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Ïðåäëîæåíû íîâûå ïîäõîäû, àëãîðèòìû è èõ ïðîãðàììíàÿ ðåàëèçàöèÿ â îáëàñòè àâòîìàòè÷åñêîãî óïðàâëåíèÿ ñëîæíûìè ñèñòåìàìè, îðèãè- íàëüíûå èíôîðìàöèîííûå òåõíîëîãèè â íàóêå, îáðàçîâàíèè, ìåäèöè- íå. Äëÿ ïðåïîäàâàòåëåé óíèâåðñèòåòîâ, íàó÷íûõ ðàáîòíèêîâ, ñïåöèàëè- ñòîâ, àñïèðàíòîâ. Ó çá³ðíèêó íàâåäåíî ðåçóëüòàòè äîñë³äæåíü, ùî ñòîñóþòüñÿ êîìï ’ þ- òåðíî¿ ³íæåíåð³¿, óïðàâë³ííÿ, òåõí³÷íî¿ ä³àãíîñòèêè, àâòîìàòèçàö³¿ ïðî- åêòóâàííÿ, îïòèì³çîâàíîãî âèêîðèñòàííÿ êîìï ’ þòåðíèõ ìåðåæ ³ ñòâî- ðåííÿ ³íòåëåêòóàëüíèõ åêñïåðòíèõ ñèñòåì. Çàïðîïîíîâàíî íîâ³ ï³äõî- äè, àëãîðèòìè òà ¿õ ïðîãðàìíà ðåàë³çàö³ÿ â îáëàñò³ àâòîìàòè÷íîãî óïðàâë³ííÿ ñêëàäíèìè ñèñòåìàìè, îðèã³íàëüí³ ³íôîðìàö³éí³ 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. Ïóòÿ- òèí, 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.). Àäðåñ ðåäàêöèîííîé êîëëåãèè: Óêðàèíà, 61166, Õàðüêîâ, ïðîñï. Ëåíèíà, 14, Õàðüêîâñêèé ãîñóäàðñòâåííûé òåõíè÷åñêèé óíèâåðñèòåò ðàäèîýëåêòðîíèêè (ÕÒÓÐÝ), òåë. 40-93-26 © Õàðê³âñüêèé äåðæàâíèé òåõí³÷íèé óí³âåðñèòåò ðàä³îåëåêòðîí³êè, 2000 x]h\UlҦM4 #$Pl(X֢nDl6j"b#"-6}qQPDm;jۇQ|D)uH{\/w?3̙DD5"^ ngDzcVDДoξ%;"?ϙr9YEZ#F#.|aoy9*蔈t6yyO9Y~C&YzdY|8yZO9uGX~nr^>&c .R4h7]yA/$p/_?KOӅ&R#vpC! 뚧9~_3,3r>/ƭ\ăԂ~pMݯ}'[hSLʪ[A (=GPYj^l >˽4)3( &*kϢm&~) mF8<`&d?1Co]_ ѧ <cO`Qw'BR2N_No@^8/ybނFL&.JwOĦWÅ-׌=N/MNrᵦIfgUf,m`Jc3i cN4k&3 Od 𛞿|z}Mnց}`΂Y:ށaO׺9} nrJ45)jR|+I4zF9zkm;|؍ ޙg_zBسܻtXW=$?k9g/%*,)sN?goǽ/,S7;Uye>~p/gp-= 5^f W"&4qGHΈ>o?Ӆ ɸwr=o=^ﺠnߏ~fbS+^+U[lom\mZbvj9A=zژ5fz|MkjP~srP3ƯWol׷rpl 'N @8< R8p &7DMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:42  %  %%(16L727/< %1k20^{Jxk^Eg-P BcX \@Y.ʂZTR@~h\cD1AB"*jn7Dn7s}g4Os9sm !,|p~(zbC&,8kL|lwn!S-%DsfrB8-\ C!x&`,MeU_EKGS :c0-QYxӮ$AIG%Jv8DA!SPg,%LUJA )e2kY…"jO4̞i)QE8ExI(}LܒIm;. a0խֹoN#6uX?% Yo}X.׻Ϣ w ]YoʢscAОq`LsxCpܚ—wR2%Z5|bE/s#jj̍-$vo tyG;٥SW(fo_c/nxg d9M#4|j6Eǧ-s6z3U_鑼f_./)`.{F'Y%mRuxVDNrqrRx{W`إ۶rGU$o1!l ϲ#_[%|VG½hmX~PY)$[,L%O;i,W+l˓_mldy;\sZ!~խ+0~̯з*m7MSGzv`;W$&ݱvkb[A6]x{vn`軙vξD8[1&'8T0Gxomd P(g_ o29=ijTb˃ﱦUKHkǚUۺtx2_k[zO ݂^>^k7lTKOaQX7(kr"/rCO \H\ L;p[Җ [y?xW3)Xڒl{ts Ϩ|RC/kMT6N =!Fvhv>-e1cAo0VVF{`o56w .D1羫JQ:OJk3(+l F]>zbmg7G2ߵn}oI`h 䋱ci7ZW89}߻K/_ ^hA7 EWy1O*^ f734lGTXb0 e>0Ix寪 X'rؑ6*d=aՠF@|W)G"'ȁ~ B{]kcN ydd2)Hay|hLjV#U(9顨6yh {dZ֛e2o~c[XaZ#D[m$nb8Mo)3yS## t]- T-ݵ &Ǿؘ,#:a?~ qy?ƣuhASfmiO)XP'[r龪E;KmNjo<5t8550^!e=8(C.mo0ct7ԉ+wPO=&P~HLokbL#/|Y<8_1ۓ)oS3`!c>9['OM* :N.ә-rA}kNWXl9L8O+"7 4!ڒ[方SZ;zu.Z\[v}^qS+ebdKI7W0GD:@'H[L[pQb14hx{nqq薜/'*ė6ƾ!햊x|d.i\AFHo} &AF>ƾ V^'r 9:&7h;8q.-νT_2MT兇J+tM_8&>}m~/\F 22 ~খdZni+Z +64FDƛ{oΉh. p3^ y)ǎ@.LuQmgG|sAw9(3smq~v >`ف}jD;Oml:FExs9|7 tE\%#:οeL\]]J<^soйE~_o oХN?sO_/s #<,_N`ARι_⾀3~WS HtހGo/ϊnL~֑c`dgz?QOJw_w:Nc?yFJCƉk(?UmX#98b;~CoC-gE;Kс˚B&ۦ6EO_NWpپPGO>/)1u^C[ ˜Ϳ9YNY!:9e7C,ѐC?) Drpj\9.;.< 󵘓IZ}u}XL[Ꮚgb,_&]~Ԉ^ȀܝWGnq"6!Rݺ팋O!\DY7ɛQ㻎x9lO_:N{שӎz`l7 a\NN}qj1tq=tXG&+I1€r&d7'ޕ?dm9:=Yu Ac sm91 XhՆ9cImgZuXg~*2w9c)-e 19w Eіb6e=cD̉L=} e3l}~xB\#*;ݒH " =q_\'-dԠN8qZW̧oƯE/.Q>ǰ)vщ]S_hX)3:g\:6o/mE˜/}sUu:m'@o7I|,:#%OB l}h.!Ƿ w/cXpns^ݐ+6d+@^2 hIfҎ{C-#W(su$wKeP:3ݐYhGWqL8<}Gc~mi;cR: s*.cPny:w g/K,,' 3 ÑÎÄÅÐÆÀÍÈÅ Ñâèðü È.Á. Ðåøåíèå çàäà÷è ìèêðîäèñêà íà ìàêðîñôåðå è ïðèìåíåíèå åå ê ìîäåëèðîâàíèþ ýëåêòðîãåíåðèðîâàííîé õåìèëþìèíåñöåíöèè.........................................................................5 Äîáðîâîëüñêèé À.Í. Èñïîëüçîâàíèå ïàðàìåòðè÷åñêîãî ïðåäñòàâëåíèÿ ïîâåðõíîñòè äëÿ îïðåäåëåíèÿ ãåîìåòðè÷åñêèõ ïàðàìåòðîâ çàëåãàíèÿ ïîëåçíûõ èñêîïàåìûõ..................................13 Àâðóíèí Î.Ã. Îïðåäåëåíèå çàêîíà äâèæåíèÿ õèðóðãè÷åñêîãî èíñòðóìåíòà â ñèñòåìàõ ìàãíèòíîãî ñòåðåîòàêñèñà.........................18 Èâàíîâ Â.Ã., Ëîìîíîñîâ Þ.Â. Íîâûé ôîðìàò õðàíåíèÿ è ïåðåäà÷è ìóëüòèìåäèéíûõ äàííûõ.................................................24 Êóçüìåíêî Â.Ì., Íåíüêî Ë.Ô. Ñèñòåìà óïðàâëåíèÿ ýêñïåäèöèîííûìè ïðåäïðèÿòèÿìè íà îñíîâå âñòðîåííîé èìèòàöèîííîé ñèñòåìû...................................................................30 Âîñêîáîéíèê Î.Í., Èâàùåíêî Â.Â. Îá èçîìîðôèçìå ìîäåëåé êîìïàðàòîðíîé èäåíòèôèêàöèè......................................................35 Ãèáêèíà Í.Â., Ëèçãèí Â.À. Êèíåòè÷åñêèå ìîäåëè ïðîèçâîäñòâà ëåêàðñòâåííûõ ïðåïàðàòîâ íà îñíîâå ïðîöåññîâ äèôôóçèè........................................................................................42 Ðàñêèí Ë.Ã., Ñåðàÿ Î.Â., Ìèíåíêîâà Ç.Å. Êëàñòåðèçàöèÿ îáúåêòîâ íà íå÷åòêèõ ìíîæåñòâàõ........................................................49 Ãåðàñèí Ñ.Í. Óñëîâèÿ ñòàáèëèçàöèè ðàñïðåäåëåíèé ìàðêîâñêèõ öåïåé ñ ïåðåìåííûì ÷èñëîì ñîñòîÿíèé..........................................52 Åðîõèí À.Ë., Ïîäóôàëîâ Ñ.Þ. Ïîñòðîåíèå áàçû çíàíèé ñèñòåì ïîääåðæêè ïðèíÿòèÿ ðåøåíèé ïðè óïðàâëåíèè ýëåêòðîñåòÿìè.................................................................................60 Êîðòóíîâ Â.È. Äèñêðåòíûå èòåðàöèîííûå ôèëüòðû îöåíèâàíèÿ âîçìóùåíèé â äèíàìè÷åñêèõ ñèñòåìàõ.........................67 Êó÷åðåíêî Å.È. Ê âîïðîñó î íåïðîòèâîðå÷èâîñòè ïðèíèìàåìûõ ðåøåíèé â íå÷åòêèõ óñëîâèÿõ ôóíêöèîíèðîâàíèÿ îáúåêòîâ àíàëèçà............................................................................................75 Êîøåâîé Í.Ä., Êóñò Ñ.Ì. Óñòðîéñòâà äëÿ èçìåðåíèÿ ïîñòîÿííûõ òîêîâ...............................................................................................81 xKHTawgөEbB!!4c MQI+*"!ڴi&H "ma-&ik(bڇ&{<7#VȜ* Dv$ ,V9b$I;EztYNe8fxipji~$̖{ uƺtSNۻĮ:Y ~=Vb}J1IFjerA߂72#u߃+T4~+}#uZMM] 03lkQ̙2Ҭksě#W=WIyf \AVRcv)w]nvv>3RMLqxݝw6SPsp{x&(gkc@WBOubY?,|%n}n˗欻R.ЭE3殇al8f\1|wh-r kp3IoY3l;}p>{G>k|p9ma˝m @h DFG6m @hy6 0|Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:42  `Mt8 PMXM(16]2^/- fM1RZ4{HDxUU/f=\a *N\~K2K-2\j+\Ŋ+[Ε5sNͭ L )3W׮W@~)v{ys<^2Ӈ}9BY=BxF0H%D d 8㧇XE,.}!D  WKP_1s\Ws[}b?MկgU{F5T$٧ yd7sB#_IU'h=mZ"60}Osufd #::kY•Bjig>ѐ/.*o~Ue<00DםrcKH֩L#6mx?~ନZu>5+եgD>`VW<u\05gq(=8{:0ShE{PuEzƗs5#´r _VIuX~-̍ͼ>vo t}W;٣?M A!׆zCNi<y A˜6)}7|Y5*S_N>%KrĽzᗔ/uTV/A/{EJqDYo%Пchw *~:VehK薔]m& OxM Ng1t'tDۺǟ iu? ~v ?X ?+V>G]ǨEO>xs0 l~ؔ؂Ǖ%~ylK_dv幈}1%ޤ*?"}]$ъfACoNoE+SLKZ7UR䯍ÖQꃬs53~@v:O?,Z|WkQyw*onpu-K&]J(y;kz5w_6k$9 Nn"o'<ȗ=%}!V=XCzs{]YIn_SN.Ҙu.㬉VGw)R ;Y> pzs{Gf7k?ewN^-J0U8]?;Ge(|;#1UE V ز]Y~>Aߔc^1qFJ2*ؤ,34df:9W/l_v~UnVZЉ~eDP?29X`> 9(>X>{&CשlMoE$M_%#ژ7((lnddup>_xE=q2$JKȇu|_Gz7<֔X>sVxkwۺN6d|֣K[!:9@ƚqoNp㛬ZCP(n%Z÷莬R&w^{E[&v ͹G+ C[-j:ˑ=rF˳؎sWhDI1^#+AE<:5Pl'*|>U*ܮ:&b=_9F>P>Y;rptP=Yoǚ2ڹ龆 XKۀ6z ݥع~~إM1e1^Nd֬hf!{$nkҸ˧+v!,BW w8)PG漍S}P77}dzV9lfh㹻;/Nfٳ%3;C HwB&_xJ\+ ~i;V>TJOm@y ݹ1 ߁?6=܃6G [gz봃{oRhW3) nȩa6%1اmgxw8oǜov,9ԡ[ɡ'|rBPnapO  bS~ُӝ~^<@/C sڑƏycJ{g*`iN]?!yɷ^nI_H~ރNegX$@"wX+bBs^r #c1E16ldT2MwGrr(ٱ7ʒv񷊲AK~Sx^?u8RGVʼΚm|ʼJ`AKWH6d^,#4dxd\$φqR8>LZGou ߝca7p\Dі>^&{PȟyGrh 鬁rn%Oq?}$fEO'8z5!AP/9?/6IY'Kc| 6g [O#ɊO7zuz/etnT\x+fD&&NJI13G38tRo qE>xx{{Z;џ!~,I'B,_\xkizSENÃ޽AZK%ƻ@yn`:[Wv/%xxkPW/8t3~h}G)1~!Uyd_yY0M0F+Gw. Azt.*3rE:w:؛%k-;&#c}T7>'ƢX6n~._3W>}xsO.o\,]76`im0KBٜ_tśu[߲ɧquh t.:RK/%ܩխmhcNeE}2ɍ/s!7VJ"0ydnZ/윋9 vCΥ_G ?uhI0ss!U2}9_\3y8sE2&oȆm{*3ḗ.ў/;qw,L~W?) bħ(=:ޢ+xk^m8Fu.O"Vg.c/QO_gGJ_> u ]3f 3,݉SJi{cI~X\5T%ny9Pb{pWNkN6w^JioG?{!o_ A x@n:vR@Cwؓ1LnÃ/0&8цm>pCмx ObYق3iQ:E˳&VɿOrO6$ wVnUd2}>,<% yB['@x/~͘bs~xϘƃ ]uaW$cB^R_y-}ѶA0W}g9q2[sM[J:ek:!q˃N R0d蟷>։s#Y$](ڬhZ=DnLsTv(eȂ5 @ǧ9ضAh Ls-K')ɰ@4~@%3s3ψK71|<c#oPZGKVti/i4tݢ† :@~% lh[Yu<~ɸM!S6t~rc]nx{81I&{ωzs-F qqz.=\'y=mY ],.R=gq:IqBtLCn\9~}Ӌ}9O.9tJ[mp .V!.omo9IԽo'= ~Ѕ0SЊ$٣}f/?%` 755Uٶs<>9'oy,,. 4 Øóëèê Ï.Â. Ìîäèôèöèðîâàííûé ìíîãîñòóïåí÷àòûé èçìåðèòåëüíûé êîíòðîëü................................................................85 Âîëêîâ Â.Ì., Çàé÷åíêî Î.Á., Îãóé À.Â. Ñèíòåç ýêâèäèñòàíòíûõ ïðåîáðàçîâàòåëåé äëÿ ìíîãîçîíäîâûõ ìèêðîâîëíîâûõ ìóëüòèìåòðîâ..................................................................................94 Òåñëÿ Þ.Ì., Äàí÷åíêî Î.Á. Ìàòðè÷í³ ³íôîðìàö³éí³ ñèñòåìè óïðàâë³ííÿ ñêëàäíèìè íàðîäíîãîñïîäàð÷èìè ïðîåêòàìè..............100 Øàáàíîâ-Êóøíàðåíêî Þ.Ï., Øëÿõîâ Â.Â. Êîìïàðàòîðíàÿ èäåíòèôèêàöèÿ àëãåáðàè÷åñêèõ ñèñòåì........................................107 Ìàíàêîâà Í.Î., Åâäîêèìîâ À.À. Ìíîãîýêñòðåìàëüíàÿ òåñòîâàÿ ôóíêöèÿ äëÿ îöåíêè ýôôåêòèâíîñòè ìåòîäîâ áåçóñëîâíîé îïòèìèçàöèè.................................................................................124 Íèêîëàåíêî Â.Ï., ×åðêàñîâà Å.Å. Âëèÿíèå ðàçâèòèÿ Èíòåðíåò íà äåÿòåëüíîñòü ñïåöñëóæá ...........................................................131 Áåëîâà Í.Â., Äîëæåíêîâà Ò.Ã. Ïðîöåäóðà íåîðäèíàðíîé êîììóòàöèè äëÿ èñïîëíèòåëüíîãî ñëîÿ L-ñåòè Ïåòðè......................................135 Õàõàíîâ Â.È., Àáó Çàíóíåõ È.Ì. Õàëèëü, Åãîðîâ À.À. Áóëåâà ôîðìà ãðàôîâûõ ìîäåëåé äëÿ îïèñàíèÿ öèôðîâûõ ñèñòåì è ñåòåé.........142 Íåâëþäîâ È.Ø., Òó÷èí Î.Â., Àëü Ìîõàäìåõ Çàôåð. Ðàçðàáîòêà àëãîðèòìà ðàáîòû êîììóòàòîðà äàò÷èêîâ ïåðâè÷íîé èíôîðìàöèè ñèñòåìû óïðàâëåíèÿ áåçîïàñíîñòüþ îáúåêòà.................................148 Áîæèíñüêèé I².À., Òêà÷åíêî Â.Ï. Äî ïèòàííÿ ïîáóäîâè àâòîìàòèçîâàíî¿ ñèñòåìè êåðóâàííÿ îá ’ ºêòàìè ãàçîïîñòà÷àííÿ îáëàñò³............................................................................................155 Æåëåáîâñêèé Ȳ.²È., Öîêóðåíêî Ì.À. 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Îïèñûâàåìûé â äàííîé ïóáëèêàöèè ïîäõîä, ïðåäëîæåííûé Ñâèðü è Ãîëîâåíêî â [1], îñíîâàí íà çàìåíå ïåðåìåí- íûõ: âìåñòî òðàäèöèîííûõ öèëèíäðè÷åñêèõ êîîðäèíàò ( r, z ) ïðåäëàãà- åòñÿ ðåøàòü äàííóþ çàäà÷ó â ñôåðè÷åñêèõ êîîðäèíàòàõ ( r ,  ). Êàê ïîêàçàíî íà ðèñóíêå, ìàêðîñôåðà ïðåäñòàâëÿåò ñîáîé èçîëÿòîð, à ìèê- ðîäèñê – ýëåêòðîä íà ïîâåðõíîñòè ñôåðû. Êîãäà ñîîòíîøåíèå ìåæäó ðàäèóñàìè ñôåðû è ìèêðîäèñêà sph d r r  , ìîæíî ïðåäïîëîæèòü, ÷òî ïîâåðõíîñòü ìèêðîäèñêà ïî÷òè ïëîñêàÿ. Ýòîò ôàêò ïîçâîëÿåò ñðàâíèâàòü ïîëó÷àåìûå ðåçóëüòàòû (÷èñëåííûå è àíàëèòè÷åñêèå) ñ òðàäèöèîííûìè ðåøåíèÿìè äëÿ ìèêðîäèñêà [2-6]. xOHTQƿf$s@ %͙ZQmjBj"J"ME fe_DJw3qdFZ߹|;s[$-KJ[WI ZkRdYOK`3]c--NG*햂!00Eeja5԰os"۞l'9a%F-pߘVRqmw\:AU).M].UY%[SidߡZtBګzZZ<7WCA$ѱ*Bt%6&ՑN )"tgslkr6jޱ{=C\T5iNSjuMR+'B+G[jƧUxsjxs?ŸTYa?3q9<œBqЋU wp*x7?9*!G_X ;VAA .{|T>_b8+ea;uݠ-p(,U%sG=o@og2}|F;z40:j 6s9FNx:m=9k<+o5?.A2}awg,Lyƞۃ\097fu;ƍk67>yruq qll/6oL6חk}.yu^{ʫڹq5ŏ|W+-@ ՎAMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:42   _drz(16j2/1Tr5{x{]UOTBX) $884ҥM716)>e'nTdif&mb1:bXTBo=n:ֽTr`g^{ku=Ւ$ɟ+3"I—G'PA8IFސ$s/:/IZ'ɚI),S&ϕڒѩ/ym#yɟ$7$%O_ RםN+[I*G]_<8<=A(3I1 (p4sTS1˫㔞0WD\R]bM_G(0ޤ-OS~XfbKHvrC.u)%IImWD=+Kƌ:$gZKd̚'[4|l?& ? 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Äàííûé ìåòîä ïîçâîëÿåò èññëåäîâàòü, êðîìå ìèêðîäèñêà, òàêæå äâóõìåðíóþ ïîëóñôåðó è ñôåðó ïóòåì èçìåíåíèÿ ãåîìåòðè÷åñêèõ ïàðà- ìåòðîâ (ðàäèóñîâ ñôåðû è ìèêðîäèñêà). Ìû èññëåäîâàëè äâóõìåðíóþ ñôåðó íîâûì ìåòîäîì è ñðàâíèâàëè ñ íàøèìè ïðåæíèìè ðåøåíèÿìè äëÿ ñôåðû [10]. Moäåëü Ðàññìîòðèì ÝÕË, êîòîðàÿ âîçíèêàåò â ïðîöåññå ðåêîìáèíàöèè ýëåêòðîãåíåðèðîâàííûõ ÷àñòèö ïðîòèâîïîëîæíîãî çíàêà è, êàê ñëåä- ñòâèå, ïîñëåäîâàòåëüíûõ ðåàêöèé ïåðåíîñà ýëåêòðîíà [7], à òàêæå äèôôóçèîííî-êîíòðîëèðóåìûé ìåõàíèçì ïåðåíîñà âåùåñòâà-ëþìèíî- ôîðà â ÝÕË ÿ÷åéêå ñ ìàêðîñôåðîé. Ìèêðîäèñê ïîëÿðèçóþò áèïîëÿð- íûìè ïåðèîäè÷åñêèìè èìïóëüñàìè íàïðÿæåíèÿ, ñ àìïëèòóäàìè, äîñòà- òî÷íûìè äëÿ îáðàçîâàíèÿ îêèñëåííûõ è âîññòàíîâëåííûõ ôîðì îðãà- íîëþìèíîôîðà, ÷òî ñîîòâåòñòâóåò àíîäíûì è êàòîäíûì ôàçàì ýëåêòðî- ëèçà. Îáëàñòü âû÷èñëåíèÿ (ñì. ðèñóíîê) ñëåäóþùàÿ: e sph max sph T D 6 r r r r     ; sph e d max r T D 6 r 0       , ãäå e T – âðåìÿ ýëåêòðîëèçà; D – êîýôôèöèåíò äèôôóçèè (äëÿ âñåõ ÷àñòèö ïðèíÿò ðàâíûì); d r – ðàäèóñ äèñêà; sph r – ðàäèóñ ñôåðû. Àíîäíàÿ ôàçà      A e A - g Óðàâíåíèå äèôôóçèîííîãî ìàññîïåðåíîñà â ñôåðè÷åñêèõ êîîðäèíà- òàõ äëÿ äàííîé ðåàêöèè âûãëÿäèò òàê:                               c tg r 1 c r 1 r c r 2 r c D t c 2 2 2 2 2 2 , (1) 0 g c c c    , (2) çäåñü  c è g c – êîíöåíòðàöèè ÷àñòèö  A è g A ñîîòâåòñòâåííî; 0 c – íà÷àëüíàÿ êîíöåíòðàöèÿ ðàáî÷åãî âåùåñòâà. 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Ïîñëåäóþùèå àíîäíûå è êàòîäíûå ôàçû ñîîòâåòñòâóþò óðàâíåíèÿì (4)-(7) ñ ãðàíè÷íûìè óñëîâèÿìè, êîòîðûå îòðàæàþò ïåðèîäè÷íîñòü ïðîöåññîâ. Ìãíîâåííûé òîê íàõîäèëè èç ñëåäóþùåãî óðàâíåíèÿ:                       d 0 sph r r 2 sph F d sin r c r c r 2 nFD ) t ( i , (9) ãäå F – êîíñòàíòà Ôàðàäåÿ. Óðàâíåíèå ìãíîâåííîé èíòåíñèâíîñòè ÝÕË èìååò âèä:              d dr sin r t , , r c k N 2 t I 2 max 0 max R sph R * ECL f A ECL , (10) çäåñü ECL  – êâàíòîâàÿ ýôôåêòèâíîñòü ÝÕË; A N – ÷èñëî Àâîãàäðî. ×èñëåííîå ðåøåíèå Ââåäåì ñëåäóþùèå áåçðàçìåðíûå ïåðåìåííûå: d r r R  ; e T t T  ; 0 c c C    ; 0 c c C    ; 0 * * c c C  ; 0 g g c c C  . (11) Ïîñëå ïðîèçâåäåííûõ çàìåí ïåðåìåííûõ àíîäíàÿ ôàçà îïèñûâàåòñÿ óðàâíåíèåì                               C tg R 1 C R 1 R C R 2 R C r T D T C 2 2 2 2 2 2 2 d e (12) ñ íà÷àëüíûìè è ãðàíè÷íûìè óñëîâèÿìè: 0 T  , max sph R R R   , max 0     , 0 ) T , , R ( C    , 1 T 0    , sph R R  , d 0     , 1 C   , max d      , 0 R C sph R R      , (13) a1x pTg݅B&vZ ) F(T1 vlqLj-2ZQJ2NFZ[IM)(U!#Lqwv57 ye1>/"YD@xD6=DOfOB]b:"~;埜e_d83&ώ # %ƙp|J%[X>`eݒ!/YJ";@/Udrɑ*첢RFI2H@Yr}2X wgb֝YukY7.}bΐ)u|Z(6Uq.l{yy22:SC2S({8SBy[`m`OX :G vV_LtQ)ZJ$]3[c/gL^گaDyH @&ϲg!>+ j??Em/2ew/~`Pm969vm>-,p{i &wVs5U ywV- t~'hLb*]>afȳwR3Vmx1tO_sFl>W)bKkجvIQnKwϸ4{w~5䪵%/w\ 6AD9W}6k>e_-ٱ/ы:9i%Rb*7Am\OvvC_Fw1?@W$̫):.>Wk{*EۮF՟K"(nE;3wK 瑗UFbǝyUs@.*{WYiwebZ zǴNu?sXih~.wsrq;+՝ys91gNuk}V={t5gCbv@"$"@"](]wQ[0Ww =R2F>}]>_7퓗6>:Nzli}09zN'2n-'ouMIgn9{Nd4zI#@܄þX*; 託޲׎K9y#ŲhrML{ J{&{P6e|9Z*6|]p | Vօ+(09`g|#7éMs<ǑʡwƑd:׆IO~Ek]oSh@f@//#K\z T-sQ7a.=q C\ޑʥZrtz;o~#sZ ^#ׯ%o7coҙ;~o n*+ܮSIf>(ﯾ9c7ߛYiⓈ@"$".g&";lMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:43  Jt xC:B(162"/ P1} n:{~x U+!b 1&D` !3H !pګE ^r|NAy \du\>CA<߿NJ:uI%wծU^UgXE&7@<셤'뗏k4vtˢhsje/[fZ4q Z;,\{?0ۋ9/F0B\Ga;#޽ua7wGܑ;(|>{G JxS]ёėr^5mώY7y,Rm]q|M{5m%1kSU$vޛtQ|~ > ^CǓQG\Qw*&ڪc.Gv#Ԓ#_OHFdڧ2kZr9rI{M. yryR`zKU.LxtuE,T;%:7yɷbxv>Fr H.K.l%+o㕗ˢ^dC噮[WxkXLÎ%\Ňƽ4yLR:_M9JW}d$:vu&$ź_4:rn*?ԖUG(CƢ";؍_K'WYeXʼcÆ<w[]nqݪO|!.^ikFObwkmSќ3.?c"fjY7?yϴF.h8Pͫ5Z^_^=FE϶Җ>]KF˰Bt(⓹{()pFDEgo7-?,&L$%#ﴢcɊ κ4;!,LyI#n&/돁Ko0x8 ŴzU$ǼR->j\zggwxLɣSK(LuxX>zAt6J5]֒7Ʋe8y's?~Zw!5m7*sٱ|_M P9o~mp.O~i!6KsT#mۙ1Gg|Uҏv|OF$6|xPa#{a2G`)9z|U_Ƹls=%Ig^ ϼ.+ A2 >0\l;AeKF(B-ܳZ|̧\ϫ\K7#yJaQ䱎v>pO  =X*CH%oyU^h<}\}׵{Ԙ1ixT=ۆg!{FJfz ;:da,y##"NQ)SgQgzNc왮۞]1{=[9iΞYٳWB n|L!Mg0@#&hLuj4mO)ƪpk٤}]M96v9 M0Url/ӄ 6)ٳ9n9>sxcM~͓$vDO5E~Kk茶}-~^1P|?ȫ/P.|8>K4=ҵcym*c~z=ي{c7\3zvSml|]BMa2V'㡳w)*kNx{Ct:SKu&?љp #nDN T/g*I_&'''qާ://'r輜#drwv,y'B>l?R_$[1fhKȮBVOX C{_ýMGA+թwd@ZR{BTekגy(osILVkOu8Fe[nn: !\!h'3>p.No">A_GMi|,NhPƎZ~?Kuhmׇ̟p{Ytg-鹊/Yw+R% َ"!EB"o.=k+[6ݓJE$장ݻgBvD;QELc:U4?zlgp &;2(>xm?x//Kn= :qoWʯWG_{YgymnĞYE-G۳ Şqᗟk|5?r?_ /_׃cFXqx旞=7~麞G1@ײeV+oub]}(J7q5iS !q#q:hG3 t`}':P{dޢ[\_G־:eփ?DYo_ǚ=#xe,HOӣOt\ym.۞^س7Ly{~g]1{cvƮqD#O/"xwLv={|2T] = `OlMZ֏uyۻ8oxE'S}SƯ){;\XwǘT2iλ W#2x!:^ثoo )?YsL՟Znd[ȏ?ex/k~nF64UO u<#Y6}m}``,f'W.:J:?|8\=|{c_EYjc6/)xw B ^VBþgk$\79o}s>Ags! {wa3њYlw+FO9OPلS05iPcyv1yu@<8G78{ 4wD{'hoo)NX$[f;A3F?O5]#>9$BftACtsD >V?J~6e y/wߦaeʯoqqDK גO5._N7} =";ST?ÀE0/YwGR~%ly'Uա>O?^Q]|L=kƄ_waxq\pJ sթ # sFP~n&d m.fFf6Gj}L69 WK7 i NߐZ5 4BxMiNݳw 27um[213 GPm?DM__"x0kA5߆;%{xNv!{/x-߼xctG޾])\)N"c-*6{xO E'UYY_xYt@'ۥ6k_ˊ+5=xhK .x-WU5 5K3> ^[ٲv:$O!6 Sg5 -&)mTGɫ^4>k7` k臕!e|ĺ99vᵛh^ێ6-@xm`kkoz 1|cΊd]Q-C}υ!:y t{/x-߼xcM5,^S^Ksf@3=_w%WИ,o<_B~|@aNa9~BvZ*5ᛍkmݲuF}g|^&|-ײ㵃Akc dMd\ujOQ I(?w@k'&ќC1Cj[+)#w7]{m]sW=QwUD#]~GϏ^;Z;~w~#VNZ_ߨСfyY>+FN0b_~b"q_iơ߯Pw$uyo%_"蝈E 2)[׽H?5$ QOJr&z Q%z9B71IF_k CZ}UOn귐\SzJB E}3}K'YZKƞܻox(|iuqoGJg}262a??OG_u0G$6!O"|_31@ɵKs}exv0ϵ\k}%R"t~t΃mn/1h%tz/~1&B~/tsPEހQE~ọ3d5yΰm]a:|CZto:eߟ2o8VߋPt._~/8b. mty7VM5=3(PlNH^U$3i!:_v芴ul}[\NHK_]r'P~.o"=rM/K7|9%%j0?Ws~>k4{KSޒtk'8',G=!4rm ӝ^/Lw;]N0tkem`te [;v!Pw}.,D7wH_./BpW:nsڱ+t|vS,C 7յQ*t|ևo+[ `~rzf>E^~齓v~ ̥JҏOC锢:X׭z9s>ӏPmֶ{6 H2=0nTj音m[eD.|tyZr2nx,)m|χ6?ȴW|q&^NrS!FƙSo!!'頞̯i쵍q&Cw]cWC,}`>f;4}qo2%sܙ/Y2m㚡Sst1M`t骾7Ow偛t5uzz(timg]}}"(Wx<f|_tYk.t c}o'w(e{d|7}ӏ'>fc|o驟MW{ρWo=#L}*O0G[c"k*s"tfP`"t#<:I\wPL6㫷q_g[7{ VfS[si n-y: ejEd|fFPZtާ>'b[Otz~W+Pty tZ;O>]CN_<6 ͗glN?2)lZ芴;\}OVmf)>]ϗ-Z芔[gz"7kzY>ƾmۼ^?f՝K;lP)kr7ѝy@1_o09ܿӵy^Oc4~⩏>wMY&?ɰM{VǀBt\~ዔۉO7/5|^ߎg|%.TKiw 0%RWQw0i#/D7w%ytyP.Fc40*ɧ;~db7[BE|>y{s>.,OWkg{-L7эlӵOҖȥtΏ+E.O󥌼 R$eӊMf)W"Mn bl~~ բlXG>* t&Gt@R}i~NWNm2O!jbɕtuWOR|р(VbG2*__Dn<]\qtԧq#ԧ{Ś>o҇9b}kaOzoݴ/'ӽ*qƧ@ƧVrmtinqHCt>]? 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Ïîëó÷åííûå âû- ÷èñëåíèÿ òàêæå ñâèäåòåëüñòâóþò î õîðîøåé ðàáîòå ïðåäëîæåííîãî ïîäõîäà è ïðåêðàñíîé ñîãëàñîâàííîñòè ðåçóëüòàòîâ âû÷èñëåíèé ìèêðî- äèñêà â òðàäèöèîííûõ êîîðäèíàòàõ ñ ðåçóëüòàòàìè, ïîëó÷åííûìè â ïðîöåññå ìîäåëèðîâàíèÿ ìèêðîäèñêà â ñôåðè÷åñêèõ êîîðäèíàòàõ. Òàáë. 2 äåìîíñòðèðóåò ñðàâíåíèå äâóõ ïîäõîäîâ ÷èñëåííîãî ðåøå- íèÿ ìèêðîäèñêà: â öèëèíäðè÷åñêèõ [3] è ñôåðè÷åñêèõ êîîðäèíàòàõ.  îáîèõ ïîäõîäàõ äëÿ ðåøåíèÿ çàäà÷è èñïîëüçîâàëàñü ðàâíîìåðíàÿ ñåòêà ïî ïðîñòðàíñòâåííûì êîîðäèíàòàì è ïðèìåíÿëñÿ ìåòîä ïåðåìåííûõ Сетка Гэвэган [3] Сходи- мость, % Данная работа Сходи- мость, %  t=1,1025x10 – 3 с 29 x 29 3,494 7,27 3,7105 1,526 250 57 x 57 3,501 7,09 3,7194 1,290 250 113 x 113 3,555 5,65 3,7285 1,048 100 225 x 225 3,611 4,17 3,731 0,982 100 449 x 449 3,656 2,97 3,761 0,186 100 t=1,48225x10 – 2 с 77 x 77 1,425 15,78 1,7131 1,247 100 153 x 153 1,498 11,47 1,7105 0,934 50 305 x 305 1,552 8,27 1,6870 0,296 50 Òàáëèöà 2 Ñðàâíåíèå äâóõ ïîäõîäîâ: ìîäåëèðîâàíèå ìèêðîäèñêà â öèëèíäðè÷åñêèõ êîîðäèíàòàõ [3] è â ñôåðè÷åñêèõ êîîðäèíàòàõ (äàííàÿ ðàáîòà) , Сетка Значение потока Сходимость %  t = 1,1025 x 10 – 3 c 29 x 29 3,7105 1,526 250 57 x 57 3,7194 1,290 250 113 x 113 3,7285 1,048 100 225 x 225 3,731 0,982 100 449 x 449 3,761 0,186 100 t = 1,48225 x 10 – 2 c 77 x 77 1,7131 1,247 100 153 x 153 1,7105 0,934 50 305 x 305 1,6870 0,296 50 Òàáëèöà 1 Ñõîäèìîñòü âû÷èñëåííûõ ðåçóëüòàòîâ â ñðàâíåíèè ñ àíàëèòè÷åñêèìè ðåøåíèÿìè [2] äëÿ äâóõ âðåìåííûõ òî÷åê ýëåêòðîëèçà 3xX]lUfenYB[-&6Hu-)]HMTP}4fKx,S0( hRKbτ1! ?6 3ӎߙ+qfxIN=9sΝs1@hĀq$.E]CD'dh-\8^k-bbû^|'î0~юư{=1^|Nc`־4NNh 1|,d?HmH y1Z˥rUY+L;|mu=]i݊IĹ=~^x-SYT!Zdى3n^z%߰W9*y5%z H j0D"ů[ ^#B9`>ןȟ!&r#F/uGȿ6{\GY0Tqmcl^Hluh O ˙vs֍$y=f'Q^J.ߐ/01]<ԜJ$F%d[N/m> W+V>4Ss*jjvSssN{g8';d?y!SĖX6oetTl'Iڲ(N!v?l>* 2E6Mbp×lBo*)w5I( =,\*+ժ{"'C~*ΰY%[sIA>ߒz-a[RSQ){Jǔڤ:5 ̏4r2A=ujz %Th 6GaK=뉴7i}11:x: F̺ZӔ Oum*+ 4k : l (>ߔnRx WK8~R q))Aԓ5%a}vBgmhJ MsӗyC_CoBExӔEۡpOS9O߿RB.m;ް6WpZqxQEqzsaV:;rT{>I~N-af8@`t1}`Z'a}Y6b7-!/2&E>'f\VpXVg1^`z*ܙuE ^6u3wїs)_O7(;5r%YʥZ0O%~s`z'(톺Bkx能/1^z,1n`(fb^^5x!2Նʚ7-YǏ$k0֋7K `Zsdasba!QGS{+]H.YƲNk6}(pJCGsd:S5H闘ca(|>7 ~S I{,2\Fܡ0)o+~Ef ^nP!mW/TET~*5S>I9 Hx^PݤLo|0kX17b Qch.OϺPX)zը>3 쏟*VQՖ*;VeEMuwH^ԦxAҘmCfG%C} u:(WɴL"ϕDmPV;I[L*$e֚@Ӿ>9GCOblLtleefUZc^v z{-@h˚ܴ(M}Rn>; ~hC_1ҔӇu(GCz/WPрVebÃ?EkR:P#C8ٍ0Y4 >0AcBE!qy:>4 ~&6O1p m7}?#{懊o]!ap[Z#>Pym9Ǽq//$kNAA+fj a˷נqE:̌zrv_+JAcHSgү4ETmԖmY@.̯k\aY/apuOb\wq1/E̯Aכ#~fOd+nx65ųnoRįy8a>b\f\b~S(k(zʯ/ iN+ۭ2)׽j`b)WXh6e>d'Fu@{@?~Fvq-R1 qʫiMG7"Tl6>`6".cmZN,cG>M|ϸC.`팴Myq0aOBQl?tćgjEpXL[uT%xY6 ?H٘"v~6W_?S\3_|!ޖW;d;x0 GO*.".v*"4i>ʯl=zk?زqvp<~!*5yܸ+Uc _}6Zb~}C<9~k4_]hcP_v"__wn`ۋ#yf>*ac+Wj$v0CVP{H|J1wmK竼L$x`LcV} J:z4X/Dwfex!J+z~?\YUa3{Ȱͮ7gpe;p<[aЂ?]n~8Ojw,GA.c77R[FnN(bՙ_K9gp0gfˈG_Ӯ"Y_C񪺾2y %}SF'/3WL≠dq1aڱ_ zfkIz+ Myf+8o_Q(j>QxQQ }Q۾zXeoU(Eɾi,W}#TT¿ȾU#ϓ{z \Gq5/>Zn2웲>Y!{Ʈn5&kw{e%T.Xd(t[u|9~徶? ~XZ[>9<2k/O0+WlѦС-K<Μï71.ٯ%.ϛhW/b}F`["ee0{=C*}WqU/=ߑyKʁ6z0<»O*J Doy~ekwp3]-ӿwֵv}}&q[e顖#YS1,=x꾯2D㩪0T.J;܏'<2 d q7sc*c OX9"~ϳE[`nTM{/u̗qZe4=GOKReOTiذC==PAſPLϻ>q*̶i9 {QXrX/\gmSLٟS`K禷y$7~9F`gG@oCqv寙_#xM5֞LCyN䥃?WlO۞s|wtq*?tY_X8&g8зB"GNI J:~[]N`7<8o7P>Twm38l/tu "Ј_vmR>8PE2s|c>Z q1~7Qk.H\6*υ:T4Nm?['}9!(0GlUuBUi7Ico-` o*Wi.= ^7v,I$r99'!ՙGٍ=}#WQ=UaB̯ZU}?xَ<m Gxd~) n |޸`bz&uMxDG{ޱ1p@PԲVVP|M49k9ίm6S8jL0_+σ:!Y%첡'F~N2=\nd0dWOMvbdٟˋ˞ M_>tgD5mGU}+۴~اCl~}_a,>ߔ>3|_޿eGwq#eX_XSO.U=}'4]I'!CCݫTB==7KztbE[%/ߠ1/Aq/]n}yp /o܌rKy,o#S6}y~{D˭/;ᕪ#il׫{Wth&`/ G%%= bGU_.O̻jGTd4_ w|?ޗyfU6ߛ_+穼enj #;Zem*kW/ߓ^»$雬 wUީ/HM[q%W@J=4%oXJ/GO}{k[nwJC|v~bwv o4:Á<>.ڱ8#>>;p7 /x5xw*;^Erje_ǬJۮy5e휷Vhcpڤo5Ukޜ~L ߘin1gO Gi`CLꀧk?0)7Ol?ZkMLq1u(ܨ&ҿUM\%cdSNJ1338۶U4{sҸ1ޫ-rFV-&I~u_6x*% l: ~ɮncW7*'翻^Uy٢!OVwiwl/ѾYx]jcNU|m6gvpv~-f i3X&kZnS9CGUhz eJ9YbLW$յi_=}::N=Mcҕ,< PM)˭ߡ>tWmlVi>zcuưlxl5 k`}f`{;˷ hg5z{E/n zZ-x_獛q FX~1+ė*H>Yk?gff&%o1F˩vS=ç|IuƁ8ycqǪ$ٚˈyxσUl=&v~L&ǿq>xM砸o1ײ^C~8ZU8T<8ޞƙm7kwR~l=x~Nƨ{k(BrA{+%6Ϛ[^y*;VEoSݝ)1"|)/rN''X/)0ݪGx1@uxfr~Ⱥ`fXOi>Y4{iM7;X~hת6}< y x`K۸ྉ'm)u ݤXE/lʊxv6_a7Tr׊ osoDr忬B/LtG@SlXĦybxKKGAcBr}zu; ;//6#睜KɝPQ/bGa kf5miCA O,M.ָC_Ӎߓ{{rNj=o-V 1gT[M2pϽIYQ9/:猏M*̢@&}+IcS {̬Zƙ+t_kmI}?z[n0F[s9ur5 yp}HeN#M2s'_z=},M7zc` [ k/kP綳%~@<_DĿC j[ O*PwhyƺjWPu~T%7n|+@ijy.h>vP`7der0IŴ!9(Y 9i#}}WB6wGy34Z_E7gj[zUQ{ju_:kJ72|Mu <g}E[|_;jߓ:EcaNKǩַh& l^>nIe?Ŝlgڒ eSuiYUSwTք*b:T%d|˲ڮbI|+R2 ;nL.{R.Crkc2"ܕЫkdGQ‘"=AHJSړJ7zW ':݂[ҼY{?мY{5SѲwY97w#p{uJ '+/7[T*W׹3sE?Rw;'J :c~x^RYOQm'_&R<ਥsm)(=xV*yB{Ze,8KI)05KU#pr W,CqUu,e1?'zYvZ}wsfLD Pi|}Ɖo3W ߶]FG^%O<l*(>oяԷ-_7gWE1UQx 별΃k wCvCwԣ:]w}u OyzdxZ/7|d|g,?kE|:}Ϻl-0T0>/Ϡ#|c{&|x<ɻuGtO`Wƒݟҳd!&\M_| ޿u`>}HazE&@$qs 6|N&)z6[t^֜ыReJb\$S#d K뼡EE{2e{/g{xͯTG ӊi[׼2O|:S:? 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Ïîëó÷åííûå ðåøåíèÿ ñðàâíèâàëèñü ñ àíàëèòè÷åñêèìè ðåøåíèÿìè [2] äëÿ äâóõ âðåìåííûõ òî÷åê. Ðåçóëüòàòû, ïîëó÷åííûå â ñôåðè÷åñêèõ êîîðäèíàòàõ (äàííàÿ ðàáîòà), äàëè ãîðàçäî ëó÷øóþ ñõîäè- ìîñòü, ÷åì ðåøåíèÿ, ïîëó÷åííûå Ãýâýãåíîì [3]. Îäíàêî è íàøè âû÷èñ- ëåíèÿ, è ðåçóëüòàòû, ïîëó÷åííûå Ãýâýãåíîì, äàëè íå ñòîëü õîðîøóþ òî÷íîñòü, êîòîðóþ ìîæíî ïîëó÷èòü ïðè èñïîëüçîâàíèè íåðàâíîìåðíîé ñåòêè ïî ïðîñòðàíñòâåííûì êîîðäèíàòàì. Îïèñàííûé ïîäõîä ïîçâîëÿåò òàêæå ÷èñëåííî ìîäåëèðîâàòü ïîëó- ñôåðó è ñôåðó ïóòåì ïðîñòîãî çàäàíèÿ íåîáõîäèìûõ ãåîìåòðè÷åñêèõ ïàðàìåòðîâ.  ïðîöåññå ñðàâíåíèÿ ðåçóëüòàòîâ äàííîãî ïîäõîäà ñ ðå- çóëüòàòàìè äëÿ ñôåðû [10] áûëà ïîëó÷åíà îøèáêà ñõîäèìîñòè 0,128 % äëÿ èíòåíñèâíîñòè ÝÕË ïðè îäèíàêîâûõ ïàðàìåòðàõ ìîäåëèðîâàíèÿ. Òàáë. 3 ïîêàçûâàåò íåêîòîðûå çíà÷åíèÿ òîêîâ ýëåêòðîëèçà è èíòåí- ñèâíîñòè ÝÕË, âû÷èñëåííûå ðàçíûìè ïîäõîäàìè: â çàäà÷å – ìèêðî- äèñê íà ñôåðå, à òàêæå äëÿ îäíîìåðíîé ìèêðîñôåðû. Ïîäõîäû ñðàâíè- âàëèñü ïðè îäèíàêîâûõ ïàðàìåòðàõ: 3 6 0 моль/cм 10 c   ; /с cм 10 D 2 5   ; мкм 991 , 21 r d  ; мкм 7 r sph  ; t = 10 –5 c; Nt = 2000; bi k = 10 10 ñì 3 /ìîëü ñ; f k = 10 7 ñ -1 ; fl  = 0,9; ECL  = 0,01; n = 1. Ðàñõîæäåíèå â ðåçóëüòàòàõ îáóñëîâëåíî òåì, ÷òî ÷èñëåííî ðåøàþòñÿ îäíîìåðíàÿ è äâóìåðíàÿ çàäà÷è. Îøèáêà ñõîäèìîñòè óìåíüøàåòñÿ ïðè óâåëè÷åíèè êîëè÷åñòâà óçëîâ ñåòêè, ÷òî âèäíî ïðè ñðàâíåíèè ðåçóëüòà- òîâ äëÿ ñåòîê   N Nr =400õ400 (äâóìåðíàÿ ñôåðà) è Nr = 400 (îäíî- ìåðíàÿ ñôåðà). Âûâîäû Ïðåäëîæåííûé ïîäõîä ê ðåøåíèþ ìèêðîäèñêà â ñôåðè÷åñêèõ êîîð- äèíàòàõ ïîçâîëÿåò ïîëó÷àòü õîðîøî ñðàâíèìûå ðåçóëüòàòû ñ òðàäèöè- îííûìè ìåòîäàìè è èçáåãàòü êðàåâûõ ýôôåêòîâ, êîòîðûå âûçûâàþò îøèáêè ðåøåíèé íà ãðàíèöàõ ìèêðîäèñêà. Îïèñàííàÿ èäåÿ – ìîäåëè- Микродиск на сфере Микросфера Сетка   N Nr A ), t ( i  с / фотон 10 , I 8 ECL Сетка Nr A ), t ( i  с / фотон 10 , I 8 ECL 40 x 40 34,186 4,2887 40 34,256 4,2824 75 x 75 34,261 4,2953 75 34,321 4,2946 100 x 100 34,33 4,2975 100 34.336 4,2967 200 x 200 34,344 4,2993 200 34,356 4,2987 400 x 400 34,36 4,3004 400 34,365 4,2992 Òàáëèöà 3 Ñðàâíåíèå ÷èñëåííûõ ðåçóëüòàòîâ, ïîëó÷åííûõ äëÿ ñôåðû â ïðîöåññå âû÷èñëåíèÿ äâóõìåðíîé çàäà÷è – ìèêðîäèñê íà ñôåðå (äàííàÿ ðàáîòà) è îäíîìåðíîé ñôåðû [10] #x{lSeƟSl6!cBDCKe $ oQ@  LQ# /H$x $"A2%HiZ:I<Ӟk@zH*LK0@W4BbYX]Sld4b. Tg- |qsH2Մd%Ge3 ݓUf oޮT"W1-Iv%ZZD^N^}5U3fff:ML3]_?kb^'(W@KTE櫽Tm-|5Ղp"b^V9][\e+OMtӇ"ocM\#5"r~z[zuˊ(,憇=X˟E~7Ba:JjT0IkBH]w-P-#=Ց8{p^g4EO5Pz~ \{}z)xD:dSrjC7g_U+t.:8c__8m1WZzNuB[bX:蠫7g7-+.fkBti-56ScCrľ{hF ְ ٷ|>_?[Y_Sr>o{BR+ngm[oq6ȉy& X-i8:5v߯x5|3tGgdL.zsׄwWS@WPwz5oD 'ߐ|O~z~ ? 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KU}>z:zS}u稫D# 9gOMP1CՓAl|q\UH~wFwԷ~{hoqb>q[J`Wם¬Mu°qڼٵc67Q^zg.=BV=<ϣ7߷o~׾j6F[{1 2naj2Ơ2A}t^ htuϛwye ?h^riE Dcǻ8REotm1:OXn?>k0WA>i~yIFi]>Ժ:mdM"Oͮ=/ w w]mW- W; #Yx4ADH֤D}₤?DP=^#1Ev뾾SuETu:C>b/k.1GRhԇ^/L{".@>|,lppM|M^$maViخ{LWYz.S ?U:oR$=xua-SπzG=dp~kdѽ7IumѸ}x[aAz?$4z.`L`>?kY?hr/]k>)}<8j=<"퇄sC{DgcqzrOC7ĸGVw=t||y~`.dЗ"{2b1\r9g Y9ߧ熑:.E1G10=303u]/`c~kϪݯb`S42w>}n}7@w3$]p׻zZ$nKoN,ݮ9A)^8R,UsT*6%>^Cգ NUθ9NM܈?%KIsV_FJΕy, gq@'u3ǾK>J(YnK]ʮCr,,>| |rk_*hP*tl7`^lgt>̮Izu~U3^U|MSNbřyvf;1?S7-vl.7!u-u6=Rt9S.>iyŧԡ<k{ |-[M <)匟s՗du *'ή̢+>C/;/ſlOo{D;6Y 'm_A7y}lmmgç^ٮïsNQLiRї#A>r >YerEuVsq'zhUE1㽑>}&}c!ާDVgxcIމ@#<_fgQW],F݋M4n#99}*:0'18:2 =X.:lwdd0g}>k}1uhLi|UՂ&T#WvzƜ(Ԯld`D'l^;v5evc21@CÇ:2(F l[ɤ/^]-L!<*2u׊G$ oP~cWVN<6 m9mB[br[iO1Azc{a#c?mV)~2K۰݊q~]To;3M>RW[)(9k/:`r=Ai{`C(/&#׶+u.=` .2}A ldӦ¯~kn_7lo򽵁_?=q-H^{(ozuqUe?`گ6@_tYùny>fSm Əv/˳\hw(ckF!—'IAANUCrK mv଻in&ۿVYɴn ^Q[C6@_blX-<[ 6 7QԃoȦy}#/'\cȡL}kQ} `/d^$f}^ߔdݧ&t;մu ÿ=M1ǯMA4kAh0|"6E|>N} 4סq=#l_kk\-\=_;6Wdd$ݶyZI${2]3Kq@-:|^aH_<%l }a lrm/`v۞q#<04ˀg>46z,3=&z9u*O.[Ѿʯ+/stgfN{{ }b0gQ\,UT\Ku[{J=,, 13 ðîâàíèå ìèêðîäèñêà íà áîëüøîé ñôåðå – äàåò âîçìîæíîñòü èñïîëüçî- âàòü äîñòîèíñòâà äàííîãî ïîäõîäà òàêæå äëÿ èññëåäîâàíèÿ ïîëóñôåðû è ñôåðû ïóòåì ïðîñòîãî èçìåíåíèÿ ðàäèóñîâ ñôåðû è ìèêðîäèñêà. Ñïèñîê ëèòåðàòóðû: 1. Svir I.B., Golovenko V.M. / J. Electrochem. Commun. 2000. Vol.3, ¹.1. P. 11-15. 2. Aoki K., Osteryoung J. / J. Electroanal. Chem. 1984. Vol. 160. P. 335. 3. Gavaghan D.J. / J. Electroanal. Chem. 456 (1998) 13. 4. Svir I.B., OleinickA.I. / J. Electroanal. Chem. Vol. 497, N2, 2000. P.1-9. 5. Amatore C.A., Fosset B. / J. Electroanal. Chem. 1992. Vol. 328. P. 21. 6. Ñâèðü È.Á./ Ðàäèîýëåêò- ðîíèêà è èíôîðìàòèêà, 2000, ¹ 3. Ñ. 24. 7. Áûõ À.È., Âàñèëüåâ Ð.Ô., Ðîæèö- êèé Í.Í. // Èòîãè íàóêè è òåõíèêè. ÂÈÍÈÒÈ. Ñåð. Ðàäèàö. õèìèÿ. Ôîòîõè- ìèÿ. 1979. ¹ 2.135 ñ. 8. Britz D. / J. Electroanal. Chem. 1996. Vol. 406. P. 15. 9. Feldberg S.W. and Goldstein C. / J. Electroanal. Chem. 1995. Vol. 397. P.1. 10 . Ñâèðü È.Á., Îëåéíèê À.È., Êîìïòîí Ð.Ã./ Ðàäèîýëåêòðîíèêà è èíôîðìàòèêà. 2000. ¹ 1. Ñ. 28-32. Ïîñòóïèëà â ðåäêîëëåãèþ 11.11.2000 Ñâèðü Èðèíà Áîðèñîâíà, êàíä. ôèç.-ìàò. íàóê, çàâ. ëàáîðàòîðèåé ìàòåìàòè÷åñêîãî è êîìïüþòåðíîãî ìîäåëèðîâàíèÿ, äîêòîðàíò êàôåäðû áèîìåäèöèíñêîé ýëåêòðîíèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðå- ñû: ÷èñëåííîå ìîäåëèðîâàíèå ýëåêòðîõèìè÷åñêèõ ïðîöåññîâ. Àä- ðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-93-64. ÓÄÊ 622:51-7; 622-007 À.Í. ÄÎÁÐÎÂÎËÜÑÊÈÉ ÈÑÏÎËÜÇÎÂÀÍÈÅ ÏÀÐÀÌÅÒÐÈ×ÅÑÊÎÃÎ ÏÐÅÄÑÒÀÂËÅÍÈß ÏÎÂÅÐÕÍÎÑÒÈ ÄËß ÎÏÐÅÄÅËÅÍÈß ÃÅÎÌÅÒÐÈ×ÅÑÊÈÕ ÏÀÐÀÌÅÒÐΠÇÀËÅÃÀÍÈß ÏÎËÅÇÍÛÕ ÈÑÊÎÏÀÅÌÛÕ Îáîáùàåòñÿ èçâåñòíûé ìåòîä òðåõ ñêâàæèí äëÿ îïðåäåëåíèÿ ãåîìåòðè÷åñêèõ ïàðàìåòðîâ çàëåãàíèÿ ïëàñòîîáðàçíûõ òåë ïîëåç- íîãî èñêîïàåìîãî íà ñëó÷àé òåë ñëîæíîé ôîðìû è àâòîìàòèçèðî- âàòü åãî. Äëÿ ãîðíîé îòðàñëè Óêðàèíû îäíîé èç àêòóàëüíåéøèõ çàäà÷ ÿâëÿåò- ñÿ àâòîìàòèçàöèÿ ïðîöåññîâ óïðàâëåíèÿ è ïðîåêòèðîâàíèÿ îáúåêòîâ ãîðíîãî ïðîèçâîäñòâà, ïëàíèðîâàíèÿ ãîðíûõ ðàáîò, ÷òî îáóñëàâëèâàåò íåîáõîäèìîñòü ðàçðàáîòêè ñîîòâåòñòâóþùèõ ìàòåìàòè÷åñêèõ ìîäåëåé. 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"N?qnR!iiTZe/ḶG~bяc'zȎalaO5aҏaBL b{-ʛӉOmIM'ݷC3,3mա i? Boq1qոo3};=XXP?2ϜߴkC<|x Gwa2KyF?q[y|~V~>|;m&L1L$v O /@ھi+v'O_WKy*?؆&L1ç1v×?q\Ay} a1/~"׏ \G6LI ~z3 wBE__FS8jkb\~.qr\'!-72/!/~}U%OM2-.|&Ӷ$jӏ)c*Rp/g.@*'xu>~G8t*wk~&CiRI"tZª]3hٷEKoRz|s"c繹6٦1a_,,;<~65^ax~8sǴ2V8 T6~l}!"-I/g{Rea [8yRػ0R) )2.yޔoy|ﻱ~ܘȃ:F.y_w,6ɂ8+/֝w_y-6+ý F;8|νsX?9{g~gH x+V-brmwRLB3V[_|Fn~^8b2]9׽ אX'.99 ە/b,7ܧK1&Zs>s؟a^!^dc[J?r%I\]f{z> K ?t1)ޏk'uKK K!uJ$mAgð,NY>x)d¿2}ǝ-l_[y3 ǿ>}/˒ y s-tWF>(ˮ}vܷI> ?ckS*P+sM>khQ.X.u3M_cٯo]4|a.-6acٙ|~w 'L?7ϹqyLn79˅*.}.o)߉߫+8T?/ex>2 "#ũ8ܤ2I} _،>` a.P^kOf>}blBcPTZot,#ˮ-̳PF\~p6 bu<,,14  ãîðíîì äåëå ðàñïîëîæåíèå òåëà ïîëåçíîãî èñêîïàåìîãî â ïðî- ñòðàíñòâå è îñîáåííîñòè åãî ôîðìû õàðàêòåðèçóþòñÿ ðÿäîì ãåîìåòðè- ÷åñêèõ ïàðàìåòðîâ, íàçûâàåìûõ òàêæå ýëåìåíòàìè çàëåãàíèÿ. Îïðåäå- ëåíèå ýòèõ ýëåìåíòîâ ÿâëÿåòñÿ îäíîé èç îñíîâíûõ çàäà÷ ãåîìåòðè÷åñ- êîãî ìîäåëèðîâàíèÿ â ïðîöåññå èññëåäîâàíèÿ ìåñòîðîæäåíèÿ. Äàííàÿ ñòàòüÿ ïîñâÿùåíà âîïðîñàì ïðåäñòàâëåíèÿ ïîâåðõíîñòè ðóä- íîãî òåëà â öåëÿõ àâòîìàòèçàöèè ïðîöåäóðû îïðåäåëåíèÿ òàêèõ ãåîìåò- ðè÷åñêèõ ïàðàìåòðîâ êàê óãîë ïàäåíèÿ è óãîë ïðîñòèðàíèÿ çàëåæè. Ðàññìîòðèì ýòè ïàðàìåòðû íà ïðèìåðå çàëåæè ïëàñòîîáðàçíîé ôîð- ìû. Ïóñòü íåîáõîäèìî îïðåäåëèòü óãîë ïàäåíèÿ è ïðîñòèðàíèÿ â òî÷êå À íà ïîâåðõíîñòè ðóäíîãî òåëà (ðèñ.1,à). Íàïðàâëåíèå íàèáîëüøåãî ñêàòà ïîâåðõíîñòè (ïàäåíèÿ) â ýòîé òî÷êå îïðåäåëÿåò íåêîòîðóþ ïðÿ- ìóþ â ïðîñòðàíñòâå, íàçûâàåìóþ ëèíèåé ïàäåíèÿ. Óãîë, îáðàçîâàííûé ëèíèåé ïàäåíèÿ è ãîðèçîíòàëüíîé ïëîñêîñòüþ, åñòü óãîë ïàäåíèÿ  . Ïðîåêöèÿ óãëà ïàäåíèÿ íà âåðòèêàëüíóþ ïëîñêîñòü yz ïîêàçàíà íà ðèñ. 1,á. Åñëè ëèíèÿ ïàäåíèÿ ïàðàëëåëüíà ïëîñêîñòè yz, òî óãîë  ïðîåöèðó- åòñÿ â íàòóðàëüíóþ âåëè÷èíó. à á â Ðèñ. 1. Ýëåìåíòû çàëåãàíèÿ çàëåæè: à – ëèíèÿ ïðîñòèðàíèÿ è ëèíèÿ ïàäåíèÿ çàëåæè; á – ëèíèÿ ïàäåíèÿ è óãîë ïàäåíèÿ  â ïëàíå; â – ëèíèÿ ïðîñòèðàíèÿ è óãîë ïðîñòèðàíèÿ  â ïëàíå Ëèíèåé ïðîñòèðàíèÿ íàçûâàþò ëèíèþ ïîâåðõíîñòè çàëåæè, ïàðàë- ëåëüíóþ ãîðèçîíòàëüíîé ïëîñêîñòè. Ïîëîæèòåëüíîå íàïðàâëåíèå ïðî- ñòèðàíèÿ âûáèðàþò òàêèì, ÷òîáû ïàäåíèå çàëåæè áûëî ñïðàâà. Óãîë  , îáðàçîâàííûé ïîëîæèòåëüíûì íàïðàâëåíèåì ëèíèè ïðîñòèðàíèÿ è îñè õ, åñòü óãîë ïðîñòèðàíèÿ. Íà ðèñ. 1,â ïîêàçàíà ïðîåêöèÿ óãëà ïðîñòèðàíèÿ  íà ãîðèçîíòàëüíóþ ïëîñêîñòü xy. Íà ïðàêòèêå óãëû ïàäåíèÿ è ïðîñòèðàíèÿ îïðåäåëÿþòñÿ ãðàôè÷åñ- êèì èëè àíàëèòè÷åñêèì ñïîñîáîì ïî ïëàíó ïîâåðõíîñòè ðóäíîãî òåëà â ãîðèçîíòàëÿõ â ðåçóëüòàòå ðåøåíèÿ çàäà÷è î òðåõ ñêâàæèíàõ [1]. Ñóù- íîñòü çàäà÷è ñîñòîèò â ñëåäóþùåì. Ïóñòü ïî ðåçóëüòàòàì èíêëèíîìåò- ðè÷åñêèõ ñúåìîê ñêâàæèí âû÷èñëåíû êîîðäèíàòû x,y,z òðåõ òî÷åê 1,2,3, â êîòîðûõ ñêâàæèíû âñòðåòèëè çàëåæü. 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Âûðàæåíèå (2) îïðåäåëÿåò âåê- òîð, íàïðàâëåííûé ïðîòèâîïîëîæíî ãðàäèåíòó ïîòåíöèàëüíîé ýíåðãèè ìàãíèòíîãî äèïîëÿ âî âíåøíåì ìàãíèòíîì ïîëå. Ñèëà, äåéñòâóþùàÿ íà õèðóðãè÷åñêèé èíñòðóìåíò ñî ñòîðîíû ìàãíèòíîãî ïîëÿ, íàïðàâëåíà â ñòîðîíó óâåëè÷åíèÿ èíäóêöèè ìàãíèòíîãî ïîëÿ. Ó÷èòûâàÿ, ÷òî íåðâíàÿ òêàíü ïî ìåõàíè÷åñêèì ñâîéñòâàì ïðåäñòàâ- ëÿåò ñîáîé âÿçêóþ æèäêîñòü [7], ñîãëàñíî ìîäåëè Ñòîêñà ñîïðîòèâëå- íèå äâèæåíèþ õèðóðãè÷åñêîãî èíñòðóìåíòà îïðåäåëÿåòñÿ òàê: v b F с     , (3) çäåñü b – êîýôôèöèåíò ñîïðîòèâëåíèÿ ñðåäû; v  – ñêîðîñòü äâèæåíèÿ õèðóðãè÷åñêîãî èíñòðóìåíòà; g m F и т   , 4) ãäå и m – ìàññà õèðóðãè÷åñêîãî èíñòðóìåíòà; g – óñêîðåíèå ñâîáîäíî- ãî ïàäåíèÿ. Àðõèìåäîâà ñèëà, äåéñòâóþùàÿ íà õèðóðãè÷åñêèé èíñòðóìåíò, ïî- ãðóæåííûé â íåðâíóþ òêàíü, îïðåäåëÿåòñÿ èç ñîîòíîøåíèÿ: ρgV F А   , (5) çäåñü ρ =1,27  10 3 êã/ì 3 – ïëîòíîñòü æåëàòèíà, ýêâèâàëåíòíîãî ïî ôè- çè÷åñêèì ñâîéñòâàì íåðâíîé òêàíè [7]; V – îáúåì ôåððîìàãíèòíîãî íàêîíå÷íèêà õèðóðãè÷åñêîãî èíñòðóìåíòà. Ñ ó÷åòîì âûðàæåíèé (2)-(5) äëÿ ñèë, äåéñòâóþùèõ íà õèðóðãè÷åñ- êèé èíñòðóìåíò ñîãëàñíî (1), óðàâíåíèå äèíàìèêè õèðóðãè÷åñêîãî èíñòðóìåíòà â âåêòîðíîé ôîðìå ïðè äâèæåíèè â íàïðàâëåíèè, ïðîòè- âîïîëîæíîì ñèëå òÿæåñòè: ρgV g m dt s d b B ) m ( dt s d m и 2 2 и          , (6) ãäå s  – âåêòîð ïåðåìåùåíèÿ õèðóðãè÷åñêîãî èíñòðóìåíòà. Òàêèì îáðàçîì, íà õèðóðãè÷åñêèé èíñòðóìåíò, äâèæóùèéñÿ ïîä äåéñòâèåì ïîíäåðîìîòîðíîé ñèëû ìàãíèòíîãî ïîëÿ, äåéñòâóþò ñèëà ñîïðîòèâëåíèÿ, ìîäóëü êîòîðîé ëèíåéíî çàâèñèò îò ñêîðîñòè ïåðåìå- ùåíèÿ, è ïîñòîÿííûå ïðîòèâîïîëîæíî íàïðàâëåííûå ñèëû òÿæåñòè è Àðõèìåäà. xklTUw-KK-mh X@BAyHDA(HxHˠhBЈT-!1JCEH H@"Yu~`o93sf=sҀ'{4. 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P+y"AF<~p'u1OEqF%=n.zE %J 6\SyiY ̑ h~[;p!1!#8.z=e^HY'ȓ8h~'$PD'HG{{C{#~Kn-) 1>I>%Y;J%!'? BQ0̇Fv[0H3 ;?!OlaU=`Wq cfIJbANdZL/ 3|-r>aKee -L=]rrF]p\?aPtEF9l0=Dn:OyXK`h7q˳ak9颭Cй"_ ad|,3x:rI( n_# 2Byog0oy 3-x`~h#rLh_J۪o85cndsi+J ?twQ}YLgcvo[X=uvS̅? #rAx!s3y)tkBв.d:C\|CEY@úE{F15%4L$1J}J&b-X kKYV@}B> G;tH~<oH]Ore qm& 2HCivUyKm;4s,\((9A;N,,g21 Ðèñ.1. Îáîáùåííàÿ ñõåìà ðàñïîëîæåíèÿ ìàãíèòíûõ êàòóøåê â ñèñòåìå MSS Îïðåäåëèì ÷èñëåííûå çíà÷åíèÿ ñèë, âõîäÿùèõ â óðàâíåíèå (1), ïðè- ìåíèòåëüíî ê Ìàãíèòíîé Ñòåðåîòàê- ñè÷åñêîé Ñèñòåìå (MSS (Stereotaxis inc.)) [3], îáëàäàþùåé íà äàííûé ìî- ìåíò íàèëó÷øèìè òåõíè÷åñêèìè õà- ðàêòåðèñòèêàìè. Ñèñòåìà ñîñòîèò èç 6 ñâåðõïðîâîäÿùèõ ìàãíèòíûõ êàòó- øåê, èçîáðàæåííûõ íà ðèñ. 1, ðàñïî- ëîæåííûõ ïàðàìè âî âçàèìíî-ïåðïåí- äèêóëÿðíûõ ïëîñêîñòÿõ (1,2 – ïåð- ïåíäèêóëÿðíî ê îñè Õ ñèñòåìû, 3,4 – Y, 5,6-Z). Ìàêñèìàëüíàÿ âåëè÷èíà ñèëû òîêà â êàòóøêàõ 100À. Âíóòðåí- íèé äèàìåòð êàòóøåê íàõîäèòñÿ â ïðå- äåëàõ 280-321ìì, âíåøíèé – 372- 411ìì, äëèíà: 37,2-71ìì. Êàòóøêè, ðàñïîëîæåííûå âäîëü îñè Z (ïðîõî- äÿùåé ïåðïåíäèêóëÿðíî ê ïëîñêîñòè ÷åðòåæà), èìåþò áîëüøèé äèà- ìåòð è ìåíüøóþ äëèíó. Õèðóðãè÷åñêèé èíñòðóìåíò, ïðåäíàçíà÷åííûé äëÿ òåðìîäåñòðóêöèè îêðóæàþùåé òêàíè ñ ïîìîùüþ âíåøíåãî âûñîêî÷àñòîòíîãî ýëåêòðî- ìàãíèòíîãî ïîëÿ (10-40 ÌÃö), âûïîëíåí â âèäå êðóãîâîãî öèëèíäðà ñ äèàìåòðîì 3ìì è äëèíîé 3ìì ìàññîé и m = 0,187ã èç ôåððîìàãíèòíîãî ìàòåðèàëà, íàìàãíè÷åííîãî äî íàñûùåíèÿ, îáëàäàþùåãî ìîäóëåì ìàã- íèòíîãî ìîìåíòà | | m  =0,016À  ì 2 . Ïðè îïðåäåëåíèè ìàãíèòíîãî ïîëÿ êàòóøêè èñïîëüçîâàëñÿ ìåòîä ýêâèâàëåíòíîãî ïðåäñòàâëåíèÿ îáìîòêè êàòóøêè â âèäå ñîâîêóïíîñòè êðóãîâûõ âèòêîâ è àëãåáðàè÷åñêîãî ñóììèðîâàíèÿ ñîîòâåòñòâóþùèõ êîìïîíåíò èíäóêöèè, ñîçäàâàåìûõ îòäåëüíûìè âèòêàìè. Äëÿ ñîêðàùå- íèÿ âðåìåíè ðàñ÷åòà îñóùåñòâëÿëàñü àïïðîêñèìàöèÿ íåñêîëüêèõ ïðî- âîäîâ îáìîòêè èäåàëèçèðîâàííûì âèòêîì ñ ó÷åòîì âûïîëíåíèÿ óñëî- âèÿ: min k cр d a  , ãäå cр a – ñðåäíèé ðàçìåð ñå÷åíèÿ èäåàëèçèðîâàííîãî îáìîòî÷íîãî ïðîâîäà; min k d – ìèíèìàëüíûé äèàìåòð ìàãíèòíîé êàòóøêè. Îïðåäåëåíèå ìàãíèòíîé èíäóêöèè îäíîãî âèòêà îñóùåñòâëÿëîñü ìåòîäîì âåêòîðíîãî ïîòåíöèàëà, ïîçâîëÿþùåãî âûðàçèòü êîìïîíåíòû âåêòîðà ìàãíèòíîé èíäóêöèè ÷åðåç ïîëíûå ýëëèïòè÷åñêèå èíòåãðàëû Ëåæàíäðà [8]. Äàííûé ìåòîä îáëàäàåò ïîâûøåííîé òî÷íîñòüþ âû÷èñ- ëåíèé ïî ñðàâíåíèþ ñ ìåòîäîì, ïðèìåíÿåìûì â ÌSS [3], êîòîðûé îñíîâàí íà èíòåðïîëÿöèè çíà÷åíèé êîìïîíåíò èíäóêöèè ìàãíèòíîãî ïîëÿ, íàéäåííûõ â îïîðíûõ òî÷êàõ ÷èñëåííûì èíòåãðèðîâàíèåì ïî îáúåìó êàòóøêè, ñîãëàñíî çàêîíó Áèî-Ñàâàðà. 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YFbpK~ >yg=z zDYdvnoJ [weo5S۸n8mvfD_kŧ}Oe$[`fwfQA 8~J6ޢ䓝&Zvy+k#f17bnhfvahswޗ,kG#]%Bfn1ܑӜl _>S)߼_ c8n]r{?gK;]Own7oQw_g{/Z 88쪞&Ĭ{8k:Lħ>PoWtO'yW-:t2n+;W<٭kS.b?HA3%U6=40C& 3/QA2L6#߈ Qt/.}ɣD&W#ksulR>:3hWwV>8$_l~3:6L_:B'65>Ó8!F?Cܑd-Uv9[F[ ~Zܜ,޽W[{owrJrTtT} \'>5WWm_T|k+gq|>%~{ĸZ)~r,, 23 íîé êàòóøêè ñòàíîâèòñÿ î÷åâèäíûì ïðèíöèï ôîðìèðîâàíèÿ óïðàâëÿ- þùèõ âîçäåéñòâèé â MSS: ïåðåìåùåíèå âäîëü êàæäîé îñè êîîðäèíàò äîëæíî îñóùåñòâëÿòüñÿ êàòóøêàìè, àêñèàëüíàÿ îñü êîòîðûõ ñîâïàäàåò ñ íàïðàâëåíèåì äâèæåíèÿ, áîêîâûå êàòóøêè (ðàñïîëîæåííûå ïåðïåí- äèêóëÿðíî ê äàííîé îñè êîîðäèíàò) èñïîëüçóþòñÿ äëÿ êîìïåíñàöèè áîêîâîãî ñìåùåíèÿ õèðóðãè÷åñêîãî èíñòðóìåíòà. Ïîä äåéñòâèåì ñèëû òÿæåñòè õèðóðãè÷åñêèé èíñòðóìåíò ïåðåìåùàåòñÿ â íåðâíîé òêàíè â óñòàíîâèâøåìñÿ ðåæèìå ñ ïîñòîÿííîé ñêîðîñòüþ ïîðÿäêà 0,2 ìì/ñ, ÷òî íåîáõîäèìî êîìïåíñèðîâàòü ôîðìèðîâàíèåì ñîîòâåòñòâóþùèõ óïðàâ- ëÿþùèõ âîçäåéñòâèé. Îïðåäåëåíèå çàêîíà äâèæåíèÿ ïîçâîëÿåò ñîçäàòü ìàòåìàòè÷åñêóþ ìîäåëü ñòåðåîòàêñè÷åñêîé ñèñòåìû, îñíîâàííóþ íà âû÷èñëåíèè êîîð- äèíàò è ñêîðîñòè äâèæåíèÿ õèðóðãè÷åñêîãî èíñòðóìåíòà â ïðîèçâîëü- íûé ìîìåíò âðåìåíè ïî èçâåñòíûì íà÷àëüíûì óñëîâèÿì. Èñïîëüçîâà- íèå äàííîé ìàòåìàòè÷åñêîé ìîäåëè ñòåðåîòàêñè÷åñêîé ñèñòåìû ïîçâî- ëÿåò ïðîãíîçèðîâàòü íàïðàâëåíèå è ñêîðîñòü äâèæåíèÿ õèðóðãè÷åñêîãî èíñòðóìåíòà ïðè ïðîèçâîëüíûõ ïàðàìåòðàõ ìàãíèòíîãî ïîëÿ ñ ó÷åòîì äåéñòâèÿ âíåøíèõ íåìàãíèòíûõ ñèë. Ýòî äîïóñêàåò ïðîâåäåíèå íåïîñ- ðåäñòâåííîãî âèçóàëüíîãî ðåíòãåíîëîãè÷åñêîãî êîíòðîëÿ â îïîðíûõ òî÷êàõ òðàåêòîðèè, ÷òî ïðèâîäèò ê ñíèæåíèþ äîçû èîíèçèðóþùåãî èçëó÷åíèÿ â íåñêîëüêî ðàç. Ôîðìèðîâàíèå óïðàâëÿþùèõ âîçäåéñòâèé íà îñíîâå èñïîëüçîâàíèÿ äàííûõ èìèòàöèîííîãî ìîäåëèðîâàíèÿ ïî- çâîëÿåò ïîâûñèòü òî÷íîñòü è ýôôåêòèâíîñòü ñèñòåì ìàãíèòíîãî óïðàâ- ëåíèÿ õèðóðãè÷åñêèì èíñòðóìåíòîì. Ñïèñîê ëèòåðàòóðû: 1. Howard M.A., Grady M.S., Ritter R.C et al. Magnetic movement of a brain thermoceptor // Neurosurgery .1989.Vol. 24, ¹ 3. Ð. 444-448. 2. Quate E.G., Wika K.G., Lawson M.A. et al. Goniometric motion controller for the superconducting coil in a magnetic stereotaxis system // IEEE Trans. Biomed. Eng. 1991. Vol. 38, ¹ 9. P.899-905. 3. Meeker D.C., Maslen E.H., Ritter R.C., Creighton F.M. Optimal realization of arbitrary forces in a magnetic stereotaxis system // IEEE Transactions on Magnetics, 1996.Vol.7, ¹ 2. Ð. 320–328. 4. Grady M.S., Howard M.A., Dacey R.G. et al. Experimental study of the magnetic stereotaxis system for catheter manipulation within the brain // J. Neurosurg.2000.¹ 93(2). P.282-288. 5. Howard M.A., Grady M.S., Ritter R.C. et al. Magnetic neurosurgery // Stereotact. Funct. Neurosurg. 1996.Vol. 66, ¹ 1-3. Ð.102-107. 6. Òàìì È.Å. Îñíîâû òåîðèè ýëåêòðè÷åñòâà. Ì.: Íàóêà, 1976. 616 ñ.7.Ritter R.C., Quate E.G., Gillies G.T. et al. Measurement of friction on straight catheters in in vitro brain and phantom material // IEEE Trans. Biomed. Eng. 1998. Vol. 45, ¹ 4. Ð.476-485. 8 Ëàíäàó Ë.Ä., Ëèôøèö Å.Ì. Ýëåêòðîäèíàìèêà ñïëîøíûõ ñðåä.Ì.: Ôèçìàò- ãèç,1959.–532 ñ. 9. Ñïðàâî÷íèê ïî ñïåöèàëüíûì ôóíêöèÿì / Ïåð. ñ àíãë./ Ïîä. ðåä. Ì. Àáðàìîâèöà è È. Ñòèãàí. Ì.: Íàóêà, 1979. 832 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 17.11.2000 Àâðóíèí Îëåã Ãðèãîðüåâè÷, àñïèðàíò êàôåäðû áèîìåäèöèíñêîé ýëåêòðîíèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêîå ìîäå- ëèðîâàíèå áèîëîãè÷åñêèõ îáúåêòîâ è ïðîöåññîâ, ðàäèîýëåêòðîí- íàÿ ìåäèöèíñêàÿ àïïàðàòóðà. Àäðåñ: Óêðàèíà, 61022, Õàðüêîâ, óë. À. Áàðáþñà, 3à, êâ.10, òåë. 43-79-32. 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ÈÂÀÍÎÂ, Þ.Â. ËÎÌÎÍÎÑΠÍÎÂÛÉ ÔÎÐÌÀÒ ÕÐÀÍÅÍÈß È ÏÅÐÅÄÀ×È ÌÓËÜÒÈÌÅÄÈÉÍÛÕ ÄÀÍÍÛÕ Îïèñûâàåòñÿ íîâûé ôîðìàò ïðåäñòàâëåíèÿ ìóëüòèìåäèéíûõ äàííûõ, îñíîâàííûé íà èñïîëüçîâàíèè ìíîãîýòàïíîãî àëãîðèò- ìà ñæàòèÿ äàííûõ. 1. Ââåäåíèå Îäíèì èç íàèáîëåå ïîïóëÿðíûõ íà ñåãîäíÿøíèé äåíü íàïðàâëåíèé â ìèðå ïåðñîíàëüíûõ êîìïüþòåðîâ ÿâëÿåòñÿ ìóëüòèìåäèà. Ñ ïîìîùüþ ïðèëîæåíèé ìóëüòèìåäèà òåêñòîâàÿ, ãðàôè÷åñêàÿ, àóäèî- è âèäåîèí- ôîðìàöèÿ îáúåäèíÿþòñÿ, è ïîëüçîâàòåëü ìîæåò óïðàâëÿòü õîäîì ïðåä- ñòàâëåíèÿ äàííîé èíôîðìàöèè. Ïðè ýòîì åå îáúåì, ïîäëåæàùèé îáðà- áîòêå èëè ïåðåäà÷å, âåñüìà âåëèê. Òàê, îäíà ìèíóòà öèôðîâîé àóäèîçà- ïèñè ñ êà÷åñòâîì ëàçåðíîãî äèñêà çàíèìàåò ïîðÿäêà 10,8 ÌÂ. Äëÿ ïðîñëóøèâàíèÿ òàêîãî ôàéëà â ðåàëüíîì ìàñøòàáå âðåìåíè íóæíî èìåòü ñêîðîñòü ïåðåäà÷è äî 1,5 ÌÂ/ñ. Ýòî ãîâîðèò î òîì, ÷òî ýôôåê- òèâíîå èñïîëüçîâàíèå ìóëüòèìåäèéíûõ äàííûõ íà ïåðñîíàëüíûõ ÝÂÌ âîçìîæíî òîëüêî ïîñëå èõ îáðàáîòêè ñïåöèàëüíîé ïðîãðàììîé ñæàòèÿ. Çà ãîäû ðàáîòû íàä ïðîáëåìîé êîìïðåññèè àóäèîèíôîðìàöèè (à èìåííî î íåé ïîéäåò ðå÷ü â ñòàòüå) íàêîïèëîñü ìíîæåñòâî ïðîäóêòîâ, ìåòîäîâ, àëãîðèòìîâ, êîòîðûå ïåðåñåêàþòñÿ ìåæäó ñîáîé, çà÷àñòóþ èìåþò íåñêîëüêî ðàçíûõ íàçâàíèé è ôóíêöèé [1]. 2. Ôîðìàòû àóäèîäàííûõ Ðàññìîòðèì ôîðìàòû ìóëüòèìåäèà, ïîçâîëÿþùèå õðàíèòü çâóêîâóþ èíôîðìàöèþ. Òàê, çàïèñü çâóêîâîãî ñèãíàëà â âèäå öèôðîâûõ äèñêðå- òèçèðîâàííûõ âåëè÷èí èçâåñòíà êàê èìïóëüñíî-êîäîâàÿ ìîäóëÿöèÿ (PCM-Pulse Code Modulation). Äèôôåðåíöèàëüíàÿ èìïóëüñíî-êîäîâàÿ ìîäóëÿöèÿ (DPCM) – ñõå- ìà êîäèðîâàíèÿ çâóêîâîé èíôîðìàöèè, êîòîðàÿ ïîäðàçóìåâàåò êâàíòî- âàíèå ðàçíîñòåé ìåæäó òåêóùèìè çíà÷åíèÿìè ñèãíàëà è ïðåäøåñòâóþ- ùèìè, à íå êîäèðîâàíèå ñàìèõ äèñêðåòíûõ âåëè÷èí. Ýòî ñâîéñòâî ïîçâîëÿåò ðàññìàòðèâàòü DPCM êàê ñõåìó ñæàòèÿ çâóêîâîé èíôîðìà- öèè. Åùå îäíîé ñõåìîé ñæàòèÿ àóäèîèíôîðìàöèè, îñíîâàííîé íà êâàí- òîâàíèè ðàçíîñòåé, ÿâëÿåòñÿ àäàïòèâíàÿ äèôôåðåíöèàëüíàÿ èìïóëüñ- íî-êîäîâàÿ ìîäóëÿöèÿ (ADPCM). ADPCM, â îòëè÷èå îò DPCM, ÿâëÿ- ÿñü àäàïòèâíûì àëãîðèòìîì, èçìåíÿåò ñõåìó êîäèðîâàíèÿ ñ ó÷åòîì îáðàáàòûâàåìûõ äàííûõ. Òàêèì îáðàçîì, äëÿ êîäèðîâàíèÿ ñèãíàëîâ íèçêîãî óðîâíÿ èñïîëüçóåòñÿ ìåíüøå áèòîâ, ÷åì äëÿ êîäèðîâàíèÿ xhe?m۝ynõHi?zhk"%daJ71@V$ЎgZPӶEJQ?J(E}z}6=Gw?_x~>|< "2Pd\DVq2yE%׾xW~u @y∻6 hpUQ4')H,r ɚΣńS:`B,6.'2R:*×L pL?YN+%Zdz͕d֏#.NuZ#Ib[r6 z:U[5ѻBJd'c4h& H IM`\ijT|:'k9oeiN!p&\i&J)7{vK8u7s߶5l3~YB*rĩS%DSL|G3m6oG9x>o}ü+෰g2Ϡғ? ={9Ea~;8 0؋(o>SݛL5mO7o@fۭ>}vgBLێc}뵖٠pss\&:nl\{̗Vv j#=5ͦgS泜+|h4G[U?~np;vہ[m,rp;v*Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:45  CH) bCC(16\W2W/<C1`R{(Vx fUsjl(H8ĕMl F.MKpJ^ qbr+m*D6R<:hT%ڙLl|g_&k>k[0z_BdW x|0l ׼q塷~/ G0|*n5~.n=uxa e[x&0^_:Ğ߼uʽ/gӥ.vWn/Om13[hk<# gdmJou>}zb˫6-ûLߧ qޤƔ}gx?x>_zߥ_9|zݯwvE3~L_}ׄ/+ߝup/u+#W5$\k_|W&}_W5aigew^Ȏv_C<x{"h%\1|+[Vmk8SSu7wrw}%.wv#c7&;G䒛{/썑K .arx5I^lkT*2/|q>j^eb3}nl: ;76_wi>7_ el\|QƤb8O)ؑ26ߛ?JBc)#6bSn~YMxWct8]# yx46>9MN G O;qxtx6cυp<9=ܐߍ3áh Nt'cRPbg)1w*Do^>WƉ^JǤkCHW)Nel\RvQ˱Qrƕz[{]tu^b[Y2t_Wv>tf$ҧOŝvRgOT'}+IaV<bVxCŎn]lً3yvܶ!Cu>kMmPt;t>"꿽!\{nþ9dޡ{-gOGjMګ|F#~wN%'[\pY bU{C/_Z?)g^yrEK_۳vX_Cf_?_?nnȨO;,m,9:|z0YHݳ繻= 28x%z&}!sKkx՗A)ɖg)tkϵ^ۉ_mck ˎ[|&v>)>1z$^tx '4\`E6:4>v'3?\`R)—W_|:k/{f~jկ*o[=~׾ncO]2 _tnm||_Gsw2󨓾1jl7>3wy{(-N/8\Qa%_\Gp,tZܳK;M%_"_]~P^}7ü"ߛWMY?'m M6Ӿ[1~l;ZZENC?l:1T7:vs`6y$݊|yoMiۄ)ysFnv+k3uL:ZfSXb*_^]Vs nl 647"Ĩ\gǩtDzsLY\oDǐ8-O)28Jo>4?9\a}[t7w"3'w<hz<-߇ؿVSyzD,}(H䓙twsJ׾G}$|٥W,K}6ɲL닶-H,-ńOunYb^Lb =ZWmvy_ݥʲ+&3e著ї C|6^ۿ/o |p~4p"u }!wo Nw}ŗFW`}1tc.4G+-qƒ!ܷxݖR.UF[1U)Wh [YȮ^m'>{hkV>{>^/7S#ؗ{fc,ʫ hJu=̾Yu>8ٜ=K #HaoCBZ*#;_c}zW{cnm;tF"~eRБnuObv;T?ʏ?iYa>9.;;~~ gs`fMّח''<eW9;xѡ*d1r yeIdӬX3eKN$6+ :8xk# gq k alU\;[A9v| ՞6ϾԳ!ଋsg=|\N|]1y*RHƭۼwгӮe~9M usEsө[9IƐ>#r;cc\QSzʊ hv_mns0¯eb??vW{L?"]Ïû&~xsF?Z^qW2l^_^cd5ALPĀë24Gt;x-1 !1u& 뺮1CG9tgP0W=ztGp&gKg_hN/Nw3Y>5AI8Y}2s7ˉݻ&N;Ţ}c6m/d7{]xunf O:CeꓫWvC7,z;(Ӷn'`kS~y}6iXg)?Msʁ{-{B'f}.iRICnWhפGeWs~8_l;|6;8e%~6ƊzjWgSHc__.=חwKt7>kث/V ~e_K8+[4s&OЈ1 ǟn^O x)a vZbݷyF1y嗸+ӲŚ8i]t*ro9>~Qwc}h;}o'1zi|ǯ7M~=Yg£۬nwOfgGaؽz͌䴯86yPˇ1g6M, ŴcyA^Z<ҭ*mnJsl7&mdtN4Z5~t_pxc/KWX&F-fa|#/x_ZƐrH_I_,L_M`dߓ_0:|W&w׋oͿ<ߝ_8%Ϸ<'rSѼ;kcCy|yH;x7y%~ )lsJyr'$> ~!nwSd/mMީm>mp*Qze^26`dJd_؝u9'jFz~+< o]BR'c&Ϳ,wcbQGT w);.D+B5-FKج嵜ȳzڎeۏvQ ů'ͤqY;_|_cS_;B|g^/zl#3n;4cGܭ%c/cc[woiV+A"9m\pd|bZ۰D9?cs<9Jx;)'ߔƁ|AGι-O[ȗ32m3'E-v`|co% X;4'<Ug{yx79w~s95ݏyT[h>g\f-j?;gz7ysagl(ז!OF}ܺU,ڠnkJu=kk'_i}k/A+z5Y6m-gd/Űmҧ.7UCwޑiN2|ϛُOSah[ϯQ9; vu{.7P?7n-EzM{'za#d\aq,5oJqk4֖Î;tºغnko~?p0|wҰΊs 9bnYg#@pcW2}L ΅XgǾIH> ^πt=ym\m] ~{`X1yۙ]zԡG}G}~7d&߻n=U{Ě=v-1_Υgėq? f|م#Nk(<1??|/[p{`'O3ݫ6h}twi`CY}o\yVn;į_>72}{s]17a潗˜nϩ}ۄߦa;3ļ/ s~Wp@ŸB1Qi#yak_-S'CK/?' {}x:١j!vfE|B/w9ʊY];d (?Xǐt^J2>}+^U^}z/W9)zձ&:C3>wSto -;T:s=ϿF|cGY_v{\c_ؔG>wg)`$ck_l(2x))~[W@hmo'G'|{o^\wʮs2v>32ľo}{wJ%&)YǟDvmxGj>{󭊘O½[ nsZO}o#ֿl- >'o4Cb=z%vn+̏7a5}[t7a;ѹo{f^͓11ww O'e>W/`A2t+ Cs3e9:ͥjwY7Cea̷jV>51g{_L_o1&5-#$^}:b[k%̷r1֗X@I8+'hߚg.6r|.CylXh;kCwiSe}O߿O|㰿A\~=jל{½Fc:s0N_9>3 UWX/_Rv_2l.Cw _rzgzlhuly˕>^B˿{ ӻ5 7PN·[`_η?OOX{}.W|8[pOzQY:H]MeeM$o=}+mz1`;t+]wSfg}u\bF}5̈;]+|Yz{w;jϧOĭ{A'2aR(KG[VyyvhrO|)w_nc;gpv9,,25 ñèãíàëà âûñîêîãî óðîâíÿ. Êà÷åñòâî àóäèîäàííûõ îïðåäåëÿþò ïóòåì èõ ñðàâíåíèÿ ñ îðèãèíàëüíûì çâóêîì, êîòîðûé áûë îöèôðîâàí è õàðàêòå- ðèçóåòñÿ òðåìÿ ïàðàìåòðàìè: – ðàçðåøåíèåì; – ÷àñòîòîé äèñêðåòèçàöèè; – êîëè÷åñòâîì çâóêîâûõ êàíàëîâ (ìîíî, ñòåðåî). Ðàçðåøåíèå îïðåäåëÿåòñÿ êîëè÷åñòâîì áèòîâ íà äèñêðåòèçèðîâàí- íóþ âåëè÷èíó, îáû÷íûå ðàçìåðû äèñêðåòèçèðîâàííûõ âåëè÷èí - 4, 8 è 16 áèòîâ. ×àñòîòà äèñêðåòèçàöèè – êîëè÷åñòâî çàìåðîâ àìïëèòóäû àíàëîãîâî- ãî ñèãíàëà çà åäèíèöó âðåìåíè. ×åì âûøå ÷àñòîòà äèñêðåòèçàöèè, òåì âûøå êà÷åñòâî çâóêà, íî ïðè ýòîì äëÿ õðàíåíèÿ äèñêðåòèçèðîâàííûõ âåëè÷èí òðåáóåòñÿ áîëüøèé îáúåì ïàìÿòè èëè äèñêîâîãî ïðîñòðàíñòâà. Îáùåïðèíÿòûìè çíà÷åíèÿìè ÷àñòîòû äèñêðåòèçàöèè ÿâëÿþòñÿ: – 44,110 êÃö – âûñîêîå êà÷åñòâî; – 22,254 êÃö – ñðåäíåå êà÷åñòâî; – 11,025 êÃö – íèçêîå êà÷åñòâî. Îáúåì äâîè÷íûõ äàííûõ, ïîëó÷åííûõ â ðåçóëüòàòå äèñêðåòèçàöèè àóäèîèíôîðìàöèè â òå÷åíèå íåñêîëüêèõ ñåêóíä, äîñòàòî÷íî âåëèê (â çàâèñèìîñòè îò ïàðàìåòðîâ îöèôðîâêè) è åäèíñòâåííûì ðåøåíèåì ïðîáëåìû õðàíåíèÿ è ïåðåäà÷è îãðîìíûõ îáúåìîâ çâóêîâîé èíôîðìà- öèè ÿâëÿåòñÿ èõ ñæàòèå. Àóäèîäàííûå, êàê è áîëüøèíñòâî äâîè÷íûõ äàííûõ, ñîäåðæàò âûñîêóþ èçáûòî÷íîñòü, êîòîðàÿ ìîæåò áûòü óäàëåíà ïðè ñæàòèè. Ýôôåêòèâíîñòü îáû÷íûõ ìåòîäîâ ñæàòèÿ, ïðèìåíÿåìûõ ìíîãèìè àðõèâàòîðàìè (zoo, pkzip è äð.) ïðè ñæàòèè àóäèîèíôîðìà- öèè, íå ïðåâûøàåò 10-20%. Àëãîðèòìû ñæàòèÿ àóäèîèíôîðìàöèè ÷àñòî ñîïðîâîæäàþòñÿ ïîòåðÿ- ìè. Òàêèå ñõåìû ñæàòèÿ ïðåäóñìàòðèâàþò îòáðàñûâàíèå äàííûõ ñ ó÷åòîì âîñïðèÿòèÿ ïñèõîàêóñòè÷åñêîé ñèñòåìû ÷åëîâå÷åñêîãî ìîçãà. ×àñòü çâóêîâ, êîòîðûå ÷åëîâåê íå â ñîñòîÿíèè ðàçëè÷èòü, ìîæåò áûòü îòáðîøåíà ïî ïðè÷èíå èõ áåñïîëåçíîñòè. Ýòîò ïðèíöèï ðåàëèçîâàí è óñïåøíî ïðèìåíÿåòñÿ â ôîðìàòå MPEG (Motion Picture Experts Group) - Layer-3 (èëè ïðîñòî ÌÐ3). Âñå ÷òî òðåáóåòñÿ äëÿ âîñïðîèçâåäåíèÿ äàííûõ MP3, êîäèðóåòñÿ íåïîñðåäñòâåííî â ïîòîê äàííûõ è, ñëåäîâà- òåëüíî, íå òðåáóåòñÿ íè çàãîëîâêà, íè äðóãèõ îïèñàíèé. Ïðè âîñïðîèç- âåäåíèè äàííûõ MP3 íóæíî èñïîëüçîâàòü ëèáî àïïàðàòíî-ïðîãðàìì- íûé, ëèáî ïðîãðàììíûé ïðîèãðûâàòåëü (player). Òàêîé ïðîèãðûâàòåëü ÷èòàåò èç ïîòîêà äàííûå MP3, ðàñïàêîâûâàåò èíôîðìàöèþ è ïîñûëàåò åå íà àóäèîñèñòåìû êîìïüþòåðà. Ñêîðîñòü âîñïðîèçâåäåíèÿ çàâèñèò òîëüêî îò ðåñóðñîâ êîìïüþòåðà, à êà÷åñòâî ïîòîêà äàííûõ MP3 îïðåäå- ëÿåòñÿ â ïðîöåññå êîäèðîâàíèÿ èíôîðìàöèè. Ìåòîäû ñæàòèÿ áåç ïîòåðü ïîçâîëÿþò ñîõðàíÿòü äàííûå â ïîëíîì îáúåìå, ò.å. îíè ïîñëå ðàñïàêîâêè ïîëíîñòüþ ñîõðàíÿþòñÿ. 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Id~~=${?z|k9N! p(퉱;)pؚ}VrX0Cf7W`N v1줡^9pgVrX0Cf7W`_%`wN굙j56al–g|2I~+‹m Y;)B[vғ_U5b'Oވo If soNݹc$Q;)Nvz8Q4۶;ivRTVvYw`a,;)c'}f47`|~,<mY$;vRdN'ICb]9>OE½R!Ord}W ɻ!_.ՑbwXʽ.rx}B扢qī7F > v`w>bof/ >lzP|(رm hfqlz+P|(W ,pzm l:ZWab 'ި^(pzmlm:ZWab 'ި^(pzۥDvĹl:ZWab 'ި^3#هsQ{ZgDc(Q'ۺuZblȃ\~)q[9 w;^oӜSzZsYl luzZc l>F+s眐,89jZYl lu8_oJ`6.,F9r> ^V,,66:k%Po{_d9Cr)9m i3FO,S8s:m^-,66:ZYalCf7Y` v1!g96Yp7՜kЛh5g-aW9'(gog>Nd9~ť]] a"a K*kuB[\^ɹ1JwY+CNG+o#!AoȑO]U9*0q}&;Y9[Ұ~+@.d m,,028 Ïîòîê àóäèîäàííûõ ñîñòîèò èç áëîêîâ äàííûõ, ïîëó÷åííûõ òàêæå â ðåçóëüòàòå äåéñòâèÿ ìíî- ãîýòàïíîãî àëãîðèòìà ñæàòèÿ, è èìååò îäèíàêîâîå ðàçðåøåíèå èíôîðìàöèè. Ðàçðåøåíèå áëî- êîâ äàííûõ â ïîòîêå àóäèîäàí- íûõ íå ïðåâûøàåò ðàçðåøåíèÿ èñõîäíîé àóäèîèíôîðìàöèè, óêàçàííîãî â çàãîëîâêå ôàéëà (ðèñ.2). Ýòî îáñòîÿòåëüñòâî ïî- çâîëÿåò äîïîëíèòåëüíî ïðèìå- íÿòü ëþáîé ñïîñîá êîäèðîâàíèÿ ïîòîêà àóäèîäàííûõ, ÷òî ïðèâî- äèò ê åù¸ áîëüøåé ñòåïåíè ñæà- òèÿ èñõîäíîé èíôîðìàöèè. Ñõå- ìà ïîòîêà àóäèîäàííûõ ïðåäñòàâ- ëåíà íà ðèñ.4. Ïðè äåêîìïðåññèè è âîñïðî- èçâåäåíèè çâóêîâîé èíôîðìàöèè íåîáõîäèìî èñïîëüçîâàòü ïðî- ãðàììíûé ïðîèãðûâàòåëü, êîòî- ðûé âîññòàíîâèò èñõîäíóþ èí- ôîðìàöèþ â WAV-ôîðìàòå. Êîëè÷åñòâî ýòàïîâ êîìïðåñ- ñèè ìíîãîýòàïíîãî àëãîðèòìà ñæàòèÿ íà îñíîâå âû÷èñëåíèÿ òî÷åê ïåðåãèáà â ñòðóêòóðå ñèã- íàëà îïðåäåëÿåòñÿ ñðåäíåêâàäðàòè÷åñêîé îøèáêîé (ÑÊÎ), âíîñèìîé äàííûì àëãîðèòìîì â ñòðóêòóðó èñõîäíîãî çâóêîâîãî ñèãíàëà. Ïðè äâóõýòàïíîì ñæàòèè ÑÊÎ äëÿ ñîîòâåòñòâóþùèõ ÷àñòîò äèñêðåòèçàöèè (Fä), ðàçðåøåíèÿ è êîëè÷åñòâà êàíàëîâ ïðèâåäåíà â òàáëèöå. Òàêèì îáðàçîì, ìíîãîýòàïíûé àëãîðèòì ñæàòèÿ íà îñíîâå âû÷èñëå- íèÿ òî÷åê ïåðåãèáà â ñòðóêòóðå ñèãíàëà íóæíî êëàññèôèöèðîâàòü êàê àëãîðèòì ñæàòèÿ ñ ïîòåðåé èíôîðìàöèè. Ñëåäîâàòåëüíî, óâåëè÷åíèå êîëè÷åñòâà ýòàïîâ êîìïðåññèè äàííûõ âëå÷åò çà ñîáîé óâåëè÷åíèå ÑÊÎ, âíîñèìîé ìíîãî- ýòàïíûì àëãîðèò- ìîì ñæàòèÿ. Ïðè äâóõýòàïíîì ñæà- òèè ÑÊÎ íå ïðå- âûøàåò 6,5% è ýòî íå îòðàæàåòñÿ íà Размер исходных данных без равнозначных смежных отсчетов N1 Размер блока данных нулевых значений 1-го этапа N2 Размер блока данных значений локальных "min" 2-го этапа N3 Размер блока данных значений локальных "max" 2-го этапа N4 Размер блока данных нулевых значений локальных "min" 2-го этапа N5 Размер блока данных нулевых значений локальных "max" 2-го этапа N6 Коэффициент коррекции линейной аппроксимации 1-го этапа K Способ кодирования потока аудиоданных LZW Ðèñ. 3. 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Ïðè çíà÷å- íèÿõ ÑÊÎ (11~15%) ñòðóêòóðà èñõîäíîãî ñèãíàëà èñêàæàåòñÿ òàê, ÷òî ïîÿâëÿþòñÿ ïîñòîðîí- íèå øóìû, ðàçëè÷èìûå ÷åëîâå- ÷åñêèì ñëóõîì. Ïîýòîìó îïòè- ìàëüíûì êîëè÷åñòâîì ÿâëÿåòñÿ 2 ýòàïà êîìïðåññèè. Ïîñëåäóþ- ùåå êîäèðîâàíèå ïîòîêà àóäèî- äàííûõ íåîáõîäèìî ïðîâîäèòü ñ èñïîëüçîâàíèåì àëãîðèòìîâ ñæà- òèÿ áåç ïîòåðü. Ïðåäëîæåííûé ôîðìàò õðà- íåíèÿ è ïåðåäà÷è àóäèîäàííûõ îáëàäàåò ðÿäîì ïðåèìóùåñòâ: – âîçìîæíîñòü ðåãóëèðîâàòü ñòåïåíü ñæàòèÿ èíôîðìàöèè â çàâèñèìîñòè îò ÑÊÎ; – äîñòàòî÷íî âûñîêèé êîýô- ôèöèåíò êîìïðåññèè äàííûõ, ïîñëå êîìáèíèðîâàííîãî èñïîëü- çîâàíèÿ ìíîãîýòàïíîãî àëãîðèò- ìà ñæàòèÿ (ñ ïîòåðåé èíôîðìàöèè) è àëãîðèòìà ñæàòèÿ áåç ïîòåðü (â ðàññìàòðèâàåìîì ñëó÷àå LZW). Ñòåïåíü ñæàòèÿ â 1,5 ðàçà ïðåâûøàåò ñæàòèå èäåíòè÷íûõ àóäèîäàííûõ ïðè ôîðìèðîâàíèè ôîðìàòà MPEG- Layer-3 (ÌÐ3). Ñïèñîê ëèòåðàòóðû: 1. Âàêóëþê Á. Êàê è çà÷åì ñæèìàþò çâóê // Êîìïüþòåð- íîå îáîçðåíèå. Ê.: Èçä-âî ÎÎÎ “ ITC ” , 1998. ¹ 34. Ñ. 20-26. 2. Ìþððåé Ä., Âàí Ðàéïåð Ó. Ýíöèêëîïåäèÿ ôîðìàòîâ ãðàôè÷åñêèõ ôàéëîâ: Ïåð. ñ àíãë. Ê.: Èçäàò. ãð. BHV, 1997. 672ñ. 3. Èâàíîâ Â.Ã., Ëîìîíîñîâ Þ.Â. Àëãîðèòì ñæàòèÿ äàííûõ íà îñíîâå âû÷èñëåíèé òî÷åê ïåðåãèáà â ñòðóêòóðå ñèãíàëà // Âåñò- íèê ÕÃÏÓ. Ñèñòåìíûé àíàëèç, óïðàâëåíèå è èíôîðìàöèîííûå òåõíîëîãèè 2000. ¹ 94. Ñ. 25-29. Ïîñòóïèëà â ðåäêîëëåãèþ 30.10.2000 Èâàíîâ Âëàäèìèð Ãåîðãèåâè÷, êàíä. òåõí. íàóê, äîöåíò, çàâåäóþ- ùèé êàôåäðîé èíôîðìàòèêè è âû÷èñëèòåëüíîé òåõíèêè Íàöèî- íàëüíîé þðèäè÷åñêîé àêàäåìèè Óêðàèíû èìåíè ß.Ìóäðîãî. Íà- ó÷íûå èíòåðåñû: êîäèðîâàíèå è ðàñïîçíàâàíèå ñèãíàëîâ ðàçëè÷- íîé ôèçè÷åñêîé ïðèðîäû. Àäðåñ: Óêðàèíà, 61024, Õàðüêîâ, óë. Ïóøêèíñêàÿ, 77, òåë. (8-0572) 19-12-02, 94-80-39, ôàêñ: (8-0572) 475-825, å-mail: uracad@kipt.kharkov.ua Ëîìîíîñîâ Þðèé Âÿ÷åñëàâîâè÷, êàíä. òåõí. íàóê, àññèñòåíò êàôåä- ðû èíôîðìàòèêè è âû÷èñëèòåëüíîé òåõíèêè Íàöèîíàëüíîé þðè- äè÷åñêîé àêàäåìèè Óêðàèíû èìåíè ß.Ìóäðîãî. Íàó÷íûå èíòåðå- ñû: ìåòîäû è àëãîðèòìû êîìïàêòíîãî ïðåäñòàâëåíèÿ äàííûõ. Àä- ðåñ: Óêðàèíà, 61024, Õàðüêîâ, óë. Ïóøêèíñêàÿ, 77, òåë. (8-0572) 19- 12-02. Ðèñ. 4. Ïîòîê àóäèîäàííûõ Блок данных нулевых значений локальных "max" 2-го этапа 6 Блок исходных данных без равнозначных смежных отсчетов 1 Блок данных нулевых значений 1-го этапа 2 Блок данных значений локальных "min" 2-го этапа 3 Блок данных значений локальных "max" 2-го этапа 4 Блок данных нулевых значений локальных "min" 2-го этапа 5 U xklUϝض mEI J ҈ AJUyC(&EIG6`%Qib(EE D>"$"H;۽2ۭD`2?{ٻ37uDLܔ.RvD@m'YVThHsEƐL&~#z&Ms) \v 79nx-fzDNۗJzY h{B';/3icl `{H4jJ(p%LϦ K>لT (2{SiH;>p$Rs7ؑV#L9t %=zNs@>tx{dS4[>f:cfA\-G2]. &~.n-qG򬞘g3d|'e6NuSP߮~_oYdE#C#*{k7qYr#ygu>fρ_jL[e:K1JvHwYCG:!? 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ÊÓÇÜÌÅÍÊÎ, Ë.Ô. ÍÅÍÜÊÎ ÑÈÑÒÅÌÀ ÓÏÐÀÂËÅÍÈß ÝÊÑÏÅÄÈÖÈÎÍÍÛÌÈ ÏÐÅÄÏÐÈßÒÈßÌÈ ÍÀ ÎÑÍÎÂÅ ÂÑÒÐÎÅÍÍÎÉ ÈÌÈÒÀÖÈÎÍÍÎÉ ÑÈÑÒÅÌÛ Ðàññìàòðèâàåòñÿ ñòðóêòóðà ñèñòåìû óïðàâëåíèÿ ýêñïåäèöè- îííûì ïðåäïðèÿòèåì, îñíîâíûìè ïðèíöèïàìè ïîñòðîåíèÿ êîòî- ðîé ÿâëÿåòñÿ ïðîãðàììíî-ÿâíûé ïðèíöèï óïðàâëåíèÿ è èñïîëü- çîâàíèå âñòðîåííîé èìèòàöèîííîé ñèñòåìû. Ïðè ñîçäàíèè âñòðî- åííîé èìèòàöèîííîé ñèñòåìû èñïîëüçóåòñÿ èäåîãðàôè÷åñêèé ïîä- õîä. Ýêñïåäèðîâàíèå ïåðèîäè÷åñêèõ èçäàíèé âêëþ÷àåò îïåðàöèè: ïðè- åìà (èäåíòèôèêàöèè êàæäîãî èç ýëåìåíòîâ âõîäíîãî ìàòåðèàëüíîãî ïîòîêà вх M , êîòîðûìè ÿâëÿþòñÿ ïà÷êè ñ ïå÷àòüþ), ðàñïðåäåëåíèÿ èõ ìåæäó ñîðòèðîâî÷íûìè óñòàíîâêàìè ïî íàêîïèòåëÿì, ôîðìèðîâàíèÿ ïîñûëîâ â àäðåñ êîíêðåòíûõ ïîëó÷àòåëåé è èõ óïàêîâêè, ôîðìèðîâà- íèÿ ãðóïï ïîñûëîâ è ïîñûëîâ â àäðåñ ðåéñîâ äîñòàâêè ïå÷àòè, ïîäãî- òîâêè ñîïðîâîäèòåëüíûõ è ïðîèçâîäñòâåííûõ äîêóìåíòîâ. Ñëåäîâà- òåëüíî, вх M äëÿ äàííîãî òåõíîëîãè÷åñêîãî ïðîöåññà ÿâëÿåòñÿ ïîòîêîì ïà÷åê èçäàíèé îò ìåñòíûõ èëè ñòîðîííèõ òèïîãðàôèé, êîòîðûå íåîá- õîäèìî îáñëóæèâàòü. Àêò îáñëóæèâàíèÿ ñîñòîèò èç äâóõ îñíîâíûõ ñîñòàâëÿþùèõ: îæèäàíèÿ îáñëóæèâàíèÿ i H è îáñëóæèâàíèÿ i K , ãäå i H – íàêîïèòåëü, â êîòîðîì îäíîâðåìåííî ìîæåò íàõîäèòüñÿ H i i L l , 0  ïà÷åê âõîäíîãî ïîòîêà вх M , H i L – åìêîñòü i -ãî íàêîïèòåëÿ, i K – êàíàë îáñëóæèâàíèÿ   I i , 1  . Âñå ýòî ïîçâîëÿåò îòíåñòè òåõíîëîãè÷åñ- êèå ïðîöåññû ýêñïåäèðîâàíèÿ ïåðèîäè÷åñêèõ èçäàíèé ê ñèñòåìàì ìàññîâîãî îáñëóæèâàíèÿ, êîòîðûå äîñòàòî÷íî ïîëíî îïèñûâàþòñÿ êàê Q -ñõåìû â âèäå:   A R Z H U W Q , , , , ,  . Çäåñü W – âõîäíîé ïîòîê, U – ïîòîê îáñëóæèâàíèÿ, R – ñîïðÿæåíèÿ ýëåìåíòîâ ñòðóêòóðû , H – ïîäìíîæåñòâî ñîáñòâåííûõ ïàðàìåòðîâ , A – îïåðàòîð àëãîðèòìà îáñëó- æèâàíèÿ çàÿâîê, Z – îïåðàòîð ñîñòîÿíèé ýëåìåíòîâ ñèñòåìû. Àëãîðèòìè÷åñêóþ ìîäåëü ïðîöåññà îáðàáîòêè çàÿâîê â ñèñòåìàõ ìàññîâîãî îáñëóæèâàíèÿ ìîæíî ïðåäñòàâèòü êàê   I h A i M , ,   , ãäå i h – ñîâîêóïíîñòü ýëåìåíòàðíûõ îïåðàòîðîâ;  – ëèíåéíûé ïîðÿäîê x[lUkvn z,EhZDECFTQ//cExK!*U(`!$TMز|fw|.-b|!a7w.gfΜٳg&ƈHK/N,O+ W$Ytы܁,QLRoH[W-B9j-¸WC:{kFg}P{dBmRɖB(5N+&ec}\|尝'1kOv-31`\If 0M2U+S$INibgȥY('yrNvC'Ŀ¦6()R٩RG̻:E9YLJ󟟰"ʱͳR-vl%'EV4nod0;,\+u3쟣;Ugq<,$/)Y9[F- [nΜ"s:GQsU>\T&ߧE=͑[4vYH}*I*/e0Sz!C}_ν.V~ z3xľ GhgV{8ys;@yt@[9l^M<sCMڡ;{e;hwvkoo}YSkrNsQkTF}:Rvmv)~)pԲ5 cn Y$Gʃ|^M2)xEҤª e)s/QI 9bW6Wǻt@iv/Vx|gb=y>NkA%kj%oݯ)Ge*N}alji>w*Ym`UxKFL>Z@XHi/"f1qѕ§RBblOG7`)*9>#5*l`WE-#"t;pOi /cgnyxg>&DֺB@.*G>JHVTN{#wՏH/[sm/R>z>.Jg''Iw?fr$TD R͕ݏ3q;E޿?{;jЗovqIvP=gn_ wC:x?fjSB,vxVnZze> 0=_@Wl>~ާ:^3J]$bS.=ҌMw8cF#_]+tgZnd:]Mnŷr5`-ƒ slYGo^-RG; 7Է/C9eΧ3shoԹ;uisRE|sI:8ewcb8GCghg,Е^瀮Nݍl6c.њ9.Zv΅'ȼh|F1N[Uo3Iuꕿ^j|Utss5a-YQ6!!Ad>ݧv9'|]U_=vU}U=v)I 8x$=#L?;I.I)g$S_|fJ9j6IV>IQ)Udc_Ʃɢ%ɒ"(Byb{W[GG@aV)Rzf)D LjIB Mɡt *=”LIS̖FAuy[e̪~,$ j'$aF٥8JrܥIEy/D#N*u֔weIorNҳqH~M4l:^ˏ{9U?D̤D%Yumo=ٝ U_}~GJ9.熠ߩڳ;UrR?ʯnQLyg<739Z;yXԽyvnۅWQ۴b\?Hi@%[;3+)[Vy}/OtIEA4,\23Y5p95'f&]޲Ciwf&w}6fÒSыI2pċKQOONNΒ:8_rǕKX%P;R):`.^S;e)9BO)x?rYu;hʷFkX+\ 3yF7ab6y*rjs N՜F*ci{skڊemdN!yNQg~#hǘK}K{)*Or% {]K+ͿbW5gs|kRU^sD/¯\O/v_P;wx~}B~Y5PNq둶}<֌6^{/8$Vw__W9"tӫ[( z/ SMlx"Ȟ_uWQzisz52R8|uEx8zk k# έ⥣w :C|szn֞@JT?j seN9UNAP*!@5yB2lNY>^MMLlO AE{A,ʹNߟ{!yE 쇬:[,g0m+9=H%LHC..NCȋK:0uy|$)JG==$pzmEz]Srp]N`϶qrqqq1=yy|QmftA=} m`^r3>p" ط5\O%>7-IVOS#{mŏI풿US>N@ڛ^>qÎ'?R _pa'==Gl:T .Nz4S%h)f }Dk9?|eZ.C~uy\ 畮UtC-Facvv-ep<ݧtedt+VFݦwOfW~]_#(x@CB;Ӆ/QI%y*V7:*1GV @zܼEG/ʩ$V*rpywY Oԓާw|H{䒗je w &cݬ8xZZ_k^vY*?e*IR2֒.c1oẓw *h2֊oY~><wSp ZY'CXn~%)oEB-@%-PeDe/8?TcPܓIiL~xRoҾtxz77{YgدWT,i~|{#?~%xLtCEq)…g;2c}bZ~86֦{ .; PʦO\?h'5A~}Yjjcfa2"<_PƋMc2m1-kh589e4~4yDʗ.mJZi۵X Gt=^^Vе[(몭Ƽm_FӶ`YrM>P |ن26yM|PO&9m߾BLW"^=Sm9ؕGg?~koߐ~a] ,owkdqťlx~E`eʵC}4oJ&ܢ~&r$۬pb} =J2E~ب6oRhcN>NnJ~x>=ẆԘ >i}FCqx7$RNL”GBjM\ 'o+s|xJ2{1tDn=_?{IyyL}vng塎v<{i{63L;G7n *p{0$Zk6fC#M=䡇Oz<'^)CW Y.$mK^7N1)oswÓ͇32YtᤇߒL%X,.sչGse]e=\n#t @ Gtp'B˯Dʝ[&?La{WB'loԳ^Ut/ugo݃3E \ZU|UvLE'{|a| eZ4)Ci;3Wu)Gȃn-e] ֻr8cS>GX.eXNS;lFk~*{SxMjܟȥ s ?O8]*| mاl6 /Q_yx# 0?ρ# pveIUzZq/Ǜs3}JYU3~m o s' O״Y=j9Lr/p|-}knghhv3]v+QIEg5Jz:LCO^קwgs^R.y[;F^7rAyE:b:lnRws&/=%cK$8ڮ{ BzVzB۩{]9|}׫pz%Z b2iI{dTȭz!s~WK^^-U_=7n;USY&  L/v)S|E x)y^J)Rb%]u}K/a#O5ņM4TI=JiozG 5h~.Vו[пY-S}iz8E]zSװ O[ mV=U?8Ҁw%, \.ਓ==_7KƀEtAxfUOI<Թk'<3͢ ߲gi٨=GO579:r} r rHS?YN!\VN1U9j7pV(fLЫ9G_8:"ڵzmw.f=zi~-"_8_^'E,Íj-YzܼlMGekdtljHS##"";");O{V/NrɃiNOh-/vjKv;gȹ&:a@ p9oosJ*IX 홦W(K6^GL[#5+N%x6H"BH,_YϞizr 4מY}eltgAɇ\`=z]w|r (gmŵcgcS>g22{T2!U69W l/6gXX_> O]n'̞ݲ6֣[ u?u?C@{f ϧ#l{ɋ减G+}|$;YyEtf;\q2_P{mM57xsoy" k y,X<~e:ynEKGS2{`[NrrOnp~[qmL9;m&EؗnKO}[S/6WyxkOI'mxL_ͨwx/ið%?p)# ĭ(ߴy,y]&~~~BK~5ϓKby? 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Ñòðóêòóðà ýëåìåíòàðíîãî îïåðàòîðà áóäåò èìåòü âèä: y i c i i h h h ,  , çäåñü y i c i h h , – i - å ýëåìåíòàðíûå îïåðàòîðû ñîñòîÿíèÿ è óñëîâèÿ ñîîòâåòñòâåííî, y i h – ôîðìèðóåò óñëîâèÿ, ïðè âûïîëíåíèè êîòîðûõ ïðîèñõîäèò ñöåïëåíèå îïåðàòîðà i h ñî ñëåäóþùèì îïåðàòî- ðîì 1  i h ïóòåì íåêîòîðîãî ëîãè÷åñêîãî óñëîâèÿ. Èíèöèàòîðîì I âû- ïîëíåíèÿ ïîñëåäîâàòåëüíîñòè îïåðàòîðîâ i h ÿâëÿåòñÿ ïîòîê çàÿâîê íà îáñëóæèâàíèå i W . Ïîýòîìó л i t i y i h h h ,  , ãäå t i h – çàäàåò ìîìåíò âðåìåíè ñöåïëåíèÿ èíèöèàòîðà ñ îïåðàòîðîì 1  i h , à л i h – ëîãè÷åñêîå óñëîâèå. Ñëåäîâàòåëüíî, Z – ïîëíîñòüþ îïðåäåëÿåò ïðîöåññû, ïðîèñ- õîäÿùèå â ñèñòåìàõ ìàññîâîãî îáñëóæèâàíèÿ. Ñîâîêóïíîñòü    , i h ïðåäñòàâëÿåò ñîáîé òðåê èíèöèàòîðà I . Àíàëèç îïåðàòîðîâ i h ïîçâîëÿ- åò âûäåëèòü áàçîâûé íàáîð îïåðàòîðîâ   б h , ïîëàãàÿ, ÷òî äëÿ ëþáîãî i h ìîæíî íàéòè ñîîòâåòñòâóþùèé îïåðàòîð   б h . Ê îñíîâíûì áàçîâûì îïåðàòîðàì ìîæíî îòíåñòè: îïåðàòîð íàêàïëèâàíèÿ б н h , îïåðàòîð çàäåð- æêè íà îáñëóæèâàíèå б з h , îïåðàòîð îáúåäèíåíèÿ ïîòîêîâ â îäèí б о h , îïåðàòîð ðàçäåëåíèÿ ïîòîêîâ б р h . Îïåðàòîð íàêàïëèâàíèÿ б н h îáåñïå÷èâàåò íàêàïëèâàíèå ýëåìåíòîâ âõîäÿùåãî ïîòîêà äî çàäàííîãî êîëè÷åñòâà    s 0 . Îïåðàòîð çàäåðæ- êè íà îáñëóæèâàíèå б з h èìååò äâå ðàçíîâèäíîñòè:   At h б з – çàäåðæêè íà âðåìÿ At ;    б з h – çàäåðæêè íà âðåìÿ  . Îïåðàòîðû îáúåäèíåíèÿ ïîòîêîâ б о h è èõ ðàçäåëåíèÿ б р h èìåþò äâå ðàçíîâèäíîñòè:   с h б о ,   с h б р – ñâîáîäíîãî îáúåäèíåíèÿ è ðàçäåëåíèÿ ïîòîêîâ ñîîòâåòñòâåííî;   у h б о ,   у h б р – óïðàâëÿþùåãî îáúåäèíåíèÿ è ðàçäåëåíèÿ ïîòîêîâ ñîîò- âåòñòâåííî. Êàæäûé èç áàçîâûõ îïåðàòîðîâ ïðåäñòàâëÿåòñÿ â âèäå ýëåìåíòàðíûõ èäåîãðàìì [1]. Êðîìå òîãî, òàê êàê òåõíîëîãè÷åñêîå îáîðóäîâàíèå ðàçìåùàåòñÿ â ïîìåùåíèè, èìåþùåì îïðåäåëåííûå ïðîñòðàíñòâåííûå ðàçìåðû, à ñàìî îáîðóäîâàíèå – îïðåäåëåííûå ïðîñòðàíñòâåííûå ðàçìåðû â ýòîì ïîìå- ùåíèè, òî â êà÷åñòâå èäåîãðàôè÷åñêîãî ýëåìåíòà âûáðàíà ïðÿìîóãîëü- íàÿ ÿ÷åéêà. Èñõîäÿ èç ýòîãî, èäåîãðàôè÷åñêîå îïèñàíèå ñòðóêòóðû òåõíîëîãè- ÷åñêîãî ïðîöåññà ñòðîèòñÿ íà îñíîâå èñïîëüçîâàíèÿ: %xilTUϛL]C)(.  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Ìàêåò ïîìåùåíèÿ ÿâëÿåòñÿ ñîâîêóïíîñòüþ ÿ÷ååê ãðàôè- ÷åñêîé ìàòðèöû     K k L l Z Z k l , 1 , , 1 ,    . ß÷åéêè ìàòðèöû äåëÿòñÿ íà äâà âèäà: c ik Z – ÿ÷åéêè, çàíÿòûå îïðåäåëåííûìè ñòðîèòåëüíûìè ýëå- ìåíòàìè: êîëîíàìè, ëåñòíèöàìè, îêíàìè, ñòåíàìè è ò.ï.; о ik Z – ÿ÷åéêè, èñïîëüçóåìûå äëÿ ðàçìåùåíèÿ òåõíîëîãè÷åñêîãî îáîðóäîâàíèÿ. Ìàêåò ïîìåùåíèÿ ñòðîèòñÿ ïóòåì îïðåäåëåíèÿ ðàçìåðîâ ïîìåùåíèÿ, îïðåäå- ëåíèÿ ðàçìåðîâ ÿ÷ååê è èõ çàïîëíåíèÿ èäåîãðàììàìè ñòðîèòåëüíûõ ýëåìåíòîâ c Id ; – èäåîãðàìì ýëåìåíòîâ (óñòðîéñòâ) òåõíîëîãè÷åñêîãî ïðîöåññà i Id . Òàêèå èäåîãðàììû ïðåäñòàâëÿþò ñîáîé ãðàôè÷åñêîå (ïëîñêîñòíîå èëè ïðîñòðàíñòâåííîå) èçîáðàæåíèå êîíêðåòíûõ òåõíè÷åñêèõ óñòðîéñòâ è ðàáî÷èõ ìåñò îáðàáîòêè ïåðèîäè÷åñêèõ èçäàíèé, âõîäÿùèõ â òåõíîëî- ãè÷åñêèé ïðîöåññ. Èäåîãðàôè÷åñêàÿ ñåòü Is òåõíîëîãè÷åñêîãî ïðîöåññà â ýòîì ñëó÷àå ÿâëÿåòñÿ ñîâîêóïíîñòüþ ÿ÷ååê: } , { o lk c lk Z Z Is  , ãäå c lk Z – ñòðîèòåëüíûå ýëåìåíòû ïîìåùåíèÿ; o lk Z – ýëåìåíòû òåõíîëîãè÷åñêîãî îáîðóäîâàíèÿ. Ïîýòîìó ïàëèòðà èäåîãðàôè÷åñêèõ ýëåìåíòîâ   i Id Id  ñîñòîèò èç ïàëèòðû òåõíîëîãè÷åñêîãî îáîðóäîâàíèÿ   o i о Id Id  è ïàëèòðû ñòðîè- òåëüíûõ ýëåìåíòîâ   o i c Id Id  . Ñèíòåç èäåîãðàôè÷åñêîé ìîäåëè ñèñòåìû ) (Is ïðîèçâîäèòñÿ íà îñíî- âå ñëåäóþùèõ ïðàâèë: 1) îáúåäèíåíèå i Id â Is îñóùåñòâëÿåòñÿ ñ ó÷åòîì îðèåíòàöèè äóã èäåîãðàôè÷åñêèõ ýëåìåíòîâ; 2) èäåîãðàôè÷åñêèé ýëåìåíò ìîæåò èìåòü íåñêîëüêî âõîäîâ è âûõî- äîâ, íî èõ îáùåå ÷èñëî íå äîëæíî ïðåâûøàòü 4-õ; 3) âûõîäíûå äàííûå èäåîãðàôè÷åñêîãî ýëåìåíòà i Id ÿâëÿþòñÿ âõîä- íûìè äàííûìè äðóãîãî j Id , åñëè îíè èìåþò ñîâìåñòíóþ àêñèîìó e è ïîðîã p âû÷èñëåíèÿ; 4) êîìïëåêñèðîâàíèå èäåîãðàôè÷åñêèõ ýëåìåíòîâ â èäåîãðàôè÷åñ- êóþ ñåòü îñóùåñòâëÿåòñÿ íà îñíîâå ïëàíîâ îòîáðàæåíèÿ } , , { f o k o l o o П П П П  , à ïðîâåðêà ïðàâèëüíîñòè êîìïëåêñèðîâàíèÿ – íà îñíîâå ïëàíà ñîäåðæàíèÿ } , , { Пc П П П k c l c c  ; 5) âîçìîæíîñòü îáúåäèíåíèÿ äâóõ èäåîãðàôè÷åñêèõ ýëåìåíòîâ â àíñàìáëü   j i Id Id Id ,  îïðåäåëÿåòñÿ àêñèîìîé âû÷èñëåíèÿ   j i Id Id e , . #xylU[豥mٶR(-(g@xH"D -$V"!@ T*@&*31/gv_זD0&̛7zD"# 2#"u n`E%Ġ9SdNO*h&3hgKILkYj2ɔL,2vIe|R .C1~9y%_5BQ&Ƭ </r%lk+_JEqJ0$*I5Vs+׻*Pa-˩gI^5:zej)%zdLgUSn3[AN,=Z1ZSCީu]_s$K o@e|+M/G{/޺Cd!>r>>J,PIѤ,p;ĝw WIL64Q dpMjOjeI25$\͚~A\C灙uwNѧ^b']VRy7md> Ny ~E.8I2Fk9()?p?0nZf֓B_&~koҤ/~CX{Ps]$@6'l![3N3w\0m{x&Ua'wrW_(Va۟a[%xlZ‡^9gR+.qx>zIWG? 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Êóçüìåíêî Â.Ì., Êîâòóíîâè÷ Ñ.À., Øóëüãà Þ.Â. Èñïîëü- çîâàíèå èäåîãðàôè÷åñêîãî ïîäõîäà ïðè àäàïòàöèè ïðîãðàììíûõ ñðåäñòâ ïîëüçîâàòåëåì/ Ñá. íàó÷. òðóäîâ ÕÃÏÓ “ Èíôîðìàöèîííûå òåõíîëîãèè: íà- óêà, òåõíèêà, òåõíîëîãèÿ, îáðàçîâàíèå, çäîðîâüå ” , âûï.7, ÷. 1. Õ.: ÕÃÏÓ, 1999. Ñ.118-121. 2. Ïåòðîâ Ý.Ã. Îðãàíèçàöèîííîå óïðàâëåíèå ãîðîäîì è åãî ïîäñèñ- òåìàìè (ìåòîäû è àëãîðèòìû). Õàðüêîâ: Âèùà øêîëà, 1986. 144 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 06.11.2000 Êóçüìåíêî Âèêòîð Ìèõàéëîâè÷, êàíä. òåõí. íàóê, äîöåíò, ïðî- ôåññîð êàôåäðû ñèñòåìîòåõíèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ìà- òåìàòè÷åñêîå è èìèòàöèîííîå ìîäåëèðîâàíèå òåõíîëîãè÷åñêèõ ïðîöåññîâ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ,, ïð. Ëåíèíà, 14, òåë. 40-93-06, ST@khture.kharkov.ua. Íåíüêî Ëåîíèä Ôåäîðîâè÷, àñïèðàíò êàôåäðû ñèñòåìîòåõíèêè, íà÷àëüíèê ÖÎÏ ÄÎÏÏ ÓÃÏÏÑ “ ÓÊÐÏÎ×ÒÀ ” . Íàó÷íûå èíòå- ðåñû: àâòîìàòèçèðîâàííûå ñèñòåìû óïðàâëåíèÿ, ïðîãðåññèâíûå èíôîðìàöèîííûå òåõíîëîãèè â ïî÷òîâîé ñâÿçè. Àäðåñ: Óêðàèíà, Êèåâ, óë. Ñàãàéäà÷íîãî, 132, êâ. 34, òåë. 220-06-74, 246-64-54. ÓÄÊ 519.7 Î.Í. ÂÎÑÊÎÁÎÉÍÈÊ, Â.Â. ÈÂÀÙÅÍÊÎ ÎÁ ÈÇÎÌÎÐÔÈÇÌÅ ÌÎÄÅËÅÉ ÊÎÌÏÀÐÀÒÎÐÍÎÉ ÈÄÅÍÒÈÔÈÊÀÖÈÈ Ðàññìàòðèâàþòñÿ ðàçëè÷íûå ìîäåëè êîìïàðàòîðíîé èäåíòè- ôèêàöèè. Ïîêàçûâàåòñÿ, ÷òî èäåíòèôèöèðóåìûé îïåðàòîð ìîæåò îáëàäàòü ñâîéñòâîì âíóòðåííåé íåëèíåéíîñòè âçàèìíî-îäíîçíà÷- íîãî õàðàêòåðà. Ïðè êîìïàðàòîðíîé ìîäèôèêàöèè èñïîëüçóþòñÿ äâå ìîäåëè êîìïà- ðàòîðà [1].  ïåðâîé ñðàâíèâàþòñÿ ñèãíàëû, ïðåîáðàçîâàííûå ïî îäíî- ìó è òîìó æå çàêîíó, ò.å. îñóùåñòâëÿåòñÿ ïðåäèêàò ýêâèâàëåíòíîñòè: ) F , F ( D ) y , x ( E y x B  , (1) ãäå A y , x  – ìíîæåñòâî âõîäíûõ ñèãíàëîâ; B F , F y x  – ìíîæåñòâî âûõîäíûõ ñèãíàëîâ; F – îòîáðàæåíèå èç À â Â; B D – ñòàíäàðòíûé ïðåäèêàò ðàâåíñòâà íà B B  , ò.å.     если , если , ) b , a ( B D 0 1 . b a ; b a   Âî âòîðîé ìîäåëè âõîäíûå ñèãíàëû ïðåîáðàçóþòñÿ ïî ðàçíûì çàêî- íàì, ò.å. îñóùåñòâëÿåòñÿ ïðåäèêàò äèôóíêöèîíàëüíîñòè [2]: ), y F , x F ( D ) y , x ( E 2 1 B  (2) xmheǯly;nܦ(;mnZJ MJ?d[&d}(tD$^DJ7 ͷse|lwkyxA~"fLDDjG=Ep4q,ԇY>ٜw(vFm`fG@ zh|'I:77iі=K3[kҫAq-Lz]kiicCc*=u1:32K6(ǐ?ٰ쵅 yU=,mɖ]6[vei6іPfO~{lAymy2Ak#>R 5m T`5OSScIcREMܲqdѯe įkB^>C1[$ 7=NR~F߁%L=1D{4pξ{od{Φ?vH43h#lvfn"L3JNmtcdj 7&-eD.> Bm6s(犣ޖȏɡߙk vFuRx/joa1"ʖvfIԢ+nN|#pwF|G@󲙇w;JϩLg=nMwuqzj/L ^!A n4x,'|IarCd_Cȿ 6!{9A.C}9S)8n57z5 A x̢zX ѽez|0D[# lqBh?ޗs}Rzk|vLK]3H^R&w*1}d (3U'Xg1T X{4/4{%En&d9=E²3jvf·ky}ɒϐWA.Ϛ An&(_`1! -evp أuu`ԵΣ|~og7M@fTNKi]5r,go鱒AXc'zr v5; 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*[>/ץ|i^NW9c5g6hFӯr{[^+%Ȳt5ܛ8X+%"Y{sy>t-+ԯ_KyzEhX6j]|<"T9|u8e_Yr<E&;BC7 |×ތϪWK&sH7G8՚Ѐp+{yM 9H{)E݋/r-?x_o]}Αh~9 rG.2b F{uI 5cu{n4F. %!#97Fֲ@{[^zzS_,NS=#Z7^q>8of /S˒Wz| >zyAi|Mηe/ j_[9CY9>c\uzmk-O7;.N\sr]?`\UT8f,=qQVЮ𭠷 Yz͒yVpm:?+_k3HΒ=[jYb2+JN.isU+8佔?{^\,fЧJ}8;t~~)*>f0O~&{.s=a%9?b 9,,36 ãäå A y , x  – ìíîæåñòâî âõîäíûõ ñèãíàëîâ; B y F , x F  2 1 – ìíîæåñòâî âûõîäíûõ ñèãíàëîâ; 2 1 F , F – îòîáðàæåíèÿ èç À â Â; B D – ñòàíäàðòíûé ïðåäèêàò ðàâåíñòâà íà B B  . Ñ òî÷êè çðåíèÿ èäåíòèôèêàöèè è ïîñòðîåíèÿ ìàòåìàòè÷åñêèõ ìîäå- ëåé ðåàëüíûõ ñèñòåì èìååò ñìûñë èçó÷àòü òîëüêî òå ïðåäèêàòû, êîòî- ðûå îïðåäåëÿþò îòîáðàæåíèå, âõîäÿùåå â ïðàâóþ ÷àñòü ðàâåíñòâ (1), (2), ñ òî÷íîñòüþ äî èçîìîðôèçìà. Ïîêàæåì, ÷òî äëÿ ïðåäèêàòîâ ýêâè- âàëåíòíîñòè è äèôóíêöèîíàëüíîñòè, è òîëüêî äëÿ íèõ âûïîëíÿåòñÿ ýòî ñâîéñòâî. Óòâåðæäåíèå 1. Ïóñòü F – îòîáðàæåíèå L â A , à G – îòîáðàæåíèå L â B è îòîáðàæåíèÿ F è G îáëàäàþò ñëåäóþùèìè ñâîéñòâàìè: äëÿ ëþáûõ L y , x  : Gy Gx Fy Fx    , òîãäà íàéäåòñÿ âçàèìíî-îäíîçíà÷- íîå ñîîòâåòñòâèå F J F J : m m   , äëÿ êîòîðîãî G F   . Äîêàçàòåëüñòâî. Íà ìíîæåñòâå L îòîáðàæåíèå F îñóùåñòâëÿåò ðàç- áèåíèå åãî íà êëàññû ñëåäóþùèì îáðàçîì: L y , x  ëåæàò â îäíîì êëàññå, åñëè Fy Fx  . Áóäåì îáîçíà÷àòü ýòî ðàçáèåíèå A  , à åãî ýëåìåíòû – a  , ïðè÷åì åñëè a x   , òî A a Fx   . Àíàëîãè÷íî ââåäåì ðàçáèåíèå B  ñ ýëåìåíòàìè b  , èíäóöèðóåìîå íà L ñ îòîáðàæåíèåì G . Äîêàæåì, ÷òî ýòè ðàçáèåíèÿ ñîâïàäàþò, ò.å. B A    . Äëÿ ýòîãî âîçüìåì ïðîèçâîëüíûé ýëåìåíò A a    è ïðîèçâîëüíûå a y , x   . Òîãäà Fy Fx  , îòñþäà b Gy Gx   , ò.å. b y , x   . Ñëåäîâàòåëüíî, ëþáàÿ ïàðà èç a  ïðèíàäëåæèò b  . Çíà÷èò, b a    . Íî ýòî âêëþ÷åíèå âûïîëíÿåòñÿ è â îáðàòíóþ ñòîðîíó. Äåéñòâèòåëüíî, åñëè b y , x     , òî b y G x G     è ýòî îçíà÷àåò, ÷òî a y F x F     , ò.å. a y , x     èëè a b    . Ïîñëåäíåå ðàâåíñòâî îçíà÷àåò, ÷òî ëþáîé ýëåìåíò ðàçáèåíèÿ A  ÿâëÿåòñÿ ýëåìåíòîì ðàçáèåíèÿ B  , è íàîáîðîò, ñëåäîâàòåëüíî, b a    . Òåïåðü ïîñòðîèì âçàèìíî-îäíîçíà÷íîå îòîáðàæåíèå G Im F Im :   . Çàôèêñèðóåì ïðîèçâîëüíûé ýëåìåíò A F Im a   . Äëÿ ýòîãî ýëåìåíòà íàéäåòñÿ x , äëÿ êîòîðîãî a Fx  , çíà÷èò, a x   . Ïîñêîëüêó b a    , òî íàéäåòñÿ b a    . Òîãäà b x   , ñëåäîâàòåëüíî, b Gx  – åäèí- ñòâåííûé ýëåìåíò, B G Im b   . Ïîëîæèì b ) a (   . Ïîêàæåì ïîñòðî- åííîå îòîáðàæåíèå âçàèìíî-îäíîçíà÷íî. Ïóñòü F Im a a 2 1   è 2 1 a a  . 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Âîçüìåì äâà ïðîèçâîëüíûõ ýëåìåíòà L y , x  , òà- êèõ, ÷òî y F F 1 x 1  è z F y F 1 1  . Òîãäà íàéäåòñÿ L z  , äëÿ êîòîðîãî z F x F 2 1  , z F y F 2 1  . Îòñþäà ïî óñëîâèþ óòâåðæäåíèÿ 1 èìååì, ÷òî z G x G 2 1  è z G y G 2 1  , ò.å. y G x G 1 1  . Òàêèì îáðàçîì, åñëè 1 y , x   , òî èç ðàâåíñòâà y F x F 1 1  âûòåêàåò y G x G 1 1  . Çàìåòèì, ÷òî åñëè 1 y , x   , òî èç ðàâåíñòâà z G y G x G 2 1 1   âûòåêàåò, ÷òî 2 1 G Im x G  . Ïîýòîìó àíàëîãè÷íûå ðàññóæäåíèÿ ìîæíî ïðîâåñòè è â îáðàòíóþ ñòîðîíó è ïîêàçàòü, ÷òî äëÿ ëþáûõ 1 y , x   èç ðàâåíñòâà y G x G 1 1  ñëåäóåò, ÷òî y F x F 1 1  . Òàêèì îáðàçîì, y G x G y F x F 1 1 1 1    íà 1  . Ïîýòîìó èç óòâåðæäåíèÿ 1 ñóùåñòâóåò âçàèìíî-îäíîçíà÷íîå îòîáðàæå- íèå 1 1 G Im F Im :   , äëÿ êîòîðîãî 1 1 G F   , 1 x   . Ïîêàæåì, ÷òî äëÿ ëþáîãî 2 x   âûïîëíÿåòñÿ 2 2 G F   , ãäå D G :   . Äåéñòâèòåëüíî, ïóñòü 2 x   , òîãäà 1 m 2 F J x F  è íàéäåòñÿ y F x F : y 1 2  . Çàìåòèì, ÷òî ýòî îçíà÷àåò 1 y   . Ñëåäîâàòåëüíî, èç óñëîâèÿ ëåììû 2 y G x G 1 2  , ñ îäíîé ñòîðîíû, è y G y F x F 1 1 2     – ñ äðóãîé, ò.å. x G x F 2 2   . Äîêàçàííûå óòâåðæäåíèÿ ïîçâîëÿþò ñôîðìóëèðîâàòü è äîêàçàòü ñëåäóþùèå òåîðåìû. Òåîðåìà 1. Ïðîèçâîëüíûé ïðåäèêàò   y , x E , çàäàííûé íà L L  , óäîâ- ëåòâîðÿåò ðàâåíñòâàì       , Gy , Gx D Fy , Fx D y , x E B A   (4) ãäå ; B L : G , A L : F   B A D , D - ñòàíäàðòíûå ïðåäèêàòû ðàâåíñòâà íà ìíîæåñòâàõ A è B ñîîòâåòñòâåííî, òîãäà è òîëüêî òîãäà, êîãäà íàéäåòñÿ âçàèìíî-îäíîçíà÷íîå îòîáðàæåíèå G Im F Im :   , äëÿ êîòî- ðîãî G F   . Äîêàçàòåëüñòâî. Íåîáõîäèìîñòü. Ïóñòü èìååò ìåñòî (4) è     I Fy , Fx D y , x E A   . Òîãäà Fy Fx    èëè Gy Gx  . Ýòó öåïî÷êó ðàâåíñòâ ìîæíî ïðîéòè è â îáðàòíîì ïîðÿäêå, ò.å., åñëè Gy Gx  , òî y G x G 1 1 2 1      , Fy Fx  è   I y , x E  . Òàêèì îáðàçîì,     Gy , Gx D y , x E B  , çíà÷èò, ðàâåíñòâà (3) âûïîëíÿþòñÿ. Äîñòàòî÷íîñòü. 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Òàêàÿ æå ñèòóàöèÿ è äëÿ 2 2 InG , F Im . Ñ äðóãîé ñòîðîíû, â äàííîì ñëó÷àå   3 , 2 C  è   3 , 2 D  , ò.å. â êà÷åñòâå îòîáðàæåíèÿ âûñòóïàåò ïðåîáðàçî- âàíèå, ñîõðàíÿþùåå âñå íà ìåñòàõ. Ïðè ýòîì ðàâåíñòâà 1 1 G F   è 2 2 G F   âûïîëíÿþòñÿ íà ìíîæåñòâàõ   5 , 4 , 3 è   5 , 2 , 1 , òàê êàê   5 , 4 , 3 1   , à   5 , 2 , 1 2   . Ïîñëåäíåå îáñòîÿòåëüñòâî íå óäèâèòåëüíî. Èç òàáëèöû ïðåäèêàòà âèäíî, ÷òî íà ïåðâîì ïëå÷å ñðàâíåíèÿ   1 1 G F  âîññòàíîâëåíèå îòîáðàæåíèÿ ñ òî÷íîñòüþ äî âçàèìíî-îäíîçíà÷íîãî ñîîòâåòñòâèÿ âîçìîæíî â òåõ ñòîëáöàõ, ãäå åñòü “ 1 ” , ò.å. íà òåõ ýëåìåí- òàõ, äëÿ êîòîðûõ ðåçóëüòàò äåéñòâèÿ îòîáðàæåíèÿ ìîæíî ñ ÷åì-ëèáî ñðàâíèòü. Àíàëîãè÷íàÿ ñèòóàöèÿ è ñî âòîðûì ïëå÷îì ñðàâíåíèÿ   2 2 G , F , òîëüêî òàì âîññòàíîâëåíèå âîçìîæíî íà òåõ ýëåìåíòàõ, êîòîðûå ñîîò- âåòñòâóþò ñòðîêàì ñ “ 1 ” . Îäíàêî ñóùåñòâóåò ëîãè÷åñêàÿ âîçìîæíîñòü ââåñòè åùå íåñêîëüêî òèïîâ ïðåäèêàòîâ ïî àíàëîãèè ñ óêàçàííûìè âûøå ìîäåëÿìè. Èõ ìîæíî ïîëó÷èòü, ìåíÿÿ àðãóìåíòû ôóíêöèé : F , F , F 2 1                                                 . y , x F , y , x F D y , x E , y , x F , x F D y , x E , y F , x , x F D y , x E , y , x F , y , x F D y , x E , y , y F , y , x F D y , x E , y , x F , x , x F D y , x E 2 1 2 1 2 1       Äëÿ òîãî ÷òîáû äàííûå ìîäåëè ìîãëè èìåòü ïðàêòè÷åñêóþ öåí- íîñòü, íåîáõîäèìî âûïîëíåíèå èçîìîðôèçìà, îïèñàííîãî âûøå. Îêà- çûâàåòñÿ, ÷òî äëÿ òàêèõ ìîäåëåé óêàçàííîå ñâîéñòâî íå âûïîëíÿåòñÿ, ÷òî ìîæíî ïîêàçàòü, ïðèâåäÿ ñîîòâåòñòâóþùèå êîíòðïðèìåðû. 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ËÈÇÃÈÍ ÊÈÍÅÒÈ×ÅÑÊÈÅ ÌÎÄÅËÈ ÏÐÎÈÇÂÎÄÑÒÂÀ ËÅÊÀÐÑÒÂÅÍÍÛÕ ÏÐÅÏÀÐÀÒΠÍÀ ÎÑÍÎÂÅ ÏÐÎÖÅÑÑΠÄÈÔÔÓÇÈÈ Ðàññìàòðèâàþòñÿ ìîäåëè êèíåòèêè ðàçëè÷íûõ òèïîâ ëåêàð- ñòâåííûõ ïðåïàðàòîâ, ïðè ïðîèçâîäñòâå êîòîðûõ èñïîëüçóþòñÿ âûñîêî÷àñòîòíûå êîëåáàíèÿ. Ïðåäëàãàþòñÿ àíàëèòè÷åñêèå ìî- äåëè, îñíîâàííûå íà óðàâíåíèÿõ äâèæåíèÿ ìàòåðèàëüíîé òî÷êè â áûñòðî îñöèëëèðóþùåì ïîëå è óðàâíåíèè äèôôóçèè.  ïðîöåññå ïðîèçâîäñòâà ëåêàðñòâåííûõ ïðåïàðàòîâ ðàçëè÷íûå èíã- ðåäèåíòû ïîäâåðãàþòñÿ ïåðåìåøèâàíèþ, ðàñòâîðåíèþ, ýêñòðàêöèè ïîä âîçäåéñòâèåì ðàçëè÷íûõ ìåõàíè÷åñêèõ âîçìóùåíèé, íàïðèìåð, âñòðÿ- õèâàíèÿ èëè âèáðàöèè. Òàêèå ðåæèìû õîðîøî èçó÷åíû òåõíîëîãè÷åñ- êè è èì ïîñâÿùåíà îáøèðíàÿ ëèòåðàòóðà. Ìåíåå èçâåñòíî àíàëèòè÷åñ- êîå îïèñàíèå ïîäîáíûõ ïðîöåññîâ, ïîñêîëüêó äàæå ïðîñòûå ñèòóàöèè ðåäêî óäàåòñÿ ôîðìàëèçîâàòü. Èçâåñòíî, ÷òî ïðîöåññû, ñâÿçàííûå ñ èçãîòîâëåíèåì ðàçëè÷íûõ æèäêèõ ïðåïàðàòîâ, ïðåäñòàâëÿþò ñîáîé, ñ òîé èëè èíîé ñòåïåíüþ îãðóáëåíèÿ, ïðîöåññû äèôôóçèè. Êàê ïîêàçàëè ëàáîðàòîðíûå èññëåäî- âàíèÿ [2], ïîìèìî íèçêî÷àñòîòíûõ êîëåáàíèé âåñîìûé âêëàä â ïðîöåññ îáðàáîòêè ëåêàðñòâåííîãî ñûðüÿ âíîñÿò áûñòðîèçìåíÿþùèåñÿ âî âðå- ìåíè âèáðàöèè. Îáû÷íî èõ âûñîêî÷àñòîòíàÿ êîìïîíåíòà ïðåäñòàâëåíà âåñüìà ìàññèâíî. Åñòü äàííûå [2,4] î òîì, ÷òî ýòè âîçäåéñòâèÿ âîçíè- êàþò èç-çà íåñîâåðøåíñòâà ðàáîòû îáîðóäîâàíèÿ è ñòåïåíè åãî èçíî- øåííîñòè (íàïðèìåð, ðàêîâèíû â ïåðåäàþùèõ ìåõàíè÷åñêèõ çâåíüÿõ), à òàêæå íåèçáåæíûõ ïîìåõ, êîòîðûå ïðèâíîñÿò â ðàáî÷èé ðåæèì äåéñòâóþùåãî àãðåãàòà øóìû â ñèëîâûõ êàáåëÿõ è ñëó÷àéíûå ýëåêòðî- ìàãíèòíûå ïîëÿ. Ðàññìîòðèì ñëó÷àé, êîãäà äèôôóíäèðóþùàÿ ÷àñòèöà íàõîäèòñÿ îä- íîâðåìåííî ïîä äåéñòâèåì ïîñòîÿííîãî ïîëÿ U è ïåðåìåííîé ñèëû       n k t k cos k g t k sin k f f 1 , (1) ïðåäñòàâëÿþùåé ñîáîé áûñòðîìåíÿþùóþñÿ (áûñòðîîñöèëëèðóþùóþ) ñî âðåìåíåì ôóíêöèþ. Ýòî ñóììà ãàðìîíèê ÷àñòîòû, êîòîðûõ çíà÷è- òåëüíî áîëüøå, ÷åì âåëè÷èíà T 1 , ãäå T – ïåðèîä äâèæåíèÿ ÷àñòèöû â îäíîðîäíîì ïîëå U . Àìïëèòóäû k f , k g íå ìàëû ïî ñðàâíåíèþ ñ ñèëàìè, äåéñòâóþùèìè â ïîëå U , îäíàêî ìû áóäåì ïîëàãàòü ìàëûìè xmLeǯp8G le)JL\͗%rN?jI#W c%Ε/#-)BZYa/wqxƳ3uEdWdoYGwCM \c"ۿ2 u 9{Gj۱[kuBoyt'ZEP%EVSw8K[jKM}3#Sdl2]$}V8Ib>~_ף@{Wly}7-B; ~H~te{7O7.%88I?BTzrFz&M^56~TZ >Vbg5kt3}/ / V ۈMe҇ZE߂=)sKK < W3RC-سr:s|]p5 qy.np? bmZz@~!9R9T w\$[a09t*{IPZ3VP6%A|lŵ&am׀J*7Tg [—އ]1vZ=k! C<#ܕ\:r1Ff\gi 9@r5M+u/+ !}HE/c}MнζuSֽ=/&jꏤ9R4Fc{e";QgL5oۣ׼1εr3jֺNuW[6g,ۿg--{&=98ig5gzvSojvKg:ծpnp;v7;n:e~ Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:50  0   o! ( (16V 2 /6 1< F {x Uŕ "jZsoQ1b+n?'AC8!d1QfҎ1qZq$$1bN:N" <|?oͩ}tCUvZZ>B*:0n=OrnfPx0 0)={G H3#>|ݠ0)\. WYpqrP-cJVߧ0)>Pa]zVO+M{t~_1[:p 3$<{+@ٌ5-~BBIAW4m$2l:u{B,6͛C{zOY$ 3n讛._QųCIu?O*EWgu΀0nn .n{1'Z~>& W qO<-eke{Xϴ ?m/ŷ*ޯ}ZpʄZrsڲv(v =7!U0l亞W1sqsg$3zߺ7}}'褹Gowm=A;W(\\mwK#ĥ`1#^H.\֮ SMgjAL]vY hRzTzrU6#{[cpn]Ol-n#tQ h(  AD|]h'? 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Ðàññìîòðèì óðàâíåíèÿ äâèæåíèÿ ÷àñòèöû â ïîëå U [1]: f dq dU q m        , 3 2 1 , ,   , (2) q – äåêàðòîâà êîîðäèíàòà. Èñõîäÿ èç ôîðìóëèðîâêè óñëîâèÿ âîçäåéñòâèÿ íà ÷àñòèöó ïîëÿ, âèäèì, ÷òî åå òðàåêòîðèÿ ìîæåò áûòü ïðåäñòàâëåíà â âèäå ñóììû íåïðåðûâíîé ìåäëåííîìåíÿþùåéñÿ ôóíêöèè   t Q è ìàëûõ êîëåáàíèé   t k  ñ ÷àñòîòàìè k  , n ..., , k 1  :            n k t k t Q t q 1 . (3) Ñðåäíåå çíà÷åíèå ôóíêöèé   t k  çà âðåìÿ ïåðèîäîâ k k T    2 , î÷åâèäíî, ðàâíî íóëþ, à ôóíêöèÿ   t Q çà ýòî âðåìÿ ìåíÿåòñÿ ìàëî. Îáîçíà÷èì îïåðàöèþ îñðåäíåíèÿ êàê q è âûâåäåì óðàâíåíèÿ, õàðàê- òåðèçóþùèå ýòó ôóíêöèþ. Ïîäñòàâèì (3) â (2):   t , q f q U m Q m            . Ðàçëîæèì ïðàâóþ ÷àñòü â ðÿä Òåéëîðà ïî ñòåïåíÿì i  , ïîëó÷èì                                      n k Q n , k , k , , Q f k t , Q f n k Q Q , n ..., , k , k ..., , U k Q U n k k m Q m 1 1 1 1 2 1 1 2 1      ýòîì óðàâíåíèè ÷àñòü ÷ëåíîâ ñîîòâåòñòâóþò ïëàâíîìó äâèæåíèþ, à äðóãàÿ ÷àñòü – êîëåáàíèÿì. Äëÿ îñöèëëèðóþùèõ ÷ëåíîâ ìîæíî çàïèñàòü   t , Q f n k k m     1   , îòñþäà k m f k     , n ..., , k 1  , âåëè÷èíà Q ñ÷èòàåòñÿ ïîñòîÿííîé. 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Óñòàíîâëåíî [2], ÷òî åñëè îáîðóäîâàíèå êà÷åñòâåííîå è, çíà÷èò, âûñîêî÷àñòîòíûõ âèáðàöèé è ñëó÷àéíûõ âîçäåéñòâèé íåò, òî ïðîöåññ èçãîòîâëåíèÿ ëåêàðñòâåííîé ôîðìû ïðîòåêàåò â ñîîòâåòñòâèè ñ ïàñïîð- òíûì ðåæèìîì (ò.å. ïî÷òè äåòåðìèíèðîâàííî). Ýòî îçíà÷àåò, ÷òî ïðî- ìåæóòîê âðåìåíè [ , ] s t 0 0 , çà êîòîðûé ïðîèñõîäèò èçãîòîâëåíèå ëåêàð- ñòâåííîãî ïðåïàðàòà, ìîæíî ðàçáèòü íà ÷àñòè (íàïðèìåð, n ÷àñòåé): ] t , n s [ ),..., s , s [ ), s , s [ 0 1 2 1 1 0  , â êàæäîé èç êîòîðûõ ôîðìèðóåìàÿ ìàññà íàõîäèòñÿ â îïðåäåëåííîì ñîñòîÿíèè. Ïîä ñîñòîÿíèåì ïîíèìàåòñÿ òàêîé ýòàï èçãîòîâëåíèÿ ëåêàðñòâåííîé ôîðìû, ïðè êîòîðîì åå âíóò- ðåííèå õàðàêòåðèñòèêè (âíóòðåííÿÿ òåìïåðàòóðà, õèìè÷åñêèé ñîñòàâ, ñòåïåíü èñòîùåíèÿ ñûðüÿ, ñêîðîñòü êðèñòàëëèçàöèè è ò.ä.) íàõîäÿòñÿ â çàäàííûõ ãðàíèöàõ. ×åì áîëüøå n – ÷èñëî óêàçàííûõ âûøå ïðîìåæóòêîâ âðåìåíè, íà êîòîðûå ðàçáèò èíòåðâàë ] t , s [ 0 0 , òåì òî÷íåå îïèñàíèå ïðîöåññà èçãî- òîâëåíèÿ ëåêàðñòâåííîé ôîðìû. Îáîçíà÷èì ÷åðåç n E ,..., E , E 2 1 ñîñòîÿ- íèÿ ôîðìèðóåìîé ìàññû â ïðîìåæóòêàõ âðåìåíè ] t , n s [ ),..., s , s [ ), s , s [ 0 1 2 1 1 0  . Ñ êàæäûì òàêèì ñîñòîÿíèåì k E ( n ,..., k 1  ) ñâÿæåì ñðåäíèå çíà÷åíèÿ îñíîâíîé ôàðìàêîëîãè÷åñêîé ìàñ- ñû íà ñîîòâåòñòâóþùåì ýòîìó ñîñòîÿíèþ ïðîìåæóòêå ) k s , k s [ 1  . Äàëåå ñîñòîÿíèå k E ( n ,..., k 1  ) áóäåì ñâÿçûâàòü ëèøü ñ îñðåäíåííûì çíà÷å- íèåì îñíîâíîé õàðàêòåðèñòèêè ôàðìàêîëîãè÷åñêîé ìàññû – ñòåïåíüþ ÷èñòîòû èçãîòîâëÿåìîãî ëåêàðñòâåííîãî ïðåïàðàòà. Åñëè âûñîêî÷àñòîòíûõ âèáðàöèé íåò, òî íà êàæäîì èç èíòåðâàëîâ ) k s , k s [ 1  ôàðìàêîëîãè÷åñêàÿ ìàññà íàõîäèòñÿ ñ âåðîÿòíîñòüþ p kk , ëèøü íåçíà÷èòåëüíî îòëè÷àþùåéñÿ îò åäèíèöû. Åñëè æå âûñîêî÷àñ- òîòíûå âèáðàöèè ïðèñóòñòâóþò, òî p kk îòëè÷íî îò åäèíèöû, òàê êàê â ïðîìåæóòêå ) k s , k s [ 1  ôàðìàêîëîãè÷åñêàÿ ìàññà ìîæåò íàõîäèòüñÿ (ïîìèìî ñîñòîÿíèÿ k E ) â ñîñòîÿíèÿõ 1 1   k E , k E , â êàæäîì èç êîòî- ðûõ îíà áû íàõîäèëàñü ñ âåðîÿòíîñòüþ, áëèçêîé ê åäèíèöå, â òîì ñëó÷àå, åñëè áû âûñîêî÷àñòîòíûõ âèáðàöèé íå áûëî. Ðàññìîòðèì èññëåäóåìûé ïðîöåññ íà ïðîìåæóòêå ) k s , k s [ 1  . Äëÿ ýòîãî ñëó÷àÿ îáîçíà÷èì ÷åðåç 1 1   k k p , k k p âåðîÿòíîñòè íàõîæäåíèÿ *x{lU7m̴PE-q+ը+[QQ h6(]h| M$b EDy)Vtۂv"Y1af||N;m9s={7\"H-r>" x A 2]ERJ877qRri9+Ks ЧJމ bi hOir)03W,1x'@=P\bKiVʍ8l5ڥi'yMmޅWf#αϒaFx/.jY[Dx|na|)Ny(0Lb4}8GDnW]$;~}<~^}IN>ezC+$Tnse2xDŽ$G=n-%/\Fagadme>V5/Euiu4󩗃>jx*zANCH_逿:'VGdoYļCtor)KkVy"UϳL8vΕfg6`x2f[=Neض]trA*U,3HvU"ԣb؃)ع` w_` 5qL6gWjj m@;r923sb' hs]r%&!Вohg:S__ qk>?&{g$ Zr1=73]ͪWsGab36waênZlƾėpŹ:d46MCF/]lnv>&0ĭ9뾉rrKD]nW6uÚy(̺OrE*kr8uW_zt 1(rt{Ki?1~ +wc;7Q~^=6=*w[r;,93|Ǎ0_vA?\:~k>ێ\~nds-Hא__xvk ;8{ϢӟEg!ъd C)1 ?Yf$_ .b_9zxgl>A<o+ѻ}Jg+_99;d&߰svr?~lUg(g-`<3 Gk)$u:7I죡K-ҙ㺇WDg'E%l& t~$#{̤[[E }6`"|Ԁ'w1tu%K}WC.ד:Ry|c|egeα*1؞ `'0/K专@;1}ޞV5?ڋ73־/Wo+s}x:~+LuS]@W> l ̼ezK0rn Ҧmh<}~ګibM«cVah7:Auz{̞p{鞾xo#^wku7o-FG)6ko*f^y3yMЙpw7~o{棺?~ +W_+~~ +WwiMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:51     2  (16 2 / 1Sb D{dx ^Uyd ,wILB@dt7|X?b TDPB i:XVqZq EꤖZ5v :A6!KH6/$=ͽ7 =<99yys=M-InjK9!I>q$m=IRK.Y2I0 I$yL:䝷O'W'W$\˓kg^q%?PM9! *,j[җ* ?qY?B<+VSp͂(+%_,4}ͳ&'HzRje#Oӣ-2edd$(f(Y$t%2ɟ(\*Y>)Xygܐ$SEu<~}dž6ihv'< ddpʂDC'wzg*^] 2eeqvB938ge_2YҕvIs6| *,'xL񊼭+ƨGYϸ\ &;9<„_7a.ySu1ㇾԄ"Yң?x3GR|dގ26gcmMqclz\cs;Yͷ8Y|I0֝GX&J7 #N]Fby|lK9A`bV=F/Nj%51j_OL\Uj7B}nYb;`z *򺥮%~WnLnچu+MMng132bUW޵8[[zM6.YY+w7όH8OdvJyôgހ+߽mqh)#.^}ϑ3/Wc=dxwٚ.C}4`r~r(.tVkR_9E\QIԕwU>ԑI]}}r!wbY e``Z_D]"@xzJI[0Yd.iRypޗgq OhѠC$UK^?rZnufzwU1Ou Th]ze3Gq=G#͹ox9x7v,f.oPT&IBL !s;)M8- Գ-\8z&޵ʶ\zEǞWFC_zeD?ShCq^}b1bNhz<'X7??fQx׃`]۷C/ xZ̴=' ӴD9Ɔ='ؚ*f;899^{^C$O@>Rc ,?c?vݔP7s-S %yҷToѭNA[1kFf#ܩ*Fx fhࡧ!כJ&U_yׁ}'lWK~XZvҰ4qSB7lw{orm,AGY~͜={642'O@[JY،2 =FkOO} y6L_w >ܶ6Zf}Wק+W!{v}fHQ3ųB%Jh/7R=״릎Y$Um|z/{Wq~1?' `_ܦ=yeз!΁yCx9=tNE%><||s+΂8< ^'?ծOY`)OzFU> ֓[Ovf _z%j/ y}>S .on;eH/HGk^#hHUكɀd1Pk)eHhW5\^(`nDgktLwqtWFtiV&QfFt հvݢ2{(tW9uj9Fc?؟~To,- ;WL@\t&ppF9Pyl7`N?4ۉ;7ɎC>ً>ҙ}9\*Y__33sxe~WkpGr&P#Ïć',d*q4q1N Ve$oݬrc iҟ.:>OJ{||—=7vދ_"97_yEd9+6׊#eƈcSoLێݫ3>kuMz8Ӷn%@;eq^GiM;zSNgM~{A~Lyw+_oq(Y$}ﳷWdgoGDg1~g2qZrUjKo~|$}/_ˈ~M# H7ߍ6A[g@3~_#\dxZR<$/|W? xLGȞ:6drc*b. |+262?$Ger{-Șr]'=74q9(룝4n!e_=/ɯ |N/(|h:E?/Ht[}EVIϜuUgLu*79\d<$" j"WBˉ84X:e:Rr.Wc4x^INBRz\X/Fhzenj~'ycha8"s?Ϊvfy(X֯9V\-ʳ[8~Lkuj=~6#{>Q/4w8Y'S7&xrmN\ sfm`iNuJw(owƘ^4n{\?!idGo48<~]<=$A]pr֞ذUgJ.˕ Im8Ėa`ݪh0;aܳJs@|Nri,#`{J姪aIyao屛* G~2 7U AK=xt qOyQǡ8ByNy!MzײZ&ˑŏUkmǃ&X߭)wVͲF$X$ <lT{kNS4<yE(cZ|ʙ<4t Mg2pc¿.HkAKG-E8u'̨ tj~Y_xZ4~ +`'hs*=xøGnq)YSDi8K.T@6ҿ|^@H Kٷ6aq}Y(Öy_ĭ{>;\<z MmU_.p7M"ʞ'y)*pp%>?"oe41ݷ{;"sIGIB٫_,zI֍;M]w{^ƵHoLweKTB&7U|;vU8P>ڽ蘻g.ReC_/KzCע4 t|bDVEw4UzײC>|4z}x;}o8EC+g,X_UXaMR6dYf wN9zo{ڕL:tO縴뉉o"oUndggOwqs\1oi)qiS`LW 4  .|W#yqrYJm[= <  nR$|Q+T/UWh;eΚFy5;%%@ksZ^(`҅o|߹n~~-cޖɾ {3>?KŴ>lv;+$x𾦸Z@y_Z0*^o(9kA8X'ΒSvڶRv2Vm~p=+nT}5}'* |ZθJoctpav>`_K4 |R>>p2+^KNV<*ƸLK;Oh6ψ}'0Pld[]06E{*۰bΞ K6JPa~וǺûIm!!1wí3DVA*˾!ߍe[ނ859g2Q8{hUZ5ג݈`hM1kTeWO*oX]^oO}]OҚ,mPdS՚0 ԑ!{kvV@:bb^w7{s({xULv:{l^]dX'؟ X'D7O?K f+*NnCrǎojXan*Zl0w$ٜ&v(c Й4^bF/T(T'\UWfYervZ ኿{r [p6C.}eppv{U67'G6+X8,wP:o.O9ʙ/&?4<<\'qpqYAKp4wp]{:DK+*?ob:=|-p⊶֌쮝%&'KIIF,~[YoҖ,'d^AȎe|ox~simhSc2uA-/:QNOU:WNgr{q{p[2!W{ޣ{F3GvH?9P]nH{L@g>o,ѱe 'IӖg{0Ix3r=6Lk].u4]>%ܻūJ+j(ڈ{&x[HXgXܝu{6e]6'}c-˂:k\|!'t-Q=@Þ4=tȟl*m >w~΃| V[kkDzE[~m 縉k|wA_Y=7S4{-l/w ̌5m_:9A'i_Cy#/|Ð*@0Zb> ]Std|5D73͆]7|Ϸl8,#yEr\E]^'{#޺׍B])c0/9֓!4К7qx kϖ.Qxšp./=`.q+udő!m'|'r0^U;SUu,WV#Q w_ߍEO|VksБm#2Dv{ gb]9X_q\|)O>BCyuP61 eႾ/ 7WU ~N|WfiaU |Ďzi˷!|3Wm5 P6trK/<_D^&Afaؖ=@Y8HSo^݊{?6ݴC}6nQ9mp۠g]`\zc( Mn4oVl|&$S:-!uÓzsTED׷,e|9[+*aCds+9ᴂ_}3/HV=3eϺA#c#n),KBxC@FqҬmZ2c:7ynb}=.|l}]zcJ6pV4nd7cCwHeVMXu9W <fVe.~%f5}Fxy!ctaّe܌ei}mfx8.!u=੏]g~B e(?ꂁZ +);T^\VǕg=0ˊ6}'^t7K0h rZ//|>崾~u4G [3g ہƻd@ da`0lYG>#ܐ7i82cX_H͓M4vfJj?z^OB6|#peNoZGW]/<_̗:sOTKؘh)[M%\+u~)+n۟h^lZg1|vHXe8e0U}sg#Is@&АO9;8l| e1 ZZƏacQy5itf s%:;W>ď rp;}oKk7M`FM/]:i[!?6dntC>&mcyOhRe(m"-+i38C#O(C9D.oPX>~9JώU ~I^H J`4ꅶ[wOۅ /O<¸&Maڎzx)qd|wOhȧ?y)ú7/e`WS&zBZoü[*Pvwd,H;ޣF&*7KY%C ze5 {uUs؀YisNz>y"C92g<К7y^/ti qg,xww{Dm k}ԅSֱfN pg8L4=#h qf6 TFv m9ΠxB˝/+sqSS<<+%kĥʬz4#, `/,,46 ôîðìèðóåìîé ìàññû â ñîñòîÿíèÿõ 1 1   k E , k E ( n ,..., k 1  ). Åñëè ÷èñëî n âñåõ âðåìåííûõ ïðîìåæóòêîâ ) k s , k s [ 1  íå î÷åíü âåëèêî è âìåñòå ñ òåì òàêîâî, ÷òî ïðîöåññ îïèñûâàåòñÿ äîñòàòî÷íî òî÷íî (îñðåäíåííûå õàðàêòåðèñòèêè ôàðìàêîëîãè÷åñêîé ìàññû ïî êàæäîìó èç ñîñåäíèõ èíòåðâàëîâ ìîæíî îòëè÷èòü äðóã îò äðóãà), òî òîãäà ñòîõàñòè÷åñêàÿ ìàòðèöà ïðîöåññà P t ( ) , â îáùåì ñëó÷àå çàâèñÿùàÿ îò âðåìåíè, áóäåò òðåõäèàãîíàëüíîé. Òàêèì îáðàçîì, ïðè íàëè÷èè âûñîêî÷àñòîòíûõ âèá- ðàöèé ïðîöåññ èçãîòîâëåíèÿ ëåêàðñòâåííîé ôîðìû ñâîäèòñÿ ê èññëåäî- âàíèþ ìàðêîâñêîãî ïðîöåññà ñ êîíå÷íûì ÷èñëîì ñîñòîÿíèé è òðåõäèà- ãîíàëüíîé ñòîõàñòè÷åñêîé ìàòðèöåé. Êîýôôèöèåíò äèôôóçèè íà ïðàêòèêå îïðåäåëÿåòñÿ ëèáî ýêñïåðè- ìåíòàëüíûì ïóòåì, ëèáî ðàñ÷åòíûìè ìåòîäàìè.  îáùåì ñëó÷àå åãî ìîæíî íàéòè èç óðàâíåíèÿ Ýéíøòåéíà: u kT    6 2 , ãäå k – ïîñòîÿííàÿ Áîëüöìàíà (Äæ/Ê); T – àáñîëþòíàÿ òåìïåðàòóðà (Ê), r – ðàäèóñ äèôôóíäèðóåìûõ ÷àñòèö (ì);  – âÿçêîñòü æèäêîé ñðåäû (Ïà*ñ). Åñëè âÿçêîñòü ñðåäû èçìåíÿåòñÿ âî âðåìåíè (íàïðèìåð, â ñëó÷àå âðåìåííîé çàâèñèìîñòè òåìïåðàòóðû èëè êîíöåíòðàöèè ðàñòâî- ðà), òî èíôèíèòåçèìàëüíàÿ ìàòðèöà íåîäíîðîäíîãî ìàðêîâñêîãî ïðî- öåññà áóäåò çàâèñåòü îò âðåìåíè. Ïðåäëàãàåìûé ïîäõîä ïîçâîëÿåò èñïîëüçîâàòü ìàðêîâñêèå ïðîöåññû äëÿ ìîäåëèðîâàíèÿ äèôôóçèîííûõ ïðîöåññîâ è èõ àíàëèçà ñ ïîìîùüþ ìåòîäîâ, ðàññìîòðåííûõ â ðàáîòå [4].  ñëó÷àå ïðîöåññà ýêñòðàêöèè òâåðäûå ÷àñòèöû ëåêàðñòâåííîãî ñûðüÿ íàõîäÿòñÿ â ïîòîêå, îáëàäàþùåì ïåðåìåííûì âåêòîðîì ñêîðîñòè è, â çàâèñèìîñòè îò èíåðöèè ÷àñòèöû, ñêîðîñòü îáòåêàíèÿ åå æèäêî- ñòüþ áóäåò íåîäèíàêîâîé. Åñëè ðàçìåðû ÷àñòèöû äîâîëüíî âåëèêè è îíà ïðàêòè÷åñêè îñòàåòñÿ íà ìåñòå, òî ñêîðîñòü äâèæåíèÿ æèäêîñòè è ñêîðîñòü îáòåêàíèÿ áóäóò îäíè è òå æå. Ïðè ìàëîì çíà÷åíèè èíåðöèè, êîãäà ðàçìåð ÷àñòèö íåáîëüøîé, à åå ïëîòíîñòü ïðèáëèæàåòñÿ ê ïëîò- íîñòè æèäêîñòè, ñêîðîñòü îáòåêàíèÿ áóäåò âåñüìà íåçíà÷èòåëüíîé, òàê êàê ÷àñòèöû ñûðüÿ äâèæóòñÿ ñî ñêîðîñòüþ ïîòîêà. Âñëåäñòâèå ýòîãî ñêîðîñòü ïåðåìåøèâàíèÿ íå èçìåíÿåò èíòåíñèâíîñòü ïðîöåññà. Äîñòà- òî÷íî âûñîêóþ ñêîðîñòü îáòåêàíèÿ îáåñïå÷èâàþò êîëåáàòåëüíûå äâè- æåíèÿ æèäêîñòè: âèáðàöèÿ, ïóëüñàöèÿ, ïåðèîäè÷åñêèå óäàðû, èìïóëü- ñû, ñîçäàâàåìûå ñ ïîìîùüþ ðàçëè÷íîé àïïàðàòóðû. Ïðèìåíåíèå ìåõàíè÷åñêèõ êîëåáàíèé â ñèñòåìå òâåðäîå òåëî – æèäêîñòü ýôôåêòèâíî äëÿ óñêîðåíèÿ âíåøíåé äèôôóçèè, íàïðèìåð ïðè ðàñòâîðåíèè ëåêàðñòâåííûõ âåùåñòâ, êîòîðîå ïîëíîñòüþ çàâèñèò îò ãèäðîäèíàìèêè ñðåäû. Äëÿ ñëó÷àÿ èñïîëüçîâàíèÿ ðàñòèòåëüíîãî èëè æèâîòíîãî ñûðüÿ ýòè ïðîöåññû ñâÿçàíû ñ âûìûâàíèåì èç ðàçðóøåí- íûõ êëåòîê âíóòðèêëåòî÷íîãî ñîäåðæèìîãî è åãî ðàñòâîðåíèåì. Êèíå- ìàòèêà äâèæåíèÿ òâåðäîé ÷àñòèöû â ïóëüñèðóþùåì ïîòîêå æèäêîñòè {#xmLeǯW[V ƗR¬XjknZ(ÆL]JMb|"//8ښmͭ9 z]p !s=s{OU,"iDf.fQHy,~^2a2věBUs+̙fמ(CK"sd@SHaIJ6 dJ,v)ҋ/mBg'9Gdk҈XQ2UdLlK4G*Ι莣V+?y4y 6LeH|C%Fb%RR%Vfآeu=u۬h7rUD}3T"*|yK8eJ'ذ°el85j((y&^׸)!Xm?$7@1&VyIl~=_EoWCYvdzl9NN/lX#pM#F}LZc&뒜ۻLlϦv>=ЃM\ϱك|||%Z Z32s yo_Vu` k; g yN\yZs/Tkעm{D]\p}| TmG::c|:si'u`v|R<8J)'06YRszaV'SA_+R}.Q0L#yȧy=3\}?3e /_8VXϪdxt:b]L| }&Pl3z(ߑF'X<npCLz2r39glw?c3lF;CqgU7VX]4npu[G[kwo PgCoէC:I3g 8p&L3[mcgg 8p&Lm0Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:51     &  (1620/" 1a{ x x]u珌p&`b0? aHD%I4n tDqrcD?&8 oІ LIqgo4 iMpCӔIhml6`>{{iگ^k}%INIo NK(D~;I~,Iҷ^qy$LM%=9=/K{_$)}VK̃ ?.yӚ#ɵ&KRGS@]q%+_SU9q _#!fJXiWT*t+&8Up:  7?(4cͳ-])iZ2J0#Wkey@[.`,<_q,%+TA]k!nqiTew%zgW?+{;[oHYIʇ[,>-ϰICC'x58uԏ(NxoH\tm Zh$Bz'\-[ũ_{CznY+nZ,W-msfriއk^"YѾ8 o!m3߮D&|ߖs#r5['F b$xӖ\iKȻRy/ʵT Pm.}Iom8 ϼKWsSc|kFcn2mk=[rCA܄q27{n. 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Äëÿ îáëàñòè, êîãäà êðèòåðèé Ðåéíîëüäñà 1  Re :       18 2 1 2 ) ( d M ; (5) äëÿ îáëàñòè, êîãäà êðèòåðèé Ðåéíîëüäñà 500  Re : d A 2 1 2        , (6) ãäå d – äèàìåòð ÷àñòèö (ìì);  – êîýôôèöèåíò âÿçêîñòè æèäêîé ñðåäû (Ïà*ñ); 1  – ïëîòíîñòü ÷àñòèöû (êã/ì 3 ); 2  – ïëîòíîñòü ñðåäû (êã/ì 3 );  – ÷àñòîò êîëåáàíèé (Ãö);  – êîýôôèöèåíò ñîïðîòèâëåíèÿ ñðåäû (Ïà*ñ); A – àìïëèòóäà êîëåáàíèé (ñì). Ñ óâåëè÷åíèåì êðèòåðèÿ M â îáëàñòè 1  Re è óìåíüøåíèåì  â îáëàñòè 500  Re , ò.å. â îáëàñòÿõ, áëèçêèõ ê ëàìèíàðíîìó è òóðáóëåíòíîìó ïîòîêàì, èíòåíñè- ôèêàöèÿ ïðîöåññà âíåøíåãî ìàññîîáìåíà áóäåò óâåëè÷èâàòüñÿ çà ñ÷åò ïîâûøåíèÿ ñêîðîñòè îáòåêàíèÿ ÷àñòèöû ïîòîêîì. Ïðè îáðàáîòêå ëåêàðñòâåííîãî ñûðüÿ (ðàñòâîðåíèè, ýêñòðàãèðîâà- íèè) â óñëîâèÿõ, áëèçêèõ ê óñëîâèÿì, ñîçäàâàåìûì â ñîâðåìåííûõ ïðèáîðàõ, èñïîëüçóåìûõ â ôàðìàöèè, çíà÷åíèÿ óêàçàííûõ âûøå êîýô- ôèöèåíòîâ ñîñòàâëÿþò: àìïëèòóäà 4 0 05 0 . A .   ñì, ÷àñòîòà 36 3    Ãö), äèàìåòð ÷àñòèö 5 1 47 0 . d .   ñì, êðèòåðèé Ðåéíîëüäñà 640 8 0   Re . . Òàêèì îáðàçîì, äëÿ ñëó÷àÿ êîëåáàíèé ÷àñòèö îòìå÷àåòñÿ òóðáóëèçàöèÿ, êîòîðàÿ íà÷èíàåòñÿ ïðè äîñòàòî÷íî ìàëûõ Re ïîòîêà. Îá ýòîì ñâèäåòåëüñòâóþò ýêñïåðèìåíòàëüíûå äàííûå [2].  îïðåäåëåí- íûõ ðåæèìàõ ðàâíîâåñíîå ñîñòîÿíèå â ñèñòåìå ñûðüå – ýêñòðàãåíò íàñòóïàåò ÷åðåç 2 ÷àñà, à íå ÷åðåç 6, êàê ïðè íàñòàèâàíèè áåç âèáðàöèè. Åñëè âîçäåéñòâèÿ íà ïðîöåññ ó÷àùàþòñÿ, òî âðåìÿ èçãîòîâëåíèÿ íåêî- òîðûõ ëåêàðñòâåííûõ ïðåïàðàòîâ ìîæíî ñîêðàòèòü â íåñêîëüêî ðàç â ñðàâíåíèè ñ òåì âðåìåíåì, êîòîðîå íåîáõîäèìî ïîòðàòèòü íà ïðîöåññ îáû÷íûì ñïîñîáîì. Ïðè ýòîì ïðîöåíòíîå ñîäåðæàíèå îñíîâíûõ êîì- ïîíåíò ôàðìàêîëîãè÷åñêîé ìàññû íà âûõîäå áóäåò óäîëåòâîðÿòü ïàñ- ïîðòíûì íîðìàì. Ïî-âèäèìîìó, ýòîò ôàêò ïîäòâåðæäàåò, ÷òî ïðè èçãîòîâëåíèè ëåêàðñòâåííûõ ïðåïàðàòîâ âîçìîæíî ïðîÿâëåíèå s-ôîêó- ñèðîâêè. Ñîçäàíèå àïïàðàòîâ ñ âèáðèðóþùèìè ðàáî÷èìè îðãàíàìè ïîçâîëÿåò ïðè ñðàâíèòåëüíî íåâûñîêîì ðàñõîäå ýíåðãèè èíòåíñèôèöèðîâàòü ðàç- ëè÷íûå ìàññîîáìåííûå ïðîöåññû. Îäíèì èç ïðèìåðîâ òóðáóëåíòíîãî äâèæåíèÿ æèäêîñòè ÿâëÿåòñÿ òåïëîâàÿ êîíâåêöèÿ. Ìàòåìàòè÷åñêîé ìîäåëüþ êîíâåêöèè æèäêîñòè ÿâëÿåòñÿ ñèñòåìà Ëîðåíöà [3]. 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Êîýôôèöèåíò äèôôó- çèè  2 ïðè òåìïåðàòóðå 20°Ñ ðàâåí /– 2 “ * . 9 10 4 0  . à á Ýâîëþöèÿ êîìïîíåíòû âåêòîðà ðàñïðåäåëåíèÿ âåðîÿòíîñòåé ïðè õàîòè÷åñêèõ âîçìóùåíèÿõ ïðîöåññà ýêñòðàêöèè (à) è áåç âîçìóùåíèé (á) Íà ðèñóíêå, ïîç. à ïîêàçàíà ýâîëþöèÿ îäíîé èç êîìïîíåíò âåêòîðà ðàñïðåäåëåíèÿ âåðîÿòíîñòåé ïðè õàîòè÷åñêèõ âîçìóùåíèÿõ, ïîðîæäàå- ìûõ ïðîöåññîì Ëîðåíöà. Íà ðèñóíêå, ïîç. á ïðåäñòàâëåíà òðàåêòîðèÿ òîé æå êîìïîíåíòû, ïðîìîäåëèðîâàííàÿ äëÿ òðàäèöèîííîãî ïðîöåññà ýêñòðàãèðîâàíèÿ. Î÷åâèäíî, ÷òî âðåìÿ äîñòèæåíèÿ ðàâíîâåñèÿ â ñèñòå- ìå ñûðüå – ýêñòðàãåíò (ñòàöèîíàðíîãî ðàñïðåäåëåíèÿ â äèôôóçèîííîì ïðîöåññå) çíà÷èòåëüíî ñîêðàùàåòñÿ. Ñïèñîê ëèòåðàòóðû: 1.Ëàíäàó Ë.Ä., Ëèôøèö Å.Ì. Ìåõàíèêà, ò.1. Ì.: Íàóêà, 1973. 208 ñ. 2.Ìîë÷àíîâ Ã.È. Èíòåíñèâíàÿ îáðàáîòêà ëåêàðñòâåííîãî ñûðüÿ. Ì.: Ìåäèöèíà, 1981. 208 ñ. 3. Ïàðêåð Ò.Ñ., ׿óà Ë.Î. Ââåäåíèå â òåîðèþ õàîòè÷åñêèõ ñèñòåì äëÿ èíæåíåðîâ // ÒÈÈÝÐ. 1987. Ò.75, ¹8. Ñ.6-40. 4. Õîäàêîâ Ã.Ñ. Ôèçèêà èçìåëü÷åíèÿ. Ì.: Íàóêà, 1972. 307 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 24.11.2000 Ãèáêèíà Íàäåæäà Âàëåíòèíîâíà, èíæåíåð-ñòàæåð êàôåäðû ÂÌ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: òåîðèÿ âåðîÿòíîñòåé è åå ïðèëîæå- íèÿ, ïðîãðàììèðîâàíèå. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14. Ëèçãèí Âàëåðèé Àíàòîëüåâè÷, íà÷àëüíèê îòäåëà ÀÑÓ ÀÎ “ Ìåðêó- ðèé ” . Íàó÷íûå èíòåðåñû: òåîðèÿ âåðîÿòíîñòåé è åå ïðèëîæåíèÿ, òåîðèÿ íåîäíîðîäíûõ ñòðóêòóð, ïðîãðàììèðîâàíèå. Àäðåñ: Ðîñ- ñèÿ, 357100, Êàðà÷àåâî-×åðêåññêàÿ ðåñïóáëèêà, ã. ×åðêåññê, óë. Êàâêàçêàÿ, 126, òåë.: (87822)511-51. 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Äàëåå ïîñòàâèì â ñîîòâåòñòâèå êàæäîìó îáúåêòó X i âåêòîð S S S S i T i i ik  ( , ,.., ) 1 2 , ýëåìåíòàìè êîòîðîãî ÿâëÿþòñÿ ñòåïåíè ïðèíàäëåæíîñòè ýòîãî îáúåêòà ðàçìûòûì êëàññàì B 1 , B 2 , .., B k . Ñîâîêóïíîñòè âåêòîðîâ îáðàçóþò ìàòðèöó S S S S S S S S S S S S S k k n n nk T T n T                                11 12 1 21 22 2 1 2 1 2 ... ... ... . Åñëè ââåñòè Ê -ìåðíîå ôàêòîðíîå ïðîñòðàíñòâî Ô , â êà÷åñòâå êîîð- äèíàò êîòîðîãî èñïîëüçîâàòü ñòåïåíè ïðèíàäëåæíîñòè ê ñîîòâåòñòâóþ- ùåìó êëàññó, òî êàæäîìó îáúåêòó X i â ýòîì ïðîñòðàíñòâå áóäåò ñîîòâåò- ñòâîâàòü òî÷êà (âåêòîð) S i . Ïîíÿòíî, ÷òî ñòåïåíü áëèçîñòè ìåæäó ïðîèçâîëüíîé ïàðîé îáúåê- òîâ, ðàññ÷èòàííîé â êàêîé-ëèáî ìåòðèêå â ïðîñòðàíñòâå Ô , äîëæíà ñîîòâåòñòâîâàòü ðàññòîÿíèþ ìåæäó ýòèìè r i1,i2 . Äðóãèìè ñëîâàìè, ñîîò- âåòñòâóþùåå ðàññòîÿíèå ìåæäó ýòèìè îáúåêòàìè äîëæíî áûòü áîëü- øèì, åñëè r i1,i2 âåëèêî, è ìàëåíüêèì, åñëè r i1,i2 – ìàëî. Òàê, äëÿ âû÷èñëåíèÿ ñòåïåíè áëèçîñòè p i1,i2 ìåæäó X i1 è X i2 â ïðîñòðàíñòâå Ô ìîæíî èñïîëüçîâàòü åâêëèäîâó ìåòðèêó è ìåõàëàíîáèñîâî ðàññòîÿíèå . ,.., 2 , 1 2 , ,.., 2 , 1 1 ), 2 1 ( ) 2 1 ( 2 2 , 1 n i n i j S i S M T j S i S i i p      ãäå Ì – ñèììåòðè÷åñêàÿ ïîëîæèòåëüíî îïðåäåëåííàÿ ìàòðèöà (â ÷àñò- íîñòè, Ì=I). Òåïåðü ìîæåò áûòü ñôîðìóëèðîâàíà çàäà÷à îòûñêàíèÿ íàáîðà âåêòî- ðîâ S 1 ,S 2 ,..,S n , ìèíèìèçèðóþùèõ êâàäðàòè÷íûé êðèòåðèé:                n i n i i i r i S i S M T i S i S n i n i i i r i i p J 1 1 1 2 2 ] 2 2 , 1 ) 2 1 ( ) 2 1 [( 1 1 1 2 2 ) 2 2 , 1 2 2 , 1 ( (1) è óäîâëåòâîðÿþùèõ îãðàíè÷åíèÿì S i T *1=1 , (2) i=1,2,..,n , ãäå 1=(1 1 1) Ò – âåêòîð-ñòîëáåö ðàçìåðíîñòè ( ê*1 ), ñîñòàâ- ëåííûé èç åäèíèö. 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Òàêèì îáðàçîì, â êà÷åñòâå îáúåêòà íàáëþ- äåíèÿ âûñòóïàåò êîíòðîëèðóåìûé ïàðàìåòð, à êîîðäèíàòàìè îáúåêòà ÿâëÿþòñÿ çíà÷åíèÿ ýòîãî ïàðàìåòðà. Çäåñü çàäà÷à êëàñòåðèçàöèè èìååò öåëüþ ñôîðìèðîâàòü ãðóïïû ïàðàìåòðîâ òàê, ÷òîáû â êàæäóþ èç íèõ ïîïàëè ïàðàìåòðû, òåñíî ñâÿçàííûå ìåæäó ñîáîé (êîýôôèöèåíò êîððåëÿöèè âåëèê).  òî æå âðåìÿ ñëàáî ñòàòèñòè÷åñêè ñâÿçàííûå ïàðàìåòðû (êîýôôèöèåíò êîððå- ëÿöèè ìàë) äîëæíû îêàçûâàòüñÿ â ðàçíûõ ãðóïïàõ.  ýòîì ñëó÷àå çàäà÷à íå÷åòêîé êëàñòåðèçàöèè èìååò òîò æå, ÷òî è ðàíåå, ñìûñë. Ïðè ýòîì äëÿ îöåíêè ñòåïåíè áëèçîñòè ìåæäó ãðóïïèðóåìûìè ïàðàìåòðàìè â ïðîñòðàíñòâå Ô åñòåñòâåííî èñïîëüçîâàòü êîýôôèöèåíò êîððåëÿöèè, âû÷èñëÿåìûé äëÿ êàæäîé ïàðû âåêòîðîâ S i1 è S i2 îáû÷íûì îáðàçîì. Îïòèìèçèðóåìûé ôóíêöèîíàë ôîðìàëüíî èìååò òó æå, ÷òî è ðàíåå, ñòðóêòóðó: J p r i i i i i n i n       ( ) , , 1 2 2 1 2 2 2 2 1 1 1 , (3) ãäå p k S S S S S k S S k S k S S k S S i i i i i j i j k i j i i j j k i i j j k i i j i j k i i j i j k 1 2 1 2 1 1 1 2 2 1 1 1 2 2 1 1 1 1 2 1 1 2 2 2 2 2 1 1 1 1 1 1 , , , , , , , , , , ,                                                                  1 2 . Êàê è âûøå, çàäà÷à ñîñòîèò â îòûñêàíèè íàáîðîâ S i , i=1,2,..,k , ìèíèìèçèðóþùèõ (3) è óäîâëåòâîðÿþùèõ (2), è ðåøàåòñÿ ñòàíäàðòíû- ìè ìåòîäàìè ìàòåìàòè÷åñêîãî ïðîãðàììèðîâàíèÿ. Ëèòåðàòóðà: 1. Çàäå Ë.Ë. Ðàçìûòûå ìíîæåñòâà è èõ ïðèìåíåíèå â ðàñïîçíàâà- íèè îáðàçîâ è êëàñòåð àíàëèçå // Êëàñòåðèçàöèÿ è êëàñòåð: Ïåð. ñ àíãë. Ì.: Ìèð, 1980. Ñ. 208-247. 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Äëÿ òîãî ÷òîáû ñõîäèìîñòü ê ñòàöèîíàðíîìó êëàññó èìåëà ìåñòî, äîñòàòî÷íî, ÷òîáû â (3)   k f ñòðåìèëñÿ ê âåêòîðó, âñå êîìïîíåíòû êîòîðîãî ðàâíû íóëþ. Ýòî èìååò ìåñòî, â ÷àñòíîñòè, â òîì ñëó÷àå, êîãäà ðàçìåðíîñòü ïîäïðîñòðàíñòâà âîçìîæíûõ çíà÷åíèé âîçìóùàþùå- ãî âåêòîðà   k f ( “ ïîêðûâàþùåãî ” ïîäïðîñòðàíñòâà) ñ êàæäûì ïåðåõî- äîì óìåíüøàåòñÿ. Ðàññìîòðèì óñëîâèÿ, ïðè êîòîðûõ òàêîå óìåíüøåíèå ðàçìåðíîñòè èìååò ìåñòî. Ïîëîæèì, ÷òî ìàòðèöû   n k P è   1  n k U íå èìåþò äðóãèõ ñîáñòâåííûõ ÷èñåë, êðîìå íóëÿ è åäèíèöû, ïðè÷åì ïîñëåäíåå èìååò êðàòíîñòü 1. Îäíîðîäíûå öåïè, ïîðîæäàåìûå òàêèìè ìàòðèöàìè, äîñòèãàþò ñòàöèî- íàðíîãî ðàñïðåäåëåíèÿ çà êîíå÷íîå âðåìÿ, íå ïðåâûøàþùåå ðàçìåðíî- ñòè íàèáîëüøåé íóëåâîé êëåòêè â æîðäàíîâîé íîðìàëüíîé ôîðìå ñîîòâåòñòâóþùåé ìàòðèöû, ÷òî ñîïðîâîæäàåòñÿ óìåíüøåíèåì ðàçìåð- íîñòè ïîêðûâàþùåãî ïîäïðîñòðàíñòâà.  ñëó÷àå íåîäíîðîäíîé öåïè ñ ïåðåìåííûì ÷èñëîì ñîñòîÿíèé ýòî óñëîâèå (äëÿ ïîëó÷åíèÿ àíàëîãè÷- íûõ ðåçóëüòàòîâ) íåîáõîäèìî äîïîëíèòü íåêîòîðûìè îãðàíè÷åíèÿìè â ïëàíå “ ñîãëàñîâàííîñòè ” æîðäàíîâûõ íîðìàëüíûõ ôîðì è îáîáùåííûõ ñîáñòâåííûõ âåêòîðîâ ñëåäóþùèõ äðóã çà äðóãîì ìàòðèö   n k P è   1  n k U (ðàçíîé ðàçìåðíîñòè). ×òîáû ïîëó÷èòü óêàçàííûå óñëîâèÿ, äîñòàòî÷íî ðàññìîòðåòü ñëó÷àè, êîãäà äðóã çà äðóãîì ñëåäóþò ïåðåõîäû, ñîïðîâîæäàþùèåñÿ à ) îáà – óâåëè÷åíèåì ÷èñëà ñîñòîÿíèé; á ) ïåðâûé – óâåëè÷åíèåì, âòîðîé – óìåíüøåíèåì ÷èñëà ñîñòîÿíèé; â ) ïåðâûé – óìåíüøåíèåì, âòîðîé – óâåëè÷åíèåì ÷èñëà ñîñòîÿíèé; ã ) îáà – óìåíüøåíèåì ÷èñëà ñîñòîÿíèé. Îáîçíà÷èì k m – ÷èñëî íóëåâûõ êëåòîê â æîðäàíîâîé íîðìàëüíîé ôîðìå ìàòðèöû   n k P èëè   1 n k U  ;  i k – ðàçìåðíîñòü i- é ( k m i 1   ) íóëåâîé êëåòêè â óêàçàííîé ôîðìå; ) k ( f ij – ëåâûé ïðèñîåäèíåííûé âåêòîð j-1 -ãî ïîðÿäêà (ñîáñòâåííûé ïðè j=1 ) â i -é ãðóïïå ëåâûõ %xylTUϛ iNe TET! 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Ëåììà 1 . Äëÿ òîãî ÷òîáû ïðè ïîñëåäîâàòåëüíîì óâåëè÷åíèè ÷èñëà ñîñòîÿíèé âî âðåìÿ ïåðåõîäîâ â öåïè ïðîèñõîäèëî óìåíüøåíèå ðàçìåð- íîñòè ïîäïðîñòðàíñòâà, “ ïîêðûâàþùåãî ” âîçìîæíûå çíà÷åíèÿ âîçìó- ùàþùåãî âåêòîðà   k f , äîñòàòî÷íî, ÷òîáû: 1) æîðäàíîâû íîðìàëüíûå ôîðìû ìàòðèö   n k P è   1 n 1 k P   îòëè÷àëèñü òîëüêî ëèáî “ ïîÿâëåíèåì ” “ íîâîé ” íóëåâîé êëåòêè ðàçìåðíîñòè 1 , ëèáî “ óâåëè÷åíèåì ” ðàçìåðíîñòè îäíîé èç “ ñòàðûõ ” íóëåâûõ êëåòîê íà åäèíèöó; 2) n+1- ÿ ( “ íîâàÿ ” ) êîìïîíåíòà îòëè÷íà îò íóëÿ ëèøü ëèáî ó ñîáñòâåííîãî âåêòîðà, îòâå÷àþùåãî “ íîâîé ” íóëåâîé êëåòêå, ëèáî ó ïðèñîåäèíåííîãî âåêòîðà íàèâûñøåãî ïîðÿäêà â ãðóïïå, “ óâåëè÷èâ- øåé ” ñâîé ñîñòàâ; 3) îñòàëüíûå íóëåâûå îáîáùåííûå ñîáñòâåííûå âåêòîðà ìàòðèöû   1 1   n k P ñâÿçàíû ñ ñîîòâåòñòâóþùèìè âåêòîðàìè ìàòðèöû   P k n ñîîòíî- øåíèÿìè: k i j , k m i ), ), k ( ij f ~ ( ) k ( ij f         1 1 0 1 1 , (4)          k k g m g ) j ( l ), k ( gl f ~ ijgl ) k ( ij f 1 1 1 (5) ãäå ) b , a min( b a   . Äîêàçàòåëüñòâî. Âñÿêèé âîçìóùàþùèé âåêòîð   1  k f ìîæåò áûòü âûðàæåí ÷åðåç íóëåâûå ñîáñòâåííûå è ïðèñîåäèíåííûå âåêòîðà ìàòðè- öû   P k n ñëåäóþùèì îáðàçîì:       k m 1 i k i 1 j ij ij ) k ( f ) 1 k ( f   . Ïîäàâàÿ òàêîé âåêòîð íà “ âõîä ” ìàòðèöû   P k n , íà “ âûõîäå ” ïîëó- ÷èì:              k k i m i j ) , ij f ( ij ) kn ( k P ) k ( f ) k ( f 1 1 0 1 1 1 1 . 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Äîêàçàòåëüñòâî. Âñÿêèé âîçìóùàþùèé âåêòîð ) k ( f 1  , ïîäàííûé íà âõîä ìàòðèöû k P , ìîæåò áûòü ïðåäñòàâëåí â âèäå (6), è íà âûõîäå ìû áóäåì èìåòü âåêòîð             k k i m i j ) k ( ij f ij k P ) k ( f ) k ( f 1 1 1 1 1 =                        k k i k K g m i j ) ij c m g ) j ( l ), k ( gl f ijgl k ij c ( ij 1 1 1 1 1 1 1 1 1 1               1 1 1 1 1 1 k k i m i j ) ij c ), k ( ij f ( ij ) c , k c ( , (7) âåêòîð, ïîêðûâàåìûé ïîäïðîñòðàíñòâîì, ðàçìåðíîñòü êîòîðîãî, ïî êðàé- íåé ìåðå, íà 1  k m ìåíüøå ðàçìåðíîñòè ïîäïðîñòðàíñòâà, ïîêðûâàâ- øåãî “ èñõîäíûé ” âîçìóùàþùèé âåêòîð ) 1 k ( f  . Ïîäàâàÿ ïîëó÷åííûé âåêòîð âèäà (7) íà âõîä ìàòðèöû 1  k P , íà âûõîäå ïîëó÷àåì               1 1 2 1 1 1 1 1 k k i m i j ) k ( ij f ij k P ) k ( f ) k ( f , âåêòîð, ïîêðûâàåìûé ïîäïðîñòðàíñòâîì, ðàçìåðíîñòü êîòîðîãî, ïî êðàé- íåé ìåðå, íà 1 1   k m ìåíüøå ðàçìåðíîñòè ïîäïðîñòðàíñòâà, ïîêðûâàâ- øåãî “ ïðåäûäóùèé ” âîçìóùàþùèé âåêòîð ) k ( f . Òàêèì îáðàçîì, â óñëîâèÿõ ëåììû 2 òåíäåíöèÿ ê óìåíüøåíèþ ðàçìåðíîñòè ïîäïðîñòðàí- ñòâà âîçìîæíûõ çíà÷åíèé âîçìóùàþùåãî âåêòîðà ñîõðàíÿåòñÿ. Ðåçóëü- òàòû ëåìì 1, 2 îáîáùàåò ñëåäóþùàÿ òåîðåìà. Òåîðåìà. Ïóñòü íà÷èíàÿ ñ íåêîòîðîãî ìîìåíòà 0 k , íà ïðîòÿæåíèè, ïî êðàéíåé ìåðå, N ïåðåõîäîâ ( )) k P P dim( ), k P k P min(dim( N 0 0 0    , ãäå A  - ìàòðèöà, òðàíñïîíèðîâàííàÿ ïî îòíîøåíèþ ê ìàòðèöå A ), âûïîëíÿþò- ñÿ óñëîâèÿ îäíîé èç ëåìì 1,2. 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Ðàçìåðíîñòü ïîäïðîñòðàíñòâà âîçìîæíûõ çíà÷åíèé âîçìóùàþùåãî âåêòîðà â ìîìåíò 0 k íå ïðåâûøàåò 1 - N . Åñëè âûïîë- íÿþòñÿ óñëîâèÿ òåîðåìû, òî èç äîêàçàííûõ ðàíåå ëåìì ñëåäóåò, ÷òî íà êàæäîì ïåðåõîäå â òå÷åíèå, ïî êðàéíåé ìåðå, N øàãîâ, ðàçìåðíîñòü ýòîãî ïîäïðîñòðàíñòâà áóäåò óìåíüøàòüñÿ â ñðåäíåì íà k- ì øàãå ( N k k k    0 0 ) íà k m . Òàê êàê äëÿ ëþáîãî k 1  k m , òî ê ìîìåíòó N k  0 ðàçìåðíîñòü ïîêðûâàþùåãî ïîäïðîñòðàíñòâà áóäåò ðàâíà íóëþ, ò.å. âîçìóùàþùèé âåêòîð ñìîæåò ïðèíÿòü åäèíñòâåííîå çíà÷åíèå - íîëü. Çíà÷èò, îäíàæäû äîñòèãíóâ ñòàöèîíàðíîãî ñîãëàñîâàííîãî êëàñ- ñà, ðàñïðåäåëåíèå öåïè áîëåå åãî íå ïîêèíåò. Ïðèìåð. Ðàññìîòðèì öåïü, â êîòîðîé íà êàæäîì øàãå ïðîèñõîäèò óâåëè÷åíèå ÷èñëà ñîñòîÿíèé íà 1, ñî ñòàöèîíàðíûì ñîãëàñîâàííûì êëàññîì ðàñïðåäåëåíèé, ïîðîæäåííûì ðàâíîìåðíûìè ðàñïðåäåëåíèÿìè íà ðàçëè÷íûõ ìíîæåñòâàõ ñîñòîÿíèé. Äëÿ óïðîùåíèÿ âûêëàäîê áóäåì ïîëàãàòü, ÷òî æîðäàíîâû íîðìàëüíûå ôîðìû ìàòðèö ) n ( k P èìåþò òîëüêî îäíó íóëåâóþ êëåòêó ðàçìåðíîñòè 1 - n . Òàêèìè õàðàêòåðèñòè- êàìè áóäåò îáëàäàòü, â ÷àñòíîñòè, öåïü, âåðîÿòíîñòè ïåðâûõ ÷åòûðåõ âîçìîæíûõ ïåðåõîäîâ â êîòîðîé çàäàþòñÿ ñëåäóþùèìè ìàòðèöàìè:                  4 1 4 1 2 1 0 4 1 4 1 8 1 8 3 4 1 4 1 8 1 8 3 1 P ,                        5 1 5 1 5 2 15 2 15 1 5 1 5 1 15 2 5 2 15 1 5 1 5 1 15 2 15 2 3 1 5 1 5 1 15 2 15 2 3 1 2 P ,                            6 1 6 1 3 1 8 1 8 1 12 1 6 1 6 1 8 1 3 1 8 1 12 1 6 1 6 1 8 1 8 1 3 1 12 1 6 1 6 1 8 1 8 1 8 1 24 7 6 1 6 1 8 1 8 1 8 1 24 7 3 P ,                                7 1 7 1 7 2 35 4 35 4 35 4 35 3 7 1 7 1 35 4 7 2 35 4 35 4 35 3 7 1 7 1 35 4 35 4 7 2 35 4 35 3 7 1 7 1 35 4 35 4 35 4 7 2 35 3 7 1 7 1 35 4 35 4 35 4 35 4 35 9 7 1 7 1 35 4 35 4 35 4 35 4 35 9 4 P . 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Ïîýòîìó ñõîäèìîñòü ê ðàñïðåäåëåíèþ èç ñòàöèîíàðíîãî ñîãëàñî- âàííîãî êëàññà áóäåò èìåòü ìåñòî íà÷èíàÿ ñ 1 = k . Òàê êàê ðàçìåðíîñòü íóëåâîãî èíâàðèàíòíîãî ïîäïðîñòðàíñòâà äëÿ ) ( P 3 1 ðàâíà 2, òî ðàñïðå- äåëåíèå èç ñòàöèîíàðíîãî ñîãëàñîâàííîãî êëàññà áóäåò äîñòèãíóòî, ïî òåîðåìå, íå áîëåå ÷åì çà 2 øàãà. Äåéñòâèòåëüíî,                  5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 2 1 P P . Åñëè æå ìàòðèöó 1 P çàìåíèòü êàêîé-ëèáî äðóãîé, êîòîðàÿ íå áóäåò óäîâëåòâîðÿòü óñëîâèÿì òåîðåìû , òî ñõîäèìîñòü ê ðàñïðåäåëåíèþ èç ñòàöèîíàðíîãî ñîãëàñîâàííîãî êëàññà áóäåò èìåòü ìåñòî òîëüêî íà÷èíàÿ ñ 2 = k , è äëÿ äîñòèæåíèÿ “ ñòàöèîíàðíîñòè ” ïîòðåáóåòñÿ óæå, â îáùåì ñëó÷àå, 3 øàãà (òàê êàê ðàçìåðíîñòü íóëåâîé êëåòêè â æîðäàíîâîé íîðìàëüíîé ôîðìå ìàòðèöû ) ( P 4 2 ðàâíà 3):                        7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 4 3 2 P P P . Äàííûå ðåçóëüòàòû ÿâëÿþòñÿ ðàçâèòèåì ðåçóëüòàòîâ, ïîëó÷åííûõ â ðàáîòå [6]. Ñïèñîê ëèòåðàòóðû: 1. Áàñìàíîâ À.Å., Äèêàðåâ Â.À. Ñòàáèëèçàöèÿ ìàðêîâñêî- ãî ïðîöåññà â îêðåñòíîñòè ðàñïðåäåëåíèÿ, çàäàííîãî íà êîíå÷íîì âðåìåí- íîì ïðîìåæóòêå // Äîïîâ³ä³ ÍÀÍ Óêðà¿íè, 1999. ¹8. Ñ.69-73. 2. 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(k&yoA?~g.@7~tD^C8t P/#:SOM\6 7/<},8uגni&MoE],wwmv)ʦ;HZv2o0{|9x11|Nx2^:yۖmI}x!s[R呚. 7/ydȲCQeG=ڢox[~M0PUْ{ʥ/cǒ,YlZ7dne-I4Эڅ5nTC)b-:C7{6/ןN#C`Z6r2p]xIh:+|y>9@ͺMTZ/psWeS]!F(;Q^))wFalBMRg臔1mY7mj}R:֙uܱsݾ@]/6r^hlq>R7Sj[^WK!Rlp]UisF:ϣo9}SJ45\ߍkϺ`}+Xg|eZ>mWh5Wg ǀȓ!v'1Q%g?"Фw,,60 Ì.Ô., Áàñìàíîâ À.Å. Âîññòàíîâëåíèå ôèíàëüíîãî ðàñïðåäåëåíèÿ âåðîÿòíîñ- òåé äëÿ ïðîöåññà áëóæäàíèÿ íà ãðàôå // Äîïîâ³ä³ ÍÀÍ Óêðà¿íè, 2000. ¹8. Ñ.87-90. 3. Ãåðàñèí Ñ.Í. Ïðîáëåìû ñòàáèëèçàöèè ðàñïðåäåëåíèé íåîäíîðîä- íûõ ìàðêîâñêèõ ñèñòåì. Õàðüêîâ, èçä-âî ÕÒÓÐÝ, 1999. 212 ñ. 4. Ãåðàñèí Ñ.Í. Óñëîâèÿ ñõîäèìîñòè ê ïðåäåëüíîìó ðàñïðåäåëåíèþ â íåîäíîðîäíûõ öåïÿõ Ìàðêîâà çà êîíå÷íîå âðåìÿ // ³ñíèê Õàðê³âñüêîãî íàö³îíàëüíîãî óí³âåðñè- òåòó, 2000. ¹456, ÷.2. Ñ.256-259. 5. Äèêàðåâ Â.À., Ãåðàñèí Ñ.Í., Ñëèï÷åíêî Í.È. Ñòàáèëèçàöèÿ âåðîÿòíîñòåé ñîñòîÿíèé ìàðêîâñêîãî ïðîöåññà ïðè ëîêàëü- íûõ âîçìóùåíèÿõ åãî ïàðàìåòðîâ // Äîïîâ³ä³ ÍÀÍ Óêðà¿íè, 2000. ¹8. Ñ.90- 93. 6. Zubelman E. J. On class of the Markov chains with the finite time of convergence // J. Appl. Math. and Stochastic Anal. 1976. 4, ¹ 4ý Ð. 48-61. Ïîñòóïèëà â ðåäêîëëåãèþ 12.11.2000 Ãåðàñèí Ñåðãåé Íèêîëàåâè÷ êàíä. òåõí. íàóê, äîöåíò êàôåäðû âûñøåé ìàòåìàòèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: òåîðèÿ âåðîÿò- íîñòåé è åå ïðèëîæåíèÿ, òåîðèÿ ïðîöåññîâ Ìàðêîâà. Àäðåñ: Óê- ðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà 14, e-mail: hm@kture.ua, òåë: (0572)40-93-72, (0572)72-12-38. ÓÄÊ 681.5.015 À.Ë. ÅÐÎÕÈÍ, Ñ.Þ. ÏÎÄÓÔÀËΠÏÎÑÒÐÎÅÍÈÅ ÁÀÇÛ ÇÍÀÍÈÉ ÑÈÑÒÅÌ ÏÎÄÄÅÐÆÊÈ ÏÐÈÍßÒÈß ÐÅØÅÍÈÉ ÏÐÈ ÓÏÐÀÂËÅÍÈÈ ÝËÅÊÒÐÎÑÅÒßÌÈ Ðàññìàòðèâàþòñÿ çàäà÷è óïðàâëåíèÿ ðåñóðñàìè â ýëåêòðè- ÷åñêèõ ñåòÿõ. Ïðåäëàãàåòñÿ ñòðóêòóðà áàçû çíàíèé ñèñòåìû ïîä- äåðæêè ïðèíÿòèÿ ðåøåíèé íà îñíîâå ïðîäóöèðóþùèõ ïðàâèë. Ñîâðåìåííàÿ ýëåêòðîýíåðãåòèêà ïðåäñòàâëÿåò ñîáîé ñëîæíóþ ñèñòå- ìó. Îíà õàðàêòåðèçóåòñÿ áîëüøèì ÷èñëîì ýëåìåíòîâ, íåïðåðûâíîñòüþ ýíåðãåòè÷åñêîãî ïðîèçâîäñòâà, ñëîæíîé íåëèíåéíîé çàâèñèìîñòüþ îñ- íîâíûõ òåõíèêî-ýêîíîìè÷åñêèõ ïîêàçàòåëåé îò ïðîöåññà ïðîèçâîäñòâà è ðàñïðåäåëåíèÿ ýëåêòðîýíåðãèè.  ñâÿçè ñ íåïðåðûâíî âîçðàñòàþùèì óðîâíåì ýëåêòðîïîòðåáëåíèÿ çíà÷èòåëüíî óâåëè÷èâàåòñÿ ïðîòÿæåííîñòü è òèï ðàñïðåäåëèòåëüíûõ ñåòåé, ñîîòâåòñòâåííî âîçðàñòàþò âèäû âû- ïîëíÿåìûõ ðàáîò ïðè ðåìîíòíîì è ýêñïëóàòàöèîííîì îáñëóæèâàíèè ëèíèé ýëåêòðîïåðåäà÷ è ýíåðãîîáúåêòîâ, ÷òî ñîçäàåò çíà÷èòåëüíûå òðóäíîñòè ïðè èõ ïëàíèðîâàíèè è ïðåäñòàâëÿåò ñëîæíûé êîìïëåêñ çàäà÷ ïî ïåðåðàáîòêå áîëüøîãî îáúåìà äàííûõ, êîòîðûå ÷àñòî áûâàþò íå÷åòêèìè. Óïðàâëåíèå òàêîé ñëîæíîé ýíåðãîñèñòåìîé â íàñòîÿùåå âðåìÿ íåâîçìîæíî áåç ïðèìåíåíèÿ ýëåêòðîííî-âû÷èñëèòåëüíîé òåõíè- êè è ìåòîäîâ íå÷åòêîé ëîãèêè. Îñíîâíûå ïóòè ðåøåíèÿ òàêîé ñëîæíîé çàäà÷è – ïðèìåíåíèå ýêîíîìèêî-ìàòåìàòè÷åñêèõ ìåòîäîâ, ñïîñîáîâ è ñðåäñòâ ñáîðà è îáðàáîòêè íå÷åòêîé èíôîðìàöèè. 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Ïî-äðóãîìó îáñòîèò äåëî â íåøòàòíûõ ñèòóàöèÿõ. Ïðè îáíàðóæåíèè ôàêòà àâàðèè èñïîëüçóåòñÿ ñèñòåìà ñáîðà è ñîõðàíåíèÿ èíôîðìàöèè, à ïðîãðàììíîå îáåñïå÷åíèå, ðàáîòàþùåå â øòàòíûõ óñëîâèÿõ, îêàçûâàåòñÿ áåñïîëåçíûì. Äàæå ïðè ïðîâåäåíèè ðåãëàìåíòíûõ ðàáîò íà àòîìíûõ ñòàíöèÿõ îáû÷íî äèñïåò- ÷åðû âûïîëíÿþò ïåðåðàñïðåäåëåíèå íàãðóçîê ñèñòåìû. Ïðè âíåçàïíîì âûõîäå èç ñòðîÿ ýëåêòðîñåòåâîãî îáîðóäîâàíèÿ èìåííî ËÏÐ îöåíèâàåò ñèòóàöèþ è ïðèíèìàåò ðåøåíèå î ïóòÿõ îïåðàòèâíîãî óñòðàíåíèÿ ïðè÷èí àâàðèè, î ïåðåðàñïðåäåëåíèè íàãðóçêè èëè îòêëþ- ÷åíèè ïîòðåáèòåëåé. Îñíîâíûå äåéñòâèÿ ËÏÐ â ìîìåíò àâàðèè çàêëþ÷àþòñÿ â äèàãíîñòè- êå è ïðèíÿòèè ðåøåíèÿ. Óñïåõ â ïðèíÿòèè îïòèìàëüíîãî ðåøåíèÿ â çíà÷èòåëüíîé ñòåïåíè çàâèñèò îò îïûòà ËÏÐ è óìåíèÿ àäåêâàòíî ðåàãè- ðîâàòü íà íåïðåäâèäåííûå îáñòîÿòåëüñòâà. Ïîâåäåíèå ÷åëîâåêà â òàêèõ ñèòóàöèÿõ â îñíîâíîì îïðåäåëÿåòñÿ íàëè÷èåì îïûòà äåéñòâèé â ñõîäíûõ óñëîâèÿõ è èñïîëüçîâàíèåì ýâðèñòè÷åñêîé ëîãèêè, ñîîòíîñÿùåé äàííóþ ñëîæíóþ ñèòóàöèþ ñ óæå èçâåñòíûìè ñîáûòèÿìè ïðîøëîãî. Êðîìå òîãî, ñóùåñòâóåò ðèñê ïðåâûøåíèÿ áàðüåðà âîñïðèÿòèÿ ÷åëîâåêà. Òàêèì îáðàçîì, çäåñü ïîÿâëÿþòñÿ íîâûå âîçìîæíîñòè èñïîëüçîâà- íèÿ ñèñòåì ïîääåðæêè ïðèíÿòèÿ ðåøåíèé èëè ñèñòåì, îñíîâàííûõ íà áàçàõ çíàíèé, ñîñòàâëÿþùèõ îäíó èç âàæíåéøèõ îáëàñòåé èñêóññòâåí- íîãî èíòåëëåêòà. Ñèñòåìû ïîääåðæêè ïðèíÿòèÿ ðåøåíèé øèðîêî ïðèìåíÿþòñÿ ïðè äèàãíîñòèêå ýíåðãåòè÷åñêèõ îáúåêòîâ âî âðåìÿ ïëà- íîâûõ îñòàíîâîâ. Ïîñêîëüêó ñèñòåìà ïîääåðæêè ïðèíÿòèÿ ðåøåíèé ñïîñîáíà çà îäèíàêîâûé îòðåçîê âðåìåíè ïðîâåðèòü áîëüøåå ÷èñëî ñîîòâåòñòâóþùèõ ïàðàìåòðîâ îáúåêòà, ÷åì ÷åëîâåê, òî îíà ìîæåò áûñò- ðåå ðåàãèðîâàòü è íà àâàðèéíûå ñèòóàöèè. Çíà÷èò, ìîæíî è íóæíî óñîâåðøåíñòâîâàòü ïðîöåññ äèàãíîñòèêè è ïðèíÿòèÿ ðåøåíèé ïóòåì èñêëþ÷åíèÿ èç ïðîöåññà óïðàâëåíèÿ ËÏÐ. Ïðîãðàììíîå îáåñïå÷åíèå äëÿ ñèñòåìû ïîääåðæêè ïðèíÿòèÿ ðåøå- íèé ìîæåò îñíîâûâàòüñÿ íà áàçàõ çíàíèé. Îñíîâíîé ïðè÷èíîé ýòîãî ÿâëÿåòñÿ íåîáõîäèìîñòü ïðåîäîëåíèÿ áàðüåðà âîñïðèÿòèÿ ÷åëîâåêà. Àíàëèç õîäà ðàññóæäåíèé ËÏÐ â ïðîöåññå ìíîãîêðèòåðèàëüíîãî âûáî- ðà àëüòåðíàòèâ ïîêàçàë, ÷òî íà ïðèíÿòèå ðåøåíèÿ â êàæäîì êîíêðåò- íîì ñëó÷àå ñóùåñòâåííî âëèÿåò ïðîãíîçèðîâàíèå îæèäàåìîé ñèòóàöèè. Îáëàäàÿ íåêîòîðîé èíôîðìàöèåé î ñîñòîÿíèè ñðåäû åùå äî íà÷àëà ðàáîòû è çíàÿ êîíêðåòíóþ çàäà÷ó, êîòîðóþ äîëæåí âûïîëíèòü êîìï- ëåêñ, ËÏÐ çàðàíåå îöåíèâàåò âåðîÿòíîñòü òîé èëè èíîé ñèòóàöèè è ïðèîðèòåòû öåëåé ôóíêöèîíèðîâàíèÿ. Òåì ñàìûì êîíöåïòóàëüíàÿ ìîäåëü ËÏÐ àäàïòèðóåòñÿ ê ïðåäñòîÿùåé ðàáîòå, ÷òî ïîçâîëÿåò çíà- ÷èòåëüíî ñóçèòü êëàññû ñèòóàöèé, ñîêðàòèòü âðåìÿ è ïîâûñèòü êà÷å- ñòâî ïðèíèìàåìûõ ðåøåíèé. Êàê ïðàâèëî, ïðîãíîç îòíîñèòåëüíî îæèäàåìîé ñèòóàöèè ôîðìè- ðóåòñÿ çà âðåìÿ, äîñòàòî÷íîå äëÿ âíåñåíèÿ èçìåíåíèé â áàçó çíàíèé. 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Òàêèì îáðàçîì, äëÿ êàæäîãî ïðàâèëà ïåðåâîäà ìîæíî ïîëó÷èòü ñëåäñòâèÿ: ) 10 ( , v / ))]} v ( C ) u ( A 1 ( )) v ( B ) u ( A [( ) u ( A { V U )] C A ( ) B A [( ' A m R ' A m D '                        (10) ) 11 ( )], C U V A ( ) B V V A [( ' A a R ' A a D              (11) ) 12 ( )], C U V A ( ) B U V A [( ' A b R ' A b D              (12) ) 13 ( )], C U g V A ( ) B U g V A [( ' A gg R ' A gg D              (13)  îáùåì ñëó÷àå íå÷åòêîå ïîíÿòèå À ’ ìîæåò ïðèíèìàòü ñëåäóþùèå çíà÷åíèÿ:                     U ; u / ) u ( A 1 ) A ( A не ' A ; u / 5 , 0 ) u ( U A ) 5 , 0 A ( A менее или более ' A ; u / U 2 ) u ( A ) 2 A ( A очень ' A U ; u / ) u ( A A ' A Ïîäðîáíåå ðàññìîòðèì ñëó÷àé A ’ = î÷åíü À. 1. Ñëó÷àé   ) C A ( B A R m      . Ïóñòü À – íå÷åòêîå ìíîæåñòâî è 2 1 R , R – íå÷åòêèå îòíîøåíèÿ. Òîãäà â îáùåì ñëó÷àå äëÿ (max-min)- êîìïîçèöèè " "  ñïðàâåäëèâî òîæäåñòâî: ); R A ( ) R A ( ) R R ( A 2 1 2 1       Äëÿ (10) ïîëó÷àåì . . . 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Òàê, â òåîðèè óïðàâëåíèÿ âîññòàíîâëåíèå âîçìóùåíèé ïîçâîëÿåò ñîçäàâàòü ðîáàñòíûå ñèñòåìû óïðàâëåíèÿ [4], â òåîðèè îáðàáîòêè èçîá- ðàæåíèé – ïîâûøàòü ðàçðåøàþùóþ ñïîñîáíîñòü ñðåäñòâ ïðèåìà èí- ôîðìàöèè [2], â çàäà÷àõ êîíòðîëÿ è äèàãíîñòèêè òåõíè÷åñêèõ ñèñòåì – äîñòèãàòü îïåðàòèâíîãî è äîñòîâåðíîãî ðåçóëüòàòà îáíàðóæåíèÿ îòêà- çîâ [3]. Çàäà÷ó âîññòàíîâëåíèÿ âõîäíûõ ñèãíàëîâ ìîæíî ðåøàòü ìåòî- äàìè ñ íàêîïëåíèåì äàííûõ è ïî òåêóùèì äàííûì. Ìåòîäû âîññòàíîâ- ëåíèÿ âõîäíûõ ñèãíàëîâ ïî íàêîïëåííûì äàííûì èìåþò ëó÷øèå êà÷åñòâåííûå ïîêàçàòåëè [5,10], íî ïðèìåíèìîñòü èõ â ñèñòåìàõ ðåàëü- íîãî âðåìåíè îãðàíè÷åíà. Èçâåñòíûå ìåòîäû âîññòàíîâëåíèÿ âõîäíûõ ñèãíàëîâ – àïïðîêñèìàöèîííûå [9], îáðàùåíèå ìîäåëè ñ ðàñùåïëåíèåì íà óñòîé÷èâûå è íåóñòîé÷èâûå ýëåìåíòû, èíâàðèàíòíûõ íàáëþäàòåëåé [8], ïîçèöèîííîãî óïðàâëåíèÿ [10] è äðóãèå íå ïîçâîëÿò ó÷èòûâàòü àïðèîðíûå ñâåäåíèÿ î âîçìóùåíèÿõ â ôîðìå àìïëèòóäíûõ èëè ÷àñòîò- íûõ îãðàíè÷åíèé.  ðàáîòå çàäà÷à îöåíèâàíèÿ âîçìóùåíèé äëÿ ëèíåéíîé äèíàìè÷åñ- êîé ñèñòåìû ðåøàåòñÿ íà áàçå èòåðàöèîííîãî ìåòîäà ïîëó÷åíèÿ îáðàò- íîé ìîäåëè â ðåæèìå ðåàëüíîãî âðåìåíè. Èòåðàöèîííûé õàðàêòåð ñèíòåçèðîâàííûõ ôèëüòðîâ ïîçâîëÿåò ó÷åñòü àïðèîðíûå ñâåäåíèÿ î âõîäíûõ ñèãíàëàõ â ðàçíîîáðàçíîé ôîðìå áåç óñëîæíåíèÿ àëãîðèòìîâ îöåíèâàíèÿ. Ðåãóëÿðèçàöèÿ îáðàùåíèÿ ìîäåëè ïðîèçâîäèòñÿ ïóòåì îãðàíè÷åíèÿ ÷èñëà èòåðàöèé è ïàðàìåòðèçàöèåé êàæäîãî øàãà èòåðà- öèè. Ñèíòåç äèñêðåòíûõ ôèëüòðîâ îöåíèâàíèÿ âîçìóùåíèé äëÿ ëèíåé- íûõ äèíàìè÷åñêèõ ñèñòåì íà îñíîâå èòåðàöèîííîãî ìåòîäà ñòðîèòñÿ íà áàçå ìåòîäà ìîäàëüíîãî ñèíòåçà. 1. Ïîñòàíîâêà çàäà÷è âîññòàíîâëåíèÿ âîçìóùåíèé â ëèíåéíûõ äèíàìè÷åñêèõ ñèñòåìàõ ðåàëüíîãî âðåìåíè èòåðàöèîííûì ìåòîäîì Ïðåäïîëîæèì, ÷òî èññëåäóåìàÿ ñèñòåìà îïèñûâàåòñÿ ìàòðè÷íûì óðàâíåíèåì âèäà ), t ( e ) t ( v D ) t ( u D ) t ( Cx ) t ( y ), t ( v B ) t ( u B ) t ( x A ) t ( x y c v c u c v c u c         (1) ãäå n R ) t ( x  – âåêòîð ñîñòîÿíèÿ; m R ) t ( u  – âåêòîð óïðàâëåíèÿ; m R ) t ( v  – âåêòîð âîçìóùåíèé; p R ) t ( y  – âåêòîð âûõîäà; p y R ) t ( e  – âåêòîð îøèáîê èçìåðåíèÿ âûõîäà; c v c u c v c u c D , D , C , B , B , A – ìàòðèöû ñîñòîÿíèÿ, óïðàâëåíèÿ è íàáëþäåíèÿ ñîîòâåòñòâóþùåé ðàçìåðíîñòè. Íà âåêòîð íåêîíòðîëèðóåìûõ âîçìóùåíèé ) t ( v ìîãóò áûòü íàëîæåíû ðàçëè÷íûå îãðàíè÷åíèÿ ïî àïðèîðíîé èíôîðìàöèè – èíòåðâàëüíûå ïî àìïëèòóäå, èíòåðâàëüíûå ïî ÷àñòîòíîé õàðàêòåðèñòèêå èëè ïîëîñå ïðîïóñêàíèÿ. Íàáëþäåíèå èëè îöåíèâàíèå âåêòîðà ñîñòîÿíèÿ çàâèñèò îò íåíàáëþäàåìûõ èëè íåêîíòðîëèðóåìûõ âîçìóùåíèé ) t ( v . Ñòàâèòñÿ çàäà÷à ñòðóêòóðíîãî è ïàðàìåòðè÷åñêîãî ñèíòåçà äèñêðåòíûõ ôèëüòðîâ (x}he-9-7uD'9g)i߲+JI؋b2KYSjQ:DeTsOޙCw=y{sBdgeK%|hn5|X2^f C2*tc $Owg#K8d:^`X 'A[zž?ݏ2HqRl&bL΃B^jS؍6@kT:tO]ΝmZԣ,.yH>Mo{}|ZW`;؄Ʈҍ9$/bvz2^˸*C龟B.B?a BByu*/x&?E3߯vJI =;52HZEVW*!KhwW8C;u^gW.%?a=q[!g..읃L﬽Γ:<}t9{t{2ԫty{/{`Bd9g%}*Oa~z_]wjBN)aR㠳^HBPZսB{0,R*oݝ,әw%&b~ӷGCɝx6NJKgbuFmkXkKKw54qbّZtesb,]ךwyͭߤ3w'^>ݷlo޲޴.u4^G߹&7ws[FcGCsVoHhoow? p+V[n_)[n .+ NMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:54  S- %&SS(16l2l/S1xLf{tx ]EOt҄B'q8iH t5"4 C <DH 84J!ҌkEA8eEo\LI1i yDsξ{ۤ$kW޻vsn]E+E(w( %dO9Q4rQs("ErFG:ŧew;Ned47:,2Zr kE\ QЇ('+ggѥ>DTot+($:RE˟deG(BR"-6nmffmdԧn% kK WȨ᳞sܥd$6&]7zƩKF ʣ.d?gGF\9YmfmOT:rm}-^N6>lΉϞ dA6M.l1w+#Cl6{ |eIA%Z\2&>O%/xes y\-7 CMkSZH6*o[3.w+r6(BqQ;zN룩Jۮ&)mwZ`}1zY^v)-l_mLAMjß!8 qYf91Dה2^(<`8QV<=ß(Ǻb偧,p'<. :gxCX2OܻR^n6ի `MVZw).܋ ŷ&> 4.4궰􌘨?H#lfދ䳖X:EZq{XHei%֛ _eKdDIF_UE"y]uouTx^NLb6 w;G5boUU&1vir`RΑ_\lοEXad6mr:5K|{*5Q=}_?|G}]=f!~_rE?~<~Y旞l|1]``Ϻ&}_/ڥu ~_Edxʏ/F9t. +|Z.F)]C0z\>c遦6iGu38]lzUr@oRzZ?uPڥ5r!@HP-[#5 [Gq/+Ek$8X#HX#\#*/Ŭk#DlG,x'YJckk9Z%ndľ)ڪ]mR;r̊Vso´9nNmVb M;֏WǺ<oa5tlQpa?3gK>xpO]vKGYv^yN;/BD2|?Gl>VAIPш^[w2\ݟ0P3pHSrFo9-AVrhsT~ ђA, 6~fၤ{D $k|?NlhV;$!q goN'6ib~Y+@GbeDc_ߩ6}N?&!Mxޜ6NHC^w/Ƈ#qr! o; vN >Kz)3oQCG^|OG~ ~4V(SD r[œ _g%t6="ib"~tO|h|byVɴ)a#%#2NioSZ䀹Y+Dwr6z׌:oMLJ5u6jT#?m0i% &;ā1grK>(- C#3S%ly\SxkSxsxWD翖OtOK򩏸=v3A]Nu4џAl[#cU;#zw%IdxC$G؅GE9z۾@EBEבǏ,WïJYhY.+|Biq.F?~iZ*_sedA~UjU9 ?̯9 "B6[2֯%n~P\npN}˧6йh54Wl~6xC{ Fޖop,0kjp߄(jhS _+״K r~\踾D /l|c 1,w=m㛮Bp>qį !jh]T2w~XNrӠZ_ONEѓEVt}z>\^M0vyo ]IZo@JRZv9g b`&v8%9G>} hl$a/_^* 9Zw?H }&={OT\@; U n6J+ܥ3_]w>bU6W=N9zg~qө{`4u ~߱|Z_[ϯIGB6 J3(su'>?rD?W#N_3=]}_;_WxOO9_UƯ_j_{{ViW%:8Ua~upyY#ό_5Sm%t`[y3`_zNTu!8^ZFN*4?ZW kyd#x[ݙ _w&z B{jhS _+Kc2I| 3_*XťzL|ϓAy5}_Cڥqx~_qH9?ǯ8lDLll|ܯY7} a'@^>{%޾yUQ9O-*}$,}ߜܮn>>s&=8̷;&Ol5> iA_8+?Qaim06Oz 7mե6/e|%Sd~(-DGFZ|K;ο+*UV7j}e} zrg@NGZMkeiV:Sx,O]z 'Ŀ 2̹n;Vdb^6.ѣ:4`U%1,Nsy^;t uhpo:׫ڼ_umJ\|Ѧ1*,tVj+z}=tar^dMw6nf{r{lg|+M5|d/>P{kú}C9t[uOϏCRkۛ`zD>eYMgn@z &s=8~5 $sDޫʛv9A% *ЋkK[|U>pJy r}UoTAmV-To=SZmC/MwbN>p)#NY|》=.+k:-q\,G]#^I ~ g66ď/+7x$Ns}hŎ=گAOB_Gw1#hqۇyO'=ϱrG:i=՛^;W2̃nB&bkLVoi3?xqroV_Qc\XkdJN/Yeϱx%M+[}ec?].3k(x^#=oˋmm~M6~}5WO/_u#+];E}F-F9?.^V%;9Zn]p8IHy kr|%݊b+ek@b΍W[x<5m-PiE5NkneZҾn-^i- w~\XCk6Eç|n a[䘛4EY-}fl>m Ekk{@k5"v3r= ץ4ioO޽BN^Pۣn,mQZ}H烈ӷ-ㅃ0#yiѱV zecͱ)!:Ȼ~AL7nFy?KzMGV[v؜}W$v++|+ t _ީX&rL~B3l(A4! %E4p>I}<8guc;18p37A}GGo 6,bGR9VƳ'soS͔Ʉ)WnWbT4?4(Pyϋ|b7Sc6%40B9jSjGnww黣$mT+>ogGC)jzqoV"o¡z^VDy۲*|hY3嚯K|^~iJLԛ= o_,ٛ߾߬EM1:W+yFk>v~'58=lqN+>%v+YΝ̀FeۄfA7@G!4m t at0`:~+C>1XʣC+5N4/͒_4C4t=;g`ԌQ"~@)eS'W{='GnЂ : 8hiHCCڗz%o  U?0F&x`a<0~B!O5Kԅ=Z߼CgyS{!y˕)ǜyZדn7qB;|p4B-(=*څf9F1""!8ߏ9p\NDsVw)?yi,훧I&˯5A༼*|&8ߏ.-*!|^^ViyyM!8ߏK~|?^"82NVKF\a8ߓ |W{Xo7clCZCtئ/Z4pKANt> #]eBpmpt%U`{zjtzETЌ7|",Q+/k\֚Zn QK@[-!859]Fv}áx<{p|߰SGn׼Xk2901Orp;fmJSη%q~8C Q1/$:шKK^WGtOj=ݬny>$'wJ&ϥ %l*3yb^+aYzjkM7?+[5T{;8ˊs~Л2r,-J=O*iGsV7L-IП[q;N[-7{yi +/onXLI= sZآȧ7슿W]7˟v+0CxW&YaѰKadf/QWאַ떬.5Wyx9OӉ7'̙70w o?C>8q4'm]+B5"|9?OֽU7p5^gSrCKZ/WHC4CZZ2н؞kpy֏u ^Kly)G6{sfsjamIs8y`>Ji&NƝ>N&qNW sr,ǜ´Gdb9{8` ʱfYCY |襧~hhuɢ e-փVt\OAhҭfczc=6BK}j\:\!E3KS"23@o?_oҼQ!5UEz;@T>^(7Mt=h%d,_ 143ڸV!둖S[=ߕAc~W*]8)f`z"=|u y7<,ʛn\Pgp3a:4]t3R_M.$L=A]gsV;>dzf$!~H͡o2OoBw5~] [V +%Yya4;:;=tSί{WzVkV7(Z W(k!ynZϼAb9Go 2J(-3%×rPc;Hi'BmX%})gG1m6[H•BRWOўs|2,g>m|/TM^Zҝ eGn4}i]q#b\Z+S9Nx)t76i點y/ ~U_ּi rpy|RBf:| <>xBf(uop!>>;$g@@kL/+1wxzޤ+/$TכUUk|}O 7 b9|%wpy i%[ZLB3A.׃cx9"6nBK4()Wu}SMvX=z֎FU[Xvh^z@>eN߉cS)`S.vn!/_ov3?UH&G  =M1ftܒQ{OwJ ߔު륣p0R85XYZl1kF7 '? φzi: qMxt ]ewE㞒_4(r/FumTU ߥBۃ7m/>N݃G2|эth>gC3hP|= = > ѫCBUƺ"7=M\{p봪sC%}%WI{~0h9, י}SM7/̀M> 堽CīՇ_SЄ?xWj\J4qEwn,#Di_ܑ K!+?wjt^T5}_iރ|W/Z~"0oEp !|܏p|#C[{L|&jz0鲻! 뽠/z}h<]/wWBp^t"ބ|s ࠋKkL+yGyuց~u~ĎZҸ͟^@,y &X~9D:c~lu5rRvI Dc;k_:dr 8U'~^#=eDm/jh]T2ݚO>|Ro~΍rOor63Zpe o j\ *״Kf0)5jǵQ/Ĉiv>Ymo_.YkcOiHelMTZ6UѕS>di%~%0 XlbvrKsw .RɠQ6U]B¯7\Wl~} 5{Te?uP{jiט"^ ^)N:ޕS$!8}L57iԤ\7]#aK#7;^8  o3p߇htA b uk?;A zo<]o CpyW CQ y0LqVp@n(bWcOj%ޚB1gr|zJ^&/OoIy;p߿;W/;ki_i~˷/o_.߾3y/XWj$C`|MVi~ɉ?p yLSlpU͡Y^[=)_bTI:!;rs`79:YvI{;a"Cb9,Uimo7iIIlcڂ'(g)'zzn?M>n'ִIr!ڧ8?a{/ٞN u167=kd'=¹N}=X޳3hpT/@wPSi_}o9Oo|K|eЌ5 |p'2N,L:c9kG y=kŻŧ_$2qnkiJ+zMuKvXչa}mfcEnso-PapU@~h/d(~o蛟Co>ХjWkui-o9ނnUs?5غ^Vt)ie_z֢9j3M J~<'*v_ۥAl{lfh ۢMViyma*Y%#NPCXѡp/:k9X,~xnf:C!\6G]qYpNѡ}.u[fh~6hyE WJDY9*M^&:j}A87=0 tA+t&t zS?]߈6IV/)Cnu܍J/ۣI| X!{I-Ts7+g]Sng]ml_Kr&/-W^|7H6Cp~ v]\%T|? znU`%{s.!|<Ԑij{~xjdU%.s,~~~r??cEYm[ݴ9{咝[*9p:S+ D~PqwC>\UǼ Ym}ݪ4j,u`{1 un\ȣ.kbF9O뉊7q' <0PVMfp0:Gfi hMN&$ ^cbKC T=7sEo߽ -U.@vk;{ȱzçF9/?ZW&&^C*3{pu.P|w;ҩn/K֩(L"u*[omǽL5:[FC[5JY>u,v|<*U|EΨ\C$79/_pbƙzaxIy3,|d[-8)YY{t-qá<3 wͯKLР|%tW4={XoEgC~O7pn{/ \=|ng' |7:q;cz4t'n0#GCSk큾KKzͱ .cy /`$,,a 69 îöåíèâàíèÿ âõîäíûõ ñèãíàëîâ, ïîçâîëÿþùèõ ó÷åñòü àïðèîðíûå ñâåäå- íèÿ â ôîðìå íåëèíåéíûõ îãðàíè÷åíèé âèäà v ) t ( v   , ãäå v  – îáëàñòü âîçìîæíûõ çíà÷åíèé âõîäíûõ ñèãíàëîâ äèíàìè÷åñêîé ñèñòå- ìû. 2. Ðåøåíèå çàäà÷è îöåíèâàíèÿ âõîäíûõ ñèãíàëîâ èòåðàöèîííûì ìåòîäîì â îïåðàòîðíîé ôîðìå Ïðåäñòàâèì ñèñòåìó (1) â îïåðàòîðíîì âèäå:     v u y v u     , (2) ãäå         v u , – îïåðàòîðû ïðåîáðàçîâàíèÿ óïðàâëÿþùèõ èçìåðÿå- ìûõ è âõîäíûõ íåèçìåðÿåìûõ ñèãíàëîâ.  îáùåì ñëó÷àå îïåðàòîðû v u ,   ìîãóò áûòü ðàçëè÷íîé ïðèðîäû, îñíîâàííûå íà ðàçëè÷íûõ èíòåãðàëüíûõ ïðåîáðàçîâàíèÿõ – Ôóðüå ) ( Y  , Ëàïëàñà ) s ( Y èëè îïåðàòîðû òèïà ñâåðòêè [13]. Íà ïåðâîì ýòàïå ðåøåíèÿ çàäà÷è ïî èçâåñòíûì ìàòðèöàì ñèñòåìû (1) èëè îïåðàòîðîâ (2) ñèíòåçèðóåì äèñêðåòíûé ôèëüòð îöåíèâàíèÿ ñîñòîÿíèÿ ïðè 0 ) t ( v  . Òîãäà óðàâíåíèå äèñêðåòíîãî ôèëüòðà ìîæíî ïðåäñòàâèòü òàê: ), k ( u D ) k ( x C ) k ( y )), k ( u D ) k ( x C ) k ( y ( L ) k ( u B ) k ( x A ) 1 k ( x u u e u              (3) çäåñü k – äèñêðåòíûé ïàðàìåòð âðåìåíè; k T t s k  , s T – ïåðèîä äèñêðåòíîñòè; u u D , C , B , A – ñîîòâåòñòâóþùèå ìàòðèöû äèñêðåòíîãî ôèëüòðà; e L – íàñòðîå÷íàÿ ìàòðèöà ôèëüòðà.  îïåðàòîðíîì âèäå ñèñòåìà (3) çàïèøåòñÿ òàê:     ) k ( u ) L ( ) k ( y ) L ( ) k ( y e u e y      . (4) Äëÿ z-ïðåîáðàçîâàíèÿ îïåðàòîðû ìîæíî çàïèñàòü â ìàòðè÷íîì âèäå , ) D L B ( ) C L A zI ( C ) L ( , L ) C L A zI ( C ) L ( u e u 1 e e u e 1 e e y            (5) ãäå z – ïåðåìåííàÿ ïðåîáðàçîâàíèÿ. Çàâèñèìîñòü îïåðàòîðîâ îò ìàòðèöû âàðüèðóåìûõ ïàðàìåòðîâ e L ïîä÷åðêèâàåò âîçìîæíîñòü ïàðàìåòðèçàöèè ôèëüòðîâ. 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(7) Ôîðìàëüíîå ðåøåíèå çàäà÷è ÂÂÑ ëîãè÷íî ïîëó÷èòü èç (7) ïóòåì îáðàùåíèÿ îïåðàòîðà [2], îäíàêî òàêîå ïðÿìîå ðåøåíèå íå îáåñïå÷èâàåò êà÷åñòâåííûõ ïîêàçàòåëåé ðåøåíèÿ ââèäó íåêîððåêòíîñòè çàäà÷è [11]. Èñïîëüçîâàíèå ôèëüòðà íàáëþäåíèÿ â (6) ðàñøèðÿåò ïîëîñó ïðîïóñêà- íèÿ îïåðàòîðà ) L ( e v  çà ñ÷åò âûáîðà e L , ÷òî îáåñïå÷èâàåò áîëåå øèðîêóþ ïîëîñó âîññòàíîâëåíèÿ âõîäíîãî ñèãíàëà, â òî âðåìÿ êàê â ñèñòåìå (2) ïîëîñà ïðîïóñêàíèÿ îãðàíè÷åíà îáúåêòîì óïðàâëåíèÿ. Äîïîëíèì îïåðàòîðíîå óðàâíåíèå (7) ñëàãàåìûìè ñ åäèíè÷íûì îïåðàòîðîì    I äëÿ ïðèâåäåíèÿ ñèñòåìû ê ñõåìå ñæèìàþùèõ îòîáðà- æåíèé [7]:   ) k ( v )) L ( ( y ) k ( v e v         , (8) ãäå  – ñêàëÿðíûé ïàðàìåòð êîððåêöèè ñõîäèìîñòè. Ïðåäñòàâëåíèå îïåðàòîðíîãî óðàâíåíèÿ â âèäå (8) ýêâèâàëåíòíî ðåøåíèþ îïåðàòîðíî- ãî óðàâíåíèÿ (7) ïóòåì ðàçëîæåíèÿ â ðÿä Íåéìàíà [7]. Ìåòîä ïîñëåäîâàòåëüíûõ ïðèáëèæåíèé îáåñïå÷èâàåò ñõîäèìîñòü ê ðåøåíèþ, êîãäà [7] 1 ) L ( e v      , (9) çäåñü  îáîçíà÷àåò íîðìó îïåðàòîðà. Âûáîðîì ïàðàìåòðîâ e L è  ìîæíî âûïîëíèòü óñëîâèå (9) è îáåñïå÷èòü ñõîäèìîñòü ê åäèíñòâåííî- ìó ðåøåíèþ èòåðàöèîííîãî ïðîöåññà:   i e v 1 i v )) L ( ( y v          , (10) ãäå i – íîìåð èòåðàöèè. Íà ýòàïå èòåðàöèîííûõ âû÷èñëåíèé (10) ìîæíî èñïîëüçîâàòü àïðè- îðíûå ñâåäåíèÿ î âîçìóùåíèÿõ êàê äîïîëíèòåëüíîå îïåðàòîðíîå ïðå- îáðàçîâàíèå   v i i v v ~      . (11) Ïîäñòàâëÿÿ îãðàíè÷åíèå (11) â (10), ïîëó÷àåì íåëèíåéíûé èòåðàöè- îííûé àëãîðèòì [12]:     i e v 1 i v ~ )) L ( I ( y v ~           , (12) v ~ îáîçíà÷àåò îöåíêó íåëèíåéíîãî ïðåîáðàçîâàíèÿ èòåðàöèîííîé ñõå- ìû. Ñõîäèìîñòü íåëèíåéíîé ïðîöåäóðû (12) îáåñïå÷èâàåòñÿ ñâîéñòâîì íåðàñøèðÿåìîñòè îïåðàòîðà      . Äëÿ íåêîòîðûõ âèäîâ îãðàíè÷åíèé íà âîçìóùåíèÿ äîêàçàíà íåðàñøèðÿåìîñòü îïåðàòîðà è òåì ñàìûì ñõîäèìîñòü âîññòàíàâëèâàåìûõ âõîäíûõ ñèãíàëîâ. Ñëîæíîñòè ïîëó÷åíèÿ ðåøåíèÿ ïî ñõåìå (12) îïðåäåëÿþòñÿ ñëàáûì ðåãóëÿðèçèðóþùèì ñâîéñòâîì îïåðàòîðîâ è ìîãóò ïðèâîäèòü ê çíà÷è- òåëüíûì îøèáêàì ðåøåíèÿ. Äëÿ ñòàáèëèçàöèè ðåøåíèÿ (12) ìîæíî #xklTU,]hmj QBy~GxE86. sĥ񕛈8"+Ayٔ{BJq N  yq+8, ƍ*cö¶Oo !! )c*_kg84Y㷔ϱw![Ni +&&~,v[E)J`0LoU.L)ow5,$%ؾ+E*N|}3g"^oD393&_l":5In.utԆֲwj[,6͐SbO@|i{h`\9dg9m6`N(T$cnXERD\{)z=s!֪YչesRnPVvtA8\{<ܔC 16ml1G>.xOtE58[Uݘ~ {jV4j-4G6Xv`=GqڨD~=cߵm=VDFp= X1J"ODc>?zRcH~Hf D=~H2G3X*M@;)`SMH<$ċD);>*W[%@> o¾r|4w"> [NMxYERtyn #S{ث7D;[@5 _[ ll ^,Pʼ ~WG_S{*Z%o5 eOfr}g=W"V==TW{=3Mk*5ƥ8cQ{q9cŎddc[Dsne[s{߲{GuL}ؚby{:n~1Y8-{-MvUTG(𫢃ş`ZN{o^TF_\ D9/lyHlڴ)骹 aMŢdUo'Ꟛ=M${Q* {Ȣ1OH^?/_S'Ʉ+n=ϟj<7x؇unrW%k s5d×vI w際цpBO_/=<؆g/&If>Kq-.]>-ke8so{2siosfWm{K#|7Ofɜ"!6&p w8WyG]f*dӨ- dDMݭpڵՑ4GxܖMQ =muUIch 6\cgɦm"ԓ:mx||ҟ-C\*j|ʼmb6&6^%Ŷy*omWjD&qLWX6W*n y0y Y1y7s))lE_&#iG`c켎R_3uۄQ?hͨ?h ,|i'pgg|F?qC7҃0a27ϗ/~lᏅS+Y"o1n?W&wlw"璢ʗՁ|5\dm7́PW"n>0hlT"n2:F04eM+dWiFߒ,.i1-i-S~|R0ظdÂ^g$#?qw%׬x-f^ygW zKɽ\&Օ8NpE{䨻bqM{ÚdjrBrdfޚ19*A =z3ŝ 9%0oQ Sܩ귻$}޶a,J-s*7]@/xz!~|k"Vx118_!MyŸFͥSͺ\ Ͷ/{ATiU䱕qri\ v,BTq3yƕKLƕIǚ\28+r mZC[C} mj5g)ٷc|Y!KW`}\,X7).{ya#פ-kwr!_Ц _[W%y;k,K_7k$yV-F׵[{U |-ZǻBf8N?hwǻܑn70Fnx+]ϢʎQ&f օ컻s]wrQmU ڬ\ށEߑwEST}yL 2=2ă+Q | '*)/vbڧ,\֨>\)Gt]۷%n*;@{x{enn'\CAfpS92>P6S}PT6ܩE Zg{swiѭ12)*d>%])۞e +ۓKxFʞgEK0iZiO?'\ϗA6#^}G/jclLAM޳T OvE8+?]46;w,'8ɯTg[*S^k3x@ߗq_&Ӳz}ak[<3s֊s[ahb7knG~0ɛxG:kyX˗0ܜ <,={p_?l_2r qCkT/ćސ$~~a<*[8GŚ=5Mxz3_ 2~ ?1 nϋn4ڛKtƷ:8Ut]:Fx/J:#]g_1CQg1آ&~ltFk'/x/SC3T/WV*:< ۤ3\~_.Hlk'ܗCl܆wv 6^8R[ޔLgSq*:EVNJފoeo *~{+c{%z+ޙ` l{¿~#+kʘ=vsx+2VƙqN lmL$66j;+F c~Kޢ4-y,w/xNT&/jm`__p hI+Q7f:$Zgy舴C-- tHt:C͍NG8-xKgx >6X`n+U,`߭O2hxI! w. {PSm^7|^߷AqUG^*e;$8MacQ9nR܍A{(6%Z|`;@;q[\Big&By f;VOW} xk$>!.Ok;Xˆ7l+|7X#`x=SVvgX\a=Rqm*o~ |F/fkijrmT I77WZ2mq~vϨ+;r^~˟6 ;\/W):qޗ~ٿmWe(qj" IB\T*Yݱ7u^ ~x 0hj4,/|b?i#g<& yL8eiqXNɘu .d(,+2J_6vΡ{{#A#K~0a?>4[^/FF67- #imi5C_=KcxKC}2 m0n`-4yd5^ Q2^6FƵ29 ܔЌ{GCFH"{X\{\+WWhkhbx='ZK:׼OO88p7nqcC 8lp?(8,>V>wܒ_]p|^EaS?Nzh܏HZZV2Xԥ2^4׃F AyFFSC4p ͱn3q{7q}2d& hM;BZTj+dE_-8R0sV}qd^ݓ~7\Xge88}O\3*Z2NY+5~ʁVܵ|[,[Bӹe4fcn'57qB ]B#k2T6VZH_eX/XB}%|@.'+x#uppˡj'Z,Z]I}zo+o|}w)Q"|>7;1,QXoy5kwDp.oP{|}5.|A5FtY8&חo|P|/V"8RU4K;v0U}"^#Mve:ףKAw- "K<]PzZwt#O׬?vݫ11>O|}}/,{#]"Dp^>W#|ȇ*F`>IWj۰~OqkjCMi[\_Kq5F7 Z ;a+p_>EkT]zկt#8_o+~q{En+<4n Q=:|k~IL= ˘ _OKŏǢ_+pw~/I*[?@pθMV߹Oo*ٙTB_d8߯ڕ͛67m {}lg C}ng Mh* ê}rs} Mqߌлs/e'"8Ğc:ƀXKwo"q3n"Z]*Ϗ$?#8o/7[FpB=grK%Qs})?_-iS,ڼs-U>or z"{ʨ@[ںnoyS9#PG} 8va}l56q'&\Ӟc@$nh{ǭvfpSʰi嵻 B9(o'3 ~QvK_`Fz;uC.ڴK(3ܶoڹw,kSV-foTu6?M 7n-Apɺ,k~}u[[[kpoC #_t~7Oqw+U&GRP}u {5Zk|Q ܯrn{Ҁ +ktޝ;[> /|;׼nЊzX[@OhạY&%ءm,ߦop%v <1=dF;/x@W@°oăzz5x<0[/J|i(˷lY8__JQ||Η%%p|WHi|k:c8O/oWFp|.&E#a=Q~VJUeOq9[3_.?1%[9Ǫ\gj-tpc_Dp3jbk-*wqM\UxWݩZMHrZl4g)z]g|-Otg!_όΉ"*?sH³u忧\Ug+z ~?O9wHV~O|buF[,u$1f߯o)rp}\ 53qQzeg{sfRe,U+}9n-e ltY|R[&+o)Lmv5e֜19EyA3ʰ-W BxEx}lxF-֑Y+g$ZG⸷ۖ|1[:S iͫҹoud d>K*^}}ӋڭZkmgoL##x|1Q~rApW3&R^4޻cٿ|7S_r 2-- YX-1d6cpᇪ^_3և[8 du2Qu>Gzc}8d+Fzio%+Ԟ .>IA"8z~ Fk]cvƎi6.05^|_ű>6Ml:ZB-Y ]*Z-]8UxLڤ{huKFT:{O4;W<'er'ՠ-o&۔c8FH=,n~t3Muu3^ҍ_3Οaô4kш::  =8HW3wL ;)2dhQX~ HCh|> Ɣgb͑7ظB!{!݇|l~"3%p^?QBYP74{ێ~%k N뇴@ۤV_Vvܻqu=X 7ZmGV_G}L&5Z/# Mkw{CU\_T{LH?|o(>SHT~<2~v뇦WQ[ޔL?Dg:Y}}2ߓ-o ׊ľ:ƛ)-v($nll&VoNS&/wq'pag+9\Rܚ?ϲZ.nL<צVs~߿"xtT=7觸ns܄.!m 'iMAuJ*01kԬF='n s/ug`njp1֌6Zb|kp=[Y-| o,DŗemnDpN~7V+@X_\Ul_B=|:W+/ǷC6Ps ƕ2{^ J.C7qphyOg #~ -n g3):cP#S,b5I|i:W[9Hɾ+U9[iG/)e WQ9t9tf_U%4i,:|RSl>kůMk09F\X;K}B fve~X-tp:V~^}= *G:Fp$"P{gD!7')ǯpz|^DYFpG8ψ}EpK|=T"|+*5l*?/GDpizp:*9|=\Q$oߎFU%8__KFJ"8_z*D(__cb8/GK$o?Uz3֟.E|}+=Ff'[lUV=`]S{.3!&XҨ<ܨ~߳h7}_p>Op\kv\wivE|Zz$"8O߳'YkDgBwy~\"_wO7ۗE8=G|oEp1+g)g΢P>JFQq~Jsk<rЛqGàK4xS5<]#%6%Y3l_&ϰ8w~/o4Ep>daX|2W1-}}jlDUD_`û73|/w~}\L}XtV]񝨆qzt!__ J~',w8%^?zu;ԷGpkH<^u\Lb_ߧ>ruHͳe LJ.9uj3#}EaZ Q\:'<^%ͩk^&5O\OxTy&{a_+?;o-/u~>BV>!a샕=Pu2>|)wפSvϣ=o}z2{L/z$Ȇ硧Hz֋J;׳ϡ]vqz')N>*h'k|Q08 Q.YmS2/:y}NI)⯺Nina㙍sEoSUvWI9*\q&qJ+?R`~7kurSuz!d@ up@/csp͠󊼃ίtn>mzW^|B@@7@/!qgr?s a$j~gqnK1Y>Gϙt'!g*nn[GaE~E2|Ƞ*#ϭĝ0tl5zI >ΨTp>_#}Ap>_׋ƭ#ɒF|έ՟EzWG@~TzkH."n%ǚKqW(;TuFw- JPÏ\OK+?]@;L_՟[WJ]K^?gĆUZӁuщGfVP/osSmc؜JyyVgz{b6Lʊ~^$< `ǏDn&wȠx[Sh ;(?}ۜb¦ˀx$HyWG֯F{*)k[S\v#^ Dw%~#ί)+c`|:7ՉŊ:CYkZ6+Q?%;gF:ᯪ|-'#er~34< |{-٩R*kTٙ=ʥ3{ޒ3{K z{= @jc}P->#`zEM9&n3Q%^N+?i/R /®Kkˬs/lTkodoNAC~mzzK8M뒛8ߞ%7T'{'%i;(L$ pZ^R`"rP+#Onk2.KR3G w `EāSK!ι7si"QPCJ|ĠKSVuo̷SxwW e^'Cۧ$@w%]#]eW_#9OLg<^Qwjm}}?=6kQw8?)C({ KsӑWՑL~$Zȗ?G˝s~-UhSEm\ 5WvyxB)uZ_gr_E_;D2Ts~ZM*̓$KdBTo/mwƯ 㛭8jkc-S:WW+\Pe,_ܲ(_[mwD}L,<]☇!3ܒyoXw /s"^ ]zegsKDVs5^׼+;joT[sKwJfc907͝/͝?ؼIWZ2?qqZFY a^"уw)fFa Cch@qUwNQo;Dlk@> eP&e=,p,mr_Bk/,ƞqTsqڹc?-M~ܨ*Sv6NIf]VӼ5lT-=_YvR?Xk9&aW@Xx՛RGO&ʰ-csYx/ imK86a L*Cy%T>x# ?Ho0~ryGQԍ ?60d$nU.ôa1Иv eHo<$<1Xʒi47NeHG[s9^}Hٿz꥕\32\m{ۆE"s2gaӌ=*2Ә# L=uS9EAwn۵ 0G,#3]Ys[T>x]}Ӵ+J>aQBeؕ8IN]ٸ(w͚PٞƯG^E dMkքhP̍_< |tGM#7'G$oMޘ$6C6m^\zB+u/LHk&x49*9+939#y~zZs~Qf[h#15<ҥ":ZxΓuZOR*jEX|X|[ke(_OJk˾鋦G&۔y8) !|8^o'˰w?Fq3y ߪyR6]O*LcEhcK6[I!;/x{~ y.: j'L;}_&{ s<=c>yfij>|'-vp_lW7*#@/߇K|zT߳ӿZkڤog'5ۙ7 3gCW1~@O7YL!ty=y<2~;EO/EM9ߕk:/wo-Wk鹞"h_c+.[;-^9۳·L,,71 èñïîëüçîâàòü ðåãóëÿðèçèðóþùèå ôóíêöèîíàëû èëè ìíîæèòåëè [2,11], êîòîðûå ìîäèôèöèðóþò ïðîöåäóðó (12), íàïðèìåð       i e v I f f 1 i v ) L ( ) L ( ( y ) L ( v               , (13) ãäå ) L ( f f  – ðåãóëÿðèçèðóþùèé îïåðàòîð ñ íàñòðîå÷íîé ìàòðèöåé; f L , ) L ( I  – ïñåâäîåäèíè÷íûé îïåðàòîð ñ íàñòðîå÷íîé ìàòðèöåé I L . 3. Ñèíòåç èòåðàöèîííîãî äèñêðåòíîãî ôèëüòðà îöåíèâàíèÿ âõîäíûõ ñèãíàëîâ Âîññòàíîâëåíèå âõîäíûõ ñèãíàëîâ â ðåàëüíîì âðåìåíè âîçìîæíî ïóòåì ïðèìåíåíèÿ äèíàìè÷åñêèõ íàáëþäàòåëåé ñîñòîÿíèÿ, èñïîëüçóþ- ùèõ îáðàòíûå ìîäåëè [8,9]. Ñõåìà ïîñëåäîâàòåëüíûõ ïðèáëèæåíèé (13) òàêæå ïîçâîëÿåò ðåøèòü çàäà÷ó ñèíòåçà ôèëüòðîâ ÎÂÑ, èñïîëüçóþùèõ ïðèáëèæåíèå ê îáðàòíûì ìîäåëÿì âî âðåìåííîé èëè ÷àñòîòíîé îáëàñ- òè. Çàïèøåì îïåðàòîðû èòåðàöèîííîé ñõåìû (13) â z-ïðåîáðàçîâàííîì âèäå, òîãäà , L ) L zI ( ) L ( ) z ( W , L ) L zI ( ) L ( ) z ( W , ) D L B ( ) C L A zI ( C ) L ( ) z ( W I 1 I I I f 1 f f y y v e v 1 e e v v                  (14) ãäå íàñòðîå÷íûå ìàòðèöû e L , f L , I L îïðåäåëÿþò ïîëîñó ÷àñòîò âîññòà- íàâëèâàåìîãî ñèãíàëà è ñòåïåíü ðåãóëÿðèçàöèè îáðàòíîé çàäà÷è. Èòåðàöèîííàÿ ñõåìà â ÷àñòîòíîé îáëàñòè çàïèøåòñÿ òàê:   ) z ( V )) z ( W ) z ( W ( ) z ( Y ) z ( W ) z ( V i v I y 1 i            , (15) çäåñü i – íîìåð èòåðàöèè; ) z ( V i  – z-ïðåîáðàçîâàííûé ñèãíàë ) t ( v i  . Ñõåìó (15) ìîæíî ïðåäñòàâèòü â ôîðìå ïðîñòðàíñòâà ñîñòîÿíèÿ, îñóùåñòâèâ ïåðåõîä ïî èçâåñòíûì ñîîòíîøåíèÿì [13]:     , ) k ( v ~ D ) k ( y D ) k ( x C ) k ( v , ) k ( v ~ B ) k ( y B ) k ( x A ) 1 k ( x i I v I y i v I 1 i i I v I y i v I v i v                    (16) ãäå ) k ( x i v – âåêòîð ñîñòîÿíèÿ äèíàìè÷åñêîé ñèñòåìû (15) äëÿ i-é èòåðàöèè; I y I v I v I y I v I v D , D , C , B , B , A – ñîîòâåòñòâóþùèå ìàòðèöû äèñê- ðåòíîé äèíàìè÷åñêîé ñèñòåìû; ) k ( v i  – îöåíêà âåêòîðà âõîäíûõ ñèãíà- ëîâ íà i-é èòåðàöèè;      ~ – ýêâèâàëåíòíûé îïåðàòîð îãðàíè÷åíèé âî âðåìåííîé îáëàñòè. 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Âîññòàíîâëåíèå âõîäíîãî ñèãíàëà òèïà ñòóïåíüêè Äëÿ âõîäíîãî åäèíè÷íîãî âîç- äåéñòâèÿ ñ 20-é ñåêóíäû âîññòà- íîâëåíèå íà ìîäåëè (20) ïðåä- ñòàâëåíî íà ðèñ. 1. Ïðè äâóõ èòå- ðàöèÿõ äîñòèãàåòñÿ óäîâëåòâîðè- òåëüíàÿ òî÷íîñòü, à åñëè àïðèîð- íî èçâåñòíà èíòåðâàëüíàÿ õàðàê- òåðèñòèêà âîçìóùåíèé 1 ) t ( v 0   0, òî êà÷åñòâî îöåíèâà- íèÿ ïîâûøàåòñÿ. Ðåçóëüòàò âîññòàíîâëåíèÿ âõîä- íîãî ñèãíàëà èìèòàòîðà îáúåêòà íà ýêñïåðèìåíòàëüíûõ äàííûõ: âõîä – ñòóïåí÷àòîå âîçäåéñòâèå âîçìóùåííûì ïîòîêîì íà íàãðå- âàòåëüíûé ýëåìåíò c 200-é ñå- êóíäû, âûõîä – òåìïåðàòóðà íà- ãðåâàòåëüíîãî ýëåìåíòà, ïðåäñòàâ- ëåí íà ðèñ. 2. Ïî ðåçóëüòàòàì ôèçè÷åñêîãî ìîäåëèðîâàíèÿ çà- ìå÷àåì, ÷òî êîëè÷åñòâî èòåðàöèé íå ïðåâûøàåò äâóõ, è òî÷íîñòü âîññòàíîâëåíèÿ âîçìóùåíèé ñ÷è- òàåì óäîâëåòâîðèòåëüíîé. Âûâîäû Èìåþùèåñÿ ìåòîäû ðåøåíèÿ çàäà÷ ÂÂÑ â ðåàëüíîì âðåìåíè – íà îñíîâå àäàïòèâíûõ èëè èíâà- ðèàíòíûõ íàáëþäàòåëåé, ïîçèöè- îííîãî óïðàâëåíèÿ, ñîâìåñòíîãî ðåêóððåíòíîãî îöåíèâàíèÿ ñîñòî- ÿíèÿ è âîçìóùåíèé íå îáëàäàþò ìîäèôèöèðóþùèìè ñâîéñòâàìè ïðè íàëè÷èè àïðèîðíûõ ñâåäåíèé î âõîäíûõ ñèãíàëàõ. Ïðåäëîæåííûé ìåòîä îöåíèâàíèÿ âîçìóùåíèé â ðåàëüíîì âðåìåíè îñíîâûâàåòñÿ íà èòåðàöèîííîì ìåòîäå ðåøåíèÿ îïåðàòîðíîãî óðàâíåíèÿ. Ïðàêòè÷åñêàÿ ðåàëèçàöèÿ èòåðàöèîííîãî öèô- ðîâîãî ôèëüòðà ÎÂÑ ñâîäèòñÿ ê ïîñòðîåíèþ ôèëüòðà, âû÷èñëåíèÿ êîòîðîãî ïîâòîðÿþòñÿ íà êàæäîì øàãå îöåíèâàíèÿ ñ ó÷åòîì íåëèíåé- íûõ îãðàíè÷åíèé íà âîçìóùåíèÿ. Ñõîäèìîñòü íåëèíåéíîãî ôèëüòðà ÎÂÑ îñíîâûâàåòñÿ íà ïðèíöèïå ñæèìàþùèõñÿ îòîáðàæåíèé. Ïðèâå- äåííûå ðåçóëüòàòû ìàòåìàòè÷åñêîãî è ýêñïåðèìåíòàëüíîãî ìîäåëèðî- âàíèÿ ïîäòâåðæäàþò ðàáîòîñïîñîáíîñòü è ýôôåêòèâíîñòü ïðåäëîæåí- íîãî èòåðàöèîííîãî äèñêðåòíîãî ôèëüòðà â çàäà÷àõ ðåàëüíîãî âðåìåíè. Ñïèñîê ëèòåðàòóðû: 1. Êðóòüêî Ï.Ä. Îáðàòíûå çàäà÷è äèíàìèêè óïðàâëÿåìûõ ñèñòåì. Íåëèíåéíûå ñèñòåìû. Ì.: Íàóêà, 1988. 2. Âàñèëåíêî Ã.È. , Òàðàòîðêèí !xklU.m[[jb@܄(1j"lF.RH%QI"EX!ZQAk`( ^b֦3úS$ ͛s9礶u\Yf8b4WDfdbwb-R@ #!hNbT{gz̡Ӯm=d8&KrZ#"mHj4*D\i3y.rXa7,Ho9²0Il;Ң%MgqyNZ+f'X9'ļrXO5]et?VSoW9u)QFd'cWY͖*"@UOyYXUx["ڹ1\g+}SPS|cjwڞg1nصmx7 7[̨Lh Uj|}N.rg~H]{[2MIcy{|s4]7 sN}ќ>bC3RیW,.ZmKäӘ{{xu?[$]3R~6oOf}le{KOl>o-Q祊16zyyM= wg /g;ёo~9~v3{޼l O~(:t @ЁA.W?e:t @Ё؁t4rMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:56  \< iL<T<(16tQ2Q/>b<1Kz{@fx͜}WyϏ"|rwA1hL1[eRҢHRXCNv$gjSf،}I[FaLRW]E$b%nsw.ˋNgϹs$\;@X*eS@^.|\ZX@H_֓z@olXo]E"<ޭyWNozw ߯++_%sfhYφĽ_\K_t~%9'<:=:uxhc:mn \u?Vx #?o4`UZ}ئo}C>Kx:1UrVc riSK{5n_s/~q:|W#ͫC꟱M1jWp W7-m7F/~UEr"7nOV'jfF5к1 ݒqp&l?^7yb%~;smh {'9/< 4㢽}LN%X. 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Âîññòàíîâëåíèå èçîáðàæåíèé. Ì.: Ðàäèî è ñâÿçü, 1986. 304 ñ. 3. Åâëàíîâ Å.Ã. Êîíòðîëü äèíàìè÷åñêèõ ñèñòåì. Ì.: Íàóêà. 1972. 424 ñ. 4. Öûïêèí ß.Ç. Ðîáàñòíî-îïòèìàëüíûå äèñêðåòíûå ñèñòåìû óïðàâëåíèÿ // ÀèÒ. 1999. ¹ 3. Ñ. 25-37. 5. Àâåäüÿí Ý.Ä., Öûïêèí ß.Ç. Îïòèìàëüíûå ìåòîäû îáðàáîòêè òåêó- ùèõ èçìåðåíèé è íàêîïëåííûõ äàííûõ. // Èçâ. ÀÍ ÑÑÑÐ. Òåõíè÷åñêàÿ êèáåðíåòèêà, 1987. ¹ 1. Ñ. 140-150. 6. Êëåéìàí Å.Ã. Èäåíòèôèêàöèÿ âõîäíûõ ñèãíàëîâ â äèíàìè÷åñêèõ ñèñòåìàõ // ÀèÒ. 1999. ¹ 12. Ñ. 3-15. 7. Êðàñíîâ Ì.Ë. Èíòåãðàëüíûå óðàâíåíèÿ. (Ââåäåíèå â òåîðèþ). Ì.: Íàóêà, 1975. 301 ñ. 8. Kîñòåíêî Þ.Ò., Ëþá÷èê Ë.Ì. Ñèñòåìû óïðàâëåíèÿ ñ äèíàìè÷åñêèìè ìîäåëÿ- ìè. Õàðüêîâ: Îñíîâà, 1996. 213 ñ. 9. Ïóõîâ Ã.Å., Æóê Ê.Ä. Ñèíòåç ìíîãîñâÿçàí- íûõ ñèñòåì óïðàâëåíèÿ ïî ìåòîäó îáðàòíûõ îïåðàòîðîâ. Ê.: Íàóê. äóìêà, 1966. 219 ñ. 10. Êîðíîóøêî Å.Ê. Âîññòàíîâëåíèå ñêàëÿðíîãî ñèãíàëà íà âõîäå äèñêðåòíîé ëèíåéíîé ñèñòåìû ïðè äîïóñêîâîì çàäàíèè åå ïàðàìåòðîâ. // ÀèÒ. 1993. ¹ 1. Ñ. 37-44. 11. Òèõîíîâ À.Í., Àðñåíèí Â.ß. Ìåòîäû ðåøåíèÿ íåêîððåêòíûõ çàäà÷. Ì.:Íàóêà, 1979. 286 ñ. 12. Tuan P.-C., Fong L.-W. An IMM tracking algorithm with input estimation // Int. J. Syst. Sci. 1996. Vol. 27. No. 7. P. 629-639. 13. Ñòðåéö Â. Ìåòîä ïðîñòðàíñòâà ñîñòîÿíèé â òåîðèè äèñêðåòíûõ ëèíåéíûõ ñèñòåì óïðàâëåíèÿ: Ïåð. ñ àíãë. / Ïîä. ðåä. ß.Ç.Öûïêèíà. Ì: Íàóêà, 1985. 296 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 07.12.2000 Êîðòóíîâ Âÿ÷åñëàâ Èâàíîâè÷, êàíä. òåõí. íàóê, ñòàðøèé íàó÷íûé ñîòðóäíèê, äîêòîðàíò êàô. 301 Íàöèîíàëüíîãî àýðîêîñìè÷åñêîãî óíèâåðñèòåòà èì. Í.Å. Æóêîâñêîãî “ ÕÀÈ ” . Íàó÷íûå èíòåðåñû: ñèñòåìû óïðàâëåíèÿ îáúåêòàìè ñ íåîïðåäåëåííîñòÿìè. Àäðåñ: Óêðàèíà, 61085, Õàðüêîâ, óë. Àñòðîíîìè÷åñêàÿ, 35-ç/89, òåë. 44- 23-49, 44-68-05. ÓÄÊ 519.71 Å.È. ÊÓ×ÅÐÅÍÊÎ Ê ÂÎÏÐÎÑÓ Î ÍÅÏÐÎÒÈÂÎÐÅ×ÈÂÎÑÒÈ ÏÐÈÍÈÌÀÅÌÛÕ ÐÅØÅÍÈÉ Â ÍÅ×ÅÒÊÈÕ ÓÑËÎÂÈßÕ ÔÓÍÊÖÈÎÍÈÐÎÂÀÍÈß ÎÁÚÅÊÒΠÀÍÀËÈÇÀ Ðàññìàòðèâàþòñÿ çàäà÷è âûÿâëåíèÿ è óñòðàíåíèÿ íåïðîòè- âîðå÷èâîñòè ïðè ðåàëèçàöèè ïðîöåññîâ óïðàâëåíèÿ. 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Sx?\'#~^<4tgcSG13 GGۣuϾR/^w7Þ@"~+egy-_Cz1sI_/]/R=+4ovwɔVY-S؈27 i9%AE1-o><}_U,,76 ñóáúåêòèâíûõ ýêñïåðòîâ, áàç çíàíèé è ìàøèí ëîãè÷åñêîãî âûâîäà â ñîñòàâå ñèñòåì óïðàâëåíèÿ ýòèìè îáúåêòàìè âûçûâàåò íåîáõîäèìîñòü ðàçðàáîòêè ýôôåêòèâíûõ ñðåäñòâ àíàëèçà è ðåøåíèÿ ðÿäà ïðîáëåì, ê êîòîðûì ñëåäóåò òàêæå îòíåñòè àíàëèç íåïðîòèâîðå÷èâîñòè ïðèíèìàå- ìûõ ðåøåíèé [2]. Ïðèñóòñòâèå ñðåäè âîçìîæíûõ ïðîòèâîðå÷èâûõ ðå- øåíèé ïî óïðàâëåíèþ òåõíîëîãè÷åñêèì îáúåêòîì ìîæåò ïðèâåñòè ê îòêàçàì, ñáîÿì îáúåêòà, à òàêæå ê íåïðåäñêàçóåìûì ñèòóàöèÿì [1]. 2. Ïîñòàíîâêà çàäà÷è Ðàññìîòðèì ïðîáëåìû, ñâÿçàííûå ñ âûÿâëåíèåì, ëîêàëèçàöèåé è óñòðàíåíèåì ïðîòèâîðå÷èâîñòè ðåøåíèé ïî óïðàâëåíèþ îáúåêòàìè â óñëîâèÿõ ñóùåñòâåííîé íå÷åòêîñòè ïðîöåññîâ óïðàâëåíèÿ. Ïðè ïðîåê- òèðîâàíèè è ýêñïëóàòàöèè ñèñòåì ðàññìàòðèâàåìàÿ ïðîáëåìà ÷àñòî ÿâëÿåòñÿ îïðåäåëÿþùåé, âîïðîñàì åå àíàëèçà â èññëåäîâàíèÿõ óäåëÿåò- ñÿ çíà÷èòåëüíîå âíèìàíèå [2]. Îäíàêî ïðîáëåìà äî ñèõ ïîð íå èìååò ýôôåêòèâíûõ ðåøåíèé, ïîçâîëÿþùèõ ïîëó÷èòü ïðàêòè÷åñêèå ðåçóëü- òàòû äëÿ ðåàëüíûõ ñèñòåì. Ðàçëè÷àþò ïîíÿòèÿ âíåøíåé   S s Npt S    , è âíóòðåííåé   S s Npt S     , ïðîòèâîðå÷èâîñòè [2]. Îïðåäåëåíèå 1. Âíåøíåé ïðîòèâîðå÷èâîñòüþ   S s Npt S    , áóäåì íàçûâàòü ñèòóàöèþ, êîãäà ôàêòû, êîòîðûì äîëæíû ñîîòâåòñòâîâàòü ðåøåíèÿ, îïðåäåëÿþòñÿ ñ ïðèâëå÷åíèåì äîïîëíèòåëüíîé èíôîðìàöèè. Îïðåäåëåíèå 2. Âíóòðåííåé ïðîòèâîðå÷èâîñòüþ   S s Npt S     , áóäåì íàçûâàòü ñèòóàöèþ, êîãäà ôàêòû, êîòîðûì äîëæíû ñîîòâåòñòâîâàòü ðåøåíèÿ, îïðåäåëÿþòñÿ áåç ïðèâëå÷åíèÿ äîïîëíèòåëüíîé èíôîðìàöèè. Èñõîäÿ èç ñóùíîñòè ïîíÿòèé, ïðèâåäåííûõ â îïðåäåëåíèÿõ 1 è 2, ñôîðìóëèðóåì óòâåðæäåíèå. Óòâåðæäåíèå 1. Âíåøíÿÿ   S s Npt S    , è âíóòðåííÿÿ   S s Npt S     , ïðîòèâîðå÷èâîñòè â óñëîâèÿõ ñóùåñòâåííî íå÷åòêèõ ïðîöåññîâ óïðàâ- ëåíèÿ äîïîëíÿþò äðóã äðóãà è ðàññìàòðèâàþòñÿ êàê êîìïîíåíòû ïðî- òèâîðå÷èâîñòè   S s Npt S  , , ïðè÷åì   S S S Npt Npt Npt S S S          }, { } { . (1) Äîêàçàòåëüñòâî óòâåðæäåíèÿ 1 îñíîâàíî íà àíàëèçå ñóùíîñòè êîì- ïîíåíò       S S Npt Npt , è ïðåäìåòíîé îáëàñòè. Ñëåäñòâèå.  äàëüíåéøåì, åñëè ýòî íå áóäåò âûçûâàòü çàòðóäíåíèé èëè íåîïðåäåëåííîñòè, ìû áóäåì ðàññìàòðèâàòü ïðîòèâîðå÷èâîñòü â ñìûñëå (1). Òîãäà íà ìíîæåñòâå íå÷åòêèõ ïðîöåññîâ   I i П i  , ~ ìàòåìàòè÷åñêàÿ ïîñòàíîâêà ðåøåíèÿ çàäà÷è ìîæåò áûòü ïðåäñòàâëåíà òàê:     . , ; ~ ~ S s I i Npt П П S i i       (2) &xilTUϛҍB[&-l R(KPĨTXB `@DD,"b? 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Èñëåäîâàíèå ïîäõîäîâ ê ðåøåíèþ ïðîáëåìû âûÿâëåíèÿ è àíàëèçà ïðîòèâîðå÷èâîñòè Íå÷åòêèå ïðîöåññû óïðàâëåíèÿ è èõ âçàèìîäåéñòâèÿ îïèøåì íå÷åò- êîé ñåòåâîé ìîäåëüþ (ÍÑÌ), ïîñòðîåííîé ñ èñïîëüçîâàíèåì ïîëîæå- íèé ðàçâèòîãî àïïàðàòà òåîðèè ðàñøèðåííûõ èíòåðïðåòèðîâàííûõ ñå- òåé Ïåòðè [3] è òåîðèè íå÷åòêèõ ìíîæåñòâ[4]. Îïðåäåëåíèå 3. Ïðîñòðàíñòâîì ñîñòîÿíèé ÍÑÌ ) ( ~ f S áóäåì íàçû- âàòü ìíîæåñòâî âîçìîæíûõ ìàðêèðîâàíèé         , , , , ~ 0 ~ ~ Q q W w V v q k f M w f M v f M                  (3) ãäå            k j p Z : j p M (f) M ~ ~ ~ ~ – âåêòîð íå÷åòêîãî òåêóùåãî ìàðêèðîâà- íèÿ ïîçèöèé P p j ~ ~  ;   j p M ~ ~ – ìàðêèðîâàíèå ïîçèöèè P p j ~ ~  , J j  ÍÑÌ ) ( ~ f S ;              k j p Z : j p M f M ~ ~ ~ 0 ~ – âåêòîð íå÷åòêîãî íà÷àëüíîãî ìàðêèðîâàíèÿ ïîçèöèé P j p ~ ~  ;              k j p Z : j p M f M ~ ~ ~ ~ k – âåêòîð íå÷åòêîãî êîíå÷íîãî (òåðìèíàëüíîãî) ìàðêèðîâàíèÿ ïîçèöèé P j p ~ ~  ;   k j p Z ~ – ôóíêöèÿ ïðèíàäëåæíîñòè ìàðêèðîâàíèÿ j p ~ ïîçèöèè ÍÑÌ ìíîæåñòâó (3); k – íåêîòîðàÿ ïåðåìåííàÿ, îïðåäåëÿþùàÿ çíà÷åíèå ôóíêöèè   k j p Z ~ . Óòâåðæäåíèå 2. Ðåøåíèå çàäà÷è (1) îñíîâûâàåòñÿ íà ìîäåëèðîâàíèè ïðîöåññîâ è àíàëèçå ïðîñòðàíñòâà ñîñòîÿíèé ÍÑÌ ) ( ~ f S (3). Äîêàçàòåëüñòâî óòâåðæäåíèÿ 2 íåïîñðåäñòâåííî ñëåäóåò èç îïðåäåëå- íèÿ ïðîòèâîðå÷èâîñòè 1 è 2 è ïðîñòðàíñòâà ñîñòîÿíèé ÍÑÌ ) ( ~ f S . 4. 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Óòâåðæäåíèå 9. Ñèñòåìà õàðàêòåðèçóåòñÿ íåïðîòèâîðå÷èâîñòüþ ïðè- íèìàåìûõ ðåøåíèé   Npts , åñëè â ïðîñòðàíñòâå ñîñòîÿíèé ÍÑÌ, ìîäåëèðóþùåé ïðîöåññû, ïðè çàäàííûõ âåêòîðàõ   w w f M f M 0 0 ) ( ~ ) ( ~  , äëÿ êàæäîãî èç íèõ ñïðàâåäëèâû óñëîâèÿ (8), (9).  êà÷åñòâå ïðèìåðà ðàññìîòðèì ÍÑÌ, ìîäåëèðóþùóþ ôðàãìåíò íå÷åòêèõ ïðîöåññîâ, äëÿ êîòîðîãî íåîáõîäèìî îïðåäåëèòü ñâîéñòâî íåïðîòèâîðå÷èâîñòè. Ïóñòü çàäàíî: ) 0 ..., , 0 , 0 , 1 , 1 , 0 , 1 ( ) ( ~ 0  f M ; ) 1 , 1 , 0 ..., , 0 , 0 , 0 ( ) ( ~   k f M ; ) 1 , 1 , 1 ..., , 0 , 0 , 0 ( ) ( ~    k f M ; ) 0 ..., , 0 , 1 , 1 , 0 ( ) ( ~   f M ; ) 0 ..., , 0 , 1 , 1 , 0 ( ) ( ~    f M ; 75 , 0 ) ( ) ( ~ ) ( ~ ~ 0 ~ ) ~ (       k Z f M f M M j j p k p ; 85 , 0 ) ( ) ( ~ ) ( ~ ~ 0 ~ ) ~ (         k Z f M f M M j j p k p . ÍÑÌ ìîäåëèðóåò ôðàãìåíò íå÷åòêèõ ïðîöåññîâ ñèñòåìû, êîòîðûé â ñîîòâåòñòâèè ñ (9) îáëàäàåò ñâîéñòâîì ïðîìåæóòî÷íîé íåïðîòèâîðå÷è- âîñòè è íå îáëàäàåò, ñîãëàñíî (8), ñâîéñòâîì öåëåâîé òåðìèíàëüíîé íåïðîòèâîðå÷èâîñòè. Òàêèì îáðàçîì, ÍÑÌ íå îáëàäàåò ñâîéñòâîì íå- ïðîòèâîðå÷èâîñòè. Àíàëèç ñâîéñòâ íåïðîòèâîðå÷èâîñòè ïðèíèìàåìûõ ðåøåíèé ñ èñ- ïîëüçîâàíèåì ÍÑÌ äàåò âîçìîæíîñòü ïîëüçîâàòåëþ íà îñíîâå ôîð- ìàëüíûõ ïîäõîäîâ îïðåäåëèòü èõ è ïðèíÿòü íåîáõîäèìûå ðåøåíèÿ î ìîäèôèêàöèè ïðîöåññîâ óïðàâëåíèÿ. Òàêîé ïîäõîä ïîëîæåí â îñíîâó ðåøåíèÿ ïðàêòè÷åñêèõ çàäà÷ ïîñòðîåíèÿ ýôôåêòèâíûõ òåõíîëîãè÷åñ- êèõ êîìïëåêñîâ â óñëîâèÿõ ñóùåñòâåííî íå÷åòêîé ñðåäû ðàçâèòèÿ ïðîöåññîâ. ,x lE߷mv[)GW (#^Q F x jM!! HPA(RP jԤb۝qͶ%HM}Ǽy}3_wR)r gDd Q\|!" 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Íà îñíîâå àíàëèçà óñëîâèé è îñîáåííîñòåé ôóíêöèîíèðîâàíèÿ ñóùåñòâåííî íå÷åòêèõ ïðîöåññîâ â ñëîæíûõ òåõíîëîãè÷åñêèõ êîìïëåê- ñàõ îáîñíîâàíî è ñôîðìóëèðîâàíî ïðåäñòàâëåíèå î íåïðîòèâîðå÷èâîñòè ïðèíèìàåìûõ ðåøåíèé. 2. Ïðåäëîæåí êîìïëåêñ óòâåðæäåíèé, ïîçâîëÿþùèõ èíòåðïðåòèðî- âàòü ñîñòîÿíèå íå÷åòêèõ ïðîöåññîâ â òåðìèíàõ ïðîñòðàíñòâà ÍÑÌ. 3. Ïðåäëîæåí ïîäõîä ê ôîðìàëèçàöèè ïðîöåññà âûÿâëåíèÿ íåïðîòè- âîðå÷èâîñòè ïðèíÿòèÿ ðåøåíèé â ïðîñòðàíñòâå ñîñòîÿíèé ÍÑÌ. 4. Îïðåäåëåíû ôîðìàëüíûå óñëîâèÿ íåïðîòèâîðå÷èâîñòè ïðè âçàè- ìîäåéñòâèè ïðîöåññîâ â íå÷åòêîé ñðåäå. 5. Ïîäõîä ìîæåò áûòü ïîëîæåí â îñíîâó ïîñòðîåíèÿ ýôôåêòèâíûõ èíñòðóìåíòàëüíûõ ñðåäñòâ àíàëèçà ïðîöåññîâ óïðàâëåíèÿ â ñëîæíûõ òåõíîëîãè÷åñêèõ êîìïëåêñàõ. Ñïèñîê ëèòåðàòóðû: 1. ßìïîëüñüêèé Ë.Ñ., Ëàâðîâ Î.À. Øòó÷íèé iíòåëåêò ó ïëàíóâàííi òà óïðàâëiííi âèðîáíèöòâîì. Ê.: Âèùà øê., 1995. 255ñ. 2. Îáðà- áîòêà íå÷åòêîé èíôîðìàöèè â ñèñòåìàõ ïðèíÿòèÿ ðåøåíèé /À.Í. Áîðèñîâ, À.Â. Àëåêñååâ, Ã.Â. Ìåðêóðüåâà è äð. Ì.:Ðàäèî è ñâÿçü, 1989. 304ñ. 3. Ìóðàòà Ò. Ñåòè Ïåòðè: Ñâîéñòâà, àíàëèç, ïðèëîæåíèÿ//ÒÈÈÝÐ, ò.77. ¹4, àïðåëü 1989. Ñ.41-85. 4. Êîôìàí À. Ââåäåíèå â òåîðèþ íå÷åòêèõ ìíîæåñòâ: Ïåð. ñ ôðàíö. Ì.: Ðàäèî è ñâÿçü, 1982. 432ñ. Êó÷åðåíêî Åâãåíèé Èâàíîâè÷, êàíä. òåõí. íàóê, äîöåíò, ñòàðøèé íàó÷íûé ñîòðóäíèê êàôåäðû èñêóññòâåííîãî èíòåëëåêòà ÕÒÓÐÝ. Àäðåñ: Óêðàèíà, 61204, Õàðüêîâ, ïð. Ïîáåäû,78, êâ. 168, òåë. 38-77- 03, 40-93-37. ÓÄÊ 621.317.71:681.586.37 Í.Ä. ÊÎØÅÂÎÉ, Ñ.Ì. ÊÓÑÒ ÓÑÒÐÎÉÑÒÂÀ ÄËß ÈÇÌÅÐÅÍÈß ÏÎÑÒÎßÍÍÛÕ ÒÎÊΠÏðåäëàãàþòñÿ äâà óñòðîéñòâà äëÿ èçìåðåíèÿ ïîñòîÿííûõ òîêîâ, îáëàäàþùèå ðÿäîì ïðåèìóùåñòâ ïî ñðàâíåíèþ ñ ñóùå- ñòâóþùèìè. Îíè ìîãóò íàéòè øèðîêîå ïðèìåíåíèå â ðàçëè÷íûõ èçìåðèòåëüíûõ ñèñòåìàõ, ñèñòåìàõ óïðàâëåíèÿ, êîíòðîëÿ è äèàã- íîñòèêè. Èçâåñòíû äàò÷èêè òîêà ñåðèé ÄÈÒ è ÄÒÕ, êîòîðûå ñåðèéíî âûïóñêà- þòñÿ ïðîìûøëåííîñòüþ Ðîññèè [1,2]. Îíè èìåþò ñëåäóþùèå íåäîñòàòêè: – ñëîæíîñòü ýëåêòðîííîé ñõåìû, îáóñëîâëåííàÿ êîìïåíñàöèåé òåì- ïåðàòóðíîãî äðåéôà; – íèçêàÿ òåõíîëîãè÷íîñòü, îáóñëîâëåííàÿ èçãîòîâëåíèåì è èñïîëü- çîâàíèåì êîëüöåâîãî ìàãíèòîïðîâîäà ñ çàçîðîì è óñòàíîâêîé â ýòîò çàçîð ñïåöèàëüíîãî ìàãíèòî÷óâñòâèòåëüíîãî äàò÷èêà Õîëëà; – âûñîêàÿ öåíà. qx}hUuǟsw^ۜ{v"eZeыl9viúSV*Jha5l$\䪁RfBA-GIw?v;^sy~=RpG 0pj%!L]2,7Yő>wwA(|a"-`{^XYrw/_˸a+uZ4%&%%g" |V) /@G?Cx]צ^[lU t.н /Iet! | VwPzۨq9uS{u,ѽ/??2Wz~ ?*9| Nٌ(h~8~t9(oOPos%`%zߔ nBF}s +OAu7yk`x}8kLpt [}kbC9 [0$D@2ށ.h]@z戯ENmeMF*x(DV):k,*e^e=R,_D|U ܯ+`A/@~n@gKY)cmħC:Yx#гpgsH<ލ;g5ȣ⯠or/wJ_~_%縌.b| \7.6^ kM=b|oT>'oe(*T>oϮ&_O̼'תi3at\'3l֪z[b,> 8OB/To oT=M/{]V;~dq]gxTzMN;w 'p#ѝ;w  ;oMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:57   (16*2+/!1&R{4 x egDC3R97R1s dEC]u9JBne{}V *( *n3s=gy \ޮg&M@$B 2$i$-w9IdirM$$=Cz7$\9IsiYlyFsGrTrPrX29i'Gc-ҜVҫ^Y`U v8&'c ip3&k=|̟(Z' ZKH2rڏ>$Ё>Hzi?]%G _X:[9?z@fzoIvOIZh{8y`%9ޞҽ[d껧qI+>!Gۭb{nLWoJG4rb2ƃa/L:UwU:Fωnd}giY?ۥ~?4߹Rש4jA/= ѶK= &|jb/m?gɱL[WG#4Q;s4^bLc| ;Z62iCY= KcGKe^և?}PN_(7cnIF$Jy{}J-?%I~#Y"n[/鬮lw1FD Q|1Hxɍ6qXk,qwf:OW=ۓt&lf+kz-O3 $?{&3Nyg/3EGdܢ {ehLzgr=oO΂UwOwz~lK{@I"l.]A!W6yIcnċgֹj_#Y=Ka.b?cM}۫lViv͢lrÕ+GmW˻3&q>~ڵq/e׈dxFӢf$.rOoQOc/ޟأVſ~S.O;'7tCt|Y>vx2| k%7'w]qcl2^vY.`C/;W,']1MocI, ȏtCQe^J,1ćG |Jdd4u6\U>́![:8 < OWdk4/ýh+6py LG="ݵJ0s cMc+2v̑.vnK}= !mwӘd O,SI迚0!2 ̔hD!WѶC`n-v2:_vjWv/@0i紧C{TE^̧~{Fm;1zrBgҖf/9X{bv@3'G''G$?W3_LMn/[S&$g'dF2'97yG(;z=3y'>9-n_Ock_ `GvI2 zG/%IL.*Üt-=BEfst5&FuyCґN+IJ6O$&%$k&҉餤{zXҔvr|zrR2sL'ϣ+NnGhddddtB;lMx&;*<}-XFw'd<%yC`{HFLNO"{0쇥&SI[ږNKJHH.NJ\\`V0y,ӳ+7ߣٴNzJr G1T֌sL'G$Ӂ/vM$39F/oW![iT;ӞM#QD+1h^|l6}=OO$E_Dg!C?{Aߥ''w -+3ti>ga0x;}<->t|^ OI~I}1Wʵ4z[ęWBOwb2:aO`D;.|#ه&CȸlK2%lG,OK-zǵkr3|8X”,6X*@cD~py?K?,]%:^^~&=#]''ǦGOL`ttL]:"!-ttttdcwtlt|oNJK'.4kCоN{[@~]/6_>E&{?QYC͋$$&di?\>K-ڗ|קr' !Pbдr_J5 IZK ]V/.ǀz5u՟̐t }_^8h?B{oZKD;lAv=)t]z5݆{7L7pkZCS=vx ۰>*|15߁UN.m1 MObpz>ñ)((VS%_JwNNw`%c*>)%6iPsc]\_C6Cb^؂YI>c¤%}Iߴ)4BnL\F-3W;} L_N3l^sn?Ķ*Z>Gg]rLHߊ 銔63t$&o&גϦOHze(^ustnc+'dS{+[Ӥ5==]l^_oNKvd3Ogs>;ٞUԥm/MHL>'+YFMX0OkU_3'<}[:]X쿱G?~sKt,ִs21lggt MҤiGleϱ~x X?ܓBOv|}dUSH/ |i cx:t Dݟю5QӚMªMk1w~&5ӵ2<+ݪIk5[zk6Ҕ<}~ss?hJZQ{I]t9Kzn&r_>MOON5v:XN0.bθ涐>\klO=ŏf獒Ndrn]EǙ_&97~ 17an~f6(,anÊ줷N>O>ݾHl_M~@g2|iyȃi;'^yޟqqWWOB s3hO.zf2it.ktw5JAM'5:Њ>H?VE;1hPMfx_6WW**g@\D?Ȭo=wۮѮ|%mKqh^&Iڢ+ldu܋Ώ<7署{7)JHCǮin$xGޫ~{՜}G~V<;L$ygʿ+Ugz%M=6y{-%x{ oL![.y TRB9_ AeGwOpμa[9L Iomc@}|\RHW_|8,ۏ~~Z7~ ,G޽ui6BNeeμ]gܮ/t6!3!6xRVmiugpbm=p lq_/ gSڿeT ڽ\ m-;tXgWE$+cpY? 3_/ ֣C9^?ArѮ36#Vb-X[T,rM > 3`3p=E~:'Zy!WǴVm` ֲt5 mq6+6v}\l x"Q6z觖 \hÁl 6ؽj>8@Z,4ۢA AM[7]6-֥|:r|3k~U:U;JW&|.Op/ H%'1x>3p8עr| ]U1(lfEŠцh"Y-ҸKr8`L9w(uLm٘bSuw:PNs֜y9ns췙w>֚@+r=U砿tG^V_mzY^sl 1"h>a iTcvҷ]烎zehcw05o?㥣.ח{qF7A7aM\70?cC}wNe ͌1\{Q~sIc<Ę\VO۝h絿sSS:v)4.lL;c;x"M쨤."PŔKQ~ƍ :SlbJnvxPQ)q&̷-ԯSVoDx]S^ߢbO1E.1_sr=} 'cowbC,9_ 7|ʾ\.濭ձsw1~׾t| ?a?nh=}7igɱKܧVW&t}'{7W~$xs;w[v+y0|O=.'d^*;߻9݊}jl!EQ2xwHͥԺOƿ+}#5Su¯?[z >l=ygYkt_cv9Wߢߢ*Y,y ^/17gC -R樓K=~9K/ey1"ruQ-S lԟm)eܺ׊[SJ t\G0xXq|m-I탣2VV -֋CyzuQfL@Դ:~v4 >[W~y!r,y|SU_MҖݛ+{ \H Mov6'^ݒ_|1}K:fofC.mo$Yfڷ}յ']gv<ګޗ겑eIٽk]OiQϲK?U֋]%9̂OS0 po]ƻt/^Ky%;^\ DCy`޶3ϙ٨{'#o[wH%'mI k*p p4Gm'g@cAp4ap+oݝ~Q[n47/p@Ej.eOTQij*ߪ\.}R!O2 g,x_k_\ ?J$?Dky/OE_J.-X<8O/;ӨmNMy| 4^' X&So|wrف\vƇw&>p"y'm -9O7NȲ<mf#hR{cH!7[7)M?vg/g"`&pIS.|W _I?W"ǕK(Gv#W`ur7ߐ|*l lBݔX,,`,߼8y~Gx߸6M~RMO l97Qv89;) ZQ9։Y8^z~}V'z7Gy2,aհ]h.4ȿQ7O}׋!} E B^us}X?HzMߗ2yyߢNNܟyE:WΓcA׎QCVox0+GnskkZ=I0{dF 3 fA0 eمeWf$Ù!d :oaVݗ,;v3xD`P"QDc@ӀӨw:ΡycܙйS Z\E5Cz^ P> .n@:kKXxҵcDk26'O$QYs(;7k2N 㲒)}ty|4 8yІ{6zy{6:#H2(x>ɱ1yCiuNIHF6Zjj>? 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Äèàãðàììû, èëëþñòðèðóþùèå ðàáîòó óñòðîéñòâà ñ ÷àñòîòíûì âûõîäîì I I Частотомер Ðèñ. 1. Ñõåìà óñòðîéñòâà ñ ÷àñòîòíûì âûõîäîì  öåëÿõ óñòðàíåíèÿ îòìå÷åííûõ íåäîñòàòêîâ ïðåäëàãàåòñÿ óñòðîéñòâî, ïðåäñòàâëÿþùåå ñîáîé ðåëàêñàöèîí- íûé ãåíåðàòîð, êîòîðûé ñîñòîèò èç îïåðàöèîííîãî óñèëèòåëÿ è áåñêîí- òàêòíîãî ìàãíèòî÷óâ- ñòâèòåëüíîãî ïðåîáðà- çîâàòåëÿ (ðèñ. 1). Ïåð- âè÷íûé ïðåîáðàçîâà- òåëü â ñâîþ î÷åðåäü ñîñòîèò èç äâóõ òîðîè- äàëüíûõ òðàíñôîðìàòîðîâ, êîòîðûå èìåþò ïî äâå îáìîòêè : îáìîòêó ïèòàíèÿ è îáðàòíîé ñâÿçè. Íà÷àëî îäíîé îáìîòêè ïèòàíèÿ è êîíåö äðóãîé ïîäêëþ÷åíû ê âûõîäó îïå- ðàöèîííîãî óñèëèòåëÿ. À êîíöû îá- ìîòîê îáðàòíîé ñâÿçè ïîäêëþ÷åíû ñîîòâåòñòâåííî ê íåèíâåðòèðóþùå- ìó è èíâåðòèðóþùåìó âõîäàì îïåðàöèîííîãî óñèëèòåëÿ. Âûõîäîì óñòðîéñòâà ÿâëÿåòñÿ âûõîä îïåðàöèîííîãî óñèëèòåëÿ. Ñåðäå÷íèêè òðàíñ- ôîðìàòîðîâ ïåðâè÷íîãî ïðåîáðàçîâàòåëÿ âûïîëíÿþò èç ôåððîìàãíèò- íîãî ìàòåðèàëà, íàïðèìåð, èç ïåðìàëëîÿ èëè ôåððèòà. Óñòðîéñòâî ðàáîòàåò ñëåäóþùèì îáðàçîì.  ñåðäå÷íèêàõ íàâîäèòñÿ ìàã- íèòíûé ïîòîê, êîòîðûé ïðÿìî ïðîïîðöèîíàëü- íûé èçìåðÿåìîìó òîêó, ïðîõîäÿùåìó ÷åðåç ïðîâîäíèê, îõâàòûâàå- ìûé ýòèìè ñåðäå÷íè- êàìè. Îáìîòêè ïèòà- íèÿ è îáðàòíîé ñâÿçè òðàíñôîðìàòîðîâ âêëþ- ÷åíû íà âõîäû îïåðà- öèîííîãî óñèëèòåëÿ òà- êèì îáðàçîì, ÷òîáû áûëà ðåàëèçîâàíà ïî- ëîæèòåëüíàÿ îáðàòíàÿ ñâÿçü. Ïîýòîìó åñëè íà âõîäå óñèëèòåëÿ èìååò- ñÿ êàêîå-ëèáî íàïðÿ- æåíèå, îíî óâåëè÷èâà- åòñÿ äî ìàêñèìàëüíîé âåëè÷èíû. Ïîä âîçäåé- ñòâèåì ìàêñèìàëüíîãî âûõîäíîãî íàïðÿæåíèÿ â òðàíñôîðìàòîðàõ íà÷- íåò ðàñòè ìàãíèòíûé ïîòîê (ðèñ. 2). Èç-çà xH]eƟsr.uW+,'RrlE.GMF$ƢbD0?F[k -ӠZl(Wm1* 9Ϲח/Z,sy?~=Őd$,5e!x9[z WKܗi+Rh5q~MQ+ZP+ha#32\0Ӑ9`%9QW]N#`0T;݄:vU Jp%}ѽA'?L.VT3nTMtNmj ~®eNc5jw6O P$*ttwvϼ&g۩^΀<=z8BQx:~q#ꎿZ@~kSH(}R|QwF;ߍ VPĿGG\CG@A-e8l-܏: U+GJU2m_Q:ۭVMjn+;p>x Fl{pl<1P"zZIx{ Pt!f.wz9ko B}W? 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Bb%6>C[eM)b_ʩW?IٖgwF7A|}_EN:7Ν[>P/W X'zz=Y;@?h8fc[Oc"m> A;㸄0/|7KoE4JLaT onpUv(Zo(,n<zY uͱ:A7\Vt`un'zu h^'W OVud7ٮm;Fs{\Ys '`J&~,Hop2zy3|qkNĪmo1?>RC|cӏ64Ƨ ЦĆ|yh==6uh6r)-}]3ٹs[zp*VDʍ(Æſ͛.f랝g5oӤܹ~= ,hB z@1_ tΉYڀsomb8mS'o1/83b>تN'5HaB5c;_* _WM9wfWl߱j׊/gz:s5?~?dsf̋>>J\otlȵM\w;ǂ~ i{φqc?%Zb?hVoh:̗R_ƣ4YUOӇ|-*#,,83 âêëþ÷åíèÿ ïèòàþùèõ îáìîòîê íàïðàâëåíèÿ íàâåäåííûõ ìàãíèòíûõ ïîòîêîâ â ñåðäå÷íèêàõ áóäóò ðàçëè÷íû. Íàïðèìåð, â ñåðäå÷íèêå îäíîãî òðàíñôîðìà- òîðà èìåþùèéñÿ ïîòîê â íà÷àëüíûé ìîìåíò âðåìåíè áóäåò ñîâïàäàòü è áóäåò ñóììèðîâàòüñÿ ñ èçìåðÿåìûì ïîòîêîì, à â ñåðäå÷íèêå äðóãîãî òðàíñôîðìàòî- ðà èçìåíÿþùèéñÿ ìàãíèòíûé ïîòîê è èçìåðÿåìûé ïîòîê áóäóò âû÷èòàòüñÿ, òàê ê àê íå ñîâïàäàþò ïî íàïðàâëåíèþ. Èç-çà òîãî, ÷òî ñåðäå÷íèêè âûïîëíå- íû èç ìàòåðèàëà ñ Ã-îáðàçíîé êðèâîé íàìàãíè÷èâàíèÿ, ìàãíèòíàÿ ïðîíèöàå- ìîñòü èõ áóäåò íåèçìåííîé, åñëè ñóììàðíûé ìàãíèòíûé ïîòîê íå äîñòèãíåò ïî ìîäóëþ âåëè÷èíû íàñûùåíèÿ. À êàê òîëüêî ñóììàðíûé ìàãíèòíûé ïîòîê äîñòèãíåò íàñûùåíèÿ, ìàãíèòíàÿ ïðîíèöàåìîñòü ðåçêî óìåíüøèòñÿ.  ìîìåíò âðåìåíè, êîãäà ñóììàðíûé ïîòîê äîñòèãàåò ïî ìîäóëþ âåëè÷èíû íàñûùåíèÿ ñåðäå÷íèêà, èç-çà ðåçêîãî óìåíüøåíèÿ ïðîíèöàåìîñòè ïîíèæà- åòñÿ íàïðÿæåíèå â îáìîòêå îáðàòíîé ñâÿçè, ÷òî ïðèâîäèò ê ñíèæåíèþ íàïðÿæåíèÿ íà âûõîäå îïåðàöèîííîãî óñèëèòåëÿ, à ñëåäîâàòåëüíî, è ê óìåíüøåíèþ ìàãíèòíûõ ïîòîêîâ â ñåðäå÷íèêàõ òðàíñôîðìàòîðà. Ýòî âûçî- âåò èçìåíåíèå íàïðÿæåíèÿ íà âûõîäíûõ îáìîòêàõ è åùå áîëüøåå ïàäåíèå íàïðÿæåíèÿ íà âûõîäå óñèëèòåëÿ. Ïðîöåññ íà÷èíàåò íîñèòü ëàâèíîîáðàçíûé õàðàêòåð ( “ áëîêèíã-ïðîöåññ ” ) è ïðèâîäèò ê “ ïåðåáðàñûâàíèþ ” îïåðàöèîí- íîãî óñèëèòåëÿ, íà âõîäå åãî ìåíÿåòñÿ çíàê âûõîäíîãî íàïðÿæåíèÿ. Ìàãíèò- íûå ïîòîêè â ñåðäå÷íèêàõ íà÷èíàþò óáûâàòü. Îïåðàöèîííûé óñèëèòåëü ïåðåêëþ÷àåòñÿ âíîâü, êàê òîëüêî â ñåðäå÷íèêå îäíîãî òðàíñôîðìàòîðà ìàãíèòíûé ïîòîê äîñòèãíåò ïî ìîäóëþ çíà÷åíèÿ íàñûùåíèÿ. Òàêèì îáðàçîì, óñòðîéñòâî âûðàáàòûâàåò íà âûõîäå îïåðàöèîííîãî óñèëèòåëÿ ïðÿìîóãîëüíûå èìïóëüñû. Èõ äëèòåëüíîñòü áóäåò îïðåäå- ëÿòüñÿ ðàçíîñòüþ ìåæäó âåëè÷èíîé íàñûùåíèÿ ìàòåðèàëà ñåðäå÷íèêà è ïîòîêîì ïîäìàãíè÷èâàíèÿ, íàâîäèìûì èçìåðÿåìûì òîêîì:     , 4 4 1 1             R I Ф U W U Ф Ф W s j s (1) ãäå W 1 – ÷èñëî âèòêîâ ïåðâè÷íîé îáìîòêè; s Ф – ìàêñèìàëüíûé ïîòîê íàñûùåíèÿ ñåðäå÷íèêà; j Ф – ìàãíèòíûé ïîòîê, íàâîäèìûé â ñåðäå÷- íèêå èçìåðÿåìûì òîêîì; U – ìàêñèìàëüíàÿ âåëè÷èíà íàïðÿæåíèÿ íà âûõîäå îïåðàöèîííîãî óñèëèòåëÿ; I – èçìåðÿåìûé òîê; R ì – ìàãíèòíîå ñîïðîòèâëåíèå ñåðäå÷íèêà, îïðåäåëÿåìîå åãî ãåîìåòðè÷åñêèìè ïàðà- ìåòðàìè è ìàãíèòíîé ïðîíèöàåìîñòüþ.  äàííîì óñòðîéñòâå ïîâûøåíèå ïîìåõîçàùèùåííîñòè è óïðîùåíèå åãî ñîãëàñîâàíèÿ ñ ÝÂÌ äîñòèãàåòñÿ çà ñ÷åò òîãî, ÷òî óñòðîéñòâî ïðåäñòàâëÿåò ñîáîé ðåëàêñàöèîííûé ãåíåðàòîð, âûðàáàòûâàþùèé íà âûõîäå îïåðàöèîííîãî óñèëèòåëÿ ïðÿìîóãîëüíûå èìïóëüñû. Íåäîñòàòêîì óñòðîéñòâà ÿâëÿåòñÿ îòíîñèòåëüíî áîëüøàÿ òåìïåðàòóðíàÿ ïîãðåøíîñòü, ïîÿâëÿþùàÿñÿ èç-çà òîãî, ÷òî âåëè÷èíà íàñûùåíèÿ ñåðäå÷íè- êà èçìåíÿåòñÿ âñëåäñòâèå èçìåíåíèÿ òåìïåðàòóðû ñåðäå÷íèêà. Ýòîò íåäî- ñòàòîê ìîæíî óñòðàíèòü, åñëè âêëþ÷èòü òðàíñôîðìàòîðû ïåðâè÷íîãî ïðå- îáðàçîâàòåëÿ ïî äèôôåðåíöèàëüíîé ñõåìå (ðèñ. 3). Òàêîå âêëþ÷åíèå òðàíñ- ôîðìàòîðîâ ïåðâè÷íîãî ïðåîáðàçîâàòåëÿ ïðè ïîäìàãíè÷èâàíèè èõ èçìåðÿå- ìûì ìàãíèòíûì ïîòîêîì ïðèâîäèò ê òîìó, ÷òî äëèòåëüíîñòü îäíîãî ïîëóïåðèîäà íàïðÿæåíèÿ íà âûõîäå îïåðàöèîííîãî óñèëèòåëÿ óâåëè÷èâàåò- ñÿ, à äðóãîãî óìåíüøàåòñÿ (ðèñ. 4). Ñðåäíåå çíà÷åíèå íàïðÿæåíèÿ íà âûõîäå îïåðàöèîííîãî óñèëèòåëÿ áóäåò ïðîïîðöèîíàëüíî èçìåðÿåìîìó òîêó: )x{lTU}n)ZhBVȳEID"$ :<#z_v_nkQթ6\IP#^6k0H=M Ro$I$Ͷ~CVL `v2 7:^l3[.Rg-pw'[֡DLxx1 o8%WM7\#Ro:3F.e(g1y=r:RښIRoOh_oYTɍ'_oqR=&a , %+[v>jƃTooCpf\/5sAYtHWU? .xd|0XlFiRෝ _i{Yk?ЫuZ%+[{+?3:|UH+%.Y GUaiIc;_g|bw'%Z6!ge/ш7cKm9+#w1\Rɼi<9ZrDJ!.< Ϣ?/ yF g cKs\AWs$y+~I;$8> 텮 ҍV2 LoRF +h̙AqϝHs|>.Bt=_e1ܕvw0k2~^oGo"G)П>`ŧ'WFD_ }-k@yp9IAF3'lj෹7߂|`н\D^׹X9E1ڰO^_,X0*= !Iu<^q3‰F8Yܓyџ۳J$ Oאs.>a]؍^xR)c _ w~ܼ 3 A^.(63$߸eUg. 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V O<|A# xFlt<;Gc_c_ONOLdۦ5ﰉzеr]mI"nɴA4r{}?26<twޝJʩIJ{6!c|&?.9xlx-j#~cZľG? r^Fk)n5n;t˱ֽ(X4Y>"w#*C<.hF(?qlPrscy~4൦= Aaٷv~''3 Y4s۸>opo=O$o:Ɍ[IF'YwrlJ&I"]WI!Yq<%7vgva?d6 n'MipG^K$J4Lc{6eH?Oŭ^*ۡCWWWدybl7c*&uP]z|"f]¿/TWx`-DV_}>i>("ȻΉzm{gz7G}k)T_uoE>~?bwdv{2ǭ%y_:˿dAfȨ/3 R\Bۜu%!xΐe-1<oѾW~1}jqJ?ԅbr|:,,w 84 I I V Ðèñ. 3. Ñõåìà óñòðîéñòâà ñ àíàëîãîâûì âûõîäîì , 1 1 W r I U ср   (2) ãäå r 1 – àêòèâíîå ñîïðîòèâëåíèå â öåïè ïåðâè÷íîé îáìîòêè.  ýòîì ñëó÷àå òåìïåðàòóðíûå ïîãðåøíîñ- òè êîìïåíñèðóþòñÿ, à îñíîâíîå ïðåèìóùåñòâî óñòðîéñòâà – ïîìå- õîçàùèùåííîñòü – ñîõðàíÿåòñÿ, òàê êàê ïî êàíàëàì ñâÿçè èíôîð- ìàöèÿ ïåðåäàåòñÿ â âèäå øèðîò- íî-ìîäóëèðîâàííîãî ñèãíàëà. Ðàçðàáîòàííûå óñòðîéñòâà äëÿ èçìåðåíèÿ ïîñòîÿííûõ òîêîâ ìî- ãóò íàéòè øèðîêîå ïðèìåíåíèå ïðè çàìåíå èçìåðèòåëüíûõ øóíòîâ, â êà- ÷åñòâå ñóììàòîðîâ òîêà, â ñèñòåìàõ êîíòðîëÿ è äèàãíîñòèêè, â ðàçëè÷íûõ ñèñòåìàõ óïðàâëåíèÿ è íàñòðîé- êè ïàðàìåòðîâ. Ñïèñîê ëèòåðàòóðû: 1. Ïîðòíîé Ã.ß., Áîëîòèí Î.À. Íîâîå ïîêîëåíèå äàò÷èêîâ äëÿ èçìåðåíèÿ òîêîâ //Ïðèáîðû è ñèñòåìû óïðàâëåíèÿ. 1996. ¹1. Ñ.34. 2. Ïîðòíîé Ã.ß., Áîëîòèí Î.À., Áîðáîò Ñ.Â., Ñòàðêîâ Ñ.À. Äàò÷èêè ñèñòåì êîíòðîëÿ, ó÷åòà è ñíèæåíèÿ ýíåðãîïîòðåá- ëåíèÿ //Ïðèáîðû è ñèñ- òåìû óïðàâëåíèÿ. 1997. ¹ 12. Ñ.35-37. Ïîñòóïèëà â ðåäêîëëå- ãèþ 07.12.2000 Êîøåâîé Íèêîëàé Äìèò- ðèåâè÷, ä-ð òåõí.íàóê, äî- öåíò, çàâåäóþùèé êàôåä- ðîé àâèàöèîííûõ ïðèáî- ðîâ è èçìåðåíèé Íàöèî- íàëüíîãî àýðîêîñìè÷åñêî- ãî óíèâåðñèòåòà èì.Í.Å.- Æóêîâñêîãî “ ÕÀÈ ” . Íà- ó÷íûå èíòåðåñû: ìàòåìà- òè÷åñêîå ìîäåëèðîâàíèå, êîíñòðóèðîâàíèå ïðèáî- ðîâ è èçìåðèòåëüíûõ ñèñ- òåì. Àäðåñ: Óêðàèíà, 61176, Õàðüêîâ, óë.Ñîëíå÷- íàÿ, 11, êâ. 10, òåë.(0572)44- 23-47, (0572)11-50-20. Êóñò Ñåðãåé Ìèõàéëî- âè÷, äèðåêòîð ÎÎÎÔ ²ÊÓÑÒ². Íàó÷íûå èíòå- ðåñû: ñèñòåìû àâòîìà- òè÷åñêîãî óïðàâëåíèÿ. Àäðåñ: Óêðàèíà, 61023, Õàðüêîâ, óë.Âåñíèíà, 5, òåë.(0572)33-13-39. t Ф 1 Фs 0 Фj - Фs Фj - Ф s 0 Ф s Ф 2 t t Uвых Т 1 Т 2 Т 0 Ðèñ. 4. 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ØÓËÈÊ ÌÎÄÈÔÈÖÈÐÎÂÀÍÍÛÉ ÌÍÎÃÎÑÒÓÏÅÍ×ÀÒÛÉ ÈÇÌÅÐÈÒÅËÜÍÛÉ ÊÎÍÒÐÎËÜ Îïèñûâàåòñÿ ìåòîäèêà ìîäèôèöèðîâàííîãî ìíîãîñòóïåí÷à- òîãî èçìåðèòåëüíîãî êîíòðîëÿ, ïîçâîëÿþùàÿ ýôôåêòèâíî ñíè- çèòü ðèñê èçãîòîâèòåëÿ è çàêàç÷èêà ïðè íåçíà÷èòåëüíîì óâåëè÷å- íèè âðåìåííûõ è ýêîíîìè÷åñêèõ çàòðàò. Äàííàÿ ìåòîäèêà ïðàê- òè÷åñêè íå òðåáóåò ìîäåðíèçàöèè ñèñòåì êîíòðîëÿ ïðåäïðèÿòèÿ è ïðèìåíåíèÿ áîëåå òî÷íûõ ïî ñðàâíåíèþ ñ ñóùåñòâóþùèìè íà ïðåäïðèÿòèè ñðåäñòâ êîíòðîëÿ. 1. Ðàçíîâèäíîñòè èçìåðèòåëüíîãî êîíòðîëÿ Ê íàñòîÿùåìó âðåìåíè òðàäèöèîííûé îäíîïàðàìåòðè÷åñêèé ÷èñëî- âîé êîíòðîëü ïðåòåðïåë îãðîìíîå êîëè÷åñòâî ìîäèôèêàöèé è ïðåä- ñòàâëÿåò ñîáîé çíà÷èòåëüíîå ìíîãîîáðàçèå ôîðì. Òàêàÿ ñèòóàöèÿ îáóñ- ëîâëåíà òåì, ÷òî â ýïîõó ðûíî÷íûõ îòíîøåíèé, êîãäà ìåæäó ôèðìà- ìè—ïðîèçâîäèòåëÿìè ïðîäóêöèè âåäåòñÿ îæåñòî÷åííàÿ áîðüáà çà ïî- òðåáèòåëÿ, êîíòðîëü êà÷åñòâà âûïóñêàåìîé ïðîäóêöèè ñòàíîâèòñÿ åäâà ëè íå ñàìîé âàæíîé ïðîáëåìîé ñîâðåìåííîãî ïðîèçâîäñòâà. Ðàññìîò- ðèì íàèáîëåå ðàñïðîñòðàíåííûå ôîðìû îäíîïàðàìåòðè÷åñêîãî ÷èñëî- âîãî êîíòðîëÿ. Îäíîé èç íèõ ÿâëÿåòñÿ òàê íàçûâàåìûé äîïóñêîâûé êîíòðîëü. Ïðè ýòîì âíà÷àëå ïðîèçâîäèòñÿ èçìåðåíèå êîíòðîëèðóåìîãî ïàðàìåòðà (ÊÏ) èçäåëèÿ, çàòåì ñîïîñòàâëåíèå ðåçóëüòàòà èçìåðåíèÿ ñ íèæíåé è âåðõíåé ãðàíèöàìè êîíòðîëüíîé íîðìû è â èòîãå ôîðìèðó- åòñÿ èñõîä êîíòðîëÿ, ôèêñèðóþùèé ïîïàäàíèå èëè íåïîïàäàíèå èçìå- ðåííîãî çíà÷åíèÿ âíóòðü ãðàíèö. Äëÿ ïîâûøåíèÿ êà÷åñòâà êîíòðîëÿ ïðè òàêîì ïîäõîäå èñïîëüçóåòñÿ áîëåå óçêàÿ, ïî ñðàâíåíèþ ñ òåõíîëî- ãè÷åñêîé íîðìîé, êîíòðîëüíàÿ íîðìà [1, 2].  ýòîì ñëó÷àå ñíèæåíèå ðèñêà çàêàç÷èêà îáåñïå÷èâàåòñÿ çà ñ÷åò óâåëè÷åíèÿ ðèñêà èçãîòîâèòåëÿ, êîòîðîå çíà÷èòåëüíî áîëüøå, ÷åì ñíèæåíèå ðèñêà çàêàç÷èêà.  ïðîìûøëåííîñòè òàêæå øèðîêî èñïîëüçóåòñÿ ìíîãîýòàïíûé èçìå- ðèòåëüíûé êîíòðîëü.  ýòîì ñëó÷àå èçäåëèÿ, ïðèçíàííûå ãîäíûìè íà ïåðâîì ýòàïå êîíòðîëÿ, ïîäâåðãàþòñÿ äàëüíåéøèì ïîâòîðíûì ïðîâåð- êàì [3]. Î÷åâèäíî, ÷òî ïðè òàêîì âàðèàíòå êîíòðîëÿ çíà÷èòåëüíî óìåíüøàåòñÿ ðèñê çàêàç÷èêà ïðè íåáîëüøîì âîçðàñòàíèè ðèñêà èçãîòî- âèòåëÿ, îäíàêî â ýòîì ñëó÷àå ðåçêî âîçðàñòàåò ñòîèìîñòü è âðåìÿ ïðîöåäóðû êîíòðîëÿ. Êðîìå òîãî, êàê áûëî îòìå÷åíî â [4], òàêóþ ïðîöåäóðó ìîæíî èìåíîâàòü òåðìèíîì êîíòðîëü ëèøü ñ áîëüøîé íàòÿæ- êîé, òàê êàê êîíòðîëü åñòü íåêàÿ åäèíàÿ, ìåòîäè÷åñêè öåëîñòíàÿ ïðîöå- äóðà. Çäåñü æå èìååòñÿ ñî÷åòàíèå íåñêîëüêèõ ñàìîñòîÿòåëüíûõ ïðîöåäóð. xhu?~ܙ\6Fke9u ktΠ8 aRb.lB`RxIxєRJT`?Y]ܾܩ {~yD"_ D\OYYtdk 7W zsaWr }닓}NB+K6;-E֕mNiV$fMܢȬԺDu6a˭H "ˇDA!0Se$Ez_'Q)LMP=KeI@u,,e+{I|A/7YRm c$92I./r *yR*V'BS";ч`՞7t q{7`wab?G,<9g!(߂wpj _5vj mėpOyFz hA{@gė` r`'pϚ~kCk nIVs2p;288@Cײ+bF3 S+oک@WZ^[up 8Ü lrUV)'u1 q> n=+41j|E  {Vv2Ν7~(| MˌIwϦi!?e Fk<9Wy2p a}Gݭ{8*@/v7܄ߌF#[pt[ZW4-_63?{ןoycxqnrVFA';nwXoѺ5onc ɫx7 G!zskf|>M|uF'SG9ږy^x:u@Y2x:uׁIMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:57  |Gr, lGtG(16\2]/G1^zX({txgeys,oW.H&ӮJY*%bqǠfZdH1 $6`1 qLj2 4"ahMva]_ 9ܳ tzg}}=khyA4G^4sM3Y= 4_~iܑɡ;/jN͇˚˛I_'Ȋ++Bo$EI0pl)?Eƶ.[]^8>abs1v(Aӵ'7'$R`s`D,0r.ЂYېՁYi@[?ˁ}}^fkvbn>iޙt[3Iݏ╕}w|e{9Y}d-ܼx㫻O]ꆗ>KK+㇚6{I4ѫIzSWt6O^#ɑrѫ8{fK+BJ1K첶}>_75Tg>޺v!^ٻ|%F+B;b>l |0c`I?jӛ?~& M͙ҰarC0>xq]:4ybӸ]&6s W[9Mi06OͣW͚b8ؔ<#-9ؼ8?W%}ؔMe] cs{_֋o'hܬͤ990CfWs_`sOr4;\U1wvxg}oz8&ͣ#]{.~ \%ݎDJįn>Z;04Q+dv!>ڱ }~}RoMZc<OU3/V>~*6o[}oɪqy\7~x_Rw_/~+gFpNx Ǘ3DljLr7^d?8/ғ/Rc鐧){N[(;1SWl^sw|h%=AIl|̡W/ȝGgvn]/#MkӦ>3 MN>}9="aLE\=ƌ_Fَvƻ+`(m͎pvх˶tW7gt:—_: EW]@d«)I(UF5g__FGJpRgFS|9+8;#ktdF@ Gڙc 'ɁWftĕ/X3Ըb/8ldn C>CV%Sj,ÓW)6(IQmVJfep8T|]\x~GɪɩvL8c G.|_?˧7uz)>5u6sj@I:s]; +Ozw_MF׭NA{ښVX{#tnI_񫇗]}_d)טdLuS/^mWɪ/>:Ź? Br;کÝ'^ut32gz)G١bD+\_s|e{teZ:%^joșXܯ~36wݷvs,j!Ğ,V6mYw|uݤ1gTYKIw6<)vp56f*){؎<˲e[trCP>'ꨫ>WaL\]PE6 O񗯇z?瓯3ޗWO =<w)>Hu6V<ܞ ʹ3鞵!icWZ2wz&lfOa)$>e~ņ)K[ "oaꣴdT՞ګObǯL Κ_omݧ;K΋fҚYwE,>>-CDvnHfl0l|]cMdS6׮r\=jT2|xu i{~9d`~'׆w_+l8n:m=[d;wÝ]A:įx>_#pCzگ~nbcvFnښe+B,'">œU~X+oHRG]=6N s]K䕁<^Y;'rFiwu9 )d᩾I5[D'vrw]>c~4Ck]xn/yR{ƒ?0k䲳81>am!TyrD $G y&hlYxOѾcwzj3?G?7ո[GWﴞ'/1*0 jp\ʓSy5ӆ|x|hNQ:fx%FiOn9T;k>i˞ܻ{mmNJzw3wvpں=[́S;k)S mWfRfOws ㍧YglnOZ ogQdIǏWJnѫOʂW%_}3xW;iۋޯ׏뭡sZu{sf9wgs'kcҞӼL+d~Fl&--XWo>^N:CvK&>0 *? 푃xqyE|LV_냣,m wwK#u<=ۈSiŘkzP/u|ǝO'17mY%4'{ˢiջCW{'!78ޙQ١v>5ʼn<>]HR|#uF'biH/k%O,.x1I_;{d&g]sý/}_E=2C^[+ۊayb|዇ŵ)=KzbDWv9PV.\ٖ1yx[Vl]>nؾ6.?]mrOq|>! uo_|@PKOwnp|<5S>}7j⍑֥G5 y/ 7Eݰ;U٢o؉ن:\͍>xcJsb_[/KUw<,TK+^J񀢑p /38|a__  M]'_Ń{7sݍpïO?Nl>@gs*Et7p5w\d#ooeSZ v$]{ӎ>nOZrݘ_Τ{ͩ[P5tvm~5h_)~>u~7`\^JG&3fDxhr{?, n \gM Q_׏?煶)`/RKIU@ !<7(ߒߦH:5Twt-rcG?A3s)4с.lO緾_guFڣ9IzD7Yy{d#Iz}/|5rOu@;SAju@[o7.j,jC[MiF[=tl+e(?):'G6~$XȠX4:K7j* 19/ypgTz 1N KEgȒ_)~>u{&}vLp8+ *NJ)"4{# H6^kțn>tX9sJt>,6D6NK:pt7D6&F1. bl)2vGS䣭Dmw}Q #Cc|4>ڧoJjY O}_,Ƞh+'tˤcV6`Kr@ұh+x2odch+:lM"6۳bJ?4y5́_o 򿷻zv_ez.0uPOqw)v';reG:wehKo~=yّDOr]},Uqlٺ -YtdGOL}ѓt/d=gNY5ʗnx.лd8S6yW.^)v؍-gm8e~-/Y2VA՗ 7hzQK$@ofDfhe e=S}kp+Ŧțu'2n|߁۵7oYvakYswqUvGCˇ^t8%X0mN4t0u@CBhfl ͜ŻC H֤$ a/X[MXd|=2;E>J//MF~O :vDoFhO;~62psұV5&~H,EX\uGdgqF 6]7nԎ I})|&lxB_C?|Tj iG]SuZp5Y:/_yQLhhdf8͔INwxc?g'*ƺ*n]w]yc@tYѦG[7u'&nҞ_kO_͹Y.?JńX?[yxa^IjOM&JvIңƋa,k.uM>i?bx]  IUv /zMd;l.H:pt(}6ɱht8Ԙl>ŀ1L##3Y>@bpBgм}=囋7Ɛ8֨5f C~*uStcMY+;*ۢݸIVd$M79t3XDX4: ;?5r_V-`:zf}j>/.RvYf;0 Vko\r*CCP}՗~Uʗͧ8|ǣ;|g,kEu;l_t'œ`_uC_zo~aقe_2Ȁ/Vlg_ugd8)a%sZCq{Ə/Y?6ŏg1ˍS~c`nG3c{jSNh]l}w8훴W[7v<;W:I>j8xv(K<üqz'ewxT_JTj,U:c=|}Z?@-_lҸwzqp[ΗVߔqr5Fw үYGAeܭfƨGG>|Sv`wy6o٨|RWeײ}O3 L,,86  [5] ïðåäëîæåíà ñõåìà êîíòðîëÿ, êîòîðàÿ ÿâëÿåòñÿ ðàçâèòèåì îïè- ñàííûõ âûøå ìåòîäèê êîíòðîëÿ. Çäåñü ïðåäëîæåí ñïîñîá êîíòðîëÿ, ïðè êîòîðîì óñòàâêè ñäâèãàþò âíóòðü ãðàíèö òåõíîëîãè÷åñêîãî äîïóñ- êà íà âåëè÷èíó ìàêñèìàëüíîé ïîãðåøíîñòè èçìåðåíèÿ, à ïðè âûõîäå èçìåðåííîãî çíà÷åíèÿ çà ïðåäåëû èíòåðâàëà, çàäàííîãî óñòàâêàìè, îñóùåñòâëÿþò ïîâòîðíûé êîíòðîëü ñ ïðèìåíåíèåì áîëåå òî÷íîãî ñðåä- ñòâà êîíòðîëÿ (ÑÊ). Òàêîé ñïîñîá ïîçâîëÿåò èçáåæàòü íåäîñòàòêà, êîòîðûé ñâîéñòâåíåí ìåòîäèêå ãàðàíòèéíîãî êîíòðîëÿ, áîëåå òîãî, ïðîèñõîäèò îäíîâðåìåííîå óìåíüøåíèå ðèñêîâ èçãîòîâèòåëÿ è çàêàç- ÷èêà. Íåäîñòàòêîì äàííîé ìåòîäèêè ÿâëÿåòñÿ òîò ôàêò, ÷òî â ïðîèç- âîäñòâåííûõ óñëîâèÿõ íå âñåãäà ìîæíî èñïîëüçîâàòü áîëåå òî÷íûå ñðåäñòâà êîíòðîëÿ ïî ïðè÷èíå èõ âûñîêîé ñòîèìîñòè.  ðàáîòå [6] ðàññìîòðåí ñïîñîá ïîâûøåíèÿ äîñòîâåðíîñòè êîíòðîëÿ, êîòîðûé ñõîäåí ñ ìíîãîýòàïíûì êîíòðîëåì. Ïîâûøåíèå äîñòîâåðíîñòè êîíòðîëÿ îñóùåñòâëÿåòñÿ ïðè ïîìîùè ìíîãîêðàòíîãî èçìåðåíèÿ êîíò- ðîëèðóåìîé âåëè÷èíû, íî íå îòäåëüíî îðãàíèçîâàííûìè ïðîöåäóðàìè êîíòðîëÿ íà êàæäîì ýòàïå, êàê ïðè ìíîãîýòàïíîé àäàïòàöèè, à åäèíîé ïðîöåäóðîé êîíòðîëÿ.  ýòîì ñëå÷àå ïðè n-êðàòíîì èçìåðåíèè ÊÏ ïîêàçàòåëè äîñòîâåðíîñòè è êà÷åñòâà êîíòðîëÿ óëó÷øàþòñÿ â n ðàç. Äàííàÿ ìåòîäèêà ïîçâîëÿåò ñíèçèòü ýêîíîìè÷åñêèå çàòðàòû ïî ñðàâíå- íèþ ñ ìíîãîýòàïíîé ìåòîäèêîé, îäíàêî âðåìåííûå çàòðàòû ïî-ïðå- æíåìó ñóùåñòâåííû.  ðàáîòå [7] ïðåäñòàâëåí äîâîëüíî èíòåðåñíûé è îðèãèíàëüíûé ìåòîä êîíòðîëÿ, êîòîðûé ïîçâîëÿåò îäíîâðåìåííî óìåíüøèòü ñðåäíèå ðèñêè èçãîòîâèòåëÿ è çàêàç÷èêà. Ìåòîä ðåàëèçóåòñÿ ïðè ïîìîùè ÑÊ, ñîñòîÿùåãî èç îäíîãî èçìåðèòåëüíîãî ñðåäñòâà è òðåõ óñòðîéñòâ ñðàâíå- íèÿ. Êàæäîå òàêîå óñòðîéñòâî èìååò ñîáñòâåííûé äîïóñê íà ñðàâíåíèå, ñîîòâåòñòâåííî [A 1 ;B 1 ], [A 2 ;B 2 ] è [A 3 ;B 3 ]. Ïðè ýòîì ìåæäó äîïóñêàìè âûïîëíÿåòñÿ ñëåäóþùåå ñîîòíîøåíèå: [A 3 ;B 3 ]  [A 2 ;B 2 ]  [a;b]  [A 1 ;B 1 ], ãäå [a;b] – òåõíîëîãè÷åñêèé äîïóñê. Åñëè ïîñëå ïåðâîãî ñðàâíåíèÿ îêàæåòñÿ, ÷òî èçìåðåííîå çíà÷åíèå êîíòðîëèðóåìîãî ïàðàìåòðà Y  [A 3 ;B 3 ] , òî ÑÊ âûðàáàòûâàåò ñèãíàë «â äîïóñêå»; åñëè ïîñëå ïåðâîãî ñðàâíåíèÿ Y îêàçûâàåòñÿ âíå [A 1 ;B 1 ] èëè Y  [A 1 ;B 1 ] — [A 2 ;B 2 ], òî ôîðìèðóåòñÿ ñèãíàë «âíå äîïóñêà» è èçäåëèå ïðèçíàåòñÿ íåãîäíûì.  ïðîòèâíîì ñëó÷àå ÑÊ âûðàáàòûâàåò ñèãíàë òîëüêî ïîñëå ïîâòîðíûõ ñðàâíåíèé: «â äîïóñêå», åñëè îöåíêà Y ïî êðàéíåé ìåðå â äâóõ èç òðåõ ñðàâíåíèé íå âûøëà çà ïðåäåëû [A 2 ;B 2 ] è íè ðàçó íå âûøëà çà ïðåäåëû [A 1 ;B 1 ], è ñèãíàë «âíå äîïóñêà» – äëÿ âñåõ äðóãèõ èñõîäîâ. 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Äàííàÿ ìåòîäèêà ïðàêòè÷åñêè ëèøåíà îïèñàííûõ âûøå íåäîñòàòêîâ è ïîçâîëÿåò çíà÷èòåëüíî ñíèçèòü ðèñê çàêàç÷èêà ïðè îòíîñèòåëüíî íåáîëüøîì âîçðàñòàíèè ðèñêà èçãîòîâèòåëÿ è íåçíà÷è- òåëüíîì ïîâûøåíèè âðåìåíè è ñòîèìîñòè êîíòðîëÿ. Çäåñü, â çàâèñèìî- ñòè îò ïîëó÷àåìîé èçìåðèòåëüíîé èíôîðìàöèè Y, êîíòðîëü îòäåëüíîãî èçäåëèÿ â ïàðòèè îñóùåñòâëÿåòñÿ çà îäèí, äâà è áîëüøåå ÷èñëî öèêëîâ îïîçíàâàíèÿ åãî êàòåãîðèè. Ïðè ýòîì â äàííîé ìåòîäèêå ââîäèòñÿ òðè êàòåãîðèè èçäåëèé: «ãîäíûå èçäåëèÿ», «íåãîäíûå èçäåëèÿ» è «ñïîðíûå èçäåëèÿ». Ãîäíûìè ïðèçíàþòñÿ òå èçäåëèÿ, ÊÏ êîòîðûõ íà îäíîì èç öèêëîâ îïîçíàâàíèÿ ïîïàë â ãàðàíòèéíóþ íîðìó; íåãîäíûìè ñ÷èòàþò- ñÿ òå èçäåëèÿ, ÊÏ êîòîðûõ íà îäíîì èç öèêëîâ îïîçíàâàíèÿ âûøåë èç òåõíîëîãè÷åñêîé íîðìû. Îñòàëüíûå èçäåëèÿ ñ÷èòàþòñÿ ñïîðíûìè è ïåðåõîäÿò íà ñëåäóþùèé öèêë îïîçíàâàíèÿ. Êîëè÷åñòâî öèêëîâ îïîç- íàâàíèÿ îïðåäåëÿåòñÿ íåîáõîäèìûì êà÷åñòâîì ïðîâåäåíèÿ êîíòðîëÿ – ÷åì áîëüøåå êîëè÷åñòâî öèêëîâ, òåì âûøå êà÷åñòâî êîíòðîëÿ. Òå èçäåëèÿ, êîòîðûå îñòàëèñü ñïîðíûìè ïî èñòå÷åíèè ïîñëåäíåãî öèêëà îïîçíàâàíèÿ, ñ÷èòàþòñÿ ãîäíûìè.  äàííîé ðàáîòå ðàññìàòðèâàåòñÿ ìåòîäèêà ìîäèôèöèðîâàííîãî ìíî- ãîñòóïåí÷àòîãî êîíòðîëÿ. Îíà îáëàäàåò âñåìè êà÷åñòâàìè, ïðèñóùèìè òðàäèöèîííîìó ìíîãîñòóïåí÷àòîìó êîíòðîëþ, è îòëè÷àåòñÿ îò íåãî òåì, ÷òî ëèøåíà åãî ãëàâíîãî íåäîñòàòêà – óâåëè÷åíèÿ ðèñêà èçãîòîâè- òåëÿ. Ýòî îñîáåííî âàæíî â íàñòîÿùåå âðåìÿ, êîãäà ïðîèçâîäèòåëü âûíóæäåí ðàáîòàòü â óñëîâèÿõ îãðàíè÷åííîñòè ïðèðîäíûõ ðåñóðñîâ, è ëîæíûé áðàê ïðèâîäèò íå òîëüêî ê óùåðáó, êîòîðûé íåñåò èçãîòîâè- òåëü, íî è ê íåöåëåñîîáðàçíîìó èñïîëüçîâàíèþ ïðèðîäíûõ ðåñóðñîâ, à òàêæå ê çàãðÿçíåíèþ îêðóæàþùåé ñðåäû, ÷òî îáóñëîâëåíî óòèëèçàöèåé ëîæíîãî áðàêà. 2. Èñõîäíûå ïîñûëêè è îáîçíà÷åíèÿ Ïóñòü ñóùåñòâóåò ïàðòèÿ èçäåëèé îáúåìà n; êîíòðîëèðóåìûé ïàðà- ìåòð èçäåëèÿ X è ïîãðåøíîñòü åãî èçìåðåíèÿ Å – íåçàâèñèìûå ñëó÷àéíûå âåëè÷èíû. Îáîçíà÷èì ÷åðåç (x) 0 f è ) (ε  f èõ ïëîòíîñòè ðàñ- ïðåäåëåíèÿ. Åñëè â ïðîöåññå êîíòðîëÿ èñïîëüçîâàíû èçìåðèòåëüíûå ñðåäñòâà ðàçíûõ êëàññîâ òî÷íîñòè, òî ïëîòíîñòü ðàñïðåäåëåíèÿ ïîãðåø- íîñòè èçìåðåíèÿ öåëåñîîáðàçíî îáîçíà÷èòü ÷åðåç ) (ε i  f . Îáîçíà÷èì ÷åðåç N=[x í , x â ] òåõíîëîãè÷åñêóþ íîðìó, à ÷åðåç   в н x , x N     – êîíòðîëüíóþ íîðìó ( [ в н x , x   ]  [x í , x â ]), è áóäåì ñ÷èòàòü, ÷òî îíè öåëèêîì ðàñïîëàãàþòñÿ â îáëàñòè íåíóëåâûõ çíà÷åíèé (x) 0 f . Áåç íàðóøåíèÿ îáùíîñòè ïîãðåøíîñòü ñðàâíåíèÿ â ïðîöåññå êîíòðîëÿ s%xklTEݶm骴F Bi+DTB( U! |C n1~<Â""؊jQ /yCyAcdC;vǮjL4?9s̽38D$?Qd(\E*1AdXLv$U%(gZ϶CJCpPR X8ՖHڕkitc#}zjn/rLm=-C(7%WH܄r)&GN;eg+GL4YrpQWkxMPt- , T  l4='=IM/Y+i}ɓ-;e^y\Bc|OgOǏ, : s5]drV'țebp+Vl:[U{ }OveE:&S*MbS08mJd_ؖDέl:)"#!YWfhʙ[ԑ,c3ù.0DZpmZ< ߃&uv.˺uy^ھ]x>OMOfs-ާg'-dct7y3+N!V|N6)pm(6UvUa{K3x3oK4·r0}/< 6^&&f#oŷ9 `?1p1kpZCz*S$rɷ!}ЫЇrӶyĶb{؞'\lѷÛ?+fbz_#k/~S@>`-0z[|y ~]_? :m?Vp?_p2ه 9bhB>im_i=ֵ$b`=.4g lBoˈ~%r98|ŸsՈm𬥄c."1χp%q}5L5yS&ʋ#(dE l7Wj/\8π[@:u7#WГs;rb/ wu>o_ ϑlӛ=`U8ׯR2 x =QCOIv8]ɓ^jOcG{uJ$M৻gK؞t2D; y'|@vm \\  XJj虾k2"7:8<>D4E3Gx'-_Ů{L'g"|Μr>wSx¶FSF"I 8x"W1$;8|{gX&٭-_S6V9V]cdVU[6x:<<+^XX>;wW+߿5*ǫScb/^9>cZGmNiGOoڹZ;6{lbգWt5Vnhp;vn_:Rܟnp;v@Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:57   ((162:/1,<{4x uǿ.˲*.D܅E%"AhML5>1#hVkL4&kF4jHj"Qh1>j}+bE}߹;XgqΜ9̙ޛ rA }?5AEA>o TAΪ N0'[')Qzx*Ό \YL. . ҂Ӄ g^5Abq%XLKគ~{Tm)JÏfG ;< J`o@9W=OV6}AMi@O4TH)_h2 ˶mۂ8Nnq6KET tGO IPAZeSI+<[k7}өOeß ۤ؀١fV |fv0γik냶NpU(}imC'eAi'^ڪSVd wRmeS62ax(i+6]aJ>zoz*fLe1<^JaNA<ӕ9^;@.[r*!67ޠ|H[r#?m2nئlyD@K:lc>.ӷMypwHmBO?Mޑ})6*,6/Rl$nMmrm+I\^`/*DfLR6 .t)x7h Z[~#nM"",im ^W5W 0k07*ADf7-Ѷi>1N=i CK>wXÓKɃcCtu> |(Cy~6 S_e꠿mWOAm\_|Wll@`L'=%#iQ!C/h=ő9zCh*̶ptE.mW@t)UQXeܡfmX{&5*9}C^Odh}F91N,=qtFAd~ǵ#xQ|x +z$؂O?(CH+GxR TY^ʛ,Z^ ͐̄LnҌ=Fji6ЮehlxP8ES6/(ՏMHg!!wġC Ț1:B0D;-N>6M7nK Ox6=ںwt{ˡ7^e|zdj1i4=«uhNF.@z`n|K46͠q4VhL2h\~'r4nmd`ޑ?yR9<Ư5#'`.e88~:lQ/e{SѺϺ.ֽ;D>,qɎUm$qՒoasgwWj"ڵ]7O wd`yAr 1=vy6Ccx c,Z]f3fi@H9h|KB5mrtGeg?^yU&ߔ|y Z碜䨊|QQgm[o*w̉,bo1|d:B K@9!i+gȧ,\iȈ=*GIW>/AR>J2) 9I̹>\#\:Nt]QΛշu grAD N9Y6jez_k:^0cf'tl|ꀟٸEȁr>+PV9Vj=圶Uv^Xm׆ngig~^X Nс3< qʱ/,YYZOEp(aUAH!mi}읠!0~128z`%rkuCZOy{xFz@SZs˦~5#ʮ<|UhFڠ=I0ө_}Xպ>[n8iyoާE]"Cb^]ZFMF.9.< 38S;sN?W FgYk}Ӹ:jsDm>Hik3oQި[W9zӛiG= Frd뮞׮WM>}c;.BztTJ~WW'YG;.I~ptx՟tP7I]"osz3G4LU.W- oƮYn]{4c50|gs3W4gο:Xx׭F:};ZWZ=m5#);D@՝|gm`͞)7k k68lLh}g29fn JK5p}]Έv͵k X pǗgHQ[}{)8q/#]𖷾]MG;ږŬm=ak9ֶ'XL_ yjnX\U5K OY o2Г俲:Xk|ֻW?&:<nn3hǞބ lI t䱧$2xѷ9UR,KʃGf4#6ڹk/iб#2팗XK{HW /p5]8|]"We$ypx..Z>7Kc=Wed8wʓ˻vޱs>Û tdy~ 1 #EfEW#8Mt-tЛH2 l_)k _/9f,;V`B;;w޷9ln$9A,/W^=$ }g{u?CeQ' Ze`?v1lq Ω,͆Wt$ !۰M,mBPM eXayzǦm2I@M~%,9>0)Gp8]8`h0=,UyFa?83y,"+1_> |\oڽ*7ɨyN"&<:Dv?+Ab;mٓ"[n)0pouӼn/2K3s)\I*,NUyGe=-x3w[xÔw+(9_4Kial'̘>ПL)gui nm0e sFڕXtC(C)yڧәµ?D,-~>pԧ[tVO3r”}|d?wh}X"VȖSSrnr Vocq9;nlmm!w G~!D~{fsǙAxBdx g|9Z &x6ͿS vwtnVs;Ty>}-G]zvۃ۝!fMcUJ1FDf%r ͣDm;bL/284C8r1XBo!5}B mՍ( Ж/h7f'48k͡WhEk ѝ&5\碻Cy>9!i]ej2"4YO C曘EnOXUǪ+$qKr ];] UwcڻJ҅U"oZP//+w.[\g@c}-z{h-? k7o)7^-1}./j|xp/{{|kbzЯ/;HWr|1278[%ԻLئC:'/rI= QKh̀{_8OTqS"~uR5bn\d}oh}-N*n Fcž-:ՊIVv|^ە|nN]#qjMzVo_5}@f/Lq MZ`|:YZ)A0!{p*O-!mIt猣QDoNTBZ6Njm&obQ@}6:xL7dD;U}["[i;a0FC[_ʻ萤Uy1t|G;Hmѹq23;Ie8<8aW1ʹco>G}&_gE-,ߕ0Y;IԻԩBR e=Q,kߡNƉ._fYJj'cAu-83E;d8kn,vF)L}e(v\i=W.\Z&O&L*$GyZ|J38)W䨃~W=΋+5UhA d'ispl;;w;_ ?T;\U1S =/b s5򇰦/?>'e>:wPN뀵ulHf{q/XCH۝M(;I~tnt# [ݝ-Fwp>]F|tf'~sjZ(5iul9ӹm~.CjI򏑷 6czY armvH>:+ Ϟyo_^lh_z-2gG,#5ʍVLŜ%0hi/h>4ɴkSCK፿v¤MS_.w}Oђ|4) }>}J>ꆒ>g}qSmu/|MjٵMV>RXm9Xmܫ\uu^:˙=_N>f?[/_n_4ϹٝsRr}Yd(u/=S^_i}.vO&_6vG}tʹ>:R}rr櫘L/_n¤/c/ǽB\6/g4j-yNyxQ *՗[/(ɗ~ܐIu6AF$rkѹ\mFrk#㫷yyG9:ђ|41I9}tGCΞ3Gw6?fmG߉>Bٵ2ьft;\>ѹ>Z6+t\ξck9ocsr/ח{Gs[b rFWȗsN#E2;y(zLs(˻SUI]/=5x$}9prYLhy+sS~7Imqy]qǓ9m1tG+zǶ :J~kR\'<oIN> !~',NH>e闞N~iZ}{BXBwW/I/5K[TXӆ~V/ Hw^_kg]lgOu%WU>h ${_~s|=Q;Q8ӥiQĝAK|uɼzonܢ_i;NK?7 ì^]ݿGg3fg~MQ=磴eIj@w3FCC(c~}_~ 5|ANTR'#I016r}eV %%]1w|Q|=5Cs#'Ɏo;#E=rwJ>} z> -(' v-ƶٷ1e2cםU߯r|\ ݏEg7;g-:/BٍLr%?H:AަWw\6#C0NB\M-<\ \{=ViZM w+ZҞ.B\=҅7oOL_^olE;Z'Z}g'穓5Ay΂w@2ms"۞=O=3= ]0/ǾHw_6έAKS9iL$iss9kUW99 V- ݽ>t9]LMO[ԕ?{:k3~W9Y>u|fgR^rcr9{9V;rno.qFްrv}5D[v|}[srrbrQt6W㿖3Zs\GCWh_}ѹc'e:6؞2gEV>τwT^T?1}ˊ˵/>}Is yA޶N0F Gȟ/˝m/L[ݴYrf;>5M)e M~[y;E`+-O Kqi(l&ǚ~L.P︾BojN{o_G䗬xM{qo);SDBvHcOOwvȀ=#sF^yg# /ޑ4<)i[=0PQ'-s4%ԓ}Mi/4꜇["Ĕ×-F}}`*!쭄?egǟط 'Ӿd;E2PN􍸚6ΔN ϳ@ګ2ZtLmk}LCЭtl>p &wR>+KnJ.viw&?9UdjrR8WFG*,^ ;T{mGI\w#bA‡<{?>+`؃-KuZ뾝!J##›ԮE a<?<xQae-up9g u;ԱQaw1EA7(WG)v)ǴQ!67&ujjb+~qֆUu6^3xxWyjY0|TW7qIpl)'x;V \XRy{ppe<u eǂ-t[,^=wsLKhC5Q8Wui:Ҡ?-iԎ_Sݶ0NT}JY[˗T5-?֖Y[Եi[U=qPBEA%\+CEmќ Ylm %u>Ƭ`&PFC]Wi̷IB1 on>xG( .z)"|>t֔c>~jMG-'y<\ráqWɷˡVÇ"g뗏~1Lme|grB/Uw |c= +~b?USWqJur"o GKgkNoO(ޢqL4 >7zҝ>%9jt"SQysoRsZvI}"& #|;Lsy*ף|zً1=SWq ~KxV9)QY?E4*"O*FZh.oj&\k; z^oݚ7=ϔ~+q i&e=*gz.TVT Ai~~rʫ\zSS}c׷gލ_21<{@s~rG)μϔ6wxjV<#-{olaI i31m=$GnhT6km늝7}LH; i?~ӕN 8oUXg۬ٽp1[,>ʼRu >|y +[MÇ|e}헏f?*+37Zsev+A#!S4?f>,nQ+-DSȽ~2gߩX Z*xأc}*ώ{TҙVZ<2^_&9^*'zG˾2cH'OEE{>XH2njc|3h)cn=R/C"钯ї>TF =sOW"_y_ېӳhTuFyzPxæ 3u}xbMuSWS\n>4v}|x_>bxZse*+GSitW;3B+eQd}s326^ںD'9k\ Hɜ>0qVMrOS" |>TF۞.KUt>NPH{K+,UO3ϫg{}}P_s9|e>#"_y8!U'MFCz':y7 ׇE~nvȚ)|>>厎XJd?vGt-ꢥn eC4H:UMrR nbq={/ьQhh֞{j]GsVexx/}jji{wgē;:Mjy+U+o4#GnNVhn,Xv݋{,xMѦڱ ǂ^,-|GwtjP,㪛{ by;ιv3bx] Om5/|r%CiA=Έ_n9x><(ۗd㫳Qu>NrᶞHpB9|R÷?s3G\5k 'yCVx50 쮫zBa'ϗ7~f<)@']tW|ߡ)9=#J/z^|g=K}9}{m~=rȈ9}izfXn`pj{*ũ 3q^=HuRυ)wzW9o.vsp>Ç-|U! Q5;#i w^Dh4s5 {usBwFv3b? d]zLX_Fe8ss 3vxIkȁ bWs}i >W }j|>AFxr$v2|NʈI%{ ;#z +ƭ?%T'n| Յ䅞 qޯ}WZO&okE:-pTkg=|(Wk;#-ڝʈ3rx}+LSTJF٠έ[{;3>G4is TJW|,#炾gԗR}e$Hg|h {ŶpB$ӣ:~5uW0yg/yg|CmiA+{Z,#:T6zu+OR݅-턶A}EvmU>Q4w;ͣv$ӎ\QGS a9@OWF+fV?1:=7}T5?WoWf-W^(2j(.32ieڝzgm񴵕wFĦɬgK+>#|D OjKUES:+#& #Ȼz~_gbp<_IӇN&`a@ >χG/ΎU*ͼN{ަ*L=Qxa#ow-Mq>SbUN}Wh`jv} wR!5פ>ge~oq#{dx~M^ʼ^!ڣQ^k^U%'(oZk>_oO:D'yJQ 6 ǩEWV';}Uh-턶A4S6q?MQS[)ᑋ6IӣߝzUc~ڹ#ùEuf?>q3?}|"^8wwخ{ ,txF{s΍/ .>tQW}==c|KW~]!myUp&goQyIޛ>FDdW=u;%{ #/Yjg=Œ_8ZQ^'IyFᑷ='mJUźOb}`IN /.Zd twFy\ءݧe"$o|vRF`zu6F>F>/M14gӊ][}>KK9_rj}ȕR &9%nom͗Dck+sB.}OIwV}5 {+0 ˻8Cy7 l 1FP˥oI*eBѱxPv=YSG?ۣ ƣN\x "=1|K(KR^>d>1ez[W;ź<|(mheOW|1_1l!Nl9}6 PStՇڍIOσ {ڇB>\>CMs|>PAZQ8wy$$P~~wECXψG>!Fi1U=wsP|ɫXžwt=vܝ}>2.E e:ozVPg}(>& &9vt}e֕O`c/>ԣ LJ:Y 1=cGGwNzՋ2)J,l9vfNyO9`ĉ +fY|L8>T2n9Ow㬲sEwܚJoKU бP.b̿*|( |}$;a<&G}G7G "a2߫ˏeewXa<ɷdaR^! {*]#-wS vnGyۃ\pym/pZVETӲ}TvK0U7u_:g3Z>יq?>|yV><#En|40QU}D͙%ˌSVd~ő%~qVn]}0%nÙR?6d!Q8Z4'3"oef;Okӟy_}> ܓe^=$ 5.ϸ~*L=ehʎ >/_y7&O[e*Ţ_ro , 2W 8FތiM[Tob<ɸ8c3Pמ@2XBA=ĭq>K}U?.h~dNt>ݜ$\rN6Yٗ ׵kd8յE6rYv|YycEk"f_WJX*6(LK̆oƎ6)-MRDF[CpeIVg6]0GMW'0Po#myFo1ZI~B 4P4Ѐ#> ;=EJt>];(;_xs~)^3k_Fex@qeO-q} Z .Z_.Z;^gc,DmZaYV"$k{O%ÕJFM!= of+6)By[vGc/!yϜZ јG؂7ޔa7ؗB _Bx4e!M]&<č~n}3^XΡ甗O˄{W$I"0׆q!)^VM5 ׏c5IlbuRK>"H122ِ|dR' t\m=)geޠg8KY(< -8'Y];n=i;|!ry:cRyS7M>Ӭ?O)|yzZn5iF"ͭU8{#]:xp]x~Yx wMxF&Vazo`v3#3Bd` c [Le1!N[(?B zczК)Ocmv%>3S^kE̜?A:@MUO Χu7gLfheneFmќ>#‹9k^[h~f|֊F[Ҧ3d:Gv&[Bߌi58dMYƵp:YɳvQ2f{~VxCɣF3Cq|{_ApBeu7^y>1|K4};A*50Qz|?,qmFO.'}G>!=q+}Z`1^A^?GM zMzBtJY 9>nϫtcާs l "Y*Q6u2_&Nk8o޷*V~V(L묎\a [3ᢰ!J1؎͘N:"mvlm5Y}\?bpqrPb4}Z^I:xCC>ASˇsߔ7E>]w*H^/l &2#~:}`4ߙ#:{`s0k"BS)gȑyʹtN BϏ^^SA@_vo f8f7kӶI:ה7Ny>.Zizk83{nQ$~ ݨVzN5om';G&'L-ـCƬu&[LOսyȋ^4r>!Nw^.x:m$䈔ęәOi?16 6,,88 ìîæíî ñ÷èòàòü ïðåíåáðåæèìî ìàëîé âåëè÷èíîé, â ïðîòèâíîì ñëó÷àå îíà ëåãêî ó÷èòûâàåòñÿ â ïîãðåøíîñòè èçìåðåíèÿ (ñì. [8]).  ïîñëåäóþùèõ ðàññóæäåíèÿõ, òàê æå êàê è ïðè ìíîãîñòóïåí÷àòîì êîíòðîëå, ñóùåñòâåííóþ ðîëü èãðàåò ïîíÿòèå ñïîðíîãî èçäåëèÿ. Òîëü- êî â îòëè÷èå îò òðàäèöèîííîãî ÌÊ ([4]) äàííîå ïîíÿòèå èìååò íå- ñêîëüêî èíîå çíà÷åíèå, ïîýòîìó ðàññìîòðèì åãî äåòàëüíåå. Êàæäîå èçäåëèå, êîòîðîå ïîäëåæèò êîíòðîëþ, îïèñûâàåòñÿ êîíê- ðåòíûì ÷èñëîâûì çíà÷åíèåì ñâîåãî êîíòðîëèðóåìîãî ïàðàìåòðà X. Ïîëíîïðàâíûì ïðåäñòàâèòåëåì ÊÏ âûñòóïàåò ðåçóëüòàò åãî èçìåðåíèÿ Y=X+E. Ïî îáå ñòîðîíû îò x í è x â – ãðàíèö òåõíîëîãè÷åñêîé íîðìû óñòàíàâëèâàþòñÿ îòðåçêè äëèíîé   ˆ k (  ˆ – ñðåäíåå àðèôìåòè÷åñêîå ïîãðåøíîñòè èçìåðåíèÿ, k – êîýôôèöèåíò, çàâèñÿùèé îò âèäà ïëîòíî- ñòè ðàñïðåäåëåíèÿ ïîãðåøíîñòè èçìåðåíèÿ  ), îïðåäåëÿþùèå çîíó ïîâåøåííûõ ðèñêîâ (ðèñêà çàêàç÷èêà è ðèñêà èçãîòîâèòåëÿ). Êîýôôè- öèåíò k âûáèðàåòñÿ òàêèì, ÷òîáû âåðîÿòíîñòü áðàêà èçäåëèÿ, èçìåðåí- íîå çíà÷åíèå ÊÏ êîòîðîãî ïîïàäàåò â ãàðàíòèéíûå äîïóñêè, áûëî ïðåíåáðåæèìî ìàëûì (íàïðèìåð äëÿ ðàâíîìåðíîãî ðàñïðåäåëåíèÿ ) (ε  f k=2). Îáðàçîâàííîå îòðåçêàìè ïîäìíîæåñòâî òî÷åê ìîæíî ïðåä- ñòàâèòü â ñëåäóþùåì âèäå:     В В Н Н x , x x , x N          , ãäå      ˆ k x x Н Н ,       ˆ k x x Н Н ,      ˆ k x x В В ,       ˆ k x x В В . Èçäåëèå, äëÿ êîòîðîãî N Y   , è áóäåì íàçûâàòü ñïîðíûì. Èçäåëèÿ, äëÿ êîòîðûõ   Н Н x , x Y     èëè   В В x , x Y     , áóäåì íàçûâàòü ñîîòâåò- ñòâåííî ñïîðíûìè ñíèçó è ñïîðíûìè ñâåðõó (ðèñ. 1). x Н  x Н  x Н x В  x В  x В N  N  N N * Y Ðèñ. 1. Äèàïàçîí âîçìîæíûõ èñõîäîâ êîíòðîëÿ 3. Ñõåìà îðãàíèçàöèè ìîäèôèöèðîâàííîãî ìíîãîñòóïåí÷àòîãî êîíòðîëÿ  çàâèñèìîñòè îò ïîëó÷àåìîé èçìåðèòåëüíîé èíôîðìàöèè Y êîíò- ðîëü îòäåëüíîãî èçäåëèÿ â ïàðòèè îñóùåñòâëÿåòñÿ çà îäèí èëè áîëüøåå ÷èñëî öèêëîâ îïîçíàâàíèÿ åãî êàòåãîðèè. Ïåðâûé öèêë ÿâëÿåòñÿ îñ- íîâíûì, ÷åðåç íåãî, êàê è ïðè ñòàíäàðòíîì ÌÊ, ïðîõîäÿò âñå èçäåëèÿ ïàðòèè, è êîíòðîëü áîëüøèíñòâà èç íèõ íà ýòîì è çàêàí÷èâàåòñÿ. ×åðåç ïîñëåäóþùèå öèêëû ïðîõîäÿò òîëüêî ñïîðíûå èçäåëèÿ. Íîìåð 1-ãî öèêëà, ðåøèâøåãî ñóäüáó (ãîäåí, íåãîäåí) òîãî èëè èíîãî ñïîðíîãî èçäåëèÿ, èìåíóåòñÿ ïîðÿäêîì ñïîðíîñòè ýòîãî èçäåëèÿ. 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Ïîãðåøíîñòè èçìåðåíèÿ i  â ðàçíûõ öèêëàõ ïîëàãàþòñÿ íåçàâè- ñèìûìè äðóã îò äðóãà. Òå èçäåëèÿ, äëÿ êîòîðûõ   N Y i è N N Y * i    , îòíîñÿòñÿ ê êàòåãîðèè ãîäíûõ èëè íåãîäíûõ ñîîòâåòñòâåííî, è êîíò- ðîëü äëÿ íèõ çàâåðøàåòñÿ ñ âûäà÷åé ñîîòâåòñòâóþùåãî èñõîäà «ãîäåí», «íåãîäåí». Òå èçäåëèÿ, äëÿ êîòîðûõ N Y i   , îòíîñÿòñÿ ê êàòåãîðèè ñïîðíûõ è ïåðåäàþòñÿ íà ñëåäóþùèé öèêë îïîçíàâàíèÿ. Åñëè, äîéäÿ äî ïîñëåäíåãî öèêëà, èçäåëèå îñòàåòñÿ ñïîðíûì, òî îíî ïåðåäàåòñÿ íà èòîãîâûé çàêëþ÷èòåëüíûé öèêë èçìåðåíèÿ, â êîòîðîì èçìåðåííîå çíà÷åíèå Y ñîïîñòàâëÿåòñÿ ñ äèàïàçîíîì âîçìîæíûõ ðåçóëüòàòîâ, ðàç- áèòûì â ñîîòâåòñòâèè ñ êëàññè÷åñêèì äîïóñêîâûì êîíòðîëåì ( N Y i  – ãîäíûå èçäåëèÿ, N Y i  – íå ãîäíûå èçäåëèÿ), èíûìè ñëîâàìè, íà çàêëþ÷èòåëüíîì öèêëå îïîçíàâàíèÿ ïðîâîäèòñÿ êëàññè÷åñêèé äîïóñ- êîâûé êîíòðîëü. Êàê è ïðè ñòàíäàðòíîì ÌÊ [4], â êàæäîì öèêëå îïîçíàâàíèÿ, ñïîðíûå èçäåëèÿ ìîãóò áûòü ëèøü îäíîé «ïîëÿðíîñòè»: ëèáî ñïîðíû- ìè ñíèçó, ëèáî ñïîðíûìè ñâåðõó. Òàêèì îáðàçîì, ïðè óòî÷íåíèè êàòåãîðèè ñïîðíîãî èçäåëèÿ â êàæäîì öèêëå îïîçíàâàíèÿ íåò íåîáõî- äèìîñòè ñîïîñòàâëÿòü ðåçóëüòàò èçìåðåíèÿ ÊÏ ñ îáåèìè çîíàìè ïîâû- øåííûõ ðèñêîâ. 4. Ðàñïðåäåëåíèå ÊÏ ïî öèêëàì Äëÿ îöåíêè ýôôåêòà ìîäèôèöèðîâàííîé ìíîãîñòóïåí÷àòîé àäàïòà- öèè âíà÷àëå âûÿñíèì, êàê ðàñïðåäåëÿåòñÿ ÷èñëî ñïîðíûõ èçäåëèé ïî öèêëàì îïîçíàâàíèÿ áåç ó÷åòà çàêëþ÷èòåëüíîãî öèêëà êîíòðîëÿ. Äëÿ ýòîãî ââåäåì â ðàññìîòðåíèå ïîíÿòèå ïëîòíîñòè ðàñïðåäåëåíèÿ ÊÏ â i- ì öèêëå ) x ( i f , ïîíèìàÿ ïîä dx ) x ( i f âåðîÿòíîñòü òîãî, ÷òî ïðîèçâîëü- íîå, íàóãàä âçÿòîå èç ïàðòèè èçäåëèå íà çàêëþ÷èòåëüíîì ýòàïå êîíòðî- ëÿ îêàæåòñÿ ñïîðíûì (äëÿ îïðåäåëåííîñòè äîïóñòèì – ñïîðíûì ñíèçó) è åãî ÊÏ ëåæèò â èíòåðâàëå [x, x+dx]. 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Ýòà õàðàê- òåðèñòèêà â ñîâîêóïíîñòè ñ ïëîòíîñòüþ ðàñïðåäåëåíèÿ ïîãðåøíîñòè èçìåðåíèÿ ) (ε  f ïîçâîëÿþò íàéòè ) x ( i f â ëþáîì öèêëå i, à òàêæå íà çàêëþ÷èòåëüíîì ýòàïå. Ïåðåïèøåì âûðàæåíèå (1), ó÷èòûâàÿ ïðè ýòîì, ÷òî ñîáûòèå ] x , x [ Y н н i     ðàâíîçíà÷íî ñîáûòèþ ] x x , x x [ E н н i       , i=1,2,…m: . m ,..., 2 , 1 i ]}, x x , x x [ E ], x x , x x [ E ],..., x x , x x [ E ], x x , x x [ E ], dx x , x [ X { P dx ) x ( н н i н н 1 i н н 2 н н 1 i                              f (2) Òàê êàê ñëó÷àéíûå âåëè÷èíû X, E 1 , E 2 , …, E i íåçàâèñèìû, íåçàâèñè- ìû è ñîáûòèÿ, ñòîÿùèå â ôèãóðíûõ ñêîáêàõ (2), òî âåðîÿòíîñòü èõ ñîâìåñòíîãî íàñòóïëåíèÿ â ïðîöåññå êîíòðîëÿ ðàâíà ïðîèçâåäåíèþ èõ âåðîÿòíîñòåé: . m ,..., 2 , 1 i ]}, x x , x x [ E { P ,..., ]} x x , x x [ E { P ]} x x , x x [ E { P ]} dx x , x [ X { P dx ) x ( н н i н н 2 н н 1 i                            f èëè , m ,..., 2 , 1 i , d ) ( ) x ( ) x ( j i 1 j x x x x j 0 i j Н j Н j              f f f ãäå ) x ( 0 f – èñõîäíàÿ ïëîòíîñòü ðàñïðåäåëåíèÿ ÊÏ èçäåëèÿ; ) ( j j   f – ïëîòíîñòü ðàñïðåäåëå- íèÿ ïîãðåøíîñòè èçìåðåíèÿ â j-ì öèêëå; j н x  – íèæíÿÿ ãðàíèöà êîíò- ðîëüíîé íîðìû ãîäíûõ èçäåëèé â j-ì öèêëå; j н x   – âåðõíÿÿ ãðàíèöà êîíòðîëüíîé íîðìû ãîäíûõ èçäåëèé â j-ì öèêëå. Äëÿ òîãî ÷òîáû îïðåäåëèòü ãîäíîñòü èëè íåãîäíîñòü èçäåëèé, îêà- çàâøèõñÿ ñïîðíûìè ïîñëå m-ãî ýòàïà êîíòðîëÿ, èõ ïîñûëàþò íà çàêëþ÷èòåëüíûé ýòàï êîíòðîëÿ, êîòîðûé ïðîâîäèòñÿ ïî êëàññè÷åñêîé ñõåìå. Ââåäåì â ðàññìîòðåíèå ïîíÿòèå ïëîòíîñòè ðàñïðåäåëåíèÿ ÊÏ íà çàêëþ÷èòåëüíîì ýòàïå – ) x ( i 1 f , ïîíèìàÿ ïîä dx ) x ( i 1 f âåðîÿòíîñòü òîãî, ÷òî ïðîèçâîëüíîå, íàóãàä âçÿòîå èç ïàðòèè èçäåëèå íà ïîñëåäíåì ýòàïå êîíòðîëÿ îêàæåòñÿ íåãîäíûì (äëÿ îïðåäåëåííîñòè – íåãîäíûì ñíèçó) è åãî ïàðàìåòð X ëåæèò â èíòåðâàëå [x, x+dx]. 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Åñëè âî âñåõ öèêëàõ îïîçíàâàíèÿ èñïîëüçóþòñÿ îäíè è òå æå èçìåðèòåëüíûå ñðåäñòâà ( ) (ε ) (ε j j    f f ) è êîíòðîëüíûå äîïóñêè îäèíàêîâû ( н j н н j н x x , x x         ), òî ðåçóëüòàò (3) ïðèìåò âèä: , m ,..., 2 , 1 i , d ) ( d ) ( ) x ( ) x ( x x i x x x x 0 i 1 Н Н Н                              f f f f . Àíàëîãè÷íûì îáðàçîì ââîäèòñÿ ïîíÿòèå ïëîòíîñòè ðàñïðåäåëåíèÿ– ) x ( i 2 f . Ïîä dx ) x ( i 2 f ïîíèìàåòñÿ âåðîÿòíîñòü òîãî, ÷òî ïðîèçâîëüíîå, íàóãàä âçÿòîå èç ïàðòèè èçäåëèå íà ïîñëåäíåì ýòàïå êîíòðîëÿ îêàæåòñÿ ãîäíûì (ãîäíûì ñíèçó) è åãî êîíòðîëèðóåìûé ïàðàìåòð X ëåæèò â èíòåðâàëå [x, x+dx]. Çàâèñèìîñòü ) x ( i 2 f äëÿ ñëó÷àÿ ) (ε ) (ε j j    f f ) è ( н j н н j н x x , x x         )) çàïèøåòñÿ ñëåäóþùèì îáðàçîì: , m ,..., 2 , 1 i , d ) ( d ) ( ) x ( ) x ( x x i x x x x 0 i 2 Н Н Н                             f f f f . Êîíêðåòèçèðóåì ïîëó÷åííûé ðåçóëüòàò äëÿ ñëó÷àÿ ðàâíîìåðíîãî ðàñïðåäåëåíèÿ ïîãðåøíîñòè èçìåðåíèÿ ) (ε  f :                 , l , l x , 0 , l , l x , 2 1 l f ãäå l – ìàêñèìàëüíàÿ ïîãðåøíîñòü ñðåäñòâà èçìåðåíèÿ. Ïðè ýòîì k=2 è l =2  ~ (ñì. [9]). Çàïèøåì çíà÷åíèå ) x ( i 1 f ïîñëå åãî èíòåãðèðîâàíèÿ:                                        l. l, l l l l l f l l l l l f l l l l f Н Н Н Н Н i Н 0 Н Н Н i Н 0 Н Н i Н 0 i 1 x x 2 x x , 0 , x x x , 2 / ) x x ( ) 2 / ) x x 2 (( ) x ( , x x x , 2 / ) x x ( ) 2 / ) x x 2 (( ) x ( , x x 2 x , ) 2 / ) x x 2 (( ) x ( ) x ( f Íà ðèñ. 2 ïðåäñòàâëåíû ãðàôèêè ) x ( i 1 f ïðè ðàçëè÷íûõ çíà÷åíèÿõ i . 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Òîãäà â íàøåì ñëó÷àå 1 p ìîæåò áûòü ëåãêî íàéäåí èç ) x ( i 1 f êàê óäâîåííàÿ ïëîùàäü ïîä ïðàâîé ïàðàáîëè÷åñêîé ÷àñòüþ ) x ( i 1 f : dx ) x ( 2 p Н Н x x m 1 m , 1     l f . Çäåñü êîýôôèöèåíò «2» ó÷èòûâàåò òàêîå æå ñèììåòðè÷íîå ïîâåäå- íèå ) x ( m 1 f â îêðåñòíîñòè âåðõíåé ãðàíèöû íîðìû x  : ) 1 m ( ) 2 m ( 2 ) m 2 1 ( ) x ( p m 1 m Н 0 m , 1           l f . (5) Ïðè óìíîæåíèè äàííîãî çíà÷åíèÿ íà îáúåì ïàðòèè n ìîæíî ïîëó- ÷èòü îöåíêó ÷èñëà îøèáî÷íî çàáðàêîâàííûõ èçäåëèé. Ðèñê èçãîòîâèòåëÿ 1 p ïðè ñòàíäàðòíîì äîïóñêîâîì êîíòðîëå ìîæ- íî îïðåäåëèòü èç âûðàæåíèÿ (5), ïðèíÿâ m=0: 2 ) x ( p Н 0 1 l f   . Òàêèì îáðàçîì, ýôôåêò äàííîé àäàïòàöèè ìîæíî îöåíèòü, åñëè âû÷èñëèòü îòíîøåíèå m , 1 1 p / p : ) m 2 1 ( ) 1 m )( 2 m ( 2 ρ 1 m 1 m       . (6) Çíà÷åíèå r ïîêàçûâàåò, âî ñêîëüêî ðàç ïåðâûé ðèñê m , 1 p ìåíüøå âòîðîãî 1 p ïðè ðàçëè÷íûõ çíà÷åíèÿõ m. Òàê, ïðè m=2 r=1,412, ïðè m=4 r=1,86, ïðè m=6 r=2,33, ïðè m=10 r=3,3. Ðèñê çàêàç÷èêà m 2 p îïðåäåëÿåòñÿ àíàëîãè÷íûì îáðàçîì (îïðåäåëÿ- åòñÿ èç ) x ( i 2 f êàê óäâîåííàÿ ïëîùàäü ïîä ëåâîé ïàðàáîëè÷åñêîé ÷àñòüþ ) x ( i 1 f : dx ) x ( 2 p Н Н x x m 2 m , 2     l f ).  ðåçóëüòàòå âû÷èñëåíèé ìîæíî ëåãêî óáåäèòñÿ â òîì, ÷òî m 1 m 2 p p  , ò.å. m 2 p îïðåäåëÿåòñÿ âûðàæåíè- åì (5), à ñëåäîâàòåëüíî, îòíîøåíèå m , 2 2 p / p ðàâíî âûðàæåíèþ (6). 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Ñïèñîê ëèòåðàòóðû: 1. Ôðóìêèí Â. Ä. è äð. Äîñòîâåðíîñòü êîíòðîëÿ ñðåäñòâ ðàäèîèçìåðåíèé è êîíòðîëüíûå äîïóñêè. Ì: Èçä-âî ñòàíäàðòîâ, 1975. 86 ñ. 2. Ôðèäìàí È. Ä. Àíàëèç âëèÿíèÿ ðàçìåðà ïðèåìî÷íîãî äîïóñêà íà ìåòðîëîãè- ÷åñêèå õàðàêòåðèñòèêè èçìåðèòåëüíîãî êîíòðîëÿ// Èçìåðèòåëüíàÿ òåõíèêà. 1988. ¹6. Ñ. 13. 3. Ðóáè÷åâ Í.À., Ôðóìêèí Â. Ä. // Èçìåðèòåëüíàÿ òåõíèêà. 1988. ¹ 9. C. 10. 4. Áîëû÷åâöåâ À. Ä. Ìíîãîñòóïåí÷àòûé èçìåðèòåëüíûé êîíòðîëü// Èçìåðèòåëüíàÿ òåõíèêà. 1990. ¹11. Ñ. 15. 5. Êàìõèí ß. Á. è äð. Èññëåäîâàíèå ýôôåêòèâíîñòè äâóõñòóïåí÷àòîãî àâòîìàòè÷åñêîãî êîíòðîëÿ ðàçìåðîâ èçäåëèé ìîäåëèðîâàíèåì íà ÝÖÂÌ // Èçìåðèòåëüíàÿ òåõíèêà.1972. ¹7. Ñ. 16. 6. Îðäèíàðöåâà Í. Ï. Ìåòðîëîãè÷åñêèå àñïåêòû òåõíè÷åñêîãî êîíòðîëÿ â èíæåíåðíûõ ðàñ÷åòàõ// Èçìåðèòåëüíàÿ òåõíèêà. 1993. ¹7. Ñ. 13. 7. Ëó÷êèí Ñ. Ë. Îá îäíîì ñïîñîáå ïîâûøåíèÿ äîñòîâåðíîñòè ðåçóëüòàòîâ êîíòðîëÿ //Ìåòðîëîãèÿ. 1976. ¹9. Ñ. 10. 8. Áîðîäà÷åâ Í. À. Îñíîâíûå âîïðîñû òåîðèè òî÷íîñòè ïðîèçâîäñòâà. Ì.: Èçä-âî ÀÍ ÑÑÑÐ, 1950. 9. Áîëû÷åâöåâ À. Ä. ×èñëîâîé èçìåðèòåëüíûé êîíòðîëü ïîâûøåííîãî êà÷åñòâà / / Èçìåðèòåëüíàÿ òåõíèêà.1990. ¹5. Ñ. 13. Ïîñòóïèëà â ðåäêîëëåãèþ 14.11.2000 Øóëèê Ïàâåë Âèêòîðîâè÷, àñïèðàíò êàôåäðû ïðèêëàäíîé ìàòå- ìàòèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ñèñòåìíûé àíàëèç è ÷èñëî- âîé èçìåðèòåëüíûé êîíòðîëü. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-94-36. ÓÄÊ 621.317 Â.Ì.ÂÎËÊÎÂ, Î.Á.ÇÀÉ×ÅÍÊÎ, À.Â.ÎÃÓÉ ÑÈÍÒÅÇ ÝÊÂÈÄÈÑÒÀÍÒÍÛÕ ÏÐÅÎÁÐÀÇÎÂÀÒÅËÅÉ ÄËß ÌÍÎÃÎÇÎÍÄÎÂÛÕ ÌÈÊÐÎÂÎËÍÎÂÛÕ ÌÓËÜÒÈÌÅÒÐΠÈññëåäóåòñÿ ïðîáëåìà îïòèìàëüíîãî ïðîåêòèðîâàíèÿ ìíî- ãîçîíäîâûõ ìèêðîâîëíîâûõ ìóëüòèìåòðîâ ñ óëó÷øåííûìè òî÷- íîñòíûìè õàðàêòåðèñòèêàìè äëÿ ðàáîòû â øèðîêîì äèàïàçîíå äëèí âîëí. Îïòèìèçàöèÿ ïðîâîäèëàñü âûáîðîì ðàñïîëîæåíèÿ äàò÷èêîâ, â êà÷åñòâå êðèòåðèÿ èñïîëüçîâàëîñü ÷èñëî îáóñëîâëåí- íîñòè ñèñòåìû ëèíåàðèçîâàííûõ óðàâíåíèé, ãäå êàæäîå óðàâíå- íèå ñîîòâåòñòâóåò îïðåäåëåííîìó äàò÷èêó. Ïîêàçûâàåòñÿ îïòè- ìàëüíîñòü ðàçìåùåíèÿ ñîñåäíèõ äàò÷èêîâ íà ðàññòîÿíèè l â /6, ÷òî â ñî÷åòàíèè ñ ïåðåêîììóòàöèåé äëÿ êðàòíûõ äëèí âîëí îáåñïå÷èâàåò óñòîé÷èâîñòü ñèñòåìû â øèðîêîì ÷àñòîòíîì äèàïà- çîíå. Ìíîãîçîíäîâûé ìèêðîâîëíîâûé ìóëüòèìåòð (ÌÌÌ) – ýòî ìíîãî- ôóíêöèîíàëüíûé ïðèáîð äèàïçîíà ÑÂ×, êîòîðûé ïðåäíàçíà÷åí äëÿ bxhUǟ~]u?]57h4GbT!J(QXXD iٲM[H@0"WQ AMAhHݻw{AQ|:yp-NDJ|"p%2/ٖ n2Ch>o~p"Ms X;m|paX/x>گL?j-.t9wIuE,܌lg< wr&bs? ~ɷ vP "^|uol-i;NOdoZvr}.?wZP'ڤ(^שּׂ6V6^'vN2dga#O`lZodȚMy>:4^DžFjZVVrgp#~&fwj?ărn-H>k3|2eq=u0ntȖ}-,@` \% {5)O#b\.R[1^׉U t/ۘ{3uQ_<ZUp 9Ĕ T*BpŸJ?Wv\=)SeIJUÉ^tE}b1hk snֽȺK_WSDKaI+$~=&.s৶ ']Ѡ1G,|3ʗ'nk8KWN"_DSaQjMM'`EM Ѐn ARRP *]1K#P$=Hԝ>}>c;a{csm3ߙd>%uSҧʣF}ՔL玹ښN߮fT>b֠ymRR͡s$Nt.}O܏4;a}Orד*|l/YT6swpLT*Y<\q۶{?^x:ucx:uMMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:58  H) HH(16]2]/H1X{rx UyϷdIƐh.K!0\ ZRtRABPD..i5Τ޴3jC)Fʌ0-_6 YrYl {n.MGg'ysynBX-8#/ >=9:^3&Bqůb!l8A`y>Q"DŽs;-pW(7;/9dM ajߠ̒ &GÎk_6Ҳ>C2TW9ӭ ' f npߔLЬ$٪\%(4"(MO J뀱*`-:7u,Bj?a>>ӛQEu}PۅmYP>M9:w_2:.zOIl@j+: w>cYXe%O\}iho,y2}Y S_{]o_=,,p󛖅XדJߖ~4v_ѷmLǦ\Y,Yqy2>.ˠ_4duY$@*XVnql?"7O1Ѯѿ(#kYRw?%&Y'~J~'৔gtӝO)SJ.U?E߶UGZ-9{Ja߄R|shaK6jExA`{Dy>-aZ 7^w+<PŹ] â[.ĹUyw{>dᩂ .+##:e>ȕ-[-N Ri,cIs?<_T/MST쇎7 t( `xY=_e sac hBݦ^;k϶X?KPڛG̋z`oP'J5%tA o}ӏ~ccӧX0`ȃF"U} n 4Run6'%(镸F ƘLV~Z* AKRoEm=Kvo!$wwVnS"|HbM ݰ6xF<ЉSmc]Gԑm蔴)oe!A >mZ:xl>'p}}@⭳]habvفhZ' ț/ ;t F y3e_r(%^cI#ܬm\e3lFvmUrE'- JAgb:2)=nՉEdz͗ϫ)<v$v⫳#糳I*7b;~U]s79i;9:B畓8'QZN~N?!=']>)Ie9 }$sƙgxA%vC wpuF8 G7s̈hHw{XY ~}qA# xO:b ȉGFx A>eS7xHf # 6аMCu!N }%.ReC!<-_]{T ̟{oAc*jh;=~;CYWORoV.h+\EcG:;N 8%?Prs9m dz :YAܤ p0{-k>~_- eჅ9܏1{o#EYA6De7{ &:[.,qLK\cox|1Dc&ɓ R}ڶ7F.qTCco_բ+_>$ttɩ wF\VNu/J )C݃|e7go{b{˴Vt5CcJk&nxaiXq3䡪@c\[D+|2M= s.-YNrU?gCs,<>eS}p~zoErafNS{噛㝖]xڡ,[Hg]V<%Wgu%u )g K:ſ1)8S5l3z^ޯӗyc?1y]!{=n8U8srhH:K8ɘ̃zu}9Ӏwj 9@p{l<|Bxq;0@vs<_~M窱:8уfژ3^6z؀;J>u ξ >˷ kWeӶL̃y|!7keGߔv|bGhR9}@]N,ϱ'tkY7b6Ƚ8;k$آrGܦN_aMS{JPq9]&U_BRLq;j5kjk=S rM:9|s +yyyj?H6=Cv{Uw&׶{Xu6}\4Gܠxa?{dv»BYJ{^OQ=ոogS>}~:MơGӐ [G /v^tA /v=}o{cӿYgŲ* ڪWgEC{-evY*2'N&Ϙi͘Xc.-.X6Bc\ _;.k'>\//r֫roz-e#ysB5?Av#n( _%~@:m|eg8F_#nݟ>̉5F1$X@qׄ;S:{|Q}Y"Nݜ85ƍ#O{>~mG5S? qI=O]Xknl.9skdXoKNS\;\*xY}٫*2'M 9 <=2ot0G%pd^[*s%n5 H^/ u@c=*juD⾐|b=$*kvk~n)uE-Q\ֶSeumXu`<%IenhO( !w,y9}gd g8h䀱l:w r :bb ^ б(ql˂y{@Gǖ=1s-t?s|Bw@6].j\*yã=,n%.# },ݗc״i*ق ܜKjI`֟WۉG>C::Gwv.-s.8.KZS`t--a zK/m-ʸۜ06کY}em#4́+wpu%=e[q#NE{瞗'O%(LZg޺s< $3}CFvC7m?`?>{'ZӲ[SG>vxx+x lnN^Nut.zwthPbWJ {9~7thn{#އK}D+[gEKW![l݊Y"WAy&OO$XoGm2Wz෬FA:m@Jj;G ' 2DŽ[Pe^wz𥳐 w' S'ܗߋ7_xڶ=Wqw; eSgΝw?Vܚ3ε97݄4E&ٔ>TyZqDx]M }+@u頻A_= C `/xG_PҾFAY܎mS&s*'JɿylRy_Oo]O>?\9/)ޞ̙|$o],>*'R=n1,oȍTX'<+Q 7:p'Ck|y,ؾCr^Qk{䯕5?`KǨr W7o\oWI.7}ʩ3{B>sqrpՍ/o0;ݜD~~cGi˒A75G_Ǟż;q©!}%BI{>y/a/@<3J<%}->Kxˠj>/˱\DxFi>zl0FSI#-?.m mpo-eYg#Ɩ=x9?ɪco;1N}D6mCީ7g{p D=vX4Nлud][ШCw1<4ck3e"|s3}1o>TxŎ ;b Wh+\pu6&^k~_%k!OD=7$Hmد<>MH}g\~9otMgԽ]oX9Cgݬwp--A</|gLǼCɳ2Սd˯^6|J⭳â=cSKFQj4ϊ{3k`w:a:):U @F!/)NB8g`^|/5BM̳34uxb"`hGϯBz%A67-G+ʈ7Ns#<7L|m;lM$Rk :d=AO~-AD]]zF.O_ϗQF;jX"[tAN佳N |ǟ%.҈|GCY_f^Kq`9&~xk_.gVDU9>]NnR)Ը=C-N'E?gX{Q:!mUsn+%9}##wx sR ;!K ^X#%m<ϧ&u8BCD.}E28~^-yӇ1­mg]*:mp?,~ͷ;|xC?${.Ǣout6B?]rznSGgH >B_UCLb[Ao>/U|>G8.?]m,.ɔ08!;k,EVߊavؠXm x w⒘t~gd؎mؾǀsaLBv ?}|S;J;H2}spWguqQDdS [z({;1ӍphpDRzDj;y/fݬ< >>yi X>]ZV:y7,>IYyYv ̇Z 96\[gD#ƾElCߜ{YN"nɿbKPD FHj۰f{b{dZMI?˅@؜1i;gP7!%mkcCr040vS𠀻/FB69em3nu;sd>uP/ߗ5-L=WEH1Ie' _lw'gkn*iWHBe%3q⬎; &Y+mlB n>/Z)^3O4ƠP1i3&~eSr`tvN\.o 7s[1)]ڱb+ -='2}S>ɪNDhSӍ׎X;8It+dqD %mבe?72s9o<'ϓ0>\Ŧ=3YbƦR)ha Pl?r -՛dtӜu~j pH7n5(ַKtgtA:4:4J~A;eٴЇP]y2''`[J}:\ߡ\^w9{Tү /<ܟZs=YW!Rylx!a}{I!Cu~iOKE&4GO!=l+eѾFm$W^o7&uicH8=|{pO]ۇoZ9_l|azx{Nxs/^I9uK+~f~$pw~S([nx7}덷ƉgЧ5=4)Y<_m {`:uwx`z^]}ɾ5ߠF2*~D9s?gnu|e|e%\)yQٕqoιwVWdp[|5⥐T~.k{ +Nܼw}a꡵ci+j|sXry#MJI<0|Y}FoدO.l(efX2FT՟qɟ~P6=TU;Gk AaH>ϳd1>|U{l/lg{Tx&('^9G5|U\AX.oOI%кqVVڣFIe~gd|ˏ'y~@^rbK4۴3%(a;'O[A>~_:{N'Ӂ5q+,E楼GEGV*Qک"[Zcs8%_9غ5뙲1:F)DzWΞ4_R?ٹwL=b۔GccŘ($l Σ;\dg],n%:Lp ;S2S~ޮjN^MgJ++Sׯ*wu3%<}j:G)w~j?5^fM53R~^셾m/lg{,֝uNT44]Mg"ƮG)gY{"8=Kq/vCJC+]8ZW%zhu|K{h?s&g>ݨ'#g>2Hyރ~OwUǞ-Pdگ  vﳫmwcqPiu>&ƒxުp]=FI,,95 èçìåðåíèÿ ïðîõîäÿùåé, ïàäàþùåé, îòðàæåííîé ìîùíîñòè, êîìïëåêñ- íîãî êîýôôèöèåíòà îòðàæåíèÿ, à òàêæå äëèíû âîëíû. Ïðèíöèï äåé- ñòâèÿ ìóëüòèìåòðà îñíîâàí íà àíàëèçå êàðòèíû ñòîÿ÷åé âîëíû ïî äèñêðåòíûì îòñ÷åòàì ñ äàò÷èêîâ, ðàçìåùåííûõ â ïåðåäàþùåì òðàêòå. Âîïðåêè òðàäèöèîííîìó ðàçìåùåíèþ äàò÷èêîâ íà ðàññòîÿíèè l â /8 äðóã îò äðóãà â ðÿäå ðàáîò óêàçûâàåòñÿ è îáîñíîâûâàåòñÿ îïòèìàëüíîcòü ðàññòîÿíèÿ l â /6, êàê, íàïðèìåð, â ðàáîòàõ [1,3]. Îòñóòñòâèåì åäèíîãî ìíåíèÿ îòíîñèòåëüíî ðàçìåùåíèÿ äàò÷èêîâ â òðàêòå ïðîäèêòîâàíà íåîáõîäèìîñòü åùå ðàç âåðíóòüñÿ ê âîïðîñó îïòèìèçàöèè ðàçìåùåíèÿ äàò÷èêîâ. Çàäà÷åé äàííîãî èññëåäîâàíèÿ ÿâëÿåòñÿ îïðåäåëåíèå è îáîñíîâàíèå âûáîðà îïòèìàëüíîãî ðàññòîÿíèÿ ìåæäó äàò÷èêàìè â ìíîãîçîíäîâîì ìèêðîâîëíîâîì ìóëüòèìåòðå. Êðèòåðèåì îïòèìàëüíîñòè ñëóæèò òîò ôàêò, ÷òî ïðè íåêîòîðîì ðàñïîëîæåíèè äàò÷èêîâ ïîãðåøíîñòü èçìåðå- íèÿ áóäåò â íàèìåíüøåé ñòåïåíè çàâèñåòü îò èõ ïîãðåøíîñòåé. Ðàññìîòðèì íåñêîëüêî ñïîñîáîâ ðàñïîëîæåíèÿ äàò÷èêîâ, â òîì ÷èñëå ýêâèäèñòàíòíîå ñ ôàçîâûì ðàññòîÿíèåì ìåæäó íèìè l â /6 è l â /8. Êîëè÷åñòâåííîé ìåðîé îïòèìàëüíîñòè ðàçìåùåíèÿ âûáðàíî ÷èñëî îáóñëîâëåííîñòè [2], ïðè÷åì ÷åì îíî ìåíüøå, òåì ìåíåå ÷óâñòâèòåëüíî ðåøåíèå ñèñòåìû ëèíåéíûõ àëãåáðàè÷åñêèõ óðàâíåíèé, îïèñûâàþùåé ìíîãîçîíäîâóþ ñèñòåìó, êî âñÿêîãî ðîäà ïîãðåøíîñòÿì ïåðâè÷íûõ ïðåîáðàçîâàòåëåé, à ñëåäîâàòåëüíî, âûøå òî÷íîñòü. Êâàäðàò ÷èñëà îáóñ- ëîâëåííîñòè ðàâåí îòíîøåíèþ ìàêñèìàëüíîãî è ìèíèìàëüíîãî ñèíãó- ëÿðíîãî ÷èñåë ìàòðèöû À, êîòîðûå ïðåäñòàâëÿþò ñîáîé íåîòðèöàòåëü- íûå êâàäðàòíûå êîðíè èç ñîáñòâåííûõ çíà÷åíèé ìàòðèöû À Ò À [4]. Êðîìå òîãî, òî÷íîñòü ìóëüòèìåòðà èëè àâòîìàòè÷åñêîãî àíàëèçàòîðà öåïåé çàâèñèò íå òîëüêî îò ðàñïîëîæåíèÿ äàò÷èêîâ, íî è îò àëãîðèòìîâ îáðàáîòêè îòñ÷åòîâ, êîòîðûå ïîçâîëÿþò îïðåäåëÿòü ïðîõîäÿùóþ ìîù- íîñòü, à òàêæå ìîäóëü è ôàçó êîýôôèöèåíòà îòðàæåíèÿ. Äëÿ îïðåäåëåíèÿ èñêîìûõ ïàðàìåòðîâ ñóùåñòâóåò äâà îñíîâíûõ ìåòîäà àíàëèçà: ãðàôîàíàëèòè÷åñêèé [2] è àíàëèòè÷åñêèé [1]. Ãðàôîà- íàëèòè÷åñêèé ìåòîä çàêëþ÷àåòñÿ â ïîñòðîåíèè íà ïëîñêîñòè êîìïëåêñ- íîãî êîýôôèöèåíòà îòðàæåíèÿ ïåðåñåêàþùèõñÿ îêðóæíîñòåé, êàæäàÿ èç êîòîðûõ ñîîòâåòñòâóåò íîðìèðîâàííîìó ïîêàçàíèþ äàò÷èêà, à òî÷êà ïåðåñå÷åíèÿ ýòèõ îêðóæíîñòåé äàåò èñêîìûé êîýôôèöèåíò îòðàæåíèÿ íàãðóçêè, íî òàêîå ðåøåíèå íå ñîäåðæèò ñâåäåíèé î ìîùíîñòè.  äàííîé ðàáîòå ðàññìîòðåí àíàëèòè÷åñêèé ïîäõîä êàê áîëåå óíèâåðñàëü- íûé è ïðèãîäíûé äëÿ àíàëèçà, ò.å. ïîçâîëÿþùèé îïðåäåëèòü íå òîëüêî ìîäóëü è ôàçó êîýôôèöèåíòà îòðàæåíèÿ, íî è ïðîõîäÿùóþ ìîùíîñòü è äëèíó âîëíû.  áîëüøèíñòâå ñëó÷àåâ ñèãíàëû â ÌÌÌ ÿâëÿþòñÿ êâàäðàòè÷íûìè ïî íàïðÿæåííîñòè ïîëÿ ( èëè ëèíåéíûìè ïî ìîùíîñòè), è êàê ïðàâèëî äàò÷èêè íå âíîñÿò ñóùåñòâåííûõ íåîäíîðîäíîñòåé â ïåðåäàþùèé òðàêò: , ) 4 cos( 2 1 2              i пад i i l Г Г P k U ^$x{Luǟ"r!3VL*( KZ[c]d-Wj0x9dzfx9PesS 6T#ђv^M~ZDmwj]k E6. ؏G-&nnb_R9ցs!r'aΠ?F1u@t1jiO.x#V-W_%[z7K"*(žZt]fѿN{ͩ%|8spqZypr4z|هR\Yk=3nzQ,f0=ӳ؝ipT'?OpFiM3HqCqT7߬)wbN;w p'N9kݥ p'N;w @Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:58  ^ "(16R2/1.{px VUༀ2[(`znRsES P0MckfWiŽ kZi:"aqsΞƴg֞}~|osn>ݧs<@\窯v.:8W\;PY)C*x`1UiapnMnf+.R]\G+Asv!ws#*٥f;=_gэѤ{坮azRn˩$NWÒ/T1`7B#&)EJ"E10t\uI) hJw^WS>KEJkU _=r(orVٿH+EMr Ouڟ?=#.<ŲjP;`OzL7i}ktYlK (K]V{Y,lz}|Cs0tȍ|is{TRM۶5jii.=27Pu8>oKr.lڲ"o6j=)GYWt|ql|ys&~'ma\STxlP/0c#}ɣGymlSp`!QDJ;0C$dd+RسiYHJ̷>ZSDmY}CfIwmksQZ'nlkdR{\эQA&df "/M=ʭNޞ W`?1 ٽJUq`b^%f^`ؚ6u`o*lV*{#HZAv넻:!D3=')Qe>ISi:xM]=Ѧ{#P>L6(>mkzF~hrg7(NK%:=!GcT6Qt.$*UZ+o_u kTJ6KGh->: # v@i$_آM  afAȆ D9et@9 $%6 Hб~uO;OԁyԠ*qN/'T6A!lh&ZlވS#U>W"c [SzX:ioUb I"Y ̞-OPnC:H (^h\ų#_t38ж>x@Mpbקmt.u1zRQzVق=ޤ:@Mm҂qM K7~(#9>ș7ɗޡa2@LJzc@WE.4< 1++` ~m^VC<^ƨ>࣑}C~9Cdv ͖&'9e*ϠiEh-=0K=]}Zn^=]m. f-P+*gM@帷ܴ AkTa%KwwMp& .j/"o-SU&V/Z"&+&OKm. Q.YYVDUk̠i֯[c\%#r23z6Sml[ͮV#=per4wpo"%p>]x-iD(3=;BqdJ^*2EOwshU 蝸;0 ?](Z藔^"/7 uZ!*n~dlVYVw-db&O+ ?НX)Y %]bCcvIYD,Q q{@N]Ό&r>-hx'-S۔zxs+Ue-* Y-Zc9J|=Y%31#Yy&s_}<,i^m|G+ 91>/OOmc9<g%}/r4*?Ks>! %~yN@9]菑gu֜G!ĎI[3>K2Nf&)b'|+16`(RhcP>ҧJVrp[sG7_(e}0==/N) pO^so{5U!}}IǪ]>#/Hmc׶AdǴc3KBZ3qXn+^1eQx%,ܛk~iqq)ՖԯTCzSvmk=9'sxڙmM;Q̝W]ۚXEUohQΏ>oТ)o!<ރZ|z@3п,K0~۝!>Bx>+Gzf8K?{'A}+;qVbL)]/Pgz%卟닥/V?ߪ8F&IxI-}]'Tt 4b̫k}vD߶ #~Lz `9Nѯoszc%oxJ;o~t6 +|}X~[ 퓥,qwd#Ķ[%='z;$Y=x0bBEX\ ɞ1f">G~zZ=鲾*3^֯rjkEU>u\OtJ4~ >sZXyOJ=,+fh#WfǧKr9T\ .R{&Ll.K9erEN9 >.uxU>Ph =x )czG`}.^:8Lϲ;Zʰ8K4K:^}h4ƅuA[|׽ׇ^Qn\x]ȂS?mlRs*9g؞ROZ\JcaXWo}EK {:o0Z9w#)J(f 3m@KgrޯAaO#&D 5) ^wwM]8Mvȴܐ~{~`YYd 񲇷Px o\x!dBrK!l/d> vC|ݦkH;7ʇBubmH.> %K/$_zu_K!>Яgg4%g}Oy8 ٧/Cx!?gBwNb$[mYzB)tU ͧToTO鹧/zOA6_6flwukY~"eM]P>ޯj<;/o{vw;ι%l|:ґ*w粁u\^%<@%Ů=x{(>zy:ŧ<ț}2}mQۋ쳵M?6أ=`ar釮> רwFV?鯝[2z<:wJ'G˱]|Zͽ7TӕWR:FUI%owʻ}T$.CAћ-Gı|tߤ5׊]{\e%MR/k $i`9|}|!\< h4}9-`]ښ"ϔ85WEcƁ=Z8#FB>KT0/Wc$-dmjF_!١|e_دTFB2\ 9Vx"D.|Tb 5L/E?<_`Ex9N}I?_9gEX)nXfE*1F~K:Wn1UeÔGK*-L6ѻ?ns՟Q*KW(fq=xd8vS^1m(ִ?e_#nw;2n}G)a]qi#yREe:a]L (~x𠗇RCv/%.˦?hb9c^|>Bx>_ɏsP 9tZ%OvA~:W^_@Y>F(v,)TKfdi;&] M  ihYLƒ^ڗgT | g9/Ss|+8oFަluƕZŲXl\ϗ&E8USu8]b) ć^,^,^vC|GϛmF>8nH۾2|;]_<;yxi{ ov0^_ovC|v0]|%ï.IQo3x~/Cr^H.Y\x!ݐ\|Ox!>x!>x!>|n_Tl$Vs~n2=R);O* ˟jO[[Ã7CPѴ<ؓJxfwHL%o3ؠJO.OmܛW)]:oP-Qy\UX?Ngڝ-^y.O9rd6W}CN'y9:E۸6>"|YuohvsӾZlvv3~l7DYm+ѢQIIyq]Vq?$K~vĶmU \~&'mcK-ԍnA1Z},u(#u5ۥl|cm|=|L+s 9~F4ӿV\V*A vM=ՏW$Vn%|,5d y#Wr}B/7Y[l1u)%SϨT.}> XybIڙ,_ݐ\wL ?$|Z8]wc;K}3- 'ǏUgm1I+@?4ER?"%:_\R}`EKo }`EWD?<+`%BFGϐ#=2omSlq}ׂ_̇$>دQ{gN܀oGi"[">F=ʀSN(R& p n8fgFgkA{%KdXLHt#+-IiGzM!=5 ƯmLߪ);d?uJ<)'U^2?֬T: 2J~YMq ۡ,rⱖ1dAg&%|?K}3#+u`=m}Ue1M9gȂWV/qU?WQ9GJֆ'xAN,<ӇCXSE9ǎgDc?Oʑ ߧetPihguHS#L{m3~{ oy4(Ǟm{bИw{b3c}yho7;-krR-c![o=)ϳEB?+rݑUђiOl:荋1WX{,,Z 96 ãäå Ð – ìîùíîñòü ïàäàþùåé âîëíû; k i – êîýôôèöèåíò ïðîïîðöèî- íàëüíîñòè, ñâÿçàííûé ñ ÷àñòîòíîé çàâèñèìîñòüþ êîýôôèöèåíòà ïðåîá- ðàçîâàíèÿ òåõíîëîãè÷åñêèì ðàçáðîñîì; íà äàííîì ýòàïå êîýôôèöèåíòû ïðîïîðöèîíàëüíîñòè ðàâíû, ÷òî ÿâëÿåòñÿ óïðîùåíèåì, â äàëüíåéøåì ïëàíèðóåòñÿ ó÷åò è ýòîãî ôàêòîðà; à – ìîäóëü êîýôôèöèåíòà îòðàæå- íèÿ íàãðóçêè, ïîäêëþ÷àåìîé ê âûõîäó ïðåîáðàçîâàòåëÿ;  – ôàçà êîýôôèöèåíòà îòðàæåíèÿ íàãðóçêè, ïðèâåäåííàÿ ê ïëîñêîñòè ïåðâîãî ÷óâñòâèòåëüíîãî ýëåìåíòà;  – äëèíà âîëíû â òðàêòå; l i – ðàññòîÿíèå îò i-ãî äî ïåðâîãî çîíäà. Îò êîýôôèöèåíòà ïðîïîðöèîíàëüíîñòè k i òðåáóåòñÿ ïîñòîÿíñòâî â ðàáî÷åé ïîëîñå ÷àñòîò, êîòîðîå ìîæåò áûòü îáåñïå÷åíî ïðèìåíåíèåì äàò÷èêîâ ñ ïîñòîÿííûì êîýôôèöèåíòîì ïðåîáðàçîâàíèÿ. Ñèñòåìà òðåõ óðàâíåíèé, åñëè ïðèíÿòü çà íóëåâóþ òî÷êó îòñ÷åòà ôàçîâîãî ðàññòîÿíèÿ âòîðîé çîíä, èìååò âèä:                 ), sin sin 2 cos 2 1 ( ), 2 1 ( ), sin sin 2 cos cos 2 1 ( 2 3 2 2 2 1          i i пад пад i i пад Г Гсоs Г P U Гсos Г P U Г Г Г P U Ñèñòåìó èñõîäíûõ ëèíåéíûõ óðàâíåíèé çàïèøåì â ìàòðè÷íîé ôîðìå , sin cos sin cos 1 0 1 1 sin cos 1 3 2 1                                         P P P U U U i i i i ãäå P=(1+à 2 )P ïàä ,  P=2ÃP ïàä . Îáîçíà÷èâ . sin cos ] [ , sin cos 1 0 1 1 sin cos 1 , ] [ 3 2 1                                           P P P x A U U U U i i i i i ïîëó÷èì [À][x]=[U i ]. Äîïóñòèì, ÷òî â ëåâîé ÷àñòè äîïóùåíà íåêîòîðàÿ ïîãðåøíîñòü  U i , òîãäà è ðåøåíèå áóäåò èìåòü ïîãðåøíîñòü  x, ïðè÷åì, òàê êàê À(õ+  x)= U i +  U i , (êîýôôèöèåíòû ñèñòåìû ñ÷èòàåì äëÿ ïðîñòîòû àáñîëþòíî òî÷íûìè), òî À  x=  U i . . , #&xlUǿԦ-@Y BmPfI9Dd9#t²⏈e 3tdfN$.Fm("Qe,d? =>Ͻ {˖,7y}{}ߞR1I-Hl(mH !}R {*jFMB8\-~`+jk`"Bjɔ~@iB[{3fʹ' X =l䲓hGw<Z5ܦw\~_cѧn/>b5e{ZMn.!MGrWt|5|-)ۣeb{{zssT33$J^?z ŒchIxkh m_M<=b[VcU Y9qopf¿tkOc6.v[{i[r<`,#qs?9XSV{+׳W|Yy%f٠)"6_Yf)m~;ԭ&u/}K^޾hXsu+l)؟.[Ll-me #3/$aoW_~ףm] N9U.t:>5{3糸<|iU2v91xO_5_aךs/n׊dlvX۩gݫ~o'1Ϧo1ǺuaU7RKHH(P>ʛ Ǜ^xqVSb' :;՛DN_:u*m{>x%FNΧvP3~D!2Z*~+aoiv6LdMK[s*r(\N?ړc/i<_D"nV# E^Ylict.;[~'7ڛ6/?݄ߥig3 Ƕb z?O=;:OjS s};Z}>o:v<5`t.K}A{fW#wY=e<˺gkl_Qv=Co ?s68R3ƽjS[Գ/X[gzuۏ? 5nvqD,3p5 `7OxV|)ֳM ``ZLm>^wZΧZ42Fn\Kӷ5/ZǶyt֌㜯OǶ}'N'm{NIɘGs+wrmf~Kd㗻r!F~CTϤ~HQ$[Q$`(T:#|^Ϗs_k>}_cyKHHHHQ:- ;RMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:58  nz #^f(162/` t1{x ^Uu$$ɀXnÈ A$%bѦ:`A$,Y+؅UQbm+J{'@s3g|wv9{>{ϹNCaa!|OQ!|`!k!B淿%0o&܂BXv@Z'',f+%0?d•hFἊ?U_jW*#5.,-@y*pPTu M_ r8JL+,! sMPv* ho߾\RY. )#0&R&_= (]2՝'_+\,=r\X]5uQŽ_#[m@9V9p+'9a/ 377qsNhI+Ayp-9&Cj99ש͂[Jv2-vݦǛÌB޷[ 1mۅW۾b:b?֦f .\1jS5{D-`zWYB;@* ox#Ԓd36g7??KL)rJAJgS *%}ʩ]*SNڟrjiOS#j/SSv &uP{_7bX۳v}^9|.Xzʳ ;t|?ՖyfW/h\R+Ry!9Q\y(|Y|Z9ab?_/;EƃC{]!էY?al-…zsZQ,Pg~s9E;T^;\D$|Lʑô}z$#bf&}t_{(h;ʾ |t95>& ˯V^\xҲ7{B{Dح yݒEZ5sqYoRq}:V~ji#ˆ!<`=ϑT>S1Ǽ9՞?m$e;N]t.bv//kv/@+ {_Zl'i= $ᛮY*>ٵb%Ư6vM{q(l#늻n1_ƌ#M#t~<_',YՆ?VT_SY@Uqxz"Ccf~ y_~y1k;鿱/>_ߵ5ZT<9F_Ÿr<9kGϸ{Hkz8)ݖ-UɳΖCGTsC/Rf`o _'Ri!}1qziܡbΙrD_db7_iLZ0l+t]hlu>.އhMwS ΂ճ荂L?}ﳄrmSyz9ZSGW~6ۦ p=shY̫C;\莼ł WIɲLhTx"WCwؽJ?:ݒ9.mpNSeѲ0.$mK{5fRm ;dIFqYc킝Q [.y XV>ճ北*>3v2RIPS 0=CI9C% y536$8B\?&oBp<{sDۚ5 4"Sah7csNƘnsSxlRnunMsމ\y,/C.v3s~vޟTw n|eB+H<mZϔޮ} F>`>\#Z)bV1eWioy8N0+Rb]K_/͋Ƀg IV 8Vo% Gݪ~-'~F~vrxc|+UoUgv ȉYYKzOmsٶ]|`O;iL@ۦ=Gdx m,o>O~#Rç wx|BH)*3?kon KekL35bz󟙎q' }vc?2u9o-_fyƸq)tA2M'<2723?:G.L@'o49m_/*~AiJzϔkj܋fo\{V]"6d7_ۋy< g;#ogezR_)xRi#6!+ wxH|mLݖl>$^2kYoct[{{cjmRS;XSd ɗcyq~^!e|Lu.СwV+Bƽw!t z֦<|G st%Z&-|y Ľ*Sg5*Nԟ>% nS{ղ>G]l9AY&4d_Umf|c0?|A_wM^mh8i*S6\"8\2yz>ppP՟׆c{NTdd)K_yH1>ۈ5k><@&`NW]B|J(Ĵ{e^2#+0:QvD| @Gmx+}qvO03JgTJxo_W=;Cwkn^kةg߻7 2.D9ꢼ+yw oifF' w%\5.2(w4 е94:JNDN?JL^*}ؗw7?w`5-/"?i.MC3uF,}nywjV]0n;4jޥv^_ŗʣz }U|7P*j9~]^-gW#7JbZMqڭ~n=!-u؅v{T|9 ?U1gWcj7f!?cq܎ ߗ3$ zT.4=4K|U(UWՏ-v)Jμ?xD e~C^US]1UՏUWՏ2_U?RnU?R}Ez֪K=]u|dzOU(>~A2kKjgtQ׏$^l÷P[ eyupvV ɫ~2R|U<{>t%>u~ͻUwӓ>[WSMί}xߴSAO>pMV~zNyMwt J~b\MU觮~p74u17VkCʞ,}ey|6kԍg ZЩ ψV*sT.cei3|(6?Q2q3I q}d QJ>σLAzsT~O{OV )E2 ɳLhw D7-xc mu_ +m*>g{'1jsC0&Hngό#8o;<.7 =0Nr)y9lC?C%+Ri&8_>cn^'$o 7YU>Cegވ9`Wo1;\7fɃd许,~'ER^GeR6i xdRƾv6:)iRW~/~]po2okb9 rs m˸/vLpţ%%B5xRQ^NeQ˯HI,PoV"gʫT6o抂6{r& :JkG =D?|Oj@wѯ w7}4+(8C_.{/6]?n#Kkho'MU(vRߩa /{7SyM)xMeoL7h})1-'pkdcrRk| h˚Sot{"558ѓ}Bu%==&@݁;Қ]k>]z;'unzQ8rաHwTZQ2<rQMs|jt|k ~BL~GEp<"8_/vF?rn c1)UƄEKkdal2H= hmCmGD#&!3T2R+=7h!d-[#Em lwkc_ACh׎=Nw -eKʞwucwLe}|2FND~&6M&|g@ȲV9|" :'tӕBlO?/M+E,/Hr_7y>VӯVP!\UVV-#3+F3sZC}. ˂*rc+Rv=glE}R&C~mXAϐ6I)[G| o=3vh>,op EKٜSi+֓Gʙ{ }vzmS?϶FcU`o>.%y7A~jJ h/?q18NAW3#ƟJ~V)-xy/k8)c<؎|قDt16|٦И7jlढUg ,G]ϯHI,P-|wѼi "Ts "ء3)AACx %=BWl_>C;sT*f}oGUweОy9Gt\gtVuhobo9ؽY{'Txfp{t ڛaoﯱ7ސNH|rۛOzzJk鿭[]Xۛ7ҽu^N{ z ށޕc/ukӘGߛ}ŷ7Q fo~ױ7z\veu/݃yco)]ތ}:VAyV>8.kLhdLTːKZnSʾ}Yrby;.\Yv~ﯤPyk(>[E?o@^ t|J4QoԑmN99OSO[;S*>,oOw(Ǘ:EכsnO-9_N> {ro! ͍-zng>Ïim;8v(rHLڂz<$OG:EnZdy"9F[mO!. V9Ռ5dy[ů1;2&.#bJd멟攞mY؇>?~HayLyn~dZxb&DNZ>mA^޼<||Ǿ<)6Z_2h:+}|ߴ\Pïko_Wp@3U0ol=߶s<'z2}blӿN_jp`K›eEB}9NüG&e|G}x[z9ۦhW_)j _~Y8teh޳b SѨ ^Yh衡W, ~;GJ'%E7Jv{HfIK%;CCUʎD{.Y:o;{'9ؚGLv֙X1{㽃/>o~E`;c?McLG(O{N Oq]3HVV`hX' הVӊ)*d{O`d_wыzJ'ﶕCͱ 6plWoX'/ؑ4E%]h4Ҟ}j_.kk̃k&PϊvpU|@).77_Ix7l6c~'m562ڿRI`ہ| /xIF@]=2#O}F=˦^[+|vv Agg𙒱^2SXɯ^@bxyACJ&)e^X#'sחNT*,fޙCޫB9 _kj='l.tΒgv>y1FjIǔAc|y'^w Z<1&[>dg||~ڄ;UU> <$;lܩu7XilaSp^K󚔽=)6Й汭(*#:P;[Pf/|"2)w=R#Mau_+9קJb\'4Vkh 7^w/dm?#x/zUڧ9q~|]e<7z|PovfO?g˶w˷,!S2A>#۬r&lIµ??2 |uqK^݉+E8L}`|ߵ;1e.`{Û;0FI#2v!B7&&q!mcg^Rdg}tO129z&Y2^Z6寄;^U[䛕|ȑg8/yz6% {z ([b*yCx?aCB С B3;d}М=[ OJ_ڟ U=K46jJam L꧍E.+Jl~챽r|ˎSwo2]m<^l7)g褔?@þx%>>4P6?t  =oKeN_V \:>+J=]L!b؃~2_;9yƈǗO>#9@zh,,797 Îòñþäà , 1 i i U U A A x x     ãäå çíàê  – äëèíà âåêòîðà, || || – íîðìà ìàòðèöû, À -1 – ìàòðèöà, îáðàòíàÿ À. Ïðîèçâåäåíèå ||À|| ||À -1 || íàçûâàþò ÷èñëîì (èëè ìåðîé) îáóñëîâëåííî- ñòè. Åñëè ýòà âåëè÷èíà, êîòîðàÿ íå ìîæåò áûòü ìåíüøå åäèíèöû, áóäåò áëèçêà ê åäèíèöå, òî ñèñòåìà ëèíåéíûõ óðàâíåíèé íàçûâàåòñÿ õîðîøî îáóñëîâëåííîé; îòíîñèòåëüíàÿ ïîãðåøíîñòü ðåøåíèÿ òàêîé ñèñòåìû áóäåò áëèçêà ê îòíîñèòåëüíîé ïîãðåøíîñòè èçâåñòíûõ ïàðàìåòðîâ ýòîé ñèñòåìû. Åñëè ìåðà îáóñëîâëåííîñòè âåëèêà, òî ñèñòåìà óðàâíåíèé íàçûâàåòñÿ ïëîõî îáóñëîâëåííîé è ïðè åå ðåøåíèè îòíîñèòåëüíàÿ ïîãðåøíîñòü ìîæåò ñóùåñòâåííî âîçðàñòè. Ñîáñòâåííûå ÷èñëà ìàòðèöû , sin cos 1 0 1 1 sin cos 1 sin 0 sin cos 1 cos 1 1 1                                A A T ëåãêî âû÷èñëèòü ñ ïðèìåíåíèåì ïàêåòà MathCad8. Ïðîâåäåííîå èññëåäîâàíèå ïîçâîëÿåò ñäåëàòü îäíîçíà÷íûé âûâîä, ÷òî íàèìåíüøåå ÷èñëî îáóñëîâëåííîñòè, ðàâíîå 2 , ñîîòâåòñòâóåò ôàçîâîìó ðàññòîÿíèþ ìåæäó ñîñåäíèìè äàò÷èêàìè â òðåõçîíäîâîé ñèñòåìå l â /6 è â ÷åòûðåõçîíäîâîé ñèñòåìå – l â /8.  äðóãèõ æå ñëó÷àÿõ ÷èñëî îáóñëîâëåííîñòè èìååò áîëüøåå çíà÷åíèå: äëÿ òðåõçîíäîâîé ñèñòåìû ñ ðàññòîÿíèåì l â /8 6  , à äëÿ ÷åòûðåõçîíäîâîé – l â /8 3  .Ýòî ñâèäåòåëüñòâóåò î ìåíüøåé óñòîé÷èâîñòè ðåøåíèé. Ñðàâíèâàÿ ýòè ðåçóëüòàòû ñ îöåíêîé ïîãðåøíîñòåé êîñâåííûõ èçìåðåíèé, ïðåäëîæåí- íîé íàìè ðàíåå, à òàêæå âûïîëíåííûõ â [5], ìîæíî ñäåëàòü çàêëþ÷åíèå î íåäîñòàòî÷íîé ýôôåêòèâíîñòè ïîñëåäíåãî. Òàê, â [5] ñäåëàí âûâîä, ÷òî â ñëó÷àå ïðèìåíåíèÿ òðåõçîíäîâîé ñèñòåìû ñ ðàññòîÿíèåì ìåæäó äàò÷èêàìè l â /6 ïîãðåøíîñòü èçìåðåíèÿ ìîäóëÿ êîýôôèöèåíòà îòðàæå- íèÿ ïðèìåðíî â äâà ðàçà ìåíüøå ïîãðåøíîñòè èçìåðåíèÿ ïðè èñïîëü- çîâàíèè ÷åòûðåõçîíäîâîé ñèñòåìû ñ ðàññòîÿíèåì ìåæäó äàò÷èêà l â /8, ÷òî íå ìîæåò ñ÷èòàòüñÿ äîñòàòî÷íî àðãóìåíòèðîâàííûì. Òî÷íîñòü àâòîìàòè÷åñêîãî àíàëèçàòîðà öåïåé è ìèêðîâîëíîâîãî ìóëüòèìåòðà çàâèñèò íå òîëüêî îò ðàñïîëîæåíèÿ äàò÷èêîâ, íî è îò àëãîðèòìîâ îáðàáîòêè îòñ÷åòîâ, êîòîðûå ìîãóò áûòü ïîëó÷åíû ïóòåì ðåøåíèÿ ñèñòåìû óðàâíåíèé ñèãíàëîâ òðåõ äàò÷èêîâ. Ðåøåíèå ñèñòåìû ïðåäâàðèòåëüíî ëèíåàðèçîâàííûõ àëãåáðàè÷åñêèõ óðàâíåíèé ñîñòîèò â âû÷èñëåíèè îáðàòíîé ìàòðèöû. Âû÷èñëåíèå îá- ðàòíîé ìàòðèöû À -1 ïðîèçâîäèëîñü â îáùåì âèäå, à íå ÷èñëåííûìè ìåòîäàìè: \"x}hUǟݖz7^nz'{[:l˚)h-eV#_0IFP$DQތʖًKPV)I%-y'ݹ!c.|>o9y"yzȌT (D^Ґ< o g"<)m#u5T72T-}gvSAgHUgF;_KO2 VOlPENXVGD^}~Jb,Hx#*x{d=@2^  3~_*d6|?O.bYZ]'$W%&Hpx ZI3OB/6`ۙG24T$I2=MtsAo1ۤ!\w$ꫣ$[kB߃2Y:O1&K693(媭q/^uIF֭"+l$G (Lr YGͩ2Rjo@F{[vT&\$e>L!`x_m:Vl:B4rCփJM-Q G yri|w 1 (?է6˚X_F|'-dS+=ˏ5f:|@+L2~gxc?7ԁ蝵Aw| |{;[1\Uɽ!Bx}pZ<֘\>@.Prye/zE6[Jk?#؅)b_%q~~Q{l,|R [{~ʔ`(X::S5<He·pfvΐv A&\ EN}4W_7tT9V&Dyӿ` hq{lx:{\8wTbqX%81X7L`O EV+W_dYZg '#y 6G֥/7W6^u\Ug'6? f};i-%@ɺxe2ʐ6Ά~ka¶  4g(vg? 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Äëÿ ýòîãî ïîòðåáóåòñÿ åùå îäèí äàò÷èê (ïÿòûé). Êðîìå òîãî, ýòî âûðàæåíèå äàåò èíôîðìàöèþ î äëèíå âîëíû êàê arccosq. 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;bQjj)_!GـiW/rɇ9c䘪9.7ˇdNN&'b+ܱ9u|hM]:/F;uu9:.<ݑC%ҷ5Sb!cGgfpO>S7׊09<|8[ߓ)]UGyǤ/ߛto?o_'Wws~`l[WދO+X+|fR;>8ryo}@gmBg]:>?z\l1{>>7,FOWmC._0m_i=w|t|k?#TBrm9K8'_Lg>@}Hʬ&f1aݍ7[xUcXyshW}_Ӏ֙8 o~](:?q]Xo rn/]>[t{#r*<\SlZu}<-Y:22k|  p̞|;Uo-c/4 ;د>Fߠͥ{ =t)hNilvOWɟ՝ "jWd԰>3 >}q; MY~xVӷowE;_o;U~e.`"Z'\'=p09szoex3Q05劥ayN_u>k9r&_295@#F(C;yM>}\v:w}o~Wv?;U\% G u]wસyaBq7Š=ky8шY=k/9 EpexJ Zx0?tN_ng]r=hg}J9zц_-(4(xV~תlr~ڗ /;ZXMe-3WϲkZIZ%^,x^Y,33ގ(K6aZa$F|=H#ߩY~.zHc x~{N̗:|^ڂiF;^ _fþG|,$:Y_dy4tZ{U{?Br~)?t+5koоӿW#9/!+>e-ELe:)Ι`8Xg|afChkc m\G[X:ec.٫(9:{D ,n"+e=ЍU l} ;1U9p's>Ȕ9k~n'>9x^.zsw:U`k7PJ#qR>^qwErR{N $?K|ܲZU{OSF ;jdC[ ) O;opJgaZes|Gy_NpVJg{%6C6ԽNk*ȂY{#Zek x hA§e@a-Эy.1#8oK[+ ^hH_ū/kkkwԔٹoϷ o\= 1pN&ۮ̓ۏGٿ;a{<;7'As}1m_˻/du :e 0>.}RRn?[>LJ^p͒-oq.Msl>"}K>ɛ\A^|oԡ؀7!o̹ʶŎk:Z%λkEXKsG}<''rg\ìtzۧu;rμH_QJs77P> u9S` vVu<8^g=xcuёiuU )7|PXA>D*po:yKx_&ߦ%V&R >L}_r+Is؀|c D{m3PxZ#c>"Oy,@@ gΞ#r—Y:|\%;K>׋~_wNs)gJ9y-~mȾi ?+>^-)t[=_>K6yZ6ׇ1voڎ(Ǻ~}q,o2nk>tXq`xa;whJv ٿD϶|[^}Db4{$|*ecN[EmV&n<ߓWZ'3?S[l=5^C|Ez퐥ؘ>9mm/@3ַdžd\0}Z&ׅ'8S(_Cy?,,100 ìåòðîâ òðåõçîíäîâîé èçìåðèòåëüíîé ëèíèè // Ðàäèîòåõíèêà, 1990. ¹95. Ñ.72- 79. 4. Êîëîòûãèí Ñ.À. Ñèíòåç ÷åòûðåõçîíäîâîãî ïðåîáðàçîâàòåëÿ äëÿ àâòîìà- òèçàöèè èçìåðåíèé íà ÑÂ× // Èññëåäîâàíèÿ â îáëàñòè àâòîìàòèçàöèè ôèçè- êî-òåõíè÷åñêèõ è ðàäèîòåõíè÷åñêèõ èçìåðåíèé. 5. Öàðèê È.Â., Ãèìïåëåâè÷ Þ.Á., Âåòðîâ È.Ë. Âëèÿíèå êîíñòðóêòèâíûõ õàðàêòåðèñòèê ìíîãîçîíäîâûõ èçìåðèòåëåé íà ïîãðåøíîñòü èçìåðåíèÿ ïàðàìåòðîâ ÑÂ× óñòðîéñòâ// Ðà- äèîòåõíèêà. 1989. Âûï.89. Ñ.108-113.6. Ïàòåíò ¹.20427À, G01R21/04 (Óêðàè- íà). Ìèêðîâîëíîâûé ìíîãîçîíäîâûé ìóëüòèìåòð / Âîëêîâ Â.Ì., Èíäèíà Î.Á., Åâäîêèìîâ Â.Â., Îãóé À.Â. 7. Ïàòåíò ¹.22620À, G01R23/06 (Óêðàèíà). Óñòðîéñòâî äëÿ èçìåðåíèÿ ñâåðõâûñîêèõ ÷àñòîò / Âîëêîâ Â.Ì., Èíäèíà Î.Á. Ïîñòóïèëà â ðåäêîëëåãèþ14.12.2000 Âîëêîâ Âëàäèìèð Ìèõàéëîâè÷, êàíä. òåõí. íàóê, äîöåíò, âåäóùèé íàó÷íûé ñîòðóäíèê êàôåäðû ÌÈÒ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ýëåêòðîäèíàìèêà, ðàäèîèçìåðåíèÿ, ìèêðîâîëíîâàÿ òåõíèêà, ìåò- ðîëîãèÿ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, (0572) 40-93-31. Çàé÷åíêî Îëüãà Áîðèñîâíà, àñïèðàíò êàôåäðû ÌÈÒ ÕÒÓÐÝ. Íà- ó÷íûå èíòåðåñû: ÑÂ× èçìåðåíèÿ, ìåòðîëîãèÿ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, (0572) 40-93-31. Îãóé Àíäðåé Âàñèëüåâè÷, àñïèðàíò êàôåäðû ÌÈÒ ÕÒÓÐÝ. Íàó÷- íûå èíòåðåñû: ÑÂ× èçìåðåíèÿ, ìåòðîëîãèÿ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, (0572) 40-93-31. ÓÄÊ 681.335. 001.53 Þ.Ì. ÒÅÑËß, Î.Á. ÄÀÍ×ÅÍÊÎ ÌÀÒÐÈ×ÍI² ²IÍÔÎÐÌÀÖI²ÉÍI² ÑÈÑÒÅÌÈ ÓÏÐÀÂËI²ÍÍß ÑÊËÀÄÍÈÌÈ ÍÀÐÎÄÍÎÃÎÑÏÎÄÀÐ×ÈÌÈ ÏÐÎÅÊÒÀÌÈ Âèêëàäàþòüñÿ êîíöåïòóàëüí³ îñíîâè ïîáóäîâè ïðîåêòíî-îð- ³ºíòîâàíèõ àâòîìàòèçîâàíèõ ³íôîðìàö³éíèõ ñèñòåì óïðàâë³ííÿ (À²ÑÓÏÐ). Êîíöåïö³ÿ áàçóºòüñÿ íà ñèñòåìíîìó àíàë³ç³ ö³ëåé ä³ÿëüíîñò³ âèðîáíè÷èõ ï³äïðèºìñòâ ³ ìåòîäîëî㳿 óïðàâë³ííÿ ïðî- åêòàìè. Îïèñóþòüñÿ îñîáëèâîñò³ ôóíêö³îíóâàííÿ ³ ðîçðîáëÿºòü- ñÿ ìàêðîñòðóêòóðà À²ÑÓÏÐ. Íàéá³ëüø âàæëèâèì àñïåêòîì ïðîáëåìè ï³äâèùåííÿ åôåêòèâíîñò³ óïðàâë³ííÿ ñêëàäíèìè îá ’ ºêòàìè º îðãàí³çàö³ÿ òà àâòîìàòèçàö³ÿ ³íôîð- ìàö³éíèõ ïðîöåñ³â [1-5]. Çá³ëüøåííÿ îáñÿãó òà ñòðóêòóðíî¿ ñêëàäíîñò³ ³íôîðìàö³¿, ùî îáðîáëÿºòüñÿ, âèìàãຠðîçøèðåííÿ êîëà êîðèñòóâà÷³â àâòîìàòèçîâàíèõ ñèñòåì ³ âèñóâຠâèìîãè ïî ñòâîðåííþ çðó÷íèõ ìå- òîä³â, ìîäåëåé òà çàñîá³â çáîðó, îáðîáêè, çáåð³ãàííÿ é âèêîðèñòàííÿ ³íôîðìàö³¿ â ïðîôåñ³éí³é ä³ÿëüíîñò³. Àíàë³ç ðîá³ò, ïðèñâÿ÷åíèõ òåîðå- jxLuǟ`8A`t'.v ҡcs56p-tZv f-7Z9]k,tYd٪;s'nlU~y>; %Un G%k.%2^9UUX8<>Ȍ%4X* @o Ue.<г0M081_Z0tO:=ߋ*_&tf Wz"ۜ;iSx [5;s  ngod);5Eix-[S9YA˿Q魔חʗ)GrVcj->9~d>:g&}{eTs*+Ѽ">F8ø-sdo!&K:K@F>'7qY0X :Tl~hOc/kaB꼆݆̗|V\96ΐrxK<w}Qre Q7_KT[Ѿ{A%_L|.ɓnM{=a^Sꍠ;_ FMρ|2~ '*]~Sr |c_J!cA/8NYWLY@Aɑ`#`%x,mh({> Xػ{Z? 68|lAb+ .OV֮uQ׏G]u7yM/;FsY`rdp):SraS0,fGYr>K8;A3S ϰk'r^.G/?/gyPDN;ÚS+j *#v .%^wsװ=Ajz(B߇vlأte HX |'ЁwI3'&ǒht}$~:r~m>VEk9U3Jok>km,Sՙi_VS>yw4}GHd}WYiT4>U-%{"J3{6]ݬZ?WM{p'N;w-[޴;w LoMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:58  | dlt(16Գ2 /18p{Ux}GUmЂó M[TeR5r .X" Ii1E!@b .!! `[`Dn˖]ei|~|}gg̙33{μ=0 =aDO<i/S> ~Waiaxsm):SO?t>aZ4eNó;e|xjaR;_:mI?SGOeN E(ʧP~]3+GwU U~'=M.-eԿ:Vs&E(ӅFcuYluE@_+2iyc.=|`pRhJ5LGL#8=rpã~sYxpְ[|Cv>odQWwK/yUû 3g]5 3lWU3mc跼r瘧-ՏDVLno->\i>y>jњ{|g^u-ͷGgl)G O<|Jӯ=c˶">znG?VQ).>џ?룫57TQu_-x|tOp?7k  ÁCa_nQV~ֻJ׏{$V{Q=Uwz!w9ëskg=Jѓl"ІͶQ7[^{{~꣟ JR}L :$G)N~W9}[Q1Tr߿rbmw.)"|o#nwԿֆjߩB BJj'#Jœr%ްUV1{x7 Ϯcc3:d#G?LkEG|SڐyK -9XxO/N kk*({dmJ徢c#BmNZϊx8Wggifg|~KUΉ؂r#%ۧde+|g+^^kk&{x,Uwc[~pTի_>/U#KJphկv%i';4ͻ|EtvTc:{9vu0"ԱudP}Q7zI~6&"k_U~Ư%c0qKagi'}xrQI +yIɘ[+<'lRR"H!wTKH㴷w.jc=P\3/s^,6xl{K#>F7[wRn:^70]]jbS6=,ޥf{nIc2:S'(\X|n#\t-V}nqg*ռ˛?̧Mtȫyt/2{gR#=G_ccNh'O&e3c C4㕧tIWr}lah9,Β].?Ysws>毪ze#{9{Y~2t9 %{.{6SVLWOWjn4C.mnRux3)RןfǠmE1`ye쑗^os|S \v+1mXdN(r6{[)qn>}x,`aT/?F/G P!{+owY+j,vQ}xWDI>6Gƚw݋Lcpc`ƖpK"9R&+׆n$7'!g-3ye ׼I*LJMŻxE'm5ڹkoXD|<?JU'?)Jd2p`\+].?bξ;bG>,n ,cK1!'otHSCY)RZ+޾e;x/Ev]u%:yG։R%Ϳ+v6k}x=16NS؁,{e}i[mmxK/m#xWwC0޸ԧp[8ZUX38{I^PpSu3vvWQ !m?*;]jpHWY뜷m6b/)["رWڐ! FJ]Ց.NX/^io '.7&%9YVS5+Ţ_ ȉR_߈dJCidъ]Sb=c?iT6>\7?erЯo} Ȩk) d`|R?b9x864/Ox;]oxV%}0/ 9%W2N^]l~AC_9m[*Fo'۱?[+;wSfgbf?vrM'mJ2y/tcwSWw[aDZxcD\t[Q0QFu )T2ɔ[ڒF{{:%ɬ9>0r69 wI.>&포BPrsPjkuraZe{a{mXSP&ɋ:47WRom3;n+bod'cC6}3rګ/DC',G<~=2n:^қ:I>uR;׏/dkcڭsy_v!U^t{wbF1)+B;^vۼC+/U<>b+Pi:`j[IEJ#|֓IW}t{(wO,?_rQڻgUon }JkwXV׆7EϦqNNp2weu'Gd+kin(=Q~`>gDW"OGƠ܏#sçOݢxd`|wN1^B}x3 f^Kw!ҶVo~kr'+<&#֧Wf+o-r>Tv`MŎcS|vGqGLT"CGdfKy讥=S>u9IŻdOb<t&~IQ{D1k([~8n Eޛ~ &u)w*7kMJ{y)'=ex]DRuˣO:}f8a=75xuNV}0KZ_%ۯy0-?;Yk}Eb{O{ɒNѻF[g);扩I}[A6>Mɋ0mM;O(X|͸;kё])@)txx䗋O+9.㘝KjL!197~|kfLog]4Uϵnw*k}OWvwgvn؟N|KӶV!n/b$xϹLA>_:L;z>m[ uڒ'mCy4%?rA,,}+E% ٿN*މ~Dn8<ά(~evGp"W0Y{ 4fi{Oqoe9 q7f[9؅{?`w" 󆡎lyc`Gu@J:`ҏi xRP?fud+hr:6}IznSt{Ffl`η(1M2ؗ}=܂'C^#rQ/6)ӗ^?ɦ-BFҕZ ?w`ޯm б~ϯT_3][7̠v=vYCg=bWȲ?$n",_;|m[FrA~#+O6c\Ӷ)%7F{B>=Tzu?zZE_'nk9O{ |Ŏ =,q s2l9>X˳:փ)%YDF~fP3,|ҿz4 yrCR7OxrQbre滄v[㶛Ky޾_9Axtv62(̟mg;<0bs7tiǞxtЧm,}{m3F.>&EiҴk\7Oq{w3Wz9oo:6.b6ў;-}Ge_wkl#gyĞmR&}/l ^9ii?IiPVG03Y'OÇpJO?:P wGOO{j|jL&~{K[x;F{gcߜsmm5yi)obM[1"s~/>DM{޳C}Noyuo?;=ߙFO-=/*WT`K߷A]aeqb{ g|XݥŻdʋgw2|O"$ފ| NRwW*/巏wKO >g-Ϲ([ĄTI>F޹@3*|MX%oHw}&'UO?ѥ 7흫g0Ւ]鷪ν=Ǵa{o'vs. |/dfSw%pO7xv[b.L*ٞ2>aCyi@<|+z^%վEz{]ɓ3gՓ~ _D}@v=x9d ji{tiK65[sN TpZyI=ꓒ^6 ʳmz?cFd_Ɠ1HW=s^'kbqM. @׾B7֍8|*dc,cM=R߷]#i~2ڦK\k~2ȮTKm=zjP \rd1^yھ5¢^K$o.ş3elF[vd][ymt*,ezG:ExU2y3vWwN_"E'v]̯ݽjglYV;=?_PG۱޹Ӆߧl6d2p@?rY"ӷ&E0wb?7![)x̳\J!~^VoTݢXzkwG1ommY=Q|u be؂.x>q+z}W=]pK6x>aL WV+'uNypt5iCKNut_t~ꠓQWb/Y[oٓ=`+NcWglGk ?~/(ډPp%Gx"K2?ZǛ*)ogq\Hq#Vt~ީ8}k:soqM`h-6Rfke2R.qB6&?|b\`ԣ=}(|Sɗ 큕f[3Y8|F3,,101 òè÷íèì ³ ïðàêòè÷íèì ðîçðîáêàì â îáëàñò³ ³íôîðìàö³éíèõ ñèñòåì [2-5], äîçâîëÿº ãîâîðèòè ïðî òå, ùî ðîçâèòîê ïîíÿòü ïðî ñèñòåìè àâòîìàòè- çàö³¿ ðîçóìîâî¿ ïðàö³ ÿê ïðî àâòîìàòèçîâàí³ ³íôîðìàö³éí³ ñèñòåìè çâ ’ ÿçàíèé ç äâîìà îñíîâíèìè ïðè÷èíàìè: 1. Áóðõëèâèé ðîçâèòîê ³íäóñò𳿠³íôîðìàö³¿ [1-3]. ßê ê³áåðíåòèêà “ ïðîéøëà ” øëÿõ â³ä “ íàóêè ïðî óïðàâë³ííÿ ” äî “ íàóêè ïðî çàêîíè ïåðåòâîðåííÿ ³íôîðìàö³¿ â ñèñòåìàõ óïðàâë³ííÿ ” [1], òàê ³ ñèñòåìè àâòîìàòèçàö³¿ óïðàâë³íñüêî¿ ä³ÿëüíîñò³ “ ïðîéøëè øëÿõ ” â³ä àâòîìàòè- çîâàíèõ ñèñòåì óïðàâë³ííÿ (ÀÑÓ) äî ³íôîðìàö³éíî-óïðàâëÿþ÷èõ ñèñ- òåì. 2. Äèñêðåäèòàö³ÿ ÀÑÓ [2]. Íåäîë³êè ÀÑÓ ìàëè, â îñíîâíîìó, ñîö- ³àëüíî-ïîë³òè÷íèé ãðóíò ³ íà ñüîãîäí³ äîáðå â³äîì³ âñ³ì ôàõ³âöÿì â îáëàñò³ àâòîìàòèçîâàíèõ ñèñòåì. Ðîçãëÿíåìî ñóòí³ñòü ³ ïðèçíà÷åííÿ àâòîìàòèçîâàíèõ ³íôîðìàö³éíèõ ñèñòåì â êîíòåêñò³ ïðîáëåìè îðãàí³çàö³¿ ïðîåêòíî-îð³ºíòîâàíèõ ñèñòåì óïðàâë³ííÿ. Íà ñüîãîäí³ äîñèòü ïîâíî ðîçðîáëåíà òåîð³ÿ àâòîìàòèçîâà- íèõ ñèñòåì óïðàâë³ííÿ ï³äïðèºìñòâàìè ÿê ñèñòåì îðãàí³çàö³éíîãî óïðàâë³ííÿ [2]. Ìåíø ãðóíòîâíî ïðîðîáëåí³ ïèòàííÿ ïîáóäîâè ³íôîð- ìàö³éíî-êåðóþ÷èõ ñèñòåì ðîçðîáêè ³ ðåàë³çàö³¿ ïðîåêò³â (²ÊÑÏ). Íà ñüîãîäí³ â Óêðà¿í³ ñòâîðèëàñÿ òàêà ñèòóàö³ÿ, êîëè ðèíêîâ³ óìîâè âèìàãàþòü â³ä ï³äïðèºìñòâ âèêîðèñòàííÿ ìåòîäîëî㳿 óïðàâë³ííÿ ïðî- åêòàìè ïðè ðåàë³çàö³¿ áàãàòüîõ âèä³â ä³ÿëüíîñò³. Öå íå ìîæå áóòè ðåàë³çîâàíî íà áàç³ òðàäèö³éíèõ, íå çîð³ºíòîâàíèõ íà óïðàâë³ííÿ ïðî- åêòàìè ÀÑÓ (ïðàêòè÷íî ïîâíà â³äñóòí³ñòü áëîê³â àíàë³çó ïðîåêòó, ñëàáêà ³íòåãðàö³ÿ ð³çíèõ àâòîìàòèçîâàíèõ ñèñòåì ïî âñ³õ åòàïàõ æèòòº- âèõ öèêë³â ïðîåêò³â). Ç ³íøîãî áîêó ³ âèêîðèñòàííÿ ²ÊÑÏ íå ìîæå äàòè í³ÿêîãî åôåêòó, ç îãëÿäó íà ôóíêö³îíàëüíó îðãàí³çàö³þ á³ëüøîñò³ ï³äïðèºìñòâ. Âèðîáíè÷à ñèñòåìà, ùî îð³ºíòóºòüñÿ íà ðåàë³çàö³þ ñêëàäíèõ íàðîä- íîãîñïîäàð÷èõ ïðîåêò³â, âèìàãຠðîçðîáêè íîâèõ ï³äõîä³â äî ïîáóäîâè ñèñòåì àâòîìàòèçîâàíîãî óïðàâë³ííÿ, ï³äõîä³â, îñíîâàíèõ íà ïðîåêòí³é îð³ºíòàö³¿ ö³ëåé òà çàäà÷ óïðàâë³ííÿ, ³ íà òðàäèö³éí³é ôóíêö³îíàëüí³é ðåàë³çàö³¿ ñèñòåì ð³øåííÿ öèõ çàäà÷ (ðèñ. 1). Òîìó ñïðàâä³ åôåêòèâíè- ìè â óìîâàõ Óêðà¿íè ìîæóòü áóòè ò³ëüêè àâòîìàòèçîâàí³ ³íôîðìàö³éí³ ñèñòåìè óïðàâë³ííÿ ðåàë³çàö³ºþ ïðîåêò³â ó ð³çíîìàí³òíèõ ãàëóçÿõ íà- ðîäíîãî ãîñïîäàðñòâà – À²ÑÓÏÐ. Îðãàí³çàö³éíî-òåõí³÷íó ñèñòåìó, îñíîâàíó íà ÅÎÌ ³ åêîíîì³êî-ìàòå- ìàòè÷íèõ ìåòîäàõ, ïðèçíà÷åíó äëÿ çáîðó, çáåð³ãàííÿ ³ îáðîáêè ³íôîðìàö³¿ ç ìåòîþ åôåêòèâíîãî óïðàâë³ííÿ ï³äïðèºìñòâàìè ïðè ðåàë³çàö³¿ ñêëàäíèõ íàðîäíîãîñïîäàðñüêèõ ïðîåêò³â, áóäåìî íàçèâàòè àâòîìàòèçîâàíîþ ³íôîð- ìàö³éíîþ ñèñòåìîþ óïðàâë³ííÿ ïðîåêòàìè (À²ÑÓÏÐ). 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C7)L]^_ϝ_71״]u^[Rw[xͫzҫ/vz: {ȑh/=뽩=Jr<>/'`G6' 3V\򁘕kqLoA[䵧]c]_5~ªć=cǃWBO]_sOS{eC=Q\*{eC;#23/YiO$o J| 'Pj=<+~03lgZI _/+6ybb~MU~EV SrBVZ+ճY픜B쯓NWh?yz]s9sCYyUbxN4ί9۴s''6 c^+?Hf#_ R> l>2"Gbj4.W*-Yil>[ڨ˯[D_wׅ5ïϙk14_ wu{|+~,JG.ѯIlyuܜƹpa@ Ა춌Z6K2k ֺ/_ֺi}voNAqe1z _~$:Y o5Xҡ(929>>3tdvїKю~T,;=WlHA͇O1# ;|X {ors3dFx想1fZbWjȸo`Dkw)%- uMχgfoL`>>$·yvϛl`RĻ',pg_vQpz Vg~xĴsfۯe` _X"8*W'2Suԕ=<2^p+Ғu)sY07~mҰ& o140% M+ѾŝW3ԍX5[S'c(̅Re:dqq岯Y|Y @~=q')̅χwqda9J/lcGRhB;?լ DmOgK QjpN?O7lFU;޷"k/lU#zU\`ℍ+_!KLFJ^JO?i>ߺ|g㭧.Zn IHrnO]i_<[9ç!$`dp2vo +\õq8}Gځqa>Kـz\yi3/̤=ut|-%_zs/_Jºw+s2ٞQ3xVۧډd;S8QMy||+`eƅzZk 'ةUd>X܅6 j[ =y-/-bWOEGU\T;YӤ{FL0Θ&%cRI(-Ö:8j搸 uʇؠ/*];l]zd_B[oO럇wIdC_0N{Xٛ/zќ |t;!Zfrt'n ۽# 'G\XfRJG 65wv⑩}7s)]:ec<=kzUPTU_|îvR辐'Wm7F3|!,5a |' g-Xvckw57ؐ].,ķgg\Ypx/1ߚgD=ُ^+pDo;;zRG=>i}DAHby|[ȺOqWZT q!_^=#VOʔN!ж|ū:yZK^_&{^|,vo@O޵8Iw.:>g՘ VWcԘ*ɒ3H}l_3 u7o=Yi}8_n8to<[Ii~oK~):q~t{K}z.:u4)~<=y(:[u_ ~&7/ 5O)ïmY+]ZSţx`SJQ=3Yb]ub͡z)jߜ!W<}C/8}sP7E4{qWUZ5F5&gr a [^;%5͇k܇{Ixj-SM{']uSh+i_gԬ|rV,f٭IմmoL㭵xdJڧ§Sgly|1r8_m.Yr%KQ.*S/LIZ ?|{ }7ᱹj0٧'ox;#OϙN[a8Ģ}.I,~_s{ScQwGx/켱-_p}yg%#N~y'#okN:Ǜ2k1Ce _ʓSV/0+tN!EtW|oOad-FAKN_JVr[NS;9AqoF=ʬgq+vmV{k';i߶6ܶh-Gg4^RGYO=}a\J&]z՗fz>vC!U/cݳl3xax"jq{/P۝;N^j|Lk~wn.{"Uٴ'<{_qqV)֟ <Ñcs6‹] }|%cn釲aQ_e^φrِgB/3^W~^3yJ+m}<\ڻ%=p2h7{ϫ9kkʾ5V?g pA\#}e8Y^y{]G^=}D1t6ɩ/y)jC?<;,4-f">1ׅ-:~}}6ٛچ1T ;:o5Vx;]1 )]GR` )LsxGv&>zt4X'ᗬ]mմv !pPN6{kOX{3ub0a\:}Va,%#eG _>(Փc /6kΘ)-;ZLuSsY eѝ?{T~$WO{jd_f_*o^LvFcsJa?32Lk \ճ#2<ʕn}O޺^ۣo=G+W[Tqwx>}jX><>W7ϧwNk/\<[[ᙢ4kN>zgKN+?ݸyܧv0~1;> wo?:BaV|s$j2?aΕnWةm>n0lW,yѷ1㗇,:e>s1VY'}` ,}Ql\xK1yWpUu(_-+_W|8F{)z6d?dNy}?@HpADCJ~95|]?o~Ӽ=3m/FyªC#U0/:RT:eI Cymcs^p<]2+UWkV -_,qS>_Exόbht^,u{gv^#į7*1v/+ 8ä9(\J^ G9+<+ k~[RU:wLvEv½*l͝3udm|"ezt(o #|6,8Wuʦv8tk\-c ڣ 6ˏ&9苝>~yX+jm3ndnBSk ;z%Wz''ʪ6_T[Rg:8`gh='Cm>N@lȿ:q;=ÎurZAkkX¢gX}Sب7G!ۈ/UJϜCW} 跲գ:>ծ:੓||c>vAx !JbV G%/l8+ڞ(4=..u=ޓ:y+aWwF=-5>2^83Qґa~=x:t,CȡjS}ɲ_{5nm]ܭUp2u;HA`?鸯&l&/wsG1rTtLm5ʭQ3F}Ƨv"owIw| c70*_1ny)F>T*OMcA\W,~]_NI`$;˫v7k/WqG駔pq\4f?tJg,fg5,,103 1. ²íòåãðàö³ÿ â îäí³é àâòîìàòèçîâàí³é ñèñòåì³ âñ³õ åòàï³â æèòòºâèõ öèêë³â ïðîåêòó. 2. ²íôîðìàö³éíå çàáåçïå÷åííÿ ïðîåêòó ÷åðåç ãíó÷êó àâòîìàòèçàö³þ ôóíêö³é óïðàâë³íñüêèõ ñòðóêòóð ï³äïðèºìñòâà. 3. Ïîäâ³éí³ñòü ìåòè: ïðîåêòíà îð³ºíòàö³ÿ – óäîñêîíàëåííÿ óïðàâë³- ííÿ ïðîåêòàìè; ôóíêö³îíàëüíà îð³ºíòàö³ÿ – óäîñêîíàëåííÿ ä³ÿëüíîñò³ ï³äïðèºìñòâ. 4. ²íôîðìàö³éíà áàçà – ç óðàõóâàííÿì âñ³õ åòàï³â æèòòºâèõ öèêë³â ïðîåêò³â. 5. Çàäà÷³, ùî ðîçâ`ÿçóþòüñÿ – çàäà÷³ óïðàâë³ííÿ ïðîåêòàìè ÷åðåç ôóíêö³îíàëüí³ çàäà÷³ ï³äïðèºìñòâà (îáë³êîâ³, ô³íàíñîâî-åêîíîì³÷í³, ï³äãîòîâêè âèðîáíèöòâà òà ³í.). 6. Ðîçðîáêà ³ âèêîðèñòàííÿ – â ðàìêàõ îäíîãî ï³äïðèºìñòâà (çà- ìîâíèêà àáî âèêîíàâöÿ ïðîåêòó). 7. Îñíîâíèé êðèòåð³é åôåêòèâíîñò³ – ìàêñèìàëüíèé ïðèáóòîê ï³äïðèºìñòâà ïðè ðåàë³çàö³¿ ïðîåêòó. À²ÑÓÏÐ íå º ³íòåãðîâàíîþ àâòîìàòèçîâàíîþ ñèñòåìîþ, â òðàäèö³é- íîìó ¿¿ ðîçóì³íí³. Âîíà íå îá ’ ºäíóº ³íø³ àâòîìàòèçîâàí³ ñèñòåìè, à º óí³òàðíîþ àâòîìàòèçîâàíîþ ñèñòåìîþ ç ÷³òêî îêðåñëåíèìè ôóíêö³ÿìè çáîðó, çáåð³ãàííÿ, îáðîáêè ³íôîðìàö³¿ ïî ïðîåêòàõ. Öå àâòîìàòèçîâàíà ³íôîðìàö³éíà ñèñòåìà óïðàâë³ííÿ, â ÿê³é ôóíêö³¿ ïðîåêòóâàííÿ, íàó- êîâèõ äîñë³äæåíü, åêñïëóàòàö³¿ â³äîáðàæàþòüñÿ â ò³é ì³ð³, â ÿê³é âîíè ðåàë³çîâàí³ íà ï³äïðèºìñòâ³. À²ÑÓÏÐ ÿâëÿº ñîáîþ ñêëàäíó ³ºðàðõ³÷íó ñòðóêòóðó, â ÿê³é âèä³ëÿ- þòüñÿ òàê³ ð³âí³ óïðàâë³ííÿ: Óïðàâë³ííÿ ïðîåêòàìè (ôóíêö³îíàëüíèé ð³âåíü). Âèêîíóºòüñÿ ð³øåííÿ çàäà÷, ïîâ ’ ÿçàíèõ ç ìàòåð³àëüíèì òà ³íôîðìàö³éíèì íàïîâíåííÿì ï³äïðèºìñòâ (ðèñ. 2). Íà öüîìó ð³âí³ â çíà÷í³é ì³ð³ ðåàë³çóþòüñÿ âèìîãè ñèñòåìíîãî ï³äõîäó äî óïðàâë³ííÿ ïðîåêòàìè, ó â³äïîâ³äíîñò³ ç ÿêèì âñÿ ñó- êóïí³ñòü ðîá³ò, ùî çàáåçïå÷óþòü äîñÿãíåííÿ ö³ëåé âèðîáíè÷î¿ ä³ÿëü- íîñò³, ðîçãëÿäàºòüñÿ íå ç ïîçèö³é âñòàíîâëåíî¿ ³ºðàðõ³¿ óïðàâë³ííÿ, à ç ïîçèö³é äîñÿãíåííÿ ö³ëåé ïðîåêòó. Ïðîöåñ ôîðìóâàííÿ ³íôîðìàö³éíèõ ïðîäóêò³â ïðîåêòó ðîçãëÿäàºòü- ñÿ â ðàìêàõ ä³ÿëüíîñò³ òèõ ñòðóêòóð, ùî ¿õ ôîðìóþòü, íà íàñòóïíèõ ð³âíÿõ À²ÑÓÏÐ. Âèä³ëåííÿ öèõ ð³âí³â ïîâ ’ ÿçàíå ³ç çàëåæí³ñòþ óïðàâë³- ííÿ ïðîåêòàìè â³ä äâîõ îñíîâíèõ ÷èííèê³â: 1. ßê îðãàí³çîâàíà ðîáîòà óïðàâë³íñüêèõ ñëóæá ï³äïðèºìñòâà - ðåàë³çàö³ÿ îðãàí³çàö³éíî¿ ñêëàäîâî¿ À²ÑÓÏÐ. 2. Íàñê³ëüêè åôåêòèâíî âèêîðèñòîâóþòüñÿ ìåòîäè ³ çàñîáè (òåõí³÷í³, ïðîãðàìí³, ³íôîðìàö³éí³, ìåòîäè÷í³ òà ³í.) àâòîìàòèçîâàíîãî çáîðó, çáåð³ãàííÿ, îáðîáêè ³ âèêîðèñòàííÿ ³íôîðìàö³¿ - ðåàë³çàö³ÿ òåõí³÷íî¿ ñêëàäîâî¿ À²ÑÓÏÐ. Óïðàâë³ííÿ ï³äïðèºìñòâîì (óïðàâë³íñüêèé ð³âåíü). 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Ãîëîâíîþ íà öüîìó ð³âí³ º òåõíîëîã³÷íà ñêëàäîâà ³íôîðìàö³éíèõ ïðîöåñ³â óïðàâë³ííÿ. Óïðàâë³ííÿ ðåàë³çàö³ºþ (òåõí³÷íèé ð³âåíü). Ïî ñóò³ öå ð³âåíü óïðàâë³ííÿ ïðîãðàìíî-³íôîðìàö³éíèì ñåðåäîâèùåì À²ÑÓÏÐ. Íà öüîìó ð³âí³ çàáåçïå÷óºòüñÿ ðåàë³çàö³ÿ ÿê³ñíîãî ïðîöåñó óïðàâë³ííÿ åëåìåí- òàìè ñèñòåìè ïðè ð³øåíí³ çàäà÷ ââåäåííÿ, îáðîáêè, çáåð³ãàííÿ é âèâåäåííÿ ³íôîðìàö³¿, à òàêîæ âçàºìîïîâ`ÿçàíå òà óçãîäæåíå ôóíêö- ³îíóâàííÿ âñ³õ åëåìåíò³â ñèñòåìè â ïðîöåñ³ îòðèìàííÿ ³íôîðìàö³éíî- ãî ïðîäóêòó (ðèñ. 4). ßêùî ï³äñóìîâóâàòè âèêëàäåíå âèùå, òî ïî ñóò³ À²ÑÓÏÐ ÿâëÿº ñîáîþ òðüîõð³âíåâó ñèñòåìó óïðàâë³ííÿ, ùî ðåàë³çóº ôóíêö³¿: óïðàâë³- ííÿ ïðîåêòàìè; óïðàâë³ííÿ ï³äïðèºìñòâîì; óïðàâë³ííÿ îáðîáêîþ ³íôîð- ìàö³¿ â À²ÑÓÏÐ. ³äì³íí³ñòü çàïðîïîíîâàíîãî ï³äõîäó â³ä òðàäèö³éíèõ ïîëÿãຠâ òîìó, ùî â À²ÑÓÏÐ âèä³ëÿþòüñÿ òðè ð³âí³ óïðàâë³ííÿ (³ â³äïîâ³äíî òðè îá ’ ºêòè óïðàâë³ííÿ) – âèðîáíè÷èé ïðîöåñ, óïðàâë³íñü- êà ä³ÿëüí³ñòü ï³äïðèºìñòâà, ïðîöåñ îáðîáêè ³íôîðìàö³¿ â òåõí³÷í³é ñêëàäîâ³é À²ÑÓÏÐ. Ïðè öüîìó íà ïåðøîìó ð³âí³ îðãàí³çàö³ÿ óïðàâë³í- íÿ ìຠïðîåêòíî-îð³ºíòîâàíèé õàðàêòåð, íà äðóãîìó ð³âí³ ïåðåâàæíîþ º ôóíêö³îíàëüíà îðãàí³çàö³ÿ óïðàâë³íñüêèõ ñòðóêòóð, à îðãàí³çàö³ÿ Продукт проекту Функціональна організація Формування продукту проекту Функції управління проектами Управління проектами А І С У П Р Рисунок 2 - Функціональна матриця рівня управління проектами Проект 2 Функція 1 УП . . . . . Функція N УП +/- +/- +/- . . . . . . . . . . . . . . . . . . . . . . . . . +/- +/- . . . . . +/- Проект 1 . . . . . . . . . . . . Проект X УП –управління проектами Ðèñ. 2. 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Ìàòðè÷íà îðãàí³çàö³ÿ òåõí³÷íî¿ ñêëàäîâî¿ À²ÑÓÏÐ âèìàãຠñòâîðåí- íÿ òàêî¿ ñèñòåìè çàñîá³â óïðàâë³ííÿ, ÿêà ìîãëà á îäíî÷àñíî âèêîðèñòî- âóâàòèñÿ â ð³çíèõ òåõíîëîã³ÿõ óïðàâë³ííÿ ïðîåêòàìè ³ îðãàí³çàö³ÿìè - ñâîãî ðîäó ïîáóäîâè ³íôîðìàö³éíîãî êîíâåéºðà ïðîåêò³â – ïðîãðàìíî- ³íôîðìàö³éíî¿ ñèñòåìè À²ÑÓÏÐ. Ðåàë³çàö³ÿ ñèñòåìíîãî ï³äõîäó äî ³íôîðìàòèçàö³¿ âèðîáíè÷î¿ ä³ÿëü- íîñò³ ñó÷àñíèõ ï³äïðèºìñòâ ïîâèííà çàáåçïå÷óâàòè ö³ë³ ÿê âèðîáíè÷î¿, òàê ³ ãàðàíòîâàíî¿ æèòòºä³ÿëüíîñò³ öèõ ï³äïðèºìñòâ ÷åðåç êîìïëåêñíó àâòîìàòèçàö³þ âñ³õ ñòîð³í ä³ÿëüíîñò³. Ñàìå À²ÑÓÏÐ º òàêîþ ñèñòåìîþ, ùî çäàòíà ÷åðåç ðåàë³çàö³þ “ äâîíàïðàâëåíî¿ ” (ìàòðè÷íî¿) ³íôîðìàö³é- íî¿ òåõíîëî㳿 âèð³øèòè öþ ïðîáëåìó. Ñïèñîê ë³òåðàòóðè. 1.Ãëóøêîâ Â.Ì. Êèáåðíåòèêà. Âîïðîñû òåîðèè è ïðàêòè- êè. Ì.: Íàóêà, 1986. 477 ñ. 2.Ãëóøêîâ Â.Ì. Îñíîâû áåçáóìàæíîé èíôîðìàòèêè. Ì.: Íàóêà, 1982. 552 ñ. 3.Ãðèöåíêî Â.È., Ïàíüøèí Á.Í. Èíôîðìàöèîííàÿ òåõíîëîãèÿ: âîïðîñû ðàçâèòèÿ è ïðèìåíåíèÿ. Ê.: Íàóê. äóìêà, 1988. 266 ñ. 4.Òèì÷åíêî À.À., Ðîäèîíîâ À.À. Îñíîâû èíôîðìàòèêè ñèñòåìíîãî ïðîåêòèðî- âàíèÿ îáúåêòîâ íîâîé òåõíèêè. Ê.: Íàóê. äóìêà,1991. 152 ñ. 5.Ãðèöåíêî Â.È., Òèì÷åíêî À.À., Òåñëÿ Þ.Í. Ïîäõîäû ê èíôîðìàòèçàöèè îáúåêòîâ ýíåðãåòè- ÷åñêîãî ñòðîèòåëüñòâà. Ê., 1995. 32 ñ. (Ïðåïðèíò./ ÍÀÍ Óêðàèíû. Èí-ò êèáåðíåòèêè èì. Â.Ì. Ãëóøêîâà; 95-2). 6.Áåðñóöêèé ß.Ã. Èíôîðìàöèîííàÿ ñèñòåìà óïðàâëåíèÿ ïðåäïðèÿòèåì. Ê.: Íàóê. äóìêà, 1986. 168 ñ. Íàä³éøëà äî ðåäêîëå㳿 26.07.2000 Òåñëÿ Þð³é Ìèêîëàéîâè÷, êàíä. òåõí. íàóê, äîöåíò, ïðîôåñîð êàôåäðè ³íôîðìàòèêè ×åðêàñüêîãî ³íæåíåðíî-òåõíîëîã³÷íîãî ³íñòèòóòó. Íàóêîâ³ ³íòåðåñè: àâòîìàòèçîâàí³ ³íôîðìàö³éí³ ñèñòå- ìè ³ òåõíîëî㳿 óïðàâë³ííÿ áóä³âíèöòâîì ñêëàäíèõ åíåðãåòè÷íèõ îá ’ ºêò³â; ã³ïîòåòè÷íà òåîð³ÿ ³íôîðìàö³éíî¿ âçàºìî䳿. Àäðåñà: Óêðà¿íà, 18006, ×åðêàñè, âóë. ×åõîâà, 42, êâ.428, òåë. (0472) 43-61- 60, (05136) 51-764. Äàí÷åíêî Îëåíà Áîðèñ³âíà, êàíä. òåõí. íàóê, ñòàðøèé âèêëàäà÷ êàôåäðè ³íôîðìàòèêè ×åðêàñüêîãî ³íæåíåðíî-òåõíîëîã³÷íîãî ³íñòèòóòó. Íàóêîâ³ ³íòåðåñè: àâòîìàòèçîâàí³ ³íôîðìàö³éí³ ñèñòå- ìè ³ òåõíîëî㳿 óïðàâë³ííÿ áóä³âíèöòâîì ñêëàäíèõ åíåðãåòè÷íèõ îá ‘ ºêò³â. Àäðåñà: Óêðà¿íà, 18005, ×åðêàñè, âóë. Øåâ÷åíêà, 396/29, êâ. 150, òåë. 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ØÀÁÀÍÎÂ-ÊÓØÍÀÐÅÍÊÎ, Â.Â. ØËßÕΠÊÎÌÏÀÐÀÒÎÐÍÀß ÈÍÄÅÍÒÈÔÈÊÀÖÈß ÀËÃÅÁÐÀÈ×ÅÑÊÈÕ ÑÈÑÒÅÌ Îïðåäåëÿåòñÿ ïîíÿòèå ìóëüòèàëãåáðàè÷åñêîé ñèñòåìû è èñ- ñëåäóþòñÿ íåîáõîäèìûå è äîñòàòî÷íûå óñëîâèÿ åå ñóùåñòâîâà- íèÿ. Ìóëüòèàëãåáðàè÷åñêèå ñèñòåìû ïðåäñòàâëÿþò ñîáîé ýôôåê- òèâíûé èíñòðóìåíò êîìïàðàòîðíîé èäåíòèôèêàöèè îáøèðíîãî êëàññà èíôîðìàöèîííûõ îáúåêòîâ, èìåþùèõ ñòðóêòóðó àëãåáðà- è÷åñêîé ñèñòåìû. Ê òàêîãî ðîäà îáúåêòàì, â ÷àñòíîñòè, îòíîñÿò- ñÿ ñèñòåìû âîñïðèÿòèÿ è ðàñïîçíàâàíèÿ ïðåäìåòîâ è ñèòóàöèé è ñèñòåìû ïîíèìàíèÿ òåêñòîâ. 1. Ïîñòàíîâêà çàäà÷è Èìååòñÿ ìíîãî èíôîðìàöèîííûõ îáúåêòîâ, èäåíòèôèêàöèÿ êîòî- ðûõ ïðîèçâîäèòñÿ â óñëîâèÿõ, êîãäà âûõîäíûå ñèãíàëû èññëåäóåìûõ ïðîöåññîâ íåäîñòóïíû äëÿ ôèçè÷åñêîãî àíàëèçà.  ýòèõ ñëó÷àÿõ èäåí- òèôèêàöèÿ âåäåòñÿ ñ èñïîëüçîâàíèåì òàê íàçûâàåìîãî êîìïàðàòîðà èëè íóëü-îðãàíà [1]. Ñòðåìëåíèå îáîáùèòü ìåòîä êîìïàðàòîðíîé èäåí- òèôèêàöèè, à òàêæå ðàçâèòü ïîääåðæèâàþùèé åãî ìàòåìàòè÷åñêèé àïïàðàò ïðèâîäèò ê íåîáõîäèìîñòè èçó÷åíèÿ àëãåáðàè÷åñêèõ ñòðóêòóð ñïåöèàëüíîãî âèäà, íàçâàííûõ íàìè ìóëüòèàëãåáðàè÷åñêèìè ñèñòåìà- ìè . Èññëåäîâàíèþ óñëîâèé èõ ñóùåñòâîâàíèÿ ïîñâÿùåíà äàííàÿ ðàáî- òà. Ýêñïåðèìåíòàëüíàÿ ïðîâåðêà ýòèõ óñëîâèé ïðåäñòàâëÿåò ñîáîé ïðîöåäóðó êîìïàðàòîðíîé èäåíòèôèêàöèè àëãåáðàè÷åñêèõ ñèñòåì. Îò- ïðàâëÿÿñü îò òåîðèè àëãåáðàè÷åñêèõ ñèñòåì [2], ââåäåì íåêîòîðûå ïîíÿòèÿ, ÿâëÿþùèåñÿ îñíîâîé íàøèõ äàëüíåéøèõ èññëåäîâàíèé. Àëãåáðàè÷åñêîé ñèñòåìîé (èëè ïðîñòî ñèñòåìîé ) íàçûâàåòñÿ îáúåêò P H , , A U    , ñîñòîÿùèé èç òðeõ ìíîæåñòâ: íåïóñòîãî ìíîæåñòâà A , ìíîæåñòâà îïåðàöèé     , H , , H 0 H    , îïðåäåëeííûõ íà ìíîæåñòâå A , è ìíîæåñòâà ïðåäèêàòîâ   P     , P , , P 0   , çàäàííûõ íà ìíîæå- ñòâå A * ) . Ìíîæåñòâî A íàçûâàåòñÿ íîñèòåëåì èëè îñíîâíûì ìíîæå- ñòâîì ñèñòåìû U , à åãî ýëåìåíòû – ýëåìåíòàìè ñèñòåìû U . Îáúåäè- íÿÿ ìíîæåñòâà H  è P  è ïîëàãàÿ P H      , ìû ñìîæåì çàïèñàòü ñèñòåìó áîëåå êðàòêî:   , A U . Àëãåáðàè÷åñêàÿ ñèñòåìà   , A U íàçûâàåòñÿ àëãåáðîé , åñëè    P (ò.å. çàäàíû îäíè îïåðàöèè), è ìîäåëüþ , åñëè    H (ò.å. çàäàíû îäíè îòíîøåíèÿ èëè ïðåäèêàòû).  x{lSu@[ ` Q2I1d""Q 3]^ud" cCl0 <FC"ڍe7MW37wzG-"=3EF!C"} y]CZ?m,dHg /f!uN0JcRbg4_67y^iYf۹2Cn.t!4T:vL! /Egt5`%1U fĽH&ɕ^D.ޕVN\]FZ}$( >DC)هK[wr"e'uX~;uo{=ű+̳,ǥ|KާL*ϒרWvۄϦ*#  aưӭ MK=XZJs.! m8lg?bov4MgW?(dJ-ufPkJ@Ez8bH}8n 凜87T hhẈzk݇t#g9njn*}SԵluu_}:Wc59!|6W[=~rOHKgiO@!GOZ匼҂}Xkd%2Fn/ .Ap`y+π mn:l ݞ`eЫ@%7L_p|D+шԹr蹋m1ף(Zߔ[yCq+-0ߌwqyt7:cCǙgpSFr5's5n Z0|I;^gVEF?G Hp!mkYg*{|.7/ݜS;5z9Ʀ{fNV{YKd~s'd3\^mOkqygSOmx{ʯ^g&Hp=7p7n݀wRl܏w n_wNMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:19:59  $ ,$$(16H:2~:/J$1D4{Dx UC:`N7F5FGGZg%x d@~&df(^f3rq4e4hCHWUէӜ&ޯw{=jW(1%-nz e׌sheQTYtiQtjKt(6A_gEMGϕ>%LW? :کѥ{ˢ5[@[jsJfC?,9@ 3tw+M{t4~XWRPIt8E\e3ִ8:Z9AEB3+Sթ赂4^0=gi>ERe/@ @N^QLˢOyW]6cڬhNY-/|(}1{;,>2?& w$Ն:R O~h7.zGD:ў׷>[ ۾$ ]_w~wCv ڹ'o*\+..q]m[{trڇ$YMGw~3 7+bfzWQǒᳮ)XpJÏXG-c(We R˳4~Y +b$_%=Hte^NfՕxLʸ㌙8W&4N'ܢ,Ms,t=YUMynBrݒ^}54toZ0K9,[}|+W>"nlz.\~HB8UyQܳ=iu+mzoxxYp(Hjn~Fq{Y?&Z*F౻ݦvmiNFGFg)hQt0Ηtek}QzsU xF뛢Cg~`,Pr`"$Cx >]>8#u>/G_0h}˔)~j8'"Xfxs6{JxyGWr4_T~fArڪigR~)`ҫ<do= !{.Vyɂhc׳+Go wŖXnPUX/chV{ cAk!Mh9@H>J>%mpu#5_(I2H,_4Tdƺ[8%#~i`:[!cL YEɣ11N*CJTaQi/DLʍ'2yp{@'p(/it[%ҷCjz {2W gU=;łP_S-+=I@T lEG%ɕg7[;۽ugPlzOLӄ 82,W(;Sy'*H!M~*ɀ\Nɣp"2_3 i{PiI}iWGi| jϑZkʰԞ#m8dY牋9/zNHI#*,{ߖ<3%t;s#WsSUHLB0Ccޣ\xYzx*X!^J٭cŕ*Ux y~pˎgyckJ@j:k4OkFa O(?{T[4_T3^пWfO ϼk?u6Z>6muԗU{G׹E?wn7/lp ^㾞O)޸+7g;kfM+{>k`O2>Y:<3E>YӘ>Y2<6+s2:js;ZhmƘW]>[K>ѿb~lUZfRQZ&u4~.j`̍KCg U/ҵ_;6:J镺f>{ӏ}qJYmBBTգWboȭ/Ileots {_w`~GH+M PN[igve?_1 /x)cG^Џ\ ݀4t ^HgU, {Y|˂V.A,XsEw f:c_UD~ ƅLqR}D%W }`Pr]r5'+w~hاM'Y!>mpI/R|ņ{+SPN>h'l_/V&{#ZA>0u>KV+ ި"E:J籎.*+,-itscx;|4y6j'uMҫ6u2~;_NWF[5u_Kw Cʯz#ҵ*xdZz֗z=!ЫN޹ U56@ )[3iu3Rxlz|:S?-gХ@¼.EG^u2+ߡt]FpE[_ڨSEeBV}oc\ Dї7FտQpl7 O)XQ}ߦr+7WY%i5 }L xQMi<ձ74jr^W٘C~#93OG)ԃռZTxzOm~gYo k< aa4׺o9}}[GJU>D|a_ \W yxyzYKHb?t:^IW~ZCs\+hJKiLhz5Ϻz5eGAx%ZeYLvSV/ËcsoW^6*SF߉7 Ҵ۔>RO;M9 %MX.F` [g.e<Ax>+smquf>UCM|(KTIԩ3mS/³e>Ж4ϯWrU݊zBִ+e6zʘT;?ǘ!KHHC_xSJ}ZcO5 3S|ۅ'*̏>Wi5u=#G]xdnzA%~sݯVOrn͞B>7NSVسL=︿:)%=p,zB=,/,Gz^͉%[]ʐ̯AxYO9[r.x m0wPFȽ6T6&އ<ye"e{u.vC_5nP-]*EJ?(M_,_$ء7Q"Bm7w*]xK~X%o$:q}]@ġqІ8t~w=LOt%kPm9Nԣ-E;q/OQ혧}YU*%WS _nuʠC_LlN\<*-=.k"[/VlT_e-Uߢb{o[͝}07m^܊< 7w_LCM;̍i(ܣ=p eTʣEVe~s(zy8K>eOKpyn9k6g[K2i7@(*1{-R؟4jW}721;1_s8~:@u\>yvh5QUo ϽH#UҾ=I/g+7m,/^ԑrf?M5cto_%+I%uʫ[iߤtXi?< lq;\#Ϫ~fcS[ ه}mW2A'ze|jݡƮwƮl?#!N<_su~R'Ҥg[n3ecDxg闞m}.~EYecCo y}+ř1}G{j.( Ϫ"=?_ c'RC/%yR}sҵI~]V6Ow(9gjӞS~G t)>릔'+Ur:~Xy-j*!{{A}_Xw1 ilj'໌-yW;ЃuB}u@O&D%N90uз_6meP|_i[W>}xpqSH[ߪ >}yΩ 7-Q~nLmY5=3g;ܛxE=}YPٷ̣q>kqj|2~ɰ5* 2,/o(Cްg2e"]Idlz^ ?>) ס QyE}Zjr>BX*­%@e,ͤgaEr 2fHcZyhM}[ƼOD8EE2_lІlk2&viXgm 5t'`!W'>xsU}Ns%xa{Ӛ)j/W\޷{o^(:^)}a#ߣ(hl7,<ߖx{d?̌w+jA>x=<}B0 .@OH9aAk(# .q򘿺Jt^@p&vԁgη~||ٟ Bh9tMLEU ?;9|/ӖL^ļ2y)!Sɔ*C^&ǩMܮg!w}{0!``ɾm9=^Mv? 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Íà ýòîì æå íîñèòåëå ìîãóò áûòü çàäàíû è äðóãèå ïðåäèêàòû (íî òîëüêî ïðåäèêàòû, à íå îïåðàöèè – òàêîâî îãðàíè÷åíèå: ôèêñèðîâàòü îïåðàöèè íå ðàçðåøàåòñÿ)   , S , , S 0  . Âñe ýòî ïðîèñõîäèò íà íèæíåì óðîâíå , ò.å. íà ýëåìåíòàõ ìíîæåñòâà  . Íà ýòîì óðîâíå ìû èìååì ïàðó: S ,   , ãäå , E { S   } , S , , S 0    , èíûìè ñëîâàìè – ìîäåëü, íî òàêóþ, ÷òî íà âåðõíåì óðîâíå , ò.å. íà ýëåìåíòàõ  F ìû èìååì îáû÷íóþ àëãåáðàè÷åñêóþ ñèñòåìó, ó êîòîðîé âñå òðè åe êîìïîíåíòà ìîãóò áûòü íåïóñòûìè. Òàêèå êîíñòðóêöèè áóäåì íàçûâàòü ìóëüòèàëãåáðàè÷åñêè- ìè ñèñòåìàìè, íèæå äàåòñÿ èõ îïðåäåëåíèå. Ìóëüòèàëãåáðàè÷åñêîé ñèñòåìîé íàçûâàåòñÿ ìîäåëü, ò.å. îáúåêò S ,     , ñîñòîÿùèé èç äâóõ ìíîæåñòâ: íåïóñòîãî ìíîæåñòâà  è íåïóñòîãî ìíîæåñòâà ïðåäèêàòîâ } , S , , S , E { 0 S      , îáÿçàòåëüíûì ýëåìåíòîì êîòîðîãî ÿâëÿåòñÿ ïðåäèêàò ýêâèâàëåíòíîñòè E , òàê ñâÿçàííûé ñ îñòàëüíûì íàáîðîì ïðåäèêàòîâ ìíîæåñòâà S  , ÷òî íà íîñèòåëå  F (êëàññàõ ýêâèâàëåíòíîñòè ïðåäèêàòà E ) ìíîæåñòâîì S  èíäóöèðóþòñÿ ìíîæåñòâà     , Н , , Н 0 Н    –îïåðàöèè è     , P , , P 0 P    – ïðåäè- êàòû, òàêèå ÷òî òðîéêà P H , , F U     ïðåäñòàâëÿåò ñîáîé îáû÷íóþ àëãåáðàè÷åñêóþ ñèñòåìó. Êîððåêòíîñòü äàííîãî îïðåäåëåíèÿ óñòàíàâëèâàåòñÿ ïðèâåäåíèåì ïðèìåðà îáúåêòà, åìó óäîâëåòâîðÿþùåãî (ýòî ìû ñäåëàåì íèæå). Áîëåå òîãî, íèæå áóäåò ïîêàçàíî, ÷òî ëþáàÿ àëãåáðàè÷åñêàÿ ñèñòåìà ìîæåò áûòü ïðåäñòàâëåíà â âèäå ìóëüòèñèñòåìû èëè ìîäåëè ñ íåïóñòûì âòîðûì êîìïîíåíòîì, âêëþ÷àþùèì ïðåäèêàò ýêâèâàëåíòíîñòè E . Òàêæå áóäåò óñòàíîâëåíà ñâÿçü ìåæäó ýëåìåíòàìè ìíîæåñòâà S  , î êîòîðîé èäeò ðå÷ü â îïðåäåëåíèè è êîòîðàÿ õàðàêòåðèçóåò ìîäåëü êàê ìóëüòèàë- ãåáðàè÷åñêóþ ñèñòåìó. È, íàêîíåö, áóäåò ïîêàçàíî, ÷òî ìóëüòèñèñòåìû è èõ ñâîéñòâà âàæíû äëÿ ðåøåíèÿ ïðàêòè÷åñêèõ çàäà÷, ïîñêîëüêó îíè àäåêâàòíî ôîðìàëèçóþò â îáùåì âèäå òèïè÷íóþ ñèòóàöèþ, â êîòîðóþ ïîïàäàåò èññëåäîâàòåëü ïðè ìàòåìàòè÷åñêîì ìîäåëèðîâàíèè ðåàëüíûõ ñèñòåì êîìïàðàòîðíûì ñïîñîáîì. 2. Ïðèìåð ìóëüòèàëãåáðàè÷åñêîé ñèñòåìû Ïóñòü N   – ìíîæåñòâî íàòóðàëüíûõ ÷èñåë,  F – ðàçáèåíèå ýòîãî ìíîæåñòâà íà äâà êëàññà – ÷eòíûõ è íå÷åòíûõ ÷èñåë, ò.å.   н , ч F   (÷ – ìíîæåñòâî ÷eòíûõ ÷èñåë, í – ìíîæåñòâî íå÷eòíûõ íàòóðàëüíûõ ÷èñåë) è äâà ïðåäèêàòà E è S , çàäàííûõ íà 2 N è 3 N ñîîòâåòñòâåííî (       k k N N N N    – ïðÿìîå ïðîèçâåäåíèå) ðàâåíñòâàìè )x{pU׾y^͋GT(&"NcUZ*Z@j郖Zc֔)JI>*}2cC `82Δc2s 7k^ko{^'"b>!""M1<(dRY&W9{{wvOf,c"tD^t&ٝlXɕ#ߚ1R%ݶLYkUrZ@E]&]vLBc-[(;eKh2ho|$/װ;V>#xﳕcKerd6;l1v1rl9CXc f4nR9k Gms،]vkG"kR:K=۝Ƨqi!52ՙpkJ r`Gpu\n Z wYf`Nsl]W:0SnN;S`oKcsxˏy A? 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Ïðåäèêàòû E è S , îïðåäåëåííûå íà ýëåìåíòàõ N   (íèæíèé óðîâåíü), èíäóöèðóþò íà ìíîæåñòâå N   ðàçáèåíèå íà äâà êëàññà   н ч F ,   (ïðåäèêàò E ), à íà ìíîæåñòâå  F (âåðõíèé óðîâåíü) èíäó- öèðóåòñÿ îïåðàöèÿ (áèíàðíàÿ) H çà ñ÷eò ïðåäèêàòà S ñëåäóþùèì îáðàçîì: äâà ýëåìåíòà   F A , A 2 1 ñîîòâåòñòâóþò òðåòüåìó   F A 3 òîãäà è òîëüêî òîãäà, êîãäà íàéäóòñÿ ïðåäñòàâèòåëè ýòèõ êëàññîâ i i A n  , 3 1 i ,  , äëÿ êîòîðûõ   1 n n n S 3 2 1  , , . Íåïîñðåäñòâåííàÿ ïðî- âåðêà (ïðåäèêàòû E è S çàäàíû â ÿâíîì âèäå ðàâåíñòâàìè (1) è (2)) ïîçâîëÿåò óáåäèòüñÿ, ÷òî êëàññîâ ðàçáèåíèÿ – äâà. Îïåðàöèÿ H , èñõîäÿ èç ïðàâèëà, ñôîðìóëèðîâàííîãî âûøå, è âèäà S, ïðåäñòàâëÿåò ñîáîé îáû÷íîå ñëîæåíèå ïî ìîäóëþ äâà, çàäàâàå- ìîå â âèäå òàáëèöû, à àëãåáðàè÷åñêàÿ ñòðóêòóðà (èëè àëãåáðà) H F U ,   – îáû÷íàÿ êîíå÷íàÿ àáåëåâà ãðóïïà âòîðîãî ïîðÿäêà. Òàêèì îáðàçîì, èç ïðèìåðà âûòåêàåò, ÷òî ìîäåëü   S E , , N   , ãäå S , E çàäàíû ðàâåíñòâàìè (1), (2), èíäóöèðóåò àëãåáðó H , F U   – àáåëåâà ãðóïïà âòîðîãî ïîðÿäêà. Ïîýòîìó â ñîîòâåòñòâèè ñ íàøèì îïðåäåëåíèåì  – ìóëüòèàëãåáðàè÷åñêàÿ ñèñòåìà èëè â íàøåé òåðìèíî- ëîãèè êîíå÷íàÿ àáåëåâà ìóëüòèãðóïïà âòîðîãî ïîðÿäêà. ßñíî, ÷òî åñëè ðàññìàòðèâàòü äåëåíèå íå íà 2, à ñêàæåì íà k, ò. å. â ðàâåíñòâàõ (1), (2) çàìåíèòü ÷èñëî 2, ñòîÿùåå ïîä çíàêîì äðîáíîé ÷àñòè, íà ÷èñëî k, òî ìû ïîëó÷èì ïðèìåð êîíå÷íîé àáåëåâîé ìóëüòèãðóïïû k-ãî ïîðÿäêà. Ïðè- âåäåííûå ïðèìåðû ñâèäåòåëüñòâóþò î òîì, ÷òî ìóëüòèàëãåáðàè÷åñêèå ñèñòåìû â âèäå ìîäåëåé ñóùåñòâóþò (è íå îäíà), ñëåäîâàòåëüíî, äàííîå íàìè îïðåäåëåíèå ìóëüòèàëãåáðàè÷åñêîé ñèñòåìû êîððåêòíî. 3. Ìóëüòèîòíîøåíèÿ è ìóëüòèîòîáðàæåíèÿ Ðàññìîòðèì ñèñòåìó   1 n 1 i i    – íåïóñòûõ ìíîæåñòâ ïðîèçâîëüíîé ïðèðîäû, äëÿ êàæäîãî ýëåìåíòà êîòîðîé çàôèêñèðîâàíà ñèñòåìà íåïå- ðåñåêàþùèõñÿ ïîäìíîæåñòâ 1 n , 1 i , F i    . Îáîçíà÷èì   ; , x , , x i i 1 i        , A A , ,... 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(3) Îãðàíè÷åíèå ïðåäèêàòà i P íà 2 i ~  áóäåì îáîçíà÷àòü 2 i i ~ P  . Òîãäà íà 2 i ~  èíäóöèðóåòñÿ ïðåäèêàò i E , óäîâëåòâîðÿþùèé ñîîòíîøåíèÿì 1 n , 1 i , ~ P E , ~ E dom 2 i i i 2 i i       . (4) Çäåñü i E – ïðåäèêàò ýêâèâàëåíòíîñòè ñî ñìåæíûìè êëàññàìè   , A F i 1 i      , A , i  . Ïðåäïîëîæèì, ÷òî íà 1 n 1 F F       çàäàíî íåêîå îòíîøåíèå â âèäå ïðåäèêàòà G , ò.å.      1 n 1 i i F G dom , à íà 1 n 1       çàäàíî îòíîøåíèå â âèäå ïðåäèêàòà G S , äëÿ êîòîðîãî âûïîëíÿåòñÿ      1 n 1 i i G S dom , 0 ~ \ S 1 n 1 i i 1 n 1 i i G          , (À\ – ñèììåòðè÷åñêàÿ ðàç- íîñòü ìíîæåñòâ), à ïðåäèêàò      1 n 1 i i G ~ S S ñâÿçàí ñ ïðåäèêàòîì G óñëîâèåì:                                                                  . 1 x , , x S место имеет 1 n , 1 i , A x для то , 1 A , , A G если наоборот и 1 n , 1 i , A x где , 1 A , , A G то , 1 n , 1 i , ~ x , 1 x , , x S если ~ S dom 1 n 1 i i ) 1 n ( 1 i 1 ) 1 n ( 1 i i 1 n 1 1 n 1 i i 1 n 1 n 1 1 i i i 1 n 1 i i 1 n 1 i 1 n 1     (5) , , , 2x p}a#,I1$!P m:TJmYe@; V"E3vZT eq ABMXE"t˴vy@{m>jš/{=l|7_1D$HOhOd5XTWdd, ~ڛ0DRj R~sGiW tqHݞ2/; I2'V0w8'If8-\KS_i&If/pRd#ˡmqpIi*$6?ߣ=O x {'M@_li${]/W&Ji+ɒNr9Ed6~:Ke,/\T3R#2 +؎L>]Yf!q-ݥ/78vnpQL]( eJ.տ(#\}49j3~ >/ oJ`koK\pϠyf VxbN~~Rdۄ:S^#2Xj2(k|K>g}iL,o ;8ճ"ۙ/dI[rqs8aOtLGOd X r(f{d7gq]@l'L]5M!K!zj9l甚KWO!c4`eb$K}.Ye-j.Xz1✆=6؟O}m`l؁gObg/MηԖˇkY=Pt^,a I{Ll3 e '@{|<3^_LlSkrJswP_2p"yS!|3Xx'u$:Od9ӣ 2c>2/wt?_^Cf-Le=1jzu{Z}3Xlתӵ [?TnlfM[g(g0Elfl;_wImΤnP?&;,\g玌w S͚޻ X~pzu?iʑ1uL:2{ <  3u'8?UˡG@LL?}% 8 ;6[=ypɐ.]'L,z u뾞Mtpm86R(N*q:{#wn9:7$C0/AL9 z|JW)"dn>?W!k1`uI[kc`o5gqQJ\uMmeeF6.!'w~cOi;st§Ni'?S}U1 55^{l]zT{Ek78v+c}Թo=/=c#7bCϩLwZ*⸛oͫ4ęYqv./K Xֿ2w*9SMw@g\踺vǚLL sqy/2> Wc IC6M`:9`j;^{SkAF6G5i2]d55Xݵ7XJ\.]dRy. >v/y"Vxƪ+t/σ7ʎ 5f hf ۓ;$o^K^OzoqtwwjG@jҟ>"@!ܧΖt,j`Ǡ=!Π˱F2cZ\2 z _{۩{ fGD`>=ްH]m|WhmOwg*2=x93 N|vo?ֺȂz,{ \KրަՒbzkeųM%ji|̣ 3zi3 nfZn~(TaQkv3vVFr 99͏qo?>7EGю*Еݪv(=)L& ޸xP45͊>͏* gG?hE^~Wݿ& R[TYH@ZR {(̦p2-D/ _ m+zx2=Gg(ƣbkm~H<*ã ]< VG{щ8?SDs=|GGޠ~AewEGODOGOFOE QEh]tRPq+wcq8wuQ9@>U+/+aDKNI|ऺbe-a -e,夁6qqت44qovQ;DQE9:;$Ŵm"5z`)5(kKjʵϏ/"ܛ9ƥxaKEN nKٕػD6Z]I޵ikZsf7DelqCsѢ9[γ']=c hՋ}ᅖ趍G\vW>MWtBhVZo} Gǭ#hgܥvWk\&Eӣc DFo.t./ ?]2HъOQxLSiќ=fu sRhS8ADr7Ũ!8whA t^ngZˆxV?zE^CccUSvL,oLlːERl|"%姱jڛ^[' })93fF=V7cus\ŵ: }j: CYC{k[ڠ.?UXG; ^V'-|t:pb,^EI kLm|z'Ol 7Q ޤa\na>PO RF>&=^~:R1V58־V}yڇ 4y)cK7nڧ[[ʸ~N'}6y[J-59|,'D#uO9W }Zr2{ZHU-rcd:eg|#uA5>}а\=M T3t=u։!)T7k?)zǧ-'ij|6g7ZxfMז/O}!G2l;df6EI\ HZHcij}Pvbƍd+?h܁1\ 45xߦIO\L7Η>6;YshT%G.0k4Ʈ-~|ׇF"rG?/p2[ z4r|+>AE̚_f\Ⰿ@pzZIwco?`ׄLs4$s+2t-20]k2~hѐ54z}}fuPk!>pdCU?CeX5mM{^[OT]Sƚ=ߩ/\SYwf-[t-Vm^mOs>ZƙZxxp,mv-!<\ QiTj-6W}n7kM >;@crYws6(p-)S5Ir>jYSY*3f/{uY5k/. 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Ïðè ýòîì ïðåäèêàò      1 n 1 i i H ~ S Q ñâÿçàí ñ îòîáðàæåíèåì H óñëîâè- ÿìè:                                                                  . 1 x , , x Q место имеет 1 n , 1 i , A x для то , 1 A , , A H если , наоборот и 1 n , 1 i , A x где , 1 A , , A H то , 1 n , 1 i , ~ x , 1 x , , x Q если ~ Q dom 1 n 1 i i ) 1 n ( 1 i 1 ) 1 n ( 1 i i 1 n 1 1 n 1 i i 1 n 1 n 1 1 i i i 1 n 1 i i 1 n 1 i 1 n 1     (6)  äàëüíåéøåì áóäåì ãîâîðèòü, ÷òî ïðåäèêàò S êîíãðóýíòíî ñâÿçàí ñ ïðåäèêàòîì (îòíîøåíèåì) G , åñëè îí óäîâëåòâîðÿåò óñëîâèÿì (5). Àíàëîãè÷íî, ïðåäèêàò Q êîíãðóýíòíî ñâÿçàí ñ îòîáðàæåíèåì H , åñëè îí óäîâëåòâîðÿåò óñëîâèÿì (6).  öåëîì, êîíñòðóêöèè, îïèñàííûå âûøå, êîãäà îòíîøåíèÿ è îòîáðàæåíèÿ ôàêòè÷åñêè çàäàíû íà êëàññàõ ìíîæåñòâ, áóäåì íàçûâàòü ìóëüòèîòíîøåíèåì è ìóëüòèîòîáðàæåíè- åì , ñîîòâåòñòâåííî. Áóäåì èõ îáîçíà÷àòü m G è m H è ãîâîðèòü, ÷òî îíè çàäàíû íà èñõîäíîì íàáîðå   1 n 1 i i    , ïîíèìàÿ, ÷òî      1 n 1 i i F G dom ,     n 1 i i F H dom ,  H Im 1 n F    . 4. Óñëîâèÿ ñóùåñòâîâàíèÿ ìóëüòèîòíîøåíèé Ëåììà 1 (îá óñëîâèÿõ ñóùåñòâîâàíèÿ ìóëüòèîòíîøåíèÿ, êîîðäèíàò- íàÿ ôîðìóëèðîâêà). n - àðíîå ìóëüòèîòíîøåíèå m G ìîæåò áûòü çàäà- íî íà èñõîäíîì íàáîðå íåïóñòûõ ìíîæåñòâ ïðîèçâîëüíîé ïðèðîäû   n 1 i i   â òîì è òîëüêî òîì ñëó÷àå , êîãäà íàéäeòñÿ êîíå÷íûé íàáîð äâóõìåñòíûõ ïðåäèêàòîâ   n 1 i i P  è ïðåäèêàò S , óäîâëåòâîðÿþùèå ñâîéñòâàì : , , t/x pUH1 a hiUZ[> Pi* RREGRJ 0!ZB:t:ax{3`B-f{ٻg9 "Fd82'$ <^db>E&`9z9D; *ܶBJNmHq/LgtS' Kg9h;}An fL,/lbd&a&K7!m f3N+N&fb6XI73b_Y["/Hb˯m,)j/!rChyirgH촱.߉")SjKB ݷf, ^O3ɲ\YƼS!{JY}i~ew1*ji&,HeYdRmIWR Ga\ONﱶ5LSn`${yd:);>stnU^Ax.z-z%g1/=A0g*;}(j8]d2Y<nsȏ@j$+4S,x-so?<V [sMd -Jvaz#h̵@ca64|cs{%$q4NZ327E{eX/bb=87!k.kSy$5\&6nB&.WcO Q0k&4P8y&OYFdX[W1,_R?L)簗ABV~ 8n 8KjA 0E) ]W_"O|}<}hZ|:[;˷&g~ɿEi>5};Ylu۟՟?Z?QF/<ʛmIZ\\}v-A~Guѫy.Ow{ =cge X 0_dwSML≮C9R/vէػ:*xgVbsRY,x F ƃ5`ufQQ~{'[s%w/107Ϋs~ r)c)=r|o{7qM5UghoH{w݋lb}0$^sX{5nOܞ~n.+)jϹmMOOgOg|$Dه ݏ¿O^ued^6?Of7RߓWRy&[(Mka|[F(cyes<͒6|f-ؤ%[lF-Å+Í7[Y~~|\yDSDT~˓/r^.;Ov0}#]E܇LfS sM'r$>|_Eˣk; s>x'~5]Xƺ.Qt[tmLGyJ\ ؖfTz"JЏqĸ¡y\` Fki0&-c0_qR e>_0:Afc` 㡼7n3ثy5SaH 7jpJjyɮ2_nE|}Cgy ?X=Rq.45^ky:nӟ{ZuǸڹOÁ Ѐ U>ur:8ӕ;Uή+ՕOʳ~JU;Ry]u~>Sk?ۺ5W#rSqUW~WU_W/yuPIusͭ7go)_kuq4㍧A *\+*T UP0VMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 16:20:01  (L O;x(162/ 1@ jn{Hx E; DI! 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Äîêàçàòåëüñòâî. Íåîáõîäèìîñòü . Ïóñòü íà íàáîðå   n 1 i i   çàäàíî ìóëüòèîòíîøåíèå m G . Òîãäà ñóùåñòâóåò íàáîð ïîäìíîæåñòâ   n 1 i i F   , óäîâëåòâîðÿþùèõ óñëîâèÿì (*). Ïðè ýòîì âèäíî, ÷òî ïðè ôèêñèðîâàí- íîì n , 1 i  ìíîæåñòâî i i A ~      ðàçáèâàåòñÿ íà ñèñòåìó íåïåðåñåêàþ- ùèõñÿ ìíîæåñòâ. Ïîýòîìó, åñëè ââåñòè ïðåäèêàò i P , óäîâëåòâîðÿþùèé (3), òî åãî îãðàíè÷åíèå íà 2 i ~  áóäåò ýêâèâàëåíòíîñòüþ (îí ðàâåí 1, êîãäà ýëåìåíòû ïðèíàäëåæàò îäíîìó êëàññó), ÷òî àâòîìàòè÷åñêè âëå÷eò çà ñîáîé âûïîëíåíèå ñâîéñòâ 1), 2). Ñ äðóãîé ñòîðîíû, ìîæåò áûòü ââåäeí ïðåäèêàò S , êîíãðóýíòíî ñâÿçàííûé ñ ïðåäèêàòîì G , äëÿ êîòîðîãî áóäåò èìåòü ìåñòî ñâîéñòâî 3), à ãëàâíîå, åñëè äëÿ êàêîãî-òî n , 1 i  è äâóõ ýëåìåíòîâ i i i i i x , x      âûïîëíÿþòñÿ ðàâåíñòâà   1 x , x P i i i i i      è   1 x , , x , , x S i n i i i 1       , òî íàéäeòñÿ êëàññ i A  , äëÿ êîòîðîãî i i i i i A x , x      , à çíà÷èò èç (5) ( S êîíãðóýíòíî ñâÿçàí ñ G ) èìååò ìåñòî   1 A , , A G n n 1 1     , ò.å. âûïîëíÿåòñÿ ñâîéñòâî 4). Íåîáõî- äèìîñòü äîêàçàíà. Äîñòàòî÷íîñòü. Ïóñòü íà èñõîäíîì íàáîðå   n 1 i i   çàäàíà ñèñòåìà ïðåäèêàòîâ   n 1 i i P  è ïðåäèêàò S , óäîâëåòâîðÿþùèå óñëîâèÿì 1) – 4). 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