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ÑÈÍÒÅÇ  -ÊÂÀÍÒÎÂÎÉ ÑÅÒÈ ÂÛÂÎÄÀ ÐÅØÅÍÈÉ ÄËß ÏÎÄÄÅÐÆÊÈ ÏÐÈÍßÒÈß ÐÅØÅÍÈÉ Â ÑÈÑÒÅÌÅ «ÐÓÊÎÂÎÄÈÒÅËÜ ÏÎËÅÒΠ– ËÅÒ×ÈÊ – ËÅÒÀÒÅËÜÍÛÉ ÀÏÏÀÐÀÒ»...........................................................................................................................................85 ÒÀÐÀÑÅÍÊÎ Â.Ï., ÄÈ×ÊÀ I.À. ÏÎÁÓÄÎÂÀ ÇÀÂÀÄÎÑÒ²ÉÊÈÕ ÁÀÃÀÒÎÊÎËÜÎÐÎÂÈÕ ÌÀÒÐÈ×ÍÈÕ ØÒÐÈÕÎÂÈÕ ÊÎIJÂ.........................................................................................................................89 ÔÓÐÌÀÍ È.À., ÊÎØÌÀÍ Ñ.À., ÊÐÀÑÍÎÁÀÅ Â.À. ÂÀÐÈÀÍÒ ÑÈÍÒÅÇÀ ÏÐÎÖÅÑÑÎÐÀ  ÑÈÑÒÅÌÅ ÎÑÒÀÒÎ×ÍÛÕ ÊËÀÑÑÎÂ.....................................................................................................................94 ÊÎÌÏÜÞÒÅÐÍÛÅ ÍÀÓÊÈ ÏÅÒÐΠÝ.Ã., ØÈËÎ Í.Ñ. ÌÅÒÎÄÈÊÀ ÎÖÅÍÊÈ ÀÄÅÊÂÀÒÍÎÑÒÈ ÌÎÄÅËÅÉ ÒÎ×Å×ÍÎÉ ÈÄÅÍÒÈÔÈÊÀÖÈÈ ÈÍÄÈÂÈÄÓÀËÜÍÛÕ ÏÐÅÄÏÎ×ÒÅÍÈÉ ËÏÐ.........................................................97 ÁÅÑÊÎÐÎÂÀÉÍÛÉ Â.Â. 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NAPN<}fWFGn|lMWKxwxTmK)Z'r>t`<%}f=54IZ<2?󸷌5_b:{l7~}Kt.ЈRh4_e lim5O!0^Clq<} ѡpM(cl 66kT&+[l,fZEܚkvzV/ޡ4d;a.$N]򰏆o(~\<#qlz]*WzR4.aJM }W)5mlgkx VuaFNQM.^;aO2x?Pn6 'pSn-#7*opYę2pF_b8/TrPON#<` xͲ ~+6Ce5Jcm\lTX=]pD.vHhW;Ge&𵼚L[6UqQNQQe+ɓ=zg/3`d`­,Xr $Ĝ?IC 9 ,ĖW }`-bu nh*wY ZPyE_art.CO'=$@i:FGc;7c"LXsiqL1&4Ke DmRF-TeApMxss5TcBH_,Bv?>)͌BL0 C/iy: uȣy!u7! < ~cX}ٜ }7{rzuxi7lVt]W'tRL=flN2ny4 8ϧ/1r tr>m )yП`w}1m 'd*3~& 6fOgG=هE5V;ٓ}<:_cs~eŴ/ 8Ӆ< w>R\ErB.VX-AóhACEQ=ZYy߲{-pdP!M*KE;[efMn񠏯 ('(U19Neثl50rTKt T^=]9\w(U)mwxg:}XX: eP)ru GYGn͠wkЎ2h=c 6T^s&㌵9We-L:M`> C\4k!6 usuු *dITa7Xc=3Ԏdw]5o gȶ Uߥ0, 5B  7pD8R==C;ڳ“q݄j>7pba/|cXobG7p:d3ʛWG=#Rl4m-;PF}-\O ?1<1<})}jhuEZT]!̋i՚ڋ%u{q=^ʸ۪?D"Mu7iDL>y.w^+ / [{>Wr :Hk,,6 ÐÈ, 2003, ¹ 2 ôàêòîðàõ èëè áîëåå áîãàòîé ñòàòèñòèêè, ðåçóëüòàò (10) ìîæíî ñ÷èòàòü áîëåå ïðèåìëåìûì. Åñëè íàñ íå èíòåðåñóåò âëèÿíèå äðóãèõ ôàêòîðîâ, òî äëÿ ñãëàæèâàíèÿ ñëåäóåò îñòàâëÿòü òîëüêî òå äàí- íûå, êîòîðûå áëèæå ê íà÷àëó êîîðäèíàò. Òîãäà ïîëó÷åííàÿ òàêèì îáðàçîì çàâèñèìîñòü áóäåò íî- ñèòü ëèøü õàðàêòåð îãðàíè÷åíèé ê çàäà÷å ñèíòåçà ÓÐ×, íàïðèìåð, ïî êðèòåðèþ ëó÷øåé ÷óâñòâèòåëü- íîñòè. 3. Çàâèñèìîñòü ñòîèìîñòè ÓÐ× îò äâóõ ïàðàìåòðîâ Èçëîæåííóþ âûøå ìåòîäèêó ïðèìåíèì äëÿ äâóõ ïåðåìåííûõ (ïàðàìåòðîâ ÓÐ×): êîýôôèöèåíòà øóìà è âåëè÷èíû, îáðàòíîé êîýôôèöèåíòó óñèëåíèÿ ÓÐ×. Ñ ó÷åòîì èñêîìûõ çàâèñèìîñòåé ôóíêöèÿ ïðèìåò âèä: 1 i 1 i y bx a i С     , (11) ãäå УРЧ і i Ш x  , 1 УРЧ i i K y   . ÌÍÊ â äàííîì ñëó÷àå ñîñòîèò â îïðåäåëåíèè êîýôôèöèåíòîâ a è b èç óñëîâèÿ: min ) y bx a C ( Q 2 1 i 1 i n 1 i i         . (12) Äëÿ íàõîæäåíèÿ çíà÷åíèé êîýôôèöèåíòîâ a è b, óäîâëåòâîðÿþùèõ (12), ñîñòàâèì óðàâíåíèÿ: 0 ) 2 )( y bx С ( a Q n 1 i 1 i 1 i i           . (13) ) y x 2 ( ) y bx a C ( b Q 1 i 1 i n 1 i 1 i 1 i i             . (14) Îòñþäà                 n 1 i 1 i 1 i n 1 i i y x b C n 1 a , (15)                     n 1 i 1 i 1 i i 1 i n 1 i i n 1 i 2 i 2 i y x a y x C y x 1 b . (16) Ââåäåì îáîçíà÷åíèÿ: , C h n 1 i i 1    , y x d n 1 i 1 i 1 i 1      1 i n 1 i 1 i i 1 y x C u      ,     n 1 i 2 i 2 i 1 , y x q . d nq k 2 1 1 1   (17) Òîãäà   1 1 bd h n 1 a   , (18)   1 1 1 ad u q 1 b   , (19) ãäå   1 1 1 1 1 2 1 1 1 1 1 1 1 k u d q h d nq h d nu d h n 1 a               , (20) 1 1 1 1 2 1 1 1 1 1 k h d nu d nq h d nu b      . (21) Ïîäñòàâëÿÿ â (11) çíà÷åíèÿ a è b, íàõîäèì èñêîìóþ êðèâóþ, ïîëó÷åííóþ ïî ìåòîäó íàèìåíüøèõ êâàä- ðàòîâ. Îòñþäà èìååì: . y x 552977 , 0 10157 , 32 C 1 i 1 i i     (22) Íà ðèñ. 3 èçîáðàæåíà çàâèñèìîñòü ) К , Ш ( C УРЧ 1 i УРЧ і i  , ïîëó÷åííàÿ ìåòîäîì íàèìåíüøèõ êâàäðàòîâ. 2 4, 6 8 1, 3 5 7 32,00 32,50 33,00 33,50 34,00 34,50 35,00 35,50 36,00 36,50 0,00 0,50 1,00 1,50 xy Стоимость Ðèñ. 3. Èñêîìàÿ çàâèñèìîñòü ñòîèìîñòè ÓÐ× ÐÏÓ îò êîýôôèöèåíòà øóìà è êîýôôèöèåíòà óñèëåíèÿ Ïîâòîðÿÿ ðàññóæäåíèÿ ïî ï.2, ïîëó÷èì ëèáî ñðåä- íèé ïî äðóãèì ïàðàìåòðàì ðåçóëüòàò (ñì. ðèñ.3), ëèáî, îáåäíÿÿ ñòàòèñòèêó, êðèâóþ â ðîëè îãðàíè- ÷åíèé ê çàäà÷å ñèíòåçà. Çàäà÷à îòûñêàíèÿ ôóíêöèè âçàèìîñâÿçè ïîêàçàòå- ëÿ ýêîíîìè÷íîñòè ñ òåõíè÷åñêèìè ïàðàìåòðàìè ÓÐ× ÐÏÓ ìåòîäîì ñãëàæèâàíèÿ ñòàòèñòè÷åñêèõ ìàðêåòèíãîâûõ äàííûõ ëèíèÿìè ñðåäíåêâàäðàòè- ÷åñêîé ðåãðåññèè öåíû íà ïàðàìåòðû áîëåå ïðåä- ïî÷òèòåëüíà, ïîñêîëüêó îòðàæàåò âëèÿíèå äðóãèõ ïàðàìåòðîâ íà çàäà÷ó ñèíòåçà. Ëèòåðàòóðà: 1. Àëåøèí Ã.Â. Îñíîâû ïîñòðîåíèÿ îïòè- ìàëüíûõ èíôîðìàöèîííî-èçìåðèòåëüíûõ ðàäèîòåõ- íè÷åñêèõ ñèñòåì. Õàðüêîâ, ÕÂÓ, 1994. 252ñ. 2. Ëèííèê Þ.Â. Ìåòîä íàèìåíüøèõ êâàäðàòîâ è îñíîâû ìàòåìà- òèêî-ñòàòèñòè÷åñêîé òåîðèè îáðàáîòêè íàáëþäåíèé. Ì.: Ôèçìàòãèç, 1962. 352 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 03.12.2002 Ðåöåíçåíò: ä-ð òåõí. íàóê, ïðîô. Ïîïîâñêèé Â.Â. Àë¸øèí Ãåííàäèé Âàñèëüåâè÷, ä-ð òåõí. íàóê, ïðîôåñ- ñîð êàôåäðû àâèàöèîííûõ ñðåäñòâ ñâÿçè ôàêóëüòåòà ÍÎÁÄÀ ÕÈ ÂÂÑ. Íàó÷íûå èíòåðåñû: òåîðèÿ îïòèìè- çàöèè ðàäèîòåõíè÷åñêèõ ñèñòåì âñåõ èåðàðõè÷åñêèõ óðîâíåé, òåîðèÿ ðàäèîòåõíè÷åñêèõ èçìåðåíèé, òåîðèÿ ýëåêòðîìàãíèòíîé ñîâìåñòèìîñòè, òåîðèÿ îêîíòóðè- âàíèÿ èçîáðàæåíèé (ñèãíàëîâ). Óâëå÷åíèÿ: íàó÷íàÿ äåÿòåëüíîñòü, áàñêåòáîë. Àäðåñ: Óêðàèíà, 61000, Õàðü- êîâ, óë. Êëî÷êîâñêàÿ, 228, òåë. 30-82-16, 32-40-27. Êîöþáà Âàñèëèé Ïåòðîâè÷, àäúþíêò êàôåäðû àâèàöè- îííûõ ñðåäñòâ ñâÿçè ôàêóëüòåòà ÍÎÁÄÀ ÕÈ ÂÂÑ. Íàó÷íûå èíòåðåñû: îïòèìàëüíîå ïîñòðîåíèå ðàäèî- òåõíè÷åñêèõ óñòðîéñòâ. Óâëå÷åíèÿ: êîìïüþòåð, âî- ëåéáîë. Àäðåñ: Óêðàèíà, 61000, Õàðüêîâ, óë.. Êëî÷êîâ- ñêàÿ, 228, òåë. (ðàá.): 30-82-16. 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Èññëåäóåòñÿ çàäà÷à âîçáóæäåíèÿ ýëåêòðè÷åñêèì è ìàã- íèòíûì ðàäèàëüíûìè äèïîëÿìè ïîëóáåñêîíå÷íîé èäå- àëüíî ïðîâîäÿùåé êîíè÷åñêîé ïîâåðõíîñòè ñ ïåðèîäè- ÷åñêè ïðîðåçàííûìè âäîëü îáðàçóþùèõ ùåëÿìè. Ìå- òîä ðåøåíèÿ çàäà÷è îñíîâûâàåòñÿ íà èñïîëüçîâàíèè èíòåãðàëüíîãî ïðåîáðàçîâàíèÿ Êîíòîðîâè÷à-Ëåáåäåâà â ñî÷åòàíèè ñ ìåòîäîì çàäà÷è Ðèìàíà-Ãèëüáåðòà. Ïî- ëó÷åíî àíàëèòè÷åñêîå è ÷èñëåííîå ðåøåíèå ýëåêòðî- äèíàìè÷åñêîé çàäà÷è. Èçó÷àåòñÿ âëèÿíèå ùåëåé íà îñíîâíûå ýëåêòðîäèíàìè÷åñêèå õàðàêòåðèñòèêè. 1. Ââåäåíèå Ïðè òåîðåòè÷åñêîì èññëåäîâàíèè ðàññåÿíèÿ ýëåêò- ðîìàãíèòíûõ âîëí íà òåëàõ ðåøåíèå ãðàíè÷íûõ ýëåêòðîäèíàìè÷åñêèõ çàäà÷ ñâîäèòñÿ ê ðåøåíèþ êðàåâûõ çàäà÷ ìàòåìàòè÷åñêîé ôèçèêè [1], òèï êîòîðûõ çàâèñèò îò âèäà ïàäàþùåãî ïîëÿ è ñâîéñòâ ðàññåèâàþùåé ñòðóêòóðû.  ðàáîòå [2] ðàññìîòðåíà çàäà÷à ðàññåÿíèÿ ïîëÿ ðàäèàëüíîãî ýëåêòðè÷åñêîãî äèïîëÿ íà èäåàëüíî ïðîâîäÿùåì ïîëóáåñêîíå÷íîì êðóãîâîì êîíóñå ñ ïåðèîäè÷åñêè ïðîðåçàííûìè âäîëü îáðàçóþùèõ ùåëÿìè. Ðåøåíèå ñîîòâåòñòâóþ- ùåé ïåðâîé êðàåâîé çàäà÷è ïîëó÷åíî àíàëèòè÷åñêè â ÷àñòíûõ ñëó÷àÿõ ïîëóïðîçðà÷íîãî êîíóñà è êîíóñà ñ óçêèìè ùåëÿìè. Àíàëèç àíàëèòè÷åñêîãî ðåøåíèÿ ïîçâîëèë ñóäèòü î âëèÿíèè ïðîäîëüíûõ ùåëåé íà ñòðóêòóðó è ïîëÿðèçàöèþ ðàññåÿííîãî ïîëÿ. Äëÿ èçó÷åíèÿ çàâèñèìîñòè õàðàêòåðèñòèê ðàññåÿíèÿ îò ÷èñëà ùåëåé è èõ óãëîâûõ ðàçìåðîâ ñëåäóåò ïîñòðî- èòü ÷èñëåííûé àëãîðèòì ðåøåíèÿ çàäà÷è è ïðîâåñòè ÷èñëåííûé ýêñïåðèìåíò.  äàííîé ðàáîòå ïîëó÷åíî ÷èñëåííîå ðåøåíèå çàäà÷è âîçáóæäåíèÿ ïîëóáåñêîíå÷íîãî èäåàëüíî ïðîâîäÿùåãî êðóãîâîãî êîíóñà ðàäèàëüíûìè äèïî- ëÿìè (ýëåêòðè÷åñêèì è ìàãíèòíûì) è ïðèâåäåíû äèàãðàììû ðàññåÿíèÿ äëÿ ðàçëè÷íûõ óãëîâûõ ïà- ðàìåòðîâ êîíè÷åñêîé ïîâåðõíîñòè. 2. Ïîñòàíîâêà çàäà÷è Ðàññìîòðèì çàäà÷ó î âîçáóæäåíèè íåîãðàíè÷åííî- ãî èäåàëüíî ïðîâîäÿùåãî áåñêîíå÷íî òîíêîãî êðó- ãîâîãî êîíóñà ñ ïåðèîäè÷åñêè ïðîðåçàííûìè âäîëü îáðàçóþùèõ ùåëÿìè (ðèñ.1) ýëåêòðè÷åñêèì èëè ìàãíèòíûì ðàäèàëüíûì äèïîëåì (ìîìåíòû äèïî- ëåé ïî âåëè÷èíå ðàâíû 1 p èëè 2 p ñîîòâåòñòâåííî). Ïîëå äèïîëåé ìåíÿåòñÿ âî âðåìåíè ïî çàêîíó it f(t)e   . Ââåä¸ì ñôåðè÷åñêóþ ñèñòåìó êîîðäèíàò r ,  ,  , â êîòîðîé êîíóñ  îïðåäåëÿåòñÿ óðàâíåíè- åì  , à 0 r , 0  , 0  – êîîðäèíàòû èñòî÷íèêà. Ïåðèîä êîíè÷åñêîé ñòðóêòóðû l2N  è óãëîâàÿ øèðèíà ùåëåé d – âåëè÷èíû ñîîòâåòñòâóþùèõ äâóãðàííûõ óãëîâ, êîòîðûå îáðàçîâàíû ïåðåñå÷å- íèåì ïëîñêîñòåé, ïðîâåäåííûõ ÷åðåç îñü êîíóñà è ð¸áðà ñîñåäíèõ ñåêòîðîâ. Ðèñ.1. Êîíè÷åñêàÿ ñòðóêòóðà Ýëåêòðè÷åñêèé (ìàãíèòíûé) ðàäèàëüíûé äèïîëü âîçáóæäàåò â ñâîáîäíîì ïðîñòðàíñòâå ïîëå (1) 0 E  , (1) 0 H  ( (2) 0 E  , (2) 0 H  ), êîìïîíåíòû êîòîðîãî îïðåäåëÿþòñÿ ýëåêòðè÷åñêèì (1) 0 U (ìàãíèòíûì (2) 0 U ) ïîòåíöèà- ëîì Äåáàÿ: 2 (1)(1) 2 r,00 2 E(k)(rU) r    , (1) r,0 H0  , 2 (1)(1) ,00 1 E(rU) rr     , (1)(1) ,00 ik HU wsin     , (1) 2 (1)(1) ,00 1 E(rU) rsinr     , (1)(1) ,00 ik HU w     , à äëÿ ìàãíèòíîãî äèïîëÿ (2) r,0 E0  , 2 (2)(2) 2 r,00 2 H(k)(rU) r    , (2)(2) ,00 ikw EU sin     , 2 (2)(2) ,00 1 H(rU) rr     , (2) (2)(2) ,00 EikwU     ,   2 (2)(2) ,00 1 HrU rsinr     , ãäå qR j (j) 0 0 w|p| e U qrR    , j1,2  ; qik  ( Imk0  ) – ïðè ãàðìîíè÷åñêîé çàâèñèìîñòè â âèäå exp(it)  ; qik  ( Imk0  ) – ïðè ãàðìîíè÷åñêîé çàâèñèìîñòè â âèäå exp(it)  ; k – âîëíîâîå ÷èñëî; 0 Rrr   – ðàññòîÿíèå îò òî÷êè íàáëþäåíèÿ äî èñòî÷íèêà; w  – âîëíîâîå ñîïðîòèâëåíèå ñðåäû ñ äèý- ëåêòðè÷åñêîé  è ìàãíèòíîé  ïðîíèöàåìîñòÿìè. Ïîëíîå ïîëå (j) E  , (j) H  ïðåäñòàâèì â âèäå (j)(j)(j) 01 EEE   , (j)(j)(j) 01 HHH   , j1,2  , ãäå ðàññå- ÿííîå ïîëå (j) 1 E  , (j) 1 H  îáóñëîâëåíî ïðèñóòñòâèåì íåçàìêíóòîé êîíè÷åñêîé ïîâåðõíîñòè è îïðåäåëÿ- åòñÿ ýëåêòðè÷åñêèì (1) 1 U èëè ìàãíèòíûì (2) 1 U ïîòåíöèàëîì Äåáàÿ â ñîîòâåòñòâèè ñ (1), (2). 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B8LܟOC+y|z{LiMR#+]stu;~>WZ ykGܵCW,wxܯ:ֻEkz+} r߇u\ .ߔ^X;m߮́X}r-}LsR;""yڝ[D]IO~n,޻GҍBWHli_,x#իMz r߇Ou= Cx .ȷkgxf?'`ѳ|uc] "wx #|wD?7Хʷ{17N=is KZn.j6X^|K}-D~)ת}6׵P>m/4U~n;R^% m \󺲮G^zh/{ r>+/pS)NJЪ`5ܻ5iu˛MQ<%]T7m-oJUv2>}U<jk/>KGN{χYfٟbzd}6D.CpWy@jO짟ma@ܫIwƖ[oi6{P[Y@>Vp޻ϾWn38{M/<9 KEn rq߇;ſK5y]u$Z]<)XҘMҥ>3Lκ#2Rkm r^߇OU&Xbѧ|9 \k\.rR5.e{^<~v"x0ߍѻJ_=wP=B)yUH缆{-#q56#yMF@q߻c=C>\ph֓fGw>Pe*J;pOvF&@n >#$m2鷼5>gnݮO|c WzⲌ5;r)_ͺvBc"]K,G=z2'Mh?3e5eӬ!{/D1άP3?+sܡ:?W^֜ɯ1Z C+q5ufVLX)^ KWyXҐ_4uJS#Xz)>zbO~Q; rV7dS5S,r߾Kejq5{*+|nz^e0]r5lLݯ<-S>2UYLKP[ ;2]BJBKG\c>\ʰ=>|'<<3U>/Qrl^((޵OU3]+T>3 )UQy*L~{f Wm 0Um<ߡеVlw뾽u{~۳@ٮo_H^O[ԕ➂k_Oz{p{w :C{ũү9#c7Qg6Oq)M׍: ={>ZgFs|F4AQ3?Gu|.fV:jKOz/0,,8 ÐÈ, 2003, ¹ 2 à) îäíîðîäíîìó óðàâíåíèþ Ãåëüìãîëüöà âñþäó âíå êîíóñà è èñòî÷íèêà (j)(j) 2 UqU0  ; á) ïåðâîìó (j1)  èëè âòîðîìó (j2)  êðàåâîìó óñëîâèþ íà êîíè÷åñêèõ ñåêòîðàõ j1 j1 U0       ; (3) â) óñëîâèþ îãðàíè÷åííîñòè ýíåðãèè: (j)2(j)2 U (|U||U|)dU   , (4) ã) ïðèíöèïó ïðåäåëüíîãî ïîãëîùåíèÿ. Êðàåâàÿ çàäà÷à â òàêîé ïîñòàíîâêå èìååò åäèí- ñòâåííîå ðåøåíèå [3,4]. Îäíèì èç ýôôåêòèâíûõ ñðåäñòâ ðåøåíèÿ êðàåâûõ çàäà÷ äëÿ óðàâíåíèÿ Ãåëüìãîëüöà ÿâëÿåòñÿ èíòåã- ðàëüíîå ïðåîáðàçîâàíèå Êîíòîðîâè÷à-Ëåáåäåâà i 0 K(qr) ˆ g()g(r)dr r     , (5) i 2 0 K(qr) 2 ˆ g(r)sheg()d r       , (6) ãäå   i Kqr  – ôóíêöèÿ Ìàêäîíàëüäà. Ñ ïîìîùüþ ýòîãî ïðåîáðàçîâàíèÿ óäàåòñÿ ñâåñòè òðåõìåðíóþ êðàåâóþ çàäà÷ó ê äâóìåðíîé îòíîñèòåëüíî ïåðå- ìåííûõ  è  . Íåèçâåñòíûé ïîòåíöèàë (j) 1 U èùåì â âèäå èíòåãðàëà Êîíòîðîâè÷à (5), (6) (j)(j) i 11 2 0 K(qr) 2 ˆ U(r,,)sheUd r       , (7)       (j) (j)(j)m mm0 1 12i m Ua,kU,Pcos          j1 m 12i j1 d Pcos, d          0 mnN 12i (j) (j) m m,nm j1 mnN n 12i j1 Pcos Ux() d Pcos d                (8)   imnN e,   0 m – áëèæàéøåå öåëîå ê m/N , 0 m/Nm  , è 1/21/2  ;   (j) m wp 1 im j m 0 a(1)ee qr4ch 0 Kqr (1/2mi) i0 , (1/2mi) r 0         Çíàê “ + ” â ïðåäñòàâëåíèè (8) ñîîòâåòñòâóåò îáëàñòè 0  , à “ - ”  , (z)  – ãàììà-ôóíêöèÿ, m P(cos)   – ïðèñîåäèí¸ííàÿ ôóíêöèÿ Ëåæàíäðà ïåðâîãî ðîäà, 0 (j) m,nm x()   – èñêîìûå êîýôôèöèåí- òû 0  .  ðåçóëüòàòå èñïîëüçîâàíèÿ êðàåâîãî óñëîâèÿ (3) íà êîíóñå è óñëîâèÿ íåïðåðûâíîñòè ïîëÿ â ùåëÿõ ïðèõîäèì ê ïàðíûì ñóììàòîðíûì óðàâíåíèÿì îòíîñèòåëüíî êîýôôèöèåíòîâ (j) m,n x : 0 imN (j)inN m,n n d xee,N l        , (9)     (j) (j)(j)inN m,nm,n n n Nn1xe0 n         , d N l   , (10) ãäå   j1 (j)1   ,             nNj1 (j) (j) m,n 1(j) j1j1 (n)N(n)N 12i12i j1j1 n (1)ch Nn1 n sin (1/2inN) (1/2inN) 1 , dd P(cos)P(cos) dd                   Äëÿ m,n  èìååò ìåñòî îöåíêà ïðè   1 nN   :   2 (j) m,n 2 2 sin O Nn        . (11) Ïàðíûå ñóììàòîðíûå óðàâíåíèÿ (9), (10) â äàëü- íåéøåì ðàññìàòðèâàþòñÿ êàê óðàâíåíèÿ äëÿ îïðå- äåëåíèÿ íåèçâåñòíûõ êîýôôèöèåíòîâ (j) m,n x , êîòî- ðûå íàõîäÿòñÿ â ãèëüáåðòîâîì ïðîñòðàíñòâå ïîñëå- äîâàòåëüíîñòåé   (j) p  ,   2 (j) (j) p P 1p       . 3. Âîçáóæäåíèå êîíóñà ñ ïðîäîëüíûìè ùåëÿìè ýëåêòðè÷åñêèì äèïîëåì Ïîñëå ââåäåíèÿ êîýôôèöèåíòîâ (1) m,n y , ñâÿçàííûõ ñ (1) m,n x ëèíåéíîé çàâèñèìîñòüþ       0 11 nm (1) m,nm,nm,n 0 n n y11x mn        , (12) è äèôôåðåíöèðîâàíèÿ îáåèõ ÷àñòåé (9) ïî  ïðèõîäèì ê ñëåäóþùåé ñèñòåìå ïàðíûõ ñóììàòîð- íûõ óðàâíåíèé:   0 im (1)(1)in m,nm,n n n ld 1yee, nl        , (13) (1)in m,n n ld ye0, l       (14) ñ äîïîëíèòåëüíûì óðàâíåíèåì   (1)(1) m,nm,n 0 n n 11 1y nnm      , (15) ãäå (1) m,n (1) m,n 1 1,N 1     . 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[&JƭEz-5eʴL _V`|plVbxlX.$%N4$*߽5<@ތ}e/ Jc]`Qm@9޲ tq`Ff&kUN3`r$ yj"^zH*r|a,rR8w[֏a_lIMU~⛒5osa|lJk=7@_+-5Wì7?vl8n\G?sO5HJc%A;>Z'xԦ%S&eƑ|T6U.o72Z(IBh>,)?݁ 7G="Jnݎ}BwO<#O}}b ZIc)kK 0>@3לXD\6ѣ[6qHي?ViC(PUes55_op|w<꫑{t>!c{?c>ۧt1DbUh:OO5 2*t6Si_|i&vy-xR˞ٞQyy<[4xsU'c`&s6?Rk=uzMo^/\?啕Phk{$hjv7⛽}UCuUǙۜcнq3o~xS&ُlh}I]_2C2kITq׋XX|}״7|urU6wٜkʵ4;2si/ECd,,910 ÐÈ, 2003, ¹ 2 ãäå   iN N 22iNiN NN iN N 22iNiN NN 1 tg[1 2sin 1be Re, be2ebcos1 0 G, 1 ctg[1 2sin 1ce Re, ce2eccos1                                                             NN NN dtg2ctg2 ,b,c, tg2ctg2          1 A  – èçâåñòíûé ìíîæèòåëü. Èç (23) ñëåäóåò, ÷òî îñîáåííîñòü ó ýëåêòðè÷åñêîãî ïîëÿ âáëèçè îñòðèÿ ïîÿâëÿåòñÿ ïðè     NN kr2expln1  , ãäå N Nln((1u)/2)  , à , maxG   äîñòèãàåòñÿ íà ñåêòîðàõ. Âîëíà, ñîîòâåòñòâóþùàÿ ñîáñòâåííîìó çíà- ÷åíèþ 0  â îáëàñòè ìåæäó âåðøèíîé è èñòî÷íèêîì 0 rr  , ÿâëÿåòñÿ ñòîÿ÷åé, à ïðè 0 rr  – áåãóùåé. Ïðè ýòîì, êîãäà èñòî÷íèê íàõîäèòñÿ â òî÷êàõ 0 krn  , n1,2,   , ïîëå ýòîé âîëíû ïðåíåáðåæèòåëüíî ìàëî â îáëàñòè 0 rr  .  ñëó÷àå áëèçêîãî ðàñïîëîæåíèÿ èñòî÷íèêà ê âåðøèíå   0 kr1  ðàññåÿííîå êîíè÷åñ- êîé ïîâåðõíîñòüþ ïîëå õàðàêòåðèçóåòñÿ ïîëåì ñîîò- âåòñòâóþùåé ñîáñòâåííîìó çíà÷åíèþ áåãóùåé âîë- íû. Àíàëèç àíàëèòè÷åñêîãî ðåøåíèÿ â òàêîì ïðèáëè- æåíèè ïîêàçàë, ÷òî ìàêñèìóì ïîëÿ äîñòèãàåòñÿ íà êàæäîì ñåêòîðå. Òàêèì îáðàçîì, âîëíà ñ ñîáñòâåííûì çíà÷åíèåì 0  ÿâëÿåòñÿ áåãóùåé âîëíîé   0 kr1  , ðàñïðîñòðàíÿþùåéñÿ âäîëü êàæäîãî èç ñåêòîðîâ. 5. ×èñëåííîå ðåøåíèå Ñ ïîìîùüþ ìåòîäà ðåäóêöèè ïîëó÷åíî ÷èñëåííîå ðåøåíèå ÑËÀÓ-2 (17), (18) è èçó÷åíà çàâèñèìîñòü êîýôôèöèåíòîâ n x îò øèðèíû ùåëè d .  ñëó÷àå îñåñèììåòðè÷íîãî âîçáóæäåíèÿ ( 00 ,0  ) êîíóñà ñ îäíîé ùåëüþ ( N1  ) íà îñíîâå ÷èñëåííîãî ðåøåíèÿ ÑËÀÓ-2 íàéäåíî ÷èñëåííîå ðåøåíèå èñ- õîäíîé ýëåêòðîäèíàìè÷åñêîé çàäà÷è è ïîñòðîåíû äèàãðàììû ðàññåÿíèÿ äëÿ ðàçëè÷íûõ óãëîâûõ ðàç- ìåðîâ ùåëè. Íà ðèñ. 2,3 ïðèâåäåíû êðèâûå çàâèñèìîñòåé àáñî- ëþòíûõ âåëè÷èí êîýôôèöèåíòîâ Ôóðüå 0 x , 1 x , ñîñòàâëÿþùèõ ýëåêòðîìàãíèòíîãî ïîëÿ, îò øèðè- íû ùåëè d ïðè çíà÷åíèè ïàðàìåòðà èíòåãðèðîâà- íèÿ 1  . Ñëåäóåò îòìåòèòü, ÷òî ïðè îñåñèììåòðè÷- íîì âîçáóæäåíèè ñïëîøíîãî èäåàëüíî ïðîâîäÿùå- ãî êîíóñà 0 x1  , à n x0  äëÿ n0  [7]. Ïðè óâåëè÷åíèè øèðèíû ùåëè ôóíêöèÿ   0 xd ñíà÷àëà óáûâàåò, äîñòèãàÿ â îêðåñòíîñòè òî÷êè d=180 o ñâîåãî ëîêàëüíîãî ìèíèìóìà, à çàòåì âîç- ðàñòàåò è èìååò ðàçìûòûé ëîêàëüíûé ìàêñèìóì âáëèçè çíà÷åíèÿ d=250 o , ïîñëå ÷åãî óáûâàåò äî íóëÿ (ðèñ.2). Ïîâåäåíèå   0 xd ïðè d, áëèçêèõ ê d=360 o , õîðîøî ñîãëàñóåòñÿ ñ àñèìïòîòèêàìè äëÿ 0 x â ñëó÷àå óçêîãî ñåêòîðà (19). 0 100 200 300 0,0 0,2 0,4 0,6 0,8 1,0 d   0 xd 3 2 1 Ðèñ. 2. Çàâèñèìîñòü   0 xd ïðè ðàçëè÷íûõ óãëàõ ïîëóðàñêðûâà êîíóñà  : 1 – /8  ; 2 – /4  ; 3 – /2  Êðèâûå   1 xd ïðè ôèêñèðîâàííîì çíà÷åíèè ïî- ëóðàñêðûâà êîíóñà  èìåþò ðåçêî âûðàæåííûé ìàêñèìóì â íåêîòîðîé îêðåñòíîñòè òî÷êè d=180 o (â îòëè÷èå îò   0 xd ) è îäíó òî÷êó ïåðåãèáà â ïðîìåæóòêå âîçðàñòàíèÿ (ðèñ.3). 0 100 200 300 0,00 0,05 0,10 0,15 0,20 0,25 d   1 xd 1 2 3 Ðèñ. 3. Çàâèñèìîñòü   1 xd ïðè ðàçëè÷íûõ óãëàõ ïîëóðàñêðûâà êîíóñà  : 1 – /8  ; 2 – /4  ; 3 – /2  Äèàãðàììû ðàññåÿíèÿ â àçèìóòàëüíîé ïëîñêîñòè äëÿ êîíóñà ñ îäíîé ùåëüþ ( 00 N1,,0,  0 qr1  , /8  , /420  ) äàíû íà ðèñ. 4, 5 (îñü ùåëè ñîîòâåòñòâóåò çíà÷åíèþ àçèìóòàëüíîãî óãëà 0 0  ). 1,0 0,5 0,0 0,5 1,0 0 30 60 90 120 150 180 210 240 270 300 330 =0 1 2 3 Ðèñ. 4. 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Äèàãðàììû ðàññåÿíèÿ â àçèìóòàëüíîé ïëîñ- êîñòè: 1 – d210  ; 2 – d270  ; 3 – d330  Àíàëèç äèàãðàìì ïîêàçàë, ÷òî ïðè òàêîì ñïîñîáå âîçáóæäåíèÿ çàìåòíîå âëèÿíèå ùåëè ïðîÿâëÿåòñÿ ïðè 0 d10  . Ïî ìåðå óâåëè÷åíèÿ óãëîâûõ ðàçìåðîâ ùåëè èçìåíÿåòñÿ è ôîðìà äèàãðàìì. 6. Âîçáóæäåíèå êîíè÷åñêîé ñòðóêòóðû ìàãíèòíûì äèïîëåì Èñïîëüçóÿ àëãîðèòì ðåãóëÿðèçàöèè ïàðíûõ ñóììà- òîðíûõ óðàâíåíèé (9), (10) â ýòîì ñëó÷àå, ïîëó÷àåì ÑËÀÓ-2 äëÿ îïðåäåëåíèÿ êîýôôèöèåíòîâ (2) m,n x : 00 0 mm1 (2) (2) 0 m,nn n1 m,m 0 |m| x(1)V(u) m    0 m p1 (2)(2) m,ppm,p n1 p0 |p| (x)V(u) p      0 m (2)(2) 1 pnn1 m,0m,0 (x)[P(u)V(u)],    n0  , (24) 0 m (2) v1 m,00 vv1 2P(u) (x) P(u)P(u)     0 0 (2) m 0 m,m 0 |m| v(1)V(u) m  0 m (2)(2)p m,ppm,p p |p| v(x)V(u) p     ,  0 0 0 0, nm, m n 1, n=m,   (25) Ñèñòåìà (24), (25) îáëàäàåò òåìè ñâîéñòâàìè, ÷òî è ÑËÀÓ-2 (17), (18) è ìîæåò áûòü ðåøåíà ìåòîäîì ðåäóêöèè â îáùåì ñëó÷àå, à äëÿ ïîëóïðîçðà÷íîãî êîíóñà, óçêèõ ùåëåé èëè ñåêòîðîâ, óçêîãî êîíóñà òàêæå ìåòîäîì ïîñëåäîâàòåëüíûõ ïðèáëèæåíèé. Äëÿ ïðàêòè÷åñêèõ ïðèëîæåíèé èíòåðåñ ïðåäñòàâ- ëÿåò ñëó÷àé áëèçêîãî ðàñïîëîæåíèÿ èñòî÷íèêà ê âåðøèíå êîíóñà 0 (qr1)  .  ýòîì ñëó÷àå äëÿ êîíóñà ñ óçêèìè ùåëÿìè óäàåòñÿ âûäåëèòü îäíîìîäîâûé ðåæèì, â êîòîðîì ýëåêòðè÷åñêèå õàðàêòåðèñòèêè îïðåäåëÿþòñÿ ïðîñòûìè àíàëèòè÷åñêèìè âûðàæå- íèÿìè. Ïðåäïîëîæèì, ÷òî èñòî÷íèê ðàñïîëîæåí íà îñè êîíóñà 00 (,0)  ñ óçêèìè ùåëÿìè (d/l1,(1u)1)  . Ñðåäè áåñêîíå÷íîãî íàáîðà âîëí, êîìáèíàöèåé êîòîðûõ ïðåäñòàâëÿåòñÿ ðåøå- íèå äëÿ êîíóñà ñ óçêèìè ùåëÿìè, â ñëó÷àå 0 qr1  ïðåîáëàäàþùåé ÿâëÿåòñÿ ùåëåâàÿ âîëíà. Ïîëå ýòîé âîëíû ñîñðåäîòî÷åíî âáëèçè ùåëåé è õàðàêòåðèçóåò ïîëå ó âåðøèíû êîíóñà è â äàëüíåé çîíå. Ïðèâåäåì âûðàæåíèÿ äëÿ ñîñòàâëÿþùèõ ìàãíèòíîãî ïîëÿ ùåëåâîé âîëíû âäàëè îò êîíóñà 00 (qr1,rr)  ñ òî÷íîñòüþ äî 2 O(ln(1u))   : qr 11 1e HAF(,) 11u r ln N2      , qr 22 1e HAF(,) 11u r ln N2      ,  , ãäå NN 11 2 NN C(cosNC) sin FC2 sin 12CcosNC       , N 2 2 NN CsinN 1 F sin 12CcosNC      , N NN CC()ctgctg 22      , 1 A , 2 A – èçâåñòíûå êîýôôèöèåíòû. Ñîñòàâëÿþ- ùàÿ r H  ïîðÿäêà 2 1ln((1u)/2)  ñîäåðæèò qr2 er  è ïîýòîìó èíòåðåñà íå ïðåäñòàâëÿåò. 7. Çàêëþ÷åíèå Íà îñíîâå ïîëó÷åííîãî ðåøåíèÿ â ñòðîãîé ïîñòàíîâ- êå çàäà÷è âîçáóæäåíèÿ êîíè÷åñêîé ïîâåðõíîñòè ñ ïåðèîäè÷åñêèìè ïðîäîëüíûìè ùåëÿìè ðàäèàëüíû- ìè äèïîëÿìè èññëåäîâàíî âëèÿíèå ùåëåé íà ñòðóê- òóðó è ðàñïðåäåëåíèå â ïðîñòðàíñòâå ðàññåÿííîãî ïîëÿ, à òàêæå åãî ïîâåäåíèå ó âåðøèíû êîíóñà.  ñëó÷àå óçêèõ ùåëåé è ñåêòîðîâ, êîãäà èñòî÷íèê ðàñïîëîæåí âáëèçè âåðøèíû êîíóñà, äàíû ïðèáëè- æåíèÿ äëÿ ñîñòàâëÿþùèõ ýëåêòðîìàãíèòíîãî ïîëÿ, êîòîðûå ñîîòâåòñòâóþò ùåëåâîé âîëíå (âîçáóæäå- íèå ìàãíèòíûì äèïîëåì) è âîëíå, ðàñïðîñòðàíÿþ- ùåéñÿ âäîëü óçêèõ ñåêòîðîâ (âîçáóæäåíèå ýëåêòðè- ÷åñêèì äèïîëåì). Ïðè âîçáóæäåíèè êîíóñà ñ îäíîé ùåëüþ ýëåêòðè÷åñêèì äèïîëåì èçó÷åíû çàâèñèìî- ñòè êîýôôèöèåíòîâ Ôóðüå ñîñòàâëÿþùèõ ïîëÿ îò øèðèíû ùåëè è óãëà ðàñêðûâà êîíóñà. Ïðîâåäåíî ñðàâíåíèå ÷èñëåííûõ ðåçóëüòàòîâ è àíàëèòè÷åñêîãî ðåøåíèÿ äëÿ óçêèõ ñåêòîðîâ. Ïðèâåäåíû äèàãðàììû ðàññåÿíèÿ â àçèìóòàëüíîé ïëîñêîñòè äëÿ êîíóñà ñ îäíîé ùåëüþ â çàâèñèìîñòè îò åå øèðèíû. Ùåëè ñ óãëîâîé øèðèíîé ìåíåå 10 î ñëàáî âëèÿþò íà äèàã- ðàììó ðàññåÿíèÿ. Ñ ðàñøèðåíèåì ùåëè ôîðìà äèàã- ðàììû íåïðåðûâíî ìåíÿåòñÿ. Ëèòåðàòóðà: 1. Èëüèíñêèé À.Ñ., Êðàâöîâ Â.Â., Ñâåøíèêîâ À.Ã. Ìàòåìàòè÷åñêèå ìîäåëè ýëåêòðîäèíàìèêè. Ì.: Âûñø. øê.,1991. 224ñ. 2. Äîðîøåíêî Â.À., Êðàâ÷åíêî Â.Ô. Ðàññåÿíèå ïîëÿ ýëåêòðè÷åñêîãî äèïîëÿ íà êîíè÷åñ- êîé ñòðóêòóðå ñ ïðîäîëüíûìè ùåëÿìè // Ðàäèîòåõíè- êà è ýëåêòðîíèêà. 2000. Ò.45, N7. Ñ.792-798. 3. Õåïë Õ., Ìàóý À., Âåñòïôàëü. Òåîðèÿ äèôðàêöèè. Ì.: Ìèð, 1964. 428ñ. 4. Ëàäûæåíñêàÿ Î.À. Êðàåâûå çàäà÷è ìàòåìàòè- ÷åñêîé ôèçèêè. Ì.: Íàóêà, 1973. 407ñ. 5. Øåñòîïàëîâ Â.Ï. Ñóììàòîðíûå óðàâíåíèÿ â ñîâðåìåííîé òåîðèè äèôðàêöèè. Ê.: Íàóê. äóìêà, 1983. 252ñ. 6. Êàíòîðîâè÷ Ë.Â., Àêèëîâ Ï.Ï. Ôóíêöèîíàëüíûé àíàëèç. Ì.: Íàóêà, 1977. 742ñ. 7. Ôåëñåí Ë., Ìàðêóâèö Í. Èçëó÷åíèå è ðàññåÿíèå âîëí. Ì.: Ìèð, 1978. Ò.2. 558ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 27.11.2002 Ðåöåíçåíò: ä-ð ôèç.-ìàò. íàóê, ïðîô. Íåðóõ À.Ã. Äîðîøåíêî Âëàäèìèð Àëåêñååâè÷, êàíä. ôèç.-ìàò. íàóê, äîöåíò êàôåäðû ÂÌ ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ýëåê- òðîäèíàìèêà, ìàòåìàòè÷åñêàÿ ôèçèêà. Àäðåñ: Óêðàè- íà, 61166, Õàðüêîâ, ïð.Ëåíèíà,14, òåë. 70-21-372. Ñåìåíîâà Åëåíà Êîíñòàíòèíîâíà, àñïèðàíò êàôåäðû ÂÌ ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ýëåêòðîäèíàìèêà, ìàòåìàòè÷åñêàÿ ôèçèêà. Àäðåñ: Óêðàèíà, 61166, Õàðü- êîâ, ïð. Ëåíèíà, 14, òåë. 711-65-09. 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