EP* {x͙kUWexLaӁڱqR ZFRRicL5`Q0J`S5M~ 6` NFDI  >߹gs3|M^kqϽ"b#x,nz|41zMDy#J}eħndo%[/`==qӻƞѱ$Vǽ2Dq P׸4gYOd~fG8kux|>33x+hg܇$(2S(0L elgUƴԣoz̊|.\ K]scalvseZʍ?X#g7o+PĤs˷#M V9_]G ;oi5si]F86+85g~*-]\=ezIƂyKFdO37٦-ёpe]_ *Գube^qf3CLu}q PWš%0gse<*ɖ6hS3'l+tBEVjn̏K=Y>ISN*y*/7y&=ż#qrϚRRZ//b^6/p%IkR#`zy8>%(_3녺%}`뽱#Kݧ|'xGN=_\]O39ܫ=k\=+O/3Yѣ?{.BJ-y`Z=~(kAka< -Бr jNPųK#8Vs^Y;< ^0ykf(/Y!gr+ؕr+d=k\Lk^4Wreio[)re)W{702xޔ̾zw>їbog_#݁d7+om_WmOHWHb+5:?JKqiSƢǨ <쾥龋qk^WۉCǭuB%Ҥ#`ܞ4n8,5nzq7πhOo~5WkW߬B;@l>AMbڭA+c^vʾo2diio~Pm3}7@{%_\7cߛ/dݟiZս4k7~RˠC냥uw;hSyX#%\~[#~ؘ-`fNdflQkbܾ1`ܞ4n6nR&7{ڵG;jVv+<~wjG8G8`CB9qGeVlu]fG;3ͳ:;iZ/ڊGvmC/>,%rYك\p[E5Hjlu߹/Tb1{s,Z9+׃'ئb|.נ{ܡy?Ϋ*hYu]* W(S,DF_.G֐*]\^ڶtNy򁔗߫Kr߽n>9啒qyKR)O^Ruyx9J&UɋO 6D`شlOǵ+:6-D\xuc;sO}?DBͧݢ" Fxf֖-\"ZA[ DZ=)tMsO@:mc48?]܏q N>:B%$౞EH7?8>ĝxT,9KgݯRV]%G˹a_"1~Xȷ#TS1/6&)7E $!cZ\cN *FvMHHb{9WTo7oGtp9A.ku>ч:Yg~JI?8zGQ[h ŅHh5c9sL@Lk"H`g4+)Rɠw'Vh}_sJ|z ~1\YcEܠ[_>i;6Аǥs>yUc9Grd[ӧl;"ęyxpo ŃyZH;18Wifތ*(]փv*ƜcW|LTvaZ?ȐE;fTV!Xg%ecG۾O\#{㉌*^1!ri@ǧT u<$}}%+yN1J9p.â޲z=( +cp܉'j# NVv8wMoiu=)W3֖dpo+|G;w rڿ 1,۹@:|m˃漣86X>}Ç.o zJƄ/Efh>g)܇~>}ڡ|< d?> /=|AΌVg'{ȵ|`?m?A}KIs-߲Ó>?GxڕoS[wDU?\ bLFU\qmxC?!>qXn+m@֟֓tϹ"FT0#²8=LJyb@V2 'N kzƺel}]OqNɽҾ4|~#c:?h[r\/t<,}I >36 3s } (oNivWοT 7\ro] SqO¯#3_9sǼ MЗ>qf =/+|mum{e*uCǥN>!cgmdc,ǿtE~>LF̿ {a8+W8p̿kcNw؎oĿ|MKP/c2gkm™8Ș|lq.m=#;ȋߢ:crX.ɽBm+6o@[ E{]muW}؉]Ͼ(\LW#6`Xwv w^m/6':>"iwNfX'8gwFh7y; yž\:[m\rG`]'R4orNu?|÷ !鋬|,./h/cCo~?4-gw~;(=G{<{iCi9{k%gPM{vJ޳SֽgēZ<|A~.s)u(-ڔfwِH?- =׊NϻEJTޙإdG'ްq'Kgkwnl\}i^0ߠc9}uW+u/dSh]kNIlz|!5ƱE젟v7P;u(:TyJ^rw6r:'9`)|1_WyJCX:`o OG1+z:M1^':w%z8Ę.&OR鈮ˀyu.B/ ^y_¿[a'6턆Px,1=Ϟ^w q=efE,Qw}Q1wTHd:=d7z:^۠IVyxF8xJ!H?Ts;XKl/Zœ:uq'rrn<=G;O؇5me=O3 {?q'ʱ9,ܬKe;aBaņ+=<㓾rLz_^8b83'}='e==O)~.x'Ȏ_O,ϓл#Ð֩g4{f׭$@wD}>>Ї{H y_bBo9>*3e( y;:yX7_,'tzT.o|y[;s2~FWlӹhztz:?.Rd|n/sܮFهr<-&?W~4tQn{9MН=hŬCcg3sEWo8icU_9sNTmEea#>qh8͉}E]bแ}/ܗU NO֞iw`% h]nlsU\CU\RzF畷e[aBg-ν)9Gڍ74}mhs ^4SQBb;+ƀĸ׉9˔oeB#سU6OTm1yHr #Wr+!]ȼQ} o_]wgCqzwnU9K:: hL|zT btz?,M^~o X:kJ)nkS|$t?rC%4-[?~}=e=-FOu6O7T4=`}" 3J?g/󛻒JNJgBܭ2ڌp[7D{Bz6-}@hįzw|;aULMmQ:x8X!cJd"PDߑ?`GV@Hߋwz/|o_)m#~_"3:oY->G ݶ~ -;ƻ}ec_ !_E{T7Fx@U_PPr͠>y.ŮmEi[]:>jet|a@9N.qTpu6ff*Sn!enK}'!{p']FpG9~g}d7퇆շo_<'aؗ& }W6gLt>eh:ɷOr{KJ۝ 6CS^vt|yTr8ϙ1Ψ|J*՜Sc}@:>%\&ON~~NԪb>㫵D+{KW)}-]nd}^|DOv.9 wl/{ JX!z[ys[Wb#ŘX{>(jN/bz'5wӂ󃿐eN\U/Ξ۪Us讀[i^\e}g\;MiE/y+g5EIO/~ کJ'К7eIȩjin3|p9Hܤ&O6{u΀s:td Zyq򦝶/i] _P&J|ζcwAijH  N]ޤAQ]yx`,, 2 ÓÄÊ 62-50  ñáîðíèêå ïðåäñòàâëåíû ðåçóëüòàòû èññëåäîâàíèé, êàñàþùèõñÿ êîìïüþòåð- íîé èíæåíåðèè, óïðàâëåíèÿ, òåõíè÷åñêîé äèàãíîñòèêè, àâòîìàòèçàöèè ïðîåêòè- ðîâàíèÿ, îïòèìèçèðîâàííîãî èñïîëüçîâàíèÿ êîìïüþòåðíûõ ñåòåé è ñîçäàíèÿ èíòåëëåêòóàëüíûõ ýêñïåðòíûõ ñèñòåì. Ïðåäëîæåíû íîâûå ïîäõîäû, àëãîðèòìû è èõ ïðîãðàììíàÿ ðåàëèçàöèÿ â îáëàñòè àâòîìàòè÷åñêîãî óïðàâëåíèÿ ñëîæíûìè ñèñòåìàìè, îðèãèíàëüíûå èíôîðìàöèîííûå òåõíîëîãèè â íàóêå, îáðàçîâàíèè, ìåäèöèíå. Äëÿ ïðåïîäàâàòåëåé óíèâåðñèòåòîâ, íàó÷íûõ ðàáîòíèêîâ, ñïåöèàëèñòîâ, àñïè- ðàíòîâ. Ó çá³ðíèêó íàâåäåíî ðåçóëüòàòè äîñë³äæåíü, ùî ñòîñóþòüñÿ êîìï ’ þòåðíî¿ ³íæåíåð³¿, óïðàâë³ííÿ, òåõí³÷íî¿ ä³àãíîñòèêè, àâòîìàòèçàö³¿ ïðîåêòóâàííÿ, îïòè- ì³çîâàíîãî âèêîðèñòàííÿ êîìï ’ þòåðíèõ ìåðåæ ³ ñòâîðåííÿ ³íòåëåêòóàëüíèõ åêñ- ïåðòíèõ ñèñòåì. Çàïðîïîíîâàíî íîâ³ ï³äõîäè, àëãîðèòìè òà ¿õ ïðîãðàìíà ðåàë³çà- ö³ÿ â îáëàñò³ àâòîìàòè÷íîãî óïðàâë³ííÿ ñêëàäíèìè ñèñòåìàìè, îðèã³íàëüí³ ³íôîð- ìàö³éí³ òåõíîëî㳿 â íàóö³, îñâ³ò³, ìåäèöèí³. Äëÿ âèêëàäà÷³â óí³âåðñèòåò³â, íàóêîâö³â, ôàõ³âö³â, àñï³ðàíò³â. Ðåäàêöèîííàÿ êîëëåãèÿ: Â.Â. Ñåìåíåö, ä-ð òåõí. íàóê, ïðîô. (ãë. ðåä.), Ì.Ô. Áîíäàðåíêî, ä-ð òåõí. íàóê, ïðîô., È.Ä. Ãîðáåíêî, ä-ð òåõí. íàóê, ïðîô., Å.Ï. Ïóòÿòèí, ä-ð òåõí. íàóê, ïðîô., Â.Ï. Òàðàñåíêî, ä-ð òåõí. íàóê, ïðîô., Ã.È. Çàãàðèé, ä-ð òåõí. íàóê, ïðîô., À.Øòåôàí, äîêòîð-èíæåíåð, Ã.Ô. Êðèâóëÿ, ä-ð òåõí. íàóê, ïðîô., Î.Ã. Ðóäåíêî, ä-ð òåõí. íàóê, ïðîô., Í.Â. Àëèïîâ, ä-ð òåõí. íàóê, ïðîô., Å.Â. Áîäÿíñêèé, ä-ð òåõí. íàóê, ïðîô., Ý.Ã. Ïåòðîâ, ä-ð òåõí. íàóê, ïðîô., Â.Ô. Øîñòàê, ä-ð òåõí. íàóê, ïðîô., Â.Ì. Ëåâûêèí, ä-ð òåõí. íàóê, ïðîô., Â.È. Õàõàíîâ, ä-ð òåõí. íàóê, ïðîô. (îòâ. ðåä.). Ñâèäåòåëüñòâî î ãîñóäàðñòâåííîé ðåãèñòðàöèè ïå÷àòíîãî ñðåäñòâà ìàññîâîé èíôîðìàöèè Ê ¹ 4619 îò 18.10.2000 ã. Àäðåñ ðåäàêöèîííîé êîëëåãèè: Óêðàèíà, 61166, Õàðüêîâ, ïðîñï. Ëåíèíà, 14, Õàðüêîâñêèé ãîñóäàðñòâåííûé òåõíè÷åñêèé óíèâåðñèòåò ðàäèîýëåêòðîíèêè (ÕÒÓÐÝ), êîìí. 321, òåë. 40-93-26 © Õàðê³âñüêèé äåðæàâíèé òåõí³÷íèé óí³âåðñèòåò ðàä³îåëåêòðîí³êè, 2001 xqheǿn[m(L&m-7-(R9+ 3#?ؠ+RPeVBL$LWsӽ󤿄/}~y߻dz%%kv 1 e-7mUut(ՇK/F-&2jwT]aNXج_?̗iӎ.7-8tcidփ<ށS`#8.8|=`GV;3p{A7<6`<;SQtB}ﯙ-=߯vW1ASh;+]cJcb+X.It1Kbb""jC qQBjh&4DU5k{wŎMJ MQU$ν]{g_*ˣ{<]eaGIN'.> Z͉öKOJn=J=%TP!l@[>6v jbhܞ^N^3ZE_[L=f2`lv(fc9`/'_7Č 3^L  nc5rV=['㢱n䕬?4D _+ ~"PLg#Ȉb{ZMޮ6ƲmU= Ϫit:y| Jc7A@Cy^P<蔃]Sz]ψג-gG7nDL%V/Y8]P}! &w 4L/Jzz5d)#yfik~G9"`=~GcŪ|Uֲy_h-:yǏRny+Yȣ;5tyJʮ5s2ܚcُu*Jaڕ/bі;MָJ=1=1o(kg~F%8ݝkD:'A%, 1>àt{ @NUZq,AG:؁(ud^7H:ץއv[ ƄeT$D?idX~QK-\{x,:Q`İkU9?]2+ڞڝMv/aMY^Dl*+3zZ# ~}*@zZmeOxYv`}]qF; 4e|O( 9tCyC!( }a54u["Dl^YYoe6eʾ5a}E@}J{9jms۰Sidn/d3t"AysۣC;a|ޕS$>dS>PXBz훼cvݷ}*'ynK'cقj0!;w ACane C9AXSݡwŵeVؒ9Z}̑Y(]?#}oRqzcBM#CNn1k\X lM-#9vd}lz}NwaU |Wb3t940^ydvUCNo/x􋾖kxA@^mh3W5( OkF`%yPC'jgi{~ֻMx )n?S7Fv+Ǜ5vg~b&qdw"OG>lA@cOG94 / 0&ؘukaіV;Rꀥ)QxSJhAo b8kV_=.cBnOz[ꋮhwd`gd+ħPߩq;w} 0Wd+ ek[ *FF NiO˘u %ƅmWZ͉v"uRvm`ViVݫy]TڍȽcXgI<ΐ9~/$]!K:v̖o|Tz¸y#]~82_wboײޮxlAxbsQ5k̀h eqM*$UQq ;(H'C{g"=!{$ H@ ]فu'C(o( 9ǹ1:< 2AX3Z+ɾؕwSjxwx[Qz^s Xr?5s|J)[Fۤáh+_{6 |h؁~!L.||u;CzISV(`O:^:ԇ^֒F18 [d.i0ݢ1Gs,3S$&X>M'Ҵ<44x9mx>7GM<- {ۿqXz ?^:ǻ/~?9Ѣ4&d.\G_9SvhIwX֢S*kU{|e:f^%0J}u(9uM$`v4f8C1xOM݁^p[T{{1ƂH&vI.l@=!׋jw=E99J{ =/ `%nV[dϊVfǹR^|ιԽU"}!* 2ߟuz揸1cjAA>]'(M`I]9/eR1h~t|=ĭE.Z/_{FO߷c[JU:>Dc|[ ;箟bB?|^o;}9՗WWN/7d)2}ӘU7d\}ǘߐ77-nOZۋzutޡ_ީMLp~}ojXЉ~wߖ<,L{w)dy܏x_{Ǘ7BN}/oMzU}+Amܥ+`}N(0tn@G8Q򪢱z`Yo tFw*U</[om`zD?:o|-tDWNF8a'!q#IiO[Jx߃_}>cn^6rЅNyHW\>@Cmߪ4 zϬ٣zx]t*-*E@~E=M.ekl/7WxS\}Nϋ.]]vѾE M\Yn#⢎'{Xv .NQY|;h;xig1~э͑l ։k!Ɓȸ)K3cgzK\%nNQߣK>ǫoIwb{uIy=%JPvYS[d?WBe従 wXv9}>}VƵ;N@>4_Ui vZoS uwz=ek{6,\ј{_.k+wϻi gn U-|!>L[;x{, ͓~Y;׋7wiJ\kKmwiPal_C;_b1XG+?7h`d9ׅI]IJSVN:A:ut*M~5q l~=<ɖyX=Qj֯½}dutrjq]1F[y.>"(yK%׃McwlY yBmc|o4 a2?C,g6{dFWGDA+vۋ]G4. E>ww, F2A4t~FY6oW7: fVfNVkcbխ=w}G웚GY3Ìa8&͹9dzG>ss״?ؠ.\ɖ u;jVHqÑfY=Y_:LeVTgxg(B`]AiN) >\~> zie/)l}!~M[R[/:h;~ۙfCoɸ8 %Dռ^ $dT_#-쩤@D.Zj0z~*_dmrv~@K`P.lW|!5$Bh\mSJҾ3N,@(1 9?}u;[IDXV%ė-q~O6!5Uk'{Iy3ğ"Fa ~rϱE?8]dw#6yrhL <+*iYrPb/b܇1a?}C+[VT<-3a4zK[,ٙ~QϹV9xOށaZ5zw蛑N=F!r[7u^E<3< #oμޜާ;ױ LXu˄w4;} *޺۟O4tCs\y7{q\kCeW&FQ(`0 _g3Q(`0 FV^:Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:08  $O.8 OO(16 a2@a/J*O1t]{ Sx{UuB$DEc$ alɃ`mKg5(DGdZfiqCIXK[ m $}s)'Ywگ^{wN#tu)}fgⲔnI)/\ޔ)_PK{'Rz )&=rꟋgtKЯ9eڈNm0΀CUm F >MRZ_Af,: AM[Ԩ4Gep|]u ȾЬ4V63,iL=*Orh´|0?ۜ[wM/u;7Z6*1Veď8:|TϥTz=̘§N7S)!~œ i+cQ`z GsewS&\}>=K7O>!EtWrU]M-.gsg. ]>O˴r yKCҰ]wU.iAOH?j~ҟvu-qhGږFƴp82AbigbFDs0GHlh_#JZaP ])3Oc^0lN{ik{ϩ0ng<^mľOW~0ʩ|%H{H>מ g N?+aϽi}M)m  ?cn6ٖ܌>ma[GNwV>4jߛ䰏b?ڢSP>Փϒ[V2YOBJ[O#[iC2#v{縘΂on?udawc)#jAk:!Ho#IʶM(-xvXr \) =u su B{?`lo&ݰVUl)b⨍:FHK^ޒC$CኯcnxvIrwqvq6r--F-C:! [6T.w } cߤ.w'n@Gۅ`gBkKBU>wI(C1n1WN㓡\9 Ǔ*oX:'S;'JځiX:bΥ )}d|*<}rYiNeL9}btގ;i3!5w=_"_.!6^^7"ۅqmԣ2i3>J^B*X0(^^MׄjM=<_vIC;2Ԅ}54Ux3j K}~}?%m%o>IOa۱J{Ľ-BݷhC Kg'fBu{Qބԗr"akLY (/ 6+_V]Fs|&ؕ߁sƳXݜ7{obl_͆xn7'_(;Q}ׁe_0WSᝊ^yW-}i{+hm-¢t6-حM :Y)FG͓ݣHݍg7SyWOz17EӶiܾgHdZ=P.u]luLܲ5!uæ-C^hW1:֧/5x=$a~ݗw5hx כ.p؁f fȶxe>a`$!Z_[)}g>:2~fVv)^MFH ?@ ;*\`ɵzsiz ;^1b @!CVQ1B:[x=rGH=<ܺcg!g!φiJ"LI3bf {t'{d*p[D?oLdN÷'Dgx*ϰȳ7siu˃~XU-`/+sj% H {ӕ骴(/znt> o:#.__~/ߏ^ΘNw:n|%ĢU;q=\:g#ﴙ狌7k6!lAo=`/ бZӘ3ո} \43FAgjU{<36LK :6RCWӋ}hJ<#(oJLM;'[6#@ C?smUCPyff3!k?C_eO}v_`wUNe<5Ft}R:Ҿ2P2\}u#nZ{~N2:|юLQ7x^HQ읤#h{0gYnyW fMavC<{ėSHzŜ,O`=lI>.Vmy}tnr1#E16-VʂeWz<7:Sf|1m<{!g.7i~n5ݤц=|ŌqcӆMbvn\<eHG@^n+/(ɫG_u.c91܊8FzOa#1;>hoO|{#vdۜ ޹zdޭ`DAl>L7'=Ċ/3noYrSҷJ_&8͂2d],Wr䅽7P6 ꃜci9&v/z o708b6\?jtaϔ%"Mj-cUz!w>8$ڕQW#Zzr0]άIL<|Pr\vfx|u$Qed(2.E>QiyQeo9yOnVU_y:lUle%2OH߷WfFDCbOr-fam]AldڣmD[[@[A[֑>rNq?=vk0al^X{vmȾ7lLXh 4+Ӗ#O=gH^3e?ȸg\|-~P~k%md(_bzr{[:O& t\"ϸr1v s+NYgd=rkCuh_;2evxGӇ3*c+u'g6 c#u-"9P]*"mZ0 ʭ]k|CIyԋRϵis+uc=2e[y2$^[gOX~58a5ʳ.bHV)˷@|J:^ 5}^\ckPn}\2PuKw.1 |Z};69mvi`-ƳzXo~77)Q0/7:O(J|y6i\=m/n ixKCim L<=Vބ,'4o: [xCq?u| ϿF_ΤoyZq_t-7_fmn,FAڒXmfc\%Qnrz7)tM[_C񸻧)sAx+m<&5,;n Ey'y׊};9>dc`+5E\s<_ʏ<ѻzw̫7+,, 4 ÔÈËÈÏÊÎÂÑÊÀß Ë.À., ØÎÑÒÀÊ È.Â. ÈÍÒÅËËÅÊÒÓÀËÜÍÀß ÈÍÒÅÃÐÈÐÎÂÀÍÍÀß ÑÈÑÒÅÌÀ ÀÂÒÎÌÀÒÈÇÈÐÎÂÀÍÍÎÉ ÎÁÐÀÁÎÒÊÈ ÏÐÎÈÇÂÎÄÑÒÂÅÍÍÛÕ ÑÈÒÓÀÖÈÉ ÑÒÐÓÊÒÓÐÍÎ-ÀÍÀËÈÒÈ×ÅÑÊÈÌ ÌÅÒÎÄÎÌ ÐÀÑÏÎÇÍÀÂÀÍÈß ÎÁÐÀÇÎÂ..................................................................................................................65 ÑÈÒÍÈÊΠÄ.Ý., ÑÈÒÍÈÊÎÂÀ Ï.Ý. ÑÂÎÉÑÒÂÀ ÍÅÇÀÂÈÑÈÌÛÕ ÑÈÑÒÅÌ ËÎÃÈ×ÅÑÊÈÕ ÂÅÊÒÎÐÎÂ..................69 ÑÈÒÍÈÊΠÄ.Ý., ĨÌÈÍÀ Â.Ì. ÎÖÅÍÊÀ ÝÔÔÅÊÒÈÂÍÎÑÒÈ ÀÂÒÎÌÀÒÈÇÈÐÎÂÀÍÍÎÉ ÊÎÍÒÐÎËÈÐÓÞÙÅÉ ÑÈÑÒÅÌÛ........................................................................................................76 ÁÓËÀÕ Å.Â. ÏÐÈÌÅÐÛ ÏÎÑÒÐÎÅÍÈß ÀËÃÎÐÈÒÌΠÔÓÍÊÖÈÎÍÈÐÎÂÀÍÈß ÄÈÑÊÐÅÒÍÛÕ ÀÂÒÎÌÀÒÎÂ Ñ ÏÑÅÂÄÎÑËÓ×ÀÉÍÛÌÈ ÏÅÐÅÕÎÄÀÌÈ...........................................................................................................................................................82 ÃÐÈÃÎÐÜÅ À.Â. ÎÖÅÍÊÀ ÑÎÑÒÎßÍÈß ÀÊÊÓÌÓËßÒÈÂÍÛÕ ÝËÅÌÅÍÒÎÂ....................................88 ËÅÂÛÊÈÍ Â.Ì., ÌÀÊÐÓØÀÍ È.À. ÀÍÀËÈÇ ÔÓÍÊÖÈÎÍÈÐÎÂÀÍÈß ÊÎÐÏÎÐÀÒÈÂÍÎÉ ÊÎÌÏÜÞÒÅÐÍÎÉ ÑÅÒÈ ÊÀÊ ÝËÅÌÅÍÒÀ ËÎÃÈÑÒÈ×ÅÑÊÎÉ ÑÈÑÒÅÌÛ..................................................93 ÆÓÐÀÂÊÀ À.B., ÌÎÑÊÎÂÊÈÍ Â.Ì., ÁÐÓÊ Â.Â. ÄÂÓÌÅÐÍÀß ÌÎÄÅËÜ ÊÎÍÊÓÐÅÍÒÍÛÕ ÂÇÀÈÌÎÄÅÉÑÒÂÈÉ Â ÝÊÎÍÎÌÈÊÅ: ÒÅÎÐÈß È ×ÈÑËÅÍÍÛÅ ÝÊÑÏÅÐÈÌÅÍÒÛ..............................98 ËÀÏÒÀ Ñ.È., ËÀÏÒÀ Ñ.Ñ., ÆÅÌ×ÓÆÊÈÍÀ Ò.Â. ÎÄÍÎÊÎÌÏÀÐÒÌÅÍÒÍÀß ÌÀÒÅÌÀÒÈ×ÅÑÊÀß ÌÎÄÅËÜ ÂÍÓÒÐÈÂÅÍÍÎÃÎ ÒÅÑÒÀ ÒÎËÅÐÀÍÒÍÎÑÒÈ Ê ÃËÞÊÎÇÅ................................103 ÏÎËÎÍÑÊÈÉ À.Ä. ÍÅÉÐÎÏÎÄÎÁÍÀß ÑÅÒÜ ÄËß ÈÄÅÍÒÈÔÈÊÀÖÈÈ ÑÎÑÒÎßÍÈß ÔÈËÜÒÐÀ ÊÀËÌÀÍÀ.....................................................................................................................................111 ÍÅÌ×ÅÍÊÎ Â.Ï., MD. ENAMUL KABIR, MD. HUMAYUN KABIR ÀÄÐÅÑÀÖÈß Â ÏÐÎÒÎÊÎËÀÕ IPv6.................................................................................................115 ÕÀÕÀÍΠÂ.È., ÑÊÂÎÐÖÎÂÀ Î.Á., ÁÀÁÈ× À.Â. ÀËÃÎÐÈÒÌ ÏÎÑÒÐÎÅÍÈß ÊÓÁÈ×ÅÑÊÈÕ ÏÎÊÐÛÒÈÉ ÄËß ÑÕÅÌ Ñ ÒÐÈÃÃÅÐÍÛÌÈ ÑÒÐÓÊÒÓÐÀÌÈ (ÌÎÄÈÔÈÖÈÐÎÂÀÍÍÛÉ Ï-ÀËÃÎÐÈÒÌ). ÌÅÒÎÄ ÃÅÍÅÒÈ×ÅÑÊÈÕ ÀËÃÎÐÈÒÌΠÄËß ÑÈÍÒÅÇÀ ÒÅÑÒΠÂÅÐÈÔÈÊÀÖÈÈ ÖÈÔÐÎÂÛÕ ÑÈÑÒÅÌ..........................................................119 SVIR I.B., OLEINICK A.I., COMPTON R.G. RING PROBLEM VIA SPHERICAL CO-ORDINATES. APPLICATION TO ELECTROGENERATED CHEMILUMINESCENCE...............128 ÐÅÔÅÐÀÒÈ ...............................................................................................................................................................134 xW_hNa~ssɲO|jH|}؅m#samE'.nHK!b.2]hD)so޶Nߤ\p<{,@PV;P(NGYീ*#2zXJ8m#; J,4TsyN1R]szVwM:#P~w.w.ӓ!9pΈ$[#r$kF'ý+֧9SD,͑4wPuv{nT;EZNBNmt1}O {k8f㌯57s&?FwD>1GOox0_$kbąvxODO#)9`-q:9'%gH6ƛ*_@1QŸn)&FY py-NŜ[!']0(xF5noGd('ɇ(F(|@ƣ k'}8â}y>+>wC}:Wߕγ u=ݜ~\ӿu2q8`q8`k~=Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:08  Zx2b JxRx(162/ `x1{4{ x ]Uy 86a&J L20)#F%)J 8*] Uؚ*VT) m6Xd"C0yDwsrΐXlo֗~s4|! g f!sBh"BChJ_᪇쒜WpkBxX婪O?3rH8qiSX.  Wp3Y1!8`7! 0OPni{spc~lI!/PАQ S+TPzzsѰBK<ϘDHOc$LsC#Jwu=5,:+O:y췍?Ӧ >aq&OLy]>񽏆[B Q=nIJlY͕8oN1\p=1'ܦ5ӴomN#xۜ,|{L^xU (򶮰KGGY)d9I^ {s[s*u*0W> )VjQ:N?dۄc|-.!ue]wg9$Mvh*.on*oRIyv4v#$-Km]vY/>)EI0Aݗl [nX_Hq'Ox5 mRz}*+2_>ٮCo7R{7f7Bo (%N;fCw;q ȯC=,^k[nS6l'⭷C`QaeOU{I}ڌRwݜ.Fh)zDCkxfnh _lݠIu w [GU>R0Х>KhO7=/5ocf⮬K4ǝ]vb;.1K=1' 8x| 5o(LFB/|AHwɏT{0sXWiE.ZխW+]}Qݗ?X6X*DbEy p mSAqaZ^ pMxVn A?_Q) 1JoU \*ㄣcy,,Ճu_jQQneFQceCQW-9愼|ʫ]101^7]# i8{ĸ2{TDe6}cnV:ҽj^ iY @ގc ~T:7ŌeJb)\ަղŕ?1(+?vu~=ō W}jJ?oR"ك7ܛcZ@][̃rwEZsOhCCMXQ#?x'kSح0lxX`wcg#3mM߄<_܋& iw~z+i?ve6qX7 _2xX_֒UzP]I3c&^ZsmHCx:f!^~s1}i^HƱ&m1 bI Ej>izI|^c]JGnU,RbiYJm}}aJP 퓺2.`u~ĀO/@;2X Z~2"}v[=Y\ؔY@Z6e\Dy*@mKzi -ƻ0{r[:_y-z!󧥙 *(j]>[K$~Y&q۬L'N׽msZzΤl=3>s:rDf/~gA 9}@Gyr!7:G/v)2?sEҿG2P+z3- LJ.M9Z _]hF]BUV2Od ȨX:gޖeZOv@J[l:ip(|*xAG.p~;Xۄ^ ];~q%ڳcOmZ$,P]߉YCe ^RXH͗qM: P޼m[ck9U2_:?eb}*OYm߸nKk!͙NVﰈ1.|Ν #˂& ,*9)Rzh)#GIJb47)tn<6@yGx ZCp`uݶAì&x@q_}:' xVpl'括,,fA[,Chgs!<4InKYp3om9@kr3^ }C=j[}.Wn xF'KbqN_IďwTjBUos/XP}n7Ӑ!O@Xڦݗ7cEJl/l}'/hlsg:ii,5apԮ6K%X{bB$p)~]<1}Uo%?'|C* X62&7衃~f|'mv*ݿ/ey_ۻRWۛ?)XĂ63t_GDW2ߥZ[u3S{ǝfB6ev]F7/qWwm%~eC6_df?DD5I-tKiM)9 1 >ZN#e虾E=t՚3v0 =kR)•:ᩜz!]g*~|QcOSb\e5i* !uAF[Q\-k[_zu eN6֑Sڻ}x1oCGJ]޼ҹogEiQO7OefOU;F[{S7۲Tjħ{Qxj_"nxևˤehyQg"+zq ޲>aZv:޼2)mS>1st?R|%CB!u?Y8ڕzœnϚ[ݸ>CW䛎Rf|8YCzAY"ChѧM(8ܓC^roɃg2ޮ C3Ksjy2j=0kobv2ۡ.[y^yd@gx)4 *4Wcu-8G(E~翴w?(fưׁz޽6͞nf;Vg|aC==ϋmƒ'ZNIO.={Z\ݱy6zƖuێ9"ו j G-f9mgw̿9އfNٽR|Wljsy'ʝޫu8OJogB?ODJߧRDzw%,kC:'9nd~a&jbd'mq%7V60g> Xh>/6}p;KǕwEʜ4Gɨ!ѼLbFoKhg|zw.nMTvtxX%M;+^7ځHNcxt+I?nβN7YVyJ_S}~GwZ~ǃ;_!_S]gF]R}ܥI }o_}H%%T{~[gR|⠼uQ^Kky!zuN wt_E#>gv@{74ߪXA ac;obƫfeuؗ\K׺Fk=BJHJa׳T\V(nCρ' oiP^(ᄎnd~= z 隴]n>s\!O_N *u-^(lP^kp13&G2kX~3nhllg]L=L 3gDsvSH|y/i=/ܗi!{֖ZKX[?j˩/=Ůg#k1(PAE=Ų e =t1~|}?u斫nyhp7Sߝq)?+8簿e2)bsG<2Zʜ28ڵ C>)?G='Rg%ߓ|ZCI}j q̹8%W1x,?{ϰgE߹~N)m'}9A8L0: eeJ= ${Eiz f]Q];Kљqz`4Ko;Q!(ibqY+j>l4JZڋmN?v-|Dѝaz̯.=^gh-\zS/DΨk9Ϩ6޵Ib7б1Xshek!ȍכFo}uoj>Z~C^јStD)eօ)pedmŵzח?pܾ5tu^25fY,Ԇo0W͑M!;cyx vY|Dkc }:#kPAț"eggN_+@jd b>_~1|sCC]wC ]kne{!oMSrǶrt6zקЦti}"~c;I~mR~֬ٛ;̽ |gTLng荧3j"AST\;̪ޑz/NCЧ5dv߷:oֈۖ8Ygtz躃chtV'4lY'`;@M*;{9DBF%Yc)92_slCѿ/'{+Rb;pw%Zv0ZUvcݱkw5wmtY'׶!H/ Tg2+cW}8:C[%nIѭ|q!or{b9v=F̀gg goñ?s7uc"7yw 2}usOTU NipO <|j?$P|'gߋA:m*A3˔ ôWv£Ho^ӟLԐХ3=<&{t!&VC3V&(ѕ>Ǔgozm!egJhCcGgṯ>7 ntd5OB@fϥKvg_v.A4>1Ҋ&ZQHܑE}`D_Υ^W:K*Մ3qvelW TW|sڛ;=ޡP58,z ,s9lrL4d(^Ϣ䛦p>OQ'gѴ̙Z^Y]=^{rS]=<Һ,/#.KCggGt/z=HܛO[O.{t}ʵt;3zZQ8P~}Twpu*>:sȢOcD^,zb隴]mW1vY'kyw5zue._qht}[FrߗIѵΜrzɧg ^r-]bT8Yiz+uxDfOe1Z[+?xnO:-#Zhn}˷S뎡}zY'KZJH߇H)}_oψWf÷^:x$%|{uSzwXQ?.PCwȋ#_5|tOZ7\_e@U{%ؽB%2}?HH>;_}HG;~\zN;b1^Ֆ*9.XNm=ֽM !g? )eTW9:[p_|?z' Jf O.nqNwX)siS;ۤ﫟yPŃb{7wUg QvWu4 Ruj\O})wEu#˃/]U!o|?J+Jaף7UƠc/>(,Tb]P0KOg#*}R;2}~Ծg'ڛu_~Yz?|c+K}@u89m8ηCV'GZ)wwa^]"<ї͋٬̶+EKfamV}k=GD L1jֲIm>u{ː>yOdcK܆[ԑ :@̅6ƛO{ |іǙ/h\6k'r{k¡2ݳֱ-5k&Hk|oIW pOɡzL9ݯWz2o#O R!7|H mULA2ݸ/1I롡m=ge$e\f^ ~cޱ6V8*u_>kXd7L|CL`}d>&oݞGFJGrAI݆|^CzR ).gZOrq s_i~A9ӡI(ХC7M±*bd<z{VӲ='|;YxjaltіQmG(E;M4~[b\[XxTYѳ=}B|g|cZ9=i ZA[Լ=N6OMkG^3e82!{ik8P90e4'+y|=X) 7٬%D2߸Kޕg쬿T^[12,s-)mI<>tX94<36mμAo }y%ZNuu }ۅ^U;<}QSX 1 qx[DCk嗶HY.i/{,CSG4ePX$l&(`_@^sߪ/(,,5 ÓÄÊ 519.86 Â.Ï. ÂÎÐÎÁÜÅÂÀ, Ñ.À. ÌÀÐÒÛÍÎÂ, Å.À. ÑËÀÁÎÑÏÈÖÊÀß, Â.À. ÐÓÄÀÊÎÂ, Ì.À. ÕÀÆÌÓÐÀÄΠÌÎÄÅËÈÐÎÂÀÍÈÅ ÍÀ ÏÝÂÌ ÏÎÂÅÐÕÍÎÑÒÅÉ ÂÈÍÒÎÂÛÕ ÎÁÌÎÒÎÊ ÌÀÃÍÈÒÍÛÕ ÑÈÑÒÅÌ Ðàññìàòðèâàþòñÿ âîïðîñû, ñâÿçàííûå ñ ïðîáëåìîé ñîçäàíèÿ ÑÀÏÐ âèíòî- âûõ îáìîòîê (ÂÎ) ìàãíèòíûõ ñèñòåì ñòåëëàðàòîðíîãî òèïà. Îñíîâíîå âíèìàíèå óäåëÿåòñÿ çàäà÷àì ôîðìîîáðàçîâàíèÿ êîìïüþòåðíûõ ìîäåëåé ïîâåðõíîñòåé ïîëþñîâ ÂÎ. Èçëàãàåòñÿ êîíöåïöèÿ êèíåìàòè÷åñêèõ ïîâåðõíîñòåé ÂÎ, à òàêæå âîïðîñû å¸ ðåàëèçàöèè ïðè ðåøåíèè êîíêðåòíûõ çàäà÷. Ðàññìàòðèâàþòñÿ âîïðîñû, ñâÿçàííûå ñ èçîáðàæåíèåì ÂÎ â ïëîñêîñòÿõ ïðîåêöèîííîãî ÷åð÷åíèÿ, âîïðîñû èíòåðôåéñà ñ ïîëüçîâàòåëåì. 1. Îáùàÿ êîíöåïöèÿ êèíåìàòè÷åñêèõ ïîâåðõíîñòåé Îäíà èç îñíîâíûõ çàäà÷ âû÷èñëèòåëüíîé ãåîìåòðèè ñîñòîèò â âûáîðå ïîäõî- äÿùåé äëÿ êîíêðåòíîé ñèòóàöèè ìàòåìàòè÷åñêîé ìîäåëè èññëåäóåìîé ïîâåðõíî- ñòè. Ïðè å¸ ðåøåíèè íàäî ó÷èòûâàòü ìíîãî ôàêòîðîâ: ïðîñòîòó îïèñàíèÿ, çàòðàòû íà õðàíåíèå è ðåäàêòèðîâàíèå, ýôôåêòèâíîñòü ïðåäñòàâëåíèÿ äëÿ ïðèëîæåíèé, íà÷àëüíûå ýòàïû òåõíîëîãèè, èíòóèòèâíûå ïðåäñòàâëåíèÿ êîíñò- ðóêòîðîâ è ò.ä. Ñðåäè äðóãèõ ìàòåìàòè÷åñêèõ ìîäåëåé ìîæíî âûäåëèòü êèíåìàòè÷åñêèå ïîâåðõíîñòè. Êèíåìàòè÷åñêàÿ ïîâåðõíîñòü ìîæåò áûòü ïîëó÷åíà â ðåçóëüòàòå äâèæåíèÿ â ïðîñòðàíñòâå ðèñóþùåé êðèâîé, ôîðìà êîòîðîé â ïðîöåññå äâèæå- íèÿ ìîæåò èçìåíÿòüñÿ èëè îñòàâàòüñÿ ïîñòîÿííîé [1]. Îïèñàíèå êèíåìàòè÷åñêîé ïîâåðõíîñòè ñêëàäûâàåòñÿ èç íåçàâèñèìîãî îïèñàíèÿ èçìåíåíèÿ ôîðìû ðèñóþ- ùåé êðèâîé è îïèñàíèÿ åå äâèæåíèÿ â ïðîñòðàíñòâå. Äëÿ ìîäåëèðîâàíèÿ ïîñòðîåíèÿ ÂÎ íåîáõîäèìî ñäåëàòü äîïóùåíèå, êîòîðîå çàêëþ÷àåòñÿ â òîì, ÷òî â êàæäûé ìîìåíò âðåìåíè ðèñóþùàÿ êðèâàÿ íàõîäèòñÿ â îäíîé ïëîñêîñòè. Òàêèì îáðàçîì, äëÿ çàäàíèÿ êèíåìàòè÷åñêîé ïîâåðõíîñòè íåîáõîäèìî çàäàòü ñåìåéñòâî ïëîñêèõ êðèâûõ è çàêîí èçìåíåíèÿ ïëîñêîñòè â ïðîñòðàíñòâå. Èíà÷å, ïóñòü   u   – ñåìåéñòâî ïëîñêèõ êðèâûõ, çàâèñÿùåå îò ïàðàìåòðà U è ïðèíàäëåæàùåå ôèêñèðîâàííîé ïëîñêîñòè 223 0u0 R,T:RR  – ñåìåéñòâî îòîáðàæåíèé ýòîé ïëîñêîñòè â ïðîñòðàíñòâå. Òîãäà ïîâåðõíîñòü çàäà- åòñÿ êîìïîçèöèåé îòîáðàæåíèé     uu u,T,  (1) ãäå u,  – êðèâîëèíåéíûå êîîðäèíàòû ïîâåðõíîñòè. Ñ ñîäåðæàòåëüíîé òî÷êè çðåíèÿ âûáîð êèíåìàòè÷åñêîé ìîäåëè öåëåñîîáðà- çåí, êîãäà äâèæåíèå ðèñóþùåé êðèâîé îïèñûâàåòñÿ äîñòàòî÷íî ïðîñòî èëè êîãäà ñàìà ìîäåëèðóåìàÿ ïîâåðõíîñòü ïðåäñòàâëÿåòñÿ ëèáî îïèñûâàåòñÿ êîíñòðóêòî- ðîì êàê êèíåìàòè÷åñêàÿ. Äðóãàÿ åñòåñòâåííàÿ ñèòóàöèÿ âîçíèêàåò, êîãäà êîíñòðóêòîð çàäàåò ïîâåðõ- íîñòü êàê íàáîð ñå÷åíèé.  ýòîì ñëó÷àå ïîâåðõíîñòü ïðåäñòàâëÿåòñÿ êàê äâèæó- ùàÿñÿ â ïðîñòðàíñòâå èçìåíÿþùàÿñÿ êðèâàÿ, ïîî÷åðåäíî ïðèíèìàþùàÿ ôîðìó ýòèõ ñå÷åíèé.  íàñòîÿùåå âðåìÿ â ÍÍÖ ÕÔÒÈ ñëîæèëàñü òåõíîëîãèÿ ïðîåêòèðîâàíèÿ ÂÎ, îòâå÷àþùàÿ òàêîìó ïðåäñòàâëåíèþ. Ïîâåðõíîñòü ïðåäñòàâëÿåòñÿ êàê íàáîð ñå- ÷åíèé, ïîñòðîåííûõ ñïåöèàëüíûì îáðàçîì. Ïðè ýòîì ïðåäïîëàãàåòñÿ, ÷òî ìåæäó ñå÷åíèÿìè ïîâåðõíîñòü èíòåðïîëèðóåòñÿ ïî êàêîìó-ëèáî ÿâíî íå óêàçàííîìó ïðîñòîìó ïðàâèëó. Êðîìå òîãî, íåêîòîðûå ÷àñòè ïîâåðõíîñòè ÂÎ çàäàþòñÿ êàê ïîâåðõíîñòè, îáðàçóùèåñÿ ïðè äâèæåíèè êðèâûõ. 6%xLUǟsArp\XH16-A?l,6(1S[KWKZSLѲ[:%_S9\zV[^yy}y3"^I/R" ^d~5DV鐞_hZ2"Owdž\&YPFw; 'l2upO=1ԊۈWYR5D&89&,Qr|o䝰B4ndp. [sp=pg(W2G Yp!#XNH͂k;3r=Zj$\T5)kPe cFe*~unwF\!{5"p?> X.Ck$#p;Vj̇ú/jWp.ko!M>C=u,΁!(Rtr1 :ZТ`~; thoH6򕱐iĶ7p69?]FQ/M*ORiԛ!T4R{1ݻD?#pz8_I<7TRo!MU[(ۘGXlߘ^ =:$6y_y~j g~Yr]¥p]%L=n7=+=(b|zyEgg>xK/ck'x3i\.'r/'7×UR(swr%p Li$[~g&\TR3&a Zc` \գA.3֮.p量hZ}k[6}h>]ALɍ_?L!]~}8܁ƙZZi7V4ߜE7{iv5l[[cz{^ٷi{gkqz\sOEQ^˧\E^ԭxusm;/So,ǩjWnV-Fѷ>E8{sG|1Eۢ7Gof]9+ş/)8ysꪐ\i04~mQ\aQJÌN?A>I1XTԐgȯ$?+/7K,)'wkQ.qSȊVq!CmV&t!*{bqjD[HaoˊǮ;USqQ:oʕs'Dc?&MʿvEo=m^Zhӽt3[Sypk)tcK688ݸ Byoj{6F*Ne_PFBzVڷ]y肔7=~k6}k}Hw QmB/->N>rDrSs:L6];} 9}>eQemc]̳ѕ*= Tچ5c6>#J/+TP/_]C-e *6 e/e7t"˛? cq8^M+p5QXMٵišz*m65zXՅn(xb:?/%U]ˌzypް$CK2-ǽ&^NWYa|uMkZz_rXǬ|濛{H֜yϪhϹB#^H_=_9zVE𖍪FO*kUל=S->wuQ=["{VE/Ή.^JF^G5.Ѿ1\+|3+|JP*ڭߛbuc ux :yZ:Gަ4nc]]k=I?}xƩ<v{)h*7J>YMMM}a?|[z0>oUm0KN:+G<3w&5}-YM?BGGӵUz݇D!O<%L𛇷PJ eIe}d}JI?U7kP\vdw6UihVm^}G+Č_Ⱥ/Z_?3W>m =墏zݸ_c|ނ謕 Gd+Ghyէo+5_Wo)]%kkF6?.ωVi2~0a8/ɚednv3| Y;鼾HJքMdɋzӗh>uռ~Ж,VxS%ơ6/Js&_t c5@Qeֲ.s_3;)>r~ikFT?/6r[?iǜ]7j޳\ׯ-f?p.p{WrN˄עkɍ^!QrteV7-oVo`pL\>{Pك}fݾJqN ):mvuס_L7Ÿ;v.[lnhʠk9]q~8gʝ9gBS~~@9(ܫ~uܹ*??=\;,b8mO=8ɆtXf<鰽%@h6gmC~H[V4-.5M{9KaY!GE*c ;1|M12&e`rӍKUlIN{#ک xH3~ᣃ" 3Duht~(zx@8먳S=Q~z=W}rSըf?V!6]IȖ2Kh@ ]X|䛷H[ 呶> tYY'u9ZV| ;Y%cd>KynTaȄp-Bf~qdzs@V%-ck V /]; m_ݪy`5<XoՁOQ&.kaM4OĹ1FH59|Ӎ0 Gz#+@!Vu{dQ=~q3~I`6AP ˪zv_*{BRj}2~7l -Cˣfe Q' mLMuQٽ KEGUo;CY^tF|u[alπC@'II~F&oMe yI>& V 7 ڗqBFY[[gL@+2~B}hO.u>ˣ)*3g*ʫӁd,onQ ځK\ݒ#3>߉ڷB軝`<%h &A@K`|";< myWW # +8!zOxGɘ8tZ>gWʭ qֆq[!> Syo؜g_ߧyKŸDlOY^fpi!_~f7tx^ <#n'[ jum2Ryo-dVUBO94O_釺=mH]fOhKp#{'(o9qox^j6u;QOy^Pwx ?LCxeW7yYʩK&ô }IKhe :a[CrQݓpY3 yMy/S:c?pbMuX E_|>lx76~#;/tʘֶ,_dhuCoPg|:amwSObVjPX*[Wy}EP-iv٬hς;KvvLnv%KƗ6x5VB,d|xMҗo1<0` );TY뗾ȷ>|^,o{|dA<[y@.ɟH(ss]+#U܁rb)Ӆ=~<<Ά8"*~8d6y>nKFH3Ȍ_WJ2#ʻPudƚuTf?alm/3;*\fo{=~o6Z2`󰼏"̮KxS۪C_Pv>6L~VFKle7 <⦓`+mE|~mG*odO*no2KIoA%t~َٛ/ ($ݭ9EQW5:[:G>CCNơ-txv=~w&әώ/ɳ4<" BeȊSfv`. iu"o ?Ky{۝>p?W-!2"J n?xOvXqf`K#e C>WaiKra]6M^֧d}ع<-P?lkiY]hK= g8JeeߠY`d΍A7sȬg'ا|k,wUGGSN ˘5y+?M~Vn3Zp,n{r_[=pM=h3oa]äxY<;^qn"o'*]y}_oެzks5f }n8Y> @rixk|9Ǻg\xՁWeVf6o6gdyA39uou qbF[h%s[(R~;^|_<$odv?HB`?Nv؝.| %aô%r;c<@&srFgY)~^MY[ 5f+Oh1sI's]<sb~ӎ6KGCP~&u48! r0G0vSf儆.(:jEmW6hBMtS?[BV=SoNTw9IjZW%g[gFsi4坯uwxB*+w;]Il= Dy|uu;aki'BvYҦSoXt_[vzyƌ͂fO_s0G5FWkKH9Sƣښ9y竦3垔ϫ5;]y|P8 e=PFh iMfO _)߯;CuݿY#O>nd9 qO\gwӸpan, zi`Uqxduwx~y7Tes/ Sm=[uFĘ c3F~E3wq1&kH7}.iOR]#mzc:jm-a]zF8_3/ gCRv6uEeEKC^8^:I{&/O=8-1!񀵃1Z>|CmIpL֏a pV[MVe{b2gxgȟ_!;tdplOpix G1pШ.ܜ;~9H/-Ü{֨~=idM =(YWo7Fo_z?]~}9쨇S2ũg܎џT4' gKuWƤ T3*æۑo{Þdvwb)[k l~!D>[┛]'M] Ű=y"g&NGhs곊3T{c[!SʳHʾ>aXINڎ*K]iNzN7a u<;5yxkC9xa=꒶ykY_'oxgC,K;U큗k_Leڥ?PNOTSp.A'4c擕Kad7 n>ʾ_|+- OlZ- ;$Z4;?tbl<്lF( aRl5q3U2/կ6}N_>Ly oWz UgUFnU38ݵ߉;7row _ ZSjzF;dae3_LfSVSdf i[ #]~WeWWfՑ >|'MPGY"Fxߧx495}/TM}~וas]=>W5}j7yvnD*ol#>(?p\Y2 -f^/[r|8ם1m>2vx5wiqݯ!?}ثG{GNo.6yJCoxo }#'܀uBt.6H:?Svds62Y_@i7Y<-{(ӳ#dMD|~諗S2ڙ|,zɱ;7CY_t7+o [#kvwзd.7ܛU䍮=򞝙Gz?h^W.&U諗s™7*]%調^$7I/|>Z#oC.U_gF2^d-JPvҋn>qh\3C ;@pwVߦ{Y_% l.q-8I;7C8]*݀fƍ҉UnjP Cc'5gd?oKքMd-;𪥮޹zUA\(c57w|FjUeӥ*t={\]TO8:`C{3iJ`VoUN~5?j4fGgFkt$o l7?XO޹*]utRt 5!QT8w{ٝ ;~dWGGf/=훛9UIah)^a{O85L=.i[K[FbзV=aManmS?}AǕǽlYeC>A/sirX.# ݄|<_])={{OeMq;Α?}EׯgB|]xaK h9-qҷ9s~GO-Or4}YJ:}с 학(ߋRn]5^yFSiU-!o!=vn2->`Ї^>h ZWڇ>QyOh_zb9xƝXg"An4ɕ?Gwb $s0dyM?ݹoGW(]%o^#o 7%WX'o$: 8sY&߼i(fs 'ɖlqTv'X\pc7mb{r:ԫ`Gّ2h+w)ɝz.yRJxV\Ic~#{a1OlL4}Qfʠy #WE˘5o$5R4㴐qwmf>;D17dK>lsҟoفKs=uٳʸ+CY|$&Q}" }4^Er{'kvo6pV)؂jI&K]Tn4!~P5_Rm{vg9{Tp\}F̳;Oٹ>4RɚIuig޿a|(*]%kmF6_.J*Ɣ%Y_-9zaHlaY~-}u܀eY*YWkνf*I>tAgj ùm5X;3 {Z4T<@Dޚۯ}\=&]5_J/iΘLםy?SsK gc|y|ԑ`_/= lN~7Nzƣ&IcgrfoAZym=ztB{+YNkҼa6j6'_: g d\@_s)_gǧσ4 М(|Mng.ϠƗ}/m%t|@ ~o[Vok+J R(Dy3dmpg[s3]g>3֙܀W)]%߲5Y!V!VtdO8\ˏ3|0Ιn?>ҙBs#lN}GNܞ;7CYN*YK:Mc%M1e}=H-yѕ~o'[xtMd=1Lӹ;7CYX*YWIFwI֗K/?\#kn36:ӝ8F LGDޚۋ<߿>WL|(ӕwFXrfͶ򚽘I S=?Bؒl],:;Vzx^g˘x8axʴOρn/'EW}b9c7&īgG?ߢCd^3UɢyS|gaz8Y\ɱ/isC}k3Y~Ss0ߟ”1/w|;nN{d~ޡxk|нI<^ j%nfg]Ab4T7gA{LOg$O瑟1sd4%ɤpv=L~+I&3?zzgD ɽwpഒ9sN/ٱdR8J&A.pj5%Il;"{ѳHқ#F˗? 3d8v7Z2=t&MyXGnR8sz.aOg"83{X|<==Dp=Kwx-AэӍ(k5h28g>X~s> zz˓m]Y7;3$OCi~Ho|c<[^|\)knN , q{ ܎b56=a$.!ӓb4YUH0)O&8l'RrDm3֙kCٖǙZTlM,(NW2qf-F2&Y|]vFEQ'btrg+R8X'<D]t~)Mvg1E~8NMʴ}Avغ< J3}YQ`z"EQa"8s0Q\Q4U*hqu( ms0 4g_7rkHOA UMq %mjǺ:B&wن@DT2CqںЩŒmj@%1ປ qA 8sNێ̵.jP'$s];}Bl.F1qB ϩV E4m$Dl`ũ;13dGgANb+GIbjqJ7tg_quҪQ"S{QzC1vNqj8m>MyJ?G1,D0b}j(=SuB=ąF.1N؞gt,#'//@D m^LX8~GUi5'jAL8d©y(Mg8L ٖUogQ!;meQ!lX.Ho8Nn;ݷE8NIùA-+g+A`c4۬]0s`e͈gANgl0Y WP3)|o"tZ%L8tHqe z>B)9sB#~s,H$[A)qZAۂ8\)sO-4tz4EZť/Gp,8-)4΂.S,ShZR\Cf/".{^{{- aB'V׾NI3m[H3r)3龻 pONܐnɫ0^,Gu8\?Np:P=ta8$F$[# GqܶN!=8G4qa:PS/^sD ^Z/^Lq+֯ʼnf\jM }f8#ʼnSf8$l30N2M̥3h8n85 bLsC%s[<_3_#-=@G#ޢbƘ Lg`$vy3^| Kk]INVl!8Jib>0yrPr8lN/gAD|옾o}V8X GU Ics}+#w-ѳ0-۱2g% ïjO8qXoCp ӓPPduNRW=oe*wSow $9AJ՝}Zq&A8VQ#U8:%~P0<{zVw83ɼ,吿GjA.UƉJ 88V)c=xdqzau8խ {NMGZ N/琻;8b>0.?AǓvdLyE73?8'pAiGPv\t-`{8og|;:#F-HTiG/s CA{tɿN+\i <-=sҳFۮUIˏK8"5m [ _ӗœ9QJS.O'Ww4LxeV'X8ʋC~r0Y()cAOn'25pʬvc51d8nOKGm>=o3gv3\jۺR iy$g*gfΧq=ӗG*MHVNfBqhkSI&H{j$+2AF^8G\KyVTy>.(w(KY5X-IZOx{F~KkX۷ U #NW3g6` \e?P4pne'h%Nǽc\tɓ,skqzU 9YXɀH5+zO|q,VC+7G*:is:f$intwI`=??Qi>p"NoP|-+i6ρ@hfF KzcP`.ݻ-ۉ|(oh==z> 7]8 -fI/vEuf̳鴒fˢpz8-ʜjs2#D1 7qڊ=}C$J>=iڟzN{m=} dCq\xӗ;^ɆT1[| p]k>;ƥa8}|vx`=usW:%asFo[±ʱzLsmFR cu&8N:}#(a~Np+%PE.Rg'D΍O.59 wQJ p{3)whcwf L7ѣs)R*~_Hu>S/w7߆YsX\Sz&mv6F5q=wDQ[8Kril'Jˁ"6I^ma5I;~8,OkEm$ebzN?Ve7FI>ַՊ53Lv^,cRpXC]g}[i׭t}j1N_?# c#DRdGS5)PJHOu7bi(Nȁ&bGU (fc3*OϷ#Y(N-#]q,y~9SFOE/G;LI|? +|3s7פSϵ~k38QCM3.gV\ 4\<_*NOGkU5g^zgzi8/azf'Z~akN8W.a~ ?B78zp:NN ʮ)\ӘKAZ~M>;4]!Jti'%C!PC[ ΂(,(|%<=_fxpL)=Vƚw)NpnK{MqA[ gùU~]Jf&ٓҗpR~`mX#~^L{w]|4Q;{Z>6Ic߰g#;`L^i?R4{G΀ǦBc% N6-2zlqCj2 ڀRzNcC5ר82NQVDRpjۂrMxt'П.ٛ⋶X`~?0H+ӕQZXV8Yd11p]m'eסو逞BpYdᐱr}':Q{u-oܾ#pj8Nj.}dYpJ_'=~XvL³gG.3〞^4Ug]^KRzNA8$bTn =9N(NiV$gZ ټȦ ][6Oٟߔ_'ѯ^w^wP>y!~ȭM`6Ϯ  \Rm(, L8<^;,\T" fa^AJ_nYhe ϕyc'@AyJ]83H]F('_p\^ß+q8 ғOxcOdß+)yoW Xg NǾϳ4=Cq4krb6k`U8-A(8b_U"qt8[EA%{L8[I|+Latu\BIpvM0a%p{;i} )'nԻ}VŸ+a\8:ÜIr㴇ѳ8=CUѓ$&wMItۇ#Y.Mxn+Z#x(-ǯd8 D}6 z>)t @O2X8k,^UWԄpĠ zPM=\A|8Qq>Y((o4zR4GCZ.Ha/@=2gL v4zN>퇱#*p\h8'k8e?ғNW9]_\ӊ.b_X(=EݴMp)8Ǔ}KqC5Ŏ)NdQ>jǎmBɈ8,MC3pi!ٿ6>-:>.ķW4tT5^hx2F)ƘSE)]V%Kt]YΞ'56lnFl>.ʟ~ۿm85\{bqݢs;mkr{ '9ḶAFG)Ty])tSƙg!$_.t6E<M)>aZ(=ey'4W=o rqy8S˂p榓0>pZ7 ֋oM)`N5*N(_zJ\FӶL.NOq6Z@)"\(GM5#qu<@: =eqxb" r`r[gG l.& $N&FN &nD69ڍ̀ ;jXp p ]zVj905 D peh8<Nq6pɱL>cV|?<M4`=V#Lq7*n=ѲOei'\8̃/=PD:)Y'[8&EeiVk%f9V'=NZfL[{ tv(O1+ix'yR`ҒF8Yؽ4>kͳN6Xf-'wa=v jU?k&SkS⸿!%4,8%q7!\)wR[ )NE_tMq|!KPMq_s#J.'UZ^pq:43sUi.Z,=IjLoT>gs}_=Eq:~ E?MJg;hQlq%Mq0[g V1qNwB8͓Wréh?%Ȇ8<J8 )ERr!N+ P q mGqO΋QTq%;ʟUJw?9/bGSŕ<(r^TŎ+yQ伨OWyQ;ʟ*yG*o? z#j ğyx28 &2.}c8]yNGO?)dѠ&2.}2ഷMgpnȎL'!S'(NOg{m^+Ѧ{WEV_-wxOYu+_m~8?_gcש HHJ+_]']6f ߷և ox 2zb##G,b}R M{w;ϧXmc)!l-~0'?(}o#Fw+y0:'zڡwȍ@F a9S} iCʷUť8ǼTǛQVfW)q##qu!M_0LC^5t-3+h6RKF.8zstul (|ҰXa|uMoa+4zm ɃY?79}UѦ7s==ZbEGׯʹ3oUto٨j.VEw|[sS->wzDQopYHsѫ{m%{T%5*=C9jg7k6}x^Կ_r\*{kyD=#oS1.RdJL*QLh~f |תG7N*ȭv`JF?<]'QcN"nKoOj?FFdVuwQ<0oB*PoQn)kd:'YlgЧV7-[zN?|P~GVm?/:Gǟ9 w2ף\Q +}Ͻ[Lz]=}聓y /O>&ۀ>:E˫>ux hQuѿR>x>(:+73g#?+o4 G[l*oV>]c[cZzvTlD;ZRg[SEɚo74 yX#!'^GWWGkeJq^3KW< m^k }U!{y wm/ou{yB O3˟pԽ?{yUigah[wM/$e<:緻vgo;MU=U2C7c̺Y?ҙGv^8Muu6D3s|OޢS e<׍*4GKӜyBͽ[*V:}4XƁgkc|B3;䷋vsƵZJFf({_7Tvp3=C~=ЃZ  m܌I4Rh<K,1l<<яu,pxšttgK6c{E/c-Pvӹ9@^{+M;4(( mc1FC'$c߬ 5yX_mW,qr,ŵ-Xa3Y5QG9OTr+g"l.ۈo8䏫Qw^0K ChWxӹsD;Ƙ/lk[~Nϱ5AiUsf ^ٖF=2|Kf(gMԷ 8 x1Uj!US6;MNJ^c<3FR@YB;VePX93IOjbLmQk95Կה(+w'@;=}GߒlFx5HcLZNZ?7:=U_InǮ''L15~]Ǽ'JtM-4˃o®3Dޣ7yIޢ}+H2ke|=496:37y lt^&}un%W`h;4<̺O; E?E"9A5Ll'c43f- Ykg-ouwf;ɵqx斱A,d;鷁vKkXeyog *&V?.ǽ:tp#ʟ?P{gn~~08sޙ]ig#o:1D>)}.Zlͱƒ9&e^RYoٗ}rbU\|r3U^ޥӸ@c?KWST.cߣs!ócd7/2FA X/u3Ygsw+=[7o@WuJ1A믪H^~^x*=G ^6omOjA\ea wֲ9l gspF:HNXbOb~N]qyGZHbbu\G(w#;kwy /*9nav5?ls~_[,¹]qlo,Wϱ[B&s>ږvv8>\pNWt*R R R R R R R R)_T_Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:08  $ R$$(16:A2pA/c$1*:b{px Wy&\# !;#ዌ# 8fq97`\DbεI6fÏa+BC pŌgd٨=|UߩKwUkfG:}{w9 }2WrU|h52[ X /+wEZjov~b|ǂkH:='Ϲue5x[;I7o'ݙ5SG2?!i ]ێ8BϭCiswc_FGrp-pL!'s*q9t+XIg!zd__gEngeV\ mv:ym6`mowzssLk V^wgx/]7[X\{mVW=/@xkX68нIkVC>Eh_/ٻ9}q5g9li5%ֺ&|znB2AȊz)Q)Gr |^Ы C#~?Y;.o [)DZmE+ez*SW:y(2< _CN˂wb>xkpu:kEzzzyo7zPtBa{` VqzJ5xAS/R/&(^"+vc=P"E/Yv W< ``6x$8L"zw^Be_mŏS9SЧl/+/I.8O,m oMmU~]R+t̍װg095@۠a^U7p UVH7,%+WZ2k`mr5츎K/[\嵐O~O#^65um~`.eYR^oMnnk+>ͨA-5W?E 4O}cmpcۿ ~!0*4_ ^\܄Wa.Uu^(=9W-fmk+06nGyX8ov~ȋjg>mD-oqq 8f:]M&_ފ, v4O 9s;e8\k UʖIJ+}öyْi۔3$M΄','IxryL|Zv=C'1pE ?1cN3_Ksc㗺3K]ӬPσR~lƂ['~$_֏1%ȯ_I 28u"]q?4IB+]?GvM1^ B[`WbYhm~_Aۖs3aMq}~0ʆl>D'jr[Z.,[Cn@\Ý֐O5! r3!䙸pY,ZkK_vFc|Yٟeпۏn}{5zN@dv[K+;W` ][#NKN7:Zw0F18]_t݁[G J֟2wbɽ'qme7?Os>qݦng#Ȟ}6e&E֔HЮbS|Yoie}z!/:/t(4냨O&ȚaY?aU:*W޳^4dM~~uᨲG0G z& Gz/(g;Wv֮dKNkdD}OB v_lײ^tJՐ=y-_X9 Z7tp VLN>r36%oҞO3Ql{/3~םǻOzŗ62#oHy|mwZ Hɻ̶vdQtpsW3T{ e;`ſEO 76E5QyEwtFM!xNpS-Kê2r\|6;`ۓql֡nոnG$~|B`/RY;K{  `UsACӜC0;4˘4τ<=-R22i2Y gw Nɓx.B'wLnOoaļ[\_ z&rq<O<ZWL}ȕ2rO l#PEZI.'x)mw:Vތ2>kg|N"> = <L~z,"[>b>Gг,g+wu~,c_1ʾnE+yBz_ZЕ'S3#. a]1`|YM_Ϣzﰴ{Fw[}g8}|v( D<z&^;t[&( >yMiw/8 %Y\)ԧ]2C5/H^Mۆ9y/(si`ꆶ}ڛzML,(HJ߮D:dzyX)bȯ*,ҹ [xqhp38Hz|yWq;ʸc =c=Τ>YlD־ks 87yc1Oǐf9ےC֑6lG^LW?<zq .B U=?C/uxIIX lݼt>x$S`o"OUyʾ+fVsȔ;(2|$.2[V ~c~ Gɗ=YȻjO nn:c~gHW_j4W'B T ]^}OH~st*C,}+v?616N‹|9Tw}z27vֻཱུۢ7/hRԧ6 KO)}`JFZLN4u7_/&KSYmZdK]<9)u?}~~@aϜ_flE}g9$:wx6pas/`;ʀGe/딬_tip07U-Pfox˵for͖u!I i>so?w qY̗q_2d=ɝ9GJX1p\Uc< xL1_ | ڐ&哧2ҤmW|3x;fcn1L9=`26 s.R|ةK!<0/9 %ʏGys"+~$[(kṧ$o¿|?䐧2d_hވ2aFv̌O#n:Ws\y@ϱg&Ӣ"i'yC9U`wיHvDzFuj\0&}ϑTx4'3ԣIx\d+u.ca!!|aӓ!r֕2æ1?zy<TN;z#ga>?gF+ew 9]]'~RΞowy{H}-e&Eޔ o8yd=m_zZOH9 FY~߀2Yꖟl$iԧdͰ_Ig{z{He}%e.m 'yQdq,O;YY&>8 -}OF:p%ӯĻ Q}Knɛ.ͯ䳶w ӽ&<[ΧSJVz?F?O}%"g-ڑ2,@yœ|=sx=esA;9O'hoiKԗ8쫴4cyY1]޾%/D8OeIWѼ e3w8fg)G1/ /@~Xv.nW~>77MG]ryϏĥ=G:"/>kd,9*R^Ó.iuGeɳeףp? ?l1tqa9yƣ:? eV~+ry*B6%}`0ϗ`6W9diݕ"g;N|%po,#}%x&U :R?!-`"oyU e03=;}k&Sˊw8o25b";3Ny2͐~K2|NpCh `tm(#4iGL5Uw4|r*ڜ:7]71wNQlꟙKп{0i_+}OWIҞ;znpm;<2ߐ[ۼ]iۜwݮ_ɾv=4}.3w.JNt.ugw.7%yS>NlVn$94\XC~ON~/u VPJqyvSڮ9Q-w}xHC <;ko|ޱ\Źa3?'naw,l6{wg/e}&<G\zm5M:f?;l@[ iqO s`ٗuw vGw2$!d1>UOc>g i'w`'_ٞ{YW0d98I!SɇÓX?p'ҽV";g>B<8/4oe?O[;~"ok~ǂyl/;c, UX#,/`D8g_y뾉nCjs܌}|%M:ݷ3}ǐ};]og]T};eesQe=Awi[^ڳs %8%k ~15&a{xy.Gw޳^dOY߁tZQo!f]L+t|G>x!s߇;+Hg?0/'Ly6gmI^sk; 4l) =f"}7 .,~(I;퓃9|t5ъ},bOnς}V x1rbx6\G@{Ǎs,{^[X辉/r>[$5 w\^{NɯmAtgo1rޗ5a}/e2zI! OJ{%zʛ!벝Z/} -]qOL3m/YW^!Yȇ7"1y! +oن%_W=eE^_}_9#=W>S\/u@d0lo~ht yoϰ=Z[ۿۿfkp۳LN.uiS{{{<- aeGu>mWqH{;̝* ]+F)ԧ=:w|5~C"{z e&E֔;mzup+?AXfwmOw#N /ҽ}vowNÿ׶CxDO2"w+w/(;\!wUwQڮvW0#e_ySmOϻ{5<4̮wyGeOkZ~s-yH8|48׬",ѽ<5.w\ ry^_%_·,g!:g¯DyNEs? 2U(Fevx+"|3}B|:'[X|>kAI ǧN\"'I\w ,c{:6d;2mIK =҇23' OZGO*#ψƭF25˞!Jֳ(9j,r$-Q/)1do+Ў>h]wVa-Q\9C3Mz EV;mRORrzY5=úfKI -g>2>Ƶ4C?2\azP&}+ Q ߳,l[2lK yPۊc'rq^^iyE+<,1YWlcZ螭b^H\hyl'}'BYo ۑ8Ueo|[{%S2^X]d [d: ksV_5"Nm2WJW\Y_p6{ǃC4_Ҧߔ3YWBR|i+q=_LnkOUؽ&iI?zB?? -O:+>6:E}7ȫ҇Y٧pLaLwfo[ݱf)WzTͮ_;Z _WPwH%-)X9SG";Y|<}=}ROpEXm:yͲb>1J&>Ll/}dsC8BKt`?~r[b:AY O"{usp9!c>} ̡k8/HC YiÙ&$|^kQ>bi}2O걭:iKғ|Yg4t_O3wϸ? 7집w)kgO/I)'ΧC|oXv4+m/9J'vEIӤ#SG+30gFȇyg:m%_h2P>L³^ڋ\g#.}:L<%fnź,|H6'c#o=SZAH lWn'ٳquo"ym]tĤ}r[lDl`yk~_'EF'|26,cȺ f=۲i73ں9\XN~eSsPy*{~η6vs-o36h|](kOn3{ml-<]\)ž5Py 7k^SL3[$_]aHLYgYW Ḽg"> S8nGZRaxYyS'%gAOxB)щ",ԭ҉;Qoo^{Li0yqbVx2zGlSy|!G~{ p<G7콉CneI~<܏\xBn8S WyeihsMV:<'B{)3-r<9˘,kV/O3le`js$E=[ӔBGX&22I e-w^ouDֿw^yl]>#RK&<-[{Bf}4O7k0p9@+vB>&$_ ֓qzB_5<3̗ `ϚBϣM|evWjo*dϐ,7~ܩ)s ߌ#wFb<ϵDK^?uKCg#r/KҔPJ}<':됦$PҔiQ1gy_;EhNq㙘y>/>Ɨ#yc9!I$[F`LӃtTAP)trQE>3z+iwM?bwμ|l;/eҞ\ewpOGz?ߵ'+ȁK*rێ+7k !؎U=ӷ뷪6Q.X~@"{ٻaOzu^䷶uHI^(_ߏ+/j7OlE&)$%7 -unjUz<<*c0[Zf=ˌ-3^wzR?KZˌH~&ho -e4@h 2[>xc4Xˌ7]-e²ך]V% /ej/f[Xfr,7B02x\6ˉ7x]hrx/YƖIpﳬCxT,t.^%ˍ\uY~x__<, [fxGnX^c[f;/3! d9`ޱ20Kޛ,e‹ @ @7? xGA ȱexǓ;O^ x.=hL.SxIx$Y]3K;<>@DǓ$(!YxIxGx/51d)Xb xX.sx؆_20@K:zxQXZ"-xK^b  N?cKg>g'ϣҥp+AE` Bgm";K" sXvmӅ(-VmO%xN3-M,,\<9KM%xlf0Dd1M%xMxvqx&^MF~+/U:Tl9IщP'rRnn|I;׺4.+\\4r/ ]{sMj[ݒknUul9ERY~A`m[0HWV(Njm㉋p>eikD[6#5@.^޿u=r<7A۪.~2%A9cu>rm xtxn.@ XGIHߵd1%s)UN,ȫz$92`-r45#:T ]Mk 0Fv\=XꋬeA"6ZY1Uc"k 0DrWvď  RO TC"u)r(<8"CvN\GH:6 VV'W"+V@e]Eж+I6E,@TixXB?::&(W/Ef ^k^)΀\LJ Mt$G%^$sDQ(@V#x^Ͱ~)^pUێȪ*Uxq3E֕x7o+ a9 0 fWZ"]OQ䨊L 1.g {U,;IM`$҈dذ rHlzPj*<7╉ROWwJ’*дgNt[*f*$ ˶h Gַ,"V΢|s.G2xjTEuh|ƌ\;MO[aZCGOA.q[7씨W5rU/f+ B]xx[Ln%~Y&|de5kj=w JU-Dz9@_L,^3^Tz|{/QTRz=k<35祍OEDSN[s>JUR_Rީ,0mٞ4[E* kv7zTդF-DAJ?3xR(_A5?!%MlX O]ּmZ_⬴|]$B[7>3VMĝz6 h_:OEi}qҍ݀H{A]4X7g&rzUx~Ř5^u^(ӍsqxDjYj?Z<3kW,7 G ZLs;{O+dK)/V96:k=/H)Ud nX BGUx-sb#P-^Ri`HۢJ@<ބBWTuf_!rv絶 s|Cuf珨8Gi920Ϥx9!g4ؼ-0P{a}1 $f gNX@iwOތ=/I>G xzn)Q2W,n50iep}fxig44T/6ه#3a欎-R4dTXerI- S=#:YST73v$]o']=xC :`8Ty>9/Qb߶r)pn^^!ci^ " S6e Ҝ! Äk;׺ebi'QlB-Τi,C,f&g3o^eusHB]/_cٓ9Hx*rN _Vt8 UӇ%^&0[1,I+4BkGp< *)@L; jf+/I)< ͬ>CJi#Ht-L+wt,U}KY[ o6J_* WbRPvGP* ^XǯfW  J$K” Pux~g4-XP=oa` p~*^2zmIF[lCi腚=N#LOeoiuc)QDnzWtA˓Wmv;e"csXnJDZx?47Of_+qcfӠ=>fW[pS6bcN?0tlpմǓ'۽na!|y%>?g?mxqa-wY]_ Y ˑHQ6I<?3\ʲ}X#x-ۇ!moĽv7.5:;Z:r[ɟ,>>_3$ks!DyMَN7W{\$2Qy*gv7925Nj.Y;WnrTY91_P@Ȟ(gx|?}"lIm&^>VP{ ^&Z-32)0sL}ƦaәNh; RmV6o\,ǧ|X_eRk͈p.xO|g *Fܥ3` ٵ.8r{l% 7+ϘTfdn_iW6& 3'sМƎ6 2:6#f/W sYGPowx}eӟF#)LgJ"#Q*maw a)ں Pn=y;>5_Ë GnneV_Q7 .*r { a3ռT 6Nz,ecrkLqVbi:;~d!/כn{a1we6C>rksF7>ЦU?ܟL+N/z5w@{)uxn[nWM5.^8 r:uoS=S#v2F=<-qRwsԋ{TDrp윃ċ|:)߿%]G!XUś-_Pq$ߎ7"MD2}P_ Jf")FXOx刷39V1/yfj喣%\]~jEDRԗ<Yxzat؛ Zz DD2dq-Û@'{ xsԟz6o[rxB.3.8 p&"Z!2.u"r(ftyr4k<"/x/ԟ> .^`_NYiӥ#yIIoO;ex)E4 J,P6?>Ji4E0>*VvJ:<^Tvsa٫L-=`+J^< ngl>;GGxH͛xqFŠI;󙽶i{s'MCەNޮ 6aYyCG! @y"KX7}u"v&~e Sֺx{)sV^ro$&{xIeZ|N8FjkQ~+to{߱gQ+8UW$Ox۟|4 rVe4,XyiQ붡/'sJ+qX~I/+7/>(y8 /L0yVxN-Ȁ\fct;mGGܛ(x}?0a@!jƓd>:4 -#$ɑȵ; B[ثNH蓱);\-~"bVbv&QP1{?%aRqFGv&9"Y9tLȏ3ҨD.]l,%y=qI̅ b?̑[cPcI֛{sCg<#c0@~)4\+% ЧcR4R3~bhQ}1H(0Cb߮qyp|a^ S9a(<~Qxr|7dh@;ËbF2"'P_rgی/<-hmlq4H~4l44\KϬF92U"'|/!7%I7n·g!y$20M#2e徬b0KƋ6 NsjTD)A,?4cԟ?O7u5xC16n,^Mig96QJ4EL6{UDYn[/3?5v[Edzd*u4>Vx8/SPJ4pBHFV9u YeJ/xŧCxC(?ZؼlU䍂xRg:["bYOi[} EHݛڡ%+šxs ?IHV$5J { ӏM|jisnZpwxj=-]L=^cXk5,I%\[< ^Q:k19n AMz xpfstKx^R4,xϖkb-kszq=Ԕ,!&uqWs[|3 ?WkBA G]]@q-|=3cz|m?Ӧ l,~' z}o\w.ZBݦY6ב&+%LP /g~k$ jቾ #JS*m-~'!Qk|$y&-KpJ1~d“֎fɰ;&tDzLXΛ:x)wRӭңCvK(׳:x^Chr|vqnx :̯7;^:$--[32VuƗZ4< aJY%f:㋼\\KaV s{$f:x¬}'\2j,1S`~3%jT5 Nf[~#5?eI۫U/mװ +$RK,(R˛~|6ozc(\G;I77LeegUoBΆ0vǶHôUCV (mi"XҦpM[e1d Ӗ&BUeV4aZ:/!3 -e~ ˱nsZtAx}S g2?cRۅ Lm"CsN1ȕk3N2;:e~+?/vlMm@\րxGڅVXzk֑_Dl.隵/eIsYcs9t|6sڰ;ݜg0;s,n(fٗlfyXP<0gZ&+o/@u|ƥm͑a:>_1:9,0'Vf6e##>&5&A;t|o~<.&iGBMb$n#\T٦x|Y8m!w?2 Ck xڱO L|=TIٙ+˛Cw$

25QCNM5ǛW4d"I&Q#gTR;xUJvWfʻ!eŚ jRvҬ.SO4Nb`iImexi X"fVP ̯Sh]x7/%UxsR2^l~ ^,ħwvYmݜ%Ll ^$ħԳίBHD6Vkj6KͯT|jm~x3JŧJ߄!l3aSh>^j~: s!/4fx3F*lᕋ/I\t*f ]r%Ilo°^jC3 Wy(uf=_Nr'v>]i&*t["ϰ UԎٷ6 [2j#{JnϒV~>D]V1[4/xK-Sc|~nO=kRBfdSR)`"׺ϙ_KBx⼨eϙ_0E$S= *R̯J|CD$4@]Dm̅TbUf,ͻjT4H]`HWEvЈ7P] /4fڒp(fR=>g~mB'35Sjj .ϠE$HRy0uQum/dy<(e78Rg̯d#K|f̯ϩԀK8g̯kAATn1h#׫NW eOPXR,/n˞( x^9uBu1\<<_N|zsE'_@T*U+Z!?'Pczh~BH`~J/8bžB+Afb|/. };w X/,B]".Y7(ß߱J:y$P^Pw\7^ވzx/QZRw̉|K[⫘^t-߼_k6aM?f/ۧ_8ċ N-MCF"ф8k4.фk4>SW= JJ㒼^,Z WvSM&&T3xM&_ d]-7^ {1dċkN j1.N kT.ǃ`JȞL rog'ET}Ɗ |U< [i4OF?vJ.4I묨$b݊ 5:x6 W6m|7wV`!LkSU;N{ /k`kk ޣ1O]s+>}f'OZt ):={1%{7[@'.,-mW?&GuM6$6w +C(# |LbG? oCH~5~1ˮ&kDZ̯݁Cy] .x8X f^G!|j3=>g:O.RKdcYtxI,g]`T\3g}c[W?{ o_Nt2Kò߃?yUe`G̨_<xApb68|MA|Nۇ AKq~ OX9^ƅO.!ӬGNBOcHl)'61yD^Bfi^FYī1굓xA̧fzF̓c0qfZJwXOH*=$o']ί2r.Kǐ/:~lpd(K>bK?a(t\snF\ʐs)ê>62uT c9=g!=UV=`t̏},g}1ÌS3Z~58;\kS==NS YeK=QKixE^\ x@^D%`y5[Qv,4x@Sq=i+y~'^y!\3Vv1H1!CR1< ({$ur5|%y2e-[~c:ƶ?DNBدE'=σI.8Xm3)ʇ3k9qʝcb u1*13r: IS0@x ^kgn^^,A>v:W7o ~7"I}kk>Ѯo6!G|eSSGPoݦ (_+\`x >p p {}y>}3GsxKkMՏm:YmKÐ9mN߿&, . .G엂W7UۃwoށUu^(=9W-f_W`[y~K~Ӿ#A}}&x?O@Q㘷%" &Ki>K /X|;>$3:Kw1d䛇N7s5'W!C7=niH~rc~2.ϵyBk*I}<%OVqm$7>)3]đUz֥^~g=Uۍ(;=<7{}IbO.xw# g8`Or?wLggo}Lx8N3i g9,r%C)AC3q,,7 Êîîðäèíàòû xyz îïðåäåëÿþòñÿ èç ñîîòíîøåíèÿ     00 xRcoscos;yRacossin;zasin.  (3) 2) Êàðêàñ îáðàçóþùèõ êðèâûõ îïðå- äåëÿåòñÿ â íîðìàëüíîì ñå÷åíèè ê ëèíèè íàâèâêè â òî÷êå M ïðè äâèæåíèè ïî  (ðèñ. 1). 3) Îïðåäåëèì ìàññèâ òî÷åê, ïðèíàä- ëåæàùèé ïîâåðõíîñòè ïîëþñà â ýòîì ñå- ÷åíèè (ðèñ. 2). Äëÿ ýòîãî íà íîðìàëè n  ê òîðîâîé ïîâåðõíîñòè â òî÷êå M îòëîæèì îòðåçîê âåëè÷èíîé h, ðàâíûé âûñîòå ïîëþñà. Íà ëèíèè ïåðåñå÷åíèÿ íîðìàëüíîé ïëîñêîñòè ñ òîðîâîé ïîâåðõíîñòüþ, èìå- þùåé ðàäèóñ ìåðèäèîíàëüíîãî ñå÷åíèÿ h a, 2  âëåâî è âïðàâî îò òî÷êè N îòêëà- äûâàåì îòðåçêè âåëè÷èíîé p è ôèêñèðó- åì òî÷êè E è G. ×åðåç ïîëó÷åííûå òî÷êè ïîä óãëîì const  ïðîâîäèì ëèíèè, êîòîðûå â òî÷- êàõ A,B,C,D ïåðåñåêàþòñÿ ñ ëèíèÿìè òî- ðîâûõ ïîâåðõíîñòåé ñ ðàäèóñàìè a è   ah.   ðàáîòå [2] èçëîæåí ìàòåìàòè÷åñêèé àïïàðàò, ïîçâîëÿþùèé çàïèñàòü êîîð- äèíàòû òî÷åê, ñîñòàâëÿþùèõ ìàññèâ A,B,C,D â äåêàðòîâîé ñèñòåìå êîîðäèíàò xyz (ðèñ.1). Ìíîæåñòâî ýòèõ ìàññèâîâ, ïîëó÷åííûõ â ðàçëè÷íûõ ìåðèäèîíàëüíûõ ñå÷åíè- ÿõ   var  , îáðàçóåò ðàñòð ÂÎ. ×àñòî óäîáíî èìåòü äîñòóï ê òî÷êàì ïîâåðõíîñòè, ëåæàùèì ìåæäó òî÷êàìè ðàñòðà. Äëÿ ýòîãî ïðîâåäåì àïïðîêñèìàöèþ êèíåìàòè÷åñêîé ïîâåðõíîñòè äðóãîé ïîâåðõíîñòüþ, ïðîõîäÿùåé ÷åðåç òî÷êè ðàñòðà, íàõîæäåíèå êîîðäèíàò òî÷åê íà êîòîðîé íå òðåáóåò áîëüøèõ çàòðàò âðåìåíè. Òîãäà ïðè íåîáõîäèìîñòè ïîëó÷èòü òî÷êó íà ïîâåðõíîñòè, êîòîðàÿ íå ïðèíàäëåæèò ðàñòðó, âû÷èñëÿåòñÿ òî÷êà íà àïïðîêñèìèðóþùåé ïîâåðõíîñòè, íàïðèìåð, ñ ïîìîùüþ ñïëàéíîâ Áåçüå [4]. Äëÿ âîññòàíîâëåíèÿ ïîâåðõíîñòè ïî Áåçüå â êàæäîé ÿ÷åéêå ñåòêè íàäî ê èìåþùèìñÿ ÷åòûðåì òî÷êàì ðàñòðà äîáàâèòü åù¸ 12 òî÷åê, ÷òîáû â êàæäîé ÿ÷åéêå îêàçàëîñü âñåãî 16 îïîðíûõ óçëîâ. Ïî ýòèì 16 óçëàì ñòðîèòñÿ àïïðîêñè- ìèðóþùàÿ ïîâåðõíîñòü Áåçüå äëÿ ÿ÷åéêè. Âîçìîæåí áîëåå ïðîñòîé ïîäõîä ê àïïðîêñèìàöèè ïîâåðõíîñòè, ñîõðàíÿþùèé âñå ïðåèìóùåñòâà ñïëàéíîâ Áåçüå, íî òðåáóþùèé ãîðàçäî ìåíüøåãî êîëè÷åñòâà äîïîëíèòåëüíûõ îïîðíûõ óçëîâ. Ýòè óçëû áóäóò äîáàâëÿòüñÿ òîëüêî îêîëî êðîìîê ïîâåðõíîñòè èëè îêîëî ëèíèé èçëîìà. Òàêàÿ ïîâåðõíîñòü îáëàäàåò ñâîé- ñòâàìè íåïðåðûâíîñòè è ãëàäêîñòè íà ñòûêàõ ÿ÷ååê. Îíà ïîëó÷åíà èç ÷åòûðåõ áèêâàäðàòè÷íûõ êóñêîâ ïîâåðõíîñòè ìåòîäîì Îâåðõàóçåðà [3]. Èçëîæåííûé àëãîðèòì ïîçâîëÿåò îïèñàòü ïîâåðõíîñòü ÂÎ ìàãíèòíûõ ñèñòåì â âèäå ñåòêè, êîîðäèíàòû óçëîâ êîòîðûõ ëèáî âû÷èñëÿþòñÿ (òî÷êè ðàñòðà), ëèáî îïðåäåëÿþòñÿ ñ ïîìîùüþ ñïëàéíîâ Áåçüå. Òàêîé òîäõîä ïîçâîëÿåò ðåøèòü çàäà÷è ïðîåêöèîííîãî ÷åð÷åíèÿ. Ðèñ. 2. Íîðìàëüíîå ñå÷åíèå ïîëþñà â òî÷êå M, ïðèíàäëåæàùåé ëèíèè íàâèâêè: 1 – ëèíèÿ ïåðåñå÷åíèÿ íîðìàëüíîé ïëîñ- êîñòüþ òîðîâûõ ïîâåðõíîñòåé; h – âûñî- òà ïîëþñà;  - óãëîâàÿ øèðèíà ïîëþñà; 2p – øèðèíà ïîëþñà â ñðåäíåì ñå÷åíèè $$xklU춥HmiI! Rj $4%-,ai$ dqI%3?s{f:DD$=J/NJ,C՛\=ќ߼f|)p*&5ŌtXejc.ٍ)q xgm`ԍbӴ"WY"vYlgGXC 4L\#o{1Rj%-FC;~} 99spg0<)W[ :dxwxWӑgiu>)1F^cwLov#˧ֿL^H 럋Ac3$[**<1}V&gn/1k5[k`>Y_F͸~rv9i3FlqRYg-*&!+'1]JdI+M;؃wc5HRd#\$$J^AwK2z>,#7Rox"Y0Y=Oi[ȕp)08:?aRC=+U<r}JbP 깟4L `vuLz1<|!b<\yX/ԐʚSIxʃv>LpX:rWo-3ȗ>e&P$Μ1V > çypTM[<G%~8jG oj|g otxT` .R|/,=YDt6y:b/s;ġ.g 3OWw)Y~y`u!< *o|grN6B-OU# ҄J_3uc J˧67uqeF 2w/7z6\ߥy;{3 yU,0ޑ"ƛx~:*dsn]Rz.YrQo>gHF3Sl=?YJZ̳S[zuڬg0opy[Fss.%[uV[$(d9j [Ýq c=WΜ]:ZmٖMgSg{lER~sϮdMy7"ikmU:gB}XJVBu[I%kvr};`wvx<+;`wvDҁL+Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09  @bB g08(162N/F1:@@{Zx\W]/O:HG !OkTKfBA-xQ"}( -gJʙӤm3IZ2Lfw{Z{Ϝ9v'kw?{3EѭoGQu(Ho57Eԫ~Q4}ͫׯ"4솤ݝO/>9灎yď^5і;wG7ESއO^ V-ZF6M3P˿ y ۓiĹk#ry ?QGH,GFa3)IaBLP]#a_,|Ê'ih昡h 9oqZu $.%WEHPqo36D}'.z%7GцuZDl36W2ɿx{f|^wF>:.jL@Q^ʡݤҤkmcsA WmnBu4lѕ{CT?F)oRңS3.)Ry9@ߊBCckW+Xkcf"DLoDr]F߃&2c>xwtIVJjv}⯯]20ꧾ\kgܨ쒱17h@<]>KƴK>EW]Rne @=Rbp%ט{c===B><=SlB{mifiHճkc{j10-ؖie ap1/Q@Ba#93CR L)ΏL)xqnLb_m  i>ӈ?qH4>样NMn#c(#GQUAEGIzd$I_vaJN^QϢ&S(z)bBq,>oA'ԭ#{gɅphyEbmS-ei&?Ϲu#똧^W^gF_e㍾UhN mE8jQkM~8&A}0Cg9 e҇X6&}هq".e@YiQ7ψ?Dz]ʟ?%g&yD^dJ^$ 3jql'1>pI=l4e}نr҆eoZhkyMNko<)پr*zۣ){ͷbMrX]vrsܼ6վbQ'=guu6^mn}Lrlpʢf>bқ/қ5yt&4cO!4}_%nilN?'0=?nOEDFWEGg^Dkq~8 _ _b߈C5{~Ƴ.GS!Nb~FB]HIuoBݛ_6ޭXgm(۟"nLt]{t 1 o@Q߃fcbCA~ o"ߗGԸtGuj{to;u~ޥmk=CglU=&m2S4MX֮a_?u1(8=(lsMĺ)tGKe_$vp;6#k _պ6.óvz%hĪUSnmh`Ju@OR>Uu-gɉ.b|?-m!Koֳ)Q7Do8hJnG78=Ȟ7|> F[ߖע[녤m]c-O˹w-&ֳz5L6;/شM5viJGe\g|u/twrGNּg#x{spvgFsg>!P?OcYPFu{FܹN2uh+c3 ̱8Vlra1raXYDZR̋W!P A4O&HQǽ{ Y;W?)cg#plC 00t&ƺtC;.F#,hm...z`%:{8V`O9:ɑy3w;U Mu}QG_gpA,6A9B OyOlO2? zx 79(7P}8F =9%ю6$evڔis p[דӈه%rxed7Ld85 Z?e/_J1@z ;1 DގWPaqzok`+!i#!įA D<Յb?үyہm46Mn2t o :3|{~Ur܄}5WRֲg~uz+?D^3f{Z}!}!L)j'c;PgNm(۟wM;X<1~g]~g]*K| pg|0\8>|>򏸿čλ.b܎(oWu+=v@;݌`^z7>>&N;2{ijC0( \<1L57Uh-*}º3wr|(og?/@_;5yӮOs݀o>{37Nv[ܴyxUl S1X#Vm='փOY4YG7uRߥۇ=Ϋ)c(Ou/A ,(X&el+1y6+>v#岟=~v+&Y:SB9(OY~ 7s+>{ b&OCz?{5bKPכ@fYƯBۡ?UyM3A6O==v0~@R|aCUώj*yZ܃ve_]u?{Mw] vA;؊(ow&d羂P=vmF0/WxmA?xFij(nC{gW-esUhee?ʛ~ Зkw=7* ;Y '&Y}.) ۋ@Ie]|wb~oB'g\ /}ϚL~s 2Vz|2-o;y:y`y@Z] B$Jg#&.Õ#.meq'';w/@ }21~ߚ7s(c{ͷ0h;ɂz7@9S |~ a=mX# 0ׁ(rN 9ImD KrSXϬBlR{o+cS s)7}lkaLW~{=b97 Z[--U=Ck; [܂9އ͚ߑ6ds~m9vBy_y*Rvp.|1 x-]vKmVA;؁/47| :- 9R7!T8̢PyfigQm*ރ Tedc8?qb1OaXG,ڇEޏ@"O-Muf ur?{V|^Evұڳ2e)3ēyerY.u,g@?@!L}eP7^Qٙnr8yzӮ6"U8ߋ-1Keo>{'q8hCRqA.c|?{sa <Jr߈s9wo /Wڿ92]^^Qd^<ׅŹÿF-t| 1d{p>'?!p"?keC=;x 3܏=8*{pRƲ}~g]ZGC^ଓf/=8mg߄ T~ڈ~ V _[>_P~N#e;ٳnm^>G{~qح\6~3u.}ӧEԽKQ-]7q1LhLg'G}npGў6q}= *"S߷!ҷ˿Cߓ}o>}qtiA27!HuO[Z복x;P<ḫ_3{~uToL߂K[QFQIr}>?{*rUbouȻNd~?* 7n0{v?j矁ľ~fd? J³ ^wl0Pv55^  ;b\q7CsFκr q|<+H6 ؜`ݕ3O^@ "^;x?P~Bu!|4oEvoj7<6bO} yNL)#M0fI;)cy,iI~9ַA F7 Υ߭ӿ"bC6.1=!縉:݈ϠuI??d2f8skMo$s_b{~+7 uk[=4Ƴy\<9@ yy{ĺ1A`cXs"X2#e]aZXXεV2v Mb;i#؆2%&i_c?k%[4ރu'QP]ud9o=jzt_:7ؗ/dJzK;jw3V%*op^m=ۊ~7Ŗg?:4I[lͺ2< GbʆZ虶0\ؑ e|, Z8ϘsێE l#P}WKxuWx6̓_ʀ:i/m턎ҩ⳴-2dJ~![QWAФbiWZo>8g7Eze_L=d$˔ʔؘQQ6 G)k Sv?L(=Y~#;ssEsEzu LhAroYT; Ek^ɧ;YƴBy֋}ȗu =Kcё=G6җ/쀶ogel3ye?thG7V6?PgoG+FWOUN)aπWygKg?w] v@ߊK6@}wB/\n_īwei< }~Hﲏ?o=ʸ~k}RPUG~}!܏ki['<?mn=ױ:HA:XG,ڇEޏ@9I(ɳ=~֑Ehj&컧;IFӮӊoqoA;e^ܫ\DF>g>ZKc95C  0zO@<o}O\?/˯a8W>Ќ#o<#w/S舺YDߜY&mS>RX-izgVIr՞Ll'zb_aƤi)L39޳hgT.ϓs| ٜ"xԧN~CSu#iv:q򓚎qWEQ1Mٖ|/Җu?|rKn߃IdVlzVw|m u{C^>|M;.߃Y{{0l{0H]B{0G߃^`"ƾ5La,kizrZHR v{?luEm ߆;|b eޱ3.mvQ/OtП?!gu~7jJv6l2柗َzg~?0@؇LJdߜǏ#FQה<^2L{1+wy ",GgᎺ;*N]R ~M~~}S=F}g)5ͻKڇ3 ,HzjȌ2>rbL>Y&,g{i6XؤaK胱Om~klYeWO^H;SXw8=)ْTij wٜ8[@=4mԡnMB%+a\z^F`b_iH{yn7ӯHKNȸXG;2҆W Ω@@QίDkPҽ>> w>L-IfZ>~D{$.cڋXւ,|Wf+ ʀk)/S.,c[҆s!i zU/)c)w:l#t4!}Xδs3v̳i=HzD8~{z)uO9Fϔ)q_^j8sh)ԅȇeR.z`^Lه2dulaZh "o(U?bJ۲}Aܪ6.{: 7} wGPVgpK>wz^O7ǸWzHyC=uFj {BRHMbS/"Cil6nXv!Cڋl#EGciϘYϘ s mY'tYO,t8~ 2H5(]o>9CWWеky|!乏ވw8X >Z#8_Я9̫O6$'KG@0PެcZ\Ҏ1Wy`{c,y7e; ĒXڲ g:e l'c4 2/mn"u}u5~))[@cÔ+sBsMu*B<#gf/f߂a:"a йw@ڙ`kl0lfG_P?SLy/r胢MٞL`i QBSڳ1/eBk aEz¶2^dZlmؗGx^n>2{ٌ`^)LߊBz!53ȚJs{|&Pqp|dwʃ1Y3϶30-3ؗ)3|L__YU>#i]M7hdh}˽g̵~#ح-\Eb"_öfQBz1urge9'&2:%y%bI/8BKbc ?mg]u;_9/m!C=e-N}vвBrw^ʍ_X0]e#ۚr}gb['J|>B=i 4YG/8|4::"}]?N%{yG=Vn"Q+Q/8î2?P7LSr_b-D+gӮR)NJ'Ψ$e>:PoyHu|4+=uԙ .[)(O-ܕr6b .)G ӌ)[U|G:f 3ޤ2_"&,(XN M౜m3moAO?m՟$v`gQv%x꾡$[= H_in@??I^ ׻=]Yfuv+cugIH~'ϓ(cQ=ɭ";1q(_iC3a`ޤ!s%Ϲ;eZ6 )πA/l#W'6 ,puK'֔o~1'w仝Z>mJdgzߡNl?OE'B`3O_J[t.mS7>ޤ̧##WuKMu|܏su^OgN,w8}po-=rB)G! 2SgL3 57ֳ\t)E̳^^hJҶunL`$e>9ںY :?iމ˦:y.wZ/9'}ݫKʿ "CCu]rs];X4_m(MYz ,g Bcȏwk,poqYR擋Om>CVi4ɃM;kP{,'kʔs mCS?zLBYi\-H&ވ4qnc7>ߊk9))|2z*H] pP3 ilZ;EO6w"PN$MY غvM5@nށov]rƙx h/s ) ~/M!sycNm9ANB"K~4~bwG}"3_?q73};1f?[붡Oʶ=EgE$Ggި{~g\' vұ+Gy^Dz њMkg-/^x;7D7ogè߇:poߧΉΓ<mF͹@(">Gt^o+p>u WL-(Z|K/^ri;Z{H x<1V 6,Jq(qW^n8[-jFI{ox8~@h2^Iw(~\6Wo,?\YW+GWo컖cǏ?.Ǐ>Jlns%Z^ˀfATV>z<.h*TT/R'"ZqTQhoxXыe{8 Sp9oˀߏ 2wWǽ ߮ǽ +3@^WuֻWaѩ){_6Nܷ/T|5rK?P{]b>=%Yn;u2$V?Rz柳nCEŏ_*w9VMZ7X:u/~gYOSzcٷ6Be=hC< -v,@0s{>w>QoL;Ν& }}NZ<:ءcd,*i;+w| PJ7;q(FطU?Fzȴ=TO?43L3Ugt:qrS} PUwܱ{b`c3;n]KSRF{w^HUj='Rv@*㧚1Y>h/?zԤW>`9Y:Mc/\G]BwUPz^=,U #S2{:_K5iTU|M{%7mԅ -y`)sL&3 fdR]nevܚΘՙ,O {18U OxBy0~E˪"W`yf{Atč! sM'} ۙu5G tF|j~&n!U7HT/3S g00aA|k]jPn ;Q7D2ogfDE|x+oyge3@ 'kR)ϓL6x"pCi4N BMHRIE8oOg04A)&b?/wMHw 'U $ί?AEIA˘pkȺ5HMoB >UA[/ӚLu+nxպSRG>Rzz>oXݒoSg}9iu(Ϻ @ט%N'EuVucl} Qت~ܲlN!]u: Ӭ09i?q/1<75~aZ!|uD y ;nƽs¯U:7g,|ڲƅ԰8#dwY]y*߮c82F\jXcϞX۹sZAkEƏ[ME(o:R$Vi1oY]l8q ]\3O&߭۝(Z{(kv@>=O(Ӳ'nQ/C@+Ԅ (@h7ش o3ҩ_U/MN|sEaf 7Tr"`%8o9@.Ea~T-o9@"WCA|K]Y3q+;-t1 iF^ʵteDt-@?'Ȅ;sxcZ]΄sZ]g0~nJ _}.7%؏ ?'7|h?O.o(Rx[+?UZUo@4LN|SofB_F?%Vܺ;;P2|a4i9sNJ1ЉRD~6瀟s@'7QT:x">: `d~ZmJZ< ?Uȩx7~U,OϖwF@_i wꍽW)R{OfU)@z4eNnX2?7p'y^^'1sk}uU)~x_PqS5JÜ< H3r|5t;h*23b^=kHkh'4|=] `_O|:_ӱ|ӻD.*ז/|=gri_9@Mp@H,r&Lү'璸^K56t&*වk$: oo=D|:@J k6ӖD|:4SeN ߴ @wJ&M tvlI||:@M^˜mWoD3V`/~Agⷛ[j 5/& 4 Nz$WM:t;:R_:W7UQ=u@/~@8a2Y|VR -/s@/~@%|3=f2?.cӥ-Q^ +PMJ }Ŏ wxmN%&_&?~ 1\O~Y&?~ ~˅/[~/_V g]M'Gg[>[ _MMOX_OR `|mGRt ~w-ieW|= Wk6 {QOjqS\z)OW7j/(c  >no`*u+ /SBBZΟ@?mT EӤGUYSt> ͳ(߯;K*r]Ҷ|O'Ů#r~= T|/jOF0_ofV Ѱ椉 > 5{\dQħW9m,hK\lp]̲r|t(?9̃ _,@t.W,x2)|e<ΞIa9EhKӖ1r9}y߹l?2 HBA+>8P6 p6K_A%_6|J 2[ٹ-/[JKVe |~ %%/.ïsJK̷=p7O H{-@x:_v l]b + <./=gb(*w?8,djrU\'W6,HcUp"?,Ȏ ƕ2{'Mtsk 8տwƈ ?輖 ˅?*G}PRnCf )=݇I3i)\8?X^?06| ;}dž403BsGYJK 1: hv(1X ?^Ny 3{=Cjc{wX+B1>| WcR wkƇt0"ƨEQKfrEN c8r?߹/#s&l0n;';Wߒߌk45v]Ÿ(``q}5h|6ǎ4jwǎZ~˩0;0~"J;0#;2^ˊ?kw߱e8_TZScw j{ȇ4@PRL𛅊%8(hW`k2_\5~s+0=?ƾWt@%X7\_ +E:jwI{uBd 32VƟlmgW^{Xn|{^n|{Xn|{XnweǷp-O^\q+:WE6ˎo9[ ә} + `y;,Z+ f f&^*s9\~G} \)88yIl3]a+M/ƑHy/[R$?9wx `t|`< .lTT׹ sڸ4vڶXJ}1f){*JxJkFǯ\~wNN/+zJ_;ྕßIhji]=gm4ҿG `lf6!|_Oz]h=;oņf+'@{z.{~ \0 y;uхǎC <ދWدsK_!Ϊ8ĿrJkW8 >e.trWثKSG,On~/bOAӽEqŏ 2~ܘmv{z|a0ӹ<A"zݝm4 ,XğM .i0$= aD:>J >'7aRO2&͂ SRdjt")MН{!@H\,~#k\:fA+/zhP. 0"i}H{a|8<Uq3k_4>pH9gɵG8?W}]߭6-Ic.Q dyQ{̿'h|850^B@׉\&*iOO릎RDAӉ ^ o_]! 7P?Q߯{ZM/xi>I?}Dʏ!xR04EL_w"\IO;P\#ShJfz,_XK d{Wr(?i+p?r{(dtI(k+@9~- Yc95NfqJ-'ЕhڥӅ*]Pݙ$SI*O~6imGv|>?'y?N`)Q~[R|b>tVOZ1d-?b;';_":t(} (|5bd_ ]S-*ħ4D(lWώvz|=+pZq߳ ,(k >z|L#7O zY_QOf4]{o_?Q_ݙsСt+YBjHg+]_9CsiZr%BjL@溳jd~_L׊2:E'v)W"~zRRvr%yD 濅LI ϦEWg7"ief;~GQ=uvif쫈_R%~܊8i莂?kc3_/>w9(ӊ|:twȀ W_j+"\z3/!x[;;W"^nLK|Z b03vڃ?r0*~~M5KqF/I,uiNSD_YrwSSp 0VeE ȃO wb R| \ďm!8y/E:_Y~2Kb 7*%9<~럍̾*'@'._ƿ'؃Wy'_}H~1-q㹱Xmpj ȃ;3| \ ?4yc˛5=~xEh{sU?_3?N\;d~n?=Q_ܓf$<{/ϧ;f,ip@=if.3r邒Wm] )ο. _yo+}9l$:5~awVy~*1=M tH?Dӧ _J9# d%sq q   apƈv~7vKw;Sײ6 k֤O6?@nlZ3lٮ5(X26X&u~shԉ\5LǽFSezR+;ӌ2fSgvfů4L{V; 0M=V:>_Ք> 8Of_ԩ%k|S;Ǧ`coI5%=XiS՘Vhe ~w5~f~ 4F{ǺR vs3`?h9#,=JhlC^}mг?n$s-8,FMW &'Il#'e"h|롫tE<$~5*)4"mj^] 'NM*TiWom/߫[6XxaQ<2y @w}5B?ߵ рF6mmӽIE+Ow Z1k/KkFk|h`9t0 7!?c[)~ [\ƌo[?(xoa>f~ƌo/&-9qwSjgTǧuƍo) =Ś|H:;kjw;~qwrlfYG᫗-cag콆@eZ`_x&Xtɉ%kǍ{)ŏ<\:+)˅Yq߀jf\j4NTK~+:'+Lkh׻gPfh[E<^ ?ngNY͈VJ"nN}0ٖv<">,P4;V?൚qƕ@b [13=*>!wkN|@hgxzCz>+fM+R[V|l`вWV,JFr^r`G?)4z;CC0f嬇RR)3˓Κ71 Zj]+ udK]'`0 >A%3Y;/K%o7*1Mˊ%5V  Rf45^FJW#RhÇe4y|='~i걸y|p^]JM]0\ :)7hڈsŭ7Bxݝ'L~,PqD#4~>;E|;k=wޙ}t[|`?o'jUHt{И;3?>^q6~^<h{7X:Nl|=%P_dbl0?f vfbHSw#+C7 7z:ubx K?>(e~![Wq|pW*?F߽b3oq?YGg=.;VL#Y{@{&]I__eΚUPzPW⟳/^sȮ;^|hK@Iݠ}n&Cn/o"nDBFc)af5~a35??HV]KǻyNCxKUQ1>;}/3,ƟzSbBK{2WO-]g*xL 6o~Ӟ ɪGޔoJ]wӮI?V!gdţWۂBI9qOmA S_<>HxC3ˣb #DyNT?=H+,ݜ6`CP'>z^"|{8Ǐz76@߫Nc_.]3FITS/|R_(?_I^q_񓓿߰WoK(ɍ/7~^NU''/wu{7\//7aɭjxjr!a(tv<]]fm"7s*Sr FOky?:׳/$ ]?Z s_WӬ|; `zh vwl~ީ^}'f~s(//~y;6j(+{Lj?h-qJ>d?;>c:68o{u<~kA|8 YsWO >5N|NO(w4p{uuᷓ70\oahj'z;9ߩމ^es}|} C_MӽS:_z|ܗOѱ+C ?9c'G{2$cu\2EQe!>=wHAq{OzVPxҒJl DRG~4`Pu9]/x֍rR5gcy!+%?=Ӊz' 8JZD&R)Birj6 #KvJV񏥿]KC{7Y-0[SKC΃[$7Mu'K ~Mg Ϳrw5<=D펳 { p)5Mȵiv_=tnk<Sy~_Xj A eEUCgL ѡW8\r|NzL˿LBʤIh1_2 -q+W&?ne;\/krV?^Zu'i tQ~A^Xҵ(jIŭ6FYHX)b1<]Hk ц#@F"xHV"MAmhLzdC㺝DꧣG5AJ{מ!O\Kn Qn]hS=VTmX7g_;tދ4+h3ё GODt?mW}&&u=يNXjO!\9)3i (=?Z]ầb|T?T?6"QʩGתkq=` Q\](ی`^Px_t$:(S=щh>p0R1j݋cǣ.ʎFF?@#hӉr!zG z!?6JSF䃶49/ɳ~zIKI)y鲌#$2ґ:aѹoM!O__0E7#<yԒ3랇 v3yi)(<P6FmHUKhaj?Dw:<#O}WSERa#bʒB`Xe{i9I۲ j+raӒ:i+}v#U T1ͱBk!- S%g&yD\WG̿L3ve9grn"_Fޘ@`)2[ˡsegL7MƸVɘ7dކȢ6 Jt^=ѻwD!ގ ߅yiP"/۵浩erºjDo[m~%7S#\s﯏ؽ f̣7 iqO{cu9U)aymt~ ^s-Hl3ѫhq-x8 _ ?d߈C5{ZGs׀M7/GSM^A؆{}=2%Z# |9IK$&9hMљ0P? DB螫{زO>mZr\= iDD"U>YMLLZlשӽϽK%w=3t {Ʀ_uޣnv(cf)MXjkð/_v?^vLyK}~&buK?_~֥{]@;-]bSOzԽum5\&"\ [UΧni3ѮMȋ'E>nmh`Jn!/ꏟ7n=ON|"sNmB_f=uCyҙOhJnG78=m=oُ}>- ˯E3ځsO/&klV~1oF㞣.w1߉9Y<YQlԽ$گ+;= @{{G3ԻrN"og4>HTosgN$Nfr>Ll|7wMz*mJc} Zt\P3'Gmo/kLlOh[z)EkeHxbO#>wrIۯ"'W&4 vb@f!m$>i*Y+)GNr头ds:\o !{.K}+Y ľ؅.(K`o 5n"gfk:ʼY 25gD.ADY)lz\ =|U|73.`75k%r^8D5&ԜW;L}2B_#JЧQG 9_Úq1XW]h/wG9ך"k/{@>UJ檐=M^i$o{+zڪ]zpǼק轓x9@)n^N답}Ďo[by]w^;w:WEo^kNj'Yxsx|O Vl_}غ|^QL}7;nKlڱzz?½=V^c39ggggggg_f՝UMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09  P'@ b@'H'(16?2,@/7V'1h9{lpx fWu36! eB#`lp*11ťCK#xXƼZKAB -HED*!FDM%D)͘=1).w9^^Zk?>0\xaxe%/]1 yðcxeN`{ӒcO2? 8M1>p0Q=9}wi-7B%[$F麗Ғv<[Ϗyǝo+veb |獉X[ι4%G6ֿx֞U_U|ͅ}WMWˇ/Aȇ)| E]؟r-*b5Qc3 >98ciXuo6},};/}_1Ǐs^=Ly1xB my)^#~{/1kRMMNjع&gIQߡ0X<{_ 'ǬQv0;Ꮄaܙ&#ٟ׃%θ5zȸj[#sH#<8{ثwǖE@,O<[o)SG,sZ| :rW/ڗ~Vs]>O:83f#ʩӷ7<#Xs%h}gDq]s:ksb|(qz[pDPoyt7ȑh1}țDsӑhbU_7b܍"uNX)ɉcɫgeϮExȚ?tҳ.y.|*[67r/)ܶnAptlZ# njή. mڞ]Dp3.`-2[Wƅv`4.kߺ=êN{:k>\|.C1|r !DߕMYݶ­eJ8ήq4[3̇EM缣KEWl%m΢}s|t]~4Sx}麧=5ν |c:̇PE7Y9sɎi>N͇̓̉Gwnp#M˸9Fi,N_Z?qw޳ٯwCg>+D>Nc~ES/ _a^4ְ3МV*'K6n><ܻOK&nt:C: sZ#uO"sw0Ggyb%#jObj.NuYE|q'__9W|WMBs:]Wɶ]Wy s:>ysގi* Y Oj^fng̩U~+?!)Z[ٯDŌsrf.$N<l $ ؁<^+_c[ן6W/R|)uGY͍imK];'b}(>5Y_ܖκin_ |';{#euN}Rduc5q]6ټ}-21:͇Uht>;6mi{swO&cY?cY֯y)g6ǟϝ[uhzN~l.ԯ-&ɊSu_{>5=_rա]ϳk:{:k lw￑ؽsY|{WpDq#|Vg+ WY̩n#D _z438o:ʸњ;^4o:GD_]YY'kYg/y.y{iފ\9}]p/_ZŻLjx>-nܦ:ۉM6ӝqܿL5<{ zsr)ǭ 8ܕLqqyxoK}3]0ZO!y)h}n \us:<81܊qV_]oЇ<8e?hNg_Z>+v|Qn,twlN8{ⱲXA &'Vw=HcA빳~G,ʣ?x!^:9Tݽ˷NY6:9z~~hm5;)^]]o_xw!jVzB=M;]O6ʞt '>GY5:ŧ7J]]>ӘYGo>7 zc–#^}8u]#K~&'Up/Ł{9Y&KNL<}n!##dOs:v~2sJ9.'|]}sXTec&ȂTV~Udz8nj{}cǧ9g+ [έّt>Dr~vo93Qس)O[O+}˩-'O/e,s5^qg\*yϦpώmOʓ'ӿ)M)n.n/q qKHX۞'+yvM퓧kzq;A{v\<ٸq7)7ōd槽{ Y'Eb7S;#86핗v<ߖo gB;5g]w㗫p85gĕ1m`. m1\0dJ}<#NǓ\MgSO[rb'o qpM3Ǎ7E58YF{l#Om%Ӟ4gj:YY/@G1TO7}s#>t&_!&^IFΝt; t_Ds/C7~c S%3sH涹l6w+st;~1}8=uLߘܞ:/N7͞NU0Lǿ?mL_[>^RfcRCA}ն%?ZѵDz=-^Ttah6U/ƤMY,^˺|Nj'rMn\\ڔvA~/~m7<=7 #8@f;VU+ώ:Cڟ]ɪY+rp%=ќc'\ϝ&LWIJ~hܻ ~#C\]'[d7%z h?k:଍//\ܤ.vS[::*͕Cͥ,sIɥɥ72rxge)r-8їb:ԟn}I 3Ѱ=zZro:|7+Ó8+֓U_r8/_ׯdĠz}Ug>|5ĚMFI_7@Ms{|?}_%Xjw}L7򱙍dW֎ j,w>ض}'7=OIu6c_&,Jrw/4}{ݔo ;ߞX/L>j'v ?uoO ˲6q-bWcڌM6o߫~wX/qĽ5o .wU6F~͒_WGMKNuf1ȽqIJBǿo'u9t&6~%Oto<Ā|cS}xtT =9^;4^s+1u->c?&i.X3Yݔׄ1dH]\$QMz,W<;?/|̍vZ -ǬxKK"9լOiZ><5K1Rk~wx >b@ӏڇG7l5|>4xt} Suo/9y7N՘)7оfJxgSc>=!:iy ֕ƨ93_R-"? 1oLτ9q-grV/1%x-W>?ayOE2c8>MwM_7:ZtWv(g7Q͈]n *vNn V78VW›L P9xՏ[gծ뛞|򭔜_~vGhi'<{=Ysh`>YJ[Я];=jo6W~KcS:?٣‹^աcûkOҼg߮.mP;g]Gn[y:VV]-t9 -5q|p ˦-!oc}{=ǑgU{&nu~J~X9]0>?#πWGUY4xƷD^M>.>zcy[gk;ݣR:u2{=vW_<9P=/@]>xv5 ^M?]Ov]s ;|N'ΰy?s&Npسi\4i3x\+O}iv+\\.#VٔWfO=\0>mc|,oSu]ݘ?d;c<)6?$+֌-¿i<m[E:¹pKzS >6ms{\㪔41N^uz}/7ϋ_ƹywV/6á'0_t;OUNyVbxKfsƭo*O1m~OЁ6=w_2|WDU_Ɗו=?2|eɉ.~?DDm3%~~:|6tk][(fil[Y.}T>-XlGn_q}">x8'v7LV$ϰ}࿹O~Kz\mwcR;آ Q+l˳ڷvF?ճ7<oX_ NϕA>m\5oJ<bY~e/왇#g7g,Sã8=,8M*/&|=:^ݟ`+ŴO\#?QNk1t(mS{~py]h MVڮ*S9)?GƮΗ|R^߮ud_zK46_t_Z {AdNs|of&dt>}+=qoôwOڭqǘ/um'@ɥ}щW9祗-}xëG^Kk|ۏ:Xg967=G]kb+9j}fOwgZ_-u~'C&fѮs]b)}u+j㼬'ZCۣO4%=?M#3c:׿M/jw]sz:߰W?˺:?{g w>cޫgSo,,b9 – Ïîñòðîåíèå ó÷àñòêîâ ñîïðÿæåíèÿ äâóõ ïîâåðõíîñòåé: ïî ëèíèÿì ñîïðÿæå- íèÿ, çàäàííûì íà êàæäîé èç ïîâåðõíîñòåé; ïî ëèíèè ñîïðÿæåíèÿ çàäàííîé òî÷êè íà îäíîé ïîâåðõíîñòè; ïî çíà÷åíèÿì ðàäèóñîâ ñîïðÿæåíèÿ, çàäàííûì â íåêîòî- ðûõ ñå÷åíèÿõ. Ýòè îïåðàöèè ðåàëèçóþòñÿ ãåîìåòðè÷åñêèì ïàêåòîì, ðàçðàáîòàííûì ñïåöè- àëüíî äëÿ ÑÀÏÐ ìàãíèòíûõ ñèñòåì. Ïàêåòîì ðåàëèçóþòñÿ ñëåäóþùèå ñõåìû ïîñòðîåíèÿ ïîâåðõíîñòè: – Ñå÷åíèå æ¸ñòêî äâèæåòñÿ ïî çàäàííîé êðèâîé, èìåÿ îäíó îáùóþ òî÷êó, è ïîâîðà÷èâàåòñÿ ñîãëàñíî ãðàíè÷íîìó óñëîâèþ. – Ñå÷åíèå æ¸ñòêî äâèæåòñÿ, îïèðàÿñü ñâîèì êîíöîì íà îäíó êðèâóþ, è âñå âðåìÿ ñîïðèêàñàåòñÿ ñî âòîðîé êðèâîé. – Ëèíåé÷àòàÿ ïîâåðõíîñòü – çàäàíû äâå ïàðàìåòðèçîâàííûå êðèâûå, ïî- âåðõíîñòü ïîëó÷àåòñÿ ñîåäèíåíèåì òî÷åê ñ îäèíàêîâûì çíà÷åíèåì ïàðàìåòðîâ ñ ïîìîùüþ îòðåçêîâ. – “ Êðèâîé öèëèíäð ”  – ïîâåðõíîñòü, îáðàçîâàííàÿ äâèæåíèåì îêðóæíîñòè, öåíòð êîòîðîé ñîâïàäàåò ñ íà÷àëîì êîîðäèíàò äâèæóùåéñÿ ïëîñêîñòè. Äëÿ çàäàíèÿ òàêèõ ïîâåðõíîñòåé ñïèñîê îáúåêòîâ, îïðåäåëÿþùèõ ïîâåðõ- íîñòü, äîëæåí áûòü ðàçëè÷íûì. Ñîîòâåòñòâåííî èçìåíÿåòñÿ è âíåøíèé èíòåð- ôåéñ. Òàêèì îáðàçîì, èçëîæåííûå â ñòàòüå ïîäõîäû ê ðåøåíèþ çàäà÷ ãåîìåòðè÷åñ- êîãî ìîäåëèðîâàíèÿ ïîâåðõíîñòåé ÂÎ ìàãíèòíûõ ñèñòåì ñ èñïîëüçîâàíèåì ñðåäñòâ âû÷èñëèòåëüíîé òåõíèêè ïîçâîëÿþò ñóùåñòâåííî ïîâûñèòü ïðîèçâîäèòåëüíîñòü òðóäà êîíñòðóêòîðîâ, òåõíîëîãîâ è îáåñïå÷èòü âûñîêóþ òî÷íîñòü ðàñ÷åòîâ. Ñïèñîê ëèòåðàòóðû: 1. Áåëîöåðêîâñêèé Î.Ì., Äàäàåâ Þ.Ã. è äð. Âîïðîñû êèáåðíåòèêè. Ïðî- áëåìû îáðàáîòêè ãðàôè÷åñêîé èíôîðìàöèè â ìàøèíîñòðîèòåëüíûõ ÑÀÏÐ. Ì.: ÂÈÍÈÒÈ, 1987. Ñ. 6-19. 2. Âîðîáüåâà Â.Ï., Ìàðòûíîâ Ñ.À., Ñëàáîñïèöêàÿ Å.À., Õàæìóðàäîâ Ì.À. Ðàç- ðàáîòêà ìàòåìàòè÷åñêîé ìîäåëè äëÿ àâòîìàòèçèðîâàííîãî ïðîåêòèðîâàíèÿ ãåîìåòðèè âèíòî- âûõ îáìîòîê ìàãíèòíûõ ñèñòåì // ÀÑÓ è ïðèáîðû àâòîìàòèêè. 1999. Âûï. 109. Ñ.100-107. 3. Overhauser A.W. Analytic definitions of curves and surfaces by parabolic blending. Scientific Research Staff Publications, Ford Motor Company, May, 1968. 4. Ôîêñ À., Ïðàòò Ì. Âû÷èñëè- òåëüíàÿ ãåîìåòðèÿ. Ì.: Ìèð, 1982. Ïîñòóïèëà â ðåäêîëëåãèþ 03.03.01 Âîðîáüåâà Âåðà Ïàâëîâíà, èíæåíåð-ïðîãðàììèñò 1-é êàòåãîðèè Õàðüêîâñêîãî Ôèçèêî-òåõíè÷åñêîãî èíñòèòóòà. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêîå ìîäåëè- ðîâàíèå ôèçè÷åñêèõ ïðîöåññîâ, ïðîãðàììèðîâàíèå. Àäðåñ: Óêðàèíà, 61108, Õàðüêîâ, óë. Àêàäåìè÷åñêàÿ, 1, òåë.35-65-94. Ìàðòûíîâ Ñåðãåé Àëåêñååâè÷, âåäóùèé èíæåíåð-òåõíîëîã Õàðüêîâñêîãî Ôè- çèêî-òåõíè÷åñêîãî èíñòèòóòà. Íàó÷íûå èíòåðåñû: àâòîìàòèçèðîâàííîå ïðîåê- òèðîâàíèå ìàãíèòíûõ ñèñòåì. Àäðåñ: Óêðàèíà, 61108, Õàðüêîâ, óë. Àêàäåìè÷åñ- êàÿ,1, òåë.35-61-13. Ñëàáîñïèöêàÿ Åëåíà Àëåêñàíäðîâíà , ìëàäøèé íàó÷íûé ñîòðóäíèê ÌÃÏ “ Òåð- ìîòðîí ” . Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêîå ìîäåëèðîâàíèå ôèçè÷åñêèõ ïðî- öåññîâ, ïðîãðàììèðîâàíèå. Àäðåñ: Óêðàèíà, 61108, Õàðüêîâ, ïðîñï. Êóð÷àòîâà, 5, êâ.37, òåë. 35-33-35. Ðóäàêîâ Âàñèëèé Àíäðååâè÷, êàíä. òåõí. íàóê, çàâ. ëàáîðàòîðèåé Õàðüêîâñêîãî Ôèçèêî-òåõíè÷åñêîãî èíñòèòóòà. Íàó÷íûå èíòåðåñû: ðàñ÷åòû ìàãíèòíîé êîí- ôèãóðàöèè ñòåëëàðàòîðíûõ ñèñòåì. Àäðåñ: Óêðàèíà, 61108, Õàðüêîâ, óë. Àêà- äåìè÷åñêàÿ, 1, òåë.35-69-92. Õàæìóðàäîâ Ìàíàï Àõìàäîâè÷, ä-ð òåõí. íàóê, ïðîôåññîð, íà÷àëüíèê îòäåëà Õàðüêîâñêîãî Ôèçèêî-òåõíè÷åñêîãî èíñòèòóòà. Íàó÷íûå èíòåðåñû: ìàòåìàòè- ÷åñêîå ìîäåëèðîâàíèå ôèçè÷åñêèõ ïðîöåññîâ è ñèñòåì, àâòîìàòèçàöèÿ ïðîåê- òèðîâàíèÿ, ïðîãðàììèðîâàíèå. Àäðåñ: Óêðàèíà, 61108, Õàðüêîâ, óë. Àêàäåìè- ÷åñêàÿ, 1, òåë. 35-68-46. (x{heǟwv93w98,b8m a)قf5MRF9͜lFEp&lcΈkuZ,$;{yݯmf?/}n.{Y,"$J <*R^"tJkSa""TH//%j6\.H@'$8\WRrczcĻ2vE붮ۡ]K2Ktk)vrtM)"һ*zՔ#A$9#xwJVۙ[և/5r|SG*cG'ގ#W~R=cx8'=vθێ;{K)`(NaZǴj?>L?3~#}w ]dxe<\z83\.yE-|j+-W@n͆OJRLɑ+T\u \K ɓ\0LI!}nWwzV[9Yz套oWI,gy E}4TJ<2>]ߓd5T* Pi?h[ m:'}Z%svAX/lFR9? `_edh6H{1TF3S-|u1v=A]`13<o_6[c!Fpp+2]e繘o3[#3^&v Up1+p>_&li|Ӥ^U")_N!p-qfp}JBm9=&J*OóJ~.iE^Iq9^{E0SYB=F+4Pz,؋]GROE4^@(n!w|&x\=Ft'Ch?|6=l'N'O(vޏX3=w~v|K#$/G𱇗=|h7lɯ{)hb=ѵ!Y ciF,w/1P:wMSmb$GzN$5y&ה5yD_|bAfGx!<aOr>ť7M+3y:5k~~x O+~Q-t'3o5+ bѯgyN_M]N\ i~ sx#s~ q=Gڝg}&?^gFkӳb@\':^&W^W5=o&Ժu?=@L{:^/s|<}gN`Μ&ώ괿7[u곶ǭ;ǻv}v7sw7o:t9mw| {knv[ٯ9L_hVU*` XVU*Q؟U*` XVU*+7W-Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09  zcA K"jcrc(16Ԁ2 /hc1z{fx{]u;8(w ciH@ e.Ԩi)0Q HQ64Ԇ"Ԣ#خCHe<~c؀ǵ>u;cH{g{㜡ROp]-ł'BIW4^vQJ4F4%n.ғGV3$'>ǧtc%ݑҟ_~ kbJ1Z OUluDD9O4nA.Я3Z9LvM_' u*YfI ɸ^19:I_/t}aZdG*NЙﺢ6sI3]&o95ϴyS:_qۉN9%ޘzOI[;$:ZS$'LYR̕/JOQGw,-PZ}AW.=^w5Iҙen;yǔ4$ ]S{(3-M(}}V~SJ#N yJ}]σgW +B~6F+K+_c˽.ЁXZ7 VcR1 ݚTN%-#ÌUCtxyQSf fߜr4\>7)-'c*?o6&%I7ѷm}pK}G%Cβ_\#8[0S „v$`qKnr]gq}S&'*똂v1uhVR=V>/i.467ԝX`,u걀̶)違CKm94P<O)Q:/JEW>P9rxjmuLIo_V%i7{6,sW^.^Guwg쓌P׾5Mz+j;KKÝO*W <)it9K7}X=gp*,SƾG9]gRmhqS#+ߚvtkWMӎtWZn۶vO\7Qs:S}<A]0[pzx nUі6urnUch>*@&AeM91^AYtibNVH/z}蟱z:(8|Fc*?j:2s)[庛{*GK,v QB5&\;{PWSk+/ Stk ?{>Յ[X]Ut=V/^-`ez;u?,50z (1u#`g =\=z[zy\sjbJ}*jѾ^ܵB5kV5UK%Ql\heՅ ꋒK:3uC;i6T-<Ւ6c %zb-mt;Q:7Rohz[+i ^(V媿"^nTOWԃ=:+0\~y,u t:(wi.eҷ'tJ|ZfNw:-uryMwϗ:^.&*~Ο_Ao FX(@&,y\$ wvnͮks Z9/K2[_ϖܪVd `} v1Ҷ='@]>n^y-vuLZ/\B/%m<6,qAs1Hp][Y拷Wc"wI6.b3~+ *jۈc̝݅%ǎf|+uΪΈbK0]}ugbkˣdoO} }!60%}.xߴgNuNwlcslw 7Vl笽5/1dT6-*:=gtrtմT%#yh59[y֥ue;Xց Ini}}Ngl48X-1 ʥeH`bW;#S˾GV!윈Mjz~%==ٱ}y^۷y}A1|#D>ppԶWDŽ䜼{s?le{/]Is93<[QO;ttD[t,yK+b^= &RzDtLytCE~! }@HMȻ,y;y6֍nO /m Nt q{M钲8|).N։R~&׏zj4l98b~@D:tiQ74蘺݂ry< '[/t}mlęiA>tl< )WUl mpzU<r&871tPY+2i> ϙ8Y7am"_Sany3WfmtctK `UVXrzFܑU"{Bd+ܭ7vtw|ԑmPbst0%`:%vr#ǶD~|22mWe~-<*ja|KDy ߳cC { %FL\c|k?k rKe|*qk{6L[U&4do;EcL)X<@»wiҀwEo3=ir5 퀞Eӎ=4Щ~8h8d_Boqܜ,pi nx6kq9(0m\1By35 !+9w { y:}XùaǢgݺk{s.x-|yv~1bC\,gZCB~lBpؽ7U / tjۣdk[aיYfy禄Ղwܖ4.o 5YW#c~My+Ea/CE[u\wbwC][Yqi8-߲-61q҆^X}=t?M]u%JFg=FwI^ʄ̱,db8imUĨ{>V 2gyiiͬ6|·+x`>Xݚ[':ٺG *|8hes~#:|O4OC߾2]upǕb2kSORz:r?{ʹ|1XORm58ڦ䃝jS׮!k^1ɀ}>ʙ u\V;`[uxa֩K=qWJYȥeA ײG?gjRr{J]Fe} u<8hS߬[\.o p8G+%Dfc`V'r0vۋƇdAѨ]b^[Go_֝ucqNG[&8בgumUG}W=f_Kdзy_?rsk<ٖ㎊ݡX}dZ?Ind@XGĶd !soL7'2Ωθp=)CnpGӶ-؟:6>I?i@v<㢄s?մ~@µ|nTD{~{ёٹf8M'·'Ne!>:.]gnk)9?ZN#8>O3uM;dUGmS>)'򜳐ۛopZɾ7EOB|'h5u]'8sLm) {͹y3V&g2o;g=!;:,pLWò<؎ r3'o*ڇ]٠Ԇ܌Lb*2W?d-eH}{zr686Z/xܜo/VdэM`OJh#A|vo*V:[x'e{q7.2'f)}CrX6wӑr-چ،v={fhS|5Xhc?mO~w̏mCu:֍g/ぇv b!>kb+Cm.;!ZQ,)eh*o̭So56}*r}ax[ɀViHg{N_s[ԽYuf;|u-CIJCkY9K<xt;"yė[[sw-ڗn![7bN]_}he}j.hW-oGC&_"%Y=BOևujY,vrg=ZxL)}>X/3w# m|lug[G:w_8˄}}^?xuj|ˌ~7+dy<`ϰ>AV7 s}8lQ7V,rjñ`;ݡc"rS:zCLZKF^i[!>M0'psqc4\5P~:QhG z}Tܗ6?oPsp>^!Gv܌Gt r]Z5$։x?"u_y..r,6/z*Fs`ݨf&93sZda{AQUJ1'Dɒ$9s=qJbN[k୘`5P3zij^5򋩩U^l!=8 ^BR\KΈS_KχyPaFI,erG`r/s,z<[zݰctqa7z1/3I_;^'`0a&ۿYR3U^]Pl0~P -STLzV>Z2d '3e,|O]=|ļ%Oѳ},w#{-v9zTU̾ϲ*|0Ws[|r2py+8F6 X|>{A" Y.%g>BbgU|KkT>dxz,% ~nVu{x[KEܙHT}j|^ղac7nwŠHl1׍-/_׉Jk].0r$ܩDjG&gb'hmM]o*"Dˉ'=QK95&0YOTg*D'izտˍ!cM5k X&`M8> X&`M5kMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09     (16F2|/ 1Ƹb{hx{WUm -R-UPORlRlP(:ڂ-$*A36(X+2 |?eA7SGoBBn$MJ -{Ͼ'$iGǓ^ZkY=n\WWq0~a8-0rKaeX5 UT tz0?WN.}u[Rͣa"&a3媮,*SMmXu24}Ӵ|~Q7|6U9<3*~h:_[8#JϩJJ%븂>J[[TX[ù27N\fT@Wi;K?1ag+|pkW/z07~˿oh]fxEWYWo{vޮT==͇]?]Xu㯹|,so{9yO'c^a#Uf֡$=wvx>pin].6\lzlG;)?8;s}Np} R .o)C{G *6&g*nl>IUNJVҦJYΨ|װ8'yw'-N<ʼn7Q8zb"C$fhދ-֐t|~\P<|rs>0ė>|rzC&MC.X6%}Fþ>aK*2G=<:4>'+zr}_|ஂ2[=eSW;Rp`>?23Zs ی7۪FղIv}xΌ}/DWt~s%D==bBmr<ש~ O\o[\8|7|o+/X,JX=4.WseEiEo^mk=wh\N~ğ Z;T}1V{UcWf-zpt!7=rE瑙v#;9{&|,{L>p"_l[._YSIL'7~ Vp6V# } -[ ;3  .r/cU3yt=E'0XhA/\pm`{IMp)hz~xٚi.x9S;"ͺuuzhy{X_^{1>S̷oXaf;DߣE/ϸR_:9|p%9yC_Əo/-O/?I?ɀY鬕%uP|xesYGjyw1nessIgl`n ().]{yuF=-=8x+sz@/ يH~VlhsێR[Xq*Q=uZ+9]WvM(+u=M*GÓ-Y.^vA%,-&>'|C+9yhS;on)7mG˫~ѻeqpQѴ({JjۦV1dsn14n)6Jx?'vU^9?w֟n8o|k^Ve]-\[m#ap#ڹ laXԼm"~d/k2۞`{_QƱNߌm{]M 6:yb^{goi$}“&kn~OỶ_e=rd ~{H7_~`W2?p9jVϜR5h;jXYR(jom<:VM?{a^]D`)ƾЧ-ڇ~IBٕN5P"9:7|vtK;0ƖEٞ;,nm'W{Q8%zKN?Glb/C9Gr~K)G>Yǖ񵴗&';~fT&+CՕɗ?mܜ`//e[vChuĞ-?RuSCg|;qu͏N%_-mFwmE'*wrG?kFŻR|LxOV+ֶGћ%ܶsK|EsCT.fw`OY[l KdypEw5Urx==vu)+VQ]_ӗ?^pW_Uŕچ`'+#A{ɺ6Ƃٺ4ƽF%xBmo›Cf;?^)ƞ<6 l|ʩ72iKr|vy~SOKSVO]/>\!S?N.{ʚbֆmaRtrl+l0˜3".[kImCѓԵOVߏd^{L8<m?M=|W `)A[t מ7֓V ϼT,` yCBho&iVxN/y{X~1=)dKN= Y`r08/MFx"7t}%GKn S?\+ϻ vs[oe2ri~Б=$4~Sgm};[QMbcz!퓡E=Gx.Bs?\Svþf8ghNG]j,fG4iU'ͻsn-"Ikv+5c6w'zr m =+vvW^Z~w6>gn{3~ٶƲ'jCOV'vȵd-VZv}xoS{yg ]Y'ڸgp-:_9P0~* ;EP};5W|l^oldʩvCz1c#>i-ޖpxz{GvC>;f-S&3}_zw.l-/뵹9['.R=tm$31οWolOM'cKz^-z݃Mn\#)rvv7Ҏz/Cm6m<~w^Nf{x#eƷ]Ho{oHY᎔o4{v~rG'I0-,64g |h3W%|)džM _KydJ}? }/H+ٿO*ꆽ#cټwվmb.?4X3CbQ.D;K#ׁ{韩 vWme0m=-:6YݕZǤcOy;Jy;[ɼ7v>n˥Fѳz`)Է_O[=?XSOȲy.rٚ~*e>l򜺝fwT`a{QbRy ]Ko.þpf{E32tִmF\ȶhWx.:Ml>)޾ iGӦOi:~c#e[v_|doVsfn[=ggi_b/J.+Jv1~]Uj!nzV4vb>kW3/c83فۈ|qIs:yЦr !4j؟|sڞewbojlwͲ-N9/o Dg^f._xI?mF]^ŗ -Y; /+ v{ʬгw js(;\;eO'Ϊț.>VLHh.`'.k'KK4=={tBE>u}ˆg]:-,zn7=oVcm_u;+EOGh[Es<|mܼD/o# Op$|#yLLxi||e{õ/amxk<\;\[ί,nҍÏկ~ͦkoyWxaRTo )Ň|__io `Rɻ{ #n-dJͣ r\월䪲 ewTmKZSuVn-6zϤ27TϽ޺5A*MR''zVg9zTsh$*Şi3s K2,/O7>r=0/3')S Ң^'.gʎ>hb%֯X{k]f7Κ+X .hIn=վnnܟ:g租)6i]Te78O~uE'NƗCV]sO Y2X1Nr>CO/5m`lW qמV'nǽdxe[$jhJGIP40M{l7 Ǜףs> DO.ե̛)=/Y`Gcى/H`y*'drK;lԕJ[~S%7e~ :oĮ3Zevg)ZYG_g'}.2^{W_S 퀥O.,-+ P۝VjcV;[>:~Ӵ֎(.R쯿Λ!>՞ҟ5fΗw2~OͩI%KpxD_b$0rLGC~\e1h!eE"KW6;e9 G9S?X]RJ'z=ϫڷ"ݙy2߅+rpdȷw~Ѿ~N=m { ]Fzs[+~;^[􉮷_񅮷39hӏȕ^?=m' Q#?glG.;pyO;hOWVtiKa]>2yBppO^{UZ=Ur_e1^oE&\Ŷdá,3oŝٜVXzz0|ށSkS>^q!}LƯUl鼲Og |EeqS]RkO }̭{IVԭm[uz%{]%9>} `KLjlR`\"/ˇ{)ok,-Y/*g/p=xif9eAyle5]y^4n}C6ڪ,ù;[(WC/9vy9pdHGO ?_C 2Y:<@_슢]s9Kx1nЧ:0N$]di'0r%FCr&'g2Ƕ*cc6y-§nօgeE̦~=77,)oϞIE(rG`zvw$y+Kt#_yM)|ˣ2WdAh|m^FƠoJڇg\deWyo `G.e~גfg5rN}k~-<=ߋs*C%sHC;/ts"=A+XtosH{;Ǐ߷ }b<[%i?CRohӶ\;}\]񫦶k,so6hVA򷻼B_TwbijhwyCQjmYw?}Ё? G &eq7ڈr6H=>yx"'|㏽yBC쯝C9W '1oWNL|Y Ҟ w=%˘2$}1~~韸ŭq(W\;xJsܡ[,,J11 2. Êðàòêèé àíàëèç ñîâðåìåííûõ ïîäõîäîâ ê ñòàíäàðòèçàöèè ïðîåêòèðîâàíèÿ ÐÈÓÑ Îäíà èç îñíîâíûõ öåëåé ñòàíäàðòèçàöèè ïðîåêòèðîâàíèÿ ÐÈÓÑ ñîñòîèò â ïîâûøåíèè ýôôåêòèâíîñòè ðàçðàáîòêè ïóòåì ñîçäàíèÿ ìåòîäîëîãèé è èíñòðó- ìåíòàëüíûõ ñðåäñòâ, ïîçâîëÿþùèõ íàãëÿäíî, íî â òî æå âðåìÿ ïîëíî ïðåäñòà- âèòü ìîäåëü ñèñòåìû ñ ðàçëè÷íûõ òî÷åê çðåíèÿ è íà ðàçëè÷íûõ ýòàïàõ ñîçäàíèÿ, à òàêæå îáëåã÷àþùèõ êîíòðîëü çà ïðîöåññîì ïðîåêòèðîâàíèÿ ñ ó÷åòîì åãî èòåðàöèîííîãî õàðàêòåðà, êîòîðûé çàêëþ÷àåòñÿ â ïîñëåäîâàòåëüíîì óòî÷íåíèè ìîäåëè îò îáùåãî ïðåäñòàâëåíèÿ çàäà÷ äî äåòàëèçèðîâàííîãî îïèñàíèÿ òåõíè- ÷åñêèõ ïîäðîáíîñòåé ðåàëèçàöèè. Ñóùåñòâóåò íåñêîëüêî ïîäõîäîâ ê ìîäåëèðîâàíèþ ÐÈÓÑ. Âàæíåéøèå èç íèõ – ñòðóêòóðíûé (àëãîðèòìè÷åñêèé) è îáúåêòíî-îðèåíòèðîâàííûé. Ñòðóêòóðíûé (àëãîðèòìè÷åñêèé) ìåòîä ïðåäñòàâëÿåò ñîáîé òðàäèöèîííûé ïîäõîä ê ñîçäàíèþ ïðèêëàäíîãî ïðîãðàììíîãî îáåñïå÷åíèÿ. Áàçîâûìè êîíöåïòó- àëüíûìè ýëåìåíòàìè òàêîãî ïîäõîäà ÿâëÿþòñÿ ïîäñèñòåìà, çàäà÷à, ôóíêöèÿ, ïðîöåäóðà, à îñíîâíîå âíèìàíèå óäåëÿåòñÿ äåêîìïîçèöèè ñëîæíûõ àëãîðèòìîâ íà áîëåå ïðîñòûå. Äàííûé ïîäõîä äîñòàòî÷íî óñïåøíî ïðèìåíÿåòñÿ, íî ïðèâîäèò ê ñîçäàíèþ ñëàáîàäàïòèðóþùèõñÿ ê èçìåíÿþùèìñÿ òðåáîâàíèÿì ñèñòåì. Ê ïðåäñòàâèòåëÿì ïîäîáíûõ ìåòîäîëîãèé îòíîñÿòñÿ øèðîêîèçâåñòíûå SADT, IDEF è SSADM. Îäèí èç íàèáîëåå ïåðñïåêòèâíûõ èíäóñòðèàëüíûõ ïîäõîäîâ ê ðàçðàáîòêå ïðîãðàììíîãî îáåñïå÷åíèÿ àâòîìàòèçèðîâàííûõ ñèñòåì áàçèðóåòñÿ íà îáúåêòíî- îðèåíòèðîâàííîì ìåòîäå. Çäåñü â êà÷åñòâå îñíîâíûõ ñòðîèòåëüíûõ áëîêîâ âûñ- òóïàþò îáúåêòû è êëàññû.  ñàìîì îáùåì ñìûñëå îáúåêò – ýòî ñóùíîñòü, îáû÷íî èçâëåêàåìàÿ èç ñëîâàðÿ ïðåäìåòíîé îáëàñòè èëè ðåøåíèÿ, à êëàññ ÿâëÿåòñÿ îïèñàíèåì ìíîæåñòâà îäíîòèïíûõ îáúåêòîâ. Êàæäûé îáúåêò õàðàêòåðèçóåòñÿ èäåíòè÷íîñòüþ, íåêîòîðûì ñîñòîÿíèåì è âîçìîæíûì ïîâåäåíèåì. Îáúåêòíî- îðèåíòèðîâàííûé ìåòîä ïðåäïîëàãàåò ñòàíäàðòíûé ñïîñîá ðàçâèòèÿ è ìîäèôè- êàöèè ðàçðàáàòûâàåìûõ ýëåìåíòîâ â ÷àñòíîñòè è âñåé ñîçäàâàåìîé ñèñòåìû â öåëîì, ÷òî íåìàëîâàæíî. Ïåðâûå îáúåêòíî-îðèåíòèðîâàííûå ìåòîäîëîãèè è ÿçûêè ìîäåëèðîâàíèÿ ïî- ÿâèëèñü â ïåðèîä ñ ñåðåäèíû 70-õ äî êîíöà 80-õ ãîäîâ âñëåä çà ñîçäàíèåì îáúåêòíî-îðèåíòèðîâàííûõ ÿçûêîâ ïðîãðàììèðîâàíèÿ. Ñ 1989 ïî 1994 ãîä ÷èñëî ðàçëè÷íûõ îáúåêòíî-îðèåíòèðîâàííûõ ìåòîäîâ âîçðîñëî ñ äåñÿòêà äî ïÿòèäåñÿ- òè è áîëåå, ñïåöèàëèçèðîâàííûõ äëÿ ðàçëè÷íûõ öåëåé.  ðåçóëüòàòå âîçíèêøåãî ñïðîñà íà óíèâåðñàëüíûé ìåòîä ñîçäàòåëè 3-õ íàèáîëåå ïîïóëÿðíûõ ìåòîäîëî- ãèé Booch, OOSE (Object Oriented Software Engeneering) è OMT (Object Modeling Technique) Ãðàäè Áó÷ (Grady Booch), Àéâàð Äæåêîáñîí (Ivar Jacobson) è Äæåéìñ Ðàìáî (James Rumbaugh) ïðåäïðèíÿëè ïîïûòêó îáúåäèíèòü ñâîè ìåòîäû. Ðå- çóëüòàòîì ýòîãî è ñòàë UML((Unified Modeling Language)).  êîíñîðöèóì UML âõîäÿò òàêèå ôèðìû êàê IBM, Microsoft, Oracle, Hewlett-Packard, Ericsson, Platinum Technology, áîëüøèíñòâî èç êîòîðûõ ñ÷èòàåò UML ìåòîäîëîãèåé, èìå- þùåé ñòðàòåãè÷åñêîå çíà÷åíèå äëÿ ñâîåãî áèçíåñà. Ñ îñåíè 1998ã. äåéñòâóþùåé ÿâëÿåòñÿ âåðñèÿ 1.3, ïîëíîå îïèñàíèå êîòîðîé ìîæíî íàéòè â [1] è íà Web-ñàéòå www.omg.org. 3. UML êàê îñíîâà èíäóñòðèàëüíîé ìåòîäîëîãèè ïðîåêòèðîâàíèÿ è ðàçâèòîå ñðåäñòâî ìîäåëèðîâàíèÿ ÐÈÓÑ Óíèôèöèðîâàííûé ÿçûê ìîäåëèðîâàíèÿ ÿâëÿåòñÿ ñòàíäàðòîì, ñ ïîìîùüþ êîòîðîãî ìîæíî âèçóàëèçèðîâàòü, ñïåöèôèöèðîâàòü, êîíñòðóèðîâàòü è äîêóìåí- òèðîâàòü àðòåôàêòû òàêèõ ñëîæíûõ ïðîãðàììíûõ ñèñòåì, êàê ÐÈÓÑ. ïðèíöèïå UML ïðèãîäåí äëÿ ìîäåëèðîâàíèÿ ëþáûõ ñèñòåì: îò ÐÈÓÑ ìàñøòàáà êîðïîðà- öèè (ïðåäïðèÿòèÿ) è ðàñïðåäåë¸ííûõ web-ñèñòåì äî âñòðîåííûõ ñèñòåì ðåàëü- íîãî âðåìåíè. )xLUǟs:pg&KpR?j#ga%,%&LHX([ɚtVk.fC+WƏ>^zw۠{w %yRz|Hn5= :@Vm!}M4~&@NsyP8 ~ E\&Xo'> A+j8T| 7">IHT@T0\F~.錷 A,8#VPNjIS&d*/kxkj!9x/8 &3n?!yof]Cyz~bq= /~Nezv9r99O|1q6e?FL6:A Hɢ%zV;k{w_{'R%rXz] ڰ\P}ΜLgm7˱{0g ] *g ZX`ۍOz[Cp@Kt |@|dJʔsdZp3pNY*0 WZG40.ŞGD*‹@_]Ķqx9y,p's{vh.u\¿E'/^R+_]˳//.~yf!-.]wp{x_ x;|l5jG{=+<~Kݰt *K rЃ {x:^ u1qxL,g{A 0MqbdQj_n|H)9ѻzyo6uX#{wo g%ya) \o9؏g)__! wW}q ^N[s|0cY>=$6;6~3=\]kz&R>n+UaϫJO[ g|dWV^iR>uM#\Af3J[[?WX[i23e}. P|qwEi/ItSN.?y; o/Ooh࿱Q/8*/|͟fiӯJçtpK:qOo>,39gr*vrS*]x\/WYi=eiÅ>W?>fӷ8fG|c+~OgGvOiTjfww/ p^|W"_Z$Y_^)dH"<.=5\y$!Pao>wͭ'v6/zWo~'_9}GWoQ?/~)eI߱U? |7/#uRevo}%[ e {]cxTrphxp7ڎawED4SvU[yEΪ&_-I[۪?b9s*=+Ӄ'p8ӛ7|^02RGUN{h$u'x2"XUDvhG=)y͹EsU&.J|K➢;lunwe cw0ze4vbb6Y|ڈ൩ p|}4ւ?2^zM؟`™ym.?L *meevv|`_xP<4J=NJV_ e4$|%.*GkWcGe<\FY+c͞RՆ[k~tSYU[?`/2[)kkywko;Pe{؋*.3X{j3.)J wV5%޲"g2z߽#Lыֶ'4H.LFkWY?c_D=1K0$/L*T1Ι{>̙ V-KuuwF3j~okwP@~>xxQԁˆkéٞ,ݖC+ vvٕn/Ux > DrЪt[Cç,No)MV mg ͍*g `͍[ gOHeVW'xKnt } =38Fk_geG?ܳecO4xDy2/c7#3`-vjN"NɞQ,1u8o7ڹ*p3i{PSt76!]~==sBOlNNmS O|;x~cI;'#'Rg뿯dJWT{Mes]ĻY=bk` с\|>6XъgV:~P}8o~Sز~jm2L82/ɼppξ{ڙď͊;Z<>ҴUfNjݞg/fK(Dh/*$p9~ɍ=C~ɵ%%[gԍolrg%̮?W0/ͅ^YT(پ]-EO[Qrh$29`Cs1VeY64ed^TX&*6~j{k5I#wN=GgWgUƳ{x~vFVp ۦ.zc .ݣS^ .>#S}iGvүrmœ>ORpis%s w{}^ʤk;ʾW[{ $:n5bXish[کw^[sxݥFƉ'%%#v/uzB /)0γ$iwƼxOܩ{U/]"֫'+U[rd5̽dc5Xs̙E;KE> 띞R#/o`ڀF| 667ؖ u|?1L*_7g!w8Ok/ed?cSQ'O&2莿]vч<:uv|amlZmO6O9>`Rw2}?6}`ϲ6OeqDTAy삯]g'pkEd|J7Sط 7VOta?[6W*l^xD4#蚬=ǯ]_}/7p~2kY L8wV%|WT:_~5EsÞG^"{ ϾEy@-"+3کv=#SHtN[*!B+1vH MY%$?//Z{hO?-KWg}3v_wr=Uwmsۉۅ, dWEGGݹLgȺqӝƆil"xBK=/|bF.zP #ү6eQ1|dfgt_{nW֬_sMیixG?8m6Eb=X [O z_*n~D`'#Wfcy/O?Cˍ} _h]ڎK7pnfj-uhx~%;ﭧalge?ٚ\w;ʘ{SvΕ-Ӳ9$<卬 I}?ĂȌ '|pƁO?ԥswgxfվjR3'⾥"s"o4;zI/mv;'Y}p3crz uחn5P ~1$CTϦfm?/Dᴃ/%Ru}u`ױXβ؛;M7-r/׻kc;\b6ڵ?}\`$C\FeRF=& k6r7xAh6ϴ~#'cXeqwWyO\;` 'gkvb35~}0.Oeyt-9o+ӫ_s}{y.)e}~rgQȬT럯l8fx{}gRdi[{mmިvپ?pnuR9=~ep='%~p_r퉑>_V%/Xo-UO? > ɘ{ 7U^^s`~wׁV;>|Wr_;vtzy#E7 fXv;߹1ӛD7яD>t/~G%'S,k֮Sӟ39zsVd#Oہfg woR' &n֟M6h{<ߔ͏e|^.-XvƓOE2<"?I;R|fj{[;ֻ57Srml(V̿-Jl]]%Y.zSF.e‡>GX{m6ȚN;Ҳwti_N&ʸ𓿹?ئ'a߯} &__)ز8µ7'Ó=v2};hMtf9$ qQYBgϾ|,x[{/-}ƒW=(Ii|u}K_Wȅgn.pv9`Kp{/{Ifi~y~wTm;ٹ{vyC'Ā'Nz{M1 e'M셏Lc{Ӿޞ/3{{B(׮?.\։e;7<Nj&6؁V*:{{<襔ѱ+Yi;ѤplLflF[ SoF,M} &~}hf> 흁e4,.V4y:0ٛy;PnErcy=YcOzcjtIGo7#'p}5çrdOہ`Z]^ OܵN._x>]P|be ]X/ړ3d~gq}gd"^c7zhϤ2Ns'쒽5} z44wɤТS]c|C;܌O<vj6;li_;gS炷UE̦wncO?AZO)9\W72ەezWXٝ#qΨd#Gcph>V^T#+% xGnc=!AsCּʎlˬkb_҂-=koy,7̱GˮԬmڧmo޾ߘ}&q;_QŇ{+;&v4~xc>W{80WcU9m>W&Cl`;6ىe+O-y;h; 66ΣuclDEtONc޾A .yx1h_f\09qދ ߛ%oXq{2쨷::ܞ۝];ػ2sޭ-11*˽WZy8z^vѩܜz;l:[ };ɾ~}&:):u9{w򎩽?1go?+vuZ3F<[kol7vʶNnWډ?U8+n=u:;CxE.rzʼ^(:!yeA4}dG-,^^$잳{quc`G{?kg{nvY~X =}nxlsؼrso xn}Ϻe0 /]`lhnհaހpc3_? ҟ\mbhrћ:ta>}N'po.ر࿔w{sRo0ۊ$"Ki~cC(k \+b#ۊikn~rWQ=>?nBݸחSezaIcqå=pS?WF/O_2̅WO9'ـB{cQ̎{ w߾)D3o3pC>~N_хG9ؼz|ʑv[pN)m<9|ڗk+~k۲L_+ F=ZK>Q۪׾9oc{ ~n~%}#˳v0v`[*ņƮ.7{*ǧG/YǿCKh)%3~ɍŇ/nؐ-_\M_g҂mӾ{mD5hwmvrv.4O|3ݨz93AJs='}*::[yRXp)>eOzCx򳿈L}yRF_|l8{ ?cS-hJsZfѮ#It_,, 12 UML íå ÿâëÿåòñÿ ÿçûêîì âèçóàëüíîãî ïðîãðàììèðîâàíèÿ. Îäíàêî ðàçðàáîòàí- íûå íà åãî îñíîâå ìîäåëè ìîãóò áûòü äîñòàòî÷íî ëåãêî, ñ ïîìîùüþ èíñòðóìåí- òàëüíûõ CASE-ñðåäñòâ, ïåðåâåäåíû íà ðàçëè÷íûå ÿçûêè ïðîãðàììèðîâàíèÿ, íàïðèìåð, Java, Object Pascal, C++, Visual Basic èëè ïðåäñòàâëåíû â âèäå òàáëèö ðåëÿöèîííîé, îáúåêòíî-ðåëÿöèîííîé áàçû äàííûõ (ÁÄ), ëèáî â âèäå óñòîé÷èâûõ îáúåêòîâ îáúåêòíî-îðèåíòèðîâàííîé ÁÄ. Ïîñòðîåíèå ìîäåëè ïîçâîëÿåò ðåøèòü ñëåäóþùèå îñíîâíûå ìåòîäîëîãè÷åñêèå è òåõíîëîãè÷åñêèå çàäà÷è: – ÷åòêî è ïîñëåäîâàòåëüíî îïðåäåëèòü ìíîãîóðîâíåâóþ ñòðóêòóðó è ïðàâèëà ïîâåäåíèÿ ñèñòåìû; – âåñüìà íàãëÿäíî âèçóàëèçèðîâàòü ïðåäñòàâëåíèÿ ñèñòåìû â òåêóùåì èëè æåëàòåëüíîì ñîñòîÿíèè; – ïîëó÷èòü ôóíêöèîíàëüíî ïîëíûé íàáîð óíèôèöèðîâàííûõ øàáëîíîâ, êîòî- ðûé çàòåì ïîçâîëÿåò êîíñòðóèðîâàòü ÐÈÓÑ ñ èñïîëüçîâàíèåì âñòðîåííîãî ìåõà- íèçìà àâòîìàòèçèðîâàííîãî ãåíåðèðîâàíèÿ ñêåëåòíîãî êîäà ïðèêëàäíûõ ïðî- ãðàìì íà îñíîâå øàáëîíîâ; – ïîäðîáíî äîêóìåíòèðîâàòü ïðèíèìàåìûå ðåøåíèÿ, èñïîëüçóÿ ïîñòðîåííûå ìîäåëè è âñòðîåííûå ãåíåðàòîðû îò÷åòîâ. Äëÿ ðåøåíèÿ ýòèõ çàäà÷ UML ñ ìåòîäîëîãè÷åñêîé òî÷êè çðåíèÿ ïîçâîëÿåò îïèñûâàòü àðõèòåêòóðó ÐÈÓÑ êîìáèíàöèåé ïÿòè îñíîâíûõ âçàèìîñâÿçàííûõ ïðåäñòàâëåíèé (âèäîâ). Âèä ñ òî÷êè çðåíèÿ ïðåöåäåíòîâ (âàðèàíòîâ) èñïîëüçîâàíèÿ (Use case view) ñîäåðæèò ïåðå÷åíü âîçìîæíûõ âàðèàíòîâ âçàèìîäåéñòâèÿ ñ ñèñòåìîé, îïèñûâà- þùèõ å¸ ïîâåäåíèå ñ òî÷êè çðåíèÿ êîíå÷íûõ ïîëüçîâàòåëåé. Îí ñëóæèò äëÿ öåëåé ôîðìàëèçàöèè òðåáîâàíèé ê ñèñòåìå è ïîçâîëÿåò çàêàç÷èêó íàãëÿäíî ïðåäñòàâèòü âíåøíþþ ñòðóêòóðó è âîçìîæíûå âàðèàíòû èñïîëüçîâàíèÿ (ïðåöå- äåíòû) ðàçðàáàòûâàåìîé ÐÈÓÑ.  UML ñòàòè÷åñêèå àñïåêòû ýòîãî âèäà ïðåä- ñòàâëåíû äèàãðàììàìè ïðåöåäåíòîâ, à äèíàìè÷åñêèå – äèàãðàììàìè âçàèìîäåé- ñòâèÿ è äåéñòâèé. Âèä ñ òî÷êè çðåíèÿ ïðîåêòèðîâàíèÿ (Design view) ñîäåðæèò, ïðåæäå âñåãî, íàáîð êëàññîâ è èíòåðôåéñîâ, ñîñòàâëÿþùèõ ñëîâàðü çàäà÷è. Îí ïîçâîëÿåò ñïåöèôèöèðîâàòü ôóíêöèîíàëüíûå òðåáîâàíèÿ ê ñèñòåìå.  UML ñòàòè÷åñêèå àñïåêòû ýòîãî âèäà ïðåäñòàâëåíû äèàãðàììàìè êëàññîâ è îáúåêòîâ, äèíàìè÷åñ- êèå – äèàãðàììàìè âçàèìîäåéñòâèÿ, ñîñòîÿíèÿ è äåéñòâèé. Âèä ñ òî÷êè çðåíèÿ ïðîöåññîâ (Process view) îïèñûâàåò ìåõàíèçìû ðàñïàðàëëå- ëèâàíèÿ è ñèíõðîíèçàöèè â ñèñòåìå è âî ìíîãîì îïðåäåëÿåò å¸ ìàñøòàáèðóåìîñòü è ïðîïóñêíóþ ñïîñîáíîñòü.  UML ñòàòè÷åñêèå è äèíàìè÷åñêèå àñïåêòû ýòîãî âèäà ïðåäñòàâëåíû òåìè æå äèàãðàììàìè, êîòîðûå îïèñûâàþò ðàññìîòðåííûé âûøå âèä ñ òî÷êè çðåíèÿ ïðîåêòèðîâàíèÿ, íî ñ àêöåíòèðîâàíèåì âíèìàíèÿ íà àêòèâíûõ êëàññàõ, ïðåäñòàâëÿþùèõ ñîáîé îòäåëüíûå íèòè (ïîòîêè) è ïðîöåññû. Âèä ñ òî÷êè çðåíèÿ ðåàëèçàöèè (Implementation view) îïèñûâàåò íàáîðû êîìïîíåíòîâ è ôàéëîâ, èñïîëüçóåìûõ äëÿ êîíñòðóèðîâàíèÿ ÐÈÓÑ; ïðèìåíÿåòñÿ êàê èíôîðìàöèîííàÿ îñíîâà ìåòîäà óïðàâëåíèÿ êîíôèãóðàöèåé å¸ âåðñèé.  UML ñòàòè÷åñêèå àñïåêòû ýòîãî âèäà ïðåäñòàâëåíû äèàãðàììàìè êîìïîíåíòîâ, äèíàìè÷åñêèå – äèàãðàììàìè âçàèìîäåéñòâèÿ, ñîñòîÿíèÿ è äåéñòâèé. Âèä ñ òî÷êè çðåíèÿ ðàçâ¸ðòûâàíèÿ (Deployment view) îïèñûâàåò ñòðóêòóðó àïïàðàòíîãî îáåñïå÷åíèÿ ÐÈÓÑ, íà êîòîðîé ïðåäñòîèò ðàçâåðíóòü ñèñòåìó, è å¸ ñâÿçü ñ ïðîãðàììíûìè êîìïîíåíòàìè.  UML ñòàòè÷åñêèå àñïåêòû ýòîãî âèäà ïðåäñòàâëåíû äèàãðàììàìè ðàçâ¸ðòûâàíèÿ, äèíàìè÷åñêèå – äèàãðàììàìè âçàè- ìîäåéñòâèÿ, ñîñòîÿíèÿ è äåéñòâèé. Êàæäûé èç ïåðå÷èñëåííûõ âèäîâ ÿâëÿåòñÿ â çíà÷èòåëüíîé ñòåïåíè íåçàâèñè- ìûì îò äðóãèõ, ÷òî ïîçâîëÿåò ðàçðàáîò÷èêàì ñôîêóñèðîâàòüñÿ íà òðåáóåìûõ àñïåêòàõ ñèñòåìû. Âàæíåéøèì áàçîâûì òèïîì äèàãðàìì UML ÿâëÿþòñÿ äèàãðàììû êëàññîâ, ïîçâîëÿþùèå âèçóàëèçèðîâàòü àáñòðàêöèè ïðåäìåòíîé îáëàñòè è ðàñïðåäåëÿòü c*xLe?! o \3<$.b.F25bHbiFd-iPGb.h֬F44K[ڰ{:ϻc6<_ylD";OW"kc";g c m%sӾՋ|n5p!Nߩ^%U&bQ~ qG|mZ!-؃ic;m7l[mA_^*0q-EbMʯ?}2Rv^*ׯ`[}Ϛ3k;4֬Λc+\Os=\e`]x#nƉ*˻F2- ;g`|,Y ;Z@(.u/R-]Ќ n:'"**Z&8rtyܖ!Urtj^0>8EFrm:GQ.?o9&7m*CVr 5^IFdى}n[I滨~;lu:v?馞{=kf3~|Cvz_N`o/>.gj_z<@Rj;d'(5sYnO]^bV".,ISe\|+~OsXg}Jü|N9eT9Rn 9xt8@ex`nz{Ee;W0nn\\, S _e}3r8Pk-s7 β}!pE*_B/@ڿ~_&&A,U:֧op^ρ_M>!IdKpZ_I:-y71 z%Pm|]$$ z~)|00@oK:(c?A@X_Ml{@zK鳵JSMyDŹq.y|xk.<%G9?#W52sp.{{ShSNy6+k`!| p3hn`!9J[@_c9=g&=fc.i>FɟDsfnW/-o:@%g!8;[o]J^/kbv#5ox?31x%`/xQmn9&_J0CYݬpPRdz}pkd[v%/21;,{ad~&bEGgϿe8[9{}-YMuo_g+ ,qZ*s"KU_{dPFzʭSZq5Owz '+n\i<_<G)@aBMAW{drf(ciJޢ)sSx5+HC?2Kv;00QIou}av3;eޥC{SήGf_Ԣ~{xG&>ٍlŏgefͤ-KdiJ^4O#b˹9yʿO K;ߨ+Y3IznnF}yӊ隷QGѷm_:=:vκd,R4Uzo?v v2ޥ{0MUMi2J̓S7k "_D\ wr-'GUo/)ꛋT$7;&oNn9=voN }!6dhCd{mY-{4ے(ۜSzhu={\<p~fAa6*ޢܝ#ߣRC9-R8K}${CxF#I&1DpW Ey)Ges]K1Hm|䒶|C92QSǁ6M?bbbϋphhTyYMa)ףEjُealG(Bŋ?Ve?6ܢ {o*w<o*mQ=|TtJ=s3lC4z{}C1,49Daxm'ۇ,g)(K#벜ضu,et5O@󼏴O+ʲeo.t`Js4xk+/߭,&҈=B;E;k;.axb_M 4m96OKz̖ zqNlwq>e_ϛ':F҄Ç8+3ɧKBֵ/14t㟳xd-aìlν [ϻp(@lxYv& m]-/?_*feOi}l]~Nvffz3[w޽eVKj٪R...~WVxfoLaU^z4:9ӳOs8m˯Xwdd}CGu+u4տ?O(ݞ]`|,GX/@Ǜܧ<Qdw+N1>oˎi x\WX />wxӁr:m?W |1TDC?)y_udj\OՏ>{OO/؁?aFܿ?}X}-K>vC}Lx3jUV7_G'/R?C l4t ti!](Wu HsIUyl9DžKsα\Q?:>͂5wc_׭w|g›YB.חF =iƹ[ʑ?:teziv n>9ׄ{Uؗ 7|/ /V96c v8H?=mqpD[ fvH6p뇱KA,<<ݡ7%8~rۿr:f=qožq⼙ן7o[.ͣ 8QVbmub^<3w#h~[I,^~'{VIIߡLﭔ{ 4A51nS{F~Jwt9l7NE'eu4~t2[=,oѾ)tK}o[̻Z e>w c}n'3֞'3/c~:鸅#<\dk;W4XYZW0^ ;e +Z=YZIN\e [N9r ݚa h̚uO56=L5Cgʮ|Z3P.Idy_zaLk f9^5Ch 'n7墭}Uto{K8Fο5Cw:}_l2͚彰X[N >?6u*s2y~v߫ '(pׅ>e]g|yCgEO>of-=N)fԿѷđ^e}F~Mw*|P+ŜB:;{n6|M_iFa15״Qދy;PטcY3>vk,ڥ5Eec*C]0ɃڻEa>ί}R腓4NKxp鄓]Iu23Neqr gn*>;m8uB?q2Xĺ28 ^?E AE"ư߼ L~y[O:{٫M, #&'f;#>.Ym&/C7~j'm육uYxžɗ]_>1co044)~tP?j*s)~FmHo+)]!3OS bŵFzs2*\S5ˆ/ek9_}h~*yyn|!1,];~lɷ}>nyiM㶎։mKG}ϻ 6^+a"l@Q(0=ʉ؅ eI/' &cWw&WU  v]2hwz#pE-~n*>ߗo}O,~bQ"r]Џydl~U. b*hסǢufuh7,zHZm;_\j*CMƞ=. #軓uYN@7N3~ľt 5 xw>m>SLT7ęTęK;Ls6Cy^8c;5Ӵ5驳Uq*o[q.Rg,qw+ fo^(m5gj{ʶu7g۞{2}C[x& ݦ}> :'#] a`n_tRVG_LƾLԾC}SؗުX7̗< r=2y~w(Lܻ.ָ 讋se>_,f;wۿ9?$.;ERڿۜM}ѿ#}za0Kfkkm(|J.7> r5J<5MB>950=D{,h5XU~ϤkLԒ?׷ w>}C+etʺވ5vh~.䤗넓Tוbe@w]ozdսK_}IʡSdyLNocԾ8 >8㽘&&}ۯIGKVgRg|vt_"֕.x(sZIc"NIǯ̃c7ߐ^#Foػ'5|ֱߩΉ::oL-fD@?`}ث4DjxʲyVqG|[n$ v@p~E_w:e-Q&cz"r]ЍE)^o>" X:1wӌU܈U1Qp[U.HK%~}F%߫^Xu߮UDbU#s`*!X2y;Vên~ǝlUybƪ5T (ֺK6켉uF%¢:XľtU,r"HY̩RG~u6_X._>[2ͦ+_X ~5r_|s:͵*TPZ<|kZS8_/^!Ǎ+ϳm=`ŽoVV [7+ؐuZ:~rN?) Z=׋K =ȸ ŲJ̻,c|M}|2z>v~5Q3U6y?>y `Gۊ٪8O5Vz=.g=omF qw$ }\lTm [I?,^ R{VI/= _\ _DN<ۄnӾ `sN.N[Meu4~v2>ƚ645ohߔnF:?(_M43Xo̗<Y\t5GٿKC>wܻ. +}3~ 65}9n69PIHlzax8 >~"Arlt/L6I6IT}b vN { Cy{3:;-ef mWzi (}7 tF6WVO3ӓOYcWQ+RoN8ɞO]tוbijozdW+ѣ/ʡ._ %g'>f3X9.JL=7 -bT*bK7[L('b2E)zEI/hPcQĢs-o'2ע:E4ݨY_!GBrr?&]z%zV2\. LLߥ_`gc/OWv?ãu2*~ :1U)ʉLx.Ƨ7y;Uçn~ǝgjU~;@|Z5h|Z#[NZ,t3^jW+im,P7JL/,Z:XľtU,r"EHY̩]_8^c&c[_eQwz=[ Oޑ_XVu/'Y gz͠f˹t/æo1O4Z5:W &N2q6=6,LgT7Z]vsn=jC\Oo35go2M߰N3D,p ŚevBxiJ\ySC= rͣ>S^ [j{pv~l52u<דsAOnw[]:w<[\lT[J);x>ںg :=Kz=`sK6{oN>TVG'c_cisnSF eL>J-fue@w];{GoNRGߜ!ѻ: Կѷ;ҧ rY[Z)G>KWޯՊJ/V;asdoNW;UlUl(U|&݃I-ݷccm2疦}|2=5_HЍ]I/ 'T^-JTYg op8? &7=q=2X=h3pۊSINT9 `rddhnINz&cstEt}R9}CMiI{SڿwcO\q crkG  |`؝B}>#.|iLx.Ed3.Ҧ|7}7}g<8ߟ?VeIWYI|JbڬJq1@?Ft`[G`}Y9z,M0wxߪѿU7 Ϥ8I#N8N膓@ڂ>8Mp:$eQ&}('b2E庠R|E,9V,mq]9W 4}@Ec}r0^~Di[/0\kDgr:_r-淊B|WIHk7o L`^ n_|G37V_o[`FVOD<3n亠^#/`j6ѯ~wk[S{#srW)][9Ses - _N\rmYGzaʡMuB?~U'ʉ^X#e1 ^1$niP~~{Y.|5^N7yF&sac7鉍 _ ۼؚbcwmHgd:%!yFaɴb^wj~tăw!'~W /9[>`}oKujXdV­eח7;?N\+KL/MuB7D'q} ?E]Q&hz>eFL*zƮN.䤗놓*uh]Wk>h>Em7鉓 / '' FQN]Tq NvmиwGny_MוI?aC}&I7 Ɉcd'<섟')k.Jf7QOܜy{Tekwd?=Kd^{H\`qsy9TiYgRL֜N'nkN='L2U LW)V߿8/zQ <򌕃Qmwzbe+bu64X]໶IWYs2o}@[$H֜OwN'oY6"O-fD@gn6K_y'c^gw5Ax|ke¿Vh{ķ_NoO@ow t7L('b2E庠R|)XT6=\5׺x@XtT`TϵEר nE{1bZN:MG+3ϗmE@NWŢ('bQ(|U;9p{*ܚL`7K`)|Oߨ{clGlg,wv@;oc ѽV\G]]5{s:S+M?fvzMȌ{~3ZFC樎fϿ|mv_>[YٶkВ]Kx96km>6W-eNFA_ K(QyW=1=QxtmkayӊE>o8=:M9]G17#|RNJ+ *e/x۱iV/k+WUyS!Swܖ/flNR q%)^hh}ٖGl_V~mFUhMof{Y<;exj UmTzKγGLvJ>='w u)W`+95itr:)P>ʒv ˢO& YKs;lEo!Yyg?lQc oP.:Jm i-vv )/u6s;|3Q47sy2}pl?FL+n!л;,56>#74lɱd$셝 fGn?[m~yOU@o{xIƎ}{d.fLo`6T,wh?":~Ty*ܒX1qr1dA$9;;rۙXϽ;GbW;QiZmCLieo߁fY)i܆(>||}Ҟ|/k^:{,lbyr8tYt:sR}bOt>R;@Щ}m3xb=i"t-4y=X6>] X[xvAofػ7=ք"=91e|ᐼͮQM9"Ɔ|FH6Om^5ў['po][=Fwy}{AN,;G9v>5JN xy=pE?ިފW0fi'Y˸OoޯVt8qَ <9x |=qv?@?G򟭀n@{@y}Iq=sw̜ujsw[:t1FzC?Gl9qni?7Gqј'wH>Z'ȶ5HX*oY _R6VX揵i3yYQ6#r}3ч7|=A!uu'ܥծ˚e\71wFoVźm}E4p~W)jG?zĮ5ohCR]펓uҎ;_N_yV.f>+/-eQP/?ftG'bxg3t|\Ebhґ϶4?1#~|9y:<Vo{scѽ螝ӫ c;A%[%,=ܽ/tƳ#={7:"@wyАcz } ı O-'xc;YRX`^,;+ٛ}X#r:s ћ5{y3m}^x_ٶ=0w=k}P+yzzy~--ϰxn_bнvǾ.KLpѩM|h5/0r-W9mlhZ-Kĺ~U6bVDg HȠ36lS<6rtăݭ\ԝu`۹ϘNѷqQ@}1-&!!9KŻ>w'тϤn޴s>$ĻB!^wy_ʖeXp}(0^7+vhI?w'dOl})`+p<{5:q?cy1؄{b8ю_6XPYevw(C,.S?߯ 7h_Wtg̣}f$ՏkA78cc{kn@1W ?Og&X'󕶞<]tou t u|GFqR&5r{a#F_'|Meݶ-SiyJq73(V~ҊdMS~Ny~I/P3Z=Bs_fyn@ XKy-׼ؘ16knp{GKʼn{hVȵ. Ǎի}PfQ({Ȍ̿ycx.=Š̾YwYM_ "F7HG1>֠;>A^ ?u>u m!~ pOzO ^RKA.|nELY-ϥ367nU {Qc {Rmp>>^g!]~B'WQ˨hwTx~]E="=yĖΞ.oyNT7:} |Ķy2ܓ(Cl&eRm?Xs}nyo{,{+"bq΄x~eW.c=\Vۄ6ڗ#<~tbc=zz4g<9#ymx;=ǔǛym ݖ\=ɵeO᧬'^Җœ:VAml/|EoGc^荼+E[.Nzc iŧߣa =Gf?լ~_ #QXgYK9g΍(q]/7HuJ47e<=wtO~A|]{s>q:RM2_g9eJ{ c?Nl~*K6mު=!arw\ D>yDH|&|-g뙃zbuWX9/kN8 z6=AG'6>e߁F9xТAǦ(/eHOVL#&^bY;-ӷ&ŢP#E付CB{T֚7k(;]Ixƨ ZV{X_~CyX5gv9Vq+9Q1v%q::!v`L&=WuEđyyQ&4d`w' ˢCM[.Ť/~NA4Ycꁗ4!7'sɎmhz5}; P/L+eL`Ɍ=9Z Z+b|.3P>.JX.oqF3ƅVBonH:ڛ{d3btkc?1/<׮zL1i%PzR>B|8`o=mE.VNvg,|_.<`4;V--(NnW!7y4gHac:l'xLoO~iEmNG6t^| \pD_f>Үz#D}6e?iE;]6V`ϯ0}N'g Epv`/h;gYOx|Ǥo| |G5'iu uxm.3>,,13 îáÿçàííîñòè ìåæäó îòäåëüíûìè ÷àñòÿìè ðàçðàáàòûâàåìîé ñèñòåìû. Òèïè÷íûé âèä äèàãðàììû êëàññîâ íà ïðèìåðå ýëåìåíòîâ ÐÈÓÑ âóçà ïðåäñòàâëåí íà ðèñ.1. +декан Студент Вуз 0..* 1..* +обучается в 0..* 1..* Курс 0..* 0..* 0..* +посещает 0..* Преподаватель 0..* 1..* 0..* +читает 1..* Факультет 1..* 1 1..* +состоит из 1 0..* 0..* 0..* 0..* 1..* 0..* +работает на 1..* 0..* 0..1 0..1 0..1 0..1 Ðèñ.1 Ìåæäó êëàññàìè Ñòóäåíò è Êóðñ ñóùåñòâóåò ñâÿçü, ïîêàçûâàþùàÿ, ÷òî ñòóäåíòû ìîãóò ïîñåùàòü êóðñû, ïðè÷¸ì êàæäûé ñòóäåíò ìîæåò ïîñåùàòü ëþáîå êîëè÷åñòâî êóðñîâ è íà êàæäîì êóðñå ìîæåò áûòü ëþáîå êîëè÷åñòâî ñëóøàòåëåé. Àíàëîãè÷íàÿ ñâÿçü ìåæäó êëàññàìè Êóðñ è Ïðåïîäàâàòåëü äåìîíñòðèðóåò, ÷òî ïðåïîäàâàòåëü ìîæåò ÷èòàòü ëþáîå ÷èñëî êóðñîâ (â òîì ÷èñëå è íè îäíîãî), è êàæäûé êóðñ äîëæåí âåñòè õîòÿ áû îäèí ïðåïîäàâàòåëü. Ñâÿçü ìåæäó êëàññàìè Âóç è Ôàêóëüòåò îòëè÷àåòñÿ îò ðàññìîòðåííûõ – îíà ïðåäñòàâëÿåò ñîáîé îòíîøåíèå àãðåãèðîâàíèÿ, íàãëÿäíî ïîêàçûâàÿ, ÷òî âóç îðãàíèçàöèîííî íàõîäèò- ñÿ âûøå, ÷åì åãî ÷àñòè – ôàêóëüòåòû. 4. Èñïîëüçîâàíèå UML äëÿ ãåíåðèðîâàíèÿ èñõîäíîãî “ ñêåëåòíîãî ” êîäà ïðîãðàìì UML – íå ïðîñòî äåêëàðàòèâíûé ãðàôè÷åñêèé ÿçûê. Êàæäîé ãðàôè÷åñêîé êîíñòðóêöèè ÿçûêà ñîîòâåòñòâóåò ÷åòêî îïðåäåë¸ííàÿ ñåìàíòèêà, ïîçâîëÿþùàÿ ïîäðîáíî è òî÷íî ñïåöèôèöèðîâàòü ñîîòâåòñòâóþùèé ýëåìåíò ÐÈÓÑ. Íàïðèìåð, ñïåöèôèêàöèÿ êëàññà, âîçìîæíî, íå èçîáðàæàåìàÿ íà äèàãðàììàõ, ìîæåò ñîäåð- æàòü ïîäðîáíûå îïèñàíèÿ åãî àòðèáóòîâ è ïîëíûå ñèãíàòóðû îïåðàöèé. Òàêèì îáðàçîì, ñîâîêóïíîñòü ñïåöèôèêàöèé ôîðìèðóåò îáøèðíûé çàäíèé ìåòàïëàí (ðåïîçèòàðèé) ìîäåëè, äåòàëèçèðóþùèé âèçóàëüíîå ïðåäñòàâëåíèå ñèñòåìû. Íåìàëîâàæíî òî, ÷òî ñïåöèôèêàöèè ìîãóò áûòü èñïîëüçîâàíû èíñòðóìåíòàëüíû- ìè CASE-ñðåäñòâàìè äëÿ ãåíåðèðîâàíèÿ íåïîñðåäñòâåííî èñïîëíÿåìîãî êîäà. Âîçìîæíî è îáðàòíîå ïðîåêòèðîâàíèå – ôîðìèðîâàíèå ñïåöèôèêàöèé íà îñíîâà- íèè ñóùåñòâóþùåãî êîäà ïðèêëàäíûõ ïðîãðàìì ÐÈÓÑ. Ïðèâåä¸ì âçÿòûé èç [2] ïðèìåð äèàãðàììû äåéñòâèé, ó÷àñòâóþùåé â íåïîñ- ðåäñòâåííîé ãåíåðàöèè ïðîãðàììíîãî êîäà. Íà ðèñ. 2 ïðèâåäåíà äèàãðàììà ñîñòîÿíèé (÷àñòíûé âèä äèàãðàììû äåéñòâèé) äëÿ ðàçáîðà ïðîñòîãî ÿçûêà, ïðåäñòàâëÿþùàÿ ñîáîé ìîäåëü àâòîìàòà äëÿ ðàçáîðà ïîòîêà ñèìâîëîâ, óäîâëåò- âîðÿþùåãî ñèíòàêñèñó ÿçûêà: “ ñîîáùåíèå: ‘ < ’ ñòðîêà ‘ > ’ ñòðîêà ‘ ; ’ “ Ïåðâàÿ ñòðîêà ïðåäñòàâëÿåò ñîáîé òýã, âòîðàÿ – òåëî ñîîáùåíèÿ. Èç ïîòîêà ñèìâîëîâ èçâëåêàþòñÿ òîëüêî ñîîáùåíèÿ, óäîâëåòâîðÿþùèå ïðàâèëàì ñèíòàêñè- ñà. Ó ýòîãî àâòîìàòà åñòü òîëüêî îäíî ñóùåñòâåííîå ñîáûòèå – ïîëó÷åíèå ñèìâîëà (âûçîâ îïåðàöèè put ñ ïàðàìåòðîì c). Ïðè ïîñòóïëåíèè ñèìâîëà, îáîçíà÷àþùåãî íà÷àëî ëåêñåìû, àâòîìàò ïåðåõîäèò â ñîñòîÿíèå “ Ïîëó÷åíèå ëåêñåìû ” . Çàòåì, ïðè ïîëó÷åíèè ñèìâîëà, ñâèäåòåëüñòâóþùåãî îá îêîí÷àíèè ëåêñåìû, àâòîìàò ïåðåõîäèò â ñîñòîÿíèå “ Ïîëó÷åíèå òåëà ” è äàëåå, äîéäÿ äî êîíå÷íîãî ñèìâîëà, âîçâðàùàåòñÿ â ñîñòîÿíèå “ Îæèäàíèå ” . $xklTEϴ.P\6b" K %B,H)(b<m@P T0@**^s֦ s7̙3g枙 "/"9I">XD*$HC >Z"+uH=s,Hj? tDP*՚\F0;tGdgJ yMy'7Q20~T هL3(^]A|hk`42-k eYWw[O|sB >I~":7h/zvO!hވ/K1*m0U9}U,L̛ɸ 2e*}zR_K6` ܈b .~E;Rso}&e؀}L܌/?kp(*,!2.S=m4xB'cWs2,A˱0K@4Vɨ1ag=WBwo5[\R(Anf5ux>@Q{r2g}EORN-=|8vv뫅Y(Yl%Y,ن} 4%+cm~#ױ/Ͱwx,CFwOcGð7ь_G rg`X>WĻu< f2u乫`OxVWw6xʬ[&eϞ~ǹp LE.2s|݈Q:F,Q霛tyA it_Yup<}~1Ѿ`>ΩSSߊ=~CcP=}JW=5:)x>?}JP:*(s4DDsFЅZ~_WG)D\ "F왋glY.Δ0y i1k&A}ڑa|bX3ˎxtxy'uœ׊7 ZvE=~O/mY5GV\uDꋕ;8=g:&xFo=s1x`9,_$FG3IN=GwO6f+`W]v +?/Ǯ]v +`W࿫Q Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09  z> ;zz(16ʔ2/z1t{]x՜Wu? -eJY f(ZY*UW )0݌V3ĘTcgLS`$a:&cFR$6:5h4"w~{ޏߏirs=oB`I!Ղ#BV$ KW0$يn˱!l=>g?\fت=#Շ]\h^;çSN#'M3O|{-,U^}Rq:= ^/4Em⚹uQUQm".}$xU:4b!mbn'놷c/JY 03%+"靠xnȒ|Vl#⩪T|l^V +R)V846[ebcsr8Ʃ/k7VClRyW>6+x4[',_'<&C!78y=&ɳDk_l,Ti=s/3kr=pb&>5Mmfl{O JX8O,))FG2 u%- (*iL-]}Q2}}}OR?zP[yRzf{>cZy`a{aȐ 2GVm?v-ico[O?P'>' X)񁧭(s3AEt1*d AQpS`-w+g1ٝqԭ2_+ײ&V;t1YL2 x,8gm\|`aQQIUC7?Ng/ؑPSk>Y3ffMK٪ϪA6b8D7?ZVsUB8ق(${͘Yl;>Ax瓿Xp9̙0/,n#qo_Y޻ ϼۓ?mqc3$^DE`_ 2 #;>ۚ(c-k^|荿ϓ|`􌵹XO}1z.FGY8w 85gFտR<0Bo&~ [SIMmz2[~눜:"阖IrqO=]. W%ry=^Hz ;Mjo琫)y犸W2k=\ѝ!~sdz?wF!a7)ѬV}^ogϩN CKt@yHu+Su(VU5zڝ*jms/^1;T@,pg_ɏ~g=jY8l4~H!6RJ}nWmJ7+].{J:9 %}+-(w^MZeY!a~?dcϗ1a,/Mio>btr׾}g6ȐF Oq&+mJZV&vIK%[ޜ۫#2s{*ȥ3{/Mm_Cҹ{|njrkWP߭8nh?T-rzxO!gd {pHSvJ9CbD6.$v_<5p&Fb$4 #Կif\` /x nbc+6a u4닻Վ]s;w 6Nn܎}a)zԕjb/}Bvnl $x9c-{>y>>sm_.FG4.MǴ7:|xv.Mϯ̼J6hmxվoKq'{{ ү(3*.L?A^&/msuۺM~meck[jUyoX1MsXAC>mt1[;]3ԌhCg}];NRT fuhތ#~d;mZ?L]ɾ^;ռK[}G<ҤĹdb,]>#X}g_Y-fSHڔMt1vus?s8k sH@Vj;y 909O_͹}^IB_{F5szX,`/"!;=WrM73J=$z 4SW[qU>Y:S%f\nEY+K;(fS)cf ԝ3𙧷yc<8p'jn;)Zꆂ `ӧ6[kﰍ3o]v<4|w3P.Ń 𶧀gpٌ?Zxc4Pھ=x.FG+Ƨ j/}N])0^1ׅMFtO}v;&_No:T2?NmN#r\#m_阶FG&缾]]GRe:/[>dURYF| ~pM=s} T{mq#>]T=7n߯@{7 Z['֬[Ny/| sh_K6kFjM`Φm_#kZ{rqL^S8yzZnͤ?껃װ_u)+O 7`w^į51; wo?.~'~L‡߉߉ߩ߉~' q;bpCJx5y ^@_W`+ep;B݄ Iܫ Gos}W@zF^Ź=\;EO_Ϣc>}Jn쑜 ?p9- -iXl O?|E?tE{x#Ao<]N3~Ư%؟5zo*(}#i_w}ڭ%*kEaVE@DJ/w~[ƟxeMlzF}~|#'EK}xh^g>qEOȿ psa =00=V?u=D89cy,&M?j`0u_$>JmWݖY)su'-mP'v5 K-׹x>x37s~Z lΘDn1w[#?wV.vmZ~JÃO3t.:4с؟*CN-lyX+,ɮEKg9>V>ɓ셶eyʅ|2*z[8+:.gF[.$~z Hsl='CiիS}hLLd16 ydǕ]-cح>㯛ڮ)ch&6r7eU'msd2~JJl-fk.69Zz]#zn(x5ݑuukv8LLMge4MJlzxv$&&} N$ >6 ;D"T| wxj8btFt8&F.&CW{4zߣ;Og&</ _dtʶq>=cd6ث} _QWw}t\,o:T &/wdh3=JHhн vH,,14 Ожидание put(c)[ c/='<' ] / return false Получение лексемы put(c)[ c=='<' ] put(c)[ c/='>' ] / token.append(c); return false Получение тела put(c)[ c/=';' ] / body.append(c); return false put(c)[ c==';' ] / return true Ðèñ. 2 Èç ïðèâåäåííîé äèàãðàììû èíñòðóìåíòàëüíîå CASE-ñðåäñòâî (íàïðèìåð, Rational Rose 2000) ìîæåò ñãåíåðèðîâàòü ñëåäóþùèé êîä íà îáúåêòíî-îðèåíòèðî- âàííîì ÿçûêå Java: class MessageParser { public boolean put(char c) { switch(state) { case Waiting: if (c== ’ < ‘ ) { state = GettingToken; token = new StringBuffer(); body = new StringBuffer(); } break; case GettingToken: if(c== ’ > ’ ) state = GettingBody; else token.append(c); break; case GettingBody: if(c== ’ ; ’ ) state = Waiting; else body.append(c); return true; } return false; } StringBuffer getToken() { return token; } C xT]HQ$ꚻAi+ kыV-e"b*ER=Z`DAOEDAA9Wi`/|sX& \K@+ eqW}p^$ k.Ȑe@璉R:Lxa-MyZg'$Y l|& +/¸5CއHAD#OQ*VpN-^RVA#hQT&֤VQjدBc\zrC |@Q>|J[|01G)ș}cFc+eA1fDo(g8^U\JʹoÏmdPܸ:'Pm..AEPb/uet71thɗqg~ }n]G52<~D1C3Qrn~fm{%eE|sܸᜱw: ̚[g| e6M/'˼/3;ʳ̘;M7i|a5;uNn75B2}~C`z{7uځ}x S+ EMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09  $ "(16*2`/*1*~{\x͜{yID].@T.^oB(jVDTJ`uF;tzI۴$NbZMیmLkRxiRX`P1js={a!v<{y<繝n#p`Y# ڄ(?c\BsChWhvCk!< NuX8eM3, ׇae(׆[Ƅu5WX! PFC_S'iWKf -?6[a2G & .} s&gkuf_` :utVXBK0faNQ]׋BU}B6Nu!>ȟ@[o16<п?aySN .[V}pі1~b֨>%|DZk? G 9B6x }ev`c$T0{`:V,I]eEDcL^N:Qz2/6nwI?t;V8ՍU!w:*.Xl֑ czf2;{''Cqʧ±G׍FBÙ' 4>\z}ĮPL0/OH%fA3?t1?dzh$Ʀ|&O(H?/f#^.eB} y"n{?\(JZu9/|RjX-Dh?;3ߥ<]|e7AW \ s/DӬM-΍<[3Ρj+ˤ3/Nȝ:[V=e`OJ|{ 8N.yy^S؊JOroK\9>FLdqVBfp狷NOE{"aS[?፰1lS\6 = }T/7T߮rG8xsjo׶ rߠѶE͢*ZG|or9}m^89.X!p?eEDi~MXyrv ~9 cFz^+cQB G wpuAW^,\,mʄZķ_"GR w SEl ~#>ݒ5R՘ mn,"Sky9M$}|+! K:ˡz#cc;y=/s-r`p]Ƴn'+O*k_&rznR ^Yn(r}@=X#K kc7vl{73};<^+,} 5F1Ι>[81?9~:[/EY%k=;fccqwf߮Ht0u{t4k1dU^W$7k7+=Ve'A%|[ڊ}g1OsX<;wǃ~8=6wz9R'n_i}4J;)nT}\?qm[@Wyqkq$nuq߭6R㦥e4JۚFiq;cB1*>"q[_Ulƪq$nuאuz♟/k;쒀# n!{YRg{]{IpS;K§&zϞ~5@b˕q2;[+@ gF|t#==9X/JX }hI;i\NI^.ӽ} J QT^\( 1pY(O_OqxSGăjGchh<\7xvXHܺVw }̝ku+Q*$x[V D/G3 v>MPBmr:g$ot hԄ{TPׅ*\_mHw}uZXXyCYk䅔1rq"ڵINs?8?#S3؇6>|s)v}P?lS?s`wW ݏ[;\Yw{W9c4:P> r>կ/>QiĿV47:Omr_;J1m#Ȁ~ǕX! M RK*/+\]^)Z~Vq\%)r/נ=hv)JEh/}:=$w7}Ӱ=|ÑffjnTX~gLgV8%T9Vf_;sL762?ԑ?p؃C/h}]ľMj0F WWEODɍn H7JV]Sbmbǝ.sFO8~:c[7ШOvs?7}Kʓ 9I++~vpQբl\OLZ'?>,F4Agt6ZL;E6<Ϧ /%1yF{l>,ȃ%*hKh=E]c9ɮ[o OG~!W|(}%莶c{}A#/}-%9y ^ˠm~C̼D.Aw#~ſU 5_6 WD<'kMΆisIo;عx &[!Jv{9أEo?<.9 o k_o#cq 8 >ƃأv{טolg*7(ivkG)̕]I=o8oַCH'C{]&CV.ۋ/}QzݥnRwrh?/\q\b]p\?`mC,G&LN +wg#rsF]+ZkT:kKU7hvxt['ksZ)ݾ=Mt:^(lR,[c$;8׫r͚4OL[_bg! &G|Ycq4r;|!4Mwcc8?hǯ17C1{k^X\tMstyrⲞ؁zUG¡U]N{D{{Ig>cl b;4lǟu,{6"EZ 3YO%Z%蓾ZURV+D.1^Kz~DJ꿧:.gn*:_y^A|!`^mEYR_ޟ5l>^'ܹe~8Y'wL~g&o?>in;hS#t8[y)}ܶJw޴s~oIs/[K>uh~?ؿa?Q 6 sjODZ&&7G}9zvAI+GMՏ#3F_<΀>?6򎋺;MݟzcB6.^N\2lxbDT'x»~c&ݽ{)Jfmۥay_Bi؊@n+:аh>p \G8MuDg<:tl.쳎ugu|Ȝ" eF'TkB Sۢ,۠~= ֪u:&mQ b?|1o> #G4vMhC*._!GWl휩b}ha̩bks%snvr=YzBIe/%k"mǏ vG_|N};$vbJ\(9UDznCFCIהco;!},xg|ơN9ޫsiW[6<`ѕ q#>^܉/⩻:~hRyͽ8&k*_O W#jU3O+/J[6Xў՚{ZIޗh%ԓ~M術.\glQ3Ek,~%w_aݱ:?v,>K6ύR)+όVye^s^ɳPy͋~;G:Yaaxq|vIQS"՜?=}~Můo7ս>-~x .sҀ^SSRy91XF,,c15 StringBuffer getBody() { return body; } private final static int Waiting = 0; final static int GettingToken = 1; final static int GettingBody = 2; int state = Waiting; StringBuffer token, body; }  çàêëþ÷åíèå îòìåòèì, ÷òî ïðèìåíåíèå îáúåêòíî - îðèåíòèðîâàííîé òåõíîëî- ãèè è UML îòíþäü íå ãàðàíòèðóåò äîñòèæåíèÿ íàèëó÷øåãî ðåçóëüòàòà, íî ïðåäîñòàâëÿåò äëÿ ýòîãî ðàçðàáîò÷èêó ìàêñèìóì ìåòîäîëîãè÷åñêèõ âîçìîæíîñ- òåé. Ãëàâíîå îòëè÷èå UML îò äðóãèõ áàçîâûõ CASE - ìåòîäîëîãèé ñîñòîèò â ïðèìåíåíèè îáúåêòíî-îðèåíòèðîâàííûõ àáñòðàêöèé, íàèáîëåå åñòåñòâåííûõ è óäîáíûõ äëÿ ÷åëîâå÷åñêîãî âîñïðèÿòèÿ. Îíè ïîçâîëÿþò ïðåäñòàâèòü çàäà÷ó â âèäå îòäåëüíûõ áëîêîâ è êîìïîíåíò, èíêàïñóëèðóþùèõ â ñåáå ñâîéñòâà è ïîâåäåí÷åñêèå ñòåðåîòèïû ýëåìåíòîâ ïðîèçâîëüíîãî óðîâíÿ àáñòðàãèðîâàíèÿ â ñî÷åòàíèè ñ òåì ôàêòîì, ÷òî çíà÷èòåëüíîå ÷èñëî ñîâðåìåííûõ ÿçûêîâ ïðîãðàì- ìèðîâàíèÿ ÿâëÿþòñÿ îáúåêòíî-îðèåíòèðîâàííûìè, à çíà÷èò, åñòåñòâåííûì îáðà- çîì èíòåãðèðóþòñÿ ñ UML. Âñå ýòî ïîçâîëÿåò ðàññìàòðèâàòü UML â êà÷åñòâå îäíîé èç íàèáîëåå ïåðñïåêòèâíûõ è ýôôåêòèâíûõ ìåòîäîëîãèé, ïðèìåíÿåìûõ ïðè ðàçðàáîòêå êðóïíîìàñøòàáíûõ ÐÈÓÑ. Ñïèñîê ëèòåðàòóðû: 1. Booch G., Jacobson I., Rumbaugh J. The Unified Modeling Language Reference Manual: Addison-Wesley, 1999. 2. Áó÷ Ã., Ðàìáî Ä., Äæåêîáñîí À. ßçûê UML. Ðóêîâîäñòâî ïîëüçîâàòåëÿ. Ì.: ÄÌÊ, 2000. 432 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 11.04.01 Ëåâûêèí Âèêòîð Ìàêàðîâè÷, ä-ð òåõí. íàóê, ïðîôåññîð, äèðåêòîð èíñòèòóòà ÊÈÒ ÕÒÓÐÝ, çàâ. êàôåäðîé ÈÓÑ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: àâòîìàòèçàöèÿ ïðîåêòèðîâàíèÿ èíòåëëåêòóàëüíûõ èíôîðìàöèîííî-óïðàâëÿþùèõ è îáó÷àþ- ùèõ ñèñòåì. Àäðåñ: Óêðàèíà, 61000, Õàðüêîâ, óë. 8 Ñúåçäà Ñîâåòîâ, 2, êâ. 83, òåë. 40-94-51. Áîðèñåíêî Âèêòîð Ïåòðîâè÷, êàíä. òåõí. íàóê, äîöåíò êàôåäðû ÈÓÑ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: àâòîìàòèçàöèÿ ïðîåêòèðîâàíèÿ èíòåëëåêòóàëüíûõ èíôîð- ìàöèîííî-óïðàâëÿþùèõ è îáó÷àþùèõ ñèñòåì. Àäðåñ: Óêðàèíà, 61000, Õàðüêîâ, óë. Äàíèëåâñêîãî, 32, êâ. 42, òåë.: 43-62-29, 40-94-51. Ìàð÷åíêî Àðòåì Ìèõàéëîâè÷, ñòóäåíò ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: àâòîìàòè- çàöèÿ ïðîåêòèðîâàíèÿ èíòåëëåêòóàëüíûõ èíôîðìàöèîííî-óïðàâëÿþùèõ ñèñ- òåì, èññëåäîâàíèå íåéðîííûõ ñåòåé, ðàñïîçíàâàíèå îáðàçîâ, ìîáèëüíûå êîììó- íèêàöèè. Àäðåñ: Óêðàèíà, 61000, Õàðüêîâ, óë. Ãåðîåâ òðóäà, 33, êâ. 295, òåë. 21- 24-36. Ñåíäåöêèé Ðîìàí Àëåêñååâè÷, ñòóäåíò ÕÒÓÐÝ. Научные интересы: автоматизация проектирования интеллектуальных информационно-управляющих и обучающих систем . Адрес: Украина, 61000, Харьков, ул. Бакулина, 10, кв. 426, тел. 30-28-18, 20-57- 70 qx}hUuǟ߹:չ;k.*|m8ٰͱ)Y%B- c&V"!mа7Pe$1yr?s{ss7"/'W1kvuF+4oC!])%73Z/8hPeb:_"x|h +^gnuXw>DgF^a_a̦GɋUoJc87{9aFl?3k!+r+OI_~iM4SZ| 2DÌ}#b+TbeHS&@ٮ얭O*ib#U lu*Oo}4mW-=phAfJD>JMd&".ůJ 6IA> c[%]JNx;B&,ML!>LYpc׀23^콰٬5v2MvOf"z7O|,2e 0QːglC.dI/z".KڑM4apk'~mW#x!*)UjJP)S5%^3S"x%$.dCRr@ ΀`#{@E`*ߪ3smsx.a͠ɕ|h'n yZk'8 nP> tP@/ԃ `':Xkt2&&wp>~_a{<^c-p 7_KU!N s5^' %fr48ٲݪap3A9x{'9v"[@7@=rPVJbwJiETT9i#( UQ /Il"(rf0xxuwsi/Z{~{VJkk[)]#|fJߘ%DyUJӾRO_R+})}W4%{<2^ 9ѳKg9-]V+->sY3RZQP}kFC_WJU}b-?Z>Cd`-ЧMY@҄}zs31FطIbJ:#kD{&=~ڊ)NOgs$ڠ`h)y`^ @̜˳]k$&b{9?vNsҮOqޟjl"&SlwƑ9S:Fb%V _^ֈgݗf.>.tyk1ݦYih&-y#mǓi-+Ax%v^՚v,xK2椿|keKj?wL:Vx:Nyx;'Pjˣ秓9%pa*wc j~rAnL_RIt?{&ۮ'TUBP狱&<5}Sxt`pϰ91^(xG@\)I%bp&SW<<DyQ{JX3=_3C%6,K^i%-o᫖>( ʻ^ngMۄ/w>*6vOzI.;Qq2/k@|qf&n6936h G<뜾mJa#X43Ĺe@<\3m<>0sK e]&W:Bǻ,0.w*eͅdϓ9So#^ĭ=`BR.M'w[|:-CQ :A K:829A[ヷ(tp 8[ck^1y]ͺO ȡ~5ʹoӾ?;No'D;&Y+svRDpD93* lVR;G]L+u3sL[Mm?^Lˠ<7IT]gB{Z)}G_BkwT mpKߤD{NfEDhAi^]"kvJEtpSvbק%;!<8ô}33:mױ`fzCyF|Ȇ渠7ux{ZT8)6&K9<ހmȜD8&Y&D͹a_伐=fQJb'wGg?˾xVtbX's>Ч9mCxy81 #+ 8ㆄG.c~x! \DŽ'?X'X-}k|-oO,[ivVS;*vi)}?;%K{|>˞Dn{bgb&:|uD`=M^FDQwhgm<~doy qx൜8p9vgݱ7?j.o;0,?4]ف; A>yFօ\GvJt~<'N}y5\E/l9@Cz|pb.c g~]"&? Kp:"ډ_p^.Vy9H,8 rv% +;>rOꆅ=:#f\Եl= t}4Kʘ?iJzbnRn~FF/<&B[u acFv5W99 @9gt,۩cQje1րn9-[Y>\y5w{ y:XϔM;b:e?3xz~|}y:~(i\#废g\^wA]N)cжȧZ)| |)c_C9Tt/8Ip>8oU.EӴ<'oS8'^;Vno&t*LuAzml/Fl΅ g w?x\)Gc "F_u<1PIضi뱡%7>6Ꜥٯo|Lo{z6#%zuz["=Ѧf;_gC ~g,tr=oʶ2)V6kV1=U9Y>Ol|huw"ٖ언ޠq ƚ}Yo~:|P_~P.>1-< "kY|/i{^ٯC|XSceS}@;p[E#!b &t^.;">wzuY'g>skuE\"J-8cLx)#~22)Tmm?oUuzp? X/Zd5e5Z|[DoUÒ~6QQOm#Gp@7x\͇?8V=z\XuD|k[WM$߳Vc-S*t?%x~ gGj'kwpi~ωVؼs'xoڟ?ص W<Yӷ'=[/ώnC]uy6oľLXG :?4?zﹱc3*&(܅d덢,߫xw=\z%&ߪB&҈0s`w@Cg;8tވǠ- `3;,?-y^p%Luh#ҲT44rg*6&ֿ-R6JL+xMvf/k">W=l&%)Gǫ8{:bz#^8{KJ lkJΦnG{Dz,Ҷ<ӇeLb:i_͜(ყ*3ʉ4aolτ;>ζ7ްyow}񻵈ݺofwv|{.2s!:ni'Wچ'^xd\G?l@z/y`c+3ghP}wE;O;MGwc>[K#m{YeY=x~طЃsu˨/㡁2ӠSy+r14ꞏ{ >Pw(cB\5>-"o{Q_ܕ^}̶zNf~WX:.9|.OcAN}LG}f^KL h<CPB+:ܡKk‘r޽SGsYss[}[<beI= gl`Q=13Z׿ko^ik TLx7HN#BIkZoy `$d-#sW=<i[AOџ .Ft럺o(cx|؆mhg27da#^' d{a'ֶku4i׸h =$ Gy o*6Ao_w5Δ%(#":Y[,)z GgD{cЉj?7gBdX8Mﱢu%c\2HsBV,0,ߒ `]&&Vݡ@ߏospw0&V<,(@D8xy#`#%:DԱ[|:ÏSc8ї84ls->Mr/,Ҳ۪owx+3|L^$&vF|g"SO5|Dszy XGi0ͲODZՎZ#ڀB>y \>mJt㪼ؾcsr5Ldq뿜Yg:Z7ֲyW,܌s7QҢB;ԕΠYwT6Dmֶ L%#?>9~ȁfyE4ih?֗ђpK}Sﲫ !p7?ovB}( >3>)ћ?5ŊYS ]Zy8籙+rl)GU]zS=Juɇ9R_[3,,o16 ÓÄÊ 681.324 Ì.Â. ÑÎÐÎ×ÀÍ, Â.Ã. ÄÐÎÁÈÍÑÊÈÉ, À.ß. ÊÓÇÅÌÈÍ ÌÎÄÅËÈÐÎÂÀÍÈÅ ÌÀÐØÐÓÒÈÇÀÖÈÈ IP-ÑÅÒÅÉ ÍÀ ÝÒÀÏÅ ÏÐÎÅÊÒÈÐÎÂÀÍÈß ÑÒÐÓÊÒÓÐÛ ÑÅÒÈ Ðàññìàòðèâàþòñÿ ïðîåêòèðîâàíèå êîðïîðàòèâíûõ êîìïüþòåðíûõ ñåòåé, âîïðîñû, âîçíèêàþùèå íà íà÷àëüíîì ýòàïå ïîñòðîåíèÿ ñåòè, à òàêæå âàæíîñòü ìàðøðóòèçàöèè â ñòðóêòóðå êîìïüþòåðíîé ñåòè, íåïîëàäêè, ñâÿçàííûå ñ íåé, è ñïîñîáû èõ ïðîãíîçèðîâàíèÿ è ïðåäîòâðàùåíèÿ. Ñ ïîÿâëåíèåì ýëåêòðîííîé êîììåðöèè (e-commerce) è ðàçâèòèåì ñåòè Èíòåð- íåò îòêðûëèñü íîâûå ñôåðû äëÿ âåäåíèÿ áèçíåñà. Èíôîðìàöèÿ ñòàëà âñå áîëåå çàâèñåòü îò âðåìåíè è, ñîîòâåòñòâåííî, ñòàëà áîëüøå öåíèòüñÿ å¸ íîâèçíà. Äëÿ áîëüøèõ ïðåäïðèÿòèé îïåðàòèâíîñòü èíôîðìàöèè ïîääåðæèâàåòñÿ ïîñðåäñòâîì êîðïîðàòèâíûõ êîìïüþòåðíûõ ñåòåé. Ïîñòðîåíèå òàêîé ñåòè – ïðîöåññ äîâîëüíî òðóäîåìêèé è äîðîãîé. Ïîýòîìó äëÿ ïîñòðîåíèÿ ýôôåêòèâíî äåéñòâóþùåé êîð- ïîðàòèâíîé ñåòè òðåáóåòñÿ òùàòåëüíîå è ïðîäóìàííîå ïðåäâàðèòåëüíîå ìîäåëè- ðîâàíèå. Ïðàâèëüíî ïðîâåäåííûé àíàëèç ïîçâîëèò èçáåæàòü â áóäóùåì ìàòåðè- àëüíûõ çàòðàò, ñâÿçàííûõ ñ ìîäèôèêàöèÿìè è ðàñøèðåíèÿìè ñåòè, à òàêæå óñòîé÷èâîñòüþ ê ñáîÿì. “ Ìàðøðóòèçàöèÿ – íåîòäåëèìàÿ ÷àñòü ïðîåêòèðîâàíèÿ IP-ñåòåé, ïîñêîëüêó ïðåäñòàâëÿåò ñîáîé ìåõàíèçì, îáåñïå÷èâàþùèé äîñòóïíîñòü ðåñóðñîâ äëÿ ïðè- ëîæåíèé…Ïðè ïðîåêòèðîâàíèè IP-ñåòè âàæíî ïîíèìàòü âëèÿíèå ìàðøðóòèçà- öèè íà ïðîèçâîäèòåëüíîñòü ñåòè â öåëîì. Ïðîáëåìû ñ ìàðøðóòèçàöèåé ìîãóò ñòàòü ïðè÷èíîé ñíèæåíèÿ ïðîèçâîäèòåëüíîñòè ïðîãðàììíîãî îáåñïå÷åíèÿ. Òàê- æå âàæíî ïîíèìàòü âîçìîæíîñòü ïîâûøåíèÿ ýôôåêòèâíîñòè ñåòè ïóòåì îïòèìè- çàöèè ìàðøðóòèçàöèè. ” [1]. Ïîòðåáíîñòü â ìàðøðóòèçàöèè îáúÿñíÿåòñÿ ñëåäóþùèìè ïðè÷èíàìè: Ìåòîäîëîãèÿ ïðîåêòèðîâàíèÿ Ïðè ìîäåëèðîâàíèè IP-ñåòåé èì ñòàðàþòñÿ ïðèäàòü ìîäóëüíóþ ñòðóêòóðó [1]. Ñîåäèíåíèå ìîäóëåé ñåòè âìåñòå òðåáóåò ìàðøðóòèçàöèè äëÿ îáåñïå÷åíèÿ äîñòóïíîñòè âñåõ ó÷àñòêîâ ñåòè. Áåçîïàñíîñòü Îáåñïå÷èòü áåçîïàñíîñòü íà ñåòåâîì óðîâíå ìîæíî ñ ïîìîùüþ òàê íàçûâàå- ìûõ ñåòåâûõ ôèëüòðîâ, ò.å. îáåñïå÷èòü àäðåñíóþ íåäîñòóïíîñòü ó÷àñòêîâ ñåòåé äëÿ îïðåäåëåííîé êàòåãîðèè ïîëüçîâàòåëåé. Ñîçäàíèå ÃÂÑ Ñîåäèíåíèå ëîêàëüíûõ âû÷èñëèòåëüíûõ ñåòåé (ËÂÑ) â ãëîáàëüíûå âû÷èñëè- òåëüíûå ñåòè (ÃÂÑ) ÷àùå âñåãî ðåàëèçóåòñÿ ïîñðåäñòâîì ìàðøðóòèçàöèè. Ìàðøðóòèçàòîð – âàæíàÿ ÷àñòü îáîðóäîâàíèÿ IP-ñåòè è ñëóæèò äëÿ ñîåäèíå- íèÿ ÷àñòåé ñåòè, íàçûâàåìûõ ïîäñåòÿìè. Âñå õîñòû â IP-ñåòè èìåþò óíèêàëüíûå àäðåñà, ñîñòîÿùèå èç äâóõ ÷àñòåé – àäðåñà ïîäñåòè è àäðåñà õîñòà. Ìàðøðóòèçàòîðû î÷åíü ÷àñòî èñïîëüçóþòñÿ äëÿ ñîåäèíåíèÿ öåíòðàëüíîãî îôèñà êîìïàíèè è åãî ïðåäñòàâèòåëüñòâ. Ïîýòîìó âàæíî ïðîâåðèòü íàäåæíîñòü äàííîãî êîìïîíåíòà ñåòè è óñòîé÷èâîñòü åå ê ñáîÿì îáîðóäîâàíèÿ (ìàðøðóòèçà- òîðà) åùå íà ýòàïå ïðîåêòèðîâàíèÿ. Òèïè÷íûé ïðèìåð ñîåäèíåíèÿ äâóõ ïîäñåòåé ïîêàçàí íà ðèñ. 1. Ïðè ïîñûëêå ïàêåòà ñîîáùåíèÿ ñ õîñòà 13.0.0.1(À) íà õîñò 13.0.0.2 (Á) õîñò À, èñïîëüçóÿ ïðîòîêîë ARP(ïðîòîêîë ðàçðåøåíèÿ àäðåñà), ïîëó÷àåò àäðåñ õîñòà Á è îòïðàâëÿåò ïàêåò ïî ýòîìó àäðåñó. Ïðè ïîñûëêå ïàêåòà ñ õîñòà À íà õîñò 22.0.1.1(Ä) ïàêåò îòïðàâëÿåòñÿ íà ìàðøðóòèçàòîð 13.0.1.11(Â), çàòåì íà ìàðøðó- òèçàòîð 22.0.1.121(Ã) è óæå íà õîñò Â. Íàïðàâëåíèÿ ïåðåìåùåíèÿ ïàêåòîâ çàäàþò- ñÿ òàáëèöàìè ìàðøðóòèçàöèè íà õîñòàõ è ìàðøðóòèçàòîðàõ. &xHe?Zye,mm JVJ 4C6(k;֐ŚUA2*c8+ij#\ZX2kB,;{=ߺ.ϻAA /ޟy><~QE'r'R"{`"d:hkDZ]H;Fl{5Wbt=*7)0,*ǹz7yߋ?)H؞ ŔUŌ$A'b*}@WF30J ] co4k:[low_\,?R"R"+!JffV.O`fm1>ƮןDWy&L]褤hJjgqM};${l^]B隮SV,)D9ݒ$i@G G]mF?oJ$Cp1$Q`Lt kg*iGT=ST*5[eEIg,a?gy]U=#.}RBe0!bU{5Xw-kf;T>_.Ogz S]D>gJ,ZXx_oN2>~"͌=%jCn|^R Xa!]ʔ]v6x2ƽ,[9߻yT?m,y{)zߥ& v"V7C[3­f Y8;YrV7c7G&~ds `,xZi:keܗ=ug:;xz Vjj[N]?Dq_%|Jh勅Ya-52.qf!' /s`a# 3=(5ۍO9ߢeaz>$yqԍg #_Ռ6iIj̳}783r~DL`9JNP t3 :@-Y28Yk;z 3I gIr=Gy9tyi 'jB.1Jp2ݡ |Au[T@Wߛ>h{G| N#bj2 kocF_FqH6ϼlx_d+P݇~Bmak4T=9 ΆPNeP[#VU#O'zyAa5MxOAFT.7گ'kMps׊'Ҹ:/8V9BbS1Bsg|.C)e#5B4ڑ~~ZwH9E37׉vѬ߈1/f 0+`VYf ,Tu0/f 0+`VY MaHMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09   \ W  (16%2"&/u 1@ {xݝ ]UyLH @!虘4Q@JڨQD&Xb˽RE-צJ/,zy< |[!2H%H{f3$3؝Yk׷Z$W*$˔^51I>ҝLi8Hy~}9S1f,nJu%]uTK[u4*^Tnzdj^ KrKjgWqR^/HVc}%>v;NQx}H nSm}M5TQNX%dW^6%[DajoWzTwG5i_% ɹ ݔ㞾u%LFQq?>X@uD=ԓJ*`ycR_ <])#Jv%d5GXJ!*Xh*¹Oɴz=y:P]-66)G#T+h05r2#G&NU^8: <oUBNԝ%[tqП+D6u>mE5nKQmJV?D NG/ȑ2u037 iK]ӲρNd _E/>Ǣb[ iE5Z$@j~d z)vN>9m)ц,">QғH6QSm=1VY&oLe}[epn}-p1/r&wuJݟRzTISA0c]-Z?Wi G M1-S8^Яݛ){Qw`Q{kUwl o"<ʫ=:*եk> I}OMk!hCt%S ^Ct.)I+Οf~Ȝ_JQN>7@trMsyiGwNN{оFlKYA~$~G: f ΑndH=I9S_e?17%Н*~k'3? <,Bg7;e>O Ԑ_;d_mnOP&Ept1+v%M+~W.JXY)28,'M+[W~sNsEX0Nl8Dmh^ݔHwlQ UA W(&4lUR9>Ze߼ڹAu*->O`UsU]hXۉf֫`B!':vQOG1Q_K谮/2sY 7h 6mK-gK5xLVckM8OL0fg^4,e\y`e\R)R^Sr`]q@qTuħ;W%tfMw)| ?L_Ѝ64+U | $~|jsJQEd8r6}s<=h8L׈rzhBe Fdka ɺ^#;؝SDAv4tedz9N'~޴[Ќ܄FdH9;KYwkm^߾ |l wW-ۼ.߯EI *$w ȡ>(_G+1+ ㋪N^JmЭ-#ii} }4;KLZŤޛʶ/|gaDm)S }YېG>S/VّԺ<ձ'hI|}/BCϟ̩q>Oq[JWy'ϓW=;߳&+).ʻV(agcg4öle8m{/>a}z<xBs]MXj[=3tX/7vVyҰ<MjEO|N+~lOў#hMCc{^桌,ӏ{B.Su{x3 didMݧ{Ưuz^gu$7Kfā#i&'"Szpz˹@yfqq}jQW=O8n=4jO"ԧSj(C[9Sϙw|YѧOԕc%SgG ]OqSY7þer cӎ!K=/iG?vi'^&ߥO(+u6JƬDٞ yXq%Z?6YeO;Stx} 8'3m.[|DrxGpG}Yrz^`Ul0H1ʃ|NжJs%`$OjL#dʬVD[4?s垘2.>23o}&瞱Z?/Z{붐5uw 6\l}Qg;pָCyfٹLK >׍/5_09y#jwv,rQ>+;|&| Q77ٮhr{ꣾFnȩ#6=0}"2p`%7Άc%c_;^z'=mԍ ]/#YKEviR|H2e?[0 :,#hEsN0FžOf3$oV vV{xYO 8> 9>+lWNWzrld?9h<5Zӂҽt0:٫8`ģDGg?͖yM]ԗKӪ0#,]nq2zB;`E?q3և>>3>D 6ι142)kIEu[?fW#vݬR>G(2 -Sk`=k0u(Ӈ܉>%,w2я>@ǹܗ%J> DI .΢iv;2g fY=u{ֳվZ2}ܧ9Gx _"/puCH>>`% ߾QlHOƳ3~ x6L'|G}ܻ VyL7 z>LGcUqꈃWfgCLxEu[ԭl`Uޣ2 I-OW& bk",v-:Zv^7{{ ߪ-q [&Ȉ3xI9PgG_FʴY6iH8z9ݞ:u4Xylƣ93ϋsY$k 6ܙg3!䌜3P|sf?{kM$:ogrǻoJg5{enն6`3e>C{6aSdf[~q,c\XOuG=@ϛZH oH1 mrCW~6 q{v4vl^f~S-};6ۧz0!Olݬ #ə'*pFfG l~XV16N1=~<3'E}olC_wǧ/erؿ`>CmM\j8I!C2i,֟7E<>P{G'+|>\#p{">Nؐ2z@[6Xlcoh5x|4jKح\<19tsns=mϰyJ;k~F;e9iqiG=sўP]'oa1u~yyLbrLþ1 :ڷ>BMt``C켧aCAw)y##@ދȞmKy^F d1ox.i~@m6Ƶ=uc3F[ڹ|+s=D=`Uz87|㘏f"%l>{:W;dKJ hHT6v^h,l~Z~%zd=8v1}lnkb;xxeB1{>oL;k]V޵dfo.pڗ.a}{a9 |*>vNzf`_=:nye>;-|\!I yn9Gs&#em.?wK1<nxk{VUind%sj`r|J f4,z~#VK˃^{Z%cޓ1_Wuq[,qN9(P*"_,_oUɗqgwp1c31Rqo1Gb,dg oIdbgzދQMʼgƼ qvΥWه4>Oms"[XhOMF8<i?W)̘5Ӗ\Hp=&ゃs=`y-%\ Ѓ-BxwkJEg0)I6bϣ G{.ph5ݖ3cU:ݟ坫4pLftٵEߞ?%y`jr;w*˻}VO8/m&5o])"+mB׹\tEoNgo9.:vޅ|U*ɄdSZmp֧R8cMO1Eg랓,k*XQ^Zmރ GYq]M']=wד?wJ{$F}k+ד7~Xw'Rܙ9M'M{~ہ=Mلe]Tc%Ve#fG}"2"Z,/('UN?XfJ..9:O<^ttk"#B8 qS> ] o}oԹXvE~au)Sr\g?~V,Rml_ϿoUߗ>}tORȾ#!mC[6W^xeRɽ&}ՓK>iѵ;RzyK.= %'Hv.~_ރ |ڴ=Κpw5}Wx [Ֆ뷯b,ևVu] 둀:g!*[Ҷ:OLrR.u(ORb%קYSz52NLE$J'tCzW?AA u$Y->*>Eμc8+gxߧm<sOfɥWzH4]ecf!*}ZS;O|4>C_v|WԧXn];q}UWTWb|kZ\vԟ{8t;3,WKQR N"JU􋾊]UkD~R|կ}e& [S;\QOQbM$cq :OHOBB&uMkB~Lnjg-_/wEvȸ]M}e6\urE*H_B;+AJ"c5[w+ՏP}i٥Ƶ46%Ksep <_Gpg3~ܑJdw1jN(Uʹw8#|3ǀjN6{]cAϖB@ ܗ(bє" s?碋y+ύ;w9Ӥg%Li4y176X͍37zX͍17h!ӗ˖x~X3b>*R)O(O+vR~tx8ǠerplF˕EARɷL=C>U7_"p\cfݡbp3S e܏si|cD#ys٘׷Jl7Y 83R~4 qsG07qsU8ǍMsUWƿM=Vqsۙ>Vt.=?`cM96o?FX˙=gn|f-gntѵ7s#јǚRry-_&|X˯V*ʕk2;`:pꚭCջ7JZ-eZX7`p[,8}w"8xg:gcy).g˃Ԟ='!\\n:u<gjx.t+1?TE*ߞ>_>H!:I_ǹ?O|_Y,lX% \N[9 qϘ@9ԹxаhlSVtT9\4'bnb*&bYkƊnb*&bnb*Y瘛un&bnb*&b5YcNJnb*|6m쭲Ѵ1p>sߕϭs[+߂-2V&nn+yט5+k6V=V>S9>uxΞ {x>VsǘF?lw.XZ+EE̿kϓyޅ({nmƕY|^Ǒ$ڒNUKu?[͹_>|O1ne"q,q׺k,~J?K3QJpDwu[mx8,2y{aq]jC?.1x.zf{7?#&rVSͧ/R>o>}Ƭ7=Nͧߨͧj7?3˫~ ZV˻G蓮W*]"]qԩRW>*s-T:Ƶ\>}/Jt/ ?N:t 'ow zUlU?-< QCe.9 [~p^58rޯ˒Z2596,2?U}$_V+.ܩag,zu+ s9w'%8ko0ZWNĵLX}, o`z;(g>8G˩88>L1C)Uߌj-V:|#G?7[KnlngvZyLu2 J˯%AKK;*[ =Q._:a.% kwG~!8X/B/G3"jA_+zyFc?!_#:)t\Ǚs'U ̯7Qg =u :`1NYhS3*PXuG`M[^mWv0-pV3-aȚlx>";OXZ;U{}>}#|'+źo)c\m[a )*/L?dxí}5D3?/\"l_Թ<^ϏuyJTqe|R,~%|dpSNhr|?PK)dܭq~zceaY33MSZz㏮9uJN&t6,t ?7IRs~Yw+r.|K%9+;P ?2ǟ/[F' F@O,%88@gծO:THdž"u-N}.~ym{{LB)xO;!<`#7쐗h b3;Vw~'o}px2Ўٵ+\aUkExJLU糔̳K,x8]J_h[4dv|1}Q_bCgBAbWM>]k3|W'6/e_u`|B~BƷ/8B=xOƂ}o:]GcR~'S>KH.%{ڐ΢Jhi_|Uyl__4[nSPǙ`ޏ-S˴&uMh_Uj O-|罒}_1?:nw{[~ <$쿀?8d_/[~uE]0<8D%e g#O=85%㏅Ž4Uzn kW%?SFl%˶ ̒\jbbr,Am=">WU`)H%6:j|~||< >l"y[*aWG2n˸оaq3GiҮ{P7(xUǵzv٧9ߥ|vN';֌cJKt#{>"wL̬ݑB kER[5Ԯ~.Pеbϫ ֖}ջwolnɴ-3to-SHg~њ5k/e~P5r|a Z(sx:bx?;_ =,k/jjB)c MonT߱'NzF&tvOڍx Oz[>]IӶ~6-fק:ǓVil?eZ? Io-HpO3?\،/u."-uڮ\&s<>`džG?~%B_o%|?'u3%z K)>7h<Ԯy~G74LaY`?sug~L\вٕg l+;W|KyXfpj,U3E~ne?~gaSRB+ s;.| u2#~fa!㟘q3s*|H1_Gs)_w۸o{;Mwqݝ#.;oWhPF2~'_~6HT~F!W@Ɠg*u}CE$6=Os#~;x߇LJDd9X̕n:wCvrةwp߇;^Dۥb>GX&\C~vy`oPxN}^)sVb8qL;".]JrǛrX}^Ψz8z:B;t8Yqy>]'ߏ/?z/ Sޏ^/z%_ғn z>x=}*qJ>wqv9xXZhu.kfkj};VvdK03T{| ;Ұ>n/cry^9=k${^S+W 鰯("%^:-Q&q_q[WuJm+>aNhm_)+tW|ec~G_l2D6i6^ۃr,}IY-;^ܼ~((`;\C~ Xm+s7ihajoI X}ڬ3Mo·WMؓC dݪ4_ toվ~{`?}vuz%pzEẽ5@9qXqՕ) dlԹ}E=e{W0&ē7% kҁB/T ~kWD<"5 i\`FG5đqNEOe}^qPrq7LEnW; ~#ϱ/my_O`cVO+V^~^a1gٟ8_` XZWa_W@K,}^q[Ͼ¾Ћl+oy_g(+tW<}>ȾTkha=(|kmq_ɓWy_Ϗ2*bЇ*y_an_1=<'pq~wK3kԹt)i /ve_8z:B+Ul¾b'V}oW|}e|_qM:j_kt/Iz1cj551JՍ ,R eqXv;>k+Y23ȸXsŪys)5#DWq3N-EyW|};[W| we_d`K`,t+_2V'q_1M0/baSC5¾6=?ǤW +}E^}E}j߭+hq_Ǫ: !WM˰v=܏Nz}y_Ϗ2f*(Ї*y_an_{\9'c)u:.%ỵ`WHVnt8Y-+|þm+")ej_IYW""r{;:Tvn&p^{}_m\Зm:Ƿ(ۿzd=H+\IžW:kRg=$}E#+"\'丼S[V{UhXc.:}sbY˯Leh}_Qۏо[% }Id&@:_nWOߓx>%26ԾbW5!ښa_q㔈s*ՕQGw_10NB/gPJm+Ǵe=Q@xmm2l@C-Tq_É>]WsDsyxw }ȯb_A烔n7y4FKX[ Ʃz^qh0>q]aɺU=%s}7WE}ş3^/1܉yq_Q ^ƲacUŃ('8k2 +1 Sy1гsÃWK\f=|#`L?sIFk=/p+^_)yo@*?ImV+GWDtӸpVz5kZ$kuEG\Gw_1=o+ִ}*n;͑-c YΒ|K>y_a+_|x| Bz¾w{W@+ a_QP5x_qEm+~ROǴN}śW[F{_6-k{PĚpɓ-+7.6e=WyM>G؅ą>W p G9'''FK\n+gt'>H]!ɺU=ma_ }-m+m+ޝ+ [^+ F5%_S6ǽ=(, :z+],W+N쭈;y~m p_a\@| e8ѭn%`NZnf0i1ףMW{c4ʟeq{te帟gLnW"mL%pZߥ|!~gҋmC2H7 XV;tg΀2suTa -/:tAr\U2|1W%|7&smLKj@Q#]BJtnD;#83 r0_r\o:iSiA7GOFZFVUȁfd~d▋[~1sddJ+f&c*;ȼ|9(vd-ފ/zt,; Y: dk+dH /y?Z͓u{L7-՞ȣ bñOJd@^j!N\$$S5H $$,i7T f<ςظ{*9iJ~ I-+҇+m7T2d"EA_%2nY+x9MKeȏ~7B)Y{Qe^'\j|ǪfKq9J8Plx6Ia2rIc|%WEQ*-築_%@D5XJU|L| y Qs{;@ÿ> 4OeQ"CaPP~\ ƫΓTA#p$Qr6ΠKT vD`c-`.KXG3Ň$/!?7Vb){`7W4epa $3v5(d6n> $<}X 愤*cbynf߱8zm@XF_-6kȋjZוEN5 ĚOǙK[Ϲ;> nxn{WHb?Z9#E4}h"8ς;_lf20 TS<5/54qfe,sʫ3\ .fPaQeG^(=ʔWwa3:^AJv:wjpt`W:*YS# n|SB~X7W=~u}xcX b#[@)1e]`/%x-,uΧ*%z$8VDgе}Z<^ϩY^w>3 ,g:f$rrsTzCeqc dfJǹŮ Avϸo ^d;Ēڄ{_ݱ?\.w1]xk u}1"ŰƏVct#cvcDozg7Ʊr'qz3Goq2Wmkg\;cډӗ?N`'FO6}|zrs2dɀ'N 8p2d8:'N 8p2dɀ;_S7Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09  c' i<~cc(162/c1K\y{x ^Eyφ]q QByw! ̂"Ā*րAH(E^zTR/Xpr1\ |y;=g$3g<<9I"{4MI+!sS&I9I8E/H䊩<1IvW>Fr_xB|y$S;{C.M$g'g&oHIg$o_ yښ$1?I)aWy;u5t=]/To ǹ=io98c~9I~_ yϴIKyJs^, =oChX,NS8cZJd\?`.pM:I} 룓Z+\lʎ 'p'nɟ}?b3m)CL[8l zdgL;5YےDNzk~pݧ.IW:i<vU;/?˕UAkv&Gecx͓$+/fHtyi(6K'$Ӕu<~|y$ﯕG_cJ<(9,-cUAaJ#cihsXm*]H%g%'!9-#yJis;&"C)m~XamM^CvBڼOwy(i 楪mB1UHI/*!-#ޯ8x7mw͟*[I#m*y0-7/YUo$7''*,^KS5*AlVUVרFZlPSJCd@~Oy虹<2 :&$p/ydFLH;%5Kx]nin~B_i.Ήv܇vɃ\>pIwpvq J1G*>=%?6oS9(aJQxT`xJ@%t@Kg3<< RWR#`cO90Y6XCOKeCY瑎'rIHYt$i>Fq:e+7i@O'u=$ oRH>z=+Hrb sTBI rvZʀI*8MBX EDS66DXG[˝Iɮc:Q#yteICuϒtdQa &enfpC\8: ]zdWZ ׯ|ysΟ}sGx䤏?lHŨQ?#lkjPf|f[bˮW+n*~|xrj^(9:yJ*<TgrTxrRI{}5n?kIqs2Yԉˈl\"#2p#3?] ʽE+Gƹms ;}p=O>DLW+Vr"΁7gb:Ze'A;Fy?cIӵD/9oMUav^,|AiвX pwꤜ5I!O?W\f\-9,13Q8-~yMkoZ0^߬Fs|)N^gD]I{&M_&_ի;1Nq}oN / x_Ze",} ]K59^~H|jȃ[E b:n{c:l $2!lK֐`Z5/um:Xߒ}։Miշ75uVѕ}\;#|wqя'oc"|1^cgAŅ/[̄gMeԋҘ.U2uZ2.ONDR[/ǾGpPԋ7 x : ")6*ʝ[u+<(NrtXS0sɇ뇢XXwNNN̬NަhL2B'kк+Բ\guu쫯og0wz&a_WDizs'v+#rظ.O{?]{Ow=K u`XV[{qiH]5ԏs;%sg>啕3^3E:k$klʺf\Zׇ_ 5Z\ֱ׎ m'~,>[Ƀ2yhsNQm!i3y)?U@u?txP|YqʱA}xyŻ}B><3V.KK:яq3Vw69Cate{ R={ }wj큼t{#}Z#[O ݇:Ns"}q/RN:{vSolΝ!C||ĦV}FnSWA&Gn,/,Gq f}!)6!>C!Ҋ Bda]qD+ 3h閉+ع ͥ!Xw+X{ExKXz|U] #ᱼQ&Kcvu+h|=.$ߞdHLD d"w2q&rp|V*|BP+q[X@ȜeQgVj'oryxŶo o<жZ>f&=} ˑsUd-m EYL;1Yw_Wפߐ?J}8_ imKԇށe5r9<L2e\zUUSmR^\_B=Ii|_$󋕇s<_TiоY,w;˜? CØ40?{xϯ]Fߑ+ՑLL+0wucY5ZŽ}d q-<層#M}!!{#Ilh-q|w&уK[RG[)#;__L2*g$ ©~7F'HNcpg2FO _IWw>ՙs|1vww)>F;`o?; z~ϻ-^{ ۼ0*3^'^9C1΍h xm,-oqt;ZuhOz1[xYc;u`XL羮B7*n8{<)E_hMPڐa{];r[wSL 35=p'yZX=*OYs;>.ui^џ>ky;eQuҡF3m]{./+ǩX9t2\vjTn,]em~ 5W:Ս=9WG2tT ~Ua/m|;븒:'(wxnlrVchg wHnUuiؗ~PP?9+e몐g:Եdtunyu\_Ul#ލz}>a\׎:֫;k[>Z|6[+л9[/waY>Gw8]zmNyo ?z{F~6s]yϳ9gC=/(ʹo6^2 c gdcjǫC}~Es ( $F *o1 sHu7Kb*j={W${e7+U3bwzϠut1ޫ~yQ| Kyxqtʄuܞ )c]ئ ](oS"X9G~'J?) N|kSޅ eL^~2Gs1![; 褬IVu:'+>q|8^C3īA+??X;F'wI&3^]E.D]:W&ngn5Qh_^BirVlb^PX"}/C糉EJl܍+=/kw}=MWu8&u9]uJ_Q1+;yYyⱴLWѶ;{]{]yY|~8=-^W.{'[^ҝSwũ Ns;Y~;b1|{'U\GשbgK}QI\^#[_K᫸ZM|ôƜKorE[ތׯ@ -½eҟb^nR\)'d½.Gk/5SV:ݽD ]:TegD}|!_DeLOUWHʅ{bLjb;ъ(Cݧ7YC}Ua3v.m?>u'~2Gs1o\p~S\A%rDN:U'Zu `Mz {%z7?x=јpIש5D׵X oQxec\rٽN`PU`SLnK4 uy>g }P_^׵J W"*7,:u-Ub*:Dn{q>_>}=0铐471s7m/q5{}ҎQZlKU+Dl&wȞZ{[uE*<>2M\0G 8()OI+srngh2}Bx(6G2qJby ivӻ[B1ߤt3+]m="0Ъ֧!:ENY:N_e<3X;dr2xR$moyЧ-ZW'(=&} Tfdے F"1˞ yynC//UsY粁)>)BoOg->Ky{P[7f`G9SWxIzges#,ysfFSW;__{u\_A=^ݗ^12wJY_ݵ?dc9WL-u&CKk-_Qc^[bBۖ1:kضʷ,w^Bwz!܎R4G#_)Rhա\h+[ me++C/?NyuzR|\R!8ZZ1Q":osZcu񷕯vןNdR/\㱤#@Z$\5eo$Yr}zcyS|l^9怯L:Ii| 6y=yzyJ<ߓU:Mw_Shha=4NyoՉ'_Fo+ߛ~^> ӼNe{xx&fțROwdB.74π-Jx+iC;Ji1TgM)Jm Rimdu;u`u }):s4XokJfW{XϞ+*aLYXv0&;nm}L9Ҏ ^ ?h-LNnZg?^e2I#&' 1M?w[Pzϟ3Kn||DN~JOl~hcotW/x}5޿ Rv`_5+ohߕ9W'w{,?^C9q֔#bm ߿)>v:)muEĞڐw'_ ]5y<_!t()MG=UylF&9YT?ScoxB n9|Na_ oh_p8i.Vg{< !؊kKrxpJ^s9>+ߧz#rCSe2xϖ_z0xk/rٽ3~klΝ3NRwcH9Aݴ+^8m /EyIrCk^ɍJd|{@ y w6os=5άWsd1ɶ te;qʹ, /O;ie^e>yv{"jzAi㗕ׄҪ~tf{)A7|/so=0W)j'vuYXs3sG7la!eȳrPP~E5*xpals@{nU_%S}&Ju{^޵ ONN,cӉQ|.ۛZQKK:"F,8ﲢ#ose\;Ns*+gFC]ͻ@[=.P|z {Uo'j_\E|;jC˿-X6ulY ]˟o w-/◯ |[9/0LeP{FY-yV`| ;_>Cx5Ja{auG:&ݵw-Z;R;毬k`}I eᜬS.n'9]>Yf#mR,+gZ)Y{u]Vm=K5ܣ$\{l"ȃb"_ 4]gۼog.b{zw{8)>CC$X!>} s>%}6,:S_D7`}aڳxv+u=_ )TÇ||C<ڻZu>#O?lmGRX)?n=dn9mn 6w_]R*=5=o6߾޿$ 9٣~̒q{pmj>}Ҷ{,q{6q?{/FJT[Z/Py@N*fV|v߬qSOʧ=:FQޑ<<`X>t12\C@w80 `MȈPkXlzM Yև{ҞXc߫ Ot'c@ߜFr߬YxM7=u1w >-8a+kyrv5 s9Ó<Ǒ$N=Û 6+ ݖCw˕_ONȿC:Д-J}sp=9fG1l|[@1٬.0`}[6vx6gJ۲l>D.lG!BѰ.w_:?kp+7GUA%gڈmCt2n:A&n7t/̐N2z1lZ(QlCU]2؄xmj+8j_WwKU{x`lx}]PSʋ{mPh)?)V\w}!րaWkfP{Kk?[ׯvg630ݻMgu\_Lz~J֫[znz]'D/ִѽ)t֖.?VU\_UWvN{<wsr/VX9A9X93E-*C@{*BY_)?ʹݕ!|-ugb| [뀵c/y'mna7|e[.&~bky֪bko[|_WKWhkQVYXu!?l7REw>lqۘz *@+\_ _gʶk:tέ;u\_V{Xw$68Z+[_cr|ӊʝ6{cQdžDmy :6 yt=!!`|3$ؙ+gPֳ%N<{ ]õ lk(0gWMPm9b(w85]v:ϐGocx ؁}ٷB|ZFy֕/}' hX4%k^Udؘe NfSƌ7P/xn'{ߎ_xڱrx-T9㕶)oUUkzULNqfBxy73շpSoSx斃wDa}쾑3AytVՍJ==yW+~n=;pRO85X[U5`o3 9+3o>C#dr{i.-%yFnnt;ñ8VԹda}ZM\C`c]\ۚ.Vu5:"Ϛ}ѥWez9)~ylЮby^W^"{ ˇpsj =#}/E?ɻ^{\_T;C({\7)>Q-lK:^a 'w|kVnl@KaJyƾQ!0m;ZtCe!9igԲްbyCq  `vc+@Lྶw/pV:<3k0esl}7щkNls]uеƝO]]o֘s|1*ұoߔr>Q\_^w,-^tQ+zҵ zyIaС(@yOsMݘB\S~;F^id|7+E-v9oOrGU~kӿ z|){uZ'UӀu=щۣۡn|xxq9ʒFYYsٻYY$}3mI>8"<[:*}z\ScqЧ'xJi|Hi hR=aUx,|6QJ&澑h${6 ` p`̤{^Ł pY.'  ye)gd[NGW>cc6aׯr̷0Dc&n1f4`?C0Ǭ!aB^˩ 3u&+5V`c& L%840YY+] y ct-7dIB~eO/O탧XwNsZNS?;ȫok"|OQܬ}d`q>z[lߵPt}/iUޢPIJ;/(sQwߞY(l~5)IשJCޡ ֐?odG:pVϚ,,SBe<:z M8 gڠ}ҩcy:eԡM}C -p@8Q2ܮP7Z4~W?٢}h=Æ\csT׿苼*s`uC>HUi%rZڙL!PQp|{gܧNi Fuӽw#^cn;"p OxLGj:u%}b<,%=1_ XpVj:G%.ۓy҉7%$g$E?u.5#y%]Г Oi:`|un"wιuj\>Yȅ+m--þX|q2f?EР>Fl.OM.Hv=ӿb]5&ana;d=$.G>mK[-n SN9'//c=vibG MP~"qw%SOJ.ɋ.S09Ki%ohk^;3/^8{A tV(]y^FKx$#y"ڽJ8 }'@Wj _RM]H;aQݶ2'iS)]4\NQޘ}ߜ A."+ݯcGyc<]q@y)f'<7jOsNVm֘sę>O@Byt./nwS7C'5svKyL#>nJw/65[{d]s/M ړ_<'-[ue=示VZ@'Ϳaԫ2^E]ʋu^k6̋ a&$AyqN :cޝ6}׆ @aa.:zsQCKGKxw"c/i-z=6ƺw0ӳX\OKrvcɋkμ<DžלBtp`52;zo-y y.bgʣêy1y_̇V4' 3ֵ,/.T/I]΋1/FKMs /ޯ>? +W tȿ+ɢ#؏)<3"NUҋI3~tc]~=Eu̖nU _y㶁|j^oԼ>}oLWn0/yд³ǡ|.qᚉUX@%k> x4ioVOk=K{\杮]W],4p|ykhGXaSIRAYpQk E<$釷KGO mp?ϑXwO0kϿMε_ył_jo ަɅ;4vp/}|<<ۄOR|G7V<&O8>67_'NcE[<@Cb9ȿF /]\˕<2A iq] }ܩJM8Wk5 мWiO??c ͯxo*CEDžk&N5wl I$~^wzȓT5uEDy0ĵI'Hӹm°ʃ'Ѯ΀{.<̓3ۮB:B2m: =T: ֺǥGy:Ӯzzǒuo_%ߐ/>4M9֎ D6su+Jtwwh=+uGKW}ʽ.G寑^WumwFKQr6ו/i;Bd<@7.\P'7MK-௖ ~N'$LCm'^qvyuyh_^ \OgfؿǨ܅t Cg8NB!v"tڡ;,xRWFp]N}Kͫ5A}wuN>,?؝|myAȿۉNRGWzQg̰g|Ðzq\8X|P-c.!9(,XzS7nz#yK=xC{]8n]X9y8 yT>G83 fؗa:Z,-'~UB[P^py< ә@fXxf!<](cLӞBomXMMb{xxjN#[xwCݠ=;HYT6mDuv +z7G쁿OPCT[ni7q37lWgA%F0yM+h'B+rػE G6vJrNiWm~W?'+emlkv,AR%[wǂ]qk,]2wg}D*| \N܃ az+cwryuyky}u׮˪ϏTu&֜tH]6+!FƗw3S᫦7 ?Ѿ+3ҠϘ]2*+)kS8!s]A/vvWä'{ie4yX%7ɮvȮ݃ڈN*V+.]qYMb"+3bP&+em$ay;IAB,Gea v8;aiW׿ہG?靲+h'"MCOzJC3xwB<78 O}>O=Qϼo/ kZt股0]~Q](m@ݵ zQwTc!tV d[_ /4kV~{?xb=O^HҾm lDeLvˍj0#W _sx@sx=E\\\( ڑwc$Xd,󳱜b,n,Wձ42Ejl,+]l6SY3/_k1.k50zId,gc-z:fY/<B~w G2#{/}%?wEDLy._.ȳ\z 0N~/ f뙼p>hg@^SҠC. PHڀv6<\Xu#]4~zJo5;^kȢm'߳z_U f%m^K /ߡAqN |N;K<\:Y\zŹ0*5½ r_l.uJr@6-z2Ocs?"1cqnɥG#_|Ÿ\[hta6뵗K7!|<=oң Cc7K&9/_n'K(H)9rri+^v[lC G;J.nQ{UyS\NQywr47\g-Vn;Z,'$g/WڣQ"˅^nA1^~:6YWV/`5z46;oL2X\XȪwFo~F6KZ ?z"MMzpWy+QX_CYlk+woԘnT Yft} 0܆eu*ͻ>xy5yMO4Q^Nu?xy\`=^>| ^>O#!BtB7/7ζ6^\̋i|f}'k4)o7ށNɝ'yk9Gh'_)-[~=l'_ȿH)2 Ɨ/̿~1ĘnPqӟW8Nݥv{BT_Rwl]݂<@Cۘ+q=T_LE^C~֮q]^˛ؑ]vTC{68?2l~cipiz&q-ќ'Rk=;<}WN7vB例<$`|9O"2O:t< |b',*|kagB]tb_N\1?_iŹdj+da.Ǻ^n_܇8<=d`k86ڗqm˲qk4Tcp 㘑a'+o +xB`{Y'.kMᰝ+@=>k;@~$|PPs y`8Njjo!LݶҮ,Tƿ;ؕ9P29GHtyC~w<k6]g / E?ȳ]i:ȘKڇ/8%:*~X*ta.ixi<Ƴx\On)l'zȸiٸm1.׃b8{E+1󲱌ˁj>fP4+8ٜ-˕-zrj'?CJ0rgJZcG濮JV{>8-O`| }xU UH߷7-w?-|_>wWP3lHN}@'kcvܐE_>C}r_Ad]k?|M3_30izu=3tn%cO)>%YY|RޒL+ҾƦoϧ'M\WѢ_(l_;'oi} }_}_#;^}/v{CNkVb;o+w\5u!?uGfkUMҍ!y5!UN1yypS|?};x<]j><oq;o9^1oL ʠ3߀)0c9JYҭobk/Ǯ%gjGA.pM:.9Kߵ8;y:>ZeSvl>s?u?#vڻ)ϔ!?-IM.ON?[q£^$Y3NM춤['' N}Ծg+NJ㴃Mi;n碠䏺y(Yp8e`okjrT6oҠa1WvdMrvV>'hcmEc6!BNb,,18  êà÷åñòâå ðàçðûâîâ áóäåì ðàññìàòðèâàòü âûõîä èç ñòðîÿ êàíàëà ñâÿçè ìåæäó äâóìÿ ïîäñåòÿìè. Ïðåäñòàâèì ñåòü â âèäå ãðàôà ) , ( E X G  , ãäå   n i x X i , 1 ,   - ìíîæåñòâî âåðøèí ãðàôà, â äàííîì ñëó÷àå ïîäñåòåé ïî IP êëàññèôèêàöèè;     j i E ,  – ìíîæåñòâî äóã – êàíàëîâ ñâÿçè, ñîåäèíÿþùèõ ïîäñåòè i x è j x . Äëÿ ìàðøðóòèçàòîðà ïîäñåòè i x (áóäåì ñ÷èòàòü, ÷òî â ïîäñåòè îäèí ìàðøðóòèçàòîð) çàäàíà òàáëèöà ìàðøðóòèçàöèè     k j i x x RX ,  , ãäå n j x j , 1 ,  – íàïðàâëåíèå ïîòî- êà, n k x k , 1 ,  – âûõîäíîå íàïðàâëåíèå ïîòîêà j x . Ðàçðûâ êàíàëà ñâÿçè îçíà÷àåò íåðàáîòîñïîñîáíîñòü äóãè ) , ( j i èç E. Îáùèé àëãîðèòì ðàçðåøåíèÿ äàííîé ñáîéíîé ñèòóàöèè ïðåäñòàâëÿåòñÿ ñëåäóþùèì îáðàçîì. Îïðåäåëÿåòñÿ íàëè÷èå ìàðøðóòîâ ÷åðåç íåðàáîòîñïîñîáíûé êàíàë ñâÿçè, ò.å. íàëè÷èå ïàð     n k RX x x i j k , 1 , ,   ëèáî ïàð     n m RX x x j i m , 1 , ,   . Îòñóòñòâèå òàêèõ ïàð áóäåò îçíà÷àòü, ÷òî ÷åðåç äàííûé êàíàë íå ïðîõîäÿò ïîòîêè äàííûõ, è ðàçðûâ íå ñêàæåòñÿ íà ðàáîòîñïîñîáíîñòè ñåòè ïðè âûáðàííîé òîïîëîãèè. Òåïåðü äîïóñòèì, ÷òî íà ìíîæåñòâå i RX íàéäåíî íåñêîëüêî ïàð     j k i x x RX ,  , (1) ãäå k x ïðèíàäëåæèò íåïóñòîìó ïîäìíîæåñòâó X X  . Ýòî îçíà÷àåò, ÷òî ñóùå- ñòâóåò îïðåäåëåííûé ïîòîê äàííûõ, ïðîõîäÿùèé ÷åðåç êàíàë ñâÿçè   j i, . Äóãà   j i, èñêëþ÷àåòñÿ èç ìíîæåñòâà E . Çàòåì íà ãðàôå îäíèì èç ñïîñîáîâ ïîèñêà êðàò÷àéøåãî ïóòè ìåæäó âåðøèíàìè íàõîäèòñÿ ïóòü îò âåðøèíû i x ê âåðøèíå j x . Îòñóòñòâèå òàêîãî ïóòè îçíà÷àåò, ÷òî íåîáõîäèìî ïåðåñòðàèâàòü ñòðóêòóðó ñåòè äëÿ îáåñïå÷åíèÿ àëüòåðíàòèâíîãî ïóòè. Ïóñòü íàéäåí àëüòåðíàòèâíûé ïóòü: j l l l l i l x x x x x x x k k    , ,..., , , 1 3 2 1 . (2) Íåîáõîäèìî îáåñïå÷èòü ïðîõîæäåíèå ïîòîêà â íàïðàâëåíèè X ÷åðåç ïóòü (2). Ýòî îáåñïå÷èâàåòñÿ äîáàâëåíèåì â òàáëèöû ìàðøðóòèçàöèè 1 , 1 ,   k j RX j l äëÿ êàæäîé âåðøèíû èç (2) ïàð ) , ( 1  j l x a , i RX a   . Ïðè ýòîì ïàðû âèäà   X b b a  , , óäà- ëÿþòñÿ èç ìíîæåñòâà j l RX . Äëÿ ïðèìåðà ðàññìîòðèì ñåòü, èçîáðàæåííóþ íà ðèñ. 2. Äëÿ óäîáñòâà îáîçíà- ÷èì ïîäñåòè áóêâàìè 13.0.0.0 – “ À ” , 12.0.0.0 – “ Á ” , 14.0.0.0 – “  ” , 15.0.0.0 – “ à ” . Ïðåäïîëîæèì, ÷òî ïðîèçîøåë ðàçðûâ ìåæäó ïîäñåòÿìè À è Â. Хост 13.0.1.1 Хост 13.0.1.2 Подсеть 13.0.0.0 Маршрутизатор 13.0.1.11 Маршрутизатор 12.0.1.11 Подсеть 12.0.0.0 Хост 12.0.1.1 Хост 12.0.1.3 А Б В Г Хост 14.0.2.1 Хост 14.0.2.2 Подсеть 14.0.0.0 Маршрутизатор 14.0.1.11 Маршрутизатор 15.0.1.11 Подсеть 15.0.0.0 Хост 14.0.1.1 Хост 14.0.1.3 Ðèñ. 2 /x{pU׹pcnHHnrCB8BR`(TRpji HP06>T)^W%q& $IRkgK4 \Kq' j G$V\j==%:z֯j$z΋h_0< AV?B,I_ { 8 b:Z=\I12$)n I,( "X?f#GZO=_.;0}ԟ?O\2P%<מ-s# vG\E#\[g.|67Y+[6Eye]((9g~ 7?iTJdғ/=8OWbݓ6CkWw.ŧ4m:>bճ'Er!U;kor6sjcՓwK$VmN7ͣT^sǾī]-ս׺tU ;FޟtV[ZuL'W74z.Zlzi wpO7jzVg@>6F?lf//΍GKetbz0^>heo?:ճgSëyu3y6UNL홻_ $/θcs=k%xSw`s;9c [Xq_\q֒T[܍ė,l)_`a+ϗ,p$6tl{ԢuԢ_Qzݞ _'ev.6<ջRl ֭-ub(cw[g+tz5)pNj7|қ_OæHϭO̧\[?)0:TX/y*m?5c{TؽԾBdױ@ Xw׿dQL%oJmN't~[S/G&uE?5t&^)Y<9KwDbw?k*QWޥC{38`9Xi&i^ >J^o`^{%=K_NYet8JQշ!jOhݖS"JowTdlVAHL33Ig? n[&KoxuJ)gspNƎc)0~ކ#)zlp</d~xV㱃V29` f탨 x/hf>Ǚ085[ź{.ЪJ5UHody^_y(U=9jH%zL{.y(߃͖MQᅵ%+߳_\E/.z+XXfԃ3Vzz7%{=cw4ǥ=v=}"ZzEf譶WugjzJc̜ךF_E?J*{R&fd[]|]OK=09+fm)votbN?3cj}7{~랝};w ̸g8}?ch4k--w=^d,~ПCq +W @\7t +W @\IMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09  Ѐ ](16t2/ 1 V{qx U}gC !6ABoȒEW / f *,؛ۦ6PbXRij( BZ-آkaKk"]! Ƙ Md2l; =s{[E-ʝ19>Ү(&E>ڢjE*l+|7E(S>GtyۣwFGw/Ou+X}(b)G SU_wz:KfH88~9An\\\ENO0u4 ?3z\ouYQGNw,D*vsgbQ1D۔^Ӣ _EӢ߽+ޯ>h&ߙ" fwoY]tۣ':i+":6<[+b\i;l]q=guPK?jF/R[#˶om8{ѭؿlf.02 +#YEKf 虊<]>z==NzͅN"탊V\+BE&%O¶*LQ1NAH[#>O6P}j9 άڑjƆ^vmИlnkw"S-lD6+kЄ z]O(k7+SUG6dzWl$>+o?-G=*Oe+v_4=,~=U omTz)Hi*ߎScF;^`7Y6IA9܇;_?1d8Eq.پ#e e_Ez,oꛣU|ހGQ+pn_hע)S/ƴ1W^B+7 ~ӏ TlM0~^H5UݼU2 έzz)7_ p=~e ۂMfLw5dFʑN]97vT_a6eg?5Wy;3|:ׯW{Ewʧ mw %_4="xpϥqMm72*E}mESMH{ŋ{ż~xدݽ%z|_$(8kUηDr_TUM vkL\|ߕREpZBܣdߊ .EG[j^n/w3co=߹R8΍zd ;iLp%ԋLB O?noP/21Z)z!wrJ6߰(eyїhW}y[-iv]ϔd\I9xyfǕJ_<xHbU}Z;{ǵEsfpn_C;Ϧ] ڧl/WWrsD5p=~Aox.`xg wG<lذi6c9^ba/_-W2F㑃Q=E>'U~i+hɅs"[]nF%{v9`!_1/C=$A;e)9( sS_nnZa^w"ov+/4x=/Rgߊޮpvxۀ  m87 z*7-]wɁE4/C̷,>+瀲4% ر"|fx7WSdwhlP3đ`UH;\qa.ݙTa&OO<D{WOׇ|x}W#E_X(zWM+8!=φCYf>#}3w-[Hcނ\Ʌ0/N'Ӝzܩ5p>xG.Zje?wPH ߰O/|>AgWʡ;L{ȼ9GV-·NYR^e<盧F/*t!uE)[5Q^}<%OԔ~ss.n?]Y>|hy n)|͙W )Sz6IEZ4:$b!5_w 眵hq8t#(#7;, D8BFw^5#f\fpn_UoN4N_tʡ/蝧דe*!Kնh^W#t_o/W8r~/| YV׌= UyU387/UWI=*/ʅȼ*_]jgڇd^%p(+3Śys*u0켊јWݫzWmy=Hkͫ2~*d(oa?'yեy]Ӝ 5d>BU+[z/8_8\E_4y~^F~ʜ_L O>H>ϕu| #GjS}j|9-m#Ʒy+闸آH}fpn=&o/W<\8%\o>=Ƅw7r#W8XG~52d b\_G%_K#{< Rk>D#SҘ0 7<>O%Ə3~ᜧSa sz<$U|\|9T2'HH1Q8F-45'}Nm[uNɜ [$E`N=!C_ Os;B:ߞҝB]9s!΅cdMMya.\i+g z(Tox>I&_X߉jPU2±_MR٤qcs+ltVd^4V(~AXIz zv .K\lܪ\38z>UV{nU_Kmdn/xg{KVx^ 65b:[}A~vnEZ#{=ƒ=kToX7 ['>lmǎ*[174SZ!T_>"WGܩIX@-=J٨6I}Z3JKJ ꋽMq&wg;ՖC帻yarMq~Ľ1.)oxw<.GF^q7iᶸh/ k{@ ;0퀿|_+X/iU-J{XJ< fJS}ӶE>wnPɟǡ #:IBr+*r@]%M]>lT VhNx?Aētƚ䵌"WFǹhl>i!S~l9| 8qr02 Xy : }g&%2q6[瑉FĠUє p{.Z>?M~nǭ7b/6ޡXv˷Cz3/?ęNąnN'tsy3w^Cw"nvN^3Vg?l˝!ΤLq_=!Tb K*!)u~8pO|%\l\.K{!BJ+8,gGKQz{tށ).W Jn(KkҀ[O{dCo`~&#swri N}yQ:n[9< 7ݗ(?c1&YIB/T]K[xY["|_E r2khM|Wu˽U:]7{hQ:y$_h]7[9ux+A]qFbޱOx֯k0g8wu35|EަaI<=TtfwkΑijb~_S>ׄ7@o/,s? P yG Uf^|qmSа7q6޿(o\od:B\* F|gÆM;f; kٹ ie>^BE"ǚ29ֱ.S|XI=hj|֣< ߩxU{ ^%*}M>mC*/W49E7%]@?LҖ=Cض[E}ˮ&86o~(-_yC6li7ڪxc\UdE1.Nl?V٩֓}`>"-óޑ1-.5;C q~?NN8c@r19Tي`X#qv㣇Ou|dzĻ^tfe'Lk&:ᯞ{ăgĜUO-Zh\Zr#e$VdOоqwFx ؇c7n^2S=ɝw!}l2..e"AEk{\9 E{+!~Z]M-<ùx\כ%[o?hn{~(zkٶcoٰa~GfѦS}lF}c>|E&}N2r;2ޢ|m`Cm /8đ>rkOL|x/W)+j9 s;5!W?nr9c{HgCU34 'F9ÔԚ8Ժ6 ^r3 CćeIw0Ҙ<8䅺G:qS?]rwzahe7j!)-Czף<晢.h 7pXI:_\/#1w\Sz~_dΝwT|I^eB|3$ף(צ@.Uixkι?UUk_?堐|/@nZΕ 8f2c;ctz@Ez~St7|38zrwp^>|p ̯]w*;EjV+=sx83K}e wA15eμk,.#Ѭ_/I~W#^Sl83 $CY YHc¸O.|Z/z0Ձ|t1o='1y gp+w1C -9Ez˷YڒF޵[LaСFhqaN[Ijr!-(-YoCsㄟm-Y!;)\Y\52%ܒ wO1yAu!x|w*GqErp|X7lV]NL4AKx? '-1~gw>4 v3g+_EW;[Y}wZlu*-O% Ъ)u~8G%=e*b g7J4v8zm"u멹΃/N|@{~{%N?׈^ǼTTߒJ Kھq΃ha<9yg 5s]@@gu?yJn$$p?bϻl>%Tuz>!-q{Gl9|ESsD|3\@Qs0,"'&^/ڔ v0]X?$9Quܥuפ_Q%w²Mt5_q8Ǖnf?M* 45-I!m7_ywh2⨋|蜞o JAS1<+NsϗaPz^(ؓjyy=^)-W͓;w? OzQҢ|s>) o[TUмp^ʚj7/њq*wunU9 SNz6IEZd99I8GGJ߭s(a>9zE>ϙtfu$Rͯwj->7 έ'rFᏄ_/5LxOf8 Vuէy}38_å_ٝy}f~52뒃wKx^ 65g:\4z}ryBERX7|/ʱ;U${Hڞ;YqEuPi F_I'd/&~U>RQ]HeYj E{-SI'z;/嘛✟9˸.{J\8u^Pa\ө?lөu<|Q'n_|3e}8"> vƖ_olƊ _V_*7TizV9oO9-A_47Jk r OYi\ |&R[q馥lz.@ ?qmiuᓏ<3|hq^aQ'0pGC}1= '2qALިE214tx;|j'QoQ ɍT-ژbIْJOjeޓ$uHlPlQPL;widz5Hw=.;:u.zsY4w=ȼ[ȃ# lCD6GS6HV+- :`6g[z N[Cvg}!qilmg-qgҾ87p~@in.io?Ѣ, %߰={4BOxl<4]qs;H#p9.ou~ON5~.G+T JnHF-DGď+QJn[[ܚ^ҳiC7< g l9 D޸n®2>޻圇zGGw|%6NA]bQu6yvto}Җ^țTS//m'/N']ӭ8,/~QLFz&Ź?Z oVEΏ) 4Kz#_>kGWlW_cCvGʽRwZ 6 YB^,K7>cǦ{ұ?nL;s;r39SgZ]m%6Ey#Z)xt{Wby#\'u.Sw>O FZxuR- V%1rLcF;W6zKJ4KN:h#yid:#-g P'yܝj89$dR$+v$o%7uQ؉%=BWX2kuN֕U2[ ˕?w\mryŞL֢3x }C 2W8ZLl1I*HYB;A̽X2E^I!-Nם3#C_E韌Qef /q FN:ULAI@g1~-1 b;Qk1OT!sWY-{γr:[pR6%>]x(X:5O~džoniD ~s;;m-MW%c0ǷWw`B0}u i/d { ^&x8}C*e}^ oRop&_/X(2K؜9gh6:lt,96O=xo`#kFFvK(/LbU|W'^#c \3?aqO.pY;|Yr;sޏ:qTt$8xliUVk4̟#ّ1PoiԥNNcؘ1)2?61C1Cl[Yx36c`3vYc`c[c% e،!bSe!]6v,DZ ؟ɡcttl3`'}q J=-mol xK>vƶolKY6x]kƮzm3fصhlvLs.T`cSc˲ ͱeќq:x]˂IΕ c&/靧}O'f J+ZuSX}&vՇdtk?mȋ{_p{戮p陸 nC>P14s-yW5܀(:}{IMaA=gwp)G[Y_ a|ҩ-yw3 dS&} |fR?'5-um/x?g]q~ja+o?-+nz{|[v`o||;V<5K{ {ez>/7EEJޡ;˶om8{q?f&>8<4)o7MV˝EEC'VExN<N(" \d GO{˞:a{ =8}rᓴ`{A ;BPr9*{6K>=}ݤt# xđ:}U/R'x%@'N$zs>ໞP'?_C'oV' :N$ӽ#sY<[z 1oʗWu*YvLu{bA~nOgͽ7圵NBOyYnrl?^t6z3:O ΀E5yy4rl>t~O0xz6z%|A/ 2&gj6;g._&^^"wÞ֎K{3l`G~l+b!Kr4}y;/re.srVQNλ 9ټ]d;C]JvܟNKsPמ{gr^8+?rsɡy&%oݙC-gc(|=j82IʜyVtގ>v(] |2[֋yϹOX1 y82s1WʟyƼ杯tޮ9?ӥ,xcߪ1w-B?fmMaߕ*Jx%ll^3O>68cwG1`ceF΁ǰߣ76ldm4`獑-bQ_q&.GWO/Uڲ埳Y.WU:'l;Ļ<\Vd\nfxLcqnU.тP'0Yc™'YFԥy^s|lEqicC1C1oƾg،!e!m+ of .k l:eM?>_0ѱctk3q`#F˂M?ld--ڗ~{4`}O^>%j?eq;7Oj)Y,..W~'qpD?Nz8Źylؘ̟٤5N.6 ط68ǁ]V?llk\Yxӏ~<;]V?l:eፎaб[c[S~z {:2{,a3Gol xc[,?#-eӂo`okƮ,ͱk1ͥeќ*x;`Esl*1SeThMԲh8 .e_pnu?7kqnnD?97_vz|;3^痊)SaHȆ\;hTfʉ6;ȽQ"qNy@s/iy9՗} WplLȹ} ʹYg&/n_<`-;_9mrWɝ&A4K.O0iX:n9d[=x\ *9݁r66緅 6g@>68cwG1`ceF΁ǰ`#kFր1sy3 (}j?znrcW׏&Kqdƺzg'Uԟ16c`3vYc`c߀}+ of l.k llk\Yx36cvYc`cׁ]/ ot ۀ|t ז,1`ߖF {S 9Kƶ7˲--eqx]kƮ4Ǯ4Esƫ ]ͱƦ4OaeS96cSˢ9t6x,;W/q@p@uߛ1k8LUK^9{x;%jN}ӎW#aæ-~>8fʑsE{7{(=Λ]_+kuOr2yw}Pq닺s~]_ռ7GCOs4ת#IyNL c<޿wC~._ማ? f 2pm GqwחsN@çw|:=}'#=awzX+VׁPW;A}>sdE)Pg7k;h?ߢ:.5qFzTgW6uo#lϚߊ !۳=94rl>`G=.ȹd;OgOD7 2&g{j6m(VT-#{Oڬk3x'.)lzg{ rehW;<]_Kw}]?0tw}Qnx-lzg{d:w̙gEg{ʼ \!?EO8 -i,R 5w&ɓ;ŹEb  Dg1˳y+~'Y_1f]4sMpFv0Ѵ(^V 6C7ݥG=ا&zZz_;8>3}GoEoE7ߢt `w[.E&)sQ=9}~;6K!c1`cFʂ96r^l ld h#-;;~A~ߐeRE A1w}]6Zd \>fqq9Luٞ83(|reqrz8 gx+=ku^;O(g] 8d6nlcc.R6g].9ǁM?lq`Տl[Yxӏ~.6ֲ68ǁ]V?l:eM?m@~-*Qǁ#LwXƶ7-]mm)߬7elk.ˮAs4ǮEsƫ lvY4?4M66eThMԲh8]˂ M貧]_zp8{]a,@yư/q𻲌/Yl;^@}03I/S|”s%ng w3x;9j#<>n糵>aJȓwF׿{wۇ9ﳾ_-7zMU3ռ $>"zgtLv[cI@,M_p(NwwfAgnfs97"bHu"j#r7-*x1 g9Pୋu:4owact,O-ꊳ#d*8nQ>FZ9 [ R"UrFhfGeU~ڪCe)?G5SZI}VZI߅J_!(?4ՃK(ׇy|,>(NkLw5`>`go:(26A׊:S:O]ߚaƚxvC??4Kv&*oˏ^w93)"r?y=+HU$/G}D, R~KT* E@=K-p׮g~H˽?ʋq9Xj7Gum>k#Tn4orո>bs2r%-حA"͑鶊U./O/㧭9r {wi^B*y{"_p9ܕs=O۾upY)39ticVJiёm2,xTeb"+3#|;ۃ zu]7:>BNt#GtF{mcpuۋo@^+g _J{KVZT`=w9_whL(d-۞]l:œ].:|, ϑˋ>nW|'q5ޓ7d5kC`<ʉlrG}O Ļ6`($= ~_\e|<_$J5K!(=+2[f62ξ@22?ĀSh7e tI+ Nv9~ TMPnfk5plZ*bLNeIԹ  ֎ Ի㹔Fr~!A0:2櫃糮>f]':k}~:xϣ6 $fM:X&N%z8N׽H$׃m-w}7rޔ爫5 Λ,z?g#Y(5~9CNA:0F}NwG5 7XI>k$ȵȯfwDkf( N!܋|` }%Q8;qgU^R>{yD/g?T6Q¸z[BP!TAx*kİ3U:!Omj{c+Nrq-7Vb} ylQ&ݾ ^"_ng_ 'e,mJ1%WT~aV2n#r:3wtan{ ~w@2fj_|6\nfF"j!dyJ'εh=DWP737?zNωƹ:u9|Mfm/ug6Ms}&?޾A9}Su)[/7l {~/P Two} ~Kg!!!!!!!!*4#_@@@@@%BMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:09  = Ax==(16nV2V/=1#JN{x} $IUv .gr Uv)G}xd (#xx TފGx, ,,,U=T"^udVWUNVefċ//^\G1/c_lu׼a?}3ٴJUE7Zsu5j ~?VF_1/>tV:/!' exnj@\;5Orqy'?A?f,gP^)2ȗj^rd9B9e@w=n?z*ŴlO^!L|\_ychIě^7n uB<+GRJ2oru5|}}<ŷE7_R˛͍~8J'ϛ :Ox |&M&[*ϛy>`GA oxܕ7ۀM[vyDs66xww;vܷ!\<>7O"BZĻ  o&ow{y4j<7y ouHg'o1 ߑᷡ&'.! *ζi'Ƌo2<}&][>)>?aTl?Y?nV\hxY5ߘLyKpN/ ^\HOiY}.<Ӹj9jie _ӌ#X3[QwZXj[)]p xoF>5Z0,hU[K|c;+/ԝok p?-}' |&>oηp|'|GϷO 6n){(wI]f ONdYYwH#+/|D^bA@ӭyɴf9ܵ%W|]jxW5|x3uϗ9aJea1<;_ִUGJG*mCM ~t?ymm;POY`;ok@-'QN-O%AȭJ.Dy#]^05?_gѝeH33߼57qR|GW*|o*\5o|]ctB`Jy7L̯.˶ŧ6Pg{n~w2!w -])V̡k|]>T _43o_<˻Z|?_rd>C^;o5L5^߬p4/KyӰzO 5nlef~|ZN[ ъH.P3{ޝ4X:V[nKSD$Yik[3TVg1x8Z'khnNZpCZո#MˏqwMktO77ucX>bew>@A4f[h,{~zi{bh ih_>4:yq K&9tk97I_rkQ-j9m(۶YdօY{dfJN[¾Op^oC $n&y y@uc,{;&-mwZ=Oyߟhkufl|2g?!k{oydcJu LbYImR -ighZ|$U .hw2a>eAӍtywJwIfQ|Hq)n/S<Ѳ4OƝg~+܁e7 Tw S p~,Ѱ:h%ka+~|Wduc`ƶ+5ce'QJ|k^j>iډߢG/~H|j;OvVF⪙84k|pSp5t#~lyY~ `Χ}u(߶Bɋ-==|V6cOIx^O, Z 9%cVk}c~{M4c:y|Ѽ[lCY7r|;:.A՝vh{K,7 _IuƇ0k׸3l5;/ԝ4Ԝq5ԝgSVg N;e!h_liPB+|x;wky'_ijS4}+E|\H/ϺB˅o faonoCŲwceD3n싱f_<)q1gj߉Rۤl.)W~o8/Ye?;Ӿ̴jYh~|)j&.Viҝ0';~?$*\Z~JoU7_nUcٲ:VpMSdMMb/SI_ZVv)a[q(e0g'무n۟3`fQi1/O^k'@3 JjjN3M:4iyA7ttaYΟ:ؼ|g\/0O̴o0IJ95[iGXlm{[ju--_QwG)hGCou׼"f~,;-t'|-o}N7[yfv-g-|X4yJַ>x,{չ= ˲)GϏAy:7wBb=k~ѬsmS w7N^[*.R'7b{\tN?{`yBuh2<|T7#0W4N3ˇfaN;ˈ~C{6"?y#]~IW*gПƇ8{~y<~ZCmYq 8%$e>WKqH|>\,vn(5lzZO24o<9Qr!'>j>+]!Lˈ~qb9SƧaZp:I Y?Ox wM]&SZWR&Z:i' ˛y{Z|C3ˆ& -Kԝi=otJo{H[ˍf ~xۦxy\5oX? #}6Mn458!ei ])YzW-9ĭsPs gG ;a0Z67K?Y˱jϾ58q/#=y<ߤI+*W=׆sk31}|~@sUWW_m>>|k!!k5]wyh>C?|؇}yЃd>?|G|ȏHQQ?|ǘFazs 7?!yyCj?c?c#G>?|'|ym>?|'}Odl6M2)b>S?|ڧ}Ot3?3c>|g}=ql'<>Cr)=;gb;|/LbgϳRD#A8$ͿlH-1Co'D9M,Brv_k΋Wxoӑ9MCn;LLN4>Sۦ3qvb;vfd RՓ" ;OS#i,R.2~̟sM#õtSBJ' .XOi8b9 |YHbbqYRԳ ?]3B}҇F Z&j&겏o =Y4*z;Рo ƈK](Xr0%wET$ya,;"%x Vtj;1; JFΨaw c F |uxEv!6cCH[ICaX1tv>5G ¤>(U:7AP| BBGwgFI@"/kw@ ISk“!f9 +Ș)f#(Z\ EEcvGŧcB ^DKzQ`q`qڭc!!jP3!? .,ci@ċqs<-[Kb 'lp MIR `A' By9\K^(A,m%N[!iZ|ED$'`J/!0 s1 | t ßĠo\(@Pd$gsa Q24-ޣQ$q֞]}d ,@bDiX0z/` ܐMqjE(<$d$PJ[Q70fOX@> <"; E-Tf gnxI -)zf-uwyY` ĐK~J?_L"$U"<%f-}OPҴ H bZf&V.h"xf^) 2V>v'A)sPBݛSB秧7GWL)1/Bԋ5 E',J@3 \C!1II-)P2K(g}YhۋY@u"-ZR P"p`9 mAVRezu9C$R|b<OɱG'5q. LTQ)0"0uEwni )J.Iȣ )VMPPưfxW$m((6,a~$ sV:(~|?MrjU!lm<ފݟ/Xc"N >W;.6e| *-%W~JH /˒E^on9}z,-01(wV [в8{{6?~,&t#{7QNrz;Bd ij; {.5ȃ󡹅bYٓE/F'b1h5۟SAX("r/BO\x@W5\'>u%s~hv۹'YtŎnD F.'~{l5 ֈ'ۢ:\3¬vg#;sEYd'kc/>+6 Z{S[ee9jp哰ZF5Fk4#-픯F+-cr1OsfuZ|PQʃ&RL a ߉1o'9K VicVyT_i}b@g*p>#I"{,p6 Q /fIaDoL  89'eY>9gNA&VxAkcAA>9(p k !&9N> 7%!k 3 '?&㜇|†1\hp`3-l/dXKig]MMrط ?vbo&B?o/`_Pݩ\ꇯ bmu0 [ybW`6&y3S :X$|K.>X󎆲,cɀS(wD>9N>š֩O+ASw5 &Ycq'8 v0oI3Gyr.+rG LZ]*)SJm4k'O0j׼q?(Szqr+;*$sn%"%e `#?|:ÖR'dB&y1%WG>) f!^HY4Η 3eo$NI>iL4l N׊[29.MRO=%or|:C!_P>q`!O$+F7G1 ncNA?A_).x,MЊkeT4V+ʒ'Y`rCkJ C'C:^<^Upe;XS]wp9x2G]VN@Ss}uuLl 'nvr,֯;00e^݂Stؔ,IMX`ɺ=gRJ~P%t4y+fb3 (Q bCXWVy^2wo,WL@Y/NjFFذS-ulnƼ{]LCqsfJT»#Y YL%s8O0h6H&>JEn}`ս|]= ZdŮ| 7mќnq0H~I49O0׹.`{X/\SM ꓵ$mi Ux# 3MX'IQ 53""糍ֺ'<"۳+!(x[$6WC@w媐Md:gֻ_>Wc8s>= L>Y>mp+lŬz͉(5'' cN6a@>Id^R!aaPIJ >uL}R * Ɛ3z' Gewֺ`|sxeXNxꓵw(M`&$HXМሖl1LlY#c׶xXOsfI8>M{UKcL55%VNPɸٺB8uaKqƋUfa^B fP]>iaf?fNߣ޺x'{kq4wЭaらIYm-_vH}L0t}dN'g?^ nJ>b;s;ۜƞO0 [Zi5!tgP0䌕J,:%2fs]I P[vsC tЁv}fY UjM 4dFT?Ś%WDp&|hӞ"VvtsYH&Q(hÎA{Rx  r-k`>;d^FMSZD~Df VfInȑhh@L?%0`0d LK4q ZZ褀- ]%1OI'u%rQ"sqߴb`T-aG%H,qF;c,%x@12Q%lJF &Z knūHا̥~؄x-?c"KO]|x]sMؖ'Mo_7 w;〃$:;V"^ u$;y{^~;p,4ݢ}-.LdT'; Ej9uWQ6 a(ML#4s:lXX#(Ĩݥpxa?!ݏN~  |UU(2%IFޠB_{mOas?]-} Zk U5ij#696:аqx?9?؞%z+Ox&e?'!O (z!@陣9˜g2R>l~Jluvu V\]Qq8S3!}!XDgo N7@Vܰitl̯Ox(YX}6wLÛ>Ak8U) 3WYtC:7#dJXՎs& QWdlC2 b9pA6vطrԫewf6g~#xѠ곦ic|@GSKh X> Ĭ8@NᷰzK,1)ŬJ{I(6F;AD1a! Eagzh2W"!N6#]S&(^3N>)a_mI 2fSI`ef^xϮO_dw$xy̏3uG gS[k># 5yS<4(7ɽܤ(}ц~b("^X$Ic9bkt^3t #/L7K},x=|ٹ}x{%V'h%m}VП O.u`.7 j_pokp451䖸b/g=E7" a6Z&+M/(O%>?v^"$>WC_ f~A&б{w?L*ڡ,'I@j_T`b&ɺ2amhvg!/tK]}fN/J}2H^`u Sd'{q|8 rUvd w[$kT{֩s͈d5&V)QD>RPRܲXW=N?9qy>dB IY&"p#m_ѽ(; #rmo'EN_6Tx?;ĭh}2Ж Y?Gd?@^e~ /k>$u2Mtu~p"U]EeBe®|ص_:';pKV;:t퀘]KWE sJW !ᓞ2~A}mLr[pk3vXa(lmn8~Y_ʰ"nlk<ϫB[.r(ES9:W!]7iIlX;2Ws ,)ṳ6x\0)F_뒆6b;$ǎ6Zq7Q9BG2Z0+厌x׳dA7Dr|2[_n-|`OfGAOhEr3cTNXAE/.H Bْ!AMEGǍJηИ`ǰsH[.?  t}2dD̾8Y#6{{!/#>M@sNDv4`=7G_r_me|:@C8WLաEoݜxpH>wd96"HhU-ryc5a^1JoE"lko ,x^8d6l]07.$a g.; V OJ;9.Smn >}2 ;ɧPbpwsOFCMS=3^Rc{cp(I5Ny %0sDsw1B<@W!O-qU TOZD2(N X Ǘ0 j>لd}4?6?I%iNVމxu*NKSs7nX Z8C:&9oMtjpHtO9ጂiǥyQzGPN2>^;iiN7d:˜Kݡ|q@$))>rnSuVtMu :1zwO' vNOx$~R?=nş⊰FIdޱ@}mNMyTd1);GZ-Haa>."OR7WQoPa)&cQx*i^m6Ilt+Ϟ p+1ʹ2$~[y.W4l&a$h&1z\MǵRhkL_;tcA5 l1*vv7[3P kџ`}qov1D .xxCf-J9>,Ѷ`1[0UȟoN$lz80~:u&86ƞ} ѩ1>uU1~ laעg?x|қٚJNq+DHĮI#:NJlnpƅVXIJ/egslr詏qA@Gqb#08~kkM-`aWTCnݬ)s)+\ЧTknWz[y:3wi^ /2?Q x4;k EcG,`K\9AN.̡Uyn֌D/?Ntr9=c]d|dIMþ1фS.d(i ɵ=M୏sBw0 /:g:؎;di|u2Ƿ'lhw3M\ZO}rJP gy4J;^5M*}a#] ࠍ8뫊/nߩ?&.}ӆ&%В0-0: -0@0 YfO;P:pk>q/m?8L1Mغ&. BG% M VC _5+6ݬq1$5P4y4uм4pNG5eb1 xkkJv=OY iRC9,$x>Յ4qް !%f١P W$1UrM+q v49+~͚>dXjc9[IǎjO_/~ۜ\zꔺ^?F 'v`g sS5i:Fq o /ox1y0bem| pI]}f;~\kj`+7V_VEAIj~4ed;Т9/q9!e+4[a,FLr=Ӊh aJ1~ Œb[~ԃeI\fAPR~ `% Ek܍Qn,o7y] Xr ]c[u?E`ƈi5m $.& x֘P4YOVpPX6,`ٝ+076`8n+@8 B._+I>ٱ6|%@_;kQ0nrcx.;nņ-:qi%hNpoKΑLu]}hy>~1j+vbmH;RuO;|?Pk/K[!E#٫TlB;2Ky=ŸF>w2?r'6rhp5T2q F?˽,b4h֚#Z8AJO/a&as_sVfc~F[^(*lʶ2F;#wfo;[R\D+ƌ\q#v5 Q$^SDEp65mI:m5݃yY,äN|,8'$gv<^cZVy7PuULb_s%}L hOgc\;qc]i' }+q8Gm;(:#B^cvW,F+3QɆ\UФ!cwv涏(LUjdIF"UYnVB68 ^z~.cw?Y|iE-R-/xPe\}]FiHbi Ys^k*p8wѡE0F[!dIoQ?1G6di,C]s;S,ɪX)\W+l 8Yb7ֻP*+O<z=Y6'5 BAENrywWU*W' *9+=q%'O%igEaOw?p>OvLCs+ղ%'Pp  ٕO9t؞W@ qԫMB!yL>6赇 w+\>vXɊ|2X|Bڝ>Na3NjqDȞ=U# eXJieJuA^cYC>Aٳ*Y)nAf|Q_hh+9POww9 ?y K^2عꄋ8dūϖϽ:-OOb `3\ߘA*So*K kW;G/,%T;KxA#]2Od1qǑ%DN/luJ|Zc-+zLJdVrK|iqFwkGSZ>V˱R·0i)WYO0b;AP;$rVF,9b!;O<ӪCݓY n{26ݝ#sn.:K*7m#,ΎEyԲ; Ųj=!la6 w"?xi *UzvI\;a: ?и LOjU%d4:-AsGLl[lޤobφZ|bOI _YD0BlO/+h89I͆<+keʆU'I&jgְ-þϧ%pIq|g $UCl0Hn/7K0~;ʫ${"~Np$95V>ӟJKQ }vq]J;$`;Q3zLX'ɅvK3?q %CFCoG̘}aɧ?x/5$Θ; CߓtZ7pKi9Grjw ٘5쒃#`+ 1?Ya LrՒrrkui)`T_<~wfj~Q B5-9\BJ&;,}9| i N _JKaU7ύOsP/Cw(# N1y 0J_p'VBV^.ttKTn&}'<g$-,MLk ^dT'!}qװ?hoz-@="\$m'7rSJr&g!`?jtOR`En{‚kbB7mU)j)FwEXi _Qxz~IA<)?Q}l;\r) l(X>VA[tm맨mŭA09z#)NbR,XFq'a[?W%V>xxޏ=bk6KY18ܭ3J7@i&<4 "1b8Ԧ^/CѠsUp8rt~Ñ~:W><߾?4Ԑ8(lL:^XWe!JNV:Kl,j%69^3Z2be䓓/~g9zR-( ɇs鉖㓦)i<|_<k'=&qO+nF>7dhNYO⤴Ҩ.3cp4˵<=+c#;J3]Lrc)AG>c{08,r[^G1ch{s%3W \+Vh̨һJK* OaX㞥 ۙr'n}nfr,372C}4%FyN 4C̪"ֶbJDIлiL]9;+Ov1ά5zsm*pY nr Iڋ!'%WSFW6~D8* |&Ʀk6U䫂ӡrII(wz}E|4 K2B4l}'w*P鋖{5;PD95ST+>KG.$pԧ,"E>Qr* Ũ&η>[&[LU]8\"̛䢲4A- ?U?WӘo?q=xS4b!j烘Rjw%rc>UVx֏n1j SШ/?^gi£RdH3xH2cKT铮)ZMbtŪ2Br3cAJ'ڟN|FW_}j0b89hk"GQ%qvEZ7YBV;չj<-ͻ9Q su+LJOJ}^Qd|I7R\%_ WyIjshif{C*LiO0-DZ~rg8"~V+*>}3wbo[`;*33cy zHԷ7r fZI"Pn~U!y#gt^b}ηhIRZVsp h,Gn~䋤Xw`sI,.$`Kt\L!,^VP=C׊Mk"i6Х-ge)vZP~17&R(;4LB?9/ @mK0'a{MO΢>w'mؓ\^ ]ȥq|r4VQWS5L ''̔cQٚ,fηMF~Mp>}ݙI96n\LtB)'wҽr4cvηʫ%?㹑XUBOH!ݤK NƯ%I]\}l7x܄\_RY- zc#i ' z_fX sKiT}Y&f}r}vX]3S EG3xڄc>6_ (P@zxc- 04'7o-R7Ui9%SSI ےrݽF3OAn)&]HX;~'o-] {<'ZLlVM'VJȥ;.]1'OұrE'TZ}l}'^;L3JgUBp0؇[2(`k?A@~|'0ϸ4^z^\Ku"Qk~lNim`@-_mQ=yZmAbd^bo3L5bbE>և0M/Qb+&O(wv]Hj-E(4.R!VE' )܎p+OiDZjXX'bLNRbBTؘ+AgI';|bdNـ;tK V42r̆Z'(/pk톨'{%,vN/lXyCi TIMv+´qR9H'9>aU1֋_=*͍AF7G[;/\5"njy!MtǶvHy<`c.Hk( Fv\Zgf}I}l5Zaψu3(Ăf2}sAօ!",IUP-ruC?T9n{bDL]$ѓOi7[@;f;.UA%ٟw< <ԢFWK62VBNvGxcd5}0!sFٶf.z9cB }) S\Mrf+Q& 'lmZ|2a=`^ ~7jưХKvfjԇG{} U538šݡ3ĿN$'P%Sd%b<.B8v e`IVHW䄓OF16^{cI #a]a '4WggSf۱J~/fIV@ s& Uq 7"/<2c ŘۈE[cQF q !v?ymxMGɤAFJ!3jCZ#/F*S^5Ni/Kr>&G1B$H)+`3$9d[@A\!}lpڬyU Ӿ663ب b3X9$qt ɪtYN-=Սp5|dحYGZfe"n^KTIV(Ο*Ϛ!+Ynǩmvl`l`lhA_-us>;C?{e|[ed sb$bqmڣglIɪ)$yCH\Lq\_v?ߞz;)k1259ii-RNE׼k-vDDrJ>D^r ͸o{嚩?__l/^`GGgnEiˉZ>p,JY$:c9tNVt؇mĞ/dirwER#u"Iģ`Ӣ͑@`o*HAl} C7ly.OWfzX$tw͵PBÃB* % Pg U\sRM|ȿFiZ0R'l!-i;8Ո[ |xaɱjÍwɸDz<9gSLKKF@LuAC^S+&RNa%JY4z(xMr3b1=79,{ W5Q;h>6)rTϹeF ۗux&GQP:ފ7`ȇU0'qJ*& X U9q"C*@\i+E"yh0aT?NPͷןd$<..eYBXubBM]Ƹ<l! S&i`PiFh8C@):Y*wJ=#,%|-mm"Hg4TJr:;H$⤇M}C4 1vM#+.s@72YP!j* {c_O<Ɏ@ЎT) yU_ᬘpքhj'g+O|Q|[x[>9%k`:}t׻9~,rlmCc>`ϲ{6?~=4*vvۅ_LʖMcS25H-(#̠v$Oow}D1hop흕 O Wel@VX$?@{vGX }tA'y`&GQ9|F~Jdi#Tȟ|ƦʇkW+'` ϣ L!c̪t|Ty|g82QS]TTbU#0MAC2A|q>ȱvN!`&VbA}>ha=<2ETOd4K3$K ʄ ɠA|i&4i`'htY8x<PpA[tI:[_xVoV֩]rW@.>NJI۝N u7u/;lV[ l']2 C[uWic Jl|pRZx!}s^\B|hGX&&^L06O 8eZMaqwiƺ Jp_ f{׺[RJ- NߑkWlnP縲r)9,.aGͶ;ф Gnş#vq֖n =`QgS=Ɓw+C.KR@9OR2!喔Rk8Qs׍w\_|IGv )_J `&X2]{}`îG!: 9чRkt^kehb8%0ιD'bz$٦x:ܕI61>nxij8ZEt(ힼZ)qK.~wbŕ3(XN'9+Enk`<'-.^ &L-)T~Yw@ h=̱8d+%;3p徹ܔ"MMZYrG9;t 'KǺr&.X枬{h9\؇]2poz7^p&qI&wIrC_%whGuwwݗꓬ'us.Bi~ rێR6Wٞ\}eg`~;y)׶}ṃPl;,*P&8!k'\h8\X5)hacsqALjvl7 NsC/ `glhom(O o s ) ] t?r7p.g*+j 01tK&4ن8|_Q{a|s|g,(::6SNJvk}kZAG/". @>4*@Q?.+q;,ߑ+Ź;$fo弛*#U핵cZ +'k`|4;e=/^f0iDMmK).lɹ&.5ͱP̀}Ofeq|+?v_X(K ҄(sgic3bs144zjt~CM\tQKG+RWjP@2b7i"M>$Q`bn_Hd9[N Μ30EkX9vIٴPOʶ>](n"#R4y㊖1@${M nM~ '3 S={ ojg%1'i ;'sx 6e_`?Oæ 0i5AnV bQ8I^;t_τw0RfcfUڞY4Z~wMycgE$&BaS׮#2<|caA\8e*5+NsJZmpmAy(M!f S5HaKіO.dcjvjV_=f}ۄTUifFxq*9C6e͊% ༌c:4lolLQN؃By]U;6񿳂'w܏0,L;*0W8 xn۝4vmUO\^t^/Q!OT;w5Hf!~9'z=266Q&t:PWa\O@]X:33[]ob bsW[ט٨扩%(Dʾ.?Q}UHUB)T流=}&vGb4BMN.J!b- [rD,BiBK'Zr?"mbo]ج{)fN;B$uvsgEfn. ۪D0K<-B$c.39abW܁`Զ*"o#_.>ZsKjT} +J·8A5{1OG;'e;)ROj.~q %j0jě.y9:ec_zỜk6߅ObC>_ӥ3IB]JzE#˽p{T^ЊZA?C"A&.'{.h8Fg|%5~; -'!&$RQtI7* LyUBKZ &1 YRW»⪫ƭ+Zj "HM=*ǹ~޼ɛSϹ=qŁ;ڧ) gekN=|້o7p@!{LOTG{Ijc#OX|-Pn~vE9(o|<4fK/v&"s*ؕ;,kmw~s}IO!-a%fvz~ܯ2r]hCg9nчO@Lt].ǎsEjA}*6^yfӤjz$Mow*6Onoeb}osxnX8PGٍ -hot7E{ ˹tYyκas:[ U7ֶ֓~D] =DyҖzX86Cr:F?kFZcc$*VwrHc[~'&+ OҲ'*S)*3gpscx"3{;اC^_ʯz7uLG{@x(~uخsWp.e#pɎ\Ky;NTOxqޜlsh7:߅~]~6lfYc^:{x+mN)ba'H 񠋃UXMK.DYo^c)RN8?+Զ;|`U;z7Ɠ2q+O;xCwOvq*cm<  c`{Tbs4(l6K}h_f^xl4%.{ۘd=QJXھ2#FAh/cϟToy?)'V`{pvL6G@j`®76y4# eh8[s˔{iM?';S9sn]mwxöi .\c 7 @>?'}~v0ޮ_xǞ/>7ӳosz׌'v* EE)pNZ8v تWZQ |l^/~VLIjo?<7V wkI}~\R|4R?P };~z tZ^9ج Xذ}$^53ԩg'<6x;7Z!(^۩y<wPN N8nދHN9GxrͅF ͧjw(s^TZ;idA7|o5Y<.!P?ZΥ*}YG2P{J[n6FF,>zYȿX^sV,W^ ,6?̽1 XM`%RT(Jļ}Ɣ+Štu3,=9EKIE^3!` `ĸ]Q&H x(#S5q*M.CP9?Ydwmyct;~ /9,r zaXAy)l[[DGkȓ1$+Q%?6 YkZQю^3#eȑ˻[xr8n6\\"[Wk[ we1H sJ9JT=r̤ c(T2y kHtY*Ԓa^ݶoD$a1*HRrW^% (Bڪe$Ēa6I(֨[,"HA^qhؒ~IGvqNNc5d sFW0d18 x#  X$rGeb)(UA*l*UAA2d-SmPiaB.mz$SXAASE)f2bn^9#)[hv֗Ul5xuh7怊@Q82Eip~љV7H Z%%*P:& QnI&Q̉GzI%\\)GPjHW!亸=1[%%2ԝ$b@1ZZ7Qk.vkN/qBOn趻m'0QtEeoIk~qxَ^[_A Q\-E%fBqx3uB%JY2h@+\D(0!I RMl<6Q6!)"DXyI?$pUNC|l jd"aNN#? k8 xB $?RZQ1UtXlв{KՔq(a3n'2Fԭ qT$VGB wæQՆ'#$hH M`nUIggyqr{gޜMx>v4h.d4ax)G6O Dͩ%*)%K8muE̷x1WjrRR,OfQ`$<օnAнۉj"T qQI(%߉^BY,Eqy~>nqS >\b1Eli|3r|\2(3˟(gF$1V'(J2ZI784Qm ߉.dIdhdgF\dQD #A94UzB*fH HQWp2]n 4l& M;X >b>_|awXQLgdP5sjHR@4hDm]V2Ǔ ^IZy#]+J]Z( aGZ=ת1!P6䒒p)4FEj[-vĺR<g@$G!%&N<xBFd@}*5"@U&(zbb ?Uy%hRd$w)R(T,IAmZ5r 9梉T@ *=Hww6oxˤE2 KYA@RX(/j5 1HG\jjH%ńUMH._$*ԉr*a¥'KlfŹVnѫȘCEƤKD*ҮAst1<;_㋙p'f@;.34> !Ғ FAGQ$!S2MNA:B'z &&RB9hԫALqG06O HU0l"6c&Y$kW\oȸKkbF}i[`'.AJ琛Ry5 (JΥN9*h] ^݋TB(ɐQZRA3SADRU鰄xnXUGŚHs"u#)2)K!#W-FiES )lP#Ct=.Щ);QJqɰXR6-OÈStM1< ~5!b96!靰JEnVgikXL5Q))X.'*I rU{WH7y᤼Dak!DDd)n([SDB7[(DJAj݈ 1J8bB'%OA昘Yd~>"]:% ;\lY7A*4ΤL*N3̚T Gw$ӓȒfj'cdRTU¤5Gƿ$%4l;HQA72@3@"JQW@q%-AJ5(|Pb=RtAl3XEwܺCڨV ՝`q!dÌ|襜MiJD"ZZjVT)=!!x@BQD@=gUH*BMXuhV1U tUq:{..ϳ8k"a9N *y0FOY]x7񐛬@$tmrZ \^ p: )(K A~Nq_\p4gx',NP&zj705T L4;IxFLۘ,0io<%F9p'^/9L 0lqhB~QpPuKd!x6H*qBX"* #IHuuHf5s[CVXaE qЇH.CeCI:Xa +l*Z}"Ϳ;i6^!x %lI쟰sFi48K|DBH0Mz@R=7L^*&u2tFvOWTa%A H:׳ə\ĭ%jMHRDJzep}R,!Tba?a:d|_E hb|2Pk4\d OϰO&c XlWdh(Xc$u[ =,CE-IK L ͨQ,!9 c`n&ؙ)tai~9Spj:N* od[lc,A?g;QƘtmxow}||GVd;ކdwA@{uUq-pw>ٺ4?)1hii" 4Q;!hhl#Mw>s܎*$)Z">uC%GϘzM7X%@Kv[M+>`FW3|Cؿ:>ǀ!x?bt@j.uj|gՋ+@ 6\|0$uMtٛh-0kˇp5#u[>-.# /PԅkL @_[{<ǘK(`Fg>'C*^>)<':##˿D mxRcr#GgX'Sf?Y9Ycamq9=*hѺ*~PlB7yM~Q\LD!^[i7dx|>՜xߟ_#7+cXbLN#MTM;6Ybw /7gnNTq}T)5$UMKMkx)H߾ZB ;ZTRR7wS)"HlLk0)Ěkbgg'a? ;N;_4!4qH_UaM?u }4?xMg!8 3J~䇗 & , ?š>k7aN}ry~*w?? S{y~?*?L[G2{ #ٯf{[_{RWav,o__WG} slK?g]rpcm_/!ߔ"n_xy'tnG =Ʋ} CP//7?%~4bM /_SXSXC/nG }= ?*Ó,, 20 ìå. Ïðèìåíèòåëüíî ê âû÷èñëèòåëüíûì ñåòÿì èõ èìèòàöèîííûå ìîäåëè âîñïðîèç- âîäÿò ïðîöåññû ãåíåðàöèè ñîîáùåíèé ïðèëîæåíèÿìè, ðàçáèåíèå ñîîáùåíèé íà ïàêåòû è êàäðû îïðåäåëåííûõ ïðîòîêîëîâ, çàäåðæêè, ñâÿçàííûå ñ îáðàáîòêîé ñîîáùåíèé, ïàêåòîâ è êàäðîâ âíóòðè îïåðàöèîííîé ñèñòåìû, ïðîöåññ ïîëó÷åíèÿ äîñòóïà êîìïüþòåðîì ê ðàçäåëÿåìîé ñåòåâîé ñðåäå, ïðîöåññ îáðàáîòêè ïîñòóïà- þùèõ ïàêåòîâ ìàðøðóòèçàòîðàìè è ò.ä. Ïðè èìèòàöèîííîì ìîäåëèðîâàíèè ñåòè íå òðåáóåòñÿ ïðèîáðåòàòü äîðîãîñòîÿùåå îáîðóäîâàíèå - åãî ðàáîòû èìèòèðóþò- ñÿ ïðîãðàììàìè, äîñòàòî÷íî òî÷íî âîñïðîèçâîäÿùèìè âñå îñíîâíûå îñîáåííîñòè è ïàðàìåòðû òàêîãî îáîðóäîâàíèÿ. Ïðîãðàììíûå ñèñòåìû ìîäåëèðîâàíèÿ ñåòåé - èíñòðóìåíò, êîòîðûé ìîæåò ïðèãîäèòüñÿ ëþáîìó àäìèíèñòðàòîðó êîðïîðàòèâíîé ñåòè, îñîáåííî ïðè ïðîåê- òèðîâàíèè íîâîé ñåòè èëè âíåñåíèè êàðäèíàëüíûõ èçìåíåíèé â óæå ñóùåñòâóþ- ùóþ ñåòü. Ïðîäóêòû äàííîé êàòåãîðèè ïîçâîëÿþò ïðîâåðèòü ïîñëåäñòâèÿ âíå- äðåíèÿ òåõ èëè èíûõ ðåøåíèé åùå äî îïëàòû ïðèîáðåòàåìîãî îáîðóäîâàíèÿ. Êîíå÷íî, áîëüøèíñòâî èç ýòèõ ïðîãðàììíûõ ïàêåòîâ ñòîÿò äîñòàòî÷íî äîðîãî, íî è âîçìîæíàÿ ýêîíîìèÿ ìîæåò áûòü òîæå âåñüìà îùóòèìîé ” [2]. Ïðè íåîáõîäèìîñòè îöåíêè îäíîãî èëè íåñêîëüêèõ ïàðàìåòðîâ ñåòè ìîæíî âîñïîëüçîâàòüñÿ ìåíåå äîðîãèìè ïàêåòàìè äëÿ ïðîâåäåíèÿ àíàëèçà. Îäíèì èç òàêèõ ïðîãðàììíûõ ïðîäóêòîâ ÿâëÿåòñÿ ñðåäñòâî àíàëèçà è ìîäåëèðîâàíèÿ ìàðøðóòèçàöèè NetArchitest, ðàçðàáîòàííîå â Õàðüêîâñêîì óíèâåðñèòåòå ðà- äèîýëåêòðîíèêè íà êàôåäðå èíôîðìàòèêè ñ èñïîëüçîâàíèåì ïðàêòè÷åñêîãî îïû- òà ïðîâåäåíèÿ èññëåäîâàíèé óñòîé÷èâîñòè ê ñáîÿì(Fehler Toleranz) ñåòåâîãî îáîðóäîâàíèÿ íà êàôåäðå èíôîðìàòèêè Òåõíè÷åñêîãî Óíèâåðñèòåòà Êàðëñðóý (Ãåðìàíèÿ). NetArchitest (ðèñ. 3) ïîçâîëÿåò ïîñòðîèòü íà íà÷àëüíîì ýòàïå ìîäå- ëèðîâàíèÿ ñòðóêòóðíóþ ìîäåëü ñåòè ñ êîíôèãóðèðîâàíèåì ìàðøðóòèçàöèè. Ñ ãîòîâîé ìîäåëüþ ìîæíî ïðîâåñòè òàêèå èññëåäîâàíèÿ: – àíàëèç ìàðøðóòîâ ïðîõîæäåíèÿ ïàêåòîâ ñåòè; Ðèñ.3 x[HTQ65A1t*Ju(bƠRPb`])!#2_J ٷs >Z{9sfBDflB˔H Gb+F^L]3v*3GçE̘K= N&,S%j}C;Ee?7!yc^b*zfmmq>[.Q.v @95doshN%vhY}}Ck"Ki"/I$IR3vX'1$F ΉYZQMJ-3gGm,י?h'1hßB1ld\nb2$oL `a ,Ct?kBa>"9TZeb|;`GN5RӬ^t*mGZzF gho.t!u+\{;:zzk^{^{}ν4B,kAB" !,4FhS!P}u!ғ;*puXVP /Svu*Qw&?jj2]-STo£>=0IC;x]i>"A!Ч]@#Jx?*a.`,VT,g%,"zZ"m}IXbk&;9o~7ϊF[ZĹaNS,}#^yG4l1җNwͣDT}j}ؼ" WN)\#-q&~%\}Tb nSbsbsycQzؼIJ@l>؜:&&|-jl.Y#~*@b_ h.6EF:9>?دꇇ~-B+ aoVmmw8ij4$"<+`>]o ;EozHڞe0Ke_!ꋒ+\ X th?lAٲϯ=7-gui]>tlMQ# 9h\[n:-ӑGp<{/V_+}WYY/~ʯ+u|m`-N녇_J9k[qüyh Ex?d;2PxNݮy3ܚ<7lHJdWx.b; ai)Q`!阥>y؀u SN`F}52=><Ǘ:Eu~ER >?ʓv6,dӏ>x&xr'/~x{v{@k'ffM3Z d>fkOyfs=qL 8{h9c. i\+d-v|79=7mdܮ-ey'q}|:[XrۿF믉7$8ᏴSc2pg`BߡqQuxouS7tCg|`oD@[1ߓOo^+V^ {^^NZO!&J&?OV9Z_>{-ts^ \w}E~syt(yvB߰GJ=`v^߾"|~{70~ {WKߎNn+}~8әo`;ox%mV4Vdz ~{B #o`#3?Yk Xk6(G@xZ3$fxmƝ.#'Ӛ ck( +y,eW@Cv fR+_c zٱڒ[6l=Y-xud^:[bˋirqng֫?xNWJz|]^-OtFowtS ]ƸX'5\@#,E| 4tPJLuOTm`Gq^]Ձc~s1rn|T>)zV-;oHElʶG[̧YMq.ExX-$,ؚS_W!lu!S9^yυu9* zfy9DO?]ǥQ׏--',~@xJ¾iʅ0'ƻ=%5׳ګxoﳫt8{|pBDY8䅧h3d4/c" 4Fz=,e,A}Bu+t) \>цmwwA͋iThVc'7znL8YfET\eS=W V*~(g W$}Vݠr?X7vۇб[ɏQؐL#7(@6q9F}:4E=tZ!OZ7u=ie5昉r4Kdn7+S N~,/3y2ڔis[::[pv;'؀qzL~ތ1C }~Q~Bvlf(7#hw1MRgmyrƓ!rبEK.=a㌙\Ϙ3v' ~l#1M>+ku r{5G5v8]uvKp>lsuEDaQo1ſ3QP%mRgQ<vN^v#Oa! VIޥ:uv ^iڮHg,XY)9ޱgM rY`L؊139MǍ,ck`C]yo\K][bEDցu Z#8ǫRY8LGZ4D^'`_>70~!>r6c>"7Β^0^{s:eczC| 9xĮev%/s{&<מ{)#TŞDDuE<ޢb7{#aXwR}iQb|#&~B&cޢk8綌,>Em~f:u>'ȗ󓥯S:_7}:94v ~=lqf+d"{~9'g.qh<]%;V`T<&r? [ +Y>:߸et| L|@=un 9׼%% 69|Cll =u\]))TZPvuEG/'`N ).툰¢ s`]P}^]gPj>-̺O4"Awj1 <ҹ*o-)C2zyAKEg&;7X_]󝟀ڞ::jsGϵ/ԙJߋb%ootM8>Iɋw4su{1xuݓU[רxފcf<80Oo_]G0tK19|5 )W56 ި(}'7E+[MUV?>lOyr(ѽiabŜ @`/6VXo5wY畏|dNIAOoSu]##:ao*aЙMs40B4=|SMzNU7>x!q_r,uQbC;I)GIk‡{IxGl=ZMy#]Kgk)\{۱k)VU<`OFl{HQO ?ռ@pxRH6m*?,ʆ!""6gg`8 i32 40{BpO %=ڥ=b@6i=Y~tǵX؝U] ,,` M)MowI]jwlo?\ tb(:Б`B 'z{G!0;vc 2_ީ7:}O<\>|_7/o' n>Z̏ =3o}UXNn~lo}Ct:xkjD^ S,j==giV79q]Vdcj[0~ le;Bs"ղ O}] dG]`x֑i9b\escBm^"kV5ϑziQy)_?-\^@~1Jo㧷dwNS4Π"nnRD{I3{n'Qۃx}t#ccc"G.FjC?}>kʝQ}@IbN {b`Njvdb)so8ؚOy*y'Lzf_Hyn 냟SX>a]Td;=c' .Hyeˇom~Y} Pp}pd{S_|{LWx.vy_`g<^#2<)ѹ&ZJ|]B۝\n0g vm?dlC zU9_# eF[sQF?ԅL; ӆ]*c.0G7&:E{x_"JgٱoWDmmG~S{nv4opO"xHEUY{;.N&^Qy\s@7xcgP̬>"ߺ W~8@yJAv}R>c}TU|xSttp={S v>bc-omz-k {FOm0>f={@wF-;((#;wx8MwM<(L>%:ؙYt8b "rnz̊F+ڐ| 9 Wbx=5e2:d8o ]A2mãML. suYc~2p#;~hJ[c`a]~;tWOHQRiji٩dm1ZZÌl#nQca+lZ5 .O5<6?n6vACep]6, J׈vd\O{4#8æȽ {R7 X=LvQ@j9; YwXwY!WM>ƾgp G#5{Z5 9֏h`y v:us߱">~wwf9˴O5;R|Nd:_}$Vpn֛>gӥiM0<8.ݐ#N׵iTóW7S'yǂcA29ӏyޫ8!΀'uq/"We沋瞎~1sOC&g} j>:.O|YAiߞ[&_=l9OmMhƔ>ޓS6/]c9V\i9_X'냗由Cl|hi]>M~։9eNw~3bj8|_&B{6'J0/ƼAu}{#طgβ˸^~m:;u}h+3mXtXrĆ o|Cl|A]$?~> ";wGG wXG^di@ѕ֎/c1phWJ.yy^H+#P ZxR?uمL:{˔dKc)Лt1!ض>w]x3tmO1>Z'q@ݪ> wμϖA>7v!'Aw?ރHA\zށω#ٺX'=j~'D(=YLS:14|Ѷ5ccdl[!붽\M&sNޜ+̥vhu6"ޏӚ *-|S٧! 3q.lɟ+kʚ|Ξ>8y%>%t 쒟ovy?@G';y}~dmh?5eyt_ǿ1evz@<tZM(WC#zW@?QZ0H{!|NxEHu|x˳zg?DV [NE nZ*v-3(O.м^uё1`OqE}ðT<~:]xq]o`=re;,kWm>mʇ!tQ"-`_ѓ]8f^/n<~hܤz!q>}kδ |9tv.hC&ۯ"~o{xٿ5!]nd)>S(?W@,,21 – ñêàíèðîâàíèå ñòðóêòóðû ñåòè íà ïðåäìåò âçàèìíîé äîñòóïíîñòè åå ó÷àñòêîâ ïî ñóùåñòâóþùåé ìàðøðóòèçàöèè; – ìîäåëèðîâàíèå ñáîåâ ó÷àñòêîâ ñåòè ñ âîçìîæíîñòüþ àâòîìàòèçèðîâàííîé ïåðåêîíôèãóðàöèè äëÿ îáåñïå÷åíèÿ ðàáîòîñïîñîáíîñòè ñåòè íà ïåðèîä ðåìîíò- íûõ ðàáîò; – ñêàíèðîâàíèå ñåòè äëÿ îïðåäåëåíèÿ êðèòè÷åñêèõ ó÷àñòêîâ, ñáîé íà êîòîðûõ íåëüçÿ îáîéòè èçìåíåíèåì ìàðøðóòèçàöèè. Ñïèñîê ëèòåðàòóðû: 1. Martin W. Murhammer, Kok-Keong Lee, Payam Motallebi, Paolo Borghi, Karl Wozabal. IP Network Design Guide, International Technical Support Organization, IBM corporation, 1999. SG24-2580-01. http://www.redbooks.ibm.com 2. Îëèôåð Í.À., Îëè- ôåð Í.Ã. Ñðåäñòâà àíàëèçà è îïòèìèçàöèè ëîêàëüíûõ ñåòåé, “ Öåíòð èíôîðìàöèîííûõ òåõíîëîãèé ” ,1998. http://www/citfroum.ru/nets/optimize/index.shtml. Ïîñòóïèëà â ðåäêîëëåãèþ 20.03.01 Ñîðî÷àí Ìèõàèë Âëàäèìèðîâè÷, ñòóäåíò 5-ãî êóðñà ÕÒÓÐÝ. Íàó÷íûå èíòåðå- ñû: ñèñòåìíûé àíàëèç, îáúåêòíî-îðèåíòèðîâàííûé àíàëèç è ïðîåêòèðîâàíèå, êîìïüþòåðíûå ñåòè. Àäðåñ: Óêðàèíà, 61174, Õàðüêîâ, ïð. Ë. Ñâîáîäû, 51-á. Äðîáèíñêèé Âëàäèìèð Ãåîðãèåâè÷, ñòóäåíò 5-ãî êóðñà ÕÒÓÐÝ. Íàó÷íûå èíòå- ðåñû: ãåíåòè÷åñêèå àëãîðèòìû, ìíîãîêðèòåðèàëüíàÿ îïòèìèçàöèÿ. Àäðåñ: Óê- ðàèíà, 61174, Õàðüêîâ, ïð. Ë. Ñâîáîäû, 51-á, ê. 732. Êóçåìèí Àëåêñàíäð ßêîâëåâè÷, êàíä. òåõí. íàóê, äîöåíò êàôåäðû èíôîðìàòè- êè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ñèñòåìíûé àíàëèç, ïðîåêòèðîâàíèå èíôîðìà- öèîííûõ ñèñòåì. Àäðåñ: Óêðàèíà, 61054, Õàðüêîâ, .óë. Äàíèëåâñêîãî, 16, êâ. 8, òåë. 43-09-36. ÓÄÊ 519.713 Å.Â. ÃÎÐÅËÎÂÀ, Í.Â. ÁÅËÎÓÑ ÊÎÌÏÜÞÒÅÐÍÛÅ ÑÈÑÒÅÌÛ ÈÄÅÍÒÈÔÈÊÀÖÈÈ È ÎÏÐÅÄÅËÅÍÈß ÌÅÑÒÎÏÎËÎÆÅÍÈß ÏÎÄÂÈÆÍÎÃÎ ÑÎÑÒÀÂÀ Àíàëèçèðóþòñÿ äåéñòâóþùèå êîìïüþòåðíûå èäåíòèôèöèðóþùèå ñèñòåìû ìåæäóíàðîäíîãî êëàññà, èññëåäóþòñÿ àëüòåðíàòèâíûå ñïîñîáû îïðåäåëåíèÿ ìåñòîïîëîæåíèÿ ñîñòàâîâ â ñèñòåìàõ êîíòðîëÿ çà äâèæåíèåì ïîåçäîâ. Îñâåùà- þòñÿ îòäåëüíûå ïðàêòè÷åñêèå è òåîðåòè÷åñêèå âîïðîñû èñïîëüçîâàíèÿ òåõíî- ëîãèé ðàñïîçíàâàíèÿ îáðàçîâ, à òàêæå ñïîñîáû ïîâûøåíèÿ íàäåæíîñòè ðàñïîç- íàþùèõ ñèñòåì. Ñóùåñòâóåò äîñòàòî÷íî áîëüøîé êðóã çàäà÷, ñâÿçàííûõ ñ èäåíòèôèêàöèåé ðàçëè÷íûõ äâèæóùèõñÿ îáúåêòîâ. Æåëåçíûå äîðîãè ñ èõ óïîðÿäî÷åííîé èíôðà- ñòðóêòóðîé, ðåãëàìåíòèðîâàííûì äâèæåíèåì ïîåçäîâ è ðàçâåòâëåííîé ñåòüþ êîììóíèêàöèé èìåþò íàèáîëåå áëàãîïðèÿòíûå ïî ñðàâíåíèþ ñ äðóãèìè âèäàìè òðàíñïîðòà óñëîâèÿ äëÿ ñëåæåíèÿ çà ïðîäâèæåíèåì ïîäâèæíîãî ñîñòàâà. Ïðè ýòîì âàæíî èäåíòèôèöèðîâàòü íå òîëüêî âåñü ñîñòàâ, íî è ìåñòîïîëîæåíèå îòäåëüíîãî âàãîíà. Äèñïåò÷åð ìîæåò çíàòü, êîãäà ïîåçä ïðîõîäèò òó èëè èíóþ ñòàíöèþ, íî ñîîáùåíèå î òîì, ÷òî ïîåçä, â ñîñòàâ êîòîðîãî äîëæåí áûòü âêëþ÷åí âàãîí ñ ãðóçîì, íàõîäèòñÿ â îïðåäåëåííîì ìåñòå, åùå íåîáÿçàòåëüíî çíà÷èò, ÷òî äàííûé âàãîí ñëåäóåò ñ íèì. Ïîýòîìó áåç èäåíòèôèêàöèè îòäåëüíûõ âàãîíîâ â ñîñòàâå ïîåçäà íåò ãàðàíòèè â òîì, ÷òî ãðóç äåéñòâèòåëüíî ïåðåìåùàåòñÿ ñîãëàñ- íî ïîëó÷àåìûì ñâåäåíèÿì î ïîåçäå. Ïàññàæèðñêèå ïîåçäà èìåþò æåñòêèé ãðàôèê äâèæåíèÿ, è îáû÷íî îí ñîáëþ- äàåòñÿ ñ äîñòàòî÷íîé ñòåïåíüþ òî÷íîñòè.  ñëó÷àå îïîçäàíèÿ äèñïåò÷åð ìîæåò äàòü îá ýòîì èçâåùåíèå ïî ëèíèè, êîòîðîå âûâîäèòñÿ íà èíôîðìàöèîííûå òàáëî íà ñòàíöèÿõ èëè ñîîáùàåòñÿ èíûì ñïîñîáîì. Ñîâðåìåííûå êîìïüþòåðèçèðîâàí- íûå ïàññàæèðñêèå èíôîðìàöèîííûå ñèñòåìû èìåþò ìîùíûå áàçû äàííûõ ïî äâèæåíèþ ïîåçäîâ è ñðåäñòâà îòîáðàæåíèÿ èíôîðìàöèè, òàê ÷òî íåîáõîäèìûå ñâåäåíèÿ ìîãóò áûòü ïåðåäàíû íà âñå ïðîìåæóòî÷íûå ñòàíöèè ïî ìàðøðóòó. (x}lU]1uPֵ"@9QhH&@t`PÇ$D8YDd.!? LDCcݮWjeG&Os}M'"/2D$T yOKŸF&q5!m{Ρ= ՔXL M>Iڞ趒yM:A6e[*Ǟ D26O-ch_H8hmYh&6Z?|qdh]v8[V2Vimerps3.&4G WAε3d8U?ũ>iO v,h`9ڢ8zLk^kk85Gam.9C e239FrQMPi?)*U.L~C<q[~Iq*M^Q#cW拗9/뼌xec{y/6t)t֧J0 Vω5g1s4N߃sJ.MUwTIqr7 -qx R*OIO9Kw5v"{74rN2Ubfx5[ɫ U))Myo&@'@%uXhSJYSG̅~vsqc_ LG)23}^Du`'(Rxa($vZh#ΖgP ^_g5Tv|>WM3~9~)\b PhS|w|{ern{KEp }"%ðSU?|Beȇ 꽘X 'lASL>Gg̿q6kol˥ 2dJ=A9s9WC cvQ=SA]2>hl?^*oR\óʖ*G|+U "x+Vs2xx |b,S(LǯglN'8 z$v5<oJԃYSZVQWuKbG\ { W§a&y`&h~P^3a 9O`X%<ɲ%`7vmg3NL665ܜk7H׽𺣡u+Ӊ-{y]ݝAv68R{y4c]Eu=Hq:EČ֚|Q-1Z7}nO<;cS곢祝gFY#}}]6z3H]Gk&L }5ڎ役&}7XČe_5kƍu}5Ǫuvw,:q+,?v;`wvv .v;`wӁ?2UqMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10    d%  (16Z=2=/" 1C7{rx}WYߴ( eV(BĊŐJ(/)/PQQ!1!?HQ0 L+T]#.;ζB[X̙;lnϜss<9/߽]C]Wz9`9wW|7 Jn}T^g/# o=,V]Y1 HWixB|MkN4)_X|7UMUaX)NM>_!7<3+-UWiR}ɒFu\A6>UÕ~T'e'M\fY@O/Yה6zpM+suxo-<=/a`ǽW^K}VG u~yʍU_뇛?aߑ J7{B|tO>q_6&G9oe lxz7Uf֡$=gvx];|҇7??;/\rm;f>J߱Lg#;ק4 tQ5f߷cϋ߻cܟN[*c?"򥾯E~; F̒>7.wJfe7_1cxOńo\#gT瞙o{.Eÿ6Oˏl)7/-97>ߔM<ߤت͟>5ϫMV`|󻅻}XñpCbApU\Y=ýUGE{p+)]|94 ' :R-jZZiꇆWZ,3JW^.+W|yhkbIUbe:5L~G<84ol MډU\<,f"Lj̶fѢ9Q[kgje}t2:nxѮ?+^4<`ʺ='cWRvI\U)R)=zl(G:i/ei~%OᕳvwN2>Kh#~>Ǐ}r u)r-Xp.˂m'ʂ͋րX'&g<"s.I]w6Ҵh6K2Niل~Mtb.Ïo&s,70t.Hvgx#'} t}&gsf*X]ϵ.k]ݩDwoNO>^;k5{%mǫ_}_S)5eS6?,v}w%+q]bg_oޙ:.mV7zEqx w ۓ΀k 3~cؠsYzEFzw?M{Xr_<e؞ @Nb;_0}]֚7~Pv)YDI{!a'11j6ytџ&NgE: c 0h̆`g$C~u2ԓ+kXh3tًD6YR'@}lhU?[ۺlf)֯N&lZ.mxO90%c{qE8Vw4dE"AO:<=::x&g%/}l~ mV=Q@{^ h~Seו)ӟ5Z|kZ/51;l1VxСQz}VT!D|%6}9cWOno;cRZ{*9FK'(7'f =9qgfܾ,m2k"yF61Yd&oA+zE9Iox6yx̱,erF^r#=Xp4o/?zL!ژBܵ>8p7!g]"]n6VL+{6NV=Om1!4+ߣ+m9}Hj[#y}Иѻ<|(']8/z4i_}iSb ܕ?ʑG\YL&} `W<* ?(tKY ج=5Jb91oATjԛVgU*60~k܅|gCGb_ltڞø#_{u2~/K{˘ybOځ'ِcss3lmۘsꪷ|هUzmOxmWxN߸g/{u||ޏ_'eGz-2w{؎/8)ǟ9Br=pt:rGǜO43v^,X-\YZ-Ҏkvońv"&gjN{v'`P[+",|8X̆_S}*9=ect<=[+L{]ot*:Kei߿}ё<++G+Izھrb*KvN/WpK/|SN? 3l҂mw(;ɳesglޞxߢEvr/<{45l;LZĔ777ϝwMr^BG93F\{l'  E|pR`hA"/Sƣ=(k-YU?x ?xg^^bµZmoLwfwjGjMxo̲nE+9TfoU{J2:ex&M>-+ɖ e~'} Gg-c>;aOʢgo1F7x]vﴰc9ZoOiߘsQѭ9AӯW辧%+|ѫ)eI,}<[dSzYI}lg? ]C37{.?f(5rXpuNZMZ2ɷ>;UDcN2nOwwahNNˈKH\>/.ğu(Ŝ1T~Bw;v=ȼ5ZqnFThnwP[6&KG]?=}/ ?8_0v۞q^PV^=/K `ƾp_-1wݍ6DzY.:qOFt[Kݦj 3~ Xx}v73dߡn_aWKe}"GM9VdI?qta`ْ1[TyUm wC~`l}Gʴo{l<8C/If=hn8H־˹y&zviTj{oEվ+v$'k/_/o ~񦡽-;>QAgˮɘJ\L0:JA?ydn-Vr fm "Gc;%}}_?\;CvB'fGC[BolwHr-V*fS.۶ 1wyg~Gµ{2|}W>x9s&9x"Gzf'u9^6G2{_tvUB'雺r7r ^,x|>pv`5n?n g kZyG fu{vFj*aܓ7[pwbxK{s/'`Oͼ`gGlra%9'|RGox鶏h2?O};/I)=|A7ӯ R%tK9AW|^ٚ쩴P^T}Oo,`V`g",WRbw7ۓL3ȯYNMmoТ{nkwy;em3rFmyzg#Fߑ G&E&Kizi#2:yߤ 02vҶq><4'ntm9_]3|5'n.\{ҞV]2&u{OOh/U x?qfx\]J$"Dy3#82/-y2P^8;D?}mNnA|kDNCNf)#;GlOW`a_γvgg:J,c7mM]~{QG+VmDoX綳 O8\1͙#m)!Om{=*j؁q mw5!]H+r-Jni#QL"^p3ʹ~?4| ?33|ංm{Yo؏U۝l!zd(K"O ʑ%,M`赓#6K ٱ%YiOh{~mV˶Ή?5]J'ډ]67Z.Jw+ofEwn=5[<-X0c~$z?}&L9|O6lox> Z\|]ݸ8Xa<‹G{ǎ쉞+-C\8G_l}A}yc&UrOxXW'C \}PrQ/ERIw'}i@h߽;vqyfh7`xds8ҙv -c_w[Q_?C^ar;A,)Ktf~?YGF'hɘzf%xpGt\3 1 ّv#־>`ƦL߉W=lkw"=^׹1CHOgtŇ&{}SU2^x}mϒȑ6_Ɯra+ؕ%c8y>*{r~ù%m~譔M,F{;9?s@#Ё.|S6b{{UmHtNEz ژ/yph'9$4}޽es1z^^A8T= g ߯_X2+u=zPl/J7[+g !kY`K}pr^rOc‹Fom'2Ne{>>mN۵qL8}٫_jҾk}ߏ-z='b&؂ە'/D Xhnw|KRD6:<ؖ<Ư/9>o뷻;s'Y;>:Vg_UhLvϽ~t4]DSSp>' Mv% C|ϿO~_O62Ȗ'[ O|3|x}ζضo-ZlX[ Np-,+J{f5=^Щ9BiN9zA+[rf¿4ڐjC<';TҞ\{rr'%>O/ǃxXp  q[Kl[)M=~m羍d995Xm0߽fbIF`YC4ͼ][LmkPeMgl;[7h;o׬nfY'fUͿG[­J͸=q0K2pquN4Gl'ڊ Z>v#gUB\DŽ=ǺM,,[22 Ðàñøèðåíèå ñôåðû òðàíñåâðîïåéñêèõ ïåðåâîçîê äåëàåò ïðîáëåìó èäåíòèôèêà- öèè è ñëåæåíèÿ çà ïðîäâèæåíèåì ãðóçîâûõ âàãîíîâ åùå áîëåå àêòóàëüíîé. Äàííîé ïðîáëåìîé çàíèìàëèñü ìíîãèå âåäóùèå êîìïàíèè ìèðà. Ïðèâåäåì ïðèìåðû äîñòèæåíèé è íåóäà÷ íàèáîëåå èçâåñòíûõ ñèñòåì[1].  êîíöå 60-õ ãîäîâ Àññîöèàöèÿ àìåðèêàíñêèõ æåëåçíûõ äîðîã (AAR) îäîáðèëà ââåäåíèå îïòè÷åñêîé ñèñòåìû èäåíòèôèêàöèè, èñïîëüçóþùåé òàáëè÷êè-ìàðêåðû ñ öâåòíûìè øòðèõî- âûìè êîäîâûìè ïîëîñêàìè, óêðåïëåííûå íà áîêîâûõ ñòåíàõ êàæäîãî âàãîíà. Ýòó ñèñòåìó ñòàëè âíåäðÿòü â íà÷àëå 70-õ ãîäîâ, è òîãäà æå âëàäåëüöû ãðóçîâûõ âàãîíîâ ñòàëè óñòàíàâëèâàòü ìàðêåðû íà ïîäâèæíîé ñîñòàâ. Êîäîâûå ìàðêåðû çàãðÿçíÿëèñü ïûëüþ îò âçâèõðÿþùåãîñÿ áàëëàñòà è èñòèðàþùèõñÿ òîðìîçíûõ êîëîäîê, âûöâåòàëè ñî âðåìåíåì ïîä âîçäåéñòâèåì ðåçêî èçìåíÿþùèõñÿ ïîãîä- íûõ óñëîâèé, ïîâðåæäàëèñü ìåõàíè÷åñêè.  ðåçóëüòàòå íàïîëüíûå ñ÷èòûâàþùèå óñòðîéñòâà íåïðàâèëüíî ñ÷èòûâàëè (èëè âîîáùå íå ñ÷èòûâàëè) ñîäåðæàùóþñÿ íà ìàðêåðàõ ïðîõîäèâøèõ ìèìî âàãîíîâ èíôîðìàöèþ.  1993 ã. â òðåõ ñòðàíàõ áûëè ïðîâåäåíû èñïûòàíèÿ òðåõ ðàçíûõ ñèñòåì, è íà îñíîâå èõ ðåçóëüòàòîâ áûëî âûáðàíî ñîâìåñòíîå òåõíè÷åñêîå ðåøåíèå êîìïàíèé Amtech è Alcatel â êà÷åñòâå äîáðîâîëüíî ïðèíèìàåìîé ñòàíäàðòíîé åâðîïåéñêîé ñèñòåìû AVI. Äëÿ ïîäòâåðæäåíèÿ ïðèåìëåìîñòè ñèñòåìû â îáùååâðîïåéñêîì ìàñøòàáå æåëåçíûå äîðîãè Ôðàíöèè, Øâåéöàðèè è Èòàëèè ïðîäåìîíñòðèðîâàëè åå ðàáîòó íà ïðèìåðå ïàññàæèðñêèõ ïîåçäîâ, îáðàùàþùèõñÿ ïî ìàðøðóòó Ïàðèæ - Âåíåöèÿ/Ôëîðåíöèÿ.  ïðîöåññå ñëåæåíèÿ çà ïðîäâèæåíèåì ãðóçîâîãî ïîåçäà ñèñòåìà AVI ñîñòàâëÿåò ñåðèþ äîêëàäîâ. Íà ñòàíöèè îòïðàâëåíèÿ ðåãèñ- òðèðóþòñÿ ñâåäåíèÿ î ëîêîìîòèâàõ è âàãîíàõ â ñîñòàâå ïîåçäà, à òàêæå ôàêò åãî îòïðàâëåíèÿ. Äàòà è âðåìÿ îòïðàâëåíèÿ ñîõðàíÿþòñÿ â çàïîìèíàþùåì óñòðîé- ñòâå. Ìîæåò òàêæå çàïèñûâàòüñÿ ìàññà êàæäîãî âàãîíà (ïðè íàëè÷èè óñòðîéñòâ âçâåøèâàíèÿ ïîäâèæíîãî ñîñòàâà â äâèæåíèè, ïîäêëþ÷åííûõ ê ñèñòåìå). Ïî ïðèáûòèè íà ñòàíöèþ íàçíà÷åíèÿ ñîñòàâ ïîåçäà äîëæåí áûòü èäåíòèôèöèðîâàí âíîâü. Ïîñëå ýòîãî èç çàïîìèíàþùåãî óñòðîéñòâà âûãðóæàåòñÿ âñÿ èíôîðìàöèÿ, çàïèñàííàÿ â ïóòè ñëåäîâàíèÿ. Áðèòàíñêàÿ ìåæäóíàðîäíàÿ àññîöèàöèÿ ãðóçîâûõ ïåðåâîçîê (BIFA) èíèöèè- ðîâàëà ðàáîòó íàä ïðîåêòîì åâðîïåéñêîé ñèñòåìû ñëåæåíèÿ çà ãðóçàìè â ñìåøàííûõ ïåðåâîçêàõ (FITE), ôèíàíñèðóåìûì Åâðîïåéñêîé êîìèññèåé.  1998ã. ââåäåíà â ýêñïëóàòàöèþ ïèëîòíàÿ ñõåìà äëÿ ñìåøàííûõ ïåðåâîçîê ïî ìàðøðóòó Ìàí÷åñòåð - Ìèëàí, â ðàìêàõ êîòîðîé ïðèåìîîòâåò÷èêàìè áûëà îñíàùåíà ïàðòèÿ ãðóçîâûõ àâòîìîáèëåé, âàãîíîâ è îáìåííûõ êóçîâîâ.  ýòîé ñõåìå çàäåéñòâîâàíû òðè îòäåëüíûå ñëåäÿùèå ñèñòåìû, îò÷åòíàÿ èíôîðìàöèÿ êîòîðûõ ñîñðåäîòî÷åíà â òàê íàçûâàåìîì öåíòðàëüíîì äåïîçèòàðèè, îñíîâàííîì íà êîìïüþòåðíîé áàçå äàííûõ, ïîñòàâëåííîé êîìïàíèåé IBM, è ãëîáàëüíîé ñåòè ýòîé êîìïàíèè. Ãðóçî- âëàäåëüöû èìåþò äîñòóï ê ýòîé èíôîðìàöèè ïî ñåòè Èíòåðíåò. Îñíîâîé ôóíêöèîíèðîâàíèÿ ñèñòåìû ÿâëÿåòñÿ íåïðåðûâíîñòü ñëåæåíèÿ. Äëÿ ýòîãî ãðóçîâûå àâòîìîáèëè, îáñëóæèâàþùèå êîíå÷íûå æåëåçíîäîðîæíûå òåðìè- íàëû ìàðøðóòà â Ìàí÷åñòåðå è Ìèëàíå, îñíàùàþòñÿ àïïàðàòóðîé ñèñòåìû ñëåæåíèÿ Star Track êîìïàíèè GEC Marconi, â êîòîðîé äëÿ îïðåäåëåíèÿ ìåñòî- ïîëîæåíèÿ èñïîëüçóþòñÿ ñïóòíèêè ñèñòåìû ãëîáàëüíîãî ïîçèöèîíèðîâàíèÿ (GPS) [2]. Èíôîðìàöèÿ ïåðåäàåòñÿ íà öåíòðàëüíûé ïîñò óïðàâëåíèÿ ïàðêîì. Íà îáìåí- íûå êóçîâà êðåïÿòñÿ òåëåìàÿêè òîé æå êîìïàíèè. Èíôîðìàöèÿ ñ íèõ ñ÷èòûâàåò- ñÿ óñòðîéñòâàìè, óñòàíîâëåííûìè íà âõîäàõ è âûõîäàõ æåëåçíîäîðîæíûõ òåð- ìèíàëîâ, à òàêæå âäîëü ëèíèé æåëåçíûõ äîðîã Âåëèêîáðèòàíèè, âõîäÿùèõ â ìàðøðóò. (Îáìåííûå êóçîâà ïåðåâîçÿòñÿ íà âàãîíàõ äëÿ ñìåøàííûõ ïåðåâîçîê, îñíàùåííûõ ïðèåìîîòâåò÷èêàìè Amtech.) Èíôîðìàöèÿ îò ñ÷èòûâàþùèõ óñò- ðîéñòâ ïåðåäàåòñÿ íà áðèòàíñêèé ïîñò óïðàâëåíèÿ ïàðêîì, à îòòóäà â öåíòðàëü- íûé äåïîçèòàðèé. Íà æåëåçíûõ äîðîãàõ Ôðàíöèè è Èòàëèè (ìåæäó Ôðåòåíîì è Ìèëàíîì) ñëåæåíèå îñóùåñòâëÿåòñÿ ñèñòåìîé AVI. Èíôîðìàöèÿ, ñ÷èòàííàÿ íà ýòîì ó÷àñòêå ìàðøðóòà, ïåðåäàåòñÿ â öåíòðàëüíûé äåïîçèòàðèé æåëåçíûìè äîðîãàìè Ôðàíöèè. Ñëåäóåò îòìåòèòü, ÷òî ñ÷èòûâàþùèå óñòðîéñòâà Amtech /x}hUǟ4{w۝׻{t/!ZX`FԦij`-^VS ̔41߶Rch G: h^~Y^8dS9۠ se+H9S*~+DhȅFq?I딓 +L< NL=JЉgYm^%sywι!Pys9`"eJݜ]}t5jMxwguɓe4UDLЙ$oǘ\iO3>}#'쀫^Єn=0>FJ|Ϡ^ Oerdh-KA=a~{{83/rL@7woU$_C x ã8@: &(2 1fޒR?:8qwI/9`<4/%f2}| FW` Σ|> O#jx0p8à?? 93Uit

!'N{:05`)>gn/e#׊p־f1煽sh^7Au 5%F 0Q1Qt֢ :܁Eo%#gCo+9牰ke@4x!l[O;5;JuQzٖ痩` z?ӛu5Ø׳ zAo_wb?F-ٝg0Z&{s9\sKzI9{j`v >480 yF->Ml4-îF0uC!oIn*4z&Zȗ[ͣV/SJv+"HJ˙6do~ޫ M)0cH-cP;r=X&x7Sk p GXyǛi }1x>8|=cG`Z tKoK:^tR{*G}rvGn{֜ꧫnH>rc]G/1K}/&O5^jť%][uWtRRwus9UZ'U^rz%.U=/dnl9ҭaVU*` XVU*`yo XVU*` XЁqMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10  a> ##aa(16h2/aa1J~X{x| Os/ Qdi,Q%dR(RIֲ}Ihv(Bٳiz̜s3sfi ٿa\x&g 2FT}lrZ+OC*܄0%n7O0oa|r=ԉdq?Y>0f @PfĆqgd ct(^:C;<׀ۀOa=X/= mAeO`]fiapUwtrO0kDx.gEal๤PPcmiZO%KJwsM m<`_2g3FG#hdW4 { Mr}QgDuF'#?P'h3uH؆B؎ 46:2GEAcX7?2O ڀ>u~ x(G_&DBZx]O%O1T8+M2օ0`/{&,X֢n!q0Q!$6Ue~vyƛ3(cy#.6`?1kȃeNX<bQJpŇsA[cc>ϋy "(S倻(> tpG<؁N$c=Bm+ Ƅyٌ& B ! yr2A趒FG >ϐd4 ҉(|lCX!1ntk@>l[ -X}B;A :w}K:쫠TJS >^ƾ~5F:@A(LGhĸ'N@mL>Ob 6z"#H;DpqD?~c6caa\ |:`{ Abc_Nc>6 h  x=C# V >QDu=n"ȵ"8W6n Vc3>Y|8rΓk>"חNq3 =64' 2 x`}yJXxC[\):б?`|,ԡLt4{{dI ގPB8NpH<9~F Qm}\wނ;`1/ ulG|cgAA?[ua<.1 .C't~uCc9ȱ_a࣒`>Љr c\ bM׀ɹ>? 5"{y!w\7(aRO_uz8/AԱpO+췀<@¸c u`Xz :>:A nNpg:n ~~'٠OeOE4-o>0?pψp Y"5]~BƗ B9Ğgqls6m9'Fr\2PO~.gc}@5 yn\@3B a-0o 2iu5ث?!_{,2^ #y]s('GQ(}`|vktl7cc| vcK220|C:!!gx4{~p~pmO0 i3dX+_Oyp#9)}5~cD7   ?h| l|F`Lm cee+@ȇ:}@r茲4e|f<AY, - 8aa|X(d@e![gؿ }ˆ"D.4X[.Ab_qaxcVm00Op;l 7A25{{;ZWhHozx/C8zCj"Ȩ zd6:07n q/?/X@ rbYFxO`?l ulkC0t0@ʐ㾱~3:Lgle6q)O`O 13C rq_:@<3x źAX7L|0UM 7N,D~Q3f)yM (ڈp%O0g!r"cxGm%itkw >yzn<7ݡ `+ Ə <܆}d|}u0gecye@AtЅq碒s^'AD[ &#]xwdp&jRz&< (!E)jn?!{Qk)@1-w *?=w7G8} @@A\g,^P3q0B+=D^Ó wqߵsޮL ߳.lmB46 =}`+ v[b{r¼ȏu~1a~ ~Ћ?С yc=9!6jub=%&9caATx+4kaaOvkC|)ܜ@~ rE%8o/#>O~#``cAm90> 4|@c?ݠ rX7С~@ q[hPX̨@s^ث ڿ݋zKF7`0BЁH| X VUdq wlN08W'1 vv: }a`{`Ck@Ƕ%}`} QA31q;a u>4x}}15@@u': l9$&ykv0!XV92 DFޭ= mu(!a{a2=@CF>A۞Q?hNuA tQ7:qa9Olր?`hHo%m܋!/n=* 5avoɨyZ'[HIcv:؆^؞[ d@r9n | !xx %vuB;b]X7 u(t@5z y@^-E 9 s}7}(6#׀_<{ 3C`_SrU; o"2&i؏-`a>x[0x`cl~ub=`cs 90>CX!ہ, ~eX62@9?1Sҿ[#ڿ[Ė޾;ğonw#cM2*8'M"WATH3vw@;}>P;,#x?qX5hsྰ.ЁO 4^g3BuS{xDF4=s930y:Bb+rB 7Iނ׆Ҋ23A _{7w:0v$Jc2cbC(C;xo` J=Ost,uH P><axyH  }C]E( :#oP3xac+~~ &n!? N¬(-d g[o 3 ᐶ6;0ڄm 4FC vr% c߱<!V/0 g$x̐,iX7w=>;QM OAo3~={tXףvt m;#x> Xȿ5ɿ<>iS' 8g_`?rP:a\gAx8 ʘrX?XrF> EPggԋ3s>w#7auW~S?$NOw[9⃽ y|gBcv!*MX7v|Ҿwx1ڈ7,|lKc8@ǸagdɾA_N h1x)(QqF2i^]3]p) f r4}nX luucԡ9a@8&N6A @2>*R b NEi$0&߼YeQG 4#a~H &ڠcʨ{ (xge J 2l :Чv;JTE9J4 PrB)T?P`w \nh+aQ;[?|2|?P?0Шy2"'1dNęnӥ +z-u}v+BmeG?>-!  ~ߢ)GtV?oxoZ5eUF抉/1ތ +MzcCb+^ʾ7Q1um$ŝuL _LYݙwoƍ5_7>gdT'0eNe31 0z!;92Sv=XlO3J"F䳺^<ˣvgr;gOm?:fy~0b*Kw0%M{"?_–[v3B-^್-R ,LrmЦ3X"0qYRX q9yy'+yF/W LjOEJ4Ta!TJzM8Iۏ e(<^đ!7xڣjv݅7Gwmc\ 31z>gzPg'LϏ18{DܘUʔ/gVj,q\?{ӎ]g?[3R̃z{5>6ruxd&e_0]T=r4eمoubk~>|?T|tc{(#9Šu7VNI<{vfČ{NtOϲjs42_"moNmgӡc8_]qͬG?$0ǚ9wQ[ >*{]F9c m6~Х'u<;{p`TwWWĝrv[w<[F0ń{z‘WMw NR 5fݸ|td^ϝ7&3CAlϵU |n˰K:)k].*l͡|^ZА;%}lNe\&JqE,c䶧zehl We˵;Cm#7XD\H+]iCg}<{5]Sv=_ٍkxT c3Frs?owr4VC%KʗfioϪfB|RM$-y6WLo۾R"UcŅ+< /2fQF_Պwj"VG%Ŧ8YXޑ7I{I+fR'o$v+߽Pye3eؼzAK5xNe7]\/@ ڪ:x.xC02љQ>^q~푧^b'f^R+E>*?[ɗitW"M=RwN DBe; Eҗ\iX4{ʼnnouկ =q64nZdNJa%zSoTw{596_BLI,wDKges+tg[56&-*]vD~摽 2\%[wSܶnM 'doW Y2+5eswA UK3=ăX<%s iGNfSԓk̾Gl[t/6O:}u{ \]+-V;DZ|ߞfkkcߢۼ'-mC1Mŏ{VfVy';-UfXc9w }mSir<4<9dVO pde/v7oorpڐ3?fbؒ6Gxw8AHP]gxb(aל9&J^Wp*E%*caTys`qD~L)[es?7̺d3$^\jx:i Wm>͢-hqJewI0si㦾/yN>'&mo$ez܎>yE-M0V\E쎚TգU̗ϛ6㼔`N&9%sAE{㌃*֞fw!Gx]Y'}j5wN<)fVaumGk/m3:%L3i5U*ʙ=/sB}˽VԓFBeN?'r(?0ɼe斑5Իjւ+'vEwF2݈eoy1\^+ImW (ko9?yLX}3kWr-_˺֐{z˖+R(x?Qonܙ:Q0i'R^{>W+H_>&qNLkf2Woe/(\ T5/ }))'_'ڃsB-:-EiILG_vyʶ3wg\wqF]իI:y25o5h t2b\kt%)v# .\^;oѱ Zy7l^=?Ě7Ym|A<3;4xyjRr̙AP'M?t~Og^M:u'5.PoI 8甆|\[1V1==+)dnԘ`˫6{_$pą,֌-Z>lZ{͉fg,Z}ʗ50fJ!"q*QM0qfe~tM/ﲪ3]ޘuYy$:J e,5k|03^u5"0vԵdyUyDd|QS"ѭ# 7=HoM̟Z`Y~VaVђ<ާKiTZdôO*ky%=\d )T]K BόMŽ"]_G^hQ(g}wfzvu皕7J8VLuOM3Ȏ dV=|yoGu Tݾ^nYW`sec6eý({"ϪCj {# d5>-yzPuwB$n72}Ïoc5dgE[jiaNX8_\8hb:nܸy%'vc^)wSwE,y.{Ժ^UdfZ/ۜ~9[!CZvv%gDYmIeZ'ztT1zVtӧi+:b$j7Wݍ)N}RPϷ NjjI%{n /.%ӽ<Oi^ DS1 q@H.%JrxI\ j,x[DׁH}kOeڜ2w \7sSϖt9i1'&".i|̜k\WcYj3޲ έQLV҉׵O ^7J\\㶵WBKrp5cI ~ô)Vo㛟D %Xhvv+΀5%?+v;k~Қ+\= tR`4֯;!.{!>,^+[:炉}"W*1M{M^%Dຓռ-#%jUjֆp]rJވ䴗;o' -=罦7YYTprgvRx\(?k',|zg}6KYq"}ΛJ狖w)ڼ#lss{?n?'ⲂFMƶ5K%XyLzLb9E-R\h¾ґ0׹: ;Sfqf)Fq%:oYwfoMzT '_o*=5_ozrⶁM;M6(CP]^u/1"}v/&+Y'uxRwEZ|pŝ gg)Z9Vosw>OI7~&$h#q,oaBT{;с7)<\ޜMlYz4%D7Z_{<0{]aa>̻coįvոxVr(jH2pIwéUu{7ҧ޾8"5O'.8|v=՝旙>m{5+@Kz6P858 j%y7zT;e23H^L~Hpq +rn˧ڽ͎bJ5yikQC̨g< d0t6 }7lM'' =6N/SJS#4k2c=7UIvwհ4<9WG;i+2)ͬj5f]=8f=vgDՖg-GW8aeO* 7~/ Ww:s31"ooB侉/ͲKN-u՝ϧn&lAՓ̬Yt;^Z^n]_-EٞսwFj, ~TP#|zLJ7"iχR]{,-2ލH2Kbλ_#U#˂n__.7<<=QOoTs}Ie`0Q̆[5ƮUR'zvrr U!;'das|^0=[l6K]ߔ9pZ|L^J)\&[jlLUͣKl<S\L8KݰM<Ѫ}SN$| z1maHC~kn1,_qp̟e4˹0* o>YwX]rf^sl8®ӴxEM,ƲE߷jEc߿êV[.>wGVXm1;AKھvNq2'Ss}󜦤ZYAçǏ7{۱bKEyR5„ټY.peIyԣO Qnʧ2??ϖe{K{Jf1Z5*6O15/ST57?ٞL'^T":g/\!`ah>W^ c7ש3kEtN([?dUPl/aFFSpcH 1~WmK}Kj š\"#( a%$YF2ak-IDWX%$CL3Z\Y!bAq:ԠR6[ђ7an통}Ûմ؅#[ Jc}"CũZb)[K qgC9+#/n8}4fgl}yLϟUɊ0(@;,v>ʒ"A~Bޡ$$^f-a;(CK|=+X[+ j""l2!"F5I;bo|"hjN[f<|$p(Z@JhRHK\|]S9eP(l?'V1NoX\{|vH`װ_|+s=ye\{][(m^w.J,^]\ӫjjO'B?]U3'(܍_Mμ.uȩo9$/ ڮ3>AnwfMb_3MS55*bƫu_c2)|ӳ2Koӏ[e}[v9t>%u5{u.8>ыyPM ͥ/q_/l,-zY G\utY%u5׼Iq)mYE``b[FWGv``мk.X-5Ge$s &ҥlhUmmmEh/.0ڪMam?l%d `HSeV@V dҶ F-g{Pʑ"tڊ Ue+޼dž//1/J8oa?e w[}X߲MqT^&!/8•IGt])/py>>.lZ#߇;/pBo _Y#u.LpLnE;EVGGUUWbue-sQ$|KcΆ%>aEeguv5 J;{#1@m.ŽK߹zѢ +7 U݈it(}|’Z=^mdi:Xrԩ^JQ_azjs닷qEMJyS(B#}Chc¤Dp%h61CAYO#[ѧ˿DU-aٶz";6<[+^FOӦU+j[2v'wmx1{A1[Ob'5|4ew0/=NҙK}^So^$aQ ޿m|ã:զ٫wT1G6@TwoMgH؛slNF͸weW=Ti%%%e?;M]Pv=իPOuEM%7qUw{g!}<(Ls ׌sGmR.vmũfi.!cEרTl^ӆmʢ N߮EȨZ.cH)%žH^m{SYz}Snd[ʕ,Lۊisx^8k^cѶO X&[{oGͲw|hޒY 70Tq-z~_{^d~Yio-#_TEnvxe+kÌF2x5=TPmc;Mwh.ɖ n][;MKf(q;wq{>Wb{ڠi:_V2yu~e|WlB%w/?Wgka,"yzM6Ic;z|Y3Z伬Unẻj*wCuףH %'_c";X)veڞ7CV:[βZ*jNW۽MR6ZpܹeL7g|)ȹԝ΢½Ç`Jfb;5w.a7Ls]$"LSBƧ-:U=d!ͮ&=|X#rFoXw˹Tjt.C*ow[ל4 0먪1t.8R"0\[2-@gߞT)c-,㷗龬M95n&a8kM+*N*,?슥׳.^IHl$5kWhG*Po7$lϦ\oy=iuTfݕ;>vUfA)b~}}Zf/7ݢb.Bȝwytţ·R*g9#ҟG$|$Kf](I frdזlof]ɯR/a3BiO+ -)agr}JtK>^M6r\Kf&{3 ZGq/N2퍃8cWxhعO3N)$e{O⺎a>Ι7PZEdwOck/n+(| '֊8\]RqE4vNQ،ϏP]$T]xmMv Yg8CWh=$Qr:~8?xvӼ,#^^uZ-blpLYq+\K=LVLhl9:X疵AFgM$?j 6/9Ѱu_@_ccfz&1FFvp~.|} ʷ'{ri:vV姍+tuy|\knbӤ_,HwJsl[w(=}:W~n{:!)q4 eϤ}|L?tڋvߊDO3ak.n{ZZ]ˉi^X=~6J;J/Xfk$,r-N_hpFDha|hݩl9n.KI"=مX/8"R?l!d.\M[y!e4 ]\.Z[->ͼSZ/[45s^*xY.H\d]HQnldnKd:jfC>0ه_b&҃YDRےTKUH=D-ASFHR=vEp9s=sa~w;[Fn&}MJU<nC?o:Vg묙Hlyp孻7+%ݾʃӲ˭w4OYywA}rکE]#Qj385?)go1ˠ7nV:jÆdh% )gOkVL'_DpcifBY#,%t9SL|렷T\S<~G;61tfs徼VWN LZb'M-`\Ƥ1VY`cA_H6 IZ6 pzFk?wD2f=-)a\,J]4V'ntQ]k)i+;0v[J7 ',hz|R+؆9'}t!!뜺Inaêi#}MqEВ8sڨZ*I\76Dɛ[>9IKᄬSWMݫ,jm籏7U"E,O3^%3k=Q^ p]DY#EveiZQ,K]NKt^Ll-yS)x6@(D`C:~{@h ?lE|~f| Y1DmШm1sƳ! ֒jهȘ,,y23 òàêæå óñòàíîâëåíû âäîëü ëèíèé æåëåçíûõ äîðîã Âåëèêîáðèòàíèè, òàê ÷òî è îáìåííûå êóçîâà, è ïåðåâîçÿùèå èõ âàãîíû íà áðèòàíñêîé òåððèòîðèè îòñëåæè- âàþòñÿ ïàðàëëåëüíî.  öåíòðàëüíîì äåïîçèòàðèè êîìïüþòåð IBM âåäåò áàçó äàííûõ ïî ñíàáæåííûì ìàÿêàìè îáìåííûì êóçîâàì è âàãîíàì, ìàðøðóòàì è ãðàôèêàì äâèæåíèÿ ïîåçäîâ ìåæäó Ìàí÷åñòåðîì è Ìèëàíîì, ìåñòîïîëîæåíèþ ñ÷èòûâàþùèõ óñòðîéñòâ.  öåíòðå óïðàâëåíèÿ óñòàíàâëèâàþò îáû÷íûé ïåðñîíàëüíûé êîìïüþòåð ñ ìîíèòîðîì, êëàâèàòóðîé, “ ìûøüþ ” , ïðèâîäîì CD-ROM è öâåòíûì ïðèíòåðîì.  êà÷åñòâå îïåðàöèîííîé ñèñòåìû èñïîëüçóåòñÿ Windows NT, ÷òî ïîçâîëÿåò ïðå- äîñòàâèòü ïîëüçîâàòåëþ ïðèâû÷íóþ ñðåäó, êîòîðóþ àäàïòèðóþò äëÿ óäîâëåòâî- ðåíèÿ êîíêðåòíûõ òðåáîâàíèé. Ýëåêòðîñíàáæåíèå îñóùåñòâëÿåòñÿ ÷åðåç èñòî÷- íèê áåñïåðåáîéíîãî ïèòàíèÿ. Êîìïüþòåð óñòàíàâëèâàþò â ëþáîì ìåñòå ïîìåùå- íèÿ äèñïåò÷åðà, îäíàêî ñëåäóåò ó÷èòûâàòü òðåáîâàíèå îá îáåñïå÷åíèè íåçàâèñè- ìîñòè ðàáîòû ñèñòåìû óïðàâëåíèÿ íà áàçå ñïóòíèêîâîé íàâèãàöèè îò ðó÷íîé òåõíîëîãèè ðåãóëèðîâàíèÿ äâèæåíèÿ ïîåçäîâ. Ýòî òðåáîâàíèå ìîæåò áûòü óäîâ- ëåòâîðåíî çà ñ÷åò òîãî, ÷òî ïðè íîðìàëüíîì õîäå ïåðåâîçî÷íîãî ïðîöåññà ýêðàí ìîíèòîðà ïåðåâîäèòñÿ â “ ñïÿùèé ” ðåæèì. Îäíàêî ñóùåñòâóåò ðÿä ñëó÷àåâ, â ÷àñòíîñòè íå íà ìàãèñòðàëüíîì, à íà ïðîìûøëåííîì òðàíñïîðòå, êîãäà ïðèìåíåíèå îïèñàííûõ âûøå òåõíîëîãèé ïðè- åìîîòâåò÷èêîâ íåïðèìåíèìî âñëåäñòâèå ñèëüíîé òåðìè÷åñêîé îáðàáîòêè ïîä- âèæíûõ åäèíèö (íàïðèìåð, ïðè ïåðåâîçêå ñïëàâîâ è ò.ï.).  ýòîì ñëó÷àå ïðåä- ñòàâëÿåòñÿ âîçìîæíûì îñóùåñòâëÿòü èäåíòèôèêàöèþ íà îñíîâå ðàçðàáîòêè ñèñòåìû ìàøèííîãî çðåíèÿ.  êà÷åñòâå îïðåäåëÿþùåãî ïðèçíàêà ìîæíî èñïîëü- çîâàòü áîðòîâîé íîìåð âàãîíà. Ïðè ýòîì, ó÷èòûâàÿ íåóäà÷íûé îïûò 60-õ ïðè ðàñïîçíàâàíèè øòðèõ-êîäîâ, ñëåäóåò îòìåòèòü, ÷òî èñïîëüçîâàíèå öèôð ëó÷øå, ïîñêîëüêó öèôðîâûå êîäû â îòëè÷èå îò øòðèõîâûõ îáëàäàþò áîëüøåé èíôîðìà- òèâíîñòüþ. ×òî êàñàåòñÿ ïðèðîäíûõ ïîìåõ, òî íà ïðîìûøëåííîì òðàíñïîðòå ëåã÷å âåñòè ïîääåðæêó êà÷åñòâà íîìåðîâ èç-çà ñïåöèôèêè âíóòðåííåãî èñïîëü- çîâàíèÿ. Ñèñòåìà ìàøèííîãî çðåíèÿ ñîñòîèò èç êàìåðû, ñíèìàþùåé âèäåî èíôîðìà- öèþ, ïëàòû ââîäà èçîáðàæåíèÿ, îöèôðîâûâàþùåé åå, è ïëàòû óïðàâëåíèÿ äâèæåíèåì, ïîçâîëÿþùåé ïåðåìåùàòü êàìåðó â ïðîñòðàíñòâå. Ïîñëåäíåå óñëî- âèå íåîáÿçàòåëüíî. Òàê, äîñòàòî÷íî ýôôåêòèâíî èñïîëüçîâàòü íà êîíòðîëüíîì ïîñòó öèôðîâîé ôîòîàïïàðàò, âûïîëíÿþùèé ñíèìêè ïî îïðåäåëåííûì óñëîâèÿì ñðàáàòûâàíèÿ àâòîìàòèêè, ìîäóëü ïåðåäà÷è èçîáðàæåíèÿ è ÝÂÌ, íà êîòîðîé âûïîëíÿåòñÿ îáðàáîòêà è ðàñïîçíàâàíèå èçîáðàæåíèÿ. Ðàññìîòðèì ïîäðîáíåå ìåòîäèêó ñîçäàíèÿ òàêîãî ðîäà ñèñòåìû è âîïðîñû ðàçðàáîòêè ïðîãðàììíîãî îáåñïå÷åíèÿ. Ñõåìàòè÷åñêîå èçîáðàæåíèå áëîêîâ ñèñòåìû ïðèâåäåíî íà ðèñóíêå. Áëîêè ñèñòåìû èäåíòèôèêàöèè íà îñíîâå ñèñòåìû ìàøèííîãî çðåíèÿ  xmheǯ8 4e2@\3g.5f >A9 g4%rE"R.gʥn01K)m5r(kX{7@5'_o_I6`a&@N؛GY 1ax/k-R"gV#ʸq7)>d-p`~W+ӌUן:>~}|`&@sp>v&A!u N|ϰةyF#%n~ K TA`qS%C]; w{#e ,#GgYd\b>N!2$OQ_Jꪒզ*j,d4OPixߧhy68< '}mVO{7bw) AC5'"~W;I>N^y{S?bx'rcy˧76spncp7ڽh|bi|^5yZWܞjgwF}VU*` XU*` XV <(Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10   PQ(162D/1v64{qx}WUgB  e6ʋYۈ!RB; M %I$JbI@ JDX^bjlvnwg v=;gfZܽ9ss{<3, *XVa07 k0 a껠 g|_}0S~q?|?}û s`UpnN.ϵVUSC]0U쬫cW?o,ˆW_|k|yc΢A\OEtVuk9־]zI}7lϞ:zzf^oUJo|U? }7Q%{g OVW|2Nտpl83,Uֆ:^Dwr(sg+P(}_I/W]GeX*PkϪ➵S::VN?y5yNՊf5ytk=Ӌ́|N?:ϯJGw?s&9^B>*зZ7Z6z>0|`Z9Q?zġ Ww_S kk_HVϡҸ) gGo8\ nb;/} jtxĮzlԊuK8KL懎O_͍= _Z^{1Î?pߜ?-_UqN'kmuyGgsDS{}xȰVsxUGGlSEm{F[vIzج]^%zvͮEơ~ȋACs xXj:Zɜ|υ{g#(ċG9-v1I!qt"qZЂj@c稭oΎpkmÑoD O=3;U_ƞAKvKuA;Xdķ|*K&E:}dvݷ]+Gڞ[&ڢ/UyxT^VߞǼD+xYN`؍ dƦMJ|2 y42j==or }}?U7mmz<5bfŶ'{߃Eoi_+]\ r=?C簧b<{Mmmga=>#᛾ȸ_|{=?}䌙9ßb\X>яkVGF}??8?u~puf;3G<2[Pr86,}.~O^z/0x2^l:39#O^gGM3`?̭tw;wU{*o[+/r.$|p.0k,N_`styU~ljmE>Ꮜ:WF6"?εy/:ƒQ˰'a*X.ǫErOlٜ,l9~3<̛C b{;U7|=Y-ܛ M~EaB+O#gZcWJ=x,rN(D{Ε4on1hJa'6zE9}U}d\L0B]%jrui<5;Ȫ3|YfZ} &ΨZ>=ũEP8sP1j> z%yS2({,ãd=Hq8XW~}EcW2_֦)Ѝ~&w|j9<#v{;A;c+cAW]GWA']xѩ6^tV d ^c-ts.3?9GҵwT_=9,{yOmo4kܢF{"ùF+pqɂ=vvspb~?12t<|@_uɱ>rOQߟyv?cLj$l￟KE"ԭk۩[$ӯbnq!=;s&@qYwƋ'r\㉍#ߵv|ubJ|8=cyeΑ5~x=G&஢/ֺ\xj_Vjr7xev ϶|KNy|:}ٽ/h;V`U%MOޮh^O&|ѝ9ۗ3_x2EcyƼm[,uƽEj7)reb;%wdb3;>6I Lzz?+8z}=0,1dXZ፜ݘK. ?ŀ~ڢYŀq],=s]wm'tEd~ -?YO@Os;亷Urq·hWk56c{pԏYhE.G1:Fo/'f.4>6\;OLć]l8YyE[C%,hgo"9.'-c8Sü@-nZLـlx7^S0wY&u_|3]4W<}Ǩ-h8j &mkћv=OY_\V W]?Ĭ5>{u,ھ=PsEl+tJm/8I?U3T<{j.u)6M҇OCk6OlL6j^zS!٭HCM|3j%÷ڰw0čS7ip[|Γo =?\ײ=eFlKwG훧d"z8:{Ngši?l}-jڹcGt{=C|0Wk/OFPȒɺ6^V3$=o?)U%,(SZRvٮݷvn4$lቊZOukf}nԯ]vk ;{a6=,S?zz=SA褿;=t{~>\=ch(Wb=3cvݵHўI@ ecG_59'(ڹ,Wokb3:vGgM`⚬Zl:WcWd.E^of5EYץ"[|@?|ho(U>?8'EH;o\V8?YUkֆV^'H'>s"|?ǞZrv͚Mb`mkvMؑ j33b. wuߗ'sS+Ix_p^2{e [LxHgǦl`?ѣn/,vy}g/S6gn. e08WFN}ֱI|=al8^1*qx}t/ zJ3ua^a]3G~7UE~m>6[b0g]IXEm_xg 2atz.l֢,s+6ryU1[ǎǺCqׇG2>/dfB_:s0L`]U[s|{W/v'Wo g^fŅ3| /_y}}cjgųKg~J|K,UIwI(xmE/ޭsc`ud-swUyFHo$w͟wTۻ}b\>b~*lKW״3:hC3uxXx zΘ aVY]U2[ao٬vZ+챑0HdM/VONb+j#(u }籱bتס/ej}K֦#z#ej`jwd-|_sX[ 9o)Rpa[m+:׷mNZWU''}o`ݖ'.v|~g]Kp=\gDޱkvm^w78E3Y]śyi?|6b{ikGQͥ'3_"=7}ECo֮tmwY.4Ż]Ulh`L/ynN61f|q~;zdԹO}7bEߟRCկ>tq3^gΉ c軾h۝u^hq~c9882?"o6e_CO>~[(; 8Yh'QL,\#;a/6@OM*KEf׬<2뾝~[/j+xYglCzuz}^ok ܿ]kp_>'.~Haceu |)d]拞Ѭeo9acSj-7l徳vwlfN\Ǟ׵ 5_#?9Dptd 2e~据g~ <󉇫|+l;zBleN{X~CD7(yfeoT]Q=|i»vR'tpy!5w5}܅`NףqzD"?9{fDOtFɉǂ ~ ?hł Kƙuj׿C}9 shվ ΍rzcs$gZ/qKn}fOO?[We,}~也o=+:ЕĄ#|w'|෋vMoZ2~~a@b,j~St\/2E>g?cHfo%v7ao'7^Uy-'>XԞ/n&O%Q}Y WFF7zƁ(l\MyekE"<'h0U3*Ǧc_6ŧ6Ã\8?|=ȾuJv{F3̙Lj`+v=Y_Hg }-fmTx;'<_vRpoʯӟ^qٔZ|/">hgdC2у߼1/I]͘|a{Ƽ_~DPx,sZ:![]vv{k=r|?HC^cMϧ>BW/xE _px֧__R#e>э_;v߹V}r sؿr ]jmX~ oy]Q~V7霪_7C%| B{.;6b2ǘ/WMG֝G>{jl]~Ը}^-Mo{cA}5o-UŻ=^71ڥٴ+ V ;6o>Բ?NgΌ&ᯝ^p"Z'vslc4女Zd~nv2b`o?{>>U%FO:ǗZa'p\fY}lOei5x;/oOۛiir??dYO1E3~UgN˘W ?[EfX;Oaa]ؿTYrv"sb3X2>h7ۛg8~?_ /5|x۸_-#Q 3n}v ɷ&|!-밷5=LȪIF>m^j9Qh2F4^&6;S_W%Oڛer&D~C%_;eD+{?~ct=J{OlЂv{6YS]lEg)Ϙ֥>1V?F| xNd,uƁux[T7T;w> ]߅,nˢNzB9Zَ!FLMcOb]5۰KfUbuxΊ-8'L,,y24 Ðàçðàáîòêó ñèñòåì ìàøèííîãî çðåíèÿ, â òîì ÷èñëå è ÷èòàþùèõ àâòîìàòîâ, ìîæíî âåñòè â äâóõ íàïðàâëåíèÿõ. Ê ïåðâîìó îòíîñÿòñÿ èññëåäîâàíèÿ, ñòàâÿùèå çàäà÷ó ðàñïîçíàâàíèÿ èçîáðàæåíèé â øèðîêîì ñìûñëå, ò.å. íåçàâèñèìî îò îðèåí- òàöèè, ìàñøòàáîâ, ïîâîðîòîâ è äåôåêòîâ îòîáðàæåíèÿ. Âñå èçâåñòíûå ðàçðàáîò- êè ýòîãî òèïà ÿâëÿþòñÿ îôèñíûìè ïðèëîæåíèÿìè è íå óäîâëåòâîðÿþò îñíîâíûì òðåáîâàíèÿì ïî áûñòðîäåéñòâèþ è íàäåæíîñòè, îãðàíè÷èâàÿ èõ èñïîëüçîâàíèå â ïðîìûøëåííûõ ïðèëîæåíèÿõ. Êî âòîðîìó íàïðàâëåíèþ îòíîñÿòñÿ ñèñòåìû ñ îãðàíè÷åííîé ñôåðîé äåéñòâèÿ, ïðèñïîñîáëåííûå äëÿ âûïîëíåíèÿ êîíêðåòíûõ çàäà÷. Íåñìîòðÿ íà òî, ÷òî â ýòèõ ñèñòåìàõ ïðèíèìàþòñÿ ðåøåíèÿ, äàëåêèå îò óíèâåðñàëüíûõ, òàêèå ïðèëîæåíèÿ óäîâëåòâîðÿþò îñíîâíûì òðåáîâàíèÿì ïî áûñòðîäåéñòâèþ è íàäåæíîñòè è ïîòîìó ìîãóò èñïîëüçîâàòüñÿ â ðàçëè÷íûõ îòðàñëÿõ ïðîìûøëåííîñòè. Ïðîåêòèðîâàíèå ñèñòåìû êîíòðîëÿ, êàê ïðàâèëî, îñóùåñòâëÿåòñÿ íà îñíîâå êîíöåïöèè äåòåðìèíèçìà, â îñíîâå êîòîðîé ëåæèò óòâåðæäåíèå, ÷òî áåç àëãîðèò- ìèçàöèè îáúåêòà óïðàâëåíèå èëè êîíòðîëü íàä íèì íåâîçìîæåí. Äåòåðìèíèðî- âàííûå ñèñòåìû ïðåäíàçíà÷åíû äëÿ ðåøåíèÿ ñðàâíèòåëüíî ïðîñòûõ çàäà÷, îäíàêî êîíòðîëü íàä íåñòàöèîíàðíûìè îáúåêòàìè îñóùåñòâèòü íà îñíîâå äàííîé êîíöåïöèè íåâîçìîæíî, îñîáåííî â òîì ñëó÷àå, êîãäà êîíòðîëèðóåìûé îáúåêò èëè ïðîöåññ íåâîçìîæíî äîñòàòî÷íî òî÷íî àëãîðèòìèçèðîâàòü. Êîíöåïöèÿ ñàìî- îðãàíèçàöèè èñõîäèò èç òîãî, ÷òî ñëîæíûå âåðîÿòíîñòíûå ñèñòåìû íå ìîãóò áûòü îïèñàíû äîñòàòî÷íî òî÷íî è âñåñòîðîííå ìàòåìàòè÷åñêèìè óðàâíåíèÿìè. Òåì íå ìåíåå êîíòðîëü è óïðàâëåíèå òàêèìè îáúåêòàìè, íå ïîääàþùèìèñÿ ñòðîãîìó ìàòåìàòè÷åñêîìó îïèñàíèþ, âîçìîæåí. Îïûò àâòîìàòèçàöèè ñëîæíûõ ïðîèç- âîäñòâ ïîêàçûâàåò, ÷òî îáå êîíöåïöèè íå èñêëþ÷àþò êîìïðîìèññíîãî èëè êîìáè- íèðîâàííîãî ðåøåíèÿ. Ïðè áîëüøîé ñëîæíîñòè îáúåêòà íóæíî ïî âîçìîæíîñòè ïîëíî îïèñàòü åãî è âñå ïîëó÷åííûå ñâåäåíèÿ èñïîëüçîâàòü äëÿ êîíòðîëèðóþùåé ñèñòåìû. Ñàìîîðãàíèçàöèÿ äîëæíà âñòóïàòü â ñèëó òîãäà, êîãäà íàéäåííûå àëãîðèòìû ñòàíîâÿòñÿ áåññèëüíûìè, è â ñòðóêòóðó óïðàâëåíèÿ ñëåäóåò âíåñòè ñóùåñòâåííóþ êîððåëÿöèþ. Äåòåðìèíèðîâàíííàÿ ÷àñòü ñèñòåìû äîëæíà áûòü òî÷íî ðàññ÷èòàíà. Ñàìîîáó÷àþùàÿ èëè ñàìîîðãàíèçóþùàÿ ñèñòåìà äîëæíà âíî- ñèòü êîððåêöèþ â äåòåðìèíèðîâàííûå ðàçîìêíóòûå ñâÿçè â çàâèñèìîñòè îò îïðåäåëåííûõ èçìåíåíèé ñîñòîÿíèé îáúåêòà. Îáó÷àþùàÿñÿ ñèñòåìà íà îñíîâå äëèòåëüíîãî íàáëþäåíèÿ çà îáúåêòîì äîëæíà íàó÷èòüñÿ êîððåêòèðîâàòü äåòåð- ìèíèðîâàííóþ ÷àñòü. Íàáëþäàÿ çà ñîñòîÿíèÿìè îáúåêòà (çà ñèòóàöèÿìè), ðàñ- ïîçíàþùàÿ ñèñòåìà äîëæíà ðàçäåëèòü âñå ýòè ñîñòîÿíèÿ íà ðàçëè÷íûå ìíîæå- ñòâà. Ïðèíàäëåæíîñòü îáúåêòà ê îäíîìó èç ìíîæåñòâ îïðåäåëÿåò êîððåêöèþ, êîòîðóþ íåîáõîäèìî âíåñòè â äåòåðìèíèðîâàííóþ ÷àñòü ïðè äàííîé ñèòóàöèè. Ïðèìåðîì òàêîé ðåàëèçàöèè ÿâëÿåòñÿ èñïîëüçîâàíèå ñî÷åòàíèÿ øðèôòîçàâèñè- ìûõ è øðèôòîíåçàâèñèìûõ àëãîðèòìîâ èëè òåõíîëîãèè àäàïòèâíîãî ðàñïîçíàâà- íèÿ. Ðàññìîòðèì ïîäðîáíåå ýòàïû ðàçðàáîòêè ïðîãðàììíîãî îáåñïå÷åíèÿ ìîäóëÿ ðàñïîçíàâàíèÿ. Âíà÷àëå íóæíî ðàçðàáîòàòü àëãîðèòì ïîëó÷åíèÿ íåîáõîäèìîé èíôîðìàöèè èç îáðàáàòûâàåìîãî èçîáðàæåíèÿ. Ïðè ýòîì ñëåäóåò âûïîëíèòü ðÿä îïåðàöèé: ñãëàæèâàíèå, óëó÷øåíèå èçîáðàæåíèÿ, ïîðîãîâîå ðàçäåëåíèå è âûäå- ëåíèå êðîìîê, ìîðôîëîãè÷åñêèé àíàëèç è ôèëüòðàöèþ, êîëè÷åñòâåííûé àíàëèç.  êà÷åñòâå èíòåãðèðîâàííîé ñðåäû ðàçðàáîòêè ìîæíî èñïîëüçîâàòü ÿçûê ãðàôè- ÷åñêîãî ïðîãðàììèðîâàíèÿ èíæåíåðíîé ñðåäû Lab View. Ê ïðåèìóùåñòâàì ãðàôè÷åñêîãî ÿçûêà ñëåäóåò îòíåñòè ïðîñòîé èíòåðôåéñ è âûñîêóþ ñêîðîñòü è ëåãêîñòü ïðîãðàììèðîâàíèÿ è îòëàäêè, òàê êàê ïðîãðàììèðîâàíèå âåäåòñÿ íà óðîâíå áëîê-ñõåì. Áîãàòûé íàáîð ôóíêöèé îáðàáîòêè èçîáðàæåíèé ïðåäîñòàâëÿ- åò ñðåäà Mat Lab, áëàãîäàðÿ âñòðîåííîìó ñêðèïò-ÿçûêó. Õîðîøèé ðåçóëüòàò äàåò èñïîëüçîâàíèå ôèëüòðîâ Âèåíåðà, îïðåäåëåíèÿ ïîðîãîâ Ïðåâèòòà èëè Ñîáåëÿ, Ãàóññîâñêîãî ïðåîáðàçîâàíèÿ è îïåðàòîðà Ëàïëàñà [3]. Ïîñëå òîãî, êàê èçîáðàæåíèå îòôèëüòðîâàíî, åãî íåîáõîäèìî âûäåëèòü ïóòåì çàêëþ÷åíèÿ â ìèíèìàëüíî îõâàòûâàþùèé ïðÿìîóãîëüíèê è èñïîëüçîâàíèÿ òåõíîëîãèè ñêàíè- [.xhUǟ3f޹v^+bMD9.2GfȖ\QFi 3Bw$XlYSAe Z3⫌9w^ {_ݠsy<{ 7IDH "w5Jd X5Md| 5D^!?<=ƎC=1ExuʳF-IiR|ⱜS.:Ļoq28v=-oGӅ26viX+ͻҳkgcg?ϋ_ޔ,_AAXN^RI|I> ?qo/Ǟ tW\\ ΃`3qI?Jw`JU`"fyk~̐2B|rlf!!:8H 8%b*UT!9)?$ԟ-)[%S p&ɐ $,KAԀ~0OY 擫ZA .3a;upPreEnۀ~>ML?lRG딟rQϗC< - :\UPy'+{t M0+}*]vY+O*mֲ@̖Wȱ}J2kXލ֓~o(KQ:gTl!&̙D8ߩ0'~~trL!ػaOkEljb0XO}r6=_DF*g}hTFz'(VaRx֐"#<oU zV`D[EX=gՇ?G%޳^)jtpN?_d&ﭜ_[ Dz7)f`:N>nW;5jʕ<{Zh;{=?;Cغ?*;* =w{5[_νiq~.Ɵucn'`O?+@)85c ޣR]p\ ֆQKzX{f9g*ч]B+9*>#tiө}=lgA!Orb깉skCߥP(#IGo3p!߇oDڄ`j>q[M^,@? ; 4,hs6z~yW3Gp'{1=p<쭝6B]1H^oc.kgnxKyŦoS3.硥sᜫuE{M]Ԃ2fr*24g:=[xo-G%;{~%-(F1nsM\H4N4Wl~/֕(Η(nb&cDkr3_&.c\$%\uNre2(&x1o=?wmމRk>FQ(`0 FQ(`0 Ul(`0 FQ(`0 ' gMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10  6 @!v~(1632"4/1 .~{|x Wy X2Y $E,Ɔ$L`vlCdOxZH0HI[&!) )t\iz-KHز-"u}L>l,ra[ፕ^aȦL~ax{a׽z0u6VB g5 {0|,9s6>3\2\:wXJdkRR)jjU-U'CoO+]U|oju*=ұﳓkMs}dntfmvTZTEu8 +ӫJ\^%RLO2\^@K: w>oxC(g#S_a8uʦ/m־VG]훏,_.{|*`|sp {omJV틕w *?T|NUd -wq=W;XAH}ǰc[+]rs`nΨғ&usLpߕT z7z>7B#Ɲ2ZS`r%d.O8X'F2/_*W #{ whSV?2e[ea;ʊ{Yw8āRiJ|pAsyNAU+rn2k;G, {"WFttj\?]$:E_r ﴾#Cd!9`],ח\z/aM9Uk㞭(;VS%pob; r1<`h1uċ-̭#Q&N,z=э&Ůcl .4O mѳ^ڀ_ Z)9}[5}M6 G4wh?y .GhK=4O";}K`CC^ bÅ3|u\|gSF?9q좰>S-rXkS0+F^e^M1f \d%%AshNnE:z,=Sg#뛶^i\9!OmQq/__OS{!bV 3tt_g_1fSy՛M˺o=7zst}S{`d0/ҮK6M[OzWyD֔,?| ֚ryww|wHch+D+O6Ó9'N걾uf֮bug\cxmDh{t^た,6RO<Zx|?>~Ț;+=[kMixx\qy_mˎi_bGdL`b'/Y{xšQ/MyG`rx7؜U ?dLGcЧش[hՓўrA;tic[m9^{N:Ȩꪸ𤂝_, xYxw`]2O{[F`fv"jE衫u1[aszZGt1c#px҆lE.|줌W|rGvC+Ϣe ma_Svo$n__jFS[GVmg'%S;ey3(tMb.z1ƣOytLOhR΅_\xzOY;SfӾ>>";?ӏ^vx"<~g ?>?a V7Njپn/[nd8*wy<lxPSr!-vZ'ӏkJ]3C~B.M\YUG > -XQN}}੓'wzlla`kxS˚{eC{N%޷#sX6o$ӫ K/Rt"?R89=J*78{\̀[ΘǮiaZކፏeVK\z{ΒWNc9ٜП1fuf1c@c ےm"ǧ/l qzlz;!^}|bFv|1@2vR '1ܓxqH?Iý.c.O=IKV^<4xIbx''>FxG/ uRO6<~ .6]1Zݮhwly,J;<1`Μ#x(9j{cc/5?Y Y9$ytNVɣ^Ȕ&m>3hnRkз .2O~a?\Y +u}7۝g6+͊`ցysз;m偢u 5t/sE{՟SF/F9gB`hwȃq&v#ڄ zh"#0i\^]PO\B/7 8~`/._;8vzGʱ8K?,l`^tw~ q_:rmXtkNml]YMdEwGOD~_&חО__Wb{ߔn*E;FmrFfS{ߨwٜ\㹍I;@.kzWF$ƴ'"wqT)z[emAW33|c9r#Gnxxdݾ};##6shyݿ'6삢Qel;;+#ٻό[Ɲyiq\)i{%΢MXY+kԼѥkn#DK|}g\ө:&Y=m$,؍k': lna6j7nͪYμ2з3q[Ipgocjk}%]]ytɣMo N)NgЊꋕf~DN.O; .Eʩ-& ۿ`kY"t۝gzvzHFWo|{>PF<G߮5B9c#y4F4,2{pm Xxf.h ?{ggg7 ^}hV2^Ԋlx8nE|f 8q>k|~Vo\mmqv]5j"]X e ӓI"X7}bԳJgo§7@zd~yA-|C GiP6_Wyeu7Rt/vKp5{c v~N0#V b=僵Μotܞ%jXeξ֗ vzuC ˾D.^e0 _, >@9;w_Vin =.8Fg{/ϰ/ZsU?нGkyCTT{Nq^N"398sbh;e} bFOs@t`DWt*oD`ѩ<ִ<{p^c4zаuutFfږ>? l\f5m,Z gOړΙ54ڳlf 3YYm?1ĕaOZNxΕN]򬐜š-WGOW鶏uDgh|lg+Gp6V;noOϢM7۪O?Ixҿ7T9Բ98sK ?k|ކyyf!XFsݷ-V=sߨa;zGi\mGzup.3#':GqD=MG|`Z}#KЯgM䐑~NNzL{ֲ?|?`)ؼrm{"ETK4/~*WXeiQlnE[ݭ.V񱳫O02s*06btǘ$\y} L@&}$~bGF~U5+Mq})>o |`Oڸso_ih+6O%حݻmKV",y s=Y&߷wcb,nz}]ѳ~kW-9h%^uVw;##}N?".O乇|ʧ}k[빇vslޭd6k~\GGxI5qL?}Zŕw*ɮ=7zP tlӂzY~Oҟ#}i+}2#?Ab 4+؎%[<mN޻;YUeoUjVv$G {dU1I7%Z3'Ƈ>O>r‡7#S:,Y "6g ꢝ7K[FF &O _g'3{_1삢gv4==V 9ȶ1Z avOveפx0ChvJ_#>GKne |h`-ɉ^{gi|EGnvE6gl ޯ UZ{igQ}~6a'_k' yq-7!Ws=ͳB.ZT5~NlĆ=D&}F1Ե}σ ڬ>SFwVuYҍ3 ToB;KZ4rmGc& *w}#/TgZo+_T{FZ㯧5G Juh5‚ʗW^?|{'~#P7ԙ)+/\a}pװX7 \ߍ[^9\U_;_~˖#]׽]T=,zo˜?_Y/ܼ|*=e^_zmEuƷ7\q(G~~[{{.ww㒷}U}~0^8u@cU1 ;sO0>S,}zp-/~GvʾY`M}U5<.|{ Q~~eg=^* 4Ovtqݑjs^wߪo åǮ;v>4|97pC4^7~qo=Ъ_{ m/k/|dTqݩY6X>%&0\ovwӿ¢烟,0ܼ3F9ZJx^m4+(o7(7eoˮ'1m7m>Z5TwC̓׷g]512Fw])b7/ ^|g\N]yqŲ_9kܻkG_T_|UmE\S:oӣ&暻wME#Y}D׏LJĤGvU~G;>:*/ɄiMEp2ؕYsM7K=f=x0m:m:nxr~fl/۱og\obd=tẈ;lܼ3U3Zk]9{;_Qq2ոNxzܹ1x}~ỵY>߮KaVSZvkc*+8>O_k?sC4?y'T7yZyby8Cg ~A(c矽l󬿏>pUk"; g,9 Xx1 }t ++}@[>oY؀^xƧ˦MOG\6yShv5#_./v|;^JM|UScS#s&'ϝG3z_B'᤽*۞!9|oGJ_Ww!\=7+ףꢦ[<5]]K+wWYng-,z gbtp$6i?{2ђ%̳K_v ?Y]~Hs'd ̳˵kvUy6j[ z %Qen[zu]RW~2.u[~Vm,V҇^V}i"߽i‘o8O,!za7615vW^kQ05OՅswP}]Λ*l{iL:Znգkj<#:%gys}ur%beVߝ߹D=‘T_W".2>S(wڛ+"'Lseyz#Ooræ.&I9ҶI,}2X'h8Y/6f{jGßaL26 5o,WKםk痮o}EVWUWG̜6{d|ޓ?uR\~FjΟUE;(ܗ=Ǵ7_ިmWϱ~x*b3o_%jõgnl=u`O߮Q{&G/Ox-{Vӷ RڛCn&ȀKh#MNutlؖ1?`-y6^.wuoxjmOصy<_IzS}1|o ?V]#L;mpS/ҡ: ŏؤ |9ف?ا*ke\c]G ߞ,kd~mn{Dz9ϲ<g}Vh3W{~J/Z>C/riXt-|SU]9txpdg'צdΓРe¥Nv F9rIP)Ϸ9`<po .uf߸j{oRo_^?؞n#}h*P,Wj߽+z"z[z xCrb8OD<['p ˄O OÃ,}RlZ|ٙr`k~/EYn+=<->u0BO7eeճG{gUmew&F7vpƾ]>T_li)^/Oʃ?py% xz>wfw`7?]ώJo<ZڻOf+7ք'cuco$f 'cC,E9Ot}hB]󠍍2KmeЧ?#|'fLhli<)j_,mw2绻,2V{F}vhzlo,~՝={8㌾%Jёt+z.~8ImK[p} -S6*VP|׸?b9 j-PWlGX~cYJ]<6oϺGuʻ+I} ={=l/as v~γ}ʒm4|eVFhQCiaU§ݾoovZ}C&nuӡG+Cd&W2;Z ?0ɳ }ioGM쯍7hL:>&o>]:&4ǜ W?,,(25 ðóþùåé ëèíèè.  òîì ñëó÷àå, åñëè ïðè ñúåìêå âûïîëíÿåòñÿ ïîçèöèîíèðîâàíèå è ñäâèã èçîáðàæåíèÿ îò ïðåäïîëàãàåìîãî ìåñòà íàõîæäåíèÿ íå ñóùåñòâåíåí, âìåñ- òî ïîñëåäîâàòåëüíîãî ïåðåáîðà ìàññèâà òî÷åê ìîæíî èñïîëüçîâàòü êâàäðàíòíîå äåðåâî. Ñóòü âêðàòöå çàêëþ÷àåòñÿ â òîì, ÷òî âñå âõîäíîå èçîáðàæåíèå ðàçáèâà- åòñÿ íà ÷åòûðå êâàäðàíòà è äàëüíåéøèé ïîèñê âåäåòñÿ â çàâèñèìîñòè îò ñòåïåíè çàïîëíåííîñòè êàæäîãî êâàäðàíòà, ò.å. äàëüíåéøåå äåëåíèå íà êâàäðàíòû âûïîë- íÿåòñÿ àäàïòèâíî, ÷òî ïîçâîëÿåò ñíèçèòü çàòðàòû ïî âðåìåíè âûïîëíåíèÿ àëãî- ðèòìà ïîèñêà. Çàòåì èçîáðàæåíèå íåîáõîäèìî îòöåíòðèðîâàòü äëÿ ñîâìåùåíèÿ ñ ýòàëîíîì. Äëÿ ýòîãî ìîæíî èñïîëüçîâàòü ãåîìåòðè÷åñêèå öåíòðû èëè öåíòðû ìàññ. Ïðè ïîèñêå îáúåêòà íà âõîäíîì èçîáðàæåíèè ìîãóò áûòü ïîìåõè, íå óäàëåííûå àëãîðèòìîì ôèëüòðàöèè âñëåäñòâèå èõ âûñîêîé êîíòðàñòíîñòè ïî ñðàâíåíèþ ñ îáùèì ôîíîì. Äëÿ òîãî ÷òîáû îïðåäåëèòü òàêèå ïîìåõè, íåîáõîäèìî ðåàëèçîâàòü àëãîðèòì èññëåäîâàíèÿ îêðåñòíîñòè òî÷êè, è â ñëó÷àå åñëè òî÷êà èëè íàáîð òî÷åê ÿâëÿåòñÿ îáîñîáëåííûì, èñêëþ÷èòü èõ èç äàëüíåéøåãî ðàññìîò- ðåíèÿ, ïîñêîëüêó àïðèîðíî èçâåñòíî, ÷òî öèôðû, âõîäÿùèå â ñîñòàâ íîìåðà, íå èìåþò îáîñîáëåííûõ ó÷àñòêîâ íåáîëüøîé ðàçìåðíîñòè. Ïðè ýòîì ñèñòåìà ðåàãè- ðóåò íå íà ÿðêîñòü ýëåìåíòîâ, à íà îòêëîíåíèÿ îò ÿðêîñòè. Äëÿ ðàñïîçíàâàíèÿ öåëåñîîáðàçíûì ïðåäñòàâëÿåòñÿ èñïîëüçîâàíèå àëãîðèòìà îáó÷åíèÿ ñ ó÷èòåëåì, êîãäà â êà÷åñòâå ó÷èòåëÿ âûñòóïàåò íàáîð äîñòàòî÷íî ðåïðåçåíòàòèâíîé âûáîðêè èçîáðàæåíèé. Ñîãëàñíî [6], îáó÷åíèåì íàçûâàåòñÿ ïðîöåäóðà ñîñòàâëåíèÿ ïðèíöèïà èëè ïðàâèëà ïðåîáðàçîâàíèÿ ïðîñòðàíñòâà (ïðèíöèïà êëàññèôèêàöèè), êîòîðîå áóäåò èñïîëüçîâàòüñÿ â ïðîöåññå ðàñïîçíà- âàíèÿ.  ïðîöåññå îáó÷åíèÿ íåîáõîäèìî ñôîðìèðîâàòü ýòàëîíû ñèìâîëîâ. Äëÿ ýòîãî èñïîëüçóåòñÿ âåðîÿòíîñòü ïîÿâëåíèÿ ÿ÷åéêè ñèìâîëà, è âåëè÷èíà ñðåäíåêâàäðà- òè÷íîãî îòêëîíåíèÿ s - ìåðà èñêàæåííîñòè ñèìâîëîâ äàåò ÷èñëîâîå âûðàæåíèå êîëè÷åñòâó ñëó÷àéíûõ èçìåíåíèé â êîíôèãóðàöèè ïèêñåëîâ ñðåäè ýêçåìïëÿðîâ ñèìâîëîâ, îáîçíà÷àþùèõ îäèí è òîò æå ñèìâîë [4]. Âàæíûì êðèòåðèåì â ñèñòåìå êîíòðîëÿ ÿâëÿåòñÿ íàäåæíîñòü ðàñïîçíàâàíèÿ: V=f(x,p), ãäå x – ðàññòîÿíèå îò äàííîãî ñèìâîëà äî öåíòðà êëàñòåðà (èäåàëüíîãî ñèìâîëà). Ôóíêöèÿ f ÿâëÿåòñÿ ÷àñòüþ êîíêðåòíîãî àëãîðèòìà âû÷èñëåíèÿ ðàññòîÿíèÿ ìåæäó ñèìâîëîì è êëàñ- òåðîì. Çàâèñèìîñòü íàäåæíîñòè îò ðàññòîÿíèÿ äî èäåàëà óêàçûâàåò íà èíòóèòèâ- íî î÷åâèäíóþ ñâÿçü ìåæäó íàäåæíîñòüþ è îòëè÷èåì ñèìâîëà îò èäåàëà. Çàâèñè- ìîñòü íàäåæíîñòè îò êà÷åñòâà ïåðâè÷íîãî ðàñïîçíàâàíèÿ îòðàæàåò òîò ôàêò, ÷òî ïðè çàôèêñèðîâàííîì õ íàäåæíîñòü ìîæåò áûòü ðàçëè÷íîé â çàâèñèìîñòè îò êà÷åñòâà ìàòåðèàëà, èç êîòîðîãî ñîñòàâëåí êëàñòåð. Âàæíûì ÿâëÿåòñÿ âûáîð ñïîñîáà âû÷èñëåíèÿ ðàññòîÿíèÿ. Ìàòåìàòè÷åñêàÿ çàïèñü äëÿ ïðîöåññà âû÷èñëå- íèÿ îöåíêè ñðàâíåíèÿ ðàñòðà ñ ýòàëîíîì èìååò ñëåäóþùèé âèä: C W P P a P i a P i i i        1 ) ( 2 , ãäå P i – âåðîÿòíîñòü â i-é ÿ÷åéêå ýòàëîíà; W – íîðìèðóþùèé êîýôôèöèåíò; Ñ – ìàñøòàáíûé êîýôôèöèåíò; à – ïîðîã, óïðàâëÿþùèé òî÷íîñòüþ; i – èíäåêñ ðåöåïòîðà. Çíà÷èòåëüíî ïîâûñèòü êà÷åñòâî è íàäåæíîñòü ðàñïîçíàâàíèÿ ìîæíî ïóòåì èñïîëüçîâàíèÿ ïîòåíöèàëîâ íà ïîëå ðåöåïòîðîâ[5], êîãäà êàæäûé âîçáóæäåííûé ýëåìåíò ïîëÿ ðåöåïòîðîâ óâåëè÷èâàåò ñîñåäíþþ îêðåñòíîñòü òî÷êè íà íåêîòî- ðóþ âåëè÷èíó, íàïðèìåð íà 0,5. Òàêèì îáðàçîì, ïîëó÷åííàÿ äðîáíàÿ ìàòðèöà õàðàêòåðèçóåò “ ðàçìàçàííîå èçîáðàæåíèå ” , è íåçíà÷èòåëüíûé ñäâèã èëè óòîë- ùåíèå ñèìâîëà íà èçîáðàæåíèè íå ïðèâåäåò ê çíà÷èìîìó óâåëè÷åíèþ ðàññòîÿ- íèÿ äî ýòàëîíà, êàê ýòî áûëî ïðè ñòàíäàðòíîì ñïîñîáå êîäèðîâàíèÿ.  öåëîì, ïðèìåíåíèå àëãîðèòìîâ ðàñïîçíàâàíèÿ â ñèñòåìàõ êîíòðîëÿ âîçìîæ- íî òîëüêî â òîì ñëó÷àå, åñëè ðàñïîçíàâàíèå äîñòàòî÷íî íàäåæíî. Äëÿ ýòîãî ðåêîìåíäóåòñÿ èñïîëüçîâàíèå øðèôòîçàâèñèìûõ àëãîðèòìîâ ðàñïîçíàâàíèÿ ñ áëîêîì íàñòðîéêè íà îïðåäåëåííûé øðèôò. Îäíàêî íàèáîëåå âàæíûì ôàêòîðîì /xLeϛBȅ \.fȼPkf$VlZ)K_-6MLi2d΅BRefb_*9&c}.9sss]"Fty`OGT/]!2WMBkj祠msg)M0#{;ިlIli5#ZjZ{ @Ĥ$X[,2Y3MF$TŤOJ2R+>3E23ً\B_6|̿s\#JZn{1/54qGNFm$W.R (́h+}W+p%{ eidfJCUYQWceVp 5K%V2DPN1beK|}sllz~Lx69F[ P.e$8y|x:6 X$֯A`8Oݢs:AX `{z|aLP]w Kfɲ3EM O? ;:x6Csl_5b9.kl$f+`[mpR'@Cuʷ* V{H9="{7mpM,%}K6< :QrUd;w-ZTDR7|{c$ߑ<)ˆ|X9${r(u] {~ǎN՛:u,co7eǏnƗ]p1S{;>ƇF㬱lŷ(CXva ϲ׎?;6nL> gc';]ڇ Wp'\ kv|YۧvcZrv|9?N 8p*TSN 8p*pG+ϩSN 8p*TS ĎMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10  J\5 &':\B\(16b~2~/.P\1~w{lzx͝{Uyϻ` KH6@ c7Q!Ѐ53 XA#ᒨ2?NthKeN@@4#nYȅ &~?vg9\9;F!\$+Ot}0 WPsBh y`V|w.! *"9yGw8!, pu(Idup*ߨ[8Vj)\ede~V^i˧[% 3]p`r L4Ƈ LA!Ч,9Gi4?ӕQPzܴƢn)e<}Y•Bүa>_9}:OG]?;tꮉSC h̺fgB&}iˣΗs']a?]KΊ󥼯b~HlWx<|(7OJF?oVk4'\.GF(soL:24xI]v{c}+^?Yk-p 7Lj[>.4c}Gi3b~QY f˄2?[}es wg~dXҀ>c2Lɡjԃx!uI-E)~ݽco쾬/pk>kBEثHc<;QôSOtn~7nr󱓧i|=md`7~`tώ=]Qˬμ3em]R4u~#:y60$ܹD!&d5O3fػ^Řכ_)pWnv<$~%BzNcN<g|`umgrr{ gϲ-#o^@'9rX<x ȶWPa@Ŗ}qpuv_#N=٥5  :xH|{Q7qx,~g|9? RNPzvzV~:^eOg>Wϧӕu>8ιH-'?_ 8ZkS|)Һ))hHѪ[k}m9x__Tvh%Xvy.Fj9Gmy/UFH솾HDig7}^xy]:&s;s$Fj9Sr[vvCc7RFZg7nw {;AG.?p@hkSNE\Y'A5@\1O*SI/VdA7cR )Ǫق^!_G39"o s`j[hun,v޽қB!O6?)z6 pڡF?n]?֊vpY|'|y3S ZJR.QJ//E߼EDC o%~F2ީg_a?N@3IJL},~O}w+7)U //՗ y77OlmڂF[_qm}KL){ڛU N楢s5^=,s=<4lH|㍢}_B_T7uX4vyߏw:G㏶ gQ'lήN6w5T>!޺>!Z>HzBjS,OFo1D m\ɘ){h4b. #BgiO'eچnms wF7#]x}ɼ$![h.E/ cggg<;y}}g.:)h,\uE{ >yzVƖwwEI/aGTg[%&6g ؚB14{*mY/7l^ 4_^V[̿SK ȇ|]ǒ1PUUm 6NE+핵 sg9\B[eٖ,b _Hq?+ 5qI8lTgoiDz&''Osߡl60/M}XZ'_rt@ǴWi+9ouh$}wIm[R~W5;kቄ%a3F7ƻ"h؟q3k}')Лnui¡Gˆ<嘾R8"ELW BuZ&w/N 5_ȍH(P~:koh=d9^'   lhy2f جcF:)sy͟>3I`3KY{ԡn} Yϼ>Xi3'nTQծа+u%t{1( ȥߌ>;:V>i~~"/T_2)]TIϞ-r~qtLn-QAEchExT￴{Wb+@VH -=y89[[Y :FA=<%:s4PƾvGI6ye]yn4<6Br]A[3R14lLehXwd}}{k}gun_d|qM#>[!]T߿LlޫlNxӾ? k* F;K~U|x؏BnH͏{<-(ԷOSdC;}+!*ݳwWW W:"z1VtS&ӭZ޷rcΈ;\8GQ>:]1V =A#{V>1_^4C#JguoB\+,h=2±ߪ DzAi_VP;6Wwi|=8eg;>iS֝}>!S]c@Wkl?J;4>[hi`>OX~ճ*.OlS={b^e=ca;yV>Krk hUN~xXbS;㇅1gB݂r/ʀ>9o#\x G,Q#y}gssObo6v'9⭳Fцuu7{մ]c1ړه&K:z.2kx >ld)Hgi>C9KV^gѡuG y `gR:in#G >p%A=/PaS{;Qξ!\n|\8d:ўGd3bn0 D%z-VR~_Rۅ<}w=f@ $8 )s/B}qw`>X"?~sj4ܕKY; ޚdf!nV>pckxlxO06p:u'|zw -ޡBzNș4yFr9Й}.cуbg<6&N/k[Sm(;L}y^  o2^=ԳMc~p 녭?~pZ?8IMgOCgSfLO 4O^߹+qֻj,wB`=gtnc |QzIMzvsTrA{O/7~c{t1 ӇCN׈BsrO>W >]bڷ}F/ħGRFG^G){=6+yv+OJcn'=?(RH]k'Nb~qEx'uұu'R6~G,*Fқn#;xlؿ*sPz| /yOJrR/ʉvWM~SYW׆g>~&/A!R}ራ%R!лчBgGh=@w+%n8}}vq]\/}:w35ܔp˃Vy,@KmO #eǿqr#!/Sl/c$6N#32J{í667 }>m7mSBϪͫT1us(gW<2v{J[iL ;NyY2ov!@n|j?EiZUެx7jL 9X?wvB"\I2 ob[! ^ 55rvJB+u ntׄku'n۶0b5bb|ylO9.W4p.!M qR;qoaYߕ w^-v1ߕֿӕLcrK}(e\/Ϋ_ܭCj_˅u-ʻ6ț)ASO+j>Z_P1q?iȍ<(8,v::)>eh!_#o8d#2h YiĄ>Aj{w^n/W:Qgu޴2_ݓΏ j8:;"+Gn=n׈NvzToװ4|,S+}ȳY(@;Mon<؃U/z}Hh>{bቫܣsF8&=w+kؙޤ=S^qg=}қn;o^ jyN o5Ц>|I K:⻽܎l;Oκ۴t߈\oxg&Y2>8~_w>3sF?$>eky(>bO^Ӊv&< nm^ʦUqĝ-\o0gXAw-6>b^e[+P-r;m7F~3燾7wm*L2~_(O l6ױ@ u٥WZܟ#`E:|onG,un޻&[*⭳ݢ1{Y{GN[O0ks%yL 3[_jS^|}/2y6 FsEJcS#v*6F-~+ Wg#>}f^^f e p|׃;b],c=Ko~!E#-pn>y0@g 73+Þ:vy],^h=%^h[!2-2,Ө=-8#o>îrw{b^=8jWhӅ;O:;(wɊC]yk7қv<΍x 9RCt FPZ_3:'e^B(CRxȡS׳^.3SYĖvOڀ>(rr~5x9>BG0sdg|6>a6U6-=tпsAC|Gx/uU찛=ձǎmpX/O]ld]#VC}|Qmϲ܎O>Ae=6hc<ۣyntsOEg5ogHٙy3?i℥\3fNiʯx gG_D։u}]Pp#r[C&i>#ȥ 1sC{}w;vG:M#p7fiG#޺(Zz ~^7 Lt_b.n';w Ik~u_\nnڵ*g;ugpە|S gonpu>Zb/ĵ,L&y7WV"zWZ9 R3%ӭWo󛗺3h 5A>u'RʨlvA-RsY=w全/X[g|G2f3o]sQ1ͷ9ӯ2Wy"o7cGw)JK[艼ϭ(@2MNjy4г2V4 iא᣺7ҫ#Ӊ cnH;vyY t!<<Jq"J\aOYWbފm)d4ob{ w>Uv_qNψ^n`<'x3,ӟm.[A99c}S&o@2G3,'Xv-ZuGo_pH~`o{؛zX⭋E~1.qى}W,nf=0sq*߇װo,7O=엣ǥ٣zql2v:.}tU>N8?Y ;ܻ#v.'+u}{{egu3i 3X .}5nݟv6Й>Km_mMmlit+_Dy:r❙adZ\|No}o8N'3l]>4ۇlۇy=򦓢{ysC~m7 GF>/Y>4s7>pOpUng=3}&]H7JwO/gg*gx2w^^.A+Tg@S#n7$r?mыaNjus|%n='SF<)L߲hza瀼/urSm/p[f박Ng#_`\:="joҜy>=ѥ1'5]댔;yg}xSo"w~M ;uOo>cY<h^;.#L0[| wpK߯`h9ig`Al@4xeNYwYy^ÿ|Iڢߪ?v o:<ѹonv<vsu<>p>A}g9]dw} b%c"$5xcgeOO7%E[樾uB{|Ws:pK] ݚrmg OG7|hhhk,,26 ÿâëÿåòñÿ òî, íàñêîëüêî ñèñòåìà ñàìà ìîæåò îïðåäåëèòü êà÷åñòâî ðàñïîçíàâàíèÿ è èñïðàâëÿòü îøèáêè. Íàïðèìåð, â êà÷åñòâå êðèòåðèÿ ðàñïîçíàâàíèÿ ìîæíî èñïîëüçîâàòü ìèíèìóì ðàçíîñòè ìåæäó ïîëó÷åííûìè è ýòàëîííûìè çíà÷åíèÿìè. Ïåðñïåêòèâíûì ÿâëÿåòñÿ ïðèìåíåíèå òåõíîëîãèè àäàïòèâíîãî ðàñïîçíàâàíèÿ, êîãäà ôîðìèðîâàíèå ýòàëîíîâ ïðîèñõîäèò â ïðîöåññå ðàñïîçíàâàíèÿ è ñèñòåìà â ñëó÷àå îøèáêè ïðîâîäèò “ äîðàñïîçíàâàíèå ” . Òàêæå, íåñìîòðÿ íà ðåñóðñîåì- êîñòü, íàäåæíîé ÿâëÿåòñÿ ñèñòåìà ãîëîñîâàíèÿ ìàøèí, ïðè óñëîâèè, ÷òî ïàðàë- ëåëüíî ðàáîòàþùèå ìàøèíû ðàñïîçíàâàíèÿ îñíîâàíû íà ðàçëè÷íûõ àëãîðèòìàõ è îáó÷àþùèõ âûáîðêàõ. Ñïèñîê ëèòåðàòóðû: 1. Ford R. Identifications and Monitoring // Modern Railways, 1998, N 592. Ñ. 25-27. 2. Rahn W.-H. Signal und Draht // Modern Railways, 1998. N 9. Ñ. 5-8. 3. Áîíäàðåâ Â., Òðåñòåð Ã., ×åðíåãà Â. Öèôðîâàÿ îáðàáîòêà ñèãíàëîâ: ìåòîäû è ñðåäñòâà. Ñåâàñòîïîëü: ÑåâÃÒÓ, 1999. 397 ñ. 4. ßí Ä.Å., Àíèñèìîâè÷ Ê.Â., Øàìèñ À.Ë. Íîâàÿ òåõíîëîãèÿ ðàñïîçíàâàíèÿ ñèìâîëîâ. Ì.: Ïðåïðèíò. 1995. 150ñ. 5. Àðêàäüåâ À.Ã., Áðàâåðìàí Ý.Ì. Îáó÷åíèå ìàøèíû êëàññèôèêàöèè îáúåêòîâ. Ì.:Íàóêà, 1971, 192ñ. 6. Âàñèëüåâ Â.È. Ðàñïîçíàþùèå ñèñòåìû. Ê.: Íàóê. äóìêà, 1969, 292ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 14.05.01 Ãîðåëîâà Åëåíà Âèêòîðîâíà, ìàãèñòð êàôåäðû ïðîãðàììíîãî îáåñïå÷åíèÿ ÝÂÌ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ïðîãðàììèðîâàíèå ñèñòåì óïðàâëåíèå è êîíòðîëÿ, èçó÷åíèå îïåðàöèîííûõ ñèñòåì ðåàëüíîãî âðåìåíè. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14. Áåëîóñ Íàòàëüÿ Âàëåíòèíîâíà, êàíä. òåõí. íàóê, äîöåíò êàôåäðû ïðîãðàììíî- ãî îáåñïå÷åíèÿ ÝÂÌ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêîå ìîäåëèðîâà- íèå ñëîæíûõ îáúåêòîâ è ñèñòåì, òåîðåòè÷åñêèå îñíîâû äèñêðåòíîé ìàòåìàòèêè. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, (0572) 40-98-21, e-mail: lgorelik@ukrpost.net. ÓÄÊ 681.519 À.Â. ÊËÈÌÅÍÊÎ ÀÂÒÎÌÀÒÈÇÀÖÈß ÏÐÎÖÅÄÓÐÛ ÔÎÐÌÈÐÎÂÀÍÈß ÌÍÎÃÎÌÅÐÍÛÕ ÁÀÇ ÄÀÍÍÛÕ Ðàññìàòðèâàåòñÿ âîïðîñ êîíâåðòèðîâàíèÿ ðåëÿöèîííûõ áàç äàííûõ (ÁÄ) â ìíîãîìåðíûå äëÿ èíôîðìàöèîííûõ ñèñòåì, èñïîëüçóþùèõ ìíîãîìåðíóþ ìî- äåëü îðãàíèçàöèè äàííûõ. Ïðåäëàãàåòñÿ àëãîðèòì ôîðìèðîâàíèÿ ìíîãîìåðíûõ ÁÄ, ïîçâîëÿþùèé ïîâûñèòü ñêîðîñòü îáðàáîòêè èíôîðìàöèè.  íàñòîÿùåå âðåìÿ âñå áîëüøå îðãàíèçàöèé óáåæäàþòñÿ â òîì, ÷òî áåç íàëè÷èÿ ñâîåâðåìåííîé è îáúåêòèâíîé èíôîðìàöèè î ñîñòîÿíèè ðûíêà, ïðîãíî- çèðîâàíèÿ åãî ïåðñïåêòèâ, ïîñòîÿííîé îöåíêè ýôôåêòèâíîñòè ôóíêöèîíèðîâà- íèÿ ñîáñòâåííûõ ñòðóêòóð è àíàëèçà âçàèìîîòíîøåíèé ñ áèçíåñ-ïàðòíåðàìè è êîíêóðåíòàìè èõ äàëüíåéøåå ðàçâèòèå ïðàêòè÷åñêè íåâîçìîæíî. Ïîýòîìó íå óäèâèòåëüíî òî âíèìàíèå, êîòîðîå ñåãîäíÿ óäåëÿåòñÿ ñðåäñòâàì ðåàëèçàöèè è êîíöåïöèÿì ïîñòðîåíèÿ èíôîðìàöèîííûõ ñèñòåì, îðèåíòèðîâàííûõ íà àíàëèòè- ÷åñêóþ îáðàáîòêó äàííûõ. È â ïåðâóþ î÷åðåäü ýòî êàñàåòñÿ ñèñòåì óïðàâëåíèÿ áàçàìè äàííûõ, îñíîâàííûìè íà ìíîãîìåðíîì ïîäõîäå [1-5]. Ìíîãîìåðíàÿ ìîäåëü îðãàíèçàöèè äàííûõ íå çàâèñèò îò ôèçè÷åñêîé ïðèðîäû èõ õðàíåíèÿ. Ñòðîèòåëüíûìè áëîêàìè ðåëÿöèîííîé ìîäåëè ÿâëÿþòñÿ ñóùíîñòè, êàæäàÿ èç êîòîðûõ âïîñëåäñòâèè ïðåäñòàâëÿåò ñîáîé îòäåëüíóþ òàáëèöó. Ñòðî- èòåëüíûìè áëîêàìè ìíîãîìåðíîé ìîäåëè ÿâëÿþòñÿ òàáëèöû ôàêòîâ (èíîãäà íàçûâàåìûå òàáëèöàìè ïîêàçàòåëåé) è èçìåðåíèé, îðãàíèçîâàííûå â ñïåöèàëü- íûå ñòðóêòóðû äàííûõ (ñõåìû). Ïîñëåäíèå âêëþ÷àþò õàðàêòåðíûå äëÿ îðãàíè- çàöèîííûõ îáúåêòîâ ïîíÿòèÿ: ïîäðàçäåëåíèÿ, âðåìåííûå ïåðèîäû, îáúåìû ïîêà- çàòåëåé è ò. ä. Òàáëèöà ôàêòîâ ñîäåðæèò â ÷èñëåííîì âûðàæåíèè òî, ÷òî â ðåçóëüòàòå íåîáõîäèìî âûÿñíèòü. )xilTUctJiK RT1Db h-(&F Dj+a+KXʪ,B1@&B"5Q 5I[KGL5ӛg{߻1EYXx2V,Q_<rhmOtxr[bSeq?vxu86h570 PIV--(]{ ]#vݎ=j\md6/C>DͳS߼Լ|9<(l:wʹqWud|9G[y5OZZ:8TV[ -B;ZBtNb&g:`8K< &6ݝqj%c%Q.;8!~ J:v܀#98ߤ&^NGNpTK`(4iRMx* L/9A5&x꼁RF< X Xklm|d5=5R?0<WF~3Q¹Ğ_o*eM!Y`c#[9Kრ#aIf'ˋB\,σE/9py.ܯW&>*K 0%~x?u6L fL̚yV׬g\a={ 5П`+CN A؅n:y{d$ylN58}#Zjɿ:Zx芰ow^:`G5>YWK*u}~*bǀr0R2? S08ZE 孵}̣6p7np*}{JЇU `o.1p9<~OOѻUR\@2V sM fPcp<O=ݣ>rŘdf%tycO#kD־9.q}joz2; ~ɾOdE>,)`<3^`XY>$| |sU p4>F ȉ&>{ɑ"˰Ee|!&*6+@iIx}_ 2>m=iț!]B}Zs38  jl&x9w N_^y=5@^a|!u|n*Л籎p X 6`~Ȅ3^~HkO{畎Tx+>uι>*ط{V\͸`, ~AXs|AjA8rDrF]ղrY)ghO-fٺbWue뎾ys̫;5cqg}KkvVOf4RO?tk}ݒnuol#+=[w/|ͯ;&OyDHu"Ո<wv;`wv??v;`wv L{Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10  ԥ :&ĥ̥(162/ڥ1<j2{ jxGUn PhiW@~y[LXMIH 5Q`CCI$Q⏘@#hXenaK}ޅ ә9̙=sfywWap7 *]{09EpMðzŵamY;&ra U/3_șuûnV+Ta%nZgJfo:aRY_gvU9<3+mL0C[N,~O`\y{_pOo|p/M[ wm;wWY~7þ/?])̇*ǹpXGχ;={ޕK+]~o.ޗ ֡4hwڞs?U1-7Loxߘm({+~B#pW:}S?pW﬽x\<}G_/|kra8˻,҇7(Ϳ75b;7mƑM*43vb$ǟ77{iͣy{wMyyyJ|Z߼r)_zYy7GYJ.2߼x17뿏 a}8R=V_ZhWwGCz(VE[{SUNl>Xc?(ђSz~>3*2Wdz(Kxr }rс=~t˚ M}} zR?;f2n:C+9|iRyc/UnƷhYPx߆ca񏍘^iό)sgN(<;9 ]=D́8{<+Ձg<,5,}'7;YG|lp|`R'W26ʛNSe_%+zrZ {|b9`euӺrx/G~IS|Ng?SÞ.m+}'J~x;f.ڕ%̯*nH_V߾lkD0E;X~prx(q롏ٱd'KbcxedlǻY{?6cu,\ڑӖ9DBG^X^5J7y\{8;t {%ڊgڢeT<((OԾ>I1lp8Q%D.9ܸuOOJYn2wdnbݾ9uƿVVss6mj!Oxth7.ߘ|a?=iw%9mֽLI`"gg'9mҾzMG ?>a|0`os}hW2?xvVTzkg*~m~GَT;>8EPVU~0#IX̓-mNU.^FzvU,{҃C2z~ [?Z0JY` 71lw+g|oUIvMіaVjoi}5[w݈ٓ\NkTlή~hwV5]rXUo .;=c?YJY[:}/IN&x)/OƭNO'ܘfƖqу:?80'*Qז2?8T1>׭ilvX3p\_4+צQ}^[fޮ0bJ>/{M{ǂEr:'y7i7`E3 puѶ{&xb;$UzhΖ Qv۩Oh~GF}.]?f~1&3c[w0@[VcSξLE&ȧ/y#z;~S#ct:Ln->(^s3]и#C?뭏qk#ʞ,n?zR=R~pwyc6k}@K6 bG"bW=e'MAS'#u\i:Ȑ#c0vz%di-X ϦWL\Ѯ,ھJZMWh3ޞ(=*v '[>Xy@=6 6zHEoIݬ5_R}W &|w'Iz+UOgg Zr>]4[t37cu,o^iޗ>VexدWĵ{x7n{ F>P/-67o9k׷Wg&UW>k).'}3Ѳ3gEnnYmzsxhw}wGjn[m}tuV_ۓw kٝx364WW?{_yRڣgIB xѣ*˞Lvr2r)WeX&}%:2}Ed5/.6j;Ͷ{m'0uu'AF}hCʰD科 Wɨg|=/}Q'Z)zt< g={E.=[yqj;Qii=;ّk.vSc8Vz._ b=?.ݥ'j+],hOk6d#6ccI[ضׇ<ӆl_Ϻ&7u+u2ц.r[_o{j+w2zB*jr >Br%ܰZ>rpI. <ޔoX>mwpᓝ5rD xxdViHi[w#DH?x'Pr=l9ǦafC#{'Sg[ G&յ^EE.r~͞'xZ]-{{wkz S_:弞~<ĎJ4oY>ysr%g85J/Ûs6Μr#K.x:Fo/SKf< v %IY_<2^yS;u%=]O;ת'~ mxƒc[geP9Ijnlx*U%llӣ74|34&E s|Y䱫WGdh98h7/1Aq86=0 Ė=~zؙk#i#'д'_}_ƕv6ߖ_F&q,n ÞXn`Ҟ2gou ovw_i\iӾ~yuТۉħ=m3_OѴ <._Nɕ`)cS._< ɮV/cƕH_ ?TѮ6*-`{۳*7?녔gڡ )0 #ϸ5ֳ(eQVb)ZɗXgO 2v؂S)Tg~m% -=^ѩ%蔓3ȤMse,l?Μ?x ۽/-{E{R-Ń]KTw1&QcwVVeNY^Ӽ݌+v1!N5-85.zx%원[9?Vcxq`gxK2l3]#/I)gWO?'|:O/}L}轨d˹"1 WT^0Μy^Y+ ӻV󃅀O:7 -O@[oӞrRc;کPHڵKS,wB$-llnv IJ;Hr-`J*YG+gC_kq\$*^:յOLs-Wuh)2,^^=Mϡ/ƯV~PSfʈQlW˙ rR׈bt|)w_\]۔,z޷Kʽ\'l"/cUΩrڣ{"g=[3c:pW>'[WnR;Xֿ55/lfiv Yɲul{'&{ξ댮޷;/\/mSkKNYJF= }[+ke]n "i|2h2b­Dhw{qk?BdϭHCƹRl.l{nO=B}=v$K&6Ƌl>myDF&vR2~_[~j~&Q48/ڽ-sNSNV:<=1Lo.|;:%W ͟_ͫGd쑹>&gO]=yecȠ<8}glM692Ɵ1jN=/ -&1O]mxzWu䗌va+3=F6:>VC Q;= io-۷߫gF:~8]Hqpy-g7vb_!lxJe~Ж.)zޏOٸ6ۆ;"8=Vޟm;{};EӘnG8Xjw@:'st߼ ya\z^r>V׏:>0z;:ԃztIſ"6Mw5Yɾg=?Dܝ"J_$kN[ߌ?Ioٿ3Gy|J5Mv]Uesl$V^ ]h,khMO[kE[JDyϧsdvJl?b[1% z/:Ӌxi+N֞:}Hd?νaǀVdz_Y~z7e1('ta-jlbI(|K9< /E\:eQ>{%6ѹG~E}9;Zzr W-ex% Z\Q+ַ3㿊bz[?X /oLGOYd b`ٗ$g,9Y2SJ䵋v@O6rR;?XϏY3)scF0x߸h۝iٯ5U<OX%h޳S8hos~_4Gs sgء! ^_r293W򔣿'iK?"ׯЩrxL{O-/ݙv^;;;JS!;m^_Y igGso-mmg3=k ;+{clʵ`WbW6쪌]HߙLd3I;21e\u}آͮIN&rZX_? ?v~/rZ~_&Fd+~k{ 1Vw^nLot7d [lzlu^. #=:=lOWtKA~qV^.)եc_/ϸkEQ}|W%OԎj^vW2} yjt{:tC2}nzO ~&[0ͺ'+OD}G'3^ƪ~Q噓v6S7s4.mO|J{N=xxcѮ|Dtܷ3'$[_vCei]a?RxK;`)qو]؃c[9{HmzYu'6ص-in ҭ]Ό#$Ǐδ%`vӭ._{2W+tN%_?O9}s.3y|o޼2 /*5% ۬~ؙƷkܙisھ:]t|;3?ek9Q0#Fە\ڣwd>_xaK8~kLOF6:2W#[ڒ]pO NӞߺx?o?|I{_37his"qqQ?T;񛱶_|#=5.6g$}ՕX6hHœlꋎLz2+Ճ5]2;Wھ0|b?|hJv?|xuμG*AtEh:}Ø3'.^;&QF9gj&)5O_Ĵ #aNͤOrWqj'M$~7R?}2{ǯ4E7]hUNMK=t:Ќ-vOhss}[\7pŻh۝s΢/P!}-_V8Lw5'fW=sM;.C'-c'ɓzzIx/ -mA}םO&~qǯ:_0UAqs\]u P|`;=RxGQH>oU`GH逫V8G"3B; yu> T\e9R'~ Šp{uG+.8BnUPEnsjA kBIjdLF"Yq|xzPe5|.A7`?]u4W~|+cA0F]{s6^C91uVK%O$.%›i{@=K/?wPp%\c7\θ ɜ?؇/pLϥ[.rG;ixȯ 8(FIlx\g{ 2 c8eP[Ʌd>ʷ\S5fPv%xaYE3Ps#p$KT䇧bSkm?z~v3c/j?.B+  p;AM-]w;A 䭡ރ`L/l7~Xu8O^B~ ,ûF ƲkXL֩Ϗ/'drg=ϣaN=T rӰqFFD.w+On^xcuRכ HNp TJmߐ5a-' E>m-9{!x7P_T͹xx1ɭċg^Ϟn՟\M{x ^EoBc4$t!@&!4 0F'Γ  $J: 3 3Ȏ2"3hd]0 Hbc@‡d{v~'+UԩsNUsI:s$|3'g_&IӕIR9&ɘW䆦$Cupw)_Jt1G{ES2'&wG[;)YLӨQm^!N'>g]SSF*zi.ySru*SĖP60uj&G6'Y3WٜxG6MlBo*eW_!6l\e%%ےJ|9y:Y$ iF6'O*lL'3ܨuyNpƦEk[E?Uߨ~%`֫)ZOOZ)죀 %AbðkK󀛤@L|( # w'o4ipo|Σ <{%kѺ1NYXpbk*kR9;5y dʞMY\|5A&6HZݯmҝb>~|&M7 :4ziN \|~a VYc ڠ.ڠܼr=S< =i`Hc2ۭoJ-׏1Ky1Rg䩔p&g4|/pjj<4$efzZ)fg|&;X}8M;/7(*P״u| {!o}n BaO?/(f.4?X{߮j.f'#f#kŹ2ٟyAGj/4!ih E_QhUe Sq_䅼)aJ| 5 .WxN ;>#;s_USO=lR=S5 R[K&\!6P;AxX=la?Waa1= z[ u.81IPvv\LN>ȳnULK_gE .*ޭka=jv=^=paU> $'/+o[\u4Lx&][F71nMiZ=<&>8)Ww)4+6^@/p4}7I(DŽyL<DyIEu/glJrRDm~%-et5Z1[iL-~IpG.YӒt?k9dMd%=Z=n[qo{ɖ/C`_Qp$XGf郒AE镇>]EcJsR$g$$|ȯԈK>),UvqkoXߟtO KOٷ*L0w yH$ϛ?Lǧ&Gyn':8(M>}:0~zp:q~T W1Mbp7#Q2 )ل"ίܧԠ98Dh\8Zsa?-( >6+cZ{T:eyDYD} nq>5M|儾FαJke8W%=uԄJQj?:aN6 Иr2ksfR؍^Iw$_{+xnZ=3_iz9*9^ 3Bڭn#:>~Q}F"Y\N1cN_:v†#Ј17_ko~x8ޑ"`*kd9nKT"_K  %GqLâKRZuISxb>CtP_OJrp9㧞H?Yv||ayDy1Pe&zو& Zƴ8Yc0z$kk4κq ҅#7Xn>7,Q\-=Ul<~\C,P|,7L☏z{t= 7 Mc׍Hs)/%M-, 2,\>17_qy̔1fP t3 p!+ePߺe+ob8WGIJiN9KAMPG7(3LSbr_P^$*[=4;}Lv>$2;K|i=|"6O޲9 =<8 (CF57E}2|jpタ<{x3&X)sw`c<}XegL7y)&rڣ99眵W\pNFSLhN==փuhݹ7G0p:"ML}yP&>fBSݞ1Óh^UG?2^O=(?7SwZ=._P pWV4`i&J=8R/C`8k7k.x$qD5YJNQ~}e{&ٯU`~} $B_QFODZNn["1\.w,'ut$w,=bn~O'~0?1 3 H$~}O[1Wc4~_(cn4a#7S2_y2Ǖ_O_z}(+SYGГ]#_Tm){Vy_Bxk2y5[&6ב3uۢl[UVS%TyJƎ6='s=ΘB{`gZ]= ,˺>yjߊ&Lt[Tfhv*T5G+OײM;sBBAyvi~S֖=GؿU- St]t +{TVo=):}yvԎ> )l2A+h -eZ~&&@]}m:٤-q<{bW!15j3GvQĬgWpcF p)`?xLj=ֳ5?ثcp,;HTVqg71ͳЎQm쟨CMUzm~EbG)y{rW֢QL_kf G&WE>+m . z 5Nʀ>dNVOAD7is5omQP|G#}~SOa Ob$w[>{cS=p%OXT?O>V훬ƾI74ZqG73''dYjo?vۦv$i]?{)&bQsy^' |\N)7ߪ e}^3ׅwI>uZxOU:v^4Px sHŻ}xQymKV\|R`nA Jw&B)g}vC|ܴOWOn8jh3G%p8$/Ǣp81d$}`q5BKްOs~>gּ_a'_2Zp+kڧ#ڧG_^q?T}Kg}X>5_/R>R.اƷ(p!*6}Z:lp*|Dt٧x4 ٧1{ٲ}Z=Ӭ`%+ۉWh+yn~׫اԂXwhk(<''~nH~o.;Pdl)vۦ٧%R'')~N1{ AYOשʬ)gV*L'e(O"=?_֭̀PTX/5!_0{w%ّKv%Z9mu[8~-bp UՀpN,hڿh QnZG?8\9r7we pGk-gvH _H}j f.Tڡ^YŅA>7g!fR.qUm^eX冻™ofŎhJ}e}:[~XK._vBP ߌyw1P&i~H v .ķN}g9Vl'n+ aNϑ5-y >,9.ۿN(n%ONo=ǕmY/O-O.¹PA7Ng;|`v28f)_L~p0~N遵!QL/F27ۼGz`14_[rB8p]3| 6}c~9kp=^4m:{l$z̀聬{9us/|*뜀_A/HO\۳w#|Œ17_GyVt( j]# ;_BRvwnOTUoW8ۗ).ݣ2ցN>GxtL!](MA}yG*;Yy1A&:|j7DK}72|-٪W{v6i] :{#S(*0;a~>RNݰ 1탇{pX>(82nڱKLV9xA^_HXTETy\LSʾ ߷]:d|lzBm[!}3cu_M'<^I9c3=3e]s )U]ʞ*6>.U;Ubv<)"TnXdoځΣ.ӓO k%= |v  nv)LS8Vr <=h|w^#pN4bpIui݉=*ً];N,rc>W8PBzgEO] :lzϤ/K6c#YCEcBo4+0W<_lj_нVF}XD (54Lrp^(lX, nSRtؽF%Y:dRK8F~z8[=]D(2S!,KY6=9`w#1BَO~mw2ߡbRާXjSĻ{)RF' E|a'34I<`ڦO/d~ =˾d?F`iF|)(4$Ϥ22H>=ʜҔvUWlLaLWM½w+6>h TѴ=s9u]-7*vZE݌~ 83HN{)[a).B2B~Nu҉K_خd흲OĶ)BǶ#p >l ߢ$wt{ɨ 778H7i}B)Ӆ.4ڳm\1/J;\Hc/%|y~נyv̄%v̄s,fP6z/fz 5|3R6ĪtK y7R铻P=p<\59Y&,/ ja}/oVob/8'Rwg\\rǍw/Wys߽ӟo8b_-mw^5\Ϙ/d p C]O4fѿu;l/߇:ÔmYiE;a ؃챊Y#9ʜ]_p[im qR6AyR9+4Uiq{uuJzD;[Nu gM|}C\+H~=\d/ߚH6p(P^T0S&\x~`DCdA:>D{ CtBM;35h?I?Ce.*cp녣hzmŜ*It- Ms 1JxS4/4Oaf3v8f[6tV#%b{vZ=9#e=X'W2d\E^<p p"Ow (gӇ N]ۖae#e:D/a2_n-c}zzmӏ) lp`w|Jq 9T/qQfEsyl{"y2N"%*ݿ,ˆ߂pRqbzL>&sdιgt.n(@7Ҝ?&yWŔ3ozkWҝ> }"Qt!GWRplmbx>:NY{V;2ppOj./Օ4iʧޙU_S٦XmupWbp18$cwYGWuz6]ͯ\>㲜LwP4S|Vg|Wp ؘ1Es4/<#>Cڝ\.G?G|Vvy!2IC|hCGjVQ6{C>Z==/#og.W}N1B֏~!&<++|F>\c%gW"?5h~yG -M!E<R/Iky6޷}i|SplN1`F쒲:^㚣L2>{ }\9C}CfocypA[=z(-Mh[BHV3j6,2|kw@rE饪LH;JCh3FWOnCo4n`r"9.۾czM|c-a݁CV ̯P7@ u \툿uG/nx8f+aږ|WC`3-tܦ7`>-R.rR!.!4[nqH(niC0,̗3+ vHtr\[}%99DmX|]-ɔľanIiXG-'iľk ~.vzhh9_wg3Ǡ1d&o٧zxmӏ) --Zv eu\Zwٛx'Yr6+;zZpvIo{QٯS 7>!<-'ttcll&&a VhA^H S5Qeh0Es|bwmSUmS|;"xet!Rw a )Քk/bݲ=2lN2ef{ƤGw}^{4XvC,HS{:3ɚ G?~ź-ݮVsBmct4 ފ9}wH0ٔ q+`_@ 9  xi M(L-6i])%Cd(hBdLTaBEv諮 Xmܣsoz!hUGz =uHz]I ?3;{΋.RcpGpԀ;0| Zf-{65[;0]p|nCŤ 򕾡7BWޢ XW;4B!sY8)T 7Op||̧jj>U-zrO]Q潥һ7ރ[OW|g~gyJgy۾gy}td;bŎ{$TGw v[>%<ź#ޱ?_p|Efj7Lm;ވ >M5>?`˓$aJ1|([ש^ZUL=|Gw[f~n^,W9OT_ɾS~%_of{Ɵ=6I#tlE~c[% (7 16'e88XeJYeQN;ѶsGp4)n4wW뗕w`c|UeG[vR?R/M{zVgV O4`io'yVЍ1AO㌽uҋ|ӍK~ݱg 2x=b?7]9ynQoxkdhEa3UXp)Ъ@=`tܮ1\o+yΊVi,= ~-ە|& s?zivtZoM5zבQ@) Ϫk/D56iovޑ63E?e6w]L1 ϯa_m;Fۢ*E?9CD33T[NvZ(^5ԲY#p?qWm)C՟lzRI~"u: 㴎vgkR^R>l&+S!2h۶+;eƜm풽Ѭ"1]װ]WC(cUS';Kc+[Sz3b:gX*iXm+_wҷ>]J[{)lwW  #A>!c-u2ݥ0Uq By_%}k+C}5] 3/%1^6HutZ~U]߁|UZ9OUAYg0բMut2 ׍D3ԣ1G̩ x_*߻mQKg`/*8e_BxyLi=1Y<~uiU\N;pϾnFW1W~LN6]/h\T+^xnr&+~eiWW w|]BjU}/b+WuǠt*^Ѕq}/Wx'׽Kt$^ǫ"aJ6yW)J>B8oky`W)nW =s<,סUʷ)O񹢯r1v|e,,G28 Äëÿ ñîçäàíèÿ ìíîãîìåðíîé ìîäåëè äàííûõ ðàçðàáîòàí àëãîðèòì ïðåäñòàâëå- íèÿ ìíîãîìåðíîé áàçû äàííûõ (ÌÁÄ), êîòîðûé îñíîâûâàåòñÿ íà ðàçáèåíèè ðàçðåæåííîé ìíîãîìåðíîé ÁÄ íà íåñêîëüêî áîëåå ïëîòíûõ ÌÁÄ. Àëãîðèòì ðàçáèåíèÿ ðàçðåæåííîé ìíîãîìåðíîé ÁÄ íà ìíîæåñòâî ïëîòíûõ ÌÁÄ. Äàíî: Ìíîãîìåðíàÿ ðàçðåæåííàÿ ÁÄ À, õàðàêòåðèçóþùàÿñÿ ìíîæåñòâîì èçìåðåíèé: }, a ,..., a ,..., a , a { A n j 2 1  ãäå n – êîëè÷åñòâî èçìåðåíèé ÌÁÄ èëè êîëè÷åñòâî õàðàêòåðèñòèê îðãàíèçàöè- îííîé ñèñòåìû. Êàæäîå èçìåðåíèå a j èìååò ñâîþ ðàçìåðíîñòü p j , îïðåäåëÿåìóþ ìíîæåñòâîì çíà÷åíèé a j . Ê ÌÁÄ À ïðè ôóíêöèîíèðîâàíèè èíôîðìàöèîííûõ ñèñòåì îñóùåñòâëÿåòñÿ ìíîæåñòâî ðàçëè÷íûõ çàïðîñîâ íà âûáîð èíôîðìàöèè Å, êîòîðûå íàçîâåì ñòðóêòóðíûìè ýëåìåíòàìè: }, e ,..., e ,..., e , e { E m i 2 1  çäåñü m – êîëè÷åñòâî ñòðóêòóðíûõ ýëåìåíòîâ. Êàæäûé ýëåìåíò å i õàðàêòåðèçóåòñÿ íàáîðîì èçìåðåíèé, ê êîòîðûì îí îáðà- ùàåòñÿ ïðè ðåàëèçàöèè çàïðîñà: } a ..., , a ..., , a , a { e 1 1 k 1 i 1 12 11 1      , } a ..., , a ..., , a , a { e 2 2 k 2 i 2 22 21 2      , ... } a ..., , a ..., , a , a { e m m mk i 1 2 m 1 m m      , ãäå ... , a , a 12 11   – ýëåìåíòû, ïðèíàäëåæàùèå ìíîæåñòâó À, ò.å. A a ij    . Íåîáõîäèìî ÌÁÄ À ðàçáèòü íà íåñêîëüêî ÌÁÄ ìåíüøåé ðàçìåðíîñòè, òàêèì îáðàçîì, ÷òîáû ïðè ðåàëèçàöèè çàïðîñîâ Å îáðàçîâûâàëîñü íàèìåíüøåå êîëè÷å- ñòâî ñâÿçåé ìåæäó íèìè, ò.å. } A ,..., A , A { A n m 2 1     , m  – êîëè÷åñòâî ÌÁÄ. Ðåøåíèå çàäà÷è äîñòèãàåòñÿ ïóòåì îáúåäèíåíèÿ ýëåìåíòîâ ìíîæåñòâà Å, ò.å.      m 1 = i n 1 j ij m 1 i i min x : e  , ãäå       случае. другом в , 0 , a a если , 1 x j ij ij è ïðè îãðàíè÷åíèÿõ ; 0 # x : M ) x p ( ij * s 1 i n 1 j ij j      . Çäåñü     s 1 i n 1 j ij j ) x p ( – ðàçìåð ñôîðìèðîâàííûõ ÌÁÄ; * M – ìàêñèìàëüíûé ðàçìåð ôîðìèðóåìûõ ÌÁÄ, îïðåäåëÿåìûé êàê M*< . 0 # x : ) x p ( ij m 1 i n 1 j ij j     Àëãîðèòì ðàçáèåíèÿ ðàçðåæåííîé ÌÁÄ íà ìíîæåñòâî ïëîòíûõ ñëåäóþùèé. 1 øàã: Êàæäîìó ñòðóêòóðíîìó ýëåìåíòó å i çàäàåòñÿ îòäåëüíàÿ ÌÁÄ i A  . Ïðè ýòîì êîëè÷åñòâî ÌÁÄ m m   . ; +x lv^lζҲQ  I1#:q(0G,|BK/mUT‡L0NL+Q6p,V27$nгy}חw[[y<9<_9oy"3JRH$G!=E vI"ݓK{ݵv^&NrNOpfvo kߘk?8melLl?2Witmm}HOJ-q5D5s)SV-·o`* kwD>k?24 ; ߉dF*kܠG]{QL)ՃNfLZ4>wvuݙ kYĈ@[M5,mqȶ4dV+is,ճoX 6B5:Q̕ѱ~ v_ÿ =:f`zuC< f¿{1N:U/b{gc>ioKc "1} ۓ5@'Z?b v`زx&iSuܮeF8B[@I^^* 𛨙ZrnE ?LWazju} ?qr\*<6`EHrQy"ɹse3XUi:qQN0#g=ggn(ܨQ~|wk4[$YS!sYJ E9OqVek/6Gf= @-Dw,s^v"4ܱ6~ܿ\5"Ïv Pgޱv* D^dh^<*\KNwj˹$|XϨ#2XyR%ĝNM[Y珡ή|}M|Yٻ}k B}D8 nP]SnLOCT jdL 8w}dK|nBG=}I|8LtMյ9IZ6}}Ӈflr{M[qyh7"4WsǯӹY7޾?ߎdAnUܢWEWsb>l|s{o!4@#&K ?O?3 @ o$8¢ndV~4bӵW{x{bzImH[o| ^)M,'>Ne̕j*tJ2 zb(qeTˣ@ۍ[/@?0v~~"TM#,1_"z$yΥy'2S+Y3:V7׿bi/Z((ǖj6ά"./Q;+A?̞Sx}v'?tZwOݍ=x7}P}jޮt(uO.zmǞ\} {J]=gO)x.vݞ_ 9o+ܽ YPf\f$h=Ӧa 3f ><¿0a 3] >FMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10  v6 V0f6n6(16M2HM/M|61GD\{Xx ]Ew`"6) B5D!&dB g(Aԋr #WgGa4h$Fd;]94TkժVZ%IrmIr܉#sJ(J $=㒤-[[I)n{]ܱML'|K'ӓɜd^0IJ_1r$+Z oUA AgTn7x:S7v[_<}pG9Lnܾrr8pmd-O)(/7uAYIG&}"LŖdi/ Οa3Ds3ZpjSE#_c2M'pQ%Ɏ>pv|7m;h>r-Pڻg'ot?ޑqv"R'0M< 3]'Gfԓ?aSi}-^O6_  y Y5=Rl(Py")P6{ͅ!P6ݔdd2oMm^huF|M ۜ|_|;[rsηo u |;XxNo37˷{U?|Ço1Az|k6>uOIrg MwkL\4Y%$G)@:YLV3ɋSzJ[^Th:clQd3K_rԭ$ #8u}k9tag:[%7mMn"./{OE*o) >Gb*f"*4鄭k iS/h&K_>,پ߮HwʾX*{lYirtr4{ճ~:o_'mGgmYAҠn<uNpG}QO(-֭HX3}|sٽt$3nzvQ(.Hꜰ-$<*\zܢw$ޝ|T~P=_CT'+wRf(I "xX+wܾrVǺ\"ǜ%S_2 &+8ۣ.7Yebf*ϲZ3xyE:E@G $34L@z B('J6;z,'sb,SOX=79Csv>hhC~Ț2a4yqk.b̯T|L1vhz.>cirtBwPOW]D9h[fR_w R:<߲_Ai=uo۰akgu=4zV~ցEvJc~_2֘Vok&#ާrmW(CY%x@{![Bp`˱>,ra1u˅x.Wb(2ȥmޠb6ZM4[T4I՟ЦBsڻxt{wO9`eػ$_w wzХV d1c@j~-4F䳽&Ձ]Ή:5gn?Xngrˢ=+OÎDYZZŸ5B{~3I4jOkݫWtu{m ?ίr@*/d@okF9M;Fuc v3;{l;r>ʲ]ɢÖŲ,gz6 ^h6f]-f[vlo2ى B6Z|'oMJ1T^nۮֆ6(-rҾ)|]@>eN}C5JٗkT~`zkl. %[PF, fO#S5 i礦Sۗ~f$\2LYfCl=U%2ܳDܾI}%Jm;=Ҿp>^ݟm`c{us:(Z({7'?zۆO~ʶ,(`!մ ,w !:ÍwZ_,fpLg|E po| G>kvM&1U Vt )4D\Z_mėC#j<\f.%UqynsѦ]\7vGUc6풽=06kěke\1xUQk̝Mz{}믏a3</./Ï?~@9O| Cod].K_<2e|֮σs3jd}yA1y69x'#<"qM;Fu ; )B|_QGׁӕ T|\;4G [2_C;kNX5 c=5CӚ/U'4qѳ-ڇljWҚC|8Gr%a)YykyB-ѫwY 7[O?_a|3µ&LV9$mWڥK|.B| z_"]+/í#cp!_+a,>/Fmfhӌ# h.٤K|ۤzW56ܡ^xU8^qk8֚Òڸ.}M87Ww27'{Jh +I5#wӂydj'Jr_ 'ҞI =e|);SyEF9kրz;WTߍʅz1}xe/=ʸ^nӭG3ik%;||( OvѾ=m=^WzYF뭙9?\BȚofF|<ӕȞ_P7mT|;#cX}sf٬9%<80pY}S:H.kX` =ɣE{D ŋi. c[x:EU{ dQz巷-rܢy+U UWdJ盯wGJAB[_%I7wqoOЖJ\*zhgPۨޏb pVe\dʹH_ݛ֏h M33(I$d-xhȟ+^0O~:*|>IV%~۔Wg#?>ڜ犜+i-uU9U|-E p9*Wclr6-au%>Eclqripqp|^.5?䌟w]+{~ɺzW콫y\o{M{k.9P0 )q{AwhL<~|wDwS'֨m'ȇ ySw٢mQ^}ewfWo6XW.~2V.l;zTSPNHi5>oN;Eӽ8Zi]Ӎ_cVjj=-}=!_\[${qq+#Qxʱg&ٳT%_8¯ٳC={DQe{ž5_ #T^|ff+̞/+l6)|X$ywݴcTlЮ[h\"[}ߦ+(fދ Y;[ \&vmދbvBbHI8t#߲!wv=wɫwB[PE'į] )+ޥǛnw. wn3ğ;7ڭ>r][fMgV mgī'y*k4aa7.t}8^Kps|р-U2sz&;L*}Mcp ׷h=Z_ Z}GUޯߑ2d{Z.?Y5=Q@NQ^ }IO'`^ vT}6ukOܻ<`N3bzZ/y]F9(Ѩ].^UI"bxX/wd.$xHnj7*mb8Pޤdwdi)/m焇2J?WB|4ۛf}6V}uߟ!w`>+wcfN9֟c/z%G>(#4p,e(O{5#?B<zJh| :鴁r֬Wv֫Mk5–f(T(t^{ݯ-=?M um7]mڬׅ_'+;Ey۴kfi[Ufi|'U|-ElZsdMGی M0~ƌ1(1o{ضl1U6LNYA> 6$lflE=>qnj?J.fpd;jeȾ8T߫:]tXX¿m@S6κ-Ɓ֭co:K &'dw/~ pi ߸ap?A1|(c˲rloXOAPO[Uȟw&9xgIUF<㡬Vs(//1Ϻ'4*I̗{_ާT#QyoVZB-'B[2 O|dЧݏBHbpBi1vzTm1||^Ue({+ %+ߛ܅Zȩ^yP/8/OJ|^DL t^\җ]o6 X7/eu` mn9 g0[ah xǁ#L:gM iuF a/pϰ*T^ ~g ?ɷt^/ r;UW辢ޗ^ʍGԟ}ԗ=䰽x½ α6,Ml(}5PΰUg:7:p(',*k73da#p=#|Cs |]}pփPyYh-?it力֡p խp~;?_>5;_@o 2c@|k͓_Kpmn|?};fЦ.޳s@o=!WjvPkOq˔5Jqti M͒E%}anO?7^#wpwk$o)Υ;4 WzSz=[\+frޢ^;[e٧=?d˅=k/(~JvZ-AX9_m'w8x-N:N#L^X2 -#zCnVxn|X|𒧧Ҏ?_Z}Rn;y!z\̎Mxm1)ꭍ/3^5KsNE[.q&fM뢿{{P6:#wa_c޸d(6\x(A-rˡh/Tʡt #FtEjO^鹳d#wJ 1dNhkY -w)x@vu#e}?7(wkx3crFS_l 8 ="V mk#x?G>QnV+ ) ~C+¯vT f 1h~">)C _nL?jviwݴc8[,GT[\DZ\kq@6Y)9ĕ*o+M G/BlFmoϫ_|Gyvb[#8x(}C>c*ZY#}{Mg͞ H:ꢑjrC0TFmUc|rנK 5}eޠMޢUG[)Oz _v1Ok>Ki͵Gϵ Z{|yej=];ZgEYSu[p s-b]T>{\{9r?O.! Yu6E.6'ޭ-N :OnΉmJ] d?'R.o9r<9wأHs8Y\xNIZ%̋5#'alqҵ#:K'tw|A_tvYStYZ֡^<yͱs.8^u<`\J)g3H^)dDѤl5Ri"v਋'wv}5Kq`fg=~ġ#(?ݳŷIHV8;ymd];2B,=++ ȹ 1"rqsbc;,Q DZ#)}cF*ƷI\xu.׾ alܛ KRL- ,>L;Y0py|Á8t 8W8r\QrmJ3Ƀh>]yur<<}S-b+q'cVf)ԛ-4>}ހV!iΧLhz]  n""- GMO{":|?{],[co}u1xs -лG!Va,ǟ_*nUF R"TȡK7|$DC|l<v𕿑h|go9AdMCTZ^nrU]!>mz[- /Y~~QňޒߌcJs3F딛 _!<) ky/yE~5r] o|\BYkKl|'6fi|!7#?=Ns3jd|q[{Ep|5r/<ƈ̵Ê>^.fCo}Y߄wyWw@WG{D2CirCyUIVOhMB|3_ie͸ɺ^O _۠ZyoTLC!Ƭ˽gMOƧG6AY֨a#NYaǁ1n~DX{ ^Mv#&uƁE&cV?Ѻ! PRMQZ\Ұ~uJdluE!o ]U8}>0.ыgO>ir\~NG!j?fs|sooKɏ|UP׆k#sx%ߓ 8 } .\G#S pV;5A18g]o!۟PnqK*8˸[7~]z#߄Cy_~ɋ#p4 U׆>9BSI^-W=f<ͬY_;4Z_{[5/.+|UY_W:Qs,N& Y>տ mk#pqh~Y:rDs5r/z[_3<;d'_߽߆ v̊}F!k^?}.A{@x<>Ex}uS9iCy֠Ẍ5-rj.~|QmMKO\xM;SWwnDz;)92"]U[A{=x`&[ޯq{Ń4X‹Ȟul71Uǜ{4g[Wκlrxͣ|K<:$UpY-{.Qmo?9[Z1_Cw_1 |voya3H3|mKv¸K%>jPaOח>oqٲcR9v/ޣuLؽm㮛vTٽجKv;]yWLqr _ɧ<6mޥb67(8h,oȽ'j[*?[d5enJqkU2n{Jm:63z6SgWͭ>j /bs_hY㿘@)@SǶ2_C>!c\ YN 5ڽݒ o.K3S.Ӊo9r9A< +Z"Jc&9y{Y*ݜl{5k7rRZ}Dzs.>+qs7E:I)^ޣwN}+Z?yw+Hܧ 5z_LE»Ju$-zQi'-&QA-]&]zCu~Φ'6 \ X^ݷ#Nsyw\>[a{SXg+[x\}' ^yoWZ}k 4"xzT)OHZj0Nm;`!M͠ik+yNr͟ k8'm?ȍ 5Y̷c~7.F`gx ^G)mq{\<@}ه58kDz*ԓǔS3\w>, ڧyw?;tS`vN#n࡙)cHX#R|UrD>pv:  q`o8MyR }Niޯ9RH5lK3|=+n9L<^cd,0J$ ~G?h?+/.K:N]#yGVctFjYOh<ʹ~1 n+˚:y+qnK[nSy@^'Op;W 8=rwj|kȹx+i]bG ,r˦O/(y_5P}oi'qԉjs9*zGpڗpqp׻8wi 8Mrn+.7n/=z) 38\X)FtO#u "纑K>}&;C'+7Uy=&WQUpZJe J7%#9+C{4Cz#?lxl쭉<)}K`?m:4&c~%3pVjpbpaJ34&^[tu]+]׷h/#{\w0EXÅ5;X굜0{Yiu;\U}&C@ "Z3ge=FRE/^הcTQw޿}B :{J"cݡc->޿~@|9T։|_+QnJM׉V<y8~^Wl DZO japά#Y/$Zu(>; ytOgX`a]~8*ϰ<ȥrrɧ´u:]eၶ|_2"IN*=c6U1߯<.U~7HYKwWg\fו=\sOO4%-} Y9v~j}U~ ^#OՆ^3zv:!8Ny8avyNzpQ#=C˙gQVC63A(:ž &< ]=۷ #oi);l~|o 7Ωm#7N>PXwqa>| qI~Cener?>m=eP-hT7l٬|[owȷ?6A~%߆[|P| }oQ~|KU7ߠw=5n1`fowȷ?6I~ o*9 mdɔ߈t'5run$<1a3_BEfsmo⯗ 9}QNURȣ}X31;w!V[˹.\"Ƿ/\yԥѺNW{4,HJfgs g(ԍEh Ks{~˕`C홦߯49Z-a;Kכe3LKޫWU)uuAܯG4Tʄ,YpMqYܚוfbo q̅ri3y,3y00^ߩ8|I[:F㲴|4R:N9W1?L}Gy* <1.,9/ORǤ$M?h;}-8v_E}tY-W^{K /!*;Qm_PHiin6GR&'K{|s3 KeIޯ1ʝZ@MS/zmVr0И~G32o?d XtJGgS)kZq'N=iw* ~.|ۼKix؈ʃ'Ƌcۥ#N,=S'<~&HB9Ӌi䝂9An00+'I23OR]7/|Hf82` u0W۴:('m6PGXmr? o}I9l?98UAYRr1/,#?3s >qB1XӦS=ў6rR9no-_?y=13w8U3yz/iQ/:LgwϢL沆,"WwA_S>.y+H4u^6Z!> U?=hQߦN7'RV2'1Gx>!-OA{!k9d <#'K=G}N/ûNl_ ~S/1~km9Iӎ봃<&X;|wˑ\uSn\WށFK۔J;Yi1Z=gt0 j~m,Ggrā}pّP3hH,Ml+/so009!DM|v xޡYsidO3{q Ԑ81&zTOh|1CGB88)QqNKf~F] X .g̤oHN9Sǹ~5m9_'|_TqA兜-hﰸr ̓gxy~羬 c)3ʡq4HH/Ӓi-t/F3˲,\(Ō;)'0IoyavVs@7 0m1?Ak/RY²;u.;v9|˻nړc!L O`EaBm`/.`w*L9ϵm AJ%7_WQ N,.x*<| ٘>"{}Mmc*.M%W7n0o<}>2m/9+ }fOۼ`#rg:J`g|aB׋n6YQOT~7E;2}' 7,,29 2 øàã: Ôîðìèðóþòñÿ ìàòðèöà | x | X ji  ïðèíàäëåæíîñòè èçìåðåíèé ÌÁÄ ê ñòðóêòóðíûì ýëåìåíòàì è ìàòðèöà | d | D ij  ñâÿçåé ìåæäó ñòðóêòóðíûìè ýëåìåí- òàìè:       случае. другом в , 0 , a a если , 1 i ji ji x     m 1 k jk ik ij ) ( d x x . 3 øàã: Ðàññ÷èòûâàåòñÿ ìàòðèöà åìêîñòè ] m [1, k }, l { L k    , îïðåäåëÿþùàÿ ðàç- ìåð êàæäîé ÌÁÄ p A  :    n 1 i ki i k x p l . 4 øàã: Ðàññ÷èòûâàåòñÿ ìàòðèöà âåñîâûõ êîýôôèöèåíòîâ ij v V  , ] n , 1 [ i  , ] m , 1 [ j   , õàðàêòåðèçóþùàÿ ñâÿçü ìåæäó ñòðóêòóðíûìè ýëåìåíòàìè: jj ii ij ij d d d v   . 5 øàã. Îïðåäåëÿåòñÿ ìàêñèìàëüíîå çíà÷åíèå ìàòðèöû V, ò.å. j i v | V | max    , ãäå i  è j  – èíäåêñû ìàêñèìàëüíîãî ýëåìåíòà ìàòðèöû V. 6 øàã: Ïðîèñõîäèò ñðàâíåíèå îáùåãî îáúåìà ÌÁÄ À  ñ çàäàííûì çíà÷åíèåì: M l ' m 1 k k    . 7 øàã: Åñëè óñëîâèå 6 øàãà èñòèííî, òî ïðîèñõîäèò îáúåäèíåíèå 2-õ ñòðóêòóð- íûõ ýëåìåíòîâ èëè 2-õ ÌÁÄ â îäíó, ò.å. ] m , 1 [ j , x x j j j i     èëè j i A A    , 1 m m     è ïðîèñõîäèò ïåðåõîä íà øàã 2. 8 øàã. Åñëè óñëîâèå 6 øàãà ëîæíî, òî îñóùåñòâëÿåòñÿ ïîèñê ñëåäóþùåãî ìàêñèìàëüíîãî ýëåìåíòà è ïðîèñõîäèò ïåðåõîä íà øàã 6. Ïîèñê ïðîäîëæàåòñÿ, ïîêà íå áóäåò íàéäåí ìàêñèìàëüíûé ýëåìåíò èëè íå áóäóò ïåðåáðàíû âñå ýëåìåíòû. 9 øàã. Ôîðìèðóþòñÿ ÌÁÄ À  ñîãëàñíî ìàòðèöå Õ, ò.å. ]. m [1, k }, x a ,..., x a ,..., x a , x a { A nk n jk j k 2 2 k 1 1 k     Ïðåäëàãàåìûé àëãîðèòì ðàçáèåíèÿ ðàçðåæåííîé ÌÁÄ íà ìíîæåñòâî ïëîòíûõ ÌÁÄ ðåàëèçîâàí àâòîðîì ïðè ðàçðàáîòêå ðÿäà èíôîðìàöèîííûõ ñèñòåì. Ëèòåðàòóðà: 1. Warehouse Cornerstones. BYTE, jan.,1997. Ð.85-90. 2. Grouðware enablers and business solutions / Morton Marjorie S., Holman Richard A., Bess David A. // IEEE Int. Conf. Syst., Man. and Cybern. “ Emergent Innov. Inf. Transfer Ðrocess and Decis. Mak. ” , Chicago, I11., Oct. 18-21, 1992. Vol. 2. Ðiscataway (N.J.), 1992. Ð. 943-948. 3. Linthicum D.S. Power Tools for Date Drilling. BYTE, jan., 1997. Ð.143-144. 4. Deje-sus E.X. Dimensions of Data. BYTE,1995, apr. p.139-143. 5. Èíôîðìàöèîííûå ñèñòåìû äëÿ îáåñïå÷åíèÿ äåÿòåëüíîñòè êàôåäð âûñøèõ ó÷åáíûõ çàâåäåíèé / Ãàéäàðîâ Ê.À.; Èçâ.âóçîâ. Ãåîä. è àýðîôîòîñúåìêà. 1992. N2. Ð.166-176. Ïîñòóïèëà â ðåäêîëëåãèþ 18.05.01 Êëèìåíêî Àëåêñàíäð Âàñèëüåâè÷ , êàíä. òåõí. íàóê, ñòàðøèé ïðåïîäàâàòåëü êàôåäðû èíôîðìàöèîííûõ óïðàâëÿþùèõ ñèñòåì ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: óïðàâëåíèå ðàñïðåäåëåííûìè èíôîðìàöèîííûìè ñèñòåìàìè. Óâëå÷åíèÿ è õîá- áè: ïóòåøåñòâèÿ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð.Ëåíèíà 14, òåë. 40-94-51. ; n-xPT[ ?Bji4 Bjf"iAi'dFPqPMi5ZCRƤ1MZc 4J 1ӪF&6'i o|R~ڙ̗{{wKĘ."iDyh: F]!B'Ѳ]`P=V/D(3>Z`七5~!6) (d=3ZLe3E*8x^'$ ӱ/s_x+"XGG][>~Ni&:,MH gXi$Dh&ɽ.Kf[$CV-n#^JxYĸ*?e3ӻ*[yl1se=M鑳ijLRI=++? $k/q$a3C"'JZ$H?qŌ*?@}%Q`r1 6ĸ]A=cGxiA79l/Iܝam^Y5}|/F)9?guK+Z=AKv{4^/3>(?-Q9kˉerꡊs]˖)gԅZGי}\W|#ZY;E7g~YsB|AL䇬#P`5߯9{wx=:40jPvcpuoI'eZW}c=G3uأP -O)~ ~sf|$rͬe-t}`;8*09"Vjoy_5Ҩ 8k:S'yklut ;}v]jŤиuɕnߣіY0gc%3cVيk`8gTgg9 8 8 \Q ;U^oT#M^|Y|h,~5 M]>/q|IxiѧȈ,sHF#_#|V #$6"ܣsX|;@RX!+@9R":7ȪkMZn:7ye(֟4dRɷչJ*.gF7>&k7/d[8T yL m+<&Mn߫+},y+)GFp ߢFK2'ѕ`1 3 ^gJnGc0_ LcGe/yCdl=h0XO|yˣK/h%Pӳ k](F< ǐpȽF= b'B+ȠokȤ=C/D;t/ˉg*{YL.SidNc=n]W OYEA3EOA5g)d 7be$ ._⌥kh oi+/ri3pngb/ m@A} <qS2 ~ *LzNKmpC{@ }ԟkҨVXoCBoN'/Ѓ.2B#Q^g`|')|qViq Kw]Rp͉1ϣAl;st~AƟG* 77cn5uAwn<~¸p*b50\^oQ^.߷s{Z*átX^gg˷rc}W`Gˣ;8^{Ow Vy0u6ka#r1X#n PO[+} ?_/w/cGZub l;9ZK &mo{_߲Խ{4Myxc}ӏ^!7BLpAo'D0 +Bhu!4Š[CwѾ(ڂ/Ⱦ!Q?n0 aq)\ +BSpe9B!v^/) QSUFM_QUoJ;>-4+c0[1>d f  }4"(Mg R,`,V\r2KAH*nӧg4<=JwgJ8gn>I֟ I6exYݸItחUwuXqr,Haꧧ7dc'/c_<;Cj9er. ퟔǬA.vݾw&E~seaDRJ[b2۶/,x숝BX*F/|CoOIo&r/>Ey6-jb,>D\RoRm/WO]ָ1,RW׆g>ھYÃJ9>!Xԥ,< Mͭ+at|8\`` C|?|)ѷ'ٱα|c,OmO [:9xT9b{V2F>Ǧh$`nX kgh>t{POshgx\mUn/ofܴJHw1 g݁V<2vS켪1%l>cɘʆTk KS4P>Ppp`guByz4ջ5yqA@]ѯtGl+OSL{ko)/W>3%g~ }V3h0 D/ 1[EIy@k45oYl47B3 /"Ey&{%)TzV*@ۢ"U,q&pzEBF)uCm ,uU!.!'LhsbrnB|jǟ=-c iU,'^ݳ2!ׂ^+zMzMz{y//D_+~I޼VO dx%̪ȜxN OkdΤzHa~Ʀ ȳנ|_)|KL<2o\x^GyvǵzL8kQgѯʕ_+EV+/:E{Z6_(VfSOޔ<. Qdx ]wifg,ytR|)0<1;֡ñ͟/cݎIGل1*7WcźЛ_Ǻ3/ź>{nS}b)nMehF a:!:~Y`ئ(}/l #aro ))lv8lTy ;Zax)o oE#6qm oM2OT^/xW[‡Zy L-( @1ߙ Q&5xHV^@ ,۱LꁷL[6r࣏.)t[F[Z/1mp爷ξ? nCтChMa%Zg z6ΰ˂7˾(Ev{6ˮn}h~ċ׏mNi;E?џqU^<6s]ms~lO rA~Xs>Lc?s۟R _:ۧY6"[bѡ–Xb[4S~>Vg&;~Mas]6(%z<^4mޜ+Ɗ1[W 8 ~>RȀFϡN3˻r[&v(@^K`yO[4چ2C>.rBeRo`W󚹍͙V[(޺y?(yϐf(M1><Ǽ핰T Y[TgxX ;#[%e&( #q6@]M`/HީIٶq=ӰҎy?ey6'LdyÛCnr{G%!~O'~p/eV ٹ~ߺ0Wu<3]y7E7'|buO Mu>1"sI3u+ H[G*U!fkD pra' S%^6]L}*=cA= \'o> 2u]mzrop."&^P wx|uʮtnJDŽ*U}6;[kq`n<ݷ?x^#`Bϭ=_vDUth^c>Bs]RtkMh/ԥ}6,-Ӷ>6CVǮ6ui+38A3>ӄ;Gu>@'cybxISg;^I8|'MYItnІq3݂rѕm5yuH/geݤWk6x@!XǤnl\q.\!+8eO@?o7])S/ x˴s x@ݭXvb$<g{n\ZQ8WkMaO87܏S}ă33:d_=׳1:s"q)~Q6?]'om!~aȁk~z{lOLXW H@}1:3"EhJgc`w_>ݸ+[8J0I|f|$a̞ucYWpi]02e䓺=N}9%cO\Hq_ B 3zcT+OXYVub>sUcqCZs)?S罶uD= ]YtUȴݜfs[.܀.j2)Ӳk{K~0N@ұ Xϝ]zR Doj{NS;@ZNf23GoRM 94G,Q7Gmmxê3gw } ?=sq=}o~C~mv-!PBv8_#9<|Γ eCضNWk©'{"GX̀]# OƱ_,~?r?u{H8ڊp3E{L"?5dU,Ò VPƎ/ٿ%XG႙ӽzϲsy<~ :E6o.-nw~UhPJs/J.6jg3=o>0 vArop"|j{6stBYNYֹqRY,xC^;ke+O`O/7<+*|jUO}Sjb"0ϻwڜFY$ձ#y>3y %=^(މB({'}/ F.# =#wQH}_;w@Ca2Rʽu:@>$9;M@hN){ejrDZwxCI>y*e܎Wu5cKd9_W}X_rgQŢut!)AI'vA@S2KiJ$xv+zoE/(P>5hgghMl;λt*Y٣ rT&nρ8B=pm/ƱGcc}- c;Jϗϟ[?ګq/nOyiH:>ݡT蜇V3ˢJ#~{}"vtߖܴcKK}= 8e^̇QKJټнhwMx\|^eUmqpË}Mv}uGa:o5;O6_s(h>pv;y޹i.ﶾI/ǒ!5[s:섾_:&o=_$EЬGB KP62)vGgvvJ]dQLe hIٯ|>>1\>y {,16xׂsks?^6}״|.|[u mBٺN޶06D95/4g-r,:o>g\ˮ|}@NQ?UpM#~^0S)y ř߼ͩW=ZpkqwCGFOz ].:'o}~ByBw=Fnժv{wZޅ[;BQ~ b=9>}ixס3<ݮy2/ [O'U1+: hDm2V ׼}>oc6cʎ3ÏȣWAֱN8Z)z\8=ʴeCJ}G_h,fׇxeTY^ wx|?D^kxx@8>{-:E v.҉7/ze`ݐ c<]|-2[?%:4Ͷ& ;-beMx59q/=\ߠO;g2ߐ pi]( {<.-U}0~:!u:vËg)\?\u,vI uL=B7P>57mWڶ/p>CuJ`/sO)rwۿuLmMf-J<ħtM6A13>4 Lۑ!q2v|ΡWh#)\O!1f7u5'dmc2æԃ}cp?9+K?LЋ% Є[ FDk:wMov} Y;;{Tw;E6wJ(O_Zoz$O^246=eRׁxl^E B RUr'Цq4gwrh3o, hFCub.ЦZ\XP< .-/dy͂v8_#9z]±§{%9Tm:|&kJJD e:/{,R;Vc`,Wc1v,\Phۤ(e}AhҜK2ۻƔk !Z+6ү's1]58 .=uH =x!dǧ.&eݞ򡃃N80Z2K> vyX۽Wʜl;w:)3hD@.7t 82)t2 g;Ј [8Uz|6?eE8mC.=~?J#avpu1lP4swܪf8'uXr6;} lЦMt"d*/0Vƺuv1'Ú7CN9E>ui\'#N^7#623}RmZ Y587o vrcp!q lTCH^)aOb%J>7'RubG?(O8=~'E|G */xѣA,9 ~Eڧ,R-#ײ(=b'gp|ć?w?Jz72* 8 +VŅTNMR[Mo; WX/!axҹu/Rhúwj]BGLL׾`[,ݗ\~.Խ˗dnozz{b\ D~¾6Hz.Gn%@M'5OC&޶G}g9L2[c c]y`U#rojlnxars+pj _ W?^<x/W`ޒN}KV;uMOE_ +|t]dl xЗw>;pޗWzoNE+Ph*2!swwGI*E. NGy%mz>M,,30 ÓÄÊ 331.45 Á.Â. ÄÇÞÍÄÇÞÊ, Í.Í. ÑÅÐÄÞÊ, À.È. ÕßÍÍÈÊßÉÍÅÍ ÂÅÐÎßÒÍÎÑÒÍÛÉ ÏÎÄÕÎÄ Ê ÀÍÀËÈÇÓ ÑÎÑÒÎßÍÈß ÇÄÎÐÎÂÜß ×ÅËÎÂÅÊÀ ÍÀ ÏÐÎÈÇÂÎÄÑÒÂÅ Ðàññìàòðèâàåòñÿ ÷åëîâåê êàê ýëåìåíò ýðãàòè÷åñêîé ñèñòåìû â ïðîöåññå òðóäîâîé äåÿòåëüíîñòè ïðè âîçäåéñòâèè íà íåãî îïàñíûõ è âðåäíûõ ôàêòîðîâ ïðîèçâîäñòâåííîé è îêðóæàþùåé ñðåäû. Ïðåäëàãàåòñÿ èñïîëüçîâàòü âåðîÿòíî- ñòíûé ïîäõîä äëÿ àíàëèçà è ïðîãíîçà ñîñòîÿíèÿ çäîðîâüÿ è ðàáîòîñïîñîáíîñòè ÷åëîâåêà íà ïðîèçâîäñòâå.  íàñòîÿùåå âðåìÿ íàáëþäàåòñÿ òåíäåíöèÿ ê ðîñòó àâòîìàòèçàöèè ïðîèçâîä- ñòâà. Êàçàëîñü áû, ÷òî ðîëü ÷åëîâåêà ïðè ýòîì ïåðåñòàëà áûòü ïåðâîñòåïåííîé. Íî ëþáàÿ òåõíîëîãè÷åñêàÿ ñèñòåìà – ýòî, ïðåæäå âñåãî, ýðãàòè÷åñêàÿ ñèñòåìà, è îñíîâíóþ ðîëü â åå ôóíêöèîíèðîâàíèè èãðàåò ÷åëîâåê [1]. Îò ñîñòîÿíèÿ åãî çäîðîâüÿ çàâèñèò ôóíêöèîíèðîâàíèå âñåé òåõíîëîãè÷åñêîé ñèñòåìû. Çäîðîâüå ÷åëîâåêà — ýòî îñíîâà åãî ðàáîòîñïîñîáíîñòè. Ïîýòîìó íà ñîõðàíå- íèå è óêðåïëåíèå çäîðîâüÿ äîëæíû áûòü íàïðàâëåíû òðåáîâàíèÿ è ðåêîìåíäà- öèè ïî îðãàíèçàöèè òåõíîëîãè÷åñêîãî ïðîöåññà, âûáîðó îáîðóäîâàíèÿ, íàçíà÷å- íèþ óñëîâèé òðóäà. Íåîáõîäèìî âñåñòîðîííå ó÷èòûâàòü âîçìîæíîñòè ÷åëîâåêà, åãî àíòðîïîìåòðè÷åñêèå, ôèçèîëîãè÷åñêèå, ïñèõîëîãè÷åñêèå è äðóãèå ñâîéñòâà è ïàðàìåòðû ïðè îðãàíèçàöèè òðóäîâîé äåÿòåëüíîñòè. Îáîçíà÷èì ÷åðåç S j (j=1,...,k) - ïàðàìåòðû, îïðåäåëÿþùèå ñîñòîÿíèå çäîðîâüÿ ÷åëîâåêà íà ïðîèçâîäñòâå. Ñîâîêóïíîñòü âñåõ âîçìîæíûõ ïîêàçàòåëåé ñîñòîÿíèÿ çäîðîâüÿ ÷åëîâåêà îïðåäåëÿåò ïîëíîå ïðîñòðàíñòâî ñîñòîÿíèé ÷åëîâåêà U. Ñîâî- êóïíîñòü ñîñòîÿíèé, ïðè êîòîðûõ ÷åëîâåê çäîðîâ è ðàáîòîñïîñîáåí, îïðåäåëÿåò îáëàñòü äîïóñòèìûõ çíà÷åíèé U*, ãðàíèöà à êîòîðîé ñîîòâåòñòâóåò ïðåäåëüíûì çíà÷åíèÿì ïîêàçàòåëåé çäîðîâüÿ. Óñëîâèå çäîðîâüÿ è ðàáîòîñïîñîáíîñòè ÷åëîâå- êà ìîæíî çàïèñàòü â âèäå: S j  U*, (j=1,..,k). (1) Âîçäåéñòâèå îïàñíûõ è âðåäíûõ ôàêòîðîâ ïðîèçâîäñòâåííîé è îêðóæàþùåé ñðåäû íà ÷åëîâåêà â îáùåì ñëó÷àå ÿâëÿåòñÿ ñëó÷àéíûì ïðîöåññîì. Áóäåì îòîæäå- ñòâëÿòü îòêëîíåíèå çäîðîâüÿ ÷åëîâåêà îò ñðåäíåñòàòèñòè÷åñêîãî çíà÷åíèÿ, ò.å. çàáîëåâàíèå (ïî îïðåäåëåíèþ Âñåìèðíîé Îðãàíèçàöèè Çäðàâîîõðàíåíèÿ) è ñíèæå- íèå ðàáîòîñïîñîáíîñòè ÷åëîâåêà íèæå íàçíà÷åííîãî óðîâíÿ, êàê âûõîä ïîêàçàòå- ëåé ñîñòîÿíèÿ çäîðîâüÿ ÷åëîâåêà çà ãðàíèöó à äîïóñòèìîé îáëàñòè U*. Èíà÷å ãîâîðÿ, ñîáûòèÿ çàáîëåâàíèÿ èëè ñíèæåíèÿ ðàáîòîñïîñîáíîñòè ÷åëîâåêà íà ïðîèç- âîäñòâå ìîæíî ðàññìàòðèâàòü êàê îòêàçû è ïðèìåíÿòü äëÿ àíàëèçà è ïðîãíîçà çäîðîâüÿ è ðàáîòîñïîñîáíîñòè âåðîÿòíîñòíûå ïîäõîäû òåîðèè íàäåæíîñòè. Áóäåì äåëèòü îòêàçû – çàáîëåâàíèÿ è ñíèæåíèå ðàáîòîñïîñîáíîñòè – íà âíåçàï- íûå è ïîñòåïåííûå. Âíåçàïíûå îòêàçû îòîæäåñòâëÿåì ñ íåñ÷àñòíûìè ñëó÷àÿìè íà ïðîèçâîäñòâå, â ðåçóëüòàòå êîòîðûõ ïðîèñõîäèò ðåçêîå óõóäøåíèå ñîñòîÿíèå çäî- ðîâüÿ ÷åëîâåêà è åãî ðàáîòîñïîñîáíîñòè ïðè âîçäåéñòâèè îïàñíûõ ïðîèçâîäñòâåí- íûõ ôàêòîðîâ. Ïðè ýòîì ïðîèñõîäèò âíåçàïíûé âûõîä õîòÿ áû îäíîãî ïàðàìåòðà S j çà ïðåäåëû îáëàñòè U*. Ïîñòåïåííûé îòêàç îòîæäåñòâëÿåì ñ ïîñëåäîâàòåëüíûì íàêîïëåíèåì îðãàíèçìîì ÷åëîâåêà âîçäåéñòâèÿ âðåäíûõ ôàêòîðîâ ïðîèçâîäñòâà è âëèÿíèÿ îêðóæàþùåé ñðåäû. Ïî ìåðå íàêîïëåíèÿ “ âðåäíîñòåé ” ìîæåò ïðîèçîéòè îñòðîå, õðîíè÷åñêîå èëè æå ïðîôåññèîíàëüíîå çàáîëåâàíèå. Íà ïåðâîì ýòàïå áûëè ïðîâåäåíû èññëåäîâàíèÿ ïî äèíàìèêå çàáîëåâàåìîñòè ïðîôåññîðñêî-ïðåïîäàâà- òåëüñêîãî ñîñòàâà è ñîòðóäíèêîâ Õàðüêîâñêîãî òåõíè÷åñêîãî óíèâåðñèòåòà ðàäèî- ýëåêòðîíèêè, ñîáðàíû è îáðàáîòàíû ñòàòèñòè÷åñêèå äàííûå (ïðè ïîìîùè ïàêåòà Matlab 5.2, MS Offise 2000) çà 5 ëåò (1992-1996 ãã.). )xklTU.}mKvbڒ(yJ)B $ZcDЂRPjM,)T#ښhDX "ۂov{RIr7?3g̜K'"8"KdGds~C"եwCDc mYUЀ*gKbR\j;q?s@_ײno݆gut Ct([HrKă3+l{M@<)M^TWL?f"^"~Zʍ[T(.Cdt0), _U. vٌQnǔk +1߰n2>k^O~a9:>;K#9?I[ɲ>+2~J/9Sr>xԠZ%7Z$R9AZ{0S6~;A=] L==Zv=X[)r 0ib!Id.K70z+X;S``S&O|Mp-(ŌKmTKM V|&:vr<lRx& !`t؏[N䥰+~E+@+#\*At<neu;V`?зK k/tqf5tOߧIag$5x1[ ľ|HFWpo`w jml~9A{PC] 0\ @6} '/P=7kB]@!y79q=skLg?g^Kx9j{& }=\'7MaE x n8a9i5'+ o3_Irdr !g%`җ]/} Uȍp!xEPš_ +3w~x?MO??c8{ѫm*>Tr1a┇x-`<13A/Nrk]& ?`.>OЛ|kGep7M`.¿s(bk߂n|1߃GlٕLM+ȻNc;FWb &9A&=WxQYGWw9V6We\7p3 7t+׏[GfD@ %r2>蝰·B6=2^E&0klX9FV7 9=A@=fv9v?}w$[&=)ݎ5WxDi5}2iSDZr+NSS,bc)-ewō63VߞrF<_9Z s:tN8p:tӁ:p=9N8p:tK2DMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10  : C$~(16v2/1X {xļy@L8~,5:M{iVmlӾ3mJ)IYbJ !$D(kE$! "")~>8 K_x2P26d6eCX!ei27\;og?c ǁ]r! b-oSF|4N .XYU \60] 14w4aYxptBUR`4 LUfpnғxqNg5w qMR3Hխy}=u. ~&{iCoeTKp>9=@sp|d@U*gznOm9o9%.iẀv36m|~g݅Oo{.9)WО*{V5-+e-3]9!O=w.R˼-$#'ldI5WR 谯T|W\X3oDjʙe|qKOO_5dK[2 ȕ5K~~IYzcŜJ4`HfXv}3nz.=ӏ(_:/7uLpEU]nf'4g7JQ66TR ?sSq:g>=K.cNxrղuMә͙:',[CXv"Yˎaݥl]JFM3dm3]9avv:MMg]1ve~A|b픹v~xE$SM\t ʸ#7YK#L 9]iجR'KXW^*dY&z?<CDD&DrN/Gc.NTXPʃ,_5?ˮMcao?Kwu3.KRظXWK &6T9}xjF9n=Mwe:3 јܣ-A%^)o?Xb_f;Ȟ@܄"U7NPӓ)Jٕ,H 9}rmˉšwW|3*ýxc;Wi#fdRܷg2ح(%~&O \ppE؄Y`E!;d~_*^|n3)dts7K9{~=pzgl xiqq`Lx)sv\n~3ybNMM|*-~F`gS+ Ul"ozd*eʌdrVl>KO<_6`FؽzƲ]{OiN+!Yh*>styz3̞hCOl,ڕkD]֝8`̯/Mciޛ?G"ƞo>y@5nѕaJ-~eV`dD_͝L\B`*ĉhI*N-֞\Zjmf$6է0dn-S1CHĔ{? I2qP2xRAJaߡǮR~s&p}t%Y+@[SYȣU@REڹ+brMtoYPrpWbZ_?RwqEvզV̘ݪ^B B"dBg]qq:6 io%rRvA%;_77T4Dg%lV&%d(H5vxL$qIlg4T}hs;b DCrP0&mmzFfvݏl#g XHE0a1; Yݏ7RϨ)Ozk73nס ]LLS@2D?npu58G4q=`-euiZB@p 0gXJ^ 5.IIk8 E2|RB")zVТ j,bJ+ZJa)R?\hs(t3[E+&ifg6} :ϹlL8KIsZn qByGlfp޴HG9 ?cpAa].RCGʨf /AgSFuHRދʌ_%VRW8g3o*R:JߟV$ݔiKnfF|HaZ^V|&e[ȡm]|do?m4X@Zcj9⛞#n"MD:Qww:yP/$.3dsj0HuLz{7~,R g1M-SL7wzE%3UM:lW~ߟ'uux-y\%uif%W{KLt}\fL vmdU,d$b,FmpB ,{0W(PP 3Jl!;ugWZcML(o/^'P=.)DwLc":t]zB<[0*>IW݇ya1Q )6Ye'NV9/: {SOgo_ҶPKjC@e ҂E'>7; 7O`߰m<$j#Pu.&ٹ6LzEsFG;jt]LylL[>0(gvMƩCQC3Cqp9[{V9bjq:U^o0 GKiE$'z|[ge]jv+@ri~vv5V*\2Hl@YDweLrgv=h:ϯ̄9FcV۷'4,*M!f?=ٔu`w.zóm?(S5Um3`S8_Uog,cOJ76zr7w-gZh>RwM-0KJq><FW4"Dz; FG˂x };Bک94,f(: DNG.*y&0lVsa` +_z~v*ŋh1Rbq$454c>N]o *d9C:4kuIR]*Vkᬳ@{Je|UG `}WT}Vm)8$ɱ=oHұ;ZQ=5oXi(}Mi˺OZHS}W)\FpVg; 3gCvSQޟbi~%Nu`@]* 9濂B@44}i>*whtMy#;"?i>:M΅'*9:3,݉|Dhzq双$A\#PgG%᳨Mેrۯ<М[`dB]#<14.7(.ן_7W0Rѯ`PIqPXOqNbkTr(n:`~A%TS }3n/xdGd[xM4r>5 & A "> adt0 ^^ۯGq3c0z^QC[ĿWQƂq$Brb‚Q)(QDvC̘T`}ņMщCxă"<K CDJ$oī M̅GG4G̍H.џ__ a[ K}ї!8A?ٷ^@kC~zFyN#}/x[!}, o.~?yF(w/,~e '8Ȩ +6mLWP5d_TGz!JBwN\T'lEn <1! xyO:aB6-$> }AxbDs!#DA ٽ_ nOv>hhoВ -b}( #N28mԿcg.C0juϐ 샭G1[+P+`Eސ x >#xQ1ACz%tDGWWFt$ %GxFC̃ CXL0&Z_c =P&څ!iъ|[T=3$NP c ~DGxԏC؅(иD?lWA'dB#*јȗ^$#ڈ5qd@ |>2;,a/o O?+tþ#9LqFy%@6FAHA?^Q=B6 lp~f[H!Q"<ӄM3 4.C#xј>DCx$G4͏:7ςtT'xT> |d{)Ϳ-r?.g8+#{9j;-Įݯ]ЦcGke@kj¹! ?} kcG?tFӀ@tԏ7*BKAPhlbm@m~1ᅬOr<{&FA%! |+vG>q_N@W`]{ϰKyFsG s A~HڇߙaUYc{ѵIO,s}@AB a !~F'DOOv!lE蟐d#A'd6 !@tD#h<4%pN#h捞'd@F6G~,a/qO9Ⱥ ѳBeH~ D{.9)oḩtP%:&tpA~xmxu ]4 @< ?A7y,cOy0ӏ=r~caPw@/B@x,Xx cco8'"9hٛS?D>h,NEmdsC~DwDA?14֟xGQ j>7\ v|%A`@^toh>HDr\'bh]Ga¹ y"&4V7scllC^xcyBݭIc(~͏h_ϐ|\Bu_Cm E%dCu QG2 >O$|%:*Qċщ'?ч6"QOB3O6Fг~h+Zְ/i4D_!}{IIFO@]dCkg@~‚s";H/H}P JBwD"@M l#Hs1!O!^ԗ3j6Ԅu6$OKIDt$ٚC%>~ER -%hsEuy#ܼxQ=F=)/@bh~C2ܡ c( ɣZH㠾l X~B| Dӯ']8_.'|4tJ4Wí] E`@TOYp&v8-T;w'SY#Veq9&"JR%(?{D8؅r߀Q 2+H}I$Cp ^*_t\fEe8j٘W\}J1_' gˉ6:RuUxQ/~W|kFJ@zLc^>vYo?~Ger-#_.~kuaw馫_[;kj& G[7ƯU)`ʂA#:paR:HA $ iEk5I)yˍZVer>$g@[Ycp Rk9Pě+AABK LpX7's1.b~ԎOE̾вthϜj7܇ TK9c.)8"F.\ERJ)ߔt`Pvd%mk~RșcQz C5oI2ս}(`Uܦ/rL@_ K¾H ?rBMW ]f\j]!Է58,I,TMR*~}_ռ1`aV4{3ᾏsDZzaֶӓM+9uTƶoV\Ks׬z)oٖ!z@ Y}74x?7rKإR]ZI-i s|g鐟n:uE x^csy^] 'LKhţn\ÒdHZ ?诶ggYoUsWZP0aU. ]{M{qK__ȒeJ,6y-`e-8??\!No:fVl"祃NQ;G63arOD=\s5sb5C\OZTNpx،-}U39~swoo]Q숝U= =W6eq6uILƎc%`ӓ'D )t#n,hA/ 5&.2~^uC qsMuj=\."OW""#4Y=kōlyn8(cVb;wW7{3^KP~hÙ"ހ8dl8Uԝ,TAvw#)V_D]/^YsYwdSרI]k$dn4:Zvs<R8Xq QDBI2 }tX~ySc3eyF|yk/*,}MYx)7tj~84OK7zJĩ&k @⽇Mg`p܂lޞNu}1 ).x\TmeJgĉKlQx_ ~z<q 2;%i7#{ED[%tY\k^{L˞q Ex|7tJS g`£ kQAX/"i'%󯮾rX)M W*HTT\ IRZe*J]T ]b-\嗭At+lZCAaZJFUl$QX \ |Ȃ &u!odtr^OIƏWnu֓dp\d+EFiG!ł ZbƧЅ/ |d K#ie]j];3돉v/*ֆTN(&FӖ-5ed2ɀYS;Ww^{Q#>W:$_εp5l]57k5dc.((LLY+[}pu,9qA)l^)L͑#> d `$dQT!Ê4-e,%#REzg(*@!LD6G<;rUڒ9t8.TDRaRUvng,ΰlwf ^|]9&9 4()/_ %+qby~X(o ;/Lz0T*uW>9 V(S?Z^o \;̴O =2*\Mƌ+c0 8׹j>34^NE7P =`aZj91YBC0<306M>&iw(/g5oaܱ}z}wvh7:hnc{+{ m(U#,޷ڞyViǷq܉WiA?=F=4;fvu,0rٴmIm*>| txsUN_@#,H/e%9}XUO/7''#5$Wtj|T,mJBBHms+vd˶0{x6SCC%18%:؝S5n5CՒ+>7IE@옽ͽF [2cj mC[$xP3Vqc۷EK9xWx]>K,qpEȰ0fHTkw a k bZg:'^jEM<OĪvk[bRfx`LeX!e}!zP ӰOI>>/G0͟..#MFDm)Ti'87*;%}FQ{-6WI?5a?^<ڢkK Cł3[I_WLtc7 .F9jC8) ?sr}3Jã&2 |zIؑ{z9`J@Ed[|Y6V0 +n"18iPSr,6!gOH?6.7L3'd%Ib'l[:qx,AT ?rpYٓwk99,Sb01]@:vfKy1탃PǦKta*<(>(.[hvd*03}3m(78 1ሓwx@ 9E >KWXd!ifRӓ]ڿJ}ž۪.x[z#j7Cϼ2_6+R4=v7~aˤt/,c%SՐ}NWM?:BqL˽ejߛRNE;0ջ}~=h<>7+Ǒ=>dmjò,>qʆ9g,ű弦F u' ľ< |OeϹaɌsoA>4ͯ86 b-|=Kfkg/9(fGҠ)ac^{g'6ilÅ/.>y\jP,w.s!аhy*2{=w$uxе3W.?kyo;lKjbق9VeQ,WJzn-5'kz L ̧2폜ʢ eZƟz;ײҳ%{w."S:%$ʹO.oVwV1%bfz%#ϪQI8rk{9Z5+zo"BzB([ԸS=5v[ 0աyЭ&Eg%jzR֧ݸ"%:Rë 3޹`^ټ7r/ KDnCw|v_k{{KSDլsYnIQ~ Yi͙`E$!/lr- n'܌wgwg0@?ǜ[Y-GfF0)T=, ufvs'ϹL-ΐ -ܟ%ӫ8y4K^Ǧ4rG[na}-4pQ\Da=x )֔ $G9csYif\oyOB^@~R;6 5nnVB|};x9ˢI(DF(8[kDenE$w 3_41YNDa\ϴöݔ%6PmqϜ;[0ݦP2}籒0ۉ6 νu!<+'o}M~ɏ׵YL[T _2*֙zRCy.ևW$H 3畤NO\C8A4>SwEÓ&Y믪rNW\p'*ʳl82\4済=Z_7w>2~K;Z݃&8K34>R%,%'$Ѐ)тݜ{ QAۜi9x/S{$7@ʙZy |+bkkDa%R6Y6h6D*t~)7k|=;5 BūL#epKctP!rr*Ԟƚw@~F Q#))i?]A>]Kh_ii£jڙ fl<2;>$1-G/ܓ<{o﷝qV=emeU #?=`5o-^]OWrIm? N=`Vbu21j?wniֱ:1̮f#œWxqLdͰk' yY/BX|oRɪ1z7,?39 r y9/$Q5,eъsWgȖF1ގio7-.[y=hv[B%lMHW`>'V3o8x !eƱc'8 =/2~ӣsY`+XKR%UJVm.ZRҮgA>qӇ[/Oޙ*>9$UxgS\m.kd5|*g( OITlޤpi膟'T&>k]Zc]~]BwR[)"ZU?$ #.ugj]VD%E>;}ak6} mH[`33 T/i'^0Me 'sW DW\(_۸vWaBvژOϱ9}MeKT6jSrAfDp`l@%Ken\ IUH;^L @lK6H4fNu8Lǯ%̝7ImU@S[JZ ͒KX:Gljs948X@F,[&J_Ǖr^Ok<AV26ANT JBD{|rKۦr `Qf.7+eӧDH뗯^o(EŪv|{[!v2h6.1Tz8seqhܫTB@jAD]y1.Jݙg ~G3Om{rəB"I cIޜ>-"ۙTxI 'q|6d򃮨'؀.HvTz|8|e$R{:4 x j3ɨ j\3ؚpu}6Z&iZk4ks؉A}1z֔G]2,VTOQ!`Qfr͌76z爞rӌ<Ŗ|r\c'n\B#7XTo6iGO^[g_P[xh mѭ1"~0GN5~p/gjn-3T/8y5\wwﲏ:fR (d'l(w͏x5i %8L}e3|~ϱMyt반rc]vپyc@YCwgYPq;Rh I6Gaƍka%ul߽r:{vZ;:Q7IB3yADHQK(ϼtU)ѡHۭ\/JrrQ=esaXd 彔 42׵=|3fͰ0W1 I2uD٠WIkE l$ H'U Xl0NO`n0jgoz NԷL[yvskmRZDNir5z*TD7A+tKJ9(e:rx6TuW1JةEr&G~aK}`檥Ek՝3+Dq?:KL(<>bC_^1qg. pWZY~+Ro/A8&+ak|2(.i)ilmy( `f=9zh_1`fxywcYP}~ /\A:dLlެvF*,g@ /1_&@kbsRӴj٦}& 3m*BJݴQ)E*DRDQ֑ q?Oyߟ羯>rss?in R'£| V$QT tFs|$-Y{7( ?O{='ۢp5`o%ߒ]0EخZǥkX,lE)}'Ɯ0T|}#M-hbE:$m;Q괇[d[Uo cl5m@sA|ٛD2bDHsZ|qEn #sUzPuQL-qhqإ&/0\0N`i?b}bÈjVT;3 #^n;ڀ5rt$H;~;vxa>vջ ێUIӦYCmhq05'ՂMshs]u웮l ",T5_MϣlL+ xw_|}y JӸ7>=n*3E"FS'~΍uE\X̸ke$wO):Y#uP~8$=o P؊|TM)x0^>"!+b̢hͭpP츅+8W 9\')zRWGt<̭vu!w}Pt6$#bڇINZD()-W.pt}#djNS;M>l}W-De?wģ񚔻jOO?]d+n, ZM\ba+K][pjhP;yO ^[4C[ODd^=P9|juVtWkG{UY:aH$fP,4{gپ=58@P_cwQߞNQ=n|_ґf7-:X'6P^iEJF؆s/Em֪HiS d%Q4_:aV\z &,/wOֽkm#kwu˺\b$QXEoHDC4 Mz(+15yc>JMʥEED8|/gXB@hdq-k ɭ$n̯ }_ dž$ z4z P3#1pp+4ŧaRyV,+elx{}՜fnͨMg dߔ*D 8TOSK.v&WymƵIx;quB)Nai.W -3/NU"hY.k.%Evl֘2;>wSNKjrL!>h HM}V5q)b'ϲ""9 [)Yf}*@aD.FԋKo ؋_Z97b39b0Tp9oiΦ7S>#wŵ!+SϠ dz҇N΋Aݐ͏SH:~꜇]FLv 4n͕&)>W2UnK(R),1!iA5CPga3%}PkA/Wdz0MJ`'n1om7X8 {!щY;nŽRo$KwAHaƈݖ.ם6e捋/7c;zry ">qⓌ>,m\W[H#Y4(G5."IͤF>7h?WDH\#Bj'{|A.s6sNE|ǒyDfO/Egk'4ݵ1Ml sG}@hj GB懍&W#f oR\YWVorx;|** WzPb#ڨ~s*UࡈX-$(3?Ɨ|tJGuwlCp%~uz]\j c̙oį r6] t#?b2Ob)OoT:}uVzT;FDx:cƿQd\^GFm2Oi3z)hVtW|-\8(VMhKjJTv곁)btRA*j1|M}0ˀwNSE LB_Y.ڍ!Ph4]#>}F[]СE( NK۰Xb%G^Q:Go_g=vR-Z֋Җ=r2'!#3fu|mS>;}B1'آn% Bs8UvDv>6E:m{}e>nsrj\јxKgD0)q9)16QOjʥ3)xB:'&it}YJ dUR&l||Oto^ 1{qԼ)X&pK6ѻۍEEt!{! kaU_}acޓhe#>OLgaUζ1Zu4( q..gw^&nڂgrVgyf%(N{<##έy!iFqbJ,Otj[ih7>ߐ)7V=kۍZB5=~  ˎ}۶'#z2}K7YYvMzo@)\ 10=-mV?iڣbZ uDH 6I]c)Zkx $I^^e=p.g e]kZ51[ADK !%GgI~eMyK7v\7ҩSR>פKrq4Nv~ka ̜j{A/u7+P8m#f<l*^ޮ>6Mw#wϛ"~F\r޺n6vKeWmk7 o+uv17" h}'2~m`v9&1 huFJ =G>f9ɿ]\q(LtV,Pvc!lQg)R qsh8i#]1׽xS6cW aFπ!lgN917TwLYFD$[% Ohu[0!AZY];nƢO4fkv{ 'nz?9}J^D.=_dV-NR3fH?[IM;#ZoR;''K{]j\Uv!*(uE> ,)RW'G5'uE Бl} g%WHKՙH|ޝh0 !Wl`z4813Юbyumdz2m-?4GR'M#[h4ٳ%B,/NP_9 s&fP2k4JZ!{(|c*Z"F~l/_ aU?:'{@z69(lvUv2}J+ ߎ̖gߔ(Wf913(G4I)"E׵9P_d˹/~ ]>]7!#K)͍aj(U7X7b͔gT*UdZkuΞ9jQSL\j ֪j:Y"1Fq,ӑSӨ>yQV"-8f"#7:A؈n WUB-x/:ݙe|frKFoe$S 案bz2@dz.t }6׭2MrKe2f"dJ;ԠFLg#]82GA腘FaJ)S'l4e[Ljښ|ur.pJ|aIߌNkܜ1zS$LOr޺9 v\}1t{hPM: K}YR6~i}7#. 'Tl.aGAHs@V7U.\*CtDؠYwJtoFwn"&^ҲLh ߛig~e^N>j"Vxn_FCf6^N) "tse[JthGFV{#iWWRKBM@cd˱r۔*qgvr*ځ8b|Nϸ~%t$K_q?3sT7lj؎tvdԨ#H7FxU)ȤY3>CXC4FϱrB+;okI f;ɵ?Yf=ghD:"oh4L6cR*D(\~k)C;Μlb_ҁabJ3c݌lL8A;~O^ !`.Ú yz6|!Dh5^9mlqsS6Nӊs\`+n^y 4ȷωlm=[};s!We] / ܊j鄺V8j'KYz(')&(,Kqq0]uocsߛ0pbWl66]ŘE-\IRGꚺ ZZ&ORE}¿ 9vN+9௩ o@>oM(Cx|^+ډgdS.NUk+Rx}!h5VCUk!j~pMs:e[syPg5s[K+FȨ&-+Xh%)(E핖z!C̀|MG})q{e.±ӗmW#ar:3ŖB ~&wMl&@+5Ddqx.;o&Q7B]" lm(,(FY5FH⦲\567c74DI`@MMLByIU=ɔIF3ZUSaJvY|w3=93dʅE|hf)e#ͨ˺; gw|uA9Ms-ߌG5G~yw9٫B;_ή~HʼnϮfnZ-rXMSh7ܙ3cMv>]hU6sҌ]<m9J-}5V]܂4# a=֍ē津l{ϔzy]7l4پcBh#C7U8H8I|wbApǔ+g86IۖK)G© npiWِ tQn w o4ܯI;"YV7 (`hg< odl8% rEL橔P݉VURṵ1o6U Ė2xQ`g*hҡ)1nQ0W^Hclu5O}WLpwJ+M=(Q*TWrSVRBB-Ǧ=Vo_3p8S<87ۡ¿6;Y '>zH+S-RA_`#~}RS$+m_ϒe2%(P5ybYֈ^0qTZ]ݿ땇hMגr`i]X)~e]xސ^a%""=6W?R^$@UJJJ`EXi+G+|<\,׺w?'srۺ饯_֝SNπbBOEZ޷.yPkUVOb<Ƙr44$'mH|[8M̮vgLJG9f=y4|m))̰6Rò&홭MyIk^ \q<&>L>i6U'ԀC?r<7W)ϠYdA"kĜ=y/f"僛?{lX,+8[ͰTu J\4Z͂ӭߋW3 c8}5䯱]T!Nxb^{(GJkĐ]R3b 'ϩ}+Uy8W]T9IyxNpy jIߝwƯ}=z͒ t _O+*BFR8^N8aMaS?2f f88>`KOlIc .!kBL?5_7'u81p 쒼_zǯ =#>r@p 00(KȺdR ! &a9c`O2Z 6NGT|c q $:0D Gȟ8;ׇXqS= p2k5%y#u'{ [P?Cl3(kAҪb= m&yt xm zO@Prߠ_ؘ'9+D|y [4a$4#It:\B6< 0l?IBKփ{uȲ@?H~A7o"W8- z4kǼ?ťh-+$G`gXVN>l;pMD$,~IH@=H$=($=z!tpPp!M7 A{ Op9Oϵ/KVx IC{I2$ ~AK<57I=LbMg07\wo88NLhI%OC7"8GIr uZ0sG` V%W=ħZ$:'&}9)_'@6\IYp!ˑe\}w"ːz$#i=6 s#(MAL"`` 7 semG9N8 s7- f 8w_P-;G': .6Shԅ:$-ȡЂJ<\톜ANw]Gx`lBb`w>Va&.;y @Az,Frj opoiIH^?HE: 2z{ M }ḺLz֏0VxO2A e'\IV `^ă@M8͒ 0||i=`\@'S?/ ;>=1'x.Ia iA,G}X0<~k0ːmUomx۶~xt|?tF }d2\ .0#\_̍`f o6q_d0&g%kgv Dդ}r@ pelG(;n\]PhGr< 9b.;9nƸ_ g6B_ʐ"eB88I߱O]9N` Ѽ0 '(UgÊ-xLWZ2 Md "s*F_78O9M0i '"4F9M5y Ae0-N9 48w4@-@VKnN&[ 'G/0)=sP(޷9'cRʨ18z x"'x7}`,x|c=1 O1~#B0$H&'MQf90xW0~&lr>8տx6X$}'M I O<~ !`0}sm%u ~3%$ inA16J4W%yƄlq'^Odul׺40l'0m^{b:uFL: Ӏ[`03[d2Ys2~}nN0ݏhm?m p4p@ ]g_e+W?g_AC`oI=qoC0L~6;a 3Ro s.<7?%;1L0= 9 M#yH<I< #  QPAN{._ȹ%$7.0\_ IN3;+|{_{1k,_x/WXO{п! y e9/}ݻ!3{C^Ip5xY<ÿn Nv#O'x*<|^_JKpex] pjr`&h{o~ 9<@Y}H^fPC^=9N cm%`|nB>9>S-Yaoq~ x#e2g3 xsNo1Z؃^nWɷS%OzXv+5)A |;hko%77ht y+ԇ!'Iq!lSj`#ŷa [uũ_ԏ\$~,6+2x[sw&ɞZ '́?,j'9 ->))3M#w. lra.;b\'la?d%?#|kc ׇ U]L|Wﱇ$go,O,9H9-m`"@, p e55?` b1;x'hÏz8"޷ yhrp) 7 A#ׇ<$MیuقNqzg3#~_gewl$٘x7OTY ^)1kXRؔ| zDϞ;7n֤E)wW-8v%MoU[9Cy?\݋ /8|NTR[+dMc៯<_vkwfV;5˗ W\Y(J|g=Z&fɿڀ͂ɚV벹Ʃvaȯl䝱`PSg7j,M2vxbsm 5}O)c*V̼aNaW*#18P]v_1cren ~\ D8_B%0~*Ɓ\έi&-oW-tNw=rE}i~U~;.\gnDݤ=gd}7\;_wX"hY/(]QkwzM@b(^ѯ=*OXv4W[\^HN̶+̛C_6>O^|ciiw&=xqߥWTW ԝ9=Y+:{\שqk1R\U>}XU~E½nZ}A:}c$;COjp d7bOWo/$Ϥȍ믲N骕!`J𽳌UU3Qmnpۡ_J s'NJ5W$n8I\@ W'Z*~qXjjsc˃o̫7*uR~InJ ]됹 %xZA{ك}+&;31vh/|߼꫅)u3v|yy9sg<~^9}zXE.6>P3Zskڬx[6_zzE;Oε[{ŵ]K\/W( Ww̷ճ|@ժO}6coT*kzp< YY!F'5]wĞed{kn7֩N=+GSiƸ;^ .ص599;FJ fYcLD6"sINNp4;鸇Wf3+T96kʓ &1vL,kjcG4 91G3cuI:vܴnse&tOqr`TW3كo-竖~Y彵y\QMBqݎj !w3+_\uϴ{̪6;O/VDε;7Cɘo 0)%ipNĸؼ&. ;8{/ٕDv!= x/L,2N$!CVLr-4Ur_4!=C}4~Ğe;oWO1J:":|tJ._QOkaV(4|7%t"߫>ş?4xr$4&z.&Z~R=CY>hP4ӎ7_S ǩ_ NRsQbRg!nu~}V] a]0P&;婠؍33VkSYxҩ+bE?>g>JeT .UsBPmsj\9;: o8w'eMdrd\L*J oap+R|xSg9'J|Eq";{qoiHU!ʉShʯHM]?Ц֕0ticǂo=ge\h\~5`U^@'Amp40 Gy~yϴ4,n$4#D5&DӑoZvxըk3e_ έ;"֑`s@4cvsuГbr/g}BMs.#8tĉCi5IU{{X>m(`g"]!^ߚrg z덈W,GD ]޲ʽiGj&xq?žNu͔)-gk#bDH;yn;xp߂g) -Pٓ&#7~lL24ԉ/tioGM5!4oәɾd(](?;Eڶ2T8@- ȠZ,? mg%(Y'ڼ9W.Y(wͻ*ɞiƄ`ЂyFJZ31ډex޾9|.d챡VRR%si]4Lt4P~v.7׋HYJ YZR9rX+HbPY,t՗ɺ-oLpL76F+iW~V0≣O o;;i_s]va%."F/vbx4f`U2ԈBf;D\O'MaEh>$֘ẇK֣$461R*srœjgw 㼤V]E- ^W[mU޷+=1͕ 9ϣd1KUeIA֦2܏T_1 Q[HX ZhT?M bm݃L{z1P*3[7@xby7\ wʉx1qȁpĹOMopb.R1C%Ȯ_j`Zp\TBJMk;87a W^V`=Sy~b|&tw:jW PyۦwמYz0߽S֟?#*B0]lW=^\ґt>i7˓8Vyww'YVq|bC ekr!kd SYY!s k踹lzpK6#Dr4WmP_؂frt2zG!qOGb'85oIE ~źu/h9h C~g]Xe7og_/,F_#zUŽ~aOƈlR*r) u>X v-Ûc)Ee_tid=Mũ>QL'773f)V!fC d}^5jU 2ϴ3}7L*p.?8DluLLem)N3mo5'˿]znUˮ"(BfѨ-Q8 ~Ń_/BZ+Eu|1|(mv# i3Esbl}cҮ-l*SF˖8QgbĦB͘GW/貓̹Cng}ˋCY0-ƓV,Ld s;E;i$eAo v[=9ev( Bܢ*MoyyeIpєБէWJ]y&.ϑ|6qJd Q<m.D bf9ꇆRc";BD ~/' ,Ta)hQ.9C!Pjc}WD԰3u")sΏVdn)=Xb8%|47R#m&"] OsȱI1סZ-3|9',3I)"_ IšF־[vIndII~:b:Sp-8w6AjImyR=? | 4JfڤV-ЀaLWzPs1ϐT=s|d GyCYMV^6Gf{> 'PrងZd_ Ɠ t>p,?,,31 Ðèñ. 3. Ïåðèîäè÷íîñòü ýïèäåìèè Àíàëèç ïîêàçàë, ÷òî âñå çàáîëåâàíèÿ ìîæíî ðàçäåëèòü íà äâå îñíîâíûå ãðóïïû. Ê ïåðâîé áóäåì îòíîñèòü çàáîëåâàíèÿ, êîòîðûå ïðÿìî íå ñâÿçàíû ñ òåêóùèì ñîñòîÿíèåì çäîðîâüÿ ÷åëîâåêà.  ýòó ãðóïïó âõîäÿò ðàçëè÷íûå ïîâðåæ- äåíèÿ îïîðíî-äâèãàòåëüíîãî àïïàðàòà ÷åëîâåêà, ïîðàæåíèÿ ýëåêòðè÷åñêèì òî- êîì, îòðàâëåíèÿ ñèëüíîäåéñòâóþùèìè ÿäîâèòûìè âåùåñòâàìè è äð. Ýòè çàáîëå- âàíèÿ îòíåñåì ê âíåçàïíûì îòêàçàì. Êî âòîðîé ãðóïïå áóäåì îòíîñèòü çàáîëåâà- íèÿ, äëÿ êîòîðûõ èìååò ìåñòî ïîñëåäîâàòåëüíîå íàêîïëåíèå “ âðåäíîñòè ” ôàêòî- ðîâ ïðîèçâîäñòâà è îêðóæàþùåé ñðåäû. Ýòè çàáîëåâàíèÿ îòíåñåì ê ïîñòåïåííûì îòêàçàì. Îäíàêî íåîáõîäèìî ÷åòêî ïðåäñòàâëÿòü, ÷òî ýòî äåëåíèå íåîäíîçíà÷íî è âåñüìà óñëîâíî. Äëÿ ïðèìåðà ïðèâåäåì äàííûå ïî çàáîëåâàåìîñòè õðîíè÷åñêèì áðîíõèòîì. Ýòî ñëó÷àéíûé ïðîöåññ, ðåàëèçàöèÿ êîòîðîãî èìååò ñëåäóþùèé âèä (ðèñ. 1): Ðèñ. 1. Äèíàìèêà âîçíèêíîâåíèÿ áðîíõèòà Äëÿ âûäåëåíèÿ ÷àñòîòû ðåãóëÿð- íûõ ñîñòàâëÿþùèõ ïðîöåññà âîñ- ïîëüçóåìñÿ ïðåîáðàçîâàíèåì Ôó- ðüå äëÿ ìàññèâà äàííûõ. Ðåàëèçóÿ îäíîìåðíîå ïðåîáðàçîâàíèå Ôóðüå ñëó÷àéíîãî ïðîöåññà (ðèñ. 1) íà îñ- íîâå 1500 òî÷åê, ïîñòðîèì ãðàôèê (ðèñ. 2) è âûäåëèì ÷àñòîòû, íà êî- òîðûõ àìïëèòóäà ñïåêòðàëüíîé ïëîòíîñòè ìàêñèìàëüíà. Ïî ïîëó÷åííûì äàííûì áûë óñ- òàíîâëåí ïåðèîä âîçíèêíîâåíèÿ ïèêà çàáîëåâàíèÿ. Îí ðàâåí 365 äíåé, ÷òî ñâèäåòåëüñòâóåò î òîì, ÷òî îáÿçàòåëüíî îäèí ðàç â ãîä âîçíèêàåò ïèê çàáîëåâàíèÿ áðîíõèòîì (ðèñ. 3). Èç äèíàìèêè âîçíèêíîâåíèÿ çàáîëåâàíèÿ (ðèñ. 1) ñëåäóåò, ÷òî ýòî äåêàáðü, ÿíâàðü. Áóäåì îòîæäåñòâëÿòü âåðîÿòíîñòü áåçîò- êàçíîé ðàáîòû îáúåêòà ñ âåðîÿòíîñòüþ ïðå- áûâàíèÿ âñåõ ïàðàìåòðîâ S â îáëàñòè U* . Ïðèíèìàÿ óñëîâèÿ ðàáîòîñïîñîáíîñòè â âèäå (1), çàïèøåì âåðîÿòíîñòü áåçîòêàçíîé ðàáî- òû îáúåêòà (çäîðîâüÿ è ðàáîòîñïîñîáíîñòè ÷åëîâåêà) â âèäå: P(t)=P[S j (t)  U j *, j=1,..,k] . (2) Èñïîëüçóÿ àïïàðàò àíàëèçà âûáðîñîâ ñëó- ÷àéíûõ ïðîöåññîâ çà ïðåäåëüíî äîïóñòèìûå çíà÷åíèÿ, ìîæíî îöåíèòü âåëè÷èíó P(t), ÷òî ïîçâîëÿåò ïðîãíîçèðîâàòü ñîñòîÿíèå çäîðî- âüÿ ÷åëîâåêà ïðè âîçäåéñòâèÿõ ðàçëè÷íûõ ôàêòîðîâ ïðîèçâîäñòâåííîé è îêðóæàþùåé Ðèñ. 2. Ãðàôèê ñïåêòðàëüíîé ïëîòíîñòè Cx{hUϝh6i6MҤ/[šW*65TCj?)"%)%TGPjh}Vb#DM0R$J+wtfg—s{Νs̬%nu"N%D^([Cd^WǫK_$2ڷBHs6a*ޡ֕tpolIZ݉wk_M%?*k3QZd}=bE:vWԵCǝ2i&&cD{W9K@ 8nTɄ KWUv˿R./2^K5|v0x; cE/jz'3 9 2_V+Oφ0UIx$fq V${B."9#!9Mp IZ$S eY@o%{4%lz?g}T)_d=[ma~V^'[y|ot[ 7;?hQ0K*,W qB,-JMcZ^ON?u`w0ތn뜮=̛,z3N=j! 1n[Vzk{MKS ZZ`P:SHɹJyb?9r !Ͱ$5 m$'G?/&5}7%Jx7Oe81I/( {W1x;neN9=gPF?xݸ@C\c-s{sYHB4\py iYG.qwݮwֲ綏-uvKk&7|Vmξ=MN3<7[N&Q}mt 3hxwy:u^rtPu^{]jMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10  u  u u (16p 2 /u 1ʄ {qx͝UuSEHDhl!Z$өM֙hmiZgRi'qXm I(^Ox^SD8Q_<:zQr˔t+n-8X|s```)ЧI]@#Jy }&)yfE4m["Ү#}E8}F-?m=?,4e]c&|1햋n aBfշ7T?& N\m>u%J }:tӐCIǾ΍i3̳;2=IՂyk#qks]v\0hsqxN=7&%Ltѭc{Wĥo>SLR׉x0{ϗ\xx&u-J3c/UU"+&F{nѰH[AѢ?6 ?yl^n hN1\מGڂ#J },6wc黉)"s?bK*6?>mgzH*\!|nbLlb{Wylz96on_w&?.6+l ahƘa^?Ip{>֤QX@hHSδ JÛ(eS<[zuZلSZg] ωEy0 >6fYDz!tR-Vo:a*nq&\23t޹V.I~]P~5f|k[OgT~*|~70~O(k;]#3>Y7w9: 1wnic} h/,[Z;As0ֳ/{oz|+' uU1jYŸ,}п>\)^3^ׁ] dr}kǹexi?%juSil7Zݶ>l^NxsԵsxz7iޖs`l-']NB ~~=)7wi?̉fODh=;ΰn o1yЏ)l ]vi #lz(G]G٦)onQ]ō4>.&UXqGMXG`"n}8ob…aN˜LcnfKi# ӟ3me8O}&=s !A/3_|e;ÎΎ&FtŭJ3E]~$Łڭ2i$ۄ\S?v`lRy0ĜeOYOwG?~£r'3$9ۢD;Q%۟ڏ0ne?he. )Dm^-#/ڹ{5 EOתuyw'qx@, 3h7>`;3n-Nh l#;!G/ hq A GdCekɾ6֔|}If=qG'AoKdw{LclZ rq7םpJtA;ǡ F 7׌-FS܉ ?fsq|CxYTv1H3{0?`}N[;618, }YvOBh-)|So W &X Wk$gW({fi?736K%7Gi"r橖r% {$Omֆǻ];6y6l+voJ;xS\6v]ewč&׵z'gߪX.vym곢{颟Wzdi'mo`RC sXU=uߪz_vu8Gj`dy1]:E`S$bN;CxAo6ڟsusN#W_W_Ej)xӟ8b ~hLG6~bg6.Gng|u,<趽i誚2c`ma}%mdxDº5})fŐϹM$Ǔ~\K+ Oci,{-qg{x6^!h;ֹAiֲϺ#N>d5L,Ø 1]_wɗsOn =F$%6١쓷ӳԻkƍꀭ'w-݁GR]{{WN>+RRq ~6@\\#%`BH]%si8#]UGO\Tzϼ L@ש-:'|{h^ ?.YiZÙ1>C3…J_*̎ݒg1?}p̸XV5>pP3!51?wG}6x aWQ&F:CX#ׄn*}oO {KpIxį4Fus$%:Ӻrztj܎aʒMTU\#q̹< +s_Z|Ky6 0Ɨγߐ 754V W$]x&j5{Vwk%89yNM &)'j} MڠyAouT>suY'`*9#_W,k=\L~cЉi|RXq!.V^ϫi<?1W<)c5Sm $VA)IpBϔOϐn{h Hc.7=1ii_Иt6 x(6$3K}uu&p<{O!@W>G%y }<)>Z^|\]8D_If`R̥F`;n}ߠ𛂳.C3Myr3U޳|~ԑ9ָW{FsS5.3~#=S30n>C>:1 |eI)N#_!c`A+%s<*tr7[ =Ӊ>.Ƨ'4ԄEKMS"/rGsHqS^FgfPws otd=O!H[|C$r ~tZG4:M,2n?||C|O'̃vd纖~I#iw~pTvP~hv@c2F3O;oe =KW;1>iƃqF9fH[I,_hϬ>gRw9ˡ:M'o>^({q~pٿ_2wxHe֍MGoh÷F1ɥŘ$3Y1>؂$v0 B'oylCϳ_(k['1O}]yy(.㶡-˹j}ﱍ 7{nl}q]#3ЯDg-PB36R{[Fy ^e0n6횗s}EzGt0`(Ü,uUs<:6£^@|"P్_oK!zߟv0}0zbuN;4?0)4[{-`CZmڞylز틝Ɩօ}G2Oh},rSyw;[Y E{)_|hEQ+Zݼ=x(ճy8Ҙ ;c>0m`+h`Zd/ҩ=8]{8֏~[}m| ohΧamv'#lKݡ}z<û_x*}9r) 85U|:ǧ`( r n8>,Go'( ̺^:ˍky;F bq>^"911V-Þuwix-7yr2 Y< |mH[ˁͣmw]֑q=Y{F">'mY|F_꾺fn/߈i~ x#<<8{CkvD(wA(gMs]<cܷ5:<~7cB1t4}\O<)kuw[x>^#e;#E;A&xYޥr7`NM>yqrjy<=w |+mKێ<6)6m#:twn {W~hJv ^cu7nz59,Goz//;"[uO) -vS {A#^ͪ(X'|^\|W > {tYӐ3=OFZF#r.D"Z<۝Xi~уb]CM]Bl. <3b6/ۘ~/v { b ptn/谬틽 Cy΃}slr^2fOr gc* LKOϋ-aԼ*mY;>{6Vfk&wCoz=x~)yc_\zMm3t_^ycmfY+ύ2w9p|O4ߛç,S"L^^4x5{q|o*ޢ:iGޫqMp>{bY]"lrܭDIt~z̎-=H}mE< ط<\2Iy.06n;؟a_c;BnC?4d\΃w#:f C|X7uCy X 1I"vd`sЪnS*{uw ]K^oiH3!7}؞1=mcbG;NžǖC"G\},9%oǺ;Qz9j{w9B3gu[t~YM'YM=<>rwgaO>Ky0?l}JYız#دƖ?n :˻ȹmn \o >1A]`Cڋ tw)GAC_j,,%32 ñðåäû [2].  ÷àñòíîñòè, çíàÿ î ïðèáëèæàþùåìñÿ ïèêå êàêîãî-ëèáî çàáîëåâàíèÿ, ìîæíî óñèëèòü ïðîôèëàêòè÷åñêèå ìåðû è àãèòàöèîííóþ ïðîïàãàíäó, òåì ñàìûì ýôôåêòèâíî è ýêîíîìíî èñïîëüçîâàòü òðóäîâûå ðåñóðñû, íå äîïóñêàÿ ñðûâîâ è ïðîñòîÿ îòäåëüíûõ òåõíîëîãè÷åñêèõ ïðîöåññîâ è ðàáîòû ïðåäïðèÿòèÿ â öåëîì. Ñïèñîê ëèòåðàòóðû: 1. Ýðãîíîìèêà è áåçîïàñíîñòü òðóäà / Ë.Ï.Áîáðîâà, Î.Ì.Ìàëüöåâà è äð. Ì.: Ìàøèíîñòðîåíèå, 1985. 112 ñ. 2. Èâàõíåíêî À.Ã., Ëàïà Â.Ã. Ïðåäñêàçàíèå ñëó÷àé- íûõ ïðîöåññîâ. Ê.: Íàóê. äóìêà, 1971. 416 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 17.06.01 Äçþíäçþê Áîðèñ Âàñèëüåâè÷, ä-ð òåõí. íàóê, ïðîôåññîð, çàâåäóþùèé êàôåä- ðîé îõðàíû òðóäà ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ýëåêòðîìàãíèòíàÿ áåçîïàñíîñòü. Õîááè: àâòîìîáèëü. Àäðåñ: Óêðàèíà, 61022, Õàðüêîâ, óë. Áîðèñà ×è÷èáàáèíà, 2, êâ.94, òåë. 40-93-60. Ñåðäþê Íàòàëüÿ Íèêîëàåâíà, àñïèðàíòêà êàôåäðû îõðàíû òðóäà ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: óïðàâëåíèå óñëîâèÿìè òðóäà íà ðàáî÷åì ìåñòå. Õîááè: äîìàøíèå æèâîòíûå. Àäðåñ: Óêðàèíà, 61202, Õàðüêîâ, óë. Öåëèíîãðàäñêàÿ, 58, ê. 504. Õÿííèêÿéíåí Àëåêñàíäð Èâàíîâè÷, êàíä. òåõí. íàóê, äîöåíò êàôåäðû îõðàíû òðóäà ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: áåçîïàñíîñòü æèçíåäåÿòåëüíîñòè â ðàçëè÷- íûõ óñëîâèÿõ. Õîááè: ãîðíûé òóðèçì. Àäðåñ: Óêðàèíà, 61204, Õàðüêîâ, óë. Ë. Ñâîáîäû, 34, êâ. 192, òåë. 37-18-61. ÓÄÊ 621.396:629.7.05 Â.À. ÃÎÐÎÕÎÂÀÒÑÊÈÉ, Î.Â. ÑÛÒÍÈÊ ÎÁÍÀÐÓÆÅÍÈÅ ÏÎÄÂÈÆÍÛÕ ÎÁÚÅÊÒΠÏÐÈ ÀÍÀËÈÇÅ ÏÎÑËÅÄÎÂÀÒÅËÜÍÎÑÒÈ ÂÈÄÅÎÊÀÄÐΠÐàññìàòðèâàåòñÿ ïðîáëåìà èäåíòèôèêàöèè äèíàìè÷íûõ îáúåêòîâ â ñëîæ- íîé ïîìåõîâîé îáñòàíîâêå ïóò¸ì àíàëèçà ôîðì â ïðîñòðàíñòâå ñïåêòðîâ. Àëãî- ðèòì îáíàðóæåíèÿ ãåîìåòðè÷åñêèõ ôîðì áàçèðóåòñÿ íà ïîñëåäîâàòåëüíîì àíàëèçå ïðîñòðàíñòâåííûõ ñïåêòðîâ â êàæäîì êàäðå è ñðàâíåíèè ñî ñïåêòðîì ìîäåëè. Èíâàðèàíòíîñòü àëãîðèòìà ê ïîâîðîòàì, ñìåùåíèÿì è ÷àñòè÷íûì çàòåíåíèÿì îáúåêòà îáóñëîâëåíà ñâîéñòâàìè ïðåîáðàçîâàíèÿ èç ïðîñòðàíñòâà ñèãíàëîâ â ïðîñòðàíñòâî ñïåêòðîâ ïàðàìåòðîâ. Ââåäåíèå  áîëüøèíñòâå çàäà÷ àíàëèçà èçîáðàæåíèé èíôîðìàöèÿ îá èññëåäóåìîì îáúåêòå ïðåäñòàâëÿåòñÿ â âèäå îïèñàíèÿ ôîðìû îáúåêòà èëè åãî ãðàíèö. Ïðèîðè- òåò ñðåäè ìíîæåñòâà ïàðàìåòðîâ èçîáðàæåíèé îòäà¸òñÿ ôîðìå ïîòîìó, ÷òî àíàëèç èçîáðàæåíèé â çðèòåëüíîé ñèñòåìå ÷åëîâåêà ïðîèñõîäèò ïóò¸ì èäåíòè- ôèêàöèè ôîðìû îáúåêòà. Ìîùíûì èíñòðóìåíòîì, ïîçâîëÿþùèì îñóùåñòâëÿòü àíàëèç ôîðì, ñòðîèòü àëãîðèòìû îáíàðóæåíèÿ, îöåíèâàíèÿ êîîðäèíàò è ðàñïîçíàâàíèÿ îáúåêòîâ íà èçîáðàæåíèÿõ, ÿâëÿåòñÿ ïðåîáðàçîâàíèå Õî [1].  àëãîðèòìàõ, îñíîâàííûõ íà ïðåîáðàçîâàíèè Õî, êàê ïðàâèëî, òðåáóåòñÿ çíàíèå àíàëèòè÷åñêîãî îïèñàíèÿ ôîðìû îáúåêòà ëèáî íàëè÷èå ýòàëîíà, à òàêæå äîëæíû áûòü çàäàíû îãðàíè÷åíèÿ íà âîçìîæíûå òðàíñôîðìàöèè îáúåêòà. Ïðè ýòîì ÷åì áîëüøå ñòåïåíåé ñâîáîäû äîïóñêàåòñÿ äëÿ âîçìîæíûõ ïðåîáðàçîâàíèé îáúåêòà, òåì æ¸ñò÷å ñòàíîâÿòñÿ òðåáîâàíèÿ ê âû÷èñëèòåëüíîé ñèñòåìå, ðåàëèçóþùåé àëãîðèòì. Íàëè÷èå ôëóêòóàöèîííûõ è ëîêàëüíûõ ïîìåõ, à òàêæå îøèáîê, âîçíèêàþùèõ íà ïðåäâàðèòåëüíûõ ýòàïàõ îáðàáîòêè èçîáðàæåíèé, åù¸ áîëüøå óñëîæíÿåò çàäà÷ó. Ïîýòîìó ïðåäñòàâëÿåò èíòåðåñ ïîñòðîåíèå àëãîðèòìîâ, èíâàðèàíòíûõ ê ôîðìå îáúåêòà è ïîçâîëÿþùèõ áûñòðî îñóùåñòâëÿòü îòáðàêîâêó ëîæíûõ îáúåê- òîâ è ôîíà, à òàêæå îöåíèâàòü êîîðäèíàòû è ïàðàìåòðû äâèæåíèÿ îáúåêòà [2]. 3&xmheǯwllj,?;8E0P /Y0JT/2)EPY,$DgV,:ۍc9_ou]snOļ ">"Sr#R ^';Q J {(qlJv!Uo;@y&+PFIً(r;:}BN>)CrsDǜTj]-q ַk34uW-sٜʇWZ$8M{,ewޕ7fw_ +w$:DJ"*M3:}jW=಩qmʨ1h(<LDJkn7۟ݲ4_$e (bK@r(Ka?\`BN1ɖ&Gނ ' LEL}e=lL[%S G, )2y~@ "yxЧC N ` *bfc4>_`+zP&%Ϣ7,TH10S#W{>` V{18By7݀^&aoDD |?{.u[a}fk#a1|<ClE? oȓ3~!u/h[obWku'ʨ5^NdeͪօNa aO{ZGFk@gjN32DG00j0g= p 3x"[DE_湃އϓ΢F] =i {[^naR<X]>\.7< ڒix&fgϹ#ׂA QbyOHvY&21>Yg݅&Zy3'3qKH9^}ń8ǹ 9ȕƔNf39 d//kյ>,6`Gbw~5wo>A<8)En0e8 7əiFޟ~#y£=r(D]g="׀frS)z}AZ5F랪;)'ĀqoooT1O')a*{ߝ]#٭ַ[SOHݽڻNNw>+<:uEfv_ʖ˥6?sr9Rgvq:g>9M']xwͽ=kRŤa(ecS)O顧N rM7o x&M7G'[7o x&Mg6~PMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:10     t#  (16F 2| /+" 1N & {'x ]EwCx>Lґ {(΅;xEA*4!!!N#H4{OWWN>t&Nkﵪ֮ZkWާ)˲k>ؔee_%@y8?Ye,kʮД?,^-<(:qqʎvlzvEvY6/[U.ɮ_qJe>e5:*Эz]PcToΕ:Zt%67+<,y0}4ުԪԮTQQZd'H1V*rͽ^/jV6<~HyNlW %.\֧g3 We}q^9,;(;2jߐ?lsM:fv.k5_sw{v軗eGgONiγY=;畦7-?̦\L]Oe)_$?fޮ;j]e.}]u~Җ_[^|UUmy[WإGY$> ~)⅛t~j{󳕷)TQ$-z@X!h36G6v́WRx@cqyM=8CҒ}möL_rh?SJr>)^ B51/1/hK^U/3񕂣4Vv7p6O_i/v= |%UrhasFuR0˔=MU!X =<;䔥;>p:u9 ϸaj?9WrAW\#R-? X'жzуo*y/~H[M 8xQYCW yx./c5cЏ(y*/˕쨜lU xL}u^1Ki]-UڒUKdw]֥>YOUyA!V'v Ve{b{"J!n0+gyّ噣.qW~S>b!ts`pN5Hq]YMM]r]\q:\|/Oգlm.lS1KT-i|۞[XN[%)NE ٬<;;';=JU|8;Eaf׳&?BwyO=GU ?ZN~e:w*M T9YĪ||6uNGI׳4B:纑7?N})7LꕳiCB͙sӂgQg3gctpt4XA;*qoƲ W  xn@ܮЫC+g̋Y޳1ۖ?kWi~9lF[* e؟v#G{ Nbi`$y6eb+e+)>.OŬ6q [9]+i<'3Oź0fxJQ>ְtva u]s9ߔOy,Ka9w2\n^kD^?Frc6PXkdT!bqtozDy_m/ᦢ!2GL@˯&XJW袍b0_kݡuVg{!##LEר2zn>u=> irc> FKN>+MX3ՅF6JzEg+rtWhR|I wqFjގ oG9V=Yzv[u øUE Bї`w؍ "q}9d&}klrzspWw|C:r]~U;IGzc=! dNa'}901$ Z#zj 8x^aBLߨ{! |5\=a]QMŸsb%z;"Xu>fz:8gLs1!ny&&yܪmByטr꣏J>y8x+D ^=/९{52 CtzBv)cɊ]}O0f ;&+C-J螾 ul{ٶcWJ;L<6oUj?`).w;CGݽ~?чD=R侒3uT2|ӔR{[vS>J;>hgY.w9ײ'yt%Ki\px.^?=GU;xog{dcYi z C~fm;;rkέש:WzsW᩷WQلz=w׽=<%?jd^ѱEԯpX98{h˸[j:j4Kh}as}.s8A|X݈Qo&P1Χ18be:D"^Zt=B97R"NsRX*[/Y:E[i:Fc=8R:H-Q7iݓПNߟB}Պub Xl;u}/G{w֋u0֡XXt2їs9:d[P/Ӹ+։cS77չ5}cQ/!NJqXGn7Ln1@h HԪ9"rTbaj⛳~pnuLs@^$!#PgTo.W=ra>3u~ە(531Qϣ<hB;9JJ_R߾CmM7EHLK xbʼn#OCqNlmK5QK{BN:Ύxϡc vxb繓F m};5#U}zs?};(GL / ;6<,yR]d֨ ?ys?:gșxdO6纯xy[؂Ϋq'8}oiX%ƐZhi#Nkq8Y4Ap:i7S3avՋf_Y*Z7wB8 BɡM4ǁ\}OpLqaI \qZ5:qZ+9N;G9T(*fӮmʅqcO8|F~w Z1}pQ͸J 㴕;SD/hÎqGѿS9*N_yw%3giq 8Ns&GMcCji̩A8\q8])<1]/ƨ0A0G~ϕ=Glϊ]J;wVw{ۻ{; 9?ko=8(>a9\4Iy++%\>臺d##l K_dfsG4KcCOѧKK$p׽Y)Zr8:\mJupv=Jimʭol˿jQAB|Zۤbņ?&ǎlk䶳 %k؞ɡ mk'1JrA>\չqpwv`)^ }Q2/}p+/e*ivSwxr K[`oM͍ hP!rhUB&KsDYdGuy^D%dy(gq}](oKqon)}ƻ.ONYY >$ާb 61Cy!߸|nU&ϼY\sN |Ƶ[?(U| Kɸ~Z6u @oMc9Cʒr2n/{/G*y/>xy\D^.Ճ@ 8xA)YawvyKo#Tg,_*;a>tm /?6Ms mñ x!SufR*%dlRjcMҥ8)᯴桻JgOe]XKy~%-]W./ 1E}ͷ4g6[O#oz}6%On}-ҹEi~w|zFwsIJU}zC cpfFֱcu OcQMB:V#{7qr×\Ϗؿ׾7p\EWAt8vG8Ю Μ!]sZ]H7n)drlw[9J7{~׸|̉ oX^ σ} $?AѸ}긥Q/qu.u7U[XEA[kmQ/nQxh0-['ڕ£ZmX@R|K`xnrxvGRbnY sv&.sv& ƜOMŗ!RmeV/xշ*ڋ i[8ļ/0Ro\B2R#4vr0/e㻷 Ƽ^j^q[xۡNv(wF7%"^:|1A"K=w{YQ]sǝ׭} 4t4H{7 Ѹ#oxxRoW8A/ yF\F_Qoxy[_z:N ^쿉E싁)2NQ( s>>לrg)ۜ)}h\{`)"ޡ#㻷|Wt)mξ"_J<<+aWS |jQ|M8Gyrn\u{d (a\5MzqwK|Zc7['Uy34H8HCvqU7ˉ)=bEڱqՔ*Ӧz<< <%7Us\u_fN_r.U#M;UhoW~p~])<WMp5#m~pDOR~P5lwy?>Rig\'岹xuӎ HW$gU~O Ƕ95sȭ{xl?^r~o8#uh+ Ab??cRxv xdUg*YEJWE/z gL?g깂:{הr)x+k{'~#LxpnZYyyQɿuxysT ص۳2RЫn nڟz>k3OIk~%A76w9;qڌsfnF 9ڥ2!Pos#u4+^<+W0+UnTλŲcph^,ܱ?U»~={/^T;>bb}jo~Q=_R˔mZw(S491)#'{=x/1/९{5^샺Ԁ/p5FR|-b%-5[0wY.ע]) yfm_ed7b׈W.:T ǔWJJs2~d_ S&vI<1_RNWJYS>Dy'<) Hm_d{+;!QX&\snZekg^/S1[q>;c Vo^l.bɣK>KqOsv vוNX['1gqsycy:n}^yrֹL`hpu7..F?b_KWŬp^ +gB{΋A~5:/3'ڥi6@'I~(7o*kbC~%U.{N4Ry1lgϩyȰ?[SĿ_?~NkzSsݗ~8KA8~=Ўz ^sOP 隹f :'j;NyHDh[&ljj"FV$1TGԞ"+SSp}_ R{[:U|u:trH/Ϻ{zނ\=m|ZAy*Q`/{''<9e##0μewyߓR^3px%ہ\mQ~XI8]Ƽ\JnWСrw&u ]u/t}haSzI/puj%dYkrtʿ{Drw`}CF f`B%{V2DVomUbF1Ң3/!osp.€#'pUON_^$?a[򜃣,KJ7*F$p_.a);{ZbF4cCY)3yD~i?E?A8yʥ-}Z`xD0360ѵa7C鰦b\MmNBrc> Hop|^S)0aϊw/nl2,˺S)mϐU<:.#hߐ{nLK{sm *k&˒(*SJc.eAsa=sz@qE@U_xѦ>뵯u ;2`W~wRhU~tpC|Ct<<ye@sg^̟M4}Iz$̟sAxPkxrDZ8b9ƍvty^MXqrG V0Lctb6߭DIkY1]pr){T35S|ź+#^a[T{F%b?_#[rp@7Kp]yת9Q}q j+:l=Om'̑e.e:&Y]<8dx$Iu׷|k#|!Z|Mnh8j*ܬ9sOd4.1۵N5˙.FaΗk*dm][[(rW_'(MQζE׮OZ@H.'c]CM*ӅLIŶ+ 7bkV$eB~g|_Q~|Bw~#baazF9׃K#K6fd64-d:ʘ(z;Y{a<X϶ &x?$pB\#'C6ֳ:!%魒-d tј)'ԍs]V@wl+8tLѧٹ|ٌWBۤAc~5{ Llh'?U<+qy"RlbfڇnˁGly;rCFrc%ݪ~Q.{;Ok㭁ebu~6i wt{qfgWTǕU/REG5rEf k|rƁ˺ևG Z&צQk.F9O]ڈ k>v2MUMcFRv\ey2(A~Dc&~ﶥ/+Գ0}MnLRBNa? ŶH.oqEѪ5z\H=B!-xP(6-0vY 8(vKVtSv쏠?o"EQY}ZS)}|10OU'WۜTk2"kŲspFnq6-pa9CyktDY heZ6NyEa8p@ 6'6qm `lRxx>q{VzC|Jih4Ner YW]5^UtQyJ.A kY&U[z veD ):ƃN&xRl z4 qIU"vykA?=@VKS>?mi;m"Gu]7mWnPCwʩC}ýnz`6;[>s澲|^s5'ﳜ㳙K\#!M']p}lnަ5Z7]"9JJJ*wȿЙuBt'S9RZ_ۻn} ~u4- }1X_w3yX5Ih^_㺯7: <5cq{oBvvҜCccvpqsN]'vݘ.p761i;1Vɗ5Jī+e\`g /?A,JDjI"ȟQwE5a7O.<Q&,+7lM^o 'Y)LӿZ&,#r׈Fu\ 5$o:?ݛ iRrOʡ[Ρrt }WSF}|bHĶ 8c_̏onY9Y<鵂2cѭ%1;ݳ\fW*_c<*Nv8V]ȃ ,P?)\(zt$p=LБ ݸRz.(Oryrsrd);Qy8_Ewr KzNQ P-G: li .%pSI\z<\#{vK4114\d5I >)hEfWNoW>M)\;_Jhwg_OjمWڿV(-Q!Z$JTWO={wH3>OFg3n{vaxA+-eo{naq>>;m9#O'}{Ew*s+OQq^e7O8L#E,)8Ez/i=C}}s6<9:kdo#ҳ;Uߢ[t4"Jˤ^Jً]ea?_Bl`TƹrON[{'`^w߶ޓ|ɽϓA*Ӧ0}(| ϓk$C>~$nԇ_~'/?}oUD9g}! 7Ip+N14'o9J ?B>_H6پ] /GF}!{(/d1~/OyQYu(72 ֌ ~(w#F;C; Y :8;`|g].KNcf˾[ko]!qo:-?sIOy`\bR/Nfe$Eq-hj'euؿb̒E8 e'ӮaIcm҆Mt1:c1Ҫ Udmt֝=]q1yاWn YFwtuC牱keӎG3{7i?\0r!Ӯ"Cڞc.zb`e(=.[u!?M=>j;#|q!87:1g—/wg=kղ% `ly6eZ_T֚͜qS.21 w5Fsb U_C 6bi)wm\ѭk2N-^epmN9 J:{@3]p Figrmșnѝ..x3C~ nzU`&'m=m%zھ`3 ~ Ρ3^EvP$פtі1ZJs95VGvN`=~zV+\ph7M}p?H"o]|[ jN!?Mg앿ko`u_\Ocq}:Ѻ\w3&\5c `N\}&ߕA8}[f}>ޝ8 ΃RY;Ͱ?hZK}VcuΩS؃*+=ww낺%mYfS/Š جO\Mz< : ׃>#'`!еA$uOQDT^Gy= R`1`OsZ׉@S'/SaI{4nꞓܳeE0os%ݨBC$/Hu4<@̞c˙{|LW_L.ltj|cַ?y]&77_A~8e=Ito d>%$@6:r: l'wDt-'z KH%-ryg2sʖsm[ٺzϴzWzo˾Vak[wxwMwM~>e7Ovm媟]Gx":vF)6l9vy>:l왷wfc悾}32lev|Om[e*k߲ӚRɳY߭j׼Xx:(|uLǬ-;w1cGy˼Ʀ}73n>nȹKfl=M۲)72ixsZo5vsv:l1rvy~lر7y|z4ۜge~}2u89ߛ{njwTM'N~}]#F @0aZ/@0a#F1Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:11  Z n  ;J R (16& 2& /K` 1  u {x^Uy0&Q후0Ẍ́@0,Dc@‡IH8biJYaݬkm \ESJWt)D몵ؾ $!$@t9{yq&Ϝ9<9=yss}[$u-IrVk•IrmIRJIrI"7'#G&>Et}סɂdIr[RR!sP$t6&)ң) }}~?Eztꚪ5c ʣ}pBBBIAW4-)f%OknRn7:NZI[~=uXR\+Aήq )/NTg›&'vEi$Ii6ipޔS/[uO|{nLMIƶoXwvgdܦӶRt.^8g:fgK;:[.\ۙxF5Sgl¼8Ɣ?OL?Ŵ^{Ut~[VGM$W+LC~{I.\ <;9'.uJ4 FRZy?ME+K[ט$2Tt)k&8neǢ֋P7zg+MȓN鄺y:[ޯn^Yn1݄ߖUÁusw+ܭ|b6%}ɮdC-ٞKv$dR}JoLɣJoI^Ov*g{5ݘS{>Z+g_Rj*.'/9eKs%mz֫dݔ ~üB8^C|yNSFyТ&&@ 'q_ó!R?1i d IXUr.,&&~oRؘ"2ɤ)#ڮkkrȃ{t 0x 06'ecq.CZ6 tĴk9Ș|y䛮^-=Dd;JD>0joN5yk. i/FW6 |e\֑dV}K?EA7 Xt_kfVxC_8<84e<^t%8K9|A r(X'dLfح;'u 7T8Z9h/RX,_*.y1aF_vk_mb[k-gB=#m!/x5S6X.7UWy.y{8 8W1 ?"O9 iE LH^xc?ϕ+k Jjgg^y>{{&^q[eRVrp-*$O:.4QJ~[=IIeoN]+?Kˣw <-{zhquFwq'z{w oꬥkےsKL]֞ ;Wǵ#6]u.7M 9Ngx-ib<rzd'%ȁ6_6j7%o+V_XW)oMRJ6 Nz#uFڛ ;n Jy=2Y`ome@6$G/,st3\J<{J~ѭSy #p^[3h˩m!Z[#iA[ߋm! X[)=[O})tvz}5o\5jQ.iS3u^XWhR/Cɔ\O~7דГ?K4o`=m+Pv2aSՍUx*;8X 9>.ײݭ:_j=<D><;4xso9CF)cxg>CTcӣ u8tOiw E;Zǎo v`1'F:͌wC4k^9y[R߬/ r3;|0N֕4gѴt6[ۡUR2_00xi<'wr4]:y |pA|er>gk`~1MULC9Id]˼UQGUbZywV2Ki]x.횔[' @y z6e(oę»L𘟸0N8~1?#ScjR y=H~5FN W'LԜoԜVPإ;Uyt1׍9^+#JPRmdoj?NcW N=0;Webx'4gǼy;-r}J$isۥ^~3޺Cvf2vݛ9+һĆLq\IԽ3$1|/^wc{XF=)*aqkCh`am=n˾ymO." z`VwC2[0=GaW2kWچ}]h;ظ؞(628бL]%!GYb>,(Gy.c\5%͏LQR6+ɂu2Oy4{w9ϐJƚaVwJ<Ӗ?OO7p-K9Rԗy4="wEއT1~Z&q,|+[zE@ó*n~Xw?K猔oNUyn 1qGZ6ArwWP<'vc/;7>4;sܻMC:cZu[|/OS^>䩪ޡ>~^MB#6L=zW*h!I4|tB}'=%A}~xãY??)7/;W1ʳvQOv#7w]Q"Rn׈ߍѪ;yPRP~?ǻ5 hc5Fyӌ\դ$k\8g9k#krEƁ{}/$lN+-)lkI`C5]5=9u ^^`3w6*K4ɛ#FGlVhӾJWAC6c6㯲WeNmFkDحjn }_wf@Ǟh=AGƛ1qC=^-@d MX7(7K-@zwYS"[0Eall?1f4f~Rn߽?m=0"%th7ֳ~$vE;<쬹{Bxv[#Rs+k b,>jk^v9|p8tOi>YmH.O>t o=yFm}~A+][5 Qp??Cc'4tk,!q1vAuҾƽƛt_{J39'mܫi?=+٦q 7>tJeŶfz@ws˛ ȝ{|r9eQwդ_So=;f>&yUЂT+wO]kPN<Wp_5q%&M>WHGm wevD?-+\>Yo /ԓV /Z՘ ?l^W'_nwϗ *?uqwl}*^e( fILNoI@8p}26y:x!6Buq:l^(k`<8#ٟ?k S=[Rc>s{ϩTcx<C7^6pEWbsHMjr u_[L4^wa׋g)Ê߭XQʻ:FVؗdjbqB=ii?VLI }U .Y[E9P|rgB\lK>'Yw,w:л|r|>?C';cdK% 1 }m^k k_:m|mㅾv~F?=l{կ'$ס:^ xoOûI}5|hIwT8_e}O }3e~MvO /w9~a;j \ˇ6B%2ΎP?>1GZ)-S~1Mz }Hcx= 'Vћԯv C/Fׇ\kw>[sE7X59sBk|͝rO:V}+{bǰ ۿYL3h.Y&b&&. kg( gT̻T|!Mc>F[y?HbX$ G)Wg=ܫ'p~.tUjeOS)o4=_e .j qIkԌaĖ8Bs_S{b-x/O_ڀ>͸O)H\řv`4өʟ0rW9o9I_4e2Q|u~M>Ϗ#S(6ݭ@>=ەGܞ9.1}knj?Ƣ,Po_׮Za6{hbcݎ9 }{{*sXm,g)`bIJ{}@4p#|,'!_uɾɷ˂S;,|%?df}ޓ <qN/`Ƀ+oR!^VjW٦2a;1 ;zM1c7{P0b^<-z~Co+nI=uX!}WnEo_a7z2 WW+;v mT?`z }|q݊6}q?p`]n CR@6JVN"Uz$[\sikUTbNa:-jW ~hLmVm3C+~2k,M ={^=>}^.[M94`kܺ4xעN[^wi*c\(yoս~ڟ?/OWbO(>n?m`E1?>-R(ŋN)]h{>–OcVPTJ1i|\^x﯃7+=ºs?z mM^y{˓|gW9x_o,Y$+:㤌Jkf.%,䦯3'9&]Bo@<r%7,Wa޿-W3>6f&O>m.)ZǗ^WJg-X,@ z\++_=Z~\dm`;ݱ>ې)&t>1>-ѥޮvߩX*Cuc߄!{ٯx:7}r+ v;&m3[/y=q߮Z~NW][G<+}[ Ŕ6ܶ|ܠuR I+5.NM?O_jʖzŨnt-il97P`,&E܇rtFØn}ѵ{f_y<MLmZCٴBv#b#y^|SLԣozB8]@v`Bxe̾M`+]e/7V_T6\\C1e|Bl=xc© Ux͝?av.Y T>bkH|K#5iͿsrw<87Ə c^.l3XTҰϰ6:˾-=!6 NEj=Okn87 t9ihOMk}Ax÷=~2d&W9 5c݇Zg]_7ߘ;+Ֆ}ՔM&땒*떼'3:Ym-D8bVPP/{:cXXO}"\:#z16I;=)zwYgTђz o*ȗwxw8SMSy~UMugYE/Q=}E}B;E}Pyzҟi`]+5kտ/ɞ,rW;r<<Ĕ`< p<#1R_1gl./_oɻE0tc{:xşl y̗YOk=+Y<.4cI|CAvd?*hNn| <69fg Zw4|%Ho|Ì ,-;'i?t#&%#S1cۓ5 W%'k \Ip:C'u]lWP|bLR0~П Vb_)˒K8ǎ!?hǁ1u+t(|ERѿA?2c_mr{HW7aU<7US}L6ij\=~KvzioX|iܾ|}Rm"cC`E^,}{wis3+</$?8)9?b;A14־94V+.Aa1t)3&(@);+k-l5'يtv3l9,_|.lphElg8؎ /j w.zsX=^NX^բߎSy $FggH͵spDT\lyG*}^۔u/tѡM76GNU;Ͳ|!;/3pV#Ӝ9M'E9Б qo\xP<;u <y|)+LX*ػFYyk١3\6$dTspkWC8-.]wzFVəy7AiČ`7/@^2} @zx=K7xJ)c`lLSޗEo2#Ѯ^e{kwVjسF:Vу8>bfxĜ/` |r3yCYa%>exkBi`Gcg=i֦Xb4{MŅrl@'Kw^~ Z}h|.6]aLB)OWBxFyOdٌ̊ί켔C-rvp>;If[7lNm鰯 N] rC()aYCݦ,W.cA&,hx.p !-p-؂<2 6_1>-^VJEr@Pv<{[\Iۘ{R<"2y ?C35,aBSg\qtLm1=l5条u4]br@yj[e͸~W,륌7oߠvNvx΀!!0-`4=o<ϥ IyTV/9>\k,,j34 ëè÷åñòâó íåèñêàæ¸ííûõ òî÷åê. Ìåæêàäðîâîå ïðåîáðàçîâàíèå Õî îñóùåñòâëÿåò ñåëåêöèþ òîëüêî òåõ öåïî÷åê, êîòîðûå äâèæóòñÿ ðåãóëÿðíî, è ÿâëÿåòñÿ ïîìåõî- çàùèù¸ííûì ê ïîÿâëåíèþ ëîæíûõ öåïî÷åê âáëèçè èñòèííîé öåïî÷êè. Î÷åâèäíî, ÷òî ñâîéñòâà àëãîðèòìà â çíà÷èòåëüíîé ìåðå çàâèñÿò îò ïàðàìåòðîâ m 1 , m 2 , x  , y  . 3. Âûáîð ïàðàìåòðîâ àëãîðèòìà Ðàññìîòðèì âíà÷àëå ïóòè âûáîðà çíà÷åíèé m 1 , m 2 . Ïðåäïîëîæèì, ÷òî íà îáúåêò äåéñòâóåò ëèøü ïîìåõà, êîòîðàÿ ïðèâîäèò ê èñ÷åçíîâåíèþ îòäåëüíûõ òî÷åê îáúåêòà. Ïóñòü p-âåðîÿòíîñòü èñ÷åçíîâåíèÿ òî÷êè â i-ì êàäðå, p - 1 q  – âåðîÿòíîñòü òîãî , ÷òî òî÷êà íå èñ÷åçàåò. Èñ÷åçíîâåíèå òî÷åê ïðîèñõîäèò íåçàâè- ñèìî âíóòðè êàäðà è â ïîñëåäîâàòåëüíîñòè êàäðîâ. Âåðîÿòíîñòü òîãî, ÷òî òî÷êà íå áóäåò ó÷àñòâîâàòü â ïðèíÿòèè ðåøåíèÿ ïî äâóì êàäðàì (i-ìó è i+1-ìó) – ðàâíà 2 * p) 1 ( 1 p    , òàê êàê òî÷êà ó÷àñòâóåò â ðåøåíèè òîëüêî òîãäà, êîãäà îíà ïðèñóòñòâóåò â îáúåêòå â îáîèõ êàäðàõ.  ñèëó çàâèñèìîñòè òî÷åê âåðîÿòíîñòü òîãî, ÷òî k òî÷åê èç n áóäóò ó÷àñòâî- âàòü â ôîðìèðîâàíèè îáúåêòà, ðàâíà k - n * *k k n k n ) p ( q C P   , ãäå * * p - 1 q  – âåðîÿòíîñòü òîãî, ÷òî òî÷êà ó÷àñòâóåò â ðåøåíèè ïî äâóì êàäðàì. Âåðîÿòíîñòü òîãî, ÷òî áîëåå (íå ìåíåå) k òî÷åê áóäåò ïðåäñòàâëÿòü îáúåêò, ðàâíà        1 k 0 i i n * i * i n k n ) p ( q C 1 R èëè       n k i i n * i * i n k n ) p ( q C 1 R . Ñ âåðîÿòíîñòüþ k n R ìîæíî ñâÿçàòü ïîðîã m 2 äëÿ ìàêñèìóìà â íàêîïèòåëå ïðè ïðèíÿòèè ðåøåíèÿ î íàëè÷èè îáúåêòà. Ñ âåðîÿòíîñòüþ 2 m n R ìîæíî óòâåðæäàòü, ÷òî äëÿ çàäàííîãî p êîëè÷åñòâî òî÷åê â ìàêñèìóìå íàêîïèòåëÿ áóäåò ïðåâûøàòü çíà÷åíèå m 2 . Åñëè çàäàòü äîñòàòî÷íî âûñîêîå 95 . 0 R k n  , òî äëÿ çàäàííîé âåðîÿòíîñòè p ïðîïàäàíèÿ òî÷åê ìîæíî ïî âûðàæåíèþ äëÿ k n R ðàññ÷èòàòü äîïóñòèìîå m 2 , ïðè÷¸ì äîëæíî âûïîëíÿòüñÿ óñëîâèå 2 m m  . Êðîìå òîãî, çíà÷åíèå m ìàêñèìóìà â íàêîïèòåëå îãðàíè÷åíî ñíèçó òåì ìèíèìàëüíûì êîëè÷åñòâîì òî÷åê m 1 , êîòîðûì âîîáùå ìîæåò áûòü ïðåäñòàâëåí îáúåêò. Î÷åâèäíî, ÷òî ïðè çàäàííûõ k n R è p óñëîâèÿ ïðàâèëüíîãî îáíàðóæåíèÿ îáúåêòà ñ âåðîÿòíîñòüþ k n R áóäóò âûãëÿäåòü êàê 1 2 m m m   . Åñëè æå p àïðèîð- íî íåèçâåñòíî, òî ïîðîã m 2 íå îïðåäåë¸í è ðåøåíèå öåëåñîîáðàçíî ïðèíèìàòü ïî ïðàâèëó 1 m m  . Êàê âèäèì, âåëè÷èíû m 1 , m 2 ïîëíîñòüþ îïðåäåëÿþòñÿ àïðèîðíûìè äàííûìè.  ñëó÷àå îòñóòñòâèÿ àïðèîðíîé èíôîðìàöèè ýòèìè ïîðîãàìè íóæíî óïðàâëÿòü â ïðîöåññå îáðàáîòêè âèäåîêàäðîâ. Ïðè ýòîì m 1 âûáèðàåòñÿ èç ñîîáðàæåíèé âûäåëåíèÿ äàííîãî îáúåêòà ñðåäè äðóãèõ (â òîì ÷èñëå è ôîíîâûõ), à m 2 – èñõîäÿ èç äîïóñòèìîãî óðîâíÿ ïîìåõ . 4. Ðåçóëüòàòû ìîäåëèðîâàíèÿ àëãîðèòìà Îñíîâíîé öåëüþ ñåðèè ýêñïåðèìåíòîâ áûëî îöåíèòü, êàê ñ óâåëè÷åíèåì êîëè÷åñòâà êàäðîâ n èçìåíÿåòñÿ âåðîÿòíîñòü îáíàðóæåíèÿ îáúåêòà, à òàêæå óòî÷íèòü óñëîâèÿ ïðèìåíèìîñòè àëãîðèòìà. -x}lWO[}bK[|٢sF+Qg"H2qL uc06@xD`FP^U̺:M09ާmc&|9=4Gj<%"ɐ#aM]!8r=-?Bdӵ~HiKE{ RY-ѡ Ls P˵R"/epX_KZB`Ɯ$!|gL]NZ_S*)H~oOmvL %.wHcsZg:ي~1݌jǥ)ѡ/yߝ[`Y@^ç;"[_ߠ~.Wy ;Gtx֣ d1,AR| :/aw0md W܎2ƿH{1|ҾFk{ѹyx;mȩ|{[m9vf'e觤?gUlu8>+e2BQc84v3dc;Щ>vt<1f]%䀕cۙD 9 |stF״v9vXmCv-^+'ѡ]i_t]>3V=mΠ!r$҉ \MeDZ-/:tPV"߇:GY\-ud>CUY/s5Ž{9Fu_|!wqjlOpVV,n5ï3OB[V湕Ț+D{ĚcOїGzzѫs3jàr_/uCʽ}F[g8> {Q/=QG2Y|Siس1ඵ9io^E~]kf4E|ts4'F̹udjy"FV}pǭ71/@w>sc/߈[<φZe~m=9hhO~/gZR+Qp>sR΂8hvcF,NWϮ_? S8cf0iq~mcado) ozZ+f+&#)G}V9'ir?8h-FCyX7^MuԷcN)*2QϬRyp d!u/-r n >g.9=s[o ףU~z{J R1DR1Tѧm-ƪ1GGV%;Bl\&g5_>"c%!'X p:T-ԗC䊐+@X @'X y<̽#w{GBNx(c;.1޽#!'Rjkޏ:G̑umk^{HP@{ >MO1/xՠJB>fY%)]aE޿JaL>FzÛN̻" /nykg)~=0p⪄++M|[Vu_$,~5LXuʂ<ܣ5BIvֽ}I;nꨝ7/h9^ᴇ;Bu*Cin5pA$472]$(K$9"g]S& ;q?~ NX!+eKt})ҥVtM~nSHus{kn>ź 10z*4E2'v;n~VoW@7R_8 ,T^~]Z7tŴOGZ/_UHj nCf戧;a&OwޭvonU_aa8Os#X.{rqJ(~Jg+gޛ]_<4,U_ f,g'2̯e4_.H.cڮvug+m< XɦG l`k7a:TeY^ 1߬1."4aOqmH/X^O1E_G5FZx1\g;{[uN2sf]=p1cΤ~-ܤ1aN)yMߵcX^Bv_hmps_NY źeĈIߎ`ϮnƱCZ9#JJ=ddrLqN3&YsYY(li+}ujG{|N)Fd__ǵJ3Bw Xybm;b  v{ ]iځ?ηtimqֳUidNФҡcxAIǧNbV` ~IyJv~뮝Ϻk8gt βl>cO=3{l}~R %#Z^B2DnwF}u ޓuz!vž+aޞ*)bx&,&S`:;d'o .kLZ$W5?iS{=zmnm|S{jKkAbJݻPP ɎzD6UOʮz.lVC{kcJk;Ϯ@?&yQz]׶=V~[wevٮZ&Ȃ;JtVjfÆ>#}l#C9ĔK <|eqnEvf cᾐFvKLҒږ$p%{ʛ2W$rf75ۓ&nw&ryL݅|8AK4`[xX-ا£$Ѥh'dk> :xԉǰ)6bx\/ojԞwh.k$3;8߾k:Rm\XYW*fۇ|^^Wgm${ۘ<>Ε:4f?ClyUk;W?{>A>]F'#j}_jב=cqc޶ ۂ= eq2,[VH`}%fgmT[c ޭ.ۆ*O{t0mI,g+GvgMϜf9 &e{7]Ĵm.Ś\{QݠzI_i<ʉC;~vKGvs,&6? X-1"9Os,tJzeXI;N|!X©?DzLu9BIi\vƊ~~Qz  jd"gTrm(}<1'TvKgF.yŵ>o1Hzz0Y:D"CnDz,Q9#U-ig7o bEj즦ٸ~*{IGu7[~?Ȇ~OQ%4AtMlYFe~SCOOfvb]cYyc2 of,ӓ3&І6A=yqqƋ xqxA-Y1KlLV|)z˟>l_6;n1o)ࠜ{bDzЋPm- m5dVrJΨaolfCQEYd ɧoOE:rܫ~'/)Q'zm'S /{c'!psQIM>Of^QbPF춈]7G'icM;׼&߶$, ')M?/,0C-|rsN %c]*O|PfQD~OV2zutx,V|Y582'nje}Ax2fv }]ϺA8bWG) `\/n)].':|T7 VYEyc)!+ә%/NVcԇO6vܗ.aYP3etNn)l2pl_Kh ;坡2Beeg !O[PKr~,Otk|'ߜxmexʽyMU~#ʐa;G d坩:d% 4Z^H5/#_JhlS)0?p=ٕ<۩yVkîG3ͲC|v/u-#dauHSf>4ީJSx'Sޞ̰n2Ƽ|DgrT _*M-{~-I;%sYgwK%6={dg:)!%?yCy,_CGw;i#zA=C0-KGy 184g}|@=i2~c@W lQYyϾ47Jhw'#>ӋN;5N{[)U廬; X|CF'&l3[t!g|0KV40a1l܎ez쟒,*ЁS7KR_fّo#$[T!V|xE-裒 f yNw}: ڤ<}O]xN="rNy7}C;k6ag&ٝgĈ}F,>kvȹY4>k~LۉϚvޥYՊͤMY3bΚ5zzO3)pVtW]Iه7ByeeʎN[u.c|.Vjݗaz";qo{2:pw$k~ 9Xr {c^BvEhc ^?7 _l{R8]J3O~LlKMJcy=s~蝹Gz0f s.{ƷbxC <@ynzn4LU>c3]tPN\Wٖӆ y?7kV-R2y+E< !> jd=I'ʵslOgڨAX|T7˝oO@_(PZnzK9pYm\@qtbܦ<Tßds35{#7 -SHZ'Cz=Cz۝Y !?6BxS:m/L ]ƽԥȝiK;6c9fb`:H]-u|9Y#z{`_,ɼO. ~H/3[? ml͝.Iwk IrhU+B̟Z{^^\uϼ5, ɰ .0[!fԝ@i >a8(MMykBK\=}t*O)nQ~'^fsg/ҿGiIpSjHwլ 图Qe߃ջj }, f[}5owc;?O»Xd bHS6y*Kai{pT>ߩXG(mߡ#>#$~`:B>8m;-^<?A" Cm]TƪϾ4^R4;qX0MIekξ4s,/fF |H&ޓ39ayo䃼+s&ۗ~|4gZ'Πҿ7>R'sY^zPV_6 u57?4 ļSO|0nC7û|gAtN6e^FO2KzR>I~P~?l J$ݣk=$K+^Z;LJ~*XW߫ti +ݫY2!ݦr5[$3DkU !]9$F21~`,Ll)?"c4<_}4ckV 'I3W><Ƙl~V0Q,{槿M2]Y;[ +c=725c"  [-7N^ڳN2 dz/y7r$׼iz{+C,sɦ~ľ-غ#-Wm"ck8579}~Î4}8\j}Ok9OVB6g!yW=_SIwl^7t4E{TNآۢanB|aru)'7M''x%8./˷ %165&y>z;NJu[)[W*Ar2%"{B-LF_\1R;K9of/?Ieٿ|~aG;r٫ˉyfJ]cx),,\-e3X]1MSu|>RC^"/d]rdBӜ('+U-T֢v><-kR ҩ[eY=}v 'ߋZR]kXY}tuP^m_PY|n[roLKOo => T݇,U1}s_?xˬw5!ʘÈQ}>-S;߈oVܢu=)ePfOѧ5⡟5rۥpAnT^n!7ʘS/#r¶;{玷Ҍ¹)yXOı{8C]d#w}Cl ̡#ףŐcslh,>lMD*CւV:`9s,բ4ss}lvW֗TW}UKxB麁WkyE}x^Kdڏ?􋴮b.U#k(v}N;UQ e=kR@V%dΘ@Qޙm$%nR}ȿ İ~|i@7ۑA5b/'M( `̳g~x7.A[wmPǺMe!zMbprde|Y yw _AH2$\H0 ջz3~׿&i 3iy>x7|? gsx1 x(g&z`in8vnڎro8O =7r!˝2"Dekm0 O>6&(Ow(5t2W(6*O?e|車iSLBڥ9Y W" TK%;U`|y.]WY Ϸ6!g&̼º e֟XHO=#Qȳmxn.` .6>nܮaF#7( _d-)_<~GVӌŻV?}(#b)q;է3D=/Y^YerC7yQڿEeK-ѭJ{*ӱ@ QiEVOF^#2 zimedr~Ryg ImR4;~3 }7dccO-SM6I&~*p#|ů~S2 0~-i!m? 6sÓ>༦|Sn8Gl6pc<ˀS_w`ޭ2K7gd") ɗ-zIR>w11?73<1|XA=\nh6 v#m]8ȳ\xx@.oQޙS&xo1mτӻ%l.vF- fc<㑦 aJg>T/g߇K1-'<\A|d߆i88xFE>#=X?MrnW2=+l E261˼Q\~3a6}X ,Qk*˕jrqڧSh6KSG2?Ev^jaa`_koSחWb 2g' {X=[=%8npy<> C&x@|ǦW^QN m= ٰfs&ݝuQn5͈윥h*t^D"MgLﻥgl7}gh)v]kg r n.Ec+&Kw2.QesjmVsb^(CF e*;E_!,3nScx=I!n{Q5+E_x\+_ sSs͓TU~ʠh+%1pc}rFؒ plɾGوdmYc: g9rF] c1 <'cаy4sA>g-2U>;]y V)}6Y O+Jq+'jx>D(|ԡjܣ^Qri;ga{Jv9 iWD_s+:ċ. |Ѵ;q>oXcзiҫ C]3u?FiH:}wVH@5+-w=w[=n'V}+dsO,C~f9`Q1N+{y]z7n蘤 mNe{K.}X_^w+ϘQUOX n-hTѠI}{M+k{1ߝ϶vIky?iM%,ef~?޵?QZxe͊*]De֍?OwpkX5魀<}DjsDѷҔ2oox޵\$wɷ!݈nƱ ]ZM=x5іjzלb yw#ns c˾5>Ƕ2zoQХo>;l匛9*9v9%scfU=7zn*5pkÁv=+5v-XMS;&?OnC WB_II`V5$x?,+DMMʨఢ<$vO^y:YЉ}ؿnp};;']~-!~=z/vU8@}Rr~mGB]w*b~2eGvzvv gonHL+w]/ znU/oz{˸ӻ^W8:HE|\3|<]})#h%ۡbNWhfJΌOz8W4KI~|4-G G~Z@5ѬOMӚ1Ne岨XgCSXN]frӦqxkF htf474vi*qڞ2x<]Oťce΍ǽ1z蜳t_OB?_B.n0)Tnl%pc+[*f܀kp-U H?} wp3ܯU\UGgop>=yߜl{U 7/># ?G?RU?)̩U̜l>7s*S͜ nTp3Vy kf^ 7s [Rn7f|W1ncÁV}Zzݭ1e_Ӿe 2G^ځ{oA'OJ卖B[it= R+o8ت4iv*ztƅ*ƿTe4_(vɯ`z\1ԯ9y2U؂f7kdU9yn f}7sU7y]nlpcTo|pU9v K]RUyn|pWDU<wU>=VUy 'kIMskoo݆*|p3*uubU~?LN ? ܬf] 7~$p5~' n$pW'{U? IOwU~e-SUn$pW'; QU? IOwU~ WU& '_(f>_~? f> 7~S͜Zn$p3y*Ifn7sKU7*If16c|1e[>φR),9G^φh\)<F i/h!N=e4MF]o 4|[jgC_FTNy>h;|ƿ(@3~Ifjm"umY _³#pd nЪOn|"p*ܬfD'7>nlOn|"p =n7v [7>O|"pc3~D'7ת7>kkɵYK~f> 7>S͜Zn|"p3y*-fn7sKU7*Df16|wiLٔ+4!mJM ?7gpEsi}O>>+87GaoqѸRmA#>\FKiwCbe4A3>\fC}&_f|8hƇzyh}e|"A3>\fkkRU^1Yw?uw" n]pT 7~=;]n|pWo(pG? UQ7FUƏ7~]nlpcTo(pG? UQ7vVUƏ7~]nlJ(p3*QfN7sjUͼn浪pG-UƏ7܌pG1np.K>1e ; yyyzCmшQDJш_%y]w_r0<[*K4Po 404_ь_%y]o 43/i̔CB]nspWo|$p# UHƖ7DUG7>]cǀ;1U HGwU> UUn|$pW# oUuYKVAHf>7yU͜ nԪp#y kUfn7s [n7UG7c ܌]̨\1Ƴ&YSt=7?f52Eyz|:ս{E<7+q§F|<'қx}gb>7+4@hcfe4A3>]fCE4,*iv=unkjȟcRbÿ npS Tʧ7?Y7>O|*pc{ۣ~S Tʧ7v{7>O|*pcs~S Tʧ77>e>|>BJw|n5pnZRf_~/IٗU-ț5yV%opopopW%oop~U~Ws779lxϱ9{&U-nws 5cTspopopWsl&pc3 UL c3Us7795xϱת9{U*[9~skcNw ĿsſN /4maei`7[ee.體 ;f)hi 5` |iU{k8$ 1[E =‡,,35 Áûëî ïðîàíàëèçèðîâàíî äâà âàðèàíòà àëãîðèòìà: îäèí ïðè 1 i   ,à äðóãîé ïðè i i 2   , êîãäà ñóùåñòâåííî ðàñò¸ò âåñ ñëåäóþùèõ ïîäðÿä îäèíàêîâûõ ðåøåíèé. Åñëè, íàïðèìåð, â òð¸õ êàäðàõ ïîäðÿä îáúåêò îáíàðóæåí, òî i  ïðèíèìàåò çíà÷åíèÿ 1,2,4. Ñóòü èñêàæåíèÿ ñîñòîÿëà â òîì, ÷òî â î÷åðåäíîì êàäðå îáúåêò èñ÷å- çàë ñ âåðîÿòíîñòüþ p 1 . Ïî êîëè÷å- ñòâó ýêñïåðèìåíòîâ, ðàâíîìó 50, îöå- íèâàëàñü âåðîÿòíîñòü îáíàðóæåíèÿ îáúåêòà àëãîðèòìîì â çàâèñèìîñòè îò ÷èñëà êàäðîâ. Ðåçóëüòàòû ìîäå- ëèðîâàíèÿ ïðèâåäåíû â òàáëèöå. Åå äàííûå ñâèäåòåëüñòâóþò î ðîñòå âå- ðîÿòíîñòè â çàâèñèìîñòè îò n. Îä- íàêî ïðè çíà÷èòåëüíûõ âåëè÷èíàõ p 1 = 0,2 (èñêàæàåòñÿ â ñðåäíåì êàæäûé ïÿòûé êàäð), äàæå ïðè n=20 íå äîñòèãàåòñÿ ñòîïðîöåíòíîå îáíàðóæåíèå. Êðîìå òîãî, âàðèàíò 2 àëãîðèòìà ( i i 2   ), îñíîâàííûé íà ñóùåñòâåííîì ðîñòå âêëàäà ñëåäó- þùèõ ïîäðÿä ðåøåíèé, íå èìååò ïðåäïîëàãàåìûõ ïðåèìóùåñòâ. Áîëåå òîãî, ïðîñòîå ñóììèðîâàíèå îòäåëüíî ïîëîæèòåëüíûõ è îòðèöàòåëüíûõ ðåøåíèé (âà- ðèàíò 1 –ïåðâàÿ ñòðîêà òàáëèöû) îêàçûâàåòñÿ äàæå íåñêîëüêî ýôôåêòèâíåå. Ýòîò ôàêò îáúÿñíÿåòñÿ òåì, ÷òî âåñ ñëåäóþùèõ ïîäðÿä îòðèöàòåëüíûõ ðåøåíèé òàêæå âîçðàñòàåò â àëãîðèòìå 2. Êðîìå òîãî, êàæäûé èñêàæ¸ííûé êàäð ïðèâî- äèò, êàê ìèíèìóì, ê äâóì îòðèöàòåëüíûì ðåøåíèÿì. 5. Îöåíêà êîîðäèíàò Ðàññìîòðåííûé àëãîðèòì ïðåäíàçíà÷åí ëèøü äëÿ îáíàðóæåíèÿ îáúåêòà. Âàæ- íîé çàäà÷åé ÿâëÿåòñÿ òàêæå îöåíêà êîîðäèíàò äâèæóùåãîñÿ îò êàäðà ê êàäðó îáúåêòà. Åñòåñòâåííî îïðåäåëÿòü êîîðäèíàòû òîëüêî ïî êàäðàì, ãäå îáíàðóæåí îáúåêò. Ïðåîáðàçîâàíèå Õî äà¸ò âàæíóþ èíôîðìàöèþ î äâèæåíèè îáúåêòà îò êàäðà ê êàäðó. Èñõîäÿ èç ýòîé èíôîðìàöèè, â êà÷åñòâå ìåòîäà îöåíêè ìîæíî ðàññìîòðåòü ëèíåéíûé ïðîãíîç     1 k x x x 1 k     , ) k n ( x x x k n      . (2) Çäåñü k – íîìåð ïîñëåäíåãî êàäðà, ãäå îáíàðóæåí îáúåêò; x 1 – êîîðäèíàòà îáúåêòà â ïåðâîì èç îáíàðóæåííûõ êàäðîâ; x n – ýêñòðàïîëèðóåìàÿ êîîðäèíàòà îáúåêòà äëÿ êàäðà K n ; x  – ñðåäíèé çà k êàäðîâ øàã äâèæåíèÿ îáúåêòà. Äëÿ îöåíêè ýôôåêòèâíîñòè (2) áûë ïðîâåäåí ýêñïåðèìåíò, àíàëîãè÷íûé ïðå- äûäóùåìó. Êðîìå èñêàæåíèÿ öåïî÷êè, âíîñèëàñü òàêæå ïîìåõà â ìîäåëèðóåìûå êîîðäèíàòû îáúåêòà. Êîîðäèíàòû ïðèíóäèòåëüíî îòêëîíÿëèñü îò èñòèííûõ íà äâå åäèíèöû â îáå ñòîðîíû îò ñðåäíåãî çíà÷åíèÿ ñ çàäàííîé âåðîÿòíîñòüþ p 2 .  ýêñïåðèìåíòå îöåíèâàëîñü îòêëîíåíèå âû÷èñëåííûõ êîîðäèíàò îáúåêòà îò èñ- òèííûõ ïðè ðàçëè÷íûõ p 2 . Ïðè ýòîì êîîðäèíàòû îáúåêòà îïðåäåëÿëèñü ïî îáíàðóæåííûì êàäðàì ñ èñïîëüçîâàíèåì ïîâòîðíîãî ïðèìåíåíèÿ ïðåîáðàçîâà- íèÿ Õî, ïîçâîëÿþùåãî îöåíèòü êîîðäèíàòû ïî öåíòðó òÿæåñòè ñîãëàñíî ïåðåìå- ùàþùèìñÿ ëîêàëüíûì ïðèçíàêàì îáúåêòà. Îñíîâíûå ðåçóëüòàòû ýêñïåðèìåíòà ñâîäÿòñÿ ê ñëåäóþùåìó. Äëÿ n=2 â ñâÿçè ñ îòñóòñòâèåì ïðåäûñòîðèè ïðîöåññà âíå çàâèñèìîñòè îò p 1 è p 2 âåðîÿòíîñòü P òî÷íîãî îïðåäåëåíèÿ êîîðäèíàò îáúåêòà ðàâíà 1. Ñ óâåëè÷åíèåì êîëè÷åñòâà êàäðîâ n âåðîÿòíîñòü P ñíèæàåòñÿ è äëÿ p 1 =0,1, p 2 =0,3, n=20 âåëè÷èíà P=0,64. Ïðè ýòîì âåðîÿòíîñòü îïðåäåëåíèÿ êîîðäèíàò ñ ïîãðåøíîñòüþ 3   ðàâíà 77 . 0 P   . Количество кадров n P 1 Вариант 2 5 10 20 1 0,92 1 1 1 0,05 2 0,9 1 1 1 1 0,86 0,94 0,98 1 0,1 2 0,74 0,92 0,96 1 1 0,66 0,76 0,86 0,94 0,2 2 0,61 0,74 0,76 0,9 /x TWϝ]v{vvlDjB-VXX T[neۂBu)ZiPh4hGm YZFIgxμ1CGiޒ?s=sϽ{'"bfH}eF )Y_+Bu n"RO~e.Vnŭ27Y]tND$!;QFdl>z}||X,hKd%gsDΦJ Φ~O*l|]mOGDfɐDjX4qO{wb]s-(}f6{2UR! ^jI=/&k&6x5ܗжlcn7 \^D1ry/o[}/LB~Ee/}Ap.EGN1&H,y hb~#;a" h}?EOz,Iu6_E ^؟63lnBJ5zЫcX`j_'bl7cN9Wf|-m[SO|{.aI›W{Uody27VЦ6aP'e ~x'1rYuk1{YC*Ԯ13Q:d!'a;BvI%MvS#lt5Reb̭FƠwb_F;y)S='`ʱv!okŽt{,'G; *u|< 59YhfX3RMg7^7s&Oa \a?!ЯIYP7y1ċ%i'pBWηw1_G`9:% jB^ZE^ARmvfXκw#׃{ݍ^Iº` ^g#kul#`+hn~ ћM {/v/1~|]%uTQy(TrY.M| WG]Tx!Y7]{ }>ײo#&Nכ:_o$gw/q, %|w~N$V9k^`oĉKnQ7 xo#QOYms!&*}^wc.g68Sg_Yw'졷{=z3> .GyUm{lHRL=8#[*, s?ܛz7ei_=K; ? nD[َf);n` dvsWsV Z_z}j/o0O;lmzu\\Ǖ=׵lw}bxםml,︪6W0>\a6uh K;>8f]$,a%Ayšt)?sI+CnA,Çߪڔ3Cn>g|YQZ산Mrᾩ2j tVѷv 1%zykA?7)No-f Ev#zOz J ^?D?1 ϻmBpsXs`/l)H&Fy.XZ61IY#V 7HpDdONh息Mhr7fr)rEnKl2漱E'76T66 ImW&r)k37Fnyz[>[pzk-֦ޖzz[|z{ڠ7rF^7JoJ峷OcMyU)Kaoö_N[ _Wbm`f eUɩѠܙ/ i'׹o X՘Y(djyU6UEo8\&UEzYanw0쒔$*%X.`Lvl yYvGŚFyY^F"_+yZ@^p!/b*y-J* 9$b%$;]̠@%ں9*rēWN:+?g-iE}.2VHVupb(BTSb>h2F$Rcy{rq +KG;С6vwٵk߂1ߊ90SV]ev}F@p`aO<1־}zhݦ} DF/5ī3u0vstᮩˑ9OX٧#~4阿ػ zFm⸮8 GO_K>+|~~y_/=&}Q?ѾZ_Bwݱ6j'>x%+18%GuMZ*=Ã=kr\==[)!k~K$*_=C9b^8*^+EN=J딸tRr߈=^U5±קjL͈pVL{ܔĬԻ)ͧ_cc^*`UZ,9O<ϕ+vpDV?H9?V,԰~?I۔[N;_b4\L|fe+h^>9撯կ:oR#yrtM٘?#?mI/tn@KXc< 8FqDXWwZ@*`/xE^iaUiɸq)h.!{]GwY_ku+';v玭5G3c'3ovi#_]ˣW8(یc8vAL!9u9GLURKQC H$5;vP"$*,Mj1$_&\)$|1#kK1[5ܶҥ>7#XudBƚqk&ccM_5C+ctgT~cM=iXmtV)c܇,~-6GLJv2Xzec9cH|cƥe!.c꣍]ƚ5']~`re99k}1.]kGWٿUbck:pQ۷p&<>{#bѮ"ysJ睨WLTniRGKOPw nysW+NOw.ZlM\wCY:$.=Xʎ22'8>Mp.{q{ycq;AOy m)sc䌇Ѓ 4/ z r}˕;*o{{p'[ó< [TO3AMYF]J;DG}|ُ =2t]FFԑe?cçfeLyP'QiM׍w;s$gēAɏn6Oޠ-9yt.z8j1~-u { ͇y}ż1/Mr^7)1-O,+p<[UZ-,}vհ0m;:'bOX9rK\E]6CuYY61gɱ'ӹ-u끜Zy9u=J;jF7rz7WWXUrR8Vc hP6ˊS+7EbfU5kZі`cz-sSd-wɑ!2!Oڃ@C~\狠3or *|ḣ[I1p}wԒuCsP$' VJw{ WS4Q1egEكIˎ>e u90gsGdjcX?9:'{%|bI.N)`Urab/ju~rFMga3*w 7C{A?!_":`D{.%'_O-cdc;f]4M zkBK;Zsltd%qNJVca>md\[dU"VV"EiAض#rLUGOsdY%2k`|$e[i9?[/084/xLKu pia+ZM#t-C4VG33bWKi"m;TƦ6X݋>~ؽvAJ%hs:ڏcGeteY^,/r"\ޔ>/Zv֏Rw(cF=cy陫)V v`JPO :.G/ 63ѥSI/5K`?pBU$ՠd@XiNC_CkeϺ::lu;A/94i7PF7?jiOM΋v 8mOu=sgZqD#BCo图 fe_&Nw[|],13~Ÿ)sG 7xgCKN[tL{]f@V>2NR#xv`U>pkdDX3;eWy=l}Pb~ƚ;~x FwvV>5•BfdU.yPRb5o\} fp zd}Ϭ.].;e6~􋟼M#]쉏Hi^ďh֞o\n{cJDa;d!xX> M~m AiJe);s9rٚGNg2-ߢ-ml {۔yC:}}1u}k6q`GZ4CD)%^e=Xˉ^;xw6@ MjǾza _\7!Oh-#䃮\i%S6mEN_gMohG“q2FA[RZ{=8Vۄk*wOw銗蕻6YvWCyӊ7X%mVĕWB-Z9[~#rpN#t#w[p[szzi=}x a'A_rꦷ|)3y~嶁MtahGݝazՁX^3)F.Nc˔: >)WM!pA:t֩(Ɠ{\xݏmCʛki86淰]$n'LJ5m]v?a5!`x, CWyx̝ˡy K/)r\+IJenکcm :d D?¼ :6 >$6^L cr;t@ހn\U:.:{)_%GcDlxn>*zzu(1=ĵ:#58pI*|Ϲn# Z M?pТ˟z|2xӺ}nЃcWهi=8hݟ{. vP-'k*`E[ecgMf\rvnɇS̟C=$=kV˛_ˆG:!9[v275k ɸi*#O<>O2/ s o3/6o@_ys2tLRu.8c_3{~#;xO8;]gGyyȭ6'(r߳cڡ;Fz}9ӌKgE~4gio==iGuނ٣(s]SV#˱8b6u+?_g,>F?Crڳ|.U O(M @n!}u py'{0%nZy!V-d_=ede& )X~L xz|\bvW?gmg=:5$0@VÍJi*Q8GsOgy5,}#SCO霢g?pY*.ÁSa{oYUN G%=QaF,{1׻ ;Cx3pYSfLnG9#sʞ= 7&+G_US4ܛ3㼵DSyo$s(sx1~M wiP8=ae=CO̿JO?EЦ'㮑d#'v9K,˂ucvgAl쓬*1NhhO;x;y?U.`ȩjw bNe{tA 0cFrgw]gg[ ]mSB#䜲 }],Z;괷LcYv|N$h'IH+%/䆝%*ai=㝅^^_'i ^e?DCkّdyL4h>,&[!*l g.vu8NwfNpx'w5TpҹNv8(_{C%嶊s:QζI]_^ s;raКb{n^Ge!?u)agu%pQ'lN 4&6S*X%\'tᮞW$ >"k5Y\} O֡:iV6eZȄY9Ж"w;J܊0K9/Mξ'E9wHh9M|s9[(X]UrCS_ ccTI_>'ϗ\)J!Y̋ me]*`-3]^\4(ܯ%ct=5j(#2\ۯ5zrs!Gnб&[f،6Bn߬lrX>5vQF%\+9<%%CFvn.݉)IiܣxA.eb\'1.is:'QZ1~ήWp\EҨGȘ5X r׭;yG-"? X U#X8;ADa|U+]"W O_>#1iJW̺5V|S6=1OŹutJС? 8!|e =tɽfW])‡=JPzul pJ˄CnW܉K }п Hu{)uKj~߀rj vL﹢gjJo5OcY{xwVϯR]sD_̗L9G7lȊ: er!?ю2 ЛɭʴG?!gw+??=sc =5_=XU ǚˀ1Navep {b.u%8-)canI bK v`Us\-k$Ϲﹱ}A{2#I0e+H(=|<?Oc]\mw9 WW*7ס5y&2tЋi`(6DyM031*|T ZwVQ0wkI5u{CBq-DN J5*ƘI1Gꞧ$ΓifO* Ԙ'89Cy~E8#E\Cw2fǜHJGgMczb' (rʭC@g_ ,JL}HKԶJO 7|𨢃 HQ‘73!sQ|kW:cg :"'q4pImKn:rB!́]_ ~sG{|GiК[ E['w+hR3&HAZ_^^0G8+{^y{'\Nap`}(;_+Y/n-et rX#)=z>meCJ 9'zq-uJm=_ݠ\X}W0^.zσ[=s7ݲ>s,=vY" (YfGB̹O;u2iwW;y(hByU3qj:1Qp3VyO~>&3T>j MJy\W>mptk?ԳAdM[c]-}ŵJsMȕJ[}mj}ziSLKiJ𢿪>L/q̞V E{7!G0xw+?_"/8~YZg{`g :Kot?~ 2t:2y/1V\kϨfu;:{wKWk?a|mMl{|,4o=71,P HQo8R6<{"_؛ֶ+W |Set] jZ[)0Usrypޞx3L^ub3NK 6>߉V蘣a/_^W:ݮ&Y8툝M.ک'j'wC]$Yڣ :cЏ:!+^>HC,7_ ᮧm|XoF|0|H~XHS0.T y[WY>zpNv!_V}zpp~w' vv)UǶ^]c{^XHgO<ħN5[-ݤO/Wʧߒ|&Xt#iۃ#[o6(y|OCbʦۯ7ejВøM'םNQ{bv\EWe_o:&)G/EH_|K/~ĮU>ܿӗi7_us-|imRRG?딾?PP+P^=(OtkDA ~P\umw2v(M/r H1N^]G4+m]N5z] yx|q^-EFq-АK0=­*mdw?g2nw{8<֩(/95j$.Y#)^Ǭ g{ -O$W>Q]7g٥p_>c`+ꬷmNJJ q}>BI3FzQv{p$ڙK>+=Nr(%¡ßrt+HOP7K7 +O͆3<_WǙ7np"g>d@byY{Cԑe-}~.E[ 8%< snYiSَl+N3BS[$U~T==DOh_<90PIFW;Z.xӪto>%H-c<3tnZ'[k.[sZYnG/q0}:Os9]pqz~(%OZ.m^.ioĦ ڀ47&O:Kzdjpg[EUsxF֣N=͡l7Ey";Z|Yk/|%t=8p[H.κA]G'pc|p`.ӎ{p6eQKGϕ 4$` V'KViWNgViXMg8?VioNYng-/Lś I>|A.;ב!2N,3`g{u{и:`q3nGcAC~󥅮>E?jfJ cCNv`'ZVCQc=dzy9GJhzVgV&?+>uDNbN$->a92ꦱg08g#oڒ뎛)#w5H81ckHq+}ή t挷4񫴺 ʜ7%慲<;[s>g}oQ/̌"IȈ2G2u;Qаf;'Q=er7ܼL OBcp[hIӢ_(ﵢg7vh{LR3I\6X'˪\ dzAȞ ݖv= :exاSLJᅎJ1t)OU6+ρ6qCGm ϸRnSڠbdžαy?Nd,,36 Ñ óâåëè÷åíèåì p 1 ïðè ôèêñèðîâàííîì p 2 çíà÷åíèÿ P è  P óìåíüøàþòñÿ, íàïðèìåð, ïðè n=10, p 1 =0,01, 86 . 0 P   , à ïðè p 1 =0,3 çíà÷åíèå 78 . 0 P   . Èç ïîëó÷åííûõ äàííûõ ñëåäóåò, ÷òî ïðè ïðîñòûõ àëãîðèòìàõ îöåíêè êîîðäè- íàò íå óäà¸òñÿ èçáåæàòü ñíèæåíèÿ òî÷íîñòè â îïðåäåëåíèè êîîðäèíàò ñ óâåëè÷å- íèåì êîëè÷åñòâà êàäðîâ n. Ýòîò ôàêò î÷åâèäåí, òàê êàê àïðèîðíî â àëãîðèòìå ïðåäïîëàãàåòñÿ ëèíåéíàÿ ìîäåëü äâèæåíèÿ â òåõ èíòåðâàëàõ âðåìåíè, ãäå îáúåêò çàòåí¸í ïîìåõîé. Ïðè ýòîì ÷åì áîëüøå èíòåðâàë âðåìåíè çàòåíåíèÿ îáúåêòà è ÷åì âûøå âåðîÿòíîñòü p 2 , õàðàêòåðèçóþùàÿ îòêëîíåíèÿ äâèæåíèÿ ðåàëüíîãî îáúåêòà îò ëèíåéíîé ìîäåëè, òåì íèæå òî÷íîñòü îïðåäåëåíèÿ êîîðäè- íàò. Äëÿ äîñòèæåíèÿ áîëåå âåñîìûõ ðåçóëüòàòîâ íåîáõîäèìî èñïîëüçîâàòü ñëîæ- íûå àëãîðèòìû îöåíêè òèïà ôèëüòðà Êàëìàíà ëèáî àíàëèçèðîâàòü èíôîðìàöèþ îäíîâðåìåííî î âñåõ èìåþùèõñÿ êàäðàõ. Âàðèàíò àëãîðèòìà îáíàðóæåíèÿ íåñêîëüêèõ îáúåêòîâ ìîæíî ïðåäñòàâèòü òàê. Îáðàáîòêà êàäðîâ ïðîâîäèòñÿ ïî àëãîðèòìó, îïèñàííîìó âûøå, íî ïðè àíàëèçå àêêóìóëÿòîðà (ìàññèâà - íàêîïèòåëÿ) âûäåëÿåòñÿ íå îäèí ãëîáàëüíûé, à íåñêîëüêî çíà÷èìûõ ëîêàëüíûõ ìàêñèìóìîâ. Çíà÷èìûå ìàêñèìóìû ìîãóò áûòü âûäåëåíû ñ ïðèìåíåíèåì ïîðîãà. Åñëè, íàïðèìåð, â òî÷êå (0,0) îêàçàëîñü çíà÷å- íèå 100, ýòî ãîâîðèò î òîì, ÷òî 100 òî÷åê ïðè ïåðåõîäå îò i-ãî ê i+1-ìó êàäðó îñòàëèñü íåïîäâèæíûìè. Òàê ìîãóò ñåëåêòèðîâàòüñÿ áîëüøèå íåïîäâèæíûå îáúåêòû. À èñòèííûé îáúåêò íàõîäèòñÿ ïî ïîñëåäîâàòåëüíîñòè êàäðîâ ñ ó÷¸òîì òîãî, ÷òî îí ìîæåò ñìåùàòüñÿ íå áîëåå ÷åì íà çàäàííûå âåëè÷èíû x  , y  îò êàäðà ê êàäðó ñ ó÷¸òîì àïðèîðíîãî êîëè÷åñòâà òî÷åê â îáúåêòå. Ñïèñîê ëèòåðàòóðû: 1. Ëàáóíåö Î.Ã. , ×åðíèíà Ñ.Ä. Òåîðèÿ è ïðèìåíåíèå ïðåîáðàçîâàíèÿ Õî // Çàðóáåæíàÿ ðàäèîýëåêòðîíèêà. 1987.¹10.Ñ 48-56. 2. Ãîðîõîâàòñêèé Â.À., Åðåñüêî Þ.Í., Ïóòÿòèí Å.Ï., Ñòðåëü÷åíêî Â.È. Ëîêàëèçàöèÿ îáúåêòîâ íà èçîáðàæåíèÿõ âèçó- àëüíûõ ñöåí // Àâòîìåòðèÿ. 1990. ¹6. Ñ. 3-7. 3. Èùåíêî Ñ.Â., Ãîðîõîâàòñêèé Â.À. Îïðåäåëåíèå ñõîäñòâà èçîáðàæåíèé â ïðîñòðàíñòâå ëîêàëüíûõ ïðèçíàêîâ // ÀÑÓ è ïðèáîðû àâòîìàòèêè. 1991. Âûï. 100. Ñ. 27-34. Ïîñòóïèëà â ðåäêîëëåãèþ 13.06.01 Ãîðîõîâàòñêèé Âëàäèìèð Àëåêñååâè÷, êàíä. òåõí. íàóê, ñòàðøèé íàó÷íûé ñîòðóäíèê, äîöåíò êàôåäðû èíôîðìàòèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìà- òè÷åñêîå ìîäåëèðîâàíèå è îïòèìèçàöèÿ ïðîöåññîâ óïðàâëåíèÿ. Àäðåñ: Óêðàè- íà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 45-39-49. Ñûòíèê Îëåã Âèêòîðîâè÷, êàíä. òåõí. íàóê, ñòàðøèé íàó÷íûé ñîòðóäíèê, äîöåíò êàôåäðû ÐÒÑ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêîå ìîäåëèðîâà- íèå è ñòàòèñòè÷åñêàÿ îïòèìèçàöèÿ. Àäðåñ: Óêðàèíà, 61115, Õàðüêîâ, óë. 17-ãî Ïàðòñúåçäà, 15, ê. 1. ÓÄÊ 681.5.015:628.21 Ñ.Â. ÄßÄÞÍ ÎÏÒÈÌÈÇÀÖÈß ÏÎÒÎÊÎÐÀÑÏÐÅÄÅËÅÍÈß Â ÑÈÑÒÅÌÀÕ ÂÎÄÎÑÍÀÁÆÅÍÈß Ñ ÁÎËÜØÈÌ ×ÈÑËÎÌ ÀÊÒÈÂÍÛÕ ÈÑÒÎ×ÍÈÊΠÏðîâîäèòñÿ ñðàâíèòåëüíûé àíàëèç ýôôåêòèâíîñòè èñïîëüçîâàíèÿ ðàçëè÷- íûõ îïòèìèçàöèîííûõ ìåòîäîâ äëÿ îïðåäåëåíèÿ îïòèìàëüíîãî ïîòîêîðàñïðå- äåëåíèÿ ïðè óïðàâëåíèè êðóïíîìàñøòàáíûìè ñèñòåìàìè âîäîñíàáæåíèÿ ñ áîëüøèì ÷èñëîì àêòèâíûõ èñòî÷íèêîâ. Ïîêàçûâàåòñÿ, ÷òî íàèáîëåå ýôôåêòèâ- íûì ïî êðèòåðèÿì çàòðàò ìàøèííîãî âðåìåíè è çàíèìàåìîìó îáúåìó ïàìÿòè ÝÂÌ ÿâëÿåòñÿ ìåòîä ïðÿìîãî ïîèñêà Õóêà è Äæèâñà.  ïðîáëåìå îïåðàòèâíîãî óïðàâëåíèÿ òåõíîëîãè÷åñêèìè ïðîöåññàìè ôóíêöè- îíèðîâàíèÿ ñèñòåì ïîäà÷è è ðàñïðåäåëåíèÿ âîäû (ÑÏÐÂ) âàæíîå ìåñòî çàíèìàåò *x lEki-R^PJ" y塀aA`DPP $bA+B H|%%r}y^"| 1"}" r/<%D Wkr.rקτT 8hgܕjPc2b*-LqyK2Qoץ&EoŞ#N9uȫr#Od6@.;dsmkbZ>BZ|t ޮ!'r-r/-vʸ`b'o1vvJ>B?w@ԻbӺ,6/e"bֻ}(5z>5F{sqGŝhn9cPp7YIy!3[Ny۸{sumY썭F,/}־l!MTfڒi._ћ#@m+7kw ϴD\5S G3&kll9Q Uwd.8R'J7-tsi\jK() Y!=u3h;YwHრh*pl8kYP'H7v.\ sBp"p8A#9lJ%`'\n §ii p8|ocsRtI0TT6Nquִ-E)x,A?;}"<'Ɍ/ILel`MYb'Rrq_dF7C/mO DrW2aCsڑ;!{<~Z87jY&8BH K|쵌fx)}js JKk#;@:x*S_.d>ϔȟw5߂RF*HeH k˭5r$Coh2 :- ӹ͛8 ;M}"Nz@j ^z\ѧȿLo]'5gmLMůL ƁXr0 u_494A>qI5qHL4.9`1_pWڛRB, {6<a>B$u)1z.ߑ OWH@>1- k_~?]׻Wk/񦐷 h#Dzwuuo(Mf-֠6Nd):3AOY7P=q)ao$r/45נg!ۈyݓ~% j&<1ۈ?x< ' ֱ4 <鷇Eψ rbߏ5>8@-X~c?`5YcWnWgn-pwPȜ@Ew@){X8=nhoQj35w>zo N;U8[py nG;ژb^7x&V8E1T@)/8Xfp)W .~p{wLo(]. |PlB mH~͸>3PKS{{oEs~cw }*{4p4PW|198iHqsG-<S-~V X*`UUV XU$~V X*`UUVo 4rMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:11  l X  -\ d (16l 2 /r 1^ dq {)x ^Uywb0F L pQlГ*m&04"k1R=#OTRS((7sxBYg7~C& +{[zK2dɓ3]*h>NK $I%ɸK&$pL_$w*/!|IrdUr^rAP8;噡@_dʶ/W5*GC ɯP>fz[!Or *l>74wx } = EBT2(yB,k?֢i%Si_L3g% >YҶ'LzS'ɴ_uZl|MLMqw̸Y{\m2ŪSWM]oX0MTxs&v?i s±,LS|꾭4dMAͱݶkji,flhzօiQmZN:Bg=֩УAr>M</x uRc)kY#R^_x)@A0ݭ2p52(/͗NyRr~a-=xyo&0&tE\1)b|kpƛxNM?'K :joÛ1ߦUț#)怰W)͛6(oޭ} O(4mod5SYUv- *T%jy#)MiئrzпS!=*X?DH>Գi%|Xs1u9ZyPO@Nx3띧rKK[8a]A=e/EM.b?VI*颍7t%E|.?yEnjCiLiiG{Pٚ#ivmRjKJ#Mz<卍-܅tWGف 3>-e#7mBzЎ O[ Kȷ5o|҇F=?ϛN꼶JA hm|xOudʠHNݷ&iV<_6r-q˞;o45y ϬK5%pwӘ2v^3[ u=S_ _kq*K6>g8pŽ?:bM}NM\cB+ Y_SodqA$ OZ拟KNUA,չBxt(>]˯NOAs5~q o~^g8D*\vJ81-_t-ռC>:-RhMi%MB~$Eybf:G#ƞ(;|&/XӖ>7Uڮޝv2ESu"HnYpMׯ5?y/ڤZU8ּٵ./7FzƦ^`XC;脜JN?۴Ќ|L :MLs{N_q4Ȟ7M7MĚۡWW^{JUQznbzW^g=r>4]/岙Z*P Иm{&+UN3ƃ[ =NUax 3uTF>?TH86 9̈́vi'/.#MKO}tn!9?prg*;U!fp& f-.i=3^3h^xmK/z~*U!ߖ}vfSOĈUoOE W,+g_@ ~LTHf+!Zg#ƺ .Q>!]uWt 3:U}f}FkM'׵³6?!m3Vg딮8Gh8W۴ΖEJmPPͣget'ڰih罰Sm$yiG[*o]$?3|yi}Bz6?ި7%O?47/$QόW7YrG2[C/{@zsjO؆sH#`\n0,:㇜h+s_q(w=x2ӹ y<ٻ3'1$I{gh&|sG-Q̻ڨ=$i Uw=(n]}=Y{׃,X&֭tr|˴HEonVng;Ke,&/_Sn#m̽oSKI wԦ!@2J1&6Ou̓ۥ4!2˅,}R=r`=g S|bs.lf^(g Z gӴ(lT!;|30OLT7?[mɦzoܾ;2w G LӲ3Tda#=]}V>g2_ mBOw~k/I4矸vs?MLѰ_x=6Qw}* TN3 &S,_bkwEz YosglPXZ$mF߷*>X Z Huw&lFfFĶWlGP=af#mӰ'?omኺTvbk6)yZ̶Mxb[rOjV>:Z=/p7'4q‰g{>9P's58bͶ(HSHo)|RF i#6Ń9Py|Ze' 6F{BhMPs{n&3:rA{ZZ={ݻ5d77yd>ux1z4O]OlZt1<ܱDz|\ノ)#M?A/͘K_8;6RGP>w\O"c>8Oe0Wnp7W{XTnݘ:{^+k%m5SzָϢ^>ᅺu*;Vr~ ,d>\dge^vkF1'R j@b>B튧+7܅ ݭy\o7^ՙo3): xx['2Ҵ7(w;# O칹/ڑv-P87]Rى].#e'wS=v>Q`'GPO*6$5"#>}O>'<D&uƷu[ȇ8/pJuveyqhkF?Pu{ܗoEcbRe,F TgcfdMh?x<+ݖ~%RS}*zh3E.UGwAk(s KNن)nItC8Mس;wޫ[>BW{1:Ew3n?Oi$MFFh;E~ޢuInbzg@/ *N&T^ZKo;V{y{=HK]?oڳ'+ZkYWpKpW:aNE^7kk7ۡ{K ?~v a'_E OpovZ#l{vD>ﱙ6 ] gY*owQ/)}KUxHH~.8`!?Z䙝YK_ Mo5{4y>bM/MTl[͆CplMʜ. '&OnØ&$YrۆĴoυj}sWp.TNWى*s-\'xX3ϞORS>n >|pZƇA[uw o>64[txMq~>WvF91xۇ`\Ry%v:1q[Ipsz;6cOb1ב7 -QoC h Uf;6,wP_ v6w:3M-ԛAE5μ>m=O~7h|r@;x}o-_Ms| 2KМh:g~<'M| +=~?,TV逍يNDc.Z>s~_՜П b֏ eaLCv؎6Gn}P7}^B9 yG<^[Tvx} %]kh̤NQxPP]={ ۃQinnJ%1\o2<N[C[ip/phG0~6 m)Z±h#ob _~<ܦ+I= Pw;yl;E?TC]h\& x3k!K}Nx8D5ďK;T%*;AmbƎ`fOnbidw@) ʍSͻ;6v7;fq2?$> (h h>#ġӼ7'_ Ȫˍ_Ygob4maڲHLup48B^Zسy772WY Jq3:Rm7ɲr~g#؍26Ŧ нMdVC {L:I_8:sQF~V3Ў3"q̛E;hG_KI4?1Oiaޠx^ѷxF q,rtoCt_%m!\IYhH{a) }Q/S`;BUƝ  7)wϸ\q1'υ4NK_$?5spgΘ|ѓ3rnڡkyIo 5.IUt-9ޢ2 a r}xUf/$_[s@ ȼ$",. e|bx-sXߝhgЫw"$c,q}C'"cƎ]5k];nfBC1/ػG"c eHelf$'cϯ=}=vkgЫmvطʿ1څXoce.Tŀ^},?#:}^!s&lYiļ;s^v1~i KgAIDi7{鳢Y|/ZL/-Bvu7>#qzv|W|NյS|mj_[uC3RIƖv*B~#_ES4ሌ*rq4-W6XUF!a;%/If'W"j?wkd%C׆ЫC{bOۡU-/I^WJUZ \L^2r6/rWOۡW-Hr\|^ᓋW fzkdٜ4YkvlN|Fm|.5#VbsZ_^5]"ѵW7е[~8N׸.IUt&.I_No]7q ?oJ[|2nO p΍K'Dѻ1wui?1*=Kzra\O.Uۇ!<5 ]߇KaOIS>k\~) OgKVC q?Pz&E|`tI] bVH_}gwyyhO9SOoL+=IbZ۪I{*ǾN4qO!| ۄ׫_^uླ8V+}< HVkၺke1<,VP8}>>|=ސvk:oi~N>SWlܺwg vBC_m+<{*O`~cwCh/^KLMY0Oa^2|G0pRzODq4>c4L{aN4[bmzSK4czRg~)W:r=Q rMk: brZl z <1u槻w.M;t+yIK<](G"mqFW%NVe}0'&۫Cd_ׁ;Y:p tNrSVk`{fpE:ju0 ou uTg];w vx.c^eo$|\Ѯ!Z"]Ϗux~u/Yxy~4/h{ αO/^KOtwvg-U`[+vvޣ]ll9_E-G컶|cq9(t)}iKTvwR)\:!~jCuL,ބOtAZI嘱R?ekj<Ї&rc~ePΒ⇄/y@^Z~{C?!Џx3'1G|}xw#"Fn{!y?#VGD#IG?ўl>5}۫rѯ@~o97m WK/B?ץm;08"d8?=it9CɅr}/9Uc\2fU4 /Y= qeݼ{5wU6?6?!槣`y_%hu8UgP?3LtRGZO4Se0eO*\pΟ=nO)tϵk=us_=q]( u=1X^Zz=G9]AX%p4k(!Yp7?UIwM:͎|HG(C]CoX?/˞MMP4uaiyUpwW_Zwzy:R|W/r!u[rȿWSltmdo;Վlѵ˕|㺖vsϷH"?ld:Tjv>WT /I@EbOi"tإ%{l/?_9(p: }hZt}bwYR:l}J&Ö>kGFطvPǛC?h:?x)iiԣ V-nP9]RRKwy ?2bSI;T^$Wi*ޠXRO*} ywuYqCF5MDz @)鴙Z/WhXF !mm4w::w8c;z&+ӞUӞl4}43B-WZcф| fg庾2T{ղ*9s;}wδ{ƱC߶1-FZ}~v]u~ \q0 z_Oml""?;+E>ZÅh k]9iYz3D('hL3QLOFs|7Gk1|kW5ܼ"gp"=&9鐏Фz,~]GkzGkUOh|EpE>""BY2-=LLJכuC"mk\ aوF}vюlƪ{9=x$6B]K~$6LJͦ8{UGkX|}jۯ,veW5\p"h "cC̺Q7y;GBK&9AVtG[]vc"~w1hsKoxK|tG|{l]N3OrfZQ J>N~gqRG[uW79=Yx6u>6irz^&%tbc2rhWo\4/ʊCV>HYK(}.~]{Yt>?"s"J7o6M-co6uLltl 7?kXה%W-{^3t@:'c޿_{.t@Hץ%7䓟ӰOcu. ֞DM( l ;. l"[CzO8? ~u0lgSY߅ 5HŢM?}Ǎ_unw9e`p_&5^H~:c] нƧK+N~';GB*vCz7?2gbba2q딟%[}iG口ndnDRu57*Ұ[clw м-CCtոu9F [@ӼIOU{P>|ͻ/o^~סs@[߾X|yb_{W]MW-~~*>^'dgZr+u'gtI[/Ӌ߈bveW+uGs<0?]̾/k%p+5mݑo?UzZgYjϡ߯0_8VRbe[Pꖫ MKO~?*@}6uTW*܅<ڭ- Ͽ_7ģg.WQpxұere{,UEg&Cgο/owv~{'?e9:FN<[_ )wA2oRo<=cIM8/e0?z*oײ?S185}F  {&;H㚟XSQS{U+IOUAsO[˿Nkw)쯍+S |tTdb~/r?Ic\W"VH ytE_-*~[},>/[פD ~]o"^~R>{/ky+нG[Rx_/_*ȡS^QWi[%ڕ =+~' iÚ]4+J,Ef9n_twB] Y&zl };CFܥ#W h|?I: Clz6ĥ6Dcp;@ä[g&}MN*ՕO]ռC1#sWwH濥akia}WA\p:[WCG6d-:vWSv^h]Lat}}'+Obu/ċVt JCze]k,/x?fBKӫħ!z+JuM] o[}mC./y~NJ%ۙ5T>dzX;g oLm'f4ӊֆё=G$~,,s37 çàäà÷à îïòèìèçàöèè ïîòîêîðàñïðåäåëåíèÿ â âîäîïðîâîäíîé ñåòè. Öåëü ýòîé çàäà÷è çàêëþ÷àåòñÿ â îïðåäåëåíèè òàêèõ çíà÷åíèé êîìïîíåíò âåêòîðîâ ðàñõîäà ) ( а вых q è äàâëåíèÿ ) ( а вых Н íà âûõîäå âñåõ íàñîñíûõ ñòàíöèé (ÍÑ), êîòîðûå ïðè èçâåñòíûõ ïðîãíîçíûõ çíà÷åíèÿõ óçëîâ ðàñõîäîâ j q , j  N â ñåòè è âûïîëíåíèè âñåõ íàêëàäûâàåìûõ îãðàíè÷åíèé îáåñïå÷èâàëè áû äîñòèæåíèå ìàêñèìóìà íå- êîòîðîãî êðèòåðèÿ, õàðàêòåðèçóþùåãî ýôôåêòèâíîñòü ôóíêöèîíèðîâàíèÿ ÑÏÐÂ. Ñëåäîâàòåëüíî, íåîáõîäèìî òàê ðàñïðåäåëèòü íàãðóçêó (ðàñõîä) ìåæäó ÍÑ, ÷òîáû ïðè îáåñïå÷åíèè çàäàííîãî êà÷åñòâà ñíàáæåíèÿ âîäîé âñåõ ïîòðåáèòåëåé äîñòèãàëñÿ ìàêñèìóì ýôôåêòèâíîñòè.  íàñòîÿùåå âðåìÿ â äîñòàòî÷íîé ìåðå èññëåäîâàíû è àïðîáèðîâàíû íà ïðàêòèêå ìåòîäû îïòèìèçàöèè äëÿ íåáîëüøîãî êîëè÷åñòâà ðàáîòàþùèõ íà ñåòü àêòèâíûõ èñòî÷íèêîâ   2 , 1 . Îäíàêî ïðè ðàçðàáîòêå ÀÑÓÒÏ âîäîñíàáæåíèÿ êðóï- íûõ ãîðîäîâ è àâòîìàòèçèðîâàííûõ ðàáî÷èõ ìåñò (ÀÐÌ) äèñïåò÷åðîâ âîäîïðî- âîäíûõ ñåòåé ïðèõîäèòñÿ ñòàëêèâàòüñÿ ñ áîëüøèì ÷èñëîì îäíîâðåìåííî ðàáîòà- þùèõ íà ñåòü íàñîñíûõ ñòàíöèé. Ðåøåíèå çàäà÷è îïòèìèçàöèè ïîòîêîðàñïðåäå- ëåíèÿ â ÑÏРóñëîæíÿåòñÿ ñ óâåëè÷åíèåì ÷èñëà ñîâìåñòíî ðàáîòàþùèõ àêòèâ- íûõ èñòî÷íèêîâ, ÿâëÿþùèõñÿ ïåðåìåííûìè îïòèìèçàöèè ðàññìàòðèâàåìîé çà- äà÷è.  äàííîé ñòàòüå ïðîâîäèòñÿ ñðàâíèòåëüíûé àíàëèç ýôôåêòèâíîñòè èñïîëüçî- âàíèÿ ðàçëè÷íûõ îïòèìèçàöèîííûõ ìåòîäîâ äëÿ îïðåäåëåíèÿ îïòèìàëüíîãî ïîòîêîðàñïðåäåëåíèÿ â ñèñòåìàõ âîäîñíàáæåíèÿ ñ áîëüøèì ÷èñëîì àêòèâíûõ èñòî÷íèêîâ.  êà÷åñòâå êðèòåðèÿ ýôôåêòèâíîñòè ôóíêöèîíèðîâàíèÿ ÑÏРáóäåì èñïîëü- çîâàòü ìèíèìóì ñóììû ýíåðãîçàòðàò íà íàñîñíûõ ñòàíöèÿõ. Îáîçíà÷èì L,M,N ñîîòâåòñòâåííî ìíîæåñòâà àêòèâíûõ ýëåìåíòîâ, ìàãèñòðàëüíûõ ó÷àñòêîâ ñåòè è ôèêòèâíûõ äóã ñ ïîòðåáèòåëÿìè; E=LUMUN.Èíäåêñ 1, ñîîòâåòñòâóþùèé ýëå- ìåíòàì ýòèõ ìíîæåñòâ, õàðàêòåðèçóåò èõ ïðèíàäëåæíîñòü ê âåòâÿì äåðåâà ãðàôà ñåòè, èíäåêñ 2 - ê õîðäàì. Òîãäà çàäà÷à îïòèìèçàöèè ðàñïðåäåëåíèÿ íàãðóçêè ìåæäó ÍÑ ïðè èõ ñîâìåñòíîé ðàáîòå íà âîäîïðîâîäíóþ ñåòü áóäåò èìåòü âèä         iєє q a выхi a выхi i а вых а вых a выхi H q P Н q Ф ) ( min ) , ( , ) ( ) ( ) ( ) ( , (1) W:     1 2 2 1 2 , 0 iєM i i i ri r r r r rєM q r signq b q r signq f , (2)       1 1 ) ( 2 1 , , 0 ) ( iєM Г i i i i ri jk rh r jєL rєN h q r signq b H H f , (3)       1 1 2 ) ( 2 1 , , 0 ) ( iєM Г i i i i ri rh jk r jєL rєL h q r signq b H H f , (4)     2 2 1 1 1 , UL rєM i r ri i UN iєM Q q b q , (5) iєL H q q H q a выхi a выхi a выхi a выхi a выхi ), ( ) ( ) ( ) ( ) ( ) ( ) (      , (6) , , jєN h h j j   (7) ãäå ; , ) ( ) ( ) ( * iєL H q P a выхi a выхi i     (8)      rєN r ri i const q b Q . 1 ; 1x{pU9 yJ$BK!L- PdHj ,T VSU#6l`4/Yw)X[b$뷛'7qckV#>. $ɝyHF[ե*͸ۭWS&gеvG(!;x]'UfϵuD׃CA![mmh[6JA%]-y#dU$%Znvc̲*@YZp0ͬ2>/Ŭ5z%E6>s:qYv}OI}.cv%y{{v}mFi%@"/L1'?"}sA3Vwg61Xϸe'?| vY;c\4u7S^xUH#ĶٯXJxhkdx鞃XwIlWa-J˹"MEL[[./m9^[h?@{6s1v?P~ ]YNY9la7WQφڋg#fpٙfճU)[ Ňн۬~ `)+M>mo0}Mv4vC!uVѹ֦K<ح =Q>iWWF[8mGw\v[o#]ճ-&I)kd4;lmA*=4fhYz3(V_>]3t"š c%5>84~9H-ψ>'_''hQϓ>_ 9s>2&/nxb;޻ml-:OAroFs#F9w|eWK-rLo|ӤE5Z(w%=|_f\|}wln1r|[8MrDq{q,% A&6ҏkU&FSP? O X8-c _e`-h/<Sn`:q.7m%`0kAwJ Ȓyp* Åܟl4s sMP΂M`_닙79kgfs)$P͘5/w[W*PnԟbLmw|lds6j>-pNR)+/~r"ǻ4%-2u47˺S.EJneٓG9(QN%4HKӌ44KAj#^i`=cF ~s S4x1S8çIX5T0 ` a&Β x%XTs.fW.Lcp!(%.U{yç˳gt-^wS9Xhpd'XeOw мH;7J-!d M0;wϙs;$d>{{^{};%I9%IޭIg]d׌d5IR;$ɔd͋$'OKmewIrJ :W='9i5IM5[Z9{%K8L~РKY*JG]=JK^/G9U8 5]5"LI1y4^ޠPu}Q{,$W H pMߓdжݫfsfY,(uUm>X s~ԾB=Di {UY)6XύOe}Y$D 𼬮%bݟ|[՚ߩq۷nCw;j;\ya6MvJ|?|Jx= z;ljIA8KdN9m{N[\pdFodZDw 'gmI2r®UədYrtGL2]ѿLEd@yI׉cg%s2NU,v*?3znZt7.:qwUgY%wdXckɛUIMzpZ\s[MZY?DY2$ݚ~> ,w*Gű\*./Mj\O?Bex5"P;z:Czrk}vUVy cc2g17z0j'wbnx\ݭ2*y]=Hb2:hNa95cgw\M\ < 3F5" $'(S4UC:&cN]>G^fߖW<_q\e+r$["|=r=|HМ&4/[4ECr/.<}fCƥ/*WC^N3}֗x|_1FLGtD  u_>YNb/ ]N:[ _w RN˕vi~ xJx Ly`ڥ,35þ )@@އxO:+|fMs엢F7C] +9yu+ XKՒɓd8y<JK&O${ۢ)?}(-٥tWmPjQ к<u3^L84)CY q 5dڣ?3?$+h7#) d +,tKB뮪E߲p{ښtO!''^j}Oj2iV*0_)R8kޡiܴ2xٳW=Y^F9Ib)P1%ٔ9WluXj]P9ƆmJk{x|Ht_EzE$/~uVT7>Uj+V܎-v]uȏuKi)W,/_^WYK}/ uTk~Vu?Х=\nן@g7ykJmvxӎ\th 9%t(ǘ\I7k8P\Y|kw.ѷvՊ}N4B\.rrH^ɋy&)v|uӎެnl>\ aGk(*O*&k&eLOr^-^ L;[ goeOeyJ MкV`>\hyMÇJ%q]^eO(|&WڥuA񬛔QsHnZ^׼H^ț5Dlؙn;i9tv.};qR1V,/_wsl Fȧ=iGcabv~ȼCvKU_!uϞy3h|tyS#(ϡ$ca#vׇO.qL\p=eԉ+ Dm1Я(b;e_'ܚ'MS h$un>Nqwj;>TX)O Il*;YlȘ8lǁn;o<;5Xbۑ3yeuy؎Usg';^_-o( _-v,*!y}k{nsU;m."ˈcP^!ݮ-by͗Ebkbm'Q( vՊvq}dE"L^q)Ѷm|cv*0bZ)4yJ+g5Yò9Y26T¢jfōʯɶ|JzTqM'O'wÆ1v!DEf [ϝb̸fLl&u>1l#) {ݣ%Uy>vx a n;p`oV({V2,%@vd>Y0O騢tm݌";\pC{+:];pP2`W]? dKHP;fy.%0vHS;d/~bV_'fF%cx<jbE_IVk2y!c8으ߓk؋jS_#\ɾq}lΑP-[G( l2'vP}޴#VYև&YVۂxnc}5h\oR1w. z\<)“7% 6˲ߤ[=[ƒ'p>r=@Mu,*;y/qlq前@0hfy.CcZk \g(#dB{xJ`L=1(-Ēm#xip{N `\5S~Ar9-}Faf ?Q=,\)Cs z`V7nL]~㙦z ;4O0YV~ㆵYmڥ=FrJZvAz{Ee=<0br-!Vm7UoW*˵|UtK~vve^CtM[=1ozz!pށ>?ѓV>wT}~|S&Fm=Ag,i$|wgOxZSYabU #u5{ v4 ,%}*g`AW߉KհoR;W~\C]w_uaճ!a6 on6o~G"j|-d-گomy.UB}yްܣ6Wf<''M=V9#tx(GUցjQZ"-[dj*+D\!ɿ}@+@}t,R&FY7bl办M>w[Mw4/%r& -/QM35۵v8qoW>)W<I7|ϔR9w`++qq E㫨pxd)`NGs۩ g*S^;RSyp׿)XչܫTv</ s Ml/*`^+^qNˊ/V/J='$nπ IʷMMhzq|?'hvQU}\;`e|@y?uCm4Ti#v8OwK{58d-?GnԦK qa G59w`ZSst\ʘ}lsp .|)GӾyb=8P.ﶺ/C ]E/gjBȞ1@^#y-C _t{!II-=ˏw*kC9!{uf 2k[3>no'&/G&<e%߹f=8Y&ӧ|QzMz\u,_/^bñ(3 ҉k rx^_+SsǬV`}Z>{wu6_ȵu6KwKc.9kנlS;B135V/מ8W︜ -_=!}gsenYY.7+0bl cR&kCӮ8u؞Q788Ѓ! 8q>=  "rMM}2]tu}(= &AcS7// uܛSwlx.O9u[#jBWR_o;B0|eTy=qqKAWO4s{Bm 4 O3o\k|Eu쓐/sC>ߙ>Iaꓚx&5b/LǚOh\p|..h\j+Ë'Zϫqexq UwZ4 G_ҷgߴl~[H{rON^ |\hyr"iCLsm2iRng[\hF"͉UU47 ܡ~U_tuܷϔos=Nu0I̽'hﲊ9aY}~.v~=i 3#όӵ(Wb.{c=4ӲzczKcz_;5z*ј޴ }OkL#wL^<.? ܡw۪jg\M ?/ 3>Ko`ot)tz6rufݶZxEydۑ+b]w],F2rEؗ ~udw;iM5{l.;g؎\LoYgr&]jc9? }/q?~|s 4 ,4QkG#~rn&k|CG E~V`S8*d}˗~n?'EOvg ' D+_ꯥDp@k7N/V^%m{\/`;Rú[7$B'oLyߤUx%AG~5ry^}Sz~s;yѳw 'gmL VPgS<9|e>XB^3/IPdǫhᝈ; ZWVQS.^[y'~[^ySJa|0WZc 7~M]"Z֗ ~]᝭m7M=ӳo:X6gtN/Ҏ9',3,%DzWc\Mu^&,3fDsFN$5(}JHLj鉟TM0{(o- 摚}>N>>ӣW7WoT?>&tkm,pߡ_$xfpf ~mZǫG++\ŗI}ke!FlN>Fž&zG 7ijm͞Ю9dxtr Tut3(G+c@,ra]?]k2|ޟ{{S<;~W֗9CthΨG;<﴾oМqxl1Kh`P6gHt9*B鐼n7T4wVhxMソ'cs!ec;.Ãb\wYNsO|>_>tr.1=c?eS`B_k|%׻}/r{ɏk}y}%I8>{ԛ3axzip?!?̉W/q/~ yoBFo7o_~*{o&!'uL_{~NT#?}''@ >Gub%G^+++kX+o7+oF .nx,Oݫw7I7ø^>o\p=p'69Caa.t|ւiSظ4 1 +|2sD_(%x ;%/ om{pUsAy}{Ќm}J~=;85kউb7>  0G \R\]gaoRX8=I2p9R眫3Y}RԵZs-_|xEr ѧ&Khv]ii{]K꟭gmA~T`]ɮ̯A% Q{~Ъ~ƶ[uW|kL^2E>0;G>VyaTcy19vrFsLv|`bx|D9F}ItMoRK.z{ik\IsWMvD$2+/%uHO)**!yW+Ui\}kKZ+q}m<^|fb"7uZ$cvM6*֗9}i=x_>0twHHf eI%2Jga1S]?bl_|LjZ|Afmŧc;`] G|jޟzߚOnM;v&v\z%ᗠ|B|AR&kcVf}Mrװ'$Ge07?y+XY7j+c۶cfߡs·_Mo66_ |^CMaeohP?[R"7po_|q{fi c>|5#~,dYQ|~.g|b7] }66ɧw/[(уM{t`I6w!m>_S_/kFf<Owy/ZS?}' gk>kq_x1=17 q[z2|/윦>}Y۬x'yQ5pڎ eg R=*YSEvvAWԾTWSYMMmZ^7(SvBMA5_Fײ{g lpm­cxlbj3|~Up~n~e/Kޓ`c hp^28 옕 s.^]??_ ^uӘ+~V~]2Fٝ+,GuF{Bz&썵_/-)W_kc,Ӏ,_?í)vu`tfc_`MYx>d/ׁh|؉?`xU{=f;-ns(Z{-k'W?+d7c5_y=iK po_Z;iE XJ`emV_go7;=nܭa ypſ0 G7AobHó/o@9ihu),6MʰDŽ0ӂȏt9N6 q.K 18.uPƲA7Tt㣂#XB|Yo0><8A/ƶ'ٕ4JSH>Yk[Son>O<OQw, p:Gqb!4gmr 8/I^\(>41zv? yFEUk+9J_T]+%!f~d4w1wS?_ '՜bnhĐRcF~9xEyO2QdϽiN#ML4SN]H2A6!L^l*"|Q$=j_h~&yм8hS@Vh$ӴsHL?g{;2Nް`g ?Rks#:WK~-`/Tv- 19& jvuze}yݰN;t(㈘9 &zKCipw-Σqgxnk8AK~ẽXQsQLmߗקvX?5>¯I=\$oDYn0/y|3Q_BLIyBl䛿7ggޑgkަprFKh2 5ѼQyn'}bsp_ j9o3n#&{ W̟.7~x865_O M y/.T{F&p'eؤ<+w=|Z)?%~58Q`# "^{;.8q{49C>1h!@JyluO\wL<7K}o0 :n> )*)GbBzQf^7&ۑZ ktbk|{9 m?e|>BX,IVr i8xx?·WPpphiO﷐?z])&a=Ss+Ӄ _뿻|.Yc$.+h~;ƺWxAx1Xn9q㺜iC0gw]·i!Mxvd1tG9kLA7eRr7 D2y?ƾ3qoWB^ XeMv/ZF3ދ=ju,H#<\5?y~mZܛ/1]ܸ.ӷ,Hs41e\>O<~=\CNQ`<,%c.7NE{Aզs㪔NBr \~Y;P-Կ͑Ma@; GDl]Ne6e\"mO;MJ~q]mtso1XN["Zef)ރ֢ChD΄c8x7H_]W{~]-0\S@G!L<2-fs4=@ >3-p1QvBmuy#sdm Zdhwwd'"Qa[ ^%_ w3; N]Ы*;?H-?byyM|atĞ{ߥfxn2͸mw_C(Ax3?V !nٸ@yaG^3.sd}a6[ {XZ-ܫvPe<0k˓Za|hLGCY*"WA *^^ݛq( ">s7d4z@4V3 ^,5s|S3&\l/ ]uߛǨu:od|-#@\Z'GKM%SwT =OF=p(,&Fo|ӴlIkx`N!]u6c CtEs*{̑,*~쇔wt'/dٰkWD"k1CΖ8tEak.q=>1NC{^㐆=f>u# ;XC?*9<`p.eɿݒ<k=#muh<>)K=|xz[eO_->`W~Y漻g']†t\ C$;OXE>ɰ_Ɖ!o(/fȧ^\d^{ƄmT`ss!Zs 8.g;m<:L 1.41\G\yQ//b=omܐ E#xYߗJT3ȽչN.RXKó| fLO?8~oyFЍ88ߴ(-GM+isYht7i}n3p<yo5䌼?R vpdy@x6K I<`c0>J?&ϗSk'R16>5})m>/{XOs?)Q|ӣ>KLzqy4鸜5&4Lw -~YǙu^0<1Oԁ!s}Cbors)5 ͩ ~]4$kaޛy[Ȏ2Ȓ4u~L{(SC1 YƅO62Cځ4ω3h.1y)a|#M@'2߫k g=>qفƩh ΰ_ҬW6pf7 yl33yB8|>{c^3\Ҕa}%ߴ]rpoZ<Ќў:3-ҮFW廿WK )c)N.P^xL4(.K[vHw3YWS{Ҷs?UaVÞ}9pUy?s4q?7>e}|*:_8W)*;U[9=҅9 W*0O]%ﲼvˍEX\.x?,KLz#aYRݵM#~jouyer\ߢ>KyUxkUcgؙUre]꥿!˕W{?'{emP̫)k5P+8eX6ԯ~?1ws;3;%N^/U-qikt3yo km/؎ȧ]7nBoEkTO4I_O?ѫ~R)PGJSbuA%AY!Q_!}nD{x_j, }N817^n Hl/acpm bp 7 xL; ۦ4p}ƅv,%X{gx⣔I> WV^xB='mVZ';:ne[^2aE7}~U[s\VỼDA6lK,2B(fH{EwNyo2*-~!2Y^GBEcJE:4>wڶd[%mA⟿yA]bU(ړY^ualov70l=8.&jE?Erܶw4-@;قn7cvym em!6JV6h9º|AqT,,38   ) ( ) ( , a выхi a выхi H q – îïòèìàëüíûå çíà÷åíèÿ ðàñõîäà è äàâëåíèÿ íà âûõîäå i-é ÍÑ; ri b 1 – ýëåìåíò öèêëîìàòè÷åñêîé ìàòðèöû   I B 1 ; iєE q i , - ðàñõîä âîäû â i-é äóãå âîäî- ïðîâîäíîé ñåòè; iєM r i , – ãèäðàâëè÷åñêîå ñîïðîòèâëåíèå i-ãî ó÷àñòêà ÑÏÐÂ; iєM h Г i , ) ( – ïåðåïàä ãåîäåçè÷åñêèõ âûñîò i-ãî ó÷àñòêà ÑÏÐÂ; iєL q q a выхi a выхi , , ) ( ) (    – íèæíÿÿ è âåðõíÿÿ ãðàíèöû çíà÷åíèÿ ðàñõîäà ÷åðåç ÍÑ, çàâèñÿùèå îò âåëè÷èíû jєN h h H j j a выхi , , ; ) (  – äàâëåíèå â j-ì óçëå ÑÏÐÂ, ñîîòâåòñòâåííî ôàêòè÷åñêîå è ìèíèìàëüíî äîïóñòèìîå; jk rh H H , – äàâëåíèå ñîîòâåòñòâåííî â íà÷àëå r-é è â êîíöå j-é äóãè. Ýòó çàäà÷ó ìîæíî ðåøèòü ìåòîäîì íåëèíåéíîãî ìàòåìàòè÷åñêîãî ïðîãðàììè- ðîâàíèÿ èëè ìåòîäîì ïîèñêîâîé îïòèìèçàöèè íà áàçå ãèäðàâëè÷åñêîãî ðàñ÷åòà âîäîïðîâîäíîé ñåòè. Åå ñïåöèôè÷åñêàÿ îñîáåííîñòü - àëãîðèòìè÷åñêîå çàäàíèå ôóíêöèè öåëè. Âìåñòî ðåøåíèÿ ñëîæíîé çàäà÷è ìàòåìàòè÷åñêîãî ïðîãðàììèðîâàíèÿ (1)-(8) öåëåñîîáðàçíî â îáëàñòè iєL H q q H q a выхi a выхi a выхi a выхi a выхi ), ( ) ( ) ( ) ( ) ( ) ( ) (      ; (9)    iєL jєN H j a выхi q q ) ( ) ( èñêàòü òàêóþ òî÷êó ,   iєL q q a выхi a выхi , ) ( ) (  , â êîòîðîé ïîñëå ðåøåíèÿ çàäà÷è ãèäðàâëè- ÷åñêîãî ðàñ÷åòà çíà÷åíèå êðèòåðèÿ (1) íàèìåíüøåå. Êàê ïîêàçàëè ïðîâåäåííûå èññëåäîâàíèÿ, ôóíêöèÿ   ) ( ) ( , а вых а вых H q Ф , îïðåäåëÿå- ìàÿ â ñîîòâåòñòâèè ñ âûðàæåíèåì (1), âñåãäà óíèìîäàëüíàÿ è âûïóêëàÿ âíèç. Èíòåðåñíûì ñâîéñòâîì ýòîé çàäà÷è ÿâëÿåòñÿ òî, ÷òî ôóíêöèÿ    Ф âíå äîïóñòè- ìîé îáëàñòè íå îïðåäåëåíà.  ýòîì ñëó÷àå äîñòàòî÷íî çàìåíèòü çíà÷åíèÿ öåëåâîé ôóíêöèè â íåäîïóñòèìûõ òî÷êàõ î÷åíü áîëüøîé ïîëîæèòåëüíîé âåëè÷èíîé, è îíè áóäóò àâòîìàòè÷åñêè îòáðàñûâàòüñÿ â ïðîöåññå ïîèñêà [5]. Ïðîñòåéøèì ìåòîäîì ðåøåíèÿ çàäà÷è îïòèìèçàöèè ïîòîêîðàñïðåäåëåíèÿ â ÑÏРÿâëÿåòñÿ ñëó÷àéíûé ïîèñê â îáëàñòè W . Äëÿ ñåòè, íà êîòîðóþ ðàáîòàåò îäèí àêòèâíûé ýëåìåíò, ðåøåíèå çàäà÷è ãèäðàâëè÷åñêîãî ðàñ÷åòà áóäåò è îïòè- ìàëüíûì ïî êðèòåðèþ (1). Ïðè ðàáîòå íà ñåòü äâóõ àêòèâíûõ èñòî÷íèêîâ òàêóþ çàäà÷ó ìîæíî ðåøèòü ìåòîäîì îäíîìåðíîé ïîèñêîâîé îïòèìèçàöèè.  ñëó÷àå áîëüøåãî ÷èñëà ïåðåìåííûõ íåîáõîäèìî èñïîëüçîâàòü ìåòîäû ìíîãîìåðíîé îï- òèìèçàöèè. Äëÿ èññëåäîâàíèÿ ýôôåêòèâíîñòè ðåøåíèÿ çàäà÷è îïòèìèçàöèè ïîòîêîðàñï- ðåäåëåíèÿ â ÑÏРáóäåì èñïîëüçîâàòü òàêæå íàèáîëåå ýôôåêòèâíûå è ðàñïðî- ñòðàíåííûå ìåòîäû: ïîêîîðäèíàòíîãî ñïóñêà; ñêàíèðîâàíèÿ ñ ïåðåìåííûì øà- ãîì; äåôîðìèðóåìîãî ìíîãîãðàííèêà Íåëäåðà-Ìèäà; ïðÿìîãî ïîèñêà Õóêà è Äæèâñà; Ðîçåíáðîêà; Ïàóýëëà [3,4,6]. Ïîñêîëüêó ôóíêöèÿ öåëè çàäàíà àëãîðèò- ìè÷åñêè, íå óäàåòñÿ ïîëó÷èòü àíàëèòè÷åñêèå âûðàæåíèÿ äëÿ åå ïðîèçâîäíûõ. Ïîýòîìó ïðèìåíåíèå ìåòîäîâ ìíîãîìåðíîé îïòèìèçàöèè áîëåå âûñîêèõ ïîðÿäêîâ íå ïðåäñòàâëÿåòñÿ âîçìîæíûì.  êà÷åñòâå êðèòåðèåâ ýôôåêòèâíîñòè ïðè ñðàâíåíèè ýòèõ ìåòîäîâ èñïîëüçî- âàëèñü çàòðàòû ìàøèííîãî âðåìåíè, íåîáõîäèìîãî äëÿ äîñòèæåíèÿ ñõîäèìîñòè àëãîðèòìîâ, è çàíèìàåìûé îáúåì ïàìÿòè ÝÂÌ. Èññëåäîâàíèÿ ïðîâîäèëèñü íà îñíîâå ìîäåëè ðåàëüíîé ÑÏÐÂ, ñîñòîÿùåé èç 382 äóã ñåòè è 10 àêòèâíûõ èñòî÷íèêîâ. Ïðè èìèòàöèîííîì ìîäåëèðîâàíèè ÷èñëî ñîâìåñòíî ðàáîòàþùèõ íà âîäîïðîâîäíóþ ñåòü àêòèâíûõ èñòî÷íèêîâ âàðüèðîâàëîñü â ïðåäåëàõ 10 3   l , ñîîòâåòñòâåííî ÷èñëî íåçàâèñèìûõ ïåðåìåííûõ 1  l . &2x lUwr)^K\hW`vXdSn,k͡r!h,?E3Ud*^J*Gx̓z+3 ϣ}t@W=PFϓR98.UKT#7_d,ȕA<\H}W$އe`rx/jsBgYkۦm탛qsy%:L~f.ԓgG ֜m"+e8\E7';k߰GOM{~5z9gbHC[)>C=6_Nyls1o[y8cvU4em6y2ps2pg2NN Od5RA=Q? ]`&%YzΥw0&~g1LigF3:8͕9Sp&Iy9}W_Ęw5R4,\\l /Rtwγ9%]PGJR }/9<'?VP6%]'s2^Yz~wm1}w`'SZJ B,y{?Ù9Ĝn3 ׀y 2[y_RdYú{S)hAd} *cԢrx6 ooF7i=} \#d 3u&3Z+zXgtrʘ*s2=Hg>g{bV*A@td:4mp꭬ oS02梅6)d>@?z? JSFe/e1 E[>C6*_8ڰ|YL=vϺ5 o_$#@>2%[^ V tR·Kx9Q>|7uƧdwA*uշp?>Eyo{r2O\'0V/(YwzYcq_c|D}P=]>n˹Fz{sMݮ}-vb~hc-c;їϝ7{]ܬo@K85oN]^Jg8<:7[n;Zo!6N}Ėo:e˹>cj'w϶K&ޗxƫL:Ol8XO{L:w>7ˀ/^ x2eˀ/7,7S=^ x2eˀ/GzQ mMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:12  0 Br  8 ( (16 2R /6 1%  {xݝ ]Uu05E-ʛ|N$$B HP`h` -_KUR]Vuեj\6EBK[IHB;KBꃝs>ϹiK6{ڒdࢉI!IҾ&Ij/<7Iڒ I?&I^zȮ_~+I~l?&wG{rIuɚ&2Q! I2輊!& {TXSn@yM.4M f{1r1>'. j}j hK)u4>SCPzzH3˃mGf%AH%g-3n4~mJc+?0NnrqI7-5I^\ճd5֒M4T绎9ʓ[dWsymy޶;NNJWysK-,8{Co2}Sy̚7gݶc{grv&~dOWo~rjHMWߜ&uE߶~#vGvJS !/T!Dy驯/E*Gݦ]¡Y_Z&K&%O''7iM. )|oj߄&&~$|~KSU:o1az'ϩ:=jo⛤em7#ͿPIG˄+͇UdgRlH7ْlORi[2HUJq;JۓԒǒ{v[p3y< 3ٝnjvgtOQzɣlSMoecRz5\8] #U>.܈sjEw^ /V4}}`t5Zd;i ]1 ψ IߕnŞ2ᒡ?|@g/θ3neoSg")UA3y7ɲ$5{}wNeQJ+ʽ#0Y|HO߬шWi~RT饪=E6 J䌹}G9AdAK~vŧkߧ@c}SDQ۸qS/ >Go/G1W|fW۠"o^\w^f\ PO_5|ץ|ټi˺yqkC~_}v}C|>(dM"aE#Jw1UiU3]Q{ɤ.fS6PZ3zڲ~g?06M{B\:GTG{&CI-gW9#kGKGa휵y5=XIbm }wچkN$! {w`^ƚXz디zt]i)۸uN:xnZ2aSh-8m<`o6My}̗רnCf;nkwv6؝ƽ'۲Rebe,K~udg̍w \ecxDu?<. ކl ;UmQ;!<]\Jy6''JvG2W]8~'Pfwuu#t ۓoӸ> 胾-0/@K2),CS7~A^%{~Bp@Ŧߕjձ.l5"46X/~2쪛Ղ깄fk| VfceͱRpWj1GpG]%(fU0` Nϥk ܺ W]8㱅)7l~IOɓJmiӔ_hm=}ю:I]l'YOp~BBc]g|_'(w 6) !Ŧ+2ޫqل87BoXkZ' "!yMX7Qw;%6rM"GFD,J>ػc6b_ѕ\g<::<@g>l{;N1M޾hyR×<@8vBfȶ_| 2Gu>}y[:;FXb/7!~!xJRviH=3v6u d<4-4hڮ3mYl,lK֖$6aN~?gU6ɟJ\"ⵠgҝo&;79mMz|=P37Gλ`ƶoyYOԹ:P~mRhݎ6md{яv[G[6?@~܆>/dv6gwµSY+99b?,jvq7=Xv㰾3ĆPqV{ {| `ޛ-=c]ĶaǺw68 ]pgQv̗6zka:I`HYnRAiK6y4P<ց!a73{Sj] gs;^/|#c[oXN}“XuXwJ& }[GƓD@s{Ljܷ҆۸OgEt";"XdM,3:,i,ixw\Jh|`XuX{,C+s0ꜺvJOqf}Y#tyF^9rOi{q0u zծCKZcew/xrqК#܇p_m[`o vіQՅ'[Rm3+*;pcYpӻg&O6Šϓb`MgHv6 ]8Z?Nʬ^[sz#kR=uJ_z<)ur<^\\GԹ?gL_i^C﹂cƏ _6zaͽ #y=y\xȓ:ӏfShi{W<\;]ߺWm7Izc"SSk-\Fص[P>q:8]1cƬΫxx/7rLxh_ǾߣA|}:s{tRߒ9ssk>{qC8'V[xTOz4ZDѴ)ORv}܆i;G_ :^g)UdpS+Յnø3RKJ\YtF1pÝɉ$7=σxuSg\[]xBNbxh|n'E~H:]G9yQЗ(=>Pwp狶̏T[ZNe6+)uݧ6ρN'|75Tq3~tfGd:аG:u[bVVG:0% -Mk`~]~h| ?X/˵m*Gc.yӘP|S^#ǀ998O"5W3\àҝJinnppk+!o}/~{ٝk"p?3}{a=&I䣤o̈́s6K1ol)텍Y6?G̵xW-4@uG̅\:s-"=3Х\_3 #2/`wbL򜏢} =sݢ N^=:SվOB.7{#|~8OdÓ{bzb.A~8FIJS{?yfM ޱcl|pW' (ςC8uW7vdz?Q!ϷvSzg̍X@,;O2go44NJlЙtxo M=7SiLncoEc6Zx)}l[p6gcvϼ}̹-µ:xexٵ-3es)MS|/O9aȁ;u%xӱ.82.O?Z4%Ev}F}w :Fd ?.+RHPoγ>|.;KD㢍/w5K'5eco,;/_#A_>)BFZz˞3ֵ{kg|$Xڈz4+5wW^xl߭\R[url/3 x~~k-sٷL{[&IōhpɝޅE;MH˟Q&;jҚRn\C\a~g/u^#~|ټߋq@w0b 1u@oY ;BшmtLo p7q:8M5ᜰ[$w0Q ߎ'~cAb,8N&ndAONWRVjH|9wyeeˊ]7MJeRb;W2<k4~S5n5w:ׄ_#בwvo=l?2yvsj]B@{pƴh N;;>7g/}7c`o?SZ=d*'0sY>N{(VƓ~乥m繝3Nf2veZ-vwCf#ϼL<^Gq{J}Q?h|.yCBo67dfh)𜆵85{t ;<–pnwc)xPp+y6|.z"C?){\^~Ӈcc'&_1\Ə:CѰ 7xv? Yy_4 =Yᐅ Xk ξeZRa+〸 } i:phZГl+h А~ -ZeOj9s}@~,Gcc[?*\5h'e}&79>7w +cwa=ZrהRg}mlotʺkx?wFѲX62 ~yHXMoy)/ w(X]oTh'z Cc#NЃջLj]BO[&R2^kμ6#=|Z6^h[z_pƶr6~D8|l_:"~û ތc16dne4ѿF4T?> _7`ٜ|Rw6k ,4nLv+>fw6]gw6 gqw6;ټM;Ҳ.ۖZ?g=7r ;ۄ[ڤDp=8/nOpećYʮgݓ*yW]^Y[v{oJ۫_'Q8=߮jkkѲmA$ 2T2AES'Yf{'hl}wwN)[b?L_`^ V Ve~;o}^>s}/m?Z}A{`4Y22u XA>2[Z4˯ vl,L r"YN?%י,3E׫iڔxl}A_ hr~0K?C=`^` Y /GIBgpIqsCݦ/ Ud~e5 >ޘ?G'/Fx]% kamb c6ެ UfTهཱུqO?xOxJT5od7f|,͌2U{]ƛ{2=qao!xU5n'u}ucloLx37s 1x3Ǫ⍟?7~^o| ]7(z@>C4Vz$GdJsv ;Qu?vnJ)?E=-Li?M5꾠}ڱGxOGxWuo xOT5n@x›8[+9{٣UոMo@xW›U8ā&wUq ٛ *7qgēwұ7*1x37q sxU&7o|m,x [[ w+Ɓ)>sG)unp}?Z#̉ R<8_ޙֿq%±_8p:G8} OlGJg4āQb"8C'xyѮuwj}/FNb"95fb<$vbBe;NTkʿ]-{h>'(5;x,ȌtdƦ8?$kJY˵8y&΃wUq>PոMo.yX;oWڹNe:.7q]U\omxnW5n2x [+9{3͞QոM\o2xW WU e~eƻ fjew'k k uxx;}Wxcy'q2nT]՚YS7kjU&gfެf=79VkWsx3nx3nxWsxU%蜽Ts]ތU} cfwU:gCcU&7wU:w|֍+ݠ=DNG.P3vc&2ָL(n N5o<R>znL[_??uh EsuR>r[i[2NP7 OWߴ&o';kE^888i[PYE|@Izp#{}rwc&Szh[ɫ*dx^_*/W@&0Y M[籽*@&~'->xɒ-_%))Jv,,g39 Ïî îáúåìó çàíèìàåìîé ïàìÿòè ÝÂÌ ðàçëè÷èå îêàçàëîñü íåñóùåñòâåííûì.  îñíîâíîì îíî îïðåäåëÿëîñü ÷èñëîì ïåðåìåííûõ l ìèíèìèçèðóåìîé ôóíêöèè, òîãäà êàê äëÿ âû÷èñëåíèÿ ôóíêöèè öåëè èñïîëüçóþòñÿ ìàññèâû çíà÷èòåëüíî áîëüøåé ðàçìåðíîñòè. Òàêèì îáðàçîì, áóäåì ñ÷èòàòü îñíîâíûì êðèòåðèé ìèíèìóìà çàòðàò ìàøèí- íîãî âðåìåíè. Ìåòîä ñêàíèðîâàíèÿ ñ ïåðåìåííûì øàãîì íàèáîëåå ïðîñò â ðåàëèçàöèè è ïîçâîëÿåò ïðè äîñòàòî÷íî ãóñòîì ðàñïîëîæåíèè èññëåäóåìûõ òî÷åê âñåãäà íàõî- äèòü ãëîáàëüíûé ýêñòðåìóì. Îäíàêî, íåñìîòðÿ íà åãî íàäåæíîñòü, îí îêàçûâàåò- ñÿ íåýôôåêòèâíûì èç-çà ÷ðåçâû÷àéíî áîëüøîãî êîëè÷åñòâà âû÷èñëåíèé ôóíê- öèè, ðåçêî âîçðàñòàþùåãî ñ óâåëè÷åíèåì ÷èñëà ïåðåìåííûõ. Íåäîñòàòêîì ìåòîäà ïîêîîðäèíàòíîãî ñïóñêà ÿâëÿåòñÿ ñóùåñòâåííàÿ çàâèñè- ìîñòü åãî ñêîðîñòè ñõîäèìîñòè îò âûáîðà ñèñòåìû êîîðäèíàò. Ìåòîä äåôîðìèðó- åìîãî ìíîãîãðàííèêà íåäîñòàòî÷íî íàäåæåí. Ìåòîä Õóêà è Äæèâñà ðàáîòàåò ïî ãðåáíÿì, åãî íåäîñòàòîê ñîñòîèò â òîì, ÷òî âîçìîæåí ïðîïóñê ãðåáíÿ. Ñóùåñòâó- þò è äðóãèå ìåòîäû ìèíèìèçàöèè, íå òðåáóþùèå âû÷èñëåíèÿ ïðîèçâîäíûõ öåëåâîé ôóíêöèè. Íî áîëüøàÿ èõ ÷àñòü èñïîëüçóåò ðàçíîñòíûå àïïðîêñèìàöèè ÷àñòíûõ ïðîèçâîäíûõ ôóíêöèé ) ( x f , ò.å. ïî ñóùåñòâó ÿâëÿåòñÿ âàðèàíòàìè ãðàäèåíòíûõ ìåòîäîâ. Ðåçóëüòàòû ÷èñëåííîãî àíàëèçà ïðè ðàáîòå íà ñåòü òðåõ àêòèâíûõ èñòî÷íèêîâ ñâèäåòåëüñòâóþò î õîðîøåé ñõîäèìîñòè âñåõ ìåòîäîâ ïðè ñðàâíèòåëüíî íåáîëü- øîì ÷èñëå èòåðàöèé k ( <30). Ìåòîä äåôîðìèðóåìîãî ìíîãîãðàííèêà íåñêîëüêî óñòóïàåò äðóãèì ìåòîäàì. Ìåòîä ïîêîîðäèíàòíîãî ñïóñêà áûñòðî ñõîäèòñÿ íà ïåðâîì ýòàïå îïðåäåëåíèÿ íàïðàâëåíèÿ ìèíèìèçàöèè, çàòåì ïðè ðàáîòå ìåòîäîì îäíîìåðíîé ìèíèìèçàöèè ïî íàïðàâëåíèþ åãî ýôôåêòèâíîñòü ñíèæàåòñÿ.  ïðîöåññå àíàëèçà â êà÷åñòâå ïðîöåäóðû ìèíèìèçàöèè ïî íàïðàâëåíèþ èñïîëüçî- âàëîñü íåñêîëüêî ìåòîäîâ (ìåòîä çîëîòîãî ñå÷åíèÿ, ìåòîä Ôèáîíà÷÷è, âû÷èñëå- íèå ìèíèìóìà ñ ïîìîùüþ êâàä- ðàòè÷íîé àïïðîêñèìàöèè ñ ëîêà- ëèçàöèåé òî÷êè ìèíèìóìà, ìå- òîä äèõîòîìèè). Âñå îíè äàþò ïðàêòè÷åñêè îäèíàêîâóþ ñõîäè- ìîñòü. Ýôôåêòèâíîñòü àëãîðèòìîâ îïòèìèçàöèè ïîòîêîðàñïðåäåëå- íèÿ â ÑÏРñóùåñòâåííî çàâè- ñèò îò ðàçìåðíîñòè çàäà÷è, ò.å. îò êîëè÷åñòâà 1  l íåçàâèñèìûõ ïåðåìåííûõ.  íåêîòîðûõ èç ðàññìàòðèâàåìûõ ìåòîäîâ íà êàæäîé èòåðàöèè âûïîëíÿåòñÿ íåñêîëüêî âû÷èñëåíèé ôóíêöèè.  òàáë.1 ïðèâåäåíî êîëè÷åñòâî âû÷èñëåíèé ôóíêöèè, íåîáõîäèìîå äëÿ äîñòèæåíèÿ îòíîñèòåëüíîé ïîãðåøíîñòè âû÷èñëåíèÿ, ðàâíîé 0,005%, äëÿ ðàçëè÷íîãî ÷èñëà ïåðåìåííûõ. Ïðåèìóùåñòâà ìåòîäà Õóêà è Äæèâñà î÷åâèäíû. Äàæå ïðè 9 ïåðåìåííûõ îí äàåò âïîëíå ïðèåìëåìóþ äëÿ ïðàêòè÷åñêèõ öåëåé ñêîðîñòü ñõîäèìîñòè, òîãäà êàê ïðè ðàáîòå ìåòîäîì äåôîðìèðóåìîãî ìíîãîãðàííèêà òðåáóåìàÿ ñòåïåíü òî÷íîñòè íå áûëà äîñòèãíóòà è ïðè 1000 âû÷èñëåíèÿõ ôóíêöèè äàæå äëÿ 5 ïåðåìåííûõ. Ñõîäèìîñòü ìåòîäà ïîêîîðäèíàòíîãî ñïóñêà ñ óâåëè÷åíèåì ÷èñëà ïåðåìåííûõ òàêæå óõóäøàåòñÿ. Ýòî ñâÿçàíî ñ òåì, ÷òî íà êàæäîé èòåðàöèè ïðîèñõîäèò n-îáðàùåíèé ê ïîäïðîãðàììå âû÷èñëåíèÿ ìèíèìóìà ôóíêöèè ïî íàïðàâëåíèþ, òðåáóþùåé äî 10 âû÷èñëåíèé ôóíêöèè (õîòÿ êîëè÷åñòâî èòåðàöèé ïðè ðàáîòå ìåòîäîâ Õóêà è Äæèâñà è ïîêîîðäèíàòíîãî ñïóñêà îòëè÷àåòñÿ íåçíà÷èòåëüíî). Òàáëèöà 1 Число переменных Метод 2 5 9 Прямой поиск Хука и Дживса 23 136 230 Покоординатный спуск 22 498 1000 Деформируемый многогранник Нелдера-Мида 29 1000 1000 Розенброка 17 174 348 Пауэлла 18 209 303 )xklTUl--}."-t &HkԔP % 6* "R4%F$Xc Q Q(ﶁhkR -]gۓ^},Dc&g̙3sϺDTdĊL+JP>H%Fk<]=r# f\dsķK il殀JuAG %ﺽ3cݒ,m?~Fy*5YL vnjL*4y?I.~߫ I!-=qM ͟Cv<#m㷩ɐ,9N;eJܟ㥪ocY%ImtzX0Y$d*)bjT]>IfH XSݎ> 6%˜!%EĸS(ڊdIK&9.80!ݲƬDM]s9L&H^jkǺ+Yh1v/]=W,{C_@יsH'EJM  o!NR0RkpʑD,O`_*>))*M]pT,[C N"f݋^I ב+3'2+tXȟWT "<^ JGk$$Gp [_o u<28 > QWՐ\~pNRel@xEjOC2"{d3?[^oq*[ CwDa|ƁK0 o&`1m{It߃VAX1'oq;/.SzAsma{ 94K>OE_ _עHYެG^ 䭡zeq`%q>aVgp <c?A:~{Stm<>D_JLmjmlV6{'zY}7c}}q4=>cuZ}q[{bl1gc{ol{kla]u^_@[=?oXum_?UnƮ?ks:tN8p:tr~N8p:tNK(Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:12  8 D  /( 0 (16d 2 /m> 1 g {x͝ Օ- Al>>nC"@$eJRWiԐ#c;&ILbwt:Τcf\3#!4>;)DP@آw:q?^5W7眽9{}V-TpE- _ Q|\B!<jaٽ!<0ѩwA!{H3tW%C>̾)) s6ğaS\u~!S~aw U7&;vq91O?|xC~f~.윰P鍢@yӱom8<^- cگKR olz 1Qm[ ;bg}dFBy>~=s}A8x!)WF˪*ݣ􏺍¡Yo II'ͳõ3 ő{7o >Ej}|sݻ͞F'u?o~o?IoV&r|7V%26ݾ υ*\o.my'<^ Dži*6ް& Eoc ؏RF:xr~W|U O>9@ɹVl /zؠ_ EQ9@~,ϺGefAoqV)z aȀ !8Aj pV(+MnvO:NG7r5CH/2slI-oưU>̌"cC|9|ゖoʌ=-=@.OĪQ5qկ/##r 2!V@rn.][ ;9"^6#^[['W 24tN~ig$' Gph/K,1z]x$fzN$ѧmm_똔ؓף>uݎ7%6J\$[Jvpg~ոzdFd@dNR#GqDcfKqI3VyEnR "M'SV~]x3cAwz~7uܞ;5IxtH uHm[dk|VѶ(Z׈gM @?^y@7+c3D5EvM7B7Po7TU9~1NP8etdu֣uN=#&AlmN]b )u܎6xosIawK'*}{rQim5h9,#1ye[q1'S病u ; }pn⤛8znx%sTwڧvkKR~l-ykKVek,%a^8_¹Z>.z.ԹJ?"Ta:E&޹ کN<KO,0:UR%!|ͿSFSʶ|-[dGdk-pl5)׏%FDؑ,ٲ^looɢJߍ=*ܽ]&+9JEˑe}K.%*\mb$Cr}m ]yW b¬"&gѷ_]BuJydžvE߶+6|]g|EֆqUQC3t3cc~\^M/(^y2'YW[!5ⵧˌt ;z}D(Շ7-Qqy=I;_ !'HBvqs0oWߺ]NJ/kGM[:]WS w[m㜃|^}xǾ{Sz1ڀgҞ^껓c[CUً JNI8Qrf=b(,F(9[XV:_;5V9rL6mROIKzxJȡ)veܶ 8BvڮHֹՅkpg۶'ȻL e1Ceױ=NP̓(xR$yyYD8U )鞽eƋ\ }giFM$ Aկ{Tl-{$^0 ˉVyV]B&d߱zh Vedv8nvu ݾ=|udeh9&6as:"5: oauCj]BC˶y)Op mu"}:_#Q6ock lAݭ1qNۈMf)Mwg~>p[cnA]"iU&on_Rϙ+z'&mbz^4Ƽ&]noiq۾@7Ii~-ק?ryncYmo\kZ0hő!g<_(Z28Ǘ5|u23v̀sLZz`_ts/׆Rcw )/1 u?;G;6S;J{ğw Hyǀ:ڂ-g_~O>ʝv{i'}Z߹x ٭ǻۍCon_ ݔݞFH솾Ce)vnx!i_=h */mcvO'"zHcKHyAz::/[ZIDzնJHo%.aףsW.,''12vRc}Ngm$6(E^h`Rf%gKD^/K۪ۦ)4OH9s>e{~Py 8}B.Ihn~3^.K0&?]ס|qN^輸~_[߅!U[Ǝ~} r;AgU"D_X5ɂĐАdhzɭOĆ/m'4nz]Bͣw+GyYJD{J>Q`ѹgḡ+>A-It_p.q\D'UynɊ2DYfhխ~bCtbgę>,9q\['[3r3FcuʸŘ]&yӨ3x:n}_qYɻ^G^vlh{;ϩE >ѧܴ/ڟ,|Rb }wu*X>%\<E|`Xmb{QV>XV컒YeW#;<9NOxwMX]><>ś)1oQI3M ~J:O*}N]eRx,`@лSwyA]Ն>' ٖSᬲO)+Ef~}>~xyTh{~*~#:۞7bbҾ?yy ommVZ!3mG}!}eߏ/sZ΁BEыue}ަze]K2 [7ik.1_By:<دܤ#e4vNiJ@ع{秬HMߪL~K{"1nx:B_~l]A]zX/emPO]ho:1?{66kvN}7<{tzO@xV vVE0YŅ7cOxA2 hjqC+̸{\)5>Pz\]H;o+)zb8]nA 5Q~ɗס?>}{ClTo*jڿE/?O/Ou:]I7oL%";6ˆ3'dKLԄqt}^c_!F <3sum'o~]?Ç~?bly7ڕLwR[uv+O; j7]8z BrC J¿NaG>꣢=_yZ)j]m(4vq;dpq m?{!ʾ]]71Fy]apzGo9?ʼn6{~.U{ORO*C^RKZxu*_}CUݢ-_>J%zg_R!zP+UZ,X{GCJ}f`lQ>Hkez[/R Vkں_ƑgnЖ>O QO{->-#x=ڧ\*;O\j?҃\~:~#|y/ˍ<# *>)v6S],jiaQk#=^D6lkђ-m'ƁncsА]m;lt ]4n|ޅ=Ofo+]?!u'miu:IONU? t)4)%~Q_1k_ZvBKy[Oޑw-M No+~ 57߸wK(fFoZ9Oh_i=xӻ9 pB9Z2P )4O=]6yA#Nyc3ц}gҏ@w^)fyO6}Jݺِ2܇ܖe]3 /x;?s &z!9UZ3t̬ q'6'oT;ү^h;>]6O`1c .`zʟ-#t.ѫmێ|ޟŇenkvaS֩G{Q2e/c:R\~ J(\?%NoggߔumX'})ڝ^9=6RN(l:}0f:u7A h*?3tQw`\[h*ܙ[ۧE[.9> 4_?Sw?V#,Yh9r]yyMD07e牔y]7N76(.m)}'Ge9Ne"=@=>gt9NȖW,{5Jvpo-)Q)sv):ݠtEiMx pwnuy_Jox ²KOx8Ѫ|Hg?;@6^}x$[W c;Ρ-ۑҎ4ӆ2S7y`?A[|ܿ0/4qx7޼t|+[e߷GEP?B8*/ OllF]u3SBH-+):e2/쐬iKxd9ݟ%?R]xb*spUv7/Χ=+gR";7(Ca1b;xF_.xK_?;oM/x 5N3 ?10~v0zvm +m9Wxt.:.؎Эo|/Qw9<}e. D>3PG ~pgnݟj<~TyL]#}Wd`WxsX| q;7n]2~t9^m{@.)}/}Ӟz [<ԅs]9/eyC>x.y ;߫C^#{*{!Zyƺ<ܜɝԞ47N1fֽcs3]4qٺ޾?S/=z 2v<.uH$@}[k JGW:ByHO .[/%F=;Ukdž_Cēm߶_ۤXAS6 +aI|kګCǮϻcOC[tP`ʿʍZy!$;U~Yߘ62_~HmŸڪfi;,{8Ujwjw_HoH熹*7G>ʚe|&T_|ו ؁st x^b? ܤ ?V [eΉ72c@9HqZ綞zjk=:ud)3[g$ 8Vzmeh3=,Էw|ˎߍL6+WiĬ_<$vyrpV)`9;,̯5~>~^w*V~?GwW7[*8i^fe{mݥ񿓹;{k57:775m1۾X*q XkJkI]kюT?]+t9[e0F@lp'7[dOaIB\tRh^q]! ީ'hZ%R<2NSZv'#kȈ '1b-0TyowMobtvN4Dsj뉭pNw:ur#[g2Mg)'z{>@!_OQ:KYh6/}g#|r]y%l.=wPRe^7izqR Ow"7wVQ_Y^SJy\C} k91iRuXޜ:xoaͺo}xûY>&7kܬf݇7>Ûuެ7+19_]J9ff݇7o|YY፽፽FףZevOJC\;BF 7_@8F+lZke?EN}ӴU Նu"I*g-'e]}"O7IbMG'eXɻH#/kzY^tکJ |ě1J7? k:Y͚f&X׬qÛ5ެn֚o,7k:Y͚f&Û߬qw's"`~u9]1sx͚o| Zx{{ލ벯@e>OoRh^np?^bdsU==dU?YS[0_GI|sJj?]wc tRV0HuGLNCIІ=4s٢?8SٽS|J~&׬A&l&i淗w`=P~'{Fw߃u\v`{#/vi .LĻnS=SY{ xkMmָS=SY{ xMoָS=SY{ x5YfOGc30cOoyx7o|YS{{ލߑa]:lSܪ勂o)ߧn'5U_]յ[8ASZO> vA`RQL̙Ѹg}Y<.ڶ?ɻHrG^ey9NU*퐟OYP{N-qRbƫff]72.ÛxoUͺ oex.ûY2&V6kܬf]72.Û8 otͺdc|GY2sxͺ o| Zx.{{ލȰ02u\oTUx Jy]v;Z\"1Zh=W93XkkA2(Opqt/a:\0ދu^u,/04J7cd FĈJÛuެn: oO70Y: f&6›جqÛuެn: o27ē9F `]0_,xo,x1Kkq>v[qqhݤ~jUonWq{_Ҫ߸E߶~#v֧w X?>*ަ}RsOLJ>.a=/z|߅x _| 6=Feseag>A[?,,40  òàáë.2 ïðèâå- äåíî êîëè÷åñòâî èòåðàöèé, íåîáõî- äèìûõ äëÿ äîñòè- æåíèÿ çàäàííîé òî÷íîñòè ñõîäèìî- ñòè ðàññìîòðåííûõ àëãîðèòìîâ, ïðè ðàçëè÷íîì ÷èñëå ïåðåìåííûõ îïòèìèçàöèè. Òàêèì îáðàçîì, ïðè ðåøåíèè çàäà÷ ïîòîêîðàñïðåäåëåíèÿ â ñèñòåìàõ âîäî- ñíàáæåíèÿ áîëüøîé ðàçìåðíîñòè (÷èñëî àêòèâíûõ èñòî÷íèêîâ, ðàáîòàþùèõ íà ñåòü, 10 3   l ) íàèáîëåå ýôôåêòèâíûì ïî êðèòåðèÿì çàòðàò ìàøèííîãî âðåìå- íè è çàíèìàåìîìó îáúåìó ïàìÿòè ÝÂÌ îêàçûâàåòñÿ ìåòîä ïðÿìîãî ïîèñêà Õóêà è Äæèâñà. Ïîëó÷åííûå ðåçóëüòàòû öåëåñîîáðàçíî èñïîëüçîâàòü ïðè ðàçðàáîòêå è ýêñï- ëóàòàöèè ÑÀÏÐ ñèñòåì âîäîñíàáæåíèÿ, ÀÑÓÒÏ âîäîñíàáæåíèÿ è ÀÐÌ äèñïåò- ÷åðîâ âîäîïðîâîäíûõ ñåòåé äëÿ îïðåäåëåíèÿ îïòèìàëüíûõ ðåæèìîâ ôóíêöèîíè- ðîâàíèÿ ÑÏÐÂ. Ñïèñîê ëèòåðàòóðû: 1.Åâäîêèìîâ À.Ã., Òåâÿøåâ À.Ä. Îïåðàòèâíîå óïðàâëåíèå ïîòîêîðàñ- ïðåäåëåíèåì â èíæåíåðíûõ ñåòÿõ. Õàðüêîâ,1980. 144ñ. 2. Êîéäà Í.Ó., Ìàðõåëü Ý.Ã. Ðàñ÷åò îïòèìàëüíîãî ïîòîêîðàñïðåäåëåíèÿ â ñåòè ñ íåñêîëüêèìè òî÷êàìè ïèòàíèÿ // Òåç.äîêë. ÕVIII ðåñï. êîíô. Ðîâíî, 1969. Ñ. 21-23. 3. Åâäîêèìîâ À.Ã. Ìèíèìèçàöèÿ ôóíêöèé è åå ïðèëîæåíèÿ ê çàäà÷àì àâòîìàòèçèðîâàííîãî óïðàâëåíèÿ èíæåíåðíûìè ñåòÿìè. Õàðüêîâ, 1985. 288ñ. 4. Õèììåëüáëàó Ä. Ïðèêëàäíîå íåëèíåéíîå ïðîãðàììèðîâàíèå. Ì., 1975. 534ñ. 5. Ðàñòðèãèí Ë.À. Ñèñòåìû ýêñòðåìàëüíîãî óïðàâëåíèÿ. Ì.,1974. 630ñ. 6. Åëèçàðîâ Å.ß., Ñàâ÷åíêî Â.Ñ. ×èñëåííûå ìåòîäû íåëèíåéíîãî ïðîãðàììèðîâàíèÿ. Äîíåöê, 1982. 66ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 10.05.01 Äÿäþí Ñåðãåé Âàñèëüåâè÷, êàíä. òåõí. íàóê, äîöåíò êàôåäðû ïðèêëàäíîé ìàòåìàòèêè è âû÷èñëèòåëüíîé òåõíèêè Õàðüêîâñêîé ãîñóäàðñòâåííîé àêàäå- ìèè ãîðîäñêîãî õîçÿéñòâà. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêîå ìîäåëèðîâàíèå, îïòèìèçàöèÿ, àâòîìàòèçèðîâàííîå óïðàâëåíèå â áîëüøèõ ñèñòåìàõ ýíåðãåòèêè. Óâëå÷åíèÿ è õîááè: ðîê-ìóçûêà, ñïîðò. Àäðåñ: Óêðàèíà, 61024, Õàðüêîâ, óë. Ãóäàíîâà, 10, êâ.22, òåë. 45-90-31, 45-50-86, 45-90-61. ÓÄÊ 519.7 Â.Â. ÈÂÀÙÅÍÊÎ, Î.Â. ÏÀÐØÈÍ ÀÊÑÈÎÌÀÒÈÊÀ ËÈÍÅÉÍÛÕ ÏÐÅÄÈÊÀÒΠÍÀ ÌÍÎÆÅÑÒÂÀÕ Ñ ÍÅÏÓÑÒÎÉ ÂÍÓÒÐÅÍÍÎÑÒÜÞ Ðàññìàòðèâàþòñÿ õàðàêòåðèñòè÷åñêèå ñâîéñòâà ëèíåéíûõ ïðåäèêàòîâ, çà- äàííûõ íà ìíîæåñòâàõ ñ íåïóñòîé âíóòðåííîñòüþ, â ÷àñòíîñòè â âèäå âûïóêëî- ãî òåëà. Äàííûé ïîäõîä îáîáùàåò ñëó÷àé, êîãäà îáëàñòüþ îïðåäåëåíèÿ ÿâëÿåòñÿ ïîëîæèòåëüíûé êîíóñ ëèíåéíîãî ïðîñòðàíñòâà. Âî ìíîãèõ ïðàêòè÷åñêèõ ñèòóàöèÿõ îãðàíè÷åíèå ìíîæåñòâà âõîäíûõ â âèäå ïîëîæèòåëüíîãî êîíóñà ïðîñòðàíñòâà íå âñåãäà êîððåêòíî. Íàïðèìåð, ïðè èçó÷åíèè îðãàíà çðåíèÿ ÷åëîâåêà îãðàíè÷èâàþòñÿ íå òîëüêî ïîëîæèòåëüíûìè, íî è èçëó÷åíèÿìè c íå î÷åíü áîëüøèìè ýíåðãèÿìè, ïîñêîëüêó ÷ðåçìåðíî èíòåí- ñèâíûå ìîãóò íàðóøèòü çðèòåëüíûé îðãàí.  ýòîì ñëó÷àå äîñòàòî÷íî ïðèåìëå- ìîé ìîäåëüþ ìíîæåñòâà âõîäíûõ ñèãíàëîâ ÿâëÿåòñÿ âûïóêëîå òåëî ëèíåéíîãî ïðîñòðàíñòâà. Ïîýòîìó â äàííîé ñòàòüå ìû ðàññìîòðèì ëèíåéíûå ïðåäèêàòû èìåííî ñ òàêîé îáëàñòüþ îïðåäåëåíèÿ. Число переменных Метод 2 5 Прямой поиск Хука и Дживса 2-3 10-12 Покоординатный спуск 2-3 10-12 Деформированный многогранник Нелдера–Мида 15-17 100 Розенброка 2-3 10-15 Пауэлла 2-3 10-15 Òàáëèöà 2 -&xilTUϝҊmi0LMXH(+1ZlPA$Qh, Fuˢ4@4R1 U\0XwڹtZ~xM{w3LDmDFdVde"z+DjHKxkۨOT=ܘM0Y uvi[VІwjk\ဌ4YN#W eslk X6eL7#W;%Kc$J>)(l $Mݍ٦ nW>;vK.Oep򞎩w5:9jOj7dNLyY:rv':ؘY2,#զl =qf̖m4C#r`Q̝؊>9+$?k:Sn껎؊pCd?8\؆4rH 9ΐ a|-i͡y#5mNNd s}GYBkwo0^O t43% π JIF:&$cFYg;#rxv7=dq@p, d׀ {9߂DYFȖ*2F*k[` (P~ طs=h8Nc.pyk29^V![3d_K1|AgO2 JKr.8}q<ܛ~?sԗyc#$^ ?1Y^Agxs}Ye 8P~!<-x][)q1LlG7Ad^ UD2|}7&̩ bpT*"cV|Ӂ8@/Ǟ5^jOƗ,ObOU rF/Ai/O3$ \GY9û^1 8TQ- Kp`4̧5y9 Yq|%K,o_,mM&LJo'˰~K^ }O4wp9""WV<59c[;luMN_K6;9;SscԮh~ϮZZkN˙)z;۩ޜ|N{kcTni\KƷvm\mhl=ό޿ώŝz76;r1M9nݰ;b<:\6wkZ3@7DzVnk;47&np;vn/Mvnp;?(t;Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:12  K   \0K K (16Tg 2g /K 1w`  {x Uy'!ڄMXMXH`IA*\(XHt.**V֦T*(h?- r!PBEy<̙w}eɞs9ss;3󎋢*E{EڡpRmqQ4.ޔw"E $pwWGяt=S㐃pщhQt~tqTS:;Hst+֎Q4dLG{`zg6x|[s[]0*_I`VJ{+PW)qM[q1dZ4^mEO1nPusg۽k:#>{/ίVy64]pi< V𥝏:BgS4M=S&xě.>:կq y~%W MyGyonMeM^?ƿ- D:TXe|kry{ǼIn|ys٧7v(Mrkgt*w+o7gx$&6Zy,[n:e{)Icr÷*Et~qL7rkg%fvnЍ|U27:#:::AgDE+qlK553=P%'X67O17CwOlD/5cYazu}4׍蕕Cx&hbAan9VOzh_SH^0;"{yeyW.V粶uJ~%Ǎ*jFɲ*MOɶeOE/EFVȲױ&+v6}̠9qnk7mMbxX MzV;lұwdͼ&D/I?pP&BEJOCp<nk"z=g]* aܓ:}чe3mm'Oq7tG?PEJO?ܽҳEpFא#+kWW]cƥ_qw%}l\ٸ ^|'i E;LpF\k5En q׸|$9\7H.H%crz jG;ν#53E$#yy-E!;줼ٽfgMWЏi3Em?G C6a+~%oY=Wx7{$Vkop=_ժEqb]kT㊭PnDU_ 0CkPӕ=eqMI}J}+>95J:'Ee<7[>:K6v[_&OLeӿɢaѿF]V*D'+:ec ZQ6MI<a'GnŸ\|.bl_+Z7gme8 }1K'}2IyxT;G پRG_wTugͪep劲+ qqz6}8\b]Btt-98"7YAoFuR)|M|/mNU 1mҽۊ?\|\8s#vD jM]f s9h>ȣ+TSW3{IKt`~}+k#5f{oeoyzou<|$2y{Ѷm^&{]^ 殕ʳs/u̽W?^>Q͖dt?*&2P Twfpl5,ձ]]k{?ݜa$}OQ:ḩ.>:IR}ʴ_S;\RNԕi.k]4?dI]6kj/gE+~> i_/ho&_mX6VEO_fGM[:]oHv=ï]WfoCi9!3C=u\!USzgۦԙz}y{/VS6j<)oQ ɍ;85'z͛> `>KRb,$xɏ`(>N2}֦,[N  2ߥm+8gT6W)Gx@|1=YZMWuA;\m%ɚh4>0/`F;i4~{gtuMoO zkcIJf:gfzdJT{b{OkG>l,[K &ܙ!9c*ҕ7i7U}ֵo# ]olt]7tdF^yJ229ѹMjߺ}53E$^FF/h׭t>dmfecZuTG؆sY;:ll~%XnP+coB^>K:rظŴ k1v0ԓ'8p0: m[5N>uo [·"[8$pv$z-O_zMRN,`Αiq;gܜs6 _s7x`Cv}Mt^y}XH7e [0)?_M-GmaWI<W*Fj o=NӷF)X+Tcoa#u K{Fגd>pmFf6nB6X3ZZ)EЕ8r݈Go2b#lQdzȝ#=ro]2~% v ١d6&U]=P z+PY;M8mHα(>h:cYcouA] qnT Qhzf͚IL'e3 Lw<*k;oE/סjG<0I5JEpFWx$@׊~7UkVh46z)B}C!9`OvwQ5_,?#ÛٟHE /_yeu:53WW+Ё7)}fze-K*;'{Lyѕ~ \Mt%#9|$r}s(+׍a :Tֺ>/^۳Ǵv{v͕^8L9y2|~%Ǡ _=VV➏}<[+|EO2? _XXa<7['(Ә|rlXMMI)7}ZOkhJ[7ՄaMM75=t@ CRk=ᎡSUdp<L-?yTqE6B%mP~%_ױ"hJFW$B{깚|$s5Iq=s+6d={ghyٹ:5~%g_ nԗ`4ފۨ3ވkuUS\uoc%VwMMڲ:gN*͜3}9Vwhs:GƐ㠃wuܷ:epzTdzTǺc7 凪mc#/s݈7t(1Guo>Oc*ql.ŲlQdKqc珊oPo8ba+lT_߶]/W~M.{0oS62lSz&Ve`Z9Bv  yU=عVnvqBTCvnѶb'yv@*s;f\x@ !xmoכ?['iGIAڋ'ɒ [?7`ͷi> oJWoocߘ,W\{{^V<]ͣ^ߊwdoC>{\7ko$B}"Fr+׿Zm7Uۑ|N>?7ѕFt Sz%hsGUf\5o;ߊ39!B\^~QWsM^teO7rXfIVEdğ3|ȟ"ޢ 9~ Q?ץva*d7BxRo |W{/jۙ?Fff1&ꁟd~SGD59u9>m?)\/Jl{|C5|1h];\ޞpunH:g(X*K3ݬχ(!,.JGU7Ý *3Z+S%mTQ\:zA"m0OI|'rRz,Ԟʳ }qYUowj ȵw4/~-~ g=+g5\?]*׉ܚ1 HڣQwL9;>q\ qTSΏ=p~.\?52p3d;Dc+ԷG#]|=2Hz؏$I渾s=>~q3 yP{gQ6x3{!8?ǁp~ ;q%9 =׏c?)o﫲BpO!8~coW r!y3}켊9"Z_{=Hy]u#}Gl $ןT`"D/,d-*kˎjzS~V+Zkӈ^^gRz Km]*^s:qݲ8a%[&n94nӱמ%&;59Wo67;_˔Ó~ *aq]ȯ|k⑖?e_98}%E\^JLTN׳or[ST^F7nІoTtHr^PvN۹ة0?P)i;5!;yW4~L4Bn-&]E_ yzXfbFW;줝X깗Z2O;l/=zdo Z~=O^ukEMXg1WM/0#|: 0[C+Z þY qpE!En1I8k'1ߥ'fħ>hh|W\RHOR$zB$ۊ^3߽OLnNNdZ9~]L @"yzQ14?H/s+1/[eb>!x7;2|Bdg5wf;"yI,&ۣyYqnh*J,GzZ y, br(/'^Cp[h|j~21<4 8操d5| 1ggc>ah: |NVx?_Χ*lpoF=zJ)q/+$ECVއ"397O7 M͹M;vj6 (!KW 'Z/?UPvwIn;ECGHUUH]nny➀L(kѼh08Z)f1GV1~^,67A;Sа*[3#y+i,C7*r_~iF=߯翑5X%Bȭ%l_& :wю w2=L蹋܍2RiϏQBp~q|G]=?+^Ϗ4jpv*kg1;lz1CYY'2>||xiPzs@f'Qq蹾oԳBpF y sM~vJEԘ7D @ǟ+pFWπQ]{\f |7+$"ak[_4G8|E=(qcfF4uT^s༼7^[PaZ~M7;_wяFx[ ^yOϳ;l1-yvy%m̒ѥ4_ o2Qwh_=M~X|ea*1~qizJw(O{-K wR(K wXLЀ}okߘ}|8e9Ϧp+{_vq۹w8m|%.*u[n E%d9Bp牢qp!E3B'췊я+UďUKOą^k-_ج|մdKD-6_$gKzQ?Qr7$%+7[ zu㶲f?z=S` [oq;lvz?.A>\6έc+k98\6f7r6>]]:C'{3:.[t~R/:vn6W+n]t%6 ٺ8[Qk]e*g-}]r YMe{tqΏwf|P{_ 1F:9pbem"_ xQq’?i rFׯѽK{NH}GEs3S㢻vB7v,uo -b욲隷Cp_2Bp+;F}4yD7[.M"Y=]! U2lBq"q%)4xjev)-3hzSnjoꨂ[sH[-6̮~-[2{~R}gt'V+TMW%}#Е>];V45Nѕ>G6Ě %C:e-扏hE~'l*TD1zp4cW&׷ɞaVX6L$#GsFR$ӵH]x d?^bZl|ɹwyN m;l:bR1!1âZ{?Kd~|/%`Q* ĀbVn1*+gDk,J^nqEq{/n?{R)W &sX1<|k:Y`άFk'?-\[_\FAq{ºOZ6T4f/SUĒM>ߥm>BV GlQ4"\ٹ:Bּ50r\ž=VF:ʟjZ][߲{Z5}6hFژWSI=}sRrfMhsu{M*enHGTF{^5/Ԣ5uD/jIs>{O1/`^sQ83v5Qݬ<Ӧ:iMݻ󅄬9);v\j0;o=]lg*>PB}A:)fp8e=2p) ϽϚ6^? w6\w SBK=mƞk,t QUso-z{}'cў_|$!#uX촵drdpe*w!ق+!,?5SS1&pX=OПFt( FdEFWo,z8sMR][i7U5yo-ފ&?f _+H 7 j7~4~"7w,{sp\y]VN_ rCn!*1d~Stt/QV'WϤaWGݫ~UhfT*5O=4?1Lu/Sɽh_ԷA\Ca?("]JVn>OU%ڸ^Y| sOR;>To7}Rek5^qf}TK:S|9[|tNz]{h3Z ~{bE{MoT5[/5mgtgdTT;יbE`}Y6O[Yg#-N;F^)]|=t-rp׊3g"}/j'1ch\4*J_ϼb3Yo+AbpP{g:p }^b?MlG;IFoYs~u(8;u*[DWS`+|!okaktX-bCu3D?1O\Ęcm\o7!VHOAflBc~?VZ'IyD:yHOdX\1 Vi%)Ԏ39gl@ xk?NY9Y5P+=<(GpxrnU\_!}>#/v.6_kcJ7adulޜ!T4g7W]Urt}[U:7[uFKybWȴ]&{.=A{K_Jktuf8`'"eE \_LQ".gG!?\у͗:KV~$m}Ed^}Ŭ|27۹jkn=MM6utbMwȚL=!BVnnzx-Bm˥DhBɻOV͟"Ktu[b(!gk1&G\~*юV[28' q,)x6ԞǏ͑o_&ޠ;\i?wW*Ԟ;Zmd۰\.͆-[\NR˙h[/p%N_wOkVqE6߻yzoBj~:|$ u>4>'}[ D/s^fךJeڻ9Pќ^fp]5.|GZyӈOB䏤`Rf ?*({G"FtϜ!zWcbIt(.T=mP'cQ%5LT%k1i҆:Y*%ޛS]+e\i >{+<?}]E$w%~χ~pN,+ɭ?RqOS?rCAfa$g@U╃:.xZ_ O**ߝmTlLVn'P?J\e[Gpm<G ]M<PGSܹ"FMIi ^!ޱpȳlo"wW*_dNz?)]>0opO{1{6O2-᛼ }@s4_6GCM;Z}W7ZeąBm.Sݜށy^~[=2_բ_bXxZؼ``? A =ѩ9se}mm:ڰ6}~K6-8 +"+7bC f\y 7O d4lakvPtIy/_6kĻ5URo4Ud4mcՉ\k'>n MdL{y6׏c=׷gY{m6[;e["77z͔ї?cOx́+ +o74~z׀5'g{}gt7D\ǎj{N:ϫ:ofeutfa{V7o{w#oz?ӞnȱKU;#zu14nG<7Ou6/i<|ߞa+??i $Tdw,wbVX[5o}F/-h~ yC.TFޑ _Z>|$k܇4 -8(= 3^_]iA^fpSV*e*o+46z fG}gӏ"Bճ' zQʕm_* o8?ံNVX<"'gSdzC?l݁tB>+z6qN0_H_Fܼ}G꼊z~r(:/:+ ,&۴dIO%seRN:|i@`) 5I;-sG0Ңhq\5Gv5w̤rk*-JG>ݣ|Pushʊ~ɳގ5ёIuatSGϮ8fZ=97<sxγ1Z9Q-ŸZ֮*?Uh8y߶+rS NO[ ZAqݡu\:Vt=:֛(T%eo0sNcoQj:?XMBMb޶^ÚbdZSMpܐl]pfucp69~:Lc ueBc9Qut)YI6V%7ix2%g\־nKQyԕi?=zMI|;>u?Ep!\:6oyۜ/vYiH @;dǮ-712׈x̩{ ;ZeSZ9)>K(R@wD |黮]_ןZ@kqjaMSbpJՔ+!e%E.MՒ2phe^-ʬd">otNMN9Y9'Ρ:_ECKU6[!ZQuY?,KPovΆ'oM7kTt/u>+pneGrxDGS^V@!F^.R^K"t]O3>F|oV]DLV~n{}\7f]:㧐HEzzLV&USx+1^ʬǀo'xU'~]{ͱ3v]}dHc1WM/Iʾ>!xho`yxM\&񐝫zS2=~LK=[ ˚͂oFsV?hDsYs6?6U2ue'Kg, jO]mqzlKE)CJu}gW`Tg땳/Olbzo >.>,$ik|||^- _y6Z_n}ieFS92C_pVș/~߉s5;YMsu#^gsbs6;um0Ě8}64>=&jOՔ{y;ޱO|(PW׈;k{WIF\?J&Fm'UǃWtno\yzm(K/ol]Ly~+ksqn{geO2 g(AWhlr zJ+?꿓gEW7UShşF2lH^'ޙU{~]!1F*׉|"eMwϽ뉂nQ[Eϵy']c,;|8w we^xd{IO2t=SOf\Qm?[ >@Aޞp7S.S7oCV}CUwwO⿃s{=n 1-FWC'~e􉚪cG[yѵo>J:r]匆uGWٝ{F_Xg0.jy_קGo>/\7;IJ/!_{$Nj㣻E|0dO63E$g^'~rح%;TycZrNŀSm8\!ۏJE*#ԯXBb~H$~c'OMuĵoósAXq')K׌cW%zcԿ$ W+s* $WKmjbat5*hn*>wE;sci_ P~>B:wכ?.QEI#t*D^ ݌^en"iV^3O- SY1[z;W= nBp~!wDܠTxG<l"Uma~ [S]/o+KTgtC>?+ףmiviT}Nsgs~%ԭtWRYMjw/Rs/v]}( $׮>XzwXV=mH|ߤupi<^f۫l]5ղwL/Q$vq]{8tmt&϶=jo[N iH!lЋo,7[MU\ca>D/fWѫ"_x-h4׾ekŷB*ϑ%=#+&_ktKBuln');mW|ٮg F2> 42zA;cUe^۳GziemW]%a+eMxހZ7LAߝ3so!Kʑ r{_/ak.ضD]? sSvjXH^n. +NSyky"Wv بTK-;{} '=p. .U<ٟG/сo>Eh=1f7jzaFЊO(^^n >Tݟi>m"L*I|Ovd92OƾLY\W'nŗO2T1_؃P?X7f: $BpӞ{CpTgĘ+;}>= M'|#gZB)}cܓ'*^c~]\1L\H|MLۦ_}xa옫\򑬛r5a3ۡbOgKڞM?%&V;pݭϤTپF~F ~k"dQf-JOW"D?)K׌#o_Y8[ ۷h_"ҶqXxw]]TjqvO_jOF/`[!&p==p(Yfcm^!h V;O m j3/T/cͳ՝֥tEc *{ 76^c1F$[cQ+Wevm |oj "_H^|52c6o-\+!݂C I^uƾW1WM/Z?W |3^ѱ*[lUal1-G-Lu-Ϻj֖[wׯ[G^B~OI{4Bcڣ~~!e2yƷW#fXڢM91H}ncѳG<+j}CTWVZՠ)lK_ v۹n]v@yʴǺ1B?}FQwgkE1 F1/#cr@`-b$ʈ b[,H.4uGSܯUS-`Ϝ2;tnzKk$s\E[4G|Lz;6uViu gP;cub~vl~1xQ[@ܡ"dep]jN5o+)"8Tz:.l?,㟂o>lkjSgyrb~lPU7?ZZ/ 7^z~D/rp w<|ŻߤLnPw sٍeEp27WǍ沼P5*V> oVMz,C7~.O8ۿDP=DC!w!8ܳ_W2<](C:SqH ">nO+ U1Zv !=wb\~jpQ7Uӕ~I?-&~jst]7Cj/IEvqe͌jz>V/V&:{K"xW缇jzݷ^gMCr nj>_G"'93}urݭqMt9?[zk)b½UW6WZy6^IJJx|}8"qiJIIos(W:RIOgX뇔U 2_dh"Д&Ї]kb/=\cz惊P}vieSZWk{m,e@ Cu!8{Q>\YjOBڿIpqCSВ˓*'G?&NDO1=?M!FE6eݷ9V߮/")ہo Y1Z.D>ߎofjC>K#[߹ndہoVvUvfϘgl+-fMź2%y3I^Lץ'5C`;VƿZעYwf.N_ɱ ^~טsl,6K'vVޡ>ި<:)~%Mz kx%Eo QG9O׹ٲ: Np(\ Z^oM8ЗmhѤEyEʗ(?)@egF glثaös 7߆?|v-4rʝX1sn_ 8ao޿}^^ l?c-U\-1Rok|.qϡK'=g-:]Q;in2o#iFYZo?? $NJ)]L4Gܷ,Dh􂇡єG)4 KN̦%u_m~wRP#fNʖyoK JKs2uN?5Xӯ k./բ:Yf3:_YTϹV|L=9u6<ݥz8|/%`>$Dߧzn*U>G)4[5"ihof_(9?{R.hFwooe>CB_$<|<|fџ_I#m++;F\#1<{}mϖZ}1M=tʳ:t7rݯ䏺LMa{GW)':>uj67[acR^2>ٜチ_DKV_+ ͯ{FeBm, ïðè óñëîâèè: L affV  . Äîïóñòèì íà V ´ V çàäàí ëèíåéíûé ïðåäèêàò. Òîãäà íåïîñðåäñòâåííàÿ ïðîâåð- êà ïîçâîëÿåò óñòàíîâèòü âûïîëíåíèå äëÿ íåãî ñëåäóþùèõ ñâîéñòâ: 1) ðåôëåêñèâíîñòü; 2) ñèììåòðè÷íîñòü; 3) òðàíçèòèâíîñòü; 4) âûïóêëàÿ àääèòèâíîñòü: ïóñòü ÷èñëà 0    , óäîâëåòâîðÿþò óñëîâèþ 1     è Å(õ, ó)= 1  `) y `, x ( E , òîãäà ; `) y y `, x x ( E 1        5) n-ìåðíîñòü: íàéäåòñÿ â V ñèñòåìà ëèíåéíî-íåçàâèñèìûõ âåêòîðîâ } ,..., { 1 1  n e e òàêàÿ, ÷òî äëÿ ëþáîãî V x  ñóùåñòâóåò òàêîå ìíîæåñòâî èíäåêñîâ 1 2 1   n ,..., , { ) x ( I è åäèíñòâåííûé íàáîð ÷èñåë ) x ( ),..., x ( n 1 1    , äëÿ êîòîðûõ âûïîëíÿþòñÿ óñëîâèÿ        ) x ( I i ) x ( I i i i i i o , ) e ) x ( , e ) x ( x ) x ( ( E 1    ïðè÷åì      ) x ( I i i )] x ( [ ) x ( 1 0   >0, 0 0  ) x ( ) x ( ) x ( i i     ïðè 0 0    ) x ( ) x ( ) x ( ), x ( I i i i    ,         ) x ( I i ) x ( I i i i . ) x ( , ) x ( ) x ( 1 1 0    ïðè ) x ( I i   . Îáîçíà÷èì 2 1 x e ) x ( , x e ) x ( ) x ( I i ) x ( I i i i i i          = 2 x , òîãäà ñâîéñòâî n-ìåðíîñòè ìîæíî çàïèñàòü òàê : ; x , x x ) x ( ( E 1 2 1 0    6) íåïðåðûâíîñòü: ôóíêöèîíàëû 1 1   n i i )} x ( a { íåïðåðûâíû â ìåòðèêå L; 7) âûïóêëàÿ ïîëóàääèòèâíîñòü: åñëè 1 0    è t ) ( y , t ) ( ) x ( ( E         1 1 =1, òî Å(õ, ó)= 1 äëÿ V y , x  ; 8) âûïóêëàÿ îäíîðîäíîñòü: ïóñòü ýëåìåíòû V t y , t x , y , x      è , ) t y , t x ( E 1      òîãäà E(x, ó) = 1. Çàìåòèì, ÷òî åñëè ïðåäèêàò E(x, ó) ëèíååí è çàäàí íà V  V, òî âñå ïåðå÷èñëåí- íûå âûøå ñâîéñòâà, êðîìå n-ìåðíîñòè, íåïîñðåäñòâåííî âûòåêàþò èç âèäà ïðåäèêàòà. Ñâîéñòâî n-ìåðíîñòè ìû îáîñíóåì íèæå. Óòâåðæäåíèå 1. Åñëè ïðåäèêàò Å(õ, ó) óäîâëåòâîðÿåò ñâîéñòâàì 1-8, òî: à) äëÿ ëþáûõ ïàð   r i i i } y , x { 1 V  V è ëþáîãî íàáîðà ÷èñåë âèäà      r i i r i i a , )} x ( { 1 1 1 0  èç ðàâåíñòâ 1  ) y , x ( E i i , _____ r , i 1  âûòåêàåò    r i i i ; ) y ( E 1 1  á) äëÿ ëþáûõ V z ,..., z , y , x r  1 è ëþáûõ ÷èñåë 1 0 1 1   r r ,..., , , ,..., ,       èç ðàâåí- ñòâà        r i i i r i i i ) z y , z xx ( E 1 1 1     âûòåêàåò . ) y , x ( E 1  Óòâåðæäåíèå 2. Ïóñòü äëÿ ëþáîãî V x  çàäàí îïåðàòîð Ax ñëåäóþùèì ñîîòíîøåíèåì: Dx pUǿ"!$!C^DaѰ)iVBA HF)}+ qL`M1&,BEی {< ut:/3|{w|o5HD2[ ODC[-YIdB+/3=Nݝ8xB_vm[FFҜ+I #$C3$I:rNJc1>JvmNIWygo1+xVO64,U!ä~P"g7>~{ݓrR|0 nЕkTaHrN+M:xWW78.1U>y~ܗsI/7}TI~+yo`td켟cPiV?~[iٖFn% (᧩Irl(̇),}=:TʸéHNDڒ$#j=j r^MdϾFh-Ñ)WЀ-cS%|Oصu?֖/hmw'phGD-L&5ػo2yUߙrs~XG)x?j])*1xm];C9@Gӱ~t1Y*1-W)o釟s_ ]uͬet5w^N}\ %@oاȆzy!G=V]3_sqkcOG7׎2oMؐ-1li_* ]qѿ {R9f=9YQތP??gb[KO =Ss:N| BWϼR`Vկ[!#;m]N/v!2vK NHO_E<0b_|5+<#XN8ncЏY3Gc6z,*ѫ}4gަ=i>kޘ=y%A/8>K%f(~&i4nF#V_~iVu:Nk-?T{6Dn_f`7';3煾Όzf!V.&n}rU@P!;^ }CKEPEƨ% {/fh͋U+L-E.b\o1:ŲSYک(YbKˈ;ޘcj֙k@+񋋅k+HN҈WBK}q&4V/yϪs߻R>0L)ޚX`hU5~biA1S>0&w^CbFwgi= 8,5(fj}*|B7ͷ"dl۷ۭ%ScUCP苯ڭuL>6=AUp3 |5UYbi>q1T[ؖ)Y$:>;_P6u-!ς.#QP.4ʂtTs_h(v>mVg"<9;dkkfY?1J'A((Hݮor"9N/oȗh8HU\]q-p`>ڂ"M|I+ppqZ;N/@8(Yh|@*vV Ŏ|zgeXK#R̯g:MoceHcFK9C~ ~Oz[|bY{!!*:"_S KNSobd|p/ t~B'yS [S9s9?a4uB1w7=<"OćA ݓ`A~!tH|YpØwv;W(|~/ôaF7DêHQzΌwVL(:Ċ&},l8x|ظqro\ͫ4y_0{0^$~8T1ߜW<ݿO[?w~u?Qe)ndn*w&y,g!sE;"ǚ9V]).臈+ax ׷OIsۙJuWy9DQt‡ZHCFGg[\Fіr!oh٥-тQQNWMDѯXG(sN * *jtg`vch#N=~>6ZQ׃m*ؘ~PyEdo<JݏIssFł6+)'悬w˥CYO{OhUIZOO*s`WmSW[nrD4n@.WwI>D$?TSEߺ- 4ō=l7:G}7~4];_ڧ/-Zש6pҢڰ-N" n-:'z:_eE>wi]p_/P˻5\=z}?IK4F*/IjlUI;|$']RԭvI^_DƗy{y)v^F>Wnw3y zS؛c($zq_1HOzi0=*(kS?*={a'&jG'*} 5>FƦ[5|'0^r^Crb8gzF^"x]m-#FL@_g-/xmdlJǫ% ^^EbJ9׉zUwz.4};ȇF* 6Ao~{{6]vLPnl[ӐkWG+5Io)~b공+ޥ4ResG7/ZUbk ﲦHbj,ҍi6mճ\ 4">s@N׿61Ikwܠdmz?<&5Pk<}tx[ꯢz.wx!7SMVW*6AJޗLB0'˽]Bi92zzS^tWK6蕒dCc){Ǘ&&/1~=RQ=pc5o}aemV5}3济)qXkڕL`)FJL֦$pS_,8M6m0VySjI[*Tiuo-},TI?Q_Bp~-}2ˋu8R{/i>XvŇ(bdv-'iIxMft$gx/kyKgăg&j[o/,jvwgvLPMؖ;$b{uhK{Y{6 W-mKӮ#sqX딼؛ߜZ~smTc*U:[uF\6h#A<|^Efke銦/}2!vust3V< ( mm 2|U5 OGc]4ĺtg:׻ih<7jml~Q1}\K7i5~/~1ҫcVoRV/|$fz߷?Лޜ2"­Kqo_e}W ._2P3q >:! _ ~ ~їU@ίU\&yWJuIU62_e'-[+qx^5xFk#6C—!o嵫!8ʫ%'TMI2_RX7B'~M.Z$ؽRljֿGȷt'$C0+}1FCm;A;K=.|{xOW>s5oQygS?ϻ(TxKK|~ïn{~i~$vuTV ;f\ig'褢_j3_[,+2n i=3:vzð/swP|C{4hw1a{%zM;&(*i`Aqv&yl-UhPU\>+u+^^T JG6|ExD]y裭A<+E:L`L)KeOwwx٩4zLi>Li+-4V}C HāN$d9 OB|QZRR<'mPkTsd>p2膾[ 6ڳ|?}y63Ɔ_"Ɲ<}۠wH10=JVp&!3u܂nm$YoRo?V;MyFo~J*w}TCΟ7AR_0+׽w䃒KڛV9Ek쏯N%?iD<?)@:%ύIMleE"3 _s#Rk~_|p|0᫞B 'W^=l7Qi|8QL^WRM5a`DX1!uo`߬@` 8k t)+szX/[hTOMf'Zi'1ZH_@6jf8C?yPkNׅIYGTD\uԇ ;~Qv^nUԳ5^Gsc9 FFa3&6.&%q"yv8GqJ8S~md{}jM!o\Vag%3.ɣPw+oJqF{D謍žU u?71뎛tV(YOdWޔĀ:t[N![=?! OhK7_쨀_{{[YE~ [}yeľl+Qnɮ;+!XiC!W{xxYl>iѪvO(xӭ !_ k>7mݏ=m\\b:^x\WqXro#{א8{=/ t=[ݴc@v}k$ Gn:nlq-U"Qw论nVOXMaO:ٴkgg?%8E̻obLEW~`5纹mn?DcYҩ _ls;~btGP4cnN,w|-ީ_:߿;SWa8v{D*/OSKz+`ɑPTHސy~E^ LzC<%٘ uh$_J. _+Z/A|8koU^1>x)Ňz$;w Fz[A;ޛz~\^pR|IzYcx'0Oyp!w#}n_VM=g?U|\y!σɒYySUտwTA.%[_j Y+o 9NU<㍐%ưl5>n!"$9wBpSc!%'tdۥ-,k=@&;V^< MQVZ-p (w+oB?n.w^߾ۅp4| br97O%fսB!l:7{{sz( _._k$5|5n!2Նns^Y#-cöTn仯DZxS.<5/=luӎ #o}`q杽i*kL|]qQT<%U˔I.P+&\)T8na>nV3&)p.ɵ[$'3&Bi-4&ʻ-;F6Y=I0;(5 Qp4BDVy:X|gpޑW1O kXYW֬w.31n lwk`Cck]gK rJh_ ,AyvIMkJM?w"}ٳA?|Æ2h+WC[&}EuaC[6z*#v {rxVӗ-Ww``͌MI}z;OZ=AY½1,|d# 73,ܽ<|d]2:@M"*&Y/S,"?|OϚ}Y?v󩯊毯`|V Cn)sW氾amFGHV%ܞ*E\Ghާ9S~_z YytzjI%(Ζ퟉aÝ C"XN[T;4(W檼EYJaU55M\#4lsbs1.6?z/$뀭$YΏ_J:s㬛s#t_D_C<쩉zpixdžnAeS\0Zy'H3%;Cpcoߍu!8+o9GOMiwZrxOm6aӤ"x>X<L{X, ~8_=0: 띤:)D4{H~ɵ6eeoZ{==:L֩~5%$I'!yINV@'ӹ.77<ݍQ霘)Pt\kվogƇ||Ww"t6ɗ轺&_4ِY:/lDux5FvO흯 'FŃ5_ñQzVH=!?t詺 oѓ'bP.P~"9Zxu{JlΗ7AtM +|yQ!=ŗw#({@?z{pxoQʾ]a?:h3頟*q5NW&S!Xkz\򾬴 ʽSy?ĉcTUOd|N98uaV*TO0o"TJOSjuŊum8W+pʽ7pv.<[9[O3Jl#Ck.{zHF=ҭĖn/ڍ%3GFуgA] F.U"_Wu~ 8S* V9BFu.x:'W"6ē2tƄtb/cރm\ll|Ɣrʶq\mukbtPl[Uϸа-3 }u_3j] bLzc*ۧzϸ@>寳羽M=ie;M_{|qσw}EܒW74oN ~g&tWkFw\tI*>>7z9&k5#d;:$&(̇~M1>n3'Kd?b;__Epo.gV a#c^ե|| ١@ ިl 9&{_a)?kmȹ] Zv8zպ) G}D2vi'6GXl4Ƕ%;E{O9XQlv"4E_ٺȣ 5GyK7Ah{oMx^g :|U?4n)9aU/ v~rmlWe~ケ2\ GL151>֙5JuO]L Dcx٠V˚`^K/Kk0T=<0 >/wƆXqO:}`k~xk㾣'+f/|>_)f/( %~:x`lk^닽G_q/4,/ywg ~ė<{ ~O!.56k^p_ e}ٷLuP~_],QB`'eykX1M ٍ,w1m}H% .kb1b\DwYyWJ&8@P#pWB~F\ o8oB4ld1o#Vg\.w S=pOBp_o(LtGyPۊcO ~-<|f8&twũWwsh*$?Zu\~"dmo}Ot/_H[Bs&m"xsϼkZ*91]4DmPYN~E::~Ò!ppknz~*yEѓoaj_=pݢz~A#q'G?/M޾K% ϡW㣛;f̧a5ujo2ޓޖ3ӣw%t끛3T^=p83or$zwTM|1m1s sv7:~ֵ+鼇cmmm}|o~8/'O}fZc^5d5啜XJ =䯓u+ϵ ߩHEڟn~*_e4lD_|Q񞽊YR7D!MwvTZ(B%V6hfͳ j$כFy{ƈ_T  ]z.zLLJ6\Q}0o/QovnA+N䅭v|<mKd|ɒdzZK:eĤQ10И}h4wi,+M;1Nt^߫ΗtƞqOMy ~3?pb1OUFKڇM>}Ԯ{J41n>n澠Fџn {JM0>u-D<ʃW<:=2:g/\ ?Q=4?k v֔\[=cEcynnW`שzL .\ _dxV3C${5m`nm=rj+ć|(u}Brxc^ a !~-mzǰlc_?]l :5ƯŒdWH53k|:8?)p)脶mݩ63e 7Ƕ4^mwh]8h:kd=NHuvElOߧ5=.]{M|!{>~S>XML'B}Byc7`Ө:O)<رWު~qg6[IC;vo}cE=cRk,}]Z٤*ߧ園S1StAc~CzB@ԛ ?#_Kn\%UE[FƦlbZN<6b|x)&h#O\ʯB1F'?2%A.~K5/d@!~Yap[)\_:~M:į"8|]Щ ⒡[Z\: OqpN ]2ꁋ &<'N3_oW*.79 @1,^*\kKcךf^}"O 2_ޣf8?VZzPک&_K ~U>Te[.؜J9 dbo#J%fό_X?%5j[=}._K~/{s-|#3,?E_}i&4_锁kY?y$ ~ Uk7Wb=Haw uVhԾ7#o .^.LWzEl7[5NVkԞթ}K7_;Oh^xT|M}thwceg_lŐܙs)=$z MqpyIPyk\wEO%; +yoy={V'{?\'x'M[0*#ŗ_M9N mv ykdl+s5`{Wklxe:/gM;|EX7I6יE/]K_UO_Dۑ_>+V~x7l+ JJ~Myt6>:8 &~Nvo>O-g><]9J | LYZ+t`y{b=]]ĿTǍ+ d[fk+mp`d.q #)XoUZ@r}+E;f/tԯ^Ƈrrv"'w57sO h a}}ltv8u*(:UƀSMYLPTۗJՔd_`o}*;&4|yRrIo?/—}W)3Pd {?%sk&o'HMrkҟmU@?{=M>3R_-;eh2ЙOpVg&ygե/S.Vb%E|cyqWR)}]Vx}O)c,Gf/![3Ny|b`usuEy}MWF:< o{z?l.+" Eżõh8FI(##WCzC랏okÝܳ{]` gyp3~rf4]%|uf/CwTZ)՟?&wtc<=qpit{<75>RNk||cχᵀ_K댱Av#cSoviă+u:\ 7}A(J뉒)fU❼9>/gN-+HWbku8=af~k?\h\XW_/6_3_k^k2ݿR40 8?Q lw;yؓ] 2}7^I\mM0;ߓOP`hz)Fo.>)-wq%>;b__ ۞!NY# XyIw }oX|D@yt  $z% {E^Ĕ6А`m3|\ٜmptf;&vFk}(8&p\p SCo7k>2F")_g{5KCQ<lh~Tyd r4(xNzD?b_/EzA=7W=6X~ 1V 4n̫klpb=n4DioQZhܾ#?|OϚ}Y?v󩯊毯R` !79߫zb>hp$I&GC:,͗l9G7g+_>_$]Ru<31 `pl~;`}9"~32T}sb'0{rP#q~nW74/7_:3eHtp5!8^w2hnɓ ܃^FF'[p7Ph1k=hCm9/<6A. DL?p # Xg3~*Џr!:tup>bG]+IT<;8gRb8 "[y}!CN|'ȱꇇcf#HLrPH.\QoUkBc,zB"<<|ɂ>>!wc>2b^ Z"r[_ԬxKQֻ?,,42 ), x ( / ) x x ( ) e ) x ( ) e ) x ( )( x ( / Ax O ) x ( I i i i i ) x ( I i i O     1 2 1          ãäå 1 1 1 2 1   n n O e ,..., e , ,..., , x , x   îïðåäåëåíû â ñâîéñòâå n-ìåðíîñòè. Òîãäà äëÿ ëþáûõ V y x  , è ÷èñåë 1 0        , , âûïîëíÿåòñÿ . Ay Ax y x ( A        Òåîðåìà 1. Äëÿ òîãî ÷òîáû ïðåäèêàò Å(õ, ó), çàäàííûé íà V ´   R , L V ´   R , L , áûë ëèíåéíûì, íåîáõîäèìî è äîñòàòî÷íî, ÷òîáû îí óäîâëåòâîðÿë óñëîâèÿì 1-8. Äîêàçàòåëüñòâî. Íåîáõîäèìîñòü. Èç çàìå÷àíèé, ñäåëàííûõ ðàíåå, ñëåäó- åò, ÷òî äëÿ îáîñíîâàíèÿ íåîáõîäèìîñòè íàäî äîêàçàòü âûïîëíåíèå ñâîéñòâà n- ìåðíîñòè äëÿ ëèíåéíîãî ïðåäèêàòà. Ïîñêîëüêó dim L > ï è affV = L, òî ìîæíî çàôèêñèðîâàòü ëèíåéíî-íåçàâèñè- ìóþ ñèñòåìó âåêòîðîâ V } e ,..., e { n   1 1 è íå ïðèíàäëåæàùóþ kerF (ÿäðó îïåðàòîðà F). Çàôèêñèðóåì òàêîâóþ è îñìîòðèì ñèñòåìó ëèíåéíèõ óðàâíåíèé äëÿ ïðîèç- âîëüíîãî V x  îòíîñèòåëüíî íåèçâåñòíûõ ÷èñåë ) x ( ),..., x ( n 1 1    âèäà                 1 1 1 1 1 1 n i i n i _____ i j i j . ) x ( n , j ), e ( f ) x ( ) x ( f   , (1) Ìàòðèöà ñèñòåìû À èìååò âèä                        ) ( ) ( ) ( ........ .......... .......... .......... ) ( ... ) ( ) ( 1 ... 1 1 1 2 1 1 1 2 1 1 1 n n n n n e f e f e f e f e f e f A . Åñëè ïîêàçàòü, ÷òî îïðåäåëèòåëü ìàòðèöû À íå ðàâåí 0, òî ñèñòåìà (1) ðàçðåøèìà åäèíñòâåííûì îáðàçîì, è ÷èñëà ) x ( ),..., x ( n 1 1    íåïðåðûâíî çàâèñÿò îò x. Ýêâèâàëåíòíûìè ïðåîáðàçîâàíèÿìè det A ìîæíî ïðèâåñòè ê ñëåäóþùåìó: . ) e e ( f )... e e ( f . .......... .......... .......... .......... ) e e ( f )... e e ( f A det n n n n 1 1 1 2 1 1 1 1 2 1        (2) Äîêàæåì òåïåðü, ÷òî ñèñòåìà âåêòîðîâ 1 2 1    n i i } e e { ëèíåéíî-íåçàâèñèìà. Äåé- ñòâèòåëüíî, åñëè îíà ëèíåéíî-çàâèñèìà, òî      1 2 1 0 n i i i , ) e e (  ïðè     1 2 2 0 n i i .  Íî òîãäà          1 2 1 1 0 n i n i i i i i , e ) ( e   ÷òî îçíà÷àåò ëèíåéíóþ çàâèñèìîñòü ïåðâîíà÷àëüíîé ñèñòåìû . e ,..., e n 1 1  Ïðîòèâîðå÷èå. Ñëåäîâàòåëüíî, ñèñòåìà 1 2 1 } {    n i i e e ëèíåéíî- íåçàâèñèìà è íå ïðèíàäëåæèò . KerF Çíà÷èò, îïðåäåëèòåëü Ãðàììà, ñòîÿùèé â ïðàâîé ÷àñòè ðàâåíñòâà (2), íå ðàâåí 0, ÷òî îçíà÷àåò . A det 0  Òåïåðü ïîëîæèì }. ) x ( : i { ) x ( I i 0    Çàìåòèì, ÷òî ìíîæåñòâî ) x ( I ìîæåò îêàçàòüñÿ ïóñòûì. Çàòåì ïîëîæèì 0 ) ( ) ( ) ( , ) ( ) ( 1 ) ( _                       x x x x x i O i x I i i O @x t7I1d#!B вţ(`&b+ȢQbU6Z5D+"Q(Hd k"KEkЁ0_w8Q;}}w{߼?.*I9G̈ H7dG5\d"ݚv=үpiF(_V֏Ȑ>婲t>`3Y`/]5Oߵ:ֲRolҪgBI]͈=`{fl7Pd&+AvD}=I 3R̛*1f`gL$$9M@J dԑ#:0d(}րUHyČF[#߈fFi_?ж"92tF_>s} Kե,Z4kx3MQw/ucu^v{ |JVi4!|ZqD~ W&=|mDic |5|~슟!=t$׿M:aKMeQ_ͮQ$g$46Q Csnf$Iq1l] maECGoW ײ~[N'OJ4}q4CӐ)%ikB6ƿk+.k]V;S]"j.SDC7jiN7N>g|6cqp;KkcXb/ʓ` Jz7Hk 9F,s< ,x dkSЗֳNz&~+Ao7>Yb!OX2x~W @W;x- ;N,jL1z)=ݮM8j~Y% y=F.M,4F^g-AjY>>{s_hPN@: -#)l9>q~y#ڏ(c ^殞a;!m͉ucbxys_>B@ϝ tDF3tO ?@ٿ}$Z7`E,螫,jV]= LcFΨIխht.zӮLڶ}wm싒ݔ}a>my=ntsv0f=e%}l3Nx+`CH5aGGXϧ${~B!5ؿrl2q\$*˛ϒIl_-N13gB:hFsebtfRtæe2YvelڹXXylc2Y2}W65d(wdż62d7yteۙ~#7CKޠ 8uC(ys v}87J1޺20us,ugu$5 ~īIGngwK䏜%, k6kݍ:-wh/'>Цlj~c UVˎHl/Xc^\;1)B$[2tD0Mbؗ0kmiyC4,o(gc{t-}q迀@>3o{N}麭tA Hmld_|nEdU)i\@f!kqߌ6 #-*޶Su櫚ڲ]l FKʖ|3vCi)yޖN;ޮ*n:DZc5w;P*,im9&rx/m5ħ(}Oh,~e{8YɘM|1H`ev{LjpA?J|dٞk XqA]gPDS`;XF XX8'61`;У6e5GϲE}u_@mDC.aй>@+]r*DOo7Ö7mOeu[d2ƒϡcgQ3і vg|;0|=6nt6舏;Tgم|}|~4~sPpGghZbG`;g^mԹsQyxcSstS-dN/^[_zF_KRZޔtgduo>HT6;2f_mN?nsBy 䁐By _{W^ocxgw?op`/鵮|kهH}Ҿx/jU${{!PwN䞞<{# ??71~= Wn#0ڼy <ԓټlNQ88+yW Fz0~n~u*/f$HU`7@_7Z;ȷI4V-V91VR7:孴Ny+V ˑ)ët 1>J" _ї8xy#tm2 t4\&l!KIf4d:2A:eMQ2򋱩Hj^~ޔy>-wz"sA6b3XKzX JCj.F?[4ޑJ]:g:phCcm xdwssfM4xd[3Nt!?[ٖኀw s to#/-d 5~m^|Y=8QFUvF8DG#*X~Ҩktm"\v־; L/{.}Kղ/d}|W~ Q.OTp{qrTYle]nL)d\ݪ}*$mTϯ&U{P.ǶDOw P9 %ct!fKL .9g.+X^ ϝVq{Nq^NFF.c4g{)rupظ =*gdwn1?8vK ZN#Ƴ+ߧ\3^4I.mo)}6ه ir]ج )8M8[<_Bܢ{!ܢ(+.s ^ҩ/XlW. wE*Rz;GfSmx\W}U|bPuT5K\mΗU= IU]ۗ?utrrMW%;Ŗ6G+sv['m/U!By 䁐By 䁟z>4By 䁐DMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:13  F(   TH6( >( (16&G 2\G /L( 1 09 {Qx} exaRsvu);)u`cmERt~F,8eifG?ceVjGBS'oeeAATBco 3_І}w~397:u_:\Ï9¹wkܨuD[9{>>ntSݹvs]0ӝy4#0/-׸N s>#tƹш;4}aº5j9awm̋&DhemA\Ctkdqsz=I:\9LCn:YSj><熸3o_ߺk|6 |AݤC>1uݵ ?O!݈Ya[Y[kãkG1%*7/jYvƹ n5^Qْny;$çw!ӍM3&Mϸ <<Z/?#trx&z*"Eh/8.3ՆTDƇB~I%]W@qi#뒖xs ?O!fQih}[I$a$‘3@/i9ae-p-㙅Rcydk+v< ׽U9 ygϡthwDߤ'uq%O^L&LNcs|n&o5?(4>D)3 8;~{&Ԭm{.)wF\B3!1,5L z~b5b H;ո  ߮\O/xֈC"k h"8?߱sWF˦5}mn?b:ЋYJysR?2d T(B+3e %{+M +9 3YL[ehgNm`~ 2qH/v~yd!ڢek~=:(S(>UQׇNe(MVpy$/jQD( CTy޷枯\d^pL>ub6}[z禔5*L!|rAJ%NX%pᙅނrׂ,YĐeЕr"4>}m[a}o5awFl;LׄϢkR4#}Kq=6/>̏eޜg_<֣):1~g gx礟g:2 GgcY j}-B7(iqv3֏>\ބDmnf`fSQo&}<n [d[qğz%})~5KSV}|cO-o@JB/.ۧy\^y/y35gы-" ʚɼGC{)hN]gN܎$v|ƹ>0v,pamWdݸRp=@5cY'qİy照nBFBoG>Pe^pz^-.i/6|N5\w,6L n}`H;'=> ̳? b{4.w1c"iV<8)".ϥC^旖X9luj8gYY6ɗm8'zVO[^<%71y྾)v]? QF}QE8UsM8Eo1|,yEV%#]Y+5"}Sycxj!.Pt}]-y=Hv5~aGD/IE\^y_@٦C`:-Ϣ!v"ժq3A/=F)8-՝CfaW| }H2]~=LJf'/59̝8'cisȫ3|sC'ΈCkwx܍H~opK1\n->~ ms{=̕W[7 /}d^)w3r-gAgr>8^s/óK>k N%/)gIkSzҔv1pӅϞD]5*( ݵFtI;YC}tM}8ۘl`%^GW[?EB w:o& WZwIo} Tc>_5Ģy= Ƀi7K}P|}X=)`{ٶmۋt^ϲBr 8"}kw}5( 9݌%|iT$;EhWX/;{t!;gwMw@;;ڏץ,|<ԃpGgE~(BUn½v9Kqo@ 7E׉b}OBكw=`J=^$<&V~ypv 㙧C]n, 6eGI̿RPDa߉qt?m}fL/E>KYuj|Lh%Oqn;Nx\N4Tr<,.w)lA }|ˀvGE4~r~e\TPʽy+?]K[ K{~pN=O=-. c8v|I'{#@pǞ<Ƕ})u}a3 M-ykY'dѕ8+\蚽6o5ϸµ +k#t:JgmW^A>0τ^ZZF6W9Z-Ly-Z%`rx&go X85vo,Bp:?~yp'|GEff=5^mu YH뱧)*]#k!#fO7/ƙuǐ$^C΀ҁxk=sW6o>Kۦ6k_%{=-½ow2t'aGդ%]X EBWq)ᄮcS]+~>Ƕ.ʽtx5aC95'-9^'t4h|}SM4ێf:mG񧱿ZX#?U3qڟq~o;Y$Qvڑ|wTڡqBV_]dt{=Ճm Qڿ}kᘟȣg˓lR^."yA/z<%KϮzm?>e<|\i>!N{ ˽r엟].!]<,4쏒Ʃl\:"rCƩ_s8tK{5NMEҟF/豒l\6W=FcLy-ccB/n^4`GM'ۇEG^>twy5_Hk3 4?ďg}Yaɦٟ &*/16č@\>w9D>n7^]osi3swY缗l}uVbx^_o1M ,\ `轰CݛVXweߏlwex52{j{ևq,7=l.N=N@wQ.z Y(\\ ]3iK}}[yw0?̳w%te ]Ic0X]G" R<+o5N~m3]<+?Вׇk<.'*D~o״H&+܃`H+v{Ƒ8ԃ㎕nG*GV~!gIșƍ8n <~S@,]|g'\#OO}S][5oN?)o~W[3<~פ~oFC5w/c=|~`tlH@5"nĵ!u[|; ;;pO%xϕߧ]Ebp߁ˡCe1xu7G_ sIO=xy@iqL{I˲7- yO[B>>h0ABG+| y4ċ{}|W`ߌQ;`n~p!x ^r0-x\ '0Sk|'%k%fнZonF>s{ks<)篶iwO60Eȓ!78VwaV7/hSmh śFWb ) w:dpu_4.dN}8'dj#$ܿ1NNY/h)ӑ&bڨu4VCh{7\ù~7{KX8]aH|c#O ˽< Z_ؿgDCC9A~߾=d@g߾58.?2.jxfPWK2%ypG`KD&w*]ḧ@1 {' {;^+v,1@w T w/N{6 7Ew-g6N+~xMt^dRM4|ge7n*w }atnB[8-N˝NCN NK++?/=? )Nĸat\ pܯ,km_U:N!NE `V~\p'9_>g)2N景q k|UIq@pOlS?!$+{ 9@aO>0  f3uޅ!H+)SU]+jnߖx/";ezZXkFhJZդ:{c[YbыB/ʔa/D[׋l{12>ً \p\WZr~(ɮ"GRؕWۮd,SeW9_%zSnqzʏ݁< w}Qd"j}hG{h0#²ẒF¦p\s6I(Ms!K7'CپÇEd( y;Oܟw=}-ut >2ƄVyXW+?w׋8m󣐡o*RcJ~`T8$O +?].pSd-.j"Mm>%پ2RDma<+H "y|e ^IK]$6ۧo5ަ z~m2<>5o)Ķ>u?uSMW }j2Ig{fCIiLjoK|^{5c=OmN _3yM9cm`~< 1_2տ"{w20ˀYaLodzM N6}o]C] % "5NM ̊=q-x<[dZ}#;~7_ y*T59IK Ӱ(g#^!nE zdHȺq/yysot?q[vZ|B+ց?#wR3һڵ .܇d1=yy3C- 5m/e1qwΙ.r ;ϞIT3Xo i|JyK)?Pvq=umd=θ d؇L@`9b[( zZ8f0ˇy\Pδp7s _#1#trI|짅CӋ:=׮/Z;fQi1 ϠARw I07csGz;rǮK;zŝDϯ a)L%xi؛!(4JO!<B'ѕ<'i;qW(D懿 J~sr5BY8_.<}4-.b>y7rq,)̇9#Ïy$9l䌲I~RߤSeN0MΨ^^D薽襗[mFc~yЋl+u9>NC=w*_^?+g鯮c< UwqÚNcs^(ϲ-_`{XKo}7SGu)$tU?c?{.wIVGic;D.(Wivgyr1>hWC c/j7ȶ+'L6]cWr{er-.RLF@QP,v}q)N+1Ѵp;1[)9pȣ5NRvfWRNEON^ 'ֳ q< ?~ Q/Kں,(I;|->2>֏thx8L:Y[ ˼1'K@/@pBWwZY"}:k7Z}Z{j۽ztݘ/8AWgÿ3'tBS;tk h:s繹nfkzL:E"}2˔h(YK-zt:_3 rQ<̌8m(B+S&HG7:y/s_ҽ eӧE9G x3'00Gf!ԀY'٫G\>Xa~܎4!%,< Rtݨo?:p@5n-!\':~ }f>qg{}z2+ V#XƎd_x1Di"ZMz MPNH`k(l;B~ 0` L'}{LR.:2/3/}-z<ցrIq/Yv oQڡ}^LOx;OAۜ[A-GVgKw8Q["۾_Yx%ܿ磷m3^H2D7~ =/_'|=NVE qϷvqn+>X'K*{ċ_97x>]0_x!xe~r3=H^Izt0Z<!*>bcw;t95!cP;k4N赯>g|}+iF`'=tVX׷R{.y>\] xjȬpц 5`Qw3f{ pzkx|xܴY#ϒ|C&\pȢVw#]xv;ܳblI[;rCO76U,'O422dr82 @'?q^/&٬*/o79y SHTxfe{yx6Nf~Gɺ~b|ƺ-ҁg|_Sgٔ-/""+"[ZY{+\|[/?"3֛^®5bXW_]t:#oj|փyzV=ПԕaUWb=jW#Swզ<);=yޓ~ix:]X6C?w"p$A :gĉ,ňk@?skx/"+#Rre}UO{lKyߌg ]؆8@نSglXl {p:Q +vUKPV~:P@혩} O{ :@P w88ͱ7{dfUՔfU\srSx' x.$x|8KwȒt'לvS/˶x{{t^{{oiePz,",>K ='gND4jz6H5 .2]{Y:[O^C.?0QHO㴯~V~Пu|;u&~΢>,B<5 <6mg:-ϢR ʚɼ@ {{MQٜ[}k&k|ԑ9_gm%wC̕d%(܈ãor3ށ8egcǹU>&]\*X,ܓcj[Bߵ[}R7=d3x@m8+ǹڕ}6}rLvӍE]盩]с H,M/m/0-?=/,F%+^ؕy`^϶]i+.P}]iuڞBQ(C$m u)\ڞ#I~i{^nµŽL!vkkGƝC+O n0,n/9 { ; }ST{wz6v7OLQhᦨrƐrHå!85^/#:'sEEy(/Nxtz}ƋFS}D|ypZ~;݃]ۥ #'Y8lrLt&xp~i{|=FKCpnGHCpi{|N痶LJt/mq}Ţ>p3dž[W˫<`^l<~5Y~pk(ɧߣH+2}S"ʗao!Wn..m/8-g۠4"|G-z[Nuor-~ LJyZoMS!>h*x-YzXE%`N\>RZ`kdC~xKäPcm]K SL_j@PTY=}}q5洠qӉTțRE2 V(oʻЛuTXs 6W9-d,ll}8UHOn_gR ע_Ӭpk6np %z!]c{Oy`8$qIyut rjrV4#4ym%cqkCmYr}S$|d|bUc]|OɇI>;=?gÞ/93+1xf5FĖ7?yh?gQ>3G0ٚs&m]RjnY:aAY~ٱ%SaIt>8@HɉBL..'VH+ CA]%W!27MqV\iXS'Y~.)RiV:27r.A7͒uH䵠~ O>}[id R{?ŴK e#eQ^K tolkV2)҄3u/BesŖ;o3#=5έz]>{+8wC _u@E&"+8{Ryw|qAmmAgϯ/]쎵Kɭ竘΢2vn`z=0f qQ_dNRUȼ7ߛۡ.?KYCn=ycy^ta.kК32J<ʕ<,FӵxSH)űl@u\^%V0f 0e@ׇL>2%Mk9vM? W2sN=+)yC}띸9$q{q2=?K.@"b|xn[EYs)mO@Fg\,Un 1AI:f"2X /]B^oؠ=j=]g2Ly O;{}b邝gՎqS=;Ԑfh76>K۾V==ֽYKSlV{uo:G6ڮ:jl4 ccӲB-ՊPO;-9v+([M2Pܙ9k*l{}`]k|et-z&q݇57.6xŸjHZoiIFN<==Wo~+o.ӥYrkR3ukH1.Wpd+KCA H{dҜ;֧ї7++osC2/V[xU6Se9+(k|]B,nrVk)٣>?DWQGvtEVnGMjmnra.Qq׍nK8|,TV01OFPvďup9b-׻l- 9wG+dXJA_B$r>oCY>J;Yo( g g9MK9wqY9h*%g"wMO|WfOˡeRQnU sF/VgY<{~oǞ}E\qq1'IxKZͷ;⺴ڗdIN֏o3/?Ip<|_۰w wn v)il7xd][dll2z`/遤Hz 遤',d!I$=@=/DY?Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:13   NH  ;  (16 2ڝ /  1 {إx E; $L`Ww&H h@2 e!<&\ |$LTUn**|>+ꮺeq}XDe/!!ppۧsLk3:]]UԩsU(.#:&nIHh vo17f"[}}|}c(4o ѹхQ0?(߮;r$L$6J\eѧ';s_ל7;:фhw®q{yjKBJ%5U˜2#eڭgFP[Vԑ\+OkD瓨zLy9q_ͳԆڶ=v옽?0kYM?dgيF?yQ7nǴ w-h`Ңn{Q?u,۪<'V9:.]UVeq:aD8/%\%E{]<m?~qq* ^?VǑ?$+ y I_w>6.y)=O6">^6΋>N87:%#)al^&l ȦhleLlre󮶺lĹH6lx|;e pdSgɦ!TlMh߉2%ӗ'RF8+_ҷO@ KCc_O"Vg ]rPr-]h~%hzMVux]P[n$gMz˨\xB |*#`=cƻVwDg2S$K\73~{lΙ?.LTE0h+rG-zAˤ ~#wӳ}=/s5Bۙ(u{=W#z1O{N]#͊NFrP3Ӆg= G<Ή{Ocy-XFuHgݗNʹ D'9Klq-NtC>_WS( _e UeWʿ{kt&j{lzhVI1y]OPETWkAv?y8|}U]LxMƣi<6An/zNud;tt$SŎBTO2tX vV@EPy?G]jz1S'z]$;(*~)Cw&h-!c遐~]ϵCzTPN~t}5C遐~?<"{3t -7F㵛zj k3t4)jɊ&l ^h8MW.-՞ʹq+G?4p +W5IZ/P:#q 7P9.2gEZɻ+z4EOEZs|DԧAH}RWoFT8>=@})uwn)r?ۃ2zU0QIrz0d%飧,69CP/5aR$Wdӌ>L^Jɦi5ivDt6z ydž _%3ŐXcY oUo|zy8J#9Bkk2T曞$_L|rhB_ћV(Hk2nmz bJ 1BIL-;B6ȰR^ zbW޷ئ鞤eg[7~0fnϝw`O3/f1x+ntGN8#]7bBtRP:=}N+`Gdyl,niG+Mw;qjot`\ߎOz,D̩!ioL1)TJ95Dw8yd켊$i֐0ES10&U%&y&k!~y bQ"z{hbKN씔_61ǗÐ}y~6C5fOB`L#8l~x=Mel A0dG(Ѻ22*= C6\lܞzt%ƻkr)ƍB8 % 7Vvih/*O;!!uGUo=B y Ai+ka>>߮NmyO%0$#K7HS& i *W۫ p#}uEhn/Wu}3pVݫ3&{]>[BtKȶx6(pV׽Ưd|Mk|ftk+)_3t팯[*u<,Z7U5;#<_3t-0pb`\/90oo&xNel/ d?L-^1:a>DɉD@N*ZO?;<90=!q\?#FO UiW w%ϖOO[@zwCӔ'?==6u_|.NhyӉ^?Tmݕ[ ivPaOo@V{9\6I8ۦpyAW|/hfy#AtwU&ЦS }HY%R+H%7(,-sa"1<K8;O L-t4_Ozhves82~":=Ņx???o VEؔ QDz|t@rr&) yFVo݇!:ʓW=Dmːk92n&"y}߮koEiGcBI_5|*@#}XߔH Ř ߲_modTlEol69$:Rmߏ4n!#p  yG{GgKslS~' {|Fpfʮd|&OO{9IU7VAUglG1 %_=[U6۳U"[dFK?^-hj+(K%:'jb31| Qc<=#I#O^_]yt1'I[OiDA-]+k@kЭ:nXβY+('ArfqJ畝OW\AY)4+GgDo[gϷruVn}#_F4_*[vܪ1uL_UDz3Bhx/@<aWE{gQΫ SDZ\'Oߡx9z&h7O@6xtٯ{,㇧NYz_tV3ʙ̵eV⪿JaK3P8D7ÓIM 1xUcp-=_u6S=TOu(%2-^{~K7ytvޚɣ< G}%LJ#ol&N"mfRvSvr{Cc9hjE{Z^aO;wd=]].|ӣ[uh.vSGT}V7L36K$V"_Furwǵ;w(gOgoYsq)z~1%VZب_\jɚ⡺wCg܏kKmCiw1|G 7q{.]us!_\R|,a<7^xŏFP:Q<p(^o+˟QhY|5r.:Vm:ΰ}JZt޿U*Cg-GV}mQh. m!'1ԅ`U+i)sJEgCF5?l&ި(ݰ o7;Lِo:gϢXo(r=Ӈٸ_{Utp<_uym)Ӆ/INt鿥 !{=h!FtB:wĉoMe O,0iDƈ6ψ{k ]^yK]yo*Ӹɦ !L1.}L6_>-:=k/O_##=s5^]C6Ŏv3;"7]>|WŇ]ɂWdoEg|UV!uOX;I47UUxWŇ*_{=_n{)_3t=99"1mF뼑֣e~Q4t~VƲm_8@FwͩqhUV_{YJ$cYO'5?1J_(R V*xp4a_yy߆6Bl0t&;쬖s-\+ΞoL|Q?Km󧾙RKOWnzf@QE11_a^ʯo/oDŽT4keByQs̋d+~o`?M+ƯS~%K wMwtjoס'cu7d?5ckVM*{_q/]{;!{t!{Ld %C鸜ĺ=pu<n\E׾Y]fiHeک[ʳ<ګyqqr-ĝ(7ǯ|e !^ى洆 Ͱ6j'"}" G' y:D7ݕ-L/JQ?~|si$߱rZ_ ;!j䢈tFsꋲ}SNpetTlmٸ+g˗~X-!M+#v'WPy:.'M>#ٗ$af_9??8UǕ/ĵXk7ֵO۞cu$q(]LP}_tFյ,hqV|lK7m,C>zRRwV^_vCE`C> 𑛉7##p+Z#6,!y*s!:K4dWdL^JW :kbHm/S@ۊ ?l 7BE%ZODe}>VPXYp6gCـod `A!~y#|y!DߏS]rR/~?ZN ཭Gt'OCs}>8@7<\P`vٯٸ"_a*C𫜳+ ZA_A>7&Ͽ mqK7[j,ſ\ m?~_l-L~$>96 Gmw#6ί=-mot^-%d;g\m7}3e¶k-n|Qo\\g܊x[>cl+CXpfbi.־Q/$QsZp5 v@kѢ-j{09ݖf+5+(MdY65uW;8%`UNwPY:8 1}zsug#l͞٤vԹv-;Nʵ/=u|K]5K|Z}$ڵ\:|Wյ7zцڲfA6gyy /5Þh&4{b- 퓞=s΃?Ë茗x[L^jLW11E|y pE۬<\Ηw+.DLBVkk`ɷj3` =~S~̷!:~\d7]d*o!^!:=8+xlPy°_?SlJvVͺ=_^^~ح>y8S_Z WvƔȱ^7H9+CFAEt]Pq#}X5,z⑼o\]2DLo&';ʃ?Mr7 _3K;3y|˷CLC+cƎ:!Zz߅45 ,ÓIΣO<}>QQ}Mۥ[Z30ltޕ<[A?7* 83zfFTkh<6+}瑦~_g]A8~ fڮۓ^hqw: *¥IgaWdTʔ*S~i { ^z1ϥ*Sj⺶< Q\r(h Yt:+_ע(hΦЦ/{7K7f~%!\. :乿MFx۟cԊ04oAR"/,/f&\xRo$_SaRy8j#~P,d0t980I(s_.W}u{1)љhg+-}\ ǃ8ui%C-ut/#'!:e;D_͙~:M(.$Ou-}6؇; 씯}gjo5T='{j.ݒ`@61NJxAc̨ 5s؊L3$N^C񯛮~CM_ǿn Ŀ|79bG2pYmP\0 W1lFm0=tQhr|_ugJ}WG@uK7fiEit472i6hyXM3`4ը^Bzi-ﱇ.m&40,ʮK hE6]kV:I:+.'QcgX8ƧztM#qV=Ц{Zg{G C}EU^4}Ц;BeB+(w]W("d2+Ջ 3_ć4_c̑ u< )!:WBt^NNbN f~ w DEOo.no.I? ]'r)"Np 9xUW<=j kWO_ 'Ӽi-Nkbobљ[ʛS@{3ލ'~9[; 訠 CCշ[Btb!:/Z ~&;<ŀly<㣉'<+Oxqiֿ+zHο+z /JT&9 帠++*Nk-}ѳG};*4ٲq&=O|J92 wJͅK*~!K3 tMWyݤ1=qɻ7׳avވ\G:̗bE ' ݙ?.L՜)yZ6΃I~#wӳ}=ɾ2_#ZFHAC&XdH?%"af򨛎bw1ЋE/1)ƐXd!u,Z'9-dbPy|}Ovht;܋y<  ƴ0:͍;8tΡ3j\kTAE|myVzNF:/.:C1{0PXɉt&'y:9iy,m =&872/f,:TǪ&yjyވ2XMu U~ !:_ !:_<,Pa'd?4ML5Z-;|$Rc_gS9z,Pybd߲/5lLкF5շwƏBq'y-沈|OzbWcO6w×7_.&;c_{Ayz Py:&HڨwR׀ տ}~fbB.H$O_׏Bt:~=Rkw^x/5`).|N4JS_A6Nq{h$2V۵ThN, ~SyJ=V?=_;frqKY/ϜupCK7nҎ%|NgM{HN~AwkksLMszl4q^S.dz-:sH;%={cX_kq܌{S7~Q,8t_aL抻;j~|? mRvTO>\//?57 _,g=t`GN1chg"۷?,vXnϳ*laF*Wv14&m,f KW/[z+`Baʌ1K~|խI'߳:q!I6'":tl. .M̠^o'k~lrճqg"TVOs̙GI%x'7Kv>j_d>+%/nR'q/rV~K7fB>ɣ-:{IV?7䓌mOu mpSo!Rz.=̿!:< -ut”CtV?8!C3])C  6~icʯDL<!:JVJrE|ӦT7UK /oڤ|e Kbߨ$+Zaom|bjTbbK6n:@|"{H:ʐ-Y;My^?TE$"aB⟏ZHp2[@hCt‘npyg;a mv;jq5D[BtK]yas_!: s?B}u ѝIUٕrNxLEcufU3/!!Oq;/Eoӵj8ve{]н=Et&/sH^G&Cj?$^gG{;}?^H*=kEeOk_+Eǿ~$O6=Ѹ!D-LMDoUTIhSϊwF|?3Ǘ_57gծ+3y4K}/} 3ծaו5?57D|"`a" a,&]D\96f/aDs^J7Vѽg۽k;Ò:Ӣx=] +ݒL2MeӽLur4˜'Fk' 9K&q?tɘ0䏿Bؑ~EwCV3le $tEVS ?w$nTG.js3|d|e#wƯ9\0}^6okEv$LvCұ*}vD6nc[|/}klwcldP_Y2d{&K0!pټzylW~*238keq6o;4k׵붏_iJ6ƶek[Mk)蔮d+Okl҃Y7mõOpW}C}gG>V3= CjlRա~|2|l:Ԡ a9ymcڔ;he/ky(]76Ͱ>Ҩskr ίe~n:|^BJ8bf xYyŚ1kߠQsB?T/6sQLGhnLBI]?;{Bt]\a\ǜ+:::<zݴ3hLtkg3 ~ Ek&'8,ZUHgrұ^՚RQ_V/]GNxhw;&oɄ*g9=_UvIrEkENoׇ֊ej^Ysvv|;AFG_ʯ3S}8_S|-LoC6BIΚWq*j `\0ˮqm]f]Òa)_`B6n:E"hi3@ ?Y2i~=H%C鸆Zt'>cѪU: 2bEoNԿW1@7(`;)S|*y$.x"A|7_˗VʠV|⢵2tOq9 }/g?YΖnױ"==Zbג#W {Z7|m>\6w>jhdfrG@#?9hE~nc\A#!:?`z!'!:_I;[I;t!:ߎnsl<*C%eϹ| 2.]7Rj*e$i/!T2+i.D{:D˻ nn+Gl0zBtho:~212D{? ʤзyCtPMK?w!D{2;(C[ZDgrW0U5C*;?if>`H5ٰ2[dW<#Α12[F=D^l~WoG薬ܝxf: CS}WP)9ѩʓx>ObD8pŖqN^ߕCn]jvǓw_5F+7UU8e#Lz'Jp8 'M]d;r1x :gkly|?`$qalWsz4ט1q8m$pᚹQNYG-e{zܹ+f{i'2t/ !:_~^WkytLd>0:w3^Ct_NgF=P}UgB?tuk=2:?'WF7ѭH+Qb|"Cdly&&7T{ObB-Q!:ޟEDžݎUq~)7ǹN1&/oA?"_/·߷ѣ!:Ϗ'[:'c^ᱦ4״3 z$O3 P#t݃,Ncr%7[Ge)C,Wmelg钊q+9>鷌G^G ̷z )OwHcn)orҟ3yebU>eyR< >5B'Lt_ME5Snu2]׻ ;yO宀":OƯjބH+?WY}gIUH/e G+Kv2u?C+t ~!j)[7{T@WdC4_m {gů48^#{ԯ~7{ ѝʛW@7*DߠnB!:u Ctg:-iC<_#`XN|qqf-7_=ctO(^Hq<{Jsej,g"oP":<KrE:VIQ_Vmnm$8xhvuA:$WVে~n%VDg|UV3]oe+F?k;o|Ϸ⏤bLJ7xy/C׋eI.~\S|m$~2~uvW`~E6nG"Homf|QW)S$CMwt,, 44       ) x ( I i ) x ( I _ i i i i i O ) e ) x ( , e ) x ( x ) x ( ( E 1    . Èç ñèììåòðè÷íîñòè è òðàíçèòèâíîñòè ñëåäóåò       ) x ( I _ i i i i ) x ( I i i O . e ) x ( , e ) x ( y ) x ( ( E 1     ñèëó îäíîçíà÷íîñòè 1 1   n i i )} x ( {  è ) x ( I ìîæíî óòâåðæäàòü, ÷òî _________ i i n , i ), y ( ) x ( 1 0      è ). y ( I ) x ( I  Ýòè ðàññóæäåíèÿ ìîãóò áûòü ïðîâåäåíû è â îáðàòíîì ïîðÿäêå, ïðè÷åì íà ïîñëåäíåì øàãå ñëåäóåò âîñïîëüçîâàòüñÿ âòîðîé ÷àñòüþ óòâåðæäåíèÿ 1. Ïîñêîëüêó 1 0   n i i )} x ( {  îäíîçíà÷íî ñâÿçàíû ïðè ïîìîùè ìíîæåñòâà ) x ( I ñ , )} x ( { n i i 1 1    òî 1  ) y , x ( E òîãäà è òîëüêî òîãäà, êîãäà . n , i ), y ( ) x ( _________ i i 1 1      Ïîêàæåì òåïåðü, ÷òî äëÿ ëþáûõ 1 0        , , è V y , x  èìååò ìåñòî ðàâåí- ñòâî 1 1      n ,. ,.., i ), y ( ) x ( ) y x ( i i i      . (4) Äåéñòâèòåëüíî, òàê êàê     1 1 n i i i e ) x ( Ax  (ýòî âûòåêàåò èç ñîîòíîøåíèé ìåæäó ) x ( i  è ) x ( i  ), òî èç óòâåðæäåíèÿ 2 èìååì         1 1 n i i i i . e )] y ( ) x ( [ Ay Ax ) y x ( A       Ñ äðóãîé ñòîðîíû,       1 1 n i i i . e ) y x ( ) y x ( A       ñèëó åäèíñòâåííîñòè ðàçëîæåíèÿ ïî ëèíåéíî-íåçàâèñèìîé ñèñòåìå 1 1 ,...,  n e e âåêòîðà ) y x ( A    ïîëó÷èì (4). Òåïåðü ðàññìîòðèì ôóíêöèîíàëû . n , k ), o ( ) x ( ) x ( g _________ i i i 1 1       Òàê êàê îò ) x ( i  îíè îòëè÷àþòñÿ òîëüêî ñäâèãîì, òî Å(õ, ó) = 1 òîãäà è òîëüêî òîãäà, êîãäà . n , i ), y ( g ) x ( g _________ i i 1 1    Äîêàæåì èõ ëèíåéíîñòü. Äåéñòâèòåëüíî,          ) x ( ) ( ) ) ( x ( ) ( ) x ( ) x ( g i i i i i i          0 0 1 0 0 0 0 1 ), x ( g )) ( ) x ( ( ) ( ) ( ) ( i i i i i                         )] ( ] / ) y x [( [ ] / ) y x [( g ] / ) y x ( )[ x ( g ) y x ( g i i i i i 0 2 2 2 2 2 2            )] ( ) y ( [ )] ( ) x ( [ )] ( / )) y ( ) x ( [( i i i i i i i 0 0 0 2 2        . n , i ), y ( g ) x ( g _________ i i 1 1     +Ax tU}a2c2 "5kTA8TJqbB2eQS1U!` b0Tvurjwsy!ck=9.&"DF -D=xV]yԴhjE }ÔuՁ l3ߠ]ZSo"+j+]A;=Fmn#RbG=Vv죾@dz zKMv9vo'smmi3}R.K_{I;5drB:!M9Q"/5ŽV z;փ-ci;ux3}/i/ %v.ǧ/x9 Lfi'nRI;REzI??:Wm"u%׈roK%&Rb0K犒'h)Vob8|>O`3CHsDCVyOw6u}[A2nFfU}YǛZ0U6Џפo߫"I;(ss8F0v>AF+$CޔR,+Sv,|ߣ~|Q2~1e-upy's,y9!Qp'iOC8k_IY+2ZY^,/o/ Se[u,i^3׭u; ?C&#;˷{b-ԗH9p+J'DTM$ƿܷg2ߟ`[y}'OƿO^ƑK/%E #.Mk)REMi}voYԸW٣LQt݃fdg (*vԇrƎwgͯnCOOqt1h=C#f~*o;J1N\&0;s߇OM"l?&VfUpvu2j݉Y;={OW"?!ZwRfi*\px LL[ pf/R"3J+]rY[eF9y:i+: u:]5>绞]o").\1{1cћX>*ʻi<|*S}#=HR`Q<;p&VϏ a;bi~я4d'{:r%]P<ގPb0))f)sE;e s]\ ;fx"w.ʞYH28Ч,dߘ=*ŽU{1wzۛ}i0]ݗpAP!` ew 6?9m NJ 'Q4vLi %Яĵuۜ3$^9۵Wz뮯o):Eڝҝs@9V78=&#xz4r IAG#HVUr85Cb桟9rXǏA8 I|Iv-Q js4[ ?NsqL(HG3SpܛGؿ?zh^0 +i_pt<935)txm!g0@ss跉> p x~Rg/m0|бg6k;]m]65;{Y朴wwN^"h+~(WMDuOW?.X9ʫ󬣓e-쳆sYo6H,&>Fu!.tϯr3IY%ls.xrz.=8Wzp_u岟 7kXX ka79ݷ|d&Ygڴfz}:irgXDo Ѽ!C/G&"s_T[wX* Gԏ:ښY8C4F^{3yrmEq[Ļg1眶?Ѧ.G i-3mN[%{ÙW*Ϻk V`9~Gqi}O V>Un83^;2Nk a/vd_"k9n[܃CkkOynf*mק5?~>g;+k>̥{훼H}7[r8vc̹+ͻ,7s*~|9z˛/Nݛ+ӹ5WolxucuN㛹|cm| Sx{7s{f @0a |%î3fPMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:14   ̞  ,@  (16 2 /  1 {lx E߉D"$NP>$ ŀJ7EyѨ,d^܋+ 5W~ U]7*(qBp}_y NUWSuΩS$T)Ir+')yM?%Iv(IǽeI2%)W6҄iI'ɭW=<%9 w&% s?rԵs:hM(a/jYS>]),k@1u3GnfF?*/v>w>*{ Ʌ}:Y/H^KU svP> ( U}OQS^~c]{ޙ@66s\cstll%ll&Sߞփz±ycjݎ>al36cc|V4pdcZP݂ݐܙJܣi,1tW?[yĝ#2 Nx a`vg){^Z#po9_/ҋ<_^Ȁ ȹ~u_*wI~dL~;(i$?NֈcLV}S >74 ɡo~B Sfco60O~OFwhvGC=C4¦j5j/R>NG&Bnm& <?V顤QQo (>Rttg-m z/RiL-/ vy-:h#yteICe%LFrw_7ߴ?yW[F嶺kpo>i];: ,d#V@O*-{/{?wW|grڵ SOf=p=, ,&-QZۯ+ u.V/RИ&(*9di ~ip Gm@pSX2+Wp/*[] bq? J6i܇/7'Ұyi:5t/<%^%st3Oi='zlyCkzo yp>t|=kzQfw9䇯#.N7zq'QEmmG/w)~^I^[^ѫ85dÊR/3tDA9}C)g}zD19@f6/*:Н.P+N;q!>%6Q7&J;W3~/ Zŧ}|S6lZWVЯWN~/ӯ;~5ZЯEZ 2Z'_eWYx_XjPS\}ٶմP:E07_.{Bau xC;!6)yzXrgYae}ZӮCwu!_-׉O\*ñbY #6M\.Sԏ\\JyKRnsk;^C;Roz9;#;|}pPO LE~vҘيK3gVT^VރWbܡN91Q"LYn~!l7:qニi 8(c<NbYR? o i ż#\Qֱ`*ձvd$ӱCǚL6PƧ~5qh:no\#p+SӱUX^EdXϸnۺEc]ߋEP">:W1ΜFS4ítuʣty[]}3lA}aDgg{5ߠ'poLaHi#A<_{):9ao)c4WN6gGЄz'7a}{,/|;Qt_Ӓj]_PˆV Qf{J2V_7]V%x?K7 |w8 i]nvQf@| +7 c?9 4}0NCVިc#NYwc[f;4vm<=Y{涻XmsQwr{%Jk[gC?KGvFJmg}<(ۛmժc]0m^_Avs_y)?%R}g37ԟSt D+x$ztP6:m#r~s?| i+2~:bp˃.i ?=X*zip'T 9 [^cȸTo .)~Dd<(Ps%cOWe.6_CÊ}o7Uӕvi#~/t\8+6]Erǖ/ݸoRf>V%WDVW7}^v5S[v/|8;ᧄY6nTGdݣjz.ͯB/m5u~sYE/ .8;gTMWڥy8R.56b|sO>dFc!Q>WM/ڥyu^EpoGy'MaE{ޟl;/Ÿe,Ӽ7TlNgQ6//ڜerԦH=>Fn)߀˵W%;j[4OT\͔sIkٓ^( X=^ݧ`{w;i\SOIWyPi!,UwLP9GpE}p;wr%:E~/?s"g)N'E9kze"jnd^Wdk7n>qеg39yzOQʠ|xӂy-=!gy]wt|^`^WDNqX5ݥ?߀˼\8vl^?-%a~iYYcNlT \>_WpsArlp"t Սk6^M+Zu Ҽ~/r'>R9_z6k!x ~W$]Z</.%pR}nhWnx8g:y_<Ɵ'=!&~^ȭTm~U{3U_f. .:Mt]'P.'Ļ'sul?.Uk4íl ,޽coX}ofxu~2샷ɱqܥr5H QO(>ޘ_^Na{74W|en:\0UWIrGK\)23nD.WNG0g& cy7#"}+BWնɺWnՠh!/׽ٙT M8n\I#rVgR>MsR_'VZ'YUJ[Iez2q9Zm3[SOƳXKCݦ55f /+_(|Ma7gWmU뢬ox~/(oo 1?]U|/X(}o1yoPOAQ: .FcgH."%619 YZ 7@x{Zh>:u2A.!;Rr4]zz׻EPrLڑQ`DxzE2+::ߕ="\(Z최guŸb69 z~3o߯s\]{ =S_xOz׼[P-5^*o+kJ9I[`]"U?dgEegimy/]}=[ q$N¾6\zmd&G};@z)=1ps9p/>)a`, =z;ѷ}O4i!)=n}J["s-a6Y{&eWоIN(1khx$ҷաoi}}P/_MlWsn1/?boԣ\c*)/7w0LG.Gew*ٹ^ڹ\ɰ$_ykzv.]ޛK}'Loo^*v^il~9 Gн5_qW4HFq6͐\xeV͛5qz,ލz4;S};o FR{+y%BsJs8lNLλKކރg}:t58?aN'̳`]ORO2mŧ,8ʓg*=C=32=sw=stzf:GWvC3tgoTxzI#xkegvZ&M|(;LJou9J^X7y\7tg|)JFV-7Nl,ص퍼*qc!-Ϲ/[U2{஺jO)tV&9lGɃIdyA2y2~Ƞh_}C118d_-lIU5f|cw<&᫭Ƥw1LB9d|)tg+_ީmj{ ߝ_ku|ke8ξ.`Vds,߫u^'rub7t fks,iUӫƉ 퓫j-`=k1Z:͗#GnN^'9$;#z4:OZځn9P7wus e;nR__sDve/{ay湟rElx'5~L˘N+rON->B޼{1^Abkb1sqk?"%p j9\ m$iE/͊tkN\5Xi6Ƴ6 65pN/!_\qk9WZ:{ۿC;sj>WiGzuכx8VhL0ogy5,G/Z ":u>Cy@ylsmfkg0/^8\&GsӋ18,Mc;P טoؾkE7lg$bXwfbpad .lߕBD yny-ͭ^Wg˨snx>\\+x<3O+SI|?Ƴ Nր&6JqMQھSTfӚbxր4;Y(')vCe" gw#5"Vߢ__eKv[vJ2~8l8g:Y? Ł9)Gϟ:[GILO0h_Cw kg}dz8j6M@NΉWU~'}UӋ3*5oXؼMz]l~a@==>qu8 /m )??Ƴn'k8gf0_%KoR &wJ'p(8aFtIzzeJ{bά]c*={6pEp[a\gy P&B?=g.\_-ރڧm 3%p t9 tx^c5oMBý ת˃F/T}9ɪG$g$&')tz两3̹Ÿ\Әs=ʴ!Jtw.{Y^'p?ϹYvFM/hyx"HpЫ"y={>WMLL W WLV|E*7fͯgNuP^wء}UN\5X7nrx6?d\9dԫJ^/xQ޴cNޭ_D:XM -cMD}Cru8(S4 +"wRI״}K5J[c{P&j^ցϕӶyq?S;c.Ú||;k6 ^v$^MWS?0"_IzKvbMy[l 'wKhf9w8n2(pʗа$ܥt0H<$r>@Ǭ!x!08Áp#y!O.c:n1'\|iMTZy—>3 ֥fFу/@.ZM ?_s7M S/qa|kxoRHp䎗N2鶋bwʟ+׼oow累v6&>˰\;Y \]=<d}>yIC/^bk7n^=ZSOgus`4bNPl;yR1Vz:Ssj\Q~ɅQ%"giadʃG[:(ם{AepIsy7M xi)?H?gSIr1^.D+:t4Տa w~-?((P4O!Kb+<ƫet@o*~SQ"|%6N/U-ͯV:ͣJZi>RUp\2py'0c_,\xUW樓(Bn?=wii׃do{⾷̘A={X{7{bLy[|蚬Zܘ-YUܭ_QfZ &4Oe7˙>e;Dfėz"'w\cJ{=QCI=q'b'+u:51_*_l ԁC~Q ʀ59٪*!_u|5$/N}  wW;N&|W{_&^ C C!ow/Kj-SfE׵nl{ZF&n*k>?Z'8Cov=CYvש9;0sIyӲI4 {ٞ$H,#fbvaoꀿ,ɃhH.߿Ifb7{dKGgO~n(<[/OCp, +FKLnem*(E`YM<;En2e ХX,VeJL~+{SfpSls4phvMeFt)-RV'Z<5Up~.'{hz݅O6q*<1֣yɷ5ֲo>Y=. ƭO= hpo|x,OEq ǧ_<(C^XeCؐ>Km}?N,wm@gq:ˤ[.Cgsӭ΂7/kLio}rMZo2<61_**^T>u {Yr<|H.,U"xxv'!efȓu딇7䛷#kl#ߨ6|OJ_4dr}+TIߥ2-{o<\գ{%*> b06ӝ8e8<0A+|Òߩzb|菬reǔD.L!: / HFoA##R0t00WX\C6֗QdLIhLϥUuݺU{D~̧hπhKȷV6%W}ꌤs_e}mz=]7FozN3K&{N9sC^I3/NJK;²{/#A:"W픃= ⽞?z%3ޛ)ϩ>>@X|grڵG{Ϸ#N'+L$I='=Pqn,?t~~$2}No}zZ1^>H:TtK5э/+3nkE}\JlȆf9Pz':)>(PO%=lπϐ)̟ oʑtg+m\L}iM/Q'"~K Ѓ~/Nd>v4 sth_>?rssX74&^m?C>;:i\s襬Msz5fz)azAVsJE*ZGLof2|y9_9:"ہ+u =Ƴn;taUٳcn_^t^|J&3z6ʢCzsx>==9 w-mv?/?}^r.n(\T4qR>̫^=u?.^G䘃ԜԸ/~t Xr 7yg4Nc-FՈ_p+pn Gy$=oi[}1X33mE'v-mRh8fܙVF9?eNqҵ =yp |6kza_6]?g81{Pw&0h'2~j[{'{XwFONnC^PS C2{/S9BK=I*ZOw(mCIۋF;y$c?K+\O &7w1PO IO.aHdzQr]ZpN+'w(ϾPw !\S8_*'#ŸM;dʧde1y9Q𱤡zM|d+a296|In7!vZn:r շH.fs]yRQsz(>䱯}0I?*rQWreu:׳eֈsm?h_5,‹kXƗZ~U]?C/rӴc;,Ḃ̗qa]ƇV>uٷZ{Crᕭ6o>[N/>4e4ȑGuer`k8C\ (NZUyHTrЙӽV[Er1[ޱiCW>VT(^_APF4gԸز`>DŮjױVC4kߜ5XK)"MNŖ7"T^c%s"5XY$ӏEVVMӋg9g_6L:X5X}^ҙ^iy"ޭl:"KV=--p`t0lEȨ: 'y1ք%||!x~7,O<u!8! *Zl+OKޑ>y֢!*;lOF䘃 {0e%LDbFRWk^ϴL*3^4*[;FנI+g1{'M1^}y#T=ϸTExپ!"k"xmXqPStu:"^rӬ)y*obt^C[Lۊ/^%"j'M׃Up_ Z[N<;V_ a?Q_ohV4{_&xb zLO)PzQ'xWM/ڥ+-/D^Ļw|E;~bpų}QTMWhޅ ])CZ_?c<{?%G 듇Y՜O]|빡vtpơwս BP?wOs!ͷE?NB܊ "ܕ~>T~^皿S}s9g;MonS3|^4V..U^ py׷w }'AX}\+}a{L'~PXc U~Y^X{#smtr-lfx[_藘^^Tl7}Uq _ߋoA#+{@9,+EzjzK~/\8ֈWq~Y&+oX)ӻ/MCE9]CզQ/23nO0 'z6$wX_'ٰҮ!V+XL]Դ-UxX/_z6WM/F=+\ߋνN Nw+WQnk+ & n\+{߿B#W3nJ{\L:M o\(XlIK%WD5VNZ2l};Q,½%s"gY%(sH*.7^FMz}evҜd>zϦ)S.}O0>WM/'%bN'X_寪Y`JLt̴4{Ϧ4ɅϺ.Wbv~͘F_!#=>)kے:>uJ}Vt>rrG}v|'}&ㆧ^¤׿Oa]c{ WA'suǼd;i2_" cB?tzbXNnEr+:t:ץ ;{DyUB~NCX-ouG4bpsȜTDˉ%4Nf{LеWN?T'+s2bPwǼC@;?(#_Mp{a_4܏TGNQ1!y 5e6 uMNdӂ۞yD_MyX 1'z)n+k-7gNnE9Z.vzb<)st>9YaySYv M#|9Pr|i9 #wX:|Ƀ誨 k${5~ m=dF7̾@ȹ}o1Yt648`4q”/x>]Nx48ʘR}S9 8"D 섮_tZU_֬;h~F:[8{˗"T:xv#ql!|&;cWI9Uk ɻ$&LLy3:OM?}_|S嚾_p~ׯ*H'+~oeYf%wM/{O||IS#V:oPk̘80`sf?O*&˿t^r),5O󒳕nֹ/)7ӟ}`Tʻ^6 壓)[ NM7x֭ҭ?9;6>%atcsg$oV7x2oS&/){?:f%xdM}Ҕ!dQ)ͯ_y넜gi(}F^IC}5u?a͠mEwfܬ]? ρSAٳ\;4x~WrYcCɊ(B|ʠWK4_'[7&UJkwfF9ŽɣCICu0gWDŒUu>STS;ȧ ӭK%r1]zPQa?Oz"tХCwKyrkg#~[zgu:i\f7L~ҋ5 @|cz-WR8]tmղ>WmS[*3[:4#x8VSPNcy$ /:Y 9A}K>ܬ-$:։VްxK[@efE:5"|]yBZ9 i 7Qxr!/9oW!_oG-KwmvR,b-oEN|Fp;*{?K.xtCPmi5an/[<(kUZi2ǂI&9=yer)Jb{z(vU(ί*\jkF19{ :rԁt]ԝCw!>.{oԩߗiB+e8W.ŀ|֌}n akc O@wyy<rymJ׬ɣ~dumD wIm zvD?Jw,PزtE!ӁNG 3?FTijKPg=zP\նa?TS懴| nJiev;dڤVڸ[X'7C/1*p/-Z<\_C7=i7?9vMf8e7jV,!j8p\ 3^k[>WM]KOb7pXhD*Pِc.B=B= ~]+Jeqу](KS+ى<ڻT?؏>~c{&g}9m}ެ Hs9a;IJZB}S~\>eӭo) L甯CߞL6#m>@{&?~otAw >a-fcpCܰO n8O&j}~|Cm+/}[(O9ιmnio|?]3inE#%W$G'^?F[Gex~yr^Q K^92iE/WD̞שS#{#t+GT: 'ZU Cz3ŸՉ>]U~1{ӎ>3<[퉢ޯ)s7O?N^q^.+v{;P/2ɳδ\!Ú.F 6,O<u!8%6[*XRgLnϨCC9KصX d{\]|M1^7C޳מԏ=OV9Ju`\ç{]'ԅ#l0ͰaZG.z؋nxǩ0xg*94ClgNk:F]%٭:}cLKia|>P?>c2l/!|@}/֢/|/g(5xo}'(W0ۡv\-Ucj\hkʻ_^bLF2^Mop<OKWw"k1s>Nz )zJOg +՗aPFG]::ԭ",>hV2zDhr Bozއz-4Н5uUF[&Ú|glߠ9:I7Q>IEL|ݻ ]Ti}r.20hڂ<7lt,W-*oCy~GC.pi~bۜC|]9RgzG<4^]7LW|:zӥGO:k"xǪ3p~~wͦU]ϥA=W?p΄KLD5q,̺lμ=y۞qnr`hNΏ!}%1R! OWt+Jn;$^U⏷Ϸh4fU>ǹ}Praz8̩JLVkkYwg,*{{zVSt=QüQޡs6xj,u=u&:<>Q}h181]gU46?[u hn}+)9uQ'> 50w $^0LV}I{8 ?=k),ʁ{ _9=w7DS~U{5}׹7sGό|~Ӳn\5h ~/ܠazoGb~2פKv E[i(7(P֐Pa=qm1G{C'º+ &ݨ/5$^5֖V,lkc<mE~9@ζIℱWgwe{m{sR?')<_ھ/O *84'ڃͼhO;)mY#wo`=Vz1eCƀk|鶟9L ݿSN&_|m@ޏnd'SZrM긕3kv008ԉzQe@aS=O׫_V?˿]>eӭ)=]:CWv::mj1{Dnb~?VvOމ|C2vHO01_*}oQ'hP|9U!ʴ͛FD^qdQtv{a؅xHޣw(9t@V9Ȉ-Ox3cw[q"#BtP.!ZQ}d e;OY"nzoCV2YJCٜ=3mr{a AWMt 1Qt4Zi%\cVÌs ڗj VjN+>G0C7\a]0X_+[t%άCiVF[_`i-5f|%.1[KpV#b-> unO~O/o ;Ny 'ms՜oUf2OЩO.o@.2ޱ͙oUx?VM3]^}<;z28?Z6'UJDze?jEkR&װe_ ͺ4ub9  qp0ps҈㣟t0QqvS(::-k"ȃ^Nn#u,qԬp;Ui-Vrm};pMnuFb;Bx1NUڼfmsENQSA~e=tSx d)kdKS`?)+1BkYkHJy]W딳XivG*rxK~%6n Vp>լX3btX '#GẬ vrSI[#Cw/WCżcpp܁P׽y}+(ͼXӋwZ,{ՄMFIqO׷Ac9dg \ G39J{:ؽ*n`Sqrms}|oNdFZo*t}6ho:MXYSwZ˕gtZfi-\ y |] \>|~zíEmQ/ؤ*gfOH .^;3Iə$1qkn*+<mR;{eh خ*gLSVMRi?5g`@g~GSlՂ.%ܐ/prqd^SI?U=ov \ؾsh8tqPG/c~{ÞPg \WHY5G;ot3&yt29x \8Id|DI)V_8f3=3邓Sۃg\19ie}yqU;%9q^VNU>9w+[mk,5sa볛ay' P'ױH^ǃ( \xQ߼z ]˵Il^)Ogcjgn5EҞXV*gs8or2[ u_QdtC_ -flc6=80uCspCˇmq㓱t_Jyo)eӕ+@ӸƗo.]y0Q/lߤۗJbL}gջ>:ݓi_c./Z ۾kbp Tp nLsMM"ouҜ?ט)Cf<ӫdVdthkFH:Fr _ykz6 wȲtnuY5vݮNϚy|)ByT>gVPsfaYz^,%M/{[m$3nнiubȣ ؍b[FY{Vo(ZrV]޷tZ9vݛ7 p::Mwxy Ł8y쓣.)Kr/θM~]ɛۗ a<:]Ii0<班'wm"Ɋtծ֓gױ[[ȸD/O?_4z{ {a-62값{/7S{CLQ߁bj{g|Eȹ]>x/NWR|´|_~J7Q S 䃻_Ȯޕ:rzU||/D!hR~u7ߨބ6p+d#5Wk^ kײ} w:oyPߘ[ .l߃2pn^p߳4cq~F N| 8/wc\_;NyVs_{\S \I9廞o+h_b>SiV~6;ꃳ'幌Khބ\F ~FCFnD?Cw:QnP.Y~RceެSC9ԁ3g Y'#J{҆ޕJlT7O5ܲ/=0VE*UIp\}wNsGCHJ碼O:,,45 Çàìåòèì, ÷òî âñå ýòî âûïîëíÿåòñÿ â ðàìêàõ âûïóêëîãî òåëà V. Îäíàêî, ïîñêîëüêó ) x ( i  íåïðåðûâíû, òî ) x ( g i òîæå íåïðåðûâíû. Òàêèì îáðàçîì, ñ ó÷åòîì îäíîðîäíîñòè è àääèòèâíîñòè ) x ( g i ëèíåéíû íà âûïóêëîì òåëå V, äëÿ êîòîðîãî affV = L. Ïîýòîìó ïî òåîðåìå î ïðîäîëæåíèè [1] îíè ìîãóò ëèíåéíûì îáðàçîì áûòü ïðîäîëæåíû íà âñå ïðîñòðàíñòâî . Íàì îñòàëîñü ïîêàçàòü, ÷òî ÷èñëî ôóíêöèîíàëîâ ìîæíî ñîêðàòèòü äî n. Ïîñêîëüêó , ) x ( n i i 1 1 1      òî       1 1 1 1 n i i n ). x ( ) x (   Òàêèì îáðàçîì, ìîæíî îáîéòèñü ïåðâûìè n-ôóíêöèîíàëàìè ), x ( i  à ñëåäîâàòåëüíî, è ) x ( g i . Òåïåðü çàäàäèìñÿ âîïðîñîì: ìîæíî ëè åùå óìåíüøèòü ýòî ÷èñëî? Äîïóñòèì, ) x ( 1  - ” ëèøíèé ” . Òîãäà èç ðåôëåêñèâíîñòè è n-ìåðíîñòè äëÿ âåêòîðà 1 e áóäåì èìåòü: , ) e , e ( E 1 1 1  ò.å.   ) e ( I , ) e ( O 1 1 1  0, . ) e ( ... ) e ( , ) e ( n 0 1 1 1 1 2 1 1         Ýòî îçíà÷àåò, ÷òî . n , i , ) e ( , ) e ( _________ i 1 2 0 1 1 1 1       Çíà÷èò, ) x ( 1  íå ÿâëÿåòñÿ ëèíåéíîé êîìáèíàöèåé îñòàëüíûõ. Àíàëîãè÷íîå óòâåðæäåíèå ñïðàâåäëèâî äëÿ . n , i ), x ( i 2   Òåì ñàìûì òåîðåìà 1 ïîëíîñòüþ äîêàçàíà. Òåïåðü ðàññìîòðèì ñàìûé îáùèé ñëó÷àé îãðàíè÷åíèé íà ìíîæåñòâî âõîäíûõ ñèãíàëîâ â âèäå ïðîèçâîëüíîãî ìíîæåñòâà  ñ íåïóñòîé âíóòðåííîñòüþ. Ïóñòü ïðîèçâîëüíûé ïðåäèêàò Å(õ,ó) çàäàí íà äåêàðòîâîì êâàäðàòå  ´  ïðîèçâîëüíîãî ìíîæåñòâà  , ïðèíàäëåæàùåãî íåêîòîðîìó ëèíåéíîìó íîðìèðî- âàííîìó ïðîñòðàíñòâó L. Áóäåì ñ÷èòàòü, ÷òî âíóòðåííîñòü  íå ïóñòà. Ýòî îçíà÷àåò, ÷òî íàéäåòñÿ ýëåìåíò   O x è ÷èñëî 0   , äëÿ êîòîðûõ : L x { ) ( u O x    O x ` x  }   - îêðåñòíîñòü ýëåìåíòà O x ðàäèóñà  ïðèíàäëåæèò ìíîæåñòâó     ) x ( u : O . Çàôèêñèðóåì ïðîèçâîëüíûé ýëåìåíò   x è ÷èñëî   x . Òîãäà, åñëè ðàññìîòðåòü   / x x ` x O   , òî ýëåìåíò ). x ( u ` x O   Äåéñòâè- òåëüíî, x 1   / è O x ` x    x    / . Òàêèì îáðàçîì, ïðåîáðàçîâàíèå    / x x x L O   = ` x “ çàãîíÿåò ” ïðîèçâîëüíûé ýëåìåíò ïðîñòðàíñòâà L ïðè ôèêñè- ðîâàííûõ O x è  â ) x ( u O  . Äëÿ ïàðû ýëåìåíòîâ õ,ó  L ìîæíî îäíîçíà÷íî íàéòè õ ’ ,ó ’ ) x ( u O   ïî ñëåäóþùåìó ïðàâèëó: , y L ` y , x L ` x     ãäå max{   x , y }. Òåïåðü ìû èìååì âîçìîæíîñòü îïðåäåëèòü ïðîäîëæåíèå (îäíîçíà÷íîå) ïðîèç- âîëüíîãî ïðåäèêàòà Å(õ, ó) ñ ìíîæåñòâà  íà âñå ïðîñòðàíñòâî L. Îïðåäåëåíèå 2. ) , x ( O  - ïðîäîëæåíèåì ïðåäèêàòà Å(õ, ó), çàäàííîãî íà äåêàð- òîâîì êâàäðàòå ìíîæåñòâà  ñ íåïóñòîé âíóòðåííîñòûî, áóäåì íàçûâàòü ïðåäè- êàò ) y , x )( , x ( E O ^  , îïðåäåëåííûé íà äåêàðòîâîì êâàäðàòå âñåãî ïðîñòðàíñòâà L ñëåäóþùèì ðàâåíñòâîì:        . y или , x если E(L , y x, если       ), y L , x ), y , x ( E ) y , x ( E ) , O x ( ^ (5) Óñòàíîâèì îäíî èíòåðåñóþùåå íàñ ñâîéñòâî ( ) , x O  ïðîäîëæåíèÿ ïðåäèêàòà Å(õ, ó). Ïóñòü ïðåäèêàò Å(õ, ó) ÿâëÿåòñÿ ëèíåéíûì, ò.å. îí îïðåäåëåí íà    ðàâåíñòâîì ]) y [ F ], x [ F ( D ) y , x ( E  (6) KAx pT yY DhTZgPAyXu_TGZBQZѪ @*y"E֖d\71c3s>sXD$-$i,׍ȯwaqΛ>3 tJ_pu-V6 MkZUzU2dO$("Ri#"2D[CodKN0p36uw~/Bs@ PD H_pp`$9W&:G7g7znvSؼO/s3Yy>ܞ@.kQ\m q32s"o1ځG$` B^*_}TsٯW?s@򢹸@'xsH BLd o_)@"9,-<>dCg)AL|ӻݑT ;d +ٿE'Bw }_ٯ#/>(x\/dwc7lۉVr>s xlgJ)tLol!>Ʀyr 8?ʣ.yUw{=E0s=oʰg0z_;4jC9$l4{B{ 9^vh6rz4\ItA:!mTsH:q˒rߜ;V'_!^Bدؐ%x"R@{3"eR_.tv'Ynu-̹ΒϹ@-o8}>gQ ;oSww*Xs YQ\y%]3h;yғ8_OiE[ߑn>w<| {Y#mcO[29%L߈RU/xu%[#=6 {Oy*+)HWN?\+ ɯW"rud rֳн V>n;]klЫylk?΁|X,Ã7 w`Ҫ :ߎFt7t)ċ9V>JF``k/-zED6.r[wS`cLy47)yA($odi'[<{ago'{۩k:S~,*ٓ+ϴj +A*6Ana\A߳Pdb+Cz3f;tlMBWQ/1oUT_< \2Ǹ'PRϿʱo/%G],kiYoN/`$5PBG`KA[ `*̩hb5&k kiT}q|h`:ǨR>>_ñ|v|'8>0ke9hccm=+KsNa ؚ֢9,~7ב|9bsHgrTCaگcf4H&#{P}-+=}C1^.&"ߌ}x;:Kp 7+duEV7!^OBsIA-0=F7wOc&(W4) e|x9:z6˸'-D5kXΪOV65l^lzM^H6$9ːgH*2? ^b+_.T,!orR o_EX{%b&]$OEv$CEf"Pj+:`6ދ]&r>/G1M 5[ӗ--PX[rw!nK>/ !jm^^-[9[rc$fYH=9~id,sx~J<$<*)j|^x`z > MwhJ-c9oXFPb[0\N 7dd2(7}t?62V-^LYzz=ރg o[l:"+o\ >Kƞ:])8Yc zWUv\JmK6RvF=@-$so#7-9^Ew8/ǮŎ_sDZQϴ_n }{  s5ibYsqSKA{?42FDKۙޢy5:cr]ߪs4+n~Ky{f9P _pcw{VbWIr'<^zԳ?dd^r^rNpVn瘪=JΟ5E-JV':Wѩq]u .0)LQRQ(訐-Y+S1Y(bXԭzNTȒ,R&q)c|a)$T{LL&m{^$?E%/gؤCN:;޵y:'%|N@G~ىP|Ymyru\НֶN= Vw'uږCD^Tm׶oHfU_םiYLt{Ҩ6GiżCGCtJ&3u>}{yeSm(c嘧̣ӹ|7¾Jd\w*xW\ZuoG2wQH}s^ĵ\uoܕ:ٚo :{]dNX =ҞΗZH _#3_eHu[_v܄뫒CϼdsJY>sg~C4C=ǿ1dU۸qz4ضu4bBDZܚ\<7aA/眵s%gTśjS(R>dfz< :4cΨ=y0ljW< >\gIß9w]!,]<9uvno?W5Bߞ f\/OߋwY-l<})-E@e$ P%)5c4$bs&SքY~[BU*['mY-%9tin͸dL'huC/:*֤벚.wn '/:;S98^8N{52exV3 /QxQ\,D\|Dp5ʭ$HHV6KyX@x:g[%Q8G4]NHWj;Zu+nn1t# |V Λg^נ.Pgn@ B)G=GŴ;UVIn/BĿ`/-ǖ(MmuڦDFǹY\Tz>LS} '})TcSFB 5$9s%m> >9~¿Q{7mIr&⫪9@u^ `.TxQVυ~^/[UfQsߦ'zW2oVhvfO%y<}<g^By݋6 >tz~[C 6mw:ϗd`>@Es|?Cekj37|o(nB& >g}Ό7 ߴ.b1>JC]zoV6\9Xs|iK-ct]t^c_w?|>\U58D/vAS-?Ϙ~ s3Cڇz{CײX߹[H3HG/mzA;juMe?GYʧ6\mGЯQ:hwGXߧ {w= <bL Rȃ5-סGZ״<;urtN]Iub}խ\)ϬXz3|KN p)ʀN#<,-{t acB`ֿ^q>7{|:6ӈʃ\eK6W]Ke`Y$%x֫Wh59J򇔪UACGcc"6#d&P߰hr:AGV8Kz`W*|*+oBVUNoOZ[{nop2XG"J}S{ [e,c} ĘE ;T3ӔO3ok<^eV-WߥzT#VTWUKշR?ީ3R[/ 1.Inzimy2kE:OSzK/6|)֦(TD jz9Wg{CzGk}OI\k^m=/{rmxf_2`_y>L|x8? snwbbٮL'w* ogo㳡|u&W)6OvygUdO^kٓnڨj6OY3>++h<];TmOa*zu ky*3Y#ڲˤy7{ "U] m^Lׂ"jʄ4(Mm^%\⸏"nr1¥}Qo^J_+Ե\{e͌ziXۼl޳_^6V;p6k\۬kYOm1Y~׵:Gy=} $ ^ Wη>ӫ<̘>Js;imb{g^<܍{?*C)~ϼ&|6kѡ_Ƽg^ɽf,FQt^ץ酾ת-Trjd+|1j!%96mS\-<[Nm9eya9Ose^ONW-ZgxdU&ʸߣ=Uܬ xiégg؅qkӄȞ\ o . vGdZ!OUT)_'}x7;$ 'Vnkf{@zisupI乜k1ױ}ӔSv'`Onu8Chy͊_[8Z(tڲw7v{XV Qќ֘jGyda.)8iʗrSGvHt k+$5>tuR eF{-Ѷ>Z{IF7I_5}~z2 }>.ّ [^X\,#gB9A9݃2tWBxc2i{ r*?Z>e~ >}dꜱSNWXPF{Ecznk{zHqTs@yW(J>bԵ.,*b~ ^!|uBxxa^Tk` :0)k&\۫U>eoto ܞ@a<7Ta(kf+5P~G|HjJ' L_Ht⏋ {>׳lfL#ͱ:[thu2iZſF⏃Uߋ ?n>Z7<_ј[coqm7n!8ң폳ɧ_d s@χ!"yF mRWa|U&eDSƒ>r,T&77&}z)7PS~SiQO.=IW)r oL&22yK#rYhoJ. \d$rH!9/;mY*G_.IP9G5=]l&9U[* Zvi?KX|m3gJ)M߃ռ~6ߩAp᱃C]<6>Bh؟cԫ屬>QJ(}bBy\;s3j} KώGW;&_V4l=U>m@?B=8-ܤ t/r^ ݗӣw;l\+NtIcxuLɧRnXx:n=W45C}G3b>钏SUk^AxduS>,C-VnV|S?~{I,}\eFrwѧʤQOm?O~'X4V]%{>];FDzH>@FA"۫u}u^R/*w{o6IE1G|Õ5&R٠Ž {oc=iJ& X:8EFwID{.,R٩x hK]E<5Xy,eXQ6 -ݪu /&W&)&Uw2O^>@-i̓lτ^m#~~:pLc[3c(clԏ 5'~}=4KhOh{Ї;)qy:-?@;߲oެ}*RUkk#ߘۋ1 d[1>e2d_F|)t)jN-yW"}zRr]}?|d}?[p *<b4KGk-޽#=gbyOAst˕ݕȎ~`3߁;W!;˴IF";Uk3GsuV)ǎL,F#m؍F|<]KۊǮP֪y2xsT/cVٖ{NOfcT녽f~%]{@}Y~߬OS_3t_h,T~_׽1Tuu* R8ŜA-Ҕekݧ|6%M4ŒmȾxM#IF-GG_I#֭m@^/Bz-PA^"VH?WlM~Td,9p4x}y#tU]B]jx)9PnN}Kr'VoIP3IoisV ^4Xz{=^۝9* @{{o4O{{սY{Os\׭v+6T?h5Y:_PZZ$wPu6f9{%F'1w.MW7u4.gf aa[^G[^njm~ɧ Ю #KaۼL–-GY#xF6ða{Jӟz{(yOJ>^8cη=v*fc|j ~{]s]=]_mؔ=22}3c|6%V 1o/9=wXPoXPqm?`?rz: ǂ~Z8%BCk!b,zEcAo;3tX!/|{k{Ǽ~Ik}8fn+@"͵O+Sjr=<4sd\M9+η>:Sϯ>2Zkv ?/C/w?}~hwĬ{N[>X^ϟP?k{`Y֚;]QP/o7\]z#vlj93eVwɗOyv$IUh,|GK/?Ƃ>nzư}kvőя_vW?Y2)їhY 近gC8g>[lZ(ݿ!o<$W(o*~WTtֳŕ"cp,H?WNt뽓T&vY14^Rt u%y?/y d4IFQ1sN)`P?8Dy띣뵣)})zy%X^4@RIUg{ / 䣗yϺA&s?L}|0,bi`&v2`/.('y*;I[h zWV 5eG__}kߵ: q2~Hs?P?s2N?ѳ̧v<*jS4y86c6zU׻ףqqBqNt> Տ՟/)p| Eϯuɯ [Ⰾ逸#J&4ee2w4ٻhj~_<}teޙz(VOz?k~n;I(0ZoPfi≍nTbH#eɩŸˌ}.Ϲj )g#S&t5eX|N~ɯ!bx\*]t$u^!ߩ|"3UIkOq^~_w=[4Oh%x,حIA}yrSB>#ַBb5݅v0o-^@nS OLO_8]eCo0 SuN֤6!|CuڥvNJ6'Lv;{7Xmxʏ2ڠ~Bx6$-W3xN[5IɅ;Ӱ[W?TmwEmkcIe䎄mWTo<$aSz_a|JFa}7z 1צN`^LQ=JX5x*_y#PFL }#95sߤG6)s83evY[em~#ٵ*۔z.mLqI9] :ތj֪#:Xԇ|coOOO1}tOT}VWs?<}|ӴzwzrUQPAGwRP8zmH +oIZX?B z]AGj!7-=X }5}A!/wգ4 O04bvoք }nA2os|wϪLi5H*+j/N޻ :#+,Qv|cgS-:qCg֣귈^cw7cwc }}c;I>lj5] /Vo&Ŭyz(;M?d2+וLo"H ;|"GN{ksʛ1\\!׃@DX+{C#Rm/UcMK擇 IĤ]v09{+GҮKs0tΟ'< (b]vt˪ҕ4rئl˰˼:k}~tWӨ@icm2i*[T^_͗`z- Ś*W6%iCO5>-lN ˑ|QWro-)CKu2Qx]6^@&:2Tw}{/ːevF"0co=8סɉk;!;Vw$+u$Es9 {/B?Iר/ez ٽ͢KGtwQQwm7+_xRs>ӛ20ܳkDg .5>+B>8o̹>| /T[w)ajk*RC>ڦ<)joԼηKjg/M=ܻm}`/P ,6eY*;)L\ ^v?p>?fD:\60pw#Y/wHs AGJ1'O~|;?wߠ"}궡977OWh1eewY#.%w׳".Pn55~kҵ\bb5Gᚚ4rGk=bBe ?P4Vi_zGYyF-ncp{qMvÛMSeor$vc>qpLHx$2FLhwnvzrY\r?OܤYjmSF`\+3{c:wܽ>i,Ǝ&VC=9k}9F;MR%ygIʋNϔ=Sێg7;9ې<\lzb1[ї ץ ٔZ=3곃/@c<-f_gVWjOq]SQ8uyq:.90 6w}Qfۈ]QF>u 從8 \k[߹gFiOoSU˰ C5p'o+]s Udkzl{K~~ѿ|(ɱܜyu_g^9s9#gt^}:}>E|n$[1xSBjj\3ocU=wU=fUvŲ$/"_93Y>s0 Ѕ:w}2 ԅ"ݶ{wa%;OKᥢEEx"7z泫K( oPz;UWމ繦Rw[_px{b_? nzŅ]H_nuEB6o;2< l7pUw5ʳw7 yјCzELbnBIU4~r˟X ]7*uMʁ\S>CRK?IH(BEqBgyh94k]O@ VO(CnBxc2+jlJ hç )Oe}TV:3: r`aA˹6K 1q;|o^GSNߝo=cc8{@u/Un^$[6CzȯCy?{~}'RNsW^S_,;{>#C~#}%VO~'5bnoi"ͧkzaElj2q۪l=OByڌSBa%jt}\ j^ܞgRObO9[tfڅ^s03&:#fF=Knȸ*\wL@/ lW`XQ~MQ6e*vc@ 7tZ3Ud1lBx en|&G'uy=̣+K?"?7ﭤWtEV9i062&OL/sקrאGPG6%|5ηiTܻQNچd LH}Lsjݢ~5ʞ ޏjMץ} ûbP(woe hn}q$f MX01yHۚ,ߖtkξ%=[|{r;4ߕ\:nbZ]^1>#،DW hO<[:e{T\w䏲"4fElۏv yȣ.l~Ʀj2l2ڊOKa?nB1DZ,F(fc3F K{.pg8H~}OJ?ZYO˧z |'э @7~Hq^7 ݘy\ q@׊¾ ;]a w|aRLBX ݩ.LJgOQ!ϸW1z[=\yG*(Hߥ0R^k++w3mmnԔ?eeGN+~5޻=t 1'59bO1x:)'mx|6L}-u 90?y6 (7}\4Z*@+S10oy}Nz7M_|{+4^k\ϗ*!].ӗѬ} ] /W=-yoobNR 2iZ._5 kz9seo61_ʧ6(׫#ae#WQˣEʬTweؕv,ek!u2\G4;Iͧ-_ qM*FO%fmskv=~jzUҾѿ-<)MҌp&uZ(6h7hI)z\1 |'lə 14~&ÀkV-6eOU|*ViV>>.)G4*!ZD]]C/Bzwvi^הO4PҞˈYDq)ŸG_kya9OsHոl>Cq^6SlƎfd|'*NZ2jxP&:2X,kF&^d"֊tL&^#D ˑ|Q.0?skH2lzxUkd>*kmjix@؛O?ۡ;5ج]<۲tx-׸-dx3V Y>N!η,o]YɻEm}оw|'ŏ{ʐcվ嶗vٷ| ղ%˷WHr$:/$oF%:WhSД!ɋy*^ TZCt <DOk ٷ[L,v};2iT}K&n}E&"NUV@,"`ya9OwNLć,RQԶnОe"eSLUYcGD^r>ʘXY&u*(>N??hʞtôM>pBῪ}28>xZ>שr bU_ ,[8VyEv.3fsU;^ͻnS/FWjnz÷ï^tp:H>%-YPfo%NU|.nS=!_ɋy*k}ď(ew1g.C&i%;|Lka{ȫdH>=LDebExؽWȸۜ!) Zw\owJon{@z:v+mtnUq 6-eamY -A+6l|ڰm WJސw[Vټke(Vh hnyz)CiOD'w}deҨU6cZ;V^ؼ} ] (zKT6{W`zMb밑w='>{ :E59=󍼓~齯#G3_Ow홏';&Md>3YNf K4۬^F=z3h0Эyf2[Sֈiڰ~K: Թ%Gkgo}+G製ǰ>zoX7<{vLJy= Qي՛&^c=hn[]*@ջ@eϜ9eRԂ}UγGqM\R+ڛ&mϼ^\({LJ.MgKP]5Clc] R~]6$Wf||M=۵ {Lmum~KM^QMN-$՛ԻZ4VO"{DAeZ1xN/8yxԼ oA=x۝9*Z`׻פfZvwl;L4@wt.5TEt=b4kzЋuXO&)E~oЌ֌~k/_!q{NQ;=I_oeB(|SLP뻃C|3TE:(fAQz53fՈ=@dq^N\7Ox5HG/mzA;5G~r͌ziXî/yi}#q^u"=vD73spLX;-U>0S(~c<= wu*ڐ7OW)o+]wXMW?OQ駡]|uTب;}*u8]V(iӔ] { u /h:Yug{gG4"7Z!)I8M˘|T|[ާ:U0cK[{ߢF"ܔ$_:p@4g~Q-oz5gK뗊W WCuz4|fM F 4]_h~+6stJ'K믔?ٳku/! z߭O5&x=;z0q)+E䟱S;izwyg̎TuQt^ߙWd.|'Ӛ^辦4.g4OIZ^XӍܥ@W9/s)kg=KޫgdyiI,EWJ= >|^:d&})N*jO>X}q@aY~E: J(g}A}V}_!skUpe8~)$}|@׼} +5o*Gp[$/gWL/W2ѢWsT#ffNSV: \/Nzx ^wA%A1xX9*\c}ʜkV]/i`!>Χp_5cy7^8>.} ȼk}1c}c4u,ׇI4^}TD:qepu{ǤcfP ك+WQ~C }hc}+oK<eo7oiM?&+ЏzQoR>0G?R>QG=_}?Qbv}esN)w Ĕ([5_iU'נ:zY}Q̕z<]٣/CoK(ݧZW_\bEd'|[^#EAgB6zh%kv$kya9O7*wk^/*/w)C"zr_+ÿ/#T?LGESCi]5hb/T5S|dBGW)V_P6SyT^l*ɼOZ|x@>6q +!a6F-I;]˗NkWܬYz }o#ަ28GSS#ϺqLLa \#mqCʹ|t9ljz|`Nhl> (ʘmף`b5F_/x?V\M|)k~jCpY/<|ʀxcٗђ@#CȚ& *Sc1W,\Y7h5 *Sr~WoHv`7]b7eea͗Hje1 ).>~ZKW]U?T>U%.}:ąIFO%}$~B=A3+4^~Bľl_{W(~Bc} +TD \l_X> C4b«}]l(FU)3_@/}m/n~X"g2u0[+yEr >ף[ u7Ix>^_7ߙ';P@VQ9ӡl }Z5ayB 556p*/Q>7QW_J+cUm5Mkc2T#G&O+ym=sGeO2Nc}smˬR**32?4~[&Oild7=I\D9&>Pz#i:B}Ma}θ( .R7T៼x ̳lhMOLjty:vKzm>Zag-qcH| r,_} ] 7t2i4UHn-{!UJ-jSf(PQNC̗̏fnt'r.趁Jx1*~bڴ^G;y=7\xC|=y97ߦs~#2qw?U[ak_ɧvL&bg2ae"𰑮VD1Y&RֈL+.K"_?Aç 3b2tR=-9>oON Z2Rt-׹^kymN}Sr͇|eO+Z|#Fc2t2mzߕn>GMݭX=;VNSX~1J}We΍Ÿ"}z& yE~_\]czmc^yruLpV׷>O'U(=Z'+V3zu36i{X׏w6 3OUV "(i 3چRytR\N=NI:%{ {:|I -5w={AyXۈsrN~N̳?Ubd;7Ey_l;d{XI 6wTS]Ȯ F?)#f[<3G9ruAg>zƛN ׇOdCHv劋W6dz8'_ep2X汖"kd^S{,CKJݧPMKwf'H[D#ˤkz2}ʿo\KLբ{^7[d?=0Lѫmϛ^KTʬr'5St$EϢZ[zϐD}u}o{R,U6r\||mӏ"ʁ|LzTތ]atM蝷SegQ1x󕕦(܁N>:1#sZM靛;57 5W~gou2FJ2'Y &;ˤTaz"T^:/1:8D/h\^";%\3Et+_sOGkGL<"ftfo{g'& uɫWw%q3S i ]NUVGJīwZd=`nO[EzM*z ˼Cz :0:sxL8 5.}>MHS2ѡطryG)Os۷F3۟_7&3g/CO:>9>DƅoZsθrp e\k"Lm p:8 0]ԴH|9vu3ap@k?gb ,,46 ãäå F: L  Ì – ëèíåéíûé îïåðàòîð, ïðîåêòèðóþùèé ïðîñòðàíñòâî L, êàêîå-òî åãî ïîäïðîñòðàíñòâî Ì, a D – ïðåäèêàò ðàâåíñòâà. Ñïðàâåäëèâî ñëåäóþùåå ñâîéñòâî. Ñâîéñòâî. Åñëè Å(õ, ó) ëèíååí, òî ), y , x )( , x ( E O ^  îïðåäåëåííûé L  L ñîîòíîøå- íèåì (5), íå çàâèñèò îò âûáîðà ýëåìåíòà   O x è ÷èñëà  . Äëÿ íåãî ) ( u O x    ÿâëÿåòñÿ îäíîçíà÷íûì ïðîäîëæåíèåì, êîòîðîå ìû áóäåì îáîçíà÷àòü ^ E (õ, ó). Äîêàçàòåëüñòâî. Ïóñòü ïðîèçâîëüíàÿ ïàðà ýëåìåíòîâ õ, ó L  ïðèíàäëåæèò    . Òîãäà èç ðàâåíñòâà (5) âûòåêàåò, ÷òî ), y , x )( , x ( E O ^  ò.å. íå çàâèñèò îò O x è  . Äîïóñòèì òåïåðü, ÷òî (õ, ó)   __   . Òîãäà, åñëè 1  ) y , x )( , x ( E O ^  , òî , ) y L , x L ( E 1    , ) y FL , x FL ( D 1    . y FL x FL    Ó÷èòûâàÿ ëèíåéíîñòü îïåðàòîðà F è âèä îïåðàòîðà L, ïîëó÷àåì , / Fy Fx / Fx Fx O O        ò.å. Fx = Fy. Öåïî÷êà âûïèñàííûõ ðàâåíñòâ ñîõðàíèòñÿ, åñëè åå ïðîâîäèòü â îáðàòíîì ïîðÿäêå. Òàêèì îáðàçîì, áóäåò ñïðàâåäëèâî ]), y [ F ], x [ F ( D ) y , x )( , x ( E O ^   (7) ò.å. íàøå ïðîäîëæåíèå íå çàâèñèò îò O x è  . Ñâîéñòâî äîêàçàíî. Çàìå÷àíèå 1. Ðàâåíñòâî (7) âûÿâëÿåò ñòðóêòóðó ïðîäîëæåíèÿ E(x,ó) â ñëó÷àå, åñëè E(x,ó) ëèíååí. Îäíîçíà÷íîå ïðîäîëæåíèå ^ E (x, y) òîæå áóäåò ëèíåéíûì ïðåäèêàòîì, òîëüêî çàäàííûì íà äåêàðòîâîì êâàäðàòå âñåãî ïðîñòðàíñòâà L. Çàìå÷àíèå 2. Åñëè ïðåäèêàò Å(õ,ó) ) Fy , Fx ( D  , òî ïðîäîëæåíèå ) y , x )( , x ( E O ^  ìîæåò ñóùåñòâåííî çàâèñåòü îò âûáîðà ) , x ( O  è íå áóäåò ëèíåéíûì ïðåäèêàòîì íà âñåì ïðîñòðàíñòâå äëÿ äþáûõ   O x è  > 0. Ïîÿñíèì ïîñëåäíåå çàìå÷àíèå íà ïðîñòîì ïðèìåðå. Ïóñòü  ìîæíî ðàçáèòü íà îáúåäèíåíèå äâóõ ìíîæåñòâ 1 V è 2 V , ñ íåïóñòûìè âíóòðåííîñòÿìè è íà 1 V  1 V ïðåäèêàò Å(õ, ó) ëèíååí, à íà 2 V  2 V òîæäåñòâåííî ðàâåí 0. Òîãäà, åñëè 2 V x O  è 2 V ) x ( u O   , òî , ) y , x )( , x ( E O ^ 0   åñëè æå 1 V x O  , òî íà äîïîëíåíèè 2 V äî âñåãî ïðîñòðàíñòâà ) y , x ( E ) , O x ( ^  áóäåò ëèíååí, à íà 2 V – òîæäåñòâåííî ðàâíûì 0.  èòîãå äâà ýòèõ ïðîäîëæåíèÿ áóäóò îòëè÷àòüñÿ äðóã îò äðóãà, íî îáà îíè íà L´L íå áóäóò ÿâëÿòüñÿ ëèíåéíûìè ïðåäèêàòàìè. Âñå ýòè ðåçóëüòàòû ïîçâîëÿþò ñôîðìóëèðîâàòü è äîêàçàòü ñëåäóþùóþ òåîðå- ìó î ëèíåéíûõ ïðåäèêàòàõ, çàäàííûõ íà ïðîèçâîëüíîì ìíîæåñòâå  ñ íåïóñòîé âíóòðåííîñòüþ. Òåîðåìà 2. Ïðîèçâîëüíûé ïðåäèêàò Å(õ, ó), çàäàííûé íà äåêàðòîâîì êâàäðàòå     , ÿâëÿåòñÿ ëèíåéíûì òîãäà è òîëüêî òîãäà, êîãäà åãî ) , x ( O  -ïðîäîëæåíèå íà âñå ïðîñòðàíñòâî L íå çàâèñèò îò âûáîðà   O x è 0   è ÿâëÿåòñÿ ëèíåéíûì ïðåäèêàòîì íà âñåì ïðîñòðàíñòâå. 5x{pW% ͛$6WP TP:2h)X tkTH X3((o)PP`)7cڙfgϞ=MqH~`dGd4Ȳ0 [Id7垴Ե6"5I7bC=Zs:K>4AZKW@x}gP\ =YqEгP")7UNy-7L9v2)UnL\Y(Ym{'}24M:H6rNINN.|ɔmw%ͫnFD$Mu{H-ˢu1XoݞNab֢(t1u u*?6?=/3iqJN#/ ~lQH5nn@n]swɖ,΋gcp+ț7^=r6NŏImVas_] PREZ?#GMdGFC3}y rY{P8y}i|̀9?5P-4 ڗ#e~rV%q1p@mA}>j5vqǡq"CŴBfWDK ͓=&-Ġ̸;cos {ds/b{%Ck|#uKY(9 !rߒ[O3쳅IE AYP1PX{#x:ݢc)ǹ[`e@A [ :o34R,ҶS.#TY^ y+:MFVS,sX+d>rWhEDjd2k{m˷+crĺk+*ݘ*m;n$ejҊk9v{ מOn~}^K✋coW$D\BJgA57BvU6yedw:`p/Z3v=!vn u^E=Vq{cq{M,-xa2{#w[E}ތw;aD`5oDl>8 \Hz6ѭeirUq/]0?%r{SrR9f,S|:0irtچq|j]Uvo:3F5lJhw+?zFsyIKFcyh|OмqnF׽k5vlKGpMIk'ͷYK]wKs]c<[̵ R{}%K|z~}ҧuWom!ڶ#k̺Sܲ菷\Kd DfRs/V< o8YvWE7r'hTG>D]2d:Ce*^0咎7NY[Tޤkϛ/+y@|[D߃.LWQJ.%%`3>ӈϧ&-.@_=mV&Ta_X2!c]JZE~t2;Xunij"AF&GuđJar܃9ekMľxG5dP\,Hs:SdKV 9{k(]q`66 =L)Q[?ƅ"`CyYqlVKq! Ed.6Q_.f'דʬ~|DLEB ~(mwao7q\L$E˺=h_5P 4 ZQ[IN.%'yrG E EP4t +o0Fo/+bo~>DX ׼*a'WʔCՌ;qRԇVc[ k&{erUBNRIz|OA|HwX/y-O&q >*OS MbAvfܴ}]Յfǫ#;]Y59|=+S~]Q : ;=F<̌>Ce*D0 ~}#t: KkRrxZ5y[aa֧\&FO][6}識Z&7Ȱ; 7~WmEm0ٚNplT*HUrb\؇\Pw@Sr'F9h4k_IV\r3yXF/@ƟbE|Emx'[ד"f~=ulKV8KA)Jm p;}+6r-`#) zATL=T"4{;q A}dlW̕!GGL15{`|gǃc<mw4wln0Oy8ߝ`A89-F'5GO<\MQoxsX83Udj| ?pf^5Anc/ٚvֱ]hc{Hq^3A6.ht WȆ;쳨\l׋S1v#< F_w#+Kd DHd DgGc/DHd D>9N Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:15  h O(16B2x/1 \={x ]u #ɝA_$͇Y4vك`%E1e0ZHR$˖@’X+$f;Ɗ+  >R 5A$XD!Mϝwg3Qw>}ݧ}S !**!IgU!xc+&=ʦު|T yVuƐ >~[Lk\+YMw 1IJÃƧzxZR7Y3G}>8j?xa`C dTrZ0O B./jVhJ5NVHCNӴR>Ұ؆ǟ<9tcyeM0Lw5jn:u.a}:tk =W:lࢊt6)up=oo!un΃"o tX=둞BM~L+2Owܢo*uu҇rA0쥞-mIg\^iU8d>Җz׳BmRP{R@!ܤ9cyF8`O#ΦhS6y¡l=lm|R\(6Vبm6 Im&R)sʉSOoYOq 7Thyz.U86vszKݯQVFQ#(2` mςd~ oI]''DzZ};UjۗԎ :4߻ iCVyZNeۃ|}uNü8#*r8n_EϹi1= .U5T#l~}#'6I~y?_2Aep1KrF0S&vA'ha_\ȼk/`f't?VnCB2:eT6FOoD`&&6iɎhB.ِ7glvN~,5Xn X>\ыeo}y0>b^`,X)y=O+W^ߺEeSXtʄvB|6j`:wPϚ~q==)}>9<^ת5J'\IXRrTOQQ%>=r`O1J[Ɗgrg;i|$2xÝfÝYWnj<ې5H{`d&]9{X8pPDGM_uS :YƟkkNjR\듚 1%Qỵ>_I Cx(˻4G9 >+4o#/}6Uksd||W5y X&M_Ii +pQt[լ JV|b[ɣ}Y[,<`NuΝw+|^?zB&2Wt?Z^VHY| z<[@ }'ډ팄zpخy )cC)6=te#[KK%Qdmwpe1'V#I3b*Z@6sIcGSZ@!3WoKՏ oUHƖ%BA~{%ܭ{%:;Xg\{%?m}XQ=l;Ƿ)`Tq68c{V#hK~S/'ݨ_FƹWrWsyws#=]^EX3`S=U_SǍ>~bcv yRi<拸蟑FAS^q[{;ç54q7 qCc-g=Cmm[~omgE ~川9~Xq61f=;﷍m>L&6mVXi76xׂvXIx,~R?t~5R }Vݻ&~cys#~HοiCXoʥ~6U_O Q;_aئCm*ms68Oڎ!U9Ⱦi+f>!8Ӑ앣9TzB% W֝{vrvʉ*瀴W7~+sخ?'ܯ3Y?ɿlyr s>z,+͂qˎ4e\|zYizS^) e;u@FlҶG _B)H%M:ƙm˼>cC3U䀱vW&[ǷnAn[ٟϺ|gѥw/|i BA?^- :ƲH!7/uk2ջt7~bAsُ \V> ߎ_lv,/. ._ƻlFქ >!{962IgWr;C3޾1Z((҇ "t\Ut6vVۗĥo]>]6ӥC7Yc}{cT.]ŸwG[/;cl,u`MtTӗQҝA6(/{c,~G9R_m(ٌ7za;'YW#={O/~q\yeW܈F[WE/ӷөI:j|5"nR_-t#?s=ux O{~=L x_~>}H;e2 eBi_4,H9}hh\B]?!KyCG+- [Kpm.OaoTxoۮ:іsA|j2gu Uь]0j좷fey"K#3L6{vBo͠ Ҧq><I^:ơAi{ /5jge8මb=y`rd ӝ)2ޣI||!CͥU{=!]7'_f?PxFz|W=~ߚ!~gjonwCjeLlQzA ;:s>tċva<4hIN]6āԖr3vOu2~Gxã= п&GM47z5;%^i >

g܅ƻu/j}XFN[^S֛ :S:B !o܎Giu)抾J)[ulg]!A6v ]#ưыg_~@d7]/X&(ceg`@cE]Q1HC4 :|juh:v^>̬?CU' %nhQyQKKKz DxÏ{eM[WgZt[/s(8Bl%=-ݱol*4ZqB+N0u'e]7}ҿ7LP#F#fQa#hsoF/]#[oƹ}9.zC7Edʹңm灨7h >>spQ m'BFX7=ڦTo#[oģު;.zxQoO)7orOs_Caz۪!z#,򮧷FO֘o 8+$*.}!5fGF5$;7縤>y/BtM$V UpT<# TiȣZBKLz1t=U&ȣ>S&Nm>|o.)Us6CZf 8/?4/Րx*Oa 'r.egp_W1bɣ|R۔>)zC/_-If<"N@ G_ xGĝ&-!}vP @߯gm]9Ym=||<ֈ/QȮFWWn(/ ygU-zs o!<(Oq`,gcsCC>u vJ\ud|X)lOD 6'HM]Ȍ\*@n'ˑ|B ˢ}}>Sޖ|CM~?oȃȏ&!,ݽ `?1X֞,&߉z.آ fh9*NuZ5vJߠ xj}AžG_.SlS^5"zc5f~ [Fg΋ Ǽqs㑮6-#TġAx|Y.| OpMy׼@O<(84m'o?l&*9OB'Mlw8;r8FK _B=A}̍/(6_řq.Ќ8GCy䔱^L@"gMylwUJr5=Q8&/LO '@Gw n EQG#ʔw:ܽWG= 9 Sy}2o= }G8+kCbJ8n}ĶPHy:$gj.i\lb W^qO0~b+ }sXnE}6G8qVFvYzy.s邼>h-DV+rGQ[֥e-|Bxę#]eQ}Zw':)k>A c腐G\ C7yLzh7.Y2&OVP1Ie•K%9Yܚ-)g߽.i+{~da[t_s !8򂖲ChZ3ӥqEY&I'yYA.[82ܦz{_~Y-sME& eO,||ʤy\r]љ},,ȁ<@29lT+?>'^~C/i Rm! f>.і)FFŽ+^;2+OR?kFc%OJxzH9Gcq~~*>;_Ry[,f`K^,3ڡˑ,rY+\}*|CG3J}%]Qx[)ungP|Y̋3+ifc0'Oi7NdIpȊ2-l71MX_~ʐdo%rE'[{EyK+N1xF!3%scq4N1Suމx}E H,W*!O&V֙iY#߲% Bt@]Ts/ G3GY$tk1k A]ϯ-m{7$H4F3#kd +đ=!2"B Su;Z:7E;i(cr^*:ݷ_+$e9|okDŽ{o޷[ŕqjֻ޷H4齽_*[mmV-xsome{yPO+uZo#cOPOs%w1Z]!2.~C@Q5dYMl<񳚀`)/az>TʼPwF!|}Fޗcv NJvʿR6HqゾKO6wm wl;i?yreXW-̺钜fwCL>k袧25HXo-;kqZx.R3&waӻWv4~Dci.se Zۑ7SϵvGG{.HHڟYt;Gnw 7ȴ7a}ސw:ؾ[}DoǣuaCmNY>ie-5 2#q sIN(\3q}>6 uozcg[no^8~?8')ltݻMYooaFީm8~,xg4A\!'Z5±F&mמ{, ڡ.=d-+CCaU#!Pc;8m?llA i{Anzz reՐ4/˄7 ]ZƪܾVGn)ڡC}\GÿH"krZF*#L80)w6Wac_Z_͘NX72-gn 4Q~rr}ES?ikjD' J N0 9oE4舺)Ր>]nOн:%QkP?,7aYGȒ8L}3"4(X>TQEM̝;ӽiqP8|)f|9TA~V s0m1,SLccKO?'[:[9Ư).=> !H;tq;%Zb;܎,seo㻦܋<&o/Xnp:nj#y4xi ?!ihMYuy+EWD/蔹&mNw*9Hm5)4.ZWݒ0'Z-ޡWjs~צK}:'_-GNP>_) Tȇ֏yA ߲wy~i|EҔw{\'!6NК?<m2/ʀG~߇_ De~Jy;:4sow~ψ{6?gu62#)>']so 1'A˯ߗSo=oe~#;d4/si\qtz\:tL>zx”oOʃ}&~:s{L[; vfM#1yM c3Í[p\:ݪrϖ!.Gr3 \ֲNuf<Ic;azIpЧvG9eWsJWTں'\٘~Zy8k1Q,{:؀9e澦)j]KY<Xi}MhնA>6E辸-^fл!o:z-Rі}yuûiηDw ]s4;@sWC|9jr'nRH[Z,kE,e\~#6/6)mN҄]{3qSE-57WTF2E{yl{^9ߑD/2pϡ!=\ yO4!lM˧t8nxR>=^!;_Wt B%ks8y/{+V]G!:FlxWc+x恿4"kyal)ʻ wFhj(tgj4U{rQۃ-L` :`B>M-cg!~ OH9h[g(|ʺ ԙSuA,cO]80kϒa)YMn57Fgwqÿ>oF}roz_8Ⱡ c69=w `w71<)gSqʦ62>. Òîãäà ïðåäèêàò Å(õ, ó) ïðîñòî îáÿçàí áûòü ëèíåéíûì, òàê êàê â ïðîòèâíîì ñëó÷àå åãî ) , x ( O  -ïðîäîëæåíèå çàâèñåëî áû îò âûáîðà  , x O è, ãëàâíîå, íå ÿâëÿëîñü áû ëèíåéíûì ïðåäèêàòîì. Òåîðåìà 2 äîêàçàíà. Ïîëó÷åííûé ðåçóëüòàò îáîáùàåò ñèòóàöèè, ðàññìîòðåííûå ðàíåå. Åãî îòíîñè- òåëüíàÿ ïðîñòîòà è â ôîðìóëèðîâêå, è â äîêàçàòåëüñòâå ÿâëÿåòñÿ ñóùåñòâåííûì ïðåèìóùåñòâîì ïåðåä äîñòàòî÷íî ãðîìîçäêèìè â ôîðìóëèðîâêå è òðóäîåìêèìè â äîêàçàòåëüñòâå òåîðåìàìè, äîêàçàííûìè â ðàáîòàõ [2-5].  ýòîì ïëîäîòâîðíîñòü èäåè ïðîäîëæåíèÿ. Îäíàêî â îòëè÷èå îò ðàíåå äîêàçàííûõ òåîðåì íåò íåïîñðåä- ñòâåííî ñôîðìóëèðîâàííûõ ñâîéñòâ èñõîäíîãî ïðåäèêàòà. Íà ïðàêòèêå ýòî îçíà- ÷àåò íåîáõîäèìîñòü ïðåäâàðèòåëüíîãî ïåðåñ÷åòà âõîäíûõ ñèãíàëîâ, ÷òî íå âñåãäà óäîáíî. Ïîýòîìó ñ òî÷êè çðåíèÿ ýêñïåðèìåíòàëüíîé ïðîâåðêè ïðåèìóùåñòâî èìåþò ðàíåå ïîëó÷åííûå ðåçóëüòàòû [3]. Ñïèñîê ëèòåðàòóðû: 1. Àõèåçåð Í.È., Ãëàçìàí È.Ì. Òåîðèÿ ëèíåéíûõ îïåðàòîðîâ â ãèëüáåðòîâîì ïðîñòðàíñòâå. Ì.: Íàóêà, 1966. 543 ñ. 2. Øàáàíîâ-Êóøíàðåíêî Þ.Ï. Òåîðèÿ èíòåëëåêòà: Ïðîáëåìû è ïåðñïåêòèâû. Ò.3. Õàðüêîâ: Âûùà øê., 1987. 158 ñ. 3. Âîñêîáîéíèê Î.Í., Èâàùåíêî Â.Â. Êîìïàðàòîðíàÿ èäåíòèôèêàöèÿ àáñòðàêòíûõ ëèíåéíûõ îïåðàòîðîâ / / ÀÑÓ è ïðèáîðû àâòîìàòèêè, 2000. Âûï.113. Ñ.35-41. 4. Ãåðàñèí Ñ.Í. Ìàòåìàòè÷åñêèå ìîäåëè ïðîöåññîâ ñåíñîðíîé ôàêòîðèçàöèè è ïðèìåíåíèå äëÿ èäåíòèôèêàöèè ëèíåéíûõ ñèñòåì ìåòîäîì ñðàâíåíèÿ // Äèññ. êàíä. òåõí. íàóê. Õàðüêîâ, 1989. 134 ñ. 5.Øëÿõîâ Â.Â. Ìàòåìàòè÷åñêèå ìîäåëè ëèíåéíûõ ïðîöåññîâ ðåöåïñèè è èõ òåõíè÷åñêèå ïðèëîæåíèÿ // Äèññ. êàíä. òåõí. íàóê. Õàðüêîâ, 1984. 138 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 12.04.01 Èâàùåíêî Âàëåðèé Âëàäèìèðîâè÷ , ñîèñêàòåëü ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêèå ìåòîäû àíàëèçà ñëîæíûõ ñèñòåì. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-93-72. Ïàðøèí Îëåã Âëàäèìèðîâè÷, êàíä. ôèç.-ìàò. íàóê, ñòàðøèé íàó÷íûé ñîòðóä- íèê êàôåäðû ÏÌ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêèå ìåòîäû àíàëèçà ñëîæíûõ ñèñòåì. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-93-72. ÓÄÊ 519.673 Â.Á.ÊËÈÌÓØÅ ÌÎÄÅËÈÐÎÂÀÍÈÅ ÊÎÐÐÅËßÖÈÎÍÍÎÃÎ ÀËÃÎÐÈÒÌÀ ÐÀÑÏÎÇÍÀÂÀÍÈß ÎÁÐÀÇΠÍÀ ÁÀÇÅ ÔÎÐÌÀËÜÍÎÉ ÃÐÀÌÌÀÒÈÊÈ Ðàññìàòðèâàþòñÿ âîïðîñû ìîäåëèðîâàíèÿ êîíêðåòíîãî êîððåëÿöèîííîãî àëãîðèòìà ðàñïîçíàâàíèÿ îáðàçîâ íà áàçå ôîðìàëüíûõ ãðàììàòèê ñ ðàçíûìè ñèñòåìàìè ïðîäóêöèé, íî îäèíàêîâûìè àëôàâèòàìè è íà÷àëüíîé àêñèîìîé. Ïðîâåäåííûé ñðàâíèòåëüíûé àíàëèç âûâîäîâ ïðåäñòàâëåíèé êîððåëÿöèîííîãî àëãîðèòìà ïîçâîëÿåò ïðåäëîæèòü àëãîðèòì ñèíòåçà ìíîãîìåñòíûõ ïðîäóêöèé, êîòîðûé äàåò âîçìîæíîñòü ñêîíñòðóèðîâàòü ôîðìàëüíóþ ãðàììàòèêó, îïòè- ìàëüíî ïîðîæäàþùóþ âûâîä ïðåäñòàâëåíèÿ êîððåëÿöèîííîãî àëãîðèòìà. Còàòüÿ èñïîëüçóåò è ðàçâèâàåò ðåçóëüòàòû, èçëîæåííûå â [1]. Cðåäè àëãîðèòìîâ ðàñïîçíàâàíèÿ îáðàçîâ âàæíîå ìåñòî çàíèìàåò êîððåëÿöè- îííûé àëãîðèòì, ÷òî îáóñëîâëåíî øèðîêèì åãî èñïîëüçîâàíèåì â êîíòóðàõ óïðàâëåíèÿ òåëåâèçèîííûõ ñëåäÿùèõ ñèñòåì. v+xilTUϛa v e(SYK b(P0JbX[!&F>(5ARMSf6 "[@)d1H*$^33OƦ~ yMssݹ/u#D$px!2 tYᡃ> %wݓ/R s 5/9ӌ+qvGƚ"&zvyDIe+)&.[2n<";۟.'/dYiR"% Hz2yl5yw.\;m{YDB 5Ϲ&6mEO5#m;SLbH5'W]"rXRE{J(OKsls4_l45wλB%כ3\]AGk9ٵ9.E-G1/>r3>x502e.|4~`1Sbr F ]%Jr _>p  6M} A#^+x3/[u߂Q^scZdi;:,F"I(?bEغ?,ƭv PI Έ?jt ]bx95`t0Y%*M> `x+C&j6 P > R3w.`>뤫$Tx! H>]IrZ$qJ RnI!Prb# 8gl&\iF<;/_y%p) 2IVOŮ=C ݦ42.?T9.[y.` s~~fn!k>뉾چp>_õ`~`Gs90:8 Fܤ%E'ZρS\EN7I3{D>CeCS9| *گ}, >%?KEiMC{!hzo7F,sbc9cю%6 iھDiknM7\coJ}~J}Kmi͵8zqh>y3zZyG[|gv +`W]v x+#Nܮ]v +`WQMMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:16  j {/(16h=2=/\1X6${x̼ <0>8XUDTǾDH$EI!ɞ-{Q ,%DQ -my]{;gfy晙gU$P0$V`ŁP,8l!D32AZ T8q9yǀ ye\>ł4C)mA7C4"_ @!ٟi>*ć]4#-4&8?c W2$ 8p @  C~dq2bbЖ0-$# pi3 @C@G1'(`B>‹I[ $jk)!aؐ(`\]Ay NClm[,.!t-4 aj z0 ]XAg|<@bN8:8#=oeqĊ0%muy "}X'.ЙqX mLݶ1: &dzI rB8F]0CNj, A[8`Yca ˟b,~@i c=n`]LG?i6'x#~'n֖n?1 `9z1^7yltpJ7SA7!&8ٌ݄ttMjnف| #&c1nB>0l"ݼQ+Eh.78W}A?LXE1.`cdRgðNՊpxKG1^c^ b~[`0s@LG\KL{ǠcaH9f+ <Nx "4^PF!z'@ЁA myBO>M'0:D>]HCB6S\K?@'.{ߘ߂ |* @lxCa1>O6e񜀳?yebwqiCw:jV]t1YXi\ML:ile54"? / 뭱/Vl#NH: 0)A<'`PX"rY "8>QMD?!MCL MC}@1qVU?&jyX}pp$l? {^@wa6\S~h~bC<~ }3 a729X$h+>#8cݣ񍝱AgrԀ( 7 ϙ{+St~'7\3L9s1p] 7'a>X`Yc a`@83x +1/Qg|ϬTz0='g7b(sn)'bglo|¿Az|44gB;@bMy !d<@Ƽ|DZ/<2xnils>ȝO4$An8>Lh')пݏ}\elƱ::_uʀ>e= k[S!؋Q%v"p/[dpރ& i>1(4116}-dn͎Pɟ,Ǹɾ vذrNYǯ3uk93a9vԆ?;}OixG>#? cگ|!s@]BL"\ 1!}B A]BtPc,@a0HwK32Eü {ƙc2bl \gq\w啘!f11C6A?p0oGg/aV`|x2>/97xHajWAtnRXշ "!:F8}1ZUF]LXZu~V5[J} ]SK2F{0 `g+ρR}R 5cŠqE@pP?9@,~ Zx}M"(g"r!4cEc#_8q<okBpsCo \!wr~ro{ `C ӄ\9^x a'?-WB DLdVX@/&d"HMdd_ 7zt?!wSL~ržo7%L(2Z^/l_+ 7z 'Kh"eAMu,bE [0"AO z"z[pտk\"ы?'/l׃=ztK®!wz2][`:tB`u.e2z, {Gx?'_"7ɘkyA] ꍷk~k<{`>3'1Z(Ǧh8l!\׼p@O?0ϸq8VsGq@%| p3B\.Bʶcq"yLë m8p61)fP/B&jƲy2@phc4zpaulPcc܉ڨe4$D۟hslp߆߬ Q|f|Ԇ~=v9+4g&ܫ ox+r!k HA'S1CG9 A #'bv}_æ#t% 1| b_u@WL+O2#=8Q?({aAw]hkhˢ<qx }F^d~Px A!3/>/2= I% 'PNC_We m@9Ā:G8}(=!x~U+fq'+pΔ[,V,.5nc;pӽ؛[7}Ƽ)=Ľ[{Ŭt}[&/70fb<s  ~ԁ{3A i}"A&ڃ2BWw|Y'tڀߍ mAq=lOd? L_lhLu@ uCS&{/t2% 4~{moa.1coN^0>v|!H!@(:'~m$mp!' 0>b@ԇv T|/fn`t,VFA`|rC__k~3p/a%u kPN|<_6Wrz46@ '[ Ņ /ߏ>d{}E_GWaE(sRoi`! <+]"P^ڨ^o?ڸ oi!a8!O$"te!djE_aT@v^HAo<$UM\!h .8b${`ygqfkS?Mc09Wro u[MIV%tVv>g]3Gl0Ԝ%9ùɲAIkcLA 0A**:1ATI2'Ff_)޹#,]3H{-$竵/umU mXH<ZAJj0]'O\VzuʖN-y;\o)ryҙoneo;q\嘸ehm<>lGVmsrܧ@ξwrC~EZ'[i*c YJYvKNQ}8 /6T[TVP&&#~ظc[&5/1HjlֆR+=O\l_)Xh.Zw4#'}FMYR,^7lZK]?%ճ}dRR|oy |eZ7Räת~mj! Иor_.G95j+URHJvws6ɇ[ Zb8xmo4\u0er%I ޿חaI}jg ,.^UXjU<Ϙ/$$-+{znb% ,BQuTޕ"גkWsJqV|Q57>E[gK1<,m ;y$mʌaK{5_5,s8mUt-CB}鳵RBٌY#I1B`+G0x9O~iX.vPS'Ov#[ۅ8ƬRMv۾w՞a e\hPL;;#'&m?1vWyʎ}/q_Bq;laP߸%isT\}Sj 8O&m~M2YB6T+S^f.EL^-p;(hLR*愜#DN^] pdrr%`1zߐIX14jh2,U|o]b)ma=tPfs1{mN~ kZK8}TYl|sQb˺VcͻXfwrdwbLbܼSIF9`_"ۓInƞ<&(ȫ|z%"lI|Utل#Lw$Izɏc$ L-eLfEEiYnj?BYMiqV=g J;K3YTeqqOڊvRTY V BǢ>{M(Dgi$Zz5u§ӵ^D]S"!@4b|2>Tpp[So[U庱.FH|kįk 9rzHQ#L Ž+gdr O jyQ]*~9X7_ee"[%/+̚VtkytluE۟M:/23}қ+^oiep%Z)]"3lVZtz9g{<5(2{]`s'W*9hLڠvmz^O]vծ^vMۮ9Fo!n3LV9a#Wc z}\FA-W}NzSEKwI-vx1Kz㓺^K)tAUR7uD]MS$~*pu.\=gE߫_* CnV-i˫/3C TOX߇gȗ+CIiuQ"}>2ᒹ:XsR,? \D,m|ء煶)@Yݯ=ڳ |VXNQhI˛;+k i2X)ZJ|@hݻ);[F 2&$J=Җ CG^-KjӒm 1N G 48V>fU;] .cSՋyVՖUg]I`[Pk)4{hq}$Mfy2jPL9)Ǚd_ΖVDG[vYa8oĭba!(h,$9v%?ZaRX n31E⾍E-멜N_gmZ,}Ps$VG>yu筫sf=[i#hA+khj'>rX6+IS[s'jHK~l7SWV@pW=,o$7:RW={HSf-=~}٤NAR%YE\HXrOKzshT%h+䄄:,>0xU7:IM~Ê4] #JD3'T\U^ԙa664?FvE@ؗ ׿t5ESjgMh+mve p=+R`Sy[茧bV{k++Co\D}ӕ7\//Tگ;?uVوsYh׳g6U~e9+w+ZfizV\](LÌtDzb<&U.Ԙ~3RWs(U N4>UҜDٜc {:[eC_ i{-RzBkK%ؤB^V)/(o͖gkj1SO0_ 5hq4HdF3y ~*nZyU֧8ITڵάYtoy$3IJ+9 5"ȺTM)ϡf,Q(FU!ì$ZQ]Yݑ^Dq?,D`p /*#M}(F"xtZ#P:d!,7}dF~fFG5a'7?3C Lқ9қ<<<ICR1Ȣ#߷26Zkl\-:op>r^ѨrVVD:gC׆Fy#pDq2|BhW_m/{N^z t{=EFOb%|P*Cc뻥@:`&.ݻ (|8A*[V͟?#kX8fR|s宙OsV͵0ke/,^۲tn.(tv6R)s+T!S 2' X$79+eYha"e92"%5KjG##;wz{=I /hR~it(E]"C=>2$n:0p$t+j)]})/ jInV&/~e#u  fw/=Fcﳪ bH}G Gؤi14y;ɾMD|?]\m٧_پc=թ{si$tتaj,>r+3z/k(Sj] R\jsxJ #m6Xn,7"uAYK.wFJW<#~^0aR/eӏzg~0qʳg›8/EOy>ii/[:^UFѼߺѧzpK +ylW Y2zZzzG5xO>0y鮷ꬺ.bt4$q<U\,wF17"($\Z(ijgϔ%nHO؍HJ첚o--7pPQ\[ڦ(wBOUĘ ~)dt8Myg*s{%K-M5"I^~jݣPS:#Vfj21ΛSy.l]ݍT;PxM5  o+xtO *V =#Nu^7KͲ%QРvT0r,7. PRT3TyNgmXQ}*G $A pp#KM#ɑBxOv9\kk5]bR8]VWX yDZ9/n~4"ݩBϭBPTֿأ8y6V%PkS/%7k/<<,!BK Gb}mz'3y$ <%ܷ~iL^K;zCJ*x`gc׏.'4mTiFʮfmxUaUy$^WC3netxﮦ@s5 %MSJ0h]ҩ"}TB>1:r#TWA᜽2r4 r}deWb N\T2}# :v Fځg2WVxv?Tvم5lD6_+7f孰afwW|w/Y_. >kW3jZLSrn':i_ v$n/fŘjxHڞ癍0_޵6t򆮔|mrٯ䰤lm t覞qUe W'K; ?OO~{u@o!I+VmƁ݌*O>,T兦e'$3uZڤ<{^Β!޾YR#V#.ܳ.8%{"X͘=S#e&P8:&ϭorC;B{O;h##YNia4ň,IQILUpXB ,vk5}9܁Zh[VVVuލձ)N& 59!1{ִ# Nްg &99<^DY2&7}jZ5tSH,3]낈fn97^[e"vYsˆٕ-}7ə2I 2+LrXNhɫ2nKlӽ=F;O7Xq'me \e yM]QAyv_-6eN:>Kp|*~˦vm-zAwNN]ijHGVG`NG&]vKk/R<)!/t,>=&P)υpjz~^hz6]>>E|wɭYLh%ZņL͈O|)/$5/`y6p/AS%Pd92]f >Z!dn325SSӝX l =55=ī)ez-z$ ~;gϋH}'y/ #"?c#v#yNj?^%ڢYg(|;Dp0{E].mt {_o2W^P,4:4tJ]Sfeh'ی^Ov~}fv}1,Q3>/yd+} n:T1]qCG;YXɮFjW#WqQyت,Ӗ9|'Řalf-ݵo]4Խ+B~'5~=`dij`'VKIj_ISѬ9>ʫ(wD5BΤ*/#= qu p0R)2 ,;{5zYCu zAGJ=6-lyBU>.< za3DY//=dgKr?2mVVAxANzʑ )m J'p8 ^0E5Ŧ 䌥l{i!{. ٖZ !\ e{O=xĻrjZ$ Dz-=QX;-F1;I۬W_otҢn Bv(x7kܮ2G]k732wqUY̘?z]޵ ؇sώMݏxқ;oՏ>P*[DW]24ǣ\:o^zjU4g*n *5"JUrvbJڱِn=Wnu!r DM( ߞ$sԐ!%;uIڥTQ}{u_V 1KG/:jޠ!jnJ랕0mPw43U07;777O>vIƨW܅wNqWtz,>eOJuoV[OPZɢf)w=tlo֡?:?|7u suׂNZwpl5<H9ȡgv4يly[]0E'E"|s\$XJmO8""9 Cth\A֙{=v|6 uӨ8t~zNտ߈4Lsl4TtvdmKnO5:'mow#pJ a/ND4byzݟ''/_oIŭS QA5@$AP4 ~**ZghkM#iYv$5A.ꯅHgܩF|,I&IT ;`!.Id7Zlk?r&HXhpЃ˱VSu/o5DLXߛ|gb`Ԙ: S ?ߓU_oh,^rn_p!ֳbb+N!S~{-,m%Wn}(p1Y]ure1TYpB~:-CbAc6NV^ qw!+)&`+{,hlA!RK^ SFJ*O^IЯİތwJ(S+_veqe91g("WG"m jC7S}#8SnY$Su\ĥp bYvTM@:|N,#Q_3~dv1ceëu[/yS}43dVjo` ;IV@91 5NJ 0 z0'׺e'z%&4RYF](=Ȁ~ru\d.#2/Mh5X`/coG{o<װhfr)-!_`q$To:Ę9~Tm@sWߨiXzœ^E3vh\NnJh`ѷe$ԆAB)BےY(hx^+_vex83,2}E{P +33}ptI#m-S5Q-k<];f"]3ɬ|XDdB{}NhSƥ[8gͮ[gT]'q(Ê~<ndUUp!Ti۲^/qU<ccFİJ-8tH.>Os[ d6ONbrxK_7›I{}|rBI'9.ܬg;;Y㧑xNR.P:bi~c­ |"Yt̏{N94s4%^%u&ymov/(RM.AUyj.gxv*s"aj|vnmK@a%m9hnlH/y{RZS4wF TԉT_Y}Ё|ғkyKB ̆Tcі|EEH#Aj6*ba>8;nGDr7.4sQI[4XEQft ?v'_ŝeLVwCZFc[SnD'U_s+Lwt{Ϗu޻۷APgtoh哻ӂ8Sxϵ C446FkW3C݄C) Id%;| _j-̬3ZXQ3ce& l€,7%N0}5wI^,]Q!V|$,3d} zzQ%5CBYL89½jRT^|l:H^Q.O)!(I"wdΠ8q.7յnW/kkfL۪Hq5=Ǘ!կ]OjX NSEf8}R8ç})R XZ@C450kSrqzkdq fGZ$mќ+)IA.LOAH1iމ=D^ߥĤ8SA D+nNsEB17!j[}#TcuP7\'FMyA&΢Sԟ*tд쎦QQgΡc,̝J 4J\"moJa<4B4Z\ďUϑE .)kE- 2؂h2TmBcJ 8{ ]kFN (!v/[n4鶇5 [v] . ݙzΛFZ7%AЫ''MoV%•<XK:,Zo#QYys8EcƝ^ҷzm˕²"\JԎ-[s6xYIƸvDų=╹^~!X;M 70E^b>~5-{ܷ/NR{l%+(z< ͓Zn˚ބԘ CfDÅݥIw .˾-40D#9LOZG}=ElVҪSW|·ܼ>zA%;Yvkc~#K ahEYⒽZBސ}}u nFD#8h1j~svڕ`x#S:822,Ycl[3'~V_ƨP̎{Q3ynpPz-=z{^O: WO:UIMߥZӯhTngeyJLzvifЮ muįR;`d񿭪`mafW 5s]Da;ӂUM=<-SPP.uhGavR*Z׻ )=]QZt)|^Yϩ*D2%EaGCJ]gH{;z }k9;dWn >|{l^fs[W7+&I6(zŪ[a {/@d =?brc(&*j,i٠At=g+odA}8Z~~o3"*c]F#~Ԩͮx]Y]>FniGY϶6pnTT%v_xzynd?b *=\0#ZE)Uw?:txǢJ߿at~1+Qw DL}oPÐeVϱs̗bF']ˊ ئj[Z@\VFjjRW;"pUv+ xݳw%iz~ǣ{4q;d9@5}#EL|Le,trV<(9;Ⱦ”wde6#Nv؄'-z:g}ˆU4$_3paW-S(ی==^ׄx$Rug`eBv$GGWVN4Ѯs{upYWd`?1s:kGVMNSI3 YnŸgڙŸgQ_W˯YW)/U>9ʞܽ-Mw#?*S>tLP#׮]qq3g$VaBo·Yr|P6:{a̒!IWjuX4LWs !w/"NQyqxrK2Qb]ۇ[y68,zŐ23n T7U i>{O+];k]rZG8bxՔi1Fkj>b#yͣ*7nl5/}(:Ywd/XϚ(D:n}OqǑs#5FRWEK:uּȺl9Zhr7UA_ՖS{?cV㢚',"'hT:GgK[-v=:%JJLu dr;Tڻ9>g,D EvQ8fNV?}X˳l%/I.Q$ uɠ1KtAP10`X#(*p9kWafzh},X2LwF:dq*Z@5_mZA`[PTp㬡Xj/E5tv +'&&e\f̼2.r?Sn~*c:+kPK٘)4 UUd6=XN{aaݪKwkcj\e}mt ]/KmOoO]t]|䠗?|W.ٹu- - )&#otm8bkOuyWCFiaV锯ֶM/D*Vwk5pp{^h:|Ehk'Djə?B|blxcuj?I^RQRa6߻om$E2X-DԯҖzn?4˙B{ܜ|jpUS$@[HٷfJ#SLF4`(zLڡ_ ʶW$o>`"ϒM`UNӼE<-Lf6|bf[OWy{ϛ=\|h]ިzWDcp>=;v9b۫i) Kjx!ܹh[D.i.lhUF\k /X{^D]jL9<{p%g;擉:]V~S 36 ya`ƺ+[>zy<6Z7o_SX09La_B-wlhE×K=rn:mY3<($rnOCm?IeyL'/ybylr^FEQ1[:v\d9 uܶ0fZH ބbO>)qUC+ֆtvw?+}~XqWlH`9p407;wO^4Yz(6)M&~1w~s@`-Oc5j'ng[aPmbkPvW3Ljʭ(XT^szn M 3BܙKGm=L>UIA4 (MV3aHHWx-"ņ5tJ$}y\䀌F?;Gߏp`TjHvͤCĪg/HiVp|kOO|x0Ԝ#Oj_4&Z Muî~p3=q=C>V,]E(j[Xxf%&lOkDwrnay?FJV &lu؂Nl%2Uə"{Ean>satLvY4%MbԼ0ͅa;kvu<{-˒(uQL@<={M6}l'Ti0FϵTr,}0}`ZMZ/9:%}Oil+{A*cX) f{ܹKuuy#ov2IA4co/i k:wdzg Uv/b4aۙ5Rl ybNt~_$69z!9wTXE.v66&=~V{˕KםV]kTvh ''nXRnt{'i]cb#]JJOzmzW)|}!2iy.Kp?w{nZoZɫs؋9ס[7NlzGG ۈx,O|l['; IY\b9̭xyQh>~*)9Gt}Zg/  95gW4|6H|^LSRH1+ xf rvD=~" {!u[)Iy9k86n}sP't--t.&j3e-|QcStOGXa:-LǸj_v:6ab`aL&I1ݶxAE)/naEvu6>Ӵ*$ZԂ~wTU֤|=QtwRv8CPT m&Y^ḡ)fڞ;1b. eGD&WVJ98VcaG](KJ m'Jcީ4C@7Be'q ?F!du:U2ȅ\[uaF #PF~ ,J&78V-F#|Hޓ:=vS ,<.jj'FW:r]Չ#M>0FGMG'nBo*sp_ͺgj{Ђle^0۩9SnŻ+ ɉYU_?8iPq;t\FUUZuXX"kvxbգ >:N=T#-I$U+^kܷW;&~!S+P;,?MM7Źnf4E{g;s7-">N&!,^rzQZDT\2_߸ͥS ݫ_Mm460U9vMkٯϻresJw]BϤ}Teׯ=<_MxaHJq)Mrjki*c/f՛tJvVs/&Jf 94rfJ()4Y}Ӆ U-E}uog_fgf6r_hxBͺоi<&֪;9T (I9S.wS)atq_TJ\YsYNldE9[mBPW\.?,JaVv1LS7zxxxk;CO6˾>{\HtbIӋY-PG7_+ Qʌfzj9kDdz>5vtdBm&_}\ u=cT(%Z}m*_|jp{_]mJ]Nw'S,Z{61卂J'#Q#KvخG23- hdgU.6F1f)]f*?R#Vc*f8QTo*S۴5}*ƼFTS):B*[Fk@ 7iX1aU̧G1-U*A>٘Yh]C!Ʋ&oGuJK_*1Gy![XgP +12uV=+Ě$͕0-izȪbg_t|* G9tGE^Z}E|K,Pa! \2tڵ\QSpX/ ~iKnL%| [Qg-nίlcEi4k#ÝrVHf<탖1 MY۵VɿNk»UʫJF4^J}5,Uq}1=c[6F^)C&{d>(͈@TfιkzO!˰M eۏ+OܸKyw;>bĮdo֨Nu?0#?i{qPEHQ,3.,q(^n 3j[BՒBʶK2?wwӼ=M5˽!(:AUpsӭKe(p!LZ Sﮰ+A=Hi 3O\IxrG*o^d66/C3b}R^β '^wkDz>Ym;~愛oL>IcWXhT ԼILWo_.8c2\PqN'HZ dV_߭wLVFhNwZ9aOޤC*̜R@[һsCM.Dy]>Z5~qL`]X]g-yRMվtJǟ]$?I4&vzg[:ks= 3ږ%oIPcS{- d=jYjGt P.wxc~/:EOr`Y9S/N32';VaΣ%֥{lKhvcrrJrh`$VP[JR'oyb%o]K7il/b-QáDN6/%ǾS+v~LM4"}IgcDV}IOS(7=*ErUξ-;yS{߉$>P3w!I͚<ߍ'=iht6#Vnٸfkd鶸9dNh]N!] 1gD\aH \1⅕eג4cK{6iոPRi-O9h9ˀy4neQIs_!8hN]'fs3ZVT+-$6H:-]x캤d1̮cϖwj Ytߣ_7Że(M]-⛖dg4+޴UE1Ff$pb* n5h;ly`yusBC4{fDfZجmߗM$AJ^9^vӧykMiҩ_3AB-JFPqܸ*67|>Rv_.FM#+&zON:Y#/\7 GdbK "oVFuH%["7RbK^^r:H>~mv+S:oVRo\дSD3ՋY'J6޵N/JvS % hy޶Ɂ^H;ғb8TyltE+:bI!L+U|:ƒmoq{aˉ+-3P4Cܐ|nZks7]1l0Z~zk[fO:iʺ32 [&"3uDQyk,iN$bE($ H%)oߑ!T#,tXs$AP,>ː4g$ \NΠ65Wg .:qLDBK jARv,'mW|d7m?%&a»Z6J^|`y0E8a+=^( `Lj,e[uDxasW)miZ9{F؎VzC6VXMaaV]%XVRM T,`i,TR梭Wk*|ɰEtKR2U9#W Gj]Q~&!HWm%4lvkK>8&ۊ.`6iHEP܋YbkBot`s>A#- Z`DžݛFe;/+w1:`~}KSi'$E*ە9M"kΜ7)zr"cVdu+:aZ#bo^z)7`Z3v$١F6g?ͯ)o;ґߨ94hdSJȎlj:ӡ\$t[ Q5~Κލ&?_~q6GlC~t˯|ʛSP PFeDQx\o EB),E;3WaG>/ HcNnx&/(j) Cz@LX\ j^,-LDq@<qRᄠW`8.Aj6._6~s)̆C$kxdSE}C;ˣkѯd Ƞ9#yd3_D}g< (E'usy?Au(N'Ǐ(xp~g( p :Bx!ߢ:1tQl CAΝ/qC!灍/_>qI\ <5|~By sW/!?9C]kA;, &{{ӑ_bڄw'戟aG *k_(g{Ɏp^3̠B ׃00 y(׿ߑK!@Y8#(: phpȇ򐏷޾x>Pk @>y___A۳ 3sk_ @| g YIho(N`ZSߩVE ygN|^g٫p6s xxq ƐFX_y(`7}` ï6@8>ġ=^. D(@6=p|iEޜa!<Sp|? yOATq:ZLGq*B[iEp}rBzFt`BSɐrn^Q__n,?pnX7AC lg @T: By?g2Oj5쫗7 aF4Qz<0. H_04_. a ~C-#_ʠq_a>8xl q쿦~e/e auuQ"GW# Ka/QQmA71QIjZQ4pV+*`; 9YV͆Sjŵ0n"wVk=墳[mѨan(6ִV~XǺP5 'j_@P]`TV:QveMVvr?|mg6D}BۘqEٸ`K7+yQo߫>. LA~ex@^1}tW^Y0`~qxÝ:M~ץA]#:.y0.?X gNA-Bְ[.hmHx(BgpP}sۦ/ 22R>(hF/Bh x9(氡! ##kPoxр("~P6uPTa#zq>΢jf͠~:.`<.LC8CեWp,f`-$)>5q|jƧ|j|jHxCQн,#<*~vA}񁼁iS~Lߕ/~ G d+X?& .>4Y:썰u\mLԝ'L cytbD _ƒ>A0d_^Ӿ_pwO 3dāv`~t{z l 27#A07y{0Ηn1ǣ{~o!"x,>f <Z|]BzxћC-ڃnjxћC×vp7p}/ 27\O>1'u@?pzOB'~=Y6&7Ͽ{_Adwc{pz"l7w 71f &-W[ xOz{f `o8o`il8'~ozˠ!C~GoI xћO{_g]`o8zzˀ݁M@X`oXpfC/_ƒAdw^Ǽ:&7Ͽֻ/ 2;zc:7<Z)4l`o8z{h2:ѻi֐ o! aa@=`xћC}/e} k߁pz"l4 |̒A07y=ޥ|Adwc*@{o8zbHVD`oAdwc ˨D~G|Laho Go7ܗ_kmx?Pްְ 3Ba.s ?ҹxYε|LX33t&"\ :sQ۫1?x9 q~׈xFM7P1? &4PH@!= i3~(i!Ө=|>4nyx}q| #Amt و_#)(oD<%ԒoS]Іxmk^{@u5Ss> DP/0?|nl3}Oeia?#?WK(MD.@.ozQ\BƤu`"/)~w0{_l#'V_됣(-ޘ~ cvTA@ rrcG'">s Lt+5d]e@B?*e}[򗑼K~F_QV_z (ۄ4"}Ńoo%U?/:޾x^ܾx7mPDt}oO&2// \q(q٠Ȇw0lE~w(>-?Ta,ex<(E 8a><4** ~=p?(O-(D#9 o>@yyF>K/`'xsdgW˝S+| _$^f3ha] 0@h;|vz :1>S U&*vl}pCa4!7xYHN3<?ܿ@OhhDUQХ}7 Hсu!ey} :n/ܟY(vсp#)ꃯ=| ^.(*DQ-VӢý1ߣo} g7}'}wC9>S-ˇ<c?ױ_m;C?iP#Pʠ:Ag^Xˠ? 4,, 48 Ðàññìîòðèì êîíêðåòíûé êîððåëÿöèîííûé àëãîðèòì ðàñïîçíàâàíèÿ îáðàçîâ. Ïóñòü â ïàìÿòè êîìïüþòåðà çíà÷åíèÿ ÿðêîñòåé ïîëÿ ýêðàíà çàïèñàíû â âèäå îäíîìåðíîãî ìàññèâà ýëåìåíòîâ ÿðêîñòè ýêðàíà: À={a1,a2,a3,a4,a5,a6,a7,a8,a9}. Ñ÷èòàåì, ÷òî íà íåêîòîðîé ÷àñòè ïëîùàäè ýêðàíà ñôîðìèðîâàí ýòàëîí, êîòî- ðûé ñîõðàíÿåòñÿ â ïàìÿòè êîìïüþòåðà â âèäå ìàññèâà ýëåìåíòîâ ÿðêîñòè ýòàëîíà Ý: Ý={ý1,ý2, ý3,ý4}. Ãðàôè÷åñêàÿ èíòåðïðåòàöèÿ ââåäåííûõ îáîçíà÷åíèé ïîêàçàíà íà ðèñóíêå. Ðàçîáüåì ïîëå ýêðàíà íà àíàëèçèðóåìûå îáëàñòè À r  A, r={1,2,…,9}, ïî ïëîùà- äè ðàâíûå ïëîùàäè ýòàëîíà. Ïðîâåðèì âñå àíàëèçèðóåìûå îáëàñòè ïî ñòåïåíè ñîîòâåòñòâèÿ ýòàëîíó, äëÿ ÷åãî âû÷èñëèì êîððåëÿöèîííóþ ôóíêöèþ     4 1 э a j j rj r  , ãäå a rj – ýëåìåíò ÿðêîñòè ýêðàíà, âõîäÿùèé â àíàëèçèðóåìóþ îáëàñòü, à ý j – ýëåìåíò ÿðêîñòè ýòàëîíà, ïîäëåæàùèé ñðàâíèâàíèþ ñ ýëåìåíòîì à rj . Îïèøåì ðàññìîòðåííûé êîððåëÿöèîííûé àëãîðèòì â òåðìèíàõ ôîðìàëüíîé ãðàììàòèêè, ïðè÷åì ïîä áóêâîé àëôàâèòà, ïðèíàäëåæàùåãî ãðàììàòèêå, áóäåì ïîíèìàòü ïîñëåäîâàòåëüíîñòü ñèìâîëîâ, íå ðàçäåëåííûõ ïðîáåëîì èëè çíàêîì ïîä÷åðêèâàíèÿ. Ãðàôè÷åñêàÿ èíòåðïðåòàöèÿ êîððåëÿöèîííîãî àëãîðèòìà Ðåàëèçàöèè êîððåëÿöèîííîãî àëãîðèòìà ìîæíî ïîñòàâèòü â ñîîòâåòñòâèå ïîë- íûé âûâîä öåïî÷êè â ÿçûêå, ïîðîæäåííîì ãðàììàòèêîé: G 1 = (U T1 , V HT1 ,  1 , P 1 ), ãäå U T1 ={k} – àëôàâèò òåðìèíàëüíûõ áóêâ; V ÍÒ1 ={sigm, a1,a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, ý1, ý2, ý3, ý4, 1ì1, 1ì2, 1ì3, 1ì4, 2ì1, 2ì2, 2ì3, 2ì4, 3ì1, 3ì2, 3ì3, 3ì4, 4ì1, 4ì2, 4ì3, 4ì4, 5ì1, 5ì2, 5ì3, 5ì4, 6ì1, 6ì2, 6ì3, 6ì4, 7ì1, 7ì2, 7ì3, 7ì4, 8ì1, 8ì2, 8ì3, 8ì4,9ì1,9ì2,9ì3,9ì4,1s1,1s2,2s1,2s2,3s1,3s2,4s1,4s2,5s1,5s2,6s1,6s2,7s1,7s2,8s1, 8s2,9s1,9s2,1s, 2s,3s,4s,5s,6s,7s,8s,9s,1c, 2c, 3c, 4c, 5c, 6c, 7c, c } – àëôàâèò íåòåðìè- íàëüíûõ áóêâ;  1 ={sigm} – íà÷àëüíàÿ àêñèîìà; Ð 1 ={p 1j | j=1,2,…,92} –ñèñòåìà ïðîäóêöèé, ïðè÷åì kxohuǿu{wd6\bYTT#-*EJB$bZ7VST *E%M}?0+^>|9w>wFܤtѓz5+i< 6s)?R4SN/p/Ua޹TwSm`05,mOm-H5K_z.J$ R) Dhb~_s?G-^ǔ׀ߠ#~v G[:9ޏ_3hJ5C]:\ V:G{rG!9xqQC/p*6akE}]p0U_h׀W.xOܖZPW>RV][@ xjCCί@^!ߟl~>oɈUcR8/2-I-aN9>|o(Xl9nr (1'Iq~D|r;M\h  ?u ƫf/!t~m--8n(5pu3wP}o+_"p#=x3zz~u"+/0^r.c|٦ {/uJ,QJǔ422fmFy<>fMj 5u>^ 5=Z!:ANu_C(s/̽j ^ ;hg{&,1H=> '``bvc3 4A=s+ilq^A`1 N?Y^q.xX;ƒ^x)Lo`O7=?-Sa3:i5j.uڬ56ײcfg؛41w %@nr2u!si?z4 6_ J.P/_ ^q^s: +YDqoxfy̏ꦓ{1NjT&S:lv':j/W)-/oz1+]ZoC'`Ib͝/z?ջDarl)|3UmLp9ߢ9}w @܁q̠\w @܁qځ"WhMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:16  > R(162/ 18{`x ]yd0O&baip ! ۣXP(ar!*x`ت6!V]<ʯcC6v@dlz9shZ}O~_w9wQ$;.Y$6,MXz~$t.VzkƔt r.Ң;gd*w uJEM](a d)?2{M5,ɤ i׿ฉ7 oyVU춥.K޸wݞ$˒+ya{>>Yi9A~[;}~ɣ߮/ܚ\˒˶&d__1Ovݼ~Q[;7FUds%_%٧aM餬n{Y.}k[uҜ-Wv9JX1/|GY)I6) ҋUhC߯Yr+%1V*Mt %o.m[v ?UF%Oys%*t*9¹m;~+xƏ̼1ܹyt|!Wu&͋pntn.U^67w0|"ss7+;w;7H:7əEs flJTCmwJ[6t^ EGܱoi $coYd>sULH>5}| $Զuz^T)5̜uOHݕ{9s7ՅɆf+JBHYs$J.쭝5ӎulrl}}rc_yjc(7=ӕx7}ctCv|I$w/Zx1bN;w&UfTcY_ޛ }7F7nu㴬\juJG?M;yΚZ߻Y{ߋ whL)<ǁlUDG=Jf )1 hGOʽE]aX 0,>Q sJ~:++{?T~X: RBB?+U!6zAXXWwM yKֱꔷլk!'|sm-w?P?>~1,Zۀ%nn)B B^djvR7ܡY?vzB]J ~Um@P F}Fy]VbW.a?ׁ]m%'Wz]WG`WqKܰ+&BwR@}/8Z5/n8C_7^ ^3؅,N/.xAl36 [("Cw:5}wޛ2=uѰpIqKܰK2B^dqu ΐ: T,pwV ggL+ UвK93Jҁ pdؠn,NnM3Ů]wԁ]mܥ/_]tВ]p_]c(kSg3 Ϙv R7Y/vzB]K ^  ř#!vYy]j+_皾ڸ۽/sî ^8C{aya u]`.dqصۀlX"v[j\U^~]F5U;8.ф)vm|vΗ3s6zKܰqЁ3Yvv>gxbl.dآ,.jջWJJVbXZʷ&}acbX1 X )Ý*G!{ߋ [}~>[y^E|&? 6!6  {,Ce#jk>lybWo ²!YyenHc_bY1?aYU<>{b'oteNѷY M˖Uo)X,VHWm>lro ²onH!Yye\w-jJv-ظ^5_n1V؄%nXƸ)e>^dX>#|GL\Hp+1nTĚT*2xĵǸGv2~1{ [-ȰEZXW&5%qXָKu`Y??ӄzsXVXք N1Kܰuϐi&.÷{Eg? 616 28FeblTUemAPXFΜ![,k\\:5ݯh?7,ЁcY,~BGwXH}`Y1z,cŲUX-pd e`veVbY{:b~%0>7 qKܰL2.C^dX6a#u1[Y㻲1&G 8!p78p2Lq Uq<"1z[a:97nb*Hye˾Rq&~c{<|O\>l[+p_V7RM" }/~1~GwXH}e`2dXv Xۂ,{̝C,},k2}JDz:iR\f?7,ЁQ}/,L^p n귘ѷYX1z,CeeO#b BawT7XvT!Yye,kR pᱬ1 _eʸ (Y,}V,1^61re8ƿz\:?12~1{ [-ȰEZXWK\v#S]8F+oqq:n)]v%nXx%{U#q #8Fdb<"X Yz<"+{[+e7=`Xf-5..:5XP_g}ռqŋޔl/_%ye/sòlF^d^eq1 X6_wu?2YT= d\m[Ė#-Ȱ7S3ܣ'c~dגp|7I6%K.Қ{E}-ޤPJ)h+oqO-M}7(S:M _7$I1d O~+od'_߾Z{>mU7쑯=g O0>:*}z?HXz~|$|XmA-dcJAsK+Ym<++oq:cn 4O+sZn_Y ך1 - ՚X"ū9xuO hiW嫕|듷%HޞVrqgnϼ)ųۖ,9|;:l'2c$Gx@UV/:鈭 &W}lk 9j`kn߼N}c}^|I%ʯz ъHgm[V/u4nq˕l9˚A::p xf?7΀Kfb1gxfo W{yGh?iPV7x?H;t,KXg /uEџ Ox!8mǍ쨬lLA96pR~t W#쫞2b TU _%pr~dg\gz|l> )%cݒw^XyO q4't,ֿ':w$6KW&gJ-2e!'|,36{@Obcn1ghcs y_1χC<2S _V7Ro)3,DǴ|&޷#*.)\.b!|[=HG@+p b!ߧ؍<0Wx[WsY#qqNbkʺJd:?:W:ik놩gя6L9:I,gKz 1[o\:0ت[Ǐw`um߄%nϸ)a>: ÐWK`DpR|YV_8Y0c>X̯zNuj, b1`1B|VJ(g-SѰc8Py]VbWoׁ]m/S{ ZU?aڄ {tЁ/>h\_ _,Q/N/O.K.7/ns_t҉J88 Cs벲"بO*aK<G*_mNw8~Ŗ՗dRՏ)َܹ,㇭ٛ =jY9cFޤs[k\ :p}{sgp ,1|Sy_xW?Ro\bk^ VׁW[]=^!ūgWpauY7x$Uū&p=j!^YyW[^qDGw=K`TV/2c~ɟ[ݴ Ёeob8ü=3g@WӲ( =^!ëϽ=dUdzw bSWVUJ_c1Me?7Ёeb*^Purek^ˤ>z>pWو>-KKW5>N|տ{U?q񻕇| -^5.J_c1 0_W ]*+|>_d_Y>8?u +@WbY5שd'#eQ/ȓ<'hq*1%Qb_M]{r~4:Z5.̘1 bb-tO}18*:}z.? ncXZ/.?lQz[u]\JصB&emո:5}؅?P?=-1V_O؄%n%XЁ/{#.e{ B)W6'DV6`G̾!~Ze+GQ VŤdw{WԲ6Y{Ů]zj.Mc9:(Į&e?7b3B \!@J#xp/vS8畷?Z_[bQsIcq`}D/p5f ~A!Xy?vՁ?uة?_cOb'?OL,_d_e[Yn:|ȨCaGaUx Y,^U=;b {-~h:E ūKցWuŻ+|Є>)c܎YWuѰ:͸&K/sëxiB="+l/1Z`SxTVVT|=ӏlW|ۂ [btO=|G3IĒ#>.*g i-^5.^xU=>[[n k&^͵s-r; ߡ?y?%nuӎ<~y晴S qlR`'b -Q]9u!n7XZ-;ʮQ[,.ֳ4|&p{Bܲg=Tnչ!XVc4)2c~ɟn1eE/ { ,Gdx/ Y,^U=:ۂ [TlE^vـ]CsژK_c{*ژX۽/s.B%v_~@aW^v#Gu/ T6#\uI=[T@ӏ8GdpVVbS҉=ĤdsWdϸdkU> QZ̊9iV۞QTZ֯VbW\ӷqWc9F&]/s.AO%v?.F_Nv|}Nzqn頑]K[ϼ ~K2lҽ+k~v-&.+oqqu`WwK[zqcktZu1 hGg5tAK"Y2oؠl;XA/nD_7Lxl\`\4dV\ [cmAӏUk_p-fB=Rչoc6?4c~ɟ`_d_x4Z'+ae8.]p+=86L&Rګ>BlṃdRWsr^b6wǐ}'~&ZyWԁWmܥ/O]tϰ>B!CqKv][$Gr"׃We{㮜:WwKxg Y,^*B ^W&jxŞJ!^YyW_^DUc5K*&B"ūQ|Y ^U|+XzFN8?l9HmA-U{3,юt7|z/A?:XmU▕ո8:pJAK…ǭ:(ĭ&<+%n%HЁ`F[e{Uu rex^xH9;T4VzVu-_V mA-q{3R6:u_jf"WqVbWb:5V״_]JBLX~T{3Ft2q{2:}z.x@ cXzn-(y[u]VصKxF]VbW:5}؅?P?>7rY;̧~.||e?7슉Ё/I/F]v}+ׁ,B c|a,vX]ߺIr8Al9I_&o 2lƔ#}޽[T)]Q0r!gh}it9^u EyaVbX67Xx1Me?7 c2NCCGlĞntte\ ,QOfo<^x>{8ſSlȳ)+ƒM*퍇7cSG*ST>SzƸo-G ÖRl}6L(qe_ˁB[6I6U/F@T{xnUWo9-.6.{\lc;Mcq1 q _熋!"\~ro`{(#ݟNd1:H鋤vDN.0ԸS /^8SYL[˰^l3،,WiHy^[>mA-Ukۧ>kxbͪdQVbib':nyR2'%` HnƓ9F!6/sR{HKH/*E_!FI* xR_V=E$\(xO Y,^{;% Uz[aK*WJ/)5_bŭŀOՁ[u[ܒkq1V7ڄ%nŸW:~Y,nn8Ї+Ł~;+Syx5*T*-x;.)*oAƥ[@-Ȱ"5<'Oя,C߸tnщ,#/O-:oYL_n/7_Ds4h/k7BZzoW+3ũ?댁{|xxyKnG\lH΋$&ĩ/s{{H w-ߊ{_,ƯzGΣ|^'{Զ=Fhkst"CTb:k׃0\E/o+EuYصlY Erx]lYmA-+#$]7[#qYLc;:/t~,G'2tf5buwh3wGm3Nrt"OI م+o#c=RglzP7g Gp=%n}H _٢rtW_~UXq7u jC7Û{GFT*W1n[nRmA_UɩYLydG9:#Ym.ߕ:dL|~{̟Pb8:0 )=~Yc4,C8?aV%oDy J/kk ͺpXV65)~9*<xV_'9Vd,trO]+gmFCO92p:JԾ''gm-v5.^}3j<ˡ1wް KܰK.Ubd1K4ݗ)tѢ_%EbBjˁGȰ ʮ.G?ܞR;ObMJt^:5t덍'zIb{a#9:dm%G~P)m+oqq1:nq_o->7#x|35 ga_8?3>-*G>=" j }.8w.=s_^1=` ="[AmA-p ըuir,g6pi!nYy[+ڸR_cS9Fòp qKpKЁ{?,~)h-Xi1u:V n{܂?í+ul#z[aK~*О|~*-Gps[\&e-v5.zs=\OU Qv5ẬKܰ+&B#îƁwܠ:ߥ\,lL xt;xƍ#[$[mA-ҺR9qa= 9u =j]_tINd#10Gm~k9:>M߅oYZyW_댅|~ߔ\M?>:T~ϳ9F?&ī/s|}H Uijy C_°;wu:Yc|lg3{h0 ózGU#^K3mA-*+%PQ%J!vYy]Wց]uBbbޱ"}~4!^5c~ɟv1esс/%዗}c6qbI~KCl=?`M޽?nꆃu#4- 1 L,V8v\rxVla >)?}g׏,A&%颓=^'2t*|+lFhX۸Oы,y{x^V脏$s:JjƁ⿕߸5댋|z>C7?Jx$uѰIK_Ud1~{\٧Nzbt>[75t^:*>"tߢ\,./8TW×tӏ*Z5|9ۂ [*Zsا~#C #{xOӚ|gXks覬. ŌK2qR~sx߸xQxﭪse}}?`H|8{_E_.;Mpվd1 STjb1YU;e+|4'ۂ [+ n7.-QVuV1Pg_Uc4,eՄk/s-JB~#ŭ{YJ7uG:ִl)-h[bq= eNᜱ# 깗Bܲoܪs--ni:vͯ' {}%nx) B~#~Y,nsre8odeE1F,ނg#Oe JcF8̪g!]'Uo 2lDJFLws^3:J _i H9Xy]^ZvչGJv_OA?a\V%v_̾Vz37Ȯ]B_^ >+؅,Ve1-Yw!`Z ]~s CwPvqG{Vb}"ď|[v_kr J딐$JZwkg?M;.t'/F]ܷ<B_욖-e|!_ 0}v b mA vd!֏]vn4:N.Tbո:M)=aޤk]/s.R tZ:#KTwqOw>d%%grTv?FN*a|-Sk"č#4e =dw]#DasL:J͹vKL^x$>sk>v $-d7c /s{ֆCJ̛<_*~Y_]-=/Qh׉,F!E&cv{)ՅQ2@/ ~p^/NJOQ ZׯEŮEFUGZdز^HTGGY=:G :W8Lrt"C_nְyXr#ϟدYn1Þ6A #VޮG?Rz?i[1JݬGX4k|#u}ߤ/s[0CJozdс_erXqu jCÍ|d_ n[xYLUa>sɩYLydG9: ˥IYmL?[i^'ڄ@G) C̷AZDe){uѰ 7oy_JG~=~~5Zk9\\٬kY٘Ãu AYu_9GƳݫkUN[dtqmjj˓ߩ`o-v5.^}YUg,|O2GJm:uQ]M؟l?7b۠_Wr#/pm~}z4i0 cXLzvϸ~[N{[a~ˮ,Ք0^y\b+W6PV6`mgRh-t#ʪpUW -Ȱ"^_Mq8w;&XXLU=r?W[|nWpx\g->u`:rǮ \KqRo%B^XLE \{ +ʠgiRv?upmׁW 61Yz?Y{[aKܳ@;H5>3M'ZzJkw&X)ٞ5$y[μ{q@r-oiKWvA`ݒ:z(/>Wԁ[u,=oW q1V5)4c~ɟn1U0ܱbqÂ6| ydGu#ִnp<-d52:7H_ۂ [iDg+Q =}-vA5Pv1h=`1qgmkV3Wo?7U؅|1{/F]G 8mTĉU8T]p[:w9Ⱦ2CqvU=kt-b  A~i])fNeXϳFcCNbks\W2:6L6i39uf~rNd1:G|~6o1=0~+oyū:c6^ ɪs&ū/s|Av%oy C_°5;cgGWJd1,^KY=#g¥b ϯ Öx5g_'GV;Ů{>k~!vYy]FxDƫ2mJX\J⇕ K1ϭn1Ě/{Ǡ_ʽ/F/K.g=sTózz-Tp X")Y .[V ÖzߘRx܃ƪ#;VR]1c~ɟVUY҇o(Y V$o* X^xÆW]z{X }pOI?N?TVUkN߼-Ȱ%,reUv=V]61jDf-V5.:j*MңKV.2Iz˼1ϭn1b]Wr|C?|׏,"=V!*UUp~AYkGg1 b*tEU`<~db<X YV|Nqm٠x_:˕z^El V!VYyUڸ(_x1M^e?7۪ЁY VQUpܦ\,)/'CpWL!O~89<<8@o  qg$ /"ިVrXոUu`UW\z, {RAcZ#2v ro20}PrmZ:hbffu>xZ'P⧕ٸXg:nyI|>SJ|寽Osש)uIKqR¯?с_#ޯ"LNsw;4>"/rfxWTƳ,Ɣƒvr|J_JKv'&iJS仓gaI9^߯&%?P٣}J|w>VaI?tϢ,?f1JPƀЁtIV/۹.SFoQ^e8% oaR=ɗzLzOTB~WIul:Qshi`lp0){;0Cl&iNKm9Y]:w^gLOiV=hgΝ J18ZJa8EuUۀ6͒}.yR_ڲK-VAV+Б0)ٕL3>,zҹ>(`1y{~Fș/¹kʨ^yzkaDFҖJ2NLy' g0$>!kkES̵~!1Vd_|1Z{eCځs>g6Z;)[!tN0̉*%wL)q^&9p;B[|O^D;i^fוt:ݣ*+k/u<YVb{A w N{LQHd߱{3Fa+!~;1}?G6Xa;NCC{aEθҸ1O`-rt:3\$/:XI:#caݝQvkSFfozʀ@uFC~gs+}{Yg9=>Ջ1>Dc{KL1^WEc~|kp;@F58kmډ}fK1[nӾ Kfc:y8ygbaH>sq-*E}4!٠֋<0EkS#/^l˕(_D%kʙW*Y6Nh'vsdZVRv>>ɬ?ӏݏ+pevҏsک~1N+G֏54!rʪ 7ӑ|vigU?p>|]z1H{>NqN;Տ3xF&OUY|\c:~N#GZ>GE?r?U׏|LGvҏsک~1}jAPe8c3~N#GZixrߏ_PY\?qMg5; qN;%i',f}"vުZlCź\e:y9OY5/ie8/S/:_O*ORӢudzof#x嘫h+ssN[%U!Z:{nC&cn^=;IGsv27SI;& f=[~QesΞnV朶/ikܤfG{n>}~.pLq_spvҟsکi' ytvC?Q;{s)UQZ:{+QJiVQZ:{~QSG:w>]樍~:KI>V)mSZ:{~OM`I(խ3rǐ޳/AZ,,49 p 11 : sigm  à1_sigm; p 12 : sigm  à2_sigm ; p 13 : sigm  à3_sigm; p 14 : sigm  à4_sigm; p 15 : sigm  à5_sigm; p 16 : sigm  à6_sigm; p 17 : sigm  à7_sigm; p 18 : sigm  à8_sigm; p 19 : sigm  à9_sigm; p 110 : sigm  à10_sigm; p 111 : sigm  à11_sigm; ð 112 : sigm  à12_sigm; p 113 : sigm  à13_sigm; p 114 : sigm  à14_sigm; ð 115 : sigm  à15_sigm; p 116 : sigm  à16_sigm; p 117 : sigm  ý1_sigm; p 118 : sigm  ý2_sigm; p 119 : sigm  ý3_sigm; p 120 : sigm  ý4; p 121 : à1_ý1  1ì1; p 122 : à2_ý2  1ì2; p 123 : à5_ý3  1ì3; p 124 : à6_ý4  1ì4; p 125 : 1ì1_1ì2  1s1; p 126 : 1ì3_1ì4  1s2; ð 127 : 1s1_1s2  1s_sigm; p 128 : à2_ý1  2ì1; p 129 : à3_ý2  2ì2; ð 130 : à6_ý3  2ì3; p 131 : à7_ý4  2ì4; p 132 : 2ì1_2ì2  2s1; p 133 : 2ì3_2ì4  2s2; p 134 : 2s1_2s2  2s_sigm; p 135 : à3_ý1  3ì1; p 136 : à4_ý2  3ì2; p 137 : à7_ý3  3ì3; p 138 : a8_ý4  3ì4; p 139 : 3ì1_3ì2  3s1; p 140 : 3ì3_3ì4  3s2; p 141 : 3s1_3s2  3s_sigm; ð 142 : à5_ý1  4ì1; p 143 : à6_ý2  4ì2; p 144 : à9_ý3  4ì3; ð 145 : à10_ý4  4ì4; p 146 : 4ì1_4ì2  4s1; p 147 : 4ì3_4ì4  4s2; ð 148 : 4s1_4s2  4s_sigm; p 149 : à6_ý1  5ì1; p 150 : à7_ý2  5ì2; ð 151 : à10_ý3  5ì3; p 152 : à11_ý4  5ì4; p 153 : 5ì1_5ì2  5s1; ð 154 : 5ì3_5ì4  5s2; p 155 : 5s1_5s2  5s_sigm; p 156 : à7_ý1  6ì1; ð 157 : à8_ý2  6ì2; p 158 : à11_ý3  6ì3; p 159 : à12_ý4  6ì4; ð 160 : 6ì1_6ì2  6s1; p 161 : 6ì3_6ì4  6s2; p 162 : 6s1_6s2  6s_sigm; ð 163 : à9_ý1  7ì1; p 164 : à10_ý2  7ì2; p 165 : à11_ý3  7ì3; ð 166 : à12_ý4  7ì4; p 167 : 7ì1_7ì2  7s1; p 168 : 7ì3_7ì4  7s2; ð 169 : 7s1_7s2  7s_sigm; p 170 : a10_ý1  8ì1; p 171 : à11_ý2  8ì2; ð 172 : à14_ý3  8ì3; p 173 : à15_ý4  8ì4; p 174 : 8ì1_8ì2  8s1; ð 175 : 8ì3_8ì4  8s2; p 176 : 8s1_8s2  8s_sigm; p 177 : à11_ý1  9ì1; ð 178 : à12_ý2  9ì2; p 179 : à15_ý3  9ì3; p 180 : à16_ý4  9ì4; ð 181 : 9ì1_9ì2  9s1; p 182 : 9ì3_9ì4  9s2; ð 183 : 9s1_9s2  9s; ð 184 : 1s_2s  1c; p 185 : 1c_3s  2c; ð 186 : 2c_4s  3c; ð 187 : 3c_5s  4c; p 188 : 4c_6s  5c; ð 189 : 5c_7s  6c; ð 190 : 6c_8s  7c; p 191 : 7ñ_9s  c; ð 192 : c  k. Îïèøåì ìàòåìàòè÷åñêèé ñìûñë ââåäåííûõ îáîçíà÷åíèé: sigm – íà÷àëüíàÿ àêñèîìà. Áóêâû, êîäèðóþùèå èñõîäíûå äàííûå, òàêîâû: à1, à2, …, à16 – áóêâû íåòåðìèíàëüíîãî àëôàâèòà, ñîîòâåòñòâóþùèå ýëåìåíòàì ÿðêîñòè ýêðàíà; è ý1, …, ý4 – áóêâû íåòåðìèíàëüíîãî àëôàâèòà, ñîîòâåòñòâóþùèå ýëåìåíòàì ÿðêîñòè ýòàëîíà. Îñòàâøèåñÿ áóêâû íåòåðìèíàëüíîãî àëôàâèòà ÿâëÿþòñÿ ïðîèçâîäíûìè îò áóêâ, êîäèðóþùèõ èñõîäíûå äàííûå; îíè íåîáõîäèìû äëÿ ñèíòåçà ñèñòåìû ïîäñòàíîâîê è èìåþò ñëåäóþùèé ñìûñë: 1ì1 = |à1-ý1|; 1ì2 = |à2-ý2|; 1ì3 = |à5-ý3|; 1ì4 = |à6-ý4|; 2ì1 = |à2-ý1|; 2ì2 = |à3-ý2|; 2ì3 = |à6-ý3|; 2ì4 = |à7-ý4|; 3ì1 = |à3-ý1|; 3ì2 = |à4-ý2|; 3ì3 = |à7-ý3|; 3ì4 = |à8-ý4|; 4ì1 = |à5-ý1|; 4ì2 = |à6-ý2|; 4ì3 = |à9-ý3|; 4ì4 = |à10-ý4|; 5ì1 = |à6-ý1|; 5ì2 = |à7-ý2|; 5ì3 = |à10-ý3|; 5ì4 = |à11-ý4|; 6ì1 = |à7-ý1|; 6ì2 = |à8-ý2|; 6ì3 = |à11-ý3|; 6ì4 = |à12-ý4|; 7ì1 = |à9-ý1|; 7ì2 = |à10-ý2|; 7ì3 = |à13-ý3|; 7ì4 = |à14-ý4|; 8ì1 = |à10-ý1|; 8ì2 = |à11-ý2|; bCxZOh\EMiSwM6E1VL(JQAAŃ4^lKr)("(J{N;*hvGg:V Cgq']/t)UrZK\oeާ.9vq~^~ ץ=84 4.FL> [ʙ#Vyہc%ujſkγډohJۊ;)-q}q!,?dgccEPnlYj59jsȻ,;;۵g^3cv[!zh?|ͳ׶ DQVlDg~@e$n/}kgdqvܾ8'<=羂soWkm >=c?bucYsm3uw,AJq_Y'̧YN!}|>Ӈ ӷ]Z~ = '16Rۻ|u{>uDuYIN{~^^G}2||'ը{){|ޟ(_%.[^͓#+#<8?yfl侉3>i|wO{6Q:|_R?ip~{>0w!Ջ7i7I/vѸ3Uq/USSt?Nן8M6[TJx7i7qv.qw]_ Ґ 3*ގ>ktgz|Vmsm^3iۍu]su_kESTv?:>v_Q7>uב\?kS?ϊ_lxgm DQ@T * D֍_VңQ@T *ب CZhMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:17    H  (16727/! 1 2w{,x]UId aZZ H! k^CM(`BeT~ j#|J[㵯hF-Ti" JB}9{{'wk묳Ϲw:BR.!cB!ʅ_BG8#BP@vƒGO8kaae>\ 7}rVה]X"t|Wd7`ѣ3*l@4I*TTTtT8#i9FzzJ*Ebg:2,:!iw8=&ƯIt}aXel[p7oϽ9Ǐg񴾟Kgڜ\|pG^utU; X0{tS\}˥}I6@{2hʲ-E{Hulle2\y{xGo 6(K)*2!ǿڔ 4h#csX)Ya^+K#_eU^} zpsDF7Mx o;|4ܨpml,5lu37iɳN77W>i|X}vh>o߭o~^]DVOm﫠ӿ>$Ds.CK):YSdmS$]P#D%鋂_a!Zi/O*"k+:ӳKd=I=*/K'ZӷLΊ|?=5k6~p zo99wJur램 3)W\ )cyڕzD.Z%NjkNN9#zDʲ\wUzUz\h=.,]ȉ=G,KwH*y=p(#z\T=)="g3="zZHY =>vL@NN9#zDʲ8*c׼.]ȉ=G,KȅW5Z999c#r6#ҡGe=`o?r'AGDurJLY*ezp⻈%9c#r6#@)_VCG=y= y897y8Rԫέ{ǹv|?nϪ-7}CO4c辛;dQcβm{]ݽMfpl[eSݥX;]| .ͺq^ ݭB.eQ/Gwȇ.W^~A㣻npu^wU^'<5]z5QzӣDwW0\w5\jbGQO8 JшW@bI=B<GϬ* tGeg R~*;H~HQf;LCu"> ` 鬎ݸ&qmPd'H.eyY?XV?GCX"Ycq*ȉNߢl+Hv+* $oHZ>KJ]fё&#ՊzsH,Deg:zlW}X s}zs\HϽgQձ&L tGurǦL[%81# U*:DzM:pS;d^{t~8x287w޴ o8|,@%2U&2{b{w8ۥt<;}`K{N8m䨽#{ֽdڝ{ P?A1Fp]6is2Bxrh :Fe rJGOIʪ5HSTAiJR#\}iیkKcJa.\$H1hOx#}6Av zG ۚ?2θqbu$\ܢ 99ܟJ|1| ǥBr˥!"p 8ݯUa}SEp@=1Ϣ傌1yM;f~_8V/ncy\+/f%|k{Эl*#3\nƸÛG0DTh ˖GB] #LTZ#'.VHv%YK'xPAhe\aP59bvh̏z;y$1c1n/cy$9r3*|$clk##GwIwhJIvHƜy$| 6|G|nG2^ARRU^{ϳ7I>}uGޗ :(D߱:gG]&*lk~pva}9X m<}7#ه;+>އ? 2Qc[++,./ú菗?F#CpN U#^a}f̏z;c>WEs,$_"c2Ak%{SixVMu8t|xV}s5W C^&\}HƬ#''=f6ۇd|1b?8FQ 9h>?'*l%_;#cz8Oa؆O:>6 O))Kr1:~C~=.tg}>\a>$Q`ۚ_+DۅQ>$#+'?"}BWbNHXXHE>d>vJ Jsj!ًdF煊{Yo~hp 0%'{y,'e誝ˍMeA\ƿrRqWVjNƸIY7'-|tXoT$W9閧82sRi9&s5.;:{SkI'sRCINNʘ?IS=õYNxOI9)LlNwא x9:Id9C>;1>ILTNZI5 9iw+w=!Gؼ=M|y"r'TM_z!fs1?7$'(Ppw s8hp_i˓iNzy8CCDsRtO"w\.%s~QTW磏 wp*^86 UnCmW TFu[vv7=7'-Akf Ϫ0lu\V9;x̋s*n>` ݏs7_ڙ>'"_HtߢCt֚&F](\mwI[;*[+hr0E{AXTx1<˪TFsXgX`HJ%9ߣmIppfFQV.NzdݢY1s֡uD{ӰG3mc1 m:u,0.8G u۲^ّ=*{YD?G8"[otbݲ߰[glK, vۘ}X1KDܳ 'tLO'sptiatic]z2ztN[pbx kb 9=BJ8Tw5c~ogAcl/kLƾ["R4EmQk2Ā|<-V&r?/Ѻ]vzc{aS6뙾/ } x={lghu=~Ʋp37d?9St vW*x ceJee$9DߑEhZ_v%wgD"ŰlzВh0NQ^wLp5xIX>`^!x>)2y<߼VZD%{E-U }ؑ5Pb~ ]/o=!t< ^Ǿw[ːK[ˀPX:RwM uwPc6v_(,UñB6iG]ۋO|h31=.#hpE:Z)Qa>ۮ>_x^Cx1i&,p >goǃLȌаPG~Uv*(T$; )iEId<1UˤvɆh}m%Iq@&;e{b0ؼ]g(zuыu :xuȹK}Cmm{y PGFHiC1Nkw]$\}-?e,+?TQGk\'s+:Kp-gp1Hf4V9w9G]w *nC?Y@Ƕy/c>ž1i29w[snNccO`O 'N6i' EB:X-=Pgn"#su7h~CP2Upf&rE8ϕSR+>4uZs ?WSGo`T$WR;Co{ ʃjGHr+og xj Mzɡ<>\G ~baʻk2cz|:Gpmvx>٣ }I^?BTvgeIϕ- h9/%e\C|-|.zl\}>5k:2Q`z^va}r\or4*S9N-?Ђe?W'>jr+ 2s7GI~M|?A#[<,\%pWS=ݨ(ֈ EKok2ÿvauE. ti۹N[øn(\*Ld$woǤL=c{CC9bVWd/Y/H׾k>aJb7z>)nogCsO]}<#y93_ ~ =X\e>6}/fЖ:4 }mms?ڹe6O`>}-4-|cNl縳#Z[N /8soڹt,'Ag6vįo?fU.{KWgyQ:{<;[.KÇc|nܭ쩾 =:)۵;,da|/wd*v#5(aһev#'vZgfc )ۍvS Olת`mn@,ndV[T!(ǿQyq7EqR~I<|I.rq Ή๖0jY/n064({h:f}໌Ay,= c+c|g4h*։px0WZ+shtgs_97h׷0ǻ+>`&V0WWccs0*W;sNw="MK|mC*\ƐuPmߒh0UXI2wꧪ4j~ڈg`#A;oc+8J4~;8ֶ]}'sx_o9]<o~3UG&fz2zE\A1Ov6ƶظKIPcwL"?*Zގ~5;-V[kmk V2hڴY芵,<}_=^̗:aΜhæEv.|]"YuVlh7Jn[ηߚcla/¹'kP6߳ǀɢsbSls zy>y~u?S6' F{Ƶli/x mF}91x# |)y>!.T~>I!%ޟsZvmx^Op_|TD1Ԃw7m%nY~|ύG,D:@߾?76|}9->_Ǿ1^K,iSqb,cż>Аu|7x 2-?ck?'9[CK~GjY=-YkdIV3pb/&x>]5zr''媷ޞgtfPG/^7ԽZlvVڛ?׋Vڷ9s|9mc'}[ Զ_%> _ify~//-F¯z-7]D}?nm}Q`s 6%Gg-cKԟߠY]Ek-љw%&{{D|;CI+[+~NseOpƻsb팧o>fݖvծ B[1oh>{ѷGŴxLe@ 6-6^1vp+Զ_%>n $L0R+)NmWٖ؀*OHF&G;[\c֌ɘU=抏{7ӁN:xHp)ho%M3s?s?u1ޙ_{}H4aSV#.$ߴ$zY>{Z?^-ۭ${~'ә:1™z]xg:gް>ݺ3=:+#]h>8ym H8xJk7;67,/3ܞ8fdoKY`5VЯY5-v{=Zߞ+z.km#:d<6)ƙ>fe2=c^Q2\g~*vi/6;u5gy!s"q :uq-CYqv6'U{hԶHO<䪔~tɮ3a&|*Hg34_|2j} WdN_& 7IRGq,a {xP1B%R49HVAllAק]6t_%k臺rė3יY4/J::t.N{O=mҧN p( :sIaznW>Mlo;x7M=Q%w){IavL'xX|4 rjkOjqo  7QY%5s}޽Z7|>Wܔ1AWU9WpO7Ǵ?h(d+l֭ 4l&ڌX{ 8)% Džd }HVb|/)E\;@c._8+Dkg#“^ֹρ1ޮz\1I#"=whNPk O`'B繕mNM^hȁlEPy3}B<>.9yBJ\x ?准J%p[{HA,%*X$/HxU4 ( B*Sq21fNNrNZ{]^d>%"f\W&r݈l"o0EW.γ(߈e}3Z/dr&v3Uܹ2=1Z'4f<=fhr|9md!n }HɤX^|ƾ*%hy8[iǬ|N1)L驹~GW[dԏD-wYޘW:{*\ym]r H7. tLsH#_9i-[C}ݺYG:=8R-rVa9,i:Z2dϓӾ9m; YZiwz%+gEVާ./s,Y &c&07X?oj:+VcC >C?"UD>(cvC'}!O=yaS/  s:BzX_b^!˄仉^dZ+ޗ[1[iN< ?k0|sڴ%FTdM> 8 "'GVu 5 ûדڣ(hw9AY-8 hbr6yt26d*e"t'|!|gz?5GX+R1{==&#/FDFȻp@c4f|0 ޯKtptU@I穕dfCv OH&ƶ8ibq0v>0~eDM V` dGw>eQA9܇*6(S;Kp7zMb<-iNi컥__|z״n#XSh +?=^x:u9=^x:uׁJcFMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:17  Pb8 R)@bHb(16hw2w/Vb1hr{uxVURR=\ $WDAI I&|.F5y&ĤfV4eMcٟ1-+&Msl|낐 (5b9g=Ϲs}{n9{^kaQP`X-P;2>6J1(sIU}] /]8",Yo/_Ezd͞Ѽ=ѻ%QEeSZ"g纬U1Zu5]C꾥:p?Bq[ʃ"As+UƫtTTtTeXܲSM5*!h|ס*aEcs_3fMKXh9nqr ?O$zy֡y*t*m"_wĬiWnTyB49%OcU8?{>Nuxd,y=Th Tn>4\6ª6,ufN?O7i{}ϫMEV7G^yWĺ 4:Yݜ.:稠 ͇? D7!D6WYLMgUG\s_MpT#=mFOE+Ѧ?Z'6G) 7Qi-mWz<.J1Cu5Lj٠>E{]LY"33\s,(5s>sqmڱI}61rmc2O5mYbvjeOvYd!XϷɮߛt*ߕߓt/]e!b|H*Nݑ!c0O0e> Һz'i ͺS*OSM*Eu({y\gb{! ؛'-6%6gK{ۤY~NٖlQm+Ygl==aZu5xdz5ؚ7zY;HͰNOڌWɶ/km:0aD2GsU;K4б zWFǺ4<:NA?~pe?Itw >Z?E[u݁[Sؓs%ꚠB>$zz>4yOX=|?=0b33;T|:1y="C9t8>54:8{Q*<>N_U<^ۑsnkbZw+ 7ӺSUBE ~v W/SŏKB'SQ_s[ĐsQlѐ*/p+xM׷>KY"oT-{%ǩŴiJ#P~KB~Z0+kٚ.4y˸CxhL4~!Au?(wI&-,SxXs53ɼz>d>3sUQyzOLcTXo̓`p*m'"}ʕe4wiO43߰++J*\?v/wKuhW6sX䄐x#\Ճ~^i쒿G '+g⧽F? mvt gyO4_v!79z[Bo%y[Tu}r}| d,T10.gY/Wl  y/yu}sI_&w(fYNBrUO (}O{}w鿐Rx;<,SǪo7 nF_S?{?Ucnߢ5mAuv,u*Z#FϨ͹Oܱukڳn/(|6ƫwY><N=G~uiԗߗy[f C]7HF-ơvh`{ m/77סV9:Otڞ|vo~'}oly#kC/{gx?wp.|/z2V}@8*ŢP]~tES ?<=x@C<4oY;O楅)K_:UI5c(.=2;e}3ol=~qzeB6D. k$60w _OB.N4uwNS]͢?<=x]up k?mr~Sa7zUhGkwss[mKC81`eOm/v+P׾G%}nMRXOt+jۭ='uٷ(kq@8q5dz@MF KR8d!|xIA@Z<_R/ph<S]tifx <⡙{7b(=`Qߎyi|kR`O4t@3S[< ]c:T[X:^o{^G(.K<J g,_z  @UJ`86z&0 օ* @OUi~cs)y[<*d@⁲l/񀷽=l@Wf{qu =xEI$P{;pr= GV6C'dL:xC&AY7qةKE*OL|z^W򝭅?Um8S>]GH^˄#ߣ?ɯQ/Q$٦ULl`롁tn*+TT*Vߎ9Z.11G3|9࿅m|KbS:v {UMnUl:"!@:OMJ|]o3Xۏ ۏu1S{]oX4O:5+'2~^۞6GMm~>vw$o׾!g*~{xB׫;淩o~+=v͜n Yo ocަc~+@,< l^qSp"0o.#}+{;5N|o ~߆wo~ߦ"l~3y'ۼ*~{xE_.޲~ni GcfY^ߖ*Ʀ㷽MaӋⷁXz`s6cow ۳Һ]ۓD=oL5.N< /m ~^4 ۏ^|3},!8oهupSa~;c3淓5ܵ`s▏!'c5rQ7_~o<[{w[}ܾ{N3w3t˥g9fQdnf.keϒOI7j\%i]ɗ/ }+ce7=/ox4}kQQ݋"GĐ߉N^;泙~=IYC\< poۃ>F}8vW;=U_?#ՍcOkќ8)ow]ÙV74o؇p U6LJ3V|m}{_JB>hLJ]ue| W/p >^4 AZև>"ć'9r6N`YN}ۇ>ffR}8ыه7s:%;᭰gg풿6|w|={p VU6LJS‡wsTWƇcE0hFc"GO8u`yt{gkxQ.=w} //osݣxO[6ft9G|y+]e }94Gypb_~bˁXx _X/Ӹ}Ӻ]}|a>|52^|9h^5}|Y|:} g;ّ[ܼymO9/uo)m2 :z=*g4?C4dDl0Yl1mJ[9 fw4k`^ʌyEr̘͡ ̘Y1_ҿ6>F]М:Q 7yӯ/=<_vr74#Vk^X*,sZ?fjEERh :xZ+L;4{Ǭ>݋E|:smٺ Z"c+pbRͻ\yy+'QE1-1U^lŷsWF^D;[=P 1!:ȋxs̘g4ˡ ̘BcHJ+9 f_Mi>C\1[Ƽ-#FbC\VD"lleت`͈ci.v?ZtE4R j0S8K$׃ۙ1-b<"CUoaWz\z66y Gw_HU=3yVpR,/bヱ) oWF^>"7MV&8hɈ؊QV9Ρn0c&7MV~ʌ*4frS'o̘MA ̘Bc&7}V>Fnj^&y+O\V?>ٿ}Cumvlry͈i4_?>c$x&sg%Gf,*®vzX) oWv׋M[UOVpEl5%[Vpec+rS<ˀxࠩC[wrrS71&y+?fpeLl3)蓷 f䦠IWfV1>y+O\cfMAд}&~-};jY͈y+-&9[][Ԗ[aW[y[ }\o]KP萷yZ׭dU4[q[? [ y+ y+x) ؊}}+#/[&y+O4dDl7\Byxs蓷̘MA32c& [y3frS$oi+3fbИMA1[&y+O\VRqXފvlry[53'[ 3fQ6jU.y;eUټv=jqpB؊}}+cVV|lEުll(M y+ r"My+2xp{ࠩC[+ϋMsC`Ln 3Uh䦠O71&y+O\1[Ln x3)h4hl5Ita߲շc[kFl̜HWgZr/g͜NɯVYdV{ {Br@|=6u `W[y *['孠MjX`@jDZ׭Hj蓷zOj ~W^[y^[KN V胼\y؊4[yY$#b+u[8>4[1+3fbИMAn0c&7MV&2c& [y3v4[yl4b?dvtey+۱U،ت9Fc+eJ#TE[5sU䭲v)V(¶aW[y Z+X7"7E|y+[*[+(VVEluR0"7E|Vy4AS]7&:Imb+rS71&y+?fpeLl3)蓷 f䦠IWfV1>y+O\c&"7MV&24bؿec+oVfw7hc}n<$ 4M8ٱc o۾T_ՏI9:bFuN3bfDcG'ulೲNDލVZr-[gw~'KfNYlżV܃]%o*8\o]KP+:bu>{4:Z4[蓷؊򼀃by[M V胼\y؊4[yY$#b+[8>4[1+3fbИMAn0c&7MV&2c& [y孠I$oUf#'3m[\fV̉4[//تsD\k[%oKNYlżw`孰䭼]aWciuc+rSA.[[yzvM;=/j׭=,NF؊o#w6ywm| 9 EwF:^Ή!u]2A/dշe"kl"wj"C.`>so1_"z4T1?{Jv} 2/)|! Cu!Ծ$f ^G<{zr<e _$w쿐YYD.bX54Znw~3|R3=͏7sZmg쒿6$Uw#<4αళE6+$Z|sH7dIT>&B>6Ek5虨?Z_DuY5O Uzm>툞SFҿTl0ψFV<{uM3­%CUIp|@=1cUɶskgmg_?~m <ڹ3p㎴rmtSo4hmMl YiY9s\Uu0<ޥ]h,OiSMp,Xˎ0s+3E3y_{V_mEZWO&u~#92.:䫠]ė@JvPj]]]76X GEzUҿyHjWFvU[>Y ߴQﱶXx {JhE./ո *TFL͟zeqeރ/2GoX[ͮ/l 5KOq3m[ɶ1mڽkpW +i]hYÛTk~|սO48^:CA݂>{["RGݼD0i܃zc: / xekwbӯA:(=0c YF6̩ѷ 2S7QQł:`i3YTNh_g_S?M9Kh􋹲'`͜#do +TfUTc h쒿6i%KN~Cభۭ=rH&8h>DJ|dg8?K28Pڶ7_jl)g=MpedEB,~=M$M"pM>&mWMV죽 \Z+Zdi&ҫ>]~*O"bQQY9xC(Ӫ+Z;5mH4S'opŎ(!9lK#vɀM54wΠt:EseEH(чDiL^=J'sR|Hyf5*4rcy&e%J䖬[")[—R^~՝!^)J5pe`|Qm MVݗHKZ<E%->)a8nwǸC#㴹Ea+_WdQjg"Ȓ>pmsV]Wm}5gqJBH刔&zߗd {yڇh<3!MsySDUʻG-~&s]׫&MLt63%J{Zl~;' ۬=86 (2M֖vO6?v -{`G)]`G o@hl#6f=ZU>RFkx 6oO::Ü3"՝ ȟ]*3s$s^5#S-|#/ !ס-Z={%:S{ux{FmS58tfJ1m9V\AXy^*}B|RuC:H|m6.`m''zTiL+_rc9)< :UYV/(UѻHM/pA m%F1=% }7Y1 du:hDV]YrB^m'~&J{ ~gO g,Y zi 7I>#eznXC B]\MPמWJ^n{1p?V((+twY\=] ݻ$oOt 9X&e\ʾ?}`(Nr^b?? q< $5H'2kӛ_j#v7M@/,g B@ 1z?A/#B6Hg铘do%zuY]+nB}?" 籉G"Ə=Mޔ n!]45wx]O{E 4;e >OA;Vg*uvM }@^hJccc[_k 7) 5vδO{t~h.=7Uu2+A]b#?UG_K* /k=/ƏH=Ϭ~֊<+?A~d7zTn5P8x(ׄ?d;хwEtm|sJ}94YO/^RI/ =*:AuIy::xJ4)\!ց *z邃\CP{[-;d埏?HU 6쭍}Cg5lYh}%TA?7M}h0 zcE;ȣvV>צoɡnWe@>|w\twۢ|xcس?Z!DioT&?ڶdΒ.'|Ug @|=5ktzhfx~/2uh_ 2_wWfDXFd(хq9|&Y2 3-X\OtzAvw Q;Fz{(7ɕgcUYقK8Yz5k7qCQ>$8B'뼵Уj};_pw+ecѻE z@pb'D~~'?s>Bk{рwH(p G}DWƩ~Fn(瓢o&y7sÂpe'd[z$ǟ%l|3F4녂~LgψEx@&н 9t;>ÝGʦG#:l!"{R?H3^NB{-?{ܮ5StzC&2װs};֙EO~0.8[!^G3;rph  2r[ckRؙ.2t!l \c|C 9].?W|H\3רjрb8xA{#kU2رq:=Go31|H_~!Kd| ^9*e n(Dс=?KgQ)8x`CrpK|4OIyZ gsO[L۶!Z'8ՍP_ ;>YOۣr߷ ~ BW7 IlUwրF-Eo4AUҺl|Ѻ\4fA/Cp"Eq*/t?+f<]p=PB^"\bԴ+k5 cli;tt+;7if]r=w~ Oh˳Z~>Kѻ3?Y<4YSGނ5͞SO]9EzT2Sn(e`^(ܮ˕рNf 8x*Nm>EURZDȟy9J'|+g(fO y>g5 \((Pu!;z@%kș;"r-R]/ɨ(6=8 ~s{ }!9$٬= .DI \mqN ]o^,d aݘ}Ƕfhg"kc8pv>)vK, $cvF{97{˹X?+W9sB/C^ k@:n0:'3_DXw&O7EҀY&ѩ͚"u\sh 9^>#_'/׏\UMcĶ^$wO;й'UIeyXI0_qz%~y37'^06unhkqgz !Rxkg*m4+MC{ʌ~(fϙ5W сi]HXr1/ޞ}J4Qp VmNK:c%U»(W"z?/6}WZ'eZVA^xrAOG!> LV2F7ƾ"B89_)\:l#fwm%JN$y4[asg|ΫVrCwE=됵pnkt?66'ҡ]:h4}Z[{{alL'ze'tgQ^'[ChEm ֗ƍyO݀naO2죰QN]VmTWO%︘N D'Y{(/&ZϺXKW(EgMGȴ3ݳ_@ck myehk6_d4L{mn nMR](2󢇮^W+A] 8{J^k Vsr.Z][:Ci&@*Ad,, 51 Èçìåíèì ïðàâèëà ïîäñòàíîâêè, îñòàâèâ áåç èçìåíåíèÿ àëôàâèòû ãðàììàòèêè G 1 . Òàêèì îáðàçîì, ìû ïîëó÷èì íîâóþ ïîðîæäàþùóþ ãðàììàòèêó G 2 . Ïóñòü èìååì G 2 = ( U Ò2 , V ÍÒ2 ,  2 , P 2 ), ãäå U Ò2 = U Ò1 ; V ÍÒ2 = V ÍÒ1 ;  2 =  1 = {sigm}, Ð 2 : {p 2j  j=1,2,...,29}, ãäå p 21 : sigm  a1_ý1_ à2_ ý2_ à5_ ý3_ à6_ ý4_sigm; p 22 : sigm  a2_ý1_à3_ ý2_ à6_ý3_ à7_ ý4_sigm; p 23 : sigm  a3_ý1_ à4_ ý2_ à7_ ý3_ à8_ ý4_sigm; p 24 : sigm  a5_ ý1_à6_ ý2_ à9_ ý3_ à10_ ý4_sigm; p 25 : sigm  a6_ ý1_ à7_ ý2_ à10_ ý3_ à11_ ý4_sigm; p 26 : sigm  a7_ ý1_ à8_ ý2_ à11_ ý3_ à12_ ý4_sigm; p 27 : sigm  a9_ ý1_ à10_ ý2_ à13_ ý3_ à14_ ý4_sigm; p 28 : sigm  a10_ ý1_ à11_ ý2_ à14_ ý3_ à15_ ý4_sigm; p 29 : sigm  a11_ ý1_ à12_ ý2_ à15_ ý3_ à16_ ý4; p 210 : a1_ý1_à2_ý2_à5_ý3_à6_ý4  1ì1_1ì2_1ì3_1ì4; p 211 : a2_ý1_à3_ý2_à6_ý3_à7_ý4  2ì1_2ì2_2ì3_2ì4; p 212 : a3_ý1_à4_ý2_à7_ý3_à8_ý4  3ì1_3ì2_3ì3_3ì4; p 213 : a5_ý1_à6_ý2_à9_ý3_à10_ý4  4ì1_4ì2_4ì3_4ì4; p 214 : a6_ý1_à7_ý2_à10_ý3_à11_ý4  5ì1_5ì2_5ì3_5ì4; p 215 : a7_ý1_à8_ý2_à11_ý3_à12_ý4  6ì1_6ì2_6ì3_6ì4; p 216 : a9_ý1_à10_ý2_à13_ý3_à14_ý4  7ì1_7ì2_7ì3_7ì4; p 217 : a10_ý1_à11_ý2_à14_ý3_à15_ý4  8ì1_8ì2_8ì3_8ì4; p 218 : a11_ý1_à12_ý2_à15_ý3_à16_ý4  9ì1_9ì2_9ì3_9ì4; p 219 : 1ì1_1ì2_1ì3_1ì4  1s; p 220 : 2ì1_2ì2_2ì3_2ì4  2s; p 221 : 3ì1_3ì2_3ì3_3ì4  3s; p 222 : 4ì1_4ì2_4ì3_4ì4  4s; p 223 : 5ì1_5ì2_5ì3_5ì4  5s; p 224 : 6ì1_6ì2_6ì3_6ì4  6s; p 225 : 7ì1_7ì2_7ì3_7ì4  7s; p 226 : 8ì1_8ì2_8ì3_8ì4  8s; p 227 : 9ì1_9ì2_9ì3_9ì4  9s; p 228 : 1s_2s_3s_4s_5s_6s_7s_8s_9s  c; p 229 : c  k. Ïðåäñòàâèì îïèñàíèå êîððåëÿöèîííîãî àëãîðèòìà â ãðàììàòèêå G 2 , ïîñòàâèâ åìó â ñîîòâåòñòâèå ïîëíûé âûâîä òåðìèíàëüíîé öåïî÷êè k â G 2 : sigm, a1_ý1_à2_ ý2_ à5_ý3_à6_ý4_sigm. Ïîñëåäîâàòåëüíî ïðèìåíÿÿ ïðîäóêöèè ð 22  ð 29 , ïîëó÷àåì öåïî÷êó a1_ý1_à2_ý2_à5_ý3_à6_ý4_a2_ý1_à3_ý2_à6_ý3_à7_ý4_a3_ý1_à4_ý2_à7_ý3_à8_ý4_à5 _ý1_à6_ý2_à9_ý3_à10_ý4_a6_ý1_à7_ý2_à10_ý3_à11_ý4_a7_ý1_à8_ý2_à11_ý3_à12 _ý4_à9_ý1_à10_ý2_à13_ý3_à14_ý4_à10_ý1_à11_ý2_à14_ý3_à15_ý4_à11_ý1_à12_ý2 _à15_ý3_à16_ý4. Çàìåòèì, ÷òî òàêèì îáðàçîì óäàëîñü âûâåñòè öåïî÷êó, ñîäåðæàùóþ âñå èñõîä- íûå äàííûå äëÿ ðàáîòû êîððåëÿöèîííîãî àëãîðèòìà. Ïðèìåíÿÿ ïîñëåäîâàòåëüíî ïðîäóêöèè ð 210  ð 226, ïîëó÷àåì öåïî÷êó è ïðîäîëæàåì âûâîä: 1s_2s_3s_4s_5s_6s_7s_8s_9ì1_9ì2_9ì3_9ì4,1s_2s_3s_4s_5s_6s_7s_8s_9s,c,k. Ïðîâåäåì ñðàâíèòåëüíûé àíàëèç ïðåäñòàâëåíèé êîððåëÿöèîííîãî àëãîðèòìà Ï kor (L 1 ) è Ï kor (L 2 ) â ÿçûêàõ L 1 è L 2 , ïîðîæäåííûõ ãðàììàòèêàìè G 1 è G 2 , ñîîòâåòñòâåííî. Òàê êàê Ï kor (L 1 ) =Ï kor (L 2 )=k , òî îñíîâíóþ èíôîðìàöèþ î êîððåëÿöèîííîì àëãîðèòìå íåñóò âûâîäû ïðåäñòàâëåíèé W 1 =W(Ï kor (L 1 )) è W 2 =W(Ï kor (L 2 )). Âñëåä- ñòâèå òîãî, ÷òî Ï kor (L 1 ) âûâîäèòñÿ çà 144 øàãà, à Ï kor (L 2 ) çà 29 øàãîâ, òî äëèíà âûâîäà l(W 1 )=144, à äëèíà âûâîäà l(W 2 )=29, òàêèì îáðàçîì, l(W 2 ) << l(W 1 ). Ï kor (L 2 ) âûâîäèòñÿ áûñòðåå çà ñ÷åò áîëåå óäà÷íîé ñèñòåìû ïðîäóêöèé P 2  G 2 . Äåéñòâèòåëüíî, â ñîñòàâ Ð 2 âõîäÿò ìíîãîìåñòíûå ïðîäóêöèè, ñ ÷èñëîì áóêâ â ïðàâîé èëè ëåâîé ÷àñòÿõ ïðîäóêöèè, äîõîäÿùèõ äî 9. Íàïðèìåð, â ïðîäóêöèÿõ ð 21  ð 28 ÷èñëî áóêâ, âõîäÿùèõ â ïðàâûå ÷àñòè – 9, à â ïðîäóêöèè ð 228 ÷èñëî áóêâ, âõîäÿùèõ â ëåâóþ ÷àñòü – 9. Âñå îñòàëüíûå ïðîäóêöèè, êðîìå ð 229 , òàêæå 7xYklU> mw[vK˫⃇@A1Ԫ( ? D" 5FP`">?Tb(+i@h1 -;3^ά- 8K>νys<{8"RGz\`F \! 0#/26OWtu& U;*;/ŬWb5fr:>2XJ\I ur-eBf.x:p$X7}q+XwBJ txJ.OOs'bGFqmy} =Z-yv.79ϋy9,5גݐn*mڍ}>phu9|ۭր{58ewTvv.}&b]tQόy=UTY;XѢgܕ>+Seɍq[,l7}rtΌؚ7Oex%XsX:賫@=snZ+Osu˜*;߇1CIrFL݋cC^a;4E뮵 hX_E_o OAf˗kN și)OfOf쇭C3mɝݙ4sż' 9.( ٝI<]ÌtNT;iZsSG-Նk=9J33cIfLVuos֕Svv=y]]e۶  D*𿨀wL.^8IنC=Lʓv7k9 ]]]R2$bLϸ-Z~*}&q&HIS|1L܈XǺKɹqlȞSR)wM3s/A 4W|]4svoK]36X#>oruv ߦ}?W>f \{M~^LQ[]xux:f.7sIA]\kl۲qK,'gW-Zw{ i;yl¶֡gQ!g}k|2NJXyqnHwnKJvb 利a>ڻX"L69eʷw VPO#+5^pTH+v-w@~ r*n-G?ofoc}w܏wn\$鯫:\_l|uf  ī@Itk(Ipi^'{)IZ'S9ho=f[ٟHjq%W@S^׀&'!aA>/߇Pg!&? 9 ~2b6cQV~ ucfZVnH굸јun1]R%-@Xߧ٩B.ղ>MͩCVi# ~\="ﹸf)=RY,8aSt޽}*;Z'`0,@ǁ> dSz y !o m.hN{?vulOy5}^axU-˜zt>=/ M^Η}oY1ー8aau?_u])ft?A66GBqYGXP;J Bk9|~㜒J3Ǵ194c2>%lsd [ROiun^+ikskSjk'̋>ϮZ363ڦU @TQ D*U @TsT_TQ D*U @TӮo$cMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:18   x l=(162/1w$z{xU SRWZ]@5YX`fb gQFJ2&Mpe3:35jZ+#kZ6KG4kd|B" > w~{;{]w{}{}~BJpAG gG Q~z[\BBGZGAl%/ᶗJN9cd8pih._>jUlUUB/P4wJW%8BW~n)`Dc|Ԑт).ACO2I'uM[0u+-_^VI~ cYsX Ya{\yЋƅu/k}y3?oo3l@YB6+Ozª6 - Rugta.+J\4#CWR˹*K&8aU}_y$鸲mul8Å/]Vί-ON)mcӥIGѷm_:7x숝BX(F#!GG;Qh%H?|!g酯/UU,'~/:K7I}sݨ "_蛽 aхZNow eJ7>Io&Rlrtvnwj#vJiRIv\ n^v۠)v#@ɩoLok-@n{8ߞjcnnwj-gtH|snvqׂeS7RICr5ڭSη7Fb7:*)ٓ-|ERkЮn-]saGخö`k(w))Lu]nDvە¹Q'U~Bma3=&\0j' 6P&-C3?.^!xG<tcy)?yڃrH.kelo-}0-%}J?Wmȟ&y/M㇖N2?ҿ/AkB#Z~dNmr_֎KUy䢟IJs@Wc$ϑF#͵1~"خlcFNjO:ŧhuq0~=7:O>SRk "\7.B>0Fln"l'"'ֶ[s\~V4ڧvZaC~zxv Яcs~Xy{xAqAC8b 6iNjoxM&8@t,>8|?yLy +O l*q]§|} D/<[r+`ɧ'*%ܖ:f*|\~c!6VC^Ј.9/}al3cNZJF\)ym쨁c؆34*v  hm>4#ÏG5{-`3S)C?6N~)[(e76#G!Pۯgyԃsr/yGRS:=N&*}>>cю Hiа;4&X%yJ@kg,N_%ŒXX@c,Սehq o ,I*Ļh(/޽JzvϷݚBCGk]: Dm*vۋnjnh)fVm6@yοy/|:.5Tu3<~ʦS~YI _Rqڭnoak8B~v#ya|ذ!8^@L8>-M ½Au6}P4Q14MWzkK+p8ߙEFivʢAN N=n=+xtzK|e{ V!h k?in{ZMl&)h<}`^(-TlYh wpu%FhxD64cky1/_G}!tG8t0  1C{pgn:DmM8K=*jʝľG;N"/ iOm3$?1nyw]y9mP^jON*hJOj~"#;YxVi 3l<[>ȄnYL'ul2q .cȅƦ&1l]%\d?jh݇ZpN8Zw8Wx[yʭAvm xO׭/:xyF!o]R<`:)zc:A;Im 2SY]:}zԡ R'ˤ l &޺{hݲO|B)h=L?Oה^I ˷=Ѡ5^끱Ƈ.K:!me12Yw5Oynץ>tۏ26~xL Jx:d?V ovv}t򟓌JƫGR CkG`%ߠ#|h/qE(=C2 Gޡ]nN[Zj(Fsr[ԅg2c,#X11wJi{/)m(QAkGwKG&I B֎b?J?-{=J`E30l/ۦ}ty9AGty:?^ܤ[l\cl~, JsAkGI%9?F2~&ďn)mpJj[̐3늺p |,\- 1{LiaW.lۊt̿+e& D;Aؚ]h. uUr:fԇt^>⇶-Ä!\]nɾ;?+vݭ$u7);~0V;W+|Rok?gyt [X;D|;qw<<*p,df膱3n<_`ƃhۏT2kz-BKqI <Ӹg.8iؚk56fRaowxl-Z?}-Z .s.}7;t2shO(XuGRƮ|^懷JmcYeAe uȻe9|XyN=(S~|?U~־ ~+ƫN 79O5~qnKu@Ldpc9?G8xNENV'EKR&-34d7̵Ž@ժnQ  dz1ztP˙# ^=ͽ2Cj-7\1Ұk =/1pJ޼ϰ#kFq3| C zc1-sܲi@G:du :-U~K)s2!\*Zzjx 0+_LuGH>w=w1t:)|nx1 WDg6K޼Yu: чߎHOwu9Jv;vT׭hI}x}{ijnUI5VۄS}xS$m f E a ?sg'ǃxY=0oYG8 oν /э=/Lo[ƒNPҘ|l˜ɏ/S 4o@aR v'>ݏnH,֟ܦ [ROU8bRj݉T}3T7UNuncxh]UPv u:ȂN򑉝Amׁ%u>qo Pه?8}bG?,Njn;83oN-y8C*6}ڗ'\ xON]&Em{~{Z\co9(LG&vc\&?Y`>A[MqiLo6GOonKuv]ڽT:.Z~;#]#G%''CiT[Zs0VtE]{֡:?v ӨO]~BlO^kLC xl-4l!bh}DZ˿J2~ W+}/ڐ}gck$6Ck=@?R*v䟭*dJs@LE2y'(g "볣B8crhn-}q@͐lw8QpV]gђ)VFsX#И8癓I:%tgQ<-&Pk:0H_>~bolw[OlߑWn_aM:ڧ~O`2iOׄtge]h7Sڰ\Rl)3L)냷Lw]x|q ~5 v]){0/ w|qhM=c]9)8||DU7~ؓ1N u[\ֵŝ-o]_UzwW<=_'[;[\ۛ=$zccmOpCj+ej'˵,h-uccpLCz6_-{mГD6۳^*ywχu~LE{|xmч݅f |tf=)SY9?ۣL{?,}CʀdmJOl mj1>B@- xd?Pk~&,^\mMPe|,Z](lŊQv!o}lkmAkGoH׼3b`#}~tRc<e|8Xü~J' vW;?* h+by݃{KZsy~.y57G2٣I懷n,wJ\ijBBGh::*}}w ޲{%;Ho|掺H\Y?qcCf_=!.tw vN{\ʹbKe c=2 gn@>.ɽsXKgEzʝwJLإ=wyJ.4a"F;ya 4sovJl[{``[H~ۧ^?~Χ_ޖc~H!N=#FLFsc>/8E1W f&oE۠*gü^\w^'<:?7͂ <.eM?&ݗĀՅb19y F\Uyg#AYfM:/RJ}_ mp:%q#8pg}tm 2=g}wRc=>g G\_w ;c.3W $[q}8m4Is\?TA`J}bߌ*>%zZvN%G*7kuU~4Cgሟ]WB UDn616֯TWb/zc>?y8b=|:heX?\{4.Ӳc}{xb2>=bbsѷuJXqU뗉6<ٷ&]A}ҟ+u7~ G=k\q668/c;|d11zOcm+ߑ>e=+wuh'7.jzͫw5 C'3}o5&oYXd,n& iLN/ؽOvg6gjUb3Is>I]3X?kBɯ>f6k/7TOJ6ThW\C>hՍ*fkcEu3֩t{7Hh̏(R 'cg9ñ|jjOuq\^9C!ϳ/F/Jjbh~CO O{?T;|!";5L|>h~u2~DPTHQb|vi5qgH,,52 ÿâëÿþòñÿ ìíîãîìåñòíûìè. Ðàññìîòðèì ñèñòåìó ïðîäóêöèé P 1  G 1 .  ñîñòàâ Ð 1 âõîäÿò ïðîäóêöèè ñ ÷èñëîì áóêâ â ïðàâîé è ëåâîé ÷àñòÿõ íå áîëåå 2, à ïðîäóêöèè ð 120 è ð 192 ÿâëÿþòñÿ îäíîìåñòíûìè. Òàêèì îáðàçîì, â îòëè÷èå îò Ð 2 , Ð 1 ñîäåðæèò òîëüêî äâóìåñòíûå è îäíîìåñòíûå ïðîäóêöèè; ñëåäîâàòåëüíî, ãðàììàòèêà G 1 ïðåäñòàâëÿåò ñîáîé àëãîðèòìè÷åñêóþ ñèñòåìó, ïîçâîëÿþùóþ îïèñûâàòü òîëüêî ïîñëåäîâàòåëüíûå àëãîðèòìû. Ïðåäëîæèì àëãîðèòì ñèíòåçà ìíîãîìåñòíûõ ïðîäóêöèé (ÑÌÏ) íà îñíîâå èìåþùåéñÿ ñèñòåìû äâóìåñòíûõ ïðîäóêöèé. Àëãîðèòì ÑÌÏ ïîøàãîâî áóäåò âûãëÿäåòü ñëåäóþùèì îáðàçîì: Øàã 1. Ïðîàíàëèçèðóåì ïðîäóêöèè ïîáóêâåííî è ïðèñâîèì áóêâàì óðîâíè. Äëÿ íà÷àëüíîé àêñèîìû sigm - 0-é óðîâåíü, à äëÿ âñåõ áóêâ, íàõîäÿùèõñÿ â ïðàâûõ ÷àñòÿõ ïðîäóêöèé, êîòîðûå ñîäåðæàò â ëåâîé ÷àñòè áóêâó sigm – 1-é óðîâåíü. Øàã 2. Äëÿ âñåõ áóêâ, âõîäÿùèõ â ïðàâûå ÷àñòè ïðîäóêöèé, ñîäåðæàùèõ â ëåâîé ÷àñòè õîòÿ áû îäíó áóêâó 1-ãî óðîâíÿ, ïðèñâîèì 2-é óðîâåíü. Øàã 3. Ïðîäîëæèì ïðîöåññ ïðèñâàèâàíèÿ áóêâå óðîâíÿ, ïîêà òåðìèíàëüíàÿ áóêâà íå ïîëó÷èò ñâîé óðîâåíü. Òàêèì îáðàçîì, åñëè ó áóêâû k  U Ò1 áóäåò n-é óðîâåíü, òî ó áóêâû ñ  V ÍÒ1 áóäåò (n-1)-é óðîâåíü. Øàã 4. Ïðîàíàëèçèðóåì ïðîäóêöèþ, èìåþùóþ íàèáîëüøèé i-é íîìåð (êîíå÷- íóþ ïðîäóêöèþ). Åñëè â ëåâîé ÷àñòè ýòîé ïðîäóêöèè èìåþòñÿ áóêâû ñ ðàçíûìè óðîâíÿìè, òî ïóòåì ïîäñòàíîâêè ëåâûõ ÷àñòåé ñîîòâåòñòâóþùèõ ïðîäóêöèé ñèíòåçèðóåì íîâóþ ïðîäóêöèþ, ñîäåðæàùóþ â ñâîåì ñîñòàâå áóêâû áîëåå íèçêî- ãî óðîâíÿ. Åñëè æå â ëåâîé ÷àñòè i-é ïðîäóêöèè íåò áóêâ ñ ðàçíûì óðîâíåì, òî íà÷èíàåì ðàáîòàòü ñ ïðîäóêöèåé, èìåþùåé (i-1)-é íîìåð. Øàã 5. Íà îñíîâå ìíîãîìåñòíîé ïðîäóêöèè, ïîëó÷åííîé ïåðâîé, ñèíòåçèðóåì íîâóþ ïðîäóêöèþ, ïîçâîëÿþùóþ âûâåñòè ëåâóþ ÷àñòü óæå ñèíòåçèðîâàííîé ìíîãîìåñòíîé ïðîäóêöèè (â äàëüíåéøåì èìåíóåìîé èñõîäíîé ïðîäóêöèåé). Äëÿ ýòîãî çàìåíèì ïðàâóþ áóêâó ëåâîé ÷àñòè èñõîäíîé ïðîäóêöèè, èñïîëüçóÿ ñîîò- âåòñòâóþùóþ ïîäñòàíîâêó, è ïîëó÷èì íîâóþ ïðîäóêöèþ, â ëåâîé ÷àñòè êîòîðîé áóäóò áóêâû ðàçíûõ óðîâíåé. Ê ýòîé ïðîäóêöèè ïðèìåíèì äåéñòâèÿ, îïèñàííûå â øàãå 4. Øàã 6. Ïðîäîëæàåì ïðîöåññ ñèíòåçà íîâûõ ïðîäóêöèé, ïîêà íå ñèíòåçèðóåì ïðîäóêöèþ, ñîäåðæàùóþ â ñâîåé ëåâîé ÷àñòè òîëüêî îäíó áóêâó sigm. Øàã 7.  íîâóþ ñèñòåìó ïðîäóêöèé âêëþ÷àåì âñå ñèíòåçèðîâàííûå ìíîãîìåñ- òíûå ïðîäóêöèè è âñå ïðîäóêöèè èñõîäíîé ñèñòåìû, íå èñïîëüçîâàííûå àëãîðèò- ìîì ÑÌÏ. Ïðîèëëþñòðèðóåì îñíîâíûå ìîìåíòû ïðåäëîæåííîãî àëãîðèòìà ÑÌÏ, èñ- ïîëüçóÿ â êà÷åñòâå èñõîäíûõ äàííûõ ñèñòåìó ïðîäóêöèé P 1  G 1 . Ïîñëå ïðèñâàèâàíèÿ óðîâíåé áóêâû ïîëó÷àþò ñëåäóþùèå óðîâíè: “ k ” – 7-é óðîâåíü, “ ñ ” - 6-é óðîâåíü, “ 7ñ, 6ñ, 5ñ, 4ñ, 3ñ, 2ñ, 1ñ ” – 5-é óðîâåíü, “ 9s, 8s, 7s, 6s, 5s, 4s, 3s, 2s, 1s ” – 4-é óðîâåíü. Ïåðâîé ïðîäóêöèåé, ê êîòîðîé ïðèìåíèì øàã 4 àëãîðèòìà ÑÌÏ, ÿâëÿåòñÿ ïðîäóêöèÿ ð 191 . Ïîñëåäîâàòåëüíî ïîíèæàÿ óðîâåíü áóêâ ëåâîé ÷àñòè ïðîäóêöèè ð 191, ïîëó÷àåì ñëåäóþùóþ ïîñëåäîâàòåëüíîñòü ïðîäóêöèé: p 191 :7ñ_9s  ñ; 6ñ_8s_9s  c; 5c_7s_8s_9s  c; 4c_6s_7s_8s_9s  c; 3c_5s_6s_7s_8s_9s  c; 2c_4s_5s_6s_7s_8s_9s  c; 1c_3s_4s_5s_6s_7s_8s_9s  c; p 34 :1s_2s_3s_4s_5s_6s_7s_8s_9s  c. Ïåðâîé ìíîãîìåñòíîé ïðîäóêöèåé áóäåò ð 34 , êîòîðàÿ ñèíòåçèðîâàíà â ðåçóëü- òàòå äåéñòâèÿ øàãà 4 àëãîðèòìà ÑÌÏ. Ïðèìåíèì ê ïðîäóêöèè ð 34 øàã 5 àëãîðèò- ,xhe{#v7vﶜשe9QB"@l$-d6\(Yk%& l(KRhϹ}5z{VHQrY""OIsEMT%nk[!ml;keY6ec˲Df07!0ɣ?iRv}f=ӷ:}_k\^~uf06H\;uYuC[Ә0,;=~K^`d]^}exAb]~\5l0}k"m,{Q-_Hm\ޭ>SdNԨc!ifuB\?jj&7|*hoT,_7z׸\4c\Hes$3# lHfȫ/fTy(GdBN]O*l96TN' Kҙ>'\X'BNic'c%MlXK&7nIcƩF}FYFvD6n:99zg{A+$YVD{-.!QBP_%-p\79(w}`=#gVA ʁ?.~:H2b|I*A<gɓHm{/h39+W.LTN RD;i/nT9x)ai"괉FD.= ׃ r50}p-؈< 3fPX ip ȟx*o_@ V\k\y|nV}gZ>*`jt">xܟ)i}c}%p;(Ly5 õp&A̕ip܆5={j`' G=P9M [c!/+pefvX~ `@ A!rƞ&@!%O!oU99#}'|3/{A5` gc1{= Fx-:F>7b?.7VЂy:b[1׵:L~ж_+I5^!O.,toGw1{ԍךU:WWJa72= {97>WyY? V&+GI<+Wš C^Ϻ~opU=Rz*s-`%6y=70~-}ʼ*s/ gAM!LQ51zN\Λ}v@H\YB %:qk|onfX0k;BS'׋~k@Y[g=lΦy^T.g@6ks fs3@_/*c|08!:apNl)k;uW#'w|8mTc{D6c&6xnqμ}W#W/6Nmu>tϭ6NuŘK;TMT~]s־+M5oӒ ̟Sp9|2wd2z1M~"7Fr&~/YN*UW^ x*U5?x^ x*UWױ Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:18    8'(1602f/1,2e{x ygh4ͳJkm6Vbr#o@/M$)mhMLMSj5ic1I5%ַјD[dAA?%g33e={sss3giId҅-I2W=Kȏ=I]Hکg0IZ]dO) /w%={': >q̴]&]ɧO&W$5O$?GF&buZBV_sxF9%v@e݀ Xf7]dsSnvO/N,mCғԒǒɣɦdKlrUX nT~M Q&BZM* dy3՛{Y_usMM/<5#*& !;.sʓC?xRID=!ytY[3t+LvbnOWeB`2{gjrf$ -Rf94u_ ŒҶ6!q,'xKT4l/Ch؝/*ݰ[@Pu]@$tqhkS/ȿ_o{F'^R?]Z/%Itk2?2c{5qYꆾx#SB S t.UzYIuB[tڥJi ;c^y9@UjėW= n;N|6(!OՁXhҪe(ryrArt#?-Lq'T-kBP9iڍwVJ/c4^W~>]pҞ@zv~b:?Wd]:N_j&)x !O|e,c\eJ^I5Ɋ7 ׮#5P+*9cև֌I.k"C7#BpQ-^ʵpӯ9 "\l{5<ɽu3cso{eLRkL2|"CQM|uQ?,9e-Zwź14B&$R3*1W,}Y)Ta:o+YL~>Wa }J*(Qι֓p}6TGV?Ép#ڰ{ cpǎs8ڈm65* *>+E}uu]R5%!ɍqn~שA H"ilc^Z1/:ƒqñD 'y+tH&42yTےn%=ă9}b!9IbFbY!lLU_e N.t/X?c7+]IRZV/J[XS"-yh%pKƚH4μ)k:@:@]<5NȻyZ ^5%_Ʉq{Nј#~>zp'Wf=jz,Q:ajBkuh*Nb_O%ƃeENtN?: qe:ŘG{p/p2 e809);MM y^]uHAY۸ ߉-g>Q'-*W1])?}^_'v/ }O<J/D}A/E:yDB>wEe0ڋ:d(Vj+ۋo^ދ:xΉ{Y+hg+0j {#mu֫X5ݔsG1_<\D8 ;4YnC6x?q hm<)np|z}U$W@./1u灮ی)뺍P&l7`6>)*[{De߾y\;Оw޶'~:_uc`s>#oN2lv,Vδ؃a.ri3ѻ.+Cʆ4Ҝi31XG=-  uП;цў֡C5RHo>i{ZCi#֥Ӫ|zD^^ CsM?~=[A1p8X1Nbhc;RD0 2K̥Gt t t &]e 7}dm{mJy.gf}^o{A_=_F TW2='Fi ) <&ӁЁЁЏlo V],mNmaA]~maeY.Z;t.̮U$c[9}{ W.UŸ_px݈-\}m( m<{   f| +EFϷ3X?圸^lH}6%i[ŋ>f_/?*x@}m_ᚍeb_Ҫ/|Wt6(1v׭bu( Đl6qyF]Z`u𼵀'*}fϞKgh9QRfZ>uy8N(m0}󼲀'*}Vz*Sh9ϟVيXӡ7 Ch9woЪ1JIG}J@v6>P>7S;ե~*(1X;;"[@9 ڥ4 gsa6%V>Z V. <کX"'|ν|!0^}z,AO;Y9Lv֊dັ+iYS[whO9IJȠ.]v%[uFm@Cfzrw۶rk_dL=)odpΞ-=K?$HJݽÆb Ulj h\&ldg3m{9j4%Fsnvף6:ۈW 21綡Qm8\:8.۰{q=b%xc/c,4b@idJzC{Q{ GUKPۅ#~y=3ڕ\p癳{ %)52ߣ>DþAS8ҾчFgyuMP А~5])^{%{v-3'(MHT_ARF'h ] OS]Wz"zmƿC|Ы[)sqʗ>Pl%)׭6SP}=?*~CNہJmJ=Juxm;}?}6bm} ^ =ǥ 6`o|<4~1?beJqLB^x}}zhUYӥzD*Z!߉ܫm{dY*dY͑Xh|Щ؁[}ͼoކX;X6=^7}͂~@蹬uˡJJCXvz ac]BCfU-c9Ucj:[m@|ӂЪG>P!<АgG/~բ' Z5|$O<#yf @*Tz-~ó<ЪIZYn~yೂؗ9k=?XKNP' t-;൤;~-96j{~?KxX߿)-\/(P_A[:lu'*۳!x-?\T~7g{n>&E ḱp% ҵcppq\ÙG +ЪpE o_bMq F _+ק3kol9kj3 ߃|QSoA=O椛DIմoݣկ/LojYQ٠7{С>nK%O.)1qµp0}n:u]>hԣ<<-x$?Y~USOG{нPfDC.ldOuCe2'Zݷ t6ц@i]55YxIHhc+/+j`Iӱ]0kaP?.m{sx c@碸+Ń?-G#s-&/ʾ:7á)rfzӆ8tt9byH8"xf;TS}gh32yTڍWKf$M ^Ogʶ+M~C˹c1tX.7%<\ 4dHtvA?˕=繷|"4x[~V>G,5C^(qSQA"sx!NqeӲyWSăhFGlNH"J?׫tD-FM-p 8P%aۦ)`+ <|m;Pf'%o7FIF|]po}buVw\Zώ?`{|>pk{گƕX:j_b" }fs=>ceq/{_3_V~o]kǼ7ә^2Xo~g{y.4\e4\=ʙ,h;W9J53cCZfڝ??@T6RY  m߱Leh߇ŜiېGF'=b:Ne}9v )g6?CU_YtvlzjM 7SebJњGgGW+~K#]amX9ڮ l]=c.E\ \q_..*+P#ē J蟾v+x.'4xҧ'|xGxO}/]01h3{'eyBgb_Yo󎖘?_s% JsgE'%m0}\TZ>o\󿥀?r xBFYgs13EY8AgboL({PL]K ;)~6/c'<}gjs`=7Z{:SUy-Փ'V!u3<|8vUCߘV!o˾UەBZ=_M%$ d)k}E8;Ͼ!3O~H>:ۨ|uޔ_vbO|8_P4#:5ozsyx0;ā53SW;@/://*d{3V|X& ~#eA+-'ŃO?gH9؏,^LNXhUt՛u-^jJf\) uwRxbACbVްxQ۰<<S偶=_*G* n`Bo٪P Xʄ\xb1 _W[ >-r\#]B+bx0_D=U$k͸3_!_hm ז#m{e:2SGcUavP=cm {o#OwVhx33szy4G~)Yakک%cN[|׋sY[yUU zsCcSyQyꚗtH97uJOJwM2hY ]QH"8Dm?@6|Q0o : #G(ݘ6U7<݁]̷[K}mGaOPm{@[*pR, 4dk=OHNҕEWE3E|y2 Zʞ]A.0ժ3 PզhX.hU*{f ]wrq$ Z؉XY\ @v Jk~Xӝ٠/46ꪣ/ZgqEbk k1J+)Q19\CK !@pT$4B2X 6Z^?(k#l`l#hȢ*ڵ<@Cfj{U,b11^@eVEf6V|4Y66S|tXGvO?u`/hU'aXhUl^6O͓ͯdXh *"6gcy@Utr78B<^S#/WCyMⷯ YQ[Аe{by<nJ?M7u܆낳I=26f,UPX)|xcyŃ?c 7+ Ъlb߫U5B~Γy#±-ɷD8}sW## C\oNJq&y5&Ըx5ԒUlkp3_rZ;SL!J́ne| ߃ئyp?Po>!OzR~lqU⁍qacPjѰVY}@y]VeE½D^Gv }lp]w91Tȁ<{ꥂ:7 peF~V*|Iܽ/JkjvyDg"|ʱ(oiw)FgeVY'2ZvF޺79[ .g?qֿ!wn_ۥwܾ,8~ppl<} x}̳پ^fM imRXQ@.SClQIftVCO3T=c'F&#=u\M)n ?|'T"E6׋MQX9eg۠/1 <\ :HLu;Q޺7i}xySp{](kq7/O{̝e|`XL8P73vͺ&>ϺDYdCNIg؎yxxz^;=%N_2uoٺAxV<5Dlh؀x] k8KnsSx ۻLXH+ sx- yZTLFа2jۜ)h4[=K|wcym-Us АA<|(OT_g Xeٟ6XC&=!/=, •mh?gekO< gv*{y<BrGV <8'p:~ktq 堛2ƅ,ۜ)rF\!i[fE{ ,nMYo>O qˎ*OYTFؔ ~E_{#}U}|m z^Mme}3Ͷ$x֍6Sr]qk>y7+MA'rpnQ>"{?Ԣ1X`)5sckTGJH汘/42Z"c : Țuׅ-3cK'[eɂǩq/h \Rx>mLt1XЪU6]]&Z9 <_偶=>rW m2@CC=抆x:5&1N _i1Ğm%/@7TѮk%>)^_YoqWqQ.;zl{i& $wo='ׯw| `뀌! !Yo\1纜օ^hnsrp=p xR)kpp$u98ܡ<>@>7R*JX@Hlho2#?o\o4c?ĵ?{\pUOhW8PO _^|1_hՀ*Ϧ{>~g?Îxx.i'&JEѩ}6ev֔̎Sjcz\SuWpm@?y%k[2Ɩt.΄뢝"\O?!Zlo/ןYjC}$Jvt7.qUE7<߻l>v@8tf{XWv]fp۶ txS>eٍ2'1^xl<:vm16(Y*[f㵢12ez 7,^Tf+aY={[ %&_ E9g h{X%Y@y3=u/RؾGY@zb}PҜ7M|pQ?̭sXk|HgTr0>sZk 8<:7Os;𳝬s2Աρ+#9@"^8r[;]eB{lCD4h]䰿_gB{q2]#)DL6oꒇw؆8@x%:>.[)\.JPf{=l֥e$/ ׈A'k*-Z =ɰZ=CpQmK._,ثC>١ř>}XWա tuh\gOUpϚG{Uۮp,w{ktk1菱f޺nI0(Кمzna9 mcr1hSk;:l\dWOA.XhJṎ==iwYw U=K{2i7tI qI ڶ.v^!o1RGп4vӮ<,_BT:G}Z(E~;9:i( աJ㕎UQι!~}6b;Pڈ{vUW{cy}q)>w<~l 9J !}hfs/1Wa8QaA,,53 ìà ÑÌÏ (èñïîëüçóÿ ïîäñòàíîâêó, îáóñëîâëåííóþ ïðîäóêöèåé ð 183 ), ðåçóëüòàòîì äåéñòâèÿ êîòîðîãî áóäåò ñëåäóþùàÿ ïðîäóêöèÿ: ð èñõ : 1s_2s_3s_4s_5s_6s_7s_8s_9s1_9s2  1s_2s_3s_4s_5s_6s_7s_8s_9s; ð èñõ áóäåò èñõîäíîé ïðîäóêöèåé äëÿ äàëüíåéøåãî äåéñòâèÿ àëãîðèòìà ÑÌÏ. Ïðèìåíÿÿ äàëåå àëãîðèòì ÑÌÏ, ïîëó÷àåì ñèñòåìó ïðîäóêöèé Ð 3 : Ð 3 ={ð 3j | j=1,2,…,5}, ãäå ð 31 :sigm  à1_ý1_à2_ý2_à5_ý3_à6_ý4_à2_ý1_à3_ý2_à6_ý3_à7_ý4_à3_ý1_à4_ý2_à7 _ý3_à8_ý4_à5_ý1_à6_ý2_à9_ý3_à10_ý4_à6_ý1_à7_ý2_à10_ý3_à11_ý4_à7_ý1_à8_ý2 _à11_ý3_à12_ý4_à9_ý1_à10_ý2_à13_ý1_à14_ý4_à10_ý1_à11_ý2_à14_ý3_à15_ý4_à11_ý1_à12_ý2_à15_ý3_à16_ ý4; ð 32 : à1_ý1_à2_ý2_à5_ý3_à6_ý4_à2_ý1_à3_ý2_à6_ý3_à7_ý4_à3_ý1_à4_ý2_à7_ý3_à8 _ý4_à5_ý1_à6_ý2_à9_ý3_à10_ý4_à6_ý1_à7_ý2_à10_ý3_à11_ý4_à7_ý1_à8_ý2_à11_ý3 _à12_ý4_à9_ý1_à10_ý2_à13_ý3_à14_ý4_à10_ý1_à11_ý2_à14_ý3_à15_ý4_à11_ý1_à12_ý2_à15_ý3_à16_ý4  1ì1_1ì2_1ì3_1ì4_2ì1_2ì2_2ì3_2ì4_3ì1_3ì2_3ì3_3ì4 _4ì1_4ì2_4ì3_4ì4_5ì1_5ì2_5ì3_5ì4_6ì1_6ì2_6ì3_6ì4_7ì1_7ì2 _7ì3_7ì4_8ì1_8ì2_8ì3_8ì4_9ì1_9ì2_9ì3_9ì4; ð 33 :1ì1_1ì2_1ì3_1ì4_2ì1_2ì2_2ì3_2ì4_3ì1_3ì2_3ì3_3ì4_4ì1_4ì2_4ì3_4ì4 _5ì1_5ì2_5ì3_5ì4_6ì1_6ì2_6ì3_6ì4_7ì1_7ì2_7ì3_7ì4_8ì1_8ì2 _8ì3_8ì4_9ì1_9ì2_9ì3_9ì4  1s_2s_3s_4s_5s_6s_7s_8s_9s; ð 34 :1s_2s_3s_4s_5s_6s_7s_8s_9s  ñ; ð 35 : ñ  k. Èñïîëüçóÿ P 3, ñôîðìèðóåì G 3 =(U Ò3 ,V ÍÒ3 ,  3 , P 3 ), ïðè÷åì U Ò3 =U Ò1 , V ÍÒ3 =V ÍÒ1 ,  3 =  1 ={sigm}. Òàêèì îáðàçîì, èìååì ãðàììàòèêó G 3 , îòëè÷àþùóþñÿ îò ãðàììà- òèê G 1 è G 2 òîëüêî ñèñòåìîé ïðîäóêöèé. Ïîëíûé âûâîä öåïî÷êè k â ãðàììàòèêå G 3 áóäåò èìåòü ñëåäóþùèé âèä: sigm,à1_ý1_à2_ý2_à5_ý3_à6_ý4_à2_ý1_à3_ý2_à6_ý3_à7_ý4_à3_ý1_à4_ý2_à7_ý3_à8 _ý4_à5_ý1_à6_ý2_à9_ý3_à10_ý4_à6_ý1_à7_ý2_à10_ý3_à11_ý4_à7_ý1_à8_ý2_à11_ý3 _à12_ý4_à9_ý1_à10_ý2_à13_ý3_à14_ý4_à10_ý1_à11_ý2_à14_ý3_à15_ý4_à11_ý1_à12 _ý2_à15_ý3_à16_ý4,1ì1_1ì2_1ì3_1ì4_2ì1_2ì2_2ì3_2ì4_3ì1_3ì2_3ì3_3ì4 _4ì1_4ì2_4ì3_4ì4_5ì1_5ì2_5ì3_5ì4_6ì1_6ì2_6ì3_6ì4_7ì1_7ì2_7ì3_7ì4 _8ì1_8ì2_8ì3_8ì4_9ì1_9ì2_9ì3_9ì4,1s_2s_3s_4s_5s_6s_7s_8s_9s, ñ, k. Âûâîä ïðåäñòàâëåíèÿ êîððåëÿöèîííîãî àëãîðèòìà W 3 =W(  kor (L 3 )) â ÿçûêå L 3 =L 3 (G 3 ) ðåàëèçóåòñÿ çà 5 øàãîâ, ñëåäîâàòåëüíî, l(W 3 )=5 è l(W 3 )Ñ7KlߛAMҵْV s5 ~t`7;wMųgs*+c~_ѹ3N[z_RҲi-h6ύռ\ݕmLmf9G{r039:uþV}gMc:5nwеu0{4B7ַnTmݓI~Q KHӤPuIJW(O(>cA6/gB ]gB9z1Wdwt1 cڏl__!^kad8ch5Rx^6#Q CiG{ZCZ81'S=|H^I6PvqzV7}6އ yz'=\w+^w,k<\+'H "[$9/EGѭo6y!'JsG[>:ɞ#{pX  X?Sg JMp;| nՠs_%dY;|,!G s{s+s_zƛ |J9z9"k@W!^ASؓOܡȕB_YhKSឞ7 0/'َQTy`'Gß"jZ5}fSgGvI/}Y >E'Qrjk]RLmɧ3, mfxoϙ<Gf#q*^<~67` 5a߀ ޝ`rrLFj*-(p{Y A3hZ$$Iy [Jߍ w}OYf ծ=qgԱ޾ quaw1s_w~i\ۻV0}}xۼLlucl}Lw9SLͳ5MW8O_'gv)2}GXלߚؘ͵Qlum*ٷ1?+S-rx2V=~[>[ w-V_F6Oc͍ku\*U @TQ D*U @Tj~Q D*U @TQ +=Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:18  GX 0GG(16d2e/H1]ȭ{(x Uu%*)&]AHR).ªL'bl*"T BG0QŎv@A#H,%q$L }lvdH8{=s=>o*!VBHpn/Dw~{^Bs 7At.}-!ܿOPPi07\> ׆SsYcCq\ɡ~TTCRAŧ(_ V[kjm0bh2[3NAUJY@%rф?IPݔ'ڢjI8jq,^1{œ.iC 7ukrwy>&+ϞpG i6ix|CQpd\5) Ls*y]ǶREu8rx§@ܘY-ST,.c Ivk&9:|Í֎<-M?v] |}V;ǎY…i*!QH?DS}A8m+1WfU,=Gbxpm.o{ IГi WKƑ!E͉#͎}O/r8(:ouQ9:rR8Z߼K㛄&aoo*͑=)9篣 nOOvZpcܷLǘBh9~`LhXOZ쓮ׇ-*-okޚY)º-umxIAbOV GH/ā(6,< >nLǧ*=R8N7E~xB#|ȧޤ9/o>Ve8 } ;qp%i|,/H} /޷6zNck`)ɚ}%#J6ʀꊎh/:A7ĭGBk<4tB&p?}m^2l#xF_ e/m:|1`ٔ>Q0s8h)•~Ѷi-JYq%z`#EgDP/랶QƉ5l϶3ZW wGEkl~Nhwxh 3Z5, KZ H J̜hĕ1Ek,E=|RZ[g.lBUL_X8q/M/<"c@@eBǦcМhqldM5lX5F`74nD{4S ɔ8N.{0;> u@VgziUfkq]vY֡}}:nې::#^L#o!^Aswep|OK l(\<,Zq ՞7㬌s9t^Ⳓehr̅s`{僒s3 G{l\9s!,;sA߬Y|s -]r9wU񬌰ݮ֩@8$ZNno(aIʃ:w3o?ϛ7-}Mkg%U86MFh9ݾ?` Gkn؍fv-PYceCv sB:bf,U É33'0~] u'EeaAntEN5C`@pY reA)(䓚DsU#*IG5_s!l'C<(4Q/Cj!:B̃U[kqҭ !!y)Xfΐr~Ȋּj7f[l?4ڏ%ڒ4? iEmstt9x:f.&ym{ﵼ~>Os<,B呷K#}o/H7RdL_Hvna0ؓc.9W LJ$C|)Ǝ pY{hG 9wiw6 @_һvom`>?} y֗C#`4C\.=mpbOcaP3o0Y=\ %G leI,]oqc$痭!CЭ?iBt)|3n;nY63Fu.r=k콦썝wP cTNn8{c4JeYOmvڒi ؏5zRpoYX{fccak}A58BDhv~v@Y-͋C *p6#NvHూ|5qlt$["{.t5! E{T}rzh[j~CJǢ̔<9KcC} 36#N[?Ao>Eоftxѵ}EQڪ8gM 3>|uq_@~@]s/L0)ܲxS71}9'^-=9 +_ܤYw[?ɜI'թ,/sWGXWj=zRhfy7d݂a6h hx^wbC_+uW{^9Ӛ$i69@#;)T?(T3.c]_9~uCp`rMΫpCw/  we+/BYо un;ώ?'?>;ApИmc ܟ/ ˏy!ŗo?=.V>ƽ !spUpF-z ?Eٝ/;PG4l񠟹9T>(S89́́e}>H9y^]>xx?9'9133loy3K}f\BV!r9pp)z#tHoYCTuKE/Q3i^HO>w[CUkB[.}3;* ?4G{Й廯" ?iY4{G%4Nshq{t>{f}~sOr>S}vٳ>KH%,۶Jm i whT:cZȥW{?v⬝7O)=tWr34T~6?N:mkՑ}8 Hg8{H>>s~gxw>cCG|y;쪀r]?b}j/c!NAؾ GN/-߉[񬍻5# EHO8y1{xLy5+XgrF#ܞ3[.q.[M<y T]&|.l߳m{/GxWo%G^ZѨFkכ^ИEz.]zrVNoY=m \!k.><717ƶo&-A<NƬttG[֜Qfq,z@^Zl= .S}ˡyIȗr5r/|?ym>40M@lF$olˇ4q0.{C֏lͻE½Oe {p >3a3sB=xS9|sf D4515T+%LB蓾҄mY^6[e|ġos>S]WҮ/8[dc7g[lcK|;8+Gu`E/wVM3Y)3X[vU sr5Ƥj-ϭkYc} ^Xoy-3G>֯ym#mrS 9sxH| rn|t`c;kl 4]9y 9_@6!ZoCC[[+Dcu?K=U#JwƦoW9ցOu\`-C,p|;m_ 0ЌqtБQͮ')|>oܮ"w/wpo0az;7?ov_U.#&ֿf/7o6) Gx`:$hBc 9m\F:9r 8Nwy1y7hh\A`R-c~Es*`;^2/-Oz7]0n80`'!IUV&foH_r=bmم=mu{AxnWE.!4)Ai\B|.e:Ӕ P!A[+i•i**Jj22Y;U=k#3;ΌH|YWϴRʼmVcZ㴙4!Ç5x=2ka v.ur~= \C'NCႊ*Y•٘1я^/~$}Of_LͷieN]$phn工GC:L|[Lɫoe ;o>h=` ~ ̀ވ9}öW㛢%:q%ISZV~Б}#<."oYh̳iLâk{w]Sأ>fivy~tzC'7-8C짧Ux>yQzU(|F!t%i?!U 3ƕZ={y5_ĵj9ƃ/GED9,'ɼd8oY[ .o.K4nMd5ߛUJn.ѽq^_ٺuqߤmuZ115[zz^_W/:?~sOpplnpygCz|4H!Gv՗1~{%AkCŵ4 ;C@H_\7#uor~&TGS X l)GXQkˑrvE~>p-YgwrےGۦ3~%}f4/Zsn`EѸf5 :Ag&ƑGjg^9đu <{7^ |O|H[kD2V 3Mzϒދr&ހ3^`s}q#< O-kv8:Wߜ&[SZ}oe˯A;u=:xҹн>Wˣ|IaSt>o!DS?;7bnqF@҈_9B$|<{&If7/1Ľ|#Vq>hc[YSpk|,2MCD]^y^3}|3~2Rpx%u&p0/# X}1~q1G07me&:p;h`ߘ2O?3Qk1MlOn߄}vžww}}ww?} ?[{+ wdK5{|ynW}[יӉ>)w~;;4wdt 뽅Bcd\O+֭V־)}aPW^7*nSߤya[p"M{͓FƄZ6e"4Bըi|z[6!2Yys ~`ek"BA 7V2?HWpz2c_bQB. h3\lKO㍺kܸ3{`;K- 9N[u>ެ|B{ qt}{mۺo>M>;on_MMyЌ'LBMN(8Y>5/e#SK*ϰmr{ミCe^"nT~=6w [eڅa!ݗ|>٫eRlٴzDڶ!n}`'tg>hؠ]~M55B'i :)A^xͱ?c_4{xsu5/|X.V8ѿY87_\DNyonM3~?vu;:&J!xI3?!Rq,gF-mz^6r]q+__,[tHa.F5 66.Nˡ}cGٶ^Gg|qovƷZ2DCIIOXy9yy?᎜o{bG{^n?_2X_z5#k;7?;`nۃp4iH9750M\rl|7Qq&:C=X#25{_r7>#d]:ƺ8ߗ< dUnjf}O,][~vN}8I҈1 Z5!kFYI{Jkf%dMip{u2k1p@ ރ5?K[)a/7W6ŷ vw|a$~!/7;\G3$>,G?D6xz]I?ߖ..Q;aoP1}CY/R[zk׀Z/ c⭂:o_YٛNߕ6bn=}:U?OUb6uKh]u_ȗFŮ^Wy ˙ctș } 럽c,="cU=|Ny'aOS璨'G$uu ݄kYmն?yts2&%ݒH]B(<}_b(EM¬!ɷ/[G[N&GVE3ɣlrc۝4"I*L9nIT%«ȗ-YR ]ѝFRmY=Gxl3exRzld,8)^_#)iErhQ`쑁=P@+P=f+> f܌B7qͰ%3쵇ҧI@Wn >F}1gll{UOm`mpc{tw>g.νC]ZwbpnzdOcK/ c(X .֜3U *oB. DB+;Ez.\L_ZdI=aXY29̜&r/'_#\ }*xNxeRYG]$Jlt @l~x v=4 #Jp ly7A* ׳Q O@~ #V/v00"uc$2AEe #?8π8x9o2'3MFڀOu1}3">E71桗Od|5~" j\ 9o:g6jx! 99@l,9>z>d q6[A5 Vc 3Hd߂$ 9:NA,TuʤLa?Ľcs3[yZg㥮t΁5s5]_&^VO }'GToߏܳĜOb|E[>|Y/C׳4kh/ЍgKcO# PtGM'J ߱xx#\B.GAFd^U9=+W9j~:m/h | FWegrE!kZl_GjO׳]kȳZwuᝒ)k*/-xyr] x6K Xց9Hm̝F KU< 9zf3d<,Gxrc=-`?y?Ȓޡ(,=#pN{2^YFֽJ=9ԣLw;?ozho3|:o|w+NJἓ,N˦v:#wĪM^C*=S/{3^{v{kƝs||frw3I>w~g *;c=ԍP[ga|^YXn⪏lFSL fn<-;v#뷞tvnp;vہ_nnp;v.Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:18  f )(16~2/1֦{tx ]UyD & =2Cj DqT v@DH Zj9YԦ'VtOrKOK]$$_w1/ka ߝ,ya.=,KV~d}?]!'+oƲtt}znMz.T*,^ӟ\xn=dMTն]kӌdq{Yҩ2O㿘Ŵ M.OߦcIY$g*R*|SOx'ʣb\+e\!ͥY5KnGz|UjW87OMޟ\*parnyn|Mbϋpnqm67oR\67w& flnNWܼF噛MߦU87ǒ^47/RE"bu&y?WBYI*)߆mt뙹s{U7=w^Vt곢BV- 2T[Ȟ W8+ ޫY:^ <KZ#r`7o/\kSDg$IK+nnڱ㮵3D>ϾiߨWHj^pњy. ?O?=#Җ.=w?#Ym+FO(duHRt/_KNZL-~N;~Frb(9+9)9MwoIސ\)o,$D,OrOP|rR]ʥ-/_0mzj~y9Xd54_wV=eF"W2VnF[hshs/hyo 5)3[DW^륪 :uݴFtJFͲIE5Εh^&)Xvܵl]eQ܄te^{6Sk鮾c&O8O`n󋾣2)Kuv _DLJZY kv?m*=+O/+6]鵛RULIu=z$Ӌ2u"zMWώiɘîG/7$1zQܛ^<ף6uC³r:FeLY%pp (y"Yɮd7^닉WUKӟz׳; j:w*Iu[*"v'ꎮfp ]~i]Ak|]S.\<ףkl]ozy!#^K._̧Ȏ/{xR .ݢO \Ywz5{Z}xw34nf~6wNڿW4|9Pk'9s|> 28ϓ>֢y-"*u3[O?_cK$(1͓Y}m]Io0O_p'!λ389O*\3ǹq,U qn^wўiWnewN \Z{c#pojpWg>¿;&wwL2 {(-vе| hD^/ɋq>)<T ^ITӵjZ.ȧ|EANj_i?~vc>R_,y_,yb(q]ʘ[6/1&vϳCQziz)(,U` o(~bE5_4y'* -#4W%n'Xș]K_ >PWU2B=j/ T V*[F3t"v J%胼`^k=`zQzᄷ:*s8WftPOAC:I zyW ^u%%$%I6&;=mN&*Uؐ +ިɦ o`*ҫV#T Y}oLV?v2}x1Ĺ3%g+'&|P#8b$ur$WU6B{Zkzõ7\p{*;_Ш>]fv~]={ߟIקfƭLWhl"S9o 7]WU[+s3jZfN[򸶾t3֓D+9n'dY?@Y 4^=[s:е6yڳ;^uvVe<*{i8`Rtp'l&sr&G~_yض zmc7tڡoˠf/=eQgI]4#\BV^U~x\M|i1w(/\E6@Zzx6DM`Q]EWş+K&|OLvxHepzEjٛ rd/Z?-2/S]-^L Y;v\D|éEY{*R2hk}E>m^&SfOO *7hyt2N}аBO"rE>CGowWt5b9vҨU:zEhT{es6sW 5D;z|b)9l"}^_A&w.!O@z'=DMh?{mG>caWNnwŗuZ11_?[@wx0| [.+Sc۩5c:}fxj :yYM vvX͠Q`';m'B;o嘯ǚ/c,R< yK<>^DK^Va_^8Z޺1y+D>uzVzSzxTVc;ݰVCې֑H ,_'é} C߬:8Oi_P߮(X?l06cU8H~C#!}hdzsw[Me>>3pn:瞘=}fČVQg.SZb^y[EENxlIiAg\r.k\]KW_i:opbʠ8ݺM~[Nn-*%=;D;mfu =X /Zc/9{acp_2BKsJnvpYۀo_ r15]/ྫྷbp廾KwQ_5k}/[9jªn"/~rМ?}yœ1>ں| ?2ܫ$bpᙟP 7oڊ#ޣp'>y~"fZ$ʿ g~7nW$3]`Gp(zsĎ8o"E:Ԛ27(Wϛ/Z||)Ǭj?\_҄x5r6ϫɃW:rN%VtNi\ěA2ڎTr"#ߦۨ9`.x|ZNe?4xU(3<AN\Ee oYJI#>8e/H;:Lvlb%G*J>RfR: )[D'g>|@;};x͌}S5OS̋j}~7pcg!Mxn.KY\+|҉ù3]y OLR.?3 ,4?Wi 6Fa}?\9۴Yky'V#kwsr:kqRUAnU_鉜M)óWq?fLv @m̡ >;:b9pw3Ltt2 @:0 a]]Qi>y5'tH 6̃'4T̃v`c=|g̱WmMYS0{L>|;xb?4.r` [?rR<~'|zUY>߇ U#UꞱ}4a}R|)!sx?|CCC{(4ԍZzZ<|D s֭ϠOT{2XS)ì]wLIo[d}l!|wAOV)B(W|z77V̧;Wt#gM?QOשC}3Fr7^ӭV"vֽҰ%2Tc{Pj:Rdud0gpo=ǰqf{K6]kuU<\y)aBo%8`|@f r7>̿gОYT3Xo&˸3nxu'e]4`;7\&'[]|=dnuτnAr!G7*@in|`>|Vi"6*[#Áq_-yTK*뫊\zӭ_>E-E8o{/}ŝ93s|* * uh_QSҴ"}|)l}R`+f/)e̫r+sPJTC:@u ~Cy6߈{W4k?J~a~_S>{L2e29E@n8XYܜNeG<#+Gͭ<cZQ7 m:tb>.`ቡRyv57) gg) %_zP>[çjO/e4&9*ǶВ ;y6%{PupPQ<;T XD#wۡ=%ZcW5z u5?o]ܺ 0{DZnaʱ6/Ṟ5E,k|{%_bya9vHUԁ$+P *;ٹ5.Ii6 br>que-24tb,د/~!oҐ e=SJg'dp6*[w4|Gbpº`8p1QuY aCYS^Lƞ'A }co䝨ϔm? t>'0`_3<mx{=z3@ɾc4L/Y\tמL>B/!-s;3A{m= I\uQhRy6+`8=2BO|cxyOAl'0ҋp  t8oELzŔn[)ת Yvk|z4^_ 7i|CK(#m5}f>}eE~ }=T`_ %pdS[=Ss ]'2Zd=w\bVtѵ:<.2B/*}{B{7ߋc ,,Ϭit/ 8J?T}X}ӏjJAαWOnJePqL~zy=֓~я4kl 4eEdžUC/c] ޡE{Szn\SL8|;X,Oy2ˬv.&dErYw[ V\[B]cX80;էfkP+o*PyZWK#pN'0!$6N5/tZWu>[V<.*"ݿ3yeS~#3t1L^qș cUdHvh?>1]<ְVK8n[Qysyc8kt\73fՈmU~x~_sݥ{=ٶm:ʼ2jM^P!o/G^Wb#k _׾8ׅ');#쵰?Gq)GZ\GY@fl _ U_8<6m]i b6ΰh0Ylr}✝fz6wElŝW}+FFHZ$&i';σ7*+<#3b9go/ODo.ˆ8q?)*šu/^vcdHmӏ2YOʧd9~Ҽ,'IP/rt1ߕ{BGNYQDv,{hyJ8sEܬd)F"~J=4Q^ LINxrjBYɌ{:~E2In_w15xA ߝ,蜲buO-˒??xhFqe٧\ܡcً;,}/ ՟_-X.-Xqr=乞 '+T|j.۵iFڇ,i1Ө^cI(p4!7BGV(J͑e~z'~u{$\_ɣu*OȻ غ,[e<^yI3 bX́@C9H;?kp/!9ozBF"y:=k||<:IB:x9AlzA+ W5wԴ裣_"O)-Oyoyjya9J<%yQyzz_n٤gr99xV]L{s8 gZEWsAw߫%+ m8,,RzLK,~M!JMCmY}|* ?]-GL/0o^~ўY}b?;c}$n[XS1X}!ϴހӲܹ]U"~I7AW/OqCg1_[wRnygcp%^x} yb=JyMX}A}O1p^c \X3"XpI \Xk [n"G}޿S~[}.] !}]Ec37gw0/Hܜ_yv]vu"s v!v5Գsp|2btN+\@mȾ;O.M35ɫ߃\+߃\vLF'#xW^c=b;%ΩYնWC;hҷ)P6@΁(%aa(߫Xi_~o^j[a_aUiøR._XQm4&1SO;!R;s0R;)` n[J;V!fk>z&Y6XiUrQSfO;l͉wzW?C/_w :ߌ o~Me߰~=u$k >CY_=0rWPH.@=tu &ᗗ!(u+XtrK2oÂd}ԍ_g0 IpW)CyNt}xu_2[\ie~ݴ&,EcRF{|Sx^;dD^zNQX%ZͿV~_c_^ov^3N7,n5o71_?37Uн=}DZ/窞2oAV֯"z3oon)n><9`^xޟ}hQؼqVagl<n.]Xl*6cx^y~/xBztuG/-v$%C`mkR }&x!N!xfl.KPvL)nC8'_WL}:}{)Cy[NBogd9X5ސ_;lvԉd'zO*ZWȖ"Rյv2e d(FWvj4ܿN)3]3EkҚoJMo +Z <^nB`M^]a{m "gӇ[ģNY8 ujUwov[<#---T;?KL׊Ucy]aTЖgjiw|hwNs3j[A@mӨ4pY#sYlotn`yvqX?p%DOJi r&X1zߣ'D׭կaa>țay(vf+Z/~wy0R1?7<ސ9ة!:_hHdkҡ3MӁ>nyS=mGZXS$|?9VGyJc1ި{~Mo͚vfD:\=cu94Ø!<~u 7SN`) ,!ɫ!M$ȺN")_oN?o?ܶ TQxwߴ oLUEs\-OyzDʱB8rub?t#W)eZ8W(N 3/_RU'~{p=;lsuгaոR={`ccW(4 XSHo;vwEy>]E >G}@slk+sTD/SWkis?΍19W'?+[ 9=e87}O+yg-/,Gn1F Ù |7.nV:ӕ2"imI5﫶1[ηAmX%鎤ЗSt} /aLW:uMAOG:鮔N/CDP/b>* uh:lKdKhǥ2@gAJ0=3L9` xX;g]V OUϙC_~WN_f7]z.D_vL_'<:$:);hO)}y~;vX' }P_>H"M6\/z }.2h^VYk芑6iv5cy-wU=tEO7܅5"2_[g[pjo>R~5Pna=kg$o1Bkd^Ttoə>J \oP ᷡr$_]]q%pa}H~2Ƿ#ۤ87ȹEߜ+M f756+7aO*ojCh)xuzۆ&@Sy;<&lMljVN?ްd=ԈEL1%PZ#vӻsv}n_:*g`(eӊ)Cyn>tKdI x)6Sz}pK*rg#^:s+IǶ{WayzXgEfO?iܩ01#as['s4ȟߖ=3U۵}}{Rȉ&~.$ ۥlxsaDf5JP>Oe6 Q\sTG=C{<W]̯wx}@O##p 껼7OyF{Owt \XߵLH}˃^Vַ E%R_hC/q_ ~Y .e1>bp}~Y .~ ./?yRO'6Xmv)l;T0omP/bnޣ}Av6{Sۉ~v1gi~v'IcKT#v-g#&Jҍt]r6nVic'yoI+a=C_(h?Ŏt"xRwOgtv:t>S&מ=pGXUQ w你 ஢ ]菮R#6_'\DSt%ght/Qv%,ٮCKˋl1HojwA;[kv~2Z"Dk~ٹdsbp^sS ޠݏ컸Pyy \Xu]qz>%pa}j]T_Žo{$cp!x.:f(:fE Wtp!~pa} Ks#x5Ovv}Gv%/Wr/.z۠`1?Ygv][nn? 7!]aյ .qW:jv4c@cuߐUukM N97vcpju"{ Čiz;P':LuFrj_\&43/3۷Z*;z3raSbݢ|l8]Q h7jeJֺElNÆ= xjN}f{H_.+y >* qCvcAcQ6V[U?bgt%Ϸ2XU:il6!pH㵜e}YvT;lv6AϟiBVhpmSwٶk>﷡ ܧ^O!Vu~U<2V_oP7+1ʠݫJ} +M ]EEkK-a'Pw)f7+%OU uTy .H7uy42OZdΞi]ϰ |v`uS3rƐr ?<׳u'"y-/MM/lp]ז(r3cn^b6,m-\gKk8׈]Z| g[%?Sz B?PڀBxeĎXNZbZ۷A_kuܭ^jYSH'f{. ͭS|G _UO#p )CNWR|E }[3L_8Ϳ@C?:;}@ky7QAmÅkJzUtP(VncpKPe%ruvε9߮)l45?[VB2Y)S y5= eLEج7_|B#berQ9sfcӕ>Y&gx'|!`H|&\H93Q}KW5j߅K4C , ʣ7j>&\M\o.G? mO ]Xa}J;vCxx\7'1//qt!2 fj;ϑNl<_ϡ3ȓr{7f~'+_YGE$RUV5xMf[bqάMb6u{CͪC1cJuyC<Ҍʫ)gP/TxT`S4rQ<4ļ{ W28h=`u:{vO`3;ir_N41Fb" Cқ_G&b"ŽبKVgGl;>.K% %uѱMuW#[uc-NB>&pR~t3q)n_I;e{oGvݨ3sj0l˜RG a;-vc_1IˬSK ~?!c..z搋UI'ƚۇMݣ=־TkF棊i%UOMH+og㙬8rF@7[Ob'x ymC[O6h738(vJhͺ|g&[ ua>OVQK觲js?z3iny+O_˸Ӿp//&,1:/<{N_>2P6ke:2m暼~~ )4bf|}'=uk-ulf+GTyncGt|k6VFku̵ fOkkcjCm|?ijO +)JNkq7,Vmy~;7F Mpi3R_jCɦĹN٫wklV;,IV:k {lPk>L* l֨|ӸdqzҳTԂC؞^39Hs|2?2d A\B:J9sy|;GefxyךaTVx<}^r߈yr9mEDf`:}] 8ɯ@y0do"Љ.W,Ǒ>rrx EOBFWJk G'>R^]dE%8věs)v%UXollXef<~oS"wv,ا qؼ sDIZ-':~]?teNދ&/r\!}ߡɻ5%csW'W"7[f 3+>s>+7'vVYq7,p^|i96y4"m؜\Riܩxi7]~ڬWmsfdk͘hO6vLN*Ҭr7=n+K7\f93iJcKci a?A-Dc4C}&MDs0rZ<Gd A @ 2dK_Z3d A @ gHƴMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:19  $ m@(16 2 /*1 {r콻Ιg3UN>\3(kBؽufELK”OM* tu(&D-=nJ`鿯4Gf͖뒫,ܸ2MS5MɅ|k7GZQ{rO{,Dg+z5$q_d /˔=)/>tR7kϧل!ϩ;uY}ˢ7m,??Sxվ,n+U]RW.bMҬ],ܢl+vak&϶:mn%u8}eqwTcsjUgxzK(mb\p#m%>ErSixS8l#HxVh+bE=+*iC=;GXK^y͝S)/|OtVtdǢSR9uؼj _MX9Ƿq1ؼK~ؤٻ:r?6}vѸ16M|&~hl+?6wri~Ic*.46VڝQ_9=mUuU-yL~Q>=GOb}TR6D-lKW ^6{)zN7/8t aoAO:aҸo{KX sY⠵FC4xyFg>ur9yڡ0s{9ͽ/X8E~]>^- gIX^| SN9{=:{+g[]3#ujܛ,ҭo ]P["M"cz loMл8QEyϒ.>E+ok}{tMVкj-uNnG}$=w.m閛-*r.8tot>DRi˝uKE7V%s"np&o<|ݧ5~q/^G8_Əvk /[o===.mҚOUы+ ~Nzmm/;nW4s Utf_9/h;C۽=I.q\UtW>^1} ۳g7~<p&pfInspE5I?_A w5PvIh/7Y^Wsq ™r1Δ(gp&|0_7xsMc˧lC:9_\K9F G}Q%uh10Ѭ7E=p8_'a~j# ȅĻ/巾i:W&lTդU[l>*`#E׿#cv{kw 4C GH61B?`u]7Fx(Xqdj6 3} ۳Ǵk^8ƨϼ0<@x.9Q6bE@oR+zhU 7H|)TJzKO:U2=.[T%·=l2}]0w( >˲WgZvQULqmo:@RQrȨ;4N)/NťtY@#Py<Ϟj@n'DsmL_MyvLu _ɸsll7?nQۍ%ڬʭ# ]f[Ǝ+^u&ۆ>^f+^zyc2vx&v{jXlbel\4NdsƯ:1_8o&aٔzCѻt:$҉M D9B1=s;@VRv_)9w4N#}_9sDM?ugqᡰNh_m50Bt~mzmIOsְF:_ߟ@<κGkkod42! ɱor|^jgLճMYpld(<;?4xܛE||d٦I;U;k6ZآEf?ZMJ᱓aj۾نKxK: =46 O{-o˿@>#z ;^.:=_:S4+]1r6֥j);sXo6q H/QGj=}~|BGKE7 L^£fKJk|{͌<&ͽMԊ%}~~9>'ܨ>VGSMavݏOM|>@#mnճޠ^ZoT 77OfHC+0,e8A6lzLC/좔," ŊԑPT?W;1om˕v4x܆=A&? 2p`s|a3 9K|o#>T?s+K.}5ȇgY7?[ |UX9w٣;n1Hd7i20_+٘n9O4.+hS~EFPy%ayo |y/kn[Va+ y,<5,3X1>SeX "tmrחIP)_qo=k-׶uEmn6^VVoMg~La au tw84p6.9B~o!޽R 8=~0`{_*G싌cc :[y5*9ntO QU p^;v"/cbݰT5 njrOjTeui&}L7-Vd\~]2ٓ$I{Dq(.T}JۤK_߬o*ѯ .kT<|cG/րѿL96gKVYt$C7Cq'Y>h,W+ M/CC1I=)ؼ/4畱*5PEcϨbctiw*Re vijg%~V0g,.KT?yn[ 7:Ə;^U"٫x9vhloRB:ux :[n :]w~U>\g=DG Py~˚!:޼=`kooѭtۢs}{tQ|u|s  ͮ|M~]Ϝu'+Y5.W|Wz݊Vo^/~?P1y0sMn(L!cCuYC`֌]rʷo_}ǯY 1:|C8ʰ7Bkp'153bԾd.)=x|_} BԻcw_cW+m쩱F{ԴU'ٵ+ m3Q9ӽI>ݻsI\h+{{q)[&i٭2MNW!>?Am(o:ŽONH.;j*tsPј6|n>+e)<^w^ߧ}{; —7_6'Y|iujAJ;wwc;# OWodQ=v"m5\ax#6B=300e 0aOGm-iF<5e/ ]-]ՙ' UAr!]J{u\\Znq#C-O lW}Q+tc"^j{xnGy쓺7~U]sӢ3-Ack}:?&aHQ:eاާCy|7mvtEr>g3>k}:yMW`#t!j!+vAxuާd5fo4^~߷YW@MU"T:7yft.< ަۧۧ3ytF[UP^kte-m3fH֧G__"cJLb6wFmy5[mfd!MN+կTk)KDUH*r7Yl؞M=uy)̰Ab<.95c5[_m5Ysom8tt&{q],wkx[7M"O||o=wDy/hdF=tn=麷=:|]~0|K{)>쐫g^vX7/ąbm^~2[([&{oIBev+޽7 /6~ |&>Pm,_WC-07gW|ss6n|疳qKi sԟ*s}A5QQ`Zgvmv\k>3#ֈYyb>_o 5 r(D>8!DRi~'4]Z[qj>6﵂-mJʯd\ϾKWdfoR3{Q/K^j䛯>#Ǎ_Nכ$Sj#/ny eWsׂ{a#-Cv{W埧٣-{-hpi6M. U,^'-WwkZmWA|_M]T/(w(Q S69'Z_#qO^`zm]=i;?B5 To<lZqk+|k~2ܔ &ӒgaF`RΌd1)i`R%1R7`BpaD.د<>*Zɻc3m(K_)}f884YoW eB roص"®l"8S4s1UaW:p˝> e`VW3]sI`NE~ot?3ot!N*tNڣ*zYyjBُ v|]v> yov\,*ϷI&U6[:ޛPynWoj }tdAloqC ߉ ]޼kUV蹾-DBt )ڼm|;fv#*ϏN >/owI1?_!:ߎBto+xJ9DItIxdbn(~\ T/\ T ^@{F*w񇳏J?G#ܨ8Y_V%RRPt0;t>ˡ[*IڷtB6“FƓ?l-oxp@h?:T|OO3ɗ5 KƆ1DޕkC㳑%52>w؇%N(mp&'>7m5;atp.gV-l /oI\evŊ|JNC;>;<_LgL(sCebݚ=., ݪS['B_ P*h%f{%l OfIٝC^o%lL˯,v՟V߽]nԒ0x ÃS ?Chl\4Wә`=/t;v ʰ tK2.`5~.>KyzN#v <^uzYWӺ}|~uhٰ+4vy/*ξd@wUQkR,9[_غ|mm'aHX/*Lþ̟Wqjr]K6xz6Ư"(g}Egҧ5aIYqmOPԣ:NUuW/KA %i~I=<~\9Ei}CLCi~xYy<,}>7K.|{F=k|K{&%LW+cn)_AcnV\)tƂzKwyji~xLaǷƿ=گߡ7c|1g$ Zh(g,y'|ʳI%,׫5ߌ9XG~)%K 81Ah 0nǪ˿X>yXaSBu& vHk>Ű5eCrtv2bGb-gs9~}\]o{ѝ[[ԵuIw6%˩9^9䛯u)F96N3 ׾#4F֥eoos͛t_EU~ ٰBKXZ/?H_!eŊ_NP<<"^x#<=Yy9ǢSb}ŠLz`;mWWm7}褪>v\iАé9x|st}ˢ7u=m,qȷj_%r{Sڕ??nܢQJE+ɳ-ohQRXU;i5gϧ.AzƘ kX?F:u=i8޿ zxY.҈t[;z8YKps/NzxXL]I6TVk;ܘ>p#~vo ۺ/o<ݶ}>:m]ez+m6/tǷgBZ 5rrU<,DPAr5[Ŀ&Zə]UsVw4- zX65bHv7{NYkvNEu͖[,EtE.Rٛ_;K-. W$^R~MRt[4+e#j.v}c%UNH3_fkzC?_{ؽM^ʆc ̆^^xpr;]r<YnC],Y[bWbKԧwdߦY:*I<$xv5=V#ax7_~_9ʹZmw'j|ҙoTᇓ~mm'eVv!ѩ1i1=qACd8rql͍@9we~_a5_Qtg8A6lϦE8n c#" \W mXQX~@UTрqD2Y?ou$aRWN~/'uxM+7=tMoMb{h E}^L,؞3_9`˗ٮOSC!-Cz^9ܐOMe.;gymh4s[96ϸ7i ߮殻kOٱ^^Ux*dݏG']슪jn)EC\tɰ&L.elQ$Kfݝ]Ft phVo+pN%9io9C6#Y&0vJLN[2 twl/}@9l&D~b^\ECj9vu4KCʐen9u4}moAABt+t&Brt[5Ctߞ{DJ'ryk蹾yg~M*o݇|{t[ٟeέ?#U뒔|qr񋹉.*O^ܿ'=oUs~s(a{6(Q(,Qci*̶3TK_5}jE&p_|^=gO%ηC"ΰ<؋a/z9ΰJ}I}kw+-t`rAL7og\ԟyʽU/ioWϖeLuO:_4wʥu^?>Y_YrYBc5i%=>ya\o4 B}|Oƥqr!yOV?AgόNYJt~O]jw.wf ~gy_F^}Yt>_7ޮǮjR]m,8Ҿ՝Ȇ#e!Y<2z_֤9vדlߊP RA?z>zN jY|ABbγNlӿ8xf9py*|puaQҮVXK_EVd=gZ gŽw'v* [t' 3,Uf[+>Iק-d20C`ċxluꖛ-#V9cu[4㹦6$ލ4ņdR6̜GWi=zGrlHYMz%/݊aa܃1ݡ0}wfSJVn* Ki>)t R/ʵ/?UىBnD޹74=[uϘ?ד]X(zDmJfk?&b22 J d & y E6zv<8yNkf߇=֒&|;(^~]f&ߩ@ κ'sBϔ![i]Fw͖c"<JPtXA  T\ܿ9C19)b۽R͏P˅Cts\y^ηu\+s>D[-g(Ďܹ&;0^6r̹~39hs]dxSr׿Zfϯl;;zww@3*̙+SӃ0sMzMJ6ZaG{vSO|)LF_7?=3a8c'ֶ`,XSP3qyWcf53=|;IEqG>jam;O'li5J9E7COrzyѮtnw*վ3YяuSw-}xWeX^+08't< i(So˃oϳ =CnY=,$xżn?Q9>Lq|]r1ݧ>*.=p]>}\{xDEl4j8\y򑟑J~yT2H8TYr'h8DgiCo|h) {q/1sI>0t85X>Üj![EeZVFw͖{;L^o[}z~%1{}MɆ d:{gY-㥳&|SNr  4=suΉz.'Mwȅt絪X9F}ѫ5w ?[,FR}l[̣{ć+O$~kK!J3^N}/EzxI{yh_)_ydh.}u'&oػ33QsצWLdl1MM.OwVDw-NНԝKor;6|?MEqOlOYwMW~]խKR~xӯGr!Z3~4Úmq~ls= d;H_\~-s=3:9{ 7 ;l&=cHk),09կ.>"69e+6yM=5Ʀ r4*K_f˽Qښ=?Ubk/b^Fj}=V[>ߝ|Qy6w=2l&lf4z ¦?۽{x/۞oqqrqo&/Gw.[}JhLח}Oq-+)3877B2zx>H>'Xi)m ei+v=l}d_,L9FuSOſkgZHo Jbdlz["u2y5r{o\mS&a{6(|2!! V%/W)!F;}a~v ͛k)h9{> }4 oz-/7Z|0/:w帚νG}fMcAA:9PsPkkBJ#gRۍcv'_ޢ5:N#wvz_;zt20CnfN}Zعq)y*o{t]+o =׷ckGoc|tmro=uhdkfDޘ홁m GY] [m8h$ v"{0,hȋgyG<:Y<-?0WTqR3Zu^أ7xG\~#~6>20b`ŋ>+#~w-nJEu!?o듟GJFV_me\INydxX߹y%mr.Yſs#_UgX߹)'{E =Ӈٰ=zLK딁NN~VNgv:W,Ч|H޵K9&(\*[i6ZMmc݄:K7}yz$'i|g*n+Y.r܅3gah qO@C8x1ۛ0{sxHqbs~ &lUɘ乻HO>yh+*^lȵƊ]o:Wrz^^f+1m xo?ҁ?р_z.y iɮW$꡻FQDgc7vG}'iIhQ,)[OCzިJv䜷Rq ky[O&kp3@x-GGOx3:䠅Ə#ci6FY|Бp-_ <#<9WT>U:T݇R狰OeѮ乩=BxQ]~<->vU*l _QZLgX-7[L!jxC2 eoƚ(kdEVcBtEn+Z[:ݤO:K nE8%D=wKtCv/X5D?l>2nҾPcwJ DWUGپ@=wJ#/䐅ItS~%r䧷YzwBΗ7A ]sΗV=屿<zIvoe=cۢ  Woo{=gonji+O+/{`D:~a{$L$ߩ]>ߩ5sxKNÊMWm-:UU3 [mFòvx-ưX~&gmbЯu!IvI}_gW{6$ h8(V TAP*:Z_h*j $A BQX;u6${e0|qEE$?UhDgGC ?}%{tI_ݗNf\v7֮an E/ps8msYFdB'; By/m[^wiΑ^e^Q̮nN./dA*&Jg_7X>_J8r0YΕGip&/G^EΨLێ8JjRװu lao瓴eR.-=d6KV_4,"vzȍX~)ؿ5~ƍv65v'v{o#)9i9Ҷ)ŭ;3%[7t!~\.i [$Q?cz5͉֚u )UG榌k@n')]dxDO>z퇐>=c\+]j|w%eg8Xۦ5Ngmi#i#1_.1zΕH-zoYO H~H_M- h( =#߻{Cbw{SI-2WRȝmRI{):g!ӣ]6cn.vtYѶUPWzh~7@jgYy/VGtZTdI3u L] i"T17D*XUa &o gr gD !F8o}wQ%v}Nt6k7w`[:,z~v=ԞgwڼߤİNcc{j@V*hgwHm'c+;jg'r{?/=ڏ/K18x֜]~PKDjlӁ3Y{:kďdtwEI13\]::Aq>GkuA֦h:Q}EAh3u#bM=Qlխc!g\0_c`I|/FѳZ=ҝ}v}b՟m]g|_sktųӌ;̫:K1Tvȍ ۣDOcG}_GZ/R^ֹdHF dЍ ergC#ivM-N,]eFs;7{V}4J? }J_ SP13oLhaN!/J=:6.(e//wP3nYgnCޝ<zs vVݯ-GiK /w"A-_ķx W}J\|] bc;`^֗a}3Ufh>&pNJ'[~J\C`-ˉU̗c_vwrBZfN,֑57fV8vX6meqc8p̆ilsflS{ l,}7CSv%?Z˹qyx  >YQWmPbذp܅{Tkd2玙O`L{ l__=P"ہ-ǟ9Zb[1雠 Z֥a%u#w.V39?0l?_G\[>N?vEr.O_s,]$cѹ|4'I d_ߛe B ;oSM8,jJSa_bLqqU4n+U2>(l*4&Sm v4#!Q,~=z+NW٭ѻ<'L~);[жmߔ7&k sWb6JUjK2{Vr:CP9ibck_nJ}}Vν65goBU1>wkra :~IgR,&l=6TLl] k[02[V|+Fi~GYoQ?#Cv&}PNt/t Ïkh< ׶a16{/a(7oX<_y'>m"?uyoйYձ}K1뻊Dmշ]oaN{m0g*ϼ[7S=@2$#@2$#Dp;dHF gz=Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:19  .S 0DS&S(16q2(r/4S1# e{xx U+! Cs:H0b@4H4406yQfxO(3=q!J:>wޫ~wU rEљrG/6( 98 *}x :,zc(N%tw*]O[^m4;:/:3:; ȝ%v|g]١6>Y SQoot4JŌ)7Zn}rܕOP6r&˵UtTnXL)d1^Wȅ|+7i,VԘ9yVD*|Yq]ͱ>-q{ׅ3E==7/Sl!Wu~ GsY/83jy1Z1rA^q07.J;7"J7>;>l5}rl+:Y#q+Imx1]D(65>iӦ^{ivޟpڑv֡vrI qH}S2!GZ-rt@W/y}U$|p?oRu`e$/yoQ#)/=|PtNtdII k:77ߡq }7[>u3rn} t}Է Kq;ԁO[$grPߜuhU45D+ |'ͱ53:i?*GFNMT]*x\OWaZ^| Q%GcCrdžBMs%!IƏz?CeiP㑼lM]QXUt9'ir_dYct]vG}vƝ4f@|1`4#㣣âKE1_"x1?N(dΊuWǷFsTE۾RY]AY&-QZMWϜgNѹэ(ݪ70t߇nTCtWYCt |9WX/os1jJ3q G+i<,!ձx d M;5\x@9Q֏Ak,&,<.Z~s<:rű,'֍oW*f:AlkGS3׿w5Nwa%>ee=MэK:myi!UHS:Ye&ەvnI Ņ<%j6L^Ն(s_Kﵽ1 ;?^Q⺷ ijTf뗮ho@;~mxii#L6"^})@:a^WQX{q[{eLKGHGG5OW] G^&Hq<]px0G<k8P`%Zj'VE+hyP쵥M>'i|[f_C"a֛DK>NW߁Wd:Qder־#ZEu8x| o]}-o5}o|F^aZ.āVt=\.+l/椿^ nX_nBX_ʴ[umc +|?+ O:@ۑyЮ1X>1!L_!:ێ>야&*Nm7 (Q2I+֟l7\63l:{x vxL2U}~ʲ80$Ѷ~7*p諸VEOioTΫ;X9[kFSje[)d֪1^k{U*R6bR{ʑw0WQ&;AclƇz‡pqr}NqcT)$VŽZX=rW%9i,~ Ζ kFNt;E2kgGʴQl yEM]{wX;vx y4ni,9y}||uP93-WCKח_4VC|y+] kwX/oseKe-@NdYfYjVesȗg1bƇMgo:p|r*og1q`yA[À6>&][{"I2뱌aź`zTy˴e6u:nVwoڦn*E)+brYJ*Cl1}D٥Mg#0RďI|ιp5[r?q8yӆUm\z+h#3 :>5٭rtvW-/_GKu͎uVYYqH-=`hs"y'sdMmM0zhpԑiz5^VOZUo:lonx5}B')Z?A _;(S˦wQV=1Ôa9Wy@)Vʣe6v/yK=1 6RZz Xf1V7n簜>_oR(펼LGMSG\ o0(z' eh{myEZ}Eb7ko6|㷎d1e2-}69)r~e2WYy[f1VMYr?&L.eME2X gq8qX# wi<ثcTͪt%5y0DeR1/ b2Fcs8)/4&WG^~:%eHMt!Dq`mvf7r^ԑ8 P&аLu@e53?ͫg^,:k#e+;3 mLSߓ3\1S6@&dǾc<ث:8t{PVT9ҀMrSAy=X>^yQZazeB,%|{cm0e%tCmܤ]%~딩"iJ>G .lxVG K- X4{_*$D{D/ͪvjV/ͺ'ď8c ӶX[zC6(}yA-#_zG>w}wqۚ!M;5!3<`8!{miIyq{γx8xE.Q zAMge:Rekk665 Dx 9(;FeG a-}gȬcUY;$(W? k2V=ͯmrcu%_͑#cystO"jNq֯kG"[/yVKK],L#OPNU\%z4>~x9?o[>o+?W' C:ns\h.TeVՉN;LkuHZ+yu_Cuѡc[%+c.Qͧs MnfS1>{)"ѥ<]Ct튳6g> j[o9<ɕ.η"Bt=u=6{@auf-]icmع.쵥M>'i*gu7qn `:@סOUG%D=MSa3B5Suҩmrv̓ȅA)CikcGOVTԵoxBtY]{sg{e$5@%WJO(}/en6?kn}0oa쵥L)ŋtqhV.Yt-r0ն>5_[*^Ŏd()-s̭ .|VyTM[^H/QP)nC͒r^7sǗ7Nact^IdS`Pؽҳսeu)nK&L.eMFE2S@F!ÇdcĎ7$+{>J>tn2M<~v]02OIuQoY#_ Yn592j~HoO9GS3Q?;3yZ9/nkb4C._P+.u4WHyC_w2y/Q?WchybyL"d2Z|* k/[LKj?NESZҷF3Euqp}-bq끧9@z1{G!Cv6VmUw|)"ks|8vnq6Vq8ˡʱGo'+&+LC'ي_a|IݯpηIIuq|N,a}:Pw w^[^(s)xaڢBU8 }Ct~Gx1Y@Gݠ17W5Ctߑ'DGy3 j]o yN7Ԧ{*_ ?Uy\ ?S@>ȗ֗-o7}tڞ},1O~0yHXf~x e,ܰEXC,֢Qkr'E2eʜo O*c髪G>t+<&0̤:Ʒ'C<Y@1ʒ eS@e| ߄e|9QC miX1} E:A.ֺR !m/ :.n֟Z_c?|$sG:?9l>#a*o u:Z;%Ķ4b qmA^`+O񍋅r-ܰ.W.dVЭx:M&YI˻:º/֫C:nwWxV(Ewс-%r- jڌ]uNYn^[rKX~ىt4ի푁`ۉL^׊5};cxO}K\*Hި8ϔZ ;U%{}V6bWI|tqn:, ['%sїFo| 3uXw7,`>!f!,0N ᵪН*0paye`2ܛb؟S,Ǯ넩 ?/2:oyHH1({v!ot?Ҹ v4Bt+O!:eJ!:oW~iJ|g Yhڈ%ӧ%#_p_>l gxpBv -Wᙤ/*|]{\a* =ߡD#+gl(%7 }5ޡV[W]ېz>g'8 ,xVp"4N9p§VZE8` OZtB M~w7o0KpiYΩ;C!y*dͰajUUT^/Cw/w֫ j̥҉8;\=󋟻r6Vu|{yab& U@q!~~=ӍavmF ty2Orܺsm>< P|=o+A嘣B3L ztYs]od#t!~>S |Ϩ#yV?hwbB8 |V@L~sZC?_S ~E:4D>wKΗjGBttޖ0-S <ݜHƛ??| /:o~_Dr|Kr*W/ C}Z6ϧ{N7GX~=D :gt=>wCt^n>˳L|{xyު ˻xgG+nѷom}._Jg|ktBv9h;zunA$E0lN#=(;N}6ÓU؞ /UkGm-U yvO+YˢZE^m`h9]C5qNFណp{\aFC(/t>P({;u?^V7O(þPSֵv$umPQ y|pNt~0Q(^;5 {v×{j?#T5!є!718I5nH!핌KkKE5Y<˟O?aNìd[>Pz;kdvcq>.YLJT]?Ig+&bl_K~{6M-r0|nSv_wbx;]~ znR] {z F5< -YL˽Y:6^#<>FG.Ҥ]ubc7o| C//>$Owp+1iBΉΊNNw7O,ila}D~- cٖT^.k=J 0b&{]+6G՜ā#E*ߏY֫ޞuAF(NșFGїhhLW9ѱ=O]C^V >jY=# T}W8=dVLe[R)޷Nyy Xժ]J6^Χm2 rOݰGz8C#l}Zi } |ǑgHnmdn0pKoݯS7uZ˘Kiޔ/nxߤ[߿5r(Ӵm]i dŁ}wnuŋxVK+||ㄊQŝCu9E[w1uN w"INԊX_g1q`:DTKFޚ [Nӟx G#/$:O}3q WNr%+-p+7C.FsrCF?_O*Wn57O(Z{2 5EEm_Fy!:o{|{P;[SB|CY__gE|i߿lV7[ߓƨ̾64+z6 :duI[r}"J9]Sy{; dzkId y ވqt4g1w8 {L]5)=!-r #=U4m܄&]sű|"GHgI/Or!Mt^}'r22N'_5$*?k~,V~}> r=4u?ݯS}bG"BttK1e9m98 i{}{[߮͋O[Lek'хeu4qh(2U$~=:ݷy}trfh޾(O+?i 7=}x+s,xVZy ҡn2[U1n? =]3ݡ6=}tsꙺ^OU ѡϭ5,s\^ӳކao5f.횡C[2GiUz zH?˦Lekӷ7|C=3BY=MzEg)J߿1Fw8qsm :u~(vK-?h}b_4k_eA_Z^/s.)zfm=~I #=YȊ69!: ]5˱W^J+D O 9D!:gckKwew'=n[{OayO(q[?SvPzp5R nXC~cR7+X&Zpяt&$ m꾝NEn\SrI8W)s$|W-r0z+ђe=нzk ޟ=]w-Tr-\csrk AO=S~qarS%h h'Y<ƟxuMvS;$3w@٢ȑ.u>8I|_TF=o  \iU:~e`2KbbzǞj 6OF>}*c<6k=L ݧF|kt'8~y~5HC}LwQ K䵇h oe-J?$Bt> |mLوb(ykUKy?B|yBtH[Ȕ |2:)o|?G&~|ܥ*O  ?_{5B|y~ txj̿$SJqD2Dq}U!~>j|k4Bt !~>'!:.6/Ct[ L 2P6?H o87sG 9 ?o9L5 -}\;DwwΧ;V9DݥqWiLΧ?_o*^d|9vTtyӽ :_^YK~m6"~&KCWPz.F7JjӻIu\l|*L*}Fa*Efj5Vnn=jlSoyH}nY|ԭm^VŶ-lJ؋ٍO|l3؏ۓ,{uq?6,5: 8݃x5ITL$,6@9g8gyO!~w)dpg pO7+{6|y 1:_gCΧ PP^Ӌ[*s,LR]ij!GKVADžE~\@S3֟|y|x:O㬺;5UOd%}Yge1xLDoDfwg&s;x°Ʌx"{{e}xƗs=rma.NnG>Ҽ;O'穊DKoHo6Ffw# ZHKG޷W|d1I KDaE6sUbP]tyyWGX2dذ?k7I6cwxL6Yd_Q#>Бg2~k}H]jl]!N5i_k/lNڵ|,T-Pzo=Ӈk>z7㢁eqw? ]@mz@mxvuz{9+[4`@;6ʮS|Lcl%U3nbQxh]6kʒa _;\PQ]ߏ[(9ε5$/S_sx619PY:,Fa)S9'Iꀋn=~wչWd&8g_Pѝ>nc:wO(۫AGr[yOF[+ 龤A\@ۭԪ1ޫ ]^9> 4kw}nb2Y?Dwty;zVB*$Bt,/{)u,??}:!~|*D{}Χ˻SV޹꠵{JW~}rS?yygBt>nG~y/{Ԡ뭼Lr jye,D˛77t}=Gs2p |~qY]^?] Bt>]yBwz* 7#ѧ8}?/Co]Z*[v q-D˱ڭgZޯv zOʋLy=݅!:_ޑ^d򻀎E^ gF]d?J"3{Zu^m1/OBwȎFkH`"<@ڻ}UGƆWDLkdV8w>UwůH➎^sw=^|>gEC/4yl2cF'lp0l8ɳ`}7gzx#~O9hI@t8'Ou Uu\"9L[CmT2zaUZfUUѓaշSҶ[ԴJ;}': _+R6!ﶖ2GWqno9c¹;1Ç0k z'( Jm1^ !}nvgRϔF= y,7IIoZ`$ץxUG6Oau|Yp^=kf69͡r<:Rݽd,rRw|NSC;WuL?L/i`h\Yxڮ"G㼜2erˮ p/4^>'~zHV?~BðH+2UzsT \I˼(W76ozFyoz"3"ǩV?O>iPn_aIV8i3n=CUˋ<ٯ wM֯_1:u AiõE=s4o'kmأ _ A69~r~?|旟3W6*~926b -~O9(ʴconRҦ݋d.q+ZӇl"qS:E&ӗ+:`YZ- gW5u_.Qi >ƟppKr9ê~pvQ9}?,Ut:{ 8@/ ԩo_y?疦o%|YY7&obؔM @icV*L`/P܃1mib'ge308y\ks.W~{k+q2c*qCNaZ~&zYg=#Qɧk;!o}ްt7sk9N n9Svعv.q9HW2. S,9h09r[pv~cN?&ז6(œ2t9D7TCUlv2P~_i<4*u,pȅd,ut;4#{v29OQ-Ke,)r"Y1CYƖFTw&ca^oRdloU.x cwSd%ijg̯+/jU]0k8ц9:5:h*y*_'dlKlKCGsIu$)C*mr.m+HCt2ۈjKkrv/`_x ۱f3qv lr r(:X>{;> v"*9imomx/2X&)/r,-v͍8h#: q*eo6 p+(ޒm):疡 Đ}w=OR7@`7cr){M@V[Er8䶼[苌TW|X+TS|-/>^ݭjKH~ [&뫌x}E`<@ǖ8oKA.-6'mRd,^*;D!c{_"Tw̳>^}=;fp>A|s=9xgkڝQZ >^y $ kQ? V`Ek4:p>yHO*kjU;U^?_׌z_Tzi]2Db*j MS=Ǯ;֧n?`Nt69t!~1~Bt9[9|f!~>Gw۫йy}Wt{컓TQ?3G~2ϤZg,S?8F:m &Qz0D xxe( ;v#W<󣋢Ӣ LBKt"R=iUkieN3<͹WY:Jtώ>׿wwy?w}F'8=࣪ھBCvП&/k[ª<ʮU5s,3);uع.5%=Qf`/9PG(2) &1s%/ O0>XT9l7Ͽ˗AYaoSNJ܃NT+>>_Q:sO_~ WP|}";BP#tһT/^&c/9GY&lZ~լ/@'e/w`2ri $oOZ4w]ڮ iSioo&h~bz7K7 ׃oLO^׊oPD>&}{ ZQE73{IdUZrAʼv,Zh'VjG%VA-{ЎD{>Cn6"Z`[=-?۱#ն!|M^^VKu*mC}]m4+~Vdz;5·)H= ᩀw،:Wnw?Nދzh3e rإYŧ+EFveWIqE{0[?{FZ!rGy/vx~"AW=m#֬mZ\l=h+pg³/?[y mVbzMx0~}֯OƊM@kv- q}Cw/16{a wv܋tVo)[Om7t<}?p]Ku}525y`q*_WP:<[o롏:b+SYz96ҥ5y< PAYAѻofooӎM|F󼊌^Xqԇg%zS.<"qyD7`DlӴOK kQ}K~2#hϣO-<[ Od3)M: -"dKYW 6ZvW%m&u />p|u̡ 0N:Z(M~ KVSmh^rqms;iEأ5%Kԋ`3pm&aw#XKH \m篃MOW"E|^@0wJ)'LhhϡL,oĦt1Ϥ:iY]|meVXSCݹi,x^B9n,"=:uj.[sګgoEԏm"gß}IoXr^k[^OrCG7w}Oh ;{ð/o+_>:5F*~)[cH$BzٖLƍ/lƬ9#yQ?F ߃!.D]o/8Na]N^5 ȧI~peJl' ׳4w;Z mM[ ֗sza+_KQck'Jh-N/Z{ql/VΆTu:,[. ü4: dQsֵw[[s-7]{Q;\:>w6u twoS{.JC 7/Ƕч/='k.gA+N&ﳠE=jQ]]QHoL9?|R.[=lz[ A @ 2d >D*oĭwMluyԧcG31R{al>aԦbޕa~cyf~V ?Ƚ¸G uaoPc 0sM)xWlOZ~W \<.~r < #5 -G(fS>%@z L7h*?6{J'v Ѝ%_obC7wtk~n#E~VJ=1އk-x=ZkҳzX{5 lc9̋H l_G]ևhlt;J;Vs=My1b%^gN.6+&qim5_[~B,m/m{+:]4{7|a9/?۶}X3CW^ּўϙb~7}P :_<֟gW[@Τ*J<ޯǼM]mUuঽ8Vbg֝o!'֡(bcǽsK,;7"(֙OEQmS"~kӈ=}ޝ.;Y5.2v*W>Чz c?]T|g\i^\ ,3Og`M|x5?L ַ[DqqIm{^"n=螈Z|a+vk ̫v{^}th {#_a:x$!8Q&\{$d_wD[KCv%;LB&?C~Ml+w$9%rKwZ'էQqrUݽ申hq^?wE "a A @ 2d F}, 2d WMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:20   s D(162/1(*{ x `]Uw*FZ" iC[max6T2Z@3 y%̈ZU'sȽ s\Q2 jZ-*)twegsshve_~(;!-wJc]ҫ((*DQCH!zblW>d)-^E*>S#^Ŋݢ%yхeQI#TZk\XXrxSD9ԀيSM/MÓUKa)i۞^c3s4rr%9]%ԅk)yJq(B.۸ik_9ƢnEiפa,D+~Bw} H EZqIS|('u^^ϰCC&/y}.Q;E_?/j9Z?iY$VGsAd#eXz8L=\ wkI=V5=(ۢ6ʻ]aҶlhAڇs\ݡ5-mI|FK&+楅.)ΐkQg)!U;qǑ1V+B%͍ %o.E}xGz|Tsz]cN..N0:GJ*ws慟ssŘxn[=~n.P=cn._|D37 MV~nVn:e7Փ'T*TnѴo/k.[o_n9L~rS Vm:rJG-8h3BއC:ecѳ+43C7# bcc<&Y>]?vpȣO%цRy'hC)zI)kQq6nQF%q__` ^')lq|h) c|,hᏥ5fk#/GK?/|*$p9d{-{L XxY%x?1( 16~_1zMșks{wM܁Jۄ^$ltRt|\;Qѵ}=kso5Z6[O|> {zݔ9n;-GNPZmknwa9{o6Gn}W(_Kj&,2gЕNXtC]fe^8:!:UwDDo> Whiċ=N=L)wA? 4֓f?.yߝr3+HJOooONZ(m3tɀ3UqDVZ? Y yQ0kŠI'trmrS$G;8%%z[ENĸwmvQ0E}\=JD?=%=AviǷ)hĦ}?3}~Vt?yOЁа49gF|o۔'{X_T_Hwtቨ/Z'ۿSxGS1w֋lPb$\~ZQҞTá1/s^'Li0FxӍe<7P0t(K3'2#if 뗕<ڧ.K,a#P},69inǓJ8@iBy4 IvHIA)ZIv͸'~ء'/;1@O s<5Vŭa˘ȵe@L#{]rX$ȖqV;8w+s *ùږ;˭rZKr;(?k^i<4+-Yzf4Cq#>kmj[lяcE]+E?ժ@wnyZڠ55F><.MҧI[Eψ~RlzH%hͪJq&٤8z!nxA֔+KǷ0eS0:d`:a3+:@4 ɌI |QfZ-&>zQoYq_=,l7=OЏ3Mr &퓙wҨ+4Nݥَnf@9ܸ+H#,N9ϕl?ɣG6;WRO7ijx~YȄuO*H>a}+|Jwb"x'!,n2D~~,@p-rm Yǧ YVNܧAG[:d9dg= ؾ/_v!,V(&T \Fv6>hxdc=o [3 .Ѽ{.3~6)zBLyA)Fذ痷 1g9~R7 k$$De'OW]g)l\ SXuWQr![M}P=02^\5B:B1.p8^c1X7߮ mױuh:zuٔuȰ,ly+G7߭Nr1tL E]*sCco" e壧ùv=saRCٓ7ile\S;BtottSTGL4~}ۮOݴRz{"6_|2e2a]s] ? F_};05ii|HN6elsS3t~]Cvƚ渾mk=~ pyQtDl?ƭmђ o~6X86;E}\7)U8aCnBXR`X΀ nGI4T7|3|. ;3F|xYb)vCk80NIa ߬,|[-nz>LAiv4ʄx{%vENǜv>qӧ>q¤O# &|K'h=%:|䤫Z+%ͫSn8..q7lm])X^Wf k߈q}Z= ^W wi=pH?jɢOF({毊u+Sn}gA.VhV Ձub%col ʧ  ;"tFvjq<$eNs6cU[[˶(>~q3Hm0cz)GV~-"ߐ~mW%6aQK;ݽx?Kǝcۆy5Efnts¤ٞN90{R9kI'v9FE`?*z‰>!i֩Tf<Өv3G3 S@c [8aҭ,g&t~2z:) M '7(l\nB|_ҀX>Z D~|eBscBXf2֠l<5xCv{ hbrɳdW<rE=H:N95Kb4w~ِYz2D7SE6BtSS !D. Y=<͗ qz q,oJ5-%lYϵ*F[']o{7~Pb:3~g|8Cqη;Myqd1w!n4{K/%_gsSnn:īܦg/Q<;ؕL&?gBj\ICDt/ W.ʱwؽ@C =O碷p'*iv,ƭmђ͙f4,|/, &>I~Vg^H .1֩ܭQ7OJ;Di:oTރQ%dvYux|nf ||0yR\r^6 NyGvy4Yʟ,9ACrbx%sxڦ>_*o,xKʾCsy;?ɻZ[% 'Wr6o-<s2u~@<[ngT<{ }+ }btqHX ϫz"şw3nпue|^$kyoh\{6`; =Zc"?qZtnI!LDgu/y^Wht̬X^:?#w0ӏ^tӫ_S֐^g!G}֒xqӫ.܉,$!G$!jm+Yz QVkl|]V I5Ur熒_m'J奅ڴymMotY[~/6-y~ԁ]Rnxg C.бWZ؋^ۅgePmo.iPgRfg v9b%nϤmwOr&V⼆3?9_k,i+5&xOyK7ҊW49_i2J#,'vߙΑM$YoNKQv(m#{{Ct,պс[ձQ8D8li 5%\QϹ*F9> t:;QW:ly\1ϧ wv ǽ3?cꄾ#^88rQ_q?Z${dyIov98C3+,Tn8fW| ˓HF>~;@^]ypYHsBt7?m\#M3a¾-z&L<ڀ']=!F/tz\3tw+}߮99f΄|k\^KEb_%^y ~naEl ٸr][+:WډJk7'y=MZ}!W>{3|'߯ou&'W=@`zOIcރJ8wY ltPZK3lhu[^ٰü}z|}ꆎrmLVr ?!LBdp~;BXMѲ+) !M>9[ͷO:1v]6W_nغS%֍*?ZMҦz64X<y,2z?DI&#M\lEт)Vɰؼ2ɫ[a{g`M 64yO~ 3]?Dxx }pO!]g&CwȋŞ-MW aj\ e,C}>~iYay6K|(yoʰsg Ƶlڦ-iۡ{Ἔ:u]_qPbI8t&f9pLU1W}H6_yEޣ40K+K7s;>nJ51RȐ:,8X92OQ.$~@kq$g-}@>=K14s_WYYc9ݧ,]x7VѤ>pa&y F@=t=ma;wWV[5CIrq*yUB7M!+g2gΓG N[(a<9rNWb+5Cݥnt(U[ۧt~cñQ%nO9UoҸL7Ʋ<0pM7.*rRkl7\cO==Ukfkn{:=О^/ }a:Iׅ|_@7OJ"Tu!:?{%ǯ%u: 7W)y`zV1XRfzjq2t}nr.>Ge:^}1?_kgB+ݮ>D7u0"~p.p Cٙ>36|_mu9ФP)؏hνGlk./;3T❲n-<'.J8-#__:r^@_&s4_9!AϹ83 4D=YF~ZɧN%n}Bsɽ*tR2uӵ5m;^׌sIO=%;팭񓚀kIeW͟ygu*p&&tu1Fס}Q5DF!:ڳfBtgN+8Buv_CBtrt/:ByNN醒ﻴ>/˗b!:ϗ[Ɔ\uϯ˭hˍ`./^pI>l{2ω{ZſZ%N?}HG {ćLRΟמLn:ϗ6CDs]_ߒsm ڝs.xHuϟcTΏ>ɷBt^#vM9e?=M;,gϣ=ޒ9 ~9l"\:6Ećj+:\ܢ4./;_'ྨ~Q'iom$oX3QP1ŹUPg}Ҹ{ ձ,> X#L:aο Sҥ8NYpgq᧮sZG_/ɧ [йyѨ'ܫIu:7M=q̹PI+GWz?obTNr4Oշ\IFw`~];pBv9gX}ݎnj>߿^o>߿s?ㆂ&@^ny!Ty͌sK=~Ws˹/dr8vuG_gtiI~/ڥ>j8yGKދ?Gc#.c84$N'_Шy=+:'Vis./7+'¿ikT ߡ0=#Ϧ9hν#a-e tOiQrQI7m},A8y*k$~Op)=猢z^MJp6տGzRSIùzno끳i#AMdCf%8sӂ }|"t% b ds@>O -P}~qp,T[ǻ[r i^.U5z&u׿[ϵU+m&Kj|4cS:1]0osozQ ot捣}.羣ozvڽʵMN"$/E9|^^dVL2y}:`czO韷X}^ngy}-\!DG}Sh;FWIbS>qO/ۢ+9S6I Fw /Y GSe%:9hJ]kNtݢ[NQh:tXXKmtauDŽ"8:~9uJ i8@CFmh,׃ 5^p:ߥP=pz=mb;ռ&׷j_^9slBL ?_\/{Pr]vth½Ip}N m-dzZD!:?;Bt~c {M>+t~N$73H |G-Rl!:ϗ$Bt~ߔ ycB7<8]J3TXR "DCKâLdžk5Z=ulU 悎~#wš *3N#ӣ9Y|%t<v&]'v=g|Vx'vP'߄|멂v^vۼ^q@ݕoh]KoX}%wG$|CVXvߦo[߬u˸\~vnƭm">`P?tܷ9M|t5pfҸ./Z#>}]~lIR1ýB,N>]$wԞR}_k{(P+Gba=(y~}CSMЙt<āWg߮9 Y,<:|PrR!: }R D7ӵ1$DwCtc ւG ήZ`>[,t>|8w~~5`!:tN6VK M߇?q(4\G|W?cD6NȽ9C`eσ CouЇ.N>h]p6k,y6B?oC"_gh/P(-$_*Aq)X<>&''$5֊_}Q)b˷UHV-_*mUH~9 a[&p',z/MN0z_KV·H}|_'mAgchbmg˲/"rLM}țw Gq?W>K4.`#g%}V^p7$߽O'{"f{T_uo{۞G(y/=ikF?=qpq `ם SNP=hQRn(lo%>3=gsDrLrmr;Kr^}l e-LZh>G~ggdϳmf%bOͲw$_xB uddNkEe_e@Zl%1Sνր~c\ Cgvlgf3GœqJg]r(-۫{Nyv9%\޾2%f+RK3~'~nOԷqY ͧa~~PRRJ:1'MuPOw) lj}R6Ԇ/]pԇ'u^mS1he1k.Q;E_?/jGOZ/Nz蕿w9iU.nLii\9un-X߭FNAiVics ù{.nQ׶$>mkӦGf4yx69k䝡4Fh"ןo>2Tc|,*EGƚ 1k I#@fv͆D~B8ϗOt%qS+ˋ/kߊ-m76 +W4YS\cr<x P f6֓q5oۿAIr!nGZʯ*SDgy%97пv)¶С7&̺4OY^|y'y]9р\kdEkq_Y}0{ c1 %L+!~6Y1W#/ )z$>g=׵[G:o?z^C6+v6cJȮC[T=Nk#:.![K Xtg3@ණ(@ }|U;qǑnv9wJ^{ҥg0>8=C3_-/,]Iq a1줣VJ|dN<'oxmҸ \}`LW`+]QLRnY~3gg/YQܺr]'#臾)!mdzkdu'/OT9\+Uګf~x T;8/%_VWǦJ9dd{5l䊌mR:X2Vo%U5c[~ʐ؊6Z"lU[IS6pʽU3yU[Iuhl9YMn/!j3 _XJ-LZ iV(Zfy`+Ur>J;XfyjKڣ)`-^|e컆,8c0,㥼jœ5S/t%?\vʷ9`o3? (=1߷ ;X}z`zR ;qvwk|ɢ$" 5N$j,%U< kD)3l;\#l14fT~)ZHYd(9ʛC#br=_OY^鼲y`-{Ba3tW# }-S'T-x?ݮBU2U(V1ʰ %63L} eyeɋ2Ŗ!lY͘5$L_3㷩W%o3Vla%҇Ėg d6(“޹lt7+ZՑev9%hrYf&&opxq|s 7o6LSfy a=?4 0i-|򡷶x/I-ԇZ u~-*@telH|,0Zl}Z0ñExmfhkkd{ lIH).zaPxm{$=}Vq)]Fs"kSv}}PvqQ@ /arݪ>f-ER"yK|ttOY:;BtL!9< 8.=MG$._WSb,3XsDe"_sbO^AN*&-N1y/(2ʒtDwl"ƕ;{vaۀ_& _\gK?5;e;6'C˰y_^/ۘ !_Y'WzwZ mvTޠ}P]Q9DLIؿƚrh|R:e%T+Sg#~ [ʣT%;W;n!k fgz|շQ^ndրNc/(dl[r?K|ß4*:g*+1ߝ'.oٟڀ$} rߌ1Y~|shuu>^ɝVԱ窡ߐwqAWA{ Ko/]nTלIN9l'ͧɗXC iM&MƇlisWT7<3l;~!] 9+GW-v)=n.kuԶ75c"؇B9xZr{ˡC)6_f^-ƾٿhkMNu\kUiS2w%Nf8UN p ~G;cYGBz?Ռ*S}#߳/p߽ -OυrcjG>G>y' =6 sd^E=*o޿\R'k! |㮢=\Ϫ7s܊|̏}gC"ѧzAkr`9w2sǚq-`|נ9.5F*(Kg tˀL4ߘ$bC i'P'+_K<Ieߠ.}CW,;Wr7gU ۠v1m]˘567+ %_:@˱{J)#+  fΎ0>Ԋx+"cēYk eSRv's{a(T5AG|EM x){>+8MEй~ňX溺7nN[s7[Dw!Ee^;~r i.k4;w`_ɴw4}Š1!Eބ"O fIs]ucN nECw'I;m NCXe)=*]bXRxby55oSc>SMh O@EP.{gA,kP˚q;d[>(oFY5Z~Pk$WGiEkb4j*΀ SWw݋{{x>sQE>xb_=ž'iFa;=^ڷk}i o&:šۉG8H}iMZM-Ob_U!ZlL2FSGyI}ֽIէh39sfVam&ZyXtimu'kv-6Zk6f?66Z5Hը4~7GE|l-qjG siM~ -]ޡ.mp*jœz[9~9_sy o|+$F&pr*C~kC[Ӹ5Bx wx^sV|NZ_=kW7 TV.KV ,ܯ.Ie7r+{' '<2hߓ|=ʞS]8A+7u̵8k_J A0bFVn0UA\U[ՠ/8k0덹2rs`êJk m|U]Xnp5^U6m*a!8Gm k XC_: 3@: 3p3\3@: 3p2oJ;Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:20  X O6HP(16J*2*/^1N {ԅx E{" &N’(w&#!`a07`dy%aY?( n"j+(]EdD !<`o{:'ݓ{!K'5UuΣ9Uݷ%KNm3o)v.]ΏQǿ%Z%ڸkrzkpk=JP;:dvEFGgGGӢkmW2_q vQۤOU6xӽm4u ԮjcUhs¾ z* *iC&ezu2PlY=}Zʤ_?]W\F-ьQ-?Qe-_0oe~?Og|VϰIC&,|EksuOˣ/=Z?~yL? Z衎-{/JמW}q;%yjg‚Zگl۶=ZP{_<[eGw_YN]G 2߆+.)NTCOQ!?Ms/M}Te'TsrCqv] [ޫvO4bʀzVy ,03kY.7з{VՉ%SjibyZ;׈g959?Gt|"5૆77nڊ/dKUֿF }蚶z_Ƿq_N=EB5<c"{7']aQN[rp_Qq NoӏNqz֨%ʻL6ϱ9eש G_ǵTh|"I׏oгʽp=_h6u mQ`\~|ZeIF:耨xP=knQ1?QEGΊH|)1iӻM&{k&Xh'~Oȣ/rZhq[^?O .t&OQ=7gKJ_ (A7"yY#CRhk^,5+p$;|kz!bsN_WOڊyc.wë!{~4 zUjB;lu$.wиhW=erGUp[Gң5ӯE_ꡯrk٫gZ#[Uw3E0/5[u7kX#GUZwӪэ Z.,lpgp)rfnZ:-]_Y\6H\K5߆፿A es!]OAy_RIxui{6=?u,U tKu}(h"EE8|YJ*dM=nœ%[: ݇t ?vR,8wj(G..e65k mS;M٬j?+ob٬w6$28/\,<<'|(J ]ՙf)p$6\[WP@uЖy̞<6y  cH/Մ~rxAеm];" Kq5 Qt6|;ẗYW o_nڊ/4W?7FKCY_\Jg|;, p ~u域*32*,|CCW7T,|(myXL0 g<hihDY}'oЃ=-߷ T4Q[]sۻ@-g{}"y[ Dl-E[S\}n] ;q} hOKur?|xSkc U29;Eٱ'ԣ/pq,T-L*r|-;~,OF`48kI_V?h eT~Cq_Tmzʾ_;kƉ3xLy">qݯ!ݐ {`:8)3Nlo^m9n=1G2+ Wo\ܳdO*AI8D2OoЗX![MB͑@lUǗ{GDT4:l75j?qGl kEWB-WϟtǪmlUWaDE(~(Ln{.!8e>R}uQ|y]r$]ACY ?rj"zJdtw`~%7?HƆ|{+d@51fwY{f=9lKbsPw.c#£s z;TtRn܏v })Ae u-pR+l}ԫ9K({f˓@'g&OߴfRwN~=?}'Wck;9,"r~IN\F<9A=/'H6t`W2ЭsIWXL/7}=kYy66=[%t; ;fH‚f)y ʦ)shʬ4tؽGJ>!f~*`'96ٶ{e- simʵ#ߩq1.+X{/u*n)q{IFMz)ّ5YeqZǞڂfؑ#uO&ɰ&ZfbGÉҳj ^e#;׋'fpގh{B!83c L@^EL0 9dFnv čֿ%E.Mߤ_ Ļu .kOy~m^ܔ]mUWUԫ9"j|\DզN^FjSЕҴ..(C׫K&7xQ} o`{-IudPyuvyF VuhKuxS~3> ':=0ַG>zV`mڳ|{ѥTi[Bٿ)}G_UKe˖e<$awФ+ʷgG`H16w^sT'˓>;2x-~ɦ]EbRKl6Q顦Ӟ:w+*ZCp;\= 2|@' OɣV^=uΙ+||GxCOWT݉qSmB.Vr;nUzjhZl-tO pg+XR_/pG6Coϳ9~M}{YWoM~5ܙm`gׁjkx(uQ+\Vs$sߙgɀP{VCp2l?4P{YNkښa4Y~:Eg6D8WfPMҮ7Wէ.TL7!gB ǨݟnC3U#ż.+ʘʺLJw鞴s.ɗ?RK\YG}yQͰe. M3wZ;VRྣ<8ådSN$rh]Z_ׅFM_~|5mrp tlJëu ã u_?v׏ȳ8K?RF3A|^k3{1^k5z]w`Bp^7=I` 33Ӈ~g̡z~ή;S矅gzs49 k[wIXMЭ@XM1'6ړن;yY>Uj9)CIrǽX]C}{S3g'XL,<~ A=QyJ&:9eQIE ƿ{8y&%OO,4Cߙc26h| z~O2p+W1ެ*ɷD3,O GGt`܄=Lvxh9{\@vϸmka}64يb`)\6Nllݺ:xh nݓrl_~ݗP],aH^VdJLE KoibC7&U?/.~ :zuf]|^8%ׯ:} }{>. w{xqZӌWY{Uʁp=ܩ9p~JK?}E~!B C!8?}!8?Ip|jGB7PkΏ8߿1"-",;O2 g]MlWv|9<2%۽B2 yɽkE'?Y5ɢqu xW<8ÿ A~E_\ÿ_Z{n"d}[罟tFBp~zV?d$.57b)Ρ{V)=0oq7ۯ{)8}~J[u%՞ "2ʯ?sJ7+ɢdI]Aboio6OYeOI^#ߓҬ%~Ǜ^>k)iv/2t>=/YSgyY~6{E(V2PFy(Tc|B~A>$ŏ*/oRzr-=w=6ڽS2|,%myVznT@ߥEy ʞSmWe:o~}VU8t˙gG+c$&h,o~ مNVNM>MRY/#_l ̕zt3/o>;z{~tj契}|b3}݇lM]{|#3 9pϪcFCxl;4:i{yzquLcσ3BYA gY#r~ijRKeU,=:|~ Avy{Ge󫬃\roUy6y??_5ǤDŽ}w܋kː9+:e_.ҷ- y.-Cpno]d=~BA@g>S{eЍʬ4 ={7l gO\c[NAysJ&eoS޾ *i`9:~5iݳ [+jۍ؈9†ؐ4cʹ@9Orϳi[Wǹh( 7 !^в7LxS?k߈_q *zwQu?c?::%:Wh*z{wL3lf숍p6f~_oKb"{eE26T3q4E#6dW-_2-ɗ\LK鴭;oMFB1rzu(d8z37ȍFl&FY+vp&/)^1]<>-RYEx\yeSbo_աj7$UݝŧV}zZ}󻽥[!)*MN0߽ /Ek5о{d;ckp$ RY4m^^\;Oz~Y{`n$:]ziJ6}K8Kj5V3i u˟Oa^yOwU"3;S/Ƀ3d7ȗT%=7^oi/IޞK%MTKR6 c*%|k$BpE#/:e_ė{%]pؗD."sÿ6%|IG2:yp'yg,[f࿈/%gO=OADbz鴧@狲i*uʶe6'ƪ+מ}P۠sm~,Ʌj,d.°سgm=L؎سw{R }gT́WnXFh^kylpY!8P癞޴۩ͤ)FةJƥJi$Cpޞoq==6N {ܷ ^L{Ϟ@>g7Ge,=k褠 |[ ÿWfe"')0'HW|D_Wsgˌ ؋3L~t=|!X+W R,we _iO/nw4KaW~Uz-Po^ Ђ!S~I=_pdm`q(mQ]vQ (Ҵ f`c0Z[ ׼O|~b%[yst9G}JLcfOS^~@rmO sV:̫m\yȘmIFMh>okT߈;S xf͖ȪS^zgfҶG.UA{){Rw=}rS cĿ~l1`_5~4>L=Ka3l{P6J4=tzu\=W6Ѓz Ѓ= 2DeVt^Wث@ t\8z?>uQ,t~ tѪy^/Y:mtlfá4CiO|*WGN'Jt'?emι'#JeY{PݣBp{NGEY 3s|[|N L !8߿a8߿|{J Mˁ#j] A~ko6ԞlD!8߿E!8?M3Yړ% ]smf:ֿF_-^S/&9;i2?՞C sor%@}˯H{_"kna83sq֗s}{?T!8)#<+gd#%Plͩ6']F(+៚`|6K0oKoH7Wu༜m89ylF,3ޟ_ڟG0r']kfv0Shv u2{tڞM?:kXN4|VW!uh튕W~m*[_۷_[1vD>I{?t_^߻5iYٓ+=٫vvd5BwY4Ͱ'G/nՀpxƓzg#v=8z?"D%uĦBf m@l}u?6|w*d? esZף/sV<*9_ z  x=Ciڗ{{׀omIR^L|o͏o^H7?V DD']#umy;ˇdx-^ۚ4Ӈ#E7Rsopb?# pyWD!~UUCp1sY b8flDZJ qB<^\QMp>"#lPYpyyM=X !8?Y(?qU/\?E!8߿+ҿDϡ|ˁSs=߿W HEm6NCqh,=dw(?54?6=ݢ"e_"G)a }Nc*_^1_z5/!8߿W1I={Z_ByF^{Ə~l>B72G>i}4}e:pdpgB 4ǿ~6x8/>ioDGw9pwO a1E>"}y"pk8<޾.H{kM6u^{߬' ]|Cy#[OR="߽ QH> N3J{g>OD|>QEa{+Fط(;Zy(G_'AkO4UQ=oۖ#àv=-˹SdIb'G|]^.yVe18)1'b`t垗ͦj^ A'*~˗xӽƏ#[%'6}ܗ[rn@eVN"8/f +7dm&j}7mO{p|rσ5{y{B&o^+k Z=e7>/[ycnw/swP;Y̷ f/4WnnWP1W}0%eλ"7Gg).Yi:`][1ɗ8{iO++<#K]~{i2;kA_e+2S@U/c0zDwb~IUЅГH7fcsO1kVF̙~ P?9&.UdRR^LW]̭_ģx@cV̨O__;@y_0`+W] /-7}\E\ }>,2WYypm ʋ>kߛ߹޵'V*ڛ,9b^' ~O \'3Ƽg?v3i 9kv7Cօ[D]:>2AɃ3C߫ߙ|}J37Gg`L1тY/'jt`rfn"Sp~(;L A9wߠ=PfEK@~^?z@[E ^Sz%*+7Wu<7<%B2/b/20O=?.(? ) Q4=tdȳI^:>P EY+G_fCݮ[#l!~AYOB˛!vVQo*zBeO/}l.180xdcm?aspғLUs *Sf{ y0f[b=q =ԣ-l3]kKD&ɣ"XSf}^*d1Ϣudۅ緩⻄SPǶhXӊ&H7LѴ ?7ΘV4Kky9NjJ':cgͰɚζ 8Wa?@<+l#߰z^2\[fqo5Gm#l;MBV3 K90w[{(dw+H?$ pFO`+Am]6m#%=Cэ7Ge鲺$Sg9| e7h/*2c_72#[_ 2r"]_7M}57m_MW;s!ۣ̘ૈ7_\/ _N+)|yC{ ^MC_~!h6|t=VIf _uNU/Bb !'r⡬seWf 8!|"2~ŷMas};#޷9|'v0Y3v7;=e*c| +DķCJ9{O6\7z W(fNoʊ);QGwow H8 j^ꭥf?WO(ѭy&~d*o= 81,ON=ޯ6XGPnh&m ߑwnLyM7ȟP={Wԟ72zVrҋ.Su Eޅsտ39_״vQ՟ҳaѳH>x(zvJ=~D䵷wVYǛ5ת i<NZ_Okxәwr#iЗTNEKF"ʰh.Z2v㲐8^5+l6KZD^86կNJ֤Ulϳ|eSϯ)5s#=xRфƳBe}8WfYqV9cBЕ]|Dl޽T:6bY ^>t_Q3q(3`DgKƿ9Z+F?>B9lI;ˀi6@o-=r΀Ug XˌZYo?SKzG/o獜3`ߥ ĘૈODO|P|e~S|yzX)B|XW;b&7Oq2 |qπU ȇ%V_Eo: :G s/3`2x-‡C}݆u=nvz:mk1A12ȋ_f2u &~Fॵ6LMhڼAe}# * Bl~#H?6T1*m“Ŋm7)qt-/47.RmRF~kۍtͭW|iǽ<ƭr>VFIC}7_;7ئ;˹A'ñfRWu nB=<@Y 1H33UnDWگTv΍ ;|Dt$/Bx缠t{ycn9-\_?ֹץ3ztZ2UG/k?' ^Sp/^S)"6~-HWQ/V;D!|s^O`Wcm1@dž>ߙޗN}h/eZƃv zBWG%csS\M;^ U:1`l̷ֲӯ_Ny.&QOWhLTEáǞ =y;ǾU6ZMБ豇z;mpt\zqBfrY ўz`㍣׋I ;##\ 62* 1@5jAs|vѳdysSF*\ggyPy~7hK5l?\ ў: O wߧ(3e_HϮVS"7Ggz礗$o,^WAn>2sSEw"Oa.ktbplOCe}tSMMSMI[=:O~2Yivou[UYy7{h٤Dbů]Smޣ٨c~1jW&Mv2zF:ׯNU~U}& w_稏4/(~mm^猙41F0QƼv4iBپvmod\rj;MbffG]-"!;b#UᙗIN8s1/v(=98Ty4KibH[9;ҶUbq}%W3sn;l%Ǩmetzhp㿬i_g9y^7>H{ H{TgYpEڛ15d6g|U8.C؜H{;}a\;*?%t=du_5u'jK6beUDllzz^/ ܙ<—PAc+W1W_~*?// .AGV/}y8u+P>F l+il O ZѾe y_}=uMQUˣ^ˎ8l% =u`=Y3w^,8E*%8;Z&W#8dC6Vܿ}ގ|;{_;/r@_M>v5I}AqD!_Xf?d(ɧFy&L.ӶY?^.a SrKrOU{SyQ2v_Bx$>7p%k=eݲ>6h6^ |Q~ηθE_ѷxthk>koT_U}=WQeԅG&M^ݪNaZ륣GnQvu4iBپv|Â)@Sw osf˷ qޙE;˙_f1˗_7͞WSNY˧pl7e^ b]F|jg,UaepSC/jY{!8kt|1tT^^3i ^IoԦ`4Eq% w"q㫞wxO*LJs4Q㠝z>pdw_,\z۴k΃|.|amѹ.C'E|s0 GPwI=|R (]NB|}_u:knﲺwW1WfI|0_3,{H:@V]j:l:m2Y{vV[YYJuy|_uU削sv0n/Wީ_I8d W_Y4C_rK>*|X- cfv"O_F+mȐ; :/r i/sdlnK4~A0whlYv|y?}j^~ c5:7ƽF@ KLtPcU&&CW`ǃLGz:gCցPj<1u5fZIn̐f s^N1%)1@,PSkTގig\j 2q\|i܍ưyDY<̼ZgVqhX 67/Qs-ׁ@*ϕ;1^ ZXϢ_B{E;/@j,v~5ĕK\KšZJ<Ӥy vs.vGV新ַgc/|SNRyNm]Ǽ9BΣ- Z#IA̹5 oǞK\w>YJFH+[3CyӮfc``bQ{Co^_cgE+Fރ~γ;F~K:NwIgOaʁּ1r{li,[,zʛv9p"yap!};^ J{cӌ.?" &1?W;٘46σ>Z!қ+$1mQ_^xw/?Wor|o:]L_9Vyl@6o{۵1kFQs_݉5/~{ \y5aj_ 70ѾéHuƇiO|G<z1=b}[DײOb~g`ggG934Ӂ?݈ìS0Gs/§v7zCblT'FoLe8LnTz9S;8$ލ˩[ߌ=ܣ nc:Q³{qSֻZ_AW)w>گ9Z7fJY~%@3#>Jt ft̚7c:o qߟ f hfӜ0Xŗq"/kJ&)3 ow\u0JqVodLty409/hfL`Dz /3"u@/Z rԇD52-S~uT?ډrs~~pHbTX8K _;?~ZI$d)Fe/]`}ʅGrRE[O_9G]筮]v]Q>u+>;Yqe|f,ϼ3}^g&0 J#۩䥞xrʵwbLs9DI[RRD0i0>ހ R9ORׂ繞=8g$uy$qʃj>@,g491#UX4,E Ṳ=]΄|3>uZ`; W9;RFc9.<UTR7 V,WQr>K YoA90Kw :@8iM_XkBzջېKqmL6 o:YvJ/V]vHyXrbԨƹ 4UuH݌/|JP rF/orf9ʖr;li`|&tNmȑ Ǒ) r8p-na?9H-湵x)z>~Y AFjMNDV"}:P`)7` -c C[r=|l {,`Υ|l77Q_Le?07{envZ`$֓*r39lYĊݬpw?}2g 9~8ZnOKWB;6wryk;u-kSÚGX8h#9F1pJM)WtpWnW*_rp+Ӿ:^.ػ?)ܰ?.o_yc,fO^6\ᖴՔS6}4<":2/k6{ ^\Ľ@ $N @$9O?ۓJuU:UuΩ_UWXEW˽sX-{(t"kQQ-oaѬâEGC֖ݶG}g(zH%:]ѥѻˣXnItj^a )b]*[ Ã*_wRYarmϮ۳6X;F9\ rr0peLF ģGKzsƩiy̾r)}\i*/ʵ@3i`/e* oR26R2~ė.H<嗷7EGWhL(:/Gr>͑}i &6ovmgy25${1>67+m9Z~m&>Mm9m#%I9괟m J;m:'u(/Z?LQ<#n%y8&.-?V>uFOG/+}m*I965% i8曃ι90F=@AK"Zf[^,o1zg}nj1էN@_7=ޡ qD](Q_]v˜ {]Bu)NIr!h;5I}=UunQoD [ECy1=@4%xկt UU9m^EhFqo㬢}CqCmdtsܦ.FqtE{+i,˵}=k n֍TkWˈ$>qy^G\5MdMcԺdrI!/z;]'.p˙}1Zjk{5S.4IϵGFOϵ- E3twV ojj"+R+f.L0NPm}St1nmGELA[&ȍ.ba\7G+Nft'P#H\QF* 1ݍjzݱ!ߓjcΗ. $D%Or/}A7ri~$4z4c"}8eNv}y#9/5@' !ݓގ Nvt+UqjW%~fw}o~8{ >c83 K|8WyccMэgec>ݼ| ;/6H۱ArWpŴ,~7˵ȑNXF0Q [ce#5|15bGb|kȸj4G;qM[8f~x!C`[?fW>4Ņdئ{'%Zt ?.ܦhVұp08–{Ru)﫺.D -7I.H(:CWnuxVmicP <,Šų߁Ex6"xVzT85Vm:s)taqV-uD55Wx8$K?U{|Wq65a]$ * ᝍOly2/O Ḙה̭1 έ>DF̋?.{-9mN\*3Bs2]aN%-9Z̉CuglU9q+FZ9ѽZ겯I-~U^Qc3r=.r#'_͉oaOI-RuݨԼ–vvy|8B۔>ro|zCdD C\ !>ԛek?\xߟwFIŕɻcjsT|̖S}lt{^쒽+~}\QaDg@Q'e(ۓ2:ߎ=)xBb wҬUb6Z]FFSZK> t_ٞSo{RF۞=J]_u#v =c5q3Cc5q5cf8I1̘.zd7Vk<p>df6ڞiNV9+LƗ6=ta3N)P )v&;Rwvh{Fmfs9c V'i0y,|hIzh,:i)O\{Qr/xa39MA,RZ\(?oKot%|P/x~{DcmJq؞vu69Fx,[ֿ?+OBzWW);2K4v~{R(׷?ߎ6ߡ*+Dw!:_߫!:/?x߫?->jZW=|?ס:'t/yo:_mގ tv(-}^{iax|llbHZoTd%X;]a4+7|l͏-v/P_(ۯVZZ>-601rFA@r~/_7w􁎱|7\;aO GR8 7{7@4bNCkg~k'kotu!c_ϒz\K,a_+ 'Z$1^$;ͣj'jn`۹f t'=dhBz~wgggy.!:hѽ]Mkdzy1ojc\>[njo˪c_?tO}Yƞ̩:U[VL9gq? tv\VZ~._O{F Ìa`%q{=~x&ϒm/_nϫ&)nZe86E@y4}U*qޮ39=RwD_%Ϭs:w>9 aI;3#Xg0#;F<7ZK8K:ZVh,?,:|>:9]xýۤ9]q^po, աQ;7{og+/G"{lc ]eǁJy~WP?Sϟ:oF r': ~~/[[eL}W&N* : e;CBt^.egڌmC~Wܺ߇e_m{G3^=ǟ'Sg^^nv\nQZnw%tfw>ib1hܗ^00E8Fcq/i]qwxddg?0 qMÀGWE7V^g> <`?7wJ%7VxnstX WZ~W6HPӏyo;NoN*:|Jo|>GejCO>s(;k6E&GGu|.83%8y> tqi r}B;|{qa~~,Wׯlo]~Wܺǡ͒_5pO|?pU%8Y# <{Η{/}cy&n_}ezڛ5cfL['H1np97;U 9e%r,xYY-EZ_0es9N|m~TFo)mkR\=+-$ĖkF4p;q¾f̂a^p/r=k5k+9p`v,t 3_#\#)Νܪv 2!헊2a.IbNlL($g:$JʽZ>gxH uA>cL bi{i9e#OdcF[T&9mѡ8ڭ)!I\zT/:$)Ch1kZ>SQf,]_Hз˰сO=XPPg!S{L[Khi+WA!zu;g]Bgy[=i=a>s$z{q_ܟ`nҘ{;ʗVjZ|FC`~//{h)wx(%'_svoy扻J{ {;ϟ8{fb'`CUӎ~ΓOdkVmj/^pY,١w)e|9\v,]_>t-v# tKݝZyJު_}&o+v_v[~o+F-×FGfjFZxW |yHg'ݛ^>+S7jW="uzjxpB1Xv@jlt9X\Nbia}ACeϝE7hWd+]f2d60m3Z|xۧ(xA">w{h Y?оmkIȏ5C] |V}gੑM=ߛW1:W+;[-QTcM7㤲gF=6:_?xG&eO&%j੿"r}evezYyU,ς~ݸzگbgɞ"! #s bu)_"dz q7ɗMIi8?Gi<4d=a, .!ۿC~7 sִ0Wn5M|v^[2^]埩o_`0$c,A#k{ⴙ=L=D1n薨0QGc:Hqmb;D t~O`;o tRϷ3+i8Nٳزa@+ÀFGC@֧>Ve-tU x󹾲~nzǀh MCtL6P7K0jY;0ѽuȟW< O*^`J{t'C^+!IC2Q$EX짱_f?qeV9~|^+/OC{ZZ> ~ڏޖQ:Δ @ r@l5K5) fwC n0:CƋG?p_Yg{C~oz۲ybaqic7{[1=Gq5,ްM =/1`\V Ի_MF7~;+bg[J~;*vִZ`Z> V VkzGӑLJ:L(8ז/8%dW32w^{\s&БfCu yUsL3Fu`ƨkmYw54kyk;u^1"ڭ阙4!:5n3ׁ'Ó|c4N[ؾs)s{ߥ<ɗz}j=/'_|);PݛEYϜk"[1-6Z,"G:b9ڍC 6wuB6n~FCyYTSq+GBFŵ ~\(Lo7QEO77)߳_=/ N5SL*\T=J_<<ܘǕo]&٨gw*SS\>ڋpl8#nty(Ər|Y;ud›%uIx^/P,<Iҫ9lrv`!Y;5@ axiY9f/]A{J哇>bJ.:hlma1J_ܧbTs]!69Ƈr A7)t^nGU]AQf{Rtu%7cF?ܣ/s/l\*lQ Qyx0wcq sޭrJ(sTv|؜{yDɯ3oNd0X9~+4t`ݖI9ųF]*_űjb3hڵ./GX[{l>!o*)mMZqP=)-y= a 86>WvU^ 62X_iv X\,uQ9r;21]sX+dW2|ͽhus-DG3~FvnCt3P:Kou$xasoߔqy')o'kaN#Z4I+wl3D˽[Yt?̞hSX{{8z} b?l/vla?fȭgԱHȞ{ rxnQd\?흐|{ \q/eq=q>Wd^R2+mkbŅdRi[DVǛ>ܔ=)hٙ[=0|۳:+C6~+۲v^acUqQadsf=y۞%3ڦgv= a_ה)5Jzs,㩾6h]2g9 q!`̰3-"#tr)h()sEsX9wjnkBtHU"DNCt܅/+jh1l}ݪg;6d{myզy[`_6g%:?}lLRt>߰7\]/΋iטSS]c:Ni/3ϯJ6"y@˽Y Bh͏>5K~XQ>2/Qfi*{ίi6w~f'2R;Qtp ]w0$QK8 8|9ф{ț<=+gs}q^um=zf@ghsq/Һg:@EX3}M_L_Sq/^k3/5ELdSu^˨߀|§71# %6^{ Og0vVM 猭pf2 |gpo/fgLVz=*mLֳ 4gn,i7Yqrz^֜}Y& [w-dzd{d]P! -ETZAe[cZ-Ϧ׫_gܨ3Zu._1gdأ-s?M2da x[*Q|9]˷;%׏_eHvff-6<[6E,AͰ1oK͉2TЉ4nմV MP69_۴kP ԿBtߛ5hnmη& $DCwګ}Yk\_ݛ{;o:kr}go~_emkDm1dwkC C? I8;ֆw64|af! >9E7Yqr2 JqU@ӻ:O3.'_#K \B\3ő=x^ ]OoCV\%-͋uC%ͽQ܋=jCkyg08*"{8iG[7~U7:ϯ 2R3JmHujiCT5}^]Wʡ_|CzRƛ޴գLu;UoM^o\|(ozm7|.W}9Uu}wўѝm$mBs%J{Pެ,ØќإYpN]co6W\θ^ KYUp\p)6Fhs įؼxG=z&t홧v|c< KinHg'h"-ڤ>iQ:1\X *Z;} ZXâJ"4U==:6yP;YD~&= ){]i&sO5נ{qhöb9Ҡ#~2}Z|f.||4s|xRqOϧ1&!l}C&vz`C ]l@yGKx}N5Y~?nPq?ēfV NtyTe?X1:a@)GѐN4'hO&7SV}7mHm6v(-R[q𤋮O0VbJf8]5I,6oc[RKCri__%z9dJo~n\L6xdëI<{5`|7$nvM^- ;|\;p] v8 h^cYIf[p`5V͒ONm8B:Qo' 8Ҽ68dy7IٜvFl/iwx{ g&{ՙHСU"b_%y3&v0 LatD06`fƞa,Ƈt`֍=:`\(itHiqt,.ݭGYGɡg/Œm;>w7g`7{&+.T*1S[夘K7fF361?Po.:b Ӭ#qxX~A>3^5ӫaQE)Oz=T-˖1J/ڳɚiI(s1#cS7]uҜi'4D6fv`ȗxM4Mr^FEqp< ޢ8BrZicj}H*NŬMl4چ5*}^/0w?$l:CҗS3I S.6*!Nhq8 ahWK/|95A=r?qƗ0Cl2::%< Ol*x٩4[mȅ5G:['2+pJ{2/=6^)H_FK匔?@7S}szD1הB 3po2lMo3!k./q'}ծGmj<ׂ8^@ves;lQ7k4opɛYt.ğ{ /E؜oSxXo-*͕p9º9Q>z詗fLK`\j~Ɵ_u5A[=6:ҙ'VaE%:B5 x |tK5Ou˼kU7@Li~S3?SCw#]A XDĤgFu$ O}PM~^e4_Zη8%x#\b9)·9i.~CHn"=|Zm԰fޥ&r/C2!rz+UMK?XL]c,T4" = ϯյrX y^] ~n2Lc] ])!{[꣝/mQ_?NH\*;@lTH/閐Dqd;?IjdֵS Oz"ITH>>_uvFf縔5#2fn\rwʍ÷ѵS9wAN$dbϙ|7ȎGs*rMkyrg g[CzOq"{.ds>5=e"^1sjb[-Q3 k3wxv'5h&Ҝxg ͉͉/G 7Y|du>q~,E[B}:?e_d~k|Q՟J'L sa˩ݜeߕwTuE6E_Hm} ˯[xlf ۰ٶM[gxʆ~A?&;ӷƮ-gPe:b s[|t_ Wn:[RR^Jyǔ(7u{wsqq7 ]!=v\[݁o|:azЀ:lyճr,}zvq4SFV)lqγryޯ{"WY2 WŀXײk\Hg t8fvHvA5(I b|;97e_L|&Gbg(Ҋr'cž&ȏc$1bn/+Yɚb4j{S0VgJ0ֳ =V!kk\˽yLGgr EFB G7 Nw'}һ2L0gd|[zk`S}11bMc4~a\0NHʡǙ? W nvTzHm#kdaWK?AUNGL,.p]/_ p'`yQr1=[?GoWzXIcq|`q,;M *$gI_E,~GW~6kj_s?ӗ_#b>+6>LՇ\<:'k;Oߡ>zCs<nfΣꛗa.~So;j~/j[ϰߘH;.\|ȕ:pS(dXWA! Ŀ́M3OŰly=wkBm<猑lǣ91rAg# בܯ5-or;%Jx.AoAWcwoNL"jD4d9<3>ϒe4wxQ+vg+|%^(.YnYv}xb1ǮɜyKmGb ގwRq7#;8hP»;6& hKDd%6+masZ{;=o *ep l:<>s?{~{=Eƛ[S qx3ԙxXMD26ƹ-L]AwSnj—g_vG^kt]O3 ɖO1.|~NCj }^yliNk~dTż !{N6**T:Uy 18 RdS0s{?(6>)Xp8_T6^bm5Gx;ݶlm1ɕU+[ox*'t;??6۪[ m}]fTrh;dcmx]9ŲͺoF4Ɲ[1n;oيomn0q{-ո6Jޞ>&&]KW{:U6 3@: 3@8PڧtHg c$Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:22  ^‚ 6NV(162/d1 -{T x x^UwBKK&(oGZ>B~1|=R FᩂD q}.XD)B(\MІ@ -c;$&!}f^㬵ZksΛՂ3kB8Cp6Q\BSBM{MdCvAFwn!|wK8r0'\KBIpN:@@_y{{(v!ӗS>Se`賳jצ>WJ+S`[vݝ݃?:>k -@W2}5 eO0W Ep/Vߚ噳ɼ~at]qz'>)5tK]·Vsȥ\B};IJ)CC#{ m{_<>/\-kBWyA}vv87*ݫ^ӛ<$׮D?A:g^/\O74'鵍i˒GGe^:?4m=`%$N`},bgMw Xt$ZC7 6t:JßSZ㏅'uk/W}՗vʺgعw=e8ڑo(Jړ޺im{UZ4xu4f$-g3."6&ld56ȇo^-7[l?H]^q[O&v͸-*'SMljI6";VznK$}F{ے}ؒD}X<$mɭږf‰ᤰDr_^nsEr߱,KUU]N>-.:C6\uk}ﱦ&JO?\r?]St쫴9[4^?7 ʭovXWsg,z"{"6M/]z\ Ni~}.o9V 7\ i >{<[P}|'c+٘[|BuYx4,~xXuXj{L>wir;%%Ji 3j;T(( S񟲌_%=Pܐ) 蓼}3ɳ :#hG޺oaq!L>,5;n!<WC`}{W+~Hdt\^F?kUH⡥ t s~*4b\/G;,7T=p.]E{HOkO#gu,c>wXj5kWο&=7ܹ 5.dޙ'>778Q՞7gz6iQ뤖H~WIOV)$]HX'C|+듳| - mkª.l #^ [Ë* W$&v¬ jCXnP ߐx1lLvJxVnT+zPJg[ՊfEsc>'!$R]c՘AРkI=ǥ_FDI_ImrEea߀9RD[$ߧTVe)يD %%b&-sh_H+jOktis}d;~/Ͻ~I/|(eK,Hp:'˶Z[؞6: ѠW=!?}zd/vQ-v s=)m=w3:Mztפ:Y7сE½_E:,6$>#?l8]g:Qt&Ď[J6XhYVQ[6f`mϨ8 +<<"ﺘ׬;R<$u_λO\<\;7ۚ.+uyOE<0HY^GδqSC(~~ hcRf R~+;]HɚJWte~x c>XsT4:/yPMD_4.J#~<^%եlλ4.!X'}Y)ZZ,V4~$L{kitV9WfҸ5i}`][S4 :`b!":)oRg-ꡥ8OJZR&,Ï׭,V-I?mA)ԗ)] 4" =LS<2?_YYƱ3d[,+Чic7=2ȗXS2׷iiL s:0>d[Fj"/ۅ!s!KLٕJӝDBC ]U9Dhw^!&_ ,<=-{lMO&rE=铱=뙇$ym='@G_~7gNW h'O;dB=$YǨ>ho}~y\qMk'eMC Z0}syr{X<'AK},kh R2uôR@'-KhtեV?SKO Ow$%}?#6|=щt9M|\VC5tG//|32<,5i`YQI+?'ӯrR~cYS~O&'$ۇwyP=4`/c+C%l ٤wOSW>%eŰ;h_rc[Zg14O_nAe2פiO[U#+ꌜ̨;TM̞RCZeH#8yrFigէ}ۻ'N%+OX?_#m|gpDOXci1<uK: _֨uGgLNެV5%QsZ}HX;4=LrݒkT'}"AtBe}{{Gqwxᵊ<됅 <}SOqSa h_Яm-8rE˝~Ж<)trF*7wh<|gYDcDH<] I^Iޏ>cw|yxtyșS]+Oj^ܫ?#'?un|Su<M)Ƒ Xsr x}xHlVxs4&ݭzٹ}Z3$X#Pȏz6bgex iB>2QLéa1v'yfZe|N>44g teԎ>vLhlB|^,/Dl@O(O,`S{R%}sFFAdxƽsϖ<0(o9֡Ֆ5вY״?+  Ƨ?ʖ%灮hzඞy#k9мzυtpT8H8H75<^;2PR,&鯗S4Orب' ?bz&qn"yKDy/2|6@.@c6#cea,8qH=Oy{\;O;ʞ#:QbwKĹJk; wp-0'sw4e˲F "D#l{HODp_?(/nEizϏaJ7=Z2~M[歫A%784'J6 .<.0wT(,wBVV\_ 8޳q۝W :_];٫M|6yͳ:5֛<|y4 7VA4ZyڕT “%͎G5/^۶-]Yν{kw;^wϼ0Iջ}/XQZ9 ;*(\x [օ{g^+# sYdw Ҿ3|{0}_nK;bك^n{H.yNRN)׊O WtneR}!z=+jf'0WnMmol "eB_ lk&^4T\Qقv)剞Kuseߏ?ZS[Q}01] 2RUŠ{+*,u芾 ާ>o!>:Woq_3J/`}1"[۩}@WIJߚ{Qo&"iL_oPMz˚ժ||}u\\Cf zu;ݢyc;l{(č"Ѷ6-_#G.rvy/Ƽ]|h]+zjoJݯ:g@9jڰ>ƾ>X#w[}jee/{lџo>N*UWn4T9x!&*&E~t=ϼ }_ߩ9IS:S$9Uy#=F{~}xvXLJ\e5H"HRby?Ml j`e/{lј̓8Fךl3camQu|[ʛL`~ޝYF} :{ ~twħqz6C)wp9~gs4KZ󬤤:x2S|2>~<+=W*};7{R1w}}U9=<+QjS,ϑ1I:CCclle<13ǰ`3Z#1sԋĿ{~;7"y;|>=}Nw@Ļ#o7-_yR֒SnwGw!y_:s y@ENgn`wuRbYB!35ۻ|c3F(?*<}`noߩþsZ5+^Oޖա98փt6'OzJj=Ǿ/ }iui Op+<~+oO+)^WPG~pg+ZE~=دQW~4~,f Ư\ 8Hz_S ~EUkyzJy˝W !:SAKvp>3&R~;7=ԭå۾,YzFy AG~g*Og6= Zx~7 cwͺWJK^$BǺ[TÑ!6֛G|_瑦+@%6^7=LFd̹'43?t!{$pG񷴼Mm |-1}}[V捞!9 X4Gb pư&_oOx۟U xNÓ;F|Xo^"Az~]Z9o!靫:g翩ۅ3싛/:n`b@t簞o9kR|?AG{zsxY&JughȷR-v(U>v3_ncO}u|`n.ZH'Y{=R}a #qY*ϨKr5J 4)+E.7޾<=u(' 7)>y߃^6.^'=+e-g=sny5s$( ͊}IBC+lle<y]@Gv:t祈ܘK[<#T4K_xZM"?_+%+ȿK@po!@BC~x1|sv)vƜ}qŅ&/u vFYIu~vO PCtU??68fz%W%tS]\C|ZgvFӹ7Vt?Hj_U,ϡUakll&{U}nTU᫸A|Yn_L. }f>TkZYD >6?X \}~g>S[ 4=*oľE} 7?)ti{R|&.ŭꇵ A|f>__Qͻz@UsKkl_s)Ѵ]˗Ol ro.$uH3d;v:XyxLC)1?{ *˲90b;nxA;q[%vA7Efb;OFp3/=}BI53Ym_Ӳ\\?={Yl:/j-Qv٦M+vn~nS}|QVS."[}eMz{u㔉߼rAP?c;`ӱ̙s`~bx.hH}d@ M܎x/P/yxĞJ=%םyO{pMQ'X2La} Ə,){?('S[U7g}{&͏|wy6gU)5()dTUZ$~Vn[g/{l>{bSyC3"s!ˋuuVlWw3#Գ cgU.\4׳UWa3y0Os";\hLi_͇Kh>՞!?u>>;~Y)mhom(s=0~~cOC}}]챙Gc6A#:uȮS>1>; Ujӓ4^ڎo;~쬤sw"Z8 /j #̮Zu^=T)QMc,&/fW;,.ߥxp8A͎$G Z)^apW <Gb^z}R%|Wg N*\sTwNGCZ#-*ħODLз$xWq[c/_4 C|sd mcy$9U&AӲGnݝ7c{ޗ ^߯g2o8oVЇk&$};dyOi@,U.'omy#{V7>m_ߪ*\s\/SBk?0V6_80Fc =VrMH-`~_3J !~KFƿUGl:a漍t2!q^A8.r/{8mkg9Cot@ ̺se %>0cq\ҠxБOi7 AkfN{wPߡ|_{.k}9q2χ#+>xڿ3^S(X~pEkfıH>D dwEW/zgowƉ5 eܘ}SocV>o/L,m9ߞՒ1g9w*YNK^SHV(;|y|knh n،d]GoV跏d~oomq[n4G*5DȚ}ڡ1~Y_Y%~ݷw߮@޶Ռ1qٌIː/Yn1U}w{聫$_J;kʗvaޕr89.q/ǺըwGѹn}'{#B|ժ#? JOU ^T~Ց;ͼX < bn9}WVFosю68 yxNWG<8eK?Ƀ<{ -Jߗ\T1>Mo=zsMdn- 9SJ8_(Vr Ǹg[7]cc,:V1RM}wݤ'ۯrOcרoP%2omWkʖ)X!謃_>i mh0{7IR$7ye;v:_W<=% ߈n@% ?suIX3|?ebP\?AP{c2qx#?="Gb~C!]_yWK@?3{h_h#T?$X*q~L&# d h1"yBƿC:SNs<U9YJb҇~#)^7̽@ohT}[0O򮑜 -S(oX|/(yߪ}{${~7=V !}$#NOSU8vGqΕĎNG.VWwnY4 . [T.'{$/I&d?@w:0=ƃO"T<8톪=AY0NQю6g5ΫAǃY˱5j \܇͠que~s\-"ϋ%;[' 봸S<'wI7=^|J"ߺx*~vC_l}>GeI?(LiK;cչ?CJ;Ꜻo{NOmC iܖ;unO%?#( u%seyύ9yMǜ ǸRГy{)ӊm_~wLb kuysyQT,^>o!` ԛo >w8PGXe붬ev!oャ_O пMCG`t =Y @,xN edp<ձnSzy1SIWjhI) *);qRV\>׸G% Oko^t>"X dZ=oUU8M_oR{H_rM/},e \ k-O VapgMĞTl0H}Q,{vvRo nΐml'z.۴|c3F(RJ:5HNW])yk|nG.g= CC߱*)?Qd[tx3IwavH3采v?'Τ[J_RJLZUk ;x?g짛]~?}r]=V̼+# IvKw%+8^ulzݘu:Ug<$=~Ƕy]-dTGV՝ spg_R1otb~Ay~jz>>Th&i%g:SΪ62->>ξ/_Q.dzwxG"GuU[?&/U0>e!"ߢg_Ky=ޚނl| -,k1~gQeA*)ػ(FVzkԎחDޢߓz_,ϑvy zoe/{lџ_z<>v{C"/ ZL{|hR{7M%v|QnuoPj;nPP^ig/gY(zz#ׇVA|)]?(of+.\W^e<g೛9Mk~~wh}={1 䦪)u^?.ׇ؛"OI~M ^njg)F߿UC ?㽾~uVu>ݢVJs^H.=7M5{}ֽu8@b_༊q}fUOkr&u{"ov.+Ƙy'vt֋eq{F|͋7Y}/T}\Fn2qY1/Fإ]ͫ.(j8|h:IXcwJ'= $'KgoU{u/Ϣ-N=S}~-dKn&od>*vl9?inS}GJQ!}r{ċi¶ﻬxl ~z]ivР;E@L¹;c9 o\]VӸ=ӎ< y2]L뱙GPG,E=z6>gM}ҞytKN<,?)j }DnAz{wlCܵ>sˏ<)R𥹄Ih)Vl blue2ev桨Y[y>*$t[ѩ]PYctIk}hΖ [m0m8]y۶gok:gƶyDuq뷤rQ{l-X@\2&8 rɕg81y|SgENPJHF%(Aӓ$&{%)&81ى׀`L= *bP+QYO \nuxlо̓jpsD] oxU}v5|!8~ta/w'9~ O1Ԡ?@y>6݌_ Ů?D%F7D~ %|!_<0Y#`r<Jj zXެIoG:,_Zݝnv"='Ѐ<},f((qRt?,r0Wv5Ȏ)v!xc*<4(XCzLy0+ʰG%Zщܢz0 8 0X3GAp/-0H "/(Z/dml0o{AX PK5/'J܊_ꤼuR($B Yr<NwA]'bjy&R< p+) gb΁ס/J㨮1FftXO7y67xŎ_Y6U{gU$`w7DMD8C5>oq 3qJމtoW|drE|1T\Ȫ[iͿkybgQFOAg?1k8qdzĥK]f 7ޥneϾY~71΅HK8d7A> *+?"e <~C`XK߻)y%\<5V}VJ? k7o~?.:$zN1DRCפ̦~yPƈ`s C^ Sմl0>@./)b!ΣHe SZY9~=q;лfζ>j嶸=_}&vtԯ㩍ޕuhO;e{OVn39nG2IQ,[Lbfbcdg:/۲{ }kY}:Sa>}h~;%]~ù:zϹmOpVپ.Lu_9kֺVtgˮΥ#XzM;ml߹;k}otu'*?^ x*UW^87^ x*UW?ka-Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:22  Z g<JR(16t-2-/`1%{4x UU(32gFFFEP `-6װ0P|!@o(TRbRٽdhO^,FQB{̚=gixᙵ^yzTxP ;KtR]7H QuU '*c2Q==o>kW;q1yG/Zs y^Ftwr4hKmٹ}u~jDvR=T6|׹Gb`P~x? .j2"U%yJ>uH}swu~@xN%ot% |^MTU{zPőNj[_5A͇綉S2=.z :[s̓9X\6b—L8p^ڙ9pBkgO'l׬p~sꩥ#k[A/ }8g9ӺSu~xU}rmd:~QmB/t䈜uHN7CTD{ǟeeq{pJu}ɥKn_U^:G=snJT=\<ѻȻTc…ޙq$[0IoݬJn^pnRO7&TE fꠛ&anoŤGuFu R"wMnGqɸ em^Uw*vN::FZNqt?yĄoÎX:'hh0?qJg2_H7*)k e|f-زEARR[>V7j[Uln50>>h)dٖ^Fu/9Src·vZklcҐKއumUs최52QWoxYC/c{]UwEA[uߗRaԖVLWktk㦖ǺM^K1$K_T3,\kPO][s gJQ ='jZmU$y&q6+NkwHh_7V [!UkA}WJ}6:Tj ]pp:zhD*޼ ҁć<{G8Mϧ#6tI/+=3t]O\rߍ"{Ӂ:dt:0җ0.,MF4:Ci(麦 F>cuP7qlzIm:V]B4 cجn`|y¥=#n{FYx e/|PYgAJY^{d叺aWToCce ѿ=\)_x{O'/_/A/8k2JG/ cc?9s^9e pnuHvN8{  VY{=8{w7 m45fckգe'X&=|>P/׽cɚ/nFa'9'8)4/<'L P9bQ %<LρxgjKwG+|)g8(oTyײfiw{Yլ?`yr;Fqgލc)?WOV,ݔ,sǼ/mmTïخF塃e  u_ 2 sɚy`3plg$cl oUqk=״3Z3ޢ;D.z6]"{ozjcbGWpavڛO:TdMDף/@^oz$zdM>F1۵G}xmx YQGX?H_xZvdTXaIj#?ˮkiW!om{w/o To/N ~;֎gV,b/N´{q!>r״:{4u/\b=߉q=K7tҴ3o5ZJ+oׯm-_#j[)SS ߛh#/ h0_`~[m]_]Ǭ8պ)CSTya|TߊT;i~lW~[{o7D8؉n1lN.XYGVYjZqPFb)㏺7T~m*"L~CXeߪ}; =~R\&k䎬g$^'D/sMݸv.h]ssBoJVwxlQ~%#=KUoEDړ /=IC& )n>׆g4%ʮi!ó e6AQ|pOFD hŰK4Ys lkћ"@k؞$֋ h-2*9Jg Z"!0 Iˈ/#%TxT׼S ?6+{l'SkQ׮u7*;y{k1gȨMy:Ź\{5Cq1}X/[;]2ebR ʳUZ Q ZNkz1׿(4\RUaz] 8[Zft0S*A [;uw54d1|<`P+eL*n'JDx>P}%Ũt5|W0ahܮM?Eq 8i֦]ַPƭo״X]1':J2GtFDMWz'{Iy^CC1Nб\X_]h1Dat)58Jy"{^ufuheO2#޷~eߧd->b_Ki?WtL=0 %'9[x7tSz=EUqؾ1&^YX~,c=Xd%۵8a*R.Ӣq61C-MiRxMtѻUEDZFzQޔC":cA_Ύ$[7炷^mFٗ+s&ac"5 f>Z&[ugNvͮZHkǽ]>#e!vtklS 3nf_P]{ZyvW9۵Y_rٵ{FyfxJ;M[)Z9ok uOJ_%'rtZ箼KQ]kg5M!]g۵R]m1-7VhPzB5QFvop oސ- be033?xt~l]zuɻJiQq!h{VWh^dkjvv{[_V%ysx0[7w҂y: ɵ*3dizV16oĶP|Bڱ8y`,%e-v֪"o^t"/zv&߀fgC+:QGDxJ ?5NTY =o[|}|^C$|h?kvkzMw6>+RO ٟ֨Y,<~~c"d[Q1y<3=PdGWw.w?#nK%Rx0IEinC#P:PN]Wo0ouSSD4yO:eh}]kܘM^]^3dЁY j(^ OKX4Lv|xy`vȳQs>B>q`HVѾP.}_ Cݺk?ͪ+a!2?;J}o-RdGW꤯ =ōQ_FݭGPyCh';B7zp^ZXB,y}8c[Rw^e=HY?} OC,}TgC„眘DV?:Q.ٯh<)Y{;C}5V67nl]i#Q*.OCsig|C!R)OBXRzc_8.CB2!ԑwBx*q*}(c8&޿åө V(8_(<p:1cgr5Rӓ!1nC48fOxT(Ӌ487y}8.cVv`*ٮTyCǜ.pKN 1;e+bՇ8tS&cf8<08EDZBkCͰ7ׄb %lQepwγ~Y<9v.n{7vL !0[% E.ϹGڡM+C/;\c^,>,^.𗼛6\e{;8qoU% ^׋*^WxAxbJt rEccQ!֑xwU Y5[w{{O7 r]w{,׿(+|liՔ[:gMgש<Bg۵k;WƴhܮM?.6>)GƐrq6fNE1s*e,1z mwO ~"N K71Aם,jkeWsrZDKwV(j0G{5_2 ɷV|K z5;?RmO;w)]8nd|I(o)ij۝K`b5=v ǝ? WiR5IUs|$s|}/9AЉs|mEΆ J.2۵G>|0[>`h'6ǎbm>Gbs{nb Ngv]cܽn"s[<|zy~1MvrHr/'X(>FwO93^퀅(K9k<ŖFqu a#ڶ4|R2Z%yLRBaocXy> (6*mQzK{v*PޮcVuTsC>8z}6ބ?`#+↍s?ؖ WT~CF@GltWRQyF bv [J a#Q*ldvW4={ p ([`p ff~haN{S؅=/$t0a5I#έaap.CEL:<ˁ)$4/J= rQE,GHY6HZn2t(kR2ԳG:}Ry\swڠ N% C7NUu[Dܹ@/w!Pzѷ2~9ig҈^Z]KG^~瑺6)- z~pJw2wϓO _PxB= }L[qxqSa*w &|o+ ʿY7;Wfv]\e,KwOBYHYOx9n;>\kPtƻ 8<\M!.aBE.-w>@wNWl'/pim?yIl?- :`8ZO|uLb(YBf]*zA<ퟫO%ѽ!"?`Hu98s;Y:8sڴ2ŭcUóDNߙz坢pBDUY _3~[i~{\N= *Ck4S=v}cq޻xt}J!=x&ow\qU!l\^@yM³B3_y&Nf*/:VN8_J器;#3*Y~vYK| {EzJ(߷ٽ6֛'fڤLWH'}[D=Gc%[ෛzj=ݶy~o)O.to=5˾o虜ߐQ]=9k'g_Nv sJ=8y\܍3,}ŹGa!B%S&r\r/me}Q?`5.! 9wqڸ=st!OuOGw?Iu!PIܘ{Cwulw?D--J.3۵G>ƘB%tx<:"rwn0R=GY WvWX߰y(>Ƶy={Ԅ7 x|k:X _O>V1,BhsQ> f2D=ΣuZyZࡎgxJO}]!u'nY=UwW=kuqV{=J{i݁qpOҵ%v*<~=נ\?Rrï{!QyJG$A8{n׆{/i+^T4y.qʦ=%ա7Ƚ"9Q7ι< ]ycxV|~.{2J{U&=|kBǾRNlپhL=dɇ{T>mQ=:~F!}nۣ/%xw: &^ǚ7-Jv~T٤R1y=vcΏozױo鈡֌?WQT& _BzfNƓ1c[|u1?{2^m&{ JݤPlvFNPn #)uJ+#?96g|Fɉy`umN[&woף!,icpq8>'a8 v[֧Ds1|(1*)B3Eʺ}*q1C,BoQy G]NpCr񩘝2Yipt mEpQ,BX" 7e((ػ;<o/ ug0mfЈ04 +pNY./^m"7=M3==J;ZiqJy|$@~x{`_]f*<6֋R'psAnW`-M/ս?oYOVPv)9 Y[V #VkkVE۶?ǽW!՝2 *^7o\M)?:de]o{*{mz3ӯ{}9Y`=LG}?6{{zH1. /WOnx/!"ahsVVL'Q]T8\46<4 mSy_Rh,z_;^6 +c*= b376,`|坭xs}(gjg:MJLdin&1}5"u3{~X{σ }/mt{`R5U a}_\J? #[/el%ԣrL7}Aws0+ >6pq:|6 KD.y`]#Ng+/J;xW>Xg |HhNq9)ȗկ>t8W)5 Бkӿvӯ,[R?_v=^Y.C+ ?^i^_ؾ}seM }zGFwEi}{&n2/niqXZLS\7}v|O8kCo~gv8H7'S~=UYs?5Q  C$š)jx ^x/䇺onݽO<#Lh_yBޯB'~27أBJ7 x 57=-J;Dmō-W+/_yQ !#ު`w2>:KPLP}l;d6̡!"2`)Ks'E=r=Bԥ =Z6BI#opwwwuw~Dmճ#/p=T]^U\[CZD>nytԩ>ȅnV[5~QdnXJ JaѪxXUtzmrf\o< hh?)= &1Ioo~-+u%( xy i-&0]HtcyMov~~gU!a|밎8xiXO֭<ހZupQ2S?-jSyh}\aݒosbǔ rukt ~Gƃ'[Cyd}bnѿ8®_?nۑsG>LSm"~賨.XT^55aYki`ܲ.&0e!lPIbۼTKU5"ۼ91~ԋ(M}XtƙzGʁ5gdnXte>n*xGyb \X^wҎT8^-W=v]{gUm{InFĘ?\X~8, /Ǎ99ui{'DHskGY&yZ8WH;v=בw_ssx"nÔ6V+ZN= :>uN?i,3ҭ6ӯD]ZܷrbU;Ek'7|_\ g )ڎecZ4nצw}l"Ga"rp甘x_͆v]y;![#b7`c>?Ƀg>OȽ*b^f= /(T4K{FiwosgV-Ed}zW~r lB^uLߏxxU!u/nvfM٭ johVGTvk@ZyQ;Ε G9ga|Y%fH_7_߸zOZl=kaxlo$o\{\Y%15wmI 0ٴ$ָV=]T9IAXp)]߮]A^3D:r#w{yTP̸ѷA|FsyGIp~GI׳<4Ji$-|o{+|{`[fϢqWo9־hfu؆f̒{& ~+*([z3mp 8po`t Geyգ qX'`)璕#߉#2LE[־EwR7KFUΪSrM퀫g8k{Yg?%qִɶU塱6&Y1[g\p)_ѸW7-Κt*u b::(FcVbbK7[Cz >ɮ+FfquҽOCB'e_ #O4!'n|BYƳ/HON_| ij}c;M-?.>1~K:z FO&~*O/?ڻ">ur'f~E+vPw 5(>!|"S,>iU^ƫ`;Y-LRݓ`Bg{K7HYmWzAgVڕ (_䧌P}Ql vn! ڠ>Bde`/Ń/+\!uYa J#_zR><ҧ=)K,=]pB&7>6SUM,> i<﷊! n BYƵ䣒P)ku1;q1C]4ޑnh 1U1M+A>@AN$dXX Q@X)#8 >a]{m6MK[?NLk-lT+gd?aߥ2.Fb\Qz!7za(4[X{M|MTϷH^s-Tn&Rl=ywzʦ$cl=6[Vooķqme3wۛШ0_7;e+Ojgh[ Q[Oa$66 ]lf/Ϸ|O@z ~RQܬ cFfI|kTyc`\ƱMclpZYi4٪9Wѷadaqm#nv TyL_IlQN6ٯh< ^&6 .|nC]f-p(" *Dw6Xiq jͿF3ϼ= |Nq5/+t?m Wnnm?@qP R>å_NUF!aڹaLTAXe,T~E*A ;~> +v0]As1P6 S2^"e=M_ xP?%1ÓHN!0aB r]; ]1H`vW4DhK6?;e`)l}H_Wio }_tCzB|pʚS*5_z\[ƱMc#Yc둵[ǵ :z*!Im 1@R֗;f~EImp):m`7Dm=y\|F~=~lQ3mW)rx;C^W~X]P,3 DưKkMK`O%20TJ{HO7H_V36o}f(oޔlF+y.ƯI}ɿ}h?kUj!4oulE7e7*ox*n<qeykUIoЃ#b}4}l5hN[%^P4|;8e>)sMXW}{?|?Jx%?OnTSW!LWJoZ>-f/͎F+vE*} Fmk')miGΝ|dſF=]ҷCHqK<&uo<ǨlYEǕ~Ikmm_B&ױx+~KtS;U_T9'ڤy'u;d?D"//(`ޓ9*Q o~Ve4qGHɈz񒐶=]Ϟg7: Sse},n=vmzrvm=m>Ƃ-%\C>T6n,Xs_n=|9\όeh6h4mGYqҭ>ϙ>[Y -|36YͮC\&Ѯ{7x /j^>w‡X{fIk'KO_W8OD}nKOK?HU )ڬFgؤG8aÎ&}'}3\vr嬙 f dL?ZQ.3$q|I|[{B:F/nGSEǻzgfjPt^3m:lUC4^~<„~NG F+\hT2[۵G}xmnfJ pggqvg1pQW7|~Bla=礃sY=ChD[<a!:GU<ҐGwϤ;OUi'lڕy5wul98{fs#mP=BkqCc ,3#nY;!eɳ-4tE}&7B!-NqDhgr'$ND9`Hȟg95{_"8G1>~4lY u s?!O )ChD=F.9G}V:e:d~'W`k1Z]f'D659QzVdem7bF.<(ןȅ(з։w$| gDw[]7_'iof/8Xc|DY H9!Y%}=]Jo %2ODgT/dJ;E\J 0_N{6UWdR mT?c S;*whO !q|!I|!sUnPޗYUt7LsE oc\wꞎZOrh*?~„~:ܝ('uGw2;f-oT_\~lm%Ey`KL mLXe7|\Ѻt1mo}[]/f2Kl'YH)[(D~œkPq9?wM_\cU)oie=Vk7IyǏjaC#%4oc hn~3~3+ϔVq18ƍc(t#%)׃1r#+;;OoTxp ?{tj\`Ҧ6ПiVQ!$Nqƒ )c\]|NzxtM\zOn;d_)u„xk=],kw=5M&8L\EdPtd)JR.b[Da>YJheXCW2u味4AI+oOeV|w ӡ[5"B;1,wT6n0l,߁wO lQ*_Omv^ƆE0E |1O/dO5!9fbFZqb|jgW{33\sCJ1.ǽHO.B{?qڮ6cCwT6XE̽ mol[{g|ж+ؠ 3ۍ3lR9])̽j{Ge͸"rXJd'gO4-͕]1?ƿzwAg1|uGuKGqpRxo0+|&oW5M:u"KoQ{۵ҹfa6]&nϷf7$wTI.<^k-x|5M+œࣱ(vTQy̷ᾋ41i*m [}bnyo\F!)*s;s9d=FvZy3>UJczsӽѪ5'#L"o={ow˻-&/7iyA`>oG 0yi1MJ,/RyFɖ0l,;|[r9ηmNjshիz:tN` -o|wҬg<]?OgW;wø4uZ8C{䝤4!yca|#'e0޻SׅU4R!-](<+3Ѡ.|9I3)߹8_:VzvJ y~;h0?3(4Y"r.s߿C5Eg Z7`n lIvo>$*n pE) 26\̲\:0B[~$F_=I`"YsҮ5T3w |Wߕwl*Yw<4I„滹7ak =U\&k^-d}y?5F*+kyoL^7 w(DsͣvP|ëi45s jɚ05;f7u\z7!!q# @ -b1-t!!jC8" SDh TC`HIAfЊʌ6{szwObc{s1wHaH%|y~ 7]Id%Atꏋ4}k0U'334 j9DDKM_i^fۀ`'ʯclG{F,e*7YR!CUOsr8Q~=l|:_@ ؠo~/hwq_y~r`NZKHHԂ 'x1vb v$W!atwގ:: e0Wԡmʃ9ɝ c8uWgAN}_ O o&'ؾ*w˟%OPɗ?޼ޑ\(2N|a go\[$a/+Y)jzJM>r >: =~ b2-&Gx\=xkSÿgH1zg^< \y ~bBmO|Y7Gz'7,#P`_Ʒa1uT2]Iö=v| e=XjF5)·P8fWs5c5 +[ MmR_96RT աNԴwn[O^Y)c zW|(r{t%Ve}ܕrK1O~}$lXue}dVSJ%˔wx:L{F,AN.XE/`=]k>J z ?&)|_@* 993{yLc"g~/AM,`oNsxgz8;:y0Y 4>= ^ur&>FJ]k.b϶JiZx 4C_߸=&U~;{w/,OZ E" Sb<ƻK |/tTZ .o(9G] _b0X1bf0sq.Ro#Mʓ)3_n zfXA[f*Cd?ļugU_kiA׫=܂:cU(M;KOQ+3}߰̕Qfazl9ؼˍ$JB7C-xx뙡9~),/~7y=Ew9֐*lLJj3^(ّ)?b1oboR(ߧ3Z=o^̗;~ۃ=?w$XG宿;~ʃy;h_q\[G~Hvhמu\Ycz0n.^Ů+rc[Ϭv?O`1nKs_=%nڏue?|}hͫ~7w{#>7SKr|swZndtGgkZ;{mF~QƷ;WRH!B @ )R ARH!B @ B kMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:23  Ą. V(16^2/Oʄ1C {x UU1PTR2IEQs2,*QQPLJrZJڵ)f7kkM^q^/bd^|Sysgl:g94zk>]]gPWNGNS@zR\O8&WqPpx-̧[{]OP>u)Kj #:#HƉKٶٽ~ԉҫOϕN>󏋎|)薻Xq?=w۳^/Y;/?i ݫr.NGo ru +jKOUC/ ! q_W-r/YSB^_x-5y~¨Fq»z9u >.8?dy9J7ǛkxsI7W0vk|rTn1lakެpz޼L›&7oͤ&SjO7W#q s~(Sp]91[bMܡi0Z>.n/mhsz,7;)SEWۻQd qKDaL/A& ?}!mww3-*wSTh Q:_+C5pE0"רMz rK<_+whǼ_Nx~>Td)U[-Nbe Nʃ{Q=k߽[\liI 5r 6]ͪ@&巷l_]y0XRGKk&NsmٲYwmV/v MNMC 3$zv}ҍ`^  f*,~͛Nҿ=`5)O?KJ-|^yڢoQ`fpNN^"mbh~PG;I!swn}w`)XȦEyTנi?Pa~>R;]r͌Υ3t^ߛ7s5+ PwpU[}udPVu+aIߨ:ʘ ]C~o.z7}#uoT.Giуo_Pgv=llRgϒw$ OOnZxx"K}#T)yO~X1WUQn[z]moܐ >,]dS%+_Z}ur8XUk*;sК,EK$(o^iQ>"UA\Azx'޶i5OHf0fܟ {>O8װwks,z0eIۮ[ IʤY~ÚU]G EG+׮X7.7 ;@XR(g!YakqP2jtpϪ.C&ZHu7%JVX&Z.ݮ,b=U8uvMB̓5pi SD"_n{veuI //¾;{~T*=0xM7 j{S>?xg!qh:Wxʽʃ7+,m6]pzh R-˻n ئi#wZMgP&Vmi%+;~w}8=xmuEM"micϨͳ "Mѐ {at\Mj1[^u3A}&tw$zWFᯄ\z ^T”w++=2p3wND<܏ZqKaqIKG8jSV}D.ebM9~$`B/zl;Dmjv {ڶg3Da~pa<{Wڰ%:UYz`ҫtƘc{N&ƗQё+'!-ӑ{H':2ӑ cӑ5u5ltSX3yFvDq/GUh9Q"+ה16i}]iZPԣg[wgoH5OܣaqւPR}z)])^W᪬a4օ;/5So{ 4 j}yN#j`m8[tu~{7hȿ;NWCTШF}DqYWe-sѹ zPKy`1~Q+&lF #CvoiCS'}^+jNuQS\-Y8֋V.v_P.)h~IDS=ܭ},~XƏV=o T7[Z~~ e^řܣerHUĬY߱m5f~nSk6e~QM7W+^Y ,3,;Hat͌qZ+͊$vwө_.R0;Uپ8Z/kYkAAzZ0T:MCշ%7?k[KݗEك /t? :X01[W|* o/9hšGPwW׮[h{:l<Ee,gښG'eG? ?wp _)Η{wھOȵs%p>CmN1˶kc4k O]*=Mivc=0 ?Fuo+YzqXǵ%4A=J~ACc/\wZY+dȍY 4ctֿ&^٘5{{G( R|lӳԙ`{! kXOV`XiCOF*YX&ZDGuvG&st5b^+חzqFoQu7}`vG%J k$X]uv#Yź[8u0 O)buuw lz낙W\>yQy2aJ- 1V] U5xs4E/Un>Lhnzrl8]LxG''q}{p9G"&sv>܋+4U/|H4wt6{i[}}qpH_|Q(:bJg\W$juipͩtFhBn[{i`ӳd!=|S7urVa~Yq=kXHޕO# J}\9k{꾯C2 6kxާ`{߻T7Y*.8J@<%6B.?dxZ|=H N.{{i|W)Dؑ+hO@<{J;?"/; aEew<;拆]`=Po s|۶KNŹWw]sٔ;8q:4{5Y$mEIx}w#Ym+k+>yK{p[xR?Gj̜Lʌ6:V-\ks6Ym}pvB =%|݌Ռ{z0;ڊ]]SlQȧ'M'2,yژiA>MN砗Hrqo?wppy\8]ypW_V۔6RQn6;yrB']3/Ĝ>;oIۛ~f~qǵy_7Xu֌|)Yw~?_y뎪u^K3ْN7*=4j,nBT;{-~.̀eo=\/?vO!w{{TiJ)mo*{=;dC5nO.t;_#YźU8y0F wah/ ggN&jsY#/\{o 7M>a.bhpMRw2W3#Y}qǵ_n#u,b@8 zHR8+f\pK{eC8zʞ܇抾<#?d7ȑ}=Ty[ O~W)^orqVuuΡNe Z9mXNa us.TqJ뫟n&z~EEogl%<}U;n|; =s2}>|@Z;m^&IB:h|>9#H qoi- ^t{ 8awnfw-p'^pX" BvW> g c.~Ƚhw\- z{PWVNƗ_Wѹ?i~MeWry`6תcE7Ԣo.}5"#E:_g 2 jFw;V` >׶q|Yq;=H&_*wƩ]ٶv%J=xGلl){s.k޹+ ~afog0g~Σzlu,ƫZjk];.]m{*4/QhH>f_R۞!{H=$`hU7.KG,dS {)fa]m{7ly;z=3!~yiJ}xI;:hwc?ӈxJzmR6}E;ۻ)Gn*}9(o6!}mVE4ѩ=q]D;1{\\MH˔)cu3&YtR}u@p]C˔a ]N[JReMvuk0Gm$N kKL @ZsF?XCS?3{g6L羯z@:FI$hx͌+n;w~QY?0!W uZ! 1"IKF,ɵ~xF #R)C:L}~ި̺U{te!WOY)?uQeח'`O%m7◕Q+9wVj9kZ;;ʾUhMn;p-wI,bN8 "->'wa/ؼ؃78xoT^"Y]3A{C P&[s5(7wFі2;G5EOՕ\?o_[0:HI mm)Es4/s?w5ɭ1K&G?#SGc}Bm1]YA㰏kv}AF:a>}X`}r2a 4 V^O_}'lXnB.֝a7hfMٮebwf"W#jBiy+iB:!Mu5$B.wu\n7 ΀8SmqRzg6GlsT;(7zhŻgU_&QYF)idC$|Si 㻲'8q8p#>|򟵆3 gnPA#c zWnxTHWڋViis-)=-~MG}%')?ɍa-"@?cg[P'!p/=c KSJ(={fjn%_s\Z۷+ ?89fѓϊ^J~2R6b|OОYy/L+6a8]*33v@}yw^EfŝkCCi=B|{D-{L^so>՜KCoqՌ{$J9B.߶Ƿ>y5\ MFxVo6me^T;=txN;a}}\;8'g !ܝ7IE.Α?}r#˜e50e,m%zSv> }ƙTbWf|_m.sŞw\l>:vH}rQ0K07I8J\OUu)0~5Gkۅu^)*4nz0{C ׻ PZ"<,G O Rص\*mعL9ҸNxc}8B|0Vomg߼߼i_ҝ۫Ppm޴qҕ|<*Cх≧FW`O(䓛5}(P{7?.\?Vܘ9rD'=CkFߗ_e 1rzWrq?NEqx}BL\$q@Eq?'8'BxR('*ݑ>4shOO?O)>ۧ?;+ ?{Q,=k+CJɅsw.sKg&1| @ٳ/7g3Ka35@\Gs^Z̅a>]~ȕ{u{C%ݜnڅ5n[H?.r*qE^`FR}9s9f)v;[yxcknWZ@s~#q6W#&pk olK`?Og|m0oZ\ꝇEdAuyae1MK#2$UpOuIv9*SœJ kWzNz犙Sٿ+;2AM$qnE,:c R:"ʨIdxc1zC| o>;zM}˩KMKCk&~xsOʝ}Y8q8 y{9<޷z𦏚-r\e\_q狚jsxU(GuU9[գ{&՛k3Fj~Pγyܙ~NfB@q<@}QyRm~q^Λo'.*^FFvڈP6%ŷI顥7 ZrH9Qu&>!MWPxAWPve봦.ՠ!kn#D3ġ'O|[q+N"{!2Nj/e-Zsg&D܉f^\Fyϻ'p1ic'"LIK3gZn:8^b?EꎸnEq y}x~_UK(fnx {u}g|w,q\y 7Xt߇$gu2 PQ5"WfffUs5t_{!'Aߚ-'S tSu橕0nO}4φkQ^#TF߶c (Zg*.GY9`K6Ӄ3B}s2Ӆ3Rջg:zG"mq:P{Z-pYoa;ф*p&(&GiۦfITWoC}skº^%>5EOe;~^g5)=4]JnB]h[+ 6a_Iz~X)]Y>%PYiOI7oԴX6gr>^HDdeQN*[]KlNj]wև.@;-Wzg$ {8ۿ 8%=s,*7*[NdRb _S%W!7~dwvnߩ¼ǎ[}|Fx\2ݝCƳPg2=Vaϸ蜬sL2*zXMr9ˏrh9W+H1Bѳ Ӌ>6q]>&mvv0UT~ w_$gn:Wqmx|va9NƐ9mOs{sz78*؛T\Yi&1r:wSٛWC:Ȫ=Y"?Kg0 Ɠ/_{HtvJuc5[3tlH]-h[sc:NM#t%tl׏DZ!qC{J/M`mz2MjS"2N㰎E`":Rb_ekt _&xDijeX 6C=Fܳ؇cmf<~[%t,y&"N}ǵ1zt)wpfb}pF6agZ+4*=FX&l㍶;kǰ^~\:YműO%u:a7V]Ljܽs7J%[GqyYW>m֮,}qx6}.O]m%,YגmWH3u~:Mvu}]YzqXǵm—~}RXޫێia_-6Q6BY[RZo-nlՎ?g(*ڎY TX^޲ͦ`ѐwͪ]qQ/P -|lĽlؘ̞B{ (~(̅Ky=Me:M}I. o[Y~/J>;˝2 \%\pq6{#?SU=vv,o-~C|A[r?G?+$lQ2. )J{-5>Lyrϙ s[s^Eݛ FWM|a Fͦ@`\?r&ח|G7 ?9)<UkT.WO.L&Է;iz 8N;~ pW̆$vYW2ށW&+Q=m/Xы^|>^iV"k["rciE W I+b7 a]Zߟ%}Xϓ?k䰫CvJpku^+.n^=d;4|7v`mt>&…Ǡ6G\'yRt IƔaZr4&asQPOt;~D+h܁4mg4Zʒ'mZ;!rylq<';1\1WL|W ?g(+[DOCɋOyϿ(uW"=i;l^;Xs@5?zX|o%sm$\,k"d#QYS;^]yJux͕WmVU蛆Nte,G7UB8]6$K^go'1¯te!W񯋰?^٠-/k z ]c*ֵzND&>,lA7z+ܯȰZ0neRa#ԞG*5GxA|Eq9'S&j-m_v]toCUvX\Edׯy:Sz]7'g'zrk{WrycqA} 2N7f7*.gYz7ja/y$OD84Wqgӹc K(_*4ޫ߷.Cn.-jT]!~7 Ig!>nc7te!?h'C (8CC`m+$ʋ a=:V#J0Pɋ8;`֥Śe]YzqX ijvyqk ߻o?NX>rq$l$d7]]Nϒ]{Qϥ+_- 8{Zs?nm lcX;Fԇ}IDd>K+$N)ZsR/cU/皣ogW#B6Vi}Lqz/]=Y fxfkua sETW1Xs2Ny!g\b=cD|ilk`=g]"Hky.]EdEu9V> 7QhgiR}'}WpU~ LI >Rڥ6m'뭬eAC|z{\cFl{ajVd";]^ح}9Yz+3:FԳf)'˱ᬥ.yn*ښE~g6ϸy=YoI62m[=kTovZm~8Mݔt6JMV75~SlR6hYOY">E, @@ϊ%'6J3x^BOHlO{oG᛬8W_YhZD%i=voyй8F;:&M%>#ocǥ V~cTsS@N 𼅛^skZYiXٵzͶ_]Z/_ >,~L15`KmۮhMozAn[=gU\Uuoe}R랝=G{^&MaNfd֏9=ȭ$zbܞey8I}2SuAp2(m[][.ClN:Tum}Nϊw eҹʕJ5IM gsths!.Q'~~ >ȵJ;zVVܩWʜ) EU'EQ/tʀ>ܣ;ߛ@i, C{ ӍJZS[V]+zBV3M/@aNJ|Qs'[C}[o`E]LIU@Z3[5mf^N}跢GD&Wz jsx?̇v*JЧLmTPC[pRIu[x'{5O[J~RItP~E`]J͒O.ч{ð n1aFOE1_ݡnIu~*7r0g cybsܫڐ~q 9<=Sb];*|ȮiCG˻kł/T뉗(=Ua[iω;c^aӶ3֩6ɏ~\e7tM9OY!"n_w}o /4P2ٕu%g^'#tDcN5г<~O}8 [sTFw^N2z3?B^vGHRe8Wھ'SL #[XSDEd&rՐ;ةq)pߵL_J/. Yx ^j?&t oȏ(yty[a-<p;'W(=@n}X߿! X?)wGԬ"σ5z6ŵ*YAV4AnVV;C1rYӅ{'[O;6"^ o{XS#Yzr>J0,nvLf/7d!VԷFIƼr'yO,? e߫t厧Mao\MbpOa8~8r Y}q~\,Q]0ܡ߫?>qAwVSS~[;W <*O#lHtg)=4v 8W_?淃X?vOOԷeX<}Ěs#>|sg>OQ1˵y5O-T?PMtq6>Kˎ)Tb.Էa u[M.zj9Gu"Φw젼7 N{ﰾo]vUfh}9baKSL;Z'M?9>A>).+BUqfjv@F.6Q ?+fD 7Sby2~-2vgqǍjj:7d2E&nHʥ߸G%t r9׳Iv*CGovWh VKi3:/M-hvlcp6ۣδf9#5hf{$_l{i-jwWLsWE͵3+*> ۛŚlj.Qi&;?gIm#lB=X?k/V(sDqmNa@qfMvOd0)M=aUWr.(-7d!72h kƩߠr'荽{_bC+ߨ?4yO)fD|]ʮpUvgTٿoKCop)q*x|2cs)6۠rEpkDG3&f'}qD|&Ja;Mqr-{7g5%rgox)ew~=l~KK8 4oa!Xnw^!WނI% 0w+o|1ܵ^'?5wF}'71?M\-YF=ƾx '}Z-O䎮|3kj"{\-tC >yAs:Unum. Ox@S׺G5t䁴;WOO%rMk͊$rmC:bt'ғ kk:rSMᙬQ#뜁m<gz:GO"-m*!Jy//Ya[}=iZqtY}H^ջ7RcPzZqI3)|ߓt`s< =)뿢Fy 8[,}y?`Kġ?|@ydKgS[3Җ ޟOgn 2&8:abcxZً;a-n9Uj`z=zioFqsSYa>nt{tܛ2BىGl{7+T=$WނFܯ|\qҹPIľQgSh)ܠ OبLXN3rO['>߭!KVGXN~0lu~zAuo3iᦣ=cD>m3Ԉ3`df;^a_X+{BU![G*mT5t&JK NriKZ$\r~^"ru\?;@Z`2Jsů+X š\$[6ŵF{X i< ?,^7~.? dl{aZ@}|W_|,+ 8Ug渜/ iF" M՜?C(=1 o3-'Νz9;Ļ3]^~oA*wk6nϗ>]Otc%Jup gz~=? B.?ox ie?/]'gԎN}(\am"ʄJ~.OG P;$|qqoʑL]Or`q|'GF WVK֎>)vx`bC&zr)>HO,ʇܺ?)-d!2A<9DZ|%4x>yNۇ6+41˭un i߰>wՇAC˯Nt(=&[Uȭ#z˯k1ug_yǯuտֳ|ErՃiG=BG]{[y޵esGB&ɭq>>(-w#r`q|'y>X^>@ְkqt )(Y.WeO-iqmRzhOMqg_se@]Q# 1npjszy|Osx=wco諗hXzss.ߏQqk/Vrj@ OSN 7;Vl-\ 8#]*;|n߭71b'!=Cl Y ;@\ =WX|K|WWvma On4+l۝D"xM յo(1PZNZEzhf[/Yk҄m]En9&g[&K]?c&[˄,7o5]/7عNz{ w-ƫ'XVWuz` Uqc8HL܄zX~(z[֟EID=yEuQҷd*1^|+!#.m\Xiɏ~6] ~=N :$^Y1Wq35JʠV]EHФʭ{N[o]F}ԭuvҥ:mg]Ի.} 2^yY2[~ӇsuG׏HZZuW*ݗ<|½<Т8~o5jE\wwiꗏdke 5:TtLcnTz闸 *)o)0(wFuC>}2>3Bf܋.V`F{"us죻#X:~W0!{݃8t{ېkLuYNF cO(nPph^OYD ,rn{AWQ$+ pkַ\p% I_Tiuԩ՛5STGoe uE/r+XE# aF?u_BcA.__T~K7Z۳D!l_f*Ա}J]"ȭ#l_ܪ/Ĺm_Otg Xɦo67F6 f-ۄs;DXP s_ =DEum#w_Z vOP V w$k-BϾF#zhOra?!NІ,~C|V~@6 [YkMg)\tU5=95k#wJ;k$XK+~fxpY-út۟yXOr>L8og|;>_&{q:N*jj{R\g(΍*=tM5r}YC5ژƺQW  yB|,7o6'nJ^B>p^%7~]E2&_^4COhK>]Emozjhkep y9@%xaoR+3<}?bm̘jژvs/ŧ7__Kٗmvwv'bMVJe L;tߜ'6xR~7Gy''`~ook)znY^լy8b71Ͼt~2a}}QR]~#tˍ їʇO;[ך򑑰{R~\-n٫khBlL>:vjqBxZa1^LTz\K\q5UJ>Oދ2+fKN_\ιq{T>Xo']o/ 6jnK!]?}1iū^~܇+D¦? 0o㿰M(tK~2xva|O[K?6o}j|@@],wm~o|w]s%ﭫfM n+焞,d?uO6 v 2 VG_?'\l7~m?PﳶzKC7Cp쁭q]+9>(mܓ\>(W䣅rbt>>hQ\hV`h/;-hr0J3/лeF-vCK5n%.|19=YzqXd)jsE[Qݷaםת;4#rn{zLx&[mq1mϒrn?︶ _.33}Lƀg*wb)}C~C͐_ ;}uΒwy61yBxQxB!!p4;G~)(Gw33ED'#Zl.&V 3C /|̘#yȽlD>t.,g Wɥ>(+(\dϞtUn`K['_w(cBO߳vm\JsAG!>齫aOHDox~\<1r.voFۣϞL lSB蜎a\!~gGB=΂YצZb([+NI7}0zһ7;q36iW S1)_1m϶~6Z?*tǧ;_vCX7a;lKyg[_e}Xԟχ~)~OhO}r)~|ܾdCEqs:1s{YJ WT/e؜Kn+зs: (n8vUΟ[>x ǰ>/Ĕ̷?oC')t 3+>JyD}qy{^ g^gcVrNP_c#XQJ_0nY=Yx[%Qgqhxog`={yo9 Yf)>Mov(D(oudžC+=/emKjPR9ϊWRCi^< 82U8^En}"^yRrJW]W'5/l󹚾A*HtH)~ /POigjtZ>&ʮP,/H,S,B.'q2\'FxB3r3ffFNО5)'|Iy'ËiqQkœUkN;74lL[ȶ a4s_[ Iڔ&Yͅ|Ƴ)l{~OryY8Ea?&O̅]/~zMyR:;F۩X =͑`HH{A&U3/^(a'Z Dž;/w? k}?vUv_ܳw]3SҴo֪@7 jߧĝ-Z';[v.m`\ُ̮l wӯv+yЇ=gsaѯEe$ #bhđӹ?&wާ:5 'b z>H#;G9\\EJNw J-9Zkka X@ٝԻVC&|b 5* 'ea/k8ee]#se, K4b|7آQ!sA`41AEqgM#ǯؿyaTYb-gor& Гqh&֫ld(iV1\yV!AE ["㻎:uL#8 jsk34JyTqp~U|<õDg9 sF2g[l0Ӵ3(-!&Y[=հso D9Ū̶]u9u/V ]a6mhnGUxN.IB!jxD)Pe\ uf7ᬲuuw貈r)a>+&0Cu[ف1=A":&x\>yԸ(L\gȱuC$P_ߑ 9ĻmA)/ysWa^oҾ0+R1cǺ7УxSw=ZŜ?M7t'Ꞵ;>\.n8yʖd(H8k1U߉-xU'ΣrJlw=" WP( ܻ+ [k&F3k7{,O/m^gp+>u_< Ôd{GpljQycw7Ι2f{}\k ЯRl/眠O7ro#<>\c8㯏>#Ly&Ns(WB^=L| ?| }}ܱfO߇=a];E1H6!ٚa\IG=ss_?_={:ovںZ.Э1n ~M` m1o0g9bvB``ƹ;Lb-QM8v.sO.ЋXH]ڈTd9x(9\Rě: U4WꈡH)ߪpu$"%VR|㷍sI\fϢAQ2ߟ U߾vAD0jE_}D(Т<"HaOH@'iWߛObN`F{ЖTYYrÔM1r;mN&*H ΒW̌P}V(GxR>俏'ݏq|[{m=ǧh.."ho/{Fz&¿Lb Ӟ^<*bCd7[E"A>syȣ:bحhw21Fu ֱ(SEruP8lX–XgHgN@lБfWsk7+,;%9̻3&5y-&ؙ~oLq<T r=9) q i@Z)ڢj!w˿SgU z޳g0~ASt nJ7ie?3r*KӞeAul!߾.;3g?㦮Z*g;]ze젭T}̺|x |` u~+CVϗmVl&p>]yfx]^] Mg]8F+ދ Y A =Kw;* +8wL+K/uU*|W86R; Ty)<>o.rLНU#^viysBޔk|⯅yxțϛYys7qM$F+7ӆhGyfc4lK</T_;0<}+땗YA$ˇ*;ԇa_gnmKCXR4(1rq MN t Cn9y.o/>K#ͳss~]C^oPowwag76tk0M={7LVk~ۇm.^>rdC/qo2NizU5 ػ3v÷ Gɫk;lwٚ!d7t4NwT.S/UgJ{3;F!wA0nx un{ԿnΣrL=V|ns}S?V^3߻f^ޙ76+Bi^h\o4V%*O *wULx*iSD[2=Ͽ1oۛaېwJ<+Oyy7G=0QtZ/\WC:ˏwnVoJ/;4xv<[6Z@3zjTZɧ?ȥ.Qzӯݨh7֝+Wca i FwC~[$*U*|AF}hTw|^_u%u*8 ƞDO{ZYso̫vȫ'\J̺M)vJcwWAny-yZrlںkƋ}qChxa _R(1%^uzWf*Yp7SXx-s1n FJ'M;2ɥ%J<-MT |ƈBݓxEj7qr ޸M4F4CHH8YfFт>YW~s~ExOg(Ҩr`Dc%ɍ>g5~R,47Z"hSz`J5ixCrcv]ˍ׭|X!o@v<'Z}W:X<7(7wdx!1*wrPU^ !~Nm(I֨Zd?= iuX&~MO5~KkqIfƷ>?O"e-aO@OO8?mtH*ɏUy)1~l!zV{Dz*nMC { F uO>O?qz!zEtAHzi[qߟ7sCe}T1>`enVsk w' GiJ>*⦡Lw"] 2_λL[y`wykᚒWxx FcVX#'[6f}D.ݒ84M7ȭ;B֓/ۘ#Fg\Jg (ó+.Aw*G*g\~ ntMShv{5j7 .)Η{{]C;FڽZ*ڽE>\:wqݼp^]9yKȭR`M~ !}1um`OdCWzﲁᆼ)l`g0؄ ›f#l`;ic62eQО%zŽWB Z}>, O_hXl~ y\6]IZp&6d]7;tڮtl<}u_r?q6ߎR{ɳMyk#Ňz-SJFV5n`4 {ŽP*]Mn[]q& CyCqmrX6U.תyA6|냷5^SuvgVI!o.}YZxoF]IkX:t¡)ߑϟēw44}맳p+σTbQ;ydZa,$_s9P^oWQ| o\.`]ї( .*wޝcwna8\h=,٘JN:nJ8{ RGkKoll1/O1FNI7C$\\۠!욥/wЀ6N{Q:fUk R>0vN`,-@N`A1\l0w /~1^#2տY ob_b//zӾ&f0?bt<g5v/D8'&[L,>X>?*Tsf_ GZ\ӄkM'=MOFQW˂=ιO}(4'Yi=E^]!?=*h縁gZX )u%sz=)B(B 1+>$]areX^Yl+[r8m< xydS'-qm,IqK#mVDAX>AmjYK9\22wĭתTƿ\ Z/Wxg~Z5xgo_F@N;$䑿*|6e2-귲GU8Hq|f3*C>##mX, _ӽö!N9#LccwLe>/ 퐸* %6Ņ+]Z_LVHߙR\`;l FJꫲt|;1J@8q-.sCHZ[޸80@ ryNV.|u%@-o#nc)N\/Z]Qs)w$6vn[Nyluv5misϺ56vf=޺+FA[~sovJ|;NIZdXZ;Jz^?)STՓcNiqvʶV2>M遱eܔv|mL NH;ސE:u1R}/-lKrB;[ůk*?+M&> BF6iܢOoR{hvswԌ{L}xk}}槁o.y {O\{3ޓ6x?C>U^dL;R 93\]gPs! Go8 umlkJ|ܔc/:S߮|'{om1-O;Nm?j\FmmSXҘ޺փ\sOqv*.t-{fǛ1 {-؝l}n76ƇgD5(+8/!/e>h~k 1c<79erSۜ{Xf" xˀo,mz:}!j'-8čQ&m>鵞^c`wN,N}YmV Xqp˺apWt3gxd\YL$!{RJ/yD##_{j2Wa/jקܜWܷ\cЙzzţ ._4NhBT>7v}s?UL>%`W17;VjI;ll}ۇ1𴦿ʧ ?O= ѬRywHz]m% KLbkש GT!NZw|MJNRzlaDsZղ0y-8sߗlsq~^kkLM>?h@e7}|LJDǝN:}S|SD$غ{hqywXGG[{Xqo flo<ӹF^0Nݱ|p2=xs޴9H_!WOO#/bB3iA`TW+r1\_,/Eg coTXx/8ӹ3#-2*:<@o$ѭv>5fВy2?6|Jzv]2SS`7>u4Է6߁oS6V|ՙ>5Y"t?Jً ġ+'[8,X 6iVku'lnNiJˌ E^@ѕ`X^B9XpMz:9$ܢsٿas`\x;hVix_ =b3OBM{&/_91xҵ=g:ǁjUq:ǔ4.+=΁k:Gg{&ެؑjnӋ,Řܛ,AϟAzG6&]}a\ZzI24yZlo&1; 66 ?-ZhZf߲^ŔX:Y mTk;Yh&'hM9~ jZZ/@jhO!;=}E{ȝe:}=ˍ򣫽*wmv_ΈAeY}3ɀeJ,>MZm36-ѧP|4\*o||@.}~ܠ_Pa-W߮v7 :uSZ>B8zCc^Թw$Y1U?RXwhn{}HG* ⇱};NJ.Qyg|iɆ<^ c]P3:jIp:=n^lX/>l8tm y *z/fhw딿>Yƈe.Ɍe#>L?X\+_]$ВW0/l^0>.tǕ7o}}l>Y`z|kf A36qח/WZڇQ (v=Sʀf}CEk ~qF{+JAh9qJo0kn5^nz,g^N]0od !^M+q̽[kW+qrbhyx "% %Y J*{Nr)Ff4k. s5^M&$KjqF|Ge5O?دɍ]nJrjIwOnY[z?ZQ?XUݐ9v #7uF  OݏXeG!~\ +9ď2Xm_-|Vz%%n|`6Rxlѐe|zV-^,zW6ȥ.Q7Is).'(q4X 2YKҟz辟u*.k\׷๣`=E_sXMs'`ݥz繜q<lE4~*s%3M<W(/gD?cvCqeN8m /Fy=.uwSl׳_@Ӗ \yܦ2iڠޠ #dr'bw93F{Q{ⵙtqJSwiM?$7vаq2s'?z#vIx+ ʗ}Nc'Dejk{jk {ffsA?p{_wma[ǯDcdJf?:kִ {,dmԇ2@iDWlnvCesnwiyORr|G$z OϞ;.Ӕq>Ok)pKmκ diSE}[!`O[8gd~Tf<^! ⵩C";DctR\ZI:Z#|qa76N{s"և!pMjOG-Ϲ-ZިskF9J^~}RIǯxqK.(px}fg_8u9qwo gmogFKk{Nǵ|ɇ8xUO.\>.o8?%U=_;=^zfmnѼzY-$p/syڃ-\Oʴ/)o~| CԳdzDR:0۵I.G<7-ꔌ[a^C\o: 'ȅSNQ^ճ}︆c#VM ȗ1Z?O.wW)eoB<և+Og=+AK0X5i[i؛o\7ȸ5 rDv:mqr&=?6V CFYzYq {zV.Q>N[B#Ӟ7OC口=6[vMe?.7K\'Sj.Q?G5*^0Gtw&]}滛/Jgh^;4"XP?iĭ dѲ |qphyE^$ <$МߧwhKSybݖ\ZkMCkنlYh}‘5Oc䏣5 ;M{ :h=$zV~ /UkɌTtaD[a]J*}749Vk>?mo ] \$~8ےf/|Y f|PzpCo˲i {Iq6,|0nLk Aq|'ᵊ`3rw$v"0nOI.u6g0Eo4V5nszZ'w/R:8=P]5޳76v'sO(_K}'=>OK8(v: Uḃ X\O$&~[>=VsE' 6>gl|XȞ8>j|Ȳ{;c-4ye|X32>f^p]S3ޣho|O\- N(?M2 RZy0-%n>(v/RA'SA -`q|LR~X|66I_L_l;z?w.txE;)ޘi 6 `?M)}[p}q؎N9~%X@{$ܑsi<~'Ļv]_vqixBdy0뽭53 _O .P'yG`6. {zh0M^E??`q|'ZDwF*W"rDӓdC>(cGݧ]Ncp_a^|}J PaO_*`{\2ށ+M)~k>gW8i-ծFŃ >?Ei}1h<}< zzn y˰ڰOj|/ɡբˍD]ֱ(,*ӿp7!Rhw1>B|E~?/Mz?H A'~4TuvDǁ=~29 Õ@ 7<{vQ7YO5x ty"o<0tItF$YȱW?]gv̹J+3;8sD :΢I^?7 /J:Su]ʶ&!^$~|Xc$^8{TM^=0:|*˰ݼJ[]3a-,:ٳSZko?odz5&TD'fL@y:|v +?7?PX,?Pu/n`7c_H(OQY;sP2+hADe[yK’`ˎeLUCۗNW k0}Mx\J\9YӴڲHo+rPF1m*Դ$}dMqgͳ::ܔct+fq|n{IsW4='.YꑗLToO*QC &wsm_ P6Vw։$}A埠Wa(pY.2+6~Ly/=TF+K{ ַ̮evi͙!+=] 7M]mo~Z~%)+nPErWiC? |8cYsV{|_~R}s*=aL୮v16WNA< "I:;6\|Bo{SB9]Gp}:O %Eg64Ueq?sdr͓twmj++Z 2}e3a}A&^K$wL#6U};]%'ݵ>O{mlpE˞!H#kM=nu8Jv|XYC;L(M?! > l<O7~bgW$#UnzO}8O <LQJhK %#ߐ3)+`=2K~&!ȗhʶzysEիWq;OzȖJi9d!sȽqSy~J1'82aSW wD=MeWxz~g%5f5lѬPzQ5 ycKgk;l:lLvv;ݝS Ŏ hӎQ˗슾dɴeٸF_ 8Ư`L\Č{lhyz(l'{̅7d5qs#Nkk*7&OsHȘ/K*|S&}Mor3Z2~)ſY~Dd;r - 3v˷|,OK<ř5vȏ-?+,1q -Ӿ3CՉ i|\y zq}hZq:tW#~D6i=/$Aڬ{Y^ K8 ^zӺK-_í77w΍>!8O;Qz å-o_[l"_tVW7'=<1_>ȕO|[a}t'l+mh(?TD"F 7cL’t} ־ wehB<^z8ܹ?RuC0>D>=Gq3jަ06US=j/pnĬG[p"ڣv|n嫚NEy*u"af=߄7~9};=:~ڷY}-Odmװ<'N}k~v:Ic~CZ>; TYqu:RեUn\p'9hd}=~0pAilǗ=s,Op`~;_avnT][ۆޯ^)#*/b{}0غS5ѐ֕n*S%[Ȇ275tl6PKT{y|s㔩4$}p\;اU2,b:_{zԑ]~P~口50tT5%~C4N٥{xfU(]8eʽAK6 wi/[*7mxن}2ZKNkc$X޶Lަָih>^fwK땟]zqN$wm Jw6'g8vL(^cuv9y϶m}>?Zsl]RG;ERA'=>J[f2os_2b+[kq|q$6ɍHhPƋb;e7K߇v`[ku矻.wv5s`Nw4?/Y yx|W |Yxu5ӊD8:\'3_TevG6ָihow4>GCEhݕr~yK=/; Nݝ/|>M8>7ȿ!fn(IGn0;EHJɣ{sf]vG^s;|/?qtSrd:J7γ[d)y-xoң/q~;_UyO䏣=}|KZQ%xIGtj!w?/SgtT =[3 |{h-;E,?8oZDnPߣۯvKm<? A'&Ȗq}ZOlhMy̷mbY0)p8Uwডv?Wsר |Z&C&*^D5b¦ _*п3"gk\!wwǍN>*wܦ<[䏣5|E?h@k$IvTXy~ 1}&Ѿ/;濤bFX{۔h?~]q?%oJfS*9 D~ =ϝTgo?m~>M' F{/,6,bmE k3-W _-woA_.DڳVPyM4IXe>QLh<?k72 w^r|h??z&KE[ ?Jcx\\(qk@.`p*|PXd!\]цH|>X-jPˋ T2\ҋ%Ǩ8'b/Й*3{L:|)ݵm>7G> :;Jh-qH@wnuӝ JW/8 b7 ~a]B+OFby;mi۩m1Ub`T' ^| m*wDB]*/c@%vf}r}оLa?MU9/>!\mlV%_gqE{xVLf[꧸ijsk[}W tq|W 2 !8ZzwŻkĻ}kmړM HܫRlOD =Rqe1#gקЖ*ȣ&-#U)3B>( 萢|֯L]xz\]bUܥ;jp+yfS@^8OQ{NHϨ=o5]-Vb™E}h4Tpw(_;[bB=5 b;|x1珆zWޢXH5گ7q(L]:Zsr9YtK8.pfΧXȟK+up 󁿟ҽ_<ЉDJk|կW,ppիpv? V|Vڽ]y:ex\zx~&@xT>!6^[# 흎3{`ҝ0;lfvldYZ;[|0n&2_v59O8}o<9A&ti2$a*ғU.Q4Gۦ/n+C4=[-o{Jj~y^$?$|u5/ĕ,[tgn9J8jh}9F $ޠӵ*3Ze`K6 |~{iy%FS/6(~U=ӷ4ݼ3_67ࣀg^]5IIi>llCkqZ!_wh}ݮi}qȈ&6ЀxJuNyc|Я{hNk*nM3 VMCkK_wh\-ӺQ8ZYD>:_KkG,1_ϗ)Sd:27̏=4̮d{2ln/Gg2#%78XȘwJ@$cSbΟ__ o`ZoƒF7ڻ7؜Q-6+×{ԯJ@b]ĕ3Z!+E=mg׫w耼cH ^ Dն}$,'~,aXu ׉ncrIk'^37,~xīƓA.CU0\;.Vzu"ܐW8hb9p=:s̖A ~H7De.ѥ\f\['JsAGezaѺO/hU@뼽`7eZ\XpSC̎]siF{h}qjIȥ.QZls?9&(N7SvܠDÝF'9f]y Mk;nkMD}P}qt j㾢7z:}޸#Cg4(=paih>6/ _ӺQ8Z@.EkTwEkkb>|Ϟ]ӗV/˔hCYӏBz~#slo<4ΗG=Isi`.%.\zWֱ{._Q*A4K[ͥNOTC򓇞siAmEš>qp>;֚‡]ʗ };k߃JЙ ޥ#.1;Bw]r?w]|R[6'=akks0wJ|4T~hH{v¸ |3Ən\{^3LC2G}voJ<㈹eGj~S1;19L_ʌ7w{-驻{$VI]~t0/VdO륢jјq쯈bh=KX_淛Vo.}_>fgi 2ZZ -?m\֋ָ) g}g^_NkG |Zo?/kh]&b@k[CگwѺx:T+zatJIMCk+0rZ7?j+口u\nPD䲇2_l2f fTEw{hαٌCsO {CwcX$'mF*$d !c3Z}V="ӱ+b3*˟qO{䏣{\V?Le Lg#,sh ϕf+v~dW]}⦡0[/<;_>G>r)f3wxpMCKlڿhӊJOpt3OwH8&|XM$+ l4flc,ܗYS*dLU[}UeWe9Uyr5B*uc!+K&hM 6+~07 ^ {?*Y}.C:`3/ޏn>#Lb&}rmLjLgP~Y`&зt=NyFxL63rmMcc=k {?V{^G mz`{^6Akx%JkuNu.i>p'bU[w\ 8ޑZeM9npﱪ+; xO{"kaPp㶍U6EiEy0sHt&q1qyf)0*s95kDlvfq =  žIBW}>0LBŵjѢ6)lS&ֽ{q5#O@x&O]vYm%g*|C^3\Du~$rMiPDAPsGG"#u#_{ =YYUcN`P4νzczVMn'χħ?%"{L~µgte֝)A1Ƨ5r:c:M_YXg-w,v_;A^MѺWm u/Lt|3^Gw;!+S GOD Z$Txzv̉;3]_=(ɴaJ%}7>wP߮36fX|Uz3̇ז +ҥqC..U\l>Qk v*A/KKhnh ׌I`\7]?P__Xؿ@mOq?[*%So籿Nl#x.pFˌ;dh.ߛ9i?Km}ůY^uI'+b>f\CޘYŮ[2ۙu6kMcmZ-3>6`jR7č JHGEiߕ7IFpR/wsWJw{ kRڮtmޢ fc[ԟVhR]FT ]`oK;;5d-px1ysfG@@wAvgP;E[畸_(|ר*]2·fCܮ ( 4]M0_,uEt^=3R:}j30[3WXg -Ƴf|/^ϼP }7-F)YQ)-c2oCOna0MËc[ކ{(6A.#7uφqؿh{q΂ eǖe|Ð6 O_'Л%i=E{ j\߆aPjèp}JÚܔzǨ_ .}ޢXUâjXa4Q^ C/8Jy$rwށ^IgF F&͠UuJ1nṅ#;' @o,M@0ҙD>o.A:e4'|ˋVOPې CH,E-֘ |+DžՇ06]Jr-[0ME7{].pˢ@wX6)]N<CVo\I8&hi[z#-q|SEy>Q|}7;nLu%Io;3zo,OK<@m.g:*ywe: eNqЫ#4FnTXWsd:9b0k(:c&jVB{ 3&;^|; ~ .í+?2fY:,O+F"%GRjT6ufئMu+rw2`cSwk7h:ÇsIY(+hϴ[ *͐# Kj21㦕/U962y[LB❹(*o;.sz_*ao oyb~{y7^OF< NZpa@:>OpwiU Hkߐ~nK}%Rtt":It8{g4P9H;8]~}vs~zkQ׿BZFOi+Xf6Non}2[8_"@v4%{+p~L|lakeSk;ab'5RPas}F)ߦ6nрie?3r8?Yy10!}hJ>wҙqS׳/cvpǔ\O*w!}z/YO/F>U^>W^s7˝_靹%Zۊ Cܤ|Gu7 ܫBstV{/&ܓ?3#F֕z0mۦLFf^}tvW[ L!资x;&OIGy?HkyT8v;5Ey9oU1o-/7qϒ0]# -!/VE\&|x ck RUGՏc`.-G_e.y<@_?}ǧ yh @/'kEՇȏ2-'O-|CO:&W( xD~2Y#n~LnW#!ˉ3VI[dvSB9ak:#mԝr| 0! W!M+TʎHۈm(mRۖ*jq\\xqZ§HC$@f|lm{})D(вڿg6RU7hБ\@xϷ|C5~!!PEZqE_|+,/ V& _v¦ k w%/cZ +)xU|`8YwG>Ñ~0!^ =p-+˾x‘s|C[]ȏt\%-DpϷ ψ ,/­].P:CB#rԁv¦ D1~hzFcwܣ6Qg??TOā3 5Z~VɃcs;(2k#ϧIYА2,,64 nn r+2jn(r+1)+jn(r+2)+jjjn+s j=1j=ns+1 CD(U+U)DD     , ïðè ir+2  . Ç íàâåäåíèõ ñï³ââ³äíîøåíü âèäíî, ùî ñï³ëüíèé ðîçïîä³ë íàáîðó êîðåëÿö³é 1k-1 C,...,C ó âèïàäêó âèêîíàííÿ ã³ïîòåçè 1 H çàëåæèòü â³ä r ³ s , òîáòî â³ä ðîçòàøóâàííÿ îá ’ ºêòà â ïîë³ çîðó. Òîìó ã³ïîòåçà 1 H ðîçïàäàºòüñÿ íà nkn1  ã³ïîòåç rs H ó çàëåæíîñò³ â³ä ðîçòàøóâàííÿ îá ’ ºêòà. ßêùî ïîçíà÷èòè ÷åðåç 1k-1 rs 1k-1 C,...,C f(x,...,x) ù³ëüí³ñòü ñï³ëüíîãî ðîçïîä³ëó êîðå- ëÿö³é ïðè âèêîíàíí³ ã³ïîòåçè rs H , à éìîâ³ðíîñò³ ã³ïîòåç ïðèéíÿòè ð³âíèìè rs P , òî 1k-1 1k-1 k-2n-1 rs 21rs1k-11k-1 C,...C r=0s=0 k-2n k-2n1k-11k-1 C,...C P(H/H)=P...f(x,...,x)dx,...,dx P...f(x,...,x)dx,...,dx.          (13) Òîä³ ôóíêö³ÿ ñåðåäíüîãî ðèçèêó ìຠâèãëÿä: 12k 1k-1 1k-1 11k-1k-2 k k-31k-1 k-2n-1 rs 2rs1k-11k-1 C,...C r=0s=0 k-2n k-2n1k-1 C,...C R()=Zq (1...f()f(x)...f(xx x...(1))dx...dxd)+ +Zq (P...f(x,...,x)dx,...,dx P...f(x,...,x)                1k-1 dx,...,dx).  (14) ̳í³ì³çóþ÷è (14) â³äîìèìè ìåòîäàìè, çíàõîäèìî ìåæó  . Ó âèïàäêó, ÿêùî çàâàäè ðîçïîä³ëåí³ îäíàêîâî çà íîðìàëüíèì çàêîíîì òà ã³ïîòåçè îäíàêîâî éìîâ³ðí³, îñíîâí³ ñï³ââ³äíîøåííÿ ñïðîùóþòüñÿ é ìàþòü òàêèé âèãëÿä: k-1 k-1 2 i 1i i=1 i=1 i k-1 k-2n-1 2k-2n i r=0s=0 i=0 k-2n (V)ki 1 R()=Zq(1exp(VF)()+ B 2M(k1)! ZqkA (()), nk-n+1 B          (15) äå k M=k+1+(1)  ; ik-i i (ki)(1)A+A(1) V 2   ; n j j=1 A=D   ; n 2 j j=1 B=D   ; ,  – õàðàêòå- ðèñòèêè íîðìàëüíîãî ðîçïîä³ëó; (x)  – ôóíêö³ÿ Ëàïëàñà; rsrs B,A – ÿñêðàâîñò³, ÿê³ â³äïîâ³äàþòü ã³ïîòåç³ rs H , òà âàãîâ³ äîáàâêè êîðåëÿö³é íà äàí³é ä³ëÿíö³ â³äïîâ³äíî. Òàêèì ÷èíîì, ï³äðàõóíîê R()  , ó âèïàäêó íîðìàëüíîãî ðîçïîä³ëó çàâàä, çâî- äèòüñÿ íå äî ïåðåáóâàííÿ K-êðàòíîãî ³íòåãðàëà, à äî ôóíêö³¿ Ëàïëàñà. Òàêèì ÷èíîì, ðîçãëÿíóò³ ïðîöåäóðè äîçâîëÿþòü: ñêîðîòèòè ÷àñ êîðåëÿö³éíî¿ îáðîáêè é âèÿâëåííÿ îá ’ ºêò³â, ùî çíàõîäÿòüñÿ â ïîë³ çîðó; óíèêíóòè âèïàäê³â ÷àñòêîâîãî âèä³ëåííÿ îá ’ ºêò³â; âèä³ëÿòè äåê³ëüêà îá ’ ºêò³â, ùî çíàõîäÿòüñÿ â ïîë³ çîðó îäíî÷àñíî. Íàä³éøëà äî ðåäêîëå㳿 03.06.01 Ëÿøåíêî  , ÿ÷åñëàâ ³êòîðîâè÷, ñòàðøèé íàóêîâèé ñï³âðîá³òíèê êàôåäðè ³íôîð- ìàòèêè ÕÒÓÐÅ. Àäðåñà: Óêðà¿íà, 61166, Õàðê³â, ïð. Ëåí³íà, 14, òåë. 26-59-44. Ïóòÿò³í Åâãåí Ïåòðîâè÷ , ä-ð òåõí. íàóê, ïðîôåñîð, çàñëóæåíèé ä³ÿ÷ íàóêè òà òåõí³êè Óêðà¿íè, çàâ³äóâà÷ êàôåäðè ³íôîðìàòèêè ÕÒÓÐÅ. Àäðåñà: Óêðà¿íà, 61166, Õàðê³â, ïð. Ëåí³íà, 14, òåë. 40-94-19. 'xXkTUTP h1LQ(-_bԕUiTjZjҚ քFIpLp|Ys/[ߞ=gΙ F!\bv PDlk3t}93[>Mj#D|@hVmD\|c3~k5<Czg,E"{f[0Ze!xr{n4WtRqA@ >ew߾sxEǷw (od*h"SQ #[%p5gFV+7p-G\j)_'m[ԽrQ!/{^/OpL5kXYPq(e|n?D5^̧Bʞ +e%^K1˩cs 0I|5֘fgJ3Vٸ& K[?_S%5ˆYHpeqslc+G8UKk#_s Tp Va9 '0ܢZ""Ij8&`86qm#Sg-|EmR3/~k};9Rև8,d+UIfgkY$r< *1F+pgeK1b&R̝S'gTD_ E F^F CP>wX)mةMt:w,YCʟ/qOjᚈbd*,=p~a Vk[ٟdp"CۏEgw^ߺBkrZQr_swxT\8gHM[<Αg[ϫOuͺݮ֨Cc8A(B,k|e'{`Cc5جc 6ZXqf0O* ż=#[ɭw8SE$@Fs$Ǒ'7_h&"Տ ,}s RtdQȩ"Q(l/[Θ"gW(gɼNh^mHќG>\%hEIl?;xK59t*dcYuFhY|uȘ+Cxm5hF"u 2o cw%WmۍD{>kՖiKvpR.+_Ob+r *A"'ƼG8cs?{(lCu cAegoM|K.KI9+6qf~usûL +5NܪA}/d']@t<ܑMlDT:O=˿t#cɷɓɭ{1El"? r盌ߋN"YKނSݣYxKjwc-?}=Fzvmlf]Oy{ڴm!k.غ}0]صzAcdu޳<]ٹl9mx]#űm6Җŏ[o>ʏq>=zv,]g kC׵Z]-:׶۬k`[~>u~^:b~ 2ˀ/ 2ˀ/O.O>w 2ˀ/ 2r`{"Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:24  ~x Znxvx(1682n/x1 Vn{xݝ Vu;(h̀&^MD8FH +DנV3I}1Mz^&ƦiMLۚP%vADňg{y@{{?yߩṋpccBRg̹!}uG>=Zso0V|r#Os {f+åaA:dUtH"P?jP~ꋊxVZxЧ]9+8H[OGЩ.ɂ.A&'#.KD:\,7u,/jVh+]iHB0܎p̒/m0cΩ}ׅ0.S;:my{orSk^X7mܼ Sͨ-Jӗ^ЙGzss*@pΰHxxWi:e[7S6\yaOfԞi-S7> (Kw>SBfbaǵ? QW W>3E|81Q,mHO^i]4l>ҖF7ͽD\mpEFs‚p<2 Tbؼѷ`Eg9Qxz5l=il^$ 6ilWbLlb{Wil6KOqt[P|]b9b^W N^_.cvacckG`,@/Uay15_@HF;D%Z J0.BACDԵZwE]wQcN 'côp\x_>Qug '\}*Cƫid.Wkh45>-F͸p݌4MѼ&|Mu 2׭f4[Uy1-Ǫ"`Ofx|F3j-cGzgf.sFոi;,~#wߞ|-Lrۮ?58:vWyv1ϋj)KǸ׻k=Ω,? i>5;*viOwx4:;4J'jwqKqAܚqEC8SpOW[~qI<. \r֪+-mGpVkCw߰}4t?+rf!^Mbxk.X*x2,WzyxT3#aYxLxi0U^`Չ`43Ȼ,ibAޱר3vãJs[6/<>R:'+ O^ͼ=8YG1@ \3y}n4o,z*1f 8s+l=[*LBx{T==j.i;3tb郊a"aOFV-?UH}H'OgEg dV*2!K51Q*qtHs & /Ph0Y{6&D}t8O5ӷw +]ku ҏDd< ^&cI)M'ǑE];cW 40u_w~\|{Kٳ-ӄZ/֓&`[xe2[:"Z/Gw< x|RwSK)#Z"#?ÒǕ kЫ_/! k[-xMW‹aR}l MJ}_R龜16/+*Tn̵nwJRz791& ;yx=144u[~_i=#1K|/%{@JʧͲsK#cr˻k$^>xNgDx%y~})k+kNu.Emgc/<4d 40ӺS,"?qA,Vj*eo77«AyY^$_<>/|;xn8kyIg7F,D$m`s>gsm v< k4) SE;Mԏ@w\t &BzݾYJoEg=O#߫_fo|VߔW8\XsJS;sحJWK]e = v9Ҧm[x/3/8o5G o:N'Edh=G@l6nt!CZ<@۬4khSEW_ȓ15:{ǹWtƺ[Y"X/.g5L3Eb- +ٰm^ 6o؟mct3?[lk9e]i2~B7F#O>چy`2n5".k, Vg87Cي3垅4x 6v(b2x~cE`S.;0^6=eDo.Gw@)d.Wێ4Oϖ-б#:(oȾ19mY~Ǭc:'m ]?ix 4hRVc$ٕ5,>U &}nភ/ Nŋ?9omXsfҽyyG|d-MVui\|s_*/P-ʠ] tAysݛŷ[vv;-(@XMq 6%%&pv89$,0*:<;DN)}:4k*^\m^&g~?Ɓmx<(&-ǿSԓ)i@=i,vSNރ|RΐlUdyS>Nj]c\/JY9*]~&k8wdO8zJQ׶<.!4d& .ylƶǸ(TBn]:u oɧ0ms]mdWq㹌GCv꡾#*)^7eC6BݑTc'c'\@ !lJ1>Mw[emWgl΅kƦSÞsϛ\0WXف}E;]*>-,!|0"F,3{-[bOyTip\~eE+Px}CQeORcw oؠ 2u{\Snteɧg)3){E*OVOsmt&vVil&mGۄ*yֽv3f>*>>{hЋ}lI{ym]{ c4NJ"ҧqlSFk~(061-Q\XXAƊVe1ks-r؆رe-sWNR ڳB c}R[mSeںBjW<2'Ӝ9Θ#nt`g+y}M9/O_?E>_G>  v i>gMCOǮ@Bw} 45bE6rq`a-W&.GKw-~7w\n᡾0t`I}Dwwf qwGUWn|q| 5_NUa6I1Ȟ|W&'}S{F27Px#_169ǨK=r:^1څS6ז;_c&ah`CxVِ}zhGhӥcnV貏MMRl.J@pҜϝ #w6)_[˱~H2dibo|Cu6}0UP^36\_YRJ/}>C?%H?~H,gao;Y+yvYǠL߉4~c|8EfHwl;|=Fmo6<".Aq߈j;mL_/`.^3E=s&3#젹<ц;ǵs'Bvu/=Iw|Դ_U4t ;,oPk}l6Q7< T?yOtWz[Z}A>|Y;<ꛬU}f^8ϳ_{y2} 06djfǬx.CvaIeћ.CG6U1&fD;C*=+^xIrSw8U#l\ec!q$m8/6AݖgNȚF'e>y~:P}阒0"Oy&)X~~? j~_សxdG|3Ig o[5~!_U'K߾{%a9x~ѧ>glb0V^˺L&.þAɛ/.m&~?o.˿ Y%=< ^; w s桌~i|C'=ng#=ܮyyUgf]:ɼNsֶCU~cwhr՜X>ɸeF)=a}7wPXC!b#r`;V-cc;` eEW[ا3mA&@~vo脇Q9[,|HpC EҽJ}yT+fҽ9_raxS‡;H՗균's^ KxMC&=U,"ᭅύQ?<\o.DGVѩx_)<}ZaO[h}ԣ j{_`CHg}is}^XHE"ܽCWf 'i=3~A呭K*SpdS S_&Ky[زwuیk>^B l߾-\rn4FV㎁O14v~G^ڧ-\.>:ₘE4B۶-ܷ&?xuSW<f}}Kw(J jLC}ځGGV6OyA]-Я"^N ([l}?&I\ӵ p?,|燄Qr{O \TW=_0Yy-ou6*#⤑Df |vQ`a?l^?_?P_SŚ/1[%wX+{Xߜ[Qki`o[_Ѷs’I5C&+㘱屇o5h2V3n߹,&}]};Lػ?/hl3O*:-ݔcgM#c_o=_8it栳׭ru3?;M:ԇ~@7{. 5'8Vz"׷Te %o%H?rxnxW=xijs`=xgT?{vz}.%bGb- ZG`I{O ݂Z-þ>f:ΓFct|̑˾/kLLX7~:_W##Wbmoخбw:o*D+>{b[`ӳ7'z}tL~KgQn?<گv(xx;m0w}QNV0c= O+Hx v9d9i<'/$/tՒK[6c.kں𐯶̝9]d:8Α9ҮQ\}稻Ɋ;GS=s$?ܝ#vڬVD!D!DnTUo'r?U%q|F"#=Vegq5savI,${66lӮw :NpqL:x6W@$jޑH˿睪;>_tyü?威Um kݍϦ=9|{iQLm>ϕ sbC<gkz䄓jiCx{9wOC޵S{n~;Qa}]H$ ߵ~R8gTcaAawlWLgʷ;o>߭Liy]y{o9=]펻ܱbƎw1{rW]frV/Ϣou?t:T >#;]cj|/euU= >P}N5f3SrV}f~r ao y|>.é"95ן]z~PwBy$/ .E ë{pwxq'8i1(a_>wi!ƹ23}b}>="z[D$gu~w㯛+;:y}m{f MsC#s9MCg´ʏp&+@f_ig:'FaKn} m}^иSM:4z%3[;؏i}wkw~;Y}mi]4ZKt׍bY 뇐-eUc.s!wC"`7%{\!o2-rr''rp<唺 8B_ھWȥ}JW]g}sq#71Z+Lf썟>l%> z+O,PrsnTm"4J^=PEs<ѧxb_L[ו?_kwޖ,.>r_=)#'S{'x2kwJ1ڻ !gӆFW]Ik?Ik9a$6Lu<]zֿ\g ػ|!1M'sqh'&rcR}$oD~ ~|t|fvSUeX߮KyꮒL<=w(UHbg$qO;34\㑌Y}1`K1+TNEV ߤhctœ8>Tv rL%{}O`T /.:Nq';o,! '_x'Y>g=fݝ>>ϩ 'ׅ*p8c_gvZ;g=Cy${f<љ`z#L@~g]z:R7/t.vh?^^.j7ȷ3ɰ.>O >)/ ;VM)_XyjMd=_`[K5p쑎g=&~nw/&@8/?|[n}}ĚG5n{~Mܝ>Uk]2x?O_8{_y_k⦡ D͑y&k #|k:XayMǚc.AO,+~m9LN]vr ZJ=~7͓n/5y~5-X+4#*m ňo鿠K_:௭e ;6~rAme&)]d #014|b:\F.rE ?doȺ%/- VI+귒G/ 5ḧ2,L Txz.B=1_alEގc_c,߉Ey@]y obC3'xChǞn">@Ā4ЇǷDn-{&z: Vwx_)q/3_Qjc>yˬ<ˊ5y$ ֵIT~MwJr,m6lc{SDl/]mn|XF/cLytU :EO/A]N/4tG]WJ ؅A[8T"~P'+{}ӭQk/cbpv?jE=B 9}]x}ٵԵųse7kN`FWƳgvG}zo`&sJGllQNsr1܃u':OBf>ĽF#D~je},7rSr'$7G]Ͻ2F |p+;*:ւ ~Ov޺V8ԑG<(׻K~atBlkagн ?2PVR`i`g~if291V><e =ɯFn;g}^H#\͉YPզ1%sbĽsy\wY3cxR귳cZSXw kT3/3Цn4$fɐ*!抐[N7S3p)* Yeq'p&*&̒%h7<}S󝵿5_MyiK~O)glgpɓn{Ӯ/qpciWS'ͭO[͝qWW^w!U- 4;גǭM4t\glܕc.ܒR7>][_<~́sSۃtbK_BXhԵ#PWLav _L~Rl LW{gNxOyd2+cϟ^l%EG%6w']-6 ;=c-q3>ؼ&&͟?zӔ #˂99Ԍ͑D?f1kCF{8 _| 2f!p$ܧB;[H_߅':N$9$ׄil oboe:\ƏxZ7y_yK݌YH:У.:8$ɹ2'}3io߿ecxxs0>8ܜlj?+oN$\l \̾WΛm0DpH4b`o4<O-ۆxeiKgy<(upE2u׷m,N7OJ}Vdseo֢Iw6;(9BOOT918_d!f -н/\'<:-tF,RZem?m@mkGkRУMœ:[xykIj[g :Wm6>DfM#s/I9e~p}8Sǻ7JvdŅn,C["(x$|e R3>>sC $tuP bq!3 vm'6ddJZ>dkx{WAh[ 8huC?G2w䙷s%&o^uBL\NB~r(Pڍwe>ڕfn%N~(1R?W]upwˌ5m<-6ڏ Jۈ3eί7^Ŀz<Y]k5:clm!Oŏc| ]iv؏e箍yyx <&?ւ)Oemc${v[&|-Z[NT[Gn xd"? uR/uHT:n~}q.xI[}юa>) ne!^hu\/,ç>t,2p' > ঍yw첓s?ڼ|fHQ\vhgm3Jwg%f_"S:5OՐxueýZxcoN 5_M#67lO[i#hf7wޝ[n w/̕u]bK94fV'B{G}bvGe{y,iGgHuNcOmk v>?@|+蔡[)6Ld)N}%Y>P]ԋ #-QzhPQpwo p5*gNv2(v{WnòOp5qf-8/`_w+3kq6IzS')\!<:1'm7/ j}Sp4mh\{cEEKM@fTN{6v~P^gm}sl=-l=WFvwrvB0 o.Mhߚzq6^l θRjvұ:u~r΃ϳ2c_c;۱LMqƛfݡhYqf>q{v>VRی˸|ʹ&K]imcpf>gƑ4lݠ~#SM^?u"g)P7<ʑ][z3v﬿wyxW;w ^.snNߕrOdoe+'ҟKt<͗rxT_j@w~~"SwuC^ J2o]z?_:}kC=y .ƿO idhvL8sOʩ9;zl_Jm#M^k /{Jy;mvipuON6[Vr/m?}_W[&/VY({857NmG h7Ri{qІ1~莃3Gxe)׺[kX)2G=l﯉oɫ߯>Hqi }.QA]NxgyS'.~mn\?1m+j}n~iL6CeGWy}m-8}?%;w;oQ։u"O^WH_g9+i~hh{Oy_t&}]xm26c?@]_Silc\eG^>}CܯEfZڞWJa좽r>6bm̊a=W/6(g|iwm\/Zfc{| ~\p; |irh򜀘?Uaq2 f0""tT|rDU9b?lko pN хծû}ya-~Kl>ͻQ5ye/U< yVޛ\֘~BhClugtcOSuЉ]I~m]Pᘇ߸}pl^uBf??cʦoOw/!zRcqXZ~?Jx3wwO}]}a{T$;ƤD/^{9A߶Gmҧʵ $/8 O{/剁kߖ 1p]pk7m{wsd߀^bo}6ׯN9 qe\;{+\mB^ 4s,H;_l8 @fCFƜuuRp!~ϘA'ܬ9Aى3 .$evV3 |8G S%:}pG+E׳yMmʹ!EF{FwigxuC]򓗏ۣN&2v Ilz,Syt3w%(Lq:6YcmդE?)7eண)uW"~ʯj8GoKZ<4C|zN7Ƕ@#OZcvؾm,4Mme3O?;K:Yc[Y~'YN&ï4^?1c3RW ?\+c?+;(оkjSh5) N[n ^`-:Wخ6zPO$avSY6@`Oo=!|,p)'Cљ95Tcmo[E:0=6?7Sm|#j_hwށ2TΥGm[8W2Ę}y>Қ~ f /s1j\~c^11'Y5/XՋz&)o#0/;gjWmG9 X>ԯ:g̡ |5o޵m~a{-)m:qB xwT%@`.x2' 1x91ێ(|,/N-U۽A//`XfS/5Ю &kJGXԣ_;1: '];ǩ텎.ۨ5m(n*D>Otq@,lMs0sW'Կ6zA/qv*Ysͬ{a~?"7gS>ԝIN+}Z_ӿ>_RASv!Fc;18G3ȃG):ӿƁ1dYy,xāゎ5>vO%:|rF|o^7!. ykZ m{>(hp}}6}}Ю n{xоՔ=avw|pUJEv] 4kv4mԾ7mk|NZvyo|HXG~Қ^ڨ Y8| ^yt˻{ |MEpojfa_}'o7Lٍp^-w'"e>Q/f+I7~ܴ?ᗴ&;1kj),K'qmȫ 6@})㏶SgYʴ./Bx_ o|O3c npWwGq&a_n0P`P8 _}B;p,#=ܷr쨍\G6=2gw QƿAZ7ty]W9HAuFh oz\y~u}ӼfwIxBvZ$w0'hYvX[Aצ<| <|:O+zmeħ?6z]K!cvMprk_u}ƈoUv>Q,?kxsU1s[m7iȘ'̏#u>':wA EK<8ꃏؤ CYYbzS׍فY,+;mB_ߗqΗ&Ѥ}<>6mh|(/gJk_r``x=ɬVbGm-cWEt)3IE)2mNܡ[tyP'r-2K#t Љ 1&B悯, (4ߣ^}Jd>{GWV YV1mY-a;s ڊ2yLT_ϱ÷!pbC퍿~S}i[?u >Cvwm}e1H\` XޞU ߎ@5z7[/zWX{ho 7;C[;^(!pIo"| w_h7N"]j ۬oB;gMؔ:| F0y<ǏmO6zybzO{6+?@ƶ~y~5g>&>C\^^:+>0[߲[~;T~%G+w\~94ؙͱLc@۲^|5e;rCdvN#V{Nzi ƿ}3Yא4={z737-"' LʙY_l)3PVظ>oCC~~h5C%Y{2V[fmp؞tl}]y-2C:ͫvAcq }R[.jm򔡣:)q1kRFL_<8fh#q^,,66 Ñîãëàñíî òåîðèè ÑÀ ìåòîäà ðàñïîçíàâàíèÿ îáðàçîâ ÏÊ âîññòàíàâëèâàåòñÿ ïî ñèíòàêñè÷åñêîìó îáðàçöó (ÑÎ). ÑÎ ïðåäñòàâëÿåò ñîáîé áèíàðíóþ òàáëèöó, â êîòîðóþ ïî ñòîëáöàì âõîäÿò çíà÷åíèÿ èñòèííîñòè îòäåëüíûõ Ñ-Ï èç çàäàííîé ñèñòåìû, à ñòðîêè ñîîòâåòñòâóþò ôðàãìåíòàì îáðàçîâ â ïðîñòðàíñòâå ïðèçíàêîâ. Öåëåñîîáðàçíà çàäà÷à îöåíêè ãðàììàòè÷åñêîãî ÏÊ äî åãî âîññòàíîâëåíèÿ. Íà îñíîâàíèè èññëåäîâàíèÿ ÑÀ ìîäåëåé ðàñïîçíàâàíèÿ îáðàçîâ [2] ðàçðàáîòà- íû àëãîðèòìû è ìåòîäèêà àíàëèçà ÒÝÄ äëÿ îöåíèâàíèÿ ñòðóêòóðíîé ïîëíîòû èñõîäíûõ ïðèçíàêîâ, ôîðìèðîâàíèÿ ñèñòåìû âòîðè÷íûõ ïðèçíàêîâ, óñòàíîâëå- íèÿ èõ ïðè÷èííî-ñëåäñòâåííûõ ñâÿçåé íåïîñðåäñòâåííî â ñòðóêòóðå ãðàììàòè- ÷åñêîãî ÏÊ. Ìåòîäèêà ïðåäíàçíà÷åíà äëÿ ðåàëèçàöèè ñëåäóþùèõ ýòàïîâ: 1. Îöåíêà ñòðóêòóðíîé ïîëíîòû ÒÝÄ Tm,n,s ñ äîïóñòèìîé îøèáêîé êëàññèôè- êàöèè. 2. Îïðåäåëåíèå êðèòåðèàëüíûõ îöåíîê ïðèçíàêîâ ÒÝÄ. 3. Îïðåäåëåíèå áàçîâîãî íàáîðà òåðìèíàëüíûõ Ñ-Ï. 4. Ôîðìèðîâàíèå èíôîðìàòèâíîé ïîäñèñòåìû ïðèçíàêîâ. 5. Ïîñòðîåíèå ÏÊ.  ðàìêàõ ïîñòàâëåííîé çàäà÷è îáó÷åíèÿ ðàñïîçíàâàíèþ îáðàçîâ äëÿ àâòîìà- òèçèðîâàííîãî àíàëèçà îáðàáîòêè ýêñïåðèìåíòàëüíûõ äàííûõ ðàññìàòðèâàþòñÿ ÷åòûðå ïîäçàäà÷è: Ñ1-çàäà÷à: ïîëó÷åíèå èíôîðìàòèâíîãî íàáîðà ïðèçíàêîâ ñ çàäàííûì çíà÷åíè- åì îöåíêè ñòðóêòóðíîé ïîëíîòû (ÎÑÏ) ïðèçíàêîâ; Ñ2-çàäà÷à: âûäà÷à èíôîðìàòèâíîãî íàáîðà ïðèçíàêîâ ÒÝÄ è ðåçóëüòàòîâ èññëåäîâàíèÿ Ñ-Ï; Ñ3-çàäà÷à: îïðåäåëåíèå áàçîâûõ Ñ-Ï, âõîäÿùèõ âî âñå íàáîðû Ñ-Ï äëÿ ïîñòðîåíèÿ ãðàììàòè÷åñêîãî ÏÊ; Ñ4-çàäà÷à: ïîñòðîåíèå ðàöèîíàëüíîãî ãðàììàòè÷åñêîãî ÏÊ. Äëÿ âñåõ çàäà÷ îáùèìè ïóíêòàìè ÿâëÿþòñÿ ãåíåðàöèÿ òåðìèíàëüíûõ Ñ-Ï, ôîðìèðîâàíèå èçáûòî÷íîãî ñòðóêòóðíî-ïîëíîãî ÑÎ, îïðåäåëåíèå êðèòåðèàëü- íûõ îöåíîê ïðèçíàêîâ ÒÝÄ. Çàäà÷è ðàçëè÷àþòñÿ êîíå÷íûìè öåëÿìè îáðàáîòêè: àíàëèç èñõîäíûõ äàííûõ è/èëè âîññòàíîâëåíèå ðàöèîíàëüíîãî ãðàììàòè÷åñêîãî ÏÊ. Ïðåäîáðàáîòêà èñõîäíûõ äàííûõ ïðåäóñìàòðèâàåò âîçìîæíîñòü èñêëþ÷èòü èç ðàññìîòðåíèÿ îáúåêòîâ, ïðèçíàêîâ è êëàññîâ èñõîäíóþ ÒÝÄ. Ýòî ïîçâîëÿåò ïðîàíàëèçèðîâàòü åå ñ ðàçíûõ òî÷åê çðåíèÿ ðàññìàòðèâàåìîé ïðîáëåìû.  ðåçóëüòàòå ðåøåíèÿ Ñ1-çàäà÷è ïîñëå ââîäà è ïðåäîáðàáîòêè ÒÝÄ, ãåíåðèðî- âàíèÿ çàäàííîãî íàáîðà Ñ-Ï, ôîðìèðîâàíèÿ ÑÎ, âûïîëíåíèÿ ýòàïîâ 1-4 ñîçäàíèÿ ÑÀ ìîäåëåé âû÷èñëÿåòñÿ ÎÑÏ èíôîðìàòèâíîãî íàáîðà. Äåëàåòñÿ àíàëèç: ñîâïà- äàåò ëè ýòà ÎÑÏ ñ ÎÑÏ èñõîäíîé ñèñòåìû ïðèçíàêîâ.  ýòîì ñëó÷àå ñèñòåìà Ñ òåðìèíàëüíûõ Ñ-Ï ìîæåò íå áûòü ñòðóêòóðíî-ïîëíîé, ò.å. äîïóñêàåòñÿ îøèáêà êëàññèôèêàöèè.  ðåøåíèè Ñ2-çàäà÷è ïîñëå ââîäà èñõîäíûõ äàííûõ è ïðåäîáðàáîòêè èõ ïî æåëàíèþ ïîëüçîâàòåëÿ ôîðìèðóåòñÿ ÑÎ. Äëÿ êàæäîé ðåàëèçàöèè óêàçûâàþòñÿ íàèìåíîâàíèÿ (íîìåðà êëàññîâ). Äàëåå ñîãëàñíî ìåòîäèêå àíàëèçà ÑÎ ðåàëèçó- þòñÿ ýòàïû 1-3. Íà îñíîâàíèè ïîñòàâëåííîé çàäà÷è âûäàåòñÿ ñîîáùåíèå îá èíôîðìàòèâíîì íàáîðå ïðèçíàêîâ ÒÝÄ è ðåçóëüòàòû èññëåäîâàíèÿ ÑÎ. Ñ3-çàäà÷à ïðåäíàçíà÷åíà äëÿ âûáîðà èç ñòðóêòóðíî-ïîëíîé ñèñòåìû òîëüêî áàçîâîãî íàáîðà. Ïðîèçâîäèòñÿ ââîä è ïðåäîáðàáîòêà ÒÝÄ. Äàëåå âûïîëíÿåòñÿ ýòàï 3. Òàê êàê áàçîâûé íàáîð òåðìèíàëüíûõ Ñ-Ï âõîäèò âî âñå òåñòîâûå ãðóïïû ÑÎ, òî îí ÿâëÿåòñÿ áàçèñîì äëÿ íàõîæäåíèÿ èíôîðìàòèâíîé ïîäñèñòåìû ïðèçíà- êîâ. Ñ4-çàäà÷à ðåøàåòñÿ ñ ïîìîùüþ àëãîðèòìà ÒÅÑÒ. Èñõîäíàÿ ÒÝÄ ìîæåò áûòü ðåêîíñòðóèðîâàíà ïîëüçîâàòåëåì íà ïðåäìåò èñêëþ÷åíèÿ îáúåêòîâ, ïðèçíàêîâ èëè êëàññîâ. Äàëåå ñîãëàñíî íàáîðó òåðìèíàëüíûõ Ñ-Ï ôîðìèðóåòñÿ ÑÎ ñ óêàçàíèåì íàèìåíîâàíèé îáúåêòîâ â âèäå íîìåðîâ êëàññîâ. Îñíîâîé ìåòîäèêè ïî-ïðåæíåìó ÿâëÿåòñÿ âûïîëíåíèå ýòàïîâ 1-5. Ïî íàéäåííîìó èíôîðìàòèâíîìó C)xmlUN׽2D B6l,ũ G  ~eX0 QL(CH 0XKf4[nk|1<]s9syd)"jLJ/S" `qV;|fkC>GٝnE:"~94 .S[*KLɇf#ݎ3}{v6Xf8ԪЪ +лjiU!=O4 xę^ Ӷjh>}̖/:gF{>ϕpGsljbb;31l96qm#;LqgkD_C;,{-2Yj U).bz%OQЇ'|cwH2ϔAʐT&F$Ve3%%[V`/u&X!r$w_݉] Шd9w!%\V9kyy)~E\9Ś$NmB?Klp:jN 7 5 {2:0M#ٱ7KUhtNa>[P._aw`xP7i"tjٳٯ]_FvboU)O&5);3rىSSe26z 4 _ž1\Uqg?gpR^gr{`/粖%Yunz;.+=;@H $~juI8}aN_@3X vW;:e(XHnI*eWSI>堚{'fGPC?3.}wYˀ@`B>gg}#q%cE>*d0^A~fTϞ~o8}h?B/8EnXqsC䮇} {O p{%x6qӋ`4R LJ΍~< ^R$_NI}'wC6^eJ{\ycoÞ<؇a3}Aq 3X=|{'֮M?%atݳT)g'K`h9wqb›EZ/ XGǛ3JV2u:J1^Nouiӈk3/ě7&KK/Vdtbikiīie8^[:F/Q=lMi8Ydf$LL2NhF" hN6G׿0zVX:`uVAY۴:`uVX:ߘ\9Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:24  L (162/1`{Pox W]v@ԡ[)/;v*` !$a&@00yH$DK4jc"QF 1A2qF]/][uc }x9wk0kֆJ/p~G?0<0%?9 k owѕa.6 a\//;ϳYypJ0iتߕ*n>_TO,wVOU*Οw-?Tu Oti!/WSJJ3SfKZ%7yEY\V充*O=5\<FY "j v?GlW B}Do1 {.{y: }|'+կd?sco,eG.6.?}'\쫦+gv\ّλ;;_-_v+K+xge󺣻6W1e-W7L_+ce:\?0eU髋qW=W_S}sC3+eY,m-w]VA-/ YO/47ޜG6<|wE͕-6oюk<6ؔM`BrFNJmUl~xdžp|81fWprبtph8:<4RO({$*zިp(_zi[J@Pqo>9x$m,Ն{MyHst2]ٚ<эƋgr']=db:<9tb_aVy׼_#=t7ұ㈂>[8>`=vx_+"Ou6"g#Ye<4_yIz/gzsS>Y%d\ SGfC{~ne\NUQGm|lq4xOg^JU[Oũ7{bѮ+ڪ:+V:V<4ƚdEd8-r֋1)GGx:0+{+E/Vl%*W8"mj90;*`}6S_4e㜜g3G}ϑI{BK,9]]ϞSK"EWYGX+zl#|·kJ\o(ޡJ])}s>^rUkU`pPݱo{_~F[>{_+ڵ%+ĬV1J"̈k;{v*ʭ!_.NTůb't2=F'`->{awVig%*ؒ+.ٕ"CWJ^Ƌg)ݞ;cͬ=gq%hוp`:sa|ct3qkgbƛFqA͈*bևo0&Mz$N[ŋmH]2B_>zt#~hvS+ػw.ݏT^}&=hHQkS;Ƕ="D+>GQr{7a=})~qw1&] VxR.WWi2{_t;qmo|n*n]SUxYϕ!`ql|Ƈ9d=?Tgܳ;=Ơ&33q84+-JLš?sx<=@QV__fSJ]xROSFמ='.ryUro̻͌0 ދvygF8tjWZ%0iw%&Jkvu:Ѝg;Lsֻއ|r?nC 6|qgarQFc?gvnj>LdأGvV nҏ#mHړ ߗͱ%ؿh?UeϾzϹ޺o849Fuukt{əmR;:9 <u+7{%+M:q|>1?X1og]!3Й)MZiV]ez zܢm}}tc'A>uZqϕis+_zٸ2,cz#][F/q3{9~:/(Yl[mf Mߥ ŇysN)3[*c8>G'701N}+E7~#er}7coXoz^XŻuȈgVصQi^?.+wzK㮒zftm@F}EwUЈ|J<)Y xf%˃G/@=؋iKdB#Hxhr-:0~|?:)uV<}I^TUdhkn;['ke tUFAzNV\QQrEiW>z__я"C'Gz+[vê6'})K'i59ok۸V){^wbm>]YxC7h w[fKf `ŢH@[lyϑ~3g>,NJrB&?ԑ2 -C3﫴s[^ ^_(j,{~ևۉ-wMgp[? Fv۸Ceխ[ύS >~|3mHQN1ʦJmJ[62Yᣇg.MnZk1Qˣn"m>h{v})<}cl?\OPGm?p;/Ov{76/s~I"rs]ԁ9M:@^9vÃ1]3sOwUѮ-U}c5x=o'ڷ8>>7R+RMZdF9Xf#WOk:< ?m{rzR:]VZ3[v*` dz.;[gsYm^e\=]S\?\1bW5}7|#y|'B {IXs0;SOh3rN<}qUD m\<\%E{q^_Z^D碶^S~;WNJJNi#ܩ;k{[r]\ޤۗ~hEv߹bM_{3>?#8:'ԉؠё-c?E79Ns%坕Ao^x|^+z?/Tݒ8y;+mo=;Un2ҭxvVڻƱ k7B|a_='^w>g7(>W7ekȒGvc=qAN|xf'b_2_Z%rJMGsڙ6&#i˾JEs߱{qo'iw߻8\S؞/kﷷ"]([F<|'{P' '"~0!MRvт'؎>yN=z9cl=Cn5`nh/,Ueo;7ۇhڿTz;־TW]y>__{6b!{N󌓇K>Ó*&'w<@?:`l+eh}^,_;Ц* ;m-K; ?/h[a/Zkߙ[so4|ނ rI]fM7Uj6~k&/՗;oϸ^kKvo~hk]Q mG7fųiONNSF{ﯤϹC=NY ~ WPԞ2}|IoWK<_Y׿[mOVa١z4enk/nqVx{}YY<-it'l]yF{iVl|Eg|ʧm%w7z\Coؿ)] Wq횳ؽxpͫ kfIlkCi'vYNt}~X>]%թm{MǬ3A~\"Nb-1ݟ`slww6ȱ-嬉}hZSG_$2` kc)U1dvs𥖷nNAV6?|>f?ҷJɳ\ 9d;+|w-տ+}wc^9xqg<Qڔ{ҧuSԭp{z!~ڛ@?2oq3Ƨm_&l=?⇧3wU֊m>h?YUxYo|>y}. Ys_xNxhw'9<1;2Yr>?41^u謁e|ڞ9_YzيO9:iOmzb⣯?TsWo[_m/{i6XDٹH ,݌Ru {|mK:3؋R=Y}`.>9mնLa&]ZXK0ÃWa!\i,fe+m[gɧ~E*kvUigY25#{qgJڝ}EhrgZ4,fRgS9Vu͚}^3.*3z;.{/߿En+|ŏ_ĕtl=qrlyRb39>|~+ԧ,U76م0 O\k˙sM[!f]۸oXV󊕦GI-ݺCw+ _HM?'?ғr|>y)=wtc *VbO{`ofeu:#wll{Qxsltѯ-ڪ˶['YOB+O~[ Ʒ2ÿ́leQ]es(<ʗ#g~S`k,%6RW|ԉ[t&6cON.:iyrb'2b9|zڞⱅ;Ï/GveɮAȳ7{jM3Q[|MZ s7R˸nfoQ+~L;>  /,Ȑ.{S=~ǽ^? r竫^+EWQrr~K% ;wk͚K5١˻ETgӋwm߂wR?xlzB3|V{K9^rX^7u,591E;ךl:ofܭ{7ۻ{2nK9eLN'z}%'&~$/k`[izYZup/N{UѮ)Uq{gLfig:(m%]#T\ Ig+}gU3f~ e6O*7w<aR|Mox=-6ܳ$n=9^MhCco0ϖ`E{aɮ-Uct]뻆KvKĀxZ28o:fޛ='M1̙?l/qLnY ^l2Dz'Swʹcg`oVnUr#NT"Jn]URIe,m?Z{}K\$UMN6)k3kdщ YCV'MtUL{^⽸dW9J Wyq+~Nv׏Sf6Ë s/iɵ/2'w?po g<w1دdH9zMxY%EBrx%sR fvC^[۝AGʉK#'QΤyo.t2r:~,%Z$es.ya3"9l*v&}h?TUmDlxyRoYIi +]9?:YNPB{i}~zxcޝ{7xJIYVxN%`3)SNx|=y _kSK}E{AY;;V<<nA[g#M_J9!+Ďg ^Jvj^?/ڞߵ-s ~s}ut_z?O)}6IF%'zٿF)-}lї'iS;='׷[ld])X׶UYϻs.s׏<F,b,,67 íàáîðó ïîäñèñòåìû ïðèçíàêîâ ñòðîèòñÿ ãðàììàòè÷åñêîå ÏÊ. Âûäàåòñÿ ñîîáùå- íèå îá îøèáêàõ êëàññèôèêàöèè è èíôîðìàöèÿ î Ñ-Ï, íàõîäÿùèõñÿ â âåðøèíàõ ÁÄÐ. Ïðîâåäåííûå èññëåäîâàíèÿ àëãîðèòìîâ îáðàáîòêè ÒÝÄ ïîêàçàëè, ÷òî êà÷åñòâî ðàñïîçíàâàíèÿ íîâûõ îáúåêòîâ íå íèæå çàäàííîãî íàïåðåä çíà÷åíèÿ å è çàâèñèò îò ìèíèìàëüíîãî çíà÷åíèÿ Ñ-Ï â íåèçáûòî÷íîé ñòðóêòóðíî-ïîëíîé ñèñòåìå è ÷èñëà ñòðóêòóðíî-ïîëíûõ ñèñòåì ïðè ôèêñèðîâàííûõ çíà÷åíèÿõ äëèíû îáó÷àþ- ùåé âûáîðêè è íàäåæíîñòè ðàñïîçíàâàíèÿ íîâûõ îáúåêòîâ. Òàêèå âûâîäû èìåþò ñìûñë, òàê êàê ïðåäâàðèòåëüíàÿ îáðàáîòêà ÒÝÄ ïðåä- íàçíà÷åíà âûÿâèòü èíôîðìàòèâíîñòü êàæäîãî èìåþùåãîñÿ Ñ-Ï äî âîññòàíîâëå- íèÿ ãðàììàòè÷åñêîãî ÏÊ, ò.å. îïðåäåëèòü ÎÑÏ è îöåíèòü êðèòåðèé, äåëàþùèé åå ïîïðàâêó íà ñòðóêòóðó ôðàãìåíòà ÑÎ, äëÿ êàæäîãî áèíàðíîãî ïðèçíàêà ÑÎ. Èòàê, ÑÀ ìîäåëü ðàñïîçíàâàíèÿ îáðàçîâ ïðåäñòàâëÿåò ñîáîé ýôôåêòèâíîå ñðåäñòâî äëÿ îïèñàíèÿ ñòðóêòóðû ñëîæíûõ îáúåêòîâ â ïðîñòðàíñòâå ðàçíîòèï- íûõ ïðèçíàêîâ è ïîëó÷åíèÿ ÏÊ, íàèáîëåå ïîëíî óäîâëåòâîðÿþùèõ òðåáîâàíèÿì, ïðåäúÿâëÿåìûì ê ñèñòåìàì ðàñïîçíàâàíèÿ îáðàçîâ. Ïðè ýòîì ðåøàþùèå ïðàâè- ëà ìîæíî ñîõðàíÿòü â íåêîòîðîé áàçå äëÿ ïðîâåäåíèÿ òåîðåòè÷åñêèõ ýêñïåðè- ìåíòîâ è ïðàêòè÷åñêîãî ïðèìåíåíèÿ ïðè ðåøåíèè ðåàëüíûõ çàäà÷, ò.å. ìîäåëèðó- åòñÿ ñïåöèàëèçèðóåìîå ðàñïîçíàþùåå óñòðîéñòâî. Ïðè ôóíêöèîíèðîâàíèè ñëîæíûõ îáúåêòîâ âîçíèêàþò ñèòóàöèè, â òîì ÷èñëå è íåøòàòíûå, äëÿ ýôôåêòèâíîé îáðàáîòêè êîòîðûõ íåîáõîäèìî èñïîëüçîâàòü îïûò ýêñïëóàòàöèè îáúåêòà, à òàêæå èíòóèòèâíûå è íå÷åòêèå çíàíèÿ ñïåöèàëèñòîâ.  ýòèõ óñëîâèÿõ äëÿ ïðèíÿòèÿ ðåøåíèé öåëåñîîáðàçíî çàäåéñòâîâàòü èíòåëëåêòó- àëüíóþ êîìïîíåíòó ñèñòåìû óïðàâëåíèÿ â ñîñòàâå áàçû çíàíèé, áàç äàííûõ õàðàêòåðèñòèê îáúåêòà è ïîäñèñòåìû âûâîäà íà çíàíèÿõ. Ïîñêîëüêó ïðîöåññû ñîâðåìåííîãî ïðîèçâîäñòâà õàðàêòåðèçóþòñÿ âûñîêîé äèíàìèêîé, èíòåëëåêòó- àëüíûå ìåòîäû ìîãóò áûòü ðåàëèçîâàíû â ôîðìå äèíàìè÷åñêîé ýêñïåðòíîé ñèñòåìû (ÄÝÑ) [3]. Íàèáîëåå öåëåñîîáðàçíûì ÿâëÿåòñÿ èñïîëüçîâàíèå ÄÝÑ íà îñíîâå åå îáúåäè- íåíèÿ ñ îïèñàííûìè âûøå òðàäèöèîííûìè ìåòîäàìè îáðàáîòêè ïðîèçâîäñòâåí- íûõ ñèòóàöèé â ðàìêàõ èíòåëëåêòóàëüíîé èíòåãðèðîâàííîé ñèñòåìû ðàñïîçíà- âàíèÿ ïðîèçâîäñòâåííûõ ñèòóàöèé (ÈÈÑ ÐÏÑ). Ñîçäàíèå òàêîé ñèñòåìû íà ïðàêòèêå ïîðîæäàåò ðÿä òåõíè÷åñêèõ ïðîáëåì, ðåøåíèå êîòîðûõ áûëî ïîëó÷åíî â ðàáîòàõ [4, 5]. Íà ðèñóíêå ïðåäñòàâëåíà åå ôóíêöèîíàëüíàÿ ñõåìà.  íàñòîÿùåå âðåìÿ ðåàëèçîâàí òðàäèöèîííûé êîíòóð óïðàâëåíèÿ â âèäå èíòåðàêòèâíîãî ïðîãðàììíîãî êîìïëåêñà (ÈÏÊ) ÊÎÄ-Ò. ÈÏÊ ïðåäíàçíà÷åí äëÿ àâòîìàòèçèðîâàííîãî àíàëèçà è îáðàáîòêè äàííûõ â óïðàâëåíèè, ïëàíèðîâàíèè è äèàãíîñòèðîâàíèè òåõíè÷åñêèõ, ìåäèöèíñêèõ è ýêîíîìè÷åñêèõ îáúåêòîâ, îïèñûâàåìûõ íàáîðàìè ïðèçíàêîâ (õàðàêòåðèñòèê), èçìåðåííûõ â ðàçíîòèïíûõ (êîëè÷åñòâåííûõ è êà÷åñòâåííûõ) øêàëàõ. Èñõîäíîé èíôîðìàöèåé ÈÏÊ àâòîìàòèçàöèè àíàëèçà è îáðàáîòêè ýêñïåðè- ìåíòàëüíûõ äàííûõ äëÿ ðàñïîçíàâàíèÿ ïðîèçâîäñòâåííûõ ñèòóàöèé ÿâëÿåòñÿ ÒÝÄ â ôîðìå ìàòðèöû “ îáúåêòû – ïðèçíàêè ” , êîòîðûå ñîñòàâëÿþò ðåàëèçàöèè ñ íàèìåíîâàíèÿìè êëàññîâ. Âûõîäíóþ èíôîðìàöèþ ÈÏÊ ñîñòàâëÿþò ñâåäåíèÿ îá èíôîðìàòèâíîñòè ïðè- çíàêîâ ÒÝÄ, èõ ðàçäåëÿþùåé ñïîñîáíîñòè è ïðàâèëî êëàññèôèêàöèè â âèäå ñàìîàíàëèçèðóþùåé äðåâîâèäíîé ðåøàþùåé ñòðóêòóðû. Âíóòðåííèå âåðøèíû ðåøàþùåãî äåðåâà îòâå÷àþò òåðìèíàëüíûì áèíàðíûì Ñ-Ï, îïèñûâàþùèì ëî- êàëüíûå çàêîíîìåðíîñòè ñòðóêòóðíîãî îáðàçà â èññëåäóåìîé ïðåäìåòíîé îáëàñ- òè, à âíåøíèå âåðøèíû (ëèñòüÿ) ñîîòâåòñòâóþò çàäàííûì êàòåãîðèÿì (êëàññàì) ïðèíèìàåìûõ ðåøåíèé.  êà÷åñòâå èíñòðóìåíòàëüíîãî ñðåäñòâà äëÿ ðàçðàáîòêè ÈÏÊ âûáðàíû ñèñòå- ìà Visual C++ è àëãîðèòìè÷åñêèé ÿçûê FORTRAN90. Àðõèòåêòóðà ÈÏÊ àâòîìàòèçàöèè àíàëèçà è îáðàáîòêè ýêñïåðèìåíòàëüíûõ äàííûõ äëÿ ðàñïîçíàâàíèÿ ïðîèçâîäñòâåííûõ ñèòóàöèé îòâå÷àåò òðåáîâàíèÿì: ,xhe?6wwmۖ?4%RPW 4~d9PԤB-76!Ta&jiO۸n$s||>|۱$3QD|"UF<&: >"x83˯N.2Hͳ 3a`.W|jk_Lqz*j(ۮkMhۙW|o3~uDJqESo&ujm-WnjrޑIb99ӒJ;>MYӑrRrʵk7cE\OXk}9}7t:ɖ$M/gP8_ߏKH쀧,&Srø9/|_}&]2O*, 'h2dd^0 Ȑ/-crt%m㳈ȷ* ϠԪu .e|PK8F`Wfb,a#At챌} 3X˩2<oop Z98+A|MⓇ hre3|ɫp!9w?$C8G[཰.2C:~}`BqfQ[3 fa_T\x ty+ܸWdw)w=GhXF/DdL7g8OׁU aԩ6vP<%vb{bk/^W}hȵ M@}\sFx\K BR~n |B4гD3ɧ/&<E6SAhOfY <ǁῘp 0f)rN[;/1Wfl}k GsJֳ[<Bp& ;@W_]~7\2 !F|,KD_xa6x(prPߺjj=ugkaz4я+0 kM2&|7R vή~ (JI}#SwV Xc:p_H%=^{[;1V;qXCqz8ùPS w^Vѓxr4؍S;7-]hB hZ`g*>8a&+\3UL 1{``T`?h@c/}wcҎE9wjx7 {@;X@.=0=yM_-].e8iX[Ě5n̩3ljƫ:C}b̜JDl=s&>G+ouDVs$ň[x1c#z﫮8uN+qzi'xōo~g~'ͳ*` XVU*` X*.*` XVU*` b`IMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:24  j? !Z?b?(16:`2p`/p?1$Z{dx՜ U;20Ƞ 0`$(,a^lIIWfT@5m~%^QUۺnRmmEV#b+*.= =\s>9: !*Մp]U(Šs{KUasTLjۥߦn//95erp0|$?\V5V, ẚ`(cP=Q )&׮WZ+Ȯogk0/Ec}ԒCY0_P*FPpht_^)+n%`-Vՙ ɼ1^G-?znXlkˇ.:cVPP[Nvb:>˦ ,W}Du9, +0a~Y;Ɲ]_do,Y+S{I[RGזMS9M-gu$jQ0瑶QJPI:9}v s9\2tYhR mIyMcZ266]zyR|}V.I4jЋt?\φvh5__kgWJU,<C^#s$|%'/$SE}‡ǔ. H*榛7ħ(o~bbPٛo6Dľ-ܢH}s&eoo*W/͕2 Bhݾ & 盛D#~6v?3?:sjo]j{ [ D},KLDﱰCPTNQ /I$W3hP9Dt ;Nz)QPoy}xnz,^$ gUzt:VDžko޿*z)-=hi)i=/mfۄyRv c{arhѿT)z /xu# ^Ȣ+h3hPk뮩*:{*npy[/i+<.T{hmʫҙ}\g};:dttOѓt<uS޶8*zC'ڕzy0 `/>~np%'O/[DC/=K2ߣ$=E+&Sѷ[@.#I\> lxn&gNS_!G҈a0\'0|3-km\,6}dl;EgO&L̵Q4aEN-icʬ?q\|xC< 9;;;I^f. >>?ע -^ˌı]| _|.!|on>3;4~:G$ %^ڜeoW?".=)r|R|pt+OKSKgG/Y耵tKGuh}Y>M2ƇN_z6y 6s?<.%q*{+opsşg_@=w[=>*;:a]ol>'W=Ӣ?Nٓ3?CϩE<̚]i[RZ.[lats&`#dQ[WQSytM㹿x>i>JAmkˣbҽ_PJs셃.|A|BLlev-8ufm݊H=s3 -E"L KK4שdϩ۰[1/z#X߸҇R9ox|V^Ա^zx$x]Ml  Slx#Ց/aAgN!:&ms;~Sgp<%狱߄X5DG੣#4ՠ["cޫE|I?#^*]?@uªY{]Vm SnsB]̙7TՇO j>,Η?aOоn ذSKHx^n㰰}_Ϋ>N'Dys^)>shr ێg6zT.?,1ob8_ϩۥEz.A=ԣJ{b ȯ%(e%V{F/qx#7/8ZRգ|@3zH _,`^ I?׸>MTu,VH|c3SE~SH:@s̸#7f60)=WпsCsb8/.*{nb`v9p ^_\I_( 4PZA1l}wxr 5„P dVe)ZLU ՚m\D}hsyU 4 >> kzx;UqEq֩%PmѨ6B[T)7q檔6n䦵e&6љ rV 7]%&7B-4\'E%9_}Ǘ +M7n?rӦt!(jܤR{8)m߹Il7/7GlK%58]1.q_!O7*9O 񕢝=|vh&˰wd\6G qB28L_x#/pruh]Q2rJqqx?Qpy8o O}dp$B%_`[ d`:T1<_ ډɲ9v#lW d™WC>7OZNy:sЦCn|AszS_}/h++[˃qdUye9u䎢*# j/o^>2C@Hᮀ;f4wg tB1=9)ߜspn8W#-Y޼>ܥ咁>~"5&*K;Ңpr-c6UԹbGWO/9wч )W#\_,AHmM*%cvsZ<.ͩҜZ͓9Pa:Pg.\vl.!#XS\V3x⥥0-(jf>p; c ~?Auuh 퓲=_Y{Ss}K(KYw${/* ~GyZ=ޘ'V{W;$Ohh*q\g`o@Ctm%X{o]ZuXqAb2O 5zIza>ݯN|y\*,o#9+օn|u=d4z5Jkiբn>|-7NUѦi%Js睙LJ1frI•kel`{~|nG14S7lP~^`>A_M߱u|jNT ?2QS\;wǧ` s7kR1Rj{5qZC<7oxwg7we=6i~~_}|_|P2RgħHs ]mL#2y6φEkJ=}]sIhϧJJ>=aN휧s7@sF|s|xOD>㲒9oļ_ܬsJV)׮8RYd{&`/8J2I&:蝀)ŷ#MCn;" +[N >{_p ^6dN` w_ |7sX[ ӊqޠ|u1bv- T%4?q?kˋF*vxoj- %+S?5{q= usb6%8bMfĖPK:ui{> uCz^֓KWj M={lһ*][w ~ ܙߪ&%zv,>f߳pc r~ ߬CoUw%F1S܏Z߯2?v?rxhEg$ji|\Z=R@ﲹi^ss?z Kpl9'ܮ:{̑<13ćg<Lp?;yλ<_PȞ 1Ey<}O 6MtJz>.s6<͎utl B;deϭJ1g*OaL؆vr=Ox56l /eClvjz}W-<wϥa]色>yT#{s@9;Džg.+́ͅlϗ2)O7@'OJ&b@E߾diÿbKsMw]xvȶ8u_-EUu5:/m*~cuiժ[uw|=Wx4[ԦoճnS{rl3Xoqm%<4dx,P{vF+%$W] p[R_x^[aߥU2s*kTMn|up4ͮn\2u ~sgtz]$^7}-mi7U|Nj_|QCM ~g{ڃIaG3,GgQU{XgtmF^~6G߱=/Z}oR8>aМ\o>;tuUDe;9} 9w'<^0X%w-]cU nhH xA{J5k֔ҹ8.=ƫ ڬ}cOky؍b[{m/x~VcU~C74};ǼkܢJ].8$cZ|׽Da^/[paU+vzi$NNpNK!iiaܲ4RD7Z/IƩ#-x_oy~^"T U܏gyg 3 B⍴*Nz9 _ ;n'g3 Ig}KuMe7D՛ujI_G^=wn36,>:},OVv?֚E+Jhuf29LL{H[E_ϗs)OR}ޅ=[ aB u-fK?Nl i#Dz `7J@V<&|l-tr :b{x.mJzuWxg߿X*%%_M-Zэm`;5z-Qmjɷ5J_k>yN&Hg.YGd5UUGI`z I?ht3X`ovM!wJv{5S>^V&Mi9iOE~O{#=5>MyMcZ6A_ >:XrVCjn{W }N!=_EvΝɯo;đ%+u%Mݿ#Kd0 g+/7xq1+ ޱS.chFK˰|h؂R%}cJĦmFӄ˳F߬|)NSm[bMɯW{0u;>!9S&]rB>c]c:<-O zG_ƥdl}EV %-9_ ;]drߩ/?=,, 68 - ÒÝÄ ìîæåò íàõîäèòüñÿ íà âíåøíåì íîñèòåëå äàííûõ; - ìàêñèìàëüíîå ÷èñëî âåêòîðîâ ÒÝÄ – 400; - ìàêñèìàëüíîå ÷èñëî ïðèçíàêîâ – 50; - ìàêñèìàëüíîå ÷èñëî êëàññîâ – 50; - ïðèçíàêè ìîãóò áûòü èçìåðåíû â ñëåäóþùèõ øêàëàõ: êîëè÷åñòâåííîé (àáñîëþòíîé), ïîðÿäêà, íàèìåíîâàíèé, îòíîøåíèé, ëîãè÷åñêîé, èíòåðâàëîâ; - ìíîæåñòâî îïîðíûõ Ñ-Ï ìîæåò áûòü ïîïîëíÿåìûì; - ñèñòåìà îñíàùåíà èíòåðàêòèâíûì ïîëüçîâàòåëüñêèì èíòåðôåéñîì. Ñ èñïîëüçîâàíèåì ÈÏÊ ÊÎÄ-Ò ðåøàëèñü çàäà÷è óïðàâëåíèÿ òåõíîëîãè÷åñêè- ìè ïðîöåññàìè âçðûâíîé øòàìïîâêè è ìåäèöèíñêîé äèàãíîñòèêè. Исходная информация Ввод данных (ТЭД, наименование классов, режимы работы) Предобработка исходных данных Подсистема анализа и обработки данных Генерация терминальных решателей (С-П) и формирование синтаксического образца Оценка структурной полноты ТЭД Определение критериальных оценок признаков исходных данных Определение базового набора терминальных решателей Подсистема построения правила принятия решений (ПК) и оценка его качества Формирование информативной подсистемы признаков Интерфейс с пользователем (типы терминальных решателей, результаты исследования синтаксичечкого образца, информативная подсистема признаков, построенное грамматическое правило классификации и его характеристики) И Н Т Е Р Ф Е Й С Динамическая экспертная система Распознавание производственных ситуаций путем вывода на знаниях Ôóíêöèîíàëüíàÿ ñõåìà èíòåëëåêòóàëüíîé èíòåãðèðîâàííîé ñèñòåìû ðàñïîçíàâàíèÿ ïðîèçâîäñòâåííûõ ñèòóàöèé xV]hTGfMXӄ& K-BIEEC A|PQ"RZZEhه4Ɣ*-T#QoEI#}(; DHK|||sΙٍj9xܠFbuS@.!kžK%7&Ӗp`mTUc9+Z5nS?r4)7nOt9w\ַԎQNΐ:'79=zSjE>Ӆ,l3{e WWbOл.oN=iRW_߉{6AHy#[iJ{țL5Opж{F"ϛ+D/$. [NBX]D+wvry<Пz+݈('"43bU1E^F^Z+^1Q}LNx2<^(fr3*9N:KYXg99Me+:L,VM챘O䵪_2w?-X BO4󬥌7sL澦.볌 8a6"1j'[~Z_椵-ܴes֖yjma;[AMl5{-'3{ɦM)X[r^vg/Cf%~ pco  La 7yyMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:24  ba u(16t2/ 1{>x ]UObD 4Dn@$1 ڄiDjlfd\0fup@cDPy 86]#!!<%9[N}^~}ϩ$I.W8+INR8jbI*K/LڡG~%b¤ VXW iaӕ>#OovKV<׭J>| ?Eu>)LWУPSЯF])dN%CiJ^nzkѴy?YdIW!%߸^a)Mz]R,讽dJrG?C`l|C}sS3'zud񋓥9;[5eq"T'&0;N^/;yA770 ;]4\cpO.Hz/Uz+m'09Y'jw/HMbƆg\Fuߦ|CG謟$'*LӠH!/M8&Lݕ*cZR^_R8W L?6WV8K(oěț3xwxr^Eszĕ⑼yT8oNW Lo&+\xsVys3$7c M7[H[SFn=~=7ƺ`)6W\FC~B}Z/Pn*nn/эѭj6>B7SQ7-*wHYftnwo~$O~B}F/Rn+nn&1t# |7[gq/Me~+yP7b{{(y1YK$%y_JV&kA)젝`=OLexIL4=xgԼO?b_?u\>Ԓy$|SϾD^qdRǸ{ k+Zrc's`N[)t.y/}8e{|q~19jͪi/iE׌5ٚjΫDuX</(R&҃*_$O)RX> d}N]F/ ׻ۅ|E{ps-cSN<uQ}3迏 'cUZս(ܖ54DMɃiHGYc_SMisP<O'mnQ:ܭy'@&IŠ/2Ⱦ|*/N_-X$wl1Mckevkx:|L?wi `'x4z^p<󅊕& |pBuC;Y-e̖V[)nL^Q it)nrҝxVB߮JZCYV@-c`8po)Vv.ʎVYl>/.[8] OAq 083dʼnh{8rmSK79pRU&yC|q.߯zߨn,qO^S>Oᅐ']8#mۘ=b

?OXelOVâُRuR5*ZֿEG?OmW(҃u=vGkrP]579 :g2x4xFnh3)ϛvIX%}uy $AƴuLyw(Gns`Fґ:1:_I3~N4f<N ̍u1_NPbͺ917tcǨ2spSS|sv9ix~<_Tٱ*j갪ȷ6-aW?˾#Z5llBʰkwP{NU`d Yz؍؍Ky3&C]3z~֎aHE2b`384rBxp y GԓzK{>x`ڸ1p ~b: 8@^9+ `T*˪C{Ne*Q[oJlxLĉ`)l?8a3`!X/I9,D (3ȳ5O*z]~L_!~ړϦ]XF>LӀ<~ |{\83onr('xM̙:zҌALK 2|ZJs{_T|Tay[fOG2;m]iv=,I#-5.Ի <M|DeR_龝kgI/x>"GǨnj-& Ͽ0v'<U~i|J;@'5yʲ-{g^27-77!8bո7ng`wƹ9a}ʹ+pчE~DՅϼƀ)g3ίL*?b4`X3(@pֱ~b/ >G t&7_SU]M'FVH <aCPr? (A~C^yx2 ~(kQ cnݷ~-M9y`iO=6s{2`{-ů^D[+;Ve*ՍLdO[-N\/Kwk91i #ke}\n]Κ|NNЎXA<'C p8t ..lgW7uCGA?Sk^+8OrͫN}8hi45g{Vk+}"_yt+@hb]]C3\&`a[uIҷ .~x<]Q<#{*kƢ~ERG]:Hhk"<י+k%6S?ܱIZW=GKJju2i}覝出UVSYlW'2ve4B>r{K؆sK67ݽVu wrMҴsxl6^-MkF8RSY3y+{)\-K7d[4|ʝ/{aY7|gMY3ypHȃB^%_'Zf]m+\LW:pcҫZ)|pT 3?m?l>✩>Q`C +gx-(fw߆{qz fG7>󔇸BOG/RN_CKuEKY'㑟njM'Wvy-q=ϴg|w*km_xd̓ukˀAnFemƕqA{ʑ!R~M^Xo`cNZOUjCOOsVI79NEC6z}st O6Q[}LcC?aނy!vhL r/dh~ʠkNiN=`'<$`t䔝,O/ 0 ̝rHWL?ʙgWbKpZ^Jht2;h]7)^TX3u<֌N)0W;L>lUT= ?dasBfC_Úy:MCX9 |y갛:@'t6> ~Z ug>4[s1_/pZ) cm|E<,s}GӉ~IR\O yOe@sus=a~.#61uX17>?*}g4vr_5kUzcx6xnNƯxʜ9LsnZ>}rѼOp[:'nQ]kV49өDJ !G[( aQ6=)o_-8ub<@?-Ry7kZ` ꪌ'oHCƸ\ai> A렎1 G6lw6B;7LI~KD꿱-d ]/ީS\N{~V~w꿯+NN1jU6-cԃ&)NW-GASR~@0G$OTUXᏹ})O40<7j$Ħk=T\;m{ ' Ǎ[叝 ?cM+Z~f띴$cz!_(=h>4|q> Wbxvq5֧LbgЕ(0 ͲsTQɾ(62 UM7N''3.xrJ-0/oHJ .[n{riהdo)7X%?f] [K k궗uwV9}4UwMji)ؔUA?;o ͪӓϦ;q}M$'K7%am..JDMPQloP@OC(W 7&WN֭=zWԒ} ZLmZ$=]s$:2ʚ$Pj>Y34"&E&@ݥ_ܭ'w C{sEgrڭPS@>IH9eaaVdՔ~\S|"s{`H/G!_S ưĔYޡQ񛁝8om׺{>4LWHޑi~O0w1Cy~Rܪ741Nwm2) ;!pb+U!*QEQq뉛|-yץHs{m79ÛY~<Ϟdope7W͓X6Q=8Ogb#otٳ57-6nAiovrO.c="x>}Nazpb'BL=ea[&-Co z vpߴq卵>iK;=oBkCiK{F*ޕ|?b *[Az-7BM5<|E| nh.Ey$[=|g8dk[S#͛L_{Ma3is'mtBoRqC=SY33pLW݇[ЭO4 C:?{YQv;tݬk%gq HG0w29s8}ӟ2(4oa=pOh(il. I7߸y?[DkDF"^^K5q[Ӧ[S5Pfk cxc&s1 ye<{iuud>XЀSaj'Tfv/Ւ oE;@?(^3B|H}fJ~3}adfO1xm6hC2Ha|t?`Lwhf9_͜=A~`8}hU\P'TVF{v Ϧ ͙&@oOxc8O g{{6yFMN#l<&< whƍ?P_[~2XO/NӋ~WoxYݰMt17~ &KSǎ {ONNz>П"% x;IM//Y 059ypXzeI#9dXL{Nldǟ,/J/P\&7._˹POwNQ{OvJzU9ZO>0硗@3 +|ə {)$ \}PG~З,ڷαH#d##̓mTH# }UHJ'h $qC撩TK,IjEɚ!YJCz!sL1gh{dO'%|% ʿY:랉[."]Q~sd?aKhק4)z߰ܲܘ^vy~+xEư|u mI*ܮ=ܼdjҎ5B6d-_!+>w-L/oמ "A"Tz*pM4$OI1V+BFv}'ߌuA2 #?kΜ9+ w .F[L[x.=vVmtdr]mڅ]EdeɬujQ<57Op$9;kܸiح-IlM5Uq ]k3E_Hf%]Ʊ̒oUf/rn^.Q@z仦 R:LZ13aZcq/Wx34gGT= ΞdO ϟ>2>iN"=_x|Ca]FϤCb|ǜIs&\4_w*ݪÁҿbu{jl~ex{V!jue.S)y3|7 ZK#;>uB򨮺ez]t6jͧ[VΛ- ~^ N|"!?W 껬?^4_$G2#Z^1߹ۧb-KHq s'̏v+&_r8oɎN=B> Oh$}ĭ`|t\8_x|½W|5黳g溸OsVZeFK,q٦](ѵ(>[qrtlYg<j o8+-D#Y'X08 &_01@{,a|{f;w'3PW]&\G]{fmgi> ˱r<'>6$ [vѽ֚1^\Po(Sr݌*3{'}K7BZm37[-_: g| 4g&z3je͡|^`~Ѿg>-z DuMjt-/_FΒc.󒼾E)6S<]g)Q5^i?k}+-}nU&f8FVnFȇCm܇@>!] eY Fdq`v &>͹ nZkZ2\g} Xv|&YẏphBgn8s=gKy gTY} c\sDg3\cK5^uu7 Y͕;h]z/_罻TgRsNTxJsaNKfs9)Wu7*9yp1FsUVz>-G8ȷ@^[8AHsf=[xUe)| w}?{kow6m;o4}B'i[4nL ܷ@f1ߡX{m*7{&П竾FOi[S0y6QϺiӫʳ.mzpac6똿0n,nM@JRZݷ[HSN]<} N8.۴,UtqL2-yſo4pܴб-lV{,.g[gb>/ ,e&WczUyf%ꇳxsV=vpٵ5B*v0gVͳd`cӊPqzknT /&xLeG!~Pÿ}Y4zG~YZ| q]~5{+Ad 7;|rx怭 sZ4610ñˈiH0J&hKø/pmInJ܌a9iOy>ψ=l=Т \߫g;&< j-S;ay}ߧw|G> w}گH5i#6cr?kΧ]hVqLi^pÅw/f⹼ѹACUqk;?չv}“ UЛ^0] jz Z+|/ѻuX&L=V T9p6Ydp_=?1B ӈ^7Sn+VŲ*[2K>cw#}^ǘ.7vB9lG溸OsVZE-{1}ܾ .>!>ӵ65F#_q'cg}GuU\'ZVSGh>\_v}W 3.%O W$1p܇5\,Uqxmt4WR i#~dR'3c$\xY[bp;T:;܀#+\9~Vpe}$&_I/Uumoq[y5zEt_IۅJߍJ}qޭmoښ^Džtt }*+!ܹ]/%Q֟6ڧ46\[IO ? \>R%pɎwSGp*ԻqCGğepcO(=ba[*F![ w!oC*;ArAHol1o]<8C3F#5*tlSeHuuLYiB):#\<+;ӣyީ9-hoP:MҟD:ϒ-=Pk"x4bӯMji,k'Y9W@uܦݳoq6[{T[#XA׋]!a;E*p~f]_ӴN|W\*\Y7 q6.:)[]w~'N"VIX䒨LWd83dgcpn)Xx#)Ѻzt 'W25d?h>n\Ng,D30 zTnv>oά1p?ZRoїczQl~W+k~bʶ}a v9ڻ 79ԋ%pN ] lIzn?1ޠ11>>.o5J|T:T{J*phaU9 mb281ltPwcz8s䤌ڭ ۮh8;f| s2uzzvj蓾V &9ɪzI gp*J } 7O*pߒqR[Aӿ~]QZc^3{vE\ӮOX7cm>9S贲쓶u:/[{lƔjKG/K}>i^Ue= Q wy[:>ɪ/<]zDqOCGU6CoPú;mRO765c/k|n:ljo7ns2Oa{㾝 ˉݗG;>\OJ |NIi-\4D4(Y{9)? h]:,`,G wF3š{} ǍM6;I#/orc6wB5dUݶK~/3c^jѧNhzP"xڤ)yph +kezq7Сk٠Wʝvi N%ϋ h'lPv>Gokq'l/>㋶4urGmi &}Qz,5_~N!ln [aڶuڶ-+6ˉ m7v1yΧ*K~ϋ?UlByOw~SSs`^Η:e~r7m:I#toە-Zi@^Ñ) d}뽕54U"3/=؁8nş_nq@/  [|̿qhuѧMgmN+C^)4'.]JvQ6Nefkbbsޡ19o rۜUe[l^ePg,!96g'﫾Ա3ΟŊwY 2{N#p<u{nt045۞*7Տ>۹.y;'KzvV0?vη_r?k]pnfvtm&is~> Ve߱i8{?k옺~ /wM/Y{<jlCi t͒o65 -=E[:lqg*Sw'+Y~> >bcSƽVlkW˙+0)wnA7F&{%n;y/evCw7Eĉ.Woep oi}[.[{F']Oӵy*p_WepFg2O{c Q*mr QO[&#mޟl,^<;Ow,F' |PFZU_Ǟh-<۹\_v!OV1?E:]s=^18޳ E;mzUܴBW}r߇iקqW}gwS}~-gj́PvvBٝ;mų;u9(?/U!g5ynyӛ!ϫG땺t2;ugz7}i;`4wKܦ\+be]Kez2U"}e +[5%='u oVեwݞZR?)Ww.Ln](>qC}9Ɏmw1Nޣz;'u(ښ=A|\gZ$b6$k$-k:$k?1]C_Õ(3][lѵowx^#?qv}Bm*d?ϯmH 4ӧ9WYs+6d}إOl@%i5 ZgJۤ_jMY,_brgg>dsg1|}j~+By_+g>y<)0Fkw`n.\D= gkT{LU }owx˹38Q~s1~wπC8Ӿp>)YzZ&|q*<{\U^_Į8{u^g/m[n[g}K6G8߽Ho=Agѣ$-ó%R; 麰e ϥyRxq<$>"u^nɘ8fBXM !}YѺawvhư VJc q)^y"ϠQ O6)֊8-dWmHUN']k"1XJ/y̒bɕeC/cR H_`Y msI,i}F~Gě R$_(ll' @c~lYN0v]i$뢔~y `BနR58wկR$ mk`|/ebXlʕbt^X>6gy:y[mz,䙚ǔ.F.͕R3 Y{< js\3px)*i*i4[63`&o_jOd6JvjkȑMqF2 +_ouq>MqYRy^ît=@^xJj[h+h[64[P`2Z*}R)8wgbY&f$$$O#-2/Xojcv!_յÚGTo9gb7;[!l6{v6tF۲y:!Bo6#gcw+}hgMz' O7;&^4KZC4cpAںg#@|A#x:~7DhcقM46Wfc}/՘R=/qac_ك@'#O|#>p}] l_o}um>n; y:\Gi})lc^ALӴoa~ N.ϰ8GK|a<:頞Z}x< ?+?[n:1<X<Yx1kw7vGrgsiT-#W>ﰟ'Yc~/a=樆7J[=sz.SA3pC߇g'!/kAG;T~`xԂ-14G]-L zad~ҝ3ׁX[.Y]vUx<U c(»A5.%;.H'bۘZ#xVngk9c{aS/xcΣQ?u-?oj$䰀BL5˳`)ٴ _n GG-}'g<㗯{ 0>ZL}XE~U35!<˃ZO}c_//cl<Yj>3^A~)_e>k |=۰쏽 G ɜ\/=xo4"\䐛[šSתtڲ?t.bUSq7'__~2Xq[5"K_kH6dp%g%;[s'3\*XZ1dhR+Z׽fi5Lv]NjǭU~Ǟ+LTs5[+V֒-_WRU[Z>vՇKRg Qxk_mX}Z`/6ևUٹZ3UؚZԏ,zնjԗ+[NNf̀7n p3f̀7_t7n p3f̀7/LMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:24   e? (162/C1] \v{dUx Uu?" bO DL"6GDpy>) )D[-*ب(QQ j->*Zೠg hϜY'+sg^S'wgfs=Zk3)˲3e^:57M 5,{YyϲI N>|p*;duz=*{YΎNN^uNFsR.5ܞ?+ag&>xUYM +l(ˊ1X+s“F: :ĩ0))e5Sg)6nƢneC3+В~@wwM^m>XjKn3=[&el4g=ov?]9l%d# ek7;i[eX݆NJW͟,s`U]VyV[w!7u/Uޗ Z3մoѶvPvHчrr^ 3=3{wNOxc~(m.ys#c%<fW+C߼smC޻F[# b\G+ٜV*Z}Og(91җHG):Ii ^ݗ#}m^:6zO5mis6Ksntisz9{mB\?VOW+uoJRh;}i6\yLMhEuBgb) *q#-]Cp,;Oq%?1Z'Ʌ12kd=a}xl.J*y6Zc.ӹ~h,Ï(M ?*hxg$, Z=沇M~J~94Z|1gMCȉ-C~x(⺃ _y2d7e .wIW`EWPveBm'sߒ+U5CsCtlvD-*w7je:Cʝ{mN;`N 4ògKa 39pD ϙ?^GS>X7Ή#%-%WѯӶNNu)v/^iQp)^v?g5-\JGZk {|D䙇[?ɨK1Kǩ;{ipKަo\}Դvk2/DP$EI[/M̋Ut{}FdHѻsar^"^nn铄#[7%oSKBO,96;|2{t{&4ӄS$%=֓(DޙoxDb:?*;/ E [͔.r Am 1UJnԙ?7HOMp҄R'\=LOaI9/?SH~~lَU~H}x=;Jp~%){}&wG Ώʋk Ӈ{ߧ 6yL${r"Ӿ<&^?!y|'$>9 [|}ef~=n{u^ _@ E={8\ݵ%P:4k f7 ϊx2+ܮ/pvx {m ]wBy;R) \h~ uO \]?|֡мloM\h/ pq;op~ P~Nz2/DP꟟OBy.ԮReOm<_>1q.4?2)!zt\]?vUy|9#??/PhOBy.Ԯ'j͊͋F&8#f״~z39CB l5#[Ќ,6ѱ)} a0l_QWCutY r{Vt"]n~z>\]򩫣 T< ;7T[۔@셻s?g(mDvϳG؎W*")O.ǿ)KZz%>U2=O KsIo>+(K=߹$hycϹsI`q+/$U)9t@ݹ$ /<^.|.%Qʯ{(bc;NQ>5Q^&Y+ nb|ew[hXYy3|˓mwu&i .BJߟX—x}8n=?ݍ|"Cir9+%UWҟ']sϪNz֍>}bI{Lo[ɽwh_=Tɟ#$/RoS!ѓ9 x9 ;/ e&^n#gܷ*%UI)G>JVrKtG](ԮgBy.ԮZRPC y璌?B7U.Ԯ?BQp)tp꟟Bz.ԮBy9VCʼ]?&<?8—BW\]?%*e^韟B\~^ثKBy.Ԯؼ~"๤ |XMC ־_ejKv.ٹrR9dM(-Pba`>yzD_ͅ|]6ݖ:]M:;J@ۼb6T;F oq;jyS<۹m4}Ly%L'H:[yr{Vzrs:~Y߹ eߦBύU l\?'w<~窼xpBt\~_?3%G NJR$:ݾ]S]}+keIieC GՇ=Mpj٪*Gl f$Λ1#r:g7@' ^ kK~>Z깴ܴhwO}J㫐+&h+S֐Z3.E !:W0~ k-߷Y7m^ZW78W Va% Oa?/%|yb?N 5v{L__ 1UvD.yf=\{n=8UJwG@>'b%Ζ?y ~ݒ~zy nWZGdwN`W+;^uUjAަvexw-pϞ)cL9OY},#nuXw\wOIY,Wu]V[84&~ }'kjjn'-|'?T|7ȕV٪kԡwPr_AޣFw2Q 8Se1|Ϟ?Ypa# ,!Ig>Iޤ-Q518?In.:/ZDv ˺X#/{3ߛL}TרMԛt~['eҟ1?Q]nﱫG{:bo.'y6ݤw#(`ߤ`zj7k;?.~ewAO3Ι an[;S!8ef+?ێWCU:ty~ZM G }Fftb^7R`mf%]oH$:aݏrta o3 7L Woiϡ7uRk7IVS8k߿M57uB:Ma_~/៕3B?Uk7Mj؉q= +-];?Q)s6?OR`MfgE7ێ6{r}{bvYʧ>l^]m^yrJpT'&;fb'}g4S[(bg$3ߨk4}ѻ<+j sU;s6 'wBdnyld]4fU|]v{m2h8Sמ&6 qz_ Inf뽗~} |!^Fx/r̵9t@2wpg`dY_Zy_-p\}OQL҇Ϧ%;msh2_l==s=?į+mmNg_\N hi]~6oe6&4b/ɀ/r@XPu4/2 _PVxg c Rx_x# ,<Wg.iE';n~;w)&s)|X}l !y[&-֚3:;+]R?.+,4+/ǽ\>%oe_ yR(|)g(+ޕ wwi!chd}NRR*òӲ7dg^l(%Sug5i7 ]򁏎N3Oݩ]s< ۆyR֍7>wҾrKNN?9?w| nC'߫U9~9SmX=Ta Ty_3xžEVvC!E^j;m3e;6y7' U-5g(pZ%|p\Us~\ Ji7?K|ao7ʅv+w뽏շ^/2_'QН:Û._Xs>x1i`( ?q'x0ȣuS_Z2NWopWb)d|+O#.D"ek[BCSlIrciA-NI?x^Z\ֽ=įb8pԒ <~A∹7?wôB5? _z)wR17Rt`%Du`1"^g3߆/pguC km?M_)->N{g1Q4|WnW0: |.Ƭ w~ʘ+G>=0Q:|kƎll4}rx~#6:"ϺW-П97P֟C G7nV3<#i}=tZ9_tbU:fp8s{X7>!J1<ǏJO{ߞ{Sv:wº8ćÞo{&rʘmA=V,<`?7г]~͚)HsAvX(mB8Ke+_ v_ p lA~$6@م_sN}'vA7` 0H!/۰ާ5|vrvAlג mhQV[;P(ě(4Qeڲ6;]u;Nb/_)6:kӇ y~XY _UV/lڷʔm *P[9&s)6ŵ: ~0J9ϯ xPur _!G#sDM nSx~=0oSy2&^oW3|SU Ej`n5gg?=069;MS(󬥷0lrU>u`C(]yӍ(ذL%ɿhA1o!*[ޜPcJ&/dOopj\uo5/8f齓ASؗ}y{-]cagmq۷^}UqsA#~?Խ7u͝oo{V'NW)}~Umw[ ]۳>u2x诧U {*?nh?x3^ƲTc9R<dRp,)n絛} &>Qj>]+<ӑ`e%v;pd _$m2/ ǝ =qüT_}"> y9ZyI}+\Xԉ-<\CnR'#X*>gߣ$^K5{YJ1yJod?GwʠX߯oC[oqaTu^ԻЕݽAsԷU6ַʁh},y"=X LٷhE ֞m-z@߄sQݣM_ߞMmw8+},=te=K݃A|!$sQR榉=)?׸ٰrSWW|9l% _kǯT3Ns|W?=06w"_MVVụ?}?R=18+t1XR_dn5 ḋo/gdQa帧)l?h ;fcQǔ) gp ov6t݇u}3D`tOP t3.ToUz 4Y]e.׿6e4]UUw?FKg1|C oƲPZs=VbUђ,nt݃3yF.RwN>]lΞ;Ξޥo ܜs=VJu"T9]"V>߿I\]}5P}snMpU16?<-ypݻjW;QRc `jWWߓ5P}oWh‫y6Y2xjAʒYKcnBȾOy<L+xMZz;grbsӶ^ʾg gs++fkת_EZZߔc.R ^S0lva9V7[ëÀdv؄Ogo'%mbvL9zgMf? f_/suȻNi/PڈF%3{onzFdOsM/1Uޭ-gP~_ `﷜ocG'p=N;0{0GHy!obEqoa6k)o[E[KOY?V< U"MQOǎ}a>nsGOۣ9E <2oWT!n}Wmx&܁%_i:Zr3_ ux$ ]B}wO􃔴Hu-7[ qljÖ>UbEԆKzM;{_w Hv`Cl-}MOtx=@!~+:]~+s:7mރ'I&|$Z}Vl.+L(2}\zWg,KCKɢe@g.LWTz~MU:HxRO9CWv8ɳ\2G*ϙҋ[J<Osf'K7ކ^NUW9h1߶M,.׫x9g;KpV*z:qqLa(mRHp gaZ]UׯۧwBh!UFe@7ۃdZ>dm^s/9҇)+3yeo_*H&^yϧ^G%xCpTc7CoDdpK{Pߑ{Pln;̷ 4cx^kc z1:{P 3Ӈ5:mnz9+^rxCقzMC}Z!o.ʂM1:E̷߯ϐ$'NT?~6.GF'U]&YnB')go#&)$+ i!nޗCf'FLf*Џ&6 ;SZtfyzdUpk8m2斋yoS#6hN3U*nĽMZg|>qo>uGlsaYke)cgTd?Um\Vu*l2v+l26_Tdϵ= > okw{p"ᾍgy |};Wd7ǝ\55/lmKut [\{TAѮjgk+ؿ| lA%>v|7uc\->uF["sl8XK_#\k;bs1߶Ny|-Qz7g rzjτȿ3m4^:R{Z1"`}ukzn9nmӏIbX`l -$3 *|琯SܢoVܕ{a&-:S~]Oۣ&F ni@|c%N}H:H't{|yx&RT-T>ja\Jf1f]Էei\w'K7g*>[\UuKuKȿȴ2wE O|O]WYk8m?rpyݍ\=Kbzi ( v/jFo4s|iXٍ|?X;|KDWo~]s+ r]c"^/~bu}|I6›// kw=;zɘ+8&&~-_r֍y6|;-%owFL3}3} AN˿,'/U֓COQׅJ4z2/F[^o]6ZՕ\WfM ^68g1YYIS#rC W]y@2t#V6=W~_>O8}"|l߃J<;CnvǵJ~[پ6oiZ#cjIS_H9Bw߼n͆,R׿& qmnl\y1|}`J_k5VGl_mٴB5}_io  _*BkkYV_oBp}0UQʾPrK>맯=!}6)K_a"IOξ7nՆ:|gW;gߝo27Mb`k)x^C|!(}2M;g]Jԁne<'OFE}\g(g{-(lJ l)l=ܱՐ=xRѸ/RnWUo̖:SsR+5'^> vodK}p Sm C>,RO.2UcO*t;B'p|-hZB`mA\&eӳ0Ҝ3K>UwE?ox(11{}]ZdYgͷc_uօE :}"DcELϿ%(*;C%T^!\]}, ZU7uU ؇^WCwzz>dcKVL'4b#g$ ϶!8WT۱.^GT9luҙagSv '' Mqt"Y '9߾*8t>}ڥFO7:zly/ &8iBO)x_e=+yϤevY9>Y=C3t|~_`=/dzـ(Zf~\wꅖ,lKɌـ"pydn WW +_WF$m@j]+c})>4pK:QY63߶F[adX%Xk  xU hp&ZZalG%(X$>6߲V)a;48_ |} %Blԝ 8tݭa%+ eӯMl-[~eZ`Nkc橞E 6y7 WZ:] QXGduK6`F É:06IFWox] ^6:` h6cUA_ l\ohy8?}ZcS ZS6dcRv$w#jbn}ۀUUW[[UpU6?'4XާURp҄R O),O(yx= [2gaismJ =Sـ[wѾ]ɶwdvOˆ[%W|G$Nu>v%uE-+lan3@^' ـ̷Dl18KY:m#6g{g /69yݦlcvp{/L_'.7α>+ eӯMl-[~eZ 숡mmf`<~Oc ?n콛jpLM?1݌%r ZC/BM6-)pT18?jvl;M ZS6>> j u:;mˑu|j}Fl<wSRm@4XާURp҄R >ɓrBYALس}@l>oFLB6Mp~+fxgy3QڈW:[?З'k|Ka4&};}aTuQD#dߊ`ϒ@;D~e,KnPw߭9_s4/K^Pߵ w6@s&XS&@~U|Ã9y>kf! Ȉ c8v$kݠ6S [6Z˿}slu | ʈ̷ʢ">^mU[ 4Cϯua?x|w*cſ=&xM =_w"wwe'ltt;Pb_<\\z+6f6ekOep.# [hD_=lÆJ[emu'>[R6z?G(&lCY1V:12 ?r;Wwgi\7:ݑ=Bc>Ak̽/$*_Z~O1b ;qۣx֖Gާl>Gt hӼҮ@9qT9Cx=Mw?nh>ddɿYosOSc8>ljw:VWԦ1-!,ӝ2КMJMJ̦^[;ˠx7cZ##y0ք?{ʦߎ[_~/S(ay?0d]'R{#s;IJEwD#(u/ljx ~|kd _~[7W-D>RrKW(3 Sl(ߛGGv7tlo cdoXw3&~{C @4OG2ja@9/o X5ɀ _ۈ/x _Ȏv%~17W ⫑~&:NMhU}8‡od;pdq{xuԟi>#>|H9O7?/'i~ ߐNΩщǪ;V mmݹ,uI%:/w4_}WN*7LfȐi cfkYwN ߮*PÇ]AKH}a8S߲x=_g/.V_?]Q}ğŜUl^~Չ$;-|5;+}ywZu5/{i\U.?ny'̑Pğ9%nE/Qa>MVt[]ihGUqA|r?mQܪfN a@ q9-V@ny|}@<kxM<Qv a;y^ҏ/7kl=,xuW֏)u6uzatfhrAE*;vdo_!uME~?ro+rSvLOM+0߆/׋_Crx^-ϐ|ؒUR ^T ć7a>Iˇ/f!m} x]{ޯ:&b,u|@|mܯCuՎZ_̇j[07mik~J>lsUl{(Z G.%sy~wðE6{'y tE?1E]S[hGob]D[~:m a sth'po GQ8nb G^&I{{l?땒!t×O`u1{|( n_Zk=^k)U;Ӎo zgSe\ _wl׍nLqK6O|?6oRk6j7Ob2߆hV+]LF5ɿ!8`7VI~ vKvO=QR nUe-ovez>v7D':|l&JEJq;5̋븾ةUo l1k a+۳e|&xU|Xسۏ=|FM-ck06.^COSE)p?Vs18:XG$CN"gI0^{n6}9=uU>u` _~c7|4cEtGܳ~|UcsCwꎌtV+ Khw9ɛ[2-jR|?_3fϼcA?~G?CTyN%[=]}RxgC~ 髳Ҽtb_}wJt8#gS47ߖ4CVXSт4n.yp_Yy+G.jG .<_/Ey[E?E |~xeCEZ޻ 1[v4dSu&~-Ek1 )qe {HW뫒!*Ғ  _#|mHU=VSj}Mܯs܁KR!~} e_YזpO1unnc)8^>EϯN|XN Jxjń?#skWyBKf7{rv| g*WP'24>+s* fD_8Y}H~YwޣA7;6֯]l6&p,YW6X}[AaNV?)CyK7ې_)] yny%*x` gJLseҁ/m&_Xy8At<ۜzh[$\]SV}s?8r|o[6:Mlb@R߶X>!dJZmTTZmg)rj|6^ήY o)P)dr>O$w@vѮcZUdŲ^H)w|I?r͇w+jSWM>5}Jo> Bl>|OFVC18Xc\}T2m'|Jo/O4Lu0AxwqU>N\QDZ>:- U |t[o˗`|#G?CJIk>S~G4Ghs}F>GR]6$Tg:D6ZJ}+DqP<若^s1ʷ3HN]^5B'U2=yqKBAX/X0*gxȸlf>xRlM ~=  obcN^Iy9}"4/Jp7l/JpoJKiL/OJ#IKtWkL]k7!w,'U]1$OF"'?&O]>(/TJ|?1:9񴤫Ժk NS×&9ӸO-,(q}'rl*ZeTǼ/w?!=]'Cz/SK~NYo/E~η )vx_&'e^8ҿ b,=y͋-rjho}6FMVU֮Iu]S|uѝl-Ij#e3/ {lղR.ߦ8KY.g|^9'{z6QNi⛻=A>#LQ _O y_V>~f>9= xl_\ ]9YW']E:!x򻺣yR4p~x1oXob#8MZ4/_ϝ=2;_wE'iJپEJwώn~gbGV:7gd)EY: wW:-/yNcp:[SUfs-:ofi $%>w$cB<*5}u|+_s(S%Sڒ3>)w&*şa2F{z}| wYe_U9Ѓ{Ӑ❲eK.P]glѻx,P#'l/۵(Wm‡X-9O2./ RUw×?Mt皨 6W  ̷P0QWo_ZM7=7ަ3*;b_!]; ;lg]6/&eW5Q}Ygۇ=;a')``Yk 6p_Wv=Wh-]Iy;J t ܧ>!)pKE18c5wB}Є5ZTs5,?)U;&?1= D3sBLΟ _vՇiOU>7;(;.;4;JodQdr&, 3qOS3||g)A}gIdWtIRoJcyD_[Dy =mNR0^vw[+û_Ç,]Y9wcrWj{i%th'%[ .i8UN\q_,;?[ H@oɮK?UqⓃ%nünV,ѷcu`UhɦvMTԓE;ILm)[/vB!8oC>Fu5U:[OTƿ_+Rr;32:Ntf>ؘ=$1+^lE}dU~3!uVu5m -*_y/ /wor'U|ShrT[חp r%5u5)kBwIgҙ⾦ș|'Brb>tm{_x x|<} Ky=WU:j^Cꨭ>=Ep҄TeGrqRXQC ɱ^SՆɻWV><)w?E=̪H}*D) z7yi#P~^^&!y_ibwU_b4؄R1&㾫<\=w_Ի}yW78鬒=`#pEw)~boRϴ>7Rq܄>5ZL q\XSvR|p!v_ݿso$gx[fOVVrrהec>-'V͟h~r|X_͞"RQ~VRg( YV^G(ïJ?tEoVV'S@<>,-ckvK~SżetE=%y?jΈ[}}EW(M*vlF~O o%ߎ* "m~әCcϖ~SG^%b*UpC_zPU}oV֫ n/~}D:(V(%m77M[vϟR~Z gBooj~ӈ=ؘ=){f;2Zo S@M1[ /br Dk×K{ߴ (W܉N ˉ 9驸kBwB[]-;q;=lQvRthίw 75z+'ɓ:UM>OwJLoeFO!9FљJIzJcca9F9 )v5m^SU^E.fgip7{Xj~Sm''=e貪h2DZLm1j(V8 ZzE* 6 Vo<",)U;) {XAə{+F'/y@ߴ ~*u/KtlWM{PkJ yY+zj7C g|[VǿiEn?$TMT檏W /3[hϮv;#x6&xe,uj/ɝ;Iux-g75qy>T@VMW(vezo4i MOPSwn~kM^R rQYӴ;N?uEg[׋+tZɿ"n-֕Ck޷3\C/s6}ל^Bc1ci% DJ}?U۵uyzd*:/9HZc`I> !+=nV^`~}3,?)qt ϫ_RQO'%8n3==8?Rcsa}sH'}%oŏd~E{#;Z|weyٻG+qeƩlxG??/_'?T,,70   ; 0 1 1 1 1 1 1 1 1 1 1 1 i i k i i k i i i k i i k i k k i k i i i k i i k i i i k i f f f f f f f f f                                                                          . 0 1 1 1 1 1 1 1 1 1 1 1 i i k i i k i i i k i i k i k k i k i i i k i i k i i i k i f f f f f f f f f                                                                        Òàêèì îáðàçîì, i i k i i i k i f f   1 1      ,îòêóäà, â ñèëó ëèíåéíîé íåçàâèñèìîñòè âåêòî- ðîâ k f f f ,..., , 2 1 , ñëåäóåò ) , 1 ( k i i i     . Ìû ïîêàçàëè, ÷òî âûïîëíåíèå ðàâåíñòâà (1) âëå÷åò ) 1 , 1 (    k i i i   , ñëåäîâà- òåëüíî, ñèñòåìà âåêòîðîâ   1 2 1 , ,..., ,  k k f f f f ëèíåéíî-íåçàâèñèìà. Ñëåäñòâèå. Åñëè ñóùåñòâóåò íîðìèðîâàííûé âåêòîð 1  k f , îðòîãîíàëüíûé âñåì âåêòîðàì ëèíåéíî-íåçàâèñèìîé ñèñòåìû   k f f f ,..., , 2 1 , òî äàííàÿ ñèñòåìà ïîïîëíÿ- åìà. Ïðîèëëþñòðèðóåì íà ïðèìåðå óòâåðæäåíèå1. Ïóñòü äàíà ñèñòåìà âåêòîðîâ   2 1 , f f : ). 010 , 100 , 010 , 101 ( ), 001 , 001 , 110 , 010 ( 2 1   f f Ïðîâåðèì ëèíåéíóþ íåçàâèñèìîñòü âåêòîðîâ äàííîé ñèñòåìû, èñïîëüçóÿ òåî- ðåìó î íåîáõîäèìûõ è äîñòàòî÷íûõ óñëîâèÿõ ëèíåéíîé íåçàâèñèìîñòè [1]. Ïîñòðîèì âåêòîðû : , 2 1 e e , 1 ), 001 , 001 , 100 , 010 ( 1 2 1 1    e f f e , 1 ), 010 , 100 , 000 , 101 ( 2 2 1 2    e f f e èç ÷åãî ìîæåì ñäåëàòü âûâîä î ëèíåéíîé íåçàâè- ñèìîñòè âåêòîðîâ 1 f è 2 f . Ðàññìîòðèì âåêòîð ). 100 , 010 , 001 , 000 ( 3  f Î÷åâèäíî, äàííûé âåêòîð îðòîãîíàëåí âåêòîðàì 1 f è 2 f . Êðîìå òîãî, 1 3  f . Ïðîâåðèì òåïåðü ëèíåéíóþ íåçàâèñèìîñòü ñèñòåìû âåêòîðîâ   3 2 1 , , f f f . Ïîñòðîèì âåêòîðû : , , 3 2 1 e e e , 1 ), 010 , 001 , 100 , 010 ( 1 3 2 1 1    e f f f e , 1 ), 010 , 000 , 000 , 101 ( 2 3 2 1 2    e f f f e . 1 ), 100 , 010 , 001 , 000 ( 3 3 2 1 3    e f f f e Ñëåäîâàòåëüíî, ñèñòåìà âåêòîðîâ   3 2 1 , , f f f òàêæå ëèíåéíî-íåçàâèñèìà. Óòâåðæäåíèå 2. Ïóñòü ñèñòåìà âåêòîðîâ   1 2 1 , ,..., ,  k k f f f f ëèíåéíî-íåçàâèñèìà è âåêòîð k f f f g ... 2 1  . Òîãäà ñèñòåìà   1 2 1 ,..., ,  k k gf f f f òàêæå ëèíåéíî-íåçàâèñèìà. Äîêàçàòåëüñòâî. Ïðåäïîëîæèì, óñëîâèÿ óòâåðæäåíèÿ âûïîëíåíû. Ïóñòü ) 1 , 1 ( ,   k i i i   òàêîâû, ÷òî 1 1 1 1 1         k k i i k i k k i i k i gf v f gf v f     , ò.å. 1 2 1 1 1 1 2 1 1 1 ... ...            k k k i i k i k k k i i k i f f f f f f f f f f     . (2) Ñëîæèì îáå ÷àñòè ýòîãî ðàâåíñòâà ñ âåêòîðîì i k i f 1   . Ó÷èòûâàÿ, ÷òî i k i i k i i i k i i k i i i k i f f f f f 1 1 1 1 1                 , à òàêæå 1 1 1 1 1 2 1 1 ...            k k i k i i k i k k k f f f f f f f   è 1 1 1 1 1 2 1 1 ...            k k i k i i k i k k k f f f f f f f   , ïîëó÷àåì 1 1 1 1 1 1            k k i k i k k i k i f f f f   . ;\x tU}e@ $2T T  *ABkš,KέZh[+*2"b *BhŪVQn=` Z:a}}~#".2Od*%2#[!r6 %(I[.;-F^Os2zZY[R'c$OnrQFI˕\?/ }Ofld I_#wA:mgm4(S-{9\9~Kz:i0[Ӛr| `~FI/?ON| _>PEV"oǎX! I_I[!]~ɤG'nXԍNWpyr1C+ ;h|#H5cVb@1|h̠NbRy1eCk_:̥Nc~1_DlGl&IZƂC,95'# igL߫幒uic] +833|n7E@7*L~1gĢ&Y8C|9+/GEXLb̭N̡-#B. W0ج}{v/ӁؽD`MEY _ _̚:Pқgʫsc[SA D鱌~WzI+_@fwkp;^c7V}kon%k2g8q][(VVM΀3r췝 ذo޼HA<b|ۃX'⮻طqzr&cf_&SuS?Fz6G&_-|jٺ! be_|+t1E~БcܫX)}@};l&[,*뢜vQ p"og+yOc^̻0R]7=>:\T>g ؃5YùgzОz]F181D (+>,;@z+eqW[ XAU3Jknc"bwKyؼ>V%24j\]m–雲5,ß:0JѬm"eM^ljup;YhZgG|P {;?bS40 )} xNRi)q\J'V#1i-_Sl0z|^8s;xXtd3Fbɞy{o \|?dsRLHƲ8(c~'`y(w |݌kcg6> ǟA@[wϭ^L+o͹4f(x$P$4<>Wn09nl=6 ?37>l:N9}7\ 87+~|۱jMSMթꛪ+ab>Yۥo=X=X qG'UrN!zM/)׺XlD栟x;'J> ` sQml`뭝(rE{%(|4ssuF-vZW2i/aojqkE׋bcٹ8ٶeɮցhlܼg*oׄghsyͭ=˅ڷkAZr50ۯ<ѧc[gG {n|ۘJ_wݨM`z޾}ǎ{Xrw`#]CɰkJ}]ZQ׋̦q>t1 3z~Ϝ ͧ3Oy䠛Pi|6FٰnmߧωQJ8ANʚ}Fi{hr4Yh\g6TjCh>'5O74q2Oͧ/&vwKߚ ͧo4}Bib~.1_K/"&fɱ2eن7LO7ٶj>m|]oU'h\S}F::g PJdtWW,J-I^Hقj<тfbCPZN`=h6=#@:c$f=JWx[ݛz0ۂf=L%lCa=MՏFѳfʦnuIȯ`d'MvG9<=? Q}ҏ9C_G:nT\|YT~0o`]7W8p!1(^Gt ߵ$'suϓ_&pkVDzejjVn-vgaH?V- Z{Az>=/52]n<,MYhd#.gY2l|1խہܘs[Nc6a:oMa:q 6ޭUkXO`=$β`\O̶x$ ϕl]ql^EG\/7IF֕갧K;~esqZ~k͢Uil_ d 4{exP"KV6NmKhgKXR:!7G(Z(zkWl3 gMyen~oW)f}t7gkY?o9hds%ZyͤLڀnys{5PP)[C~89R&gelŽ^]9R.@\֚K_V mmޣݩb4ؚ|Bckּ[Sw._B.gKVؖ stfvf/V6;ď bp*AꋥKZà5>ь^|h\}lBYi&絊^Wu.[m25N4\b-ۊհ:Pok.5_mUښ[qӖpusVkrČg4;hZ:]k5tx4Mݵy;vKMM? z_ן伫MNߪּիZg}vnRk!v'vp@r>YS״خуuƮ ͫMZnLn}Sacu61:Tl1p-ќ^خO={[Mnɸ͍6NڳFv2.5vYyVYrڜٶ雭j?:gu 8d2pz!!!!!1 tm/Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:25  P ^PP(16v2v/P1e{x E;A h AT'0uƀ8HPPTtB.#:"/#_*]eq}lVqWP׊a"^pǤ1:U]uU眪(Sx(:QIQ.%$פ7DsEyhMmbԽM=W $pT·Ey_E-ΈNNNޣ\ ԥWڽEJN.j;L~[{îizһ]vVx6I`oWΉ {(PWh)jL] 1d tݞ߼ E͊$ "KTvݵ5a1_c⧖MjjtGMygGwSz9vkn 7$7= ?vItO$c?ake❦,JWSS]3[=z>_R/JYʻV5RM{'ﶲ]M'mX2wL c MO|_< Vݏ&:Bg]S0]/=A&s~+޷xW+%͉y~%V N?Ay?MiH[#=7PSQzy<":-:Sc© 8Vi6oy-)7ǼMEɧ[=7 *3+~x$&6ZyMz7g {_TX-rKyKTZ7W(Q+z$Z==u6ZV+~?Qp)Qݵ:z@ DTTxivwJ=s=O 4ey:8b#z']i#2iۼ3_xd=c(b,}^99o4h_铟;icҾ\yf|?01Id^qN?gy/-ujH*!ϙma~kE<,jiNиRzٟ3%Z|$qm8& |=|Rpf/]5%?i3nQZ4=[:{͘Le}u5v]S'NO,kr/X3Xv]zJtp4/:>:$:JwFGF>(GO=z|dW+~r(;o?{19oy|4oe@ac. B];핗ѽ]( up7>G}Fssy7HsdZL*60Ks _O5.#XO7M/mْx46z\F̞O;S)]skmjup8].SoTtUç Eݢkh|p/М]NN! $KHF&L8讗DW-{InOh+ \'YR^.]NO|j) h6&g?WL۵vUp\LfŔcn3]sk/D_J׿]^!9i}w19;s]ұ#Ћr-G/(#&29ZCѵ!9tSvJ$rs]7e4G!2$v*v^:Z/ :q] 7*\KXz蚕n#g=O:RY[Is mM?)쭴PW(6YLtJVT+l}m,++n%yT6~+phwՋeh{;4a4)Cm'6!qoekr8Mmw{~gPP5,ht@S>ZNq};P9 Y̳t]{` j8m߉+k[g뚋zqJ/g(\2A<83Kr 5I3PJ@1}5zdT ѫ{YOuW^;+s ZصuģO(L?Ṯ~brx$$_1UhN9ZB`Nz|x4b⹌^!Rl|1us]^k9z\F/30C~xH8^լvYГ:}n^Ku>hE9/_<++_:sqkS}2=y76M]zJYۊ VyW彫$oU;$a*o6Wy4 8UNS}Ok@ohP'ČU{઼wx{W+FҾ%>E)OGE^6c]d6vQla`f *pK~] ~/3c]Cl}EkZf턮mژ}̕fVٷ )#r.GxJdyϯyy @X3>]g|| O;F+cni>]m&\K3>& OHZЏFwj#]I7$= g}C<^g|Ն򮥻\ԡ]|G4>  Q e|KLljl|-^DC=SL'kE4NoЋr- 'Df>7j])? DZ1Z*p{+`hJ{Aۦj1=qz.4ŃL0 *­3Ӿ2_d> \}YPd >C;OwP?p~xVsc-|̛Ƌp!dBxt^<Un\}nv P^>-p~dBxP?<P< P<oP=KF)͑^ͮB֙΅MKx4c}n3[:kGv 4]hwie\g{7혞#o폽ԱXz}] _@= U`?*wž^`u"i '!ur_GS*P| ko$O)Oto7s nkC5Whl_ [#o yZ#|?ra'?odyFEtLOdg־ًzW nDWUU隣էc)R7gs Yg}9~.sM'yT`SxntEd~'.fpk< uoA5Tm{0w81E =W2QgrQ0f6+i_{"rY-|/K*o dc5{ߴ& euʄy=/[}bj) / j=/>o{='e6ޱǝE]zzo._O P)~U\}\}@<=l*(B[*89:C<[9$\\!\ ;k;Z8zP@֎-_<⼅cdUޯʷMH4^ /y=-޷UྨTiW>!wK:ɻ3}Y]/ ׳/bpӴyU1_16b7e6>}ZxJd\P^O\Cr3kӪi'?7Gs^bh|s;C<]'FªkN[C_7MӕvI^gƓz^=]3ϗv)]sUkə5p4]uo6fwBp:!83뵱]=z֜\֙1^5{8l:t;?Fy'ΡaU$%fBK~oǔ_AW+ov6>ST?T?{#%,"%gﮀ]|=cr=EOS uP8|y{ ~A1b/(oXMSi !*NBdH̾ls:KtF%Ϟllj)9yek5,{Hmz;V՝av|mbQϖnkwC>7 s0uJm@ukQDi { e$Swٯ.g?tv~+\nַT oNeqh1(_gϿw3.,Y y_3z\}ABpc^q~o\6{~)S?=]8Bg yc7d#;OnS~[^N1{:[“SGl<*wM"XJW8t2>9YFWf?<-5 n\}3eM^ӵ}l;f\Fא\%ݜiC/o"8k64^_7un;K^Ek<9I] k/ߖ>aB_C7-P7:jv:C*9׹hr^^y+Foa!FdAg)Md?}Uȍ*xg2y(:S.jؙ8+jE?I|~ WxPS[z_d(,QOR=|,Gn!f{{btiDlL&_jr^.ͳ7 GE<{M]KCQ,¯؛7rC< [F2{༽vh#;.,QؘsdJUΑFWd52ߨLpe ߶ZfGߴ޸v<|ۖ1z}< }kձ<;ٳzxسgGHv$c:Ԁj֎,F{ &+2խ\fzi-g&yV:aG#Îev#oIu=*{b;`v~m l}Rv~T_zټPi+-֥{D,ýZ=_ڦ--JlO5_`h=kԗէCY ߖn;Կ=Ee_Ϸ 翳14NS}e~fmvFcY,_M_!}UAlL yz7MYK廒:LZgxy7Muvm繌!y2;7R~h|;]iذS?e|MggLnʧc6g{7혮Хa:F7ѯ/\VVƞ}u'k&M<'*^Jpv^C̯wpS1__Խ,1{)XĤgbMtvJs GDEgFgDF'2Uyj٤F35a3睍mbS\1gr:Cg`ȿa%ZU3tO<%Y_?9`Jfx;,n5!c7cIeD)PV(oƛgb,^]EDo# #c#Ϭ.fw,&o=0oL/[F) -|7+W,v!</ J{ 4\=j1{a9"n{pD:m V2V,N}kYykZa\KxJ};5״\Pr"GKhU]e=O:_z5ilִL\"qx\E9h?e1m:pB:q{adݴ;wpD/u`=_q"q__ǵ@}if|A/C64Vv :t }PB27ffZ͇;at;PΫon]_EE3gm;[6pbpsfN;,C(i@ӆ=gC}/N{o$pe[.IO[3B<<{*{_>P}svKlP}]˫%<$2hnh>OBgڶÌ81[x2GѾ7^ku'4 ?s]} T~nhPpشywҳWFϮs^ᅁ^*z\yYwRρ򟧳HC_;upXlWf] !_&|OlRρ3ÏϨ-lբ*CUYjgs_ϨٔCUΨʿԉT5;5lc혮{x}&FU79l kOjt]\3,'\}ծi R[3%'ĬuSZ7߳iiyx1'2vowrWg_~8NﲮͿ ?wl!~^gVx>]k?uni=uO0fYL0݇|/=\9sRZxSog/%7/\9oU'|I:+3Rw\ ͅt QFl㼍M'+|]R:KJ|HeP_k;Iy'*/s5-QKVu>cQ$o4O$+nh6rNsqg_[ 7ۇmζ/v36ɵm-/-"ϿVzJnhe|X F;mcm/V}~Pd8[ഊϧ%ԆuC8tm;P`x[ꠊٓڷa]}.}k& \qnص<.Ԕ,'fx!O~Ncl*Y(Z2Y𺏗]4Flow)7Wx49hܢ2Eِ>Sk':7M ׏ՙtu{=Qͳ}nRFѕJ(νoL7N٠ܘ܇s?^K%UQU>gm[FUq8hߵ닔cMm 7efflo`g{7zӦ>s4-S>Km+PKfhWel.>}҃Goۇs 3I ¹}gxZy}bXVW5y6wHlV8S({u96y96~M\ V^wm \^|}4^|}N*h[b#vNN#L!i/mOU__q-Q"NiȾV{f)}ag> m@ۮV`o-z-H6Rچ ޤqzŜ'6Vmh em~Lv/̜PnP{oSҥmf'Sz+/9h_N_]\McہU˳&yfav^=QĿz.7:"Oeׇ׊!8a$Jև~gSrBk<C? jLf?t]$k#T&XyFڐ+!;U"sR}N'}+a-Isx.Ӈ7e=+EJc(ØLlWn 3wC_ Ӌr^.[5KoD/5쳽=CD^Wz~ )~16>J 7be8`~bZhcs>Bxېa.̕mG;;urOE?Ǘyґ+_"Hlαl6fz)MGy 9Qd> \Y}'c*X;p}5u%py_%ԗ7-z? \^}с~>!=T_M;Q`>$mxj]C|zjWV՚By?+:!$T \^}̩!ݷ:y]ZP'bt!t_еXa5W8}EpFWqj46bd uoLgm$ol:1k?|r-lPlЬ6mӘov@1XED;'Y;DQn2:y*zE}\'}>hM=c1Um/ P jfלзɷ|χh^\|WH[Ϟ$ߦC.o+̷|%o_}>X!Jnhli?asO47Bg=0CahP_j*D|-U&oV&ӿShYEБ4WB_kG/ޞ>{zQK}ې)}<L}JD2z-V^Ur>7M/oƍvܛ^U|u|"kM0=$l|kH:KX6Y劑gӱȻDi X+ҰkZ!!aH27& M #Ї:~[b<8OЄ?Y m#?W2O#zdI\^}Oթ`}ΟjX 7$py1~Ƕl9bPS<>~N8k~uBtXo1pQF~wLO6C;כ50!1'S&o\3z}}'V򿽶w:]&_/͛O=cwg!i>סUjMc5btڈ^ogm>]1f_LCWӯ/J*GupoY[P/gwkh{qۀL`o3H[ ,yDsO Qr٣l!,[ݖo&p<졫9һqtPyNm㹥4{;0^WzԎŔݴJiEvӁbw:Wʇ?$b1a/[/v!pO 9kQO]6g!aýKpn6ܗUQ %l.6ܐcH<ǥ꛵l :aurH]qi@GYk.m8c21 ukUg>c27"JnH{4gL4w{/Ըҧ1ߣ$[ "8/ytft˺Xu %ģ1(LyÊ!zU1?jKfk-^uOg~ =ZӸxxx͐r^?<+jg߈iz/gShFB<]!c8ѯ/Zy O$: `]z˕A>i0'|l1\|D|C;.o#Чɫ{d/_r66w Jnhn+\9{/섞7?B{7.w{dIFokwӷIFonBQƐ%ު&py/A \Y}9G?M$@Idz3W3zReϓuYTP8'r~ 7 yOUIyGfp?z ̆7*µ瓲U|v'>xVOl4uix΂|FWmky8/ys!7#ZgCW5TO]PⰝ֓)wct幌!?Q t͛/>Ȍ㓼#˃ÞJI(t7to|{~LnΙ:'UvI&IX)ҌOx.m8wG#fdb˴)d[MS$ e4'lۅ#lg[-^yx69y㽒k>uT{`Uv>l1yQA96̱} ǵo;;\m)J pv08_-9n߆#c oke())'?ձ}6,x dGdk_ydcϷ4fm:Oi V݇`li^u-מOluTGp1gCs}OzHZ s2ԝ7Ro3Ow**n+\9;C9o\ӆzw_U2m) \ctx~SIo'>a>q$+?sozfw=}itPuċLq(yi{4ETg^ck QfTكu dzJ+$6zy&<ѕJ4%[7uڪ|#戍f4SoK)R\i^ަ=26M4wh|B[;kUq]O?$ ?ZŸqYVyx{=ڦ1{rlIQR|b;ˋ$iJ6%RX\uӥDuu7AiSsC_p֗k{_;뉆_n.8{ ;gb- pR X]XRQ~@d !!Oh43?\¦{wI'lN7j.o'uҼo, n80CZhOOlp60$JnH')I5uY:Is/ғmɎFo,^=z-!tʜGWYn:.m*灆uʵ'!uhlz"2D3ӆſi[^X7hߴ )j2] Bwrߔiz/g{7(?s:yx~gR߱E{D_u[Γz0z:QCpBҾqt@tAE3=ϾՕ Quwݑ<.XC 'OKl};(|D&}Mъz8y*MSp>jC?yQzNjeоM1B-tUJ+m wF#U~m'TlcP`\[!tgtȽS!3Xv)S!Q;6:2zMTG{Eu3&eS~0z3gT1ܴY1(>+$cPܛs?2zA;{T:8C*~J}x qxEƠ\џ2 qcy{T7Bߓ{?6߇\7rM9/[:`,ĤC}] / '_|ubPzX".ϗ@@ힹf\b^⽈/$"c;/ 8{zW~6ԗ>5xHmR=߹ey'/ִߐ˞-uF>z_NY5K@=CB>gˌ^UF^Yc?1Ϟ^ekC*2߱1>n/U|Yc^\My}g+PWKAV3͞m~,"'srh"e FgEֆ& >omÃM|==h`cb>kmWibn~Q iPyk6£j7PrymWC6S3#6yy,-k[_UZӏ(:l؟ xP)VЧqOu]OoyzwLg}T_&D$+<͛B{C:H>O=ǟ_`,99Ehpmz~Qo.vrhT7ll?X/hTG|P`)N^nY&)v#ԎbyY}S\"\{>)G:0gK^E<r^o3 =  } !Rі;kߴ}M5:iMb?hhK>|<|m0GD ޾#}Cm[rTU4M'uXLf%&c|k= լ=:6>$Rg#9<؇3PO19Cʡj Qۣf}1iv6>dg@)߯/:Q{gEg6)1m!4730iHןRՆ~%+LJtPw,"~lHVj+Gtwu/ڠ-K2iI]<ThvG;i{ R^2<ৠ/(,Ihym%/=fH1xxZy{(@n کק7סWu75Nؘ*Z Ua2; _uh{ y vklg}#徬CWuTfaIf_Vc뒇\+Jl)Ru k:ŸY<"PK4gvV;gZ:ݮٕ)[t[wu3m1GLU?ǷjǖnBX~|o.qKRXZeЏ;'qc5zw[$ϛЏq(*[)oޘぢsۻ;|=tHߪt O#dekf.>>U\^Ud6>qX}e2 YYħat`tfU֟)|it-v]UewG7굢kh,atۧ`tpyg Ruk䟵53>}dKGfȚfgI+|.W 6ͬyf#wSiߘ.>o?`K7? ~`×sk=WKV1_ :<$7PR`EtzOo[/[غhw%[B^ b҈o>G'.G|`XqRڃyIBu6[7ƏzV*^͏uȏ\!׏ȏN:r@qto_dҴ!?دvF̑U# |C OrXF/ǢLmHwnڔ碱oK~U,Ǡ7>0mv&_EMd~;%|gq3X!vRrCo1CS6m;CVNu|p52 ^^?)/O{]? =Xnu| c}WEuy504Sƃ/Z1G*cCyǸ;m<wȢcZš5aX]ǽr`<''AvXT1dUT.Ϗec; c{cco}нȏ^ԁ?VA>- 2?yJ,c=@~p_mgٽ̿e>-QҁԃO||a7O rq/w_ w`v&Zig{<[h2H } ?XEϞ/g 3$?BBg/ {]*^qInF-#~=~z9zFE>> ^J>Y^]ܐ 9H ڙ|Pc]*_ LXƷG޻1~sQO|򕡗>}ayUx@4 DcP&o=x-oB;Ǯf^i"Z:VpޭԞcYJ}6]g{x`9Wcn߰7?!=6komկ/*r,ע5:ʳhH;.R>mL??av5"gM}i>L3^UB}J }*Fk?f\y)yf{oWk<<{Jnhe~>Y[49 DTE|4@ziQ?|Q>T4<{sj(=)'ԳOU?{Kix0wx.w ڙ|-}J|-Vc>Vn U4'??V)QthD3= <}5 *>6IqV#} Wc 8Ky+=S8_R~).kK˕Ʒ̡(9cUuXc3)}Fw+5)ngI,GWB8)}"]':i3tmKϦglm4b">~%G{N+:%f<>Tcocޣ$T+5es e1ܐf)gy*\/yo 1)ØkJVL!4'\]WHZ>(0~{Kgx<.:k!P`|D0|f~pŽ+0Tnm!h\PN6oT7R|rX"X z[)O:-nM`~ ^0ޭt5zU ׵Ձz~iz-? ^e];$P(u@+u?ýkwph u_QwXr Y꯳E3⍯+ ]1XK*lKڽDr~v܏BCj W\'lN0o孟3VȞ#F2>rOvFȪٕEv4>-aNO^,R$7򮥻\5m)%]o-1|p4/:>:$:*:8:6:2n!܁7=^ۋ^}M:Wh< 7XIykPJn{Sa\ew7̱ܛjtMS_etQ ȣ嚑CMM 2/yrzRvIF)Pm ᧤?K]CxUլ-UZ7uZEh}Ur(yoct6sK}+y댦}wӎ"{:Yq" W_ 8ODC_ =&?Px,,p71  ñèëó ëèíåéíîé íåçàâèñèìîñòè âåêòîðîâ 1 2 1 , ,..., ,  k k f f f f ïîëó÷àåì 1 1    k k   . Óìíîæèì îáå ÷àñòè ðàâåíñòâà (2) íà âåêòîð i k i f 1   . Ó÷èòûâàÿ, ÷òî i i k i i k i i i k i i i k i i k i i i k i f f f f f f     1 1 1 1 1 1 ,                                               , à òàêæå , 0 ... ... 1 1 2 1 1 1 1 2 1 1                           i k i k k k i k i k k k f f f f f f f f f f   ïîëó÷àåì i i k i i i k i f f   1 1      , îòêóäà, â ñèëó ëèíåéíîé íåçàâèñèìîñòè âåêòîðîâ k f f f ,..., , 2 1 , íàõîäèì ) 1 , 1 (    k i i i   . Ìû ïîêàçàëè, ÷òî èç (2) ñëåäóåò ) , 1 ( k i i i     . Ñëåäîâàòåëüíî, ñèñòåìà âåêòîðîâ   1 2 1 , ,..., ,  k k gf f f f ëèíåéíî-íåçàâèñèìà. Óòâåðæäåíèå 2 äîêàçàíî. Ïðèâåäåì ïðèìåð, èëëþñòðèðóþùèé äîêàçàííîå óòâåðæäåíèå. Ïóñòü äàíà ñèñòåìà âåêòîðîâ   3 2 1 , , f f f : ). 100 , 010 , 001 , 100 ( ), 010 , 001 , 110 , 001 ( ), 001 , 101 , 010 , 110 ( 3 2 1    f f f Äàííàÿ ñèñòåìà âåêòîðîâ ëèíåéíî-íåçàâèñèìà, ÷òî ñëåäóåò èç òîãî, ÷òî âåêòî- ðû ), 001 , 100 , 000 , 010 ( 3 2 1 1   f f f e ), 010 , 000 , 100 , 001 ( 3 2 1 2   f f f e ) 100 , 010 , 001 , 000 ( 3 2 1 3   f f f e íîðìèðîâàíû. Ïîñòðîèì âåêòîð 2 1 f f g  : ), 100 , 010 , 001 , 000 ( ) 101 , 110 , 001 , 110 )( 110 , 010 , 101 , 001 (   g ò.å. . 1  g Âåêòîð ). 100 , 010 , 001 , 000 ( 3  gf Ïðîâåðèì òåïåðü ëèíåéíóþ íåçàâèñèìîñòü ñèñòåìû âåêòîðîâ   3 2 1 , , gf f f . Ïîñòðîèì àíàëîãè÷íûì îáðàçîì âåêòîðû 3 2 1 , , e e e : ), 001 , 100 , 000 , 110 ( 3 2 1 1   gf f f e ), 010 , 000 , 100 , 001 ( 3 2 1 2   gf f f e ) 100 , 010 , 001 , 000 ( 3 2 1 3   gf f f e . Î÷åâèäíî, âåêòîðû 3 2 1 , , e e e íîðìèðîâàíû, ñëåäîâàòåëüíî, ñèñòåìà âåêòî- ðîâ   3 2 1 , , gf f f ëèíåéíî-íåçàâèñèìà. Òåîðåìà 1. Ëèíåéíî-íåçàâèñèìàÿ ñèñòåìà âåêòîðîâ   k f f f ,..., , 2 1 ïîïîëíÿåìà, åñëè è òîëüêî åñëè âåêòîð k f f f g ,..., , 2 1  íîðìèðîâàí. Äîêàçàòåëüñòâî. Íåîáõîäèìîñòü. Ïóñòü ñèñòåìà   k f f f ,..., , 2 1 ïîïîëíÿåìà. Òîãäà ñóùåñòâóåò âåêòîð 1  k f òàêîé, ÷òî ñèñòåìà   1 2 1 , ,..., ,  k k f f f f ëèíåéíî-íåçàâè- ñèìà.  ñèëó óòâåðæäåíèÿ 2 ñèñòåìà   1 2 1 , ,..., ,  k k gf f f f ëèíåéíî-íåçàâèñèìà, ñëåäî- âàòåëüíî, 1 1   k gf , îòêóäà ïîëó÷àåì 1  g . Äîñòàòî÷íîñòü âûòåêàåò èç óòâåðæäåíèÿ 1. Äåéñòâèòåëüíî, âåêòîð g ïî ïðåäïîëîæåíèþ íîðìèðîâàí è îðòîãîíàëåí êàæäîìó âåêòîðó ) , 1 ( k i f i  . Òåîðåìà 1 äîêàçàíà. Ïðèâåäåì ïðèìåð. Ïóñòü äàíà ëèíåéíî-íåçàâèñèìàÿ ñèñòåìà âåêòîðîâ   2 1 , f f : Fx pU׹4KnÄ$DQfĊTkA5L):-"@Ū<y(Z(*jVi: osv g^{>X}ES>,`pc1w6 *%DN5"FCԵQ-Om|/L;[ΎXvGYfKL{I.;%[8M vL/HGǻ#w-E']ݶR Z$vwiLyn'eJv|`H_ZDnw(Un}=`ʚ*w)B)ޛe\p) d 6.ϗr-6 ÁZ+KF`@0 \ #Xev: N>(>9 _' \/^NQߊw]4&h{|+ O4psdn׀W`>xlϭs_'= ??q h=tzM/n%UWf=9v:)Gם`4~ g V1^aNGv+{/zTGgoe=ce TYHU+<ȑR9VZ!ewX6E+DT,o .o7ճq|P-ﹸx)9ߓm<}>}1г3Ξ軁9.FqsfMڐΞ8\K>]3]е=$tme[iUM:TƮ P~`~gȣn =`UkX+9F[TvL\4^>."^ujDy߈[ȗ>XCۘRNՏM٢1csveMnSyeK3yTX% t} /΍j7jɍԝa<_+SߘxJ5յ]:+br˳`TF§kkWzFcG\?㏋]T'_zM&$SfFOAz76fo|;F{W0RdeNOvx% %omo;҃Xt%yrJY=` |2ѭt,31>ϰ`sR?k` @CR1";[=1Ϛ\?jm]e2({)|HEN?|u͍9 9`1T4J#1W\t ^qLh skko&u:kirU9k]귝ո6'동U⋲N O.vsǾ[קbtO* 7#dw`="O~9CA+i]քv=b~H.Y!s}ϝ?7M^`{0'lS5/>vmD kI`dѯ6zgo~e SI0h~-j]z?ZP {#'_<^^si:~跌q{λt-lcX~;R[w_陡k@ct-M7q zf=]U)׈)z @B=z k.Fo~V6 KsBr_Kݭt=/[gHrϻ]Rpz20YnJr$؛1vI;8M6ܴS7|2w7ɮrFv<~|s'\ƃD$_1j}'VYsCMdܴmHᦍM{n:_A9ri3VОӍɩ槝x'vAbjb[_@yqI`'\^O`/I~z/?O;֒3>yq'4?_m&O{48u ٍ)Ypo݃R+";|Pz<_:u~Β'cOXyr%\Kt`bhg#PgXKy % ][rO,_%VEDhꕔk-q{0X`20 j7>?l`LploFW zj 7^Aii=#gÍNϲv_υ/@?͌}(톺'ef v:H>>V,%N7Ɨ`Yo>:a ) |e72#Sļ5@Wksյ̵k-,KXUOJXZa j 'c'R&O^'32>GcL?od{^RS1]/._oxzC6|PSwrZy ܞ+eꩌgWNx?ߴ{ꇯ]`[ʛ7v>stWAO~li wz3-`dl<wN-[Wu4̱;~|ϩޓ0}} };ݔA?P=z @B| =>=z @o"eMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:26  Jw rV:B(162 /vP1 `{"x _EuoB@aC6!K(5BdԀ[HEE__ >'Gi- +K"49{>vod̜;sΙs<~(PIQLt)"yEkxͫhRgr4EP %p*[E r߾ϋѹ[yWe`wQ6rSOU2ivʷT7x+oE/In]\ߨ4Gv%7(ג"LYI1dO^/ nmQi;;$Yd(z@\p|0~V#,S6뎖l~ܤ ;=tO C[|fo\_:#|hZ{q?I. 8mqV~;,뚶[9r?;.+zJ3zdZthRE.WO{~`ioG CGGtr=)~>o~iTm9^/ż񒯫@?A~>]qH]#>7;TyttN6 gGH X͛}[+M`ɻQϻ^x?z>7xj2,D۸,E7!?9f܊4j)9OQ[wӢE=)[>96v\q-f/[-gZ4x@Oኋg}}A̺  noZtZ: 0Fȵb:o=>3:~EkқT LNDGD%5]-Z|3RR*$<:}zttCO-q ͒;G h?Dկ/#1g=܇ňoܾ7&p-oӆ뛻y \YyKԿMJ;B k!w|r,ܛ?15K{*o+o/TZ1pemʛ_PyU- 'eq%ԇKq,Cxcٱ|.9?<bҌUѕsdumN.xfJsg.gӕ9ȼwI)o,e.yDEy8~[n"|et]99dN;C}j)ZzDWksS>]WxW]JKkѕ, ם+wk7uGet^nMaF] 5_S&PiFR])M+xn4yrr{WsOwup4]ױ][|4t%_KH1.k2Vu ಾ$~G9Fr#-9 :rca+Gf,zU_T'U3r3OLhRmњh#Q+7z zH1k׊un}|eWCtt:KM<]o7INPxMq+e GG)I*p'Д3kspbKF*{YNRxr9`-&aKLIG8RT?Nߖ3ahZ\u)c&]; ɁEƁcDU_:_vep!8/m<esIx) BFK6ӏ^- uXtw)< !]]Ue"zG}xzHrweA|2%.%^0cNkdy;'͘z'fL ~u\^jR) [lazezDW#\Fle꒫"K| [r"o젣/&d+NzrQbُ5CHCr<y/SdW}\|G-^c=d>@٪Z2 ZV[| #e'̓5sNNۼEZ[vj7';յW;X8-ĚNy;'8SqwEOPy._W5˧B4kRg ~YWV5·$++BH<ϧ''py63drݧxe:O'bgc*}7hZ,1[o"8+eѕYZ5:Mn<]tշN-{S#?,#{!L m|BM]J4vzoО]u&4 ][\WX!_K1z.WݔNcٰԣG0QƟh6!*%y:,WUihdvCISz%rkl$Og媏u-yǂ{c29X*Ww[M"\FlU~d*7LɆW|Gzz yوќ/nO6wCysFd&|8VnwMś,ix'~0F:pCa![물Xϼ?¥GCGUo߯{7%/bK6lߦ=ɷ"4 riir<y\w0u޽@>?-䯃#ڃu%l*{0Z`[jLwW9h^1>" y{c3[-$l&awE747=s;!׺[`y~LWw7#^]XT8-\ߝ(꘡߻a{m $)+ =轡1VZ_pa\UL,'?ON=,E2mkE*/>S~1z{ѿ`,lhmQwW"z7ǂzINh$gב~Vgt9NNm î:tziӻt u"_+2 =RzeE;#:4!VC 4?2i.up]OhLYdoJ{M0=#Gl<ԣ0י+nfy0??/QeKo:a#iބt^1Y4YEQtu'aKĶ&~ ={E74iuB'^ 4ٱ;i%p"ui4b}w_:&pb:OV^k4]O:MO'4L̊7~O|.lU=䘮]%cOjS8hٰ=N9=rԣNJU KD4Hyoz?Np4,P{guiMy4 S_~F1x_K٧:x2HH6vML7&|wpwtnlW.゗.0?cU(R$pe}pJQKWc8sDUUutqgVp_x~y|2O A71Cp^W`Cpg3q *Uϡӿ ]ZXTy6}bR5-UJys7/-} nе*ˠa]|ȂVwe2(jZ|>S2EJ/]ot]w2:8U **"_ҧY]!] )U (튰2߮gLnbzٰr~Q*Wm(E>= ?s"MCk1O߰2IOq*s~=S_'D Osa,:z?aݜ%'ssX#u8ERurO-g?wAHH`=O#u+te=pvB:i"U:F'iL_6d!g;0p]pAc̣CaTv6tw֡!S{rRY {ſP C7$^4.CbK6e"d1 6ld y_ h_FeVCn+?^gc*uȳ=+!{_7?MK?Z“џpN1H])k}mA9n+{ԯw ]Bz[[Y^|FW ZA.@Fup4])mdٰt-t NO;h?Dsۅ9ѓvQ c*mx{{#o@CC]-itHkaTG?)}oXzrcz=,պ6{~z)L_Cܻ׳1}t4"%Ӏ#GrI],Յ8ށ组y2, Z]%p\(?|Rt+ݖ)i7)N[4]&Ru!1zng{nW=n3!śzn'Z榢.E?nwV/ ݵ{wB:';//sxgiuNYtױy\/) ;+_˵ckֽӢ*wYr$'d\2.ewV'>\TpӴK?݅|NL'FW?nFC *gWHgٻofٰԣ'vy(rY4tA9VE[9Gv(u?bAtꇏNezpEz 0䭪|AmBB߰xk#BzQg6{;Ss$9FyNhDŽom,RòHIP'g;?~$R|1B~|moyQ8;mA͕&)mNΈΊNS?VR'D(6IJ/׳OMW)‡WXoGCIVeB:xsQFW//\,V;Zń)WFαɁ%SE$w!ײ5S޿1ϧ0V!{4%brM6lct܀zzɄث)M2!iȄ5r1xEs}l囦-9ۚi+nBe^[=P|ԹFib_V3dMdcG.^țȩ!N;dZ-咆oOXZϬ[zXSSo[k<Ϫ턁!-6%;wC_8:KgDn߽8ճ:lH%ic]QD7<SNL`D ]9s?lҫg :^J;|v=2-:4âmG7?>}-V˕O{'gޫ_~x翄~m+;^|, "Ş0Ce/g>2F~iu/ Յ:˩iI^׏W>w闽r3qēc8Nc}noSK/~e:NҨWu" 1VOGUmEmjF&__B/. a>s{ EC:W\*Yazև|^"}t3~x<~BMM!biszYf=ߛrFۯ7݀xU,Rً>[ZgWNcCoFo!g_6 )1y3xeY4c3(㙯X^;C[o Y_O}xk[ƋP?\A+;loAЯk_c[3OCmfGEszzhE}-lR}sU"\{>)~7|,F9e?a| %{ ٽwƪmC/U$sw,w~M9e ?C*$2aսi4UuE;!6Wx/<.Wy ?a:YW)г[ճHCbrHZ4,nSx/!g~n[W>iȱJG6a~8-F9Αojf\LU!;q|ҶT¡37ޤ]ٯ"Isk|>= 4pFߪzQOh'iԓ}`z^Vt؊obo͕[#Pi_{5't{Zfʱn<=m z$fȵǺ4m>w`?kQx;w3‡?o}/{M^ۀRaA4xoYiOC/QPoOq7;ͅ t6Nܗ^w|͒S.tߣ+0G4lh?;pUu<Ի͞^ezU*/rYc}^Msꚧ3?6c+9*ZUu|M^yа^1_W]?k Vt ?">u4yp=덹~@mu4`T~ *ec{*٦)ߞfm<֪iuύekn.oc:~ٰ" ʞAco[w-3 -k_~׊?i~G>G].,txpm]8 /"O- y,x`,OI<|of˷|ouG: q;%[O~]tRCxg g6|KxP)j/;u|ƀwUgQ!Lܪo$vq{AW'aK_tV+tlm>I?JzO KX>0v~I\K f#lMzrvc>=$8zŕg;cK5 ׆7NW%ED7#gJ:Ya]aU'N}\tXt%>g3uEKA~ <]\]#g hCgu6nn<]pdr]csѽl ?Tv3jЫ:5繵N}Y^:^aK^<=9~Bspn{tW"8?v֎նw΁u>Q+;կy,NU 8tA9޻@sVeVSrK^oaB=Lo겵whm~Vuf@H2r&#Д>tǏلejL=z{Ya9ö>[7_s4$as}̧X}Mb~[~}WESNp|-R|ۦn~va:^12a+y2mj驯ꄞ1jg2m=$ǸwhqWEd z]$Z{;he&~qg:xuVx#o%iƆi`?7OBp[4&|ygPՀ3P5O;wM-^c9cxhr#ɍ4~Ŵ0tp?Æ^9O.ތ]nVܩAA8æO݈kwv';>槅z7>d*pk| $Uq "%k<^ª-UEp/yBэ5Co5/i\3U욡qq:LJXvMzZ]j2c758F8dTFm0=lP #̧= kH˵0RҰP栜1_oo {q3>?O6 [kq~t t[/v ooק&+x60_5$ղAw1^bV5,oٍ>EɢiE*(ϯs&>kOrObC4^7?ձͽ\Bˬ|CovO[7ˣ<:yA_nHlUU'/kN^e-NZddmtF4ƦU~MW"8);oft3upS~*gS˨u3ޔ^Nf|]]?( 1Wa up]O*ك(ߠWɅ!JgDF/l9|{=mhU\^.sGkC -ۯ{U.97{ezY6ls 捞^d}1=s=I{;ULo=tO# nηcKczjE>Vwщxљm_n3iF'k}<'ɻwBxB9; +ѭ9O-kUynjWnyyM00Mx| [YK-kq<>߷P$ }Ӓ#޾kk'eXy1+oEO^&Sph)x4 o8h߰h-=:/|_R?[qyϝ0t=7xɻ&qN/+;I#pn{V-Um(:Dz: $(hgzY:wr5'1ӿihm6)لBwpgu<[ [̌zHǦU4t}GG/eȖþ_o;l7㏆pdPk4k)VMtvhZYB4z4vcL3/oCotkg铢K8;Scv+c&V}~/6G>'SәM>i]!NM>v3x|+ x-fXO޶ ɴJgo7$WR oH#~ ɵڿ!yߐ\Y|+dM:Pߐ<\~ߐoH_C! [;ut/T8{|S{i+NKA_;%o8jn9靡vՒVx-m=ؠpR]^~\LHN3WZK%..H:2F}w)؞Ds%vm/S?œױx9ay-'2e\Sh'{H=Hm/w'}Nv;@/0*je+>߄;7ua4?L;!uE];cN>~N?ط4*R^c'$ud0^xzm@^^auh'6/M^$:P&\߿Su+,U>~K.堜̮L-e:+FO^~@~7W+lBz=qX vBy}KCryn^J{{M'ڔ'6OUSkќwZ7Lgr~|?R>Y+6y>Cpѕ E7tIoCJ>|cwŶ{ @2RNzqb i?Lkt=') hJf!mLrԡ+);ؘnX6&h+TVp& O!;<#G=tI1.S${ڸ^+!D/;+oOV?3oӫ yzI޾4koer&;3z=Z;&o[kzɓ׌ݾ?WNҚ@}`{ȇ"WBk @u*pY|RnXeC`ihm YU֡7eb;OF)ߏ'{)ׄloRgtl Sxpn4yrω5:=:+MRnPUpSԱl {m`wEzla)M7W]yo)<e 3X;(=c >*D]~OD>F/A?=8Ȩ!kۚǺS`y/F Ǧy|5?ҎR}+!nuCcmW]b9»yiy79OV]LufJuK~Ai'>=,'TwS8{W3I.N>m[}tvC{KBX.;x!?f0VpI)e.g#8pma~QY/,t'w\H'fmvщ5xyc}4AN%zX!9!9NN㵟Yhf]*Z2}M;L!ٮ!8OѷBpzU(wM&R!ӌSOw.Cޮ"E Y@t"+YEtmBLwl }*Ԁotѧ~D`Vq(O5_!ݴ,:t(馟(>V*etr]w::}nj"O-A ѫN!8:TiszR;bKVŖꇷ |Yѕܐ+|&.}%ۈ]+ö認e#ƽrIԖ)N!OLoɆm @>wx݊zV(N)G3Nؽ;]8l )ҟC|ƝC 괭Е4P;YcU Ƿ,tYjp(jJ)9cI:!5 vX{g#;{urf};{HnL|E_.2dU!>Rem7 ȃT6TY~ ~ƻadtsW O"O[ZEl3׊?|P0SgtڐSt;Uޟ\O2LB| ??9o +w "xJd\˚_VZ˚O.Ot36scupSԿl݊bZ:r,(vy8_tm_.]Wꯟ.ф+] ѕ)2կ3#]);oVtCt- cECWY_7Ul)ê'hBOͯIN]'GyFl9MӬmSu__cQ^Yl k kƻUl>~mr:}Km> ۘB=z_OSOaS[-S{iWqr1{-7(cxʊ3e>PW)mֱvp+ۿ6!8kl3lgg(L> w5\-S7;$1EvwS,2W.05$ֲ ;H'VՃmc%w6Q"oyx{/G9V޻!8__kL Qr@m7זσu hބg2]<-k*7)>o7 <|S_1Ч\?k?4zF*pWhBw UX-~ޮB۱_[K.*p^yi /Λ[gg\?yjVq=zcqY?Oh;={۵ΟW9K|*.&Cp^9hɟ[4ω1$Oێ:TE][ol;;5R8ȿa~9Nͱsf'Py ɄK3gO*~i{B_]']s.}t ko߯#|,6W\Kqz_;uk!> =:ӊsLޮEKp _;oſ&ۓޱGm>aK|<ﴛ]t*o'}k~)6Vmsvlm;_lLFF/߿V(>H<;'}`DK w_ʄ}~c5י{r@ܥ^(@|\^g| of"/3t6<b "pU!Oɔwvo(#lw´pꗅ ouP~WP;<= P;<=*T??B…Lyy};φZ;~<[w ءu{y1 1iY@oݯdncً8Kg2bn6Ѡ*pCb*p_x[g|RM߲z]]4a{5sf7r 9>jQzjV~m;R48/#Cp7gs)/+Gss \~YPKyy9P;pvxJߕ R.oP~(;~ool) a?ƿo#z׉?n~;m)~շBpg|ҿ' ~?'~K`o'oX$~W6~Z'u[?ȆM=rșy$0 5DZN}uX'yI.Rd+ '%-1L-~7Xnx4%vcr#^!XjX+zpQK+*+ .Q%ˋ(*:Stm c:5FԜb|'_fZk5X]uj, ~-~w(QHw#[34k0`XЇ/J|v E"8+ewV'{{'&%uݐo@5£k @?:*>R<ׯTO&*}PnP~ .@hh|*P&*Ys ^GZ0EpFWƧ<@|ݐN9m_JwNyBp^,'넷D8W_!Nx[&U fZ y/םMx6 WGg&` .KTK+Skv _dór{Og+R <[&_QZҾ89(}QDכf+|㺇aيZCDk?>=a9Z=U7;K%t% vۛK:UJ9<:w`,8‘T]]>|V'|诧phbUCxE ٥1{ҦaZ& -~,n\.Nإ:yL]jMO-!Cr)hL@SO?3e4*FkNݥN҈9Rc?zy>TPL~迢k)¡C4z?o~E~mΧ_g,azێ诳̙3 x8-獿D7csn&Cm+Klߘ+%yY!m !kHHfMx[ݛ6tM̆mE:J t֓:i`9NV<#h/L~&;R /zS*{ /MHEqmrWCѰD;2:} ~*߮= //8u BOD_< P[Z⇖*0S0Kut*kwy>g zt]Z!eɕuzф\V- St)NS?d~)+Co} n|mBе}N9et 5&qݯ)|Fií3?ys4D˻V}yWHUqS@Kz7|etߴqוBkZ!8L=ҧY=m CCWSv׻t I¡>FK+4x0{W׊L?dms{z&[(Wif"r1|EΉZh1;'wbX!w-9lmg9^֍(;zJ.x@G@Ҕ,,q72 ). 100 , 010 , 001 , 100 ( ), 001 , 101 , 010 , 110 ( 2 1   f f Ïîñòðîèì âåêòîð 2 1 f f g  : ), 010 , 000 , 100 , 001 ( ) 011 , 101 , 110 , 011 )( 110 , 010 , 101 , 001 (   g ò.å. . 1  g Ïðîâåðèì òåïåðü ëèíåéíóþ íåçàâèñèìîñòü ñèñòåìû âåêòîðîâ   g f f , , 2 1 . Ïîñòðîèì âåêòîðû 3 2 1 , , e e e : ), 001 , 101 , 010 , 010 ( 2 1 1   g f f e ), 100 , 010 , 001 , 000 ( 2 1 2   g f f e ) 010 , 000 , 100 , 001 ( 2 1 3   g f f e . Î÷åâèäíî, âåêòîðû 3 2 1 , , e e e íîðìèðîâàíû, ñëåäîâàòåëüíî, ñèñòåìà âåêòîðîâ   g f f , , 2 1 ëèíåéíî-íåçàâèñèìà. Òàêèì îáðàçîì, íàì óäàëîñü ïîïîëíèòü ñèñòåìó âåêòîðîâ   2 1 , f f åùå îäíèì âåêòîðîì 2 1 f f g  . Íà âîïðîñ, ìîæíî ëè ïîïîëíèòü ñèñòåìó   g f f f k , ,..., , 2 1 , ãäå k f f f g .. 2 1  , îòâå÷à- åò ñëåäóþùåå Óòâåðæäåíèå 3. Ñèñòåìà âåêòîðîâ   g f f f k , ,..., , 2 1 , ãäå k f f f g .. 2 1  , íåïîïîëíÿå- ìà. Äîêàçàòåëüñòâî. Èç òåîðåìû 1 ñëåäóåò, ÷òî äëÿ òîãî, ÷òîáû ñèñòå- ìà   g f f f k , ,..., , 2 1 áûëà ïîïîëíÿåìîé, íåîáõîäèìî âûïîëíåíèå ðàâåíñòâà 1 ... 2 1  g f f f k . Òàê êàê ) ... ( ... ... 2 1 2 1 2 1 k k k f f f f f f g f f f  , òî 0 0 ... 2 1   g f f f k . Òà- êèì îáðàçîì, íåîáõîäèìîå óñëîâèå òåîðåìû 1 íå âûïîëíÿåòñÿ. Ýòî ãîâîðèò î òîì, ÷òî ñèñòåìà   g f f f k , ,..., , 2 1 íåïîïîëíÿåìà. Óòâåðæäåíèå 3 äîêàçàíî. Òåîðåìà 2. Ïóñòü ñèñòåìà âåêòîðîâ   k s s s ,..., , 2 1 ëèíåéíî-íåçàâèñèìà. Ïóñòü òàêæå ñèñòåìà âåêòîðîâ   k a a a ,..., , 2 1 òàêîâà, ÷òî ) , 1 , ( 0 k j i a s j i   . Òîãäà ñèñòå- ìà   k f f f ,..., , 2 1 , ãäå ) , 1 ( k i va s f i i i   , ÿâëÿåòñÿ ëèíåéíî-íåçàâèñèìîé. Äîêàçàòåëüñòâî. Ïðåäïîëîæèì, óñëîâèÿ òåîðåìû âûïîëíåíû. Ïóñòü ) , 1 ( , k i i i    òàêîâû, ÷òî i i k i i i k i f f   1 1      , îòêóäà ) ( ) ( 1 1 i i i i k i i i i i k i a v s a v s          . (3) Óìíîæèì îáå ÷àñòè (3) íà âåêòîð i k i s 1   . Ó÷èòûâàÿ, ÷òî , , 1 1 1 1 1 1 i i k i i k i i i k i i i k i i k i i i k i s s s s s s                                                   à òàêæå , 0 1 1 1 1                                           i k i i i k i i k i i i k i S a s a   ïîëó÷àåì ñëåäóþùåå ðàâåíñòâî: , 1 1 i i k i i i k i S S        îòêóäà, â ñèëó ëèíåéíîé íåçàâèñèìîñòè âåêòîðîâ k S S S ,..., , 2 1 , âûòå- êàåò ) , 1 ( k i i i     . Òåîðåìà 2 äîêàçàíà. Fx pU׹!41@&!C'38Uk">Fm+Zm-E;C/PJ"@#": B"J;bI~랳{Iۙ0Y{^+$b N"E%802MdZG_!2AEܿs\ټ9=OY~8OF~v\w@^d!hV+LI V"ܕ~+y}W}Ț*]oMVyM2P̏0?Ԇ@eFf}|WCyۣy`A2N2;W6K JLMlyl_﯂-ǗӘ~XrQK/!S .ϖG[vJ,H.Ư_ep2 J$UJyj|:i*#vti7=dY͹2.yT5e PadL".{xH۝-=d+P9b*ipV<yk=#?re{n~mDJ VƯ:׷U ·ON'FN~0eRVzTH[ N;KuX. Vۙ۫@(itT~+>?|UZ,V^Ϧ;x~p {eo^/΄MvTǭmʟNVN={4^tm>t.hyʐݬ]q3(g{:WOqr:xɨ,'ãfӽP^LP7]gf6ng޽SٗXCCR4gDG.bxF_0[m00X_׵5ka 봊=.`13gJiCsFψR3|x {}@ 1 P?μqr`vc?q?=ʶm7w|}v{}+bb>ϒZ"wyԆn5QmDitJiH+_~8}r˭WsYmn~kckh)%X갻ѯ1q,VN-jΫ%G=MW؈2{=1n.\$ͫ<5Z?S_-gt.θ80y[~Fo|]l_ KVv4waKqq:f8:_Foo׸M܍-G͝s:Tp5<_cn3c#{c;㋱{8/]Μ-թe_㧞^{u>m}k4s *-0goQ]'R]QB<>}9?2& 'hmM`װO bO&FxY{]/wgo33|#9jm4k=L+?>vDDEѩ__zΥfrg9zw qS ?sd8u].BЃw#i W=c657Z!W@Vua8$cZlrfZ<ߟ ٽ[[}7k IF 38F {썞~Wuh.4V'!.M踝̸{X)~!y>kLT'H۬p/6?xH\cu@"7T89VCc5eW>%!֌|ֈԶI͵+b5NT~Lj025F֏X AdY磎؊:##x\ 6xbu1]x8}  NCrU _汞vK*$'8Wo<ظ=_Oo=9~ 6?d-r;\y,Zμ{ bg̱uZÓ' ͒ezo@MN{Xw#Y~Yw:.Gp ?5 ^'xx-/9o,ڪ3I7uh]jmSMl ٞ36Q>dHI80iB:ƆYZwF cn Z (.LNմ&g,oqm|^7nɭ{k89Q=YmF{d]L|Mmi>G֏qΠ#V[|h-dtOwk/` ` ` ` ` ` ` ` |j`l@@@@1 %Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:27  B TBB(16`2`/wB1< dS\{пx ^EuoW$$|Xp#P"m|$v bV?MZ)Z[Vւ"nI Dw{n޽s?6Ƽd̜;33g93wqQ]pƸ(Zp(hK5((zFѸ@0U@wDJgНW^s4?:?Z-.Ίޭ+P{%ueLVKM K4uznR[^\rݐMeuW_aBB.ECerM ޛ^[є{,D˔I~}?EWGXnv-q]x%Q45S/Vڤ=8=ѧ..)ک#:s1vS8~W~˂zRsgcƽXU}/VMj:0i۞m=GQ?MkǴ Mϼ(RF+G.)NSF)!{w;5veWŻrW櫣WƼ@?[yޑG~oSQzy~I7ktʔ˕YV MPLYG5ѳѯCQE> /NS<3l[pB~_2B}BV>mTO֩_*mW moV8] W dۦ\mpڥѿgǢ~lnKXRΚh ֨ODYod8>*w]¿(Wyw{ݩ{L..׈3+AAVc1ѥ5J Ju= 3N, >~O=eI%6AK'6 x|A+:i)߭ qozEO ')y~y QB" =oA~5Hs󹪋7X^MHruz l]$$ԐEM>4\1^DH=CĀ׌{Dܰy9o7AoK߸vfԚݻlՔ/5^hyƍG\2#.A))ߴO`<7B.Z{9Qq֓oU-^SG$.AHqQߢ9Ee퍇N:EzBMˡgV`r /UnB#oi{n4bBCE> lF1γ4Їu3qI\1f$Yui<+.Z$]Shewb|2軍)xqw~|'^[ gbɥ~&c}k4fs1L;۴=)z޼r> -xH#5lL0}djzjCW^Ɖ 5 ҕzՎѕt]CzѢOA#ڣ,|G/kfUAzy~5#oTs~ROB5!z[BEpFWB@$+R=~4t|ˣ>Z|[q.]W%R0]8$]F8dnanD{%|inF>. :>nzz6e4sӉc6u`E++pl>#tK$U|b7Ò: ܭh5ߺ;VŋpSGWlįҿX`^lJ^wVKflB׿VY:^sx͛HCs+&]6@ 4MWuzk/GCWc]I54^TOJd]m\J8+:zjֶ"hMt_<+2o9L6{%GmۙbvL6mmӏiIaNTwi>_W u(cfE}\ ]Lu+z4`?^;Om>Ibp[kWEkMB~ll!]^ {mXmk^;Y 'Z/&tךf)k@!IDz \^}=z[(~׷ž* *8>P}t>f< q&dm}kԪku>Po|F9ooж-+'?̚Zk_~X睛UģCVO=eBLKuCpʌ^n^u4׉GC/t:ϛ>kzn6yeAz4B@W)CGWqQS?}[JOPOTk^g|Yc)YcQt>lHoJttBgߞy"GgǷ0ߓٯ GP`~%Gg7^f|}b6^ 4= wZnp~aep8s܎wǧ }MRFF9*3z1F2!~uRgg?to yUeu jK[׶[R睛tGtve: gZ ~>ٍ^d%ӫYI?==R睛x49?H+;NooٴiI^F׾W:~2Ss >.](|rhH߶lV?a~/|6_?ׇwx[M'&;`-p@p* 6'@lt=*=_/fScb&`'\Lʹ'o?`Y9ꢌN D`|Lv`7:rփ::@'9F;-'<4#̙є2Xg=Y>:Wov.'^Y腎mps57TUCٓqXv/;~iA;xؚ2rWFWRѵGYf;1;O,>;7M/ꟊ 7q&cҟB:[42 _t{:iKp-h!qH8d>m)Hnf-2~nz>-iuCl +>>l,"6eXS>ӔuiYP{X[4Ʒۭ|5Mj?Bs}o-^y 7çf`MWĞ^\b;gj؝5.u`RhoI^z_ B:i !Y/{•=NvtŽVkGa<E׏y (yh1(_:M_vհ=¬8[ף&"z>6{T6o\}A !+}[+WYۊ࿥5z<]~1~߅Le)]s!٠G @hlt=M=Cot] 8)[6mՇO]*3>yv{s|R~_`6R>L?ϻUfq.Zk@鹹U H^),=.>]QgGN[|= 8Cޣ99 ~Q3`zٴ=KiJ3'a8]:=O6+DٙQ|eVZT-1Kc_)-۳:yH+xm'lNoZƩb@|2}ٳ>,8Z9ѣ k%8BNH;W+X; \Y}oӋr6ݣBpy (BMs-.]U&P}LKI .ɽ* ;B\>l E,.<[࿥f|vVدPwޚgls_kݚ}RmtFMU*|6*Kkyt# ~߄۪iZw,? <5gA#;[;k2]v.kAM};|VpQ7UxWkx<7'.kv"Ǒ#6+fd&+Ǵml&o'm֍ vxXfQP^k2We_ڠtm''MLLbx~[ ro{ߎST/aމr{㔏A]RQ֌V. kFoSlhFm(ᔴ%C@CsH{`h^'N}y:^h|(0Ɵ"5Fځ\3NuW P}=z]17%pym &pe=(׷lO%py_xޔ}v]?Ԕ^ToMY>g5m~=\(bxmwZL_'m)Y=uɘ6%:y#홳s}thG=z\k.c8 ׿%pe'A>Ԅ{+B&pyCټۣCv3<^Ϟ)?ձg{[ "{9c\1fN18oϬ3!83ȸU"z7a$gof])ɸ5z{)3RwO63թsrVgD) :ׇ3F׳_q53y<{;KCgwupXzR?EwwߛޟM{"{bS dЉ% >ZLy"Z{~tK=5 ;?wwp/ =N1r֚(;RyvPѐ\֚FOZڨɹC!uqoAr"!>sWǵ=Gy?kviou [˳pG=` pMVFO~f}>*<8I<ߊ?go/uTv еGkE[G;6yWxe66zA;+5C:-}ѕ;G 탫?9Cm#J=et͎z#WrazWxB_m\u߭ES|bƺ鰔]Ǐm+ Vl t)5hi(vv^>aש{4 >f` '%N'~P~۞c}.3f{O]]%QSSgv_cƉNљ8>~߲/ϛCl\_p^&݃H5m϶MNpSϺC1mɣfwLKcp=yҔqV~v+ *pqqb6r͞XN'&wu>txd޷ξ4pެgS #_Q!<NnHwi<vX  +DAR߄̞5zꛨ]N|}|}mjη#!$ތw/yzZ?)Ӑftbl[nR{ǧ&1'l||-58K"8Hvяf,nYs'g0o?0/U"87/up-'/'#=d];B-Rk TI{ʺ\kwϻ\gD3^~.Q^#:],N;סRvߵs|'ywr ݫovA6mfi2ֻveeQk@]^A3ֱO.7[m{Zn>?KE_*OղīqmiyOn\;/IQy7; I* i?V f`CW/ߠ*aPi:qW=)w{bwH tlCL-;Nac,dordhV|ռq3{q^K'.)ILiv97:elVB;&vepmŻކZcZf#=&|`vr5vة<>3#͍[_yT]+µ&s<6mwMӯL'ɉ5qJ&>Bp^'!ȵ]NW22.OAwU:ɮ;x?^خ>tkw^>f:w?'Cp 3pԡ+Qf+[+TfFFT-Ke>wS`oz[z'e{*>TvkEv{N|rK[9i}J ~Bl?)~ެhH={8Ϸ|MzxX_PfFR^iW }M ƀIq;o= +y`嶿`^ϳ 7< qKg)h:ȣ'iXfo53WHi*[-=mѶ~Gk QQ蒃k=i7w>{d |/4 P@].y'_;vy=2R4C1EkQ}Pټ |}94_Zevo -O "(ky#Xk?3WO|}6l=#E8lZLX?*>Q\S?E]:!=b/uy I{ " ` !;q>i 1AEU =z>?r}){G#齦g&4+boOoW)w;?D]I[{}JK]j=4z=Mb=jձR$fgu+3mO]r<^pEm1tPAmpgiu:QUُM{:ESs޷uE|hh=޹QEtmbkѬ9+46z=D:atBp~ݕ;k ?'l:C*{>q<'C:d]L<]0]9B)]3py3N_:lF?5'up]Oxީc>M!y x6^uwQk ק?Eи|T1W^O5lldK ^?*}H0Oh-D>v_/<`e+oppAL:x6ɧ|Ol үXwW*V2];Ay jc熔>Iaxer0X|C߳ѯ'cܶ &_ڷ0z=Sh`딶n1ƥЁUEH>Uye[F#5oν{$掵 g]zxWp㲍/' {{w҆7gV71yso9|"hKʭ//7I\(dѧu<4g_qu򛒺kbq#}AsYs3pwcUT=j4pn~x}M'ig>Iw&/1eity=t#X* p`㾨nbJ ;󡪮ӿ̿S^PV|>T^P^0,B5mB63^˂\^~=/X1z}NCA?dJ~|x~l"8q!ML+uʸƷqbmx\\;юMqËԆm;BϤr">?r~rn`/aR9P{&w{]I|Th)0F@fM[cZ >n=S:KY 2V~zU<"6ًĔPFd۠jc_YCƶJJBޗwh(JC=nI'5ƺWy^GyBd!Gk ДT ^\s!1]e/ {N=;t.#<{NF#;O޾$w~cL䅧W9ܩw)3Ӈ<ӍfyU"6pFL!]W= @/g(m:BpL}&(v@[o]e ,,v6l \dW[&Od7h'HHe|܇4(4>s;dF l8/){WA.Կ,\> sl\hx澆E-?5 <ö' }6.>1fN3-R~\=[2psX UkÓz|TfJw֡]kƜ'y|֜8WQh񟈟Br֟ +ρ 񣩡qXU|^Kr8,wx]2&9B:Ra3S:X`I4 d^yB9R9<񑚓]{C|_<齾{}}UVGΕ͒G^H{ .8'**P}yɁ߫3b<[A}u9f&j|r;CEn~ƪ]Ug|B_%Z:KH5?W/|cΦ=NSCn/,VܼH1ae($_2_|eQu M:)<:Tۏ8oj(no?ࣷ-!߾2;C?XQVz%kLǟ]-c=| Nq]x%]Lw?SG 8kh/<_G8KDk.f/8fP}c3eq$}=pݽӌYCl\V|MU}ѷ_t}#t`Ҷ=Z7%::9{,T?MkǴ ~hl,G]?MW2ߪXɔ)ck,!^[H]]+a|t<D2C^L(O3'TkKefߣ񙭟2PרogK:aac]+ҭX)0w}N嚊qR4'4H(#X̬$,vm=Z +'|K <|qqBu@;^>bh9dՐYkNu;Y3_⾓{/*o@a] !8곹Qvxv:Is䯭}c|C z(Re.7?~2sSn?Gg\2*]?F[lc3 ұh3ykйج3Ze{5߻x4v>2zEY ”^_;)W}Ǘ_ }U?WH6l r=Sg萱Uűeb|/swI6 v[ިЧ@bKMf M{َMR~6ve ԁm(#__ǵPV6/+I͖>{l#l0p(]vM/(=C٧|p:c ѥx}l5h|a೶eJ8GDw7*&ͮ]/u5 _I8%$f}5r eFz$ٓLᖴᄐA?.Di*onFi__9gsX|Ǔ=h f*|@o6qY /i`pinM!8o_"t$ Ka6v'7#7h^d?7F{tuPW4Y&`x*YU Ӷ}Q.wIYaolm:Xlƶ/ bCjBIsz w?}x+ycE4JW^r@wC*ww:zUesrPK/_5 A=?ה.C"d:4gEgW;Ge~D~'U5v -+das:Yncٛ}n@6;mRȦ/)٭ώWS7bw-`6B6lnE*g=k3.Ũ~a+mi=|Tw]{plwaeݯ^D+[)(bM{u7$yhVW0l_aߋ}' >^*U:Xch_${˒9lԏ?ɺxC*늾>`xTJ f{LV9unJmy ߞ_ǬE%ͽO{8#j e͜{bĞ! -hv6=o[$͡>ƏDLѿG-Qr6>g^"xږپV^͵[sΦ}lm|m@[!凾BB B *pNjOBpsW}p!8gT lm4kisº>&ca):>eXW&i+;8.+PEpFy*LYL񓪋mG9澲4iIZ_++z~X+3>2SȑblچvO)'\ί1|Eԇh⬯*CT\/ }^<֯/u2ab2M7OSU?֨?ңd7w2ǤGQ|S+_pծ!\ck|J'u§o(0V9oI|MOۧ4s1;KrK24cR!zfИ Yc{ϗ@zM66?nG{/h6F86N]gV7wB [Y}{]to]9u}ۗ&~X$k Ǎx=d7-T9e~*kMzA&ss'#Qe|8/*f~A SFҐެ:t+VK!{sױ7L˔k$5xy_,9pF7P3|/jF^U5vax\;2Zh\VՔ^9TmA-}Ufg_E8C^l"iV^?swI|/RZ&9{eM!Cp\Q}'rybI}?)I9A$'."I?x__5_(LP?+ěk/avctXJWhl>Ǘ߰gSTJT՘o ^m:.b A)WBD&m_|91L}¹/?@CI#h{$I[yIVYϐ˅ _~ŗC_}$m2[vd7/w5{9`TȦ[WMnY3%:&:*q³'<]M׏ 3ޡ^-|0_uռmr^ nSoTcJ-_xJj,W7%+Bpy%>@no8]p'Tip |"W@-ԗK_} >X-T.>׋l+;ڵRc;bfClzCuK*+zi=*}*yVM:YebP@gho?51Ⱍ\pi"_t Y2@{*-?=k8r2pmܷ5ߧr9|Y Gr?dUy9-.&]ss3w -S9?/=$'HC^?;ס_}Qez%|2{R׼:\^zRD 'Fzidkg^ѧqpg==D1'6*NRUvnOC:wmkwmg0_Qz{s&7ys^ޑ+uu}m=֙i%S ђ>'^]%k*๊R|V[ׯsmR!PR<6cuTXG?__*⡣CP3%WV>Ox5 ['=Y;7{'7+IgN_~_ݥ%i+\ mߔO՗Z_|3eZ?K[;1C9{,0 /26f*+L[=] H .OVCx,n5U =k~ ~]1gוnye{Dx &pOK6W0u<MsEYɷu>cpР>ntu23U3=اaj|U|:%6q~{G5P}KǁCH#+!o> *qwVg^ }bUyW'Ȧ8l#mz-21$gyyoZd/g3p~(/?3p~YhO*ПaY*VO@a[ߘ B;-C/*Hu$=w*vwR=R6],h[W{}SUiW|I;+M1S7;Əo7eLX6OK%0W?H 7GSMyI^e߭[e/' 4j*Q++N\q !_;d}%2xs8^oT0_ ŗ^=_NڗhI}9iMƩ۹s%jBN/d[{Ytf|(T.QP_xqhѣV4.CpY1ORU ~ku_ۊއe)O_k,J￉CeEpec>_7Mz:~h8f69/H!Tft{ߪiثv/1]ؿV\/bB(C%2za^M+^OoM|zkaV^͎CkFkMͦM@oOEvÙ*>t?R)Cδ'*7:>#(znt;'>SQ̻4 _,, 73 Ñëåäóþùèé ïðèìåð èëëþñòðèðóåò äàííóþ òåîðåìó. Ðàññìîòðèì ëèíåéíî-íåçàâèñèìóþ ñèñòåìó âåêòîðîâ   2 1 , s s : ). 100 , 001 , 010 , 001 ( ), 010 , 110 , 101 , 001 ( 2 1   s s Âåêòîðû ) 001 , 000 , 000 , 110 ( 1  a è ) 001 , 000 , 000 , 010 ( 2  a îðòîãîíàëüíû êàæäîìó èç âåêòîðîâ 1 s è 2 s . Ïðîâåðèì ëèíåéíóþ íåçàâèñèìîñòü âåêòîðîâ   2 1 , f f , ãäå ) 2 , 1 (   i va s f i i i : ). 101 , 001 , 010 , 011 ( ), 011 , 110 , 101 , 111 ( 2 1   f f Ïîñòðîèâ âåêòîðû ) 010 , 110 , 101 , 100 ( 2 1 1   f f e è ) 100 , 001 , 010 , 000 ( 2 1 2   f f e , óáåæ- äàåìñÿ â èõ íîðìèðîâàííîñòè, ÷òî äîêàçûâàåò ëèíåéíóþ íåçàâèñèìîñòü âåêòîðîâ 2 1 , f f . Ëåììà. Ïóñòü ýëåìåíòû áóëåâîé àëãåáðû ) 1 , 1 , , 1 (    n k n i a ik òàêîâû, ÷òî ïðè âñåõ ) 1 , 1 ( 0     n k a a j i jk ik . Òîãäà 0 1 1 1                 ik a n k n i . (4) Äîêàçàòåëüñòâî. Ðàñêðûâàÿ ñêîáêè â âûðàæåíèè (4), ïîëó÷àåì ñëàãàåìûå âèäà , ,... , 2 1 1 n nk k k a a a ãäå 1 , 1 ,..., , 2 1   n k k k n . Î÷åâèäíî, ñðåäè äàííûõ n ÷èñåë íàéäóò- ñÿ õîòÿ áû äâà ñîâïàäàþùèõ, òàê êàê â ïðîòèâíîì ñëó÷àå ïîëó÷èì n ðàçëè÷íûõ ÷èñåë, ÷òî ïðîòèâîðå÷èò óñëîâèþ ëåììû. Ñëåäîâàòåëüíî, 0 ,... , 2 1 1  n nk k k a a a äëÿ ëþáûõ íàáîðîâ n k k k ,..., , ( 2 1 ). Òîãäà 0 ... 2 2 1 1 1 1 ) ,..., 2 , 1 ( 1 1 1                    n nk k k n i k n k k k ik n k n i a a a a . Ëåììà äîêàçàíà. Òåîðåìà 3. Åñëè â n-ìåðíîì ïðîñòðàíñòâå âåêòîðû 1 2 1 ,..., ,  n f f f ëèíåéíî- íåçàâèñèìû è âåêòîð 1 2 1 ,..., ,   n f f f g íîðìèðîâàí, òî âåêòîðû 1 2 1 ,..., ,  n f f f ïîïàðíî-îðòîãîíàëüíû. Äîêàçàòåëüñòâî. Èç äîêàçàòåëüñòâà òåîðåìû î íåîáõîäèìûõ è äîñòàòî÷- íûõ óñëîâèÿõ ëèíåéíîé íåçàâèñèìîñòè âåêòîðîâ [1] ñëåäóåò, ÷òî ëèíåéíàÿ íåçàâèñèìîñòü âåêòîðîâ 1 2 1 ,..., ,  n f f f âëå÷åò íîðìèðîâàííîñòü âåêòîðîâ ) 1 , 1 ( ... ... 1 1 1 2 1       n i f f f f f f e n i i i i . Ïóñòü   1 , 1 , ,..., , 2 1    n i f in i i i    . Òîãäà , 2 , 1 2 , 1 2 2 , 1 22 12 1 , 1 1 , 1 1 1 , 1 21 11 ,..., , ... , ,..., , ... (        n i i i n i i i i e             ................................................................................... ) ,..., ... , 1 , 1 , 1 2 1 n n n i in n i n n          . Òàê êàê 1 , 1   g e i , òî F>x pU׹rC !ȣ5PR+աbUJ*R:Ѐ}Q^"4EP<D0r6CB.R gZߏ쟀u4%g݂"- ,:^dL|9ez0N㰟UZ.ⅾll+(iU`XZu$EndyI\ e]_Di$s\YlSKx)ccډg9m̻%;c.!IvZyb ߉HdGb;Uc5јS> 3غ+*),P~'MT\^C̳3'mIO>z2n-5Ʈ+/x 5CsX.Nm+&/rn<1:F׈QU'N#V'9~ c ?o[3$TVZ޲dw ^!AxKG=p9 n-%| KSL*$X#P}$_ϸ>#NNk+Lyn$ݬB6yPV׫KAzy0vMd8HۿI3YO=5;нl5V~il](YGŬ"m(g77< 5X}%|Gy}L܈>kYi2|ZgP)R*uȳHoûi xVc5Ğ b\c `X賃`1ȓ]bR$$H.>KJ?3@V;(s$rrN|'7ghk5 \ll#4aMހь8 s7:0k巰{i׃ fHJ09|" 'O3sc0 (=h%m{tc) 4&k#m3s;@1"YoVmg޳["ՑDֵc ܎d$8xY{tr\< @D0Sm0}4FtCkyKpcrsd'F']'_Ϗ"CIL˃[&v&-SZA{bkY59VĔPs&5l!vޛr!ehz-3ͥsׂr8Ws"5o95Kn跉יI&nw[U>KɌS>lw92.~)pys-?STy]U*:f:?v;_[k*um*]9|r8r7Ga3:ߚQW~w0b,V6Wm:RwPӿf7?]W=!}M5sה*w7@+װڦwa&>"/E<Ý&̋{ZSBz<ڑO]PBY=Wg.g</=2cM9XK[]+i &F= PlWFL|cy1og,U߬}&si|Ӷzv=53hlvmwSw^мb,=7ß1-gxQ;>tr[(߳[~E{o^;;>oZ o6_f4,tɛNjh>kS "_"l:.Ug=ƃ h4Π-'ÛɠU~֔;lNH0]͕wkv X T9YCK#!?fC欅KNGk^PM/KBMBJGwQz-^6,FlΊϪJ~ugwunXӗk>4r zɩtm٬V*}*&ʘWmsr;{ lhJ9zq(Y(VYCM XԲ\+YэX.?ޛ5i~5fOUm>h|mPZ3zߞ+џyV}єGVvG#9R}FSjRǪzZ,zqzae_at˚L7ژ^M[:ug6G2f,1]~cLu_*יF1b 1c y1c @sMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:28  a J(162H/1[ +{x E;@F$$z<`I JDX?'ab@u5(E@V@|!jDT\qAa]v^1$aHP߾}:g:D:uSzt!Q]p(Zã-H'Dr_ECQ EI)(ӄ_]KDF ⨢]ip31D]㕢oR]acrݝZeC&)LUV(誐aH )g5A*b7CYQkrO=m[Eʤ]]W\(Dm(~yۢ t}?(j^j{gzst40|}~8i~tDݫ[Um#:sC$JQMG٭u~WԮ<\\bsspĊh UHNmu[ִFG$m8kWt|WjB5 (QmB.~ >d zZ, u(A|clP"e@Ɩ6O/3A2[N_c?,sKk~ý{QD֌&xpP;[_\B= |l9WWQ{Boa?$z0\_BB9.oI|_Xn79_+۾~8[v>ܿppx_>f<>&-yp6~a(D\+i\ݲ-W!ޏ;~ԮCF| ,?J?cÝB'h3p߇4Mqn'w_PBpKv3NUr\;UOh#v~8,wQ;!C&w]HoO'g|3ѷߙJ=s-\1}Ԇt\d<ZI8no?~2p?sw,o#S|oWeo6][8vp2mO?L f-?<}p۪n+c̕/h/N)]O_^"xh#z(g] sMNs9)ɟeL.[NhDN zr+i 6DӤۋ'Xn(''9ϝR ,Tr"p̓3ygˑ^!CN`˞4 5.cɸ/҈4"Ew%<ⰼ}@yHgb*Q>KK)| Kߡ.;Uw>X6(GЦ I>&]ߧs$#<)Vyyu+ \`.ZFOGOEkm+T/z%+q^NдtO8CL`_>RF=]CܛHZǽ'^_eԁ?"IWܩ:?vɽ:bu&FSes^Zs0hPl}x?E`'<#F5UޗvNWcYډ+[a3Uݣ0?A:~',ؕ~td77KU ߯tQ?RvI<Xn^4LlSJ>6_ o~6?2whc`7g`giۓb? <u|+=\8Ž;-Q'KнnCuf+c/^."F&!}i3fUt9f0&OQ"ג1U}GJ_7Gо Iiqsyڢ{?[-9O[I{EBoq_z~-z9(gNJeGmJtN~uu5"xHo)> n׶nvӶ t&Cyj*{VXp<] NΔӿ>bU^W ַoOb^k?2s5Pޑ,K ,pkl`(# r_w9Rzm~6_p2U_B \܌E38՞_k)& [_XdNqiz9׶.Zφ7Dc.N=VNѽe5-`Gmcp˿[mO(VY)ooyT ~Z3u3EZDcu9q_V*y~V:7١;?VbK33/&oy6&<|k_IyQeѲ[Պ ᜭ]y维Qd>/rdK3w^r]lb}4Ge.s_]jzI¹qCb_|'/0SлGyލ޸%/3D,\{Ol)fi{6[DW*ଯF(w+in8Wl׬9CU9FmU6{R>X9 f7 ӡApDk8˵o{WN\&|oY߾*"!z+g0< /}L}—N҆oM&|>/ٯ>Q|H[}i/}oy.}CJ=mSvE(j|fiWOЕ|ۿ7Q@gݦw+qL٭eYgvXɾ}O< u8r? .wd'- ] u>Jc,kjzxn .P}<٠7*|n'y]`\x p^Ny|#7˵6H0oZr]+"g]jϽD8W<]vˁ-~i#7)o!|-joy8A2H0! rJڶ_yίcLco9-dwy]6G {lt/]3w~iׇF|"q@zÖؼt=]\)=^NƵmrw|r&x|ySye+Bv{9v㟻5}?n8 wOOG/bDn >\ !EY]9=\ d鳐HI-oD'4"-9cޞ%r`L;55S߭0W4~B< 3b! M?f$j3Pp iBtn Wgq> $Cl~ft湞;?)Y~ڗs}YP/ˏGh-O%oڡ*zLeTlN"G=2r{g5v9i~'y7dKw܅첪$wG߃hwee%B٨ zrmCCz}NΖm,4cܑ ;ߏa"{"pЯ+A<8(*w:[t#㱈ۆzV"lW(_mM۳%ni;hӄ5k m{wH9b%sVV]Vl!;֜#Sw{菺_7 ;$w%{;g1.R%N5n~zq$9D_.5۞:t:u ).9Ͻs4x%&:<{{= e&Ot\2`&6k8[wG/T̙җvS%Jl!^FF&g]W1eZ JuӊK8Nw(wm?۳ &MP e SAS< IE[E_ޗX_>SH}N}8ͯ|:_ξ/O+hNO@mϪ2j=D3lw8>g% == ؟Ӫ^;9s|~yO-8?wՂsͧZpmjp99p9 5oj۵ P?< P?<^ =s= =b]<</BpٹjE bjgu#;7μoȻ[KGI2fwEf,I8lā &ș~9ٚ" 5eBp}J`7DZz{y[WKg*ёmsaZ~/Ȟr.R}1?.M ;ҏ ~hWzE=Vc]="}9ϽI{SE,܏Wp2|O?j@Xe[ypSKgjD'ϒ3M ֙&t鳶}wM ,92~88-?wav́>2Xv́OiM D︝z5~x|Wz&n!}}/Gwg%@Izep[u$ΫOx ~f9K OaRu~&of{BRٕzpk%]FIgҰl&G֙!oW.# De~O ;LkE;VkEf"V,K"piʅGRU^)3晜+x z~nTSO3mQ@ .eJcm_[iԵ{d@2~^Uv{V|bg&$[9ʜ0\|=Uo'e/)_f%gu؟ۤ|_lcr[= ~"EVv3R¥ogmű~h|O>Rx`eHOQpGxb.ו=E)=8 /g+T<7aA^\w+Cc/^͕>FЙƾ'og4IeɈ 6H[lģEF#m!+4̮Co_suqsq2.cɸh[\]@<z3D?wnow/Όug?67N.Or߈j~|O(tfL3cFTΙ1gFTv|>v[jJ3nv?M;| U`oG~rӭ/8;q‹sb|]W󃴤<=;!׷9Pv|wz*|m})?tȹzFs`kÏ?'ߦwƻh1Yh75C<@U"iDL_ ʗ*f׾$m凊|y/?MB6b/X"Uu"u}@-aW niq%MmohWFҾWt/B zok/?Pmjp/. <ן}C~g_4 .U q}p59 =;1 }q|1ag|f{ gL2p+5_(ck;os+gT!?KG{^^_<4 $Qobp)· [Sy~KR=c~g8Ϗ^Hb=@ypKҏ6c֏JMhЋX=zݛ~, F婜 я7dϾ=1<~f9|oя?x?$\q`nW~%Mؤa]+?*+i" Y!6?ϟoB1bpV[O-bpkv)w"ϽTD"pȃo I}W{mGOQ6`vI~x z^7~e%[}exl*g MNT>|7ߩmnݚu+_㚣 pnj58)ae/cCWߊOÓ:B/>t|d?7=6ySFLՙ{`4MOj 54<|.kY;v<4 ɓ[Z8!cA_ /Q|k7Ќu_|ߤA˗ڎ{J>}h[,o=jvI)MVٯU e2hN[$eI[y_}/ f_1ˏS}T1O|h_Z3$)I_pjl(|Іk/Ŗ+3hwKfyyx;ݣ 6EJf pEfA 08?Ys>BynX*]!*}SBt.>Oɏ-BBt.\OREE)Ǿ\&-s}Ǿ?!e<{=Ƹ^{=ޡu~k*vU7ʦ|.UNJOrCx=Fpy [Z3Eɂ2\v:syj\RuȮ12ݓ*a~2~Q~䠤wIs#R7ֽlɻ"sʯ"Qqg3?"}RNzKDs+TOds$s?+<hsOz6Ӿ~$WXuhoG"ϝvs/ֺa|34*w@mE}~"qo/2pw 9ED~Ԃz;DBp3~]~ kS*zل<ӈ~,{ݲgM^ 3y{FzlcGXUף@ޓg9rǷ`RXy|?wߏss?39=dMڴX+' ٴeJL^UoE@Eml4-Rݛ|7c+ ?YNž%ү 'Km{0U{O[$uI,߻ bCOƹCkҽX8(FeMڞbRͷor CE:[SxvY(&Ki}(I[?I[s"Zi+_˶T}VPi嵿_=Ͻ[| bƗ~}Q@g|)7!^<9p*wd57@CsNCr3y(8 5uCvo{UN-^<{E۪&Ϥ]:z@z-m-ty6FO(CzzT%l[~Oߠ"p|_#$Gߕ$'}Z{}W>GfLNz,GN^o ?1 rg U)m_ޒ}u'EOtCHOt<7=P&'-ppcߗsCuL)OʓEyR>I! >'r';G;}᫗gz'SϴBfj3ݟ[skNj"R{=E-n^ҳ_ْ}/?ҳdz{|I:w9pC'㡡s;ar>V_(~郵߆ ݇vf6a ųfͽw%ҫ(dRqR l݇֐OV_7k_C\.3e{lỔ5Q-i+?BIʧ$m~\"JL9V ^ތ5ܭ1;Nz(LUxrgu ;9Yx4{wQI1Bh2㣔4ll3V4dȯۊϾ}/OZƯyeN1Ov9c| |Z{{dz=H[ތw Mppsf:8 YnIh\ $9ur_#4>i!4LR5{UƯq]\qpdvqZk39ԫ96It\uK%j>=X`2VLRcNlʾZ뼃X\gR;Xzcex|Q過d:_~-͚ _5+k"Ұڙ띃x5;Y֚G:E6m>ĨZ|!|K?g)$[bk2+,7C828){Byy~O֚(sD\pR#>e߼C#o^ۤF^#->~+[n: Ykz:kOeM, OnJ#wQ(w:grG$_xqmh|6@5I󅡷2hrDzEZnq&|G=WyQL9-_f=NQpuϺvJ>^~1[*UD?kZw|'躖UNc! .ɞ߿tE+VRn9Cug]j{/U~6w)ƯV*>{={6WzB-_.jGCO[)H/>:cx"Д'̃+LԟɊ +BeDoxT%meD>zƞf[묽MBk@oGKEhh:ZUKy⥲Ke}fu#{[E_h̅ա:rf HI>x`Q<6Zw@ Дɸ}k䢹>[F޵-FfC5{Ol~.G<ߚzv|84;{ZdӦvO&((;ypW(&t+ |\s9]? |S7)htlԷTS28ވ/P}V5φogqkfݕoO?㕦g^y~1,>~#r q01rrU=6~s :s׮lyBoWJ̕JRmɈJ=Pk-rlÊFfm>d޻#k|깉_mkL_s^I~XcghZ.7ĮS"ZOB_Ch|g~Jٳ2=+[ny?YA2.P_B…2/>vYƏ!8i0K?(VԄ"2)69:MC?Fᵫyz5 ~(X`ޭ/qUfGį_VG/$oV }8^`v&1tѕOԎ7'*lpf+$.W_5ٯ^Ѣ"o:Y$!@9sچncz(0v/dQ#hͼHlIagjȃ+0J7UNɣMβN+* _ )rv^Ư*Ha_~:͝HWw.'"Rڛ?T䝈8|B+4;L-ơ4k6q-.-y_Cп»)ypW䧹ɴ~ޱEi_WڥAEx6r]tƷΎW/kb~ٴyWVp0ʘ g ^6nT'5YWz*lf VſI|DW2(y4y0!Xhܪ`p{ߤ01)c|X3w*V2KVQ7*{NgtV }\Z`WV4SJա~oŞɷv-,<(#@']s: ˷۔7[A 5fnTn; jܰBX"DQKIߓn&EksʎbDO""Lm=3y}.'Ἒ|}16;_)p,XIg^ɦٴ{G;!.]~] ,sTV3\U6\?6pLp_$+bʱoRn/Ӄs6O=}=gtL>{.`Sx`C}*q O76ϖ S>~cD[s-)g-{ma3yĸm-4~m][ lM[ڀl.a[H=lBҍ.0;Mi[q&9o'm \2VsXzBlW=?%7oU+`іAoa$MaE=4S2hat!6ۯqܕ|EΏΕl΋K!Ex׷=v3Gv040|ؿ}ڹ'>х__u=m3ɑCɊwkB-?+תa SpĊ!;Ggwl۲5:"iYGǪΣS1φy2/۹7|,R_p6gswF3Ϸ3~Q[Z|7\ex<߮Sٝ ^߈qoл͇Kx?itkG<>_ˢL' c:oc{t望KmA7>veYvfž>$i_Lj1j1m'es}=B j=^ɝėo,^{۾M<5GLaWY{}uF_EWU\{LdK5C䳵"ӂ/xgkz: fZB6;t%QEQ4n=7to*qWLm\_1_Lofza_#?ܞzVՆ1*3yBnkɓKSn}#?2IwyQM(BF_DάtEaާ]y KF~:$~{~!+7q_a dt=~ߊG˿WY\D~_9m9?vѻEA_jJjvck:4gʯfGtr~xbQNO3I^>9dP#^Kolز8g |F+p1n+j9Þ#S*߻wLM{ë{k] q ̪ste"SH+֕(츲ȖԽRD:J%JoP: ybY->* 'U>']ze$T0d`DzW_'MI#]wG+*Li$9$S `T lD3ˤ ^FJl$!C RފJ*Eo$H>c*>dKM@.OH,go;q,1s2QiH#$'f˩H]Gبk3mV0޳d\+ˬY]]kr!XO`x(_[ FXy\XsLBY@umJ ;UF=t/Un~$DIۃҧ׻zK=ު^F_׀{.ӿID oUI%rGLҡ>JT292h߅p}6ө͏Nm̫-s ;ɿ .'xxI92hȥ;Ϥ 5:Y*d>< @s2ϋv뺘|_} MqUS 'KFҪ,9 ckS]ay UY/C7T-6py+ |bE+px$sRޞ7Orp<2[9zF+kמ庣ḟ7\[ճ\&= rp=} rzWbyг_4ʳWe!\e\Llpv 3s*x 8\~5\&olr>otCry՗pr&2p|P ~ wo4hKP#Oi*1QYr7|=^N@ƌƖ3F`+=s9S.QmIQm׵2U=veme܅=v6{g>θ[xǬ{uIƞZ;{\N8y*U=vT+?poT)&we8`"{>Ѽ=qe3a@K;&aծ4f.=Lb&Ɣm{Oʎu:}[7E: |sP{>2+K92-}/f>j32I%O+@4=w} fW~-a~LrQWuoItIҘst=}rλk-V.{< u85ĺdo{8E\m_vӹtgO[gӪsFI>nS|gcMgmr9yϚjLorkk(ۯM^+(XޮSKM튝hgzldz̷q6Rmw:Nv^: jsטS{\E?s*l+yi3s+|Pۮc,2A(*WVvs` ];罳yz6}gšo_" D0a @ccUB( UGZ  T-@zu+N:MM|S fO"{+ն}|^;e InM?H+s{: S.,ڽ l>|]Lwyj/Y~XK <+~+!DyD.w~w`d $ZGҮ}<nETkpr.BȚy}%gk<IoD#w/f_,d_LS6]_J7W}qjKkx}`yoEUQ BxӐ&|0LYSn㥱s[zI<ڟ8 K>A@O#Kua71H"3N&LY_)7 ` nkj $M@_4/=o=ROtVp܎4<gy.1 )+瓁]YEܗ'!>jNR  FXvW_vp}|ZSrg Z>vR瑪qeHZHEL>K3r<hz}*&,EN8wa'OͮLߏiIYZ }as*H{(|cC+d&@dv=H߀1UHǫ?rN$9^12/GW07ŝI㭫7o͇myw>j5 웏#1;Un dD+7^K9i.iigf2@.ldڍ_r.GkEY'-#ٕzgѻ>a=6} NC6$ ;6ȗrge;3/p Cc&]qw#5CxlCw} 6;R\x[v呸 {q vm$W]q ^~q ZepcLlȉer_Sh; G\k=XÑ!ʸ}ƱFرX6][̄JkK [q [-u'2VG/@" D0K`B "Z" D0?8IFMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:28  @ : C0 8 (16+2+/"F 1!hȬ{/x E;$#A%00H$Fn>TĕAX]n@E#^$UPQ₊ ^^"[܅uyebvR]UI mh6\y\"mPiߡliS!dyDrwrg<+y0y(tz8yD$O)}SdImVRҖ>@KJ&KtlsOmTLgpoFGHw(ֲ9nb {Nق1)++>׿R~Yٽ!xV~CcY15n듦(yVdW&JmOKXqxk㲧3i-}npE<>!sd{>#V^2=++0/V5=-P]|c{'vWewOO^:9@woLOI>zJ:N+w([T:W9zb]69Xc}]7<'L)\"B ^d̽N]p$3ڈ#*/=(;"oz|m! _)StNzQ#~<_OS*PuixSLC<~+%.T~[[ߢO =.|:~%bJKI`,Gir?͟uIzO4^qm']M'%)3'Gqd,EOzI:$]Kɲlss5QOI ?C^z=DMg:M1|18ZNJ?u&cg-M ^Gxa%^6a}W'WUxe#K ׮&y7į^Ձ;Dw.{>V_3}GPwn&Z,qrz=t=ug5[݃.tW;~AeJz06]ro!d?5&4PGW CXP˔:{!r;ϑ-~J5Z+^:FSO<N{;MaU $+Ό=e:zɊ:{!Yql 2:Ycn:|o\|!l55ϣ1?I* X!,(Ï%c-TY'YW?$ÊSte篶=g8D>j_T7)_~Vk-\Ke/_ڃ: Xzz3c{ sΊ,0{Hc/ΜiΔ'8kff0N=x=g;y 4窬 bkbڳ6u|[mٻ2cݷcgnEK`#G$G_nӳ.f]8 y}}K5=ù[+wW;o^hrNsM}fU>[|#7~F3EB9"<ڒ}uӌ4ؘ=N=+Umwo 篌o_}E2{>o{y&cn/Ueӯ6 0:vs _=d̿(ݛ<e ~{G <W-]yȼu@8)Q8?n%2='RwRwT:įDUk"vj1;bd;zӧY [.;Q ЩG& 2;ן]CtaJOSLp"`>Rv]u`cvͪU!U ~h2_&*VoΗ_sVwP#m2Ȯ:vU?߅gfW$!Q \zZ]ffvPl^7ٕyux\ٺWM;%|&cn:z:~q_a=z̽tć!wNCpԶ3O j27M!V!Kksr*]"֢k>jzj1m4>fiV֏2X_oпs+KIV{I/)dJI|Lyw 1HgTVA=|A} [A'Ø)i'"6bR{J.X<߮Eksa)Cq-<7 Gw_Dי8bZ󋬍~,lwZz _|#_X munEs6YQ+Vw)aٹ|!|$aeNYJŠ׺{0y˧S1} )M7wg5z \^ŷ[=۰fm='6XtҎsϷazgeKpQiO:}{.Vx fK{p>\t~MD.jL3au"љ/L5#[e~u*6]Q -ٚH)Ey 5e_X-]yCaϙUUiNzf [mX5hv ]{I<Ǟe+eywB=OC4lP`]5 --tF%i{6@lO͊6e#=/ʼnFw9W71' @u>sAO3) ]/[$u;Kbߝ<6;"sb=3|c (3[C;* wi(0#M<.f͢cQ4J}=׿t<w GhF^9l9z/Fޗ k̿Xy̷Z0>_tm;m_$0?epݡ:18_?}cu:!Gw?JP{zw1F'^N\;٪c]_'Eo'-E+(8${hh*${xD;'&xiBSud5IyS;!od9ku5_u|m}CjlP_`2U1=6/vOfe=7[Qj7joCU/BlcC>>R`\=|۫^\7ޣ;@!B' 'lu姗Zq %/L?߮>^? ^zm~+[2ηGۛ8N/OmU7b os!k첶)3yO3W޷:ZbsŐ~Ե/|t1 oo߮^Wz}Jܷ^~)o6C̈́\:(w ptp}wd3}X|{9lUǷ'q^طK=piZߞ{hߞ飄XnnprW~>@Zq?LnB'u:|J&!9=l8͆a9aV'(ȝojoSaՖTH%=l${e ɞ? $i,FS_.Cp޷kTwnږkdž 8z\W([v+?};a~:.ƗmBxpU۳58?|AlW7Ba|} 0:kLW- `v7홏|WŴ=[>|{Ǥvn7+tΰr-Q&5vGz^) VNRr?>bηqFu; rOb|VzE1u`JCM<^soWa g*(ylh;4/#*Z`w=z'NJ gY(p6{}G2W?G$?~2~θ"c*N͙i wٹc y+m?4~Y1uyokwq>des5ޟ x>ć(>\Iz]MZd׌M֟7d=W8a_ir|u TYnΡf:jIKa0^.w|<;\@8V;P_hxeN|v[|A\? U| |`|mO=x/N }CrƦ+;9EGGKvߪ:n˿Mp1/vOR(*^K'~gUG\ҫć~pԻ3+[{DaHa'ɲowo˾ smU'+dT֯9y)o49㷦pΙomi1{|Uͫc;; ]F֕>!h-UmwƯu:e#~;ɘaUg >8{mBUwcn:L-_Umz]+=P훫;M8Kq\_it|-آfgQLl=}٥{Ivviю ;ճJW8ۀau̷Y]|bmme}hpE_s3)JWP-W_J+6]W*}fKP|".7Py*U2=O&+_ZJGMg:3J/K*@͝7愹b>mN4ciϥ[l8 /Sb}6ZqM9 1tDݙ O<{̓O[>h)=ڀ&N,>R8ژT~<>|M/5Ɨ=c+tSfU81OhǼ؉?p06喇xzd+!y'5|gZjNQ ); 4qx__:n+9v|L0kC>Ov;DIG#;qMϹ0# C N.hfuꂹrM*NeDvTkվu&~rPd~oȽEBT7=kNT%C+Ϯ1{|U>4Jݜ~I7 qͩܛ-Mnŀ92 %zars17W}=}O;_|"-V^/BYb:BkL?539K"]]!3r |%/Ea|z̽*|! _$:+,XkzsŴ=~RnǦ/T (.唡ӧabD7W@7=UM-t}nL7[n*9G ͝ Gy`MlI|8b9y%_CK _^]{gߙҷƴ&V^9oؚHzD[/l)뮉4.`MďY\)cM5XQI~)|d*r7D—ճX7U 䱞gxXEa稏{+,TPrʛPOWٝݝ~a5/{o0 X`bg.pom6#{d'+Sڲd߃Χ/Fv*|d'C癒g +z|d+JdzH?q!=|mC2u6֑bzHڂOR9m]u2qA Ure?!=Zgd-%n]7tIriۺ9ZP}Dr__vu{K^Ko +|m>9Ls=Z鞾M/P!"}T/U4N_Nߪ>ߗ_NImTVU {| 9c2uq5/ Ĉ2͛lO֗W,Y0GYw*'0nΜn+bڛ;Q}Ο^. Dwc/jK h\,tuhڏ|1E:qҟאRZ+|C BQwH6Bv=U_x[ a\ a~Umoo+9ZNӤT{pe.x/1P?wkd^#hl SQK~s{1]]g~i3ὸ)?;;2".](_4Kzx$c$u>"Pґj}P:[NEq[Ǽԁc^1/u.3egg=&ڄ_:m0So&t1g_I? ѻ.~?M}75n+s-z=n)yQ!z=.8׃;Vm].̳pWXҬ">B-#">B-#4 [+wX~3Br o6+oKg_XDojLN\a,{8Oš\-y͜>X\&e*-{oЀNSuohN4uz~ :u,dOKcٓIrp/|{D8ӻ+`&{&m}]4{Mi5`'-Rm8>Bp G8qg?^ˁJڞڄȁ: j]93~jx]^Wsi2ux9s=/y}^7b>wvi:=w';xPA\e]Ŵ*#YY?83+I(=L7*qh/6es':ǙNſG{voqY^@̙Y>.U_~;/ze^;uN%+ot}),z 雁La$o {U;wd6f3|/{gHwqo 9$,iz<u`eG{6+zfjֶ[֦ϳ9UZrE%R/R[}ܜW(]\ֺ߱퓤+_tWO/'e6oh2'vWK4Y4bM/.Y/?/u=ٟI__y 8_~">~{k|½}'g|(1~S%tcpc.~2{8}9?P =\ޗ\ޗLD=- 8q.4?o sz?Btм !8 c[k3+7^S2"K. "€OJ!"-|uޫyB笀+X{~ 믯m Ǟ>n(תwF߻RZ3-4i)>"N2r.=0o&e7(P Uv~/M%^{*g~3UF%0hv,_, T݇XZWX2nb^2ڦ8d<`LV͒|%|I}B/?K/30|dwfi"R=C-降X>֏=x;|( )ܷt̶zaoeGKn|v=g]/ӣs֞vQѫU!PlE*NvjwZ\YjzV]+[^^F_we h}_IO{EzC5E~t{r̷H"]<D[/dfۛڻDC6]{_{Cqfz=G|Nza8u{Za߇j7A^x]©A+OӀcDּl޷Hʁ/y9P'S|+6D4Xs!]eC0&D9Na^ѓ#Wmp~^=-ܽ+Vs9p=Jl{#߶,=}JJ?B\h~p.\?+9xnT25 ߛenȟلȋ:8\;7>gME=\dĐTV| |+Z|?827}z==:y8?ߋcY^[U7:ZϮ$^z~=s@hZ5gGNO8}ż;ԫ>Q7Ν:BD7[UwɷK9Y-{Enkog~p ViBUΏ> }y=#g%Vo)~P84Y|>donMV-P|Y-h} ooO۟O#pk^wo6!'f,G{g:Jd|Vjb}[‛fz>GU}8+&tXܞRj6>F}NB|qkK>3w@R&G qZ}{,L~Ӻc-Cpl} [eBbMRs\v)6ohlY5-ل:<҄' au}']7PJTf!}g"}зwqD8BcFwuE -Hz] wMNMV+\#+-E^{k;V\xIH>-I^8x:#[|:?WOjUӛ /Gbo<=-^`.' pLgԿr'޵DO{Tuq҄4j=%ߍQE{T!}"==:pߒO1D'_]ܵ_C Yb%N{F))ե&^G~$RX~R3YgOf fB~1lgyy?Ӭe{JE=O_{JCy;(oX_u2J=tԟ".I,=ʿ3 ˵Sd29i9HlH򤮦Qoz㿷{E@;9O]!|` G=Kyϲޥ9h27USֽIV^R1{xI9=QGvk~ԨtĎ䜭ZX1M|y*'x?IM۹7lq |km#W!yh>zğ_KБ-Zï^rz%+~=$=w:;D!8(Bp9=u3o=i pn46ie~[W3*H'R Rq{ [>5۱iZ/WѿYUot_R` _k=P&p~;༿xm_o1ۂʜ֝&xc/_!5쯤^WgUxe ^/٪c]{2"8ϯշ{~4k-~O:¯?&k\zV[6bTL>I`OEs8\R?A}{~{kWl PB#oI?t~[k1# C /:6]`eRy/.|m\瓯Gtslsߊْ+˟- 7O}1Fx%ٻ㱹i{=猑g>3u39=!t=7>6p~֗_g{]"\b, } +/?LX%w ? H{q="Z[]M1iBu|ْ٭A=oowu˱D|誌щbpW-yG^-uMoI.i27MZ._c]B&ht^o+869};U'Y[k_E2-g |i:Jį;K'>1Řbr+nioZP?Z51߶>" k,]0sS^^W|@|@}&tNsnV ¹<#ג{dm܃?[?{·?^{peRUZWbe^A:W4щ谜ŰKtXҡWO4!|Ox$6&x^KMº.d _,r+Vt]L+#u]uYC*{O+)FsY}zP'lY\AzCҧOTXt'kӛoӧmw]'wϜqoi0Գ6`)ݷ}YM1uM7}ٯQg-1.ڵo&LWBw{u -ᅪ2۾JҜmv i+?]ַgH\7]KzDۀ3\%ߞ9d'+~p|( )Q/ xw-YtiBpTUkm(tu6ddnk&R)< E|57tr֘o nDrzM tͬcA8ᕶd[ҙo\ 3띁&*יkC|^qa&WLw~>6׃Bp[u<lc SKr]8rHV7JyF(8QJ=ht OE֓z}09^;wdnkovd}}Sc蹾/ f`fe{qη7_Vv82zOEd7$'$NONg\t 7&^@sqz]͇;*zgc穚_}= NnWk9\wS&sC/ɱ+_a9F=/HW(Op [۽}S[i)mi`_٠^|WLܰheI:uzw #ɘ<_3G~5!v;!6v۾;deLRe(V2??NٽʣPGUwrֿ%߽}Pw,ywk x5zc}#l9}310Z؞6f~> 8e\_ӒO+elUt^*N>mlj=_^i ᖶ _&nGnrA4m/zhxz5O[Uzh/φd~=/7OeWhEeiW ҾxayzgIWȳ瀂݊}a:Ŵ )W9m']Sn<௞ErdGiLyFtZn;z3rO`8_sc꣛[h/81ft)oXIf/QueOqLP2g{{ b0eh#=Oh>IA ږ֓}ٻG.{hE{2]c=Pesx*`=_KԷ3vVް̆HצBKVt'"L}:N-7{J|MNvR avsѾƦ3sqy`bbGlmO\~cn/QŇćzHWȇ':{5i[vO)Vٽ쵺=l=ThSm +ləeWccg)ֱ/]v{ WfG-6hxmpb>L}ӊ}}\y kʊc]#No6"$ _ԗO+>' *(ocϿC}Feۧc#UvNJlr =4yY>79{}w㭊?7_-ʋ~Z^(Q: OWc*ҫcX[ǟ\w)pL*ӕ׎\c{ٯM|  x@} ;( dcŪ3Ӈ2+%C[tuE=pi6+&g+LfUp!Җ/vwޚ̏*T}4>k;Kų!Y5įw~][ѱѩ7mI|;ɛxoj7>]OC˺zuD=Al&hM}%s߆>~deWB9Ć*>| t6hZN޿M9NXwo[_Y [>fOi _}ˏ#?d~Z/Wҿ0nڨEb ܒ~_>nu 5W|4_vO&ERZMg4]4ߦ 8eZj8Nޫt^nD7G9>9iM7fHZ(]AK_n6oΞ)?y>3p/6LM=a\#?9h=˷9]i<,CFL6#]Ҏ~ݸm9kR1==$ggf9W$&Aӑ-ܛ*~ڰ V->_:2^~Ƚ~4{=W'k{|dɂ/]HY>-N ߁m&nf{`䣂^2YCv;gkM;~l4ٿwm t1V8!~-ڿ\Lza 8k 2H[k[CZ $~a[Ca(W02p_7`gG ў>_]h o5&Zêk+ q_>B=pi']d Ђ؋0|QFje~{:M_uW~WX#0w5 ̷ Y?N5gӏY \{q \5%W$1Iΰ\uj G|.>;|o>f立S=:;NCmK9'I/k| m2sD{!m2B!ޒ> pl?5-J>3xqs _pyvj;qٚ5ػK{H9zE2}J-Z&-3>|'!8o'{M _K|nPxkH/Ro:G<36z{*Zgx 񿪴&suylMw=K=E=doWSэBukOUꎹ !/~0R!*|pPZ\ud1|j9k'(mm>ʞWf[]2ö:R ^(öeՈ2{>Zo%Ey@NWOW2; ;; ~[91mb|'[d7x[{\ B[lbW-Fb~?^K {++A8R㾾>Է:. %}wf?l5u^p1}ohۘb! jkۋ+Vz#[Mpq5 pq9y0#Ԏwݫ:18?4[3ƞ8c`m_^E:>[u51o.: K2x&pK[۴ h?P݆}_xِ,^Cp~kɷ> l;}w5Ƴ(H%W.0tbC1jv.al.a]p2;cԎooi1,O߰f=ϱ|lb#6{9(LrbE3W2ߪX|CǾOh<#*ZoWq-.w*wP/9|/gfy8I tSOg.Goy#7z:k|A|` Xe,sOvێ{EG(gԷ|e!e_݇%jg]gNGsEa?=y*{f}uFvY&b.HJd2K_ON Je|ji27MW.ګ1^ꃣJW6ck=f5~,ZZWUi aNMW~ Dz{EJ=ϯu~[$įЄue/?-=/NJ=󣅾dnqT}C?&+38+'7[ xmYBtc!5^]NOƽG4,;ɫ4s ;Dy*9xv?l~+7~cL7?\tFK;,EE%yd*>ȂN%;Il/<5-O@=oJNu3&<{1=/gx*i Zwn<^l, rmZ+^۩.^{̷~e_Woc=Om%:OPNs/y5:pKՇ:EFeiB MξQ~οL9F?"GwC~ %rwBGwUêOKīc{PoH1DO^gI/M6%m;n =^M ^+'8>/(+*2€~ǯC <`2O&RJN,,75 Î÷åâèäíî, ñèñòåìû âåêòîðîâ   1 2 1 1 ,..., ,   n f f f F è   n n f f f f F , ,..., , 1 3 2 2   ÿâëÿþòñÿ ëèíåéíî-íåçàâèñèìûìè è ïîïîëíÿåìûìè, îòêóäà, â ñèëó òåîðåìû 1, âåêòîðû 1 2 1 ...  n f f f è n f f f ... 3 2 íîðìèðîâàíû. Èç òåîðåìû 3 âûòåêàåò, ÷òî ñèñòåìû 1 F è 2 F ñîñòîÿò èç ïîïàðíî-îðòîãîíàëüíûõ âåêòîðîâ. Ñëåäîâàòåëüíî, è âåêòîðû ñèñòåìû F ïîïàðíî-îðòîãîíàëüíû. Íîðìèðîâàííîñòü âåêòîðîâ n f f f ,..., , 2 1 âûòåêàåò èç èõ ëèíåéíîé íåçàâèñèìîñòè. Òåîðåìà 4 äîêàçàíà. Òåîðåìà 5. Ïóñòü â n-ìåðíîì ïðîñòðàíñòâå èìååòñÿ ñèñòåìà n ëèíåéíî- íåçàâèñèìûõ âåêòîðîâ   n i f in i i i , 1 , ,..., , 2 1      . Òîãäà âåêòîðû   n j g nj j j i , 1 , ,..., , 2 1      îáðàçóþò îðòîãîíàëüíóþ ñèñòåìó. Äîêàçàòåëüñòâî. Ïóñòü ñèñòåìà âåêòîðîâ   n i i f F 1   ëèíåéíî-íåçàâèñèìà.  ñèëó òåîðåìû 1 âåêòîð 1 2 1 ...  n f f f íîðìèðîâàí. Èç äîêàçàòåëüñòâà òåîðåìû 3 âèäíî, ÷òî äëÿ êîîðäèíàò âåêòîðîâ âûïîëíÿþòñÿ ðàâåíñòâà (5). Äëÿ îïðåäåëåííî- ñòè ðàññìîòðèì ïåðâûå äâå êîîðäèíàòû âåêòîðà 11 1 :  f è 12  . Óìíîæèì îáå ÷àñòè âñåõ ðàâåíñòâ, êðîìå ïåðâîãî, íà 11  . Ïîëó÷èì . ... , 1 , 2 , ... ... 11 , 1 2 1 2 11 11 , , 1 2 1 2 11                                    k n k k n k k k n ik k i k k n k n i (7) Ïðèìåíèâ îïåðàöèþ êîíúþíêöèè ê îáåèì ÷àñòÿì ðàâåíñòâ (7), ïîëó÷èì                         k n k k n k k k n ik k i k k n k n i , 1 2 1 2 , , 1 2 1 2 1 2 11 11 ... ... ...           . Òîãäà ) 8 ( . ... ... ... , 1 2 1 3 , , 1 2 1 3 1 2 11 12 11                         k n k k n k k k n ik k i k k n k n i            Ââåäåì ñëåäóþùèå îáîçíà÷åíèÿ: . ... , 1 , 2 , , 3 , ... ... , 1 2 1 , 1 , 1 , 1 2 1 k n k k nk k n k i ik k i k k ik a n i n k a                   Òîãäà ðàâåíñòâî (8) ïåðåïèøåòñÿ â âèäå , 3 2 11 12 11              ik n k n i a    ãäå j i a a jk ik   , 0 ïðè âñåõ n k ,..., 4 , 3  .  ñèëó ëåììû 0 3 2              ik n k n i a , îòêóäà 0 12 11    . Àíàëîãè÷íî ïîêàçûâàåòñÿ, ÷òî k j n k n i ik ij      , , 1 ; 1 , 1 , 0   . Ïðîâåäÿ òàêèå æå ðàññóæäåíèÿ äëÿ âåêòîðîâ n f f f ,..., , 3 2 , ìîæíî ïîêàçàòü, ÷òî k j n k j nk nj    ; , 1 , ; 0   . Ìû äîêàçàëè îðòîãîíàëüíîñòü ñèñòåìû âåêòîðîâ   n j g j , 1  . Òåîðåìà 5 äîêàçàíà. Òåîðåìà 6. Ïóñòü âåêòîðû k f f f ,..., , 2 1 òàêîâû, ÷òî äëÿ ëþáûõ k    ,..., , 2 1 èç G i k i i i k i f f 1 1       âëå÷åò k i i , 1 , 1    . Òîãäà ñèñòåìà k f f f ,..., , 2 1 ëèíåéíî-íåçàâèñèìà. Äîêàçàòåëüñòâî. Ïóñòü êîýôôèöèåíòû ) , 1 ( k i G i i     òàêîâû, ÷òî 1 1 i i k i i i k i f f        (9) Kx tU} $#/1ɃLZbVX@jUt"X%B* 3AFd! P`jO~;K.Yֿ>{s9q~'""#opDRDRI"MUS.rrR4=+@dQ戧W:իʢc5#7KnsP0RΒAn=y\Y%Y@Q@.p~#]oeY@?]+pϒ7=i;<j)w7Aki,H}F]πY`MCvHi҂,)#} <<.߁אrmdIpZ'7U4zNHsL]ʣ͑*燑-9J׷@ƞ:EG8M"Cݠ<ɓ"ue,x /zǢzǡw zӝ\y{+:Gӓrd.ǃBn}5WIR ;"Ï$pnR$} 6CMr h&Key .vӤ,\^N7Ә\Cy\k:91 L nCh(k_I[$@01P$ }A/`sJbc?/cS'%5;ɔݑLYdJ7S>!}. y'QˑN Hgg˻.y ik/PV*-I7Xvc8bcb}#.IΔrl;HOU{$sޑذ-{GvQ5~NC,\:0^M1x &3"%<x k#E)[g)u]Vla.maN^ 9^fEȎ;| PaO0 |m/+0G^$o[/bo({s^}.9OIM܅ igb?!):73@cCИ9^5o`"r#Medw̍4$w# Y̛,x;w- .P>⽘ieMZͧnI)!ޣﻒtmLH?Eƒ9;YKW֯kX\yy'z0W^g=*Hd< |1IY_G`㉉u_aǗWDZ_1_, \ m|g>z7>qzAYt;gb4/y͹o z7t=me,d-1DqɑnkJ}[X3I׍{{"oݛbYM9_/&ߏW 9AYmOO\b\ s[v4muyO3q9}|юx mroL'%-I3&2NW`m ,feVc4LcNgOn|؆=5͓$Iu=:{ Oi9 ?dfz'6}]Yxa-e˯՝X\<ӏD4b\zC2E|7b<_|X&=wyWg,hF ds}x#Au֨N㾊TB_p Y?#8΀Қ)ĸb}ș`нPN#ޛF҃D#_1E<x5X\zϖ!Ŝ)CS{*'?d=k^+J)7~k6>2_tՑ+i:a%}h8CD~ĔϩV{I*)Yƾi Zg٢v|h!6Fj^߮Xάߝ]KnK_mՙXջɷYmm8+5B,Nc{umXkoD:B,ɯ*5sӓ)ci!Lz=*/G_2&o_Aw{vյMȷn9lwqkO l?V^N-h lN:-J9ػ*G}+vϐVVƌ]l? Ndull5ᓱ:z6vNm9s$63KyJQ~.S]LiĬ뢮+Ygzcf:0-2kw<_:5h oSmҷck; ~<L>ΔR>e f]]=v >?׵ѴNX5_/m,ikBuZ{mt0>PL݋LEq 8ڭ{z}L]S}>m/񤉙Є~jodz%&97.fOj_.Y&6j;c=l"0f.بfu|g87{F1g4ٱ1;_7ldi^u23b+{}DHD DHD D~;z;G2dʯۚ<s'jyw[~ >O ]k;l@>Cɗ4eף"w 7JA90.ܖ;<{EsP1**ŇPEtsR<>p7~ ܁Q g'Nۣ̜>I|B!$ʻX٘8L7T>M<ބ=Gv1xp.;"gO#v^2W> [5nC Z܍#/MғSA_61*8Ҧ<~~@H&tE{a Y 􍲒s@uϑiq;a0"UW\Cgy"5%"r!ʅO8I6˿3ClD(V!ŮT*y撼#pI8r˔JVYI>-bLG;lũJ*G̱w-&h;qiOc1\;6͘T*䬣ij5Ugda)ȴW u>yB# 3U_Hu!} ݘKD DHD DHD্/0;DHD AHNMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:29  ,, j\$(16~2/21_{`x ]UOEHB( Ao$H HxᡣR MD ӚѦUl|iQ^f[T(0ZDJH0$ w:9<[ ;>z$YpZO,P8n||W7'Vg'IcI]z[% mI_$+ ~Q[%'$g%g$HNZ I>MU/ ie;(rl?My`w;b+W(줰~{ X}Q0]aBKAy":lMVBXu3 EJ&ӔN3g%YBu'bߘyS\si%=}Ρ'I_{l}āWflP8wNg)M<-dP\=/UIӵ2'iw‹I?gio~œ S5JCD=m{WOJ'g=iYQGi_:=rm 5*p#9wkBcNPAɁ)/EU K&u+L x̥?ʋxE*]sRdartS;zX+owW!o '>[꛵O^䥪e!E崁'Oۉ O ,ybgpL!{? C=IrD8˷UgW+J[ꯔ`>Q)󏹷W(*' )j'ڒ~P2Ň Pck9d{`vUP6ڨ>U짴Sl%n[?jLݦ=uqRۅgO.۸~b4^Xqצ1em}ɒ?k}9|"]RY2G7l\_7?)wţKo(]IvglgiQ+F׫&%G&&''G%+#8Ygs%D7[kyP)-З(@_|rh55h;Qi^8k$K{~rio]y([sH/̡̲ !;H6?:u~ʿ:I5o0CiNDqp[w0΂o>vY.Y&auH1,?Rz)nmRÇ;՟ =՟tcM5۟ b~qz}7:w%u|b4F(_zuIvK\[^ ܄^Oܽ[RE/5;qzNPW+&__WN^"}]{bG 4Jz1NOW5څE^1:zyv :w~v3fd/h.6oldMUGqzv|W^ =Vv |@lN/y€Rymَwrw~&+0|`~#xVͩ恇*?w lo5}2T~6lK{q8~[d^,'h߲rۭUWf/bd$/^ حЗxϼF֯ ݺP%wʈ BZƍ>[uI׷k띶;2mv7b̮ңcמ$Fkb1k"W;evS"(Ө}YP7=l)mШ|z6O$;1zЋ6E_{^V۾,[sH/iReUֽ Z |^6YBe2A;3 sn -)n)*xNW)Zg :> θמSgUg~uP:WE:+ tQ 7t}1ۿ,5.hU5턇zh7K _bz{g9==#$u^!7AcOb֥+7~%j7u>aU~q qOZ|BObczWV=WW> jwѹBc_1}M>Y~}I uL8<PO. |RW3<{tyn'>O.}rP yP1s%i~Xc^^(>D^&|L3eC2bЇ>_|;@}~=KâQ|/P@rA\'G<}e &>-E )WCE.}E}uh9W7|m'\F<=vȆtU{:*ߑ3eK}}6pgQpy߉Iw_M<{.O{`|/\l%&pgSpaٳϦ /t?_̈́i7 <cm>O mNQL1Dj~]t.' ]iLWUt}aDjyݲ>j_|]tw% GBWڅSƼ2aK4 mh_ z$⏴7E8:IDG1HGdwuNҟji~+3_0 w_=7]S6#a "?.D'iE|٧dԿ+9/v縥G };u.P, Fi}cpgi)Qu5[pojR & I2]T85&j%oh}}e Z\=8m'H%Ю%t_9rMK6G٦Mp݄O4'esEٔv4NOj W!աnzhs.PKྣ\hsw>8lB:zM>⸞]Kt4cz}^?ڜXίR}-\7Mbӕ\d q^m_֝G|/v|:Ej_dt a`ˤi^r^y:[jB?~3%uvs N"e}^>'ybe;rnMQYlb& ;k=_}'ۖ::Fa'&Ox&&З렡~dpBULpEڻ6TO2f#Q}Pݴe4^|Rg}ѽ#;6z/Zܻ~xK<rU.g Gs_Å6Xn#l2{ozKFZSmj h4邱̞Yd]:w5_lٚCzUZVYy?#h}#_e+o ڙ^Ew-_ٖ6E2q)o4YszձYl[,k O*z1+1@$_/MFl&bYU|}8Nv|WL8#w/)p`}D'^rxT |JW\h{cW^zs=[?|xM܄^ZR|?|}/څE^yybkuַf;.މ4sܞv9$sүM&y:llxhnl?d7MCatb ?v2uP/[-. حЗ_J7*b+ |zڵT^^ѝU#Xtp>*Ğ 6kzvYޮ-Kyp]Ru⹔On>|g䀪3Wg~g7:+f1 R͘B8:+z_+[&~-%E]@@ܗ՗;%pc%u+fqm0"@zKN%{TegKyv?ΛcG2/ّ$nGҮ *> HxdOcqI[$9}}[C!\OΜZI&n'}f~tO܏sB>X \ѷL"Tg>}T槏9m]\7:#'k>y|K^{/;|n>TÅT͠qTϡl~OJ[(᪟KkXF&.+>v?.-UcS5^n_* ir{~y_R|M{`nl`;A3X+'6R[KSY}R7KeU*Ms`P#GXۛ'P|{-eZ4ɝھ[:|N&lny"Ȕh|^{pU]t%.Y-ƻ~SzܷCgyW|*ً*_85&1 ߪI4Xi 뷉Gb.IU6LL^_s€b/^/Cy5]ៈ]3}w7MZG^K^$5.k WUt11Yu!\! p?|]/.ПeUÿ+8Nov\L:''jggR_wM֑k}q]KX\k^=> +y/bI>3H<&6w)?$v:Au(Wtp= f>'>2Ȗߕ*E$gςJ{%6ԷMV%kTN)Y~qEh{TrWx{P#һ+My:Ä1qY}hCʨ==-EЏ Za- _!]"]?V0DCdT]uIFwpҵ_\MKuFS6Cy .:>MKR7QYRh;vO Jy6DA;sM롭t6K~\h+wa_UdzY[g C=mb }`G} .7@ίrϺ.nMW|̒> Ic:i۫MWhrԺ*7Ql=6|S|۵auԮ=A}dHl:/XgNݦ6`K1 ؛)~l7RޮO+;U*޸q lVI%P5ׇZne^ {;_Q &vb˻_ԼWMAN]n;}ZUcoP9ؾ7Mm_3OT۱7 mϧthة[9{N ?+xXϤvЕ7ٟe &疢Qh;Ѿ z';ыdB M߲2}cYUvg}{oA?򷬄[VvxeGP]pM%TT>+c^:x$h7K#_uNߵ2{۝{?h&#_|@)AZ| &_۱tпo}ī7*_M܄^[ճh%(Hv||gz%>SE\xa( .y-6i6-y/OzoD^վ%*}rm\Ю%Y lⴺ_~y:|_ _W{wT;}g;Ӗ:f1}fklwp>Khn }a./e2_ث v5 1M8kr㮶˾WrQho([xC]:4mwRBCWm3sڶmsemfulK(y gP^^mz/ ~Å`ѵ{u}fe Z3cYU6"P_ƟyOs|tLLoz6ҭy[_Pg\#d#&6'rjOh[7B}=Mgcp-qO .sV .>ݺ6>#9.'$O ͻe#o]&k̉s:(n)lmx>W!|b#<HXO$m+iMo-zIml?,o=*~.7} 竘}( Hs.:|>}*2ܻD܌w{4ܿve^ [̷;>fvI~]x#evI'Le?Fι+}]].)MH*wxk$#Fڵ>%U@LahUmLטy{[nU]VڛKvR8]v³-*o5qnw5#LW.ڣuZ&iB:$Wڵ?d ѯ9Vskh?kϕ7MeU+K^?lgyy599-uCGo02{j\L=buKS^ *.Sʒ{@ҡBMjP^ڢdOV}fM9_bj]`b/b6 gzlI` Cr~GE9p~W<}ӦNnZtYWWC3ꦨPz:yT %Ii&WXv`ԅg]/U gE~L(iAWl,"\!Ђ*\-U%;3GRwQc68^>~B@<6x~3B|KF?RwOOmÃkg ^U68˪z6Z/_gF;h3=*[ |t W %[ޡ\ ]jKqm5ڵ(ӕ|]cmR[[, }h40{6GNi`|ZC;[g 3eXavI*Fe1<4s wp*:7$ s$PǏK=gs=?=S]}S>p ' a~@1g)M<-d)^zw9G |p&O&e]%OHoIrNC~VœSkW{l]=)Ӟ{ܭHOObEg*?%J?4NLv1 SՔ=7q]3P\JY?Kn7ZM鶫@7bF.OrM"]H6S]5TNn[M6_Nɇ~OHq mV݈qn່nMˑOr/JT M.QYbzl&3V쏇|o~~^LJKl]~n':}¹oj; ϲSv|QZc-k]:s_VJAs~oiWNf5Rf4oP~gkS :p q)3 )|,9O{~ExzZAa{HUkf2ƆҰFϽpo֩gϒgLm腙Ym?Ѹ'^;iY'[?ucBuThmcHXX֜2xx4wF$<9v Y]N9w}Ge'-aii^%y'𤡅QO>Qx7i=B7 z󷽡)tKz^2bT="dTћS4OL}KXxMW6{'i&Ʒ7I9_}/ybQ܀Tq|5SY)zsQrv9:|.b~E}PZ\Ya 3S%ڿ3'&fπL*|u#gɯV\LriMb>Gg[W+nlklӓ8l |VC;hߘ=:-i?w!_(-% _ly&r3c֍;nsNG|cO]6v_&iz7$i@6z>˝be(L?fnŜ&|=29J~ő=c>U {L 1Y!_:]thMJ8*}a}ɯSQ;? y=}ɚ=T}\#9; m$wG;i'%}lW&-&Kk5~o~ >D:VO#]"Y[a~rFLQz*-L.ӗL0uٺtn8J7mZOYR@*Bn;sA݅*V#onHn闛3uz㉿RT<=K-bβn)NvzvmPv;yr ] "iV?o=4n 7 7ݿWj|obo!9=rxW*~=Uwsrg3q/Ń~~T~x4딺Y<-JoMz7)M`> wWI;Z .)2{cXG@>Ju@ۿ1Ħ N @Q@'*{9~Nf1~{3]91tߪ.qZA1}Y*>W!e'S!:&**'BDwAx5N\[Lg+@=;iZ АGzqѸ@l=7^`(.'Zr'GV+.WT=q@?=y !飐C4rxr#|=Ǔ}IeG 6ƓwdPGRdzJяYx{ /g=}PP{!y=kfL.H}!yv|d<2rIeG9xA1eN#m + gцRg_RSO$y M9ZSٓ[=<) e76Qzf>kٷ`)=W͓%ϒNO3>#SZ7ĬG-sAĔ3zz?Ć%M.l~ }џp_=?b~mh *#*;Fm:4B7 $y}JwJzyʴ?*n!ܻOgkQ4N)85ns[` BYuiw W4'ʀ%Iy2 'zgy +{2ن{O) ;[ReG,F_e-Mϥ2 k ewI{͝ά~gAsv!V*{Kdҵ7k\V-ƍԹoדǣ X6)w=53`y ǪjFo ݏkD#nIZ TK<?rbb794+¹G_ϴ&O[1< iݏq#}.k[[ ^ ' h}yPu~ʜ\.3FLSs]h˳WO}Bcg~@|v{Bx|_4gd amA00>09ʡ1e!3o0vn㾁#8O6k\*yO\E(ݛ ;eýK ?exa}zG $Y=r+߰c׺D=>pk)RhT74^xwL{TOQ]xn>*/Ku?B*q ̇W^$&GXyTVu~&2MŰ/7%0e𙳚V;Ϫpq+cHwf= 6])#m8:P澈xoۚg8<ݏ8/3G|t=u zsǘw(l{~ԽSe\gԽ*"7ڲsdKprAV#֤7+6j]1zB b}G>x$a}9Ζn+Ӏg;@ y<ù.s ڒ4D2s#OokΓ4|C;t;I=s!o}۵y6Tש썂JAa= 1ԐQ_ s$;qEP-y M_@vD|v*z-]Ωϑ4Ɓןq+'6I.Mgbϋ=7Czbσ<ݧ ::r;6ã*:wf`B641}y#pW> O<.NNp `Y ݝ5tbݔ!_sCi#RO1*ɔ v<-3Em8`ؔa1c|x(@W)QI{J?҇7Ґbovy$2 o,.bP}}4{ kdMa!Όkb\;ML=ӖYa{G?:~I;~/p0fRAZAPrs*O g,,H76 Ïðèáàâèì ê îáåèì ÷àñòÿì ðàâåíñòâà (9) âåêòîð i i k i f  1   . Òîãäà   i k i i i i k i i i k i i i k i f f f f 1 1 1 1                 , îòêóäà   i k i i i i k i f f 1 1         . Èç óñëîâèÿ òåîðåìû ñëåäóåò k i i i , 1 , 1      . Ïðèáàâèì ê îáåèì ÷àñòÿì ðàâåíñòâà (9) âåêòîð i i k i f  1   . Òîãäà i i k i i i k i i i k i i i k i f f f f     1 1 1 1            , îòêóäà i i i k i i k i f f ) ( 1 1        . Ïî óñëîâèþ òåîðåìû ïîñëåäíåå ðàâåíñòâî âëå÷åò k i i i , 1 , 1      . Òàêèì îáðà- çîì, ìû ïîëó÷èëè     1    i i i i     , îòêóäà 1   i i i i     , ÷òî îçíà÷àåò ) , 1 ( k i i i     . Ìû ïîêàçàëè, ÷òî âûïîëíåíèå ðàâåíñòâà (9) âëå÷åò ðàâåíñòâî êîýôôèöèåíòîâ ) , 1 ( k i i i     . Çíà÷èò, âåêòîðû ëèíåéíî-íåçàâèñèìû. Òåîðåìà 6 äîêàçàíà. Ñïèñîê ëèòåðàòóðû: 1. Ìàëüöåâ À.È. Àëãåáðàè÷åñêèå ñèñòåìû. Ì.: Íàóêà, 1970. 392ñ. 2. Ñèòíèêîâ Ä.Ý., Ñèòíèêîâà Ï.Ý. Ëèíåéíàÿ íåçàâèñèìîñòü ëîãè÷åñêèõ âåêòîðîâ // Ðàäèî- ýëåêòðîíèêà è èíôîðìàòèêà. 2000. ¹4. Ñ. 97-100. Ïîñòóïèëà â ðåäêîëëåãèþ 11.05.01 Ñèòíèêîâ Äìèòðèé Ýäóàðäîâè÷, êàíä. òåõí. íàóê, äîöåíò êàôåäðû èíôîðìàöè- îííûõ òåõíîëîãèé Õàðüêîâñêîé ãîñóäàðñòâåííîé àêàäåìèè êóëüòóðû. Íàó÷íûå èíòåðåñû: ëîãè÷åñêàÿ îáðàáîòêà äàííûõ. Àäðåñ: Óêðàèíà, 61000, Õàðüêîâ, Áóðñàöêèé Ñïóñê, 4, òåë. 12-82-82. Ñèòíèêîâà Ïîëèíà Ýäóàðäîâíà, êàíä. òåõí. íàóê, äîöåíò êàôåäðû èíôîðìàöè- îííûõ òåõíîëîãèé è äîêóìåíòîâåäåíèÿ Õàðüêîâñêîãî ãóìàíèòàðíîãî èíñòèòóòà “ Íàðîäíàÿ óêðàèíñêàÿ àêàäåìèÿ ” . Íàó÷íûå èíòåðåñû: ëîãè÷åñêàÿ îáðàáîòêà äàííûõ. Àäðåñ: Óêðàèíà, 61000, Õàðüêîâ, óë. Ëåðìîíòîâñêàÿ, 27, òåë. 40-10-09- (4-50). ÓÄÊ 378.146:517.11 Ä.Ý. ÑÈÒÍÈÊÎÂ, Â.Ì. ĨÌÈÍÀ ÎÖÅÍÊÀ ÝÔÔÅÊÒÈÂÍÎÑÒÈ ÀÂÒÎÌÀÒÈÇÈÐÎÂÀÍÍÎÉ ÊÎÍÒÐÎËÈÐÓÞÙÅÉ ÑÈÑÒÅÌÛ Ðàññìàòðèâàåòñÿ ïîäõîä ê îöåíêå ýôôåêòèâíîñòè àâòîìàòèçèðîâàííîé êîí- òðîëèðóþùåé ñèñòåìû îöåíèâàíèÿ çíàíèé, ìîäåëèðóþùåé ëîãèêó ïðåïîäàâà- òåëÿ ïðè âûñòàâëåíèè îöåíêè. Äîêàçûâàåòñÿ ïðèíàäëåæíîñòü ýìïèðè÷åñêîãî ðàñïðåäåëåíèÿ êîíòðîëüíûõ è ýêñïåðòíûõ ãðóïï ê íîðìàëüíîìó. Ïîëó÷åíû óðàâíåíèÿ ôóíêöèé íîðìàëüíûõ ðàñïðåäåëåíèé äëÿ êîíòðîëüíûõ è ýêñïåðè- ìåíòàëüíûõ ãðóïï. Äîêàçûâàåòñÿ ãèïîòåçà î áëèçîñòè ðåçóëüòàòîâ îöåíèâàíèÿ çíàíèé ïðåïîäàâàòåëÿìè-ýêñïåðòàìè è àâòîìàòèçèðîâàííîé êîíòðîëèðóþùåé ñèñòåìîé. Êàê îöåíèâàòü çíàíèÿ ñòóäåíòîâ ïðè àâòîìàòèçèðîâàííîì êîíòðîëå? Íàèáî- ëåå ðàñïðîñòðàíåííûå ðåéòèíãîâûå ñèñòåìû îöåíêè çíàíèé íå äàþò æåëàåìîé òî÷íîñòè ïðè èçìåðåíèè ïîëó÷åííûõ çíàíèé, âûñòàâëÿåìàÿ îòìåòêà íåñ¸ò ñêî- ðåå êîëè÷åñòâåííóþ, à íå êà÷åñòâåííóþ õàðàêòåðèñòèêó, äà è íå ñîîòâåòñòâóåò ïðèíÿòîé ïÿòèáàëëüíîé ñèñòåìå. ×òîáû îáëåã÷èòü ðåøåíèå ýòîé ïðîáëåìû, ñëåäóåò îáðàòèòüñÿ ê ëîãèêå îöåíèâàíèÿ çíàíèé ïðè òðàäèöèîííîì êîíòðîëå ñ $0x}lUǟs[j[zBjIxQSTe+ 0` :&Pcj_, +(̉&/6&Y† }{o=\n˥My~oDD4SFKLY"?%=Xo~k^KJTVULLdeP=VHrOv4ۅr9C5{챋v̕&ϗ$_`v~< TߌWoi[]K2.r "S@XR &d]"h^l ;LʷyuyM?ˉw{qx5> R$&D}8~g ǰ);OA 8%A.mG^#%̗2r[`X߭]`f[={y+f|3<@q eoLvye6L-<|+!o/D+GZɍ#چ(n&eb|Jf%_a9p%8>׃]G7Ъ"Un?+Xv=?A+j[7xbCs\c}*qWg^ύ?&ͬ{#B\sgw ?$!Gtݗyoo<r9TF$ܮ=BeFg,u][ӹ^jk^|ov+̨ӯ[0ui&+;ufh9bWKXjy-Up2D6>,[S-/kw UP1cO̫=!ˀ:ZbM'^ɯ}G%ǼIĥ|Ao|ב dۼٗ:9&o_y7|@,3a17笛- \NwX9@e7rr{ǀJsl83kѳjU2ax?Q‰իt2czn; 2븎i̕aO`,-+JJ:gggse:PJC`}X̽7!9o s%jPFsj$}ww|<}OIHZQ(w(w2?Q# j$536r5|Rq#͆ p ي\/ce{IfŎNH:sSb77-nnf7;@ajz77'yv9 gӈ*P їsby/M (f{ 2B3M%W \ '#Wvpl_Aj _H, K4|9/36Џud={gX U nOwZ"Ќa< "7I]Q>O19;3<|1݇{DN~6ۑ6֭AEuleֻXݙ9ʗ9}v;[Z$t_`'*0b1&|1-ۄ쏜W \dZ[nD,AoGw4'aVY 3v8 &@<<2b#~=$YԚ:*>T A, ⊀-ϸ \h1 ݝ F&E[.j`+d)o:o <~K.ګ,1!ysHM?ݷVI:\GTؼ7I'ij{DᄒO}H}S_B~.R cK5LxP[a$u}y Ieϼ=I}o_8Tm}H5cӷ)|KҽRl=xet޷%oIm泯sj7tSIm_*ofƽcjcG.e+];sππππππππππππππdA@ Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:29   W9(16t2/N1 b]{x]Uuτ`bHDJN d&"?y1<62Ċ/-hV >kKGR XmfH&aB}>;ޙa$bOgk{ܖ$I%I.;r|U|aL\$sc$Ԓ:1IڔNY_$>3y(2v94L{¤/57漮[״\ =d|-a|'_<hg*LG3(eʒ;'&z: &y&0mWJ)+@cS)mɯߤor#ڵCZ@[Kx\qxd;E`8RqH9pu~ 2 ]Üt`F8u tnu[ezS Gi}r$]rR @O*'FAҞY![q*Չ)F QcF4!^8xh>;󙗖p2,֟Zrc:0@#Ϯ}IZm-}8N`>Bs+҇؍4ˑS1R tG:oO{/c@ѿG}x߫]ޯ\.T6 .WZY=O<_w?symuZ#DčqCa|-np{Œia|El}`)* [48sTNQ?I mmcC{N6w㹬ejk+ޫЮj4"+j23Y( :9y֫Z5dk=bڗqt+Z#i3{`E3DZPĎyE_{,'RèfBH8i̫2P*9^s/k8cyf.ce~糬18?eɓzQУ e:i}1MSg=\3||SsiK/r{T7._Z|)/Vv:̕ a.>08KwN38e\p%o}jCYFB3\¨Xj#/vJjhJű!G a$ę w`%\_J16 }r#=O]t4O?ᐻ.xp\/apZirދ~ZX=7d&ع%?07 {[bf$upOyL}8xeo>+LKa`8ad@Wk?եX2a/QMx-Ol<:Sk @73SȐ0u -{\˜|VH$YZC@ed7J #79s;ª=TvVՖW;hvaeAg.6zttg~Fa sBfg1M†G?m5xM8 yTi%9ho@ 'cx^~:z1{ N5#j~jp n▍J}2wA>9/Ԧy>+>^-{ E]4)G"~vjKg+ ﭴ .GRgcG~7EN7 &-7cOÜyG̍tәnF{V~ #jtV}~l-;oͺպaNqOuҭ[1XF~L<% =pSu$4tٴJ+F9`+ϊ s-Ea﫜r<+Ёp}cP9v0`,ʐ2=詡)X=ȍ>iFj 0i+,C66[܅d^HP Sx.;\^+)>e/ϕ#ə2ȁ |r8򺮦aYz\q=r%<3}6>ʠ\CKXMW*p`%? _7պVɞqU0 p8:pBi78ax I+ ˭ ]76y3Y\KUc]dM{hד# 0vZTr:&p.P} "ycl&<.9nqS93y('$5a{')J*nVߤW[7xIVkAx0r&IScߒ6qɸYmOeo1q@B?! ~OeɏPvi<\\Fy;:t¤Dz8~ qxΏߨ_\-٦[2 31gF g.!ڢy·,+xecXbF:9p`qSꄮ$g3F3}&X9?o ;?w=;|w -3 '0 :VI# ΠMW}xo>;w|xj}ʸyGy8M8t>ʐgXgx-,zpoK!C&I_Muŏx 9ņ؉p_" Ȑב/2G%_Ѫq˂5AHg~yl(DsSYc`=O3v+C~F[_x9xQyM9,+,U]'ԃ G(Aъv`>_Uڃ {A}l 7zy`-e 5յAMdd)N/%9o[Nib_1^#铆!?׶N9~"vJ }(02>^ss zW6:QP6%;}ֳxn_3n'_n+$x38o 4 C> -ʭu]Jp 786Cȯ ҡ~xopL}cw>qv!Qxpr.)FCYoz0BW 1FEhYJ tθL5rKdqyb%}ϓ3_Z밆ڵWZH}Z|2C9"G;L?%dyӄ-j]"RsҰ g:*$kqJ[WLwoJY}޳}'g_7R7IK}`S;iڧ}Mӓ+A ,)?wݾ}ӓo㇧a}{'}uwwQ+ \5=.4}㒳{g?C]eڲ8$9;@ufDF-__"}% oSBA.RU:o"d®wws_+:+xM>:/iInYr–hy0ʈlI6竳rC)2ȇ~˫SyVEYcC幗N>2a췩8ftϬkݳpˋIb0qB'G3Gև3KdO7}_2ȕ:uԏr>ݴw҇O0tVn{!y߷}h;clvXѵ 286N9U>8h{a;6egADcQBLeEҰ蒋p-é}g }~W.Ct➫yn! . 6*E>_z/lyc[nmIBTϖ(bJ_rNf([~a wlmy_ϴUly|o͔ٶ5p֖̽,}qy+_zsy$|ݟLrS/3"[N9lm9mm/lGq=k˗)4l+KM)39rf|weF ҠףZ"Ϝ+Vgʷ4+J:y6ί,g%N+T뵵"H^aohN96D^kg5æۚU8܂H^*ڋXx[ -_똩}EIG"_u_$ʸ٠MS7N--YX(y$N^_˫Q._+߿<c=ѯV91; 뵓@ k4O%vxV MG6**oip7W5NI>4]dqz0k$\%g-8C FVv`;rҸiPJ."7)n[v%<->aDn0iɇLXOb\˞:XO̕<\Ko0p8s7ϯ-*_q$E8U}Y-&6BK\+= owjKow 0xGU/`<381Iwisp8?$P򑟲].q0;eu!??q\_'ԇ>ՖHkp`)o>W=&n%ŷUy' RuDfG _m {#s1J B#zh)g;nQyy) FN&0pӾ?W* ;KYӴ!(F*"/Ski)3p7Kay}LJ4hS"K^9dz} TxizoiT"+}A E&DlYߓ%P-mz^0#3wͬGۇ1F:F^ʙI]ZHF:>p8.}r8il9ƨur+$/֣gz)"Y^4"f%]|zn mSw/TI!.2SW)K>R4ޫv{Hj˅jJ鸢}-co0]؋?rr'- ?ZoAit5UF,w7c:}0^H^){Iauks,FC 4{;[ yHvܿ:ݿ4pyM8-NQs|k}^e44Ir~Qs ~D#S/X?PI~Ǔ9**'Wު3˨6̭ty8I~~GsWY "Lk|θ\{ƻ^~Y]Y8Vv&7mQ^΀{V^d%?ZyoЎTs< rZ:oo_}޶Ut_agAL=Ӂ?iM'CfzC9%E]3V++m$h#{ν7s6Gr 7xR>| ޟ ,bp #8?pw8 uCήQ<)o\sFd{j"_4S|ݖ/Q3E .h^/i =(yߩ'z [H H#u<iv㌇|תXEk4Ӣ|EY+g.S/d{y~"S<^,|iW@Ec<~{|򚿄z1ӍI==E?N/ޙ:>Y*4sҪ])UfCu3X7~uu8m#^G)C^ʸ_,p`AOs_- an@iy9rվ}Δen[p_tGT3yo~ !]4˨>#6siGrLa[bteO ˋ>83IK;:xWǩ/c 6 8ه)sftfaN֞Cs>l/r4Uu^Q~l/ \,Lu\ͰOb#sZ0}l\^~pO9{LfKk|/:Ai/'Gc/)K^^THή ^{y:u^.uŏ/{{ X%m7㵪כ#]s.V=6plh3o75Ͱ<|>kΧ{E6d.fgCATdC?EFcC)Pچ^؎#~@yJpl('W~SeMVڏmhm5'6n 5lhk8m4Æ6sO Ec62z//^7ʆ\ U@P ۑ||6t48Em(iPyPm$VBM{U_|xpwhi VSi,vv|;w%ě[T}')n Vl7#ǵI{&z6 +)&\0:GQ/pY߲旊'qjrbM?nij)kL!>~kɡ}t'3ؗ͘%w Z߳_!8}7$Srfn^޴9/mT+{w%孕~bK|5Zk;ϷўY뽷7cty}V^ۤp~Nk=9!ק社ѻ 4=zJZ<~|TyrߥrGM8[qN cs\t_ sD9ڒ~Zv\⟪k"x.b#'3Gy"oT!j>[؞ .51ȅ=9_g M>ч1A)Ʉ6,_5]LZ.hIޟ~io-m]&ߖ,)J崚soCm蝞|t;iʊǿ=Ey0KtߞCG;{6ۄW>i}V A jK_wIL~Q,^NY =RƆUk+( VBWU u y'U)R'0vm9@_$[Q恷6~G?fK},.CQ*,e.=ھt ^\L'֝E|y'7ֱiu@דWs1ƈUWvg|ečm^q_]!X\{?{cQ9 y>>e<>h2r͏ 0>#?˫SNHD Zp軌~<Ǟ8&aըͱmK[w;֯pw⾭x;q|Sm`K>6-K뢾ڿGw8@F+H&c2#-7aF98.8Ælȿ>^mC uȆ*<01=c4t$GWm#Z ѹ;'~'r'"2--/oul=&m,oCQlHn dCF02C!BQiP;o:TTO2by6n Ѿ2NQcyIc oC~kU},ؐ; m̆oF-/dgXnVǪz)_YnmWsA]=@}i_';O擝.w`]r>mJpaؙ.e]'<̺i3tp<6ղeږUIhmbsmY_m[ƞ7Wx]UPO[*WZMwnoܭ5O 5O9P~≽mE뜴BElŶ =-lrlY[^[f [6v2ud!ze ;թp]-b[Fڲ<੧ˋAK}?VnԸWm.iæߛO+`L-e* UllesUm6 Ϩ./nh#ohnh~3i/hFK힌~3iEoʧ͈<6<"Cgs9;nh/hkF{MFo&-xoNjІʇ?^"о"HF<-}?3;Ͷ1mӆ~3Vd|h2mcƎmshcKxml'n5h3BqmhӿmxFϡM6z y{)^B;_&ɝu֓ :>~R(wκ{gntV}{ysw]pB27~$Mw㶅8~(;q|="݉|=2iZ~ 5Yk{/{҅ʟ"} {p.K{pKX)wǴ P4Uj-֕v*vw{Xg>׼{i顼"_yNԥץ@-@tendܷꔩҰݔ@nwgH?CDI+w[vXeBgH)|hmqؗWzeA! 5ocF>:]N)B'{iA5Tpoi6ɋ}7nzO)sjk>ݒ3$g1c@<=3;| |eўøu~5&9 :&SF]0uT=;*~^ƖZt,?~*{x=߶c#[/>>Iiّ  {0v#ods0,)byղH^<{y9a13Qrs 1>PNxmy!;ۀknׄ ƂN3.Kzfw V 6?Z-+[kFC]pnϻ=9;lM+e۶̲Xϖw U [6vsed_H:+ ~c5\[̛kˎL'eCըͱȫNAdž^N҇_b#[F*2le.˞+=(brاf=p~m=Ɓ6gڜ=W9C6g)3=rFshsAu996?ڜs\͙x{YFdhAF{2 u _$*F#BrXnCg?ITk(Oš?S>ߩ܇?ϹI9Yy~q U'kwtg[)@Pműooxe*auJXݤf_$dž^f uC'O3Oh_}>'`B9υGʓ; %W'Hޟ/ywzi؁=|Gm;j>v߾ajw q?3'3&_a3/^ƕIVŷ-O㲱,$+Ϝ<#ڿuT9uoM*x_kJ~9wJџz/sD,@ق)_Q8{RvPxd/zmۮڡA;}uϔs]:Rom_0vWVUo~a;};C|G[\'f t'ODZ_1y'l%p,,77 ëè÷íûì ó÷àñòèåì ïðåïîäàâàòåëÿ. Äëÿ äîñòèæåíèÿ ïîñòàâëåííîé öåëè èñïîëüçó- åòñÿ ìàòåìàòè÷åñêèé àïïàðàò, áàçèðóþùèéñÿ íà ðàçäåëàõ àëãåáðû ëîãèêè, òåî- ðèè êîíå÷íûõ ïðåäèêàòîâ, áóëåâîé àëãåáðû è òåîðèè ãðàôîâ. Ðàçðàáîòàíà öåëî- ñòíàÿ òåõíîëîãèÿ îöåíêè óðîâíÿ ïîäãîòîâëåííîñòè èñïûòóåìîãî ÷åëîâåêî-ìà- øèííîé ñèñòåìîé â óñëîâèÿõ íå÷åòêî ôîðìàëèçóåìûõ ïîíÿòèé, ñóáúåêòèâíîé ëîãèêè ïðåïîäàâàòåëÿ, çîíàõ íåïîëíîé óâåðåííîñòè â ïîãðàíè÷íîé îáëàñòè ìåæ- äó ñîìíèòåëüíûìè áàëëàìè è ïðåäîòâðàùåíèåì “ óãàäûâàíèÿ ” èñïûòóåìûì îò- âåòîâ íà çàäàíèÿ òåñòà [1-3]. Ïðè ïðàêòè÷åñêîì èñïîëüçîâàíèè äàííîãî ìåòîäà àâòîìàòèçèðîâàííîãî êîíò- ðîëÿ, ìîäåëèðóþùåãî ëîãèêó ïðåïîäàâàòåëÿ ïðè âûñòàâëåíèè îöåíêè, íåèçáåæ- íî âîçíèêàåò íåîáõîäèìîñòü íåïîñðåäñòâåííîé îöåíêè ýôôåêòèâíîñòè ïðåäñòàâ- ëåííîãî ïðîãðàììíîãî êîìïëåêñà. Íèæå èçëàãàåòñÿ ìåòîä òàêîé îöåíêè, áàçèðó- þùèéñÿ, ïðåæäå âñåãî, íà ïðåäñòàâëåíèè àâòîìàòèçèðîâàííîãî êîíòðîëÿ â âèäå öåëåóñòðåìëåííîé ñëîæíîé ñèñòåìû, öåëüþ ôóíêöèîíèðîâàíèÿ êîòîðîé ÿâëÿåò- ñÿ èçìåðåíèå îïðåäåëåííîãî çàðàíåå óðîâíÿ çíàíèé îáó÷àåìîãî â îáëàñòè äàííîé ó÷åáíîé äèñöèïëèíû Äëÿ ïðîâåðêè ìåòîäà, ïîçâîëÿþùåãî ìîäåëèðîâàòü ëîãèêó ïðåïîäàâàòåëÿ ïðè àâòîìàòèçèðîâàííîì êîíòðîëå, ïðîâåäåíà àïðîáàöèÿ ïðåäëîæåííîé ìåòîäèêè êîíòðîëÿ çíàíèé îáó÷àåìûõ â Õàðüêîâñêîì ãîñóäàðñòâåííîì àãðàðíîì óíèâåðñè- òåòå íà êàôåäðå ýêîíîìè÷åñêîé êèáåðíåòèêè. Äëÿ îöåíêè ýôôåêòèâíîñòè àâòî- ìàòèçèðîâàííîé êîíòðîëèðóþùåé ñèñòåìû áûëî ïðîâåäåíî 160 ÷åëîâåêî-ïðîâå- ðîê. Ñòóäåíòû áûëè îðãàíèçîâàíû â ãðóïïû: êîíòðîëüíûå è ýêñïåðèìåíòàëüíûå.  êîíòðîëüíûé áëîê âîøëè ãðóïïû ¹ 1–3 (îáùåå êîëè÷åñòâî îáó÷àåìûõ 80 ÷åë.), â ýêñïåðèìåíòàëüíûé áëîê – ãðóïïû ¹ 4–6 (ñ ÷èñëîì îáó÷àåìûõ 80 ÷åë.). Ýêñïåðèìåíòàëüíûå è êîíòðîëüíûå ãðóïïû ïîñòàâëåíû â îäèíàêîâûå óñëîâèÿ îáó÷åíèÿ, çà èñêëþ÷åíèåì ôîðìû êîíòðîëÿ. Óðîâåíü ñïîñîáíîñòåé îáó÷àåìûõ â áëîêàõ êîíòðîëüíûõ è ýêñïåðèìåíòàëüíûõ ãðóïï ïîäáèðàëñÿ îäèíàêîâûì. Òðå- áîâàíèÿ ê çíàíèÿì èñïûòóåìûõ îãîâîðåíû çàðàíåå è áûëè åäèíûìè êàê ó ãðóïïû ýêñïåðòîâ-ïðåïîäàâàòåëåé, òàê è ó àâòîìàòèçèðîâàííîé ñèñòåìû. Óðîâåíü çíàíèé îáó÷àåìûõ îöåíèâàëñÿ ïî ïÿòèáàëëüíîé ñèñòåìå. Êàæäûé èç íèõ ìîæåò ïîëó÷èòü 2, 3, 4 èëè 5 â çàâèñèìîñòè îò ðÿäà ôàêòîðîâ, êîòîðûå ïîëíîñòüþ ó÷åñòü íåâîçìîæíî. Ïîýòîìó èññëåäîâàíèÿ íåñóò èçâåñòíóþ äîëþ óñëîâíîñòè. Ñ ýòîé òî÷êè çðåíèÿ îöåíêó ìîæíî ðàññìàòðè- âàòü, êàê ñëó÷àéíóþ âåëè÷èíó, ò.å. êàæäîå èç çíà÷å- íèé i x ñèñòåìû îöåíîê èìååò âåðîÿòíîñòü i p (i = 1, 2, 3, 4). Î÷åâèäíî, ÷òî 1 p 4 1 i i    . Ýòà ñóììàðíàÿ âåðî- ÿòíîñòü âñåãäà ðàñïðåäåëåíà ìåæäó îòäåëüíûìè çíà- ÷åíèÿìè îöåíîê â ñîîòâåòñòâèè ñ çàêîíîì ðàñïðåäåëåíèÿ, êîòîðûé â ïðîñòåéøåì ñëó÷àå ìîæåò áûòü ïðåäñòàâëåí â ñëåäóþùåì âèäå (òàáë. 1). Òàêîé ðÿä íàçûâàåòñÿ ðÿäîì ðàñïðåäåëåíèÿ [4]. Êîëè÷åñòâî ýëåìåíòîâ â íåì ðàâíî k, êîòîðîå îáîçíà÷àåò êîëè÷åñòâî îöåíîê, äëÿ ïÿòèáàëëüíîé ñèñòåìû îöåíèâàíèÿ   5 , 4 , 3 , 2 4 k  . Ðÿä ðàñïðåäåëåíèÿ ïîëíîñòüþ õàðàêòåðèçóåò îöåíêó êàê ñëó÷àéíóþ âåëè÷èíó. Îí ñòðîèòñÿ ïî äàííûì ýêñïåðèìåíòà ñëåäóþùèì îáðàçîì. Ïîñëå èçó÷åíèÿ êàæäîé òåìû â êîíòðîëüíîé ãðóïïå ïðîâîäèòñÿ îïðîñ îáó÷àå- ìûõ. Èç îáùåãî êîëè÷åñòâà îöåíîê N, ïîëó÷åííûõ çà âðåìÿ ýêñïåðèìåíòà, îïðåäåëÿåòñÿ êîëè÷åñòâî äâîåê 1 n , òðîåê 2 n , ÷åòâåðîê 3 n è ïÿòåðîê 4 n . Çàòåì íàõîäÿòñÿ ÷àñòîòû ïî ñëåäóþùåé ôîðìóëå: N n p i * i  , (1) i x 1 x 2 x . . . k x p 1 p 2 p . . . k p Òàáëèöà 1 Çàêîí ðàñïðåäåëåíèÿ ñóììàðíîé âåðîÿòíîñòè _-x}Luσ` "W 1]5Mg1W9_X&iflfN].J5Ri`|CMUsxb\t{~9w~繿{D~",1D"Z/BCu]"Hכ)7g½5vMF (ew!S\#ƻ5|4'Վ:sO g*&O!_v/@B'7tx#v"Br>D&Ndh5|.Dҳ885= WcDOvhwp 둞i}{)=,c  fQbr8NO(n&;d5ϥ H=d `z:;u,A$5:`仿u;n].E3Of 7gʲ&Bb-88"j/\l{QϏS8{z!8+g1{Mn:얐9CޅZ+g7\`z8[I*,oUs8hO^!sL5?OAm4g"4 ֧lSkFN{`&DqڛZr8Q^"f*V1unwn?b,2OKyг~>]q-8>⒴6ܕkr5y35ro~sw>K_@׻qCvPb4f ŷjP/VCs{Wqsc4@jX uh-uqcM$bX($jˁrZ>!jيli;%[Жrz⨾7'~Ϸlݒ)kM홮Wwou\wh e}B9s:tN8p:tSR:N8p:tN4yMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:30  $> x9>>(16]2]/%*>1\PV{x |U'5@-q[V)@)P P ݊EZ LAQP T.YdE`EWWWQvUti4-R(HKwff:I3 7wν{ι{j<ϻ\;_Ա:ŞW{N:-WR2tja;_yw~=:Uޜ+kEEr^A\ѤD_e續FW%;j9@/ WN+t4J7*MT1w1J(5+)t/R_3cNTJm:H-><C*ǘ3E |Zi;;͜pza_ 矿c}I^ kp/iꭘx2o˽-^o2O/=fcX+=?~ȭ˝~{BBVM amzoay-. 5hlMr`ӥHF GC|򼳔& Uhz#̇9{=`)cX£y /I*]3|r+7ۍV(/ƷM>ȭoJOy|[6 z'r)KUmV|Gf%t 4nz{|:]=v5}ss*ݩ}[\(d߱ԯUeJF/uٹl~_B>ks|M FtV!`n/:O֗M4Nʾ[:୔6-v|Cw]5?qE>Rk\յCgv]~"'T8Qe^Kw[+z;흭Fu zo]rӞ Χx'>tM}vc2;;;]g}\5Ζ!bl+wW~Rəw[~O gjo>7;aܖCvfJTz&#wjizU-tn6/r3^/%ھ*zdN#É xb7q^Bo$hvM`vc/||9M~S{5 HnDRt`XZ{!+N ?&p 6U7W^{{JGpx½uIo׫|h@ͱ(>lSVmSl1Ǎ*$eh/.!M92NVn>K+joVHƑwK7|V Z՛ڹ|O~Fu} B%8>'$WB,?h[2UE%zEUH7˩wS?|z3(bS/ΑKC9FR6f99o_Rs~N@[;'s} #@Cz} Sf['+} f'}` oV@?mJAgp7+B`ׁ-vՅۨJIvtݯVnvyZDߛMC.wi=J{(%|2 pCv98vYB#<7/-F%հZS~sz&;4~ΦQ#/ǵCs##m^_kH& 7n}V`XE#Q+A{OgSO |!5[ieˣ_;gɣjgKc.2~8*%'C h,ڙJ}vk}9_b#n> 8՛wej]]Z=VύqV̵Ft~I{FT ,7vfBV97Xn0[cW Zں#Kc,wxI|HD]WONbBH?/_R,sMgS{FUMJ n'Lq.ؠR)=o,cy|ye`y.h '=\kCZ=rG{5 *Q5}R_l{qW {ӈy!ei_{Q+-D&}r>_zi}.ѽ&YhDEM S|rdo `{W@e' vx ?yA0yʟԪzBWc<$XV%Gp]*c}Z 'Epdk({U“j L膬g&ulLjo$٭:Ks緉]|]ߠ&p2xkJ. 8Ve N%k{lt0۠|FO .x)g39<׭spGpoL֪L{eSL6z/f^WxV&q@]~&[*+%coاilA08!_7-\I[ <˻[AmP~6o{TJ#;tT8d[8 ڌ+ =6vlo:'؍[fn;u̖X{g0C}9/r+ 6ӧ=ʭ?{cɟ:>(<1㟞G{t~cMVc klR)Ȋ?%='d;zT%ϊO6ԧga8ޓg2X ,%|6͡Br-=shd9.|f\^0Yܧz{nzGO lsY?..i1٢-Yʾ@>Wd`ޢi2 )ݹ9]pwXG痼tż}BwU8.W$y׀$pn3`]:Y}o99kx Vf.|!evr4_ۆr!F33s~߫R~\e/= S<~Te&&]mTztZ vj_gYXF`kCAcFgw?Sȭk?T/9= ǵǵ%9uOԥ{6W}Z,i}rnnglgMBޏk\ֽUݴ^o=0;smmJcf~]Ӂ.l~C9 zty~?=.XL =㇎FW6N>vhg5Ygm\ӏs?t 鏶xp-..\JV~M65pu} $+ kK+g]qJ-Ji{xKjRnGq=;|zF}1F)d EѴSYLP9zW1dv:ǹJ˒GjB$_)tCtTw/^Iؑ5>3㫄~Ыu_dUUFLȒwhߦ|d Yy]ZxYЎd86e8vpŎ*wņՎ;tv4vGedG',Ȏ9Ρ,y$ʎN {r2 g v}'l>'ƞƱs]y #k DITQaG#͎^{Q"ۉlQGYϨq=7}f[W.vװMzu0R~snɭ[貟1 WrUP)mM|xЪԤ:#&^qxW–gv8良W/^ղb<*&Ҟġg˳|a]}Tk Oo^ړ !IT;זHI4{av$~]-QBrm9ظ6%52b{dy.*>afGbHJ黄:(7{jfO'(ӿ6o]=2~9{?=Mm?^_wawy%/Dj'k5~K*)5hwKvCs.#mwͮ_kw/\v=q=n}z` ߀5\l-rcۅǿ*wf_ 곘}mUeJMG:^U֪w,kqJ?^ܾZƿ$%/հ OܾNr%}]C7:׵Ko(v}z7r+{S+e{2`{غ* v u]z~;k㗲[ݺyMau.O>{N gg5j|쳿Um+7bq_vGFlv;p<"nyYA͒G۬aTMXq GiYxdn=HcfG$=bq{=16=)f/?ύw>'J){м3T˻0br~4m72r6:^M9xMDb+7[L)-Fpy_rŭoGqFW7<[g->N|8_r{G_򙭫Z6:%i{իģƞ!oJI:Mھ*e|ϚQ%[bڹJmkVkrUd~U;~CCU2fw$o ;&yz|(L;.1'4 `,.ԇ 9w;_o3.vջ)M z' f1= ֖&~;6wHg/[[z2AI[tTͿ!w*WV%|(v~Rd~ebĐ%k=d:%b81w/?(,5j(ʽ1*C')ZT!0տfRTod:ݼtߨ2<[ S4MW6v+u*12lR֝=Y{ʫXwfu'nWBOb~dPoH|3ȯ;Qg1Ś䥾]oz6k/xm,G~?-6j %? _R?,0ױuwc|+أW0j+ܣ{woז~f5u׉1}êį?44qJ\m~ןm~U/ڹίwJEfH_'ƥsZdV)庎}9u}U mWR~v,p]ivx:w7S_ma ٩zs7B8՛-Z|^+Byύ*Do͡J)4D-%"Pv~⺔oL_[%'މgSScrwցi'2N&wNVDgĘ&(ew*JxRmysEڹzR׋MWп*q'?X\"~r[ M6𧔣\a!mJaqnV7Q z!ƈ>Ő,WEPvrhz&-4EԙT?v:)1c)G2ncv8Q[n]Btt!o4o䞍m\Q kGdBY?ܳ~hFt} sIx`ީky_o:ݛwh~>Vj\m뽶s 7FbAa܈wл] ]wn9$n dˣq2dbM$,hч w ɧyG ]~u4~'9w&8y]_ws6د94#l.Z׮M*s=j_.bp>/k+ىUׯɂ;n7g{'Ikڕ;wȎ2eeʼww6~W{S~1R;SKƍZS?/xgz\Ok%i7C* >>f¡1W¯rmͯ湸/xgzHhwrwWz=j=-ƧCs\Su(Һ9aX51fWq=i*8&\u^?%(p~-E?VύnwZ=7~-&|cMkrRRi)f;5h^p߫Db\#E/VIK?(Wf*r"w~!jrkşHN"GNVϕ˗N ߮ AZ{SZ=7nkaܰryREm4ە#[${E]'t=wM$%ؔ#7{K41K:)4~c"813}qZ%=s~7ѩœI =vw*Y?5JVׅy`xꞧ%֗])j!y]'_Ak'R-= _o+x M>v,IVl-nVB&H<"'SlheSC,I uT藔sף .~ӥ!|5ҟKω&^c&e.~TϾKD??0h]*jϟ}F}Dt[SéwcZ=WNڄDZ=w zup(7#{]J䮜8HOcr)c;c|RX1͗Xz_4So7V/ NEk$1xqZve;~}É_,RNz7+slM/>GM*r\m_njTޙ>+>&u}wt757]Y+'_Mw8עߌ6eny$Q4ydO4щonmfMW?mJD7oQa5{G c$s )nTVryZu}|/zD5mgoXrJ}Gʍ}"nY>|dzܘ`AvfkMrb?g<g<OrF_;u04~Ox́Y,د۔C-X'ʛ#(^I;[?Gk'*Y]݊궄պ^#94/ 1ҩnb)k*% x$>DkEL&3*}YUdb<'%PNZ=73A›Vύ,i=IbZJYry\ZKC,~kH֗Xҥ$wG:nP[$I\ydUJ' P~OUzthRN|!\NC<6og6a~R ~oSAv4H,y](/7fac~NU?VύREMR%1n,uucKR׍^F"K#5Rxԥ?c|k,텱ԽFC,_\W|~N®K^Qw~X,nYJ'Re^RO,UXSJ*rQMUY{X,[Ռ6k <ƅ,["j}ۿL-OEcBo͹3&]~!nUa]z"sJu#Z.G3֩Cm]Qo@o?`E| fz?V_cxw֟v#;7\ bm')T|7=@__L;!N:H9S(u6Z9n`NRKw)F_^eRG= )\~6S9u]pn'?RܭJddfO:s$_GS,L??}kzf_JgDS!KUf&r3@f% =fW}bcvU _<2}䫨J|x]|+fo׮O}`?Oa?:+Gr3K):.,)BT\ o}ש!O h|,ܣJfxKO)YOawo P§DeȈQ>=(r}Z*I9򉎰rY#|7 CU#yOoԽWD´VcY,d;4۹|kYܷW ە_f_AP?׵@Y< HįP^LNN>,^DH>P9:iJuȾ@7m+96u9w>N_lN7JBb4q{ SװMC ިmO|61f}m"<o w{$l?X[8Ɯ>pNsEb*U^S@敕߰Le+ ϪG32/ abl~C+oPvdGS4&ɕȏٴ_jcIhw<հAi/xmiM%|(vC\WhW{}m~I|ݷz U='sF[:PvU+;0l<2G\t]w*^#W+oQN*WA'ͺKnU$g:}Y4d#TZź+Yw͕\?kzU-G] @):xkΙSF;rkr+k uاfXN] 6Y9 ?Ж'k}|q|CjDrE;>*;Dei\{[EU(xGmP-=szhAýn}+pVib4V|%3fڸ}'>`8p1x%ރ|- 7vYuEv20u9{iݦ2N2.aex1Ɯo&_P+&eV:f?{? 4x={*J^Kmp ]w׮Nf}gOU?5%t;fi'ԯr]rSCoVk;mJȻ6RACmk -wJL]Ԭ4Ci<%/9\Fc|˨a۷;~WޒFzK}wa'i_rt隷>-y6=#\8..LËU3>hwtR|gu<ѷݐ;7JuLvأ7g~ty:;ID }'z+y-!NU;v!%[2ϟk3HYSV8p=y̾0248 $|1~-uw /xLį1?Ԙ]~1?c3j9$Us ޭk{u{'Ou.zJh!)Ļa7Y 9G*PyGԆܔ A!3Md$8ykBi!㑑55OڊڵoU;i?OuOwG {7vc}`:6lwÙq/͆N!ЛN1ޚNN˱!FȆT"6zN 9Q+M8ؐY -¹0HW19!ջȱ!ͱRm^fC.eC ޙ v>•ʧkmC !kQDZs uMaMVW`}C]?"{ХAϥM]I*[[=Q9@o[/jr5K=S[o s8vq~4x[=\=x6t{oM=c i S62yFx!:=n__iqX =qp*5f_A|%~Gn*=qكAsTvK4&\Z0nj_h1+w<>h=&+[{g4{>zpE냟~){K a}L{b1{kz=0ޚ~݋~Sc p *2޲#eݨ>F#o] ; !t3ulDo͡Dñ{Ԙ]~d7ԺqW4#I&hL2u)_h7l`#ݰ&+[F#o] DVv5m_OR 8vc~˯Rv#>lܸyƠ؍ϧ uhTf7yzpơjEMi=coVG  gύ~s 6{ڇB?aR0aLIZ،،?K&o\;4i~`Ac޽Ɯ5́ ́͸燰 a?΃o R&gYy6y!w | W͏f΋[m !< O mz𞗜q;/΃/&4)y^46464v^4a]:C&\Y־ q߂|`#Rx{Sư׀l`-y~ lw^cƎ;l9Flkyf~lwyz%b}DJi5Juσz>{ܳS_Z{=څzm:?(Ѻ7Mi!9SU|Ro9164vCzFuv;Kӣ&Q:׆9>Y ?Jڕ}p' q&,^/Cy֮܏p'ě8N 2]):S%̯r])?G1.7 4ڿI2U+E@rp&N)׻J8/]a=tzq=`s!zW6Z^&lbk&C)/o`3vҚJ6֩s[911eLsc㷘ڔ$a[mF)G)0ʉ@#ЬMJߟs֔SCNYI4hЀD%hJK_UI4܉K;q8֮A\b6p'.%[rp?FcoҝBwqܭn(fH¿]xqKЮ탵}JZۛp%DwkWā#c*Np:{%j TT9ԧ".L%M\"ksğ#ǟk%I\ߡ%/I/׸K9qƍ LXrؼM\%ȉKZƇ&>49>t^&.L%7;07q ` '.׸Y;9kM\%ȉK;9gL-[7q'zbCu A6o `M2&2 Ǎw^47wȋ-،y-o6~.35h[9779>񙀍ϔ9>4gʋff΋k_6As5h́͸͸l|ż_+Bs|żhl l h lT`EsTh S9779>2񑁍 24Gy،،y@A߼ˋ *E߾ Dķ{u78૎{Nw?<r+u/c,MG9e6{5:ޮO9mvʨc}QfG[=9}nnxa$[:Ѫ?z|Ans]bq5֏?)?.V^*ryގΈPʑ^kV7IptVe꣘+Mb8p46ic&UKoi}w_ |E-#󳒹N}ϼ$tԱ Kn}t Ж rr`[pk`TDɤNKwnRs[b包%?ekerw EB]wzvNt\(;8fs:D6-KT䌾]56?:ݝot]za^ ]/-qyOg ں9yh_+Lovw:/{|m^US4],i| ~f~ׅP;lNR`DL6^kmg2ߥθ+vW<fgiiƯVk >Z6Uj̕+[TIEwr&wD)ԁUK-R]r_P%Ӂ:ԝdLQb-Ha7Y ؖ{.M%ٚ˸ٚql#_ ֎mJIVd:_=7[dppvpU2/tvp< 84ϖc8֮>_ &ה#[K#ଡ)?_ eZJ̷R ,a/}" Ϻ<dž,/0I币 ͸a}\!~%a>IƜ5́ ́ ́a!%?4n2erlh^yo`_B4)МyM(́ ͏ h>7R{Fh/"Ҽhlh^+^ {Cؿ a_^ue YTv_r5 Og F ll(yƖ;ll u9ѩFl-yf lXvō#vi~(U+:ZU6ҎΠ_ B7^H^Gh5to:,I_ʉO75߽}'ݾLgĖ=wbS '{i//,Zl޶YiR9_MÑVX6;t$~v$Glr3fkq4jRq,}0 ϻx1OkW ϣ ӄi8xL" O MqzZRx/TsSOsd6T`ρi^66z-/o`@lf9j˹k g?Ck^|~ Zքk%7jeO75#E;D&;>\,qm1/g6#fGuw^+=[K4MSgo_*taJkAQ98xPîk_2 Ƈ[K ڰFfr]ԁw %TOx[ϥM{P<^<x[I~f.qm+%쌵;i0𙇮k6l_kP|~R!$ߐCɇ"KD|t%ȇLKd̾KCCNxr r7ko/< fUO?\Kb]3@ŶOb4$C(w@tmC'zl}Q|@j><~|(s3[v?D_ o= 1}; ܵW`;޳:K\z]a*5Jq7nGMݸ]g=SJ]hڦr/nk-sx1Y %r][?{Z-O6 _J֎ڔ|T/9a94‰swp^DH+Bw&n}NFcNL})ڕզ,-p'yqv>[3[20ܛԞ!T|]XN)^PN,mci&l;yyylG'q6q<`k<1<6ϣ71D`C61D`7k aLWø_2n/6eJ&vʸQ8&v׸k<OC_amMmw:}gD>+Fy 6:T`S^6z 5`Ӳ9薼`36;/1`3ǀ˂߮ݤ2y7*sZ*Xi;΁SdGi1'kXZ+ۘSyKsbNbNo"ڿ<έ?t1mhM!).)ӝߺfYm1'Ǽ\E3~smbIۍM6%&_ĒZS;geK =Uj.s.G|cIsԍ; -<K%'z9+IsLlF2U%q!a1!D}g) ܳXô)p4`PAs6=zgNÓ}>8֮sgNÓ}>8֮gNÓ}>8֮G&;(6Zar *d}&&v>h`Nay;1nN͡{3HfĸY#5nN^"=¸;;}Ь/3rg.}%́͸͸m4Ϛ61/`yf]jsui^46f4v^4g4}c4qhzx^46f4v^4g4}k4C@s6m( &:+ؖ<`cC 6v 1`c>6s`2s׀ ^ 6`3M1`3Dz෻6jPGlrQ]Q㉩@_=yt;[HI~XИrACo[?k%A_.o{6ItRҬgί=y~`4 nޡ~M~ojwj2>?>idAf'Ȏ yjn@pgGϢi0pmg߅sW&sTC{K%$P>uL0U>ޛU]X;vAmN1*72M#+!K+q(21QU}?x~U&Wh #[8{sCe ~R&'[^-ont\>quϬ7%v7+m\ӷ=J'MR-=-g[{Ԙ+I϶7~8϶?s|h_L䰜{Nӷ{nrgimOqI*{_`vզSzstm>4' 쓎>iڕl=K::;}qܭ]9%@զ;pg4O:+YÖ&yFF*k[-}Y9wIuXO^y^lW8{4n ?UfxHϫM71F`2sYc4yfD>i`O:q&͸o5nI6Wr7U`p7ռ>i`서}ft& L⺌.Щ&|r9 l~;(g~:j&Raqĸߌ،y l7odt ͱy،،y6^h9Cz ׅq;/-f ͙%/31n0n`Es uv^{]9>4gʋk.yќ._6{]^h،y`4'+xΜST,,e 78 ãäå * i p – i-ÿ ÷àñòîòà (ò.å. ÷àñòîòà îöåíêè ) 1 i (  ), à i n – i-ÿ ÷àñòîñòü;   k ..., , 2 , 1 i  , k – êîëè÷åñòâî îöåíîê íà øêàëå. Ð åçóëüòàòû ðàñ÷åòîâ ïî äàí- íûì ýêñïåðèìåí- òà ñâåäåíû â òàáë. 2, íàçûâà- åìóþ ñòàòèñòè- ÷åñêèì ðÿäîì, â êîòîðîé îöåíêè ðàñïîëàãàþòñÿ â ïîðÿäêå èõ âîç- ðàñòàíèÿ. Öåëüþ äàííîé ñòàòüè ÿâëÿåòñÿ ñðàâíåíèå òî÷íîñòè îöåíèâàíèÿ çíàíèé ïðåïî- äàâàòåëÿìè-ýêñïåðòàìè â êîíòðîëüíûõ ãðóïïàõ è àâòîìàòèçèðîâàííîé ñèñòåìîé êîíòðîëÿ çíàíèé, ìîäåëèðóþùåé ëîãèêó ïðåïîäàâàòåëÿ â ýêñïåðèìåíòàëüíûõ ãðóïïàõ. Äëÿ äàëüíåéøåãî àíàëèçà íåîáõîäèìî âû÷èñëèòü òàêèå ÷èñëîâûå õà- ðàêòåðèñòèêè ñòàòèñòè÷åñêîãî ðàñïðåäåëåíèÿ, êàê ìàòåìàòè÷åñêîå îæèäàíèå * m , äèñïåðñèÿ * D , ñðåäíåêâàäðàòè÷åñêîå îòêëîíåíèå *  , àñèììåòðèÿ * k S , ýêñöåññ * x E è êîýôôèöèåíò âàðèàöèè * V ïî ñëåäóþùèì ôîðìóëàì:    k 1 i * i i * p x m ; (2)       k 1 i * i 2 i * p * m x D ; (3)         k 1 i * i 2 i * * p * m x D ; (4)   3 * k 1 i * i 3 i * k D p * m x S           ; (5)   3 D p * m x E 4 * k 1 i * i 4 i * x            ; (6) 100 m V * * *    ; (7) ãäå * i p – i-ÿ ÷àñòîòà (ò.å. ÷àñòîòà îöåíêè ) 1 i (  ) ðàññ÷èòûâàåòñÿ ïî ôîðìóëå (1);   k 1 i x – çíà÷åíèÿ îöåíîê, k – êîëè÷åñòâî îöåíîê íà øêàëå (äëÿ ïÿòèáàëëüíîé ñèñòåìû 4 k  ). Ðàñ÷åòû ïî ôîðìóëàì (2)–(7) äëÿ ãðóïï êîíòðîëüíîãî è ýêñïåðè- ìåíòàëüíîãî áëîêà ñâåäåíû â òàáë. 3. Группы * m * D *  * V * k S * x E Контрольные 3,725 0,874 0,935 25,103 -0,13 -0,935 Экспериментальные 3,921 0,823 0,907 23,136 -0,35 -0,834 Òàáëèöà 3 ×èñëîâûå õàðàêòåðèñòèêè ñòàòèñòè÷åñêèõ ðàñïðåäåëåíèé Òàáëèöà 2 Ñòàòèñòè÷åñêèå ðÿäû êîíòðîëüíûõ è ýêñïåðèìåíòàëüíûõ ãðóïï Группы i x 2 3 4 5 i n 23 78 81 58 Контрольные * i p 0,096 0,325 0,338 0,242 i n 15 64 86 75 Экспериментальные * i p 0,063 0,267 0,358 0,313 'x{lǿ =rh{VC4ahd P]26ǖ]gؒNQ`fcva1 "(q+*-8P˻﻾=9Aso~a|JF=7T;^&'_r"ѝ5{5<箮=z,񈎞@tޅف{7ל_2}cu"{=iz]‹RK^ď[8MWgko|-w5F yS嬊62F- [/8TÝm2—P}7?|8%z|ܟ |Mr1n7)wWbn`*^]W?VxUZηs6xr{(~%4uӝ^zpa侠#l/[͹. ҟ\ˋ'yYa%|z z< `7@m]ߖTJsO؍t3UTM8 雝+sgH;w6_'ۿk 7]w]w}$f󵀾 :׀pV9C{^S>re Nc|B?K[l$>}\a6Z8M8Sh/blvZakҗw7l~O[Ou'cisHތ'0N߯c8-9;}d<'{pپiE#ȑ/l 5Z#wdU}O-:FVTYTmEýn)3WcoXnrn׊8 kyN so~k_p^Ɉ=Nt7{6V#ۡ- Bd4)Fh%۝"f[-`mL)N Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:30  (^ CQ (162/k .1{x ]EOƄIN턐NH03$hB+! A1BPQè1+9θfk`o-u S҄NHH ߮>}^$kW޻jSnC$7}!IVȽsL|ag̒$iX$iH&NnHN=(I+]'=oH!O>*⇾,Vi /d)n@OA8ܢ4h>ҖJH$S)IJy~rUq W&(#efg4ķ\IJ?:+&Ѐxb|\ l&w ^6ת,l&6bJz^6oYGܦ0|lw"c{0ٙ]d['y:ٟ<+ຕE{!}2Kgٕl9甔RJl㓍ɉ)tp?)(j؝x:Ž??bٓeIYƴb.4N3^I(붐Fk<Ǹw˹OjF7KpҊd7JJɋn:;?#/ qj`<ݦ\ީJ#-;3xL6) z@pBwNQIbn´ƏiA˴>Ԭ4yMc%ct& ]p*eMh㮏tp%<]pcόr[nyxV{ա?D6LϨ?ɑFvRE|;,P>nl>ؘRyuvhip~UwԔVu6aUaN' ø$dx`ҩJpKٓXhcwiБT* > V9p'KAƨmS4C~skfSS~u3mVZ7%Z9x)Yw{;K?\MɄ#A-s&}G*&ɮ_xڤOV$g'*䝲E 3?L=^!y% K;W)˔wEi'mO_V˵9Yμma-ytT& _?G"$YoIg.kyOS.?~,cx^6g7vP0j\_w17;9Ym.k#%9ڃ#SDs(YM׋ ].~YUS6 kBam5ՙe١)bzZao]ՙέZ}3^lGviJ8IHq~xD .pqS.38ԏoG:;OߠtwSZPsO|WyRX`={xtx}[NU@Z*upWhBVgy>6Ntx?F|gFQi ۬޹N^'fݍZޒgrJHϞRH{%;?ٙJ ZW~{,8hxwQ880L .Kc<7msہu!n9 3<$9.xNy!EugtGzv9 z#aS܎-'5vhw$?7 aAzvHZ5EƘ1* .x 3|/əƬs#δ",p p.Mùf~]:yoydG;*vQGG]7vP(WѼFG[^tKhGHg~FoJvyIzspŏJ콆bһa)x;Ӵ]j0=mǐލ rƁO91_[;Ϻ|ĽW ]XA'jl߉Y7%ϖO9n͑wv}n]N˯.\I.'Jr ||7$"t9{!y]NVRyr;Ѓ}Wk^)đfi8x@a6P\<<}pP6qElK43$9yHo *-Np{nQݝr<> *ײg#Ƹٚ prv/, {&LczC u3,~A_ӈ=Ѹ~|pKӀ'ۑG٢>0[&!=$-rk.sV$̕>V$B6ݩD.Fx83yÌ$o5vjio-b8 <|p8>.4daI8 ^Nt8lxwߌs+t'j|GsGo8r8v(=.g9'|Fy`NҒҘkG iҿTw=igZnr >i̼i μ1Mox6Pg'e\\0y8Lۈo&̴2 p cz"~).|g(muY|-#!`, e^^02I|f)ydb4d e-~䃛`=UܿUM[Te#N{Ҫٹm*Zs1G{h-Zx9ߌM\>v \ínZrW31ע_jlu];:~$ڹKvCs)Wŷe_i;z&X;7;CwBokd!ozg8=%e3|?zƁ<2`[q1~9۶!ȫO]Z4"Ry}[oL%2 7/&{Kff׼c"4I;QMoh-g qЉy|q"S>Mxbx{#3Sq̑_=-Ji8^3jߐO(Nq-b]z;*.ڗҀ2KF^hb;w& ^^pkQa/gL(n]:EIk&J8nGy9"P/=94F53U( ɸ"nAb_Z8wDeh27e-CH={]xX_ٸ5N{|Ї~ˤ 2> CZw Z>nqj_v1_eг'atÊ^ #qM;CdXKZE6)yؤvZd|^PU7ӝJ;WE8Yp7ga-*ٮ8dpj߿Wf & 5B=hߗn.ʶ%>6"q۲$>hXPp ~ۖU C9ޞ۲s}! Y7b]jCȧ)^諞x!xmOtۿ|z\;AQn`z1F['j߈;:B'b~$EJ߰l^U|c^]лUkeGk__0hn(?k ^j}n{d̮~[C9hog #H>iG5U.ﭱQuYAb[Ii*].~lt+qsS[O)m} _s ݮ.V ؙ_s=`t}K7Qgps{36БyZgYG:#ĭ['R;Hs:ql ~m /ncmKJ~7't9iش-dq9YLwp';Q8Qs>[-*Iݬ>5ᛨrx7@lKwhl^Asx|Kg9L9G2%$c(7-3z1^s C95#ώr9x#r+=2WdCi].~4{J{!W!5G)A;$7>42-Їtpt5I'#0gZ1^ OC4p;ofxž;bGnuQi ߬c{ɾVOh|ro}͟ 7䳊4"3Ax{03$(O=1 .uˀ 8eEçy\L<|` P/msy}fo(}ޜPu9 %,ճKosyK0R緤~}HHU` 9O'虞.52oa8Ҁޑ#n8Ӛt⦻ura:Z.|d<t![<;LF.?=w}}|S(n*a^n n6Ž7Fe_!]=w`A}L7|p=O8zf|c|4g0 8O:cqn>4,emlKp04ϏkSRJ["?C?Ӊ0kco0m5cP4083,qO^K O0)|ixqt_#y( q c_7uu tA]|]QY-:`(0fb@gm ڒVf0}@XM[ޚg٥vc!N 0q9gYGc00yX E.OqSÓ>[ }޳{P~J|^mxvfaggz'WzBgБqgzs*ъ[I7)yo܌Q8H8>myxrn'Uxh ׆;>>QY {d1-l\&xLg WX総06wGXp m, `-uz$cmB0{9}'0:񘦦g8!L^K1Cm4xo m0mn;c4/*wim ǽh8Nt }֋ϙJ_WCEJ;QEGyJR@ꋒg ]:7f@OIaɃNo:o!t 7b} ַN}Uӷ4pV1z;3nDK ʈ#6Ag+ ZU%LΝ&_ VIGKZ1=vl,ע_Bmƭ[O}Ko<8Cַ_+78Ejg/J;Wirc}˻Z{ w(uzBߔ?ɎJBؗ3Tag_4d;Rύ[=Ngksv8ӱct9 ^C_𡃁1>Ƈ 0v 8qyJ,pࡼٱuKGi +{NQ~ҘhNh?CC?=Uj7Վj emW}_i7cQE۲z_vz NXrq$>p,>IĝE(z$mZ4at?Ǫ؉όm?#3'~(v"b;2-'9n7z"yw4yXd6n>(i_}PW5?^?rl)i9J{˕>lUOmUU%bSUߍ`y|s=ljk֋=Jy>pl](={I4|dUkaf}4?>^? Hy%絾X/^ƶ*d9ޭr1_/px2/6|O :VE*cyF}~RgQn]0GGīggT떓L {FOXg(8ޝy"{o0n./Jeˏkݢ{l)0m"\Sl/KvcJdo2s _jT~Ap7t )\VpwHp+2'e=%{sWBcO&rSImj}FvjO9}Ǹ8 v6PG6/p=5}LFn&s&Gw%}?4g B[- 'ݣ/f; AzN[$I{O;zH3 q䀸GtHxIyG-vG_:p~0>pq=q:.`(m0v孚zd+0\I?/K:N:_fÓϧ=KaV + RR wOnr$b)mI9_\1X.xJKMe_N(IOI2Ǩg&#/o vҐ׫My;{f^/"Qwo_2 1C>s}8 um*@~Ưn c7kQ$K./s\;UӒd>2=y/x7]90v{N&X9Εk~Ì-k/K O=uȷ6Vп2QCyLa!|ӜZ㘇z[ HYrK諑CjB ڊL$9 _! {t`^oV"~i[7[~q|/K{} ;1IMi-Ig]5A6i.a@W8|±ñ-*nLZfrf.^S| B6jk /fyr;`⳻%+vw`3>Oj˟!88󨷶zv}Dz*ת9z{{d0Ɠw| wNt7ʘ,V\p湶0&z`kJz.E"y\2n7kls_myCoϛ1?@%~2K]TsYM܇_zwG5Ứ*9ozrU@8ږ2ŵ[NvߴBN_sH:ejK?v쒕/.dyc#]qH0qc9x)KlO|yVkl<ڼ곏63'KЉM,j}CYռޞ. Lt^/]yz-Z nfoY[nsEznvɫwdSUs1oW=|]2K·B쒁YM].{6|WKnK=ߔ[6.!߻m~;Ûk7klPvILiC7@UlSQnd~ \;@'r]-<Цy/IC/CQOu_{~ok46j]1Z?(IZ7uoZ{fVYݏduOuݏNhn\ kMsM<9wNREk%ugT'4ߐZӜ7uooꞯ-z AsmYr~FVwWV( rN}*{|hM=[k׍u׺;T'-3޷9zcԍWԍOԍ.uרyo7uS7^FΩ1Fy-~ԗKpxK־SWՖu*r>rJNmKʋrdxNaqAc4[!*o,c0rH'7MmSnz| \`SjXwR7NfIZwR7:љ7k?fGݬ6X>z5>n.k?ڏ~SiRXQ7k?fGZQ7v ucߵcuzd ^]FYo6k-kuzې Z䋪]|t gu 5߬U7kƧn5fNuYQ7s u3ԫߌ1ƧnXsFkJk2muoj^%k bĥx F)7/N*h^Yj4YMNdc1YuӆkTU$h:)OIҠ뤢Nmg4жrTvIuRvs:=M5띢Nmwd5m4}\_,nڇnG=&9Nڮu>$fTѫԉ^G֫߬u>$fT~˩>:ugV7kpbV:{:''o*ZJ CeӳY/І}Ys(Ď_*W/~3R1Q)s3R9TE}tV7iԍ^+Y7~K7k ~K7^Fo]/~Ǩ=F1~ Cs4W5cI]/GPfѡZ/9Go]/Mz9zCsw:7{Esہkz5BslhP/9nM^4WS^Ǽ\rQ/.{p@QzSjdA_ݹ8 {;S|@o󾥹*oИzIRGy*aE+ʮ@mrs4U&%9([rXCվrXSS9)yOy䅡<ޢ8)?*_8B0,?"J*?==OJ>\\| =:Ƽ9 >TI&'mG{F~:qUz5G\0^eIyUzņVɟܴ*=cB]іói3o<7ExU;sS[)0t̬nݔV%U-m˔S7|$<h:|D>,MrGIٷ.C>awҐv<+p~+BX~}4>m 'hܘ\[Ԇ {P'nWܥlUw)-J٪kWv _ޞ:}$8#F42!*9Ti!QD,,79 Ïî ðåçóëüòàòàì äàííûõ, ïðèâåäåííûõ â òàáë. 3, ìîæíî ñäåëàòü ñëåäóþùèå âûâîäû. Çíà÷åíèÿ ïîêàçàòåëåé ñòàòèñòè÷åñêèõ õàðàêòåðèñòèê äëÿ êîíòðîëüíûõ è ýêñïåðèìåíòàëüíûõ ãðóïï ðàçëè÷àþòñÿ î÷åíü ñëàáî. Ìàòåìàòè÷åñêîå îæèäà- íèå * m , ñîîòâåòñòâóþùåå ñðåäíåìó áàëëó, â ýêñïåðèìåíòàëüíûõ ãðóïïàõ (3,921) áîëüøå, ÷åì â êîíòðîëüíûõ (3,725). Ýòî ñâÿçàíî ñ òåì ôàêòîì, ÷òî çà ñ÷åò ââåäåíèÿ àâòîìàòèçèðîâàííîãî êîíòðîëÿ çíàíèé â ó÷åáíîì ïðîöåññå âûñâîáîäè- ëîñü âðåìÿ, êîòîðîå áûëî èñïîëüçîâàíî äëÿ äîïîëíèòåëüíûõ çàíÿòèé ñ îáó÷àå- ìûìè. Ýòî è ïðèâåëî ê áîëåå âûñîêîìó óðîâíþ çíàíèé ðåñïîíäåíòîâ ýêñïåðèìåí- òàëüíûõ ãðóïï. Ñòåïåíü ðàçáðàñûâàíèÿ çíà÷åíèé îöåíêè îêîëî ìàòåìàòè÷åñêîãî îæèäàíèÿ * m , êîòîðóþ õàðàêòåðèçóåò äèñïåðñèÿ * D , ïðàêòè÷åñêè îäèíàêîâà, ÷òî ãîâîðèò î áëèçêîé òî÷íîñòè ðàñïîçíàâàíèÿ ñòóäåíòîâ ñ ðàçëè÷íûì óðîâíåì çíàíèé. Ñîãëàñíî äàííûì ýêñïåðèìåíòà ãðóïïà ïðåïîäàâàòåëåé-ýêñïåðòîâ ðàç- ëè÷àåò ñèëüíûõ è ñëàáûõ ñòóäåíòîâ íåìíîãî ëó÷øå, ÷åì àâòîìàòèçèðîâàííàÿ êîíòðîëèðóþùàÿ ñèñòåìà. Ðàññìîòðåííûå ïàðàìåòðû òàêæå ïîâëèÿëè íà çíà÷å- íèå àñèììåòðèè * k S , õàðàêòåðèçóùåå ïðèìåðíîå ñìåùåíèå êðèâîé ôàêòè÷åñêîãî ðàñïðåäåëåíèÿ îò öåíòðà êðèâîé íîðìàëüíîãî ðàñïðåäåëåíèÿ, è çíà÷åíèå ýêñöåñ- ñà * x E , êîòîðîå ãàðàíòèðóåò îòëè÷èå ôàêòè÷åñêîãî ðàñïðåäåëåíèÿ îò íîðìàëüíî- ãî çàêîíà ïî êîíöåíòðàöèè îòäåëüíûõ çíà÷åíèé îòíîñèòåëüíî öåíòðà êðèâîé íîðìàëüíîãî ðàñïðåäåëåíèÿ. Ïî äàííûì òàáë. 3 êîýôôèöèåíòû âàðèàöèè % 30 V *  ; ñëåäîâàòåëüíî, ñîâîêóïíîñòè îöåíîê ìîæíî ñ÷èòàòü îäíîðîäíûìè. Âàðèàöèÿ * V â ýêñïåðòíûõ ãðóïïàõ (23,136) íèæå, ÷åì â êîíòðîëüíûõ (25,103). Ýòî îáúÿñíÿåòñÿ ìåíüøåé ìåðîé âëèÿíèÿ ñóáúåêòèâíîãî ôàêòîðà, ïîñêîëüêó êîýôôèöèåíò âàðèà- öèè ìîæåò õàðàêòåðèçîâàòü îòíîñèòåëüíóþ ìåðó âëèÿíèÿ ñëó÷àéíûõ ïðè÷èí, êîòîðûå ìîãóò áûòü îïðåäåëåíû êàê ñóáúåêòèâíûé ôàêòîð. Ïðè òðàäèöèîííîé ôîðìå êîíòðîëÿ – ýòî îðãàíèçàöèÿ êîíòðîëÿ, ïîäãîòîâêà ãðóïïû ê êàæäîé ôîðìå êîíòðîëÿ, ïîâåäåíèå èñïûòóåìûõ, âîçìîæíîñòü èñïîëüçîâàíèÿ øïàðãàëîê, íà- ñòðîåíèå ïðåïîäàâàòåëÿ, åãî ëè÷íîå îòíîøåíèå ê îáó÷àåìûì è ò.ä. ×òîáû áîëåå íàãëÿäíî ïðåäñòàâèòü ðàçëè÷èÿ â ðàñïðåäåëåíèÿõ êîíòðîëüíûõ è ýêñïåðèìåíòàëüíûõ ãðóïï (òàáë. 2), ïîñòðîèì ñîîòâåòñòâóþùèå ãðàôèêè ôóíê- öèé âûðàâíèâàþùèõ êðèâûõ. Äëÿ ýòîãî ïðîâåðèì, íåñóò ëè äàííûå âûáîðêè õàðàêòåð íîðìàëüíîãî ðàñïðåäåëåíèÿ. Ïðè âû÷èñëåíèè ýìïèðè÷åñêèõ ïîêàçàòåëåé àñèììåòðèè * k S è ýêñöåññà * x E âñåãäà äîïóñêàþòñÿ îøèáêè, âåëè÷èíû êîòîðûõ ðàññ÷èòûâàþòñÿ ïî ñëåäóþùèì ôîðìóëàì: N 6 S   è N 6 2 E   , ãäå N – ÷èñëî íàáëþäåíèé. Åñëè 3 S S * k   è 3 E E * x   , òî ìîæíî ñäåëàòü çàêëþ÷åíèå, ÷òî ðàñïðåäåëåíèå îöåíîê ïîä÷èíÿåòñÿ (â ïåðâîì ïðèáëèæåíèè) íîðìàëüíîìó çàêîíó. Âû÷èñëèâ îñíîâíûå îøèáêè àñèì- ìåòðèè S  è ýêñöåññà E  , çàïîëíèì òàáë. 4. Группы S  E  S * k S  E * x E  Контрольные 0,158 0,316 0,834 2,956 Экспериментальные 0,158 0,316 2,189 2,639 Òàáëèöà 4 Ïîêàçàòåëü ïðèíàäëåæíîñòè êðèâîé ê íîðìàëüíîìó ðàñïðåäåëåíèþ V(xilTUϛʰtOۙnP)`ШHJ!PQQ, ѢD1E0*J Ei)M i-Y\EhEBy<7{ι޽DE}ClM$)r F_Ad2:ClkEzl!5Hl=OQ(>i2lC 9'KL1 kMfB>I2ǰU0G)=6Y2y.z$+X)U2H*a@OaYL=1=Iz2TSZn<d|]'&Jף-=R‰[eL>y9)趠+A $Z17f;AhYB 8z5g|j%MĮ g=AFkk_.ݤJSľmqLn^L5\-Wzo[>#CZFRÑ#%>ooo AvgSmĶVOVPþ]?]5;˘&t%ß<<?5>gҩ|Ia/ +.jN^&DmRk=S~_o|//7+YodCmNdYYtEmU xYuSaoWmMy6-\`2ϛJ8^&EF>9xc/]p 2ޫ%J"9`+O!gt015*7򩅋+~'g}P -#%|r$ fN$e]$b0_b8X積2rmqFpj>? Ӿ0겊oB&:8⸉l ւOx-1kܑķ|D-GVSǕ`HiG\䬃 ֻJ>s@(s߇\jx"]DSr0_˴N50<z3A&1Vo*+wg@-nzr8pA<'Pj޳z*৊g7x~vMc>UO#A5v5T;\r3ٓy&F vMBcexgB_ *Eu~.I|{uµDɗ5΅K\`O}^'GV#SGD˺% %`1s0b{toB/v+rLYs#_{O6CJΚ=f~4jq]鍳^WzlWvJκٝî'>泺!i@s鉏@U.N|.W#O3u5;kwvΐħokCwWx;뉟m هڝ;Lǘwz40^iU[=)TwSUU+;~Y*`UUV X* ǿշ*`UUV XT^KMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:30  h 8X`(1662l/n1.\p{x VU;4/^@AeD1/豢&G+2KԉէX9eόSJs$f34#|}mX󬵞g=Y뾼(T8ENE|F.SORgh(.W|RU h .^1k$NuuuѬTX]2oգH%1(KǷ';bg]S0ZLC{Aǂp5G!h+\e5žR(HZGrP>+ȒǏNp(Wl^Wd'YalJeﳱݰ*ٯCy/(0eVlځ6vWX;G qN_tꗱ}7 EvW_ siހimRkʊmF+t[<%o]+,}޳QIyd(Ga $c :EW6BУc\Ayx/|+(4*@OyhYiQ4)80UJ6s\3/Q0/V|B)Rt]&m/|Ɨz/#//CH[6~93c≁VD;4[ʾ_7*kLm\U]-x`y^)yymqom}AtM\8}Zb+n阱3ɷS]4+[EF[C!U iԁ[ZxƯ [Z~(S[G;+:5}XuD-_XX3F󍏏8Lm|^-]=:^Шp1|q53o{S3QtOttWc>'~yt'-T@+7%&zK| |xϹ{>ݾgwRko1=#5 Bڏ?); c )]T2'OBJǸMxvqtF5$ݞ>jDw1=ơcƵK-s?b c:wijj!CR.;};sP#1z޺rG(ר1U[}OƻfUPǻ:T ݋~wx*JtH"ɗ+=ïH'hfv\N V@й`Âqڿ{>?뺡CE?*,UnTȎk쬌. zlZD1Q?3O\]+J55?_vFn ȥ؟rIgBeo֦4_{Jfr ;zg6mc8|g8V@>`/7A / "=<8G!u2'Fd Y}!+Zhc-̻/t}{t3{а=ӦҸ)Rܗ:LRM/K'/IE{w X ,/ݿ;4vOd햎X h}vxz?Q;u6Oh *?p~`ov"o*[O9@33ylc,nC9^qsy gg_𭴾9> ކz_EbcUh6 m8}Q{nN-)szۡv딟{m]oOluU:.6Qq.] ag@|G>83!G 9c2o{xPnf4gKO39נ 󵍉3Q9 ri[OҖ W _SvzȠirͶwRMў^^{nr 6s-0ݹ|X {y[Opr~={A XwM+pkgNx*6b*طẽ7gi#v;qF^X8ۋ2v5vGڋ5_zN\ggE9t}6j,m{a;ۑqeo>lu#hx;<w>bkupe^2yx"zelT♗ z=}=iѮ);3s,!L30阇W0텞48h½z=R:%}&xe0;tP4ޛB_pAWԎH p)8W?xe2'c([d̵G;~OWbrٌ.yjاw3zSgB.c3S7={9y.}]`L6qʇ;O>y t}sct2YmI:S/p 7CyEp<:>hx"V)l7)wpYus}A]Zzzm!Пu¶3VQ<>N?4 |6 /i]Ӗ>3ed R_qdT(ZLwYnT.5Y>ӳ*0睩Dѧfuwg*i#tk⳼ ~&ۙ 45xW9g>{WVڴJVh\:i/1B<9ef2$n9<~5JAҖc9ND}s/ԕX/^ޮwsD JԿIlx5]s|#=.du_O/)[#~(itֻ<717Ciz-^㐀y9\}SQo {t}AMm}v}mpy^(ZE:|GGO|~Y͡gۮ8q;|_#=Lx> ]$PQOut]Q_p<7f'%|oqxSzr#ޛXb{ǔzǤq8p5|o!+S.|2\Awtv_bqnzcמOȥ9`]e\8>fWOH=H9]EGͦ]@My4T:ZaY^ Q1*=#ܯ~Mm=]cʫ `jݝg+Gk9`(<Ϡp_ +p޳O>(}zO(=(/&CkҦ \skJü6dB yƇ3Tm|!/l@r=?TY_i%tqyg^ϡM{B:~ipk3h0ȞgȦi~SS:  4]xq|"{`&|%u9ߑL=z˫wbn9zQ;@ۙ3p=֛׫/tΗDZpoi,/Џ4]h"?h\,[ 5shvO==ơV;ϠY3ث轀oh'-L94&+<π.{`<;$ty5TG ]QytEwqF<-Z`ϡ~_pnG~\}S_k?frb?\~ܓ}o8%=*]^yT*q.<Ϡ W]5HUgx/=j6QHePO1 V@> }2gl8~g ֹ?`Ƿx0Aʇw(2r=OlVٳ)~'$9x9~"'|jOl{ѽ$;_K9tG iy zY'+eu ݖPNb2.`yە,"{_Ȟ.M'W7u+X(擣0a:q)uYs q>, )c:Ҧu<}8u#u{W0{`o򓹿 7VH~ oXɷ v-.a4[XW+ Ղ|C}szt>^cCYow_T%Sr t&J_b!}(:O-Zgįr|oR>{ 7OҸ["p`>xݖՁi:+D/f]J9 q|uAS2 '\-8NKr}xiK([(s5=POQ[Ibu> '.}s {Vڈ/g/ m/xg/;jw}^0oi[ *U<בf#x,RKǏֲkD.Zx!w;K-/|>ZU77(ٚ!Z8&D*.c]O'9?mjy-ks;^=ya A͌?a~~YRm_86!q,ć3xap\8Q>߁}Z>|=窌|!>o\yBw1>ﵝշgDu1ߢ3}{gǤ4#(nmDX8yX}2(y,̋$I_ju\:*+ߝsRrګh9[tX%Y,vA}ψ%8]Ez- N7+>W>$"'fXf 6.;+H[7eѢ˄,s$˧He/N#xJ{ ȲT pƴ=}tpTYp Γɴ!ި$gVI 2}^7i%U~AX9}sAj叒eT/(x _ 2-W@vxD<,[y"o-H絯m>dd]?E5Eؾ*x _ L+>^㹈ل@t(ӡ;oWiCq NYk_5ڰ}ȲB<"T;T]ڵ2d>X x<!oo#l:=hP72lIڞ{Tӽq:JVp{^c@“'S<~NA:}h ,ȴ}G57H.݌ ?P#G9I~ š^ eS֞҆4A0ֽxX<z;ez0#Ê4MMyZ!>?CD;y,gciP7@+P/Y:eXWW8G x&gW6l9L[8G d]FǔWޗAcx<~<-km_5ڰ}S>&yVatȴ*#ÓJSE{RqxxҞu.H7(?۾ja](]rxAQ]cl[S_dN}ϊbc7e>mqEa{p s-2t4mD$9ܞR<#y͇/j~IQK*\i˶m>da^!Z$y^Zd|Up=5ガMR頨YiB=5*Zۥ lцCY킬uFԖ&Fw\adדtLY2'\w#kW hHhJkܡ*;95 'S5PO${%d*yv-5E \nn!ܟ)͞~[c {8xQ(OS9eMge{[d=KF{r^!?t?AJ^{ĥѾ:A{+H[frT ۇ,=r&h߾g4}fj)oߣ4F|8 a g&]:2[5)u%4qU ۇ,%25HQ85JLϧ)- ^&& N,uMV٣^W6lpVv g4Y4fDK.uo+,zgxW rF JFSKi+›y16lGT7gW rv DT9R2 d8Zv{nXysnxUS:!)xtux5 +\*_fXI/9[5ʛS߳+4np_\Ҁ?Eẇ}A<0 ?GAA7dڏeA!Aݺ?bΫ70B4/ p 4[Qpo"-*/2 g{w  O<;[{hFgጌKGЀY}Q8_%M3_wjMc)Xnd} {i֐M^['Ⱥ?[а^b?|pv}2MH^3D)ׄt:ٯ*| MwMÞ R74Ni:4w >kc*XOMy9گRȻr~RBZLi+аA(FvSh5 4ia:(Ѐ?Xsi?< i>*tI_|K+8.ć*>Z=fUyִCZY.?D z+Ĉv+x3F mF*U.3WK, $|rՂZmNT9 ᅟqU&vm\bߙ9F*lM5/Ys8-{Ÿzg]'Uğqg]/sCAB7^qHkL'ε>uR] ;(?Z"?Mw+TcU[GcY<9 ]Bݘ6=.B77D.iܒ}};>c=>V#]X[>~AxJ}x2*#yj=vzmS-] t##QsKZGnQ刐w>e&gOqoH渏;?DԹZwQ&?JϻoQAy>~#렱Yٻc??&u6{љ\ys+^ئk[j؏sS~mek@SGt*&!hݐNez"?GBwm%N|y/?2^읰]xYFGFxB[({B ~9p|Kk+Ǐ>6(Ĉzr]7i4ԾV'ʝ+%/:t]g\.ΟU8^Fj\6kgSqx4E|IѢGWpW ye9ޔu[4^V.>MljK) I/QYq@~gG鸶58t>zps/Ǒq8G^6dtWRzp}U?V*)o(珕|(* _uMUz&#u'_h9mW;u?&=lM 31~g!8iT؁| v^:Cװ?|Ax_WJ7sWdl%+olpEmz6ߩzEϧlPUS |'e5Q_;K:=gdi/mGݒ}3qhMC9#.O_)ugli썝b֦~Y~c/o< h&,]xQNz'21 :x@%N{ϸ_"IMe` Y{Ny'm%,aUz-6_'K/YgvcFy'Ȏ ZIRkNo-ǽm}X?=5l9cQ+)Mz9<њvB/]WC]lpXmAC> C:h\q4!n:_ eG8>홛9@SSf٪#|k?މ{g2?t\_+{<93֬1tv"mC-;Hݱlyaae #mAްa}-JIm9mј+y#md܋:+FkҌ We4J6Hm u'O :a|' LmieOwV<<_=BF+9<Ίl@6S/[^$icg) ln<y5>'=JOƪAV|dGd`-'E*of*nsϳ56ډNnѯ{4ywoZ!_C`{C^b,.O:C7@xͩ 5ɘo E>Z83 "~ZyW?$+<'gIEW3Q9!+E$ zN=/Fp#2A϶mlw4M$-er!8 lݔGNċ'|b7ݸPV5.{|5 ,Kv -+Bᔡ()ͽ΢x |9t1KHm[h\#lg484@oq<<`7 H:r.k˓o1=mo=FݏPgsEvMжGqN;tمnGD9YrFIqƐ&CRrxY[M,>^x`;zޅsҼȃGhCt:'M=jy#Ez%O$AWV'xh/m+= iҽk䅯@8:I \CRVV3Dó mL;B3MFwuCk4ߥ߅bs&֓Wyxs >_*4*LUf6隙 p>~koaE-X3})Y; oQw`Q&:}c wf& e!`G?i׍ RU1-s 8T(Rr L3|H3JuHmp9Ye=2z&v#so} n@53o焴KѯauNT^QYW=x}2muN=-jrzUO v*{7)Wm?S1~1atX wY`zڎ!n尡n`XqIy:g}+b_lS=YycE[dK%+,{x^zZ~݀!hZV˛|#n2<{e>_(oxhpߏqS̳#>oH^{*s)=k"z'ջsഝzɁ.Ox @_zɃ)Oa=vueG|ʘe;kO7Aʣm1qItE6+ g^;*͢-G9mϠ+&'gU'`.WeV $K-Niv{u>b[c!l ࠱هo:#no'.ѽi쳤MFypƛo&6,4JHuoٖy7+w~pj'a_ũ_˽*9v5QVA0f:_.Ͼ*@"mu\+/jTك˝,}B^nΧ+P}eѥnx.^ni7{DZ]Шp\~[?&(n([S7tg~3/ǽ%kq;r7v?}{ٮ}c'ƋOVz^h?9PqaŹG>lWx3^i\}{6>twg=Mx6Ρ3+󾒜0f~+|J딿U&uhwn:drkH+o>$ d ԓ߇F߶+6XḲllu#h}|0Og 8hLbws8fT~BxNe&w6hų8yJMjӚ5^[Yw(˱Oxz@{7<1 kAg!dƺ5# yx'4Cjv2M6K ַ)Cu/d/Z݉ }q|+o[HmjK8ի˲XMҒEǯ1aK5=N#XױlNaK|W/-CYԵ3o*fh*;$[xls]7gislq\`xL.Uh>W|U)z9zDpp*Z7$yΑ#!e m0>ArΓ#`:+[+syȪ! v4[|h Djw.9|.im { "v"!{]=-,òΔ@.ȡ@/ڣG.yr7&Îr?߶R qO+݉X*k mw#~Ao~8Nww)5S*6[r%ݫ=N_S jv%_:X1~Ξ*ᎠdHO0~Dž~+$cEfLjJS%S;v!Cd /+r;fls쌓=)[݃طRVxe'zz6X2Lev@/{\).M/2N?댟jJ :OPѹ2֮ iXۃ8Cs۰=a16ħ*4^#;sP9ZxYsYCxF>Kӄ}YN&t,>լ1=kUoYsbQ5@ymCWt:!rkUW9slu T6Z$!]q$ؙxbWp.ݟ[{-o%[*xcEZ+i-;Lf*&k`y[~iAV>}׽ @1:ͬ ^|YZ~\dퟰh%!Kzn{ "ƱQJnԂ5(glz#%mr)`T=`:c_22"Z!H<²KB԰PN;]b4HO=Ajgfڳzzgar_-[}[bz^ҾOԠlDGmZf$xX'/xn| <<Ǟ"#:|'e/}?*yDe̐ ;٣&e*$qCK3c!>NO wV)"ހ\^RocO᭠q m ܟXROW"7óOV8\X{5ܩ,tc}kՄRd!xe$ȼ#qC 4ۨ(8MA0l`/6ޯ—>c~cW5\gyk.4rjỹV3r9x%<)ȵX|\G] XLYF9QJ[c3(g" ֞w9o A-{p .Ay{a/~sX2xj^}o}M2ho8Oѓٛ9É_>\cp&&܌)kntN);{y~^;U6>%תWEoNƦ>wBⷯSod*6'߹^Sőj>U8S٘RW97i|]9s>YbLvY3w3|5ߕݟ[n p+VX]72n p+VWw,Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:30  "W^ ;WW(16p2Hp/(W1*h*{x ]EC0IL"ގ 4bjB<\5H(2 $$>&,p-Ǿ-\)-oBh _6-{Kzka_$yߨGoIX񽏅&%AcѴ1Ѵ}&,I 4>jR$psQB+T#kPOgݶuÄpTFG_$VޕėMLcp#&QYGe^:#9둜4NBz =ǟ>599/\ Xy0-.Ŵ gvZ*Gy%MQO' 3v XSb{Q7\/IlusʉnU\M7o,ĺAPQQo1Q&Z/_AuHSKX/Rn?{UxPJ_acx:)'9SdxT3 Sd@Sa@ +K&_:)XvқYmJ}4Y*Y^2|܃TT;L*[mQGEpPNKe.'K=پN}F6>Ї$zrpX*] }(lŶ&W~S}cW_>tɧI#>J}*ڧ0էǷ8]K>n4椉ġ?L pg;M^ek=QV#V50O[#iR6Z>OCDX['KX]HSfĬ:`/EߴokGbU}ӯ'447yݟ W8wZlVAZ 9{_eErdq3VFɪ~ݿ  nV5M"u+ ==ʘ4N '^A지 x:dN jvZ7'OT™?NېLI%d?K:J<+nyPqbjg}ւw.Ƌ/R^ȫ2Wi<3?Z36KHw&BwAz_PZ>"ҕJz?j;V6UĘ*}>t[)zfXM&> wf(=35{bV'gC7ߒο'trM R?6Hjp+}Wtv׃7+g/gr]er -WdlT+O uh*?gzw.dti~xG!yH~puZ>n<:LT^={S{P:֭?sW!*Vڽ]y7bYKz߆w7Dq[vB+w,O|7jw#njý&qmy(w ŝ%sqf>*A^,RoBzЯ77}f- QS>>4Sa/)5s3@U*kl Wc7KI*cNF^LREoRR^bH'M0gLq83p2'MλMO^qߐO[ɂ-ɵYOV󃑽=i3FbM| q[k{q#qPY(Mä/`]Žhp$N~m%{2ϕQϪѺ* 'qdsn|ŧIHr/2_Wy>yݣ||ev{^wJ˵{OoQ|eFzCosVj'W/;_ٳo 5F}򼏄)<43/8s-B{j\7!虤/;z֚ʛfVI?L3j agve`tg^pNgBa6Nw)/}k΅r;d![?B8snI S0 JϏm߶-ǁg,)ρNd|w+,Vsc/RpRO̓3)/Qz4Nxc6;]DӘMе34_ngÏѼRs{p"f 'Q7>#7ys O5PxUѸ&Y|58sp;3np4p}gS}yp2\ M697q7z 'xŋ4f ދiטƶ nѸsp37 77n}KnL9L.y|D1ut+-(?NW=kF.OQ@Qƭlg |DTUU|ЯZ}BoLmɸ[õ5e6I+ޤ4~ᖗ{{݆'L9y8uBâQ UF|]O<~Jz9xD()PF7ȭS+vkǨw:h 9hSOrh]a~Gdrb>7zǫmX숭'+m{(;[u+}c[;MG6߀ik%Ґ3u=g%n[r7 еuvb#m}HlCo@hw0 {K~HrE^ R Gkz-!N{=JgeL~=w}׭pO+}#j}w&~QcMbt,AzR>(*45^ik~dҥk{s56/{>ݚWgێvZXv+[VѸ| Rerkw+`k>ڀXOvշ X U7x5 )^(g=K^G8]o{O?e{]1}ڂ\D^8p8|˖޵*xnP>>< yG]g7w9s%}`|sR]!|s><( e-JW_px&3$h,]y;(oW)arp~w)'W}g G_^Է3E_ U(Vǫ[amɏN= +ɶ Fk2=;2*TCҝO.>tp3Jw p.~WA'k%s ? ɯu ~VXΌ,Vt\;;;ҝzx+ݩ7YlWik玫gN&";򳫟to3zn=WxCeg0;'tzRNulwҽzJk(q+LN|JS/yM*"N.PW&75S^{4,tu[yk: Ef]!tiv<]<ɏtOuc+&6ZrbiGz=/Rh\i{hNp@~!ҍA ݛ732?c/eM7wc7wcݘfɛ1n [6KϙcW" ̱תs 1p3=7znY5pkFך]7ntd]7Jܽ򹉒CQ&hU#|'(VO?1_?0>  UPƥjA yN*UHԛ0'9?Vދ; [ ~)v>;'ԡj35.hJqv;MdݾX{zFJYZ#)w͝ypnƝyJo`\QC͝Z͝y n7ܙ7ެtq [߶5Y1iwZh.oI;mЎOjS\?l'>Y(tq6t_ч }E*{p'7z n|bhl$n7~"K"unpv4kܜ!ܜ!Ygf7V}p S 5Lpf5ؖ͘7 'eִ Mf~ nh7s4sY=ont ѵFȻvkI!Eٵ3Qƚg3UE'+NJ4qf Yit;Q!ٌ*юUD;iwhyYEA;YvN$tdG}jk..V2ؓE*UjFHg?7z fg~ n7?7, ܉v4kg??MFu ܬ[fjָn3p7?7k&Y3݌mAؖ/Ҽi1_)7Yqopop3ǚ=7znY]k+g Rvv?bbv&Ϥ?@ +N?{gЈF4?f﨟Pv"Ϡ,OB y8>'YEA;YvN5?Æ~G"ґfo3p㟁=w3p0Í7h g n֎f n3p㟁YYͺլq㟁 gnnLpfĶ+U._0,ݿ޴^' Â7QTU.О9=NÙά\) '_R;]|C04`xrZr SNUF&*˽S+ezC@ N֠UQ`[][!~|zޣJ!hS_篌W&6K&#ř 9؈ ߀ ),n4pnKv;4e Y)]o"w+?P8VD~]1m1kX!ǿ=_5KRx  t'du(d݋K|c\ܶ.0mz[Nm=oG\zB>cl ߁hx$agg)\&aaqtx_W5>+ֿ%w42iƾTCdo|QGpoIv: <RW 3{.݋_/4}?Ep1KpxW!:,3sNî~J I'<րNB~]<2}x>=S٪֟%-맾2MYM;'h~'vol^mÊ2ݠ2ߒGU۔=?-|Z6%f$ߣY^+,Zw<(.7G'gb'yp Z֓";Aex{L'Fk歉nonXO;Evn9y[?j[,z|+z;^AO-QVuZqUk=x8d'DW,*vB?o'=ө%rD. \% G;m𻝆 c}W}%#1}%4t+WT&M0A9^lZu }~.tЯ}&>~S9 ^/)cJs x^C dy ˩Obic8O}2hWUپ,>mS|bdH{uIŦ+hI[P`,w&c_?}h#1bBRǝ- rd1Ãh,%5Q~7~_m<w6b_8hP/L.Ԍ=+>kD'H ^С0[y G!/%a2b^_ҵSuhJס)#-)T=uC?KoyYj9^^e{F c&N ס^E 8Iy` n<]EN '¹ĶG`5&,p/8"W߶i[B@-CZ.J%a>ӹuےd϶MþSτ%]ؕ釧uAC~.@]6+T#+=8&2>%a+/W|2Y萖˽QePK՗@{m>7 ا5JvTCX) q;c@rM=Z#9lF>X^SI^9խ}~EK;ݲL^ ?ܾ Y^kU0byU_u:;pw#sXOKhkIѼdT9yYxr姾Cr oF"ך.㡯Xv'?\.o?׊B:>%ۓoE\~C)j߭?\Bvk{' }a/jε^RFw|dG<%xf?^=1yc{/1Rθݎc/I[b܆~(G?k.mW~B{%+r[Ѿ޷]mae}"Q=->&sǬZ4}/ޠwj ؎ҫd_~v W$J,jvpS^X dY=5RZf ڱ5揄t_8xGڭxk4._oS]'X⋤雲RrcugoIv9|- MQR}q.c4RwCw,}">lR9Jz>V}fE/&v+5'""S^y< r+>a8d0`_(UE7%>NWL~uo?߿ ~{E |} /yX=U}4hZh?^ -낺OvlhT[ݍXy:5~/U`; J(笿T5_{H݁ V',VaIZ(Gk|pSf?;%=Ӽ3\#;Se'~Ax!̚䛇 uz:)H_;s[$ov>6קudcr'e`Q B}}d~<2Wϻʀs= 2b6/7xMe|/6΃qպ/}c3@/ٕ[TWTvʊOuHBk$}VMzᛘt ~[dxN5 _Foѐ{Ṫu&;hzh8d %Q2//*Xfx[)#v<:7,;M[&'Mۑܰ:#'1!߯$.޺]ik\@Kj'?z*Tٱ*+҃UgDn7%Cb譳uu|ŝjUnTf1CøyD=r"P=a O:r\61}{l8y*`Ldy:h(țȜΠcMtvx ܽ3y 25s^ GOvfGɨz}z^_S`? Fggߟ^c>|J~OSQN?mUjUaB^ /yG' &886<,+ˋ67N6Dl~Z~*~IW?W3*n/U|O!Ooc7eyUR/Q #tf ?HNKs$яg~*h`݆DԹ @?m' )|]'O&yB<lOSˀu]([Wdseb[mwq3e ?!CU` 2,6,<)vxF ~OwW( $<">¯eUG]IReL@a\<8I{~z>Ll*BCT6_eE4oP_:=")O'In.RNfGZ.,W6!UOFȐxEekgNC98Ns>ܿq|%@r8wٓ/3^ښvt?-10=a~ܕsteu-ҕ~.!e Jf}g[_`-.=Sn ){r|zd^#k iW()h l2=2c.ǞXuibTZ30:!fiSn<~b~ Z!vM*Ei.Y~ΊVTB35tVQd6CVm$zK{ʻ:oĬyBp7N'&5  QB?tz rn7MJVLvHl]9Y?-ec}>yqe붊.9x-ἄ='(Q%^gȄu#u ~QVRZ:˗]~d]&{ u@:1zVI|S.wgďMᆭ_v-bڦ޺ӆ>'5 }YOL_÷yt~+;d ʀ-& % %wn8b<(v=}UsʁN$.$ ovⵚ'd/Y޼W!ҖreHqѮ=jkItzCLcEQ<.ԗH3稇8P@:tVkuڦ:(ҡ%c9]gRJA+DF0\^k:w$G5z!q'Ǡ}[>EnMGmu-c76G> cNqjkN]<^+⥟]-U~8ќBNWcS̏ z g(_yb׻=6Fh@Z]Yd)Fb}Ge'HT-X|R_!=GW^gNѰTFz3~T~?]mdΛyb%i gy!eֳ ?*O OpӏRyK?,pn =uܧv)C 2)3 zЯ4zd} k-*`;+H;/ƫzZ3mbL+nif ?\,SF:N? T2qR8H?^i^kd2}#Ϊ<[~YzF. iB+2B77v;tzՕ4M+bW`y̝~jd?z mcqڲ7,vPg>CxI;C`l]nE)G& Kxz]U*;AE=֕|lzmHLm0:iÖt:B6+Vѐu "}xXu;sbQ*ބcNqNk:c^1~~`xypQ!ðMm5cu80~P_@^f!"c8c'ޟIm;sX]΀/`x%x#$1*e /]@[e xmJ .bRmL۴'mRמA05=-8, to NSܢg~NUYB }AK~gV7ĥDMf6PxI[aQ`o鞣$Ӿҷz^;7gYӼefken9XO[xLvLEbsk:Ѯ4:E~L'i܏7=#@inӏ䁃sEԨ+31+GGc`<,,F81 ( 4 k  ), è ñòàòèñòè÷åñêîé ôóíêöèåé ðàñïðåäåëåíèÿ ýêñïåðèìåíòàëüíûõ ãðóïï ) x ( F * * k . Èñõîäÿ èç äàííûõ òàáë. 2, ïîñòðîèì òàáë. 5 è âû÷èñëèì çíà÷åíèÿ ðàçíî- ñòè ) x ( ) x ( * * k * k F F  . Òàáëèöà 5 Ñòàòèñòè÷åñêèå ðÿäû ðàñïðåäåëåíèÿ êîíòðîëüíûõ è ýêñïåðèìåíòàëüíûõ ãðóïï Частоты Оценка x Контрольных групп ) x ( F * k Экспериментальных групп ) x ( F * * k ) x ( ) x ( * * k * k F F  2 0,096 0,063 0,033 3 0,325 0,267 0,058 4 0,338 0,358 0,021 5 0,242 0,313 0,071 Ïî äàííûì òàáë. 5 íàéäåì ìåðó ðàñõîæäåíèÿ: 071 , 0 ) x ( ) x ( D    ** k * k F F max . Çàòåì âû÷èñëèì ôàêòè÷åñêîå çíà÷åíèå  – êðèòåðèÿ Êîëìîãîðîâà ïî ôîðìóëå: n D   , (9) ãäå n – êîëè÷åñòâî íàáëþäåíèé, êîòîðîå ìîæíî íàéòè, èñõîäÿ èç äàííûõ òàáë. 2, ïî ôîðìóëå:    k 1 i i n n , äëÿ êîíòðîëüíûõ è ýêñïåðèìåíòàëüíûõ ãðóïï 240 n  . Èòàê, èç (9) ñëåäóåò, ÷òî äëÿ ðàññìàòðèâàåìîãî ïðèìåðà 097 , 1   . Ôàêòè÷åñêîå çíà÷åíèå  –êðèòåðèÿ ìåíüøå êðèòè÷åñêîãî 36 , 1 05 , 0   (ïðè óðîâíå çíà÷èìîñòè, ðàâíîì 0,05) [5]. Çíà÷èò, ñëåäóåò ñîãëàñèòüñÿ ñ ãèïîòåçîé, êîòîðàÿ óòâåðæäàåò ñõîäíîå êà÷åñòâî îöåíèâàíèÿ çíàíèé ó ïðåïîäàâàòåëåé-ýêñïåðòîâ è ïðè àâòîìàòèçèðîâàííîì êîíòðîëå, ìîäåëèðóþùåì ëîãèêó ïðåïîäàâàòåëÿ ïðè âûñòàâëåíèè îöåíêè. Ñïìñîê ëèòåðàòóðû: 1. Ñèòí³êîâ Ä.Å., Àñººâ Ã.Ã., Âàêóëåíêî Â.Ì. Ëîã³÷í³ çàñîáè îö³íþ- âàííÿ çíàíü ñòóäåíò³â// ³ñíèê ÕIJÊ. Á³áë³îòåêîçíàâñòâî. Äîêóìåíòîçíàâñòâî. ²íôîðìà- òèêà. 1999. Âèï.1. Ñ.176-181. 2. Àñååâ Ã.Ã., Ñèòíèêîâ Ä.Ý., Äåìèíà Â.Ì. Îá îäíîì ëîãèêî- àëãåáðàè÷åñêîì ïîäõîäå ê ïîñòðîåíèþ àâòîìàòèçèðîâàííûõ ñèñòåì êîíòðîëÿ çíàíèé // Âåñòíèê ÕÃÏÓ. Ñèñòåìíûé àíàëèç, óïðàâëåíèå è èíôîðìàöèîííûå òåõíîëîãèè. 1999. Âûï.51. Ñ. 193-198. 3. Ñèòíèêîâ Ä.Ý., Äåìèíà Â.Ì. Ïðåäñòàâëåíèå ïðîöåññà ôîðìèðîâà- íèÿ îöåíêè çíàíèé â âèäå ëîãè÷åñêèõ óðàâíåíèé ñ êîíå÷íûìè ïðåäèêàòàìè // Âåñòíèê ÕÃÏÓ. Ñèñòåìíûé àíàëèç, óïðàâëåíèå è èíôîðìàöèîííûå òåõíîëîãèè. 2000. Âûï.93. Ñ. 115-119. 4. Ñóçäàëü Â.Ã. Âûñîêîäâîðñêèé È.À. Ïðîãðàììèðîâàíèå ó÷åáíîãî ìàòåðèàëà è îöåíêà ýôôåêòèâíîñòè åãî ðåàëèçàöèè // Ïðîãðàììèðîâàííîå îáó÷åíèå: Ñá. ñò. Ë., 1968. Ñ.76-103. 5. Ãîðêàâèé Â.Ê. Ñòàòèñòèêà: ϳäðó÷íèê. Ê.: Âèùà øê., 1995. 415ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 11.05.01 Ñèòíèêîâ Äìèòðèé Ýäóàðäîâè÷, êàíä. òåõí. íàóê, äîöåíò, çàâåäóþùèé êàôåäðîé. èíôîðìàöèîííî-äîêóìåíòíûõ ñèñòåì Õàðüêîâñêîé ãîñóäàðñòâåííîé àêàäåìèè êóëü- òóðû. Íàó÷íûå èíòåðåñû ñâÿçàíû ñ ëîãèêî-àëãåáðàè÷åñêèìè ìåòîäàìè ïðåäñòàâ- ëåíèÿ è îáðàáîòêè çíàíèé. Àäðåñ: Óêðàèíà, 61000, Õàðüêîâ, óë. ×óãóåâñêàÿ, 33, êâ. 7, òåë. 27-79-81. Äåìèíà Âèêòîðèÿ Ìèõàéëîâíà, àññèñòåíò êàôåäðû ýêîíîìè÷åñêîé êèáåðíåòèêè Õàðüêîâñêîãî ãîñóäàðñòâåííîãî àãðàðíîãî óíèâåðñèòåòà, àñïèðàíò êàôåäðû èí- ôîðìàöèîííûõ ñèñòåì è òåõíîëîãèé Õàðüêîâñêîé ãîñóäàðñòâåííîé àêàäåìèè êóëü- òóðû. Íàó÷íûå èíòåðåñû ñâÿçàíû ñ àâòîìàòèçèðîâàííûì êîíòðîëåì â ñèñòåìå òðàäèöèîííîãî è äèñòàíöèîííîãî îáðàçîâàíèÿ. Àäðåñ: Óêðàèíà, 61000, Õàðüêîâñ- êàÿ îáëàñòü, Õàðüêîâñêèé ðàéîí, ó÷. ãîð. ÕÃÀÓ, äîì 28, êâ. 70, ðàá. òåë. 99-74-50. /,xlƟZnii AgQpDC40L`*04Std8R" nXE :%pF"{{vTBK<=ys}OHŒEE\OjWƤ_1g }td?=/2čK3MuG)nJ33Q_~^<8l&Ws&TY1lH<7^LFo`:SËq{t주F{ίxN8zr^/ۘnRT{.wYZRաs]χ:pu?dݖ6?*Vrna]vHoBv8^΢F >k`,9r>ۓHH~wb8 =4NY5l큁v&z?gy%AwiLktNٝ]qqugfcnݵI& [0Kj>)^Ĩ0#`ءJ}`;)>eS..lfI7YE)j>ޖE^~YRq|}!Mtq@vEM6iGuQO4A{_u!= V߀@7SJz(GZii**j[y^ 2s:L" dSK `NqNQxcGUg/ȣ/5W`fr'k>Vʝ;oWMZXFKp5=aoA)j%mu!yU2(:>F^ϑIǔqc<퉴c s_h V]ؕlФCV1)<Miwqc^1OѾYCjFa$1k|'X'k~yp=02ZG W̝Ϡ_%\wlýIlj=ɳuKր ~ 8A['zuq h`iy`2X .c6؞SsT\BޱZjTWZ]ƹ -TʧgF K1k{?x ;'_Y6[+_||~n+mf>{;[ͭ[ hsݽwo׶w[q7v*' #ݼ\>c}aeBW(BN|z+#f[o]6 | +n0T T T T T T TLR࿺k)Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:31  ΰ:q ?ư(162/L԰1 :{`x Ey7@ D =ᒓD PR9BQUw@)&zc~ ZmaE *Փ%.~ɞ=Kb؜<3;tκD$Y0C=W/U m-)g+cZ\aͥY5C_}H_#hnO:W87_\Yks;Hȹ\|&3=/¹ln^lnMXqbW)07(;7TI$MmZsj~8g-*/M},͑U!i{+Sږ/`4 gL&?aD¹ipU]{g8xj~>vS}\9S wVrk~rtrl2sda2O/zf(@%)wE]3">R&hfZ_NMP,N|b*gOK0UyQ3)]ߙ:9)&y*?%Y'$7|T~ɛqནzJ1> 6sj6IuwOMfq=jN0;r4&9esCJ*z`1t^9aZr_i{~bUo(k{[5c0Q!\ VƓ[ T-7Zɿi]1?&uՎMuւݷ<7XsOOl]~L).⿷_ed3>&v;l||⺲q 1ߞ<K>s\ZR#)Kޒܚܘܤ9ukS͐[%ɊU񷒛Us,_+OKm0GR8Z9xWh)PF M|1VR (.D,?~?|n,#{x7u Ϧ/ČGNO_oRV+~E(?)/ו*A}M}US=RS֥1A i@qk_UcX(c,S%*M=EKAM3j IGvJߧ(0V;x?ib`=>$8k/v/V}s& 3O*'7}]~3W{i+G7%oi|O_sc:fR >BaF~ .?9bo2TqTP~|^Iq]q ?/1KXKC8\9R[eùD)v}//ْܟogQޤԽ)]$57e~wZy@O '3'o3toux1&7!a;%07hxwu}n:.4('pӮӞy>z=<ۂy坦: :ʄwe6.S(ߕul7v|̠RR%;ҲT;ḿV͂ޤgކ|6Kϼn8n~|ynGڴi~yH iaZ:vhu~. sh:nKu ݡ]@(8e\z&Qu~d5"ÿАNnN.sz?on6ʘ10X#8x <.ie䇰縌6O4 m8澈:Y(Nm'p$‡ FLXy1zXehۄ%xl%?[ےxH^5wGӚw-(Hff=x\2Xʁ'=඀a}'uilOЖg.M6@ؙK6N4mS(T};>+Δ*y)ij7eY͸d6>>(灷ް+r3?I>16h{bO|c}tjsIi=B >b%;d/5xX 6 ;[eSy ;]kOoj J ?|?p<18)ILL+A1c4^adhq}!{>z5~Wr5G1/O׊)Gp>%_*N'틳h&~*ﯽ :wNܫ[=>2V߃67<$*%Kߌ<у 3t^pER݋[C_ZeΝ7n\pc+dq4&_a̻dԤ??EK~'=65ʶ/tdw8WCg!\,j͞MS5Z˓J{ yԷhjgkSB/S|,Us}K}߶cp8 TU` zW,:_XY;\e18` '.iμ.'/M_-+=4q֌H|yl(SBߡW{mSU1S՞O7-} '΀f^rʖcR7Uqҟg3;t)wF$ZYp~3;X4"^翚ֿbUZSXcNh1-YO+!۲~I&,^pgYHzwB ˑ|WE.@2YR682dӯ^$ܹZei@C|Pjxo/ |- 7{]|=p&WS6Xؐ {kۙ2S(s{xʀ }G[;5, .w=1 (wpYwMy2ux_`\~tsu39O apug ncə;W0G ZdxbHc u"R ]{tM>&ԫ>!Z?{t*kPuٖ;7a3͑E4Wvݯ4Isց]/:;j5#֟28UkxӶitpm~I'KDk5(]W'2~yb@g~?n?\u:Xj6?;?D:Kv; ։IW1Xɧ SBtP?B7P t3ޓf)f?F''#R]go(h.Ve{͞@~^Є.<#x-ȯ/zի-Wi4Yͮc՝F3\c}7EN=߯ȯ5R>gӏ5bR`_c)cޯ^;|U!ʐt?g"8UHlg3fGlSC?1`w_O2b/Ա?~b(wOlm(P|av\z;fq7T636C諁O.Č1{3u41xiҎu p8 hJDqB;[8/CM_9ehT68#1calOWkXes[zZӫ8+tȄ i,ރMUMoc}Oz4%GUŢ UfHٻ'5rcի^Upʼ^O^юxGĦ>) G%[%5sHnE7 _ӕ徆Y 1_Ӌ< ڙ~Gv^j!psT[T\9Em8zп~Vy%X|M[,w|:{fE)Nr&G^? _!l1[ҬycXA1ԧAtANܣW[g ult*՗3K}=P ~[ gT1j.ƴ|h?(WпTgqo}7\z9duKr&t&V[y>Ջq.cT δ,mԺ$woIZ:XoVoⱔmn2xNPO{;^Y*L ^瞥h\nBO&[,Y7!]W7{ng)%{=A2%0cp y: 18k~cڭ;0Юμr>~&ZCwqz}#;p[u|dvrdIPgWYֻe^g9Kz ev5bxl28~mηsA}wkԡk~i}zqz nG['7{U9"+ȧYKԌzM,x{ܟT\7([p˾5l_Q)8_V,i5Kx}/ )\A(]y ѵ*.׋o߿%:\~?ޥ=ߤd{rٷC7$ٛ|1nJzN/k_y{O{'x3ss)s]+uy_ۅ8R̓37Up1_zo= iO|f{v~OW0f|סvN^߽ m<ޤtWk㭺 P?<m\Lg+o઴!i/}BpUGkWYjo0ܢ5]]ZMyhw|V%;![,Dپ$]|_(#3 1T y/Keyϑy%?i[[uyRA0q|5|dJΏD϶ԡITA!q|> |D^]/z>(X;;J֧~Ң>U}P^g>IEu{y>C ӲȘM̧J>]UY>~pYrU'C6?v|:3·!eߡc<Nr'HؿЗ9!(m턿3ϟoo|Q~/űab}~ola _bMU1]ܯ^~N F퀻gw1|ipOw1oa|ߒim =sγ >6Å~9>O C} ў}%ܣ4ys0w Gzğ* 1[y@Sa%۩?w5y~<>!Z|swI1K4횤k><|4g^ cѡW[3fNz1]Cg킸GMuhg%+zH>ΕPs?OZ4^NW|bߺe~凗u%?[h9@m >8{P1Ip7=oe`8Wk,<= W(L<|b|TK.~Zxڡڛjk=J෵X7IL n0QM?RSRq|}I$xt!eХH]=#z&WGXz?8}\|`'ܤ׎񗞑gGlT.4.XDC^:VpSep%<#KuI$-=yZoH!y'UfzxO ]=/^?lVsHn;IG|8G{~[ Q#h'#m^^lP2'_sczQhTvwЫ?|nwՆSo@+]5pyW_[Xz ӫyI<X1סW%%.sM5mz6f(߭1:_,:]*EE:Wܖt"@T/o\La bRW7 r,Wf/:C*|ض.Zn/|m~$&t7.h{IdtXEMXuuUu3.7 ICt2h{%ǼOeܶy> {lMӗ &m+JAޮy/2|*"V{9Ax!܃`π 4j?I_+P~+Vܫ3{¹vVØC ^79E>yR:8r;7S<|ҴaH@]u_ MWDӧۊCg"{}޲ONc!XF"B ]Ga3WfQ~&~ݧ߃ qE4ki?i 9{~^ kOAs,e<:%suWs1w[i6b_1ulW(uh|+zH>gӏ2}V2 }%3P΀W/ +9w~oey&I/yᖿ>Oa9 rݰ.w|W}Hc 5QvS+ۤeK~} JoRIKxHL {bx c!l8( ,觫Tx VO~hH;: ٱ+?S]!O ׿=HkBh\xtw;]j#ˊؓw*p_TO Pլs@Ont;Hk@|'7"7\*(X{s?%k/|? .^ 02W H{k/| +m }thMOҕ~{es:-ooNK!ʾ9u|sqEκ^n. 5; 흥g.}пK~5S^}'п/~iOoҩ$?:]]ᬣ<75Zg诚.j!upSU|"^^nHšvB<]ɳݻm}Ocqo}inmG_!l2yIfR3s?7l?P Q~lg6tgҧΕ2yDgLܐ\%eoV$+ue_֓ʳWS9T>=Ja:̽{xܗƜ<(.w0Q@ֻ)ֱ\g"NnB~;){PWݔGnD M ,+fuyzDW eEwS%|f]eeHׇΟ5f@]9e1WNǻ)1ʻ)dg_^W9KBTG+vpy3bzER]z7u1סW!煥;7Wѻ)WnJU.Q1סW%Yw٤JW]:Un@ Y٦wU1סW8zPp=aM17O˹\iݔmتCJ|x_j~Ȇć˜T:k>,z7t Ma^`5s(IpUuuUۿ7ߛWεMVC˿nl6ϧ{EktXlPߓ=}.E0އdxiE("@x.~nU8D 5v)]`>~doyR߇;>~~AwMWpt"WLxӔW/Te_3zB..MNig'd ** Bfu2/I!(#$ˁoC럕 ^r@SU6^"m{Im[e_]M#Ӌ7h ^TnzQYmmOm;Lw,-pY&m3ݤ83Qx a#/tG/|35~{7iҬNsh7ˠe:Rf*0Q҉YF>s(2Y-xXSL}Sбr}! B}/ 4/ۋ.,LЬζ9h` y |Cox<:[WG%-;<Θlj:,3iJt3<3+8Ӌ:EkT[Ы; ox,m-L/u*?2Giv=,m:cC*oX۬Uz\6kzt%W^ .^&颱.Bnv|_̓*|ݶTd;ϓz!_+_*:-?`n۹Ы _cTd;ӫDn~״ҫ _nl[6f>m{l&266tZ1kZRM(I+D+`ཅ:'+vs|B]ݿC"s Uj|lo~cY,5ܻgr/j®n|W[z_]ox]™O{IZ‹%^Zd/^ +{e8Θ-%8n>05!}py ġ;i?+Xӫy{ytz@Y6:WywlP˦Wh/SY{y=UfKԡW Az5_C˦cˆ˟+YTeaknе ee<29I;kL}d \i175ƪcC*|w%#su8s/=GBuGr1סWr^AWTvM<9[ilP߇Wl$m"ye#"ᜨYKEl֟A-|c͕*YKx{YKZ6ҳ8?1~FԡC9MyOԳ"ٯ%?_aMM+oP#ԡ78xIѲZeh@+3X܄=;sqc߶cp8bf **`Bv𻃦Y}k{#u$XGJϯh~ 4?w(kM/#3w lΘCz}Jr4?VdVAװŠ+k:vɧlQ&/?r@^>_S.>hb׹VSIޣ'`5(ӣ(7O)cDIHe|e(ow(nѯܯ1yL=&[*Տ{՟(~Md-˗+u^ ෫VnWB{op$34p)dwkB?#e s ~Uhud 6_W^tL#a%_MܗWюՎM/~zuK>d3nr%)NNMLNIr-iӋHim^OZ;jʦWwsWy:cC*>'Άʗ'Ei9Qopg^#O/L/h統[~>gӏ ̛o-. taui^ eVe|w&!oPئ#>nS9[Lܓmfiw-jcCz&ִ,ҦХ2=4k)K{ho*֩gkS†0K9mTyw|q)IL}ﰞ]F=ڰJ>0]Y٢ۻD+S)}ѧM_2N |-ߧ<ۺc<)'bT}JIk T%M~)X$wE.Z~4ˎeϽ)T`=h/5O>O7l4 uقoh3/kc>r~Y*3n<_=Vem݈@F$q݈z4Fwndya9O#H7P>m +QʐZQ9  yڤ/~<Γ=6fTK46f4EYUyzwH/}"Y^tJk\ݵ1<팹’<[Z<ɧŚ0#)eٚ51yVe-i'rucIߟlhK I& iádV*Wzi{y\K|&xq9{1ȳ~u sqGw}]eޯ.OMCo_nMk=+J4g+듒qR6S2 s٬vWuŊ|Q^Q>'k't)u"AdHT=—6ş&~|*9q췲V*p׈'LKx%C|KD˞y4Ve(lyߓ[eQHM?^DWhnzxO ]Wvn^U i{ÉؽΩOgNP$ZYmJꤒ(IStn`݇ozm^^5 NZ.3:rƖ3&:8W] Qp/EXPꌹ"]^8E6_/ѡCz!PBjV~WguUxNoku$E#tb.e */ 7Iɯ t|qr~M@*}:C*|ضWdq>^ȇun#btm^7oە\5SA %v3:‡K|MC hsCzUsdؾJb$_vy&{&+)P%`iXlPckgP NMĖ'Ɋg >W~xe0Yv(UxgCaJeձ6߭i%fk"pJ ~<@yG.DkgBGCx)cVh'!M{_]~ ָU|v '!p>cɽmG};O|oh-4[7'[0 mIX!C$T0/wyA% B 9߬&iĺbz4Ԧ}^o~3\^…ܬ>fb7ka"po{& Fdў:fk:8C*=R|zJ:?Ny܀Ev^gNQf8]+] w~ _w8< yn~- ҿ3\h1"m*|՞";c+>%ڬ]cwArۋ#i<.L崁]^p. 0+Wf^e!:vV.6e4* mm<ץ[mSfI*#UN:-~Ѯ/ۆ=KOl7e(sp z8Wq|Qu;|E]`]s>U*8M_r~K N_g?v]|m{<]؋O~[+K~;MM Vٹ;}>k팵nipM w(OX/N+3eORikspo< ;ïmdo}0~-ִtdeH٢/w.T= #K!f?GzWO{ @<^Ss|(3pK|C12:Q_!~29o5s*_$e8Lg*{ԯw?wRcR݃}^7{OR6*(o,ILCMx9 lQ$. }U$ߢο*ɧ?$_}%rwIߨ|Y>ɱ֔O|*V"pI#}5JjϽOs3J߇b42*OCyw=Okw+poR1Icpy[kҥ&m$pm [D:Gc,:~mn<?dRb }9u'?}(5/ot[*пOm+pwJӿ7$N>ӤtE%OoMvo+}l,q,Pq^qޱ% 8˧K;о\Ώ3{UހpّO5OB}NNL~:cC*>Kxz\{&^1n_}jvZtvϙ*zgwg|H|?z"y {nK)env!գsO_f(ޖ*_qF7~m2V{^t*O2g6l!m ꈲ:5%7wMyGVLoZ3'yObqɴ>@i`({ϛF/]552my:W}|͓<]_wv_zO;\Ci;hgϟp8+Uv~#~Ngjrr w2/SLgm&uc" Az_=veu y>EX>Wfo a|7}uU;7lxZUZ`~N KH_9}*x{iB,h+߶hi<,D=&i]e)>aHcz2 k=u\džm*+}J62!ͺ>gv^Y}XNy &)EH>Εg ;9БǴ|⼬ Y(*+0ǤrTQdZš,t,rL"YNc!|[ Kl-Y&dX]pߖO0Y$F?* ')ٗ5_Y1YseaO٨$ UYkv^Y5! -/,Gi?~P(,,)Y5L=Ag)y[bBc.L!ehB! z-Y[OE_Sio+ݕ%}eۅMhY|`;E" XWKew^ٙqΘ- )" BuB4*_ g{ꌹrG{k +Kx!hR߫ژxw|ڼMf(x@w9P~BYSS3\1}d:ߺKt⁽Ewi CO(Ytieǿ ݥIi_" to]Q&p}3YyZxJ ]᪺K٘- yWwBꅲ0pYhz@w1fhNw0mAΑszUڃPko +~ވzI:]he}[{y.5\]>8]9ۧ1ɄG8o4]b/qN,,82 ÓÄÊ 681.3+681.5:007 Å.Â. ÁÓËÀÕ ÏÐÈÌÅÐÛ ÏÎÑÒÐÎÅÍÈß ÀËÃÎÐÈÒÌΠÔÓÍÊÖÈÎÍÈÐÎÂÀÍÈß ÄÈÑÊÐÅÒÍÛÕ ÀÂÒÎÌÀÒÎÂ Ñ ÏÑÅÂÄÎÑËÓ×ÀÉÍÛÌÈ ÏÅÐÅÕÎÄÀÌÈ Îïèñûâàþòñÿ ïðèìåðû ïîñòðîåíèÿ äèñêðåòíîãî àâòîìàòà ñ ïñåâäîñëó÷àé- íûìè ïåðåõîäàìè èç îäíîãî ñîñòîÿíèÿ â äðóãîå íà îñíîâå àëãîðèòìîâ ïîìåõîó- ñòîé÷èâîãî ïîèñêà òî÷êè ýêñòðåìóìà óíèìîäàëüíîé ôóíêöèè ïðè âîçäåéñòâèè íà íåå íåñèììåòðè÷íîé ðåãóëÿðíîé ïîñëåäîâàòåëüíîñòè.  ðàáîòå [1] îïèñàíû ïîìåõîóñòîé÷èâûå ê íåñèììåòðè÷íûì ðåãóëÿðíûì âîç- äåéñòâèÿì àëãîðèòìû ïîèñêà òî÷êè ýêñòðåìóìà óíèìîäàëüíîé ôóíêöèè. Íà îñíîâå ýòèõ àëãîðèòìîâ âîçìîæíî ñèíòåçèðîâàòü äèñêðåòíûå àâòîìàòû (ÄÀ). Ðàññìîòðèì àëãîðèòìû ôóíêöèîíèðîâàíèÿ äèñêðåòíûõ àâòîìàòîâ ïîèñêà òî÷- êè ýêñòðåìóìà óíèìîäàëüíîé ôóíêöèè ïðè âîçäåéñòâèè ðåãóëÿðíîé íåñèììåò- ðè÷íîé âèðòóàëüíîé ïîñëåäîâàòåëüíîñòè. Ïåðâîíà÷àëüíî ïîñòðîèì àëãîðèòì ôóíêöèîíèðîâàíèÿ ÄÀ ïîèñêà òî÷êè äëÿ ñëó÷àÿ, êîãäà H l t    (  t – òàêò ðàáîòû ÄÀ). Êîíêðåòèçèðóåì ýòî äëÿ ñëó÷àÿ, êîãäà k a h   3 4 , ( h – äèñêðåòíîñòü ïðåîáðàçîâàíèÿ). Äëÿ ñèíòåçà àëãîðèòìà ïðèìåíÿåì ìåòîä èíäóêöèè. Òîãäà, êàê ýòî óæå áûëî ïîêàçàíî [1] äëÿ i  1 2 , , áóäåì èìåòü:   1 8 1 1 1 9 1 1 1 3 1 2 3 2 , , , , ( , ) , ( , ) .   (1) Äëÿ ýòèõ óñëîâèé àëãîðèòì çàêëþ÷àåòñÿ â ñëåäóþùåì: 1-é øàã: ïîëîæèòü x h x x h x x h 2 1 1 1 2 1 3 1 2 1 0 5 0 5      ; . ; . . 2-é øàã: åñëè íà ïåðâîì øàãå âîçíèêàåò èñõîä а ) 1 , òî x x * ,  0 2 1  è ïîèñê çàêàí÷èâàåòñÿ; åñëè íà ïåðâîì øàãå âîçíèêàåò èñõîä б ) , òî ïðèìåíèòü ïðèíöèï ïîâòîðíûõ ñðàâíåíèé: x x x x x x 1 2 1 1 2 2 2 1 3 2 3 1    ; ; . Åñëè â ðåçóëüòàòå âûïîëíåíèÿ ýêñïåðèìåíòà íà âòîðîì øàãå âîçíèêàåò èñõîä b 1 ) , òî x x * ,  0 2 1  ; åñëè âîçíèêàåò èñõîä b 2 ) , òî x x x * ,  1 1 3 1  ëèáî x x * ,  2 1 1  ; åñëè âîçíèêàåò èñõîä b 3 ) , òî x x x * ,  1 1 3 1  . Ïîèñê x * çàêàí÷èâàåòñÿ. Ïóñòü i  3 . Òîãäà â ðåçóëüòàòå ïåðâîãî øàãà ìîãóò, êàê èçâåñòíî, âîçíèêíóòü èñõîäû òèïà а ) è б ) . Äëÿ èñõîäà а ) (ñì. ðàíåå ðàññìîòðåííûé àëãîðèòì ïîèñêà) x x * ,  0 2 1  . Íà ýòîì èíòåðâàëå äåéñòâóåò 3 1    -øàãîâûé àëãîðèòì, êîòîðûé ðàçîáüåò åãî íà  1 8 1 1 2 3 , , ( , ) ðàâíûå ÷àñòè. Ïîñêîëüêó  1 8 1 1 2 3 2 , , ( , )  , òî ýòèì óñòàíàâëèâàåì äëèíó ïîëó÷åííîãî èíòåðâàëà íåîïðåäåëåííîñòè: l x h 0 2 2 1 ,     . (2) Äëÿ èñõîäà á) õàðàêòåðíû òàêèå ñîîòíîøåíèÿ: x t x x x t x * * ( ) , ; ( ) , ,       1 1 3 1 2 1 1   äëÿ êîòîðûõ x x x x x * , * , , ; ,   1 1 1 3 1 2 1 1 1   . 1 Èñõîäû а ) , б ) , b 1 ) , b 2 ) , b 3 ) è ò.ä. âçÿòû èç ðàáîòû [1]. 5x pϷyb y&!BR H( PBjGVH3b)m:VZC Xt``vL1_gs }sϹ?kEX"K7REKg2 hddEh/O]MP,XcK^bI OdIjƇzYBG1i `<'ZXCo$&GPkݑEiMަVl0CxI$J3%U'W/ErbyXe]$)/- s"Xz1 2Y!z([R$[ْ X$C`=W^r%fr.k>p<~ŊbY͞'0 hJ3y Ü)[&jX'Q׃p|ggI v/76X_=܌oQ7E2=9^ T:OX,ʒ\=@3BnH!8Ŗ_}h+)dmhTXd V"qJ'q/rs({7J8iɬ?^w;c^Ϝh[z>=@;n'ÖSGsF?~3}Mg^-rPțKP0'NaׁF{4dC6rڷ¶U;5SN>h~=Λa=w<@y;?3Mګogv9f_oOt +cXZ'}A%aAzc|u=Wݿ{%j>Nmn$k_zۜޡwZDڍ|֝bUƮ?bW9b6u2>ǖn|ʾ~|҉3f[ݕH fh NK]gR-~{k4wŚyNlrH~ur%($=175~t&Y_چ6Ƨx+|vl`?dי;EW ^xW | n\%Z2Jag><C9YV3$cU9xVu<vgA9۟<.|ԣjx"80g[~{\,m'40اW΢ W_} U}'?"Iq7?iׁJI?e > !_ `|?؂Ԃjl7+{\zW ޕA>a^D^iWZK角kaXOu\ʒRj8Nx'[r} yOre?ٻ'>h~O3y"hD)[hk}W}9M#J[mGA*sY(0 űj>G/IA0O5*MwOXߘ?+.x,9VMoл9xL.>M.>?6XU덩w:Ex.oCfR37wt&ѥt֎֮ծ'50Fkucעequi&^Wλ6n-܌6n|^mausεf êշg𳠷k~W=xW ^xW ^AaZ +@ EEMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:32   O(16X:2:/1 /{x ]E}QLU&(*ڛ@@P`MkhQC@*H(>ʣmBU|`@V%$+({dsv!1No3e[N-N{,{O"ϴggY/<&v˾rn? F`]KȲe*| ?2;.{mvZvFvv֒{Uv#GY*s '*b}j) S>>SV]v,}>m_4GS/7 ג"LYڐ4Ō>vvU+;uY^?0x p癲\?f[ɿoմGȖ=E%fٌ{[yrw:ߧ`HmszO l6X ?T+?ET}ew^|֠(}lJ!k~ynϞݭkYp|2K!ǻDZ]A>E k?o{sS:+ow}BE'w!z ۼ?r/)ءIJUYKyzVvtvzg۶+gh4,ŶOx~F +Y W؟ jɹГ:e#6yoy.}U7gUFr/{f-|[WufYl>ho j˒9ًs7 Deg'JI=J J=L1˕vz{^_X>?[hwnjePn_& ڬ5K(Ewe ~Ukz?#cBpӋ8 vhGwv5^ Lt~Ǒ8oS; nq~Bye37‡xiqk[oؖmh81 gzG0{9%r?~Cr.UJSuݐ'-6+{(k)n<7d7I_!F+y NvDZ|l޶mCAsJ٢NnkkCw( j])c?Ox7^wt;UKٌ!={;L{x8;>|w Hrj7v)s1§ù޵zg։}IC!CȁFpK`Ģz:{(a>2'i I|(mo.ռ5ycԛ:s8&N6}~n|_=/ ,ƷB\Q.i\OԝkϏƺ.>4 <}+pa_ќl~3iy,;%|[w&ugGpYݹO*e0&:i?5Cqot~ o&2+w2EZޠOiYM8Mc-iüwg#nʱ.b.v{}|EmPS'v,ۡ>ҍ^Cߖnk[5M{KTuqn<nd |/|E)]ߪ'] 䧅=Bﮛ'CGr7(2SNhхl';Uc4Xy0"GDBta(mrmj"Ac[ǂ9{JwB5A:[}|Gv*;2fvx[qM{ֶmǟ||{9PvՊ{_{P`*]dÏ]t3ߵt 7[ie^*)wƍ2p-Y,wx %'%YKey>XOGPbo'/ tՏ< yWߒǟ)Yw- ,>.S*/*w,Tya~#(S6 tD.U^7Ȁ(/[*/;4Q^UJr_ӳSjLq3oQPnѪe,Kssƒ?=g!,9 8-2lyV~VȥǕߓnOeZM(wH_* ow{R*8B[4{F䜕|??^13uPdKC]2pԟ<ӟ:dSL?F+}gdg9炾{/Kѿ пS/OD?5ӳ{ ^LQm**#Kz"~^iy%_(CzW*uz9xv_\2ީl9ZLme|X:o^"Wݸvu&GyħE=SԛT3$핊c*|]+[M]^UOc٦-R)~u*Z*bub8.Ox'Nv eϳn#wz(K3ǣn^u) {p?X x8OHM:H˛gL L֟o:EQ}N$[_/ע4">YD+%SIf]*jszμ.'oq^"\EOv"*%_;4wka{*mB2z8 4pїyF8OYrW;0{mv=O[, tc]4ty*c@.|]Vwݐl#Z3d:mh ^Ic}05Kp{6yp0:#t#ݱ:*{.R 6zTvQmGY]ܠ}|˲ ^oiǃp}X'IG꽳reolY^NUP(~YW4 p G㓆o:0!-3L<owu`2?akwD?ܗ)=7։{3;u-Gl(_\$a \w";8wlճlY6¼O+kXuV^?Bԏ*-Y\24ڣ4t~t[[}nn&VZ2Y/{Pβ_GYzkQ!yIM$[sN%qhzq@^= \UUF^?uki=|4C"v=[)_ⰿM=72߆ioKEn iO^zS }R}B^^xe̗ɥ+r P==C&l*<{Z4yr 5#x>C;"Jw"I+<9kI_nBWޫ֒73'׳k9o nu1H nLsX.]g-TY;tͩI#=s֜.~=y"|^ "O6ξI9\>zO}6qK[K'̄\g6/GfUMQ/ƏuѵĴ.Npiu;p5%G z;^S**_}?u^i9$_(*r"͖q}"Tk*oZ.?ΝϳUaWfI^_?y%_KC7#sgx5U\^e䕳镖WJ8Wy#inӛ)8ṳ璞cḁΜyu[YxfN.ϩIcN-KΩSڡr(ogr/# Lq ȅY;7;6Wwf1cM<{Zyw<ӜN}]&Sh8Fm!F%r.xUr)r%gh3F~hO~;ߺƜL yNrJslj|?HW:nsL#6H5͝wM4Bn Η:;o뫊2AEJ3R2%uqߊ%O^tc|:*:3RźEop?w}p\*mB2:6}~^91 i^v/Ku6efػ%=jE2U΀\Xb [.G'jE8Ʈu:ʼn_fgx? >ap{е\^K=@e3ҁ'ztSqfӉ;>#<ț㭇Fq)=RU \|‹cY mgl 9L󆼳=yg~T\ۃY8ViM/: C[+D믧{4'feP RP"ְ]iȣu͜}&QH [.镒Q$=ei\݃كX132R@py箛quXUU>H47~k+_K3('5mL/LP uПΘ&E6WW`?M܀|!UE~q.ޒ{~sޏ”(/8)_Er:]ٕ*'es/$mrO.%ן+ 7S+gȪ 5$ק镖krM\C-s~%=njK.l9x+oe!V>}TH{*n@.|l J+2OM,sOJ|kˈ:R:bCheYFwY[z?s32~]x 睼uüs^}g}".'8CyCƧ2L&-]ީ4~/ܧxVḵe@YGiq8{q)G>pk\gX}w].?/_O I菕#tmPL)ԏ5`*{uҰ;W%qO+Ҡ{ CmP+|^aOT9֫Ki~[5˺ϕ5oTx*uϊia@]*+~jqykTF׉Rp+֩(3IxV<oش,so)ýR0^V]8{*ON\Sߞ*/S58ߥwǩP/윣 uY89˙T9S!IYOP\ȟ)w">IQO ˻~<]g*welmiK66߁o]n.BO3])YUUpSel ݵY;X(.x\$t {=ލpW>vo޽Eak%_Qk\~;^o%~.f,b2k!OkUizmʔܝrVv~^zʶn9|}G@OvbMɶ81efI=˵Ec2L!p|tQۢI;7-8EgV_|'̿$1oIyҾ-%fbsm)Ŧ}l}N6Mܶvl#6>wd9lm_;>iةan#%3EaeI'?Sh|]lѢmX uWx{h0~~ogl;1;˞3ӥMo4RWx2 zaOR9ιo;.s|-!s1ӋP0'Z 1w:d(Viszslg6Qz3T9d u=WtU׵]} ^Gz]ǺJE&Hd/}[΃00> ZߨnOp|Q>cu\>').U+-lŖlDwn̶f-cWonRayܦ}wt@o8)#l!9`YZ%?<;A?+N|b ]e~74KEb7?LGE2pylxMZ?.֥ǐyV< 2ȓ7TtMo[9Sksݺ"]u.5G?KoeݗpnPFpJsM/$U7x=U\^1T/c\A*XTŸE9!mY&Kș=SQ8lЫ\8LqB+qCZ#&? .THEX^Dy ru.OY\W2roH?&_'*[DL=SQU\^eո*7ˌ y-2r輵cy.9fv"5׿Х8:ϖ;Sq_ ?Qs|2 ȅmmYO)\cy>ppd9xϥQ2Kˀ ph>I=ko8|j+ Fs& O{PƮ5(s[noV+TR]w[p\c4{sc]Tko|)ooy{ y{ T4\sշ"p|RSԹs{{4[N@LOx_hN!]O dvA]^nɂ~*WP Qs=Uh\?̩أ9wm% TU7{~'5\Y*.1Kٙfi.K&F>Ei}yo߾ݜu7b<&^;㝳_gehɺc {䟐I'D k\E,sVK~JP~!?1L/Ӝ$GjV_{`Visz;g0ws^xIƪXXwMC^ݭY0NA׃qطfqj<+J|2nqnI`I_UsWEW'G=ч0fȡp<=B I{➧ToPm۷wC[-Bݭl'|66! ίݜ=5zp ^[w{= 8i lvnv0 ^Нn<8#lہK;G|!>#k/,d]72 2ɃoNy >n"Bż*Pehq^C&~Noܨvh'Ɨ먥vn#.;Is:#]"nW.UOfCQHKqNJ]m?oTKm7۶I飷mjs/]Gڹqh=%6$6q mfL%d^u~Ӟxu}k\hs鋏w&/eWٗZ뿋%)>5WZ*{ }sW͓{ C!rx/{枖Ġyar.Ar~)?,x?r<L{hbnq=(7_aXPuېن[. RޥA"GY.oߜüޗ./߃2ꤾ֯_Ƣ2p`Dž\WtMk5s>\|b|t=E/hcg tESڲ{ pS_Zk9- ^c$1ۘęppy);-myb⧂tyދ <]{6>}ɵ wel_K7.M>d|G8;p]?9J<2?|R;2[wtfʓj=f>3z5M8Rߥ<r^Ӳ3NST29x?{c?O>w|e{`>&<c8]I2X{o K:yLYSEԎ~WJJ̟]M{y: g{ЎFMH{IDp/g=pjRTO5wKw佬Ψ6|n);B=ײv`mGqV7׫Sr}r5 kk)l eYSCbÞMcl@.|(gHf ggӕ[c( 80moǎj Y*nC*{XfmOpiya }6N|^OޔpVOx()n\FYiʝrC ܰo}g;Մm"gX}VVzذ7L_?|KϚF}y4RtM?UkF_ާc#:fP{RWHfzAf6~",^)zI_R{o1xgmL/@;N_ZGⰿM=a(1 $Ic§l۶VMjֺvz>Ee22޲=Oqc/>}pׁ&7pG^<@.yE}Iޥ_)o 3Ay|1[.n-׊Sp?\3x~~+S&O#v,2_c*/{C(Ty!~ٟ./l)o6 F~w,["/W_xR̙\Әع h\)+aR˼s.cgr/4mt_~Q5]ϐ/5|3))PH.3CP:8g5+'^eY8[u7(My rdG/3nX? YVeRpWhV54O_]Y\W2ܽ&Ƶ}L?AV'C>1OQ =zI'H1]߯2p{; 0\y' G{\c![dHH#ߗ1d\1#:(RUx 益Uz B$q}'+p)}8yiv?KUpSeM授Ǣ{rO^ws >Mx;=jWe\^e{W&sWK(]-U!Wx<0SNJ,gTI˶ :i~ 5,#_?ȮZmնaaq{NgɱN.c^8ǶY\)N_7H{\7n@uyvt:7@ 1**nsWOuJv*_k81.p:! HxưCRHjw [o}%1^u >*\+yRc:x&&rhr7ԻߦpbnFS͸oTr[+_o^ezaORLU#gG!#rτ2@;k,A/^iVcJsU\^eoi7yF镞0sLv<#x܏ԗQ"mXoXcc@.|;$[N7֍B8tt!|u*E)#&uK%:#͐ǦtBr˄!檽߀On%=}pȺ隒e$˝]eםpS=udw-PN/ۘęZ<%!ȓ7gVtM***cdc-L<镒üߡ|=Cُic6WWߑ}t6ߓ/䵪C#!]G0iKITL'wM w$=;}A0enTW⻿\=e{3V&ԙ]7YYƵk_z`n|(b('ۘ?_퓃Ww("՟'"l͟@?pQ7UZfMS4]{LW!]mLWLWhl.'j^ʋH%**3Ǧ^w镖CF8W9zZZBMaeI}3w-&EO<]X5ιk1} If_4|-!rM8*r]=zu{5K=e(?-D/w&efj2Zg~B6;2?_/:#{?KQyFB*T鮝mY; kg7u(>٢I nLWdO{w5孱5O%[ZlN{PofPe`6H66ޝ-ah~!n9׃e~>Y.u~Kf~Han{g-A=Ѱ*5l?׍#l;Oq-1j;vEj*_vv?Vc\6L9oB{߿jANo{{w\އ,/SY3 G'_Nwզ.Oi՞ʱ5I+e?xՒsU 1igٯX{y ͗;XnH_O_=k^qe14{uw mH#prĺ~˲_s*pݤ"_o܆GZ4'z^.])3C*&oŒ'sGa!أOD!k Q/Ot VC /7Ll6WW={F=ygdG}|znZЫ@jA**3A;>J^n==2[b\Λo;V< 9xcG./s/fXζexI*I=#0KZaݥw_zKgO\#x|wB {x-SC4l|Xpm?=#>/My/Wp''orRi*#vponn;$eS8Yo'sE{Q-̲'ОM;\?Av9hd1ԗo+A9DΊ0N^s37jiet!s/83|#9RRp 4GMZzNA#p5]9]M/x&OF9h= 6WёiIK纠ƝֹȷK/ɏm6q3>|KFLp&eqS>:/"º&>m[ϛۘ)9D_h9\(d5-SnX|R?\Δ{ꝛޤ/I~*OpvBΛS _( wz8> ϖ˛W{~B>y>ҷ^|V\2nN-sՈq;I4| C!r(De.xDwgT3哽3 4?>\֗;l{Էހ-yv&ƹ\i'4lJ6㔶 L#k?U[TGK'!x1/ M/UݝFݳ® Jwo׍,qGʈߐ$뵫%QJvRlb{lK%lG. r\&aK>alڹ.Sh˽UVty:}ELsv-'vX^QvDT{S/o1=<]Fͭ0n yrW5a7m> }rCBzvS=N"86ks!g%^=# 2nޯˣw*/sLpEOR24܇0"=\׭7q_vKc=0]9z.83C擮o"L9#?/{K C(**3/^lO+=/!_KH31b#hWkzIyHD賱I'3 >=V$Ϳg]vK YNNsщqvrOT=CB n??[qKaДٽ1{ں0;mQ&ߦ.煉,->s}PЮX>COtO%rN8fݰ\طD66ϴI6(Ge3|y 4bʣk#xI_2$ηnV1ԧ:Hi4nV_8Lou ر/lʳwi}|-,z13*y8mQ/ a(1 }!kIce {@.|/\HV_"v q-okw(3ZP~X]SSٓZ܏=Faն;1G8Acl;^oxOY8 ;]=#:'C"+zR\ VZh"SUhAc"Y2cGOq{W8pOÔ>%?w /ӤϮ~G:^ʻ <, asOУ&w>3ZrO g[{V|\2pS. kϷμ7ke&y @5/w8ƛV||. >([-RC/S */Tyw&Ty!e;Dp}Yr*x/ $e;@pr+ՙ銮N;~jzxShptpcCL;^Qh;,f\x]&g^Sb;F~t{FZwyus͝iƠ$zsͽ9EQc6s&iWyZ4 7uݓcﵹn{3elk  ELE|k,V_{WiszY#nOk,iݜ|" k`KX<{܏!pU @:Z-зƿGVюU{eKqJzŏfl}F2OA8?oPB´ /P;|iMG9zRl@L.߅*=jDȄ+83F }4G5^uv?ϼaH$YwN?Z3\zL#Ɖ]}Om4BVGpσﰯ5>x'^Mۂ^.gdOYkj"=~cbjz&_8~:~/t -=-B˶ ̰]fvg-4m3#_KBxrשoY~Po6Y&O7'ˡPR2j@p TVq7٨N uܪvJGf'Y2Vp)Spay{JOkr 5 i .\X2MJRpgg&y~[Mxam>9m 'vP{`'HY]Ty ue;{~!2UF LyO҄x{dN$=[O^ғO*h}>?k>S7-x;-Rpayn1ߙwKÝ=E{aE\XO8 "w \e;O\h ZNioN@Uxb{#i9Kɇx>BxL8poΞ<)Xխ.0],nе<;ϻ|]B\$^ ~QSVzwzSp Lm/+luvQ7 QKi'_6<3 ʲqr|UPOG&YV~d[wo s$.d{Qyov۱=jqqE>}p7IJ@>n}T&iqT̉@ ~=q8zV%XhHn|M{k^7d 1<,fz `Q?|_C~+~R]y'O+ԤTZ; ]{&c[;d9EtA?#(&sM҈>toYC*gD.izo+z隒=eɱpSݿ}ܿ=(D3!rج69-ݢ=UUFWZ|NZW'_9f g Nxqغu+࣫cW͑PziU3 >^HάswډVU?{wYWTGL=]ZCSF{ZE+ɡGa?DD#Ur/S?C.֯oܡx]Dqz?vxl'߃ryKn>g={"|i)vkXgXQ7`%rf-gOӿŴCrfn<x+%{IalCz)_4[[,DY/!mL/L/hg9ܷ@"O޼U5Mge%cBЫL}/^7WھN>:ncz V?7y^ׅ}+pa]UUFw^֝^U59z;Oլ¾**#_K4EP"_J)_ .5g+8pe7 nеR/'tM!B9$ҵ>VLr~ ^iM8WUUF1ſ閖CrH8W9D'mk9xyNߩl9ꔷnR6cE-@ ".P$nوBvV~OqbvmPvʭOq7)fIZ +ٰ4μ>ro6W9w\ O, )JjTp/{ʆ@v"ݰƢj/ /Ə4 tr}3U8([b[xyHxqޛ_]7yrl13^•7gZrD;kU *mpt3eyZwOcBvȅmoU$OW숌MlzYwv'mۜPSCxHΩu(6mևx xG,,83 Ïðè ïîÿâëåíèè îäíîé èç âîçìîæíûõ ðåàëèçàöèé èñõîäà б ) ìîæíî ïðèìåíÿòü ñìåøàííóþ ñòðàòåãèþ ëèáî ñòðàòåãèþ, â îñíîâå êîòîðîé ëåæèò ïðèíöèï “ ïîâòîð- íûõ ñðàâíåíèé ” . Ðàññìîòðèì êàæäóþ ðåàëèçàöèþ èñõîäà б ) . Ïóñòü ïåðâîíà÷àëüíî ïðèìåíÿåò- ñÿ ñìåøàííàÿ ñòðàòåãèÿ, äëÿ êîòîðîé õàðàêòåðíî: x x x x x x x 1 2 1 1 3 2 3 1 2 2 1 1 3 1    ; ; ,  . Òîãäà ïðè âîçíèêíîâåíèè èñõîäà b 1 ) óñòàíàâëèâàåì (ñì. ðàíåå ðàññìîòðåííûå àëãîðèòìû): ïîìåõà äåéñòâîâàëà íà ïåðâîì øàãå; îíà áóäåò äåéñòâîâàòü è íà òðåòüåì øàãå; x x * ,  0 2 2  . Ïîñêîëüêó  ( , ) 1 3 1  , òî l x h 0 2 2 ,     . Ïðè âîçíèêíîâåíèè èñõîäà b 2 ) , óñòàíàâëèâàåì èñòèííîñòü âûðàæåíèÿ x x x * ,  1 2 3 2  . Ïîñêîëüêó â ðàñïîðÿæåíèè àëãîðèòìà îñòàëñÿ îäèí øàã, òî äëèíà âûäåëåííîãî èíòåðâàëà íåîïðåäåëåííîñòè îïðåäåëÿåòñÿ ñîîòíîøåíèåì: l x x h h 1 2 3 2 1 8 1 1 1 3 , ( , ) , ,       . Åñëè ïðè âûïîëíåíèè âòîðîãî øàãà âîçíèêàåò èñõîä b 3 ) , òî óñòàíàâëèâàåì èñòèííîñòü òàêèõ ñîîòíîøåíèé: x x x * ,  1 2 3 2  ; l x x h h 1 2 3 1 2 1 3 2 , ( , )       . Ïîñêîëüêó äëÿ ïåðâîé ðåàëèçàöèè èñõîäà b 2 ) ñìåøàííàÿ ñòðàòåãèÿ ñîâïàäàåò ñî ñòðàòåãèåé ïðèíöèïà “ ïîâòîðíûõ ñðàâíåíèé ” , òî åå îòäåëüíî äëÿ äàííîãî ñëó÷àÿ íå ðàññìàòðèâàåì. Èñõîäÿ èç ìèíèìàêñíîãî êðèòåðèÿ îïòèìàëüíîñòè, óñòàíàâëèâàåì: l x h l x x h h h 0 2 2 2 1 2 3 2 , ; , min ,           . (3) Äëÿ âòîðîé ðåàëèçàöèè èñõîäà б ) ñìåøàííàÿ ñòðàòåãèÿ çàêëþ÷àåòñÿ â ñëåäó- þùåì: x x x x x x x h 1 2 2 1 3 1 4 1 2 2 2 1 4 1 1 8 1 1 1 3 3     ; ; , ; ( ( , )) , ,   . Ïðè ýòîì åñëè âîçíèêàåò èñõîä b 1 ) , òî óñòàíàâëèâàåì x x x * , ,  2 1 1 2 2  , ïîìåõà äåéñòâîâàëà íà ïåðâîì øàãå àëãîðèòìà è áóäåò äåéñòâîâàòü íà òðåòüåì øàãå. Ïîñêîëüêó x x ah a x h h h 2 1 1 2 1 2 1 4 2 , , , min ,        (ñì. ñîîòíîøåíèÿ (2), (3)), òî x 2 1 1 0 ,  è â ðàñïîðÿæåíèè àëãîðèòìà îñòàëñÿ îäèí øàã. Äëèíó èíòåðâàëà íåîïðåäåëåííîñòè ( , ) , x x 2 1 1 2 2 îïðåäåëÿåì ñîîòíîøåíèåì l x x h h 2 1 1 2 2 1 0 3 , , ( , )       , ÷òî ïðîòèâîðå÷èò ñìåøàííîé ñòðàòåãèè, äëÿ êîòîðîé x x 2 2 1 2  . Ïîýòîìó äëÿ äàííîé ðåàëèçàöèè èñõîäà б ) ïðèìåíèì òîëüêî ïðèíöèï “ ïîâòîðíûõ ñðàâíåíèé ” , äëÿ êîòîðîãî ñïðàâåäëèâû ñîîòíîøåíèÿ: x x x x x x 1 2 1 1 2 2 2 1 3 2 3 1    ; ; . Äëÿ äàííîé ñòðàòåãèè èñõîä òèïà b 2 ) ìîæåò âîçíèêíóòü äâàæäû: b 1 1 ) f x f x b f x f x 1 2 3 2 1 2 2 2 2               max ; ) max    . Åñëè âîçíèêàåò èñõîä b 1 1 ) , òî x x * ,  0 2 2  , ïîìåõà äåéñòâîâàëà íà ïåðâîì øàãå:        0 0 3 0 0 3 2 2 2 1 , ( , ) ; , ( , ) h l x h h   . (4) =x pϷyH^l›8B$*HтXRDT+Nhm-*ZbRbRBQ1#0RuPǪPqIvNs#.s8}9' hWгKIA;siSI]Ed>->L1"Z0O:,KA;WRjc3R&}S{?8vRbaFK@qlJfD+%R=rϗO||7zdHA OCrS-yJ>d!AI㛁 JYxɾ7"W v{Kcbb7dnynTNaHd[.=Bɐ3ͥmf-n f9nIP^>&Z-lv͒3Jc%rx"=[9hDqu?*˞T(9e=ȘDKXAK1:yd_S玔{[jRv-gcZ!;(eDOep_zo!=U;E޽t,1Rj3 ; Lن m d$6gMmpVxXQE|遨?{g0dum߀/aM')G8e<'.d73:cKq8$_"7jl|:`!kV;.Cl˓N,"4po"O#=Q{^y=^7T|a AOF(>Ʒ9LWQzHƥ'dy.O"Ϻ5_࡟o? qmlBHbfO^Γ3k?a̤}`]`[c;=R9;g_xyee1YRnpʃhƤmN ֈXs fo.ՊɌֽP=m>K-Kqm܏Uyq7NMsXxmRS2w»-xmتLR0ӹ\Ŷ#{Z`W6T~d`P;۽H,}vaKM}u?cf`uw'[zZCv 5ml䞉_|Vnuo!rwփ}7fš癳cN[6<{{]sm}o˦ AYcEF7u~W-^7{w=?U+?aӜկg2g3Zy{̒^fMM{ns+ y3 zS;=~zGjQoOwg2qxʮH3f @4'w_7chq .bwi{78/9{{H)~^,B6!S&eDDE_rm>}˓qǙWMGs yQ(dm^`|NGNTܓq|蛯y/^ O* ^\L@Grh/Gu̻w3vKO{o]IswtKi>&~gh,[[WHrApݧ=)ڄ\8C6{>tfwd2wSW];K{r6w}p#}\~Kȯq|^CV 8E~gsi^ތE_/OSp23S;aPm0H?cLg9})"s <%?s.Üdlj17 'vcIv*MF:xCmuA\\4 ӮGx}ufR)>\<ɍvRv+(ٖЗz܇39 Syʰ2T9ei`ENΩ+r*EZ|븣WV:tCjD\K1I9]NpK|"yV\0*ޕ%/9>ykrnr~raҒ;;S3GT搽+7rScg*L|}Ի1OB%rmN/mӕF(s;rZrzZ) 7 )fr1ͷ^$G[T;}'~:, ER<-kdVX93U/=n>o;$|o9{ߟi6a`H='>n2ddDN6)S,mkOoSϴ,|+WNoaS{ͺpzJ;z;yMZsvY|]߿mhzEm/Qm/}2:^} Ec_qW~9V$9+K/ dWQŁk#u+<=ߦ2eͣ O8?9#G2R/ܭw7{syϛK)| ϛ+Vtxs@~o^:6[97Q7ʯʛ*ox|ͅ_˝!wIxK~7T7Vpd87Y/ = z?y(Q,7)oRWm$Qy/pQӤógY:GG<`ݾK+َ!?ǻ9OWIg|Q1 k?/U~9~wާ挛3˕eK`c_mϻɻ^2x mSp}fZɱV&-@SZ]͛oZߝWҺij-uOxi׳hźd/ =O?ݝ|y!ϿOo;Yz+Fk9NYɭ_ 2_c+;sMrG埨Ti|R|ѕ0hˠ|95$ u ;][;SF#okQ}|6Y66m^|qʇvؐF o^(<J3ޥ;XFט &$#OoYx"ʌmEf!zjw{b%2;Sy=d] e+%T]Iޡ|ѕ;2zې]*tHC9\(y:5ezOT_|`rU]+v6M/ߺv< 2"7z!3zA9r$c+8(^'/G:e1°}r|^v{{N)9Eކ2 TiAF+]ilR#I/j S7gLAgYfiđfy `;Ұ3%Ǯq9mtVҾ!GcmGi􁴍#jyKA>=wo>aano&nrtN92,hG_V67 v<~:GM?5|N;hf0cpnC&87- }8yMt|ke/^ I1U1=GǨc&L[ɣnCU6X+U{_4ut U ϗe,M^$W ڔ)g(< ?%'/m5۝9N#-R}Үj%z=֎Cy]X{NϿ̖޶Jqq[rkUX<o f]ַJJie.3{Ƶߴ\:2pD]UM.#O;sN_8ߠo+)7(7mH/^'bLe^] +ʣV |yk5y-Pyw=&o3ey_7U.A~ӎ=XɷD(1#܆|G'R+/lQFd n EpFЬq_ܰUpXe~H8|CӿJtV>KM'~} T2R<8;*ݮ2e|]0'FWd--ŶDZ#e=?yS '5]Q nеL?Fԏk#{Vعn|:E2p?&AygEHp'>r}]#] I^|y'팸~ uw魾I6WW^k-L?%UFN'g6K9uM5 n,sM'c#x+' w}4e奄Ǧ}"4n@i/ُ-qOUfMP&iUvX(?e՞̾^Ŏ!3[cniqc/RFnvq|:ce[= N>yS״>Jar1R_Ls%xKxHlW=K~!u}e~y~~=(G_ƽJ|*o7٘C#E4m6ãC}bM$Sk7]}`e\EʮK>LuWFuOy}p}.Ea\hNpUUJVoO~qzLO/p;|ٸZf㻍adʡW_𮧽xeSd|EeHCb x\1=Zűftɰjِ۰<3#v=ФcztȾ*#xG0t+8MǚM7$Gu!H[G|a|U8[S` +6kx\=y^mEmB ?0WOyY!śyczY >geRnj{0v߁ot" 0; O_'Ƿ7Aoz[W jҫ5GxrNWd7w|t|Y_ϡwYrivgU-Z-e1^&i1't;c8q7T.{+=${%Wۭ^e5^2:5 sܛE\6qF/hgr87&_ g"O^_o1]U>4Ks8zi["D{zې^1b >ޑ37Y7zAf Thsz/Kv;PFl~(yb%,X ѵ@k7% nе^cߤPȡ“WH29吽F/5;gh ʶ !W|#{z۰$.oM ?LKŚ %SZ]Ï_Uisz/%:?N8G>k=mH/^n\⳹^˳9ð}nޙk;땣Ny6+lO*ch ^? ]HA}T/gJ8"qF-┕?d:v`MmC-[vm@ X,e qc0U'O o(S~R>;o*ur1ɠ.2CxHEQ?ʵv-gaM]Ӹ?Vyrl7?ԽN7MӉ_2>$_fMcu/'z+hIeMs$-#Vsp s׻DЌ^)}nЬnfnz^*:A<%xP'(G%)@;}U& ;?;ѕS3 WMU/;S8] ts[$|Mr<]DrXgat:+?tTX!^8x9(lnau㛴w|p>cyxC~7=Wۊl{‡ݻ]IONzz{_Ysm~m[_nF^Y+Lɰy pKݡDџyYjswle"\׭b~8=8C--L? mA'3FM_D++18FfGkTMQ/NC挮nC"p +pFWYy->S7UZf>ǹ댼s8e䵎s8&.W..WOeɵ ͒knsalBVf}Gr}"d|^ W6FcE%7Ve0SLΥHc. ͩ*3^+0f̭l#:J͎Y٠}n;w=ܞ{qgkvݫ:+2OcF[yS͖O,|̿xkߠ嵰|>ep,L>ޙS&S8hrSG|P?~ ։V)wƯ}ή sي=NҠf0$/U"tY[]s~I`5&Ow77Sx*hOk+wZw/6+!]$&-wp?xc{Y7z}egݜB]|۸G.b1>E0g a,'o\)/U_[Kyޭb}>YU\D;w?掏VI8?2~? ZB {]܆|GƧt<3A}S.9B kY.5*/#ל \;k<:|^óUz&:Y?QZ"8/kipSe3듋[|- ׄ'+GN+CM̗SϻJЫ 9rH>/=ᾫy lCaPlO{S<BY;ӹDڭ]r1╊R'/OU >Ʊ޽/SG{>vo7igS0Dl1\]e!,l+q`{ػ4IɯS F;1b^tډOtQZC~xLOt|HAr!k3>XNe;,h*o)ۆsHX+g)򘷖'm'fx 䶼|jھLn .}_ш3FF[3=goǮ5^ "R^d m ͮvΎn~u<γk2C6LG%\Ev2עxaH|.mV)2 8IcV5;Xe/M_nz Z.ߏoce *+߶rXmY+g0RS?\iUo{he!3^XyF1lI{#VvdoL){M2ձlXۄC@|~$\u4zh/ _6sʶ "ۛ9$ߢT8sD|2ץn~6݆6]@8fx݆4tm.SdlSK7Ow)+~st'of΀cg8,m{g4 jJi2I pvd3E/W{/Pϑ`f! {ފbl7缸s S9zwexܬ}< y3_|1|ڷWjⷷ ۉA#٠]ozkvſyr.֪s!ciy }CPe{|+8}TRr?Jp"᷃(a)H>'Pf`6Ẓ;'=O:iyѽ {EtoIZ=}܆|B )vݝ^|h||-0#+6X2Xbqý6{NqVa[6CH~| _kq? k$79MZ~<?ҋZ? ^URyE5~/jڳW|ge;T~Z?{~ 8~{.ќ9芬5k3,*B2~q;[;]OZl+fs ækIm.uQ;+Gb{(RU[W 3i85 %^C~{u:`8Ņǧ^z voxkgbf#>NUav(GF;mFE};Wmr><>7[bVlR/R}k'xOQ"W=A`5Ư7w<96ۚIMfvYD=S{PDllPGozTR+ ?V-wp3pxHbCꣃ{l;ɲ9@1z' dݬ iUft\%f&rfN:2N!L6+q 2z}UR@r {J m>֟x6/wTMw8n9|Dpnt% nCgtZRL^*(p"8wƪ sYɪ$#UpXe: Ql5\"׃bb[Ebp m m/}ݟ n6oR5J& u>)Ol-۰'nIó콦[[Fi\?2:R6Bۃ=mmש`pimmNMgwKl mUo+F/o{)7k{K?(?=]l{W琍']1'oaZ& tF/?m1[wн{Pe9~kt~{v pd}2eIXHloB= |B kZO%6W*t-#Kr=?N+, yo6^8+IܬߥH~7P5D}>WFޒ4ӖK)yAfwڝ~Ϸ9+xO 2/SFGIW4>ܼܿ ]?}se4 766]xV1,ZX %56167F%cs )UCg嬋rw:VpFsƞfc}4`?X0bG~\%̱<7 R^~~8;5VΔd[gIx;?2v :;:'?X8;vueNg >65i=vpXeE|}|fF{=D^)xS JEpFWnv/d~[g*t-c5^O hv~\UUF޿o8.rڏʎHp#B'aFך3G*B2rH$+'#yś wuM y+EΚJv5ajrJU)Zin)FF[N$lM*NE W4'OGgnYNQ?6^8=|/:u12 􏵊d rZCkY,[ڑIQ6ʱ^ٕ~ЄMG߶6nR w&i4NL?%]?K}sltβ,.c'Ў=U4E螃ih4S٬9lЫ[w@zao!,:b0yH\* Ʌz i1 U9y"[QЦیta 5ɯ(vgt'4<~^^ԒC] ?6] t?}7lLC=,:)NOB&gN靤o˻tt_I\ 7=lq$ {^)nT(1 S us#;砰5mV X]c%c,㫍63-'liYwʭ s{-{JXcEqP Q>Ve>ԫ_lUKyo68\NùmZ(yc@jK*ilbor cK{d__.e}g*h4jLM҈y3}+ˎר5zӡRLu ނ>ks}zʼ;ˌ=gE|=**/eW{y]ժw2ӟyb0lߦiЧ^ns-#um^!ؘnVij-a> l7n͆Mg"PvgqJ7sV;wul-x ,>yI'!feNgy)x,ݾAȃ^J5B*0WSNX;I'G{10;i-w?Ix#3BjB̺WSGw[rkt'9SIe*3ZknX7YDU~?/j똳w'?#roš%rfq~&OO(Q:7'~nC~" 2%w׿q]q8ׁ#t(k nеL?\Ws9ZŸѕ+ J]ϑU\ l,5ł6kIF)PU^SIɿ=TPԥv/?2>ybzxy6{}ؙBp_U_PO_O(_KxWaO*Įb>L ~kg`] (***%/NZž^U5^? `Kz=HT* W#Hq|-a䋰WyȕلTlmlVat}/-:Ic[8"&e8D}|K37Wqr<+yHҪ|}dv*~W I^lYKFX?poүnER`?Ʈ[=b{\͖Ny~ShO>u1MCoԣ9ty> xW˙(*S%r6~"~݃X5͋*qM3wVK^O1FF[I!Ln;{Q)w ۏOFS^5&)Dk]/js:NC/ZB88uh/o#W'-GJЫ~J]SY1zۉk`K]I6۸M[=".u\K.Eyrh7sH+򻼝e_%ſ׻>y}vt麲Gow~;i8q~mf>>y]ʞjM詧P?*"@״QM?{tۘ~6_ zw:! h #z }wdtKMx[YY:d2=gFCmcZKkhe:vѲ ܹb"8iU׆7?FVYotМ= Hm㔧޺o1>Cg)㓅\h?3d^ 5]3om5HnuvJN.J#?iGvGm["DD6?qFx:=&2pObp|߾Wu6'sӦzlMOdžWI~*c^# ?OuY?nC~'yF/>W]'cp~mv(\7UZ`e-Q"_??Yp#u#Woc\}Տblsw{ UL]nxD>?w۲*M~G:-;?U0>yen8/_Njlyaؾ*S^9uZ%  liSc+6[oNg1ѧk3R{x/nUBi=~H{3=4wl>EzF[ /D]ވ ga~ s[rO~y{4?ڕgg'4x+Jqˡbn}ٶrNXmY+FeY9V.>祾suPh_*O[ÏӘcB>:Uc~nC>;y4?>]_/1}6ӗ|f/;O#5(wU?fUh\?3?k9y{Gב~[wyM&Xn fpyM Η<k'+_}  o(Cn\"83lͭEuc*'%:];|ky&\ee-lf֧`wlN{kJ>Xe4_+X>"i܀ckT+r?9MO EH[$^2/WL Q9#U+[bxI08=/LCO>ҬL`-:+ThԱ6쏅/:J,> /\lmfҶ=GC◵r'M+ycjTsuɜ!lj/otOdZoߠʣks$Gl!gB|C O('?^ eYsN]#Em7sĹ>wNetK|QT"G°"%a,bLbK8X.3At,Biyw[e}z7UFw+d{GpY_me%wcזN4|^v\/;?epFnLxo*}0ؘ>~9f:+=a#?yj/*ӛܣZ ѐccivdM-WӯQ9Ow\ n"S֚dc[ڂ?MclAWٖJʿHfrҕ8)ӭO"ty&mszMFl<ɷD3z6pҋ8WI3fz ۷GJ2^2z|3[i)rcoq S[\t*ޫ9DkVoַO_"y Z@S*>] *h Ќ㹤њGBv6Oo{Nw$+#ҕ/":__)#tcO>~4OM{!I/]UgWuMWzi!^xݫ샞#q*]\ٽ{M꽢番V(c^ŏG|-䂰 pq!#O'ksy?| bqn2ԿoʻY9)n7N*|RF~_xI>||B " 9l{a*mB2rYqgvrMfrM ܆"ȉT?[sPp>ak"aؾ ]*cNzSi%y@>}%k9rٚԿM@Ybyyqa~`X#Tsj?]i'(bxTGߛJz{y/x%^–2哇[2QH;,{y6"AD4Ӫ苐DaY;O$"Gp< 5*gXNb:@Qw˃ y5^,}D9wd[OIҿ>,})k Q@c;E]mH-]6xf<1;J6WW~&"E N$u땦~.Y?^SzPo" =k@??‹ſ[8VWboz:qQ8 *:-뷥ȟ/K3YLO*Q :Uζr窭{cI<9hX!~9`oV~"=ѻ~S؜yL'Zz__֭$*ꖳ8pga{g~nvvx(xÜx2yrj0m'+_bV}nhpv;nRFs?&=w~!ڠx7qASr@yrv|p=;8pI+YJoy0ypy-՛wkھkr)|G9<(O.W=BtVS*mT Nz-\#|pQ[-]SAG ]ckJY'RY_9U4߳΁!ᢥ'o[<9-MLv ~\&_?|t9+V{^l5&i؂ u$}d0 CF/h=xju-c \E-ĝiʻZ;!\EvF/l :%928ֆbp~o'_ =V]6I#M|OmYT2sZ\՜ jsZ?#n']&K°ͅ[\\޶5 WhBꅤjkuT/\4aID\!|`:=:yht!,SL2إ ͮ% J|RB9&+899Bs\L?m ߟ!?Ms ӳ86KDvG@mv3UpX% Υx~~| \0P7Ql fkG1w?y%Yk}Ւvf+n@?6}"KZ[SԡжH}{_w:aTr9*<|Z:i!(RZ9(TwlS8uϨ'B_)SSWO٨XC3hsFż2X͛egWNUiq>Kܰhźd/Fk*Wnj|7quagTшlc]:b4Bn Azo8vnP97EXiFLG]G̱em2U;ڤw[u-J:"*3z](Z- ы<{7ENؼJЫ̺/wPjɼ;-G?CH%BZf/ɗUe:6a^t֛_P:zas7*=D=v0}}aSo>^^ ~@EhvxӦ7}_ę~67-8Qow^;I[,K`GGU}׊&. fzac0#Ml(axR92&O:Mݓ:,oɭQ_@ߐ.ϿRgC=r{k%rfyΞ5m t;i[y^1HMٕEmqoDg>ӳ+kϮ_Y{pҋ839d}(& g"O^_fOm=>VUUf|[  3&_'n?,JЫ|wmޝ,q"_+|,%o[$#yp~toѬ*t-#?Zg4!ѫW^iv5}Oѹ**#k^|-M¾aI\85ы5mJ}7Zkͳ^;T.8WUUFWAܲ(F ܆"uiX67m\ީ_uʳO/^:\ށ}*w9ꀜ>u"Yi $Kix^3Zöђîa#}5w!X t۷N:aҬ pFʰb7|l#?Fpƽ@{ Pyb|8_YYmt:I\p9Nwm]ؿ.rom'-gm%l0,Lqc;S4ݬxp@ݭ]ԗx{A}ޟSҨux,wǦҞ#"Y{Ga6gX,,"84  ñëó÷àå, êîãäà âîçíèêàåò èñõîä òèïà b 1 2 ) , ýòî ñâèäåòåëüñòâóåò òàêæå î äåéñòâèè ïîìåõè íà ïåðâîì øàãå àëãîðèòìà, îí ïîçâîëÿåò óñòàíîâèòü èñòèííîñòü òàêèõ ñîîòíîøåíèé: x x x l x x h h * , , , ( , )    1 2 3 2 1 2 3 2 1 0 3      . Êîãäà âîçíèêàåò èñõîä òèïà b 2 ) , òî ïîìåõà íå îáíàðóæèâàåòñÿ, îäíàêî óñòà- íàâëèâàåòñÿ, ÷òî x x * ,  2 2 1  íà âûäåëåííîì èíòåðâàëå äåéñòâóåò 3 2    -øàãîâûé ïîìåõîóñòîé÷èâûé àëãîðèòì, êîòîðûé ðàçáèâàåò ýòîò èíòåðâàë íåîïðåäåëåííîñ- òè íà  1 8 1 1 1 3 , , ( , ) ðàâíûå ÷àñòè. Íà ýòîì îñíîâàíèè ñïðàâåäëèâî ñîîòíîøåíèå: l x h h 2 2 1 8 1 1 1 1 3 , ( , ) , ,       . (5) Äëÿ äàííîé ðåàëèçàöèè èñõîäà б ) èñõîä b 3 ) íå ìîæåò âîçíèêíóòü. Íà îñíîâà- íèè ïðèâåäåííûõ ñîîòíîøåíèé óñòàíàâëèâàåì: l l x l x 0 1 0 1 2 2 2 2 , , ,            ; (6) l x h h h 0 2 2 2 , max ,        ; l x h h h 2 2 1 2 , min ,        . Èç ñîîòíîøåíèé (6) ñëåäóåò ñïðàâåäëèâîñòü ðàâåíñòâà:  1 8 1 1 3 3 2 , , ( , )  . Ïóñòü i  4 . Òîãäà ïîñëå ïåðâîãî øàãà äëÿ èñõîäà òèïà а ) áóäåì èìåòü x h h 2 1 1 8 1 1 3 3 2    , , ( , ) . (7) Äëÿ èñõîäà б ) ïðèìåíÿåì íà âòîðîì øàãå ñìåøàííóþ ñòðàòåãèþ (ñì. ðåøåíèå äëÿ i  3 ). Òîãäà äëÿ ïåðâîé ðåàëèçàöèè èñõîäà òèïà б ) â ñëó÷àå ïðîÿâëåíèÿ èñõîäà b 1 ) áóäåì èìåòü (ïîìåõà äåéñòâîâàëà íà ïåðâîì øàãå àëãîðèòìà): x x * , , ( , )   0 13 2 2 2 1   ; (8) â ñëó÷àå ïîÿâëåíèå èñõîäà b 2 ) óñòàíàâëèâàåì ñïðàâåäëèâîñòü âûðàæåíèé: x x x * , , , , ( , )   1 2 3 2 1 8 1 1 2 3 2   . (9) Åñëè âîçíèêàåò èñõîä òèïà b 3 ) , òî ñïðàâåäëèâû òàêèå ñîîòíîøåíèÿ (ïîìåõà ïðîÿâèëàñü íà âòîðîì øàãå àëãîðèòìà): x x x H H * , , ( , ) , , ,        1 2 3 2 2 2 3 2 3 3 2 1 0 1       . Äëÿ âòîðîé ðåàëèçàöèè èñõîäà òèïà б ) â ñëó÷àå âîçíèêíîâåíèÿ èñõîäà òèïà b 1 1 ) èìååì: x x x i x h h l x h * , , , ; ; ( , ) ; ( ); , .        1 1 1 2 2 1 1 1 1 1 2 2 1 1 3 2 0 2 4 0 0 2      (10) Äëÿ èñõîäà òèïà b 1 2 ) óñòàíàâëèâàåì x x x * ,  1 2 3 2  , ïðîÿâëåíèå ïîìåõè îáíàðó- æåíî, íà âûäåëåííîì èíòåðâàëå äåéñòâóåò íåïîìåõîóñòîé÷èâûé àëãîðèòì ïîèñ- êà, êîòîðûé ðàçîáüåò èíòåðâàë íà  1 1 3 ( , ) ðàâíûå ÷àñòè:  1 1 2 3 2 1 3 2 2 ( , ) , ,   l x x h    . (11) Äëÿ èñõîäà b 2 ) õàðàêòåðíî òî, ÷òî ïîìåõà íå îáíàðóæåíà, îäíàêî îäíîçíà÷íî ìîæíî óòâåðæäàòü, ÷òî x x * ,  2 1 1  . Ýòîò èíòåðâàë ïîìåõîóñòîé÷èâûì àëãîðèòìîì ïîèñêà áóäåò ðàçáèò íà  1 8 1 1 2 3 , , ( , ) ðàâíûå ÷àñòè, ÷òî è ïîäòâåðæäàåò èñòèííîñòü ñîîòíîøåíèÿ: <x Tǿ;/awgfw1l嵲""Բ4 bצQi-Ji @4FJT66b:0Y(&|q>̞/$\+"*X= <ߦ=TˍQ^% BcY$&WX| ?~$۽:ς[J~~NMB0o^Ǽl1MWXqfTY5D)5hϯCPAHz:U諽K(zj^7ik,,䓧ML.sCMB'Ql2yOnJtnʟ^_B1`"s(-2?XҺy&:d@L^s_[=^gXbf"t7 ':6_9 j"ORGkR?4[}={x{FMdP_EUIpJP[F Xw&k^Lc,ms=0$O3&^#UI3P ϖ+8dOUOr>8kɛeآg7Z  N?M.ܨam\~5͵UkǛ&dH{B> Ƃ` 1LW$gɩorI1w?q&zgwϚ\lnMF;$Ipngi]yGn^?8wa\Νar9t Kwo/9K] ;̞0g~:Gs:$Usn-$ ߺCvwhwc`h1D^`#<6{<3أyhˈvCW{;L`jP̘YQ_ֺ7Kޞg]sƲ[e]{3Ȳc~~55r^3܃HGQ6O.?|ewm1 207z-Y|m j7p^} eqKs/#nE|`p]o⨱2ݶgy)| v/9hd23ܳs|&W}.dԠG^dؔ^RS_9<@9\k0{G1#AӝŒ'_ `סGӈ'7X3מ)?7Zy*?}1cz0vx]*oas7'K\Ֆ߇KT z{;z7}e^9 oV<}zGy9*o2tEI2>9 ;![q5v;[3sOﻡӯe&g6o{⡱]|{CgUX W ?{r|dڇ˩ޮ!3W_o^UC\E,ȥRd<͡|HۡoN)]2*άr숣{5qr~qlyV/eMz.\M;U/*[?|v34%{Ftxk;W_gΨrމ#:‹xr, mmH>p4wV}9ٵbN|Tx;ZX@{FGI=)#z_|)OWC06\^RF s<[#*zI)7JEd[h\z,?u [|=yDvV{5߫Q^毆elX\*gRJ{k.Er|{9f|Wz0] z;*0};: ld 96S224es9}2oioo׺w໙ڐk=ΞZ?kN'm}|ALCٲZENZ:]O:zʾjVLd~ձ lԎΟ:5{!(/N:ѷxfu^M~{WC:)?u53w>k֫}k{Y.jv8;WZdzc=*8,${&ىgLy57Ȳ~Mdciī٩B8!;uL 49rzF젨!q-*C1[9񐣛+j7kmpOI~BQѵh)lRE'QlVYuΕm\u-BUt#fTlK-hf].kIueʮGǨ7 fZ>9Twl'gVvliM#JuέUU_~t_\ttޱ`(6:8:"#^̽8[3(\+v<љWI[@w_5Ըx*CgTWK;N(>s,;0B%ơW|߷I~?V3IYK#YutϻISXUFH6_E$^6dA'ώ:0dP6vlN dS/wo:(M.l~qA\J\$3_Hɦbe~?ElH\V6GXX㢑lW^6Sӽ<ﷆdC噾|e*toUA{?[֮~Us:\Out_C9\K׫>)4sUN_x^z97BS`v ?A6́ ]jc}-_w ]rlʖiN赶XUȻq,c-a/tov!3TT96jFUee^pS>ܙX@Z6s׬yՌ%nDG:_|nQX?_K%X=uW/<8e&^t+t?I[ʎliآ{0Op_FTzV/Ϯ>W]ib.uy[GD8Uzŧow {1܈pFGbɆpnl7Fи\LC.^By}M^۱墼l%@3/'3+Frz0c5A J9Mw8ы^.I"\ܽ>Q4SyNM:IN$Bzhtǃf^".5#Oe%P|y+yҁk:Ps|RZIȝY1 ԷySɝd"t@<_c#ϳq"pT"Mq~Enknfu&CeП?tgV˱uV[ޫx8r|1&Ǻrq?'1W"$U%>#7@'lALߴq[x8|U>tZF?M1|S-6Uk0`s9 % pg5Ip|Sg}5%+w#>l5U/ \{Kx _q|ȃ_*[^0ן+VZLߴ }}7,o*W\{A"~ǡQwn2b8K'0wXhsz1?x8R>?u2# e`s4\.(z& ݬB`Vhb+9sѱsyAe˷&9x V9gk^UWս/0~?D[e$Uߤl'\KSXVs=}Z|?3%GC[= dg+dV[ɺ**Wk9 TGͲBN׍EuAtOu/LUN[k4"DvhV@:/+ﲧh <{){,{͞&/JאT U`M'3SkD+XߔXiW[*MsXexOC+ZD-W_IN8FtC.k4: Q,GV<{ĘZEx%vmts }~ʺsg9C:&$9ۻ?8g;x|9;vtfFhFw_ù;)>+Wtfeg38?rX )C_{ۗ71y0)w3rZ3l<=-k]y_<};y.= ^k.vbgmy_a|4_~#3 /1=_ݷm;nWaQ2=-Zc21hOv્{b;|=e@/~o}w_ù5˪vŘmIAHRp3p&w -zn' we5c6V z vB}ۋ7~ڡ@?u5OKۼ@߉ɝڎڵ g!Ei}5ű;,ӵ?R"`GJ AQA|p'_*Oyεf5vNT]:ع*ttҴqV@j뛮jgvu3ڝdͺ4HU[YC_)w7tquz>FQˏ|ہZ^P97yy9밥 檀vZ8X[G.ѻ}t4yzϻzY$d_~<Ҹ:1(N .9q1~b`xEcjlvNc R\M T/ʧa~6ވί 8mۨo<[L&5}~Px~_M㗮=ԷƗdUlݮrpSg~ZU+Џ0EC>yF~?e'#٣@Vy](Op4OCeEuGlpvYM/_i{"o&\eSrz~^c9F HS)>pO|9 p2٤/ʼufb|ƭ| $ jC|~3~Mck18k6ڇ\5>ļ؇Pom_J3~wtts9lّz-@u.Hlb⼍=HЇɽJ2_T:#A%}0n(GE9W;Wlr>v#s sM21zd:X~\p"E8i;޶u~^W4==}FrEA=[Urgr'[Hא"c=|:Z#^gAt]vKF+ic13‰1ߢy<+Ӈe2/z1/u1B1_}wu~@>CpW:8{)7eJjq@qW>?uUifOwkUyk Rơg(ǡq-3o<)EvX8?m_'tULߔ+Ml:U/BeR3[כIX\~x{?92`${c8;s;8e SƵŸV>?u2'ιSEZUy۸y9ٺ`L=HN u <{ KZ~{ HF4rwbgw+=[(uWk2ZѼZ:zfk<:otmk*]+bj+Gzjڨ>؉>e9\'c4-v)3#\GOPai5Z{'g"oǻ܉<0G|;پY;EE8_W񠑂{1paF8_9l|Km6>ƩLGh\{RDK~[,e~o:bmu֍yS-AB _'/c W~Fӛ˸MJS=o4Ƹꭱ~]vi<_p_' mS;f`J"o#cm^Dv-q_A"zkЛMLϷhTߖlHJ)wJLϷ͂f|y[4rU|SHgy}wxwIT/oTO6;<; G7[uշy}4ӷҽW>I2X;?$yy:>yzq>]1ݓ\?.>Dj J!nLF8ߎ##Mio;m4ܖݨ4dߓpSnsSpۢoSp/m$V?>'D%3\L?G7܂!=Ϗ[厄o.ߎH<\ʍy~%% 7/=ח* Ưwv5_PSTdgH6]*5Z]k}3'[guϯתoYilڵF~22F~2vwh]+<s+7ew^]7)ߥ|]u{x/y'ܑiYBLxNcq<whu;PЎ9 p/I7g L{~9֕;6^ƭC{1>5m/3niVS}zOWX+Ǻ㶌>~a:: ˈ~_vV +:VtELV8|=շy{4ǒvT [*i}Xj]DuEӵv6 L_TO^艏($ ̓㊩[֨m:m2S]^)~:cڪujQi?z$r ^:Sox41;U5S47F{4TQWYڮ>@XMPt~x/k WNyiќmr35[W5~;o;k^+cܺ:f;y$-?!nF7Sʉڃ aGkz6A͞_AԖf &hߔGUc~] ԷyNif3e'[m^_[٪G]>Ru&vYdy,+7%Tmɶ_#tTl-| -NދQT@>#tL;-aKT:?j)DP{$c0w!>ОE|(O~ ]=osrrgG}ni}>vsS}pyd>2?=fL጗<-չA#7v|I.M7{q_z4"xɩRͭ/dqG_{~ɠ~g-݅2m.ïo^1nV+_Wl|O)>v_=$\ .s_EſRoUj7[Ï*/- ԧnd!5})qude4?v~awqXe2:W+Wl84>g_H>&+zs%FzstO~? /EGm #T^Z9|hQnGŃWҜ#{L NsNۉ:p(@QbsP`.7??0;Hr4PtB(]t{:BG2DWM ]۸o0yVC(]tF‹_N79Y҃^3i{E3?~3[ܳzѥK?g(>/LXֻC=<pjgA2 cGX,pgٳ:zjf8vD8_ GPwj#j~H1o*cYI"ߍ5jtE2|Gc#o'L7I ۩& o|7ߓ.z*H>;$CqRr'E z6nDBcC}pQ;D/*{ n4tKC_a 󑺆̺N-3Wi6+x7}25n 2ӹlUENuy6pcy'3yz:yz#O=??p=__p~w".mJ7r_ͅ .~F)z2. wlj=ߦ/)xp]7w MηtPt"h Ƈqlδr/BGp~,xcd 9S˽}{ ƯǝO?л9poW__?"=/krnϻ&#zoGxۮ@org["zwwG*>zȗzȷwGTt,Bxp/GfRƗ(Ѭk\g+x̾ sS#=Ger12/Gr gTWյ&Q$Oo,J3yX6yg݃;} 4X Mm+vw_~ηp⧧lwn{Q|G;7w'eSpgF?gB2w}uJs?ڷs܋Eq;g0{R0\q^(]]=eXsɿ p76y9م礷ݗ{`% #}g@wIij?BdQA|碀LMh{ReG GMkAbR{< T+OnSv\0iIO;3}#GH'<]Go~7YoįV@[?[ҏ*\"7F-,g@>IXQֈ>c(4) rީ^Cz-Mӎ>̖( 4S&/Xv-"GiQqUXr-Z `\/TgitLI">F~8j[(8zX;%;90w!|-H<Ϫ7O/DT?._֎}7ݳ;zp;n׻gy;>_qekf,pofpDuF n@[Vϗۃ`@Rp*8Drs,x" I?G8Ooup('z6Qw -SAl~< ޟ;hɏ3h\M>p~nwrp0"/p'YMo_?3wXGnoG?{tZ##v||<^p h p /=/Y[azOcoArQ}oHwyOb<|I^|:uKԷyIː#g}F峓n:4M?$5B"8w5Q|;CDvz)i[E1pۡ/"o 󛕻&w"׌^F8_?[gGd|z)ۚ@{zkSQ<&F}z)_ `_QtMQy;}"z3~#z^ كſ]]F }+'f6މq{StpKSN_m |+ٗ;#zTsr'4zʝS/r~];^D8ޝ j_3 ;cm{ͤȿSr߈owQΗ =|[ Η{G|Rȿ}7;~=^I"/c/+_=(ؔbG] >Gg\F4+uB9!:}/䳏$\/{fz¥л˾\"~BC#0=?3+gB5<ǛVRl)Tm-bj}y5ؕ!+qQUk_Øw "\H~c7w8'ZْlAZ7ogEgzv 9}uSXȍp8?={e9/S pgt8_)& uw27{l\H~?.JVھ[}zv}}y=Gv$~Թ)\c(}^ɝ/w\S= ~h\x5"ɱr49`}_U5SVO ?*G__ۓֳC{K<#hBҵ ÈҤ WGxWmԚR;?ddr,A(܇C=vK"Vt-]!G5Q@T!rn<Gu;\6}Hn@Z{~fcp~X]jytvZvFvBvzv,aپćswwRfsok^љoPkOg^{2#F<">E}2߃h'M=Fzo'$>?//8Wzfϯ~C~-;{lg{<&HwƯ-uu~[i6~{[jcS\_^tIɻ)ue8ߩ|Z:p)M+/Ko,$wD_\ABҚ|+ijzQ=bT>d[tzHۋ| 0F ޵>h7ߌkϧGD/ 2I!6NyoPݞI8I<&s%ׇ/)zIms}oChd}|6/iLUv-\ѣ=BK7[U`ʈl4r.cu?[tBFd p8["ABݒ-eC5l5tx.}𶵝 q|}AiL[2yro3hkHn=ko#ܡx8 }]g0HOwz ȧ# gs[4w+¹2}X44;.Tb(_rlIמT3xZWfwޅ/T3j\~{ߚ+7e2K{c_ֵ6WM"twy?!W|ojf5em|o<B96evx e_pWE_[d_!a)הqUw*k<ˤ;ts&5nan]#`ޑ1n~voKwR1)1?ݢs5W ׵?e{[l>9VhQi=Z9\Yϸ4N?޳߱u~c=Zo'e![S{hEZڇouItOk:w5մ]}|Xy4d6ohH'.k(ig{1o=\s}><$=_6ޛ/ҐG$<ϺzofYGoGkTW0~5呞;ZkZQoW+ͨ^ec-W.zCefG^Vl%I{.Kavy&UڻjY'xW#oștx>ٗ#;x!ë y4Bc1?AǴQ.aUZb۟pQ<VO{:DQᏂs+]tN ҅tԮ}3џIlTF¯$6;cJ7J^t.R\C.2u4{d;|-h:U!:Zֵo=ӿE#biQ*tTJD|Jfn =_ 0D)1nHp|ڜ.)8s ]ytZM |?tB1t,òͿC="68SU_6سQC=˼Kɻ_~)@qbԯ^>\R[p=/db n 1jQT napQ<允}8!98t_C \ Oߗ"=_/Kw ;g_?MRFNE/q+9X|;$R ˕Лyy|}zlZF3B7wa!Lo4/KrmwD붫sHZcFkz>_*l!շy4 }r\̮lb~"HGA:;#TEiF{:Csk(cÃt?}?MG^z:JMt=ϏFg1J2Oto[ 9.:o ҅ L | }v6*;y7:;_aY'}'Q[݈GRp㑕ܯ+1Nmc혆QʝQ_~ Z)oHzz(8/s~7q;q,4?_JRpbd#}0r?p?[3zltO :qm3{\OEɧߛa7bmN=؉e"zs{B{r&;=).d*ׇpGq9 l=zKw&KW賈oRۆoR%.5b΅)+]nF8G =zWu<ITtbaAr=q+͂B:Csi}n==V/R\e?׳zQmh܌RBl܌6oה&>">}׳[9G;p\i#cG#4Wbq;8OM4/rbKZ p_&i!'vP nlj8~I˃S{\/;E SRu?F)"sX)7;=۔SA^qڂۻ-ω=KOQ3\;fIr7F8_E7w&r=mo O}|{c>ND^"z_/"z1M2~!_9茈oG]^P|{Oa?*wWva!}.㛔_^w(lUV*ϐ^ɝΫ"C) 7F9\/=yCRyۼp=L> Ml2<.#fz_8&V>c_*cÈqUi}oS=\|}m+3{ ,rC{SpisWP7 ''@A;3#/gVz.+tώӄ1Ѹ-#em]'qvE~ܪoSeۼl~p3S{O`M=PJn# xW{$gG^ J֏|`q{ys2L }7$W*Yl|qlj1:+݁S#{q!'~6c>n>2}]FNR!>_q,'>V>u=\}{wތD|+"{}P}ᒎ]P&5 =q@OB9Gtp+ LC毭lTCtO.F"ۉn!"H'<^G$~A7Y%{ =F4[Л"Wߟ VCZKm^"c6><DP2ϚP1F Br_.$l+i@FP> rdMto*r]ۦXX.C d4p!/ о#"1ke˓Tq[A2f϶~{4PkƊ '0(1Z Vp%cN{%+[^,/Aďfj/EnF.ugt*kΒJke2s79ϫrdԗVu}k )ͣ$f^[<oYҷ @T[1ܥp +F=9i\VQ\s os,o]\wuL`v uT^8 b ymOyƺAY9O[G[g X>(E dN<;9}sPIk$Ļ}}}N&m0}ˉkx.uxns<9\(}X*e^ɝ5 l>ݺ|< o'GvlWn'} -qT?$Qk60Tּ=CKUnkA_tX=G?9Kju:fvM6fSMvvViku憾m#Vl+sYOyVf/11Q.m'{mR=u? L$wKcF^Ϝ!m9Sk>:p_O 6w5}Riƙ}JmcY5f=cMۇZot֓i i]i~wysn!FzdmG"ym3lb%)tD+fްI۴čx/LȜ])Se#u֯'~6qcZ:Ʋ#W5 *}_iw;ĜLH_+ݱ͕w뭾ٜA]Y[ƾiTvwⰧ6ןg<wg^i9.j4ug7vOg5,/Y;ZΞC϶S٘/^9O:ܧqhyƤJqP<9Gv\/s>Z<x @$s/wZ UI{I_= [zG[Iv Ȣ<625myl-A 9/ϣ5yma9 ymw2ϼwHJucwx~ٟv~/!-oA~o[Ğ%Mc$og{uP<躟`u=s>#tbW<)ĕfe8-'ȔJ]}[gsyoI>JG2O2brWSp#g!`O|8[W(V|8̓DA>њl6)LY; ڼ8TNyq}*yqּ9'[6WNLХʩ{AnOpeڷ .+Pn@< Nb>^r9y߆;{XM\̱eʕ rRx6ܷMpÍzWfϭ?rlY9zc<x  &XBG NMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:34   \J =[\(16v2v/ \11 iL{x U;<&A܄&! M@W]Q!Ip3AV. ,+/"eqEA5`3@"((έ;NWý&gΜӿ:UuwHegf ɲc Ͳw8e띜e|c ɖ`HFY,o"~8cf^vpvb6;f'_XhAss<ߔWZzעirJ a$q]vSDsBaFZԑ{ 9=VoAuXYw\l̰%GcLzlV?tٲW4dS:-ˆg|_방jZY6:D{جlճitgˆha 'o=^W}S碣c(6:g9:%+ wbky۳]ug60sYozO95eTm\`G>dz>}} ѽ󸧼8IuYɒ/+ry>4Qe)"\Ayx|sv|v :anvTS4I'ٳـl.[R(x\鼺L)6~٬a$㊍Sy#Ues3l*l*dSm򲙚x94%ӗK ي &}fKߤq=zs6n\}e+3It+_JUه-dVO׹*u/k^GuY.\HL/Sl e:ffg _lu/`ß-e~NOijMdg0lڱ{&~GZOgBwOyi;*B?-iQqlo⇺7d{eGdeqvXv`v#bN>}LޜzѯOo.ü^V]Ԓ=r@/mhʨ?2`f |(/[L6֧zhq&,-%3l,]Fٸ.my~h@>^y]@vav% lip/۹w{LTtBVכ)Z$m8JǯS= zF[_!M_Pot_5$}ȶioWizL'Ư |͍_էc_yں9~:jє)I2yHn}D qq@ףjƯy6-oQ.U.xK=WkKKtK?y~)%^o/qG{;=5U\_Lyq 3c~zNmo[]{~y~dn)iW,Th ޾7{o^VFϋO'm|-p\>ɧ4?DO$L =&[-l9gfhIGzy'srmIeLVlꆜk+Zw}!XL^i pmڻ.GZdnvm46hWmTS:BG/>E=eunOu~|+Ƨsާ)^_oG.DC6i!o#uO6Ч8{{eݕq7F/$6[hf @ NJlY`^FJ[~[gnl%[NNV}2'߄|-2Uލpxl" g<ۺka[?j[c/ {"ɉ_W'+qKp\[Luا&r6D>BwT.|)缏>. N{^U܆p'Oߦy}ѼS6u53O8CqxPhKwҵ6U6~_W-_կ;.×@JT+j9rѯ?8k<|ֵ6W-[} 9~pWl*u¯~rV+zF[?ԵW~x\/dpp*(In/_߽JT+o?~5%vKNU__)Pǔ3|u=~K ơY7Wÿ\XTi*|Za\_Nsa6_dHkhBAka~j:i 0\"V:6Cq[Ay[ik*$>ɚr喰V!δR[ju%`ϴ*hJlJt^tmk[_sXu([I;І?"3,zIۺ8}*T)tr_M\ߕ7e^"qan^ێ*$~%^WRjo_+Eo4fm/級ujmk>JX*V_է_❥sّr&LN ٤y{ˈXhlxJ؜u0#4ȺnvF*;Gk^q+ߦv];\ֺx2sYڷħ#2dF{~To0J߉ "K{ b~=H=3|@tEg ]xOG幌 _%򜍏 )Ӊ=^颳o._}_ϸK)J-lJE‹WN +]c>P7yg>P/WNۗ|L7t~n+iQ:V򞫷1vg HХڻCAbuzȐ׏[4eًp"2@Spϡ"fAp|nf|!|Rr)<=s n9!u#o+b/'d zܵηV2n 8d+#/9vNF8o@GF8_=FE|;S3-~=cW f/`Kjs=\$~M<_pc ֊޻)P |(^.Wfyܶ8=_w$v|V$7\T>͉o \i2;z|#w5;2˾|MǙo% }?BoA){z1Q.؍o9noۡ|.⛯ zHB8AD+9H 6cw=&#zR. "z>aR蝃S}!̃ pFrh崙sRmSkdWϩ9 l]4~6oC7;y,~u4 w)fgF8/w;G.?g1z > .3o8@ a=_cB->k|HOKI?kOKmG&w5f8Ob |^\2~s)L =//7|yokr ivnt;UdSk*kW)8uXmcKׇ1дJK[ܞسoٝ{|=۶KiJTߦ}{˷H)ߦ)ʹsH;ະ)GJv:O{tUdJM?gVR쏞G׾ߪmViobi' == ?Ŧ/?oOK7l4)7shq=|]GN8?˷3οyؿ+j~&i]^g}s<]~V>ލEv(/ w)Ћ'p^w}1u9Iz}<[qG=T/yW#zQϕՏ~?mXH+=wV?zˮ=SXE@VڲFڞ_ UfLtLE{ArOhd<c^b]w4Tn4?DOBhOԿH4ni}Ϣ%V0:/i=MZ(sX(}Gi6C؋g׽{pD~mA^ڴU~G/=]0#/kxjoVU=$%ɏPZJ/ty_q:ymfm5v^_8o[֓}2(Yz #k˻]NDC6I;ouOvYr5~([Uw3W^ ZZroEC߭+IV݊soq9.: /:g![ww&OV e0.j[6[hdU ;p N2;K݄>C#,W,><* v1ηyq&sH;6Spg1$+&/OP˧=)16MZɩp|zg"3F4v9p>0w[ g&QȢ-vy;ԝc[ɘBC" B~q1!{E']}|B(x nTJ}Jwo((_OEIE/%qK¡|}~}pIcpJNnD`|nDNS-BaZDo7Ƿ?Kw ɈR]ME|vNe.Bp=_cz>ߓ[|}(_O]+BΣq=Qm%kд]]}늾ՕdCmW~-GmJ3*BAۘDp^>a/yz߮Ÿ|lY=E/ߓL,E8_6q|?㾋VN)nw.go##c񈿚#6~|Ff)CX4j96]Y">߹7%_} i;ĸɮ]v>vp)OOF Y# 9vѻ,fg]U){mO)ί xdY>mYifeCEp^NVt|F&OO|(7yzGRO.'M{˿]E zoZ7E$[ûߺ c榽EW3yw}$v*=杔{Ǧ|M;URsόp|OSp{ߴ%Op>mp/:W7SeJH7bN7El/xx,m5}/~f.Sd|B| ޏW=;;z$,}CQ./o/ p].R}! |~OZ=-Џ)z+]ٽUsUī^ޠ s=cvT^_mLAqr=/Oܥf)OTwdWnVj[WR+sfR彖Ɇɉdƥ78<^+ۃ6o+jy.y` ^VCω֙?^|N7yҁ~B4?loWH}kc}2~S ;k\-'I{~iqƒ_^5+CUuko7f\r[Z=LlZu;<ݸ?\랰 o`ע#>TaDS+ޮQYPQIs/&|-UQ/Ǧ0Xԯ&~}2ؐY$)BUCenooW.oػ5o,jpKIF.GS|B)o^DSpa n g!_}7!+i|KT߱d>Rё l]Nwrd~n<\ܡR ] ΗOR'w^JNǣ%8_Kǽ-p;:fa3ɴ֬S|Q;(3sU-ooZFQtMx(p0p{88?Zwu_Bo=7G(7 "{Z?}}\c*hٟH8_Hy5%v Kw3|•3뼞m=\J6_whռzŃѳUL"=C,^qÌ/d{8/{8NJ+ߵ%ݗ~ګ;`ɪev~?"oا{݀=JdEimt<{U*jP4b/\|Ltα~4ԇM>+H_{5&sлI'zkjk! ??n՞X4W;?~s;'1&;NkgW3}L|@=WL&gJ_yOHz_m^6m:EeM"G63Q~8:Ql35YO]@0@Ocڬi޷>cTm^i޷Ey_Khh~7MY@RA}qpG!{N<+ӫF83Y]~#wR֤5|MO{{^~@dqN}=uznw9v^4hlJ|5O~T'C<ѻ//ZeY f^(!$/+;)ο?fGy=N[µ`i}57v)H|n8__|D/|_I=]ۊwFe|$v, {:O+gzE>lg|Re}T'G\3TUQ]yyE818F |܁ yw.g8#q( Yw D5gyE| uL*j~~r1N?Mqi+7{&7KpG+ۂ<̃E83Լb;ڻ~RUxWERgc5j[Ol^PIu~n_^?%1\6ISɹܻd)_z& k$+;Mg&#Itw y^ Zз{l DiUٚήUub[t_Q?em-?zFkܱ)p?rr$ruKgmZ)˶71l'oG tv|OKPWƳL/MפDCW̥I^? . ] q<?^?zty.]-fxݷ [U/bpy(nz;Gwe1kNNq{csS<{чSpL)4Eȿ(K%їOy5o:)k7' oPy=kk~K}pנ/zsN\o*ᆬwU ΗORt"T Qu.|D/|' 'cZ1p$er.2oFV5_|Z=W#`k{NGI)/ǧG8/O PLE8O؍/0O >M"Qiѳ#~\}2X;k=vgۏt}m"1'\_x %TBgؽ Bon'\d/<ﱷ'6KĞyz•ѳ~y;5fDŽUdJ?C4[) ;u+X?`픾ف#(~_=/7v^D8:]1{ ='{-v*|oQqK}`Jd -%vӛ^ GObz;S>]c{Ѿ*}JN*vLqvT׾Wv$dz<\=nlw#[3'r'p|OG8/lp>so5|0L"pSJhףVgT}{ܑ$O"}U6BoߢQ湚+m[`:-lf3T6\zEۖ# 8p({% =&ۖ76>=$ޑ-a'S[ӷKwejRn'2m[ F; gAOv-j|o-=R'1o w=O_i?꽾wB'tm!BAi VK'ӝDG׊ ߫{n===W1&-Ee z9_L1$z|crֽ$Mt"~=eBQ_/EֹU/߰FlmX6baTG%GĩKG#3Len{UQ׽HGՏ/Nc}fݐsE8;\U:uУu;a e#z{+]#4%\ /lTC0:;^'NU{{Unߏ+}yA k[+򍋦8)n_8½>0F?½ e6΀`~q둷eC-PV4?y_ y19c s) Sp_ e8HPe^Nm{n|mΦJx@ZOXumXޢ&+&'rn1OuG{nEvsc"xo:>+Ù|_uv̳֯~pM~,73.m:T|_S_|]>V?F8D?bN$q%ɯh3=4y>N*~[hwWh|TV/mݳkEKԆ/ֻ n]YýTޚjcgs=sZv";owt@Pou><^[g^mL/-o^hH'PŽw}{=]q4f`l)w4sͧ{#,bKWPbuKS<zTUG=[Id:k6/AT=pvigY 3R_A%[k75O{Uq!r_7_4eV0 Yn( g<.#*[;>V/Dk~%5:OzڹݳwƭG_wmC[FeӏԽ}R3l]y3kܺ{E3r< yK7Ϸ{/w‡6٧J>):O祬eCG0d<}N|k?|joo׏Om֬_gYvvf/̎䯽Fdg|#I ٤s6Rd#Y}/-cyM<<&Q釈&Zċ@;WI^.̦Si"xj'lb'XC3[@|p =g֝-$}g6T0|X1"ɉ߇O"zwS nWRzW(5$߯:?T5yn_A{XSq*u¯{=2ÏSP׃ p3~\ `>G{ωEϪM254'fE6>hHhNl:颡991Ӝ4?l]`WyR֛ tw|V3djfK2}k9W2~itI{bW-=P[{ɵ֭Q[sږBָ־DKt{VRwZi__ (e_o[w8_qv#zw3E8~3xM)|)8s n& %v^p|_;)v6Ku;.>=}*cNر߆7c=Ug]Z$~_1w ֊kܽC|{) \)RKF4GAJ'2; 8v9 \JN["yzErM[Do7wKw;|B "z|WKw679p\^J<Er+9p)8AD+9H7F|}/]"/~0%>lj4_X67Uϧo'1xoޢ4NΪ4X},vjۼTZd3ӿ#[yc9S=;9p^vop^?M|˷BO)}q=vI8"x[¼X ND<_ȋm|VTɮjH|m@E8a_ В7Dg)cݔP˷_$/Rp7OmC~iS UlHoNj='6koԶy4/Ƈ;:Jp^J)oN,}E_3[_;~Ew~tHZڳ ؞ ck^3<^>ςc-ǞHO6}xo¢c=o*EyT4p9^ۣVy*Ww\eMhRҵ'))|пE~OHҘn-ރ|P\eO0.F; '{dngtʫZX@XߞQhb՝tO]m0܉=o$կ{"_oz98ҦJ{OľwA}aS\}_IIۺ|7?ukK~Y{جs>x듊)PeD|NW2)Y:mf/̎-o.Oh&.KbȒl^KLfnvP{Ǔyd'r*i feEg=r,@P}*aAmy@|6;}ܟ pÞC0:Jsh.۸o=qDĞEMAhh}2bS-HLtvdU:JO҅ӳ_wahW? `gҸ{};ٷkUp$nO?-p8H :Z ad(-n+D8_ p=bU|_Rp~)khu^ɁdK蒈#\SV,=|Spc["oiz kst'jk&E[I>jԝc[ɘB-Ez|7CNjۏR.CKM,z|\ iܳ؃|?OS||\J$/5tP+9\њw&M p)#z~R==;bd`Wv"ߢ=>_ *W|> p>g)~ 9.ڋAh/p~e;{=~m ` 2Θ|Dl|;_lֿaE"UT)v咢-~^lG\3;k߿նy?Oi=ܰLq |\$gc߅3 @Wo~F)mXl^ ŃUk/Ytͽ7$z/Ak˛%w\0jh;Pst#DubXy,,86     1 8 1 1 1 8 1 1 1 1 8 1 1 6 3 5 3 2 3 4 3 8 , , , , , , ( , ) min ( , ), ( , ) ( , ) ;      x h x h x h 1 1 2 1 3 1 2 4 6    ; ; . Ïóñòü i  7 . Òîãäà ñïðàâåäëèâû òàêèå ñîîòíîøåíèÿ: èñõîä а ) : x h h 2 1 1 8 1 1 6 3 8    , , ,   ; ïåðâàÿ ðåàëèçàöèÿ èñõîäà б ) : b x x x l x x h x b x x x l x x h h b x x x l x x h h 1 1 1 1 2 2 1 1 1 1 1 2 2 1 1 1 2 1 1 3 1 1 1 3 1 1 8 1 1 3 1 1 3 1 2 3 1 1 3 1 2 2 0 2 3 4 4 0 5 3 4 2 1 3 3 8 ) , , , , ( , ) , , , ; ) , , , ( , ) ; ) , , , , , ( , ) ; * , , , * , , *                                  âòîðàÿ ðåàëèçàöèÿ èñõîäà б ) : b x x x x h h h x b x x x l x x h b x x l x h h 1 1 2 1 1 2 2 2 1 1 1 8 1 1 1 2 1 1 1 2 1 2 3 2 1 1 2 3 2 2 2 1 2 2 1 8 1 1 6 3 2 3 4 0 2 3 4 4 1 1 5 3 4 ) , , min , , , , ; ) , , , , , ; ) , , , ( , ) . * , , , , , * * , ,                                Èñõîäÿ èç ìèíèìàêñíîãî êðèòåðèÿ, óñòàíàâëèâàåì:     1 8 1 1 1 8 1 1 1 1 8 1 1 7 3 6 3 2 3 4 3 8 , , , , , , ( , ) min ( , ), ( , ) ( , ) ;      x h x h x h 1 1 2 1 3 1 2 4 6    ; ; . Ïîêàçàíî, ÷òî äëÿ i  8 èìåþò ìåñòî ñîîòíîøåíèÿ:    1 8 1 1 1 8 1 1 1 8 1 1 1 1 2 1 3 1 8 3 8 1 3 8 2 3 16 4 8 12 , , , , , , ( , ) ( , ) ( , ) ; ; ; .         x h x h x h Äëÿ äðóãèõ çíà÷åíèé ïàðàìåòðà i ñïðàâåäëèâû ñîîòíîøåíèÿ:       1 8 1 1 1 8 1 1 1 8 1 1 1 1 1 8 1 1 2 1 1 8 1 1 3 1 2 1 1 8 1 1 3 1 3 2 3 3 3 1 3 3 3 , , , , , , , , , , , , ( , ) ( , ) ( , ); , ; , ; , . i i i x h i x h i x x i                  Ðàññìîòðèì äðóãîé õàðàêòåðíûé ñëó÷àé, äëÿ êîòîðîãî ïàðàìåòðû àëãîðèòìà ïðèíèìàþò çíà÷åíèÿ l H a k     1 2 4 3 , , , . Äëÿ íà÷àëüíûõ çíà÷åíèé i ñîîòâåòñòâåííî áóäåì èìåòü:    1 8 1 2 1 8 1 2 1 8 1 2 0 3 1 3 1 2 3 2 , , , , , , , , ; ,          . Ïóñòü i  3 . Òîãäà áóäåì ñîîòâåòñòâåííî èìåòü: èñõîä а ) : x h h 2 1 1 8 1 2 2 3 2    , , ,   ; ïåðâàÿ ðåàëèçàöèÿ èñõîäà б ) : b x x x x i x h b x x x l x x h h b x x x l x x h 1 1 1 1 2 1 1 1 1 1 1 2 1 2 1 1 3 1 1 1 3 1 1 8 1 2 3 1 1 3 1 2 1 1 3 1 0 1 1 3 2 2 1 3 1 3 2 2 ) , , , , , , ; ) , , , ( , ) ; ) , , , , , ; * , , * , , *                            âòîðàÿ ðåàëèçàöèÿ èñõîäà б ) : b x x x x i x h b x x x i l x x h b x x l x h h 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 2 1 2 3 2 1 1 1 2 3 2 2 2 2 2 2 1 8 1 2 0 1 1 3 2 2 1 1 3 2 2 1 1 1 3 ) , , , , , , ; ) , , , , , , ; ) , , , , . * , , * * , ,                               5ax p@X$,ya+j,*eSQA(.XTdl :{Z*Z u*+Pt*XE!oCnJ3ϹwswycƘ:tGΫod𯘴)RېӆCO?Kop3wq)lU,9XbZy%Sb~v3L0[b&0uNz$3y&3ȩX 9U9gxqilsIFjzy[-[bC&oY8ߤ䛷M9єyLv4׌cLˑf㿟q\jhOBpM4OOg/c(Ck.$k}Ln:N{b!ڌMRZlk.a7E.IIa҇G[;qWNR9ϥMo:XYX_~5bp:KuvQWyy>fu~=ȇ@в.EJA`R.6K$ozFQV_!}^Įg]g!P~Qm^£9`1!s}3:p?t0<< bil,_Nz>9i gz>=%G#xȤyovEf>?;FL}9 _ƩX{3v\G%ShDhzMd-MXK39ńR yW]G(ožl*<ΩՖS%qù >>~ >} Oo©ߒ(_d_Z p߼@ȮHic<2zS} 'mHm_ _d ­UE\[z¹>Xo fWSipEpP+`47`*ەZPX1SuE i>{7ֲllϖ^[ٜ%U6{GolO+; )kΖl l99gpZ;N#rM2ٛYf1Җ-[9[e-7^4 {W=?]Mb?嬬W/ p{N4A c'E{vz3;ڳA4Gc9Šg胭>y|$1WA澈 np2v~HO&߳ه#SVo?%ѐ];:=^V|_ywyg/ imH^r|"6Xeob˞ֽv}q[gmemz6dal;ezKǟ馻S|/!X5}KV /XI,>_ r<B> D zp@'޽xҚ+ۙ3؝ߍW)Fʮa:snbcçZOOZx  Yg}JtJwݻDfj~6XƁ;RܟJI5"eLc^nОV{bZn=(/=Q8CYp:}|Jűid3F1Vj2 52o'^D3iw?>{VKykПgk)چy^hL|N~^#9>|h&ͳ\Oeu}:f u]ʜ2.Wl'~|I?a7f=n`mY,w`A7=9]9$=}O(ihim?rfgO7pDV~}#8@g8ڭ׃aw'/Mi @־G $D G WLz:uNgtic"=NSv /^)wO;n N6ýȓw-MY,΅K~0 ]B% rByoeRp@gnF=: J-o~c:p {N |.{MEx eIF~D#ƋC>GN3G5~tm`ÈƝڽJl[VF-Vj'ۦ'mͷ~5ͼf863Du?Θ68KER.uwb󆭳ۧۗkD}=bٱI-6hQܾ;բNZfLWʅʔ3cθߺ~׶kFܶ&õC~]÷=Uw!2Qn{Wxg\qϡ3q tPOCwUVutۆ_9{kdv[:W4NT ݵy:wԱجT/NR.wr/X鱮DW)]@ʮr֦'kd~S?oۖs9gY(r]WmнWvٻ3y=gpC_5"3kj|{9ٽMqB&)-;[{pýIpCy"w6~6rh#;ڡX @` ,X @` 87TeG4&n2yieNfOdA<FXe\7tR2Kc\9-%.@'=HݸݸuvVc Xbppaו )?n Ֆ[5>@7r38p#ȋ)^ H ฼CN+$}kܔY,bgyG&?P7?rf}<=C˰EVbOP&r)@@ύg5+䧦فo2?ߏ9ޠ'rkf#+ ~O=!{E4vwxS%.AA@d q ýCq ZSVݍKp !^q GJ\B{'G)@O ?4>3yA1'Hk|Btic" >!Oͻţ)>Ab\$^Atc#7`)[ex0-$_P5N~-{doM}M[&Nɻd7qս#~A2gsI%5Am%gZ %Am"RcDYTwp%B.sp׎~ܕmK[#=>B򇸧J &79X&#H|k7oOCΘCO\ ,X @` 8b-p> &X @`%UMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:34  w Hx(1628/1Z1{,7xUUHǐ*e6 I=QHЬu4Hu\>h7Lo+{>zr&gK^{_'DD@}Zc3XڇG ƙs9s1Z)6E3[mHֳhQT:S)ttSQAJV)cQk'fLuÐhNtetitytuT\]\RW)c?]jjJC/JTo w(L{ TAs``SP*c˔ PhM[op/b+jOYbP&| 'נy>%gU;5$FF#R[[mP/}>z蕇_8sF|Ҩsc{;ra?߽cjx_wL=}a|8-'B\ : fm+Few(X#Q:,mmjf<|xaȘ8\66 i^(:JK'9"g]S'F(!l9ZNlhS/k2gFGǺT%ϫP|P(>{JȯkTPn},lт)#$y͈]9!x}Vt;yٱϩM!4:^7&9Ja\MBt0fyzk[4hoReݤ3U˨'*EgQzm_⛔1-L8%(kD?tTrL8mSݭ1JXpi|4 \|1|JCy2A`iXY%6 z[ֆ]C\85h0G#nR)MQ~){7eHP|XV_ ^B7TV^() vӸЬoRo нTcb!]JE6Hzͻu ?Ν>}sw[xhqGrȊ7fڣ΋Y<r/Gd=.X{4;Fo*]AB=zv4g̔{nq?$:qz1L|n=YG'G;':3:%0nVW˺/@I trxб?Gӽ=틑av^ d-$C78OȖ]xQxۥLyx&fS<ݏwJYQI1q%vyWm ;K$?MѪymʜ6y{ϗL{LU?Uqӓsf:<=4t>9z+ߋ9x? 4M"E}zv= 4ȺՊFlh?kgil+ itleKzlq9_ٱI}תN-a4|y滤Ҕ_3%PðCut!Byj7K/g xfy뚯Mp56 y?z-u$1yx1r50=T0oʜo.׸vߛN~S=xǺ~QzʷEr; `G}>!~N">,||jw_Bx%7{Eźm1^5v;?vz%H{Gfy]۳4.~XyVZxYEq/4zCڊ7|ѳqۨ +ڶܱ"8.ѭZ zCm\ゾ͎ l\0FF.SW}I"xWݲiw-xwܻ:>sUWW#Z|H^I}gzG};L=cYvΕM[16mkP?]II/^ {fS/q]{gh[~O.!%xfڹ gvH<AV, >`+&:F>9]_vrGe_/vx夬Ϯ7jm]ʦGݟ#݁v_v2}=YOj6x)}{<󬞾ܬ91wh{{cb;CR`ϕXs}b4 O}G]]sʵglÜb6l~jv:CkTvg*ϨǜR}]!{ߖ{Hzg2ϰS@*<ò1;G&o/J=&'/JL6}CJCǟEOYz!ing!<Bz*cjyzvBxg Y,*36e]@{`̄|mvg1gYn J(w!PZ|VYI SEJK'L*om$'WBv#{,^z;O{Y9 _zP򻁔@y)Zpw7LoSo;Oǻ;C9Mz$}4wA2<|ktZ\-Lj'_,LoVWH%4<wEC4ZN]ʑ;@ɣ ꒦ 3o~h>@%N`bu |O?ؔ=eݐTCW_gē]ɱ6,-x{GyyZ}o֏„MamJMFa޷&4:쎩|7{jMJmbec0mbl*A9ޟ|zE"bؚCDHX5EyZ"m~-tG:`:Ι;8kKCxx\(:^|]}4e Gݐwg‰ծv,fcJ>|Ү=\qBMн@=2=J~eORF凜|ڨ t W>?_cޜLQ_#{~@׵:?0/7J5En*ajdh3{WW3W](__.zϵ,5^OkyRw[\Ɋ~CmlߗM{MCמV> ~ſ?VZ{1߉2<C.#4:HoYa>T !>grG6_|BXWôݮ1Qy):u2K^#$w={Է|I9BI\2|W?#tržTc}".vb"sôOwiq5)sjWו}S*6?V^řIj}w;$ h,^n`U9ϬSFٽ mVs&vf`[W c۟.= c sޮWaoiSe'6z h,Mʊćiޞ4)+BsZ>,MʊCR+ФC<'*IY3244WVIYoܙ<@J哲"4\$ZhRV M) Y>)+By_(Z 4)S8.0nu垛&]&THl/D?MΪlTF6uKGCCh!Fƫ_mR὚5\Y>^^^+]#?|/ )u?%Vk\h~xR6'8Fgl\soUsϵu ȋzM^GV^q} oOjmhvx+x)gH}jr__rU=?Z8|ޱ~\hZqISϏk^Ռ&Bj]5\ky1*2^Y7nds3}ٴ6V@lFqk#> s4S>?4eiRy(K"4+(KP|@J> h&T'A*Ф >e]|=Н,C啲btgAtC.eENޱ]|>=H%K"tGGAt eRVw'@|Ot+㕲(oVPڈ#6m~酨GoE[LQ<;33m߇w M eW"51s9xƞ4V= `(džQΙiκ|k.yćC}+=ohVFx#^5y^6Iv$?7_(rpƫ.4tu[Eqx]sya{tK_?Pyl[={hZoJ_>J1ڹ.7Kz!b{LNsxK)~3А jnj}{_r ym_HwG lD17u\ ]z$E߁B/,O̜'":4jV]{8|qXmRzߵϺQ_M{ N8G'GwFDgF?J޿/榊|Y^-܋l#eBxaCxh MrxO^ՄG1=1}g5ҧn8i3m0&ݺkU`{yM:/qQ&:I޻+ջX0'CS7]!Uf[[on5onm&Kz'z2~qS^ֶu:knִ)/8{O߳Pڱ4,"K?Tq2| ݼOrI kx˷FQQwh*HwkeoQo7:$k1S\y1K$|]U7JtiJ?cDФVGûX.t{YA=u{a{  o?u(l'n-kLyzە.B/׆aH w{zvB/c{1*c&;+z {߬wTy<6{}9{>=_Ef-y6n6~R4i5!|yϷ%Ǿ~yT'DϷj<};yyC]UsPtc~q ߜ3.^~-'oxW!; = xٍٚ?%hY^_CP=rԅwQҏ҅wQYDe\wɩŲ߫F5\s7(S@I\e=y!ǿLJls5lg6W7{6͚CSM9_g6'K繴J 5;RDu =wUmT~Ӿ;M4}vIK#P3=, z+8p{'ށ!eI5ԇsDC˺x_<8;m{Q6H |eJNjT%s,灲7Bx{Be{IƻΤ8ӢW r7Pf@ߑO+[s;~@!u'3shz|k6Z~@VǹU=ߍsn 4/۹;sS8_IdL%`C !z!Y&@5밽f=<W#>FUinR4;6y, 8a9GrԷ|߲>^ݿe?Ⱦ\);$ c{R3:z7[oH{~C߿w*<#6 6cv)6vJ7/K62l {TV*6M-hutYyGz m1yfӽ}}OoiX[ⴗ!C>\,o%/Hv]sۜe\ zY|^9]ꖎo M=d-a/p>Yx Pv֟+ڶܱO6k퓅/=JTGٳ,oQlf^M͖+j[=yzz}ͮECΜq=It^W'[q.EѾ\y_io0.}+yfɫQ>Yxd>5_m_m HE/S.ioE}O}}W=Z^렽M?S *grv1ȢgWy}SuCgF>iA&mƲuu %Û$z&)ΓHε?ϯk]=tocx睾k\z]e[dfS-o];#Z۰[c>XUqU(߃w"J5kIn)% Q~&v?4q,d]giʑM4@9ękioP^oO >L`4K>t 6V y?"\y}_=dYf Rd\eO%}!ؤ~F$Yx[監n}/w ɳ"ȷ)gC]:|=]>Z߷JP~/:N^^a=vn=ﯥgtc.:o5?&'dz$9jlL_Wf7rL%ȞTQ3z?[ ofCJ} 5oUzvB/1/hBx?A/6ΐugU]}њ_-;mWG kpni\ZKVll@u4g y_ZGތ:pΣgT}U ~GZK'=(iOmQ]FǓ\+=X oQ >.fߎOZ>{= oǠym+MFͱw^i7;^{oM |wCxoi vαaѮ;}^iRy;=rtZS_:*G/usMo<9ȀkK`|+]An<3x; nzR vBߛtdDov7zC{{~="16r"ך<`~Af$MGq:)Q!]R\RҼNsiߚY/fhR9*͇U~_Hۦ[RG^⽂c_ #9'UW^'TI86ȇ 泊oQWEhv/ҷ}c})g<iohB|OZ϶<)&e C;?Ryߓ7~+] {vmB/E(LdG&iG˱/rm49bZh g3ڱQb4?vMXZ}fxپ!4M&c/F;b]c딧i3,mӖ mhYԣ h?O"3ZnH,[/-c)m)"0>甗}jd\51IvvOl?oorQ _gj;[5ТI##Y)N"hy}0/!0x\渼vi-[OaTI4cǣ+}~[s?~zo#R[ndĚ;1JCZW*N8뜅5߿4A/0SrѦc #-ykq:\!4:;:DY:^;gnӛ>aiVmS{4+#F#c:p$m9Wm0ŋZʍ3jz^ˍ(̕[s" T ۽ [ 7BF]In#g o. ٳ 52?` !9Ez4fW<7 _ssvKy7 廓&9gsNS-ѽџHx6_U{fe=#!i4NBrвFhpA9uGxtft1¸?Zyc_M*cZy6k?'I֝;co9+.ϦlT-Z7}ceZ~F}G|VNe&rrFe!hQF@|[vC3}O|BxXQnG< :,+ЕĚL׶tEa߸M 3 bΰV^GOfSK[6*|ZMg/([JV:YT~~B-}E0Z]đtH[mBp%Rg!,hS~ 9[Q|[MRmʉZI>mҚtdEKR|!=|&?;6KyRpdH^o,} ^"KbUzvhȣz_G~re8gs32枭o<}Dߐ6<#vhX> A}pM??m肃Kih4y}96w(hkhsM;c{F'(ۨp;2XLfnfm҄& XO3c*}UԦD%);I?Wk}o6\Cpcߐq[ pkrgkX)5R_UQ{5\y{[h>>c?)OHP8=җձ{ź0O7C&g2yPB|=+4 [Ǖ" ׶3Y;QuCH+x%tpmΧ':eЧqp!r=M?*k7=zީP>2f#/c?6uVX_fu|Ps[/T{Rj[tw_@=kf')>x*>u[y ohhui/6eб-i@x%nO( י\ZA*L۫54EI3F{bI#̀GǩKF3d̈́S\1V{4_ޟR!Jm.3DHOW#4NO"1'}iPRt~|ωg2hVqñwC]MȖEK䍽uqɐ-xu]گϏx')?Sh'CmY h4[ Lic @y]uge[K{Mr_ t&14[fA-M˚|&`Y uEگ*\iy 1OѼSސey+}Q7J@{ך7h^}BM)_tS0dE h40̓77aȰ'h^~RҴ_^ڼX|~2 4)[f5 4ׅ?:%~]8di!7 銁xuC M_7 Y޼A|><֯6k^6'h^ _o^| Cxt-,f_OzSCorV h4|ӂZ9u!@"sZAώY8o9}+ˬȀN/ʼntPtI4c3@X*](yY\&T&pw9ej/fb}Cڗ*K+ ʸeUgT}.mN>Nf|k[Ǘb郬RnN.3=RQiuŽԉ[90|,Ι|MeLR;k-s2|OgT<^?j p 6?Tx' ?fǷN;>^H.{5lGG=؏+&בw1z <0peb+/oM vY3<\ĮYydL&X\Szh˥I*dS2YB߈kxv#$ *oKw-+Q[z"P0F( w;?m!UVlgׁ s=<ÙeOﮣ@9O/8كjΓK/[ѯsCyz+ߗ=WYeșzsPU2ʫA䁂ʄ+Z@b9D]x  PYNKeAIt92 G9(xѱ6Ԟ1Jgfxj}]ϓ9kο@N?գfQF&ђ18r1|r1ꫛg6tKWp<9q6ѝQ|7" x9fGdh~?CLcWghW׿X /@=_N[>*y{?xޜUM>67^,DWXs:H#uz抁~?>>>>>@~.AUFTJZkb^~-Fя%7NnڅjffWu{IvU"SK70wd8}圏FگWw\vHUޞD~o{` W :px r15OP:bȻF;@yUk:7v_HSeV)9V&Ӥ(ɝ^rؕ7Xu>M`*@W9 m02Z`76:*uzMȌ]m@Grz|:9  2ߡjeK֚b N!}bU&fXrվĪ=>*NNJy'[hgVmlk<|Gnc0ʤr.<.UI{䖎W,ظiEkwy ;{_ /|Wv|=L;*{ӌc`ȷ$wJz-Ht0StK{g^ƿwvb؍V}[czl Ҿ:nxL-lf{͘$n=_ïJS vw>M\T)SvK:k=K\ZG6^OG9j :[ڧPO7oLz4H];ƴmll~nn%lmL,w}[^yomݗKw[Mѳ|8F|||||Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:35  * I7t|(16121/1f"),o{kxݜVyϻ%,$bG`RCcG6IEjqL3Nkf6a0jFMˮ,Bw߻?u9{Za- w&Q_إ!d%`-VTfQg2K[H1e4\"cGU_6if{Z=~ٓgٴၾ`Ǥ\精=yIK|{Ni]":_]7Q77eoRZNꛗKM|sߤ7)|}VoLɢ=VPp=|d:Ň˭E^9l6qk׌nn`o 0?LװH}]$'U"1 !~CU7Ïë! τχsE*/LA`$)YK`^q{ʵiIu_8vk]IyG[!̘Elخtv;Rlo#,}ݎZZ/4b)v;N}?nm9)̼g3ۖ69tI8-n]vF;_k fwmմO6Y0Q^zr8EnU<}RyT§;ӵ':#di;{Zp{k ՇcU!\[c4Wa7i||jX=N+ki .ܺTn۶J^% ~7hOEuGB(VV+R* / &:>%{O ԉ}L`!ϕ}Eͳ? Șʟb_>쨽" 7lWOԟ4ѷ}?q}xۍ}mZvlv/)U\/u |0qc+tڌ[_|jգ[ZSy㴏;!="Lmfvy?X/S. BGbV+7?~p߲:m+ӯ{/ O#ڋ,κ7f,of<@`ỷۋt /J곂bU%r|up[ H^r}xKgڏYx]u^~%Z {3T7_#碾+ˢ!~k$s`i)`mE33xч6']El=y=cVᡟ瑎DCyS}4ڽ ߟu(忛so\qĥJIGU9s\Aɹ*6ѷvXAo-[p}UPqm`pUqI5aK Ѱ',ݓ;7 v- [Y8,l] ~حW!gO S:y6AizNџ~EI8L䓕Ǣ<j,ˠ 1X+@|[Ŝɇ};7HhWG G,'vźe ;ӝ蒥{9S{`v咺G/)_v#{hL311TᆳwerbivИalGU}=l|<{s?86L`S=p荘M`ئS{ Z07M@x(~17J4mǺmͱCMll'[wlї?99>mbkv*luL`u"Z{l_cC&G2VJш丟ښgvC|;.k9zY>uY':`mc#l =ϽRsl^'xCbbt W [٥NG|2I+gxa'vZj"-uO.DmOO(^/miV~Gg @G7)hgqSYi5F΢mBOm{T!菿Onȏ=E%i]ƣe`9ϯ5v{=߸{@ħsr8QJ8b7˓m{9>w\B tc}:n?ѵmI<%mal/i{.9 '{y}<'|&>qp_A}Ni"񇥲܊skܧ񄋽'`on>EYm3JxC/3u>wp?C}#ѽǡR^ڌO>Gozˀ\\>|`ؿCvM|;Evϵx$~ӏ{0揯BK\y_Y 5r}i-^*pUkY(<'Vϋ̗,2/oEOvC2%3E{aNgs5uX}]Щ6xS7?u~{rǷE떍LpА804J۷SƆؕ|W&DE[#YQCs+SS&},QZ31xSC<[Kh:\#R7m~3xO}R^xhG_،Ǣ ./fE+}g),3lPfd1yn+k'O%{U6(s>X7ڭb7<ƨCM(y1 KYQR^㐃\^u}Xmt-o9

Ή(ѿucR߱>}Sl#cO @sEȦ:~d[DT8\eƈ L].o|%ěݸejjZvtpxȡtTޣ~>Uz${j|`/+E-%@7˨S\B\ :GOzfj9%xSliBpytJ ?8oyO>ᆻnY+۱~WdS֭~c"t)N;o/D:,pɻxa/ vl^=@/֫~9BLZ<9KK36Ďu^x$~R۠?S;4댃<9oz9%>f?~i137k~0S h ^y1yfxdtC 3Q~_fwݨs_ +4d3_L?K:u>O=?c7/3/e:o-\,|9]vnl 7\Nm:^L]jW{)y֛Uy|Khx;oT⩹3C/^iu_J|Ơ XoȤ۔K~x[6NGXԝZv4/K K>?g!vwM#b¾%?.pg '!Y'jݻ;6=m /mo,|nvȱ-M :xJd6uJl}vse ?oW} qL\D#}wk̠7O))widXǚI<ѺO^9::8#ȕӥPy}IЮ*pU](kmLr$7eBCp9fsW wNOw_ſ8(9Siv?8QrB J d4ސұI?pW{8v1yGaכlUaxvIw-/~cЫK6>U6%&h$3:e:Ҽʺ!p^3G8E/%ftJz'q[8sf>ȇ||bÜO՞-h['6>8ej"U *:z`>s&ߗ C(Z vZƏw~~O*GT<]%~JN!s؆ؙ2`M)!}me㾮W7Q1g?}8cAC>k)ǀǢdCCǮS{9pւ6YYUUV܅{Niخ`ߏiukDz]6.х54˹e5®:J:$WzKמ7F|hWQi]/`ȻXsd.eBC&*?!Zxލ7vԾf.{hȳLds8Z/=\=˅[ [#kMCCJ`?'2scӼO^'/3ŧ>`gdߒn~.=W= [3߲ߒ\w7 *R9`ՂB?hb9CC&~W1ӷڎkFLn_̛={SRtUKmMCCJ_V&V34dNB&vf:/9t'f:3w|4$T x,pz^\x[:d o!_Őzs#։LeА9WUN)ȍP bO-OYW~4L9?$^lLPL9#*[>-Z]#eӼuzFs -^wƎf`]ڹ|:X7SAGȲ}Зma}R" μ0AqQsh*/n"&2!E|Cɜ|O\7r5 m$sG{dUӬQ^?4d~AUs]'nng/LI_{q?}}8LHc!ײgG;r!?<$[R?Ŕgn[w9騫7vu?~dU 죐{\h#k/2\!wrwnqZ[3kd1f?0Mb RZ1p M'Ke[f*qӼ?#ő+kyLJVٮS>]7`'_haEҿYhOk;gɜ\[f딶|s g-a_aT.^Om# ǡL%Y,ٚA*GN ?;M;D+Uِ @ !ًvZ<<}ygm~,4M;7暟;7uV.x[t+-\,,88 ÓÄÊ 519.713 À.Â. ÃÐÈÃÎÐÜÅ ÎÖÅÍÊÀ ÑÎÑÒÎßÍÈß ÀÊÊÓÌÓËßÒÈÂÍÛÕ ÝËÅÌÅÍÒΠÂâîäÿòñÿ ïîíÿòèÿ àêêóìóëÿòèâíîãî ýëåìåíòà è àêêóìóëÿòèâíîãî ïðîöåññà. Ðàññìàòðèâàþòñÿ îñíîâíûå ïîêàçàòåëè, õàðàêòåðèçóþùèå ñîñòîÿíèå àêêóìó- ëÿòèâíûõ ýëåìåíòîâ. Ïðèâîäÿòñÿ ñîîòíîøåíèÿ, îïèñûâàþùèå èõ ñïîñîáíîñòü íàêàïëèâàòü, ñîõðàíÿòü è ðàñõîäîâàòü ýíåðãèþ, à òàêæå ãðàôèêè çàâèñèìîñ- òåé, ïîçâîëÿþùèå îöåíèòü òåêóùåå ñîñòîÿíèå, îïòèìèçèðîâàòü ðåæèìû ðàáîòû è ïðîãíîçèðîâàòü ñðîê èõ ñëóæáû. Ñëîâî “ àêêóìóëÿòîð ” èçâåñòíî âñåì è âûçûâàåò ïðàêòè÷åñêè ó êàæäîãî ÷åëîâåêà îäèíàêîâûå àññîöèàöèè, êàê ïðàâèëî, ñâÿçàííûå ñ àâòîìîáèëåì. Îäíàêî ìàëî êòî çàäóìûâàåòñÿ íàä òåì, ÷òî àêêóìóëÿòîðû è àêêóìóëÿòèâíûå ïðîöåññû îêðóæàþò íàñ ïîâñþäó. Ðàññìîòðèì îáùèå âîïðîñû, êàñàþùèåñÿ èõ âîçíèêíîâåíèÿ.  ñàìîì îáùåì ñëó÷àå àêêóìóëÿòèâíûé ýëåìåíò (ÀÝ) – ýòî ìàòåðèàëüíîå îáðàçîâàíèå, ñïîñîáíîå íàêàïëèâàòü, ñîõðàíÿòü è îòäàâàòü íàêîïëåííîå, ïîâòî- ðÿÿ ýòó ïîñëåäîâàòåëüíîñòü äåéñòâèé ìíîãîêðàòíî. Àêêóìóëÿòèâíûå ïðîöåññû (ÀÏ) – ýòî ïðîöåññû, îáåñïå÷èâàþùèå âîçíèêíî- âåíèå, íàêîïëåíèå, ñîõðàíåíèå, îòäà÷ó íàêîïëåííîãî è èñ÷åçíîâåíèå èëè òðàíñ- ôîðìàöèþ àêêóìóëÿòèâíûõ ýëåìåíòîâ.  ñâîþ î÷åðåäü, ÀÝ îïðåäåëÿþò âîçíèê- íîâåíèå, ñóùåñòâîâàíèå â òîé èëè èíîé ôîðìå è èçìåíåíèå ÀÏ.  îñíîâå òàêîãî âçàèìîâëèÿíèÿ àêêóìóëÿòèâíûõ ýëåìåíòîâ è ïðîöåññîâ ëå- æèò èõ äèàëåêòè÷åñêîå åäèíñòâî. Àêêóìóëÿòèâíûå ýëåìåíòû è ïðîöåññû ïðèñóòñòâóþò âî âñåì ìíîãîîáðàçíîì îêðóæàþùåì íàñ ìèðå è êàñàþòñÿ íå òîëüêî ôèçè÷åñêèõ, íî è äóõîâíûõ ñòîðîí ñóùåñòâîâàíèÿ ÷åëîâåêà. Ðàññìîòðèì áîëåå ïîäðîáíî ÀÝ. Ïîñêîëüêó ýòî, â ñâîåì áîëüøèíñòâå, ìàòåðè- àëüíîå îáðàçîâàíèå, òî îñíîâó åãî ñîñòàâëÿåò ýíåðãîíîñèòåëü, êîòîðûé ìîæåò áûòü ðàçëè÷íûì â êàæäîì êîíêðåòíîì ñëó÷àå. Ýíåðãîíîñèòåëü, îáëàäàÿ ðÿäîì ñâîéñòâ, ñïîñîáåí îïðåäåëÿòü òå èëè èíûå ñâîéñòâà àêêóìóëÿòèâíîãî ýëåìåíòà. Ñþäà îòíîñÿòñÿ: ýíåðãîåìêîñòü; âðåìÿ ñîõðàíåíèÿ íàêîïëåííîé ýíåðãèè; ñêî- ðîñòü íàêîïëåíèÿ è îòäà÷è ( “ ðàçðÿäà ” ); ñðîê ñëóæáû; ñîõðàíåíèå ýëåìåíòà ïðè èçìåíåíèè êà÷åñòâà ëèáî ïîëíîé çàìåíå ýíåðãîíîñèòåëÿ[1]. Íåìàëîâàæíîé ñîñòàâíîé ÷àñòüþ ÀÝ ÿâëÿåòñÿ è åãî “ îáîëî÷êà ” , êîòîðàÿ ìîæåò èçìåíÿòüñÿ â ñîîòâåòñòâèè ñ çàêîíàìè äèàëåêòèêè, äîëæíà ñîîòâåòñòâî- âàòü ýíåðãîíîñèòåëþ, îáåñïå÷èâàÿ åãî ðàçâèòèå.  öåëÿõ ïîëó÷åíèÿ îñíîâíûõ ñîîòíîøåíèé, õàðàêòåðèçóþùèõ àêêóìóëÿòèâ- íûé ýëåìåíò, ââåäåì ñëåäóþùèå îáîçíà÷åíèÿ: à) Q – åìêîñòü ýëåìåíòà (êîëè÷åñòâî íàêîïëåííîãî); á) q – êîýôôèöèåíò, õàðàêòåðèçóþùèé êà÷åñòâî ýíåðãîíîñèòåëÿ ÀÝ (ñïîñîá- íîñòü íàêàïëèâàòü ëèáî îòäàâàòü ýíåðãèþ); â) V – ñêîðîñòü ïîäâîäà ýíåðãèè - “ çàðÿäà ” ; ã) W – ñêîðîñòü îòäà÷è ýíåðãèè – “ ðàçðÿäà ” ; ä) tç – âðåìÿ “ çàðÿäà ” ; å) tð – âðåìÿ “ ðàçðÿäà ” ; æ) z – êîýôôèöèåíò, ó÷èòûâàþùèé ñïîñîáíîñòü ýíåðãîíîñèòåëÿ ïðèíèìàòü ýíåðãèþ – “ çàðÿä ” (ïðèíèìàåò çíà÷åíèÿ îò 0 äî 1); ç) r – êîýôôèöèåíò, ó÷èòûâàþùèé ñïîñîáíîñòü ýíåðãîíîñèòåëÿ îòäàâàòü ýíåðãèþ (ïðèíèìàåò çíà÷åíèÿ îò 0 äî 1); è) rñ – êîýôôèöèåíò, õàðàêòåðèçóþùèé ïîòåðþ íàêîïëåííîé ýíåðãèè – “ ñàìîðàçðÿä ” ÀÝ, ïðîèñõîäÿùèé â îòñóòñòâèå ïîòðåáëåíèÿ – “ ðàçðÿäà ” (ïðèíè- ìàåò çíà÷åíèÿ îò 0 äî 1); &xhu?߻mu6lǔõrRG45HD( 3Y$C I% jin>ݳ=]w, G>{>ssTԃ H+0}&VY!kPaml&׍./x V3zPa\lXa$_6\llep|wA v9%Ą3=mQ^WkL[^϶xn̯ȏ䍊WQx"UymS4}޵쓐UHn1 ?ofAѩW_: mk{:׶n5?=Ϯk>u $R$ZE%3=43BFj~!۰=SJD[Cл !1Kg&Ew6z zX:x5QRȧ-}9S%FʩBVSA 85Xi)C⧶RzͅOkAջҔPG,J*2gyн䴣ߎf-b.%;F$b:5W"#!_Ge/ p LZQg3v uz!}̥}uϱu }2S]sOEq)< e9#"XVp\jHW'Amqp vmk EџO^1 1ݰo*'*)~>9 k%W U,;|ȟQ3{7ս3MX?@e4hY1l~g"(jq)3wOjbkv SgĽ8p,A:쁯޴֠K}u̷Al^&G^վOgwN|uz`OvD?9oDOb8$޻,>/tM1ă4#eO*W]i՘1pWJ _\pECKg܃;ȹʍXme]FneĴ>Bo#|c\dWLCV;D[DQGiE69ŷH&ok~dqڲ1{(V*>*F}Nl9Nt3tqd;'׸2Nw26_yv|&.ۖKL.݈'&'ffw:\9Tޭw֨r撟c-[-vn.*L3sr~3عx;w p'N;w r'N;w p'ۅMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:35  R2  RR(16n2o/R1 h{8sx ]ug|8 `һ` P) !1X+-)%Ę%8TڤU,DS2D 0DNbx &ߝ7og*33g|̙s{ !\Ӆ>_”s.87p!<"lWU|= ? #9甏NyJ+•0 µOYzBuv}AKz]ʶOW`$!s1>"A!ЧY@W9F͂zo E VuUu,B2|bY WߌpߑuuŒpv!gNJSeaWE #3:'MS9W.+uekY֑)AN.83=*W5HұUn;}j W|pY6?9,:+O~,b{Wĥ>SeBzbqڂӾ8m pZ+K],c˪Yq> #c.6T1IcS :儫ecyd;́) !(il^c_Dw`ojb){g IIlRMm_~yl GF<"@bW*DYm!jLhȜ,""~v}[˅Xϖr>֫;Lh@=V-3%@~7.%1ApM>}"o{jLA.2;=D 2^(2OT7ȼcxАQ6h1Ęۨh^Sg(لH}Jb$(b9!:iͮh3#k9:f=e'o,mQ*c͂GTgrր-ѢsL2Lr^@!nmtnz_?c]@.ӸHC.I;V#r3I &kbbc[%%?˄̏)6-Ƴ)6:1 pkV!a,ҕ#F kd7m~)8&ӴįߺBʇw_pM>8Fł/ȄLm+2?U#Z'c](-ƺJm2V1Аyx'c챻UQc]*םaw+e@"jei4\vpHo\3 '<ɬD8bxp_Gx}ЌK<<> M%ƾ*?&?RmkC"\':Y;4h7R{v`^SfإxVlL<W=%x^Z?64c;O\#"gW8 x4?ƾI8|>+xKD{R"}E|җ <&#`d ѷwh % 13wS˄LYuBvq/} 5^ܹ8wtOoz#x#ε8F!מ{. \'tC[p Q:-G.1D.ǧb[W/Bx&˚U}^M46v$&f c7u}8#OuQO zXۤuL_!>:tb 6&6#qEۡo-V9[:C4'EwǜHp|d )88;pq64O<D_F_[s 6mk4?2ho@N_ty˔K}<C[dW>~ovGLJbb*&bbKML )6Đh2Wʿ m PwqQ׬w+BT=F߉NwpW]);+yĦ\LJ1a|#ǹݪW#)p?h=7>)%| ~H.纒jLhTH4}hE8C=aB[խƪ7k։=JYƚ2.yԙ~~>=߹Otށԝ_-P }9%v B%;iҥvp`S͹r(>[{Qy5UtxmlShl딗:2lG_gg߁]evpg>/,).﫳#+'JSZSVe'6~!Ks׺ ^m}>ř7 t4mzEU^[AC1_77 Ж w|< ڎҧ|ӀHbf+q1X3hCiGh5*_ע زIt~y^N7KEcAϻj=%:yrY'4db&=WI8{7yM"XFo_guJO}oCs闓-l[y8G6a2[-3 x0Y8-f{! :4:VаUlE_"`N!s@0F&4d+&ȉJ+O|e%::my@C&o*|.ƽMg"pߐf #ǷWhN{&;Q5zBvxsAD\ə.@Ϫ[!kT9P.0i-/Sws)Nm^\̦uz߶fo CO$y"sv>do}fwU87{= 9JHx7op4 :=-kx'nlw:X6__3io#ߟRc~6_ɾ?+ʽo o(?[h#q?HN8<ϾqڇϾ]ʓMsY ~u{WQ*Iミ>SjlEߵ'/4VJcƘ4Dkj#1Rz)Z!`8|XcX`?<*m?c'|˜^4ƤF]ٖZ:ZA{kˋ=7V0lR=2w]Zv?D;3h&ǷBs c[z|ךt +ǔg-rR:u^A!@f?9n3LѮ?+" rBÿ]m/q3(p,~ 9 J32Jj7UC[ց|?3-Ԗyڄ @5!_Es'yh>fhȜ?̵Ե?ҎIh;;H33 ;ET83hh(vrL9.C"8 eZf^JRy #{c7ЖvJ7t 4cPB?KEb\ɥ_L/4,P ^+|K.Mv3|/%ϴҳֹq{~[*τZi#Xch4^+|ky8ވ8v,hLC O-}`-p犿)׮ 0#әwHf?6{dqmmݳoS{Ŏ0TqF+ -k`~̶uMqÛm6^oۿoڧ-H:_8U8dCpM/i|jS~koE9ƅ>=؞t5xη"]Q3>hK|Mm!ogА)e"'9MI) <=!_7A{߶!Dy yot!V)XY. ;=["AI.bs z0d9R͝3}=-\9dEC/c!?zI]~|1.kG]А!އ`Or~z119dhCWoDS֯>G1eNd_&%s ^ <JU~pM7};]/4U7;  cX,xC1Ucyo,#wGW5r!w2?gc~>vyO.n1ln]ӳ՘3cuE7u$GWIge;U*ro7y>VYKuՂ%~H_h;Y_Ư?=,q4U}395cO[=X>uܽKe8B?9AkJI5c։֮FGu*O wp{B>=k~x2JXd=u\ 8'wq /dwsG9B0[޳Bs^ ^r8ux>QLg~z+(w; 6-7%czun/}SBwuBch5f>dotuN W( ?쁞zJ<OoK}A{ 釞ubǼ@bkdBCS=:po?Y$CDcLy.}MX""x(${J>K o3GCc%ۙ} ɿ_`slQ9qF975tεh桭ez!xlG,}YeRMo5|\S@eUL^wxbbhdyvwbNilX߱9<;_\gk$ZNGߙ-t6:m%)?|5|yа?%4pȯKx) Бk5rcoI?sLnx}hr<B~q4=;L0\}:c6]'NNKmy/2~Jd\ӆn2 P,sZ9x볊xxp"la,,u89 ê) D – êîýôôèöèåíò, õàðàêòåðèçóþùèé ñïîñîáíîñòü ÀÝ ñîõðàíÿòü íàêîïëåí- íóþ ýíåðãèþ ïðè îòñóòñòâèè ïðîöåññîâ “ çàðÿäà ” - “ ðàçðÿäà ” ; ë) P – ïðîäîëæèòåëüíîñòü ñóùåñòâîâàíèÿ ÀÝ; ì) ÝÏ – ýíåðãèÿ, ïîäâîäèìàÿ ê ÀÝ è ïîòðåáëÿåìàÿ èì ïðè “ çàðÿäå ” ; í) ÝÎ – ýíåðãèÿ, îòâîäèìàÿ îò ýëåìåíòà ïðè “ ðàçðÿäå ” ; î) G – îáúåì ýëåìåíòà, êîòîðûé çàíèìàåò ýíåðãîíîñèòåëü. Ðàññìîòðèì ñâÿçè, èìåþùèåñÿ ìåæäó ýòèìè ïîêàçàòåëÿìè. Åìêîñòü Q ýëåìåíòà îïðåäåëÿåòñÿ åãî îáúåìîì G, êà÷åñòâîì ýíåðãîíîñèòåëÿ q, êîëè÷åñòâîì ïîñòóïàþùåé ýíåðãèè ÝÏ, ñïîñîáíîñòüþ ñîõðàíÿòü íàêîïëåííóþ ýíåðãèþ D è êîëè÷åñòâîì îòäàâàåìîé ýíåðãèè ÝÎ. Ïðè ýòîì ïîêàçàòåëè Q, G, q, êàê è âñå îñòàëüíûå, â îáùåì ñëó÷àå, íîñÿò äèíàìè÷åñêèé õàðàêòåð. Ñâÿçàíî ýòî ñ òåì, ÷òî ñî âðåìåíåì ïðîèñõîäÿò êàê îáðàòèìûå, òàê è íåîáðàòèìûå èçìåíåíèÿ ñîñòîÿíèÿ ÀÝ è ñîîòâåòñòâåííî äàííûõ ïîêàçàòåëåé. Íàèáîëåå ïîäâåðæåí òàêèì èçìåíåíèÿì ýíåðãîíîñèòåëü. Âñå ýòè ïîêàçàòåëè öåëåñîîáðàçíî ðàññìàòðèâàòü êàê ôóíêöèè âðåìåíè. Ýòî ïîçâîëèò ñ áîëüøåé ñòåïåíüþ äîñòîâåðíîñòè îïèñûâàòü àêêóìóëÿòèâíûå ýëåìåí- òû è ïðîöåññû. Òàê, ôóíêöèÿ Q(t) îïèñûâàåò èçìåíåíèå åìêîñòè ýëåìåíòà âî âðåìåíè, G(t) – èçìåíåíèå îáúåìà, q(t) – èçìåíåíèå ñîñòàâà (õàðàêòåðà) ýíåðãî- íîñèòåëÿ è òàê äàëåå. Ïðèìåíÿÿ ââåäåííûå îáîçíà÷åíèÿ, îïðåäåëÿåì â îáùåì âèäå ýíåðãåòè÷åñêóþ åìêîñòü àêêóìóëÿòèâíîãî ýëåìåíòà â äàííûé ìîìåíò âðåìåíè: Q = ÝÏ(t) – ÝÎ(t). Âûðàæåíèå ó÷èòûâàåò âñå òðè âðåìåíè ñóùåñòâîâàíèÿ àêêóìóëÿòèâíîãî ýëå- ìåíòà: ïðîøëîå, íàñòîÿùåå, áóäóùåå. Ýíåðãèÿ (êîëè÷åñòâî “ çàðÿäà ” ), ïîäâîäèìàÿ ê ÀÝ – ÝÏ, õàðàêòåðèçóåòñÿ ñêîðîñòüþ V è âðåìåíåì tç íàêîïëåíèÿ “ çàðÿäà ” . Àíàëîãè÷íî, ÝÎ – õàðàêòåðèçóåòñÿ ñêîðîñòüþ W è âðåìåíåì tð “ ðàçðÿäà ” . Ñëåäóåò îòìåòèòü, ÷òî â îáùåì ñëó÷àå V è W òàêæå ÿâëÿþòñÿ ôóíêöèÿìè t, ò.å. ìîãóò èçìåíÿòüñÿ â çàâèñèìîñòè îò èçìåíåíèÿ îêðóæàþùåé îáñòàíîâêè. Äëÿ êîíêðåòíîãî ìîìåíòà âðåìåíè çàâèñèìîñòè èìåþò âèä ÝÏ = V(t) * tç è ÝÎ = W(t) * tð . Ñ ó÷åòîì ïîêàçàòåëÿ q (êîýôôèöèåíò êà÷åñòâà ýíåðãîíîñèòåëÿ) ïðèâåäåííûå âûðàæåíèÿ ïðèíèìàþò âèä ÝÏ = q * V(t) * tç è ÝÎ = q * W(t) * tð. Îòìåòèì, ÷òî äëÿ ðàçëè÷íûõ òèïîâ ÀÝ q ìîæåò áûòü ðàçëè÷íûì äëÿ ÝÏ(t) è ÝÎ(t). Ó÷èòûâàåòñÿ äàííàÿ îñîáåííîñòü ñ ïîìîùüþ êîýôôèöèåíòîâ z, r, rñ, çíà÷åíèÿ êîòîðûõ òàêæå èçìåíÿþòñÿ ñ òå÷åíèåì âðåìåíè. Âåëè÷èíà êîýôôèöèåíòà q äëÿ ïîäâîäèìîé ê ÀÝ ýíåðãèè ñ ó÷åòîì “ ñàìîðàç- ðÿäà ” îïðåäåëÿåòñÿ âûðàæåíèåì q = z(t) - rñ(t). Âåëè÷èíà êîýôôèöèåíòà q äëÿ îòâîäèìîé îò ÀÝ ýíåðãèè ñ ó÷åòîì “ ñàìîðàçðÿ- äà ” îïðåäåëÿåòñÿ âûðàæåíèåì q = r(t) + rñ(t). Ïîñòóïàþùåå ê ÀÝ è îòâîäèìîå îò íåãî êîëè÷åñòâî “ çàðÿäîâ ” îïðåäåëÿåòñÿ âûðàæåíèÿìè: ÝÏ = ( z(t) - rñ(t) ) * V * tç , ÝÎ = ( r(t) + rñ(t) ) * W * tð. Âàæíîé ÿâëÿåòñÿ è ñïîñîáíîñòü ñàìîãî ÀÝ ñîõðàíÿòü ïîëó÷àåìóþ ýíåðãèþ, ÷òî õàðàêòåðèçóåòñÿ âåëè÷èíîé D, òàêæå ÿâëÿþùåéñÿ ôóíêöèåé âðåìåíè äëÿ ÀÝ, íå ñâÿçàííûõ ñ äóõîâíîé ñôåðîé. Âåëè÷èíà D çàâèñèò îò êîýôôèöèåíòà rñ(t) è ïðèìåíÿåòñÿ äëÿ îöåíêè ñîñòîÿíèÿ ÀÝ ïî åãî ñïîñîáíîñòè ñîõðàíÿòü íàêîïëåí- íûé çàðÿä â îòñóòñòâèå ïðîöåññîâ “ çàðÿäà ” - “ ðàçðÿäà ” èëè ïðè äëèòåëüíîì õðàíåíèè ÀÝ ( “ çàìîðîæåííîå ” ñîñòîÿíèå). )x]le1CYF0A`@:e2LPfD`^HB" D"H1B 2!.F Pڮ7t\xo|޷>󤈔y^nDZ &+DT<Kc.rM-W -fg@GL,19?bG}y}>UbǐG|"K8z4YuW|C)kܙ^4zt%]c.Uӭ|ڇ2퐯'mefKt @;97c;y[|Kz69EStlo.KtǑkP?Y;tIϥ}؛bJN9]&!2]zSڬfc,[_v̲dʙ>neocUWq+Zlmu7cm]֖iLH'%rd ;9K# f;r8J&bP4qNu `"G@%twMؐ\F~n{㰍uCYQ3$߃&Sk3rpOd(5 t&p"S*~)~ED0PdBrꩱ^ 蝼@ /rmM ?\,r ^߁AF5u4cM{b_d)Qb0 /gj x=epA$z t_\?B2א${Nd_7ɲ.XcgaJZh3DwqWP*:7ȥЛD{Հ ǶPXC DgDVׂt ^|.7:u_m| y2KUSg@c+-69)`4JO{w@܉ j鹺F!ߕg#Q Y} [sXX5y]/:#mX4\eph%z/h_c?~ B}4CNΰnu57Ⱥep;59B/6H0 ].K+X5~? Brp Ϣ rK}KUΝƚG-a} r sg(x|vX8䜛ʩϟ̽BħbUbx)>u377Ju}=ZYt@Zu}?Y'SϐRy 3z_"oõp!1}-T E &*]}Gu <é~iﴟͧwd|#`jNX߅?oRop>t;1y&q˝so_ӃOW qk#7t{\6ǃrq7?AsyXx5ͥ-_Z#;96/vƺmr3dʑ^-?,k^5KlysKZ}͝^'=O=kl~}Ε)t̝#S|&[QbL%w.>gOI%knJu^x:u~^x:u `Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:35   p !(16l2/{ 1t{x͝ UuLH %I "jM5HY- 6@HK D [D]b`QKBmр qf$0 o7Djo眳>>Z?N9L eY*3^,5yk?L>TFMUoJ|ZTR[| _ CfE0N.* RFДqh?"(K=nz[adp2K+$oB2]Y#5]D|zL7tv5MxR:A?Z}d4hڞ\am~^S)`̶;y{|r?ޠLPjmN23Zm|C}Yf(U;)i•ͅE֛7 n"K\fvaW+RVlwYlU۬hS~ 'Z X'YWfkǽv|E}i s!K )GLEWSkxoꀇe1O*^Yl?TŚ(G+j~'m?>1TS;WƉuv۳2g <6+VT~vGZƱ}=};uP]RUtՕ:Zm`̹dkk@G&~O]6)M1&`wj{ј׫+^vD\"?gbVَXߨ*qWpUόszLk^:B)<y2I=Ǡ!h'7;\M-U{Xk!*\ޗc'%9hmOoXS_bJՌ90JMש^ˑ,f'q l~(OXg9iuOHcӾ0˵ld>e?iLŞuzn7^2;|`i:r+*ˌ7XRK2; h*27mO66guYl+%|>w')pj]^oKcx lcc[Rm澘4>-?]'G}Mh DxOSo |hln-;UVٌ fwڬ[eˮlejz%X7P,eX2&?'=W([g&YL}1w~P1A;,؟rGEzظQZd٬{QtN錝J#v*Qk13C@پd='fsQ:gʲcŗڇtdqnJGi7)-x) llL|-E :Fiac窙&ocvOmJ~8sxL;zӕ߻mߛC5xaپK^댪F3~Cc5wלɰ_\˱)O.pr*#FpǐKCQmw5xĚw뜽 >P|వgZsp=!Cn:_-{?m+kM}| |}d}L>O>XabԂ@"`sٜg4uYa[vՂUxCz?@wѝ+ zYw@e?AxRiwRi~1Ax\mbo3s{X7Noټ'ބ07Oܲ1ǹ-j[Q̉n`y;wkWxbA.rTz#EϞ;N[Ќ|>Է}F}G;~l_y>zbsC lpD12O_'bF,g{Rx1o-zBOVUM]+=TOAƃ"]O;Ȣ듦/>&8G}?zu[ `׳D\qG-]Ռe.3dV)iQ{D?1roO;#cfHtR:s]GGoa/Vx .e|YGp@K=pw:go>*޲yшteϣK1G#. u'ϛ]?xr]R$M5` tt^xZS"\.8-V;*3|J._NHrw}PK>Kx'/G>FZؗGw'53l &౭G6`YU'̏/ԳÏ| ûSn3 &pcO7˲⭒9ۏFh-6g GΫGo8DǷm؝GNG6֡l^Z9O2RXFQ2lg/v?+mw<ؾyFy -E.jU֪nTQw`}g}wb|'4,Yf I-`t [wOХ둷R{g^mkE9M6y(VcN-w4A+Z(2? o%l-,@$ nnR*+1Ctړ&fBGwQ_X޶Ji|Σʞ;<d#t Byź^W#_3 7ؼz:[NcSgz}0{N8755<gr2az|F쳮Яu]c[ 4nǼ>_vSHY2׉'t(;k(+*JNTRz,-oFnޛ^|w*$x{γ~QvO81y:vX[R]KYVvúwTm n^>>|h? R |]d>/ؕλP2.헚fW01&rRI]'Hko -3~Bmy'E߭{λ :5u([-M"-ɽeڿ\^@r([ uY0WJVZNj2{즖uU-~:}}\^pSToĘg~q?ٹ7<7ًԈ}|ǚ9+;;{|Ow4;A|˓g'V|3>g?kU W]l}C/EX< \r\>NiS紅+[bSKѦа"Jm}!.Lm%SIip>n^UW8f(s Jm@ MqLt\.r!Wɀr;EG'Gd׏6 mWqt.ۺ[?+omCm+!Zuom:mqn)fXяo\71nf¾8O0ewŷ~8'BnyN(qߌ |B̽6A:%yN[sylR;5ݲ9Fx Zlü!)LQbyn'\mST|b̎bm{ )SN 8űC~k\ gtJ$Y_Weaoy>7mrR;#?܇ L|HY7d,tXUJUl/\YΝ3>שjbE%5qY!iF=oBU}7yL޺G?svKyM~CR-ӹ۱lקe2Ӿi_,w('Jj .k p.(mߎkKW[PwM0J!F{ AP9ȈzW}͉Ick+yOCv&J_zޚWi2/m 2Pf\u Bەv]]~ o{)nu[Ql_؜^z;S#N-+l?Zgݯ1vjӽL}3µW65>ue.nݬ!GcxG0,Z|H1Xy5J2^k%uC'7 . Z 4tt!iN%Z1qH{á2ij>>@ E/f0)+p>\ۖ}t9eHGb/te!374Ơt ȉקwJ!w񝢎!Ɗx7bX +;=Vzxw+/`tvLu<O=8S~xۅF{I}}NM[q>uא<|5V0ZJW6L2bk= #8gT\GHٗ(ۏ{ r QGw-Y{>׽τSNBxQkr,c}ANw^ocyG:V`Z_}S>2|}yyOAphYԁ^yIeAn]P"v&ډ•шeIg:Oɧ@@<?+eOԺ@,C倧L=u4q extI(`1S/5x_RU |sҴeP СȠ.8.|SKuw.c>Ǯc${ Yk5CbLl3N7Ǽ+tOk;:ngq uW;Vm^Kl9͓uxGAѿdxhųL=߰ㆆ\OJ?ǀw+?\;[h޳E+?c}± ^ }o*ϼ9_w WַDkgqe'VUew!g`_&es ]7{^R+Ygggי+wZĄg0^A":='gw[۸$ɬv?OiS8燪keϥ{Ks5_;dXeN(E/37?*3 &i'm8FFUjuƈǩYVڇh;թ6} C1SigrrAXS9_=.[/چ  n}Q<ݦnyqw,REHłg ~%?/_9{6i㩼&m]_/UTGdummCedӆ(hAM+7U~pѝo괪ndJX'.8GpC|\;'ic/-I~`xgL՝)3%kd^" wkSHh85iۢ? xWU~ɸ_% ^ZE_.k{!i㌼6։VFӫ+Yk$s cWWU~pqYg6X1❠:TwdLc$X \(|PP 6>IW~rQ9;G2Hy`b'}WUm$i!ї/UA}P2KA```E_-U_z+6#o复ol&٤$cdm-!*c㇬5d`k⸢QIĭ Q ,8F|k +w*MxjyS޼^F-Msg>èٙsTxIJGkm~)o <+aI+-W7plHl*mg#m`mL}ϰ 16;ol@|wpv<>www*|aZNw/ ;߽Jw|w֘oj[k >6hu*=,w~7 s_*H?>3\7oYU|Itm\.h5.3V͟J̏,,90 Ñ ó÷åòîì âîçìîæíîãî èçìåíåíèÿ îáúåìà ýëåìåíòà G(t) è êîýôôèöèåíòîâ z(t), r(t), rñ(t) âûðàæåíèå äëÿ õàðàêòåðèñòèêè èìåþùåãîñÿ â ÀÝ “ çàðÿäà ” íà äàííûé ìîìåíò âðåìåíè èìååò âèä Q = G(t) * ( ( z(t) - rñ(t) ) * V(t) * tç - ( r(t) + rñ(t) ) * W(t) * tð ) . Âûøå îòìå÷àëàñü äèàëåêòè÷åñêàÿ ñâÿçü àêêóìóëÿòèâíûõ ýëåìåíòîâ è ïðî- öåññîâ. Äàííîå îáñòîÿòåëüñòâî ïîçâîëÿåò óòâåðæäàòü, ÷òî ÀÝ â ëþáîì ñëó÷àå – îòêðûòàÿ ñèñòåìà, ñóùåñòâóþùàÿ âî âçàèìíîé ñâÿçè ïîñðåäñòâîì ÀÏ ñ äðóãèìè ïîäîáíûìè ñèñòåìàìè ðàçëè÷íûõ óðîâíåé îðãàíèçàöèè. Âàæíîé âåëè÷èíîé äëÿ ÀÝ ëþáîãî òèïà ÿâëÿåòñÿ ïðîäîëæèòåëüíîñòü åãî ñóùåñòâîâàíèÿ Ð, êîòîðàÿ îïðåäåëÿåòñÿ “ ïîâåäåíèåì ” - æèçíåñïîñîáíîñòüþ ÀÝ â ãðóïïå èëè ñèñòåìå îêðóæàþùèõ åãî ÀÝ. Ðàññìîòðèì âîïðîñ î êðèòåðèÿõ, îïðåäåëÿþùèõ æèçíåñïîñîáíîñòü ÀÝ. Äëÿ ðàçíûõ òèïîâ ÀÝ îíè ìîãóò îòëè÷àòüñÿ, íî îáùèå ìîìåíòû ïðèñóòñòâóþò äëÿ âñåõ [2,3]. Íà ïåðâûé âçãëÿä, îñíîâíûì êðèòåðèåì æèçíåñïîñîáíîñòè ÀÝ ÿâëÿåòñÿ áà- ëàíñ ìåæäó ïîòðåáëÿåìîé è îòäàâàåìîé ýíåðãèåé. Î÷åâèäíî, ÷òî íàðóøåíèå ýòîãî áàëàíñà âûçûâàåò îáðàòèìûå ëèáî íåîáðàòèìûå èçìåíåíèÿ êàê â îòäåëü- íîì ÀÝ, òàê è â îêðóæàþùèõ åãî ÀÝ. Ïåðâûå èç íèõ - íå âî âñåõ ñëó÷àÿõ, à âòîðûå – â áîëüøèíñòâå ñâîåì - óìåíüøàþò ñðîê ñóùåñòâîâàíèÿ îòäåëüíîãî ÀÝ. Òàê, íà ïðèìåðå îáû÷íîãî àêêóìóëÿòîðà âèäíî, ÷òî íåîáðàòèìûå èçìåíåíèÿ åãî ñîñòîÿíèÿ âîçíèêàþò êàê ïðè åãî “ ïåðåçàðÿäå ” (èçáûòîê ïîòðåáëÿåìîé – ïîäâîäèìîé ê íåìó ýíåðãèè), òàê è ïðè ñèëüíîì “ ðàçðÿäå ” (ïîâûøåííûé – ÷ðåçìåðíûé îòâîä ýíåðãèè áåç ïîäçàðÿäêè). È òî, è äðóãîå â êîíå÷íîì ñ÷åòå ñîêðàùàåò ñðîê ñóùåñòâîâàíèÿ ÀÝ. Äàííûé êðèòåðèé íå â ïîëíîé ìåðå îòðàæàåò ñîñòîÿíèå ÀÝ, ïîñêîëüêó îñíîâíîå ïðåäíàçíà÷åíèå ÀÝ – ýòî íàêîïëåíèå ìàêñèìàëüíî âîçìîæíîãî êîëè÷å- ñòâà “ ýíåðãèè ” , åå ñîõðàíåíèå äëèòåëüíîå âðåìÿ áåç ïîòåðü è îáåñïå÷åíèå ñâîåâðåìåííîé îòäà÷è òðåáóåìîãî åå êîëè÷åñòâà. Èìåííî ýòè òðè êðèòåðèÿ è îïðåäåëÿþò òåêóùåå ñîñòîÿíèå ÀÝ, à èõ èçìåíå- íèÿ âî âðåìåíè ïîçâîëÿþò îöåíèòü âîçìîæíûé ñðîê åãî ñóùåñòâîâàíèÿ. Ïðîàíàëèçèðóåì äàííîå ïðåäïîëîæåíèå íà ïðèìåðå îáû÷íîãî àâòîìîáèëüíîãî àêêóìóëÿòîðà. Íîâûé àêêóìóëÿòîð, îáëàäàÿ ñëåäóþùèìè ñîîòíîøåíèÿìè ïîêàçàòåëåé: z(t) >> rñ(t) è z(t) > r(t), çàðÿæàåòñÿ äî âåëè÷èíû, îïðåäåëÿåìîé ïàðàìåòðàìè åãî êîíñòðóêöèè, è ïðè íåîáõîäèìîñòè ðàçðÿæàåòñÿ, îòäàâàÿ ýíåðãèþ. Ñâîåâðåìåííûé çàðÿä (ïîïîëíåíèå ýíåðãèè), ñîõðàíåíèå áàëàíñà ìåæäó z(t) è r(t), à òàêæå ìàëàÿ è ïîñòîÿííàÿ âåëè÷èíà rñ(t) îïðåäåëÿþò ãðàôèê ñîñòîÿíèÿ àêêóìóëÿòîðà, ïîñòðîåííûé â îñÿõ D*Q = f(t) (ðèñ.1) êàê ïðÿìàÿ ñ ïîñòîÿííûìè êîîðäèíàòàìè ïî îñè D*Q â ðàçëè÷íûå ìîìåíòû âðåìåíè. Íåîáõîäèìî îòìåòèòü íàëè÷èå çîíû ðàçáðîñà ïàðàìåòðîâ, ÷òî âûçâàíî âëèÿíèåì âíåøíåé (îêðóæàþ- ùåé) ñðåäû íà ÀÝ. Ãðàôèê çàâèñèìîñòè Q = f(z(t) - rñ(t)) õàðàêòåðèçóåò ñïîñîáíîñòü íàêàïëèâàòü ïîäâîäèìóþ ýíåðãèþ â çàâèñèìîñòè îò ñîñòîÿíèÿ ýíåðãîíî- ñèòåëÿ è â äàííîì ñëó÷àå ïðåäñòàâëÿåò ñîáîé òî÷êó ñ ïîñòîÿííûìè êîîðäèíàòàìè â ðàçëè÷íûå ìîìåíòû âðåìå- íè. Íåîáõîäèìî îòìåòèòü íàëè÷èå çîíû âîçìîæíûõ îòêëî- íåíèé íàêîïëåííîé ýíåðãèè (çîíà øòðèõîâêè), ÷òî òàêæå âûçâàíî âëèÿíèåì âíåøíåé (îêðóæàþùåé) ñðåäû íà ÀÝ (ðèñ.2). Ãðàôèê çàâèñèìîñòè Q = f(r(t) + rñ(t)) õàðàêòåðèçóåò ñïîñîáíîñòü îòäàâàòü íàêîïëåííóþ ýíåðãèþ â çàâèñèìîñòè îò ñîñòîÿíèÿ ýíåðãîíîñèòåëÿ è â äàííîì ñëó÷àå òàêæå ïðåäñòàâëÿåò ñîáîé òî÷êó ñ ïîñòîÿííûìè êîîðäèíàòàìè â ðàçëè÷íûå ìîìåíòû âðåìåíè. Íàëè÷èå çîíû âîçìîæíûõ D  Q t Ðèñ.1 +xmLeǯysBSdr ʆ"3 4uEӾm)L*߶4WJ lÚK7t~КT~sx}?&3E$'QIx!)5 I դxT[/rŲs P\nH^lv ;rGt.2C~t)3Tw@ .=X9kl{ 72$H9t;A6r ܏=@ԇ2^a߃}I}]CJkYcku.,ecob/ֳ/g7*,!o 8 4ֶf.H{PO#ڣGWlbyHAyՃ<~7_PVW13`OGۀd!G~~bEԤFU>w@^trq KqnHGƝKn. 7aDjljɠ `#@orΧޕۜp>U k}KM䭆ٗCe`ZK۩s\~f;g`"{ ,dow9rւ`6(5Q3[\% "j՚b[=˹z}*|]F;Ŀxrn7)lˈ^}+[\ZZK ZW^δ;)G$湟A:pGJGul^MJ kI;_V":P>; |z/1|V:Ce cn| vu bۏڣv3%Z%^]|YkM頻W›k!9p4rXS58mr$@/Bu~JSȞu/'SPcsMw<:l` .QS>_|cRt2{nbؾؼCwZsN|o5Tv'>mر8.6~I=|ÉwkN֡94Á7ν֦o$mgčGkn},@>Nw0Ә?np;v$vnp;vށMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:35   >)(16*2`/1vK{Px՝ VUM,{a`h5 NXd&*"Πb;)IlLJ͔FtK4WM D9{xνr]}Z{ZsQ]*8=GM"> v Eq4(,}Gln!wQt!]"=g4:DSѹт&83:_.@nsYj{ QS]O5:hzVQz Ui֕ڊ*8@ZSc|L)@LӢ?M[  *P~g1'&h;_\Qې}a 1%N:8oas l ~Duv4eݠcHxq>wǸ7;cRVF[ 2=`4>9]‹ĻCeIӨmmZ?(zwчRm[rLt3TQm_. ?g}(.hQx0{os3Aa|xT4.Q,}H[^aY4l1җF7M-CP &V_Gꂽ*yyc06?/)"wncbs` c\{Xxgc`b\۾ csWؼTq^Qy]w&O ƋVl9Z=-LZj>m3*CUIu5ZlWEi(sTQ7gFoT[AM )Ys׃>X@i>7Y:6tꢃs=M }a|ahU>EdӚlR\?-nU3 1h:|4G$D]ܗce܌ucc7? <.]9t7t7T*@td#t6~OE[w0@*s7z"‚DPљ5}@X{t^WVy#'fGUI{UY?=ެRMr 1П3c 9`M>;'vUgwz.lٔch.0&ڣ]NnhqV{x1aXYZpjͤm5[4Gme[H:E;3fvD2&6]XwhEmVdkQ-R &*Zk3XfctYѽZ!rݛ%Ú? d|`Ӱv\V}\u|[M\3ߌvPl|o>7Ӛ[~J6de'՘%*zKmltP ﬩Sj^(ݮ6EcWSflu9& 2.cs >)p ]5SϺ86 l~hKj>On}ɬ"7z[Dņ۳s$6=gdgյٜpqc-L]oQ"g[ m6 5恩 fN&;&74^Xٔ"XNUOuY{v\W&SN-{2.c<>e-S^s,w8obwۢ)1[kAnA+oQwk?}&ۙ=Sم|80K3>v~͸m(S1}"u5Yۅ(Ȣ 9tC?|h304rQdw%;NwIpuY`[;\;^7ᶰ<2m[ uiXs`}aR.`.Z[<6?GϏf}4ΥT˼rwND2+%:wO"3Evp#KmɵmR!mHua_9>!o K<\//Og6ܠ;捊Κ5_iZ3/-oدgžXha'7#pٶ}}鶿mGm ۠><[#ɵ):ͣ /K'KGnEw d=s&;y <1H{~qGf PK iW='*l2_./,/l'Eء5״X[ 8mx[8{0s̕7_uY_}SD=!1~]gd<Ȭqn"{8{zQ[1u<{,;Mc_-k C^Z9,GԘzCYfX|5-m'QƨN?/ߛ?/dzX<+v>aEOt5.^w wNxUEβ`lb]NAkm[]28I ~IP)M>} U=S<7Ora;vWl^K j>Aч~_4- :[vոqk C2CU {>]֟n`xd1Lf :3\ѓc.= C\Zx'i`Sw`T}?%n>>,)SWyintwgjCE:f<06O ȱx~/%z'dhlaswe{ÞB~דQ9y  N1Ǻ^Ro꾃7ObxX? 8mS7GN%BpOĎHn:wdop3duV~BѶ*ӖM|c!ex`N#,Ǻ<0`cs}}KX.~NfѪ:͉=?U A~<'}$NY4m#@e>gX=KKe l6M*mm/vٹ3L]_GlwxM#cm2臇~|]Wyk$AəJ=BsY1h+q]3޹ η 3,7SrVTv%o=lM]*BN) },ݹuOXOا \޷8NU9R<X<ìw+Vqλ+Ky֊'N9S21ؓxna?|k,r`l Cr覮}<67ر˱±1~cޟ4 r_zOѷL}e=(:yَwٯml!WXXNMӶ:6P}#Ei=;q^؇;OGf7`k7Oqwpf"oRu/)px5sv4ČFV\^qr2 7ʱpMȡ;cƾQt.)sDc- s`؝3⛅ᙜlǷ8Ue>3ʶ{A)`#:mz990r'I6ŶʶmcUٖ"f .t@'\Wsgx|:S_AH}32M}G e`xGVէe#=ۑa7躞Hf;u0>kx\3fs 'v1:q9 mnȄ}t;9, ǻpK秝:JERO~/ꕿ7^2t$H؋y|Se+kql#gE6= "K/.-5,zZy`F>s?^ @w_oyBepΘ/Z:S  bU_&1}nRe\kGjйEk}9DrUsex|N!(>?Ј9Q>g^s$Ouº0Ѫpx?P֦g#g~ÿ秓.}uxp|Oh'5ǬO9{^#u4ǿn :[0l ~J[OϿo#Ke6:-/;͟r{h|K(},PkOs}.E* v{z/'ª{َ$j25jaCG4 ,Y  AkuQy\.et/cO*3{u{E<گb޿n+] :d;o wwƛ=?Omdl ::{n\*X"{`;*vv)^Oo\kD;Cmbx'Ufxz7'z(yL6-0;N9v>mq7/qshGHog§%9;<{AWΓtm=N}9':`tsO`3eMgFU_$^X)0Ӫz3=n/h>uB94,;WOZa?V=^O\mm<lO= 7):{:{Ԣm<,Ϗ.kjyvU cCw;5ƆcSʚ:ԅvد)뇱cpnqm DUN,u=᳷g} cymL,?-ӇAu?L8'KxQ):FRFQ;~UkI{3jdǍB;TaOb 7`>τ~G1.q`A&eqqazxGV'˿YwX~CMcD;lon o"?lf0& 'H`Ee`S(9ݖ!>zځ?D?ݝT~xΠchc$[7_ i-=zp9_aX/o]5ɡ]cu?s͸Yٶ-*.#g>ī#6g}z).ɇ`KbMmdlzx).0)]\@E;c&pC{Rf\3vtLb'm5ևN3 >rd贉mhe# d[x_mx䒟.;u/I}bᇮ(A>i &bvm74 v}rLxGo߄g$h{G2 yOOqf_Zua9, 9c=Vc/x "*v#Y1afɝ1@Fs87jQΛ /ؙ$3 =w9uc7_=dEuv?: =.>@[soEg }8J]Θ#DOSǿӳHDy^=Ǖ?w8o{q}VK[6F̟'ve2iCW!Ye9{t8M"n-sQ/Uv'EL߬OͮTgȞ] e2u?Tzˌ/9`I>]3@v%].>ꥅsϺuBfR=IQ(Yi֟zpzPNmݾ * ÌTnkÖnoHl*9cy7;8{gY|spnG$8LDeXk>뗛>OӵL%t狼~? m҃)n]H?fvrM >}&E:K-z.¨+`{ZsoS  n皲7k^L?XpN2X'Z(kU ӗS;S{fpgbٯ);%Bف :e_)d߬gI,ݘAHc{${dpgq*궓x\ۨeɴVb&Aߤpp S/YnL=bzZG8U{%#H BMУgXF*G^uDLofg$ L\zZs>|F}tQg׼>W^T9O;[hڗnN3} Y-L*޹[Rymk=T#a#Mz#Mr=hS|f*I֏ۦ 1'EPV8lwU12jxD.7z-E}F=}>Sz}VϪzu_C{^"uXgi /ؾ}e۷?WwAѠ?SGgd}S'aÑaG[v>B>/>w2-s? ~o3N nګAj估L9U8mG'&y8~4y0~Y5/G~exlجlwcF&1R̻/ s{Cj8E?+xۣ#jxa~=h{5x0SK?W KK̛{w o+~\qw2Wm׈c>0Ɠ"`A֞qsG[㷥[C3ج&61)8Mק3ğ%Ys.8- 8PiCִh||Lu<']c=_p뺾^on7Tz׻qt $s໪s&Im]]JZOFuH~=%Xݥm̮d<:[Uwtlt?/9޻ϖx h 9L檗pݵL_.K~Ɯ-E;^ߢ^~N]G8~Ϥq_覅Iɜ\M?Y4mt]&egQD9Ϣtp'H]>#\>Kgm@|.ʕzh' |jVymX[q볖^a|H ϫqG|,ry+Ϭܦx& O༡k]FᘘW9ChXb]|nwO7b' 8?`mo7 w7b?:kU#^U %U#6e =X7XA; &y~U0O0?#_GfE$#qE5DtGŶFq ysʎM!WQߣ//VXǘp#t?}O|,ߤ_5 )|lm[4Us^5o0~`UI>y#]|2B< q=.}鑿K]=#r sgI'K_&ڦ? V2a@oѷ] ǥJa]?g.ܧU# of|U{xQR֛}x,]Y.,{vGe#{L ۛ}o(^_I G?bj)[iĹ{y4Ig~}>!W\oU{6 |A'g4`▵9Fdo(ol/%yUMaYh/cLϏFg*OY/ݞut?9R7sΣ|myHx"w-y.s*`}@{R>gɜ]rG@ba!w^džr1LuɝOȝ,̞VΝ勇ɝ6ɝ,.T?6ɝuv9w&wI1˹=6YjrC-O2gY;?_m0F{"w~ewm6*XQocp>a`dY׫r<ُT~M\Co:{jgsW7ndz<8Kr{ϝזC9? H.qpcqN" &9f}bv*cX >wtqu]ķ"A0X󹿴2q92" 7 =<|( :ӞWZ͝o{!ywɝ׊ܹpw{􀭧K\dsΝN;Esyf]b·((.+a9Ca~vΏ]Sk7N?۔g_a6!&t>#8[OERᝍm88UBo[WB1C0N-q:~ic)2P2x׬ޥg<g _w4Dp]xv@w471Ĩ@l4Kog<5ٺ+xd|0x.˧gTso`̗= vzF zkͪp6 >-.Uxq1_!A&]]hZ'pYms&~,Qa;YkfFk5G6)dF.SE[/3_,\!䮐b_* _*dUkUZV*K ZXrC`ƝEm<)J ɶN꛹=#3ɠd` ӂu*Cqyk`kE36>1V1ђ:Twt9F0CpࣂSE)Lɝ*)Am\q Α\ՙsct# |UT5ѯ:}MKUA_)Xq#oηUmt"h<)*WIIɯTA?(x4hc$Qu6F(]s%}&*&OFO ֩V4>Vwkp g}n6Z4-5[oSz_Aips_NjL^4MWןW<-ջQbrvUDҧ&6L3:Y+d繟ǻ w 8xexs}2U{XYuHX--amO1E˜lD3'^ԝ|χMs B{)B{-#{Bݨgfx[mb722 {8,Rvܙ&VsEAx sE<.WԶנ,W0WYտN@f Sr`rE\Q8\ѮЃyXiT@ P }R(a9Mxocbt;sXZقcԧ0+˲rE]џ?k>{w|@<\Q&W]iǍ<:'#=1e+D7hQ`9;\wgP?d|]㟄Q;_\:]Z>Z3l0}!ȖuJ`OP7 crE!V[؞Gn{e~㿥~A;:c4]2m.ӯѪn^{cyݥSBg4G4g{W_~PѿUbo{fIf hל}6Ex&ktsʜSネ}}#8q0F{:D~fQ3P/lmbpt[S>hlxqZC*q߸;|=: ?rv:G~~|$%Oi,(M_5?\|?oLRFlT2\ppҚ KޗM&y{7YrV|%']_WMtyFtCrho:1=4Mߟ~&~#?ZNMJ;tN\Ꮵ%17yΔLtMޣ03T7꿓3]<=(|3962Oٺ@@y}ll&WG/fzC kۻoP*ڥ#mh/&o'ߓ|.Ncfq.W}N>ޝVVӡilA6ߖnINJg_qgmMӽsMɴ>Y[dKKLKNHnKOnMP2J>,|1>Iw&Ň$Ӗe6́4!%e$ qUI;ɮR^)=*>8=Q}0;~w:'w{/IŗÓg$ү'?OW'3髊Mt27%so%醸-u ]NOO?7='ugyQ5}wtl{ſ3[{KчOF sCaLiȳᏝ^|?X|m ˬǦ3Kgx] Y ssg(+U%g7 58:`}!s _2nःs$ '1L?7(qda(؋;cRVFM[OGwH@qͣW([rL} <ʮЃ}<ˣ_ߨ=ŸΣM=p.^3~HthH,X)Ca,nbue0?qӄw6oV"XW"/XzXlB7Nv٥X^"Y_4ߙ;"wo%?Xd(ӱXbQػQ, Q,^x>_^z]u..P6!,,91 îòêëîíåíèé íàêîïëåííîé ýíåðãèè (çîíà øòðèõîâêè) òàê- æå âûçâàíî âëèÿíèåì âíåøíåé (îêðóæàþùåé) ñðåäû íà ÀÝ (ðèñ.3). Ãðàôèê çàâèñèìîñòè Q = f(t) îòðàæàåò íàêîïèòåëüíóþ ñïîñîáíîñòü ÀÝ â ïðîöåññå åãî ðàáîòû, ò.å. ïðè ïîñòîÿííî ïðîèñõîäÿùåì ïðîöåññå “ çàðÿä ” - “ ðàçðÿä ” è äëÿ ðàñ- ñìàòðèâàåìîãî ñëó÷àÿ ÿâëÿåòñÿ ïðÿìîé ëèíèåé. Çîíà, îãðàíè÷åííàÿ ïóíêòèðíîé ëèíèåé, îòðàæàåò âîçìîæíûé “ íåäîçàðÿä ” ÀÝ èç-çà íåêîððåêòíî âûáðàííîãî ìîìåíòà âðåìåíè äëÿ âûïîëíåíèÿ çàìåðîâ (ðèñ.4). Ñâÿçàíî ýòî ñ íåîáõîäèìîñòüþ ïðàâèëüíîãî èçìåðåíèÿ ïàðàìåòðà, êî- òîðûé õàðàêòåðèçóåò ïðîöåññ îêîí÷àíèÿ íàêîïëåíèÿ ýíåð- ãèè â ÀÝ. Äëÿ ðàññìàòðèâàåìîãî àêêóìóëÿòîðà – ýòî íàïðÿæåíèå íà åãî êëåììàõ. Åñëè åãî âåëè÷èíà íå äîñòèã- ëà ïàñïîðòíîãî çíà÷åíèÿ (ïðè óñëîâèè, ÷òî ÀÝ íîâûé), òî ìîìåíò îöåíêè Q(t) åùå íå íàñòóïèë. Ýêñïëóàòàöèÿ ïðèâîäèò ê èçìåíåíèÿì ñîñòîÿíèÿ ÀÝ, êîòîðûå âûçûâàþò èçìåíåíèÿ åãî ïîêàçàòåëåé. Òàê, z íà÷èíàåò óìåíüøàòüñÿ, ÷òî ñâÿçàíî ñ èçíîñîì ýëåìåíòîâ êîíñòðóêöèè (ýíåðãîíîñèòåëÿ) [2,3], îáåñïå÷èâàþùèõ íà- êîïëåíèå çàðÿäà (ðàçðóøåíèåì ïëàñòèí), è èçìåíåíèåì ñîñòàâà ýëåêòðîëèòà (â ïåðâóþ î÷åðåäü, åãî ïëîòíîñòè). Òàêèå æå èçìåíåíèÿ ïðîèñõîäÿò è ñ âåëè÷èíîé r. Óâåëè- ÷èâàåòñÿ rñ è, êàê ðåçóëüòàò, – óìåíüøàþòñÿ D è Q. Ñ ó÷åòîì ýòèõ èçìåíåíèé ãðàôèê çàâèñèìîñòè D*Q = f(t) ïðèìåò âèä ëèíèè. Õàðàêòåð äàííîé ëèíèè áóäåò îïðåäåëÿòüñÿ ñêîðîñòüþ èçìåíåíèÿ z, r è rñ è èõ ñîîòíî- øåíèåì. Íà ðèñ.5 ïðåäñòàâëåíû âîçìîæíûå âàðèàíòû çàâèñèìîñòè D*Q = f(t). Òàê, ëèíèÿ 1 – áûñòðûé – êàòàñ- òðîôè÷åñêèé âûõîä èç ñòðîÿ ÀÝ. Ëèíèÿ 2 – íàèáîëåå âåðîÿòíûé – ïðàêòè÷åñêèé ïóòü ñóùåñòâîâàíèÿ ÀÝ. Ëè- íèÿ 3 – òåîðåòè÷åñêèé (èäåàëüíûé) âàðèàíò ñóùåñòâîâà- íèÿ ÀÝ. Ãðàôèê çàâèñèìîñòè Q = f(z(t) - rñ(t)) èìååò (óñëîâíî) âèä, óêàçàííûé íà ðèñ.6. Ñâÿçàíî ýòî ñ òåì, ÷òî ôîðìà ãðàôèêà òàêæå çàâèñèò îò õàðàêòåðà èçìåíåíèé z è rñ è èõ ñîîòíîøåíèÿ. Ãðàôèê çàâèñèìîñòè Q = f(r(t) + rñ(t)) èìååò âèä, óêàçàííûé íà ðèñ.7. Ôîðìà ëèíèè ÿâëÿåòñÿ óñëîâíîé, òàê êàê îïðåäåëÿåòñÿ â êàæäîì êîíêðåòíîì ñëó÷àå õàðàêòå- ðîì èçìåíåíèé r è rñ è èõ ñîîòíîøåíèåì. Èçìåíåíèå âåëè÷èíû íàêîïëåííîé ýíåðãèè - çàâèñè- ìîñòü Q = f(t) èìååò âèä, ïðèâåäåííûé íà ðèñ.8. Åå ôîðìà ìîæåò ñîâïàäàòü ñ ôîðìîé ãðàôèêîâ D*Q = f(t) (ðèñ.5), íî íà ïðàêòèêå îíè ðàçëè÷íû, ÷òî îáóñëîâëåíî ðàçëè÷íîé ñóùíîñòüþ ïîêàçàòåëåé D è Q. Îñíîâíîå îòëè÷èå â òîì, ÷òî D –ïîêàçàòåëü ñîñòîÿíèÿ ÀÝ â ðåæèìå õðàíåíèÿ ýíåðãèè, à Q – â ðåæèìå ýêñïëóàòàöèè (äèíàìèêå). Ñóòü æå ïðîöåññîâ, ïðîèñõîäÿùèõ â ÀÝ â ñîîòâåòñòâèè ñ ëèíè- ÿìè, èçîáðàæåííûìè íà ðèñ. 8 è 5, ñîâïàäàåò. Òåîðåòè÷åñêè ÀÝ, êàê è âñå â îêðóæàþùåì ìèðå, äîëæåí ñóùåñòâîâàòü îïðåäåëåííûé îòðåçîê âðåìåíè â èäåàëüíîé èëè íîðìàëü- íîé ôîðìå, à çàòåì ïðåêðàùàòü ñâîå ñóùåñòâîâàíèå, ÷òî âîâñå íå îçíà÷àåò åãî ãèáåëè, à ïðè áîëåå äåòàëüíîì ðàññìîòðåíèè ÿâëÿåòñÿ ïåðåõîäîì â íîâîå êà÷å- ñòâî – â íîâûé âèä ÀÝ. Q z-rc Δ=z-rc Ðèñ. 2 Q r+rc Δ=r+rc Ðèñ. 3 Ðèñ. 4 Q t Ðèñ. 5 D, Q t 1 2 3 'x}LUe”"\..7P8L&82"aS+ts,RhQ2ʴEklNȷ9Mmf\fV y:C.}ޟ;91SDREfK zP# "/߿,+vCؠ8ԫQ=#ꍩr(ޫ)^+ 9[PḖ3jtܚ8.VDKɗ |ʱJ=ͦQAY -^"="F#6EO?t;coC~ʺ`8[-yª.Dc հJ\JdYJ7e PLc%(cWRQR4 )5E x͜ds=cO1utӲ͵l3iY 4Y,FM&K"P#ыmp%g4;3&O$#Q>WqpJ=ϘR= |f.W.g`I}'`8j͈4J~ A)r |:eF&Lq1bg78CRW@|lt4ƞKo6c줿3&6UR> go^{jr#7g.IĻXfc['2݈EZҌAqi%n3ҤPb ;s3%)$B.@J)-Y`> f '}qȻ`[]bᅬb)2$<{Xe*q'pHp"d#AV[ vbNE:ϬQe?\nJzw7G*삯{e<\ O7ro_lY_ 'p!gSgB; ~..M,R@*r/J|{%>Y=L#usp%:3cĨ=dd !\ WM-wCfkwUAM2 7-I1I4q2]RW#]p>s©p`F"8^!C:b{E!hos+ ;3:p;a|5U5RC]+ur?#=H2<枌@@ z<7BXR|΀E@nD. '<3vֽ:q?x@y$ꈩyh#29_No7!yuMĔr8bi.̦sRײOu~P1E5GRܳAg3;S7TGG$1wpjq$5u|=>\wbvM&`M5k X&`M` cY&`M5k G%c|Microsoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:35  0R 1800(16K2K/01D{ x՝ UxQPCp.8LA41'z9 LY/zY  {VWD}?.C{{޿}97*)q;E׺Q~:4tQQG];(&:lfnE?dф$8+H*@nr^J~+?.mQSmʟS4}f9S&*Ӡڊvl'X[~.SEc|Ԑނa@O28Єi}z);UPzܴ1cQ61K땧Mϼ$K*>m+McGGvт^jt!=߾XwĠKꎀUhk |+!Ef򥰯bi|pc/䁯囩L%'c ΏNđ erֽ7G&l-P83yh>)GfI_:_黎l\+,HW/K/g%YtDw7ВJ/E 3}Jd$ [vk;)㵮чx)3V?y}9PqK:%12nY*Y{xh1?uȇem(KJ-rSy>w}c]][CWOEz]4tGVx-_Sy]}CY*}{7K!MvgEE?e.w=&RG‹Hk>YY'YoNC<`;1%:]CЩܽP P鐵M ~޲|J͠!3lh%͂YY>ʌz hs:ɤ_+{­on.J[J%v,SQly خ$l8Ŗ؟qyp'P.mc,?s}q.*V6S&q>2e 1g}~w\/7rvR|Z/А߫EX7^V=i>кv,ry:lO}:9 b˱G DeR|J+Y?l?՞z̻ g^"- ўS|Ŷ\.DRvhL™.`J \&-[l/2m}h;-klG|mqSRzY]:)Cy?u-6؛:- ʮc{Bm հO7-Ekx-D֯Pq؍[x jآY~-]:8˾Ϸ}FsR'ha @o0 mAL뛲}{-ZI ZCџ]rLpX;i] )g+/2" {*" 1|a{+evX.^,PէծTfYǡN eR!o~/uzLzFȣly3<Ƞ| /xk,F#tN*~-Y垘y"m&?s6ۚD9;a5]+-ɯ9C^Y#ch} x>Xuu_@\G\t`= =԰m!"̋WI`Kmt`>2|2q~3sV<cv>Et>n(Yb5"u6K~\V_"NC.jȅX|ɝ :G޹2Ԑ J e2++n_NRtHQm7hk6mm Pnmv<!6vLa.!s`,=\^]jflљ]nGlIlA&)eq >gK D~ ߟ6G4\TۜQ> 3"2DcV{?xaxwv0y!ri:yZ'ks\g~1G=ְ 17 ‡GjQbG쳺 };T'Y|=sӆ-n|ֽY(3VSP}\?B>g>lt/VVshG g<>UÕOUo s]v+` Ɔޠy?E=tG| H_ 4"\&~ܕ`;U`ch'cNeӑQk:\?[Jc<ϠM(~e \K)˼Lh=\1,wBu_!(MݡctK9q:^^')z6zHr!r׷7oG'T|(-?ďZP;yR=>hSd&Ѽ/Jmj2O<:R6jkGq ¼`|oj߭T6s±=ܛcaz[֍|6'fobq3|c<) 3>ҩGqepy˥>b)90ZoqHoDʉv| [;sސ/3~]oh;_QG-~z.,­/F 3ro!ru2Ԑ _ob7=Fml-AFJm;icۆc4m$}cjА?wǦ'4Go_>O}ɧXmOG#!`lk C'N-~\5Kȃײ[^(|O}~\+\)Z~woqj7@w򼟶~rv^[y+VsKr0^wU_J %s Jñ;.kh7lZXv}זLN]QޏCOEz%߮{,FEr~F~ˇ{@^Z)Ԣn?c j[G/4땴Z.`%v9O]I!)#_q1l0V4Z?.a q_/ Zof~"IUp;W'ٓsE%wkE6jvn684Iցmc;`W:f|?ո5'oј֬;ɜ'I;(%W'?m=N 8š[Xecx%\!\XgJiu(vc+ڣ.8ǜƹ-Qvm[EK3[,|pA` VWUnpI"iO"WfZo(ĉM8$x܌`̌qQ>c[gRH]ԶLB#Set=N@>W+4Jh) u=Z\ģ0~ڶmpG;ڃvpޭ-(ϳkf&3Nc@7i[?Ri| kSsGsa.PkhO G,+;cE k57;PWpEOBSyЯ} [ ¹I:E% fb\9fdD|''ߑd}GW^s1R=(Ix u-j9<hyZ'f*sAn}Js`>Gn'bٺ{,=; v>g-D)F1st 5F,xc!_(?;Jϱ$"_^woge}Zһ}4|̿ }y#Щ\!_Yz^v 4i2tdZeAw7Mj[­t$5 {#9bm;gcv,GTʩ̟q R N/<֏Sׁ ˡ\[.X)#tON=^u}VNk1fKHz ?v:B&ehu~IytKRVܞT˰_ 'G%K?ʩ~S$>Q E+iJ>Nr ^cO9oO{C(W򶋽w*~#TM!?@ҋʏ|y{9Hl!}9`®U2:8u,;g<)qP>ˠm>)4ڧ z7Nhax(q_)P*Tw[Cao];Cܚ`,^,P)E> )S[oR3Q}n<X<] xR9:">q;E8?49uF]S} wL3`2Ϫu P"!#c'9y|&cq+&v1NbcwjP=uN}FTݢ>SD&߳{>߿+$ 13$y[c*8n=J9> :o:VQmcȥ}!oU!=j*Jp%k\e<_sue܅ ~}mQ,y\ע?fp&=@}Bgo9B[uζ">IP#<"Z%-Ӷ| [z-aR^I莉RZ(7ouٲ!O=QYqCwzjC%ȇmxs}ǴZ'k}{3OWUz` uxO[ sz|! :!q{юQ 1"]&ںkwzvߐw^Gc WR|w&c:W5|8OEcI ݗ~+l]3c-_'2n[c_'eQP/xGy }"}.?j[mstXS\`cZ4뎺gG\ʤb(ANV*5_npE:],ZzGIӋbI b=؅p~?ƿ'﹋n%cֵ1|>OLC #$pG&2(e_G~UE 7\E"ZQI{R;u#wuo{Pufoei.£(a}k;h,hs;e%/-Զ9Գ/Nuzxi-řtuDA^h/ W0Ax>MHvʜ^qբs-n<ԛwײ.w>jN;9}I2lK%Os:5xLLN֋L/(Ssm}PX mGX+C; /[˙Nf,9N$L<^u$>Y>3of&ߛ{&Dd3"++2݆GWqf2uQK6n7=7q:`׳u%ik9|qx@ g{@s\6~@3:.O8%6ĖWְ-"[ Z3lf gV~3ingvZ$ 6g~МͮÃϮgcXыuc=0~1Z֫u]Rp y[Eo ߀VPȔi*X(/x<&.`#,g*{H]Cދ^!JA3ﲐZNx/{n콈~ýziѽm['wRأ,,7z[̯^=YwW\ԝtx󆽻] ^m%s{G/肳g3* ;|#rgiaK=XϐW>kכy3[ݺoWB~gl {zDQ} }#tہilJ*tthz RtĨ*oGmh _-y?͌vv@AicCٷ0x~9Qs3*d+MĆGWM0>>/{}Mx"꟥dbBc.|ϿG/>v-e郞ܴ{d~Z0TpHvx_g anzw_{6L2Ϫ ի7HKToZ1;f#(ƀ:w3_~J?ϟĖǮ\uD Qy6јwȕ'x`(U翤XM4 Ɇ"e_:=~B9NӪ/SV~Ƃը5-}12)J[VMϐXJ#Y6ޫZ烧4dJ&x! &D/MZUO~FY ,0?g* w=tI%x?-x[zPB}XdOm([لkMY,!6TןY_:eCb.Kcgfb?uLb)B Nqpxu|L&c[+Z(f%_\.B&њw/W/Rrioƍ ^TgNiud ෂPo6G񩠍E'xJOΓd<)YOI<łD&k5q8NZq|mԋC]Tvn]2{|B{-P( D6@ǧE%8Q#Ugꎔud\%Zp`SE*)Fژ^nAIunRݛ$&ɺY2o1ߣD~qwǃ6}9>:Ϫd='(\s6/XwNW[śf+ ~L yyDyYNx;d+Cf9L U&oa !Sk wow; ?{7fY~XC}GwW&;%IseojyJyF\o.݌3?ZX߉6E+wD[:l} IgH)9>ޢ~Oƾzg/s?A]#ύ= ̄A?S/}Pڭky?8Q<5 9gہuY!\כ;oz]G9VhBO + cbP"9_g nNpN̯xgG<S[4EcYzO~,%hR1>=zaZRy?*+3]@&מ_np5)5rG~ RL90΂}ۿXr Fӝ:Z弟2BG[tޏ> #{T$⬿Q)4\0~'#គc( }2Q'/zX{3žJS֧jA`ms 2Fu}9L<}q= m쩿r҃8\_BgO^gs)ı 7g38M*wV|rStH|]hr蕸.xG<<9!<ߕLH~ڻ?dxm5vOvMI>^MJ_k?GN7GkSCmdt;,L$3'O$ߌ$__ )y7/'wG<.:a<:t^]!܏J8m);p18 mKǟ: <5_Nx`>z͠꽵N{dH},vUs~om-.f#_l+{k#T{kӢ{kaL]v|W+ֺ*^mxuңʱ֠?WJ*g0y̍6v>"wH_><әJwH-'Vg'~W ⧤E~mO7_Ow/ۤӕ~O)`? 6O-ձaiݮ>9ѫyk)-WGGἥI+.~C[v>w-xlZ$#Q4P՗nߎz$Gmɉ5y}|rB N#9*/9:sdJ.N7ud%L&{KS]v=t2(]~^TO^IKL7ۧ˓%;?I:$''#L'?KM~FŦdohdnW?*ZjS 4iΌމ-I7&FI&kw)oKώMƇW[S{/OƗ]3җg Uᖴ\dݱgtЛ|6VJ8񌶝ON8Ҙ3I-'_(Yz~.+k/ɕv'XeSqM+JV(=_KBlDߎ> &g?VK "9MrlPl lׁz*%UJhK,9C$-,ղx>3ar} eKL xQt2ddgOV'*"j8y-5P5AR A#1B!RoiCQ,bI 4g-`<H-|-6b:??nF!{]nG/M|:yQUPXͪ|Il5gjW=pYN 5O͑~Ei:;7vX;wϑrNw)]u"3> o"f2]r%fp >D> wu_o#U+'W]wNx@f/BS4 oP1Oݥ:7Pwy$'XP``3zL W8kٌ1zmj31^joo5Τxݦc̯| >O<ջzg{N nwt?ߜpqYWt9WVwNW{֚s 07`n܀s07`n܀s O7wMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:35  L 4Ё؁(16Z2/1f{lxݜ{]}mրB!k0kbLpB1/Z"i )- hRFhkUIӤB)*Q%КMX k{/~g0c{|wMz^3{͜9giQ*WMM鯦 PvJoK}镗J˿;N2uǦwzHN҇Iϧ/R[o 4n;>A$4TW7[_z+OTH?'CfY*UUkGUPfyJSu3{UXm)YfIȼ^0qzK_*t}iZlQN=/tխ9)GdKmr,>4?O[զ^KҲ>mF$:}GE)ӗke+_or-L* O# ژ5Iʱ;m$]'W}3fllzE5۶/~'p숝RL zW&kw^tskJcW:_*g-C^#s7' j'v/')goR/r|XU7O^ȡ7)z+|TGߤ7|}VoNdџRp1=|nr,>D^+\2G_nv}목Zsz(r៭\k3_1\oE=uL{P1TIjLMyi];S~*'0my boLO\o)1'sM/r|ݗv<9ƚv")g1Cc3w UÝϡiϤy=S_XtւW/.1'3m)u-9yG9qbpw߸AW^?-Z}i9oKF_nmU9A{R:YS|[y{i:#?3gISzA?U<Ng7Oo\woO_Z3/(It`?6wvC߶v%U;6oTTI(m7~n(p_vbgo='W8h=qa/SN4I{gxwi?!<:;Q]3WtI4ؿw~SC߶U^CA1o wnIϩӳi^ι2=d+DVa/@YT9C2W嬬@ 0*^ bC7?^ɼ:p_o?T{&ȿH|p٦I? זvVH'uX1W9KEVE Q7?wZuiq#osjOg*!G{V<uSܠ~'p|\q!~95qɏY[[>yy꿠J >VDWUſ+tSR{FfU<JG1v>Sǯ.a-.bZ#ݓj slwci/򧥇Xy;Q]~^^<+fMA0k όk^*,뤴U5 hG~ГihU =rЕi:=]\[:dBC ׯ}U&;< =MwSU#9=&]52uҜʤXnK4U(|2bsހڮY^5$X`Tk\SZiyǫUmD^/<ҝۯV7gKNV};q?Bm9yCR!>hI!Ro|r7ܳw]!6j^H3mӿ~4v 2* 覴U^Po8mVDTp!#mmnRK#n-kJ[x qC!NS_(Leߴh) <ЃW` B34NR1>4iS<o9+E&M(b iŮ䋥-m] :$k CU lv)j8PX]JAK5۟;1$]v+K; كu#a=Tk =:\xe~hC^ަ1Ŷ}#\x; om9WKEd­ͷHh,G=/ca=cTobòAQ [nqaq"9bv̆1l.Fj.yV6:Mhm\_8;C浞CK[؊8c0bi wMq\ߦGO&Sy*~d{#*s0*(l?, g睲-m۫6XrM+.4֌W 5mӚ#*] 7m[EKklAf W=p>ۧ gDlWo<8y" 9[ty둹^ 3U#օ?W2' Zxs߲-Bdܭ)rToU]&&=V)-qF8ME{fS UdpBD4(Ya$%NJ6a6v|-> :}ZYL4SC n蜆60rz {lzLb6stٖ^C pb[v~L+* Q6 sRX NX[S1Ftb(,º>QEc6c-֋a^3}t]. G--dg=8-c@o@6p t7}Ώm(&?jlDF8uG)>{w;p#-m B8 ;b@9uDL&dqY2W tEYfEm=k݀LڶƴͳUl/G xb:u1Z mǪa|̋qm yx~IuGNl)N'p[ד~Yc;'*^w|G -NH'll'z@wpYٮ9u ? rG|g x^X<)#Dz̃=ϖ=ѣTWm}`F/皺9g\=4 s2'p_#̉ܳJ^@+Tĝ gjwnqLFgtv5Cq2|fXց5x1lMg2C ߠg n3eA<{x^:_"OV+<"xvߠ#ݥ-g`x*gM9dØU2; x<%?3W~@xѯs].iW8N< n=·e!ݜwu ϓgf06gz~G\7u+kw`i/ J<)q;ގgez8o3qPk/Ev3rLga9ϭ x2c4C4: e)ȱ?<,&OMiK? q4SaGb4N{LX8/47#|nyCo|J/}>_zdM$_c@z>Ynۧw)ȅu y63a_m#[Z/߈b' Lݱ7]5kp ec&DɍV-W[m.NqJ- ؆o;oxJ/;8O#]Ϝ-r]gbW#2142c6jb\-1'h+ps<'}vbWbRm]wָe4䳗rDY>us[ ,mղ&MƔUss{^պF^27MEw7->49hvfhX>1AǤ@XVZݱTk‘gOC~[=XyvS8{:7s;0([󾋓W녇_ĮMnƉdC7GƺY?뵮boن< xh) rx>cz,5eX}4{F_ {HLeY b-A؁MiP[1< FpH&xwCmI%uWXX~' :jǡK6^6ζ}ٻM9Ci}6Ca- xsCk*t |@ؤoxQvI秭bD2q}b~H_ao2>vg=7ųVaĂN'?zPێȤm9_UcU ]Z.Hoᛣ}%H|O@oh9urۼ9tlKt\q3M8cq\aShmaY*2نA߶F|<h1Z\7uU*lGs^U~`E*kDgQ\qauU(H>27%7mpO{ ; OWM%x&Cqn?</)k=mc<0Զ3?\W_qGs#N$Z˓*~=I|^kG|lXGwo丝![9ӂ6lOv>k@ܛY,?GƻkMNĩ,n6_ːw:UyON|p;o5>ޣ/b]Y\n`] m,Ԇ [rzdQy8 LܿVc\Mq$?OF:c'^d_irWZo㙒Η@#:{1Γ=^Jr$&NыuJM rZ1tmiyroyc E`,y<|+~t!OKpkNl|SCTle"3v-r*3$"Wqw)<#^\׺qoR#nN8o߁8j?_Ҷ| _@vc6m 0Z` |KjBiWכ:?M Cέ~;V?Q6!ۣ ,2*Zֽa >Uc]"s{@0hrBc>L *2-0`; j ~{x쌽僧BT-$-' 7|N؉hgǺ⛨*#;g>)x[r 9?י6:E'iS<:_':8j詑Kf0S{4_ psM2{ |!~2(?# NtЉ̶NH:=Uys*8-8<R'm|lgi@qaw5v_-6o;ec$ڹ #~hD'q %N׈\5no8K{8CHǗn]tyGmZj-i6-pۇqhx<`)3|5sN|<|bk+ו>q.:NR|bp- Oqy/*Bq.|JggPq(@*EDsA.b'ė}xyu]]ns9k:׶rc=7}gZז8^'9Y1?#G9oW9nc h;ZrD|_;Iq7{.浲nt@X/A:GX<>=x,Rf@KZڦ9bN=zs%46ޑ-<pGkE aܶ p#Zpȶ?x.-81un\P!J٫orxOӹro/|I_ԒQw@qgqstz#jǓw9=s,t o[ 88E;03І6?]F{~un]YAOX`OrǃbX@X.Sf(8y s#Wt9v >C[f5Ǐ o=I,,93 ÓÄÊ 681.324.01 Â.Ì. ËÅÂÛÊÈÍ, È.À. ÌÀÊÐÓØÀÍ ÀÍÀËÈÇ ÔÓÍÊÖÈÎÍÈÐÎÂÀÍÈß ÊÎÐÏÎÐÀÒÈÂÍÎÉ ÊÎÌÏÜÞÒÅÐÍÎÉ ÑÅÒÈ ÊÀÊ ÝËÅÌÅÍÒÀ ËÎÃÈÑÒÈ×ÅÑÊÎÉ ÑÈÑÒÅÌÛ Îáîñíîâûâàåòñÿ âîçìîæíîñòü ýôôåêòèâíîé îðãàíèçàöèè èíôîðìàöèîííîãî ïîäðàçäåëåíèÿ íà îñíîâàíèè ñïåöèàëüíî ðàçðàáîòàííûõ ñðåäñòâ ìîíèòîðèíãà. Èçëàãàþòñÿ ôàêòîðû, îïðåäåëÿþùèå ýêñïëóàòàöèîííóþ ñîñòàâëÿþùóþ êîðïî- ðàòèâíîé êîìïüþòåðíîé ñåòè. Ïðèâîäÿòñÿ êîíêðåòíûå ïðèìåðû, èëëþñòðèðóþ- ùèå ðàáîòó ñðåäñòâ ìîíèòîðèíãà êîìïüþòåðíîé ñåòè èíôîðìàöèîííîãî ïîäðàç- äåëåíèÿ ìàøèíîñòðîèòåëüíîãî ïðåäïðèÿòèÿ.  óñëîâèÿõ ïåðåõîäà ê ðûíî÷íûì îòíîøåíèÿì ëîãèñòè÷åñêàÿ ñèñòåìà ïðèìå- íÿåòñÿ â ïðàêòè÷åñêîé äåÿòåëüíîñòè ðàçëè÷íûõ ïðåäïðèÿòèé. Àêòóàëüíîñòü è âîçðàñòàþùèé èíòåðåñ ê ëîãèñòèêå è å¸ ìåòîäàì îáóñëîâëåíû ïîòåíöèàëüíûìè âîçìîæíîñòÿìè ïîâûøåíèÿ ýôôåêòèâíîñòè ôóíêöèîíèðîâàíèÿ ïðåäïðèÿòèÿ. Ïðèíöèïèàëüíîé îñîáåííîñòüþ ëîãèñòè÷åñêîãî ïîäõîäà ÿâëÿåòñÿ îáúåäèíåíèå âñåõ ñóáúåêòîâ ïðîèçâîäñòâåííî-ñáûòîâîé ñèñòåìû (ÏÑÑ) ñ ïðîòèâîðå÷èâûìè ýêîíîìè÷åñêèìè èíòåðåñàìè â ñèñòåìó íà îñíîâå åäèíîé äëÿ ÏÑÑ öåëè, à íå îòäåëüíî âçÿòûõ å¸ ýëåìåíòîâ. Ïåðåõîä îò “ ðûíêà ïðîäàâöà ” ê “ ðûíêó ïîêóïàòåëÿ ” , êîãäà ïðåäëîæåíèå ôîðìèðóåòñÿ ïîä âîçäåéñòâèåì ïîòðåáèòåëüñêîãî ñïðîñà, âûçûâàåò íåîáõîäè- ìîñòü ãèáêîãî è ïðåäåëüíî îïåðàòèâíîãî ðåàãèðîâàíèÿ ïðîèçâîäñòâåííûõ è òîð- ãîâûõ ñèñòåì íà áûñòðî èçìåíÿþùèåñÿ ïðèîðèòåòû ïîòðåáèòåëÿ. Ïðèñïîñîáëåíèå ê èíòåðåñàì êëèåíòóðû â óñëîâèÿõ îñòðîé êîíêóðåíöèè ïîòðåáîâàëî îò ïðåäïðèÿòèé àäåêâàòíîé ðåàêöèè íà ýòè óñëîâèÿ. Ðåçóëüòàòîì ñòàëî ïîâûøåíèå êà÷åñòâà îáñëóæèâàíèÿ, ïðåæäå âñåãî ñîêðàùåíèå âðåìåíè âûïîëíåíèÿ çàêàçîâ è áåçóñëîâíîå ñîáëþäåíèå ñîãëàñîâàííîãî ãðàôèêà ïîñòàâîê. Òåì ñàìûì ôàêòîð âðåìåíè íàðÿäó ñ öåíîé è êà÷åñòâîì ïðîäóêöèè ïðåäïðèÿòèÿ îïðåäåëÿåò åå óñïåõ íà ñîâðåìåííîì ðûíêå. Ëîãèñòè÷åñêèé ïîäõîä çàêëþ÷àåòñÿ â ñîâìåñòíîì ðåøåíèè çàäà÷ ïî óïðàâëå- íèþ ìàòåðèàëüíûìè è ñâÿçàííûìè ñ íèìè èíôîðìàöèîííûìè ïîòîêàìè äëÿ âñåõ ýëåìåíòîâ ëîãèñòè÷åñêîé ñèñòåìû. Îò ðàöèîíàëüíîñòè óïðàâëåíèÿ èíôîðìàöè- îííûìè ïîòîêàìè íàïðÿìóþ çàâèñèò ýôôåêòèâíîñòü óïðàâëåíèÿ ìàòåðèàëüíûìè ïîòîêàìè [3]. Âçàèìîñâÿçü ìåæäó ìàòåðèàëüíûìè è èíôîðìàöèîííûìè ïîòîêàìè îòîáðà- æàåòñÿ â ñòðóêòóðå ëîãèñòè÷åñêîé öåïè, òîé, ïî êîòîðîé ïðîõîäÿò òîâàðíûé è èíôîðìàöèîííûé ïîòîêè îò ïîñòàâùèêà äî ïîòðåáèòåëÿ. ×åðåç êàæäîå çâåíî ëîãèñòè÷åñêîé öåïè ïðîõîäèò áîëüøîå êîëè÷åñòâî åäèíèö òîâàðîâ. Ïðè ýòîì âíóòðè êàæäîãî çâåíà òîâàðû íåîäíîêðàòíî ïåðåìåùàþòñÿ ïî ìåñòàì õðàíåíèÿ è îáðàáîòêè. Âñÿ ñèñòåìà äâèæåíèÿ òîâàðîâ ìîæåò áûòü ïðåäñòàâëåíà â âèäå íåïðåðûâíûõ äèñêðåòíûõ ïîòîêîâ, ñêîðîñòü êîòîðûõ çàâèñèò îò ìîùíîñòè ïðî- èçâîäñòâà, ðèòìè÷íîñòè ïîñòàâîê, ðàçìåðîâ èìåþùèõñÿ çàïàñîâ, à òàêæå îò ñêîðîñòè ðåàëèçàöèè è ïîòðåáëåíèÿ. Ñëåäîâàòåëüíî, äëÿ òîãî, ÷òîáû ýôôåêòèâíî óïðàâëÿòü ýòîé äèíàìè÷íîé ñèñòåìîé, íåîáõîäèìî â ëþáîé ìîìåíò âðåìåíè èìåòü äåòàëüíóþ èíôîðìàöèþ î âõîäÿùèõ è âûõîäÿùèõ èç íå¸ ìàòåðèàëüíûõ ïîòîêàõ, à òàêæå î ìàòåðèàëüíûõ ïîòîêàõ, öèðêóëèðóþùèõ âíóòðè å¸ [2]. Èëëþñòðàöèåé ê ñêàçàííîìó ìîæåò ñëóæèòü ðèñ. 1, ãäå ïîêàçàíà âçàèìîñâÿçü ìàòåðèàëüíûõ è èíôîðìàöèîííûõ ïîòîêîâ â ëîãèñòè÷åñêîé öåïè. Ñáîð, ïåðåäà÷à, îáðàáîòêà è ñèñòåìàòèçàöèÿ äàííûõ ñ ïîñëåäóþùåé âûäà÷åé ãîòîâîé èíôîðìà- öèè îáåñïå÷èâàåòñÿ ñîâîêóïíîñòüþ òåõíè÷åñêèõ ñðåäñòâ, âêëþ÷àþùèõ êîïüþòå- &x}heϳ7gw޹y/ީƕm?`1M#ZKp)2B**4%dX`JRKAAonϹwO^ A~=<Ͻ,󘈄rDj&# ,SiӐ\c"I Rvr2ak5S= :gI_t#geC4~!/:+/,KIyܾ~0VVP֎T`n_8KS{̾/MMyWX]P.7RJ -)Lb(vjƊsOk'yJ\&JJ#\ʝ]3fIS uȧL c`G8EwN&-0p.;vWmQH;Jmw;5Ϡ}LeR&xk?Z `/=,J58[|N8(QlsD}(0}!5P[㋮ǿDџMsbf>/d|T<v[k2 Hx k9.E#cH ""~ڶ!6abaiE7(Oe ؋|R%ap`Fvl E/傠XcQ:kO z߂=d, H&IXg 3q;ӹ3_=|>/v>)?tMӨu=Df 7%u_]p|*`+7S{sZGEGn$:߃f|,d), ;\G@=1`9^jxd3^ /ܾxIb> &v+,#F.G~l6S8)א /'f}n0sw (s@ S1,3ES](SqpDЯE=zH耹S[C8LO ^ѷ^{zh2+^XW3C(_C1^א%܇wEm;`W5r5xZ^I^ m} ފ|tay $b4=Q>>R;Z=}_[YV6};^OSttv]7گlXcXѶcU+9iGv5R}VTA3iu>>mL׵v]L>[߲gI>'y4\NtRaѾr?qNjfCp'N;w p'N_B;w p'N;uMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:05 14:25:35   a!(162R/1> {lxUz8$$@vQHH6dAG* KD-? "U 4m% R%Bq~^fөCm=}z7מsΜ9̙3<ϻ5M*}4;^6M?ws/WtӴ};y/܍Uu_0MiDվG7=|tCN?0=8mW7׿^[ _*Y^U)ՁwU]kQ>ZWVk/WU:^DJ5S WڔgJRÚnYxQ6R_!~qpIgY5}/{ӫ^/GC?ԭ__:=9ᗿK~;Ĺ[[ON%7T斓\ wu.c7ۙ<|>0jҝuګPu*N_;mo޻es1y]on{N9۷QeʟJO@۫,`!y7D\W7O_? {YgKX~,V02e?uy()w}*67Myb?m+1#mS>m/}C*\mj6lS6;mRGt= jhi{:?=>tzڝG s0 Ux EWftn_kb=?=vJ;ۙ*g+]\/MW wWOػf yڄݧWVf+!/w9+ܚ mp;!`:ڇv/z j_Ǖ`|N ]J zzwKKCBo[|Zgg' ׶T>b1\ma<]6se(,25"702J]z9zՕmc \Ơ}K?'Kv :yl^Y;xwmJW*`/)&;xpK7{;lƹ]I {JT}u`SM}}pU_{Svqldo/(ؽ;Qi) ]?^\Z7bifn{a=.VAh휩.W\YߧV~ U@O SdoT{,KydaW';RM>6,|BCG': -8z<֨&Sh8yGpem_:M/؛ >XK'Jk;s>mvsgf=˴/}Q39w5r|ЯVqHZnTr"?(&ZLwVݎO]xQgZUmv%s3riAtrgڌТCztG7 O8aGJ乳FpYb( ]I?'?#8X{%kdlU" l*GrmGƸ_Gv}ܺ-صaߞ+<>^;c)ZKSl\JƵOx2+xނ]KpC+nGI`lVo['}1?n}h]c̞=_qp:\ΜXg8dt 'F`C|R9>WN\+ص|<N_}fΫcGW9&w֯3_Cv7΀n2 9[7w% > 28zEgּvۋ<4jc+dڀÃg6Wx6.4Zнժ^sps|nyYorkfJ.yG+垏\Ki*'7tyڧZ]_ڈ')}e[cdo᛾х'\l hu+U~ x8`NTՓ̽[D<R}dnƘtkem؜qm޷2> vWocC'1Yja#̼=[I߆9~^_іƾ+ʶk(y5#2Grh/v;O< .C.Ŏ3q$:m3YmVs҉0P1r[?89u/2p{.q;넟,-!rI*cpy%WLƿ'( =QuD+O}:8X"'cՇy7>^}5mO8k|4ɾOmh7=|j7&a׺_x^[y͝MWl'\u|V=D,YcdN*+Fd.i6B1_x ЫǮ{l h [WFq(?=V;zk7 )\?S98=9x|c#J|u6t}֊^ihY9UEg=-I<'zfyWt)cGf>9V^:چWrtYwx.'w+OʹBx ?vK=+v=Jbn::w]j٤ GBI/m'纋031%ڕqrߩ?~/ /v?Yͺ˸r+r如]sё&}+_~~mD;׻Ackݰ1OjN*2쒏|#1K r-96&ypxiʡS9 HV[o3/MR7lp.=m{c;s1dܬq`60k*jhV\M.I`Rd<)6lII[qx:I/k}HkTyM1i{BouwBdʥQGc9r9V4Uڎkl:t>x>Ey?W;QC5?W^=~`\Z3ΎiA1CQ'[TZO=VoyoZ3! %# |v&Qio<*u>Џ1C(oԺT[cx.ئum1iڑ*h_͓ pu->[`]>,eAwdODf$ze2FY:>6C =\A}صAވS3 ~}[_Tiޏ잂UzHxN=:Vqo<{N4S>7/;Cƃ99)',"I"iOviZymR贕F=}E/`?ȓ_˜[Vdh:Z镥xmkt ݤTY=L譏~^j=S^r-{wT?|7yXtfl͘Ќ .S(+4z(D:?npRK,؝$܋y;=[cFH~KWps]_+cD/vEF}-{_/8CG/#KXӭf\YWyfIF?]%;E=Qϥ%'KԱOG"h_3ʾ}X΢сGɌ<\JcUGN~xs8(yPFxeLhK>}^w?igg񳱇XckZ=Atl7 Q|7ַ"s}FHYY"- ҷ) |E6(52ʹlS& p) ɵ .QwX~gڦ}rx}N.%^0? >m!1;^^?0U1Z{ vww}?o[nXoz?YF|M[[ԇVe=Zr]D?.ۦOtwʁ63>:}6~'cvE~Fx4ﭠ1vڎc7~s5gh_LLV`r@/8u:_8HKn#\n3 ͞ c!&٣ md|kF?cc̒zZf}&G<6Gv=pU{vw GSލ O: ߶t9^I?c;{QOxG>dI^/6YCw<#yncI'@/$mК_x*6 밁+;_>EgJ DgTxN|:Xg~uNbG>!2!lW:\ֺ6R/ jїuၞ_P^`i;}ol r=?56a=Qi޿[@5s=x36߬AXo<'m[4F,7RkuE&gȌNV=+ЂEo.:q,oUCNF;sPg+9?<2M/}6?)_G=q~21whny8;~82P[G|k8nyZ o^/4 N}[~nb'mw|}/uט`9Ie)~=6|r2Ҏ |Oヵ˞^щzxዟznl-sQCĀ''_2M߷o(vpv/|'e .ĻgߩXYsb{WΜ#x>: O9S>QhN"cYWKsؒu+r}S$O#%e>"1tdDMkn\M{,:d?7=m-Gwde*(9vs|h C^JY[2F>]l=m/64ah .0_J9tGwWtl-&+>q-3';k$2KgHz|epnfɦox]Ѳg5V@aO>^D'"dg]_ϓ ;`?t@3;Kns6Q)6Cʚ]G⋴_v!Z>>_c+8CG殜1Wg;=RoX;;ڂ}KnһDtZ!)XɅ۰OWlswCj˜ r1l,~F94F'`у~ࢋQ#?4pхXϺJhKGb2ovg=:a.w6ʭk-_]:<;{^@M[yhC;Vrs֗-?^=CF_` ~7/h DZE\ٟӱ2?36exDZq_O.E?}[E%nܪ&[GƮ,K.{^̾;˖7g2_=?R'3IY_{5Jt6h3y>zSmB;7<&<<8X| h/;밃^m:q^GyY Vdgn@unepinZxeD ]d>ʏz#Бqt/Mt_c [|8^J෶hN5vLR#~_׺_Xvt;_s/4x%23o3{9Cy >+G~r)^]{RΘ ^c{ф6I|=y"f5?[Mz)?l%C2k\M+nWl/d<2ԿNlOe-DF#c6pڂKx?874tJ:}\g+X=_t oƎo,֧=YwM>^LYVnOUDv=bt9[-@S8-zic}Ft]oR7}}z1I;T{(