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A5 >=8 8<5NB ?@02> =0 ACI5AB2>20=85. 4=0:> 4;O :>=:@5B=>9 ?@0:B8:8 10=:0 1>;LH5 2A53> ?>4E>48B :;0AA8D8:0F8O, @0745;ONI0O 2A5 @8A:8 =0 B@8 1>;LH85 3@C??K 2 7028A8<>AB8 >B <5B>4>2, :>B>@K5 ?@8<5=ONBAO 4;O C?@02;5=8O 8<8: @8A:8 :>=B@035=B>2, ?>78F8>==K5 (@K=>G=K5) @8A:8, >?5@0F8>==K5 @8A:8 [20, A.98]. 8A:8 :>=B@035=B>2 0==K5 @8A:8 E0@0:B5@87CNB 7028A8<>ABL 10=:0 >B D8=0=A>2>3> A>AB>O=8O 8 ?>2545=8O 53> :;85=B>2 8;8 8E >?@545;5==KE 3@C??. 0I8B0 >B @8A:>2 :>=B@035=B>2 >ACI5AB2;O5BAO ?>A@54AB2>< CAB0=>2;5=8O 8=48284C0;L=KE 8;8 3@C??>2KE ;8<8B>2 =0 =8E 8 4825@A8D8:0F88 0:B82=KE 8 ?0AA82=KE >?5@0F89 10=:0. 8A:8 :>=B@035=B>2, 2 A2>N >G5@54L, 45;OBAO =0 425 3@C??K: :@548B=K5 @8A:8 8 @8A:8 7028A8<>AB8 >B B@51>20=89 :;85=B>2 8;8 3@C??K :;85=B>2. @548B=K9 @8A: >?@545;O5BAO :0: >B=>A8B5;L=0O 25;8G8=0 ?>B5@L, ?@8E>4OI8EAO =0 548=8FC 2K40==KE :@548B>2, 8 @0AAG8BK205BAO =0 >A=>25 :@548B=>9 8AB>@88 10=:0. @548B=K9 @8A: O2;O5BAO =081>;55 ACI5AB25==K< @8A:>< 2 10=:>2A:>9 AD5@5, 0 B0:65 =081>;55 @0A?@>AB@0=5==>9 ?@8G8=>9 D8=0=A>2KE C1KB:>2 2 10=:0E.  H8@>:>< :>=B5:AB5 40==K9 @8A: E0@0:B5@5= 4;O 1>;LH8=AB20 10=:>2A:8E >?5@0F89, >= ?@8ACI 2A5< 10;0=A>2K< 0:B820<, :>B>@K<8 2;0455B 10=:. 1I89 >1J5< ?>B5@L >B :@548B=KE >?5@0F89 <>6=> >F5=8BL :0: A>2>:C?=CN AC<<C >1O70B5;LAB2 705<I8:0 (8;8 8E 3@C??K) ?5@54 10=:><, C<=>65==CN =0 25@>OB=>ABL ?>B5@L ?@8 ?@>2545=88 :@548B=KE >?5@0F89. >4 25@>OB=>ABLN ?>B5@L >B ?@>2545=8O :@548B=KE >?5@0F89 ?>=8<05< A@54=NN 70 ?@54H5AB2CNICN 8AB>@8N @0728B8O 10=:0 4>;N =52>72@0B>2 :@548B>2 8 =52K?>;=5=8O ?@>G8E >1O70B5;LAB2 :;85=B0<8 (8;8 8E 3@C??0<8), 8<5NI8<8 ?>E>685 E0@0:B5@8AB8:8 8 ?>:070B5;8 :@548B>A?>A>1=>AB8. !>2>:C?=0O AC<<0 >1O70B5;LAB2 2:;NG05B: - 2K40==K5 :@548BK; - CGB5==K5 25:A5;O :;85=B0; - >25@4@0DB ?> @0AG5B=><C AG5BC 705<I8:0; - 30@0=B88 8 ?>@CG8B5;LAB20, 2KAB02;5==K5 2 ?>;L7C 40==>3> 705<I8:0; - 2A5 4@C385 ?@8=OBK5 =0 A51O 10=:>< >1O70B5;LAB20 ?> 2K?>;=5=8N ?;0B5659 70 :;85=B0 ?@8 >BACBAB288 45=53 =0 53> @0AG5B=>< AG5B5 (10=:>2A:85 0:F5?BK 8 ?>4B25@645==K5 0::@548B82K); - 4518B>@A:CN 704>;65==>ABL, 2>7=8:0NICN ?@8 :>=25@B0F88 20;NBK, ?>:C?:5 F5==KE 1C<03 ?> 70O2:0< :;85=B0 8 70:;NG5=88 @07;8G=>3> 2840 2AB@5G=KE A45;>: ( , !K 8 B.?.); - ?@>G85 7010;0=A>2K5 >1O70B5;LAB20 8 :>=B@0:BK (=0?@8<5@, D>@20@4=K5 :>=B@0:BK =0 <><5=B C@53C;8@>20=8O @0AG5B>2) 70 2KG5B>< AC<<K @K=>G=>9 AB>8<>AB8 70;>3>2 8 ?@>G8E 284>2 >15A?5G5=8O, ?>;CG5==KE >B :;85=B0. 8<8BK, >3@0=8G820NI85 >1J5<K :@548B=KE >?5@0F89 A >4=8< 8;8 3@C??>9 :;85=B>2, CAB0=02;820NBAO 8AE>4O 87 B>3> C@>2=O ?>B5@L, :>B>@K9 10=: A>3;0A5= ?>=5AB8 2 A2O78 A @50;870F859 :@548B=KE @8A:>2. @548B=K9 ;8<8B @025= >B=>H5=8N >1J5<0 4>?CAB8<KE ?>B5@L : 25@>OB=>AB8 ?>B5@L >B :@548B=KE >?5@0F89. 1J5< 4>?CAB8<KE ?>B5@L <>6=> >?@545;8BL, =0?@8<5@, :0: 4>;N :0?8B0;0 10=:0, B0: :0: 8<5==> :0?8B0; 2K?>;=O5B 70I8B=K5 DC=:F88 ?@8 @50;870F88 10=:>2A:8E @8A:>2. @8 C?@02;5=88 @5AC@A0<8 =5>1E>48<> >3@0=8G820BL :@548B=K5 @8A:8 A0<KE @07=>>1@07=KE 3@C?? 0:B82=KE >?5@0F89. SUM gi E ai(t) <= lim ai, 345 lim ai; - >3@0=8G5=8O =0 >1J5<K 0:B82=KE >?5@0F89 >?@545;5==>3> 2840; gi - :>MDD8F85=BK, >?@545;ONI85 :><18=0F8N @07;8G=KE 284>2 0:B82=KE >?5@0F89 2 7028A8<>AB8 >B ACI=>AB8 >3@0=8G5=8O; ai(t) - B5:CI0O AB>8<>ABL 0:B820 10=:0. "5:CI0O AB>8<>ABL :@548B>2 >F5=8205BAO :0: 8E 10;0=A>20O AB>8<>ABL 70 2KG5B>< >68405<>3> >1J5<0 =52>72@0B0. 'B>1K ?>;CG8BL A>3;0A>20==CN A8AB5<C ;8<8B>2, CG8BK20NICN 2A5 A>AB02;ONI85 A>2>:C?=>3> :@548B=>3> @8A:0, <>6=> ?@54AB028BL 53> :0: :><?>78F8N @8A:>2, 2>7=8:0NI8E ?@8 ?@>2545=88 >B45;L=KE 284>2 >?5@0F89. @8 MB>< 2K45;5=85 A>AB02;ONI8E A>2>:C?=>3> :@548B=>3> @8A:0 <>65B 84B8 2 =5A:>;L:8E =0?@02;5=8OE (@8A. 3). 4=0:> =5B =5>1E>48<>AB8 CAB0=02;820BL 2A5 2>7<>6=K5 284K ;8<8B>2, B0: :0: 8=0G5 =52>7<>6=> 1C45B 8E :>=B@>;8@>20BL. 0=: >?@545;O5B B>;L:> B5 87 =8E, :>B>@K5 A2O70=K A @50;L=> ACI5AB2CNI8<8 :@548B=K<8 @8A:0<8 (2 7028A8<>AB8 >B A8BC0F88 2 10=:5 8 >:@C60NI59 53> A@545). > ?@8 MB>< 2 7028A8<>AB8 >B <5AB0 2 85@0@E8G5A:>9 A8AB5<5, 345 40==K9 10=: =0E>48BAO, =5>1E>48<> >15A?5G8BL 53> A>3;0A>20==>ABL A> 2A5<8 4@C38<8 ;8<8B0<8 1>;55 2KA>:>3> C@>2=O, 8=0G5 A8AB5<0 >3@0=8G5=89 <>65B 1KBL ?@>B82>@5G82>9. 0=: 4>;65= >?@545;OBL 25;8G8=C 2A5E A2>8E :@548B=KE ;8<8B>2 =0 548=>9 <5B>48G5A:>9 >A=>25 8 @53C;O@=> 8E ?5@5A<0B@820BL, CG8BK20O ?@>8AE>4OI85 87<5=5=8O 2=CB@8 10=:0, 2 53> :;85=BA:>9 1075, 0 B0:65 2 M:>=><8:5 2 F5;><.   8A. 3. !B@C:BC@0 :@548B=KE ;8<8B>2 10=:0 8A: 7028A8<>AB8 >B B@51>20=89 :;85=B>2 8;8 3@C??K :;85=B>2 A2O70= A B5<, GB> ?@8 4>A@>G=>< 87JOB88 @5AC@A>2 :>=B@035=B0<8 10=: <>65B AB>;:=CBLAO A =5>1E>48<>ABLN ?@8>1@5B0BL MB8 @5AC@AK =0 <5610=:>2A:>< @K=:5 ?> 4>AB0B>G=> 2KA>:>9 F5=5 4;O ?>445@60=8O A2>59 ;8:284=>AB8. >;8G5AB25==> 40==K9 @8A: <>6=> @0AAG8B0BL :0: @07=8FC <564C ?@>F5=B0<8, C?;0G5==K<8 ?> ?>2KH5==>9 AB02:5, 8 4>3>2>@=K<8 ?@>F5=B0<8. @>F5=BK, C?;0G5==K5 ?> ?>2KH5==>9 AB02:5, @0AAG8BK20NBAO 8AE>4O 87 =082KAH59 AB02:8 <5610=:>2A:>3> @K=:0, :>B>@CN 10=: 4;O ?>445@60=8O A2>59 ;8:284=>AB8 2K=C645= 1C45B C?;0B8BL 70 @5AC@AK 2 A;CG05 4>A@>G=>3> 87JOB8O :;85=B>< A2>8E A@54AB2. 0I8B>9 >B @8A:>2 :>=B@035=B>2 B0: 65, :0: 8 >B :@548B=KE @8A:>2, A;C68B CAB0=>2;5=85 ;8<8B0 ?@82;5G5=8O A@54AB2 >B >4=>3> 705<I8:0 8;8 3@C??K 705<I8:>2. @8 MB>< 2 A>2>:C?=K9 >1J5< >1O70B5;LAB2 10=:0 ?5@54 53> :>=B@035=B0<8 2:;NG0NBAO: - =5A=8605<0O 25;8G8=0 >AB0B:>2 =0 @0AG5B=KE AG5B0E 8 :@548B>@A:>9 704>;65==>AB8; - 45?>78BK; - >1J5< @07<5I5==KE C 40==>3> 705<I8:0 25:A5;59 10=:0 8 4@C38E F5==KE 1C<03, ?@54?>;030NI8E 2>72@0B A@54AB2 ?@8 8E ?@54JO2;5=88. 8A:8 7028A8<>AB8 10=:0 >B :;85=B0 (8;8 8E 3@C??K) @0AA<0B@820NBAO ?@5645 2A53> 2 >B=>H5=88 >4=>3> 8;8 3@C??K 2708<>A2O70==KE :;85=B>2. > >=8 B0:65 4>;6=K CG8BK20BLAO ?> 3@C??0< :>=B@035=B>2, D>@<8@C5<K<: 0) 2 7028A8<>AB8 >B A?5F8D8:8 8E 45OB5;L=>AB8 (10=:8, ?@>G85 N@848G5A:85 ;8F0, =0A5;5=85); 1) 2 7028A8<>AB8 >B 8E D>@<K A>1AB25==>AB8 (D545@0;L=0O, <C=8F8?0;L=0O, G0AB=K5 D8@<K - @57845=BK, G0AB=K5 D8@<K - =5@57845=BK, D878G5A:85 ;8F0 - @57845=BK, D878G5A:85 ;8F0 - =5@57845=BK). 06=59H85 ;8<8BK 745AL - >3@0=8G5=85 >1J5<>2 ?@82;5G5=8O A@54AB2 =0 <5610=:>2A:>< @K=:5 8 >B =0A5;5=8O. 5@2K9 8AB>G=8: @5AC@A>2 <>65B ?>425AB8 87-70 B>3>, GB> <5610=:>2A:89 @K=>: ?@54>AB02;O5B, :0: ?@028;>, :>@>B:85 @5AC@AK 8 =081>;55 1KAB@> @5038@C5B =0 2A5 ?>;8B8G5A:85 A>1KB8O 8 M:>=><8G5A:85 <5@K 2>7459AB28O A> AB>@>=K &5=B@0;L=>3> 10=:0. 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