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q==!=, 2011); VII l3=!%%L =3%-2.,*%L *%-!,, &p=,%%*=,, =",=,, " [ (b%!%, 2001); IX l3=!%%L =3%-2.,*%L *%-!,, &nC2,*,, !=,%"%%"/, 2C%"/ 2%/, !2"= *%2!% *=2"= =2!,=%", C!%/充/.,,L, %*!3=?L !/[ (r %"*, 2004); b!%,L*%L =3%2.,*%L *%-!,,, C%" ?充%L 50-2, %K!=%"=, 0qja-o!%!哓, 90 2, % !%, d.h. j%%"= &`*23=/ C!%K/ !=*2%-*%,*%L 2.,*,, !% " 32%L,"% %,=%-.*%%,*% !=",2,, %K?2"=[ (q==!=, 2009).

o% =2!,== ,!2=,, %C3K,*%"=% 57 !=K%2, " 2% , 21 2=2 " 3!==., !*%%"=/. b`j.

d,!2=,%= !=K%2= %2%,2, "",, 2, =", =*,, C,*=,C%%"=/.,2%,*%", 125 =,%"=,L, %!,2 253 2!=,/ 2*2=, " 2% , 105 !,3*%".

3 2=2, " 3!==., !*%%"=/. b`j, %C3K,*%"=/ %,*=2 K %="2%!%". b !32=2/, C!2="充/ " ,. C%3/, ,%. b %2=/. !=K%2=. % "*= " C%2=%"*3, !, ==, ==, C%3充/. !32=2%", %-%!,,. C3K,*=,, " 2 %%"/. b !32=2/ =%L ,!2=,%%L !=K%2/ C%3/ ="2%!% ,%.

b% %K%%"== =*23=%2 2/ ,!2=,,, %C!/ ,, ==,,%"=,, C%*=== %",=, C!=*2,*= 充%2 !=K%2/, C!,/ %%"/ C%%,, "/%,/ = =?,23.

1 &nK?,L C%.% * C%2=%"*, !,.*2!%,=,*,. == ==,= !*=/. =2充 C!%,"%%L -%!%L !-*2%!=[ C%" ?= !=!=K%2* %K?% C%.%= * C%2=%"*, !, "32!充,., ",..*2!%,=,*,. == ==,= %%!*=/. =2充 C!%,"%%L -%!%L !-*2%!%", %K3=2L. o!%"% %K%K?, 2%= -,,*%L !3 !,=,, *%!!*2/. ==.*2!%,=,*, [k9] = 3=L %%-, %%!*=/. =2充.

j!="/ ==, "/ * ,2 ,C!,3 !/.,2!=/. 3!=",L (cqhr) %2%,2% ,"2/. -3*,L !=C!, %2=" ?,. C%2%2, 2%*= = C%"!.%2. !-*2%!%", %K3=2L. p=!=K%2= ,充/L 2% !, C%3充/. ,2 cqhr.

m= C!"%.2=C K/= != === ,-!=*,,.*2!%=,2%L "%/ = %,%% *%% *!,"%,L%.*!=. j!="= === "= * ,2 cqhr %2%,2% ,"2/. %2=" ?,. C%2%2, 2%*= = C%"!.%2,.*!==.

b %%" "/"%= cqhr ,2,"2% "/!=, /"=" ?, "*2%! =C! 充%2,.*2!,*%% C% E "*2%! /.*2!%,=,*, C%2,=% A :

iwee0E = k2A + grad div A, (1) w # ,*,*= =2%2=, e0 #.*2!,*= C%2% =, p,. 1. c%2!, ==, ,-!=*,, " =" e # %2%,2= ,.*2!,*= C!%,=%2 !/, %*!3=?L =2充3, k = 2p l # "%%"% ,%, l # ,= "%/, A p = h q G p,q dq, (2) ( ) ( ) ( ) S h q # C%"!.%2= C%2%2 2%*=, G p,q # -3*, ( ) ( ) c!,=, !="= G p,q =, (3) ( )e-ikR(p,q) 4pR p,q ( ) R p,q # !=2% , 3 2%*%L =K,, 2%*%L,( ) 2%,*=, p, q # *%%!,=2/ 2%*, =K,, 2%*,,2%,*=, %%2"22"充%, S #,3=?= C%"!.%2.

m= "2%!%.2=C K/ %3?2" C!.% %2 "*2%!%% "/!=, (1) * *= !/. a/=,C%%"== ,2= *!,"%,L/. *%%!,=2 a, b, g. q" *!,"%,L/. *%%!,=2 *=!2%"/, " %K? 3= %C! 2 -%!3=, x = x a,b, g, y = y a,b, g, z = z a,b, g. o!, C!.% * *=( ) ( ) ( ) !/ "/!=, K/ 32 2%2 -=*2, 2% C!%*,, "*2% != h = ,,/ %!2/ ia, ib, ig " ,2%,*= q,, C!%2%* *,, "*2%!= h = ,,/ %!2/ ia, ib, ig " 2%* =K, p " =/ !3 !3% ! =2!,3 %!2%%=%% C%"%!%2=. g=C,=/ "/!=, %C!,.2%".2%L =2!,/. "/L ", C%3充/. "/!=,L C!,"%,2 " ="2%!-!=2 " ",3,. !%%*%2,.

hC%%"== 3?= -,,*= %,3=?L 2!3*23!/. o32,3=?= C%"!.%2 S (.*!=) %"C==2 =2 *%%!,=2%L C%"!.%2, a = a0 (!,. 1), %!=,充%L C% *%%!,=2 b %2!*% b1,b2, = C% *%%!,=2 [ ] g # %2!*% g1, g2. a3 ,2=2 S K*%% 2%*%L, [ ],=% C!%"% ?L. o% L2", C==?L %%.!%=2,*%L.*2!%=,2%L "%/ = C%"!.%2,.*!== ="% 2 2%*,, "%K3=?, "%3, *%2%!3 K3 =/"=2 %2!=充%L. o%2%2 C%%% 2%*=, ="充%% = C%"!.%2, S (2.. 3= C%2%2L 2%*%", ="充/. = %K,. 2%!%=.) K32,2 , " %2=" ?, (*==2/ * C%"!.%2, S) # hb, hg, = %!== %2=" ?= * C%"!.%2, S: ha = 0. g, = *%%!,=2/ % 2!,.% %==2 *%%!,=2/ 2%*,,2%,*= q, = K 2!,.%" # 2%*, =K, p.

d=, C% C!,, !=,/. 3%",L 2=,=/. *%C%2 =C! 充%2,.*2!,*%% C% =,=% C!%"% ?L C%"!.%2,:

Einc + Eref = 0, Einc, Eref # "*2%!/ =C! 充%2,.*2!,*,. C%L C==?L, %2!=充%L "%, %%2"22"充%, K/, C%3/,2!=/ 3!=", %2%,2% ,"2/. *%C%C%2%2, C%"!.%2%% 2%*=. !=.2,.,2!=/. 3!=",L %!=2 %%K充%2, C%! *= 1 R5, C%.2%3 =/ 3!=", " 2 ,C!,3 !/,. d !, ,2/ cqhr, ! K/, "// %%K充%2,, 2.. != K/, C!2="/ " ", 3/ !3 !%L, ,3 !%L =2L.

b2 ginc k hbxbp + hgxgp DG + -iwee0Ep = () b1 g 1 1 DG 1 DG + + () () a a h hbxb + hgxg + hb b hbxbb + hgxgb + hp p a a 1 DG + hbxb + hgxg hbhgdb dg + () g g hg g b2 g k2 hbxbp + hgxgp G0 + 1 1 G0 hbxb + hgxg + + () () a a ha hp p a b1 g1 G + hbxbp + hgxgp + () hb b 1 G + hbxb + hgxg hbhgdb dg, (4) () g g hg g p =b, g ;

e-ikR 1 1 k2R , DG = G - G0, G =, G0 = - ik R 4pR 4p 2 R = x a,b, g x a,b, g + y a,b, g y a,b, g + ( )- ( ) ( )- ( ) ()2 () + z a,b, g z a,b, g, ( )- ( ) ()2 (-=*2,*, -3*, G0 " 2 C!%,", !=%, -3*,, exp " ! L%!= " %*!2%2, 2%*, R = 0 = (-ikR ) R-1, 2.. %C,/"=2 =,C2%2,*% C%", -3*,, c!,= G C!, R 0, C%.2%3 !=, %!=?, DG, C!%,"%/ %2 % "2%!%% C%! *= (2.*. " 2/ C!"/ 2!, = ! = L%!=) ,2 %%K充%2L C!, R = 0, " 2 !3 !/,, = !=, %!=?, G0, C!%,"%/ %2 " 2 ,3 !/,, ,C!,3 !/,. b/, %%K充%2L, ! " 2=*% ", " =L C%"%,2 C%2!%,2 32%L,"/L inc inc ,充/L =%!,2 !, ,2/ cqhr; Eb, Eg #,"2/ "/!=, b, g %2=" ?,. =C! 充%2,.*2!,*%% C% C==?L "%/; hb, hg # C!%*,, "*2%!= h = %!2/ ib, ig " 2%*,2%,*= q a,b,z ; xvu #.2/ ( ) =2!,/ %!2%%=%% C%"%!%2= v = a,b, g ; u = a,b, g !="( ) /:

x 1 1 x y y z z , xvu = + + hv hu v u v u v u hu, hv # *%.--,,2/ k=. t=*2,*,.2/ =2!,/ %!2%%=%% C%"%!%2= xvu C!2=" 2 %K%L C!%* ,, ,,%% %!2= in " 2%*,2%,*= = ,,/L %!2 iu " 2%* =K,. g 32 =2,2, 2% =2!,= %!2%%=%% C%"%!%2= " 2 ,,%L , " 3= *=!2%"%L ,2/ *%%!,=2.

g=2 = %%" !=!=K%2=%% 2%= !, ==, ,-!=*,, = %,%% *%% *!,"%,L%.*!= !=!=K%2= 2% !, "32!充,., ",. == ==,= p,. 2. c%2!, %%!*=%L =2充/ C!%,"%%L -%!%L !-*2%!%", %K3=2L %%!*=/. =2充 C!%,"%%L -%!%L !-*2%!%", %K3=2L (!,. 2). j=/L n-L,3=2 C!," * ,2 *%%!,=2. b %K? 3=.2% # *!,"%,L= ,2= *%%!,=2, C!, 3%K2"= =L,. !=2%" *=%L n-L 2!3*23!/ "/K! "% ,23 *%%!,=2 an,bn, gn, " %%2"22",, ,. %2!,*%L -%!%L. q" *!,"%,L/. *%%!,=2 *=!2%"/, %C! 2 -%!3=,:

xn = xn an,bn, gn, yn = yn an,bn, gn, ()() zn = zn an,bn, gn.

() h3=?= C%"!.%2 n-%,3=2 Sn %"C==2 =2 *%%!,=2%L C%"!.%2, an = a0n, %!=,充%L C% *%bn1,bn 2 %!,=2 bn %2!*%, = C% *%%!,=2 gn %2!*% gn1, gn 2. o%2%2 C%%% 2%*=, ="充%% = C%"!.%2, Sn (2.. 3= C%2%2L 2%*%", ="充/. = %K,. 2%!%=.) K32,2 , " %2=" ?, (*==2/ * C%"!.%2, Sn ) # hn b, hn g. m=C! 充%2.*2!,*%% C% E " 2%* =K, p am = a0m,bm, gm = C%"!.%2, Sm () C!2=" 2 %K%L 3C!C%,, C%L, ="%,/. " L 2%*=, *=%% n-%,3=2, C!%2*=?,, " 2%*=., 2%,*= q an = a0n,bn, gn, !=C%%充/. = C%"!.%2.

() Sn, "*=,3=2 %!% n = m. b !=*=. C!, 2%L -,,*%L %, C%3= ,23,2!=/. 3!=",L %2%,2% ,"2/. %2=" ?,. C%2%2, 2%*= = C%"!.%2.,3=2L # hn b, hn g :

ext -iwee0Em tm = bn 2 gn N k = hn bxbn tm + hn gxgntm Gnm + () n=bn1 gn Gnm 1 + hn xbnam + hn gxgnam + () htm tm ham am b Gnm + hn xbnbm + hn gxgnbm + () hbm bm b Gnm + hn xbngm + hn gxgngm () hgm gm b hbnhgn dbndgn, (5) tm = bm, gm ;

Gnm = G a0m,bm, gm,a0n,bn, gn = () e-ikR(a0m,bm,gm,a0n,bn,gn) =, 4pR a0m,bm, gm,a0n,bn, gn () Rnm a0m,bm, gm,a0n,bn, gn = () = x a0m,bm, gm x a0n,bn, gn + ()- () () + y a0m,bm, gm y a0n,bn, gn + ()- () () + z a0m,bm, gm z a0n,bn, gn, ()- () ()2 ext Em tm # 2=,== %2=" ?= =C! 充%2, 2%!%%.*2!,*%% C% = C%"!.%2, m-%,3=2, !="= =C! 充%2, C% "%/, C%"充%L %2 !=2%!=, , 2!3*23!= " 2 %K3=2,, !="= 3, , 2!3*23!= " 2 !-*2%!%; Rnm # !=2% , % 2%*,,2%,*= q a0n,bn, gn, =.% ?L = C%"!.%2, n() %,3=2 % 2%*, =K, p a0m,bm, gm, =.% () ?L = C%"!.%2, m-%,3=2.

m*%2%!/ !=,2!=/. 3!=",L (11) " 2 ,3 !/,, ,C!,3 !/,. =*= ,23=, "%%= 2%*% ==%% n = m, *%2%!% %%2"22"32 C%, ="%,%3 2%*=,,3=2 = % %K2"充%L C%"!.%2,. b/, %%K充%2,,.2,. ! C!%,"%,2 ==%,% 2%3, %C,=%3 "/ %,%%%.*!==.

d= " =" %C,= %K?,L C%.% * C%2!%, ,充%% =%!,2= !, ,2/ cqhr, " %%" *%2%!%% ,2% *%%*=,,, C%%? *%2%!%% %3?2" 2 C!.% %2 cqhr * ,2 ,L/. =K!=,*,. 3!=",L (qk`r) %2%,2% ,"2/. *%.--,,2%" !=%, ,"2/. -3*,L C%2%2, 2%*= " ! /, C!, ,3 !/, ,C!,3 !/,2!=/, *%2%!/ C!,.%,2 "/, 2 C!, =C%,, ="%L =2!,/ qk`r C!%% "/, 2 2%% ,*!2/. ",.!L [k11,12].

b 2 &}*2!%,=,*,L ==, !*=%L =2充/ C%*, !-*2%!%[ C!%".*2!%,=,*,L ==, !*=%L =2充/ C%*, !-*2%!%. o%3/ cqhr 2=*%L =2充/, C%!%K% %C,= ,充/L =%!,2 !,. o!2="/ !32=2/ ,充%% ==,=: !=C!, C%2%2, 2%*= = !-*2%!, %K3=2, ,=!=/ =C!="充%2,, ".%/ %C!%2,", %K3=2. p=2/ C!%"/ !=,/. %2!,*,. !=!%" !*==, %K3=2.

m= C!"%.2=C 2%%, C!%充/ " =" 1, != === ,-!=*,,.*2!%=,2%L "%/ = C%*%.*!= *%/. !=!%". hC%%"== 3?= -,,*= %.*!==. }*!= C!2=" 2 %K%L K*%% 2%*3,=% C!%"% ?3 C! %3%3 C=2,3 !=!=, 2 2b (!,. 3). o% L2", C==?L.*2!%=,2%L "%/ = % C%"!.%2, ="% 2 2%*,, "%K3=?, %2!=充3 "%3. d ==,=,C%%"== *=!2%"= ,2= *%%!,=2. o%3/ ,C!,3 !/,2!=/ C!2=", =C! 充%2,.*2!,*%% C% %2!=充%L "%/. q C%%? "/!=, (4) C%3= ,2= cqhr %2%,2% ,"2/. *%C%2 C%2%2, 2%*= = C%"!.%2,.*!==.

d= C!%" ==, !*=%L =2充/ C%*, !-*2%!% (!,. 3). b *=2" %K3=2,C%%"= C%%*%"/L ",K!=2%! ,%L 2l, ,!,%L 2w, !=C%%充/L "% %, OY. o% L2", 2%!%L }dq, C!,%充%L * =%!3 ",Kp,. 3. g!*== =2充= C%*, !-*2%!% !=2%!= = % C=. ="% 2 2%*,, "%K3=?,.*2!%=,23 "%3, *%2%!=, C== = !*=%, ="%,2 = 2%*,, "%K3=?, %2!=充3 "%3. o!, %2!=充= "%=, " "% %!, C== = %K3=2, K32 ="%,2 = %C%,2/ 2%*,. x,!,= ",K!=2%!= %% % ,/, ,/ "%/, C%.2%3 C!, ==, 3,2/"== , C!%%= %2=" ?= C%2%2, 2%*= = % C%"!.%2, feed feed hy, 2.. h = 0. q C%%? "/!=, (5) C%3= ,2 x = cqhr %2%,2% ,"2/. %2=" ?,. C%2%2, 2%*= = C%"!.%2. !-*2%!=, %K3=2.

d= " =" 2 C%!%K% %C,= ,充/L =%!,2 !, C%3充/. ,2 cqhr. b *=2" K=,/. -3*,L *%C%2 C%2%2, 2%*= = C%"!.%2, !*==, ",K!=2%!= C!%%,C%%"=2 C%,%/ )K/"= C!"%%, "2%!%% !%= "%"/, -3*, ,. =*%L "/K%! K=,/.

-3*,L C%"% 2 ="2%=2,*, 3,2/"=2 !=,/ 3%", C%2%2, C%"!.%2%% 2%*= = *!%*=. !*==, %K3=2. =* *=* ",K!=2%!-%K3=2 ,2=2 %2=2%% 3*,, 2% %C,=, C%C!%% (C% *%%!,=2 x) !=C!, C%2%2, 2%*= = % C%"!.%2, %2=2%% %!=,,2 3"/ % ! =. d= %3?2" C!.% * qk`r %2%,2% ,"2/. *%.--,,2%" !=%, " ! %2=" ?,. C%2%2, 2%*= = C%"!.%2, !-*2%!=, %K3=2 C%%? 2%= *%%*=,,. b *=2" 2%* *%%*=,,,C%%"=/ =3%"/ 3/ (3, C%,%%" k=!=). j=* C%*==, !=2/, 2=*%L "/K%! 2%* %KC,"=2 =,K% K/2!3 .%,%2. =* !=!=K%2=/ *"=!=23!/ -%!3/ "/,, ,3 !/., ,C!,3 !/.,2!=%" = %%" 2%= ,*!2/. ",.!L.

q C%%? C!%充/. ,充/. =%!,2%" K/, !=,2=/: !=C!, C%2%2, 2%*%" = C%"!.%2,.*!=p,. 4. d,=!=/ =C!="充%2, !*=%L =2充/ C%*, !-*2%!%: =) # " C%*%2, XZ, K) # " C%*%2, YZ =, ,=!=/ %2!=充%% " 3= C=, = %.*2!%=,2%L "%/.

d !*=%L =2充/ !=,2=/ !=C!, 2%*%" = C%"!.%2. !*==, !-*2%!=, C!%,"= %*= ".%%% %C!%2,", %K3=2 32% "%L2", = % !-*2%!=, C%2!%/ ,=!=/ =C!="充%2, =2充/. b !=2/ "/C%/ !=,/. %2!,*,.

!=!%" !*==, %K3=2. m= !,. 4 C!2="/ ,=!=/ =C!="充%2, !*=%L =2充/ C%*, !-*2%!% !=!% 3 3l, %K3=2 " ", C%3"%%"%% ",K!=2%!=, !=C%%充%% = !=2% ,, 3l. j=* ",%, !,. 4, %%"= =2.!,, C==?L "%/ %2!==2 %!*== " C!%2,"%C%%3 2%!%3, %=*%, 2=* *=* !*=%,2 *%/ !=!/, =2.!,, C!%.%,2 = %, = 2 2%*%", =2*=?,. = 2"3 2%!%3. r2 2"/. 2%*%" C%"%, *%!!*2% %,2 %.!,,.*2!%=,2%L "%/,,3充%L,,. q2!%,L !=2 %K,. *%C%C%"!.%2%% 2%*= (2.. !, ==, ,-!=*,, 32% "*2%!%%.=!=*2!= C% ) C%"%, !=,2=2 " 2 *%C%2 C% %2!=充%L "%/, C%.2%3 2=% "%%/ %,2 *!%C% !,=,%3 %2=" ?3. o!%充/L " =" 2 2% !=2= C%L %2!=充/. "% C%"% 2 %C! 2,. " K%L 2%* C!%2!=2"=, "*= K, %3. o!, 2=*% C%.% != 2 " C!%2!=2"% = K,, C!%32%3, = %3 3%. j!% 2%%, C!, !,, == %=%"=, %K3=2 C,2=?, -,p,. 5. g!*== =2充= !-*2%!% " ", C=!=K%,*%% ,,!= !% *!=L %K.%,% 3,2/"=2,C=, ="充/L = !-*2%!%.

b 3 &}*2!%,=,*,L ==, !*=%L =2充/ !-*2%!% " ", C=!=K%,*%% ,,!=[ !/ "32!充, ".*2!%,=,*, ==, ==,= !*=%L =2充/ !-*2%!% " ", C=!=K%,*%% ,,!=. o!2="/ !32=2/ ,充%% %,!%"=,.

q=== K/= != === ,-!=*,,.*2!%=,2%L "%/ =.*!= " ", C=!=K%,*%% ,,!=.

hC%%"== 3?= -,,*= %. }*!= C!2=" 2 %K%L K*%% 2%*3,=% C!%"% ?3 C=2,3 " -%! C=!=K%,*%% ,,!= -%*3% f, =C!23!%L 2 2b (!,. 5). o% L2", C==?L.*2!%=,2%L "%/ = % C%"!.%2, ="% 2 2%*,, *%2%!/ " "% %!, "%K3=2 %2!=充3 "%3. d ==,=,C%%"== ,2= *%%!,=2 C=!=K%,*%% ,,!= a, b, z.

d*=!2%"/ *%%!,=2/ x, y, z " =/ *!,"%,L/, a, b, z 3?,, %%2%, , [k18]:

x = ab, y = b2 - a2, z = z.

( ) o%3/ "/!=, .2%" =2!,/ %!2%%=%% C%"%!%2= ".2%L ,2 *%%!,=2. o%3/ ,3 !/,2!=/ C!2=", =C! 充%2,.*2!,*%% C% %2!=充%L "%/. q C%%? "/!=,L (4) C%3= ,2= cqhr, %2%,2% ,"2/. *%C%2 C%2%2, 2%*= = C%"!.%2,.*!== C!, C=,, = %.*2!%=,2%L "%/.

d= C!%" ==, !*=%L =2充/ !-*2%!% " ", C=!=K%,*%% ,,!= (!,. 5). b *=2" %K3=2,C%%"= C%%*%"/L ",K!=2%! ,%L 2l, ,!,%L 2w, p,. 6. d,=!=/ =C!="充%2, !*=%L =2充/ !-*2%!% " ", C=!=K%,*%% ,,!=:

=) " %!,%2=%L C%*%2, j=p 2, K) " "!2,*=%L C%*%2, q =p !=C%%充/L "% %, OZ. t,,*= % ",K!=2%!= ==%,= %, %K3=2,,C%%"=%L " =" 2. q C%%? "/!=,L (5) C%3= ,2= cqhr, %2%,2% ,"2/. %2=" ?,. 2%*= = C%"!.%2. !*==, %K3=2.

g=2 " =" C%!%K% %C,= ,充/L =%!,2 !, C%3充/. ,2 cqhr. b *=2" K=,/. -3*,L *%C%2 C%2%2, 2%*= = C%"!.%2, !*==, %K3=2, *=*, " =" 2, C!%%,C%%"=2 C%,%/ )K/"= C!"%%, "2%!%% !%= "%"/, -3*, ,.

o!.% * qk`r %2%,2% ,"2/. *%.--,,2%" !=%, " ! %2=" ?,. C%2%2, 2%*= = C%"!.%2, !-*2%!=, %K3=2 C!%,"%,2 2=*, C%%K% *=*, " =" 2.

q C%%? !=!=K%2=/. ,充/. =%!,2%" K/, !=,2=/: !=C!, C%2%2, 2%*%" = C%"!.%2,.*!== C!, "%K3,, % "%=, C%*,, -!,*,, ,,!,*, -!%2=,, !=,2=/ ,=!=/ %2!=充%% C%, =",,%2, }op %2 =C!=", C=, "%/.

d !*=%L =2充/ !=,2=/ !=C!, 2%*%" = C%"!.%2. !*==, !-*2%!=, C!%,"= %*= ".%%% %C!%2,", %K3=2 32% "%L2", = % !-*2%!=, C%2!%/ ,=!=/ =C!="充%2, =2充/.

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Z11 b,h = ( ) awm0m1m2r1r=-, h2b2 m1r1 + m2r2i ctg r1d - a m1r1g2 + m2r2g1i ctg r1d ( ) ( ) ()2 () Z12 b,h = ( ) ( ) hbwm0m1m2r1r2 m1r1 + m2r2i ctg r1d () =-, h2b2 m1r1 + m2r2i ctg r1d a m1r1g2 + m2r2g1i ctg r1d c ( ) ( ) ()- () Z21 b,h =-Z12 b,h, ( ) ( ) Z22 = hbwm0m1m2r1r2 m1r1g2 + m2r2g1i ctg r1d ( ) () =, h2b2 m1r1 + m2r2i ctg r1d a m1r1g2 + m2r2g1i ctg r1d g ( ) ( ) ()- () rj = k2ejmj - b2 - h2, gj = k2ejmj - b2, j = 12,, ( ) () a = r1 2e2m2 - h2 m2r2 2e1m1 - h2 ctg r1d.

( ) (k )+ (k )i m1 }2/ =2!,/ C%"!.%2/.,C=%" C%*%2, z = d " /"=2 t3!-%K!=/ x,y-%2=" ?,. =C! 充%2,.*2!,*%% C% Ex,y ".2%L C%*%2, t3!-%K!==, x,y-%2=" ?,. C%2%2, 2%*= = C%"!.%2, Fx,y :

Ey Fy Z11 Z12 = Ex Fx Z21 Z22 , Ex,y b,h = Ex,y x, y,z = d eibx+ihydx dy, ( ) () 4p- - a l l Fx,y b,h = hx,y x, y eibx+ihydx dy, ( ) ( ) y 4p-a -l Ex,y # x,y-%2=" ?, =C! 充%2,.*2!,*%% C% " C%*%2, z = d, hx,y # x,y-%2=" ?, C%2%2, 2%*= = C%"!.%2, C=2,/ 4. g 32%, 2% C%"!.%2= C%2%2 2%*= = C%*%2, z = d %2,= %2 3 2%*% = =?L = L C=2, 4.

p,. 8. l,*!%C%%*%"/L ",K!=2%! o%3/ "/!=,, " /"=?, =C! 充%2.*2!,*%% C% " K%L 2%* C!%2!=2"= C%2%2 2%*= = C%"!.%2, C=2,/.

5 &}*2!%,=,*,L ==, ,*!%C%%*%"%% ",K!=2%!= C!%,"%%L ,!,/[ C%" ?=.*2!%,=,*%3 ==,3 ,*!%C%%*%"%% ",K!=2%!=. o%3% cqhr %2%,2% C%2%2, 2%*= = % C%"!.%2,. o!% ,充/L 2% % !,. o!2="/ !32=2/ !=2%" 2%*=, ".%%% %C!%2,", C!, !=,/. %2!,*,. !=!=. ",K!=2%!=.

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a l Ey x, y,z = d = hy x, y Z11 x, y ; x, y dx dy, () ( ) () -a -l 1 Z11 x, y, x, y = Z11 b,h e-ib(x-x )e-ih(y-y )dbdh.

() ( ) 4p- - g=2 C%%? !=,%% 3%", 2=,=%L %2=" ?L =C! 充%2,.*2!,*%% C% = C%"!.%2,,=%% C!%"%,*= C%3% ,3 !%,2!=% 3!=", %2%,2% C%2%2, 2%*= = C%"!.%2, ",K!=2%!=:

a l ext -Ey x, y = hy x, y Z11 b,h Z11 b,h ( ) ( ) ( )- ( ) () 4p - - -a -l a l iwm e-ib(x-x )e-ih(y-y )dbdhdxdy + hy x, y ( ) 2p -a -l a x - x - 2 y - y ( )2 ( )2 m1m2 dxdy, d - (6) ( ) k2 e2 + e1 R5 m2 + m1 R ( ) Z11 b,h =,C2%2,*% C!2=", Z11 b,h C!, b , ( ) ( ) h :

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2ln # ,!,= C%%*, n-L ,,!,*%L (C==!%L) !=*,.

q,2/ qhr,2 ",:

2p j c,p - j fj j ctg dj + ( ) 2p 2 2p N c,p + fnc,p j Tn j j,j dj = ( ) ( ) n=c,p,ext =-2iwee0ajEj j j, j = 1,N, (8) ( ) ) c,p c,p fnc,p j = dfn j dj, Tn j j,j # %2=2%% !%%*, ( ) ( ) ( ) c,p,ext,"2/ !3 !/ =2, !, Ej j j # =C! 充%2 ( ) 2%!%% C%, C!,%充%% * =%!3 j-%,3=2.

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C%2%2L 2%*%" %2 C%C!%L (=,32=%L) *%%!,=2/ C!C%==, *"=,2=2,*,,:

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fn t = dfn lt dt ; J0 mDn # -3*, a哓 C!"%% !%=;

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. 4. 1. q. 38-40.

2. m=%" b.`., j" d.q., l"" q.b. t3*,%= ".%%% %C!%2,", 2%*%%.*2!,*%% ",K!=2%!= // o,= " ft. 2001. . 27. 21. q. 29-34.

3. m=%" b.`., j" d.q., l=2"" h.b. l2% !=2= C%%*%"/. ",K!=2%!%", !=C%%充/. = ,,!,*%L C%"!.%2, // t,,*= "%%"/. C!%哓%", !=,%2.,*, ,2/. 2001. . 4. 4. q. 37-41.

4. m=%" b.`., j" d.q. m%"/L 2% !=2= C%%*%"/.

",K!=2%!/.,3=2L // h"2, "3%". }*2!%,*=.

2002. 5. q. 73-78.

5. m=%" b.`., j" d.q. q,3 !%,2!=% C!2=",.*2!%=,2%% C% " K,L % 2!3K=2%%.*2!,*%% ",K!=2%!= // t,,*= "%%"/. C!%哓%", !=,%2.,*, ,2/. 2004. . 7. 3. q. 5-9.

6. m=%" b.`., j" d.q., j=2, q.b. o!,, ,3 !%%,2!=%% 3!=", !% c,K!2= * !=*!3%"%L C%%*%"%L =2充/ // t,,*= "%%"/. C!%哓%", !=,%2.,*, ,2/. 2004. . 7. 4. q. 12-17.

7. m=%" b.`., j" d.q. p=2 ".%%% %C!%2,",.*2!,*%% ",K!=2%!= 2%% ,3 !%%,2!=%% 3!=", // `2充/. 2005. b/C. 3(94). q.7-11.

8. m=%" b.`., j" d.q., e-!%"= `.`. q,3 !%,2!=% C!2=",.*2!%=,2%% C% " K,L %.*2!,*%% ",K!=2%!= // `2充/. 2005. b/C. 4(95). q. 22-27.

9. m=%" b.`., j" d.q. p=2 !=C!,L 2%*%" = " =/. C%%*%"/..*2!,*,. ",K!=2%!=., !=C%%充/.

*%-%!% = ,,!,*%L C%"!.%2,, 2%% ,3 !/.,2!=/. 3!=",L // t,,*= "%%"/. C!%哓%", !=,%2.,*, ,2/. 2005. . 8. 3. q. 5-10.

10. m=%" b.`., j" d.q. p, ==, % !=C!,, 2%*= " C==!%L C%%*%"%L *%"%L =2充 2%% ,3 !%%,2!=%% 3!=", // t,,*= "%%"/. C!%哓%", !=,%2.,*, ,2/. 2005. . 8. 3. q. 34-38.

11. m=%" b.`., j" d.q. q,3 !%,2!=% 3!=", !% c,K!2= " 2%!,, 3*%L *!3%"%L C%%*%"%L =2充/ // d%*=/ `*=,, =3*. 2006. b/C. 407. . 3. q. 329-331.

(C!"%: Neganov V.A., Klyuev D.S. Singular Integral Equations with the Hilbert Kernel in Theory of Narrow Circular Strip Antennas // Doklady Physics. 2006. Vol. 51. 3. P. 122-124) 12. m=%" b.`., j" d.q. p=2 ".%%% %C!%2,", 3*%L C%%*%"%L *%"%L =2充/ = %%" ,3 !%%,2!=%% 3!=", !% c,K!2= // h"2, "3%".

}*2!%,*=. 4. 2006. q. 76-80.

13. m=%" b.`., j" d.q. q,3 !/,2!=/ 3!=", " 2%!,, *%-%!/. ,,!,*,. C%%*%"/.,3=?,. 2!3*23! // t,,*= "%%"/. C!%哓%", !=,%2.,*, ,2/. 2006. . 9. 4. q. 13-26.

14. m=%" b.`., j" d.q., b%!%%L `.`. p=2 ".%%% %C!%2,", "3. " =/..*2!,*,. ",K!=2%!%", *%-%!% !=C%%充/. = ,,!,*%L C%"!.%2, // t,,*= "%%"/. C!%哓%", !=,%2.,*, ,2/. 2007.

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