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C1;8:0F88. > B5<5 48AA5@B0F88 >?C1;8:>20=> B@8 <>=>3@0D88 8 28 =0CG=KE @01>B 87 =8E 45AOBL @01>B 2 ?5@8>48G5A:8E 6C@=0;0E 87 ?5@5G=O, @5:><5=4>20==>3>  4;O ?C1;8:0F88 >A=>2=KE @57C;LB0B>2 =0 A>8A:0=85 CG5=>9 AB5?5=8 4>:B>@0 =0C:. !B@C:BC@0 8 >1J5< 48AA5@B0F88. 8AA5@B0F8O A>AB>8B 87 22545=8O, H5AB8 @0745;>2, 2K2>4>2 ?> @0745;0<, 70:;NG5=8O, A?8A:0 ;8B5@0BC@K. 01>B0 2K?>;=5=0 =0 303-E AB@0=8F0E <0H8=>?8A=>3> B5:AB0, A>45@68B 89 @8AC=:>2 8 8 B01;8F. 81;8>3@0D8G5A:89 A?8A>: 2:;NG05B 305 =08<5=>20=89. !  "+ > 22545=88 >1>A=>20=0 0:BC0;L=>ABL B5<K 48AA5@B0F8>==>9 @01>BK, AD>@<C;8@>20=0 F5;L 8 7040G8 8AA;54>20=89, >B<5G5=K ?>;CG5==K5 2 @01>B5 =0CG=K5 @57C;LB0BK, 8E ?@0:B8G5A:0O F5==>ABL, @50;870F8O, 0?@>10F8O 8 AB@C:BC@0 48AA5@B0F88.  ?5@2>< @0745;5 48AA5@B0F88 @07@01>B0=0 :>=F5?F8O 0=0;8B8G5A:>3> 8AA;54>20=8O <548F8=A:8E CG@5645=89. @8 @07@01>B:5 <>45;59 8 8AA;54>20=88 DC=:F8>=8@>20=8O <548F8=A:8E CG@5645=89, 2 B>< G8A;5 8 A0=0B>@=>-:C@>@B=KE CG@5645=89 (!#) >?@545;ONB ?>=OB8O: A8AB5<0, ?>4A8AB5<0, M;5<5=B, A2O78, A2>9AB20 M;5<5=B>2 8 A2O759 >1J5:B0, F5;L DC=:F8>=8@>20=8O, 70:>=><5@=>AB8 F5;5>1@07>20=8O 8 70:>=><5@=>AB8 A8AB5<K. 2545=> >?@545;5=85 <548F8=A:>3> CG@5645=8O: S(<A, QA, R, QR, B, Z, CU, (T, N, LN>. (1) 345: A={ai}, i(I={1,2,& ,n}  <=>65AB2> M;5<5=B>2 <548F8=A:>3> CG@5645=8O;QA <=>65AB2> A2>9AB2 M;5<5=B>2, R={rj}, j(J={1,2,& ,m}  <=>65AB2> DC=:F8>=0;L=KE 8 8=D>@<0F8>==KE A2O759 <564C M;5<5=B0<8; QR <=>65AB2> A2>9AB2 A2O759 M;5<5=B>2; B 25:B>@ :>=AB@C:B82=KE ?0@0<5B@>2; Z F5;L 8;8 A>2>:C?=>ABL F5;59, >15A?5G820NI0O 4>AB865=85 M:AB@5<0;L=KE 7=0G5=89 :@8B5@852 >?B8<870F88 DC=:F8>=8@>20=8O; U CA;>28O F5;5>1@07>20=8O; (T 8=B5@20; 2@5<5=8, 2 B5G5=85 :>B>@>3> 1C45B ACI5AB2>20BL <548F8=A:>5 CG@5645=85; N =01;N40B5;8 8;8 ;8F0 (A>2>:C?=>ABL ;8F), ?@8=8<0NI8E @5H5=8O, LN O7K: >1I5=8O =01;N40B5;59. >4 AB@C:BC@>9 <548F8=A:>3> CG@5645=8O ?>=8<05BAO 2=CB@5==OO >@30=870F8O, 2:;NG0NI0O :>;8G5AB2>, A>AB02 M;5<5=B>2, 284K, E0@0:B5@ A2O759 8 >B=>H5=89 <564C =8<8. >4 M;5<5=B>< <548F8=A:>3> CG@5645=8O ?>=8<05BAO ;N1>9 =545;8<K9 >1J5:B >B=>A8B5;L=> @5H05<>9 7040G8, (?0F85=BK, <548F8=A:89 ?5@A>=0;, ;8F0 C?@02;5=G5A:>3> A>AB020 8 A>AB020 >1A;C6820=8O <548F8=A:>3> CG@5645=8O, ?@81>@K, M;5<5=BK >1>@C4>20=8O 8 ?@>G55). >4 A2O7O<8 ?>=8<0NBAO ;N1K5 8=D>@<0F8>==K5 8 DC=:F8>=0;L=K5 A2O78, ACI5AB2CNI85 2 AB@C:BC@5 <548F8=A:>3> CG@5645=8O 8 >15A?5G820NI85 53> 48=0<8G=>5 DC=:F8>=8@>20=85. 0AA<>B@5=K 8725AB=K5 <5B>4K AB@C:BC@8@>20=8O F5;8 DC=:F8>=8@>20=8O (<5B>4 "" , <5B>4K ...'5@=O:0, !..0;C520, . >;C1:>20, $.. 5@53C4>20). 0@0483<0 <548F8=A:>3> CG@5645=8O, :0: >B:@KB>9 A8AB5<K, 70:>=><5@=>AB8 F5;>AB=>AB8 (M<5@465=B=>AB8), 85@0@E8G5A:>9 C?>@O4>G5==>AB8, M:28D8=0;L=>AB8 ?>72>;ONB AD>@<C;8@>20BL 70:>=><5@=>AB8 F5;5>1@07>20=8O A CG5B>< 2708<>459AB28O 2=5H=8E 8 2=CB@5==8E D0:B>@>2. !B@C:BC@0 F5;59 O2;O5BAO >A=>2>9 4;O @07@01>B:8 8;8 :>@@5:B8@>2:8 >@30=870F8>==>9 AB@C:BC@K 8=D>@<0F8>==>-C?@02;ONI59 A8AB5<K (#!). &5;L-8450; <548F8=A:>3> CG@5645=8O A2O70=0 A A8AB5<>9 F5==>AB59 2=5H=59 A@54K 8 A>B@C4=8:>2 CG@5645=8O. !D>@<C;8@>20=K >A=>2=K5 C@>2=8 A8AB5<K F5==>AB59 ?@8<5=8B5;L=> : A?5F8D8:5 CG@5645=8O. 07@01>B0= <5B>4 AB@C:BC@870F88 F5;59, CG8BK20NI89 AB@C:BC@C <548F8=A:>3> CG@5645=8O, DC=:F88 8 7040G8, @5H05<K5 M;5<5=B0<8 8 ?>4A8AB5<0<8, :@8B5@88 MDD5:B82=>AB8 DC=:F8>=8@>20=8O, GB> ?>72>;O5B A8=B578@>20BL >@30=870F8>==CN AB@C:BC@C <548F8=A:>3> CG@5645=8O. >45;L AB@C:BC@870F88 F5;8 D>@<0;87C5BAO 3@0D><, :>B>@K9 8<55B 85@0@E8G5A:CN AB@C:BC@C (A<. @8A.1).  EMBED Word.Picture.6  8A.1 !B@C:BC@870F8O F5;59 A2O70=0 A @5H5=85< 7040G: >?@545;5=85 >B=>H5=8O <564C <=>65AB2>< F5;59 8 A>2>:C?=>ABLN :@8B5@852, >?@545;ONI8E MDD5:B82=>ABL DC=:F8>=8@>20=8O <548F8=A:>3> CG@5645=8O, 0 8<5==>: 3;>10;L=>9 F5;8 Z <548F8=A:>3> CG@5645=8O; >?@545;5=85 <=>65AB20 ?>4F5;59 Z={z1z2,& ,zn} 3;>10;L=>9 F5;8; 7040=85 <=>65AB20 :@8B5@852 K={k1,k2,& ,km}; >?@545;5=85 >B=>H5=89 <564C <=>65AB2>< M;5<5=B>2 8 ?>4A8AB5<, 8 A>2>:C?=>ABLN 7040G, @5H05<KE =0 MB>< <=>65AB25, 0 8<5==>: <=>65AB20 M;5<5=B>2 8 ?>4A8AB5< <548F8=A:>3> CG@5645=8O S={s1,s2,& ,sk} 8 <=>65AB20 @5H05<KE 8<8 7040G F={f1,f2,& ,fr}; >?@545;5=85 <=>65AB20 D={d1,d2,& ,db} 2@0G51=KE 8 >@30=870F8>==>-45;>2KE ?@>F5AA>2; >B=>H5=89 <564C >@30=870F8>==>9 AB@C:BC@>9 8 7040G0<8, =0?@02;5==K<8 =0 4>AB865=85 7040==>9 F5;8. @8 AB@C:BC@8@>20=88 F5;59 >ACI5AB2;O5BAO 845=B8D8:0F8O 3@0D8:>2 A>>B25BAB28O <564C ?0@0<5B@0<8 <548F8=A:>3> CG@5645=8O 8 @5H05<K<8 7040G0<8. 0@0<5B@K <548F8=A:>3> CG@5645=8O 7040=K 2 2845 25:B>@0 :>=AB@C:B82=KE ?0@0<5B@>2 B={b1,b2,& ,bv}. ;O CG5B0 2;8O=8O 2=5H=59 A@54K 22>48BAO 25:B>@ :>=AB@C:B82=KE ?0@0<5B@>2 2=5H=59 A@54K. 5H5=85 7040G8 >?@545;5=8O A>AB>O=8O <548F8=A:>3> CG@5645=8O A2O70=> A 2K1>@>< <=>65AB20 :@8B5@852 K={k1,k2,& ,km} >F5=:8 A>AB>O=8O <548F8=A:>3> CG@5645=8O 8 >F5=:8 MDD5:B82=>AB8 53> DC=:F8>=8@>20=8O. !>>B25BAB285  >?@545;O5B >B>1@065=85 M;5<5=B>2 <=>65AB20 7040G F={f1,f2,& ,fr} 2 <=>65AB2> :@8B5@852 K={k1,k2,& ,km}. ;>10;L=0O F5;L 45:><?>78@>20=0 =0 <=>65AB2> Z={z1z2,& ,zn}, M;5<5=BK :>B>@>3> <>3CB 1KBL >?@545;5=K A ?@8<5=5=85< <5B>4>2, =0?@02;5==KE =0 0:B82870F8N 8A?>;L7>20=8O 8=BC8F88 8 >?KB0 A?5F80;8AB>2. 564C <=>65AB2>< ?>4F5;59 Z={z1z2,& ,zn} 8 <=>65AB2>< :@8B5@852 K={k1,k2,& ,km} CAB0=02;8205BAO A>>B25BAB285 G, 2 >1I5< A;CG05 B0:65 =5G5B:>5. @8<5=5=85 <5B>40 AB@C:BC@870F88 F5;8 <548F8=A:>3> CG@5645=8O ?>72>;O5B ?5@5E>48BL : AB@>3>9 ?>AB0=>2:5 7040G <>45;8@>20=8O 8 ?@>5:B8@>20=8O #!. @>872545= 0=0;87 C?@02;O5<>AB8 2 <548F8=A:8E CG@5645=8OE. #?@02;5=85 A2>48BAO : @5H5=8N 7040G C?@02;5=8O 45OB5;L=>ABLN <548F8=A:>3> CG@5645=8O, C?@02;5=85 B@C4>2K<8 @5AC@A0<8, C?@02;5=85 2=5H=8<8 A2O7O<8 8 A>25@H5=AB2>20=85 C?@02;5=8O. !D>@<C;8@>20=0 A>2>:C?=>ABL F5;59 <548F8=A:8E CG@5645=89, O2;ONI8EAO >A=>2>?>;030NI8<8 A ?>78F89 <5=546<5=B0: 1)F5;L A>25@H5=AB2>20=8O A8AB5<K C?@02;5=8O <548F8=A:8< CG@5645=85< 2 A<KA;5 ?>2KH5=8O MDD5:B82=>AB8 DC=:F8>=8@>20=8O CG@5645=8O, A>25@H5=AB2>20=8O AB@0B538G5A:>3> 8 >?5@0B82=>3> ?@>3=>78@>20=8O @57C;LB0B>2 ?@8=OB8O @5H5=89; 2)F5;L A>25@H5=AB2>20=8O A@54AB2 8 A?>A>1>2 C?@02;5=8O 2 >B=>H5=88 @C:>2>48B5;59, >B25BAB25==KE 70 ?@8=OB85 @5H5=89, 40;L=59H53> @0728B8O <548F8=A:>3> CG@5645=8O, 1>;55 :0G5AB25==>3> 2K?>;=5=8O 4>;6=>AB=KE >1O70==>AB59; 3)F5;L A>25@H5=AB2>20=8O >@30=870F8>==>9 AB@C:BC@K <548F8=A:>3> CG@5645=8O, ?@8<5=5=85 1>;55 381:8E AB@C:BC@=KE @5H5=89, A>25@H5=AB2>20=85 :><<C=8:0F89 2=CB@8 <548F8=A:>3> CG@5645=8O 8 2=5 53>, MDD5:B82=>5 @0745;5=85 B@C40 8 45;538@>20=85 ?>;=><>G89; 4)F5;L A>25@H5=AB2>20=8O AB8;O @01>BK @C:>2>48B5;59, >B25BAB25==KE 70 ?@8=OB85 C?@02;5=G5A:8E @5H5=89, =0?@02;5==0O =0 @5H5=85 7040G A>25@H5=AB2>20=8O @01>BK 04<8=8AB@0B82=>3> 0??0@0B0, C;CGH5=85 2708<>>B=>H5=89 2=CB@8 <548F8=A:>3> CG@5645=8O, 045:20B=>9 >F5=:8 A2>8E A?>A>1=>AB59, 2>7<>6=>AB59 8 7=0=89; 5)F5;L A>25@H5=AB2>20=8O <5B>4>2 >F5=>: @50:F89 2=5H=59 A@54K =0 ?@8=8<05<K5 C?@02;5=G5A:85 @5H5=8O, ?>8A: MDD5:B82=KE <>45;59 8 <5B>48: >F5=:8 A>AB>O=89 8 <=5=89 A>F80;L=KE A;>52 =0A5;5=8O >B=>A8B5;L=> DC=:F8>=8@>20=8O <548F8=A:>3> CG@5645=8O. 0AA<>B@5=K >A>15==>AB8 ?>4E>4>2 : <>45;8@>20=8N. 0B5<0B8G5A:>5 <>45;8@>20=85 <548F8=A:>3> CG@5645=8O AB028B F5;LN ?@>3=>78@>20=85 @0728B8O A>1KB89, 2K720==>5 ?@8=OBK< @5H5=85< 8 ?@54>AB02;5=85< ;8FC, ?@8=8<0NI5<C @5H5=85, 4>AB0B>G=> ?>;=>9 8=D>@<0F88 > ?>A;54AB28OE 53> 459AB289. >=F5?F88 <>45;8@>20=8O <548F8=A:>3> CG@5645=8O AD>@<C;8@>20=K =0 A8AB5<=>< C@>2=5 A;54CNI8< >1@07><: -A;010O D>@<0;87C5<>ABL <548F8=A:>3> CG@5645=8O, 2>-?5@2KE, 2;8O5B =0 2K1>@ ?@028; 2K2>40 @5H5=8O, 2>-2B>@KE, B@51C5B ?@8<5=5=8O <5B>4>2 8A:CAAB25==>3> 8=B5;;5:B0; -2;8O=85 G5;>25G5A:>3> D0:B>@0 =0 ?@8=OB85 @5H5=89, ?@8<5=5=85 <>45;8@>20=8O, <5B>4>2 B5>@88 8A:CAAB25==>3> 8=B5;;5:B0 B0:65 >?@545;O5B ?>AB@>5=85 A8AB5<K ?>445@6:8 @5H5=89; -?@8 @07@01>B:5 <>45;8 <548F8=A:>3> CG@5645=8O 22>48BAO 25:B>@ :>=AB@C:B82=KE ?0@0<5B@>2 2 ?@>AB@0=AB25 A>AB>O=89; -:064>9 B>G:5 ?@>AB@0=AB20 A>AB>O=89 A>>B25BAB2C5B D8:A8@>20==>5 <=>65AB2> ?@028; 8 0:A8><, 2 A2>N >G5@54L, >?@545;ONI8E <=>65AB2> 20@80=B>2 2K1>@0 @5H5=89. 07@01>B0==K9 <5B>4 AB@C:BC@870F88 F5;59 ?>72>;8; >?@545;8BL >A=>2=K5 7040G8 8 AB@C:BC@C <548F8=A:>3> CG@5645=8O, 7040G8 >A=>2=KE ?>4@0745;5=89 1>;L=8G=>3> CG@5645=8O, F5;8, 7040G8 8 B8?>2CN AB@C:BC@C ?>;8:;8=8G5A:8E 8 0<1C;0B>@=KE CG@5645=89, 0 B0:65 A0=0B>@=>-:C@>@B=KE CG@5645=89. > 2B>@>< @0745;5 48AA5@B0F88 ?@>872545=0 @07@01>B:0 <5B>4>2 <>45;8@>20=8O 2 CA;>28OE 0?@8>@=>9 =5>?@545;5==>AB8. ?@545;5=K F5;8 8 7040G8 <>45;8@>20=8O. ;O >1J5:B>2 <548F8=A:8E CG@5645=89 7040G8 <>45;8@>20=8O A2O70=K A 4803=>AB8:>9 A>AB>O=89 ?0F85=B>2, 2K1>@>< <5B>4>2 ;5G5=8O, >?B8<0;L=>9 >@30=870F859 DC=:F8>=8@>20=8O <548F8=A:>3> CG@5645=8O, ?@>5:B8@>20=85< #! 4;O <548F8=A:8E CG@5645=89. @54;>65= <5B>4 ?>AB@>5=8O :>=F5?BC0;L=>9 <>45;8, >A=>20==K9 =0 B5>@5B8:>-<=>65AB25==KE ?@54AB02;5=8OE. 2545=> ?>=OB85 25:B>@0 :>=AB@C:B82=KE ?0@0<5B@>2 <548F8=A:>3> CG@5645=8O Z={Z1,Z2,& ,Zn}, 345 Zi - i-9 M;5<5=B CG@5645=8O. E>4=K5 ?0@0<5B@K <548F8=A:>3> CG@5645=8O  MB> A>2>:C?=>ABL ?@02>2KE CAB0=>2>: V, C?@02;ONI8E @5H5=89 U, ?0@0<5B@>2 ?0F85=B>2 PP, A>1AB25==KE 2>7<CI5=89 W 8 >F5=>: S @50:F89 A>F80;L=KE A;>52 =0 45OB5;L=>ABL <548F8=A:>3> CG@5645=8O. =>65AB2> 2E>4=KE ?0@0<5B@>2 >?@545;8<, :0: X=V(U(PP(W(S. KE>4=K5 ?0@0<5B@K <548F8=A:>3> CG@5645=8O  MB> :@8B5@88 MDD5:B82=>AB8 DC=:F8>=8@>20=8O K, ?0@0<5B@>2 ?0F85=B>2 PW, ?@8=8<05<K5 @5H5=8O R, A2O70==K5 A C?@02;5=85< 45OB5;L=>ABLN <548F8=A:>3> CG@5645=8O. =>65AB2> 2KE>4=KE ?0@0<5B@>2 >?@545;8<, :0: Y=K(PW(R. 564C M;5<5=B0<8 <=>65AB20 Y, M;5<5=B0<8 <=>65AB2 X 8 Z ACI5AB2C5B A>>B25BAB285 (DC=:F8O 2KE>40):  EMBED Equation.2 =<{(V(U(PP(W(S)((Z1(Z2(& (Zn)}, (K(PW(R),  EMBED Equation.2 >, (2) 345  EMBED Equation.2  - =5G5B:89 3@0D8: =5G5B:>3> A>>B25BAB28O  EMBED Equation.2 . 564C M;5<5=B0<8 <=>65AB20 Z, M;5<5=B0<8 <=>65AB2 X 8 Z ACI5AB2C5B A>>B25BAB285 (DC=:F8O ?5@5E>4>2), :>B>@>5 2 >1I5< A;CG05 B0:65 A;54C5B @0AA<0B@820BL :0: =5G5B:>5 A>>B25BAB285:  EMBED Equation.2 =<{(V(U(PP(W(S)((Z1(Z2(& (Zn)}, (Z1(Z2(& (Zn),  EMBED Equation.2 >, (3) 345  EMBED Equation.2  - =5G5B:89 3@0D8: =5G5B:>3> A>>B25BAB28O  EMBED Equation.2 . 0 ?@8<5@5 A0=0B>@8O @0A=K5 :0<=8 @0AA<>B@5= ?5@5G5=L :@8B5@852, :>B>@K5 <>3CB CG0AB2>20BL 2 >F5=:5 MDD5:B82=>AB8 DC=:F8>=8@>20=8O <548F8=A:>3> CG@5645=8O, 2 7028A8<>AB8 >B 53> =07=0G5=8O: :04@K, :20;8D8:0F8O, :>5G=K9 D>=4, ;5G51=>-4803=>AB8G5A:0O @01>B0, ?>:070B5;8 @01>BK >B45;5=89, G0AB>B0 ?@8<5=5=8O 5AB5AB25==KE 8 ?@5D>@<8@>20==KE ;5G51=KE D0:B>@>2, ?>:070B5;8 @01>BK :018=5B>2, ?>:070B5;8 @01>BK ?0;0BK 8=B5=A82=>9 B5@0?88, G0AB>B0 2=>2L 2KO2;5==KE 701>;520=89. ?B8<870F8O ;N1>3> >4=>3> 87 =0720==KE :@8B5@852 =5 @5H05B 7040GC AB@C:BC@=>3> >?B8<0;L=>3> A8=B570. >MB><C ?@54;>65= 8=B53@0;L=K9 :@8B5@89 2840: Q=b1f1+b2f2+& +bnfn, (4) 345 fi - i-9 :@8B5@89, b1,b2,& ,bn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i,T((i),X,G,M>,  EMBED Equation.2  345 (i - =0720=85 i->9 ; T((i)-B5@<-<=>65AB2>  (i; %->1;0ABL >?@545;5=8O M;5<5=B0 <=>65AB20 T((i); G-A8=B0:A8G5A:>5 ?@028;> (3@0<<0B8:0), ?>@>640NI55 M;5<5=BK (j-5 =5G5B:85 ?5@5<5==K5)  EMBED Equation.2 ; M-A5<0=B8G5A:>5 ?@028;>, :>B>@>5 AB028B 2 A>>B25BAB285 :064>9 =5G5B:>9 ?5@5<5==>9 ()  EMBED Equation.2  =5G5B:>5 <=>65AB2>  EMBED Equation.2 -A<KA;   EMBED Equation.2 . 5G5B:85 ?5@5<5==K5 ()  EMBED Equation.2  7040NBAO 2 2845 B@>9:8 <=>65AB2  EMBED Equation.2  345  EMBED Equation.2 -=08<5=>20=85 ; %-107>2>5 <=>65AB2>;  EMBED Equation.2 -=5G5B:>5 ?>4<=>65AB2> <=>65AB20 %,  EMBED Equation.2 -DC=:F88 ?@8=04;56=>AB8. >45;L ?@8=OB8O @5H5=89 2 2845 =5G5B:>9 :;0AA8D8:0F8>==>9 A8AB5<K 70405BAO =01>@>< (W,(,H), (5) 345 W-<=>65AB2> ?@87=0:>2-D0:B>@>2, (-@07185=85 W =0 =5G5B:85 MB0;>==K5 :;0AAK  EMBED Equation.2 , H-<=>65AB2> ?@8=8<05<KE @5H5=89. >45;L 2 2845 =5G5B:>9 :;0AA8D8:0F8>==>9 A8AB5<K ?@54AB02;O5BAO B01;8F59 A>>B25BAB28O, A>45@60I59  EMBED Equation.2  AB@>: 8 (n+1) AB>;1F>2.  AB@>:0E 70?8AK20NBAO 2A5 2>7<>6=K5 :><18=0F88 7=0G5=89  (i (87 B5@<-<=>65AB2 T((i)), 0 2 (n+1)-< AB>;1F5 - A>>B25BAB2CNI85 MB8< :><18=0F8O< C?@02;ONI85 @5H5=8O  EMBED Equation.2 . >45;L 2KG8A;5=8O AB5?5=8 8AB8==>AB8 =5G5B:8E ?@028; 2K2>40 70405BAO B@>9:>9 (W,T,H), (6) 345 " - =5G5B:>5 >B=>H5=85 =0 <=>65AB25 W(H.  <>45;8 <=>65AB2> H @0AA<0B@8205BAO :0: <=>65AB2>  87 B5@<-<=>65AB20 -?@8=8<05<>5 @5H5=85. -;5<5=BK <=>65AB20 W - <=>65AB20, A>AB02;ONI53> ?@O<>5 ?@>872545=85 <=>65AB2 2E>4=KE D0:B>@>2, =0?@8<5@, >?8AK20NI8E A>AB>O=85 ?0F85=B0, W=W1(W2(& (Wn, >?@545;ONBAO ?@8 :>=:@5B=>9 ?>AB0=>2:5 7040G8 ?@8=OB8O @5H5=8O 8;8 >F5=:8 53> ?>A;54AB289. -:A?5@B >?8AK205B ?@8=OB85 @5H5=89 2 2845 =5:>B>@>3> <=>65AB20 ", A>45@60I53> 2KA:07K20=8O (j, EMBED Equation.2 . ;O :064>3> 2KA:07K20=8O (j 2K2>48BAO DC=:F8O ?@8=04;56=>AB8  EMBED Equation.2  ;O >B=>H5=8O " 7=0G5=8O DC=:F88 ?@8=04;56=>AB8 >?@545;ONBAO G5@57 >1>1I5==CN >?5@0F8N (, B0: GB>  EMBED Equation.2  (7) !8BC0F8>==0O <>45;L ?@8=OB8O @5H5=89 >A=>20=0 =0 0=0;875 @50;L=KE =5G5B:8E A8BC0F89 8 A>?>AB02;5=88 8E A MB0;>==K<8 =5G5B:8<8 A8BC0F8O<8, :>B>@K5 >?@545;ONB M:A?5@BK 8 8< A>?>AB02;ONB @5H5=8O. @8<5=8B5;L=> : 2@0G51=>9 45OB5;L=>AB8 7040G0 A2>48BAO : A>?>AB02;5=8N @50;L=>3> A>AB>O=8O ?0F85=B0 A MB0;>==K<8 A>AB>O=8O<8 8 2KO2;5=8N =081>;55 1;87:>3> MB0;>==>3> A>AB>O=8O, 0 70B5< 2 A>>B25BAB288 A MB>9 =5G5B:>9 MB0;>==>9 A8BC0F859 >ACI5AB2;O5BAO ?@8=OB85 @5H5=8O, =0?@8<5@, ?>AB0=>2:0 4803=>70 701>;520=8O 8;8 2K1>@ =07=0G5=89. -B0;>==K5 A8BC0F88 7040NBAO 2 2845 M;5<5=B>2 <=>65AB20 EMBED Equation , <=>65AB2> @5H5=89 A>AB>8B 87 M;5<5=B>2 h1,h2,...,hm. !>AB>O=85 ?0F85=B0 E0@0:B5@87C5BAO =5:>B>@>9 @50;L=>9 =5G5B:>9 A8BC0F859 \EMBED Equation . @0G0<8-A?5F80;8AB0<8 4;O ?@8=OB8O @5H5=89 7040NBAO MB0;>==K5 =5G5B:85 A8BC0F88 \EMBED Equation . ;O >?@545;5=8O 1;87>AB8 @50;L=KE 8 =5G5B:8E MB0;>==KE A8BC0F89 =5>1E>48<> ?@8<5=8BL 87 =5G5B:>9 ;>38:8 B0:85 >?5@0F88, :0: >?@545;5=85 AB5?5=8 2:;NG5=8O, >?@545;5=85 AB5?5=8 =5G5B:>3> @025=AB20, >?@545;5=85 AB5?5=8 =5G5B:>9 M:2820;5=A88. 5G5B:>5 A>>B25BAB285 =0 M;5<5=B0E <=>65AB20 S* =5G5B:8E MB0;>==KE A8BC0F89 8 M;5<5=B0E <=>65AB20 H ?@8=OB8O @5H5=89 70405BAO 2 2845 B@>9:8 <=>65AB2 \EMBED Equation , 2 :>B>@>9 \EMBED Equation =5G5B:>5 <=>65AB2> 2 S*(H. >45;L =5G5B:>3> 3@C??>2>3> ?@8=OB8O @5H5=89 ?@8<5=5=0 ?@8 @07@01>B:5 8=B5;;5:BC0;L=KE A8AB5< ?@8=OB8O @5H5=89 2 <548F8=A:>9 ?@0:B8:5 2 CA;>28OE 45D8F8B0 8AE>4=KE 40==KE > ?0F85=B5. >45;L =5G5B:>3> 2K1>@0 20@80=B>2 ?@8=OB8O @5H5=89 >?@545;O5BAO 7040=85< 107>2>3> <=>65AB20 20@80=B>2 2K1>@0, =5G5B:8< >B=>H5=85< =0 <=>65AB25 20@80=B>2 2K1>@0, <5E0=87<>< 2K1>@0. $>@<0;L=> <>45;L >?@545;5=0 2 2845 A;54CNI53> =01>@0:  EMBED Equation.2 , (8) 345: X - C=825@A0;L=>5 <=>65AB2> 20@80=B>2 2K1>@0 2 2845 ?5@5G=O 459AB289, @5H5=89, ?;0=>2, AB@0B5389 8;8 4@C38E >1J5:B>2 2K1>@0; {(,T((),X,G,M} - <=>65AB2>, 7040NI55 ;8=328AB8G5A:85 ?5@5<5==K5 =0 <=>65AB25 20@80=B>2 2K1>@>2; { EMBED Equation.2 } - <=>65AB2> =5G5B:8E ?@028; 2K1>@0;  EMBED Equation.2  - <=>65AB2> =5G5B:8E :@8B5@852 2K1>@0;  EMBED Equation.2  - ?@028;> 03@538@>20=8O =5G5B:8E 20@80=B>2 2K1>@0;  - :;0AA <5E0=87<>2 =5G5B:>3> 2K1>@0. @>1;5<0 3@C??>2>3> ?@8=OB8O @5H5=89 2 <548F8=A:>9 ?@0:B8:5 A2>48BAO : 03@538@>20=8N 8=48284C0;L=KE ?@54?>GB5=89 f1,f2,& ,fn (n-G8A;> 2@0G59-M:A?5@B>2) 2 548=>5 (3@C??>2>5) ?@54?>GB5=85 f. 0AA<>B@5=K 284K >F5=>: 2 <548F8=A:>9 ?@0:B8:5. ><8<> :>;8G5AB25==KE >F5=>:, A>>B25BAB2CNI8E 7=0G5=8O< 8=AB@C<5=B0;L=KE 87<5@5=89, AC1J5:B82=K5 <=5=8O 2@0G59-M:A?5@B>2 E0@0:B5@87CNB 10;;L=K<8, @0=3>2K<8 >F5=:0<8, @0=68@>20=85< 8 ?>?0@=K< A@02=5=85<. 5B>4 ?>?0@=>3> A@02=5=8O ?@8<5=8< 4;O 2KO2;5=8O ?@54?>GB5=8O 2@0G59. >?0@=>5 A@02=5=85 B5@0?52B8G5A:8E :C@A>2 >?@545;5=> 18=0@=K< >B=>H5=85< =0 <=>65AB25 B5@0?52B8G5A:8E :C@A>2 , :0: <=>65AB2> C?>@O4>G5==KE ?0@ (ai,aj) B0:8E, GB> 0 ?@54?>GB8B5;L=55 b.  18=0@=K< >B=>H5=8O< ?@8<5=8<K B5>@5B8:>-<=>65AB25==K5 >?5@0F88, =0?@8<5@, P-1={(ai,aj)((aj,ai,)(P}, GB> >7=0G05B - aj ?@54?>GB8B5;L=55 ai, B.5. B5@0?52B8G5A:89 :C@A ai, <5=55 ?@54?>GB8B5;5=, G5< aj. !>>B=>H5=85 (ai,aj)(P(P-1 ?>:07K205B, GB> B5@0?52B8G5A:85 :C@AK ai, 8 aj A@02=8<K ?> ?@54?>GB5=8N, B. 5. ai ?@54?>GB8B5;L=55 aj 8;8, =0>1>@>B, aj ?@54?>GB8B5;L=55 ai. A;8 65 (ai,aj)(P(P-1, B> ai 8 aj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ord.Picture.8  8A.2 @8 C?@02;5=88 A>25@H0NBAO 459AB28O 8 ?@8=8<0NBAO @5H5=8O: -3@C??0 459AB289 8 @5H5=89, A2O70==KE A >1A;C6820=85< ?0F85=B>2; -3@C??0 :><<5@G5A:8E 459AB289 8 @5H5=89 (?@>4060 ?CB52>: 2 !# 8 CA;C3, ?>:C?:0 <0B5@80;>2, <548:0<5=B>2, >1>@C4>20=8O); -3@C??0 D8=0=A>2KE 459AB289 8 @5H5=89; -3@C??0 AB@0E>2KE 459AB289 8 @5H5=89 (AB@0E>20=85 8 >E@0=0); -3@C??0 CG5B=KE 459AB289 (1CE30;B5@8O, :0;L:C;OF88, CG5B, AB0B8AB8:0); -3@C??0 04<8=8AB@0B82=KE 459AB289 8 @5H5=89 (?@>3=>7, >@30=870F8O, ?@8:07K 8 C:070=8O, :>>@48=0F8O, :>=B@>;L). 5@5G8A;5==K5 3@C??K 459AB289 C?@02;5=8O @50;87>20=K 2 #! ?@8 @07@01>B:5 ?@>3@0<<=KE <>4C;59 ?@8=OB8O @5H5=89. 0AA<>B@5=K D0:B>@K, 2;8ONI85 =0 ?@>F5AA ?@8=OB8O <5=5465@A:8E @5H5=89, <5B>4>;>38G5A:85 >A=>2K ?@8=OB8O @5H5=89. @54;>65=> @5H5=85 7040G8 ?;0=8@>20=8O 2 <5=546<5=B5 <548F8=A:>3> CG@5645=8O. -;5<5=BK AB@0B538G5A:>3> 8 B0:B8G5A:>3> ?;0=8@>20=8O @0AA<>B@5=K =0 ?@8<5@5 ?;0=8@>20=8O 4;O !#. 07@01>B0= <5B>4 ?;0=8@>20=8O 4;O !#. 07@01>B0=> AB@C:BC@8@>20=85 F5;59 A0=0B>@=>-:C@>@B=>3> <5=546<5=B0, :>B>@>5 ?@54AB02;O5B A>1>9 :><?>78F8N A>>B25BAB289. 0B5<0B8G5A:0O <>45;L AB@C:BC@8@>20=8O F5;59 70405BAO 2 2845 3@0D0. CABL n- G8A;> C@>2=59 85@0@E88 45@520 F5;59. =>65AB2> 7040G >?@545;8<, :0: M={m1,m2,& ,mk}. =>65AB2> F5;59 =0 (n-1)-< C@>2=5 85@0@E88 - Zn-1={z1,z2,& ,zr(n-1)}, <=>65AB2> F5;59 =0 (n-2)-< C@>2=5 85@0@E88 - Zn-2={z1,z2,& ,zr(n-2)}, & , <=>65AB2> F5;59 =0 2-< C@>2=5 85@0@E88 - Z2={z1,z2,& ,zr2}. 0 ?5@2>< C@>2=5 85@0@E88 ACI5AB2C5B 3;>10;L=0O F5;L - Z1={z1}. 0 <=>65AB20E M 8 Zn-1 >?@545;5=> A>>B25BAB285 qn-1=(M,Zn-1,Qn-1), 345 Qn-1 3@0D8: A>>B25BAB28O qn-1. 0 <=>65AB20E Zn-1 8 Zn-2 >?@545;5=> A>>B25BAB285 qn-2=(Zn-1,Zn-2,Qn-2), 345 Qn-2 3@0D8: A>>B25BAB28O qn-2. =0;>38G=K5 A>>B25BAB28O 7040NBAO =0 2A5E C@>2=OE 85@0@E88 45@520 F5;59 2?;>BL 4> ?5@2>3> C@>2=O, 345 A>>B25BAB285 8<55B 284 q1=(Z2,Z2,Q1), 345 Q1 3@0D8: A>>B25BAB28O q1. $>@<0;L=> <0B5<0B8G5A:0O <>45;L AB@C:BC@8@>20=8O F5;59 70405BAO :><?>78F859 A>>B25BAB289 qn-1,qn-2,& ,q1 8 8<55B A;54CNI89 284: q(qn-1,qn-2,& ,q1)={M,Zn-1,Zn-2,& ,Z1,(Qn-1>Qn-2>& >Q1)}, (9) 345 (Qn-1>Qn-2>& >Q1)  :><?>78F8O A>>B25BAB289 qn-1,qn-2,& ,q1. A=>2=K5 7040G8 ?@8 AB@C:BC@8@>20=88 F5;59 A2O70=K A >?@545;5=85< 3@0D8:>2 Qn-1,Qn-2,& ,Q1 A>>B25BAB289 qn-1,qn-2,& ,q1. @54;>65=> @5H5=85 7040G8 C?@02;5=8O ?5@A>=0;><. 5E0=87< C?@02;5=8O ?5@A>=0;>< A>AB>8B 87 42CE :@C?=KE :><?>=5=B>2 - >@30=870F88 C?@02;5=8O 8 A8AB5<K @C:>2>4AB20 A>B@C4=8:0<8 <548F8=A:>3> CG@5645=8O. 040G0 >B1>@0 :04@>2 =0?@02;5=0 =0 B>, GB>1K =09B8 :0=4840B>2, 8<5NI8E =5>1E>48<CN 4;O 2K?>;=5=8O @01>BK :20;8D8:0F8N. @8 @5H5=88 7040G8 =09<0 A>B@C4=8:>2 <548F8=A:>3> CG@5645=8O ?5@5<5==K5 7040G8 <>3CB 1KBL 7040=K :0: 2 2845 G8A;5==KE 7=0G5=89, B0: 8 2 2845 =5G5B:8E ?5@5<5==KE. >45;8 ?@8=OB8O @5H5=89 > =09<5 A>B@C4=8:>2 <548F8=A:>3> CG@5645=8O >B=>AOBAO : <>45;O< A8BC0F8>==>3> C?@02;5=8O, B.5. CAB0=>2;5=8N A>>B25BAB28O <564C =01>@0<8 =5G5B:8E ?5@5<5==KE, 27OBKE 87 B5@<>2 ;8=328AB8G5A:8E ?5@5<5==KE (), 8 M;5<5=B0<8 <=>65AB20 @5H5=89. @8=OBK <>45;8 2K2>40 @5H5=89, @50;87>20==K5 ;81> =0 >A=>25 A>?>AB02;5=8O =01>@>2 =5G5B:8E A8BC0F89 8 ?@8=8<05<KE @5H5=89, ;81> 2 2845 =5G5B:>3> >B=>H5=8O =0 ?@O<>< ?@>872545=88 <=>65AB20 ?@028; =5G5B:>3> ;>38G5A:>3> 2K2>40 8 =5G5B:>3> <=>65AB20 ?@8=8<05<KE @5H5=89, ;81> 2 2845 A8BC0F8>==>9 <>45;8. @8 @5H5=88 7040G8 ?;0=8@>20=8O =09<0 A>B@C4=8:>2 <548F8=A:>3> CG@5645=8O <=>65AB2> H ?@8=8<05<KE @5H5=89 > =09<5 A>B@C4=8:>2 @0AA<0B@8205BAO :0: <=>65AB2>, A>45@60I55 =5G5B:85 ?5@5<5==K5 (B5@<-<=>65AB2>)   ?@8=8<05<>5 @5H5=85. 0?@8<5@,  (2>7<>6=>ABL =09<0 =0 @01>BC <>65B A>45@60BL =5G5B:85 ?5@5<5==K5 T(()={<(1 A>B@C4=8: >G5=L <0;> A>>B25BAB2CNI89>, <(2 A>B@C4=8: =54>AB0B>G=> A>>B25BAB2CNI89>, <(3 >1KG=K9 A>B@C4=8:>, <(4 ?>4E>4OI89 A>B@C4=8: >, <(5 >G5=L E>@>H89 A>B@C4=8:>}. 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5$7$8$9DH$gdR%$a$gdR%$a$gdR% $`a$gd9{ $`a$gdj $`a$gdae$-DM a$gdehjxln<>@BLNPRTV  >@BDFH|~\np꺳h9{ haehR% haehaehR%hR%5H*hR%hR%5mH sH  jchR%hR%5hR%hR%5 hR%hR% hR%h7h7hR%A   0 2 l n p t v x z | ~                     !!!2!6!!!!!!!<">"l"n"p"r"t"v"x"z"|"~""""""";;;;׫ jhR%hR%5mH sH h9{ jhR%hR%5mH sH hR%hR%5H*hR%hR%5mH sH  hR%hR%hR%hR%5hR%hR%5H*mH sH A""""""""""#L#N#P#T#V#X#Z#\#^#`#b#f#h#l#n########$$$$$$$$$$$$$$$$%%%H%J%L%N%P%R%T%V%X%%%%02X߾ѼjhR%hR%UU h{t5hNhR%hR%5H*hR%hR%5H*mH sH hR%hR%5hR%hR%5mH sH  hR%hR% h9{5C >?@545;8BAO ?> D>@<C;5  EMBED Equation.2  (10) ?@545;5=85 >?B8<0;L=>3> @5H5=8O hi 87 <=>65AB20 H >?@545;8BAO @5H0NI8< ?@028;><:  EMBED Equation.2  (11) @8=OB85 >?B8<0;L=KE @5H5=89 2 CA;>28OE =5>?@545;5==>AB8 <>65B @0AA<0B@820BLAO A ?>78F89 0=0;870 2=5H=59 A@54K, :>B>@0O B0:65 0?@8>@8 G0AB8G=> =5>?@545;5=0.  MB>< A;CG05 >?B8<870F8O @5H5=8O ?@>8AE>48B A ?@8<5=5=85< >?B8<870F8>==KE :@8B5@852: :@8B5@89 0;L40, :@8B5@89 C@28F0, :@8B5@89 0?;0A0, :@8B5@89 !M28460. K1>@ :@8B5@8O A>>B25BAB2C5B A?5F8D8:5 7040G8 ?@8=OB8O @5H5=89 A ?>AB02;5==K<8 F5;O<8. &5;5A>>1@07=> 8<5BL <>4C;L ?@8=OB8O @5H5=89 2 #!, GB> ?>72>;8B <>45;8@>20BL ?@8=OB85 @5H5=89 ?@8 @07=KE :@8B5@8OE 8 0=0;878@>20BL ?>;CG5==K5 @57C;LB0BK. 0AA<>B@5=K 7040G8 ?@8=OB8O @5H5=89 =0 >A=>25 B5>@5B8:>-83@>2KE <>45;59. @8<5=8B5;L=> : <5=546<5=BC !# 4;O 7040G ?@8=OB8O @5H5=89 =0 >A=>25 B5>@5B8:>-83@>2KE <>45;59 =5>1E>48<> @07@010BK20BL ?@>3@0<<=K5 <>4C;8, ?@54AB02;ONI85 A>1>9 @5H0NI85 :><?>=5=BK #!. =B5@D59A=K5 >:=0 8=B5@?@5B8@CNB A<KA;>2K5 ?>=OB8O @5H5=89, :>=5G=K5 @57C;LB0BK, A>AB>O=8O 2=5H=59 A@54K, A>>B25BAB2CNI85 >F5=:8 ?>;57=>AB8 AC1J5:B82=KE 25@>OB=>AB59. C:>2>48B5;N ?@54>AB02;5=0 2>7<>6=>ABL >F5=:8 A;>682H59AO A8BC0F88, ?@8=OB8O @5H5=8O 8 ?@>3=>70 53> ?>A;54AB289. 0AA<>B@5=K =5G5B:85 <>45;8 ?@8=OB8O @5H5=89. ;O @5H5=8O 7040G C?@02;5=8O <548F8=A:8<8 CG@5645=8O<8 A ?@8<5=5=85< <>45;59 =0 >A=>25 8A:CAAB25==>3> 8=B5;;5:B0 @07@01>B0=K @5H0NI85 :><?>=5=BK #!.  ?@>3@0<<=KE <>4C;OE D>@<0;87CNBAO 7=0=8O M:A?5@B>2 4;O 7040=8O ;8=328AB8G5A:8E 8 =5G5B:8E ?5@5<5==KE, 0 B0:65 ?@028; 2K2>40 @5H5=89.  G5B25@B>< @0745;5 48AA5@B0F88 @0AA<>B@5=0 D>@<0;870F8O AB@C:BC@K 8 2K?>;=5= 0=0;87 DC=:F8>=8@>20=8O CG@5645=89 A0=0B>@=>-:C@>@B=>3> =07=0G5=8O: -0=0;87 DC=:F8>=8@>20=8O A0<>3> !# A CG5B>< AB@C:BC@K 8 <=>3>G8A;5==KE DC=:F8>=0;L=KE A2O759 <564C M;5<5=B0<8 !#; -0=0;87 DC=:F8>=8@>20=8O 2=5H=59 A@54K, >?@545;ONI89 <=>65AB2> C?@02;ONI8E 8 2>7<CI0NI8E D0:B>@>2; -0=0;87 DC=:F8>=8@>20=8O 2708<>A2O759 <564C !# 8 2=5H=59 A@54>9. 57C;LB0BK 0=0;870 DC=:F8>=8@>20=8O !# >?@545;8;8 AB@0B538N F1 4>AB865=8O MDD5:B82=>9 @01>BK 2=CB@5==8E ?>4@0745;5=89 8 A;C61 !#. 57C;LB0BK 0=0;870 DC=:F8>=8@>20=8O 2=5H=59 A@54K >?@545;8;8 AB@0B538N F2, >B>1@060NICN M2>;NF8N 2=5H=59 A@54K 8 <=>65AB2> @50:F89 =0 2KE>4=K5 ?0@0<5B@K !#. =0;87 DC=:F8>=8@>20=8O 2708<>A2O759 >?@545;8;8 AB@0B538N F3 A>25@H5=AB2>20=8O 2708<>A2O759 <564C !# 8 2=5H=59 A@54>9. =0;87 DC=:F8>=8@>20=8O !# (A<. @8A.3) ?>72>;O5B AB@C:BC@8@>20BL F5;8, 2KO28BL A@54AB20 8 MDD5:BK 2708<>459AB28O !# 8 2=5H=59 A@54K, 0 70B5< ?5@59B8 : @07@01>B:5 :>=F5?BC0;L=>9 <>45;8, >?8AK20NI59 2708<>459AB285 !# 8 2=5H=59 A@54K.  EMBED Word.Picture.6  8A.3 0AA<>B@5=0 D>@<0;870F8O !# =0 ?@8<5@5 A0=0B>@8O @0A=K5 :0<=8. 07@01>B0=0 >@30=870F8>==0O AB@C:BC@0 A0=0B>@8O, 2 A>AB02 :>B>@>9 2E>4OB ?>4@0745;5=8O, >B45;K, A;C61K A0=0B>@8O, @0745;5==K5 8 >1J548=5==K5 ?> DC=:F8>=0;L=K< ?@87=0:0<. 564C M;5<5=B0<8 >@30=870F8>==>9 AB@C:BC@K CAB0=02;820NB 8 D>@<0;87CNB 8=D>@<0F8>==K5 A2O78 8 4>:C<5=B>>1>@>B.  =0AB>OI55 2@5<O 2 @01>B5 A0=0B>@8O ?>O28;0AL >A>15==>ABL, :>B>@0O A>AB>8B 2 B><, GB> ?0F85=BK ?>ABC?0NB 157 A0=0B>@=>-:C@>@B=KE :0@B 8 A0=0B>@89 ?5@5H5; : DC=:F8O< ?>;8:;8=8:8, => A ?@>6820=85< ?0F85=B>2 2 ?><5I5=8OE A0=0B>@8O. 0F85=BK ?>ABC?0NB 157 >1A;54>20=8O 8 =5>1E>48<> :0G5AB25==> 845=B8D8F8@>20BL 8E A>AB>O=8O. >ABC?82H89 2 A0=0B>@89 ?0F85=B ?@>E>48B ?@>F54C@C ?@85<0. ;3>@8B< ?@85<0 8 >1A;C6820=8O ?0F85=B0 - >A=>20 4;O @5H5=8O 7040G8 C?@02;5=8O >1A;C6820=85< ?0F85=B0, ?@>5:B8@>20=8O #!. ACI5AB2;5=0 D>@<0;870F8O F5;8 A0=0B>@8O @0A=K5 :0<=8. @8 A8AB5<=>< ?>4E>45 >F5=:8 A>AB>O=8O >@30=87<0 ?0F85=B0 F5;5A>>1@07=> 225AB8 25:B>@ A>AB>O=89 ?0F85=B0 B={b1,b2,& ,bn}, bi,  EMBED Equation.3 . ><?>=5=BK bi 2 A2>N >G5@54L >1J548=ONBAO 2 ?>4<=>65AB20 A C?>@O4>G5==K<8 M;5<5=B0<8 ?> 7040==>9 A>2>:C?=>AB8 B5E 8;8 8=KE ?@87=0:>2. 1J548=5=85 2> 2@0G51=>9 ?@0:B8:5 2K?>;=O5BAO ?> ?@87=0:C 2KO2;5=8O A8=4@><>2 8 A8<?B><>2 B5E 8;8 8=KE 701>;520=89. ;O 2KO2;5=8O :064>3> A8<?B><0 701>;520=8O Ni 845=B8D8F8@CNB A>>B25BAB285 q=(B,Si,Qi), 345 Qi - 3@0D8: A>>B25BAB28O, ?>4;560I89 845=B8D8:0F88. "0:65 8 4;O 2KO2;5=8O :064>3> A8=4@><0 701>;520=8O Ni 845=B8D8F8@CNB A>>B25BAB285 p=(B,Di,Pi), 345 Pi - 3@0D8: A>>B25BAB28O, ?>4;560I89 845=B8D8:0F88. ;O >?@545;5=8O =>7>;>388 Ni 845=B8D8F8@CNB A>>B25BAB285 f=(B,S(D,F), 345 F - 3@0D8: A>>B25BAB28O, ?>4;560I89 845=B8D8:0F88, S=S1(S2(& (Sk, D=D1(D2(& (Dp. 2545=85 25:B>@0 A>AB>O=89 ?0F85=B0 ?>72>;O5B 3>2>@8BL, GB> 7040G0 4803=>AB8:8 :0:>3>-;81> 701>;520=8O A2O70=0 A >?@545;5=85< :><?>=5=B 25:B>@0 B, 0 ?>A;5 845=B8D8:0F88 :><?>=5=B 25:B>@0 B A;54C5B ;>38G5A:89 2K2>4 > =0;8G88 701>;520=8O, AB5?5=8 53> ?@>O2;5=8O. >AB0=>2:0 7040G8 4803=>AB8:8 A2O70=0 A @5H5=85< 7040G8 >?@545;5=8O =01>@0 8A:><KE :><?>=5=B 25:B>@0 B. 040G0 4803=>AB8:8 ?@54AB028<0 2 2845 =01>@0: Z={U,MB,C,MD}, (12) 345 U - :><?;5:A =0G0;L=KE CA;>289 8 >3@0=8G5=89, MB - 2K1@0==K5 <5B>4K 4;O A>?>AB02;5=8O 8 845=B8D8:0F88 25:B>@0 B A =5:>B>@K< 7040==K< C@>2=5< 4>AB>25@=>AB8, C - F5;L @5H5=8O 7040G8, MD - 2K1@0==K5 <5B>4K 4803=>AB8:8.  7028A8<>AB8 >B ?>AB02;5==>9 7040G8 <5B>4K 845=B8D8:0F88 25:B>@0 B @0=68@>20=K M:A?5@B=K< ?CB5< ?> AB5?5=8 206=>AB8, GB> ?>72>;8B D>@<0;87>20BL <5B>4K 845=B8D8:0F88, :0: A>2>:C?=>ABL =5G5B:8E <=>65AB2, :064>5 87 :>B>@KE ?@54=07=0G5=> 4;O @5H5=8O :>=:@5B=>9 7040G8. @8<5=5=85 ?@>3@0<<=>3> ?@>4C:B0 2 2845 A8AB5< 4803=>AB8:8 ?>72>;O5B 1KAB@> 8 MDD5:B82=> @5H0BL 7040G8 ?@>D8;0:B8:8 8 :;8=8:8 701>;520=89. !0<K< ?@>ABK< ?CB5< O2;O5BAO A>740=85 107K 40==KE ?0F85=B>2, ?>ABC?82H8E 2 !#. 5>1E>48<K 02B><0B878@>20==K5 @01>G85 <5AB0 <548F8=A:>3> ?5@A>=0;0 A :><?>=5=B0<8 ?>445@6:8 ?@>F5AA>2 ?@8=OB8O @5H5=89. ;O ?0F85=B0, ?>ABC?82H53> 2 !#, 4>;65= A>AB02;OBLAO AB0=40@B=K9 548=K9 4>:C<5=B  8AB>@8O 1>;57=8, CB25@645==0O 8=8AB5@AB2>< 74@02>>E@0=5=8O $.  A0=0B>@88 @0A=K5 :0<=8 8<55BAO B0:0O 8AB>@8O 1>;57=8. !CI5AB2>20=85 8AB>@88 1>;57=8 ?>72>;8B A>740BL ?@54?>AK;:8 : >ACI5AB2;5=8N A8AB5<=>3> ?>4E>40 : 8AA;54>20=8N A>AB>O=8O ?0F85=B0 8 ?@>F5AAC @01>BK A =8< <548F8=A:>3> ?5@A>=0;0. 07@01>B0=0 <>45;L 4803=>AB8:8, ;5G5=8O 8 @5018;8B0F88, :0: C?@02;O5<KE A;CG09=KE ?@>F5AA>2. >=OB85 C?@02;O5<>3> A;CG09=>3> ?@>F5AA0 A =57028A8<K<8 ?@8@0I5=8O<8 2 ?@>AB@0=AB25 25:B>@0 A>AB>O=89 >@30=87<0 A>>B25BAB2C5B 7040G0< 0??@>:A8<0F88 42865=8O 25:B>@0 A>AB>O=89. #?@02;O5<K9 A;CG09=K9 ?@>F5AA A =57028A8<K<8 ?@8@0I5=8O<8 <>6=> @0AA<0B@820BL 2 2845 25:B>@0, :><?>=5=BK :>B>@>3> =5ACB 8=D>@<0F8N : M;5<5=B0< 8<<C==>9 A8AB5<K >@30=87<0. C45< @0AA<0B@820BL A>AB>O=85 >@30=87<0, :0: B>G:C <=>65AB20 B=1(2(& (n, 0 C?@02;5=8O :0: M;5<5=BK <=>65AB20 Y={y1,y2,& ,yn}, 345 n - G8A;> @0AA<0B@8205<KE :><?>=5=B >@30=87<0. C45< AG8B0BL, GB> 7040=K ?@>AB@0=AB20: D07>2>5 (,() 8 ?@>AB@0=AB2> C?@02;5=8O (Y,(), 345 ( 8 ( A83<0-0;351@K, 7040==K5 =0 <=>65AB20E  8 Y A>>B25BAB25==>. =>65AB2> Y @0AA<0B@8205<, :0: <=>65AB2> A83=0;>2 F5=B@0;L=>9 =5@2=>9 A8AB5<K. $>@<0;L=>5 >?8A0=85 87<5=5=89 A>AB>O=8O >@30=87<0 >?@545;8< ?>A@54AB2>< 7040=8O A5<59AB20 C?@02;O5<KE CA;>2=KE 25@>OB=>AB59 {pt+1(M/(t,Yt)), M((, t(0}, (13) 345 t,Yt=[(B0,Y0)(B1,Y1),& , (Bt,Yt)], B0={b1(t=0),b2(t=0),& ,bn(t=0)}, B1={b1(t=1),b2(t=1),& ,bn(t=1)}, Bt={b1(t),b2(t),& ,bn(t)}, Y0={y1(t=0),y2(t=0),& ,yn(t=0)}, Y1={y1(t=1),y2(t=1),& ,yn(t=1)}, Yt={y1(t),y2(t),& ,yn(t)}, pt+1(M/(t,Yt))=P[(Bt+1,Yt+1)(M/(t,Yt). 0640O DC=:F8O pt+1(M/(t,Yt)) O2;O5BAO @0A?@545;5=85< 25@>OB=>AB59 =0 B(Y ?@8 2A5E ?>A;54>20B5;L=>ABOE (t,Yt) 2A52>7<>6=KE ?0@ (Bt,Yt). ;O ;N1>3>  :0640O DC=:F8O pt+1(./(t,Yt) 87<5@8<0 ?> A>2>:C?=>AB8 ((t,Yt)), B.5. =0 ?@>AB@0=AB25 B(Yt+1. 50:F88 A8AB5< >@30=87<0, <KHF 8;8 3@C?? <KHF =0 C?@02;5=8O >?@545;8< 2 2845 25:B>@=KE DC=:F89 Ft((), t(1 A> 7=0G5=8O<8 2  8 7040==KE =0 87<5@8<>< ?@>AB@0=AB25 ((,(), 345 ( - A83<0-0;351@0 =0 <=>65AB25 (. >45;LN 87<5=5=8O A>AB>O=89 >@30=87<0 1C45B =07K20BLAO C?@02;O5<K9 A;CG09=K9 ?@>F5AA, D>@<0;L=> 7040==K9 2 2845 :;0AA0 =5>1@K20NI8EAO A;CG09=KE ?@>F5AA>2 =0 ((,() A> 7=0G5=8O<8 2 D07>2>< ?@>AB@0=AB25 (,(), E0@0:B5@87C5<K9 A5<59AB2>< C?@02;O5<KE CA;>2=KE 25@>OB=>AB59 pt+1(M/(t,Yt)). A;8 3>2>@8BL >1 C?@02;5=8OE, D>@<8@C5<KE F5=B@0;L=>9 =5@2=>9 A8AB5<>9 8 ?>AK;05<KE A8AB5<0< >@30=87<0, B> D>@<0;L=> MB8 C?@02;5=8O <>3CB 1KBL 7040=K B0:65 2 2845 AB>E0AB8G5A:8E @0A?@545;5=89, 0 8<5==>: {Yt(N/(Bt),Yt-1), N((, t(1}, (14) 345 Yt(N/(Bt),Yt-1)=P(Yt(N/(Bt),Yt-1) - 25@>OB=>AB=>5 @0A?@545;5=85 8;8 ?@028;> 2K1>@0 C?@02;5=8O F5=B@0;L=>9 =5@2=>9 A8AB5<>9. 0==>5 >?8A0=85 =>A8B >1>1I0NI89 E0@0:B5@, ?>B><C GB> <>6=> ?@54;>68BL 20@80=B 2K@>645==>3> @0=4><878@>20==>3> ?@028;0, :>B>@>5 ?@54AB02;5=> 2 2845 DC=:F88 ft((Bt),Yt-1) =0 Bt(Ut A> 7=0G5=8O<8 2 Y. @54;0305<0O <>45;L =>A8B D>@<0;L=K9, >1>1I0NI89 E0@0:B5@, 0 >B;8G85 ?@54;0305<>9 <>45;8 A>AB>8B 2 ?>=OB88 C?@02;O5<>AB8 A;CG09=KE ?@>F5AA>2, ?@>O2;ONI59AO 2 B><, GB> ?>8A: =C6=>3> C?@02;5=8O 4;O ?>445@60=8O CAB>9G82>3> A>AB>O=8O >@30=87<0 ?@>8AE>48B A CG5B>< ?@548AB>@88 ((t),Yt-1). >45;L 2 2845 C?@02;O5<>3> A;CG09=>3> ?@>F5AA0 >B>1@0605B C@02=>25H820=85 <=>3>725==>9 A8AB5<K, :>B>@>9 O2;O5BAO >@30=87< G5;>25:0, ?>72>;O5B D>@<0;87>20BL 48=0<8G5A:85 87<5=5=8O A>AB>O=89 >@30=87<0. @54;0305<0O <>45;L D>@<0;L=>3> >?8A0=8O 48=0<8:8 A>AB>O=89 >@30=87<0, C?@02;O5<>3> A;CG09=>3> ?@>F5AA0 045:20B=> >?8AK205B 4803=>AB8:C, ;5G5=85 8 @5018;8B0F8N =0 :>=F5?BC0;L=>< C@>2=5.  ?OB>< @0745;5 48AA5@B0F88 @0AA<>B@5=K 7040G8 @07@01>B:8 <>45;59 ?@8<5=5=8O =>2KE 8=D>@<0F8>==KE B5E=>;>389 ?@8 ?@>5:B8@>20=88 8=D>@<0F8>==KE A8AB5< <548F8=A:8E CG@5645=89. =0;87 >@30=870F8>==>-C?@02;5=G5A:>9 AB@C:BC@K <548F8=A:>3> CG@5645=8O ?>72>;8; ?5@59B8 : DC=:F8>=0;L=>9 AB@C:BC@5 #!. ?@545;5=> <=>65AB2> 7040G, A3@C??8@>20==KE ?> >?@545;5==K< ?@87=0:0<, 8 ?>72>;ONI8E 2 DC=:F8>=0;L=>9 AB@C:BC@5 #! 2K45;8BL <548F8=A:CN ?>4A8AB5<C, >15A?5G820NICN ?>4A8AB5<C 8 C?@02;5=G5A:CN ?>4A8AB5<C. !B@C:BC@=K5 M;5<5=BK #! ( ?>4A8AB5<0 >?5@0B82=>9 ?>445@6:8 >A=>2=KE ?@>F5AA>2 DC=:F8>=8@>20=8O CG@5645=8O 8 ?>4A8AB5<0 =0:>?;5=8O 8 >1@01>B:8 40==KE. 0AA<>B@5=K B@51>20=8O : ?@>5:B=K< @5H5=8O<  . 0AG5B M:>=><8G5A:>9 MDD5:B82=>AB8 2K?>;=O5BAO A 8A?>;L7>20=85< :>MDD8F85=B0 ?>2KH5=8O >?5@0B82=>AB8 ?@8=OB8O @5H5=89, 40==K<8 A>:@0I5=8O D>=40 70@01>B=>9 ?;0BK, A 8A?>;L7>20=85< :><?;5:A=>3> :>MDD8F85=B0 MDD5:B82=>AB8 C?@02;5=8O. 07@01>B0= <5B>4 0=0;8B8G5A:>3> A8=B570 >@30=870F8>==>9 AB@C:BC@K. 0 @8A.4 ?@82545=0 >@30=870F8>==0O AB@C:BC@0 #! A0=0B>@8O @0A=K5 :0<=8.  EMBED Word.Picture.8  8A.4 !8=B57 >@30=870F8>==>9 AB@C:BC@K A2O70= A ?@>5:B8@>20=85< AB@C:BC@K #!, 8<5NI59 >?B8<0;L=>5 @0A?@545;5=85 7040G ?> ?>4A8AB5<0<. @8 0=0;875 ?@>F5AA>2 ?@>5:B8@>20=8O 22545=> ?>=OB85 M;5<5=B0@=>9 >?5@0F88. 064>9 M;5<5=B0@=>9 >?5@0F88 li ?>AB028< 2 A>>B25BAB285 2E>4=>9 Xi=(x1i,...,xmi) 8 2KE>4=>9 Yi=(y1i,...,yni) 25:B>@K. !2O7L >?5@0F89 ?@54AB028< 3@0D>< 1(,1), =5 A>45@60I8< ?5B;8, <=>65AB2> 25@H8=  :>B>@>3> A>>B25BAB2C5B >?5@0F8O< l1 ,...,ln, 0 :0640O 4C30  EMBED Equation.3  ?>:07K205B, GB> 2KE>4 >?5@0F88 li O2;O5BAO 2E>4>< >?5@0F88 lj. @5>1@07>20=85 >?5@0F89 A2O70=> A 70B@0B>9 @5AC@A>2, ?>MB><C ?><8<> ;>38G5A:8E A2O759 <564C >?5@0F8O<8 =5>1E>48<> CG5ABL A2O78, >1CA;>2;5==K5 =0;8G85< >3@0=8G5=89 (r[fi(ui)](ur; li(Er , 345 ur - :>;8G5AB2> @5AC@A>2 r-3> B8?0, Er(E-?>4<=>65AB2> >?5@0F89, 70=OBKE 2K?>;=5=85< r-9 DC=:F88 8;8 ?>B@51;ONI8E @5AC@AK r-3> B8?0. -B8 A2O78 <>6=> 87>1@078BL 3@0D8G5A:8, ?>AB@>82 @5AC@A=K9 3@0D 2((V,H2), 2 :>B>@>< <=>65AB2> 25@H8= V=V1,...,Vm ?@54AB02;ONB A>1>9 8AB>G=8:8 @5AC@A>2. 0640O 4C30  EMBED Equation.3  ?>:07K205B, GB> 4;O >?5@0F88 lj B@51CNBAO @5AC@AK r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"5>@8O, <5B>4K 8 A@54AB20.  >2>G5@:0AA:: . "#, 2004. 27.81>@>2 .., 0:0@>2 !.!. =D>@<0F8>==K9 0=0;87 ?0F85=B0 2 ;5G51=>9 ?@0:B8:5//0B5@80;K <564C=0@>4=>9 =0CG=>9 :>=D5@5=F88 =D>@<0F8>==K9 ?>4E>4 2 5AB5AB25==KE, 3C<0=8B0@=KE 8 B5E=8G5A:8E =0C:0E. '.0ABL 2.  "030=@>3: " "#, 2004.. 28.$8=052 .., 81>@>2 .., 0:0@>2 !.!. =D>@<0F8>==K5 A5B8 ;5G51=KE CG@5645=89, 02B><0B878@>20==K5 @01>G85 <5AB0 2@0G0 8 @538AB@0B>@0//0B5@80;K XVII A5@>AA89A:>9 =0CG=>-B5E=8G5A:>9 :>=D5@5=F88 ABC45=B>2, <>;>4KE CG5=KE 8 A?5F80;8AB>2 8><54A8AB5<K - 2004.  O70=L:  ", 2004. 29.81>@>2 .., 0:0@>2 !.!. "@51>20=8O : @0A?@545;5==>9 8=D>@<0F8>==>9 A8AB5<5 CG@5645=89 A0=0B>@=>-:C@>@B=>3> =07=0G5=8O//0B5@80;K XVII A5@>AA89A:>9 =0CG=>-B5E=8G5A:>9 :>=D5@5=F88 ABC45=B>2, <>;>4KE CG5=KE 8 A?5F80;8AB>2 8><54A8AB5<K - 2005  O70=L:  ", 2005. 30.0:0@>2 !.!., $8=052 .., 81>@>2 .. @30=870F8>==0O AB@C:BC@0 8=D>@<0F8>==>9 <548F8=A:>9 A8AB5<K//0B5@80;K <564C=0@>4=>9 =0CG=>9 :>=D5@5=F88 &8D@>2K5 <5B>4K 8 B5E=>;>388. '0ABL 2.  "030=@>3: " "#, 2005. 8G=K9 2:;04 02B>@0 2 >?C1;8:>20==K5 2 A>02B>@AB25 @01>BK [1,2,3] ?>AB0=>2:0 7040G ?@>5:B8@>20=8O #!, @07@01>B:0 <>45;59 ?@8=OB8O @5H5=89 4;O 7040G C?@02;5=8O <548F8=A:8< CG@5645=85<;[4,12,15,18,19,22] >?@545;5=85 7040G8 4803=>AB8:8, @07@01>B:0 <>45;8 845=B8D8:0F88 A>AB>O=89 ?0F85=B0, ;5G5=8O 8 @5018;8B0F88; [5,7,11] <>45;8 3@C??>2>3> ?@8=OB8O @5H5=89; [6,14,21,23,29] 8458 B5E=8G5A:8E @5H5=89 ?@>5:B8@>20=8O #!, @07@01>B:0 <>45;59 AB@C:BC@=>3> A8=B570; [8] <5B>4 AB@C:BC@870F88 F5;8; [16] ?@8=F8? ?>AB@>5=8O =B5@=5BA8AB5<K A0=0B>@8O; [10,27] <5B>4K >1@01>B:8 8=D>@<0F88; [13]  845O ?@8=OB8O @5H5=8O > =09<5 @01>B=8:>2 A ?@8<5=5=85< M:A?5@B=KE >F5=>:; [20,24] >?@545;5=85 ?@>1;5<K 8 ?>AB0=>2:0 7040G8 ?@>5:B8@>20=8O @0A?@545;5==KE 8=D>@<0F8>==>-C?@02;ONI8E A8AB5<; [25,26] 845O B5E=8G5A:>3> @5H5=8O ?@8<5=5=8O A5B59 A0=0B>@8O; [28] AB@C:BC@0 02B><0B878@>20==KE @01>G8E <5AB 2@0G59 8 @538AB@0B>@0; [30] D>@<0;L=0O <>45;L >@30=870F8>==>9 AB@C:BC@K 8=D>@<0F8>==>9 A8AB5<K.     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