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(3) 7 A>>B=>H5=8O (3) 2K2>4OBAO CA;>28O, A2O7K20NI85 ;N1>9 87 ?0@0<5B@>2, ?@8=OBK9 70 =58725AB=CN 25;8G8=C, A 4@C38<8, 8725AB=K<8 ?0@0<5B@0<8. 0?@8<5@, 5A;8 8725AB=K A@54=85 4;8B5;L=>AB8 ?5@5=0;04>: 8 @5AC@AK ?>B>:>2, 8 ?>B>: j O2;O5BAO 1>;55 381:8<, G5< ?>B>: i , B> CA;>285 4;O <8=8<0;L=>3> G8A;0 ?5@5=0;04>:, ?@8 :>B>@>< ?>B>: j O2;O5BAO 8 1>;55 MDD5:B82=K< (?> ?>:070B5;N 2K?CA:0 =0 548=8FC @5AC@A>2), 8<55B 284: Nmin > (T (r ij " 1)) / (pi ( rij " kij )) , (4) =0;>38G=K5 CA;>28O <>3CB 1KBL 2K2545=K 87 A>>B=>H5=8O (3) 4;O A;CG052, :>340 «A2>1>4=K<8» O2;ONBAO 4@C385 ?5@5<5==K5, =0?@8<5@, r ij 8;8 kij , 0 N D8:A8@>20=>. "0:85 ?@8<5@K 2 48AA5@B0F88 @0AA<>B@5=K.  @01>B5 ?@>2545=> A@02=5=85 -, - 8  -?>B>:>2 A F5;LN >?@545;8BL, ?@8 :0:>< C@>2=5 =5AB018;L=>AB8 0AA>@B8<5=B0 :064K9 87 =8E O2;O5BAO =081>;55 MDD5:B82=K<. 0@0<5B@K 70B@0B @5AC@A>2 8 4;8B5;L=>AB8 ?5@5=0;04:8 =08<5=55 381:>3> -?>B>:0 1K;8 ?@8=OBK 70 548=8FC.  @0AG5B0E ?>;CG5=K A;54CNI85 7=0G5=8O: -?>B>: -- pA=0,75; -?>B>:  p=0,4;  -?>B>:  p =0,1. !>>B=>H5=8O <564C MB8<8 ?0@0<5B@0<8 8<5NB 284: @=0,56@ (k =0,56), @ =0,13@ (k =0,13) (A@54=85 4;8B5;L=>AB8 ?5@5=0;04:8 >F5=820;8AL 2 4>;OE >B ?@>4>;68B5;L=>AB8 @01>G59 A<5=K). B=>A8B5;L=K5 70B@0BK =0 DC=:F8>=8@>20=85 ?>B>:>2 ?@8=OBK @02=K<8 Res=1; Res=1,2; Res =1.8 (2 MB>< A;CG05 >F5=:8 @5AC@A>2 D0:B8G5A:8 A>2?040NB A :>MDD8F85=B0<8 A2O78: Resj=rij ). 0AG5BK ?> A>>B=>H5=8N (4) ?>:070;8: 5A;8 4;O ?@8<5@0 ?@8=OBL, GB> A@54=89 >1J5< 2K?CA:0 2 A<5=C @025= V=300 HB/A<, 0 4;8B5;L=>ABL ?5@8>40 T=20 A<5=, B> -?>B>: O2;O5BAO 1>;55 MDD5:B82=K<, G5< -?>B>:, 5A;8 G8A;> ?5@5=0;04>: ?@52KH05B 8 548=8F 70 ?5@8>4 (Nmin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×M , 8 4;O :064>9 i-9 >?5@0F88 (2 >1I5< A;CG05, ?>78F88, ?> :>B>@>9 ?@>872>48BAO A@02=5=85, =0?@8<5@, B8?C >1>@C4>20=8O) >?@545;O5BAO ?>:070B5;L ?>2B>@O5<>AB8 ri , @02=K9 G8A;C mi 8745;89, 2 B5E=>;>38OE :>B>@KE ?@8ACBAB2C5B 40==0O >?5@0F8O, C<5=LH5==><C =0 548=8FC, B> 5ABL, ri = mi --1, mi ¬ {1,2,& ,M}. 0:A8<0;L=>5 7=0G5=85 ?>:070B5;O ?>2B>@O5<>AB8 rmax = (M  1). 0:A8<0;L=0O (8450;L=0O) AB5?5=L >4=>@>4=>AB8 3@C??K 8745;89 4>AB8305BAO, :>340 2A5 >?5@0F88 (?>78F88) 8<5NB ?>:070B5;L ?>2B>@O5<>AB8 @02=K9 rmax.  :0G5AB25 >F5=:8 AB5?5=8 >4=>@>4=>AB8 3@C??K 8745;89 G ?@8=OB :>MDD8F85=B, >?@545;O5<K9 ?> D>@<C;5 K>4(G)=(" ri )/(N×rmax ) 8;8 K>4(G)=(" ri )/(N×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«?CAB>9»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