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A?>;L7>20=85 <>45;8 A8AB5<K @5G52>A?@8OB8O ?>72>;O5B ?>;CG8BL 25:B>@K ?@87=0:>2, :>B>@K5 A>45@60B :0: A?5:B@0;L=CN, B0: 8 2@5<5==CN 8=D>@<0F8N, GB> =0<=>3> 8=D>@<0B82=55. 4=0:> ACI5AB2CNI85 <>45;8 3@><>74:8, <54;5==> @01>B0NB, 0 ?>;CG05<K5 ?@8 MB>< 40==K5 O2;ONBAO 8=D>@<0B82=K<8, => 2 B>65 2@5<O 8 G@57<5@=> 871KB>G=K<8, GB> =5 ?>72>;O5B 8E H8@>:> 8A?>;L7>20BL. 5A<>B@O =0 =0;8G85 87;>65==KE 2KH5 =54>AB0B:>2, ?@54;0305BAO 2 <>4C;5 &! 8A?>;L7>20BL <>45;L @5G52>A?@8OB8O, A<O3G82 =54>AB0B:8 A;54CNI8< >1@07><.  :0G5AB25 <>45;8 1078;O@=>9 <5<1@0=K ?@54;0305BAO 8A?>;L7>20BL <5B>4K 2592;5B-0=0;870. @8 MB>< B0:65 =5>1E>48<> =09B8 <5B>4 A60B8O ?>;CG5==KE 40==KE 157 ?>B5@8 8=D>@<0B82=>AB8. >45;L A8AB5<K @5G52>A?@8OB8O @01>B05B 2 B@8 MB0?0. 0 ?5@2>< MB0?5 >ACI5AB2;O5BAO <>45;8@>20=85 ?@5>1@07>20=89 2> 2=5H=5<, A@54=5< 8 2=CB@5==5< CE5. 0 2B>@><  <>45;8@>20=85 A?5:B@0;L=KE ?@5>1@07>20=89 2 C;8B:5 =0 1078;O@=>9 <5<1@0=5. 0 B@5BL5< MB0?5  <>45;8@>20=85 ?@5>1@07>20=89 A<5I5=8O 1078;O@=>9 <5<1@0=K 2 =5@2=K5 8<?C;LAK 2 >@30=5 >@B8. @5>1@07>20=85 A83=0;0 2 A8AB5<5 =0@C6=>3>, A@54=53>, 2=CB@5==53> CE0 <>6=> ?@54AB028BL :0: :0A:04 D8;LB@>2, AC<<8@CNI55 2>7459AB285 :>B>@KE 0=0;>38G=> A;54CNI5<C 2K@065=8N:  EMBED Equation.3 . (1) !<KA; MB>3> ?@5>1@07>20=8O 70:;NG05BAO 2 B><, GB> G5;>25G5A:89 A;CE 2>A?@8=8<05B A83=0;K A @07;8G=>9 G0AB>B>9 8 @02=>9 0<?;8BC4>9 :0: A83=0;K A @07;8G=K< C@>2=5< 3@><:>AB8. ! F5;LN >B@065=8O 40==KE ?@5>1@07>20=89 2 @07@010BK205<CN <>45;L 1K;0 22545=0 DC=:F8O yc(x), :><?5=A8@CNI0O 3@><:>ABL A83=0;0 =0 @07=KE G0AB>B=KE A>AB02;ONI8E. 0==0O DC=:F8O O2;O5BAO >1@0B=>9 ?> >B=>H5=8N : DC=:F88 y(x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quation.3 ,  EMBED Equation.3 . 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"0:8< >1@07><, ?@54;0305BAO 8=B5@?@5B8@>20BL 2KE>4K =59@>==KE A5B59 2 2845 =5G5B:8E AB5?5=59 ?@8=04;56=>AB8 ?@87=0:>2 0:CAB8G5A:>9 :;0AA8D8:0F88 72C:>2, 0 0;3>@8B< @0A?>7=020=8O D>=5< AB@>8BL =0 >A=>25 ?@028; =5G5B:>3> 2K2>40. @8 @07@01>B:5 <5B>40 @0A?>7=020=8O D>=5< 2 A8AB5<C ?@028; =5G5B:>3> 2K2>40 1K;0 22545=0 ;8=328AB8G5A:0O ?5@5<5==0O <(, T, X, G, M>, >?8AK20NICN 2E>4=K5 40==K5.  40==>< A;CG05 ( =  E>4=>9 @5G52>9 25:B>@ ; "  107>2>5 B5@<-<=>65AB2>, A>AB>OI55 87 =5G5B:8E ?5@5<5==KE <(, X, (>, 8<5=0 :>B>@KE A>>B25BAB2CNB ?@87=0:0< 0:CAB8G5A:>9 :;0AA8D8:0F88 72C:>2. 1;0ABLN >?@545;5=8O X =5G5B:8E ?5@5<5==KE O2;O5BAO <=>3><5@=>5 ?@>AB@0=AB2> 25:B>@>2 @5G52KE ?@87=0:>2. @8 MB>< DC=:F8O, >?8AK20NI0O AB5?5=L ?@8=04;56=>AB8 @5G52KE 25:B>@>2 87 X : A>>B25BAB2CNI59 =5G5B:>9 ?5@5<5==>9, D>@<8@C5BAO =0 MB0?5 >1CG5=8O =59@>==>9 A5B8. 5>1E>48<> >B<5B8BL, GB> :;0AA8G5A:89 A?>A>1 2KG8A;5=8O ;>38G5A:>9 A2O7:8   2 40==>< A;CG05 =5 ?>4E>48B, B.:. =5 >B@0605B 2 ?>;=>9 <5@5 55 A<KA;>2CN =03@C7:C. >MB><C 2 48AA5@B0F88 ?@54;0305BAO 8A?>;L7>20BL =5AB0=40@B=CN DC=:F8N, :>B>@0O M:2820;5=B=0 2KG8A;5=8N 35><5B@8G5A:>3> A@54=53>:  EMBED Equation.3 , (5) 345  EMBED Equation.3   AB5?5=L ?@8=04;56=>AB8 : A>>B25BAB2CNI59 =5G5B:>9 ?5@5<5==>9  EMBED Equation.3 . 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(7) "0:8< >1@07><, 1K;0 AD>@<8@>20=0 1070 87 36 =5G5B:8E =5G5B:8E ?@>4C:F89, 0=0;>38G=KE 2K@065=8N (7) 8 ?>;=>ABLN >?8AK20NI8E <=>65AB2> :;0AA>2 @0A?>7=0205<KE D>=5<. @8 @07@01>B:5 <5B>40 @0A?>7=020=8O A;>2, =5>1E>48<> @5H8BL 425 7040G8. 5@20O 70:;NG05BAO 2 @07@01>B:5 <5B>40 D>@<8@>20=8O H01;>=0 MB0;>==>3> A;>20 A>3;0A=> 2K1@0==>9 2 ?5@2>< @0745;5 <>45;8 A;>20. B>@0O  2 @07@01>B:5 <5B>40 A@02=5=8O 2E>4=>3> A;>20 A H01;>=><. CABL =0 2E>4 ?>4A8AB5<K :>=B@>;O :;NG52KE A;>2 ?>405BAO @5G52>9 A83=0;, A>>B25BAB2CNI89 A;>2C  =>;L . @54?>;>68<, GB> =0 2KE>45 0:CAB8:>-D>=5B8G5A:>3> <>4C;O 1K;0 ?>;CG5=0 ?>A;54>20B5;L=>ABL D>=5B8G5A:8E 25:B>@>2. ">340 8<55BAO 2>7<>6=>ABL 0=0;870 AB5?5=59 ?@8=04;56=>AB8 2A5E B@84F0B8 H5AB8 D>=5<. >2545=85 2> 2@5<5=8 AB5?5=8 ?@8=04;56=>AB8 4;O 3@C??K A>3;0A=KE D>=5< [=], [; ] 8 4;O D>=5<K [] ?>:070=> =0 @8AC=:5 4. 0: 284=> 87 @8AC=:0, AB5?5=L ?@8=04;56=>AB8 2 =0G0;5 D>=5<K 2>7@0AB05B, 70B5< 4>AB8305B >?@545;5==>3> <0:A8<C<0 2 A5@548=5 8 C1K205B 2 :>=F5, GB> >1JOA=O5BAO MDD5:B0<8 :>0@B8:C;OF88, B.5. 42865=8O<8 >@30=>2 @5G5>1@07>20=8O. >MB><C ?@54;0305BAO ?@54AB028BL <>45;L A;>20 2 2845 =01>@0 =5G5B:8E DC=:F89, :>B>@K5 1C4CB >B@060BL ?>2545=85 2> 2@5<5=8 AB5?5=8 ?@8=04;56=>AB8 :064>9 D>=5<K 2 A;>25, =0?@8<5@, :0: MB> ?>:070=> =0 @8AC=:5 5. @8 MB>< DC=:F8O, 8A?>;L7CNI0OAO 2 MB0;>==>< A;>25, 8<55B A;54CNI89 284:  EMBED Equation.3 , (8) 345 f1(x;a1,c1) 8 f2(x;a2,c2) ?@54AB02;ONB A>1>9 A83<>840;L=K5 DC=:F88, a1>0, a2<0- ?0@0<5B@K, >?@545;ONI85 =0:;>= DC=:F89, c1<c2- A<5I5=85, x=1,2,& ,n =><5@0 25:B>@>2 2 MB0;>==>< A;>25. "0:8< >1@07><, A ?><>ILN =01>@0 ?@>ABKE DC=:F89 <>6=> >?8A0BL ?>2545=85 AB5?5=8 ?@8=04;56=>AB8 :064>9 D>=5<K 2 MB0;>==>< A;>25. ;O >?@545;5=8O AB5?5=8 AE>65AB8 2E>4=>3> 8 MB0;>==>3> A;>2 8A?>;L7CNBAO <5B>4K =5G5B:>3> 48=0<8G5A:>3> ?@>3@0<<8@>20=8O, :>B>@K5 >A=>20=K =0 =01;N45=88, GB> >?B8<0;L=K9 ?CBL : B>G:5 (i, j) 2 42C<5@=>9 <0B@8F5 4>;65= ?@>E>48BL ;81> G5@57 B>G:8 (i-1, j), (i-1, j-1), (i, j-1), ;81> G5@57 B>G:8 (i, j-1), (i-1, j-1), (i-2, j-1). >7<>6=K5 20@80=BK 2K1>@0 >?B8<0;L=>3> ?CB8 ?>;=>ABLN 7028AOB >B @5H05<>9 7040G8. 1I89 >?B8<0;L=K9 ?CBL : B>G:5 (i, j) A 8A?>;L7>20=85< ?@028; =5G5B:>9 ;>38:8 >?@545;O5BAO A;54CNI8< A>>B=>H5=85<:  EMBED Equation.3  (9) 345 F(i,j) DC=:F8O M:2820;5=B=>AB8, >?@545;ONI0O A>>B25BAB285 <564C ?0@0<5B@0<8 MB0;>==>9 <>45;8 A;>20 2 <><5=B i 8 =58725AB=K< 2E>4=K< A;>2>< 2 <><5=B j; max(D) DC=:F8O 2K1>@0 >?B8<0;L=>3> 87 B@5E 2>7<>6=KE ?CB59.  :0G5AB25 DC=:F88 M:2820;5=B=>AB8 F(i,j) ?@54;0305BAO 8A?>;L7>20BL DC=:F8N M:2820;5=B=>AB8 ?> ?;>I048:  EMBED Equation.3  (10) 45AL 2 2K@065=88 (10) (xi(k) 7=0G5=85 AB5?5=8 ?@8=04;56=>AB8 k-9 D>=5<K 2 MB0;>==>< A;>25 2 <><5=B 2@5<5=8 i, (xj(k) 7=0G5=85 AB5?5=8 ?@8=04;56=>AB8 k-9 D>=5<K 2> 2E>4=>< A;>25 2 <><5=B 2@5<5=8 j. @>F54C@0 @5:C@A82=> 2KG8A;O5B @0AAB>O=85 AB>;15F 70 AB>;1F><, GB>1K >?@545;8BL >?B8<0;L=>5 >1I55 @0AAB>O=85 87 =0G0;L=>9 B>G:8 2 :>=5G=CN. ?5@0F8O =5G5B:>9 :>=JN=:F88 2KG8A;O5BAO 2 A>>B25BAB288 A 2K@065=85< (5).  48AA5@B0F88 1K;> @07@01>B0=> 420 <5B>40 D>@<8@>20=8O H01;>=0 MB0;>==>3> A;>20. 5@2K9 >A=>20= =0 ?@>F54C@5 >1CG5=8O. ;O MB>3> B@51C5BAO =0;8G85 @07<5G5==>9 107K 40==KE A;>2, 345 :064><C 72C:>2><C D09;C ?>AB02;5= 2 A>>B25BAB285 B5:AB>2K9 D09;, 2 :>B>@>< ?5@5G8A;5=K D>=5<K, 2E>4OI85 2 A>AB02 A;>20, 0 B0: 65 C:070=K 8E =0G0;> 8 :>=5F. 0 ?5@2>< MB0?5 ?@>F54C@K >1CG5=8O >?@545;O5BAO 4;8=0 MB0;>==>3> A;>20 L 2 :04@0E ?> 256 >BAG5B>2 A H03>< 128. 0;55 >?@545;O5BAO 4;8=0 8 F5=B@ :064>9 D>=5<K, ?>A;5 G53> 2KG8A;ONBAO ?0@0<5B@K A1 8 A2, >?@545;ONI85 284 DC=:F88 ?@8=04;56=>AB8 2 2K@065=88 (8). 0==0O ?@>F54C@0 2K?>;=O5BAO 4;O :064>3> A;>20, ?@8 MB>< =5>1E>48<>, GB>1K 2 >1CG5=88 CG0AB2>20;> :0: <>6=> 1>;LH55 :>;8G5AB2> 48:B>@>2. 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"030=@>3, 2000. A. 128-130. .@:>2 ..., 015=:> .., $54>@>2 .. @8<5=5=85 2592;5B-?@5>1@07>20=8O 4;O ?@54>1@01>B:8 @5G52KE A83=0;>2 2 A8AB5<5 @0A?>7=020=8O @5G8. 725AB8O " "#. !?5F80;L=K9 2K?CA:  0B5@80;K XLVI =0CG=>-B5E=8G5A:>9 :>=D5@5=F88 . "030=@>3: " "#, 2001. !1(19). .@:>2 ..., 015=:> .., $54>@>2 .. 0A?>7=020=85 D>=5< @CAA:>3> O7K:0 A ?><>ILN =59@>==KE A5B59 =0 >A=>25 2592;5B-?@5>1@07>20=8O. 0CG=>-B5E=8G5A:89 6C@=0;  59@>:><?LNB5@K. 07@01>B:0, ?@8<5=5=85 . !7-8, 2001. .@:>2 ... !8AB5<0 18><5B@8G5A:>9 0CB5=B8D8:0F88 ?>;L7>20B5;O ?> 3>;>AC A 8A?>;L7>20=85< =59@>==KE A5B59. 725AB8O " "#. "030=@>3: " "#, 2003. !4. A. 149-151. 0:0@528G .., 015=:> .., $54>@>2 .., .@:>2 ... "5:AB>=57028A8<0O 0CB5=B8D8:0F8O / 845=B8D8:0F8O ?> 3>;>AC 2 A8AB5<0E C?@02;5=8O 4>ABC?><. X A5@>AA89A:0O =0CG=>-?@0:B8G5A:0O :>=D5@5=F8O  @>1;5<K 8=D>@<0F8>==>9 157>?0A=>AB8 2 A8AB5<5 2KAH59 H:>;K . : $, 2003. A. 28-29. .@:>2 ..., 015=:> .., $54>@>2 .. 5B>4 D>@<8@>20=8O 25:B>@>2 ?@87=0:>2 =0 >A=>25 0:CAB8G5A:>9 <>45;8 @5G52>A?@8OB8O A 8A?>;L7>20=85< 2592;5B-?@5>1@07>20=8O 4;O A8AB5<K @0A?>7=020=8O @5G8. 0B5@80;K VI 564C=0@>4=>9 =0CG=>-?@0:B8G5A:>9 :>=D5@5=F88  =D>@<0F8>==0O 157>?0A=>ABL . "030=@>3: " "#, 2004. 015=:> .., $54>@>2 .., .@:>2 ... CB5=B8D8:0F8O 48:B>@0 A 8A?>;L7>20=85< 87<5=O5<>3> <=>65AB20 :;NG52KE A;>2. 725AB8O " "#. !?5F80;L=K9 2K?CA:  0B5@80;K =0CG=>9 :>=D5@5=F88 " "# . "030=@>3: " "#, 2004. !1. .@:>2 ... 59@>-=5G5B:89 0;3>@8B< @0A?>7=020=8O D>=5<. 0B5@80;K <564C=0@>4=>9 =0CG=>9 :>=D5@5=F88  >45;8@>20=85 CAB>9G82>3> @538>=0;L=>3> @0728B8O . 0;LG8:, 2005. A. 225-227. .@:>2 ... =0;87 @0A?>7=020=8O A;>2 A 8A?>;L7>20=85< <5B>4>2 =5G5B:>3> 48=0<8G5A:>3> ?@>3@0<<8@>20=8O.  A:CAAB25==K9 8=B5;;5:B . ISSN 1561-5359, 2005. !4. 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