X Y 5 Z 2404 [0\0 234 ] = \ ] Y^\_ 054 ] ` 0_\04 4 a = ] 8 b 8b 8 c d X e e \0] 4 `4Z e \ 5023 f \ 5 g h i] 50] 5 `0 4 j k lmn l m

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X Y 5 Z 2404 [0\0 234 ] = \ 5 044 ] Y^\_ 054 ] ` 0_\04 4 a45 5 50 0 4 2 = ] 8 b 8b 8 c d X e e \0] 4 `4Z e \ 5023 f \ 5 g h i] 50] 5 `0 4 j k lmn l m <g 1 234Z0 4045Z f opk qn r \ 5 g h i] 50] 5 `0 4 r \ 1045r [0\0 234 0 = \ 5 044 0 Y^\_ 054 0 ` 0_\04 0 4 a45 5 5 0 4 2 = ] 8 b 8b 8 c d X e e \0] 4 r 0\ s e 4 `4Ze 5 \4 t ukn vnpw r \ 5 g h i] 50] 5 `0 4 r g 0 r [0\0 234 0 = \ 5 044 0 Y^\_ 054 0 ` 0_\04 0 4 U 50] 5 `0 e 45 5 5 ] 8 x 8y 8 /50 2 X e e \0] 4 r 0\ s e 4 `4Ze 5 \4 x0\ s > = 4 h 1 > f [0\0 234 0 = \ 5 044 0 Y^\_ 054 0 ` 0_\04 0 4 a45 5 5 g h 5] g 0 Z ] 8 y 8U 8 <Y X e e \0] 4 z s 5 5 5> { 69VW =8 ` ] 48 4 h 0\ 4 \ 0 5 1 44 = 05 } 996 86W~ 896 [0\0 234 ] = \ i 5 044 ] Y^\_054 ] ` 0_\04 4 a45 5 50 0 4 2 = ] 8 b 8b 8 c d X e e \0] 4 \ 0 f ] e 8r \ 8 Wr =8 U r VV ~~ 8 / \ 0 5 1 0e ] _ 4 h4 ] 53> Y Y2 50 0 [0\0 234 = = \ i 5 044 = Y^\_ 054 = ` 0_\04 > 4 a45 5 5 0 4 2 = ] 8 b 8b 8 c d X e e \0] 4 8 y 5 0g0 5 h 2 4 { 69VW =8 `04Ze 0 05 3 \ 0 5 1 44 = 05 4\ \ 5 g h i] 50] 5 `0 4 4hY = y 44 a 4 4

W ƒo u u uj vˆ qv j u u o ƒv Š ŒŒk Ž } 0 5 1 > >s04 50 05 `0 ] 20\ 4 ^ =040 1 0 4 54Z 24 r Zh 44Z Y50 4 0] 0i >55 e 2 \ _04 0] 502 5 2s0 40 \4 \4 i5 5 g 1 44 e 2 54 5 ] e 0\Z 5 5 4Z] Y044 5>] \0 0hi ` 2 54 5 \ Z r 50 4Z \2> 0 234Z 2 e ] > 8 <Yi 50 0]Z0 0 >55 > ] \02 ^ 5> = \ \ 4 ] `0 ] Y044 5>] r 5 ] 5 `0`4Z0 5 `4 r 5 r \ 2 8 x ] h Y 5 44 e \ 0 5 1 ]05 \ 0d 04 > ] \0234Z h \ ` 0\04Z 20\ 4 > 2^ 1 Z \>s 4 0 4 53 =2 Y 44Z h] s 04 e 8 xz> 204Z g g 0 5Z 2 >4 > 5 5 4Z 40 \ 4 \ 4 50e 5 5 g 1 ] e 0\ Z =2 Y 4Z ] > 4 h]04` 53 ]05 24 e 5 5 Z 0 4 5 \ Z 8 xz> 204Z g g 0 5Z Y2 =2 Y 44Z h] s 04 e r h4 ^ s Y50 4 0 >55 e \ ` ] 2 54 5 2 > ] e 0\Z 8 um pkœ Ž b 2> = \ g h `0 50 5 ] i e 0\Z r 2 r 40 \4 \4Z 5 45 0]04 8 x20\i 5 0 40 \4 \ 4 5 20e 50] 0 5 Z 41045 1 5 044Z 40e 0s05 r 5 _0 \0e5 > 2 5>_05 2 `05 Y h ^5> 40 \i 4 \4 5 20 2 54 5 0\Z \ 23 4 204 > \0e5 > 5 2 5808 0 5 2 r 50 h ^s 0 00 5 5 g 1 ^ 8 b \ Y4Z0 2 54 5i 4Z0 40 \ 4 \4 5 > 2>^ 5> 2 0] s 05 4 > 24 Z 10 5 5 g 1 44 e 0\0 8 a20\ 4 0 5 10 40 Y \ ] 5 `0 2 _ 04 > r >h 44Z 04 0] ] =2 Y 4 r Y0i 0`04 0] Y0h 4 5 ] 5 er ]4 = \ = h \ ` 8 <\ 4 ] h 5 2 54 54Z 40 \ 4 \ 4 50e r 4 Y2^\ 0]Z 0i 234Z 2 > ] > r > 2>^ 5> 54 50234 0h 0 0 0 \ Z 2 54 5 \ Z r >h 44Z0 4 2 ` 0] 0h 44 = 50 ] 2 4 2 4Z ` 2 5i 4 5 \ Z 8 b 5 ] _ 4 20\ 53 h] _ 4 0 2 >4 0 4 2 44Z 40 \4 \4 50e 4 ]05 Z 0 4 54Z h] s 04 e r h4 ^ s Y50 4 =2 Y 44Z 0 >55 e r Y044 2 ` 0 Y50 4 > 0 >5i 5 > Y2 h ` 2 54 5 8 a h\03 5 `0 _ 4 ] 5 053 h i \ ` h2 ` ]05 0 4 54Z h] s 04 e h ] 5 5 ]05 2 _ 04 > 0 >55 > 54 50234 ] = ` 2 54 5 f 4 \ ` ] 2 \ 4 ] 8 x 2 > ]02 \4Z d023g Z Y 0_ 4Z h 4 ] i 5 e 4 Y 23d 5 45 r _ ^s 50 5 ^ X _i

4 e > 2>05> 5 _ 0 h \ ` 20\ 4 > 2 >4 > =2 Y 4Z ] > 4 ]05i Z 0 4 54Z 24 r =040 0]Z Y50 4 0] \ \ 4Z 0 >55 e 8 h 44Z0 h \ ` ] = 5 YZ53 0d04Z ]05 \ ] ] 50] 5 `0 = ] \02 i 4 > 8 ƒœkk ŒŒ kkn h 2^` 05> 50 0i 5 `0 ] 20\ 4 0 4 54Z 24 r =040 0]Z Y50 4 \ \ 4Z 0 >55 e 5 2s 0 40 \ 4 \ 4 i5 5 g 1 44 e ] e 0\Z 8 }2> \ 5 _04 > 4 4 e 102 YZ2 5 204Z 20\ ^s 0 h \ ` f V8 U 05 \ ] 50 g 4 1 e ] 20 4 = 0 0]044 = 4 e5 4 i 2 5 `0 0 Z _04 0 \2> 5041 2 2 Y ] 20 4 i >_044 e i 5 50`04 > r h4 ^s0= Y50 4 \ \4 = 0 >55 > r ] i \02 0] = 5 `0`4 e Y044 53^ \ 20] r \ 2 e4z] 5 ] \0i 234 e _ \ 5 Y0 40`4 e =2 Y 4Z Y \4 e = 4 10e 8 b 5 ] ] 5 053 Y 45 2 2 h 1 \ 2> 54 50234 2 > ` 2 54 5 f 4 \ 4 ] \ 4 ] 8 6 8 a20\ 53 4 2 = `4 ^ h \ ` Y Y50 4 0 >55 > \ i 2 e4z] 5 ] 40`4 e =2 Y 4Z r = 4 `044Z] = h 45 234Z] \ 4 ] 8 W 8 b 2 ` 53 450= 234 0 0\ 5 204 0 \2> 02 ` 4Z h Z d 04 > Y \4 e 0 4 5 _ \ 5 8 xz\02 53 40] 24 ^ ` 53 4 e5 \2> ]05 0 4 54Z 24 4 2 5 `0 0 Z _ 04 > r \ Y4Z0 \2> 0\04 > ` 2044Z `05 8 b 05 `05Z \2> 50 h4 `04 e ]05 h \ ` r 5 Z0 5 055 ^ 5 ] ] 2 >] 8 a 0h 23i 5 5Z 0\5 53 = g `0 ] \08 8 5 4 53 50 2 >4 > ]05 ] e 0\Z 5 5 r ] s4 5 ` 2 54 5 r 5 2s 4Z 0 40= 2 > r 54 d04 > 5 2s 4 2 0 2 ` 0 5 40`4 e =2 Y 4Z 2 2 h 1 0 >5i 5 > 54 50234 ` 2 54 5 4 ]05 Z =040 0]Z 24 8 l w p kœ Œ Œp wp V8 x ] h \ ` Y 0\0204 g ]Z Y50 0] = 502 r ] \02 i 0] = = \ \ 4 ] `0 e Y044 53^ ; 5 `0`4Z] 5 `4 ] 2 \ i 20] 5 0 \ {5 0 \ e Zd e 2 Y \4 e = 4 10e r 2 `04Z 50 h] _ 4 5 h ]04Z Y \ 4 e 0 4 5 {5 0 \ e Z d e r 5 _0 Y \4 e 0 4 5 {5 0 \ e Zd Y0h= 4 `4Z] 5 ] 8 a ]0404 0 ] _05 s05 044 5 53 0d04 0 h \ ` Y Y50 4 502 Y 200 2 _ 4 e =0 ]05 r ] \02 0]Z 50] ] = \ \ 4 ] `0 Y044 50e 8 68 x h \ `0 0 0`4 ] Y50 4 ] \02 0] = 5 `0`4Z] \ 20] 1 2 4\ \ 2 e4z] 5 ] \0 234 e _ \ 5 Y0 40`4 e =2 Y 4Z

7 Z> 204Z s 05 044Z0 h2 ` > ]0_\ ]05 ] 0 4 54Z 24 h2 `4Z 0= 2 2 h 1 > 54 50234 ` 2 54 5 \ Z f 4 \ 2 \ 4 ] 8 W 8 x 0h 235 50 404 > ]05 0 4 54Z h] s 04 e r =0i 40 0]Z Y50 4 0 >55 > 5 ] \ 2 e4 e _ \ 5 Y0 40`4 e 40`4 e =2 Y 4Z r Y4 _ 04Z s 05 044Z0 h2 ` > 8 e\04z h ] 5 ]05 0 4 54Z 24 5 =2 Y 4Z ] si 4 5 ` 2 54 5 r 2 2 h 1 0 >55 > =2 Y 4Z 5 8 8 5 4 204 Y > 23 5 5 g ] 4 h]04i ` 5 ] 2 5 \ 0 4 54Z h] s 04 e f 24Z 4 Y \4 e 0 i 4 5 > 2>^ 5> 4 \ h40044z ]0_\ Y e 450 2 5 5 r ]0_ 5 `4 e h 40 4 5 55 ^58 l pk kwk Ž 040 1 0 4 54Z 24 Y50 4 \ \ 4Z 0 >55 e >s 04Z ]4 = ` 2044Z 0 20\ 4 > 2 i Y 5 4Z Z5 r ] 50 05 `0 Y 58 <\ 4 \ 0 5 1 0 Z0 20\ 05> h \ ` 4 50234 ] 2 >4 2 2 h 1 0 >5i 5 > r Y50 0] = \ 2 e4z] 5 ] _ \ 5 r 4 ]05 Z Y h i ^ s > 0 4 54Z h] s 04 e \ 0= 2 _ 04 > 54 50234 ` 2 54 5 \Z f 0 4 h 5 ` 8 b 5 ] ] s4 53 ` =2 Y 4 0= h 20= 4 > 5 055 ^ 5 50 4Z] h4 `04 >] r s ] ] e 0\08 x 5 e 5 4 0 0d 0]Z Y 50 h \ ` Z> 204Z i s 05 044Z 0 h2 ` > ]0_\ ]05 ] 0 4 54Z 24 h2 `i 4Z 2 2 h 1 > 0 >55 > 54 50234 ` 2 54 5 f 4 \ \ 4 ] 8 } 44Z0 20\ 4 > Z> 2 50 4 ^ 23 ` 2 54 5 2 > ] e 0\Z 0505 044 e = \ g h `0 e 40 \4 \i 4 5 r 2 Y2>^s0e 2 53 \ 24 e Y2 Z \ h] s04 e 4 0 4 53 \Z r `5 > 2>05> 4 Z] 5 20\ 4 > 8 x 0h 235 50 0\044Z 20\ 4 e 5 4 204 s 05 4 0 450 2 50e 5 5 5 `0 e 5 4 5 0440e ] \Z \ 0\02044 e 50 4 e 02 ` 4Z r 5 055 ^ s 0e h \ 44Z] ] \023i 4Z] ]05 ] h \ ` r 4 5 5 = 5 55 ^5 24 Z0 h] s0i 4 > ] e 0 4 5 r 5808 5 h 4 h 4 {504 0\5 2>05> h Zi 5 e \2> Z \ =2 Y 44Z h] s04 e 4 0 4 53 \Z 8 Š m Œm wkœ 5 5 5 ] r `5 4 4 0 0d 04 e ] 5 044Z h \ ` Y 0\0204 h ] 5 g ]Z Y \i 4 e = 4 1Z 5 ]05 \4 e 0\Z 4 \>s > 40e 5 `4 =2 Y 44Z h] s 04 e ] = 5 YZ 53 h Y 5 4Z ]05 \Z 5 4 204 > i 50 5 5 5 `4 ZhZ 0]Z] ] 0 4 54Z] 24 ] 8

b 5 044Z 0 ] 50] 5 `0 0 ] \02 ] = 5 YZ53 23h 4Z h\ i 4 50] \ 5 41 44 = ] 4 5 4= ] 5 e 8 Œ k Œ wp ŒŒ Y h 05> 4 0 5i 4 ] ]0404 h 054Z ] 50] 5 `0 ]05 \ r 404 2 `04i 4Z 0h 235 5 0h 235 5 ] \ = 5 8 š k n m Ž / 5020] 2 `4 f b 2 `04Z 4 2 5 `0 0 0d 04 > h \ ` Y Y50 4 5 `0`4 e = \i \ 4 ] `0 e Y044 5 \ 2> 5 ] \ 2 e4 e _ \ 5 Y0 40`4 er 5 40`4 e =2 Y 4Z g ]0r \ Y4 e \2> 0\04 > ` 2044Z `05 ] 2 5 \ Y h ^ s > 0 4 54Z 24 8 b 5 i 04Z = g r 22^5 ^s 0 0h 235 5Z 5 `05 8 }2> 4 2 h Ys0= 0d04 > h \ ` Y Y50 4 0 >55 > 5 i ] \ 2 e4 e _ \ 5 40`4 e =2 Y 4Z r 4 e\044 = 450= 234 e g ]0 r h Y 5 4 ]05 \ 0\0204 > 2 `05 2^ \ Z 450i = 234 = Z _ 04 > r 2 _ 044Z 4 2 _ 50234 e \0e5 50234 e 4 = ` 2 Y h ^s > h 0 >55 0] 24 r h ] 5 5 ]05 h \ ` r `5 Y5 2 h] _ 4 5 Z ` 204 > \ Y4Z 450= 2 8 a20\ 4Z ]05 \ `0 0 0 5Z 2 >4 > 0 40e = 4 1Z 5 _ \ 5 Y \4 e 0 4 5 2 Y {5 0 \ e Zd 4 g ] 4 i \>s 0= > Y2 h 5 e = 4 1Z 0 >55 > r ] \02 0] = 5 `0`4 e Y044 53^ 8 x 5 =0 2 `04Z 50 h] _ 4 5 h ]04Z Y \ 4 e 0 4 5 {5 0 \ e Zd e r 5 _0 Y \4 e 0 4 5 {5 0 \ e Zd Y0h= 4 `4Z] 5 ] 8 b \= 5 204Z Y2 1 \ 2 \Z 50]0 Y 5Z 5 5 0 8 u Ž ah2 _044Z0 \ 0 5 1 0h 235 5Z \ 2 i \ Z 2 3 f 4 0] 4 0 œ Y 5 = \ 2 = `0 10 a45 5 5 0 4 2 = ] 8 b 8b 8 c d Xy 69V6 =8 4 h 0\ 4 `04 = 05 [ h `0 = 4 204 > a45 5 5 0 4 2 = ] 8 b 8b 8 c d Xy 69V6 =8 4 0] 4 0 g0\ Z Zd0e ] 50] 5 U ž ] 8 8Ÿ 8 ] i 4 69V6 =8 4 h 0\ 4 `04 = 05 a45 5 5 g h 5] g0 Z ] 8 y 8U 8 <Y Xy 69VW =8 4 x0 e e 4g0 041 {b 2 \4Z0 50 4 2 = = \ 5 = \ g h / 4 5ib050 Y =r 69V9 =8 8 Š p m Ž b 50]0 \ 0 5 1 Y2 4 7 Y 5r h 5 i Z ; 5 53 0\ s h\ 4 > r 0 ]04\ 44Z xy r V ; ž \ x0 e e 4g 0 041 8 q pm p ŒŒ Ž X Y 5 5 5 h x 0\04 > r `0i 5Z 0 =2 r z 2^`04 > 2 50 5 Z VW 4 ]04 4 er h 4

4 5 44Z 8 <Ys e Y 0] \ 0 5 1 5 2>05 VW9 5 4 1 r 2^` > 6W 4 8 okœ Ž y 5 Y2 = \ 04 4 `4 ] \ 502^ Y 5Z \ 5 g h i] 50] 5 `0 4 8 8 ` = 4 r \ 5 g h i ] 50] 5 `0 4 r g0 U ž ] 8 8Ÿ 8 ] 4 y 8/ 8 / 4 h 5 4 ^ ] s3 0\04 20\ 4 e \ 44 e Y 508 ƒ ql ƒl ƒˆ q ƒ ˆ u l ˆ u o ƒv k h 4 5 234 53 50]Z \ 0 5 1 r 00 4 `4 > 4 h4 5 `0 > h4 ` ] 53 r g ] 2 4 1023 Y 5Z r 0 0i ` 204Z 2 _ 04 > r Z 4 ]Z0 4 h s 5 8 5 h2 = 05> \0 _ 4 0 \ 0 5 1 =2 ] 8 n 102> Y 4 4 > 5 234 5 0\04 > 0\5 2>0] e Y 50 50 05 `0 = 20\ 4 > =040 1 h] s 04 e Y50 4 \ _04 = _044Z 502 20\ ^s ] Z \ ] hi ] s 04 e 4 0 4 53 Y h 4 0] 4 40e 24 e 5 5 Z 0\i 5 204 Yh 4Z e 4 2 h ]0^ s > 5 e 50]0 Y 5 50] r `5 YZ \ 0 5 1 ] _ 4 YZ2 0\02 53> 4 2 ` 4 h4z 20\ 4 > 5 234 5 0h 235 5 0d 04 > ] 20 ] \0234Z h \ ` h] _ i 4 53^ ]0404 > 4 5 0 8 x 410 2 Z V 4 4 0 4 2 h g 234Z Y 5 ] 50]Z \ 0 5 1 Y h4 `04 4 h4 0\i 5 2>0] = 20\ 4 > h] _ 4 53 0= 5 `0 = 2 _ 04 > 1023^ \045 g 1 =2 Y 44Z h] s 04 e 20\ 4Z] > 204 >] 4 0 4 5 \Z 8 ah 0\044 = 2 0 V Yh 4 = 4 2 h 50 05 `0 20i \ 4 e 2^1 \ \4Z h] s04 e 20\ ^s ] Z \ ] 4 0 4 53 20\ 05r `5 40 24 53^ 20\ 44Z] > 2>^ 5> Y20]Z 2 >4 > 2 54 54Z 40 \ 4 \ 4 50e ] e 0\ Z r Y044 50e 0230i g \4 =2 Y 4Z ] > 4 ]05 Z 0 4 54Z h] s04 er h4 i ^ s Y50 4 =2 Y 44Z 0 >55 e 8 /20\ 05 `053 r `5 \2> 5 5 Z 5 5 g 1 ] e 0\ Z 50 4Z > 204 > 54 i 50234 0h 0 0 \ 2 54 5 \Z r >h 44Z0 4 2 ` 0] 0h 44 i = 50 ] 2 4 2 4Z ` 5 h4 ^ s ` 2 54 5 8 b 5 ] 0\5 2>05 450 0 20\ 4 0 2 >4 > 2 54 54Z 40 \4 \ 4 50e \ Z 4 ]05 Z 0 4 54Z h] s 04 e r Y044 Y50 4 0 >55 e Y2 h ` 2 54 5 8 a h\03 5 `0 _ 4 i ] 5 053 h \ ` h2 ` ]05 0 4 54Z h] s 04 e h i

: ] 5 5 ]05 2 _ 04 > 0 >55 > 54 50234 ` 2 54 5 f 4 \ ` ] 2 \ 4 ] 8 ]0 5 = r 0\044Z e 4 2 h Y 5 20\ 0] e 50]0 h 2 r `5 0h 235 5Z 50 05 `0 0d 04 e h \ ` =040 1 0 4 54Z h] s 04 e 0\ 5 204Z 4 4 ] ] e Ys 0e 450= 234 e g i ]0r 5 \4 4 2 h 53 hih 2 _ 4Z \Z450= 234Z Z i _ 04 e 8 x 5 ] 2 ` 0 Ys 0 450= 234Z0 0\ 5 204 > \ 24 50234 5 0Y ^ 5 h Y 5 01 234Z ]05 \ Z ` 204 > 5 450= 2 4 2 h \2> 2 `04 > \ 5 5 `4 5Z 4 2 5 `0 Z _ 04 e r \ ^ s 0\04 0 4 4 0 ` 2044Z `05 ]05 i 0 4 54 = 2404 > 8 n \2> \ 2 e4 = 5 Y0 40`4 e =2 Y 4Z i 20\ ^ 5> 0 4 54Z0 h] s 04 > 5 5 g 1 44 e \0 234 e _ \i 5 ]05 ] ` 2 54 5 r 5 055 ^s ] 0 234Z] 2 i >] ] e 0\0 r h4 ^s 0 Y50 4 \ \4 = 0 >5i 5 > 8 b 5 ] 4 ] _05 YZ53 2 _04 4 \ 0 4 53^ h\02 2 54 50e h \ ` V r 5 \ 40e h \ ` 6 8 x h\020 68V \ 4 g h i `0 > 5 4 h \ ` f ] 5 0] 0 0 >55 0 1 2 4\ `0 0 502 ] \02 05> 5 `0`4Z] \ 20] ] ]045 ] r 40h 4 ] ]045 R 0]04 d0\d ] \ _04 0 Y2 h = 4 1Z h\02 2 0 t = 0 5 >44 e 53^ r 4 2044 e = h 45 234 \ 23 r i V x \ ^s0e 40 h] s044z] 2 _04 0] 5 e = 4 1Z 8 b2 54 53 0 40= 2 > r 2 54 53 4 _ 40= ; 8 ž 2s 4 0 40= 2 > 4 ρ1 ρ2 ρ1 < ρ r 4 _ 4 e 2 e ; Y0 40`4 =2 Y e 8 } 2 _ s e> 4 204 5 i H 1 50234Z \ 23 2 = 05> 4 ` 20 4 = h 450 0 40] x z = z0 2 0r h 50] 4 = h 450 ; 4 _ 40] 8 z = z0 x ª«] 5 05> 2 ` e r =\ \ 23 2 2 h 4 4 \ 2 0] ` 8 x 50 ] 4 5041 2 50e Φ(x, z, t) Φ = U r U = (u, v) r =\0 ; 5 055 044 = h 45 234 > 0 5 234 > ] 4045Z u, v 0 5 5 h 234 e 5 ` 0 5 ] 50] 5 `0 > 5 4 \4 e h \ ` Z=2>\ 5 20\ ^s ] Y h ] f Φ(x, z, t) = θ(t)δ(z z 0 )δ (x + V t), Φ(x, z, t) 0 t < 0, 2 Φ 1 + g Φ 1 t 2 z = 0 z = H, Φ 1 z = Φ 2 z = 0, ( z 2 Φ 1 ρ 1 + g Φ ) ( 1 2 Φ 2 = ρ t 2 2 + g Φ ) 2 z = 0. z t 2 z z\03 ; \0235 ig 4 1 > r δ(.) δ (.) ; 00 h \4 > r ; 04 0 Y \i g

~ 4 = \04 > { { 1, t > 0, Φ1 (x, z, t), z > 0, θ(t) = Φ(x, z, t) = 0, t < 0, Φ 2 (x, z, t), z < 0. z\03 \ 200 0 Y h4 `04 > 4>^5 2 5 23 0\02 5 e =2 Z r 5 e 4 YZ2 0\04Z 8 a20\ 05> 5 4 d >> 5 4 0 4 54Z 24 \ 2 5 \ 2> 8 / 5 e 1023^ s05 2>05> 0\0234Ze 0 0 \ \2> 405 1 i 4 4 = 0d04 > 8 x 0h 235 50 \2> 5 4 d0e> ` 5 i t 0 4 54Z h] s04 e 50]0 5`05 r >h 44 e 0 >5i ξ = x+v t 5 0] r 4 e\04 20\ ^ s 00 450= 234 0 0\ 5 204 0 f η(ξ) = R 4πV + (ρ 2 ( k V 2 g) + ρ 1 ( k V 2 + g))e k z 0 + (ρ 2 ρ 1 )( k V 2 g)e k z 0 e ikξ dk, (ρ 2 ch k H + ρ 1 sh k H)( k V 2 g)(1 ψ( k )) =\0 ω 2 ψ( k ) = 1( k ) r ω 2 k 2 V 2 1 (k) = gk(ρ 2 ρ 1 ) thkh ; \ 0 44 0 54 d 0i 4 0 \2> 4 5 044 24 \ 2 e4 e ρ 2 + ρ 1 th_ kh \ 5 Y0 40`4 e =2 Y 4Z r k ; 24 0 ` 2 r ; ` 5 5 8 } 200 ] s3^ 50 Z`05 > i ω1 4 ] \0 4 \ 5> 0\02 24 Z h] s 04 e Y \4 e 0 4 5 8 b h 4 r `5 24 > 5 5 0\02>05> 2 \ ] ξ + \ 2^ \Z450= 234 = Z _04 > k = g/v 2 r =\0 ; k = k ψ kψ \0e5 50234Ze 043 404 > 8 b0 Ze 2^ 5 055 05 ψ(k) = 1 0 4 54 e ] \0 2ρ η 1 ge gz 0/V 2 (ξ) = R V 3 (ρ 2 ch(g/v 2 ) + ρ 1 sh(g/v 2 ))(1 ψ(g/v 2 )) sin(gξ/v 2 ). x5 e 2^ 5 0` 05 4 5 0440e ] \0 k = kψ η (ξ) = R (ρ 2(kV 2 g) + ρ 1 (kv 2 + g))e kz 0 + (ρ 2 ρ 1 )(kv 2 g)e kz 0 V (ρ 2 ch kh + ρ 1 sh kh)(kv 2 g)( ψ (k)) sin kξ. k=kψ <5]05 ] r `5 4 5 044>> ] \ s05 05 5808 404 0 ]005 ψ(k) = 1 0s05 044Ze 043 2 ` 0r =\ h4 `04 0 ]043d0 40 5 = kψ V r 5 0 0\02>05> h 54 d04 > V±²³ ( V±²³ 2 = gh 1 ρ ) 1. (1) x ª«4 2 = `4 e 5 4 0 ] 5 04 h \ ` 6 hy _\04 0 4 54Z h] s 04 e \ _ 04 0 >55 > r ] i \02 0] = 5 `0`4Z] \ 20] r \ 2 0] ` 2 54 5 8 x 4 ` 234Ze ρ 2

V9 ] ]045 0]04 \ 23 4 \ 5> 5 ` 0 8 5 4 204 r `5 \2> (0, z0 ) 5 1 4 4 e ` 5 h Z d 04 > Y \4 e 0 4 5 50]0 5`05 r >h 44 e \ _ s ]> 0 >55 0] r 0\2 20\ ^s00 450i ξ = 234 0 0\ 5 204 0 f η(ξ) = R 2πV + ρ 2 k e k z 0 (ρ 2 ch k H + ρ 1 sh k H)( k g/v 2 )(1 ψ( k )) e ikξ dk, =\0r Zd0r ω 2 ψ( k ) = 1( k ) r ω 2 k 2 V 2 1 (k) = gk(ρ 2 ρ 1 ) thkh ; \ 0 4i 4 0 54 d 04 0 \2> 4 5 044 24 \ 2 e4 e ρ 2 + ρ 1 thkh _ \ 5 Y0 40`4 e =2 Y 4Z 8 x 24 > 5 5 0\02>05> ]] e \ ] \ f 0 4 5i 4 e 2ρ η 2 ge gz 0/V 2 (ξ) = R V 3 (ρ 2 ch(gh/v 2 ) + ρ 1 sh(gh/v 2 ))(1 ψ(g/v 2 )) sin(gξ/v 2 ) 4 5 0440e 2ρ 2 ke kz 0 η (ξ) = R (ρ 2 chkh + ρ 1 shkh)(k g/v 2 )( ψ (k)) sin(kξ). k=kψ z\03 ; 0s05 044Ze 043 404 > 8 h \ `0 Y kψ ψ(k) = 1 Y50 4 0 >55 > 4 \ 2 0] ` r 4 5 044>> ] \ h4 05r 0i 2 8 /20\ 50234 r Y 2 ` > 24 > V < V±²³ = gh (1 ρ1 /ρ 2 ) 5 5 h] s 04 e Y \ 4 e 0 4 5 Y \05 0\02>53> \ 4 ] 50] _0 2 `05 ] ] \ \ 4 Z] 24 Z] ` 2 ] r h2 `4Z Y i \ 5 2 d 3 ] 2 5 \Z 8 x h4 4 04 0 4 5 0440e ] \Z Y 2 204 g g 0 i 5 ] 5 5 g 1 \4 \4Z 5 4 5 55 058 b 0 4 54 > _0 ] \ s05 05 2^YZ h4 `04 > 02 ` 4Z 5 4 Y0= ^s0i = 5 r 2 `0 e h \ `0 Y Y50 4 0 >55 > 5 ] \4 \4 e _ \ 5 Y0 40`4 e =2 Y 4Z ] 8r 4 ]0 r µ ¹ º» ¼ µ ½«¾ À Á ¼  ëº Ä ž0 05 `0 > = \ ]0 4 8 ž8v8 ; œ 8iU 8f i 50 h\ 5r V~ : 8 x h\020 6 86 \>5> 0h 235 5Z `05 ] 2 5 \ 0 4 5i 4Z 24 4 2 h 8 8 VÅ 6 \0] 45 4 g g 0 5 2 >4 > ` 2 54 5 4 h]0404 0 ] 2 5 \ Z 0 4 54 e 24Z r h4 i ^ s 0e Y50 4 \ 2> 8 X `05Z 02 3 h4 `04 > ]05 r 5 055 ^s 0 234Z] 2 >] 5 Z5 = ] > 8 ž r 2 54 53 0 i 40= 2 > ] > ] _ 4 ZY 53 ρ1 = 1022 =Æ] 3r 2 54 53 4 _ 40=

VV B пов., м 0.8 Поверхностная мода H 50м z 0 7м 0.6 z 0 4м 0.4 0.2 B пов., м 0.05 6.5 7 7.5 8 Поверхностная мода H 70м z 0 1м z 0 1м z 0 4м z 0 7м z 0 7м 0.04 0.03 0.01 6.5 7 7.5 8 z 0 4м z 0 1м z 0 1м z 0 4м z 0 7м ÇÈÉÊ ËÊ ÌÍÎÏÈÐÑÒÓ ÎÔÕÖ ØÙÔÉÐÙÔÚ ÍÔÒÓ Î È ÔÛÐÖÜÝÙÈÈ Î ÖÎÞÐÉÐÕÈÞ ÙÝÒ ÉÏÔÖÍ ÉÜÝßÜÝ ÎÏÔÐÙÔÉÐÈ È ÎÔÒ ÙÈÍ Õ ÉÏÑßÝÞØ H = 50 Í È H = 70 ÍÊ ; 0\02 =Æ] ρ2 1023 3 ρ 2 1029 =Æ] 38 ž ] 2 54 5>] 5 0` ^5 h4 `04 > ]05 0\02 8 = g δ = ρ1 /ρ 2 0.993 δ 0.999 VÅ 6 `05Z \ 2 3 \2> 5 0 45 ] s 4 5 ` 2 54 5 f δ 1 = 0.996 r δ 2 = 0.998 δ 3 = 0.999 8 U ]045 \ 2> h \ 2> 1 i R 4 234Z] 5 0= \ _04 > f ] V R/V = 1600 2 8 b 2 _04 0 0 >55 > \ 2> = 4 ` 2 3 5 0]> = h 45 ] f z0 = 7 ] r 4 ] ] 0 r 1 5 4 h 5 4> = 4 1Z h\02 2 0 \Z 8 8 V 0\04Z Z0 ] 2 5 \ 0 4 54 e ] \Z Bàáâ ³r i ` 5 44Z0 4 \ 2 0] ` 2 54 5 0 4 0 5 2 4 \ 4 ] 4 _i 4 0 5 2 4 \2> 2 ` 0 ] ] 8 z\03 20\ 05 5]05 53r H = 50 H = 70

V6 0.25 Внутренняя мода H 50м препятствие над скачком 0.996 0.2 0.15 0.1 0.998 0.05 0.999 0.4 0.6 0.8 1 1.2 1.4 0.06 Внутренняя мода H 50м препятствие под скачком 0.05 0.04 0.03 0.996 0.01 0.999 0.998 0.4 0.6 0.8 1 1.2 1.4 ÇÈÉÊ ãê ÌÍÎÏÈÐÑÒÓ ÕÙÑÐ ÖÙÙÖÚ ÍÔÒÓ Î È ÔÛÐÖÜÝÙÈÈ Î ÖÎÞÐÉÐÕÈÞ ÙÝÒ ÉÏÔÖÍ ÉÜÝßÜÝ ÎÏÔÐÙÔÉÐÈ È ÎÔÒ ÙÈÍ Õ ÉÏÑßÝÖ H = 50 ÍÊ `5 4 _\ e e 5 `0 ]0s04Z 5 = Z 5 `0 r 5 05i 5 ^s 0 5 0] h4 `04 >] δi i = 1, 2, 3 r `5 hz 05 4 40h ] 53 0 4 54 e ] \Z 5 ] s4 5 ` 2 54 5 \Z r 5808 5 > ] \ > 2>05> 40 0\5 044 h `05 Y50 4 > \ 2> 8 } 200r 4 = g i \ 4 r `5 ] 2 5 \ Z h] s 04 e 4 \ ` ] 2 54 5 s 05 044 Zd0 5 055 ^s ] 2 5 \ \ ` ] 8 8 6 0\04Z Z0r 5 055 ^s 0 ] 2 5 \ ] 4 5 04i 40e ] \Z Bâä ³r ` 5 44Z0 4 \ 2 0] ` 2 54 5 0 4 0 ` 5 \ 4 ] 4 _ 4 0 ` 5 \2> 2 ` > H = 50 ] 8 0\5 2044Z = g i \4 r `5 > 204 > ] 2 5 \ 4 5 0440e 0 4 54 e ] \ Z 4

VW 450 20 5 Y50 4 > 0 >55 > V s05 044 h4004z ]0_i \ Y e 8 ž r 4 5 044>> ] \ h ] 5 5 δ > 2>05> 2 d3 40Y 23d 5> V r Y2 53 > 204 > 0 4 54 e ] \Z s0i 5 044 \ 4 5 5 4 Y 23d V 8 Ÿ5 Y 2 204 { >h e 4 i 5 0440e ] \Z 5 5 0 ` 2 54 5 ] 8 V 8 ]0 5 = r h 8 6 \4 r `5 0\04 0 4 5 0440e ] \Z h2 `i 4 2 ` > Y50 4 > \ 2> 4 \ ` ] 2 54 5 \ 4 ] r `0] g ]0r 5 02 ` 40 ] 2 5 \Z 8 Ÿ5 hz 05 4 50 i 4 ^ 23 ` 2 54 5 40 \4 \4 5 r Y2 ^s0e Z \ h] i s04 e 4 0 4 53 \Z 8 } 44Ze gg0 5 0\5 2>05> _ 4Z] \2> \ 2340ed 0= h 5 > ]05 \ 45 2 ^ s 0= ] 4 5 4= ] i 5 e r 4 44Z 4 \ 44Z r 2 ` 0]Z 0\ 5 ] \ 5 41 44 = h 4\ 4 > 0 4 5 ] > 8 n 20\ 4Z ]05 \ `0 0 0 5Z 2 >4 > 0 i 40e = 4 1Z 5 _ \ 5 Y \4 e 0 4 5 2 Y {5 0 \ e Zdi 4 g ] 4 \>s0= > Y2 h 5 e = 4 1Z 0 >55 > r ] \02 i 0] = 5 `0`4 e Y044 53^ 5 `4 ] ] s4 5 Q 2 \ 20] ] ]045 ] M 8 / 53 5 4 c 4 204 \ 23 2 _ 5023i 4 e X r Y044 53 2 _04 4 =2 Y 40 H 5 ` 0 \ 4 5 ] X = 0 r Y = H 8 }2> 0d04 > 5 2044 e h \ ` \>5> 20\ ^s 0 Y0h h]0 4Z0 0 0]044Z0 f x = X H, y = Y H, q = Q ch, m = M ch 2, E = gh c = 1 =\0 ; ` 2 [ \ =2 Y 40 Y044 5 8 ]0 2 5 = F r 2, 1023^ `0i F 5 044 e 450 05 1 0h 235 5 `05 2 ` 0 Y50 4 > 5 `4 i 0\04 Y0h h]0 4Ze ]05 g ] 20 yd yd = Y /D, =\0 D ; h]0 4 > 5 2s 4 Y50 0] = 502 r 5808 \ 20 4 h 5 i x + r ; h]0 4 0 ] 5 5 `0 0 ]0s04 0 D = Q/c Y x + 0 5 2 502 r ] \02 0] = 5 `4 ] Y2 h 504 r 404 ^ 502 ] r ] \02 0]Z] 5 `4 ] Y0h= 4 `4 ] 5 0 8 x h\020 W 8V 20\ 05> Y50 4 0 Y044 5 \ {5 0 \ e Z di e r h\020 W86 ; Y2 h Y \4 e 0 4 5 8 X0h 235 5Z `05 0\5 204Z h\020 W8W8 x h\020 W8 \>5> Z \Z r \02 44Z0 0h 235 5 ] ` 204i 4 = ] \02 4 > 8 V8 a5 `4 5 0 {5 0 \ e Z d ] \02 05 2 Y0 40`i 4 0 h 5 2044 0 502 r 40 ]]05 `4 0 54 50234 = h 45 0= 2 2 i

V h 1 8 b ] 2Z h4 `04 > ] s4 5 \ 20 4 h 5 q q 1 5 502 ]0s04 4 h ]0 4 4 `05 0 53 0e 5 2s 4Z 404 ^ 502 ] r 5 055 ^ s ] Y50 4 ^ 5 `4 Y0h= 4 `4Z] 5 ] 8 b ]043d04 ]05 54 50234 = ]0s04 > 40 5 0] 5> 4 i q yd 2^ r 5 ] h \ `0 Y 5Z 4 g ]Z 502 r Y50 4 0 5 = ] i \02 05> 5 `4 ] 504 r 4 2 ` 0] 20\ 40e 4023h> 040Y 0= 53 5808 ` 5 53 5 Y0h= 4 `4Z] 4 h4 `04 > ]05 8 q 68 } 23 ] ]045 ] 5 0 \ {5 0 \ e Zd e ] \02 05 m 1 2 4\ `0 0 502 8 / YZ 4 0] ]05 54 50234 0 r = m/(2π) _04 0 g ]Z 5 = 502 404 ^ = Z] 1 2 4\ ] \ r 5 0` ^s ] Y50 4 ^ 5 = _0 \ 2> Y0h= 4 `4Z] 5 ] r ]043d i r 05> r 5 4 >3 40h4 ` 50234Z] 8 b 5 ] ] \02 4 r = 0.35 Y50 0] = \ {5 0 \ e Zd e 502 \ 20] 00 55 0 ] _ 4 40 ` 5Z 53 r 50] ]Z] ` 5 > 5 Y0h= 4 `4Z] 8 r 0.35 W 8 a5 `4 5 0 Y \4 e = 4 10e ] \02 05 40 ]]05 `i 4 0 h 5 2044 0 502 = g 44 e 0 4 53^ 8 <54 d04 0 ] 2 i ad 5 \Z 24Z 4 0 40e ` 5 5 e 0 4 5 5 2s 40 502 5 4 5> ]043d0 989Vr 02 r 5 ] ] \02 4 Y50 0] = q 1 E 3 502 5 `4 ] Y \ 4 ^ 0 4 53 ] _ 4 h ]04 53 {5 0 \ e Z di e Z 2404 2 e 8 <\4 5 Y \4 e q 1 E 3 0 4 53^ 4023h> h ]04>53 Y0h= 4 `4Z] 4 h4 `04 > 8 q E 8 å2 r 5 ] \02 4 Y50 0] = 502 r 0.35 E 5 \ 20] Y \4 ^ 0 4 53 ] _ 4 h ]04 53 {5 0 \ e Z d e 2 Y ` 5 53 5 Y0h= 4 `4Z] 8 n 20\ 05> 24 > 5 5 0 4 54Z h] s 04 e r h4 ^ s Y50 4 \ \4Z 0 >55 e 5 ] \ 2 e4 e \0 234 e _ \ 5 40`4 e =2 Y 4Z r = 4 `044Z] = i h 45 234Z] \4 ] 8 x h\020 8V 0\04 g h `0 > 5 4 h \ ` 8 b 0 >55 0 ] \02 05> 5 `0`4Z] \ 20] ] ]045 ] r 2 2 h 4i m 4Z] 054 5 2 > ` 2 54 5 r 2 Y \ 4 ] r 2 Y 4 \ 4 ] 8 ž 2i s 4 0 40= 2 > ; r 4 _ 40= ; r 2 54 5 ; 5 055 044 H H1 8 ` 2 \ 4 5 2 _04 4 40 h] s044 e = i ρ 1 ρ2 ρ1 < ρ 4 10 ]0_\ 2 >] 2 _ \ 5 r 3 4 204 \ 23 x 5 e = 4 1Z r 3 y ; 0 5 234 0 8 b 0 >55 0 2 2 h 4 4 2 Y 4 \ = i y 4 10e h\02 \ 2 0 r 2 Y \ 40e8 / 53 5 4 d0= > 5 4 8 X0d04 > h \ ` \>5> ] 50 ] 2Z x V h] s 04 e 8 x ª«æ ] 5 05> 2 ` e r =\ \ 23 4 \ 5>

V7 \ ` ] 2 54 5 r 5808 5 ` 0 8 X0d04 0 s05> \0 h2 i (0, h) _ 04 > ] 20 4 i >_ 044 e 5 450= 2 [ 30 24 Z] ` 2 ] 8 x 5 =0 \2> ] e 02 ` 4Z h Z d 04 > Y \4 e 0 4 5 2 `04 20\ ^s00 Z _04 0f ζ(x) ζ(x) = m πv 0 k 2 ch k(h 1 h) cos kxdk ch kh ch kh 1 {k 2 + [δk 2 + (1 δ)ν 2 ] th kh thkh 1 kν(thkh + thkh 1 )}. z\03 δ = ρ1 /ρ 2 r ν = g/v 2 r g ; 04 0 Y \4 = \04 > r k ; 24 0 ` 2 8 } 200 s05 2>05> 0 0 \ Y0h h]0 4Z] 0 0]044Z] f X = νx, Z = ζ H, ξ = k ν, M = m gh V H2, E = νh = V = 1 2 F 2, E 1 = νh 1 = gh 1 V = 1 2 F 2, E 0 = νh = gh 1 V = 1 (2) 2 F 2, 0 =\0 r r ; ` 2 [ \ 5 055 044 =2 Y 40 0 40= 2 > r =2 i F F1 F0 Y 40 4 _ 40= 2 > 5 >4 ^ 5 \ 2> \ 40 h] s044 e 0 4 5 h\02 8 x 5 0 0]044Z Y0h h]0 4 0 h Z d 04 0 Y \ 4 e 0 4 i 5 h Z 05> \0 Z(X) Z(X) = ME π 0 ξ 2 ch(e 1 E 0 )ξ cos Xξ dξ ch Eξ ch E 1 ξ {ξ 2 + [δξ 2 + (1 δ)] theξ the 1 ξ ξ(theξ + the 1 ξ)}. (3) a ] > 24 > 5 5 S(X) 0\02>05> 4 2>] h4 ]04 50i 2> \Z450= 234 = Z _04 > r 2 _044Z] 4 2 _ 50234 e \0ei 5 50234 e r 5808 2 _ 50234Z] 4>] 404 > ξ 2 + [δξ 2 + (1 δ)] theξ th E 1 ξ ξ(theξ + the 1 ξ) = 0. (4) }2> Z` 204 > 450= 2 W YZ2 h Y 5 4 = 4 234 > ]05 \ 0\0204 > 2 `05 5 40e 8 x 5 =0 5 4 204 r `5 404 0 ]005 \ 2 _ 50234Z 4> 2 E > Eâä ³ cr = β + 1 + (β + 1) 2 4εβ 2εβ 5> YZ \ 4 2 _ 50234Ze 043 (5) E > Eàáâ ³ cr = β + 1 (β + 1) 2 4εβ, (6) 2εβ

V =\0 ; 54 50234Ze 0 0 \ 2 54 5 ]0_\ ε = 1 δ = (ρ2 ρ 1 )/ρ 2 >] r 2 8 a450= 4 0 W 0\04 ] s3^ β = H1 /H = E 1 /E 50 Z`05 r 0h 235 50 \2> 2 `04 20\ ^s00 Z _04 0f S(X) S(X) = 2ME s j=1 g 1 (ξ j ) g 2 (ξ j) sinξ jx. z\03 ξj ; 4 404 > r s ; 2 `05 r g 1 (ξ, E, γ, β) = ξ2 ch(β γ)eξ cheξ ch βeξ, g 2(ξ, ε, E, β) = = ξ 2 + [(1 ε)ξ 2 + ε] theξ th βeξ ξ(theξ + thβeξ), =\0 γ = h/h = E0 /E 8 ž ] Y h ] r 24 Z 0 h] s 04 > E > Eçèé cr 0\5 2>^5 ]] \ ] \ ; 4 5 0440e h4 ^s0e hih 4 2 ` > 2 > ` 0 4 54 e h `05 40 0\5 044 = Y50 4 > 0 >5i 5 > 8 b0 > ] \ 5 055 05 ]043d0] 4^ r 5 > ; Y 23d0] ξ1 8 x 2 ` 0 5 5 2 d3 h \4 e 0 4 54 e ξ 2 Eêëçé cr < E < Eçèé cr S(X) ] \Z r 0 4 54Z0 24Z 40 Y h ^5> 8 E < Eêëçé cr S(X) 0 /20\ 50234 r 4 5 044>> ] \ h4 05 2 E > Eçèé cr gh(β + 1 (β + 1) V < Vcr çèé = 2 4εβ), (7) 2 0 4 54 > ; r 5808 02 E > Eêëçé cr gh(β + 1 + (β + 1) V < Vcr êëçé = 2 4εβ). (8) 2 <5]05 ] r `5 8 V çèé < V êëçé cr cr x ª«æ 4 2 = `4 e 5 4 0 20\ 4 h \ ` =0i 40 1 0 4 54Z h] s 04 e Y50 0]Z] 0 >55 0] r ] \02 i 0]Z] 5 `0`4Z] \ 20] r 5 Ze 2 2 h 4 4 \ ` ] 2 54 5 r 5808 5 ` 0 (0, h) 0 < h < H 8 b h 4 r `5 0 0]044Z 6 \2> Y0h hi ]0 4 e 02 ` 4Z 5 2 404 > Y \ 4 e = 4 1Z 0\2 20\ ^ s 00 0\5 204 0 f Z(X) = ME 2π X 2 (E E 0 ) 2 (X 2 + (E E 0 ) 2 ) ME g 1 (ξ, E, E 0, E 1, ε) cos Xξ dξ, (9) 2 2π g 2 (ξ, E, E 1, ε) 0

V =\0 g 1 (ξ,e,e 0,E 1,ε) = ξ { e Eξ [((1 ε)ξ + ε) the 1 ξ ξ] [ch(e E 0 )ξ ξ sh(e E 0 )ξ] + (ξ + 1) {[ε ch E 0 ξ (1 ε)ξ sh E 0 ξ] th E 1 ξ ξ ch E 0 ξ}} / ch Eξ, g 2 (ξ,e,e 1,ε) = ξ 2 + [(1 ε)ξ 2 + ε] theξ the 1 ξ ξ(theξ + the 1 ξ). b 23 \Z450= 234Z0 Z _04 > W ~ ]0^5 \4 50 _0 i 2^ r 2 _ 044Z0 4 2 _ 50234 e \0e5 50234 e r 5 24 > 5 5 h] s 04 e Y \4 e 0 4 5 r h4 ^ s Y50 4 0 >55 > 4 \ 2 0] ` r Y \05 0\02>53> 50] _ 0 2 `05 ] ] \ 50] _0 24 Z] ` 2 ] r `5 ] 5 044 ] Zd0 2 ` 0 0= 2 i 2 h 1 \ 2 0] ` 8 b 5 ] 50 s 05 4 > 4 5 0440e 0 4 54 e ] \ 5 4 5> 40 h]044z] ] 8 7Å 2 Å: 8 } 200 ] s3^ 50 Z`05 2 `04 20\ ^s00 Z _04 0 \2> 24 e ` 5 0 4 54Z h] s 04 e h Y50 0]Z] 0 >55 0] f S(X) = ME s j=1 g 1 (ξ j ) g 2 (ξ j) sinξ jx. z\03r Zd0r ; 2 _ 50234Z0 4 404 > r ; ξj s 2 `05 8 x h\020 86 \>5> 0h 235 5Z `05 ]05 0 i 4 54Z 24 4 2 h 8 X `05Z 02 3 h4 `04 > 50 5 0\ Z r 5 055 ^ s 0 234Z] 2 >] ] > 8 ž r 2 54 53 0 i 40= 2 > ρ1 = 1023 =Æ] 3r 2 54 53 4 _ 40= ZY 2 3r 4 ` 4 > ρ 2 = 1024 =Æ] 3 Y 23d08 ž ] h4 `04 >] 2 54 50e 5 055 05 ] 4 i ] 234 0 h4 `04 0 ]05 r 4 0 9899V8 U ]045 \ 2> YZ2 ZY 4 ε m 1 4 234Z] 5 5 f ] V m/v = 1600 2 8 0 h] s044 0 i 2 _04 0 ` 2 54 5 5 055 2 =2 Y 4 ] ] ] r H = 50 H = 70 2 2 h 1 > 0 >55 > \ 2> = 4 ` 2 3 5 0]> = h 45 ] f h = 7, 4 ] 4 \ ` ] r 5 \ 4 ] 8 1 8 WÅ7 \2> 2 ` > ] r ] 0\04Z = g h i H = 50 h = 4 ] 5 ] 2 5 \ 0 4 54Z 24 Bàáâ ³ 5 5 4 Y0= ^s0= 5 h2 `4Z h4 `04 > ]05 8 V ε β 5 = g \4 r `5 h] s04 > h `05 4 5 0440e 0 4 54 e ] \ > 2>^5i > 4 450 2 5 5 r s 05 044 h40044z ]0_\ Y e f 0 V âä ³ ]Æ 5 055 044 r \ 200 Z \> h Y2 5 2 40e4 5 6.5 8.5 cr h \ ` Y ì 23d 5> 0 4 54Z0 24Z 0 05 ^5 0 54 Z 53> 50 0e ] 2Z h] s04 e 8 x 0 ] 450 20 ]043i d 5> { Y 5 05 4 5 044>> ] \ r 5 ] ; 0 4 54 > 8

V: Β 1 Β 2 Β 3 Β 4 Β 5 0.015 0.015 Β 6 0.01 0.01 0.005 0.2 0.3 0.4 0.5 0.6 0.7 0.005 1 2 3 4 5 6 0.2 0.3 0.4 0.5 0.6 0.7 ε = 0.001 ε = 0.001 0.04 0.03 0.04 0.03 Β 1 Β 2 Β 3 Β 4 Β 5 Β 6 0.01 0.2 0.4 0.6 0.8 1 0.01 1 2 3 4 5 6 0.2 0.4 0.6 0.8 1 ε = 0.002 ε = 0.002 0.08 0.06 0.08 0.06 Β 1 Β 2 Β 3 Β 4 Β 5 Β 6 0.04 0.04 0.4 0.6 0.8 1 1.2 1 2 3 4 5 6 0.4 0.6 0.8 1 1.2 ε = 0.004 ε = 0.004 ÇÈÉÊ íê ÌÍÎÏÈÐÑÒÓ ÕÙÑÐ ÖÙÙÖÚ ÍÔÒÓ ÎÔÕÖ ØÙÔÉÐÙÓØ ÕÔîÍÑï ÖÙÈÚ Î È ÔÛÐÖÜÝÙÈÈ Î ÖÎÞÐð ÉÐÕÈÞ ÎÔÒ ÉÏÔÖÍ ÉÜÝßÜÝ ÎÏÔÐÙÔÉÐÈ Î È ÛÖÉÜÔÙÖßÙÔÚ ñïöõóö ò ÝóÈÜÈô È ÜÔÙÖßÙÔÚ ñî ÝÕÓÖô òïñûèùýø ÒÏÞ õöéðè îùýßöùèú ÎÝ ÝÍÖÐ Ý β ñéôôðùôõöùèþ ÐÔÏïÈÙ ÙÈöÙÖòÔ È ÕÖ ØÙÖòÔ ÉÏÔÖÕ ÒÕÑØÉÏÔÚÙÔÚ öèòüôéðèô β1 = 0.5ø β 2 = 1ø β 3 = 3ø β 4 = 5ø β 5 = 10ø β 6 = 25 Ê

V~ Β 1 Β 2 Β 3 Β 4 Β 5 Β 6 0.07 0.07 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.01 0.2 0.3 0.4 0.5 0.6 0.7 0.01 1 2 3 4 5 6 0.2 0.3 0.4 0.5 0.6 0.7 ε = 0.001 ε = 0.001 Β 1 Β 2 Β 3 Β 4 Β 5 Β 6 0.14 0.14 0.12 0.12 0.1 0.1 0.08 0.08 0.06 0.06 0.04 0.04 0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 0.2 0.4 0.6 0.8 1 ε = 0.002 ε = 0.002 Β 1 Β 2 Β 3 Β 4 Β 5 Β 6 0.25 0.2 0.15 0.1 0.25 0.2 0.15 0.1 0.05 0.2 0.4 0.6 0.8 1 1.2 0.05 1 2 3 4 5 6 0.2 0.4 0.6 0.8 1 1.2 ε = 0.004 ε = 0.004 ÇÈÉÊ ù Ê ÌÍÎÏÈÐÑÒÓ ÕÙÑÐ ÖÙÙÖÚ ÍÔÒÓ ÎÔÕÖ ØÙÔÉÐÙÓØ ÕÔîÍÑï ÖÙÈÚ Î È ÔÛÐÖÜÝÙÈÈ Î ÖÎÞÐð ÉÐÕÈÞ ÙÝÒ ÉÏÔÖÍ ÉÜÝßÜÝ ÎÏÔÐÙÔÉÐÈ Î È ÛÖÉÜÔÙÖßÙÔÚ ñïöõóö ò ÝóÈÜÈô È ÜÔÙÖßÙÔÚ ñî ÝÕÓÖô òïñûèùýø ÒÏÞ õöéðè îùýßöùèú ÎÝ ÝÍÖÐ Ý β ñéôôðùôõöùèþ ÐÔÏïÈÙ ÙÈöÙÖòÔ È ÕÖ ØÙÖòÔ ÉÏÔÖÕ ÒÕÑØÉÏÔÚÙÔÚ öèòüôéðèô β1 = 0.5ø β 2 = 1ø β 3 = 3ø β 4 = 5ø β 5 = 10ø β 6 = 25 Ê

69 B пов., м h 1м B пов., м h 1м 0.25 0.25 0.2 h 4м 0.2 h 4м 0.15 0.1 h 7м 0.15 0.1 h 7м 0.05 0.05 6.5 7 7.5 8 6.5 7 7.5 8 B пов., м h 7м B пов., м h 7м 0.8 0.8 0.6 h 4м 0.6 h 4м 0.4 h 1м 0.4 h 1м 0.2 0.2 6.5 7 7.5 8 6.5 7 7.5 8 ÇÈÉÊ úê ÌÍÎÏÈÐÑÒÓ ÎÔÕÖ ØÙÔÉÐÙÔÚ ÍÔÒÓ Î È ÔÛÐÖÜÝÙÈÈ Î ÖÎÞÐÉÐÕÈÞ ÎÔÒ ÉÏÔÖÍ ÉÜÝßÜÝ ÎÏÔÐÙÔÉÐÈ ñõö ØÙÞÞ ÎÝ Ý ò ÝóÈÜÔÕô È ÙÝÒ ÙÈÍ ñùèö ÙÞÞ ÎÝ ÝôÊ b `0] \2> 4 5 0440e ] \Z 50 4 d 04 0 \ h 4 00 s 0i 5 4 > 02 `04 ] s4 5 2 > ` 2 54 5 ε r `5 5 05i 5 05 50 ^ 00 h4 4 04 > 2 7 8 x 102> 4 =2>\4 5 i 404 > ] 2 5 \ B(V ) Y50 4 0 >55 > 5 ] Y0 40`4 e 40`4 e =2 Y 4Z = g 4 8 WÅ7 0\5 204Z ] 5 05i 5 044 20 8 X0h 235 5Z `05 ] 2 5 \Z 4 5 0440e ] \Z \2> 2 ` > 2 2 h 1 \ 2> \ 2 0] ` 4 \ 4 ] 0\04Z 4 8 W 5 055 044 8 b Z = g 5 04Z \2> 5 0 h4 `04 e ] s4 5 ` ε r Z0 = g ; \2> d05 h4 `04 e ]05 β ε {0.001, 0.002, 0.004} r β {0.5, 1, 3, 5, 10, 25} 8 }2> _\ = h4 `04 > β 5 02 e 1 g e r 4 e 4 ]0 4\0 β r h 4 h4 `04 0 5 i `0 e 5 ] ] 234 e 5 5 V r 5 e h4 05 4 5 044>> ] \ 8 /20\ 05 5]05 53r `5 ] 2 > 00 02 ` 4 40 0 Zd 05 1 Å 1.5 ]Æ8 }2> 0 4 54 e ] \Z 8 7 0 4>> = g 5 055 i 05 Y50 4 ^ 0 >55 > \ 2 0] ` r 4 _ 4>> ; 4 \ 4 ] 8 x02 ` i 4Z ε YZ2 ZY 4Z 50] _0 ]Z] r `5 2 ` 0 4 5 0440e ] \Z r

6V β {0.5, 2, 10} 8 \4 r \2> _\ = g 44 = 2 _04 > 0i >55 > 5 0 40`4 e =2 Y 4Z Z0 4 Z = g r 5 05i 5 ^s 0 h2 `4Z] h4 `04 >] ε β r 2 ^5> 8 Ÿ5 hz 05 4 5 r `5 ] 2 5 \ Z 0 4 54 e ] \ Z 5 `0 40 h >5 5 ] s 4 5 2 > ` 2 54 5 ε \ h 40 h4 `04 e ε r 50 4 ] \2> 0 23i 4Z ] 2 e 5 54 d04 > 5 2s 4 4 _ 40= 0 40= 2 0 β β > 0.5 8 ž ] Y h ] r 5 ] 2 ` 0 =2 Y 44Z0 h] s04 > Zi \0 4 0 4 53 {40 h ]0` ^ 5 2 54 54 ^ 40 \4 \ 4 53 4 2 ` 0 5 4 _ 40e = 4 1Z 8 ah = g 5 _0 20\ 05r `5 ] 2 i > 0 4 54 > ] \ h 234 > 2>05> 54 50234 Y 23d h4 `04 > 5 V V 6 ]Æ 8 ûm k g ] 2 4Z 4 4Z0 0h 235 5Z \ 0 5 1 8 V8 X0d04 2 > h \ ` Y 0\0204 g ]Z 502 r ] \02 0] i = 5 `0`4 e Y044 53^ 5 `4 ] 2 \ 20] 5 0 \ 5 0 \ e Zd e Y \4 e = 4 10e8 b 0\04 404 0 g ] 502 r ] \02 i 0]Z Y044 53^ r Y50 4 20\40e 504 \ Y \4 e 0 4 53^ 8 b 2 `04Z 50 h] _ 4 5 h ]04Z Y \ 4 e 0 i 4 5 {5 0 \ e Zd e r 5 _0 Y \4 e 0 4 5 {5 0 \ e Zdi Y0h= 4 `4Z] 5 ] 8 6 8 a20\ 4Z 0 4 54Z0 h] s 04 > \ 2 e4 e \0 234 e _ \ 5 r h4 ^s 0 Y50 4 2 Y \ _04 = h 45 234 ] 4 204 054 5 2 > ` 2 54 5 \ \4 = 0 >55 > r ] \02 0] = 5 `0`4Z] \ 20] 8 b h 4 r `5 ] 2 > h Yi 50 0]Z] 0 >55 0] h] _ 4 Y h 4 0 \ h2 `4Z 5 i 0 4 54Z 24 8 5 4 204 r `5 24Z 0 = 5 Y 2 2044Z0 4 2 ` 0] Y \4 e 0 4 5 Y h ^5> 2^YZ h4 `04 > 02 i ` 4Z 5 4 Y0= ^s0= 5 V 2 Y h >5 5 5 5 g 1 r \4 ] 2 > 4 4 ` 4 ^5 h 234 > 2>53> 2 d3 54 50234 Y 23d h4 `04 > V 40 ]0400 6 ]Æ 8 b ]05 Z 24 5 i = 5 Y 2 2044Z 4 2 ` 0] 2 > ` 2 54 5 s05 044Z] Y h ] h >5 5 02 ` 4Z 0= ] s 4 5 8 x ] 2 > 5 0 2i 4Z Y h ^5> r =\ 02 ` 4 5 V 40 0 Zd 05 1 Å 1.5 ]Æ8 W8 x 2 > 0\Z\ s0e h \ ` 5 4 204 50 2 >4 > g i 5 40`4 5 =2 Y 4Z ] > 4 ]05 Z 0 4 54Z h] s 04 e 8 b h 4 r `5 h Y50 0]Z] 0 >55 0] h] _ 4 Y h 4 0 50 _0 5 0 4 54Z 24 8 x ] 2 > ]05 Z 24 r Y 2 i 2044Z 4 2 ` 0] Y \ 4 e 0 4 5 r 5 `0 40 h >5 5 5 2i s 4Z 4 _ 40= 2 > r 5 0]> 5 400 s05 044 h >5 ]05 Z

66 \ h 4 s 05 4 > 24 r Y 2 2044Z 4 2 ` 0] 2 > ` 2 5i 4 5 8 8 xz> 204 Y > 23 5 5 g ] 4 0 4 5i 4Z h] s04 e 0 234Z 2 > ] > 8 ž r h] s04 > 4 Y \i 4 e = 4 10 > 2>^ 5> 4 \ h40044z ]0_\ Y e 450 2 5 5 r ]0_ 5 `4 e h 40 5 h4 `04 e 5 `0 e i 5 4 5 0440e ] \Z \ 0\02044 e 50 4 e 02 ` 4Z h >s0e 5 ]05 h \ ` 4 5 55 ^5r 5808 5 h 4 0\5 2>05> h Z5 e \2> Z \ =2 Y 44Z h] s04 e 4 0 4 53 \Z 8 /20\ > 4>5 e ] e = \ 5 0 50 ] 4 2 = r 5 e ]0_ 5 `4Z e 450 2 ] _ 4 0\02 53 {h 4 504 \2> Z \ 4 0 4 53 \ Y4Z = \ \ 4 ] `0 h] s 04 e 8 78 }2> 4 2 h Ys0= 0d04 > h \ ` Y Y50 4 0 >55 > i 5 ] \ 2 e4 e _ \ 5 40`4 e =2 Y 4Z r 4 e\044 = 450= 23i 4 e g ]0 r h Y 5 4 ]05 \ 0\0204 > 2 `05 2^ \ Z 4i 50= 234 = Z _ 04 > r 2 _ 044Z 4 2 _ 50234 e \0e5 50234 e 4 = ` 2 Y h ^s > h 0 >55 0] ] \ 24 r h ] 5 5 ]05 h \ ` 8 q Œm p m n ü m ý wþ k wp V8 ľ ÿ À ¼ µ ¹ º º ¼ ¹ Á b 0 4 54Z0 gg0 i 5Z Y50 4 0 >55 e 40 \ 4 \4 i5 5 g 1 44 e 0\0 ÆÆ } 2 \Z y \0] 4 8 ; 69VV8 ; ž8 9r 8 ; 8 :6Å:6~8 68 ľ ÿ À ¼ µ ¹ º º ¼ ¹ Á ¼ ¹» <Y50 4 0 0 >55 e 5 5 g 1 44Z] 5 ] Y \ 4 e = 4 10e ÆÆ < 0i 4 2 = > 8 ; 69VV8 ; ž8 7Vr 8 ; 8 ~ Å~:W8 W8 ľ ÿ À ¼ µ ¹ º º ¼ ¹ Á U \02 4 0 Y50 i 4 > 0= \ 5 0 Y \4 e = 4 10e ÆÆ x054 U ž ] 8 8Ÿ 8 ] 4 8 /0 8 å505 044Z0 4 8 / 01 8 Z 8 U 50] 5 `0 0 ] \02 i 4 08 ; 69VV8 ; / 8 VV~Å V 98 8 ľ ÿ À ¼ µ ¹ º º ¼ ¹ Á b 0 4 54Z0 h] i s 04 > Y50 4 0 >55 e 5 5 g 1 44Z] 5 ] 40`4 e =2 Y 4Z ÆÆ < 0 4 2 = > 8 ; 69V68 ; ž8 76r 8 ; / 8 :67Å:W78 78 ľ ÿ À ¼ µ ¹ º º ¼ ¹ Á ¼ ¹» U \023 h] s04 > 0 4 5 5 5 g 1 44 e ] e 0\Z ÆÆ ž \Z x0 e e 4g 0 041 { b 2 \ 4Z 0 50 4 2 = = \ 5 = \i g h ; /by8f r 69V98 ; 8 6VVÅ6V78