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( <0E :>MDD8F85=B, CG8BK20NI89 G8A;> 68B5;59 2 =0A5;5==>< ?C=:B5, ?@8=8<05BAO ?> B01;8F5 2 ?. 2 . 2 [ 3 ] G. <0E @0AAG8BK205BAO, 0 70B5< ?@8=8<05BAO 1;8609H89 B01;8G=K9 ?> ?@8;>65=8N 1 40==KE C:070=89. 0AE>4 2>4K =0 E>7O9AB25==>- ?8BL52K5 =C64K 2 >1I5AB25==KE 740=8OE 7028A8B >B =07=0G5=8O 740=8O 8 >?@545;O5BAO ?> D>@<C;5 E M B E D E q u a t i o n . 3 , 345 q >1. 74. =>@<0 @0AE>40 2>4K ?>B@518B5;O<8 2 ACB:8 4;O >1I5AB25==KE 740=89 ?@8=8<05BAO ?> ?@8;>65=8N 3 [ 4 ] N 87. :>;8G5AB2> 87<5@8B5;59 ( ?> 7040=8N) 1I89 @0AE>4 2>4K ?> ?>A5;:C ( Q E M B E D E q u a t i o n . 3 = Q ACB. <0E + Q >1. 74. 0AG5B=K5 25;8G8=K E>7O9AB25==>- ?8BL52>3> 2>4>?>B@51;5=8O 2 ?@>872>4AB25==KE 8 2A?><>30B5;L=KE 740=8OE ?@><KH;5==KE ?@54?@8OB88 >?@545;O5BAO ?> D>@<C;0<: 2>4>?>B@51;5=85 2 A<5=C Q E M B E D E q u a t i o n . 3 Q E M B E D E q u a t i o n . 3 . = ( q E M B E D E q u a t i o n . 3 N A<) / 1 0 0 0 , 345 E M B E D E q u a t i o n . 3 =>@<0 2>4>?>B@51;5=8O =0 >4=>3> G5;>25:0 2 A<5=C, ?@8=8<05BAO A>3;0A=> ?. 2 . 4 [ 3 ] 8 ?@8;>65=8O 3 [ 4 ] ; N A<. :>;8G5AB2> @01>B0NI8E 2 A<5=C ( ?> 7040=8N) ; !CB>G=>5 2>4>?>B@51;5=85 Q E M B E D E q u a t i o n . 3 Q E M B E D E q u a t i o n . 3 = Q E M B E D E q u a t i o n . 3 n A<. , 345 n A<. :>;8G5AB2> A<5= ( ?> 7040=8N) . >;8G5AB2> 2>4K =0 ?>;L7>20=85 4CH5< 2 1KB>2KE ?><5I5=8OE ?@><KH;5==KE ?@54?@8OB88 >?@545;O5BAO ?> D>@<C;0<: 2>4>?>B@51;5=85 2 A<5=C Q E M B E D E q u a t i o n . 3 Q E M B E D E q u a t i o n . 3 = 0 , 5 ( N A , 345 ( = 1 G ?@>4>;68B5;L=>ABL 459AB28O 4CH0 ?>A;5 A<5=K ( ?@8;>65=8O 3 [ 4 ] ) 0 , 5 <3 / G =>@<0 @0AE>40 2>4K G5@57 >4=C 4CH52CN A5B:C ( ?@8;>65=8O 3 [ 4 ] ) N A :>;8G5AB2> 4CH52KE A5B>:, HB. N A = E M B E D E q u a t i o n . 3 / 5 , 345 E M B E D E q u a t i o n . 3 :>;8G5AB2> @01>G8E, ?@8=8<0NI8E 4CH ?>A;5 A<5=K ( ?> 7040=8N) >4 >4=>9 4CH52>9 A5B:>9 2 B5G5=85 G0A0, 8AE>4O 87 A0=8B0@=KE =>@<, <>5BAO 5 G5;>25:; ACB>G=>5 2>4>?>B@51;5=85 =0 4CH Q E M B E D E q u a t i o n . 3 Q E M B E D E q u a t i o n . 3 = Q E M B E D E q u a t i o n . 3 n A<. , 345 n A<. :>;8G5AB2> A<5= ( ?> 7040=8N) 0AE>4 2>4K =0 ?@>872>4AB25==K5 =C64K ?@54?@8OB8O ?@8=8<05BAO ?> 7040=8N Q E M B E D E q u a t i o n . 3 , :>B>@K9 @0A?@545;O5BAO @02=><5@=> ?> G0A0< A<5=K ( A5<8G0A>20O A<5=0 A ?5@5@K2>< =0 >154 >48= G0A, 2 B5G5=85 :>B>@>3> ?@>872>4AB2> =5 >AB0=02;8205BAO) . @8=8<05BAO @01>B0 A5<8G0A>2KE A<5=: A 8 4> 1 6 G ?5@20O A<5=0; A 1 6 4> 2 4 G 2B>@0O A<5=0; A 2 4 4> 8 G B@5BLO A<5=0. '0A>2>9 @0AE>4 2>4K q E M B E D E q u a t i o n . 3 = E M B E D E q u a t i o n . 3 !CB>G=>5 2>4>?>B@51;5=85 =0 ?@>872>4AB25==K5 =C64K Q E M B E D E q u a t i o n . 3 = Q E M B E D E q u a t i o n . 3 n A<. !C<<0@=K9 @0AE>4 2>4K ?> ?@54?@8OB8N 70 ACB:8 ( Q E M B E D E q u a t i o n . 3 = Q + Q E M B E D E q u a t i o n . 3 + Q E M B E D E q u a t i o n . 3 1I89 @0AE>4 2>4K ?> ?>A5;:C 8 ?@54?@8OB8N 70 ACB:8 ( Q E M B E D E q u a t i o n . 3 = ( Q E M B E D E q u a t i o n . 3 + ( Q E M B E D E q u a t i o n . 3 ;O >?@545;5=8O @568<0 @01>BK =0A>A=KE AB0=F89, 5<:>AB8 10:>2 2>4>=0?>@=KE 10H5= 8 @575@2C0@>2 G8AB>9 2>4K A>AB02;O5BAO B01;8F0 ?>G0A>2>3> ACB>G=>3> 2>4>?>B@51;5=8O 8 AB@>8BAO 3@0D8: 2>4>?>B@51;5=8O ?> G0A0< ACB>:. @8<5@. ?@545;8BL E>7O9AB25==>- ?8BL52>5 8 ?@>872>4AB25==>5 2>4>?>B@51;5=85 2 A8AB5<5 2>4>A=0165=8O, >1A;C6820NI89 =0A5;5==K9 ?C=:B 8 ?@54?@8OB85. '8A;> 68B5;59 2 =0A5;5==>< ?C=:B5 1 0 0 0 0 G5;>25:. 40=8O >1>@C4>20=K 2=CB@5==8< 2>4>?@>2>4><, :0=0;870F859 8 A8AB5<>9 F5=B@0;87>20==>3> 3>@OG53> 2>4>A=0165=8O. 0AB@>9:0 740=89 2 3 MB060. =0A5;5==>< ?C=:B5 8<55BAO 3>AB8=8F0 A >1I8<8 20==0<8 8 4CH52K<8 >1J5<>< 1>;55 2 5 0 0 0 <3 =0 3 0 0 <5AB, 740=85 3>AB8=8FK B@5EMB06=>5. 038AB@0;L=0O 2>4>?@>2>4=0O A5BL 8 2>4>2>4K ?@>;>65=K 87 AB0;L=KE B@C1. ;8=0 2>4>2>4>2 >B ! - 2 4> 2>4>=0?>@=>9 10H=8 L 2>4 = 1 0 0 0 <. @><KH;5==>5 ?@54?@8OB85 ?> ?>60@=>9 >?0A=>AB8 >B=>A8BAO : :0B53>@88 , 420 ?@>872>4AB25==KE :>@?CA0 2 AB5?5=8 >3=5AB>9:>AB8 >48= >1J5<>< 2 0 BKA <3 , 4@C3>9 >1J5<>< 4 0 BKA. <3 , H8@8=0 740=88 1>;55 6 0 <, ?;>I04L B5@@8B>@88 ?@54?@8OB8O 4> 1 5 0 30. @54?@8OB85 @01>B05B 2 B@8 A<5=K, :>;8G5AB2> @01>G8E 2 :064>9 A<5=5 N A< = 1 0 0 G5;>25:. 0AE>4 2>4K =0 ?@>872>4AB25==K5 =C64K Q E M B E D E q u a t i o n . 3 = 4 0 0 <3 / A<5=C. CH ?@8=8<05B 7 0 % @01>G8E 2 A<5=C. 5=?;0= 2>4>?@>2>4=>9 A5B8 ?@82545= =0 @8A. 1 . 1 . 2 . 1 . ?@545;=85 2>4>?>B@518B5;59. 1J548=5==K9 E>7O9AB25==>- ?8BL52>9, ?@>872>4AB25==K9 8 ?@>B82>?>60@=K9 2>4>?@>2>4 4>;65= >15A?5G820BL @0AE>4 2>4K =0 E>7O9AB25==>- ?8BL52K5 =C64K ?>A5;:0, E>7O9AB25==>- ?8BL52K5 =C64K ?@54?@8OB8O, E>7O9AB25==>- ?8BL52K5 =C64K >1I5AB25==KE 740=89, ?@>872>4AB25==K5 =C64K ?@54?@8OB8O, BCH5=85 2>7<>6=KE ?>60@>2 2 ?>A5;:5 8 =0 ?@54?@8OB88. 2 . 2 0AG5B B@51C5<KE @0AE>4>2 2>4K 4;O ?>A5;:0 8 ?@54?@8OB8O. ?@545;5=85 2>4>?>B@51;5=8O =0G8=05< A ?>A5;:0, ?>A:>;L:C >= O2;O5BAO >A=>2=K< ?>B@518B5;5<. >A5;>:. A>>B25BAB288 A ?. 2 . 1 . B01;. 1 [ 3 ] =>@<C 2>4>?>B@51;5=8O =0 >4=>3> G5;>25:0 ?@8=8<05< 3 0 0 ;/ ACB. !CB>G=K9 @0AE>4 E M B E D E q u a t i o n . 3 ACB. < = E M B E D E q u a t i o n . 3 <3 / ACB. !CB>G=K9 @0AE>4 A CG5B>< ?@8<5G0=8O 4 ?. 2 . 1 [ 3 ] E M B E D E q u a t i o n . 3 = 1 , 2 E M B E D E q u a t i o n . 3 = 1 , 2 3 0 0 0 = 3 6 0 0 <3 / ACB. 0AG5B=K9 @0AE>4 2>4K 2 ACB:8 =081>;LH53> 2>4>?>B@51;5=8O E M B E D E q u a t i o n . 3 = ACB. <0E E M B E D E q u a t i o n . 3 = 1 , 1 3 6 0 0 = 3 9 6 0 <3 / ACB. A>3;0A=> ?. 2 . 2 [ 3 ] , ?@8=8<05< ACB. <0E = 1 , 1 . 0AG5B=K9 G0A>2>9 <0:A8<0;L=K9 @0AE>4 2>4K E M B E D E q u a t i o n . 3 0:A8<0;L=K9 :>MDD8F85=B G0A>2>9 =5@02=><5@=>AB8 2>4>?>B@51;5=8O G. <0E = ( <0E ( <0E ?@8=8<05< ?> ?. 2 . 2 8 B01;. 2 [ 3 ] ( <0E= 1 , 2 ; ( <0E= 2 , B>340 G. <0E= 1 , 2 2 = 2 , 4 > ?@8;>65=8N 1 40==KE C:070=89 ?@8=8<05< G. <0E= 2 , 5 q G. <0E= E M B E D E q u a t i o n . 3 = 4 1 2 , 5 <3 / G. 0AE>4 2>4K =0 E>7O9AB25==>- ?8BL52K5 =C64K 3>AB8=8FK E M B E D E q u a t i o n . 3 <3 / ACB. q <5AB = 1 2 0 ;/ ACB ( ?@8;>65=85 3 [ 4 ] ) >MDD8F85=B G0A>2>9 =5@02=><5@=>AB8 2>4>?>B@51;5=8O 4;O 3>AB8=8FK ?@8=8<05< ?> ?@8;>65=8N 1 40==KE C:070=88. !C<<0@=K9 @0AE>4 2>4K ?> ?>A5;:C E M B E D E q u a t i o n . 3 <3 / ACB. @54?@8OB85. A>>B25BAB288 ?. 2 . 4 [ 3 ] , ?@8;>65=8O 3 [ 4 ] 8 A>3;0A=> =><5@C 7040=8O, =>@<C 2>4>?>B@51;5=8O =0 E>7O9AB25==>- ?8BL52K5 =C64K =0 >4=>3> G5;>25:0 2 A<5=C ?@8=8<05< E M B E D E q u a t i o n . 3 S H A P E \ * M E R G E F O R M A T 1 >4>?@85<=8:8 2 !0<>B5G=K5 ;8=88 3 0A>A=0O AB0=F8O 1 ?>4J5<0 4 G8AB=K5 A>>@C65=8O 5 0<5@0 ?5@5:;NG5=8O 6 575@2C0@K G8AB>9 2>4K 7 0A>A=0O AB0=F8O 2 ?>4J5<0 8 >4>2>4K 9 >4>=0?>@=0O 10H=O 1 0 >4>?@>2>4=0O A5BL ?>A5;:0 1 1 @54?@8OB85 8A. 1 . 1 . 0AG5B=0O AE5<0 E>7O9AB25==>- ?@>B82>?>60@=>3> 2>4>?@>2>40 ?>A5;:0 8 ?@54?@8OB8O. >4>?>B@51;5=85 2 A<5=C E M B E D E q u a t i o n . 3 <3 / A<. !CB>G=>5 2>4>?>B@51;5=85 E M B E D E q u a t i o n . 3 = 7 , 5 <3 / ACB. 0AE>4 2>4K =0 4CH52K5 2 A<5=C Q E M B E D E q u a t i o n . 3 = 0 , 5 ( N A >;8G5AB2> 4CH52KE A5B>: E M B E D E q u a t i o n . 3 HB. E M B E D E q u a t i o n . 3 <3 / A<. ACB:8 E M B E D E q u a t i o n . 3 = 2 1 <3 / ACB. 0AE>4 2>4K =0 ?@>872>4AB25==K5 =C64K 2 A<5=C Q E M B E D E q u a t i o n . 3 = 4 0 0 <3 / A< ( ?> 7040=8N) , 2 G0A: E M B E D E q u a t i o n . 3 <3 / A< !CB>G=>5 2>4>?>B@51;5=85 =0 ?@>872>4AB25==K5 =C64K E M B E D E q u a t i o n . 3 <3 / ACB. "0:8< >1@07><, @0AG5B=K9 ACB>G=K9 @0AE>4 2>4K ?> ?@54?@8OB8N A>AB028B E M B E D E q u a t i o n . 3 <3 / ACB. !C<<0@=K9 @0AE>4 2>4K 70 ACB:8 ?> ?>A5;:C 8 ?@54?@8OB8N @025= E M B E D E q u a t i o n . 3 <3 / ACB. !>AB02;O5< B01;8FC AC<<0@=>3> 2>4>?>B@51;5=8O ?> G0A0< ACB>: ( B01;. 1 . 1 ) >OA=5=85 : B01;8F5 1 . 1 . 3@0D5 1 ?@82545=K G0A>2K5 ?@><56CB:8 >B 0 4> 2 4 G. 3@0D5 2 @0AE>4 2>4K ?>A5;:>< ?> G0A0< ACB>: 2 ?@>F5=B0E >B ACB>G=>3> 2>4>?>B@51;5=8O A>3;0A=> ?@8;>65=8N 1 ?@8 G = 2 , 5 . 3@0D5 3 @0AE>4 2>4K ?>A5;:>< =0 E>7O9AB25==>- ?8BL52K5 =C64K 70 :064K9 G0A ACB>: 2 <3 ( =0?@8<5@, A 1 0 4> 1 1 G @0AE>4C5BAO 4 , 1 % >B E M B E D E q u a t i o n . 3 <3 / G) 3@0D5 4 @0AE>4 2>4K =0 E>7O9AB25==>- ?8BL52K5 =C64K >1I5AB25==>3> 740=8O ( 2 =0H5< ?@8<5@5 3>AB8=8F0) ?> G0A0< ACB>: 2 ?@>F5=B0E >B ACB>G=>3> @0AE>40. 0A?@545;5=85 @0AE>4>2 ?> G0A0< ACB>: ?@8=OB> ?> ?@8;>65=8N 1 ?@8 G= 2 , 5 . >4>?>B@51;5=85 ?> G0A0< ACB>: 2 ?>A5;:5 8 =0 ?@><KH;5==>< ?@54?@8OB88 "01;8F0 1 . 1 >A5;>: @54?@8OB85 A53> 70 ACB:8 '0AK ACB>: 0 E>7O9AB25==>- ?8BL52>5 2>4>?>B@51;5=85 1I5AB25==>5 740=85 ( 3>AB8=8F0) =0 E>7O9AB25==>- ?8BL52>5 2>4>?>B@51;5=85 % >B Q ACB. <0E ?@8 G= 2 , 5 Q ?@G, <3 / G % >B Q >1. 74. ?@8 G= 2 5 Q G , <3 / G % >B Q ?@A<. E- ? ?@8 G= 3 Q G , <3 / G E M B E D E q u a t i o n . 3 , <3 / G E M B E D E q u a t i o n . 3 . , <3 / G E M B E D E q u a t i o n . 3 <3 / G % >B ACB>G=>3> 2>4>?>B@51;5=8O 0 - 1 0 , 6 2 3 , 7 6 0 , 2 0 , 0 7 2 1 2 , 5 0 , 3 1 2 5 7 5 0 8 1 , 1 1 , 5 5 1 - 2 0 , 6 2 3 , 7 6 0 , 2 0 , 0 7 2 6 , 2 5 0 , 1 6 5 0 7 4 1 , 4 2 2 - 3 1 , 2 4 7 , 5 2 0 , 5 0 , 1 8 6 , 2 5 0 , 1 6 5 0 9 7 , 8 6 1 , 8 7 3 - 4 2 , 0 7 9 , 2 0 , 2 0 , 0 7 2 6 , 2 5 0 , 1 6 5 0 1 2 9 , 4 3 2 , 4 8 4 - 5 3 , 5 1 3 8 , 6 0 , 5 0 , 1 8 1 8,750,4650189,243,625-63,5138,60,50,1837,50,9350189,713,636-74,5178,23,01,086,250,1650229,444,397-810,2403,925,01,86,250,1650455,888,738-98,8348,488,02,8812,50,31750408,677,829-106,5257,410,03,66,250,1650311,165,9610-114,1162,366,02,166,250,1650214,684,1111-124,1162,3610,03,66,250,1650216,124,1412-133,5138,610,03,618,750,4650192,663,6913-143.5138,66,02,1637,50,9350191,693,6714-154,7186,125,01,86,250,1650238,084,5615-166,2245,528,53,066,250,1650298,745,7216-1710,4411,845,51,9812,50,31750471,139.017-189,4372,245,01,86,250,1650424,28,1218-197,3289,085,01,86,250,1650341,046,5319-201,663,365,01,86,250,1650115,322,220-211,663,362,00,7218,750,4650114,542,1921-221,039,60,40,14437,50,935090,671,7422-230,623,763,01,086,250,1650751,4423-240,623,760,50,186,250,165074,11,42 A53> 1 0 0 3 9 6 0 1 0 0 3 6 3 0 0 7 , 5 2 1 1 2 0 0 5 2 2 4 , 5 1 0 0 3@0D5 5 :>;8G5AB2> 2>4K 2 <3 , @0AE>4C5<>5 3>AB8=8F59 =0 E>7O9AB25==>- ?8BL52K5 =C64K 70 :064K9 G0A ACB>: ( =0?@8<5@, A 1 0 4> 1 1 G @0AE>4C5BAO 6 % ACB>G=>3> @0AE>40 3>AB8=8FK 3 6 E 6 % / 1 0 0 % = 2 , 1 6 <3 / G) 3@0D5 6 @0AE>4 =0 E>7O9AB25==>- ?8BL52K5 =C64K ?@54?@8OB8O ?> G0A0< A<5=K 2 ?@>F5=B0E >B A<5==>3> @0AE>40. 0A?@545;5=85 @0AE>4>2 ?> G0A0< A<5=K ?@8=OB> ?> ?@8;>65=8N 1 ?@8 G = 3 B01;. 1 . 1 40=> @0A?@545;5=85 @0AE>4>2 =0 E>7O9AB25==>- ?8BL52K5 =C64K ?@54?@8OB8O 4;O B@5EA<5==>9 @01>BK. ;O 42CEA<5==>9 @01>BK 2 3@0D5 6 A 0 4> 1 G 70?8AK205BAO 1 2 , 5 % >B Q A<, A 1 4> 9 G ?@>G5@:8 8 A 9 G 70?8AK20NBAO % :0: 2 B01;. 1 . 1 . 3@0D5 7 :>;8G5AB2> 2>4K 2 <3 , @0AE>4C5<>5 ?@54?@8OB85< =0 E>7O9AB25==>- ?8BL52K5 =C64K 70 :064K9 G0A A<5=K ( =0?@8<5@, A 1 0 4> 1 1 G @0AE>4C5BAO 6 , 2 5 % A<5==>3> @0AE>40 ?@54?@8OB8O E M B E D E q u a t i o n . 3 <3 / G) . 3@0D5 8 @0AE>4 2>4K =0 @01>BC 4CH0, :>B>@K9 CG8BK205BAO 2 B5G5=85 G0A0 ?>A;5 @01>BK :064>9 A<5=K ( =0?@8<5@, ?5@20O A<5=0 70:0=G8205BAO 2 1 6 G, 4CH @01>B05B A 1 6 4> 1 7 G) . 3@0D5 9 @0AE>4 2>4K =0 ?@>872>4AB25==K5 =C64K, @02=><5@=> @0A?@545;5= ?> G0A0< A<5=K ( Q E M B E D E q u a t i o n . 3 = 4 0 0 <3 , ?@>4>;68B5;L=>ABL A<5=K 8 G) . 3@0D5 1 0 AC<<0 @0AE>4>2 2A5E ?>B@518B5;59 2 >?@545;5==K9 G0A ACB>: 2 <3 ( =0?@8<5@, A 8 4> 9 G @0AE>4C5BAO E M B E D E q u a t i o n . 3 <3 / G) = = E M B E D E q u a t i o n . 3 <3 / G. 3@0D5 1 1 AC<<0 @0AE>4>2 2A5E ?>B@518B5;59 2 >?@545;5==K9 G0A ACB>: 2 ?@>F5=B0E >B AC<<0@=>3> ACB>G=>3> @0AE>40 , =0?@8<5@, AC<<0@=K9 ACB>G=K9 @0AE>4 5 2 0 6 <3 , 0 AC<<0@=K9 @0AE>4 A 8 4> 9 G 4 0 8 , 6 7 GB> A>AB02;O5B E M B E D E q u a t i o n . 3 @8 A>AB02;5=88 B01;8FK =5>1E>48<> 4;O :>=B@>;O AC<<8@>20BL 3@0DK, =0?@8<5@, AC<<0 3@0DK 3 4>;6=0 1KBL @02=0 Q E M B E D E q u a t i o n . 3 8 B. 4. 7 B01;. 1 . 1 284=>, GB> ?> ?>A5;:C 8 ?@54?@8OB8N =081>;LH55 2>4>?>B@51;5=85 ?@>8AE>48B A 1 6 4> 1 7 G, 2 MB> 2@5<O =0 2A5 =C64K @0AE>4C5BAO 4 7 1 , 1 3 <3 / G 8;8 E M B E D E q u a t i o n . 3 = E M B E D E q u a t i o n . 3 ;/ A > ?@54?@8OB8N @0AG5B=K9 @0AE>4 E M B E D E q u a t i o n . 3 ;/ A 0AG5B=K9 @0AE>4 >1I5AB25==>3> 740=8O ( 3>AB8=8FK) E M B E D E q u a t i o n . 3 ;/ A !>1AB25==> ?>A5;>: @0AE>4C5B E M B E D E q u a t i o n . 3 = 1 3 0 , 8 7 1 5 , 9 2 0 , 5 5 = 1 1 4 , 4 ;/ A > 40==K< 3@0DK 1 1 B01;. 1 . 1 AB@>8< 3@0D8: 2>4>?>B@51;5=8O >1J548=5==>3> 2>4>?@>2>40 ?> G0A0< ACB>: '0AK ACB>: 8A. 1 . 2 . @0D8: 2>4>?>B@51;5=8O 2 . 3 ?@545;5=85 @0AG5B=KE @0AE>4>2 2>4K =0 ?>60@>BCH5=8O. 0AG5B=K5 @0AE>4K 2>4K 4;O =0@C6=>3> ?>60@>BCH5=8O 2 =0A5;5==KE ?C=:B0E 8 =0 ?@><KH;5==KE ?@54?@8OB8OE >?@545;ONBAO ?> !8 4 . 0 1 - 0 2 - 2 0 0 9 , ?. ?. 2 . 1 2 2 . 2 3 , 0 4;O 2=CB@5==53> ?>60@>BCH5=8O ?> !8 4 . 0 1 - 4 1 - 2 0 0 6 , ?. ?. 4 . 1 4 . 6 . =0A5;5==KE ?C=:B0E G8A;> >4=>2@5<5==KE ?>60@>2 8 @0AE>4 2>4K =0 >48= ?>60@ 7028AOB >B :>;8G5AB20 68B5;59 8 MB06=>AB8 70AB@>9:8. 0 ?@><KH;5==KE ?@54?@8OB8OE G8A;> >4=>2@5<5==KE ?>60@>2 7028A8B >B ?;>I048 B5@@8B>@88 ?@54?@8OB88, 0 @0AG5B=K9 @0AE>4 2>4K =0 =0@C6=>5 ?>60@>BCH5=85 >B AB5?5=8 >3=5AB>9:>AB8 740=88, :0B53>@88 ?@>872>4AB20 ?> ?>60@>- 8 27@K2>>?0A=>AB8, >1J5<0 740=88, =0;8G8O D>=0@59, H8@8=K 740=8O, =0;8G8O 02B><0B8G5A:8E CAB0=>2>: ?>60@>BCH5=8O. 0AG5B=>5 :>;8G5AB2> >4=>2@5<5==KE ?>60@>2 4;O >1J548=5==KE 2>4>?@>2>4>2, >1A;C6820NI8E =0A5;5==K5 ?C=:BK 8 ?@><KH;5==K5 ?@54?@8OB8O, 7028A8B >B ?;>I048 B5@@8B>@88 ?@54?@8OB8O 8 :>;8G5AB20 68B5;59 2 =0A5;5==>< ?C=:B5 ( ?. 2 . 2 3 [ 3 ] ) . 0AG5B=K5 @0AE>4K 2>4K 4;O 2=CB@5==53> ?>60@>BCH5=8O 8 @0AG5B=>5 :>;8G5AB2> AB@C9 2 =0A5;5==KE ?C=:B0E 7028A8B >B =07=0G5=8O 740=8O, 2KA>BK ( MB06=>AB8) , >1J5<0, 0 =0 ?@><KH;5==KE ?@54?@8OB8OE >B AB5?5=8 >3=5AB>9:>AB8 740=88, :0B53>@88 ?@>872>4AB20 ?> ?>60@=>9 >?0A=>AB8, >1J5<0 740=89. ?@545;8< @0AG5B=K5 @0AE>4K 2>4K 4;O ?>60@>BCH5=8O ?> 40==K< ?@82545==>3> ?@8<5@0. "0: :0: 2>4>?@>2>4 2 ?>A5;:5 ?@>5:B8@C5BAO >1J548=5==K<, B> A>3;0A=> !8 4 . 0 1 - 0 2 - 2 0 0 9 , ?. 2 . 2 3 ?@8 :>;8G5AB25 68B5;59 1 0 0 0 0 G5;>25: ?@8=8<05< 420 >4=>2@5<5==KE ?>60@0 ( ?. 2 . 1 2 , B01;. 5 [ 3 ] ) ?@8 B@5EMB06=>9 70AB@>9:5 A @0AE>4>< 2>4K 1 5 ;/ A =0 >48= ?>60@ E M B E D E q u a t i o n . 3 ;/ A 0AE>4 2>4K =0 2=CB@5==55 ?>60@>BCH5=8O 2 ?>A5;:5 ?@8 =0;8G88 3>AB8=8FK, 740=85 B@5EMB06=>5 >1J5<>< 1>;55 2 5 0 0 0 <3 , A>3;0A=> !8 4 . 0 1 - 4 1 - 2 0 0 6 , ?. 4 . 1 B01;. 1 ?@8=8<05< 425 AB@C8 ?@>872>48B5;L=>ABLN 2 , 5 ;/ A :0640O E M B E D E q u a t i o n . 3 ;/ A !>3;0A=> !8 4 . 0 1 - 0 2 - 2 0 0 9 , ?. 2 . 2 2 =0 ?@54?@8OB88 ?@8=8<05< >48= ?>60@, B0: :0: ?;>I04L ?@54?@8OB8O <5=55 1 5 0 30. !>3;0A=> ?. 2 . 1 4 , B01;. 7 , ?@8<5G0=8O 1 [ 3 ] , @0AG5B=K9 @0AE>4 2>4K 4;O 740=8O >1J5<>< 2 0 BKA. <3 Q E M B E D E q u a t i o n . 3 = 2 0 ;/ A, 0 4;O 740=89 >1J5<>< 4 0 BKA. <3 Q E M B E D E q u a t i o n . 3 = 2 0 ;/ A. "0:8< >1@07><, Q E M B E D E q u a t i o n . 3 = 2 0 + 2 0 = 4 0 ;/ A !>3;0A=> !8 4 . 0 1 - 0 2 - 2 0 0 9 , ?. 4 . 1 B01;. 2 @0AG5B=K9 @0AE>4 2>4K =0 2=CB@5==55 ?>60@>BCH5=85 2 ?@>872>4AB25==KE 740=8OE ?@54?@8OB8O ?@8=8<05< 87 @0AG5B0 42CE AB@C9 ?@>872>48B5;L=>ABLN 5 ;/ A :0640O, B>340 Q E M B E D E q u a t i o n . 3 = 2 2 5 = 2 0 ;/ A "0:8< >1@07>< E M B E D E q u a t i o n . 3 ;/ A E M B E D E q u a t i o n . 3 ;/ A E M B E D E q u a t i o n . 3 ?>MB><C A>3;0A=> ?. 2 . 2 3 !8 4 . 0 1 - 0 2 - 2 0 0 9 , @0AE>4 2>4K =0 F5;8 ?>60@>BCH5=8O 2 ?>A5;:5 8 =0 ?@54?@8OB88 >?@545;O5< :0: AC<<C @0AE>40 2>4K =0 ?@54?@8OB88 8 5 0 % @0AE>40 2 ?>A5;:5 E M B E D E q u a t i o n . 3 ;/ A. @8<5G0=85: 2 40==>< A;CG05 4;O >?@545;5=8O @0AE>40 2>4K =0 F5;8 ?>60@>BCH5=8O 2 ?>A5;:5 8 =0 ?@54?@8OB88 :>;8G5AB2> 68B5;59 27OB> 1>;55 2 5 BKA. G5;. 8 ?;>I04L ?@54?@8OB8O 1>;55 1 5 0 30 2 F5;OE ?>:070BL A;CH0B5;O< :0: ?@028;L=> ?>;L7>20BLAO ?. 2 . 2 3 !8 4 . 0 1 - 0 2 - 2 0 0 9 @8 >?@545;5=88 @0AG5B=KE @0AE>4>2 2>4K =0 F5;8 ?>60@>BCH5=8O =5>1E>48<> 2=8<0B5;L=> 87CG8BL ?. 2 . 2 3 !8 4 . 0 1 - 0 2 - 2 0 0 9 . 3 . 84@02;8G5A:89 @0AG5B 2>4>?@>2>4=>9 A5B8. 84@02;8G5A:89 @0AG5B 2>4>?@>2>4=>9 A5B8 2K?>;=O5BAO 420 @070 ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88 ( 2 >1KG=>5 2@5<O) 8 ?@8 ?>60@5. &5;L 384@02;8G5A:>3> @0AG5B0 >?@545;8BL ?>B5@8 =0?>@0 2 A5B8 2 MB8E 42CE A;CG0OE. 84@02;8G5A:89 @0AG5B A5B8 2K?>;=O5BAO 2 A;54CNI59 ?>A;54>20B5;L=>AB8: 1 ) >?@545;O5BAO @02=><5@=> @0A?@545;5==K9 @0AE>4 2KG8B0=85< AC<<K A>A@54>B>G5==KE @0AE>4>2 87 >1I53> @0AE>40 2 G0A <0:A8<0;L=>3> 2>4>?>B@51;5=8O E M B E D E q u a t i o n . 3 , 345 n :>;8G5AB2> A>A@54>B>G5==KE >B1>@>2 2>4K; 2 ) ?@545;O5BAO C45;L=K9 @0AE>4 2>4K q C4. , B. 5. @02=><5@=> @0A?@545;5==K9 @0AE>4, ?@8E>4OI89AO =0 548=8FC 4;8=K 2>4>?@>2>4=>9 A5B8 E M B E D E q u a t i o n . 3 345 L j - 4;8=0 CG0AB:0; m - :>;8G5AB2> CG0AB:>2; j - =><5@ CG0AB:0; 3 ) >?@545;ONBAO @02=><5@=> @0A?@545;5==K5 @0AE>4K ?> 4;8=5 CG0AB:>2 ( ?CB52K5 >B1>@K) E M B E D E q u a t i o n . 3 ; 4 ) >?@545;ONBAO C7;>2K5 @0AE>4K 2>4K, :>B>@K<8 70<5=ONBAO ?CB52K5 >B1>@K E M B E D E q u a t i o n . 3 , 345 ( Q ?CB. j AC<<0 ?CB52KE >B1>@>2 =0 CG0AB:0E, ?@8;530NI8E : 40==><C C7;C; 5 ) : C7;>2K< @0AE>40< 4>102;ONBAO A>A@54>B>G5==K5 @0AE>4K, 0 ?@8 ?>60@5 : >4=><C 87 C7;>2KE @0AE>4>2 4>102;O5BAO 5I5 @0AE>4 2>4K =0 ?>60@>BCH5=8O; 6 ) 2K?>;=O5BAO ?@5420@8B5;L=>5 @0A?@545;5=85 @0AE>4>2 ?> CG0AB:0< A5B8. @8 @0A?@545;5=88 4;O :064>3> C7;0 4>;6=> 2K?>;=OBAO A;54CNI55 CA;>285 ( ?5@2K9 70:>= 8@E3>D0) : AC<<0 @0AE>4>2 2>4K, ?>4E>4OI8E : :064><C C7;C, @02=0 AC<<5 @0AE>4>2 2>4K, 2KE>4OI8E 87 C7;0. 0A?@545;5=85 @0AE>4>2 <>6=> =0G8=0BL >B 48:BCNI59 B>G:8, B. 5. :>=5G=>9 B>G:8 ?>40G8 2>4K, 0 <>6=> >B =0G0;L=>9 B>G:8, B. 5. B>G:8 ?>42>40 2>4K 2 A5BL ( A<. 2 . 1 ) . 5@54 @0A?@545;5=85< @0AE>4>2 =5>1E>48<> =0<5B8BL =0?@02;5=85 ?>B>:>2 2>4K 2 A5B8 >B B>G:8 22>40 2>4K 2 A5BL 4> 48:BCNI59 B>G:8. @5420@8B5;L=>5 @0A?@545;5=85 2K?>;=O5BAO ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88 8 ?@8 ?>60@5. 7 ) ?@545;ONBAO 480<5B@K B@C1 CG0AB:>2 A5B8 ?> ?@5420@8B5;L=> @0A?@545;5==K< @0AE>40< ?@8 ?>60@5 8 7=0G5=8N M:>=><8G5A:>3> D0:B>@0 A 8A?>;L7>20=85< B01;8F ?@545;L=KE M:>=><8G5A:8E @0AE>4>2 [ 5 ] ( ?@8;>65=8O 2 ) . -:>=><8G5A:89 D0:B>@ CG8BK205B AB>8<>ABL M;5:B@>M=5@388, =0A>A=KE CAB0=>2>:, AB>8<>ABL AB@>8B5;LAB20 2>4>?@>2>4=>9 A5B8 8 A>>@C65=89 8 B. ?. =0G5=8O M:>=><8G5A:>3> D0:B>@0 C:070=K 2 B01;. 3 . 1 "01;8F0 3 . 1 . 0B5@80; B@C1 !B0;L 'C3C= 5;57>15B>= A15AB>- F5<5=B ;0AB<0AA0 -:>=><8G5A- :89 D0:B>@ 1 1 1 0 , 7 5 0 , 5 @545;L=K< @0AE>4>< 4;O 40==>3> 480<5B@0 B@C1 O2;O5BAO B0:>9 @0AE>4, ?@8 :>B>@>< MB>B 480<5B@ M:>=><8G5A:89 @02=>F5=5= A;54CNI5<C A>@B0<5=B=><C 480<5B@C. @8 @0AE>45, ?@52KH0NI5< ?@545;L=K9, A;54C5B ?@8=8<0BL A;54CNI89 A>@B0<5=B=K9 480<5B@. @545;L=K5 M:>=><8G5A:85 @0AE>4K 4;O B@C1 87 AB0;8, GC3C=0, 0A15AB>F5<5=B0 8 ?;0AB<0AAK ?@8 C:070==KE 7=0G5=8OE M:>=><8G5A:>3> D0:B>@0 - ?@82545=K 2 ?@8;>65=88 2 40==KE <5B>48G5A:8E C:070=89; 8 ) K?>;=O5BAO C2O7:0 A5B8. ;O :064>3> :>;LF0 2K18@05BAO CA;>2=> ?>;>68B5;L=K5 =0?@02;5=8O, =0?@8<5@, =0?@02;5=8O 42865=8O ?> G0A>2>9 AB@5;:5. A;8 =0?@02;5=85 42865=8O ?>B>:0 2>4K =0 CG0AB:5 A>2?0405B A CA;>2=> ?>;>68B5;L=K< =0?@02;5=85<, B> ?>B5@8 =0?>@0 ( h =0 MB>< CG0AB:5 AG8B0NBAO ?>;>68B5;L=K<8, 0 5A;8 =5 A>2?040NB, B> >B@8F0B5;L=K<8 ( @8A. 2 . 1 ) . #2O70BL A5BL 7=0G8B 4>18BLAO 2K?>;=5=8O A;54CNI8E A>>B=>H5=89: E M B E D E q u a t i o n . 3 j = 0 4;O C7;>2 ( ?5@2K9 70:>= 8@E3>D0 ) . E M B E D E q u a t i o n . 3 i = 0 4;O :>;5F ( 2B>@>9 70:>= 8@E3>D0 ) . 345, n - :>;8G5AB2> CG0AB:>2 2 :>;LF5; m - :>;8G5AB2> @0AE>4>2, ?>4E>4OI8E : C7;C 8 >BE>4OI8E >B =53>. 5@2>5 A>>B=>H5=85 ( 4;O C7;>2) 4;O =0945==KE @0AE>4>2 2>4K 4>;6=> A>1;N40BLAO, B. :. >=> 8A?>;L7>20;>AL ?@8 ?@5420@8B5;L=>< @0A?@545;5=88 @0AE>4>2 ?> CG0AB:0<. 8A. 3 . 1 . >;LF520O 2>4>?@>2>4=0O A5BL K?>;=5=8O 2B>@>3> A>>B=>H5=8O ( 4;O :>;5F) 4>1820NBAO C2O7:>9 2>4>?@>2>4=>9 A5B8. ;O :>;LF0 ( @8A. 2 . 1 ) <>6=> 70?8A0BL E M B E D E q u a t i o n . 3 1 = ( h , B. 5. h 3 + h 4 h 1 h 2 = ( h 5;8G8=0 ( h =07K205BAO =52O7:>9. A;8 AC<<0 CA;>2=> ?>;>68B5;L=KE ?>B5@L =0?>@0 1>;LH5 AC<<K CA;>2=> >B@8F0B5;L=KE ?>B5@L =0?>@0, B> ( h ( 0 . =0G8B, GB>1K C<5=LH8BL 25;8G8=C ( h ( ?@81;878BL 55 : =C;N) , =5>1E>48<> @0AE>4K =0 CG0AB:0E A CA;>2=> ?>;>68B5;L=K<8 ?>B5@O<8 =0?>@0 C<5=LH8BL, 0 =0 CG0AB:0E A CA;>2=> >B@8F0B5;L=K<8 ?>B5@O<8 =0?>@0 C25;8G8BL =0 25;8G8=C =5:>B>@>3> ?>?@02>G=>3> @0AE>40. A;8 ( h ( 0 , B>, =0>1>@>B, @0AE>4K =0 CG0AB:0E A CA;>2=> ?>;>68B5;L=K<8 ?>B5@O<8 =0?>@0 =04> C25;8G8BL, 0 =0 CG0AB:0E A CA;>2=> >B@8F0B5;L=K<8 ?>B5@O<8 =0?>@0 C<5=LH8BL =0 25;8G8=C ?>?@02>G=>3> @0AE>40. #2O7:0 A5B8 ( 22545=85 ?>?@02>G=>3> @0AE>40) ?@>4>;605BAO 4> B5E ?>@, ?>:0 =5 1C45B 2K?>;=OBLAO A>>B=>H5=85 ( h E M B E D E q u a t i o n . 3 ( h 4>?. , 345 ( h 4>? 4>?CAB8<0O 25;8G8=0 =52O7:8. >6=> ?@8=OBL ( h 4>? E M B E D E q u a t i o n . 3 1 <. A;8 A5BL A>AB>8B 87 =5A:>;L:8E :>;5F, B> =5>1E>48<> 4>1820BLAO 2K?>;=5=8O C:070==>3> A>>B=>H5=8O 4;O :064>3> :>;LF0. >B5@8 =0?>@0 h =0 CG0AB:5 A;54C5B >?@545;OBL ?> D>@<C;0<: E M B E D E q u a t i o n . 3 , 345 i 384@02;8G5A:89 C:;>=, B. 5. ?>B5@8 =0?>@0 =0 548=8FC 4;8=K B@C1>?@>2>40; L 4;8=0 B@C1>?@>2>40, <; ( :>MDD8F85=B 384@02;8G5A:>3> A>?@>B82;5=8O, >?@545;O5<K9 ?> D>@<C;5 E M B E D E q u a t i o n . 3 d @ @0AG5B=K9 2=CB@5==89 480<5B@ B@C1, <; v A@54=OO ?> A5G5=8N A:>@>ABL 42865=8O 2>4K, </ A; q CA:>@5=85 A2>1>4=>3> ?045=8O, </ A2 =0G5=8O ?>:070B5;O AB5?5=8 m 8 :>MDD8F85=B>2 0 , 1 8 ! 4;O AB0;L=KE, GC3C==KE, 65;57>15B>==KE, 0A15AB>F5<5=B=KE, ?;0AB<0AA>2KE 8 AB5:;O==KE B@C1 4>;6=K ?@8=8<0BLAO ?> ?@8;>65=8N 1 0 [ 3 ] . 0AG5B=K5 2=CB@5==85 480<5B@K B@C1 ?@82545=K 2 ?@8;>65=88 2 . 0AG5B=K5 2=CB@5==85 480<5B@K 65;57>15B>==KE B@C1 =0 >A=>20=88 !" 1 2 5 8 6 - 7 4 , !" 1 6 9 5 3 - 7 8 A;54C5B ?@8=8<0BL @02=K<8 480<5B@0< CA;>2=KE ?@>E>4>2. >?@02>G=K9 @0AE>4 ( q 4;O :>;LF0 <>6=> >?@545;8BL ?> D>@<C;5 E M B E D E q u a t i o n . 3 ( q = ( h / 2 ( E M B E D E q u a t i o n . 3 i ) , 345 h i ?>B5@8 =0?>@0 =0 CG0AB:5; q i @0AE>4 2>4K ?> CG0AB:C; n :>;8G5AB2> CG0AB:>2 2 :>;LF5. ;O :064>3> :>;LF0 ?>;CG05BAO A2>O 25;8G8=0 ?>?@02>G=>3> @0AE>40. A;8 CG0AB>: A5B8 O2;O5BAO >1I8< 4;O 42CE :>;5F, B> ?>?@02>G=K9 @0AE>4 =0 B0:>< CG0AB:5 >?@545;O5BAO :0: AC<<0 ?>?@02>G=KE @0AE>4>2 ( A CG5B>< 8E 7=0:>2) 4;O :064>3> :>;LF0. 3 . 1 @8<5@ 384@02;8G5A:>3> @0AG5B0 2>4>?@>2>4=>9 A5B8. 0AG5B=0O AE5<0 2>4>?@>2>4=>9 A5B8 ?>:070=> =0 @8A. 2 . 2 . ?5@2>< @0745;5 4;O ?@82545==>3> ?@8<5@0 >1I89 @0AE>4 2>4K 2 G0A <0:A8<0;L=>3> 2>4>?>B@51;5=8O A>AB02;O5B 1 3 0 , 8 7 ;/ A, 2 B>< G8A;5 A>A@54>B>G5==K9 @0AE>4 ?@54?@8OB8O @025= 1 5 , 9 2 ;/ A, 0 A>A@54>B>G5==K9 @0AE>4 >1I5AB25==>3> 740=8O @025= 0 , 5 5 ;/ A. 8A. 3 . 2 !E5<0 2>4>?@>2>4=>9 A5B8. 1 . ?@545;O5< @02=><5@=> @0A?@545;5==K9 @0AE>4 E M B E D E q u a t i o n . 3 = 1 3 0 , 8 7 ( 1 5 , 9 2 + 0 , 5 5 ) = 1 1 4 , 4 ;/ A 2 . ?@545;8< C45;L=K9 @0AE>4 q C4. = Q E M B E D E q u a t i o n . 3 / E M B E D E q u a t i o n . 3 j ; E M B E D E q u a t i o n . 3 = L 1 - 2 + L 2 - 3 + L 3 - 4 + L 4 - 5 + L 5 - 6 + L 6 - 7 + L 7 - 1 + L 7 - 4 = = 5 0 0 + 1 5 0 0 + 1 0 0 0 + 1 5 0 0 + 5 0 0 + 1 0 0 0 + 2 0 0 0 = 9 5 0 0 <. q C4. = 1 1 4 , 4 / 9 5 0 0 = 0 , 0 1 2 ;/ ( A <) ; 3 ?@545;8< ?CB52K5 >B1>@K E M B E D E q u a t i o n . 3 57C;LB0BK ?@82545=K 2 B01;8F5 3 . 2 . CB52K5 @0AE>4K "01;8F0 3 . 2 ><5@ CG0AB:0 ;8=0 CG0AB:0, < CB52>9 >B1>@, ;/ A 1 2 2 3 3 4 4 5 5 6 6 7 7 1 7 4 5 0 0 1 5 0 0 1 0 0 0 1 5 0 0 1 5 0 0 5 0 0 1 0 0 0 2 0 0 0 6 , 0 2 1 8 , 0 6 1 2 , 0 4 1 8 , 0 6 1 8 , 0 6 6 , 0 2 1 2 , 0 4 2 4 , 0 8 E M B E D E q u a t i o n . 3 E M B E D E q u a t i o n . 3 ?CB. j = 1 1 4 , 4 ;/ A 4 ?@545;8< C7;>2K5 @0AE>4K. q 1 = 0 , 5 ( Q ?CB. 1 - 2 + Q ?CB. 7 - 1 ) = 0 , 5 ( 6 , 0 2 + 1 2 , 0 4 ) = 9 , 0 3 ;/ A q 2 = 0 , 5 ( Q ?CB. 2 - 3 + Q ?CB. 2 - 1 ) = 0 , 5 ( 1 8 , 0 6 + 6 , 0 2 ) = 1 2 , 0 4 ;/ A q 3 = 0 , 5 ( Q ?CB. 2 - 3 + Q ?CB. 3 - 4 ) = 0 , 5 ( 1 8 , 0 6 + 1 2 , 0 4 ) = 1 5 , 0 5 ;/ A q 4 = 0 , 5 ( Q ?CB. 3 - 4 + Q ?CB. 4 - 5 + Q 4 - 7 ) = 0 , 5 ( 1 2 , 0 4 + 1 8 , 0 6 + 2 4 , 0 8 ) = 2 7 , 0 9 ;/ A q 5 = 0 , 5 ( Q ?CB. 4 - 5 + Q ?CB. 5 - 6 ) = 0 , 5 ( 1 8 , 0 6 + 1 8 , 0 6 ) = 1 8 , 0 6 ;/ A q 6 = 0 , 5 ( Q ?CB. 5 - 6 + Q ?CB. 6 - 7 ) = 0 , 5 ( 1 8 , 0 6 + 6 , 0 2 ) = 1 2 , 0 4 ;/ A q 7 = 0 , 5 ( Q ?CB. 6 - 7 + Q ?CB. 7 - 1 + Q 7 - 4 ) = 0 , 5 ( 6 , 0 2 + 1 2 , 0 4 + 2 4 , 0 8 ) = 2 1 , 0 7 ;/ A #7;>2K5 @0AE>4K "01;8F0 3 . 3 ><5@ C7;0 #7;>2>9 @0AE>4 , ;/ A 1 2 3 4 5 6 7 9 , 0 3 1 2 , 0 4 1 5 , 0 5 2 7 , 0 9 1 8 , 0 6 1 2 , 0 4 2 1 , 0 7 ( q C7;. = 1 1 4 , 4 ;/ A 5 . >1028< : C7;>2K< @0AE>40< A>A@54>B>G5==K5 @0AE>4K. C7;>2><C @0AE>4C 2 B>G:5 5 4>102;O5BAO A>A@54>B>G5==K9 @0AE>4 ?@54?@8OB8O, 0 2 B>G:5 3 A>A@54>B>G5==K9 @0AE>4 >1I5AB25==>3> 740=8O ( 2<5AB> B>G:8 3 <>6=> 27OBL ;N1CN 4@C3CN) . ">340 q 5 = 1 8 , 0 6 + 1 5 , 9 2 = 3 3 , 9 8 ;/ A; q 3 = 1 5 , 0 5 + 0 , 5 5 = 1 5 , 6 ;/ A ! CG5B>< A>A@54>B>G5==KE @0AE>4>2 ( q C7;. = 1 3 0 , 8 7 ;/ A 5;8G8=K C7;>2KE @0AE>4>2 ?>:070=K =0 @8A. 3 . 3 8A. 3 . 3 0AG5B=0O AE5<0 2>4>?@>2>4=>9 A5B8 A C7;>2K<8 @0AE>40<8. 6 K?>;=8< ?@5420@8B5;L=>5 @0A?@545;5=85 @0AE>4>2 2>4K ?> CG0AB:0< A5B8. !45;05< MB> A=0G0;0 4;O 2>4>?@>2>4=>9 A5B8 ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88 ( 157 ?>60@0) . K15@5< 48:BCNICN B>G:C, B. 5. :>=5G=CN B>G:C ?>40G8 2>4K. 40==>< ?@8<5@5 70 48:BCNICN B>G:C ?@8<5< B>G:C 5 . @5420@8B5;L=> =0<5B8< =0?@02;5=8O 42865=8O 2>4K >B B>G:8 1 : B>G:5 5 ( @8A. 3 . 3 ) . >B>:8 2>4K <>3CB ?>4>9B8 : B>G:5 5 ?> B@5< =0?@02;5=8O<: ?5@2>5 1 - 2 - 3 - 4 - 5 2B>@>5 1 - 7 - 4 - 5 B@5BL5 1 - 7 - 6 - 5 ;O C7;0 1 4>;6=> 2K?>;=OBLAO A>>B=>H5=85 q 1 + q 1 - 2 + q 1 - 7 = Q ?>A. ?@. 5;8G8=K q 1 = 9 , 0 3 ;/ A 8 Q ?>A. ?@ = 1 3 0 , 8 7 ;/ A 8725AB=K, 0 q 1 - 2 8 q 1 - 7 =58725AB=K. 0405<AO ?@>872>;L=> >4=>9 87 MB8E 25;8G8=. >7L<5<, =0?@8<5@, q 1 - 2 = 4 0 ;/ A. ">340 q 1 - 7 = Q ?>A. ?@ - ( q 1 + q 1 - 2 ) = 1 3 0 , 8 7 - ( 9 , 0 3 + 4 0 ) = 8 1 , 8 4 ;/ A ;O B>G:8 7 4>;6=> 2K?>;=OBLAO A;54CNI55 A>>B=>H5=85: q 1 - 7 = q 7 + q 7 - 4 + q 7 - 6 =0G5=85 q 1 - 7 = 8 1 , 8 4 ;/ A 8 q 7 = 2 1 , 0 7 ;/ A 8725AB=K, 0 q 7 - 4 8 q 7 - 6 =58725AB=K. 0405<AO ?@>872>;L=> >4=>9 87 MB8E 25;8G8= 8 ?@8=8<05<, =0?@8<5@, q 7 - 4 = 2 5 ;/ A. ">340: q 7 - 6 = q 1 - 7 ( q 7 + q 7 - 4 ) = 8 1 , 8 4 ( 2 1 , 0 7 + 2 5 ) = 3 5 , 7 7 ;/ A 0AE>4K 2>4K ?> 4@C38< CG0AB:0< A5B8 <>6=> >?@545;OBL 87 A;54CNI8E A>>B=>H5=89: q 2 - 3 = q 1 - 2 q 2 = 4 0 1 2 , 0 4 = 2 7 , 9 6 ;/ A; q 3 - 4 = q 2 - 3 q 3 = 2 7 , 9 6 1 5 , 6 = 1 2 , 3 6 ;/ A; q 4 - 5 = q 7 - 4 + q 3 - 4 q 4 = 2 5 + 1 2 , 3 6 2 7 , 0 9 = 1 0 , 2 7 ;/ A; q 6 - 5 = q 7 - 6 q 6 = 3 5 , 7 7 1 2 , 0 4 = 2 3 , 7 3 ;/ A; @>25@:0: q 5 = q 4 - 5 + q 6 - 5 = 1 0 , 2 7 + 2 3 , 7 3 = 3 4 ;/ A. >6=> =0G8=0BL ?@5420@8B5;L=> @0A?@545;OBL @0AE>4K A C7;0 5 , 0 =5 A C7;0 1 . 0AE>4K 2>4K 1C4CB CB>G=OBLAO 2 40;L=59H5< ?@8 2K?>;=5=88 C2O7:8 2>4>?@>2>4=>9 A5B8. !E5<0 2>4>?@>2>4=>9 A5B8 A ?@5420@8B5;L=> @0A?@545;5==K<8 @0AE>40<8 2 >1KG=>5 2@5<O ?>:070=0 =0 @8A. 3 . 4 . @8 ?>60@5 2>4>?@>2>4=0O A5BL 4>;6=0 >15A?5G820BL ?>40GC 2>4K =0 ?>60@>BCH5=85 ?@8 <0:A8<0;L=>< G0A>2>< @0AE>45 2>4K =0 4@C385 =C64K, 70 8A:;NG5=85< @0AE>4>2 2>4K =0 ?@><KH;5==>< ?@54?@8OB88 =0 4CH, ?>;82:C B5@@8B>@88 8 B. ?. ( ?. 2 . 2 1 !8 2 . 0 4 . 0 2 8 4 ) , 5A;8 MB8 @0AE>4K 2>H;8 2 @0AE>4 2 G0A <0:A8<0;L=>3> 2>4>?>B@51;5=8O. ;NG: L , <; d , <<; q , ;/ A. 8A. 3 . 4 0AG5B=0O AE5<0 2>4>?@>2>4=>9 A5B8 A ?@5420@8B5;L=> @0A?@545;5==K<8 @0AE>40<8 ?@8 E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88. ;O 2>4>?@>2>4=>9 A5B8, ?>:070==>9 =0 @8A. 3 . 2 , @0AE>4 2>4K 4;O ?>60@>BCH5=8O A;54C5B 4>1028BL : C7;>2><C @0AE>4C 2 B>G:5 5 , 345 >ACI5AB2;O5BAO >B1>@ 2>4K =0 ?@><KH;5==>5 ?@54?@8OB85 8 :>B>@0O O2;O5BAO =081>;55 C40;5==>9 >B <5AB0 22>40 ( >B B>G:8 1 ) , B. 5. E M B E D E q u a t i o n . 3 ;/ A. 84@02;8G5A:89 @0AG5B A5B8 ?@8 ?>60@5: E M B E D E q u a t i o n . 3 ; ;/ A "0:, :0: E M B E D E q u a t i o n . 3 , B> C7;>2K5 @0AE>4K ?@8 ?>60@5 1C4CB 4@C385, G5< 2 G0A <0:A8<0;L=>3> 2>4>?>B@51;5=8O 157 ?>60@0. ?@545;8< C7;>2K5 @0AE>4K B0:, :0: MB> 45;0;>AL 157 ?>60@0. 02=><5@=> @0A?@545;5==K9 @0AE>4 ?>A5;:0 1C45B @025= E M B E D E q u a t i o n . 3 = 2 0 8 , 3 7 ( 1 5 , 9 2 + 0 , 5 5 + 7 7 , 5 ) = 1 1 4 , 4 ;/ A >1028< : C7;>2><C @0AE>4C 2 B>G:5 5 A>A@54>B>G5==K9 @0AE>4 ?@54?@8OB8O: E M B E D E q u a t i o n . 3 = 9 3 , 4 2 + 1 8 , 0 6 = 1 1 1 , 5 ;/ A K?>;=8< ?@5420@8B5;L=>5 @0A?@545;5=85 @0AE>4>2 2>4K ?> CG0AB:0< A5B8. E M B E D E q u a t i o n . 3 = q 1 + q 1 - 2 + q 1 - 7 ; 0405<AO ?@>872>;L=> q 1 - 2 = 6 0 ;/ A; q 1 - 7 = E M B E D E q u a t i o n . 3 ( q 1 + q 1 - 2 ) = 2 0 8 , 3 7 ( 9 , 0 3 + 6 0 ) = 1 3 9 , 3 4 ;/ A; q 1 - 7 = q 7 + q 7 - 4 q 7 - 6 ; 0405<AO ?@>872>;L=> q 7 - 4 = 4 0 ;/ A; q 7 - 6 = q 1 - 7 ( q 7 + q 7 - 4 ) = 1 3 9 , 3 4 ( 2 1 , 0 7 + 4 0 ) = 7 8 , 2 7 ;/ A; q 2 - 3 = q 1 - 2 q 2 = 6 0 1 2 , 0 4 = 4 7 , 9 6 ;/ A; q 3 - 4 = q 2 - 3 q 3 = 4 7 , 9 6 1 5 , 6 = 3 2 , 9 6 ;/ A; q 4 - 5 = q 7 - 4 + q 3 - 4 q 4 = 4 0 + 3 2 , 9 6 2 7 , 0 9 = 4 5 , 2 7 ;/ A; q 6 - 5 = q 7 - 6 q 6 = 7 8 , 2 7 1 2 , 0 4 = 6 6 , 2 3 ;/ A; @>25@:0 q 5 = q 4 - 5 + q 6 - 5 = 4 5 , 2 7 + 6 6 , 2 3 = 1 1 1 , 5 ;/ A; 0AG5B=0O AE5<0 2>4>?@>2>4=>9 A5B8 A C7;>2K<8 8 ?@5420@8B5;L=> @0A?@545;5==K<8 @0AE>40<8 ?@8 ?>60@5 ?>:070=0 =0 @8A. 3 . 5 8A. 3 . 5 . 7 ?@545;8< 480<5B@K B@C1 CG0AB:>2 A5B8. ;O AB0;L=KE B@C1 - = 1 . > M:>=><8G5A:><C D0:B>@C 8 ?@5420@8B5;L=> @0A?@545;5==K< @0AE>40< 2>4K ?> CG0AB:0< A5B8 ?@8 ?>60@5 ?> ?@8;>65=8N 2 >?@545;ONBAO 480<5B@K B@C1 CG0AB:>2 2>4>?@>2>4=>9 A5B8: d 1 - 2 = 0 , 2 5 <; d 3 - 4 = 0 , 2 <; d 5 - 6 = 0 , 3 <; d 4 - 7 = 0 , 2 <; d 2 - 3 = 0 , 2 5 <; d 4 - 5 = 0 , 2 5 <; d 6 - 7 = 0 , 3 <; d 1 - 7 = 0 , 4 <. !>>B25BAB2CNI85 @0AG5B=K5 2=CB@5==85 480<5B@K >?@545;ONBAO ?> !"5 3 9 - 8 9 8 @02=K ( ?@8;>65=85 2 ) : d 1 - 2 = 0 , 2 6 0 <; d 3 - 4 = 0 , 2 0 9 <; d 5 - 6 = 0 , 3 1 1 <; d 4 - 7 = 0 , 2 0 9 <; d 2 - 3 = 0 , 2 6 0 <; d 4 - 5 = 0 , 2 6 0 <; d 6 - 7 = 0 , 3 1 1 <; d 1 - 7 = 0 , 4 1 2 <. 1KG=> @5:><5=4CNB >?@545;OBL 480<5B@K ?> ?@5420@8B5;L=> @0A?@545;5==K< @0AE>40< 157 CG5B0 @0AE>40 2>4K =0 ?>60@>BCH5=8O, 0 70B5< ?@>25@OBL 2>4>?@>2>4=CN A5BL A =0945==K< B0:8< >1@07>< 480<5B@0<8 =0 2>7<>6=>ABL ?@>?CA:0 @0AE>4>2 2>4K ?@8 ?>60@5. @8 MB>< 2 A>>B25BAB288 A ?. 2 . 3 0 [ 3 ] <0:A8<0;L=K9 A2>1>4=K9 =0?>@ 2 A5B8 >1J548=5==>3> 2>4>?@>2>40 =5 4>;65= ?@52KH0BL 6 0 <. A;8 2 =0H5< ?@8<5@5 >?@545;OBL 480<5B@K ?> ?@5420@8B5;L=K< @0AE>40< ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88 ( B. 5. 157 CG5B0 @0AE>40 2>4K =0 ?>60@>BCH5=8O) , B> :0: ?>:07K205B @0AG5BK ?@8 MB8E 480<5B@0E ?>B5@8 =0?>@0 2 A5B8 ?@8 ?>60@5 1>;55 6 0 <. -B> >1JOA=O5BAO B5<, GB> 4;O A@02=8B5;L=> =51>;LH8E =0A5;5==KE ?C=:B>2 A>>B=>H5=85 @0AE>4>2 2>4K ?> CG0AB:0< 2>4>?@>2>4=>9 A5B8 ?@8 ?>60@5 8 ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88 4>2>;L=> 1>;LH>5. >MB><C 480<5B@K B@C1 =5:>B>@KE CG0AB:>2 A;54C5B C25;8G8BL 8 70=>2> 2K?>;=8BL 384@02;8G5A:89 @0AG5B A5B8 ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88 8 ?@8 ?>60@5. A2O78 A 2KH587;>65==K<, 4;O C?@>I5=8O @0AG5B>2, 2 :C@A>2>9 @01>B5 4>?CA:05BAO >?@545;OBL 480<5B@K CG0AB:>2 A5B8 ?> ?@5420@8B5;L=K< @0AE>40< ?@8 ?>60@5. 8 K?>;=O5< C2O7:C 2>4>?@>2>4=>9 A5B8 ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88. @8 C2O7:5 ?>B5@8 =0?>@0 2 AB0;L=KE B@C10E A;54C5B >?@545;OBL ?> D>@<C;5 E M B E D E q u a t i o n . 3 #2O7:C C4>1=> 2K?>;=OBL 2 2845 B01;8FK ( B01;. 3 . 4 ) . #2O7:0 A5B8 157 8A?>;L7>20=8O :><?LNB5@0 ?@>4>;605BAO 4> B5E ?>@, ?>:0 25;8G8=0 =52O7:8 2 :064>< :>;LF5 =5 1C45B <5=55 1 <. >OA=5=85 : B01;8F5 3 . 4 . 3@0D5 1 ?@82545=> :>;8G5AB2> :>;5F 2>4>?@>2>4=>9 A5B8; 3@0D5 2 CG0AB:8 2>4>?@>2>4=>9 A5B8; 3@0D5 3 @0AE>4 2>4K ?> CG0AB:0< A5B8 2 ;/ A; 3@0D5 4 @0AG5B=K9 2=CB@5==89 480<5B@ B@C1 ?> CG0AB:0< A5B8 A>3;0A=> ?@8;>65=8N 2 40==KE <5B>48G5A:8E C:070=89 2 <5B@0E. 3@0D5 5 4;8=0 CG0AB:0 A5B8 ?> 7040=8N. 3@0D5 6 A@54=OO A:>@>ABL 2>4K ?> CG0AB:0< A5B8, =0?@8<5@, 4;O CG0AB:0 1 - 2 , GB>1K >?@545;8BL A@54=NN A:>@>ABL, >?@545;O5< A=0G0;0 ?;>I04L 682>3> A5G5=8O B@C1 ?> D>@<C;5 E M B E D E q u a t i o n . 3 !@54=OO A:>@>ABL 42865=8O ?>B>:0 >?@545;O5BAO ?> D>@<C;5 E M B E D E q u a t i o n . 3 </ A. 3@0D5 7 384@02;8G5A:>5 A>?@>B82;5=85 >?@545;O5< ?> D>@<C;5: E M B E D E q u a t i o n . 3 0?@8<5@, 4;O CG0AB:0 1 - 2 : E M B E D E q u a t i o n . 3 3@0D5 8 ?@82545=K 2=CB@5==85 480<5B@K B@C1 ( =0?@8<5@, 4;O CG0AB:0 1 - 2 d E M B E D E q u a t i o n . 3 = 0 , 2 6 0 1 , 1 9 = 0 , 2 0 1 <) . 3@0D5 9 ?@82545=K ?>B5@8 =0?>@0 =0 548=8FC 4;8=K B@C1>?@>2>40 ( " 384@02;8G5A:89 C:;>=" ) ( A CG5B>< 384@02;8G5A:>3> A>?@>B82;5=8O, >?@545;O5<K9 ?> D>@<C;5, =0?@8<5@, 4;O CG0AB:0 1 - 2 E M B E D E q u a t i o n . 3 3@0D5 1 0 ?@82545=K ?>B5@8 =0?>@0 ?> CG0AB:0< A5B8, >?@545;O5<K9 ?> D>@<C;5 h = i * L , 345 L 4;8=0 CG0AB:0 ( =0?@8<5@, 4;O CG0AB:0 1 - 2 h = 2 , 2 3 * 1 0 - 3 * 5 0 0 = 1 , 1 2 <) . 3@0D0E 1 1 ( 1 7 ?5@2>5 8A?@02;5=85, 25;8G8=0 ( h - MB> =52O7:0, ( q - ?>?@02>G=K9 @0AE>4 4;O :>;LF0, :>B>@K9 <>6=> >?@545;8BL ?> D>@<C;5 ( q = ( h / 2 ( E M B E D E q u a t i o n . 3 ) , 345 h ?>B5@8 =0?>@0 =0 CG0AB:5; q - @0AE>4 2>4K ?> CG0AB:C. !;54C5B 8<5BL 2 284C, GB> 4;O CG0AB:0 4 - 7 ( @8A. 3 . 4 ; 3 . 5 ) , :>B>@K9 O2;O5BAO >1I8< 4;O >1>8E :>;5F, 22>4OBAO 425 ?>?@02:8 - 87 ?5@2>3> :>;LF0 8 87 2B>@>3>. =0: ?>?@02>G=>3> @0AE>40 ?@8 ?5@5=>A5 87 >4=>3> :>;LF0 2 4@C3>5 A;54C5B A>E@0=OBL. >B>:8 2>4K >B B>G:8 1 : B>G:5 5 ( 48:BCNI59 B>G:5) , :0: 284=> ?> =0?@02;5=8O< AB@5;>: =0 @8A. 3 . 4 , <>3CB ?>9B8 ?> B@5< =0?@02;5=8O<: ?5@2>5: 1 - 2 - 3 - 4 - 5 , 2B>@>5: 1 - 7 - 4 - 5 , B@5BL5: 1 - 7 - 6 - 5 . !@54=85 ?>B5@8 =0?>@0 2 A5B8 <>6=> >?@545;8BL ?> D>@<C;5 h A = ( h 1 + h 2 + h 3 ) / 3 , 345 h 1 = h 1 - 2 + h 2 - 3 + h 3 - 4 + h 4 - 5 ; h 2 = h 1 - 7 + h 7 - 4 + h 4 - 5 ; h 3 = h 1 - 7 + h 7 - 6 + h 6 - 5 ; >B5@8 =0?>@0 2 A5B8 ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88 h 1 = 1 , 0 6 + 1 , 6 3 + 0 , 6 4 + 0 , 0 9 = 3 , 4 2 <; h 2 = 1 + 1 , 8 4 + 0 , 0 9 = 2 , 9 3 <; h 3 = 1 + 0 , 7 + 1 , 2 9 = 2 , 9 9 <; h A = E M B E D E q u a t i o n . 3 <. 0AG5B=0O AE5<0 2>4>?@>2>4=>9 A5B8 A >:>=G0B5;L=> @0A?@545;5==K<8 @0AE>40<8 ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88 =0 @8A. 3 . 6 . L , <; d , <<; q , ;/ A ;NG: h , <; v , </ A 8A. 3 . 6 0AG5B=0O AE5<0 2>4>?@>2>4=>9 A5B8 A >:>=G0B5;L=> @0A?@545;5==K<8 @0AE>40<8 ?@8 E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88. #2O7:0 2>4>?@>2>4=>9 A5B8 ?@8 ?>60@5 @5420@8B5;L=>5 @0A?@545;5=85 @0AE>4>2 2>4K ?> CG0AB:0< 2>4>?@>2>4=>9 A5B8 ?@8 ?>60@5 2K?>;=5=> 2 ?C=:B5 6 @0745;0 3 . 1 . 0AG5B=0O AE5<0 ?>:070=0 =0 @8A. 3 . 5 . #2O7:0 A5B8 ?@8 ?>60@5 2K?>;=O5BAO B0: 65, :0: MB> 1K;> A45;0=> ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88. 8A. 3 . 7 . 0AG5B=0O AE5<0 2>4>?@>2>4=>9 A5B8 A >:>=G0B5;L=> @0A?@545;5==K<8 @0AE>40<8 ?@8 ?>60@5. ?@545;O5< A@54=85 ?>B5@8 2 A5B8 ?> D>@<C;5: h A = ( h 1 + h 2 + h 3 ) / 3 , 345 h 1 = h 1 - 2 + h 2 - 3 + h 3 - 4 + h 4 - 5 ; h 2 = h 1 - 7 + h 7 - 4 + h 4 - 5 ; h 3 = h 1 - 7 + h 7 - 6 + h 6 - 5 ; >B5@8 =0?>@0 2 A5B8 ?@8 ?>60@5: h 1 = 2 , 1 3 + 4 , 1 + 3 , 8 7 + 1 , 4 1 = 1 1 , 5 1 <; h 2 = 2 , 4 + 6 , 7 2 + 1 , 4 1 = 1 0 , 5 3 <; h 3 = 2 , 4 + 2 , 2 5 + 5 , 2 = 9 , 8 5 <; h A = ( 1 1 , 5 1 + 1 0 , 5 3 + 9 , 8 5 ) / 3 = 3 1 , 8 9 / 3 = 1 0 , 6 3 <. 0AG5B=0O AE5<0 2>4>?@>2>4=>9 A5B8 A >:>=G0B5;L=> @0A?@545;5==K<8 @0AE>40<8 ?@8 ?>60@5 ?>:070=0 =0 @8A. 3 . 7 . #2O7:0 A5B8 ?@8 <0:A8<0;L=>< E>7O9AB25==>- ?@>872>4AB25==>< 2>4>?>B@51;5=88 "01;8F0 3 . 4 . ><5@ :>;LF0 #G0AB>: A5B8 0AE>4 q , ;/ A 0AG5B=K9 2=CB@. 480<5B@, d @, , < ;8=0 L , <. !:>@>ABL V , </ A ( 1 + 3 , 5 1 / v ) 0 , 1 9 0 , 5 6 1 v 2 d @1 , 1 9 , < 8@02;8G5A:89 C:;>= ( 1 0 3 >B@8 =0?>@0 h , < 1 2 3 4 5 6 7 8 9 1 0 1 1 - 2 2 - 3 3 - 4 4 - 7 7 - 1 4 0 2 7 , 9 6 1 2 , 3 6 2 5 8 1 , 8 4 0 , 2 6 0 0 , 2 6 0 0 , 2 0 9 0 , 2 0 9 0 , 4 1 2 5 0 0 1 5 0 0 1 0 0 0 2 0 0 0 1 0 0 0 0 , 7 5 5 0 , 5 2 7 0 , 3 6 3 0 , 7 3 5 0 , 6 1 1 0 , 4 4 9 0 , 2 3 6 0 , 1 1 9 0 , 4 28 0,3060,201 0,201 0,155 0,155 0,3482,23 1,17 0,77 2,76 0,881,12 1,75 0,77 -5,52 -0,88 12345678910 24-5 5-6 7-6 7-410,27 23,73 35,77 250,260 0,311 0,311 0,2091500 1500 500 20000,194 0,312 0,470 0,7350,04 0,093 0,189 0,4280,201 0,249 0,249 0,1550,20 0,37 0,76 2,760,30 -0,55 -0,38 5,52 @>4>;65=85 B01;. 3 . 4 5@2>5 8A?@02;5=85 B>@>5 h / q , ( < A) / ; ( q 1 , ;/ A q 1 = q + ( q 1 , ;/ A v , <\ A ( 1 + 3 , 5 1 / v ) 0 , 1 9 0 , 5 6 1 v 2 i 1 0 3 h , < h / q , ( < A) / ; ( q 1 , ;/ A q 1 = q + ( q 1 , ;/ A 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 1 - 2 2 - 3 3 - 4 4 - 7 7 - 1 0 , 0 2 8 0 , 0 6 2 6 0 , 0 6 2 3 0 , 2 2 0 8 0 , 0 1 0 7 3 ,6 3,6 3,6 -3,6-3,6 3,643,6 31,56 15,96 20 85,440,833 0,596 0,409 0,588 0,6420,524 0,292 0,189 0,28 0,3252,6 1,5 1,2 1,8 0,931,3 2,25 1,2 -3,6 -0,930,0298 0,0713 0,0752 0,18 0,0109-0,3 -0,3 -0,3 0,3-4,7 0,343,3 31,26 15,66 15,6 85,74(h = 2,76; ((h/q) = 0,3844; (h = 0,22; ((h/q) = 0,3672; (q1 = (h/2((h/q) = 2,76/20,3844 = 3,6 ;/ A; ( q = 0 , 3 ;/ A; 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 4 - 5 5 - 6 7 - 6 7 - 4 0 , 0 2 9 2 0 , 0 2 3 2 0 , 0 1 0 6 0 , 2 2 0 8 - 8 , 6 8 , 6 8 , 6 - 8 , 6 + 3 , 6 1 , 6 7 3 2 , 3 3 4 4 , 3 7 2 0 0 , 0 3 2 0 , 4 2 5 0 , 5 8 4 0 , 5 8 8 0 , 0 0 2 0 , 1 5 9 0 , 2 8 1 0 , 2 8 0 , 0 0 9 0 , 6 1 , 1 0 , 8 0 , 0 1 3 - 0 , 9 - 0 , 5 5 3 , 6 0 , 0 0 8 0 , 0 3 0 , 0 1 2 0 , 1 8 - 4 , 7 4 , 7 4 , 7 4 , 7 + 0 , 3 - 3 , 0 3 3 7 , 0 3 4 9 , 0 7 1 5 , 6 ( h = 4 , 8 9 ; ( ( h / q ) = 0 , 2 8 3 8 ; ( h = 2 , 1 6 ; ( ( h / q ) = 0 , 2 3 ; ( q 1 = ( h / 2 ( ( h / q ) = 4 , 8 9 / 2 0 , 2 8 3 8 = 8 , 6 ;/ A; ( q = 4 , 7 ;/ A; @>4>;65=85 B01;. 3 . 4 8A?@02;5=85 "@5BL5 8A?@02;5=85 v , <\ A ( 1 + 3 , 5 1 / v ) 0 , 1 9 0 , 5 6 1 v 2 i 1 0 3 h , 8 ` b r , : d f h z | ~ d f * , 绯xoh_h_h_h_h_ h 5NH aJ h 5aJ h) A h) A aJ h h 5CJ aJ h) A h CJ aJ h) A CJ aJ h 5I CJ aJ h h h) A 5\aJ h) A h) A 5\aJ h) A h) A CJ aJ h hn 5CJ aJ hn hn 5CJ aJ hn 5CJ aJ h h) A 5CJ aJ h hv 5CJ aJ % , . 0 2 4 6 8 : f h n p r t v x z gd $ 1$ $1$ a$gdv $1$ a$ $1$ a$gdv z | ~ $ P L N P $$ 1$ a$gd gd $$ 1$ `a$gd $1$ a$ " $ & ( P < > J L P R T \ ^ ` b d v : < n p 2 4 l n 8 : n ¹ h 5I CJ aJ h) A h) A CJ NH aJ h) A h) A CJ aJ h) A h) A aJ h aJ hP hP hn h h 5NH aJ h h 5aJ h h h 5I 5aJ h 5aJ