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"+ > 22545=88 >B@065=0 0:BC0;L=>ABL 7040G 3;>10;L=>9 CA;>2=>9 >?B8<870F88, >?@545;ONBAO F5;8 8 7040G8 8AA;54>20=8O, ?>:070=0 =0CG=0O =>287=0 8 ?@0:B8G5A:0O F5==>ABL 48AA5@B0F8>==>9 @01>BK.  ?5@2>9 3;025 ?@54AB02;5=0 <0B5<0B8G5A:0O <>45;L >1J5:B0 3;>10;L=>->?B8<0;L=>3> 2K1>@0, >?8AK20NI0O H8@>:89 :;0AA ?>AB0=>2>: <=>3>:@8B5@80;L=KE <=>3><5@=KE 7040G CA;>2=>9 >?B8<870F88 A =52K?C:;K<8 >3@0=8G5=8O<8. CABL >1J5:B 8AA;54>20=8O E0@0:B5@87C5BAO =01>@>< ?0@0<5B@>2  EMBED Equation.3  ( SEQ $>@<C;0 \* ARABIC \s 1 1) 8 25:B>@-DC=:F859 E0@0:B5@8AB8:  EMBED Equation.3 , ( SEQ $>@<C;0 \* ARABIC \s 1 2) >?@545;5==KE B0:8< >1@07><, GB> C<5=LH5=85 7=0G5=89 E0@0:B5@8AB8: A>>B25BAB2C5B ;CGH5<C 2K1>@C. @54?>;0305<, GB>: >>@48=0BK 25:B>@0  EMBED Equation.3  <>3CB =5?@5@K2=> 87<5=OBLAO 2 7040==KE ?@545;0E, :>B>@K5 7040NB 38?5@8=B5@20;  EMBED Equation.DSMT4 . ( SEQ $>@<C;0 \* ARABIC \s 1 3) 0640O E0@0:B5@8AB8:0  EMBED Equation.DSMT4  O2;O5BAO ;8?H8F52>9 DC=:F859 A A>>B25BAB2CNI59 :>=AB0=B>9 8?H8F0, :>B>@0O <>65B 1KBL =5 7040=0. 0 G0ABL E0@0:B5@8AB8: 87  REF _Ref270951520 \h  (2), =><5@0 :>B>@KE >?@545;ONBAO <=>65AB2><  EMBED Equation.DSMT4 , ( SEQ $>@<C;0 \* ARABIC \s 1 4) =0:;04K20NBAO DC=:F8>=0;L=K5 >3@0=8G5=8O  EMBED Equation.DSMT4 . ( SEQ $>@<C;0 \* ARABIC \s 1 5) '0ABL E0@0:B5@8AB8: 87  REF _Ref270951520 \h  (2), =><5@0 :>B>@KE >?@545;ONBAO <=>65AB2><  EMBED Equation.DSMT4 , ( SEQ $>@<C;0 \* ARABIC \s 1 6) @0AA<0B@8205BAO :0: 25:B>@=K9 :@8B5@89 MDD5:B82=>AB8  EMBED Equation.DSMT4 , ( SEQ $>@<C;0 \* ARABIC \s 1 7) 345  EMBED Equation.DSMT4 . ( SEQ $>@<C;0 \* ARABIC \s 1 8) ?B8<0;L=K9 2K1>@ >A=>20= =0 ?@54?>;0305<>9 ;5:A8:>3@0D8G5A:>9 C?>@O4>G5==>AB8 G0AB=KE :@8B5@852 fi ?> 206=>AB8 8 >?@545;O5BAO A;54CNI59 ?@>F54C@>9 (<5B>4 CABC?>:): 8=8<878@C5BAO ?5@2K9 ?> 206=>AB8 :@8B5@89 f1 8 >?@545;O5BAO 53> <8=8<0;L=>5 7=0G5=85 f1*. 07=0G05BAO 25;8G8=0 4>?CAB8<>3> C25;8G5=8O  EMBED Equation.DSMT4  7=0G5=8O ?5@2>3> :@8B5@8O (CABC?:0). I5BAO <8=8<0;L=>5 7=0G5=85 2B>@>3> :@8B5@8O ?@8 CA;>288, GB> ?5@2K9 =5 ?@52KA8B 7=0G5=85  EMBED Equation.DSMT4 . 0B5< =07=0G05BAO 25;8G8=0 CABC?:8  EMBED Equation.DSMT4  ?> 2B>@><C :@8B5@8N 8 B.4. "0:8< >1@07><, 4;O 7040==>3> =01>@0 CABC?>:  EMBED Equation.DSMT4  >?B8<0;L=K9 2K1>@  EMBED Equation.DSMT4  O2;O5BAO @5H5=85< @5:C@A82=>9 7040G8:  EMBED Equation.DSMT4 , ( SEQ $>@<C;0 \* ARABIC \s 1 9)  EMBED Equation.DSMT4  ( SEQ $>@<C;0 \* ARABIC \s 1 10) 5>1E>48<> >B<5B8BL, GB> ?@8 A>>B25BAB2CNI5< 2K1>@5 CABC?>: <>6=> ?>;CG8BL ;N1>5 B@51C5<>5 0@5B>->?B8<0;L=>5 @5H5=85.  1.2 ?@82545= ?@8<5@ >?8A0=8O 2KG8A;8B5;L=>-B@C4>5<:>9 7040G8 >?B8<870F88 ?@>D8;O :>;5A0 4;O @5;LA>2KE 284>2 B@0=A?>@B0 2> 22545==KE B5@<8=0E. @>D8;L :>;5A0 >?8AK205BAO A ?><>ILN B-A?;09=0, ?>AB@>5==>3> =0 >A=>25 <=>65AB20 B>G5: =0 :@><:5, >A=>20=88 :@><:8 8 ?>25@E=>AB8 :0G5=8O :>;5A0.  :0G5AB25 :><?>=5=B 25:B>@0 y ?0@0<5B@>2 7040G8 >?B8<870F88 2K1@0=K >@48=0BK ?>4286=KE B>G5: A?;09=0, ?@8 MB>< 01AF8AAK 40==KE B>G5: D8:A8@>20=K.  >?8AK205<>9 7040G5 G8A;> ?>4286=KE B>G5: (G8A;> ?5@5<5==KE) N=11, 3@0=8FK 87<5=5=8O ?0@0<5B@>2 [ 1, 1]; <8=8<878@C5BAO @07=>ABL @048CA>2 2@0I5=8O, 0 >3@0=8G5=8O 22>4OBAO 87 A>>1@065=89 CAB>9G82>AB8. "0:8< >1@07><, 2>7=8:05B 7040G0 >?B8<870F88 A G8A;>< ?0@0<5B@>2 N=11, G8A;>< >3@0=8G5=89 m=6; F5;520O DC=:F8O 8 DC=:F88 >3@0=8G5=89  <=>3>M:AB@5<0;L=K5. 040G0 O2;O5BAO 2KG8A;8B5;L=>-B@C4>5<:>9: ?@>25@:0 >3@0=8G5=89 7040G8 8 2KG8A;5=85 7=0G5=8O F5;52>9 DC=:F88 2 >4=>9 B>G:5 70=8<05B 1>;55 45AOB8 A5:C=4 (Intel Xeon 3 F). 57C;LB0BK @5H5=8O >?8A0==>9 7040G8 A 8A?>;L7>20=85< ?@54AB02;O5<>3> 2 @01>B5 ?@>3@0<<=>3> :><?;5:A0 87;>65=K 2 3;025 4.  1.3 ?@54AB02;5=K MDD5:B82=K5 G8A;5==K5 <5B>4K @5H5=8O 7040G 2 @0AA<>B@5==>9 ?>AB0=>2:5, >?8A0=K ?@8=F8?K @0A?0@0;;5;820=8O <5B>4>2, ?@54;>65=0 <>48D8:0F8O AE5<K <=>65AB25==KE @0725@B>:, ?>72>;ONI0O AB@>8BL A5<59AB2> <=>65AB25==KE >B>1@065=89 8 ACI5AB25==> ?>2KH0NI0O ?>B5=F80; 8A?>;L7>20=8O ?0@0;;5;L=KE 2KG8A;5=89 2 ?@>F5AA5 G8A;5==>3> @5H5=8O 7040G 3;>10;L=>9 >?B8<870F88. 5H5=85 <=>3><5@=KE 7040G >?B8<870F88 ACI5AB25==> 70B@C4=O5BAO M:A?>=5=F80;L=K< @>AB>< G8A;0 8A?KB0=89 A @>AB>< @07<5@=>AB8, E0@0:B5@=K< =5 B>;L:> 4;O <5B>40 ?>;=>3> ?5@51>@0, => 8 4;O >?B8<0;L=KE 0;3>@8B<>2 <=>3>M:AB@5<0;L=>9 >?B8<870F88, O2;ONI8EAO 1>;55 M:>=><=K<8, G5< ?5@51>@.  B><C 65, 4;O MB8E 0;3>@8B<>2 E0@0:B5@=K B@C4>5<:85 @5H0NI85 ?@028;0, B@51CNI85 ?>AB@>5=8O >?B8<0;L=KE ?>:@KB89 A;>6=KE <=>3><5@=KE >1;0AB59. 0: A;54AB285, F5;5A>>1@07=K< O2;O5BAO ?@8<5=5=85 ?>4E>4>2, 5A;8 8 =5 C<5=LH0NI8E M:A?>=5=F80;L=K9 @>AB G8A;0 8A?KB0=89, B>, ?> :@09=59 <5@5, C?@>I0NI8E @5H0NI85 ?@028;0. 48= 87 B8?>2KE ?>4E>4>2  @54C:F8O @07<5@=>AB8. 54C:F8O @07<5@=>AB8 @5H05<KE <=>3>M:AB@5<0;L=KE 7040G <>65B 1KBL 2K?>;=5=0, >A=>2K20OAL =0 8725AB=>< D0:B5, GB> 4;O =5?@5@K2=>9 DC=:F88 2K?>;=O5BAO  EMBED Equation.DSMT4 . ( SEQ $>@<C;0 \* ARABIC \s 1 11) K@065=85  REF _Ref270951842 \h (11), >1KG=> =07K205<>5 <=>3>H03>2>9 @54C:F859 @07<5@=>AB8, ?>72>;O5B A25AB8 @5H5=85 <=>3><5@=>9 7040G8 >?B8<870F88 : @5H5=8N >4=><5@=>9 7040G8  EMBED Equation.DSMT4 , ( SEQ $>@<C;0 \* ARABIC \s 1 12) 345  EMBED Equation.DSMT4 , ( SEQ $>@<C;0 \* ARABIC \s 1 13)  EMBED Equation.DSMT4 , ( SEQ $>@<C;0 \* ARABIC \s 1 14) ?@8G5< :064>5 2KG8A;5=85 7=0G5=8O >4=><5@=>9 DC=:F88  EMBED Equation.DSMT4  4;O 7040==>3> y1 ?@54?>;0305B <8=8<870F8N ?> y2 DC=:F88  EMBED Equation.DSMT4  8 B.4. 06=> >B<5B8BL, GB> <=>3>H03>20O AE5<0 2 7=0G8B5;L=>9 AB5?5=8 A>459AB2C5B ?>AB@>5=8N ?0@0;;5;L=KE 0;3>@8B<>2. "0:, CG8BK20O >4=>@>4=K9 E0@0:B5@ 2KG8A;5=89 2 <=>3>H03>2>9 AE5<5, 7040205<K9 D>@<C;>9  REF _Ref270951842 \h (11), >=0 <>65B 1KBL 5AB5AB25==K< >1@07>< @0A?0@0;;5;5=0 =0 ;N1>< 87 N-1 C@>2=59 <8=8<870F88. @C3>9 >1I89 ?>4E>4 : @54C:F88 >A=>20= =0 8A?>;L7>20=88 >B>1@065=89, =07K205<KE :@82K<8 (@0725@B:0<8) 50=>, :>B>@K5 A>?>AB02;ONB ;N1>9 ;8?H8F52>9 2 38?5@:C15  EMBED Equation.DSMT4  DC=:F88  EMBED Equation.DSMT4  >4=><5@=CN DC=:F8N  EMBED Equation.DSMT4 , C4>2;5B2>@ONICN =0 >B@57:5 [0, 1] @02=><5@=><C CA;>28N 5;L45@0 A ?>:070B5;5< 1/N.  EMBED Equation.DSMT4 . ( SEQ $>@<C;0 \* ARABIC \s 1 15) @8 G8A;5==>< ?>AB@>5=88 @0725@B:8 70405BAO B>G=>ABL M, :>B>@0O >?@545;O5B <0:A8<0;L=CN ?>3@5H=>ABL >F5=:8 :064>9 :>>@48=0BK DC=:F88  EMBED Equation.DSMT4  @02=CN 2 (M+1). F5=:8 B>G5: :@82>9 A>?>AB02;ONB @02=><5@=>9 A H03>< 2 NM A5B:5 =0 >B@57:5 [0,1] @02=><5@=CN A H03>< 2 M A5B:C 2 38?5@:C15 P. 54C:F8O <=>3><5@=KE 7040G : >4=><5@=K< A ?><>ILN @0725@B>: A>E@0=O5B =5?@5@K2=>ABL 8 @02=><5@=CN >3@0=8G5==>ABL @07=>AB59 ?@8 >3@0=8G5==>9 20@80F88 0@3C<5=B0, >4=0:> B5@O5B G0ABL 8=D>@<0F88 > 1;87>AB8 B>G5: 2 <=>3><5@=>< ?@>AB@0=AB25. >7<>6=K9 A?>A>1 CG5B0 MB>9 8=D>@<0F88 A>AB>8B 2 A;54CNI5<. 2>48BAO 38?5@:C1  EMBED Equation.DSMT4  ( SEQ $>@<C;0 \* ARABIC \s 1 16) A 4;8=>9 @51@0, @02=>9 2, 8 A5<59AB2> 38?5@:C1>2  EMBED Equation.DSMT4 , ( SEQ $>@<C;0 \* ARABIC \s 1 17) 345 38?5@:C1 Pl+1 ?>;CG05BAO ?CB5< A42830 38?5@:C10 Pl 24>;L 3;02=>9 4803>=0;8 =0 H03  2 l ?> :064>9 :>>@48=0B5, 8 4;O :064>3> 38?5@:C10 Pl, 0d"ld"L 22>48BAO A2>O @0725@B:0 yl(x) B8?0 :@82>9 50=>, >B>1@060NI0O >B@57>: [0,1] =0 MB>B 38?5@:C1. @81;865==>5 ?>AB@>5=85 @0725@B:8 yl(x) 4;O B>G=>AB8, A>>B25BAB2CNI59 @07185=8N A =><5@>< M+1 ?>@>6405B 2 38?5@:C15 Pl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ef281254758 \* Lower \h \* MERGEFORMAT @8A. 1 ?@54AB02;5=K 38?5@:C1K P0-P3 8AE>4=>9 <=>65AB25==>9 @0725@B:8 4;O L = 3.  SHAPE \* MERGEFORMAT  8A.  SEQ 8A. \* ARABIC \s 1 1. 8?5@:C1K 8AE>4=>9 <=>65AB25==>9 @0725@B:8 (N = 2, L = 3) @8 MB>< ;52K9 =86=89 C3>; 38?5@:C10 P0 A>2?0405B A ;52K< =86=8< C3;>< 38?5@:C10 P. >AB@>8< 5I5 B@8 <=>65AB25==KE @0725@B:8, 2 :064>9 87 :>B>@KE ?>;>65=85 107>2>3> 38?5@:C10 P0 2K18@05BAO B0:, GB>1K C =53> A 38?5@:C1>< P A>2?040; >48= 87 B@5E >AB02H8EAO C3;>2. 5B@C4=> ?>:070BL, GB> 2A5 G5BK@5 <=>65AB25==KE @0725@B:8 1C4CB >1;040BL >4=>9 8 B>;L:> >4=>9 >1I59 @0725@B:>9, 7040205<>9 2 :064>9 87 =8E 38?5@:C1><  EMBED Equation.DSMT4 . ( SEQ $>@<C;0 \* ARABIC \s 1 18) 048< >1I55 >?8A0=85 ?@028;0 ?>AB@>5=8O :064>9 <=>65AB25==>9 @0725@B:8 4;O ?@>872>;L=>3> N. 2545< 42>8G=CN =C<5@0F8N <=>65AB25==KE @0725@B>:, A>AB>OICN 87 N @07@O4>2:  EMBED Equation.DSMT4 . 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( SEQ $>@<C;0 \* ARABIC \s 1 21) "> 5ABL ?> ?5@5<5==K<, :>B>@K< 2 42>8G=>< =><5@5 <=>65AB25==>9 @0725@B:8 A>>B25BAB2C5B 548=8F0, A4283 1C45B 2K?>;=OBLAO =0 2-l, 0 ?> >AB0;L=K< =0  2-l. @54;>65==0O 2 @01>B5 <>48D8F8@>20==0O <=>65AB25==0O @0725@B:0 7=0G8B5;L=> ?>2KH05B ?>B5=F80; 8A?>;L7>20=8O ?0@0;;5;87<0 2 ?@>F5AA5 ?>8A:0 3;>10;L=> >?B8<C<0. "0: C65 4;O B@5E<5@=KE 7040G ?@8 B>G=>AB8 ?>AB@>5=8O ?@81;865=8O @0725@B:8 M=10, >1I55 G8A;> 4>ABC?=KE @0725@B>: 2 A5<59AB25 <=>65AB25==KE @0725@B>: A>AB028B M"23 1=79.  >1I5< 65 A;CG05 G8A;> @0725@B>: <>65B 1KBL ?>;CG5=> A>3;0A=> A;54CNI5<C ?@028;C. #B25@645=85. ;O 7040G @07<5@=>AB8 N ?@8 B>G=>AB8 ?@81;865==>3> ?>AB@>5=8O :@82KE 50=> M <0:A8<0;L=>5 G8A;> @0725@B>: 2 A5<59AB25 <=>65AB25==KE @0725@B>: @02=> M"2N 1.  1.4 87;>65=0 AE5<0 8=45:A=>3> <5B>40, @07@01>B0==>3> 2 @0<:0E 8=D>@<0F8>==>-AB0B8AB8G5A:>3> ?>4E>40 : 3;>10;L=><C ?>8A:C, :>B>@K9 >ACI5AB2;O5B MDD5:B82=K9 A?>A>1 CG5B0 >3@0=8G5=89 2 7040G0E CA;>2=>9 >?B8<870F88. 3> E0@0:B5@=>9 G5@B>9 O2;O5BAO @0745;L=K9 CG5B :064>3> 87 >3@0=8G5=89 7040G8, ?@8 MB>< HB@0D=K5 DC=:F88 =5 8A?>;L7CNBAO. > 2B>@>9 3;025 @0AA<0B@8205BAO 8=D>@<0F8>==>-0;3>@8B<8G5A:0O <>45;L ?@>F5AA0 ?0@0;;5;L=>3> 3;>10;L=>3> ?>8A:0, ?>AB@>5==0O =0 ?@54;>65==>9 2 @01>B5 =>2>9 :;0AA8D8:0F88 <>45;59 >1J5:B0 8AA;54>20=89. =D>@<0F8>==>-0;3>@8B<8G5A:0O <>45;L 2:;NG05B 2>7<>6=CN G0AB8G=CN 2KG8A;8<>ABL DC=:F8>=0;>2, 0 B0:65 ?>;=CN 8 G0AB8G=CN 8=D>@<0F8>==CN A>2<5AB8<>ABL @07;8G=KE ?>AB0=>2>: 7040G8 >?B8<870F88 4;O >4=>3> 8 B>3> 65 >1J5:B0. 1J5:B 8AA;54>20=89 2 7040G0E @0F8>=0;L=>3> 2K1>@0 >?8AK205BAO =01>@>< ?0@0<5B@>2, A2>9AB20<8, :>B>@K5 >?@545;5==K< >1@07>< 7028AOB >B MB8E ?0@0<5B@>2, 8 F5;LN @0F8>=0;L=>3> 2K1>@0. !?5F8D8F8@>202 E0@0:B5@ MB8E 7028A8<>AB59 2 2845 =01>@0 DC=:F8>=0;L=KE E0@0:B5@8AB8:, 7040==KE =0 ?@>AB@0=AB25 ?0@0<5B@>2, ?>AB0=>2I8: ?>;CG05B <>45;L >1J5:B0, 0 2K1@02 87 <=>65AB20 DC=:F8>=0;>2 :@8B5@89 MDD5:B82=>AB8 8 >?@545;82, :0:8< >3@0=8G5=8O< 4>;6=K C4>2;5B2>@OBL DC=:F8>=0;K,  7040GC @0F8>=0;L=>3> 2K1>@0. @8 MB>< B8?8G=>9 O2;O5BAO A8BC0F8O, :>340 2K1>@ @0F8>=0;L=>3> 20@80=B0 <=>3>:@8B5@80;5=, :@><5 B>3> >B=N4L =5 2A5340 >G5284=>, :0:85 DC=:F8>=0;K 27OBL 2 :0G5AB25 :@8B5@852, 0 A0<8 G0AB=K5 :@8B5@88 >1KG=> ?@>B82>@5G82K. ?@8>@=>9 8=D>@<0F88 4;O ?@8=OB8O B0:>3> @5H5=8O >1KG=> =54>AB0B>G=>, >=0 ?>O2;O5BAO 8 =0:0?;8205BAO 2 ?@>F5AA5 8AA;54>20=89, ?@82>4O : =5>1E>48<>AB8 CB>G=5=8O ?>AB0=>2>: 7040G (A<5=5 2K1>@0 :@8B5@852 8 >3@0=8G5=89), B> 5ABL 2>7=8:=>25=8N =01>@0 7040G >?B8<0;L=>3> 2K1>@0, @5H0BL :>B>@K5 B@51C5BAO A>2<5AB=>.  2.1 ?@54;>65=0 =>20O AE5<0 85@0@E8G5A:>3> >?8A0=8O >1J5:B0 8AA;54>20=89, 2:;NG0NI0O B@8 107>2KE M;5<5=B0: >1J5:B >?B8<870F88 O=<y,D,w(y)>  ( SEQ $>@<C;0 \* ARABIC \s 1 22) ?@54AB02;O5B <>45;L >1J5:B0 8AA;54>20=89, >?8AK205BAO =01>@>< ?0@0<5B@>2, >1;0ABLN 87<5=5=8O 8E 7=0G5=89 8 DC=:F8>=0;0<8; 7040=85 >?B8<870F88 Z=<F,f,G,g,q>  ( SEQ $>@<C;0 \* ARABIC \s 1 23) ?@54AB02;O5B ?5@2CN G0ABL ?>AB0=>2:8 7040G8 >?B8<0;L=>3> 2K1>@0, >?8AK205BAO <=>65AB2>< :@8B5@852 8 >3@0=8G5=89; 7040G0 >?B8<870F88 z=<y,D,u,U>  ( SEQ $>@<C;0 \* ARABIC \s 1 24) ?@54AB02;O5B 2B>@CN G0ABL ?>AB0=>2:8 7040G8 >?B8<0;L=>3> 2K1>@0, >?8AK205BAO >1;0ABLN ?>8A:0.  @01>B5 ?@54;>65=0 @0AH8@5==0O <>45;L >1J5:B0 8AA;54>20=89 =0 A;CG09, :>340 =5:>B>@K5 2E>4OI85 2 =55 DC=:F8>=0;K <>3CB 1KBL 2KG8A;8<K =5 2> 2A5E B>G:0E >1;0AB8 D.  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