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A;8 F5=B@ BO65AB8 ?0;>G:8 @0A?>;>65= =865 B>G:8 :@5?;5=8O, B> F8;8=4@ A>25@H05B :>;510B5;L=>5 42865=85.  40==>9 G0AB8 @01>BK :>;510=8O 4>;6=K 1KBL <0;K<8. 1.1 7<5@LB5 7028A8<>ABL ?5@8>40 :>;510=89 F8;8=4@0 >B @0AAB>O=8O >B >A8 F8;8=4@0 4> F5=B@0 <0AA ?0;>G:8. >AB@>9B5 3@0D8: ?>;CG5==>9 7028A8<>AB8. 1.2 >:068B5 (B5>@5B8G5A:8), GB> 40==0O 7028A8<>ABL 8<55B AB5?5==>9 284 T = Cz± . (1) 1.3 @>25@LB5 2K?>;=8<>ABL 40==>9 D>@<C;K =0 >A=>20=88 20H8E M:A?5@8<5=B0;L=KE 40==KE. ?@545;8B5 ?>:070B5;L AB5?5=8 ± . '0ABL 2. 0BCE0=85 :>;510=89. >;510=8O F8;8=4@0 O2;ONBAO 70BCE0NI8<8 87-70 =0;8G8O B@5=8O :0G5=8O. !8;0 B@5=8O :0G5=8O >?8AK205BAO D>@<C;>9 k F = N , (2) R 345 N - A8;0 =>@<0;L=>9 @50:F88, R - @048CA F8;8=4@0, k - :>MDD8F85=B B@5=8O :0G5=8O, 8<5NI89 @07<5@=>ABL 4;8=K. @8 87CG5=88 70BCE0=8O @5:><5=4C5BAO 8AA;54>20BL :>;510=8O A 1>;LH>9 0<?;8BC4>9. 2.1 7<5@LB5 7028A8<>AB8 >B:;>=5=8O >B ?>;>65=8O @02=>25A8O >A8 F8;8=4@0 (2 B>G:0E >AB0=>2:8) >B G8A;0 A>25@H5==KE :>;510=89 ?@8 42CE ?>;>65=8OE ?0;>G:8. 2.2 >AB@>9B5 3@0D8:8 7028A8<>AB8 M=5@388 F8;8=4@0 (?>4A:07:0  2 B>G:0E >AB0=>2:8) >B ?@>945==>3> ?CB8. 0AAG8B09B5 ?> MB8< 40==K< :>MDD8F85=B B@5=8O :0G5=8O F8;8=4@0. 040=85 2. =B5@D5@5=F8O =0 1C<035. 1>@C4>20=85: ?@>7@0G=0O ?;5=:0 !1 A =0=5A5==K<8 ?0@0;;5;L=K<8 ?@O<K<8 ;8=8O<8, ?@>7@0G=0O ?;5=:0 !2 A =0=5A5==K<8 :>;LF0<8, =01>@ 87 B@5E ;8AB>2 1C<038 A =0=5A5==K<8 HB@8E0<8, :=>?:8 :0=F5;O@A:85, :0@B>==0O ?0?:0, ;8=59:0. @8 =0;>65=88 ?;5=:8 A =0=5A5==K<8 HB@8E0<8 =0 1C<06=K5 ;8ABK B0:65 A =0=5A5==K<8 HB@8E0<8 2>7=8:0NB ?>;>AK <C0@0, :>B>@K5 <>3CB <>45;8@>20BL 8=B5@D5@5=F8N 2>;=. CABL ?@>?CA:0=85 ?;5=:8 7028A8B >B :>>@48=0B ?> =5:>B>@><C 70:>=C 1 Ä = (1+ cosÕ(x, y)), 2 ">340 ?@>?CA:0=85 42CE =0;>65==KE ?;5=>: (8;8, GB> @02=>A8;L=> ?;5=:8 8 ;8AB0 1C<038) @02=> 1 Ä = Ä1 Å"Ä = (1+ cosÕ1(x, y))(1+ cosÕ2(x, y)) = 2 4 1 = (1+ cosÕ1(x, y)+ cosÕ2(x, y)+ cosÕ1(x, y)Å" cosÕ2(x, y)) = (1) 4 1 1 1 ëø1+ = cosÕ1(x, y)+ cosÕ2(x, y)+ cos(Õ1(x, y)+ Õ2(x, y))+ cos(Õ1(x, y)-Õ2(x, y))öø ìø ÷ø 4 2 2 íø øø A;8 Õ1(x, y), Õ2(x, y) O2;ONBAO 1KAB@><5=ONI8<8AO DC=:F8O<8 :>>@48=0B, B> H8@>:85 (?> A@02=5=8N A> HB@8E0<8 >B45;L=KE ?;5=>:) B5<=K5 ?>;>AK 8 A25B;K5 ?>;>AK <C0@0 >?8AK20NBAO ?>A;54=8< A;0305<K< 2 2K@065=88 (1). 0A?@545;5=85 MB8E ?>;>A >?@545;O5BAO @07=>ABLN DC=:F89 Õ1(x, y), Õ2(x, y), :>B>@K5 <>3CB A;C68BL 0=0;>3>< D07 :>;510=89 8=B5@D5@8@CNI8E 2>;=. 0 ?;5=:0E 8 ;8AB0E =0=5A5=K H:0;K  2 :0G5AB25 548=8F 87<5@5=8O 4;8=K 8A?>;L7C9B5 548=8FK MB8E H:0;. 1.1 0A?>;>68B5 ?;5=:C !1 =0 ;8AB5 !1, =0 :>B>@>< =0=5A5=K B0:85 65 HB@8E8, :0: 8 =0 ?;5=:5, B0: GB>1K ?;5=:C <>6=> 1K;> ?>2>@0G820BL 2>:@C3 >A8, 2 :0G5AB25 :>B>@>9 8A?>;L7C9B5 :=>?:C, 2>B:=CBCN 2 :0@B>==CN ?0?:C. -B0 >AL >B<5G5=0 =0 ?;5=:5 8 ;8AB5 1C<038 :@C6:>< 2 ;52>9 G0AB8 ;8AB0. 7<5@LB5 7028A8<>ABL @0AAB>O=8O <564C ?>;>A0<8 <C0@0 >B C3;0 <564C HB@8E0<8 =0 1C<035 8 =0 ?;5=:5. >AB@>9B5 3@0D8: ?>;CG5==>9 7028A8<>AB8. >;CG8B5 B5>@5B8G5A:CN 7028A8<>ABL H8@8=K ?>;>A <C0@0 >B C3;0 <564C HB@8E0<8. > 40==K<, ?>;CG5==K< 2 ? 1.1 >?@545;8B5 H8@8=C ?>;>A, =0=5A5==KE =0 ?;5=:C 8 ;8AB 1C<038 !1. @82548B5 >?B8G5A:CN 8=B5@D5@5=F8>==CN AE5<C, :>B>@CN <>45;8@C5B 40==K9 >?KB A ?>;>A0<8 <C0@0. 2. 0A?>;>68B5 ?;5=:C !1 =0 ;8AB5 !2, ?5@8>4 HB@8E>2 =0 :>B>@>9 >B;8G05BAO >B ?5@8>40 HB@8E>2 =0 ?;5=:5. 7<5@LB5 7028A8<>ABL @0AAB>O=8O <564C ?>;>A0<8 <C0@0 >B C3;0 <564C HB@8E0<8 =0 1C<035 8 =0 ?;5=:5. >AB@>9B5 3@0D8: ?>;CG5==>9 7028A8<>AB8. ?@545;8B5 ?5@8>4 HB@8E>2 =0 ;8AB5 !2. @82548B5 >?B8G5A:CN 8=B5@D5@5=F8>==CN AE5<C, :>B>@CN <>45;8@C5B 40==K9 >?KB A ?>;>A0<8 <C0@0. 3. 0A?>;>68B5 ?;5=:C !2 =0 ;8AB5 !3. @8 A42835 ?;5=:8 2>7=8:0NB ?0@0;;5;L=K5 ?>;>AK <C0@0. 7<5@LB5 7028A8<>ABL H8@8=K ?>;>AK >B A42830 ?;5=:8. >AB@>9B5 3@0D8: ?>;CG5==>9 7028A8<>AB8. @>?CA:0=85 ?;5=:8 (8 @0A?@545;5=85 ?>;>A =0 ;8AB5 1C<038) 2 MB>< M:A?5@8<5=B5 >?8AK205BAO DC=:F859 ëø öø 1 ìø1+ ëø x2 +2y2 öø÷ø . ìø ÷ø Ä = cosìø2À ìø 2 D0 ÷øøø íø øø÷ø íø @82548B5 >?B8G5A:CN 8=B5@D5@5=F8>==CN AE5<C, :>B>@CN <>45;8@C5B 40==K9 >?KB A ?>;>A0<8 <C0@0. >;CG8B5 B5>@5B8G5A:CN 7028A8<>ABL H8@8=K ?>;>AK <C0@0 >B A42830 ?;5=:8. ?@545;8B5 ?> ?>;CG5==K< 40==K< ?0@0<5B@ D0 . ::C@0B=> A>2<5I09B5 ?;5=:8 8 ;8ABK 1C<038. !;548B5, GB>1K ?;5=:0 ?;>B=> ?@8;530;0 : ;8ABC! >4A:07:0. >6=> ?>:070BL, GB> ?@8 =0;>65=88 A8AB5< 42CE ?0@0;;5;L=KE ?>;>A H8@8=0 ?>;>A <C0@0 D A2O70=0 A ?5@8>40<8 @5H5B>: d1 8 d2 A>>B=>H5=85< 1 1 1 2 = + - cos± , 2 D2 d12 d2 d1d2 345 ± - C3>; <564C ?>;>A0<8.

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