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AB>B=8< =54>;V:>< @O4V2, ?>1C4>20=8E 70 0@8D<5B8G=8<8 ?@>3@5AVO<8, T =5@V2=><V@=89 @>7?>4V; G;5=V2 @O4C 2 7040=8E <560E. &5 ?>OA=NTBLAO B8<, I> 2V4=>H5==O q =0ABC?=8E G;5=V2  EMBED Equation.3  4> ?>?5@54=VE  EMBED Equation.3  7<5=HCNBLAO 7V 71V;LH5==O< 7=0G5=L G;5=V2 25 @O4C. # =0H><C ?@8:;04V 4;O ?5@H8E G;5=V2  EMBED Equation.3  , 0 4;O >AB0==VE  EMBED Equation.3 .  0@8D<5B8G=8E ?@>3@5AVOE, O: ?>:07CT 40=89 ?@8:;04, A?>AB5@V30TBLAO @>7@V465=VABL G;5=V2 C 7>=V <0;8E 25;8G8= V A3CI5=VABL G;5=V2 C 7>=V 25;8:8E 25;8G8=. AB>@VN AB2>@5==O @O4V2 :@0I8E G8A5; ?>2'O7CNBL V7 4>A;V465==O<8 D@0=FC7L:>3> V=65=5@0 (0@;O 5=0@0, O:89 C 1877 - 1879 @@. @>7@>182 A?5F8DV:0FVN =0 :0=0B8 ?>2VB@O=8E :C;L 7 B0:8< @>7@0EC=:><, I>1 <>6=0 1C;> WE 283>B>28B8 70740;53V4L =570;56=> 2V4 ?>40;LH>3> 28:>@8AB0==O. ;O @>7@0EC=:C 5=0@ 70AB>AC202 35><5B@8G=C ?@>3@5AVN. O48 :@0I8E G8A5;, ?>1C4>20=V 70 35><5B@8G=8<8 ?@>3@5AVO<8, <0NBL AB0;5 2V4=>H5==O :>6=>3> =0ABC?=>3> G;5=0 @O4C  EMBED Equation.3  4> ?>?5@54=L>3>  EMBED Equation.3 . &5 2V4=>H5==O =07820NBL 7=0<5==8:>< ?@>3@5AVW  EMBED Equation.3 . 0?@8:;04, @O4 G8A5;: 1; 1,6; 2,5; 4; 6,3; 10; 16;.., - CB2>@NT 35><5B@8G=C ?@>3@5AVN 7V 7=0<5==8:>< q =1,6. 5><5B@8G=0 ?@>3@5AVO CB2>@5=0 70 70:>=><  EMBED Equation.3 , I> <>6=0 70?8A0B8 B0:8< A?>A>1><:  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 , EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3  V B.?., 45  EMBED Equation.3 - ?5@H89 G;5= ?@>3@5AVW; q - 7=0<5==8: ?@>3@5AVW; ? = 1,2,3,4,.., - ?>@O4:>289 =><5@ G;5=0 ?@>D5AVW. @0DV: 35><5B@8G=>W ?@>3@5AVW ?>40=89 =0 @8A.2.  8AC=>: 2  @0DV: 35><5B@8G=>W ?@>3@5AVW 0@07 4;O ?>1C4>28 @O4V2 :@0I8E G8A5; 28:>@8AB>2CNBL >1842V A8AB5<8, 0;5 G0ABVH5 70AB>A>2CNBL @O48, ?>1C4>20=V 70 35><5B@8G=8<8 ?@>3@5AVO<8. 030B>@VG=8< 4>A2V4>< CAB0=>2;5=>, I> 28<>38 2AVE 30;C759 ?@><8A;>2>ABV =091V;LH ?>2=> 704>2>;L=ONBL @O48 :@0I8E G8A5;, I> A:;040NBL 35><5B@8G=V ?@>3@5AVW 7V 7=0<5==8:><  EMBED Equation.3 , 45 E  ?>:07=8: ABC?5=O, I> 4>@V2=NT 5, 10, 20, 40, 80, 160. 0 707=0G5=8< ?@8=F8?>< ?>1C4>20=89 !" 8032-84. V= A:;045=89 7 C@0EC20==O< @5:><5=40FV9 V6=0@>4=>W >@30=V70FVW 7V AB0=40@B870FVW (ISO), 2AB0=>2;NT 4 >A=>2=V @O48 :@0I8E G8A5; V 2 4>40B:>2V. "01;8FO 1  A=>2=V ?0@0<5B@8 @O4V2 :@0I8E G8A5; O4#<>2=0 ?>7=0G:0 @O4C=0<5==8: ?@>3@5AV9'8A;> G;5=V2 C 45AOB:>2><C V=B5@20;VA=>2=89R5 R10 R20 R40 EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  5 10 20 40>40B:>2VR80 R160 EMBED Equation.3   EMBED Equation.3 80 160 @8 2AB0=>2;5==V @>7<V@V2, ?0@0<5B@V2 9 V=H8E G8A;>28E E0@0:B5@8AB8: WE 7=0G5==O 20@B> 1@0B8 7 >A=>2=8E @O4V2 :@0I8E G8A5;. @8 FL><C =5>1EV4=> =04020B8 ?5@5203C 25;8G8=0< @O4C R5, 0=V6 25;8G8=0< @O4C R10, 25;8G8=0< @O4C R10, 0=V6 25;8G8=0< R20, 25;8G8=0< R20, 0=V6 25;8G8=0< R40.  >:@5<8E B5E=VG=> >1@C=B>20=8E 28?04:0E AB0=40@B>< 4>?CA:0TBLAO 70AB>AC20==O 4>40B:>28E @O4V2 R80 V R160. A=>2=V @O48 =02545=V 2 B01;8FV 2, 4>40B:>2V 2 B01;8FV 3. >7=0G5==O @O4V2, >1<565=8E <560<8 V G8A;0<8, 28:>=CTBLAO B0:8< A?>A>1><: R5(...,40,...) - >A=>2=89 @O4 R5, =5 >1<565=89 25@E=L>N V =86=L>N <560<8, 0;5 7 >1>2'O7:>2>N =0O2=VABN G;5=0 40. R10(1,25,...) - >A=>2=89 @O4 r10, >1<565=89 G;5=>< 1,25 O: =86=L>N <565N. R40(75,...,300) - >A=>2=89 @O4 R40, >1<565=89 G;5=>< 75 O: =86=L>N <565N, G;5=>< 300 O: 25@E=L>N <565N. 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4,004,004,004,00246003,98110,474,25256254,21700,784,504,50266504,46680,744,75276754,73150,395,005,005,00287005,0119-0,245,30297255,30680,175,605,60307505,62340,426,00317755,95660,736,306,306,306,30328006,3096-0,156,70338256,68340,257,107,10348507,07950,297,50358757,49890,018,008,008,00369007,94330,718,50379258,41401,029,009,00389508,91250,989,50399759,44060,6310,010,010,010,040010,0000,00 "01;8FO 3  >40B:>2V @O48 R80R160R80R160R80R160R80R160123456781,001,0001,221,2201,501,5001,851,8501,0151,2301,5251,8751,031,0301,251,2501,551,5501,901,9901,0451,2651,5751,9251,061,601,281,2801,601,6001,951,9501,0751,3001,6251,9751,091,0901,321,3201,651,6502,002,0001,1051,3401,6752,0301,121,1201,361,3601,701,7002,062,0601,1351,3801,7252,0901,151,1501,401,4001,751,7502,122,1201,1651.4251,7752,150@>4>265==O B01;. 3 123456781,181,1801,4651,4501,801,8002,182,1801,1901,4751,8252,2102,242,2403,253,2504,754,7506,906,9002,2703,3004,8157,0002,302,3003,353,3504,874,8707,107,1002,3303,4004,9307,2002,362,3603,453,4505,005,0007,307,3002,2953,5005,0757,4002,432,4303,553,5505,155,1507,507,5002,4653,6005,2257,6252,502,5003,653,6505,305,3007,757,7502,5403,7005,3757,8752,582,5803,753,7505,454,4508,008,0002,6153,8105,5258,1252,652,6503,873,8705,605,6008,258,2502,6853,9355,7008,3752,722,7204,004,0005,805,8008,508,5002.7604,0605,9008,6252,802,8004,124,1206,006,008,758,7502,8504,1356,0758,8752,902,9004,254,2506,156,1509,009,0002,9504,3156,2259,1253,003,0004,374,3706,306,3009,249,2503,0354,4406,4009,3753,073,0704,504,5006,506,5009,509,5003,1104,5806,6009,6253,153,1504,624,6206,706,7009,759,7503,2004,6856,8009,87510,0010,000 @V< >A=>2=8E V 4>40B:>28E @O4V2 :@0I8E G8A5;, 4>?CA:0TBLAO 70AB>A>2C20B8 281V@:>2V @O48. 81V@:>2V @O48 :@0I8E G8A5; >45@6CNBL 2818@0==O< :>6=>3> 2, 3, 4,..., ?-3> G;5=0 >A=>2=>3> G8 4>40B:>2>3> 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:@0I8E G8A5;, ?>2'O70=V AB5?V==>N 70;56=VABN, B> 7=0<5==8:8 @O4V2, O:V 2>=8 CB2>@OBL, B0:>6 72'O70=V B0:>N A0<>N AB5?V==>N 70;56=VABN; - @O48 :@0I8E G8A5; 157<56=V 2 >1>E =0?@O<:0E. ;O ?5@5E>4C 2V4 :@0I8E G8A5;, =02545=8E C B01;8FV 2, C 1C4L-O:89 V=H89 45AOB:>289 V=B5@20;, ?>B@V1=> ?><=>68B8 FV G8A;0 =0 10*, 45 : - FV;5 4>40B=5 G8 2V4'T<=5 G8A;>, I> 287=0G0T ?>;>65==O 45AOB:>2>3> V=B5@20;C (=><5@ V=B5@20;C) 70 2V4=>H5==O< 4> V=B5@20;C 2V4 1 4> 10, 4;O O:>3> : = 0. #AV 45AOB:>2V V=B5@20;8 C 1V: 71V;LH5==O 01A>;NB=8E 7=0G5=L 1C4CBL <0B8 4>40B=5 : V 2 1V: 7<5=H5==O - 2V4'T<=5. "0:, 45AOB:>2V V=B5@20;8, @>7<VI5=V 70 G8A;>< 10, 1C4CBL <0B8 B0:V =><5@8: : = +1; +2; +3; +4 V B.4., 0 @>7<VI5=V 70 >48=8F5N 2V4?>2V4=>: : = -1; -3; -4 V B.?. @8 : = 1 :@0IV G8A;0 1C4CBL @>7<VI5=V 2 V=B5@20;V 2V4 10 4> 100, 0 ?@8 : - 2 - 2 V=B5@20;V 2V4 100 4> 1000. 0 0=0;>3VTN ?@8 : = -1 :@0IV G8A;0 1C4CBL @>7<VIC20B8AO 2 V=B5@20;V 2V4 0,1 4> 1,0 , 0 ?@8 : = -2 - 2 V=B5@20;V 2V4 0,1 4> 0,01. @0:B8G=> 7<5=H5==O :@0I8E G8A5; =0 10* 72>48BLAO 4> ?5@5=5A5==O :><8, I> 2E>48BL C :>6=5 G8A;>, =0 : 7=0:V2 ?@02>@CG (?@8 +:) G8 ;V2>@CG (?@8 +:). 0?@8:;04:  EMBED Equation.3  ;  EMBED Equation.3 . )>1 >45@60B8 ?>@O4:>289 =><5@ :@0I>3> G8A;0 N, I> 2V4?>2V40T 1C4L-O:><C V=B5@20;C, 28:>@8AB>2CNBL B0:C 70;56=VABL: N = NT + : " 40 , 45 NT - =><5@ G8A;0 ?> B01;8FV 2 (: = 0); - =><5@0 :@0I8E G8A5; N 2V4 0 4> 40 O2;ONBL A>1>N ;>30@8D<8 G8A5; @O4C R40 ?@8 >A=>2V ;>30@8D<V2, I> 4>@V2=NNBL 7=0<5==8:C ?@>3@5AVW (4;O @O4C R40, q=1,06). >30@8D<VG=89 72'O7>: <V6 =><5@0<8 :@0I8E G8A5; V 2V4?>2V4=8<8 :@0I8<8 G8A;0<8 2 FL><C 28?04:C 28@060TBLAO B0:8< A?>A>1><: q = 1, q1=1,06, q2 =1,12, q3=1,18, q40 = 10. 8:>@8AB>2CNG8 2;0AB82>ABV ;>30@8D<V2, <>6=0 7=0G=> A?@>AB8B8 V ?@8A:>@8B8 >1G8A;5==O, =5>1EV4=VABL C O:8E G0AB> 28=8:0T ?@8 ?>1C4>2V @O4V2 ?0@0<5B@V2: N3,15 +N1,6 = 20 + 8 =28, N1-N0,06 = 0 - (49) = 49. ><5@C 28 2V4?>2V40T G8A;> 5, 0 =><5@C 49 - G8A;> 17. )>1 ?V4=5AB8 :@0IV G8A;0 4> FV;>3> 4>40B=>3> 01> 2V4'T<=>3> AB5?5=O, ?>B@V1=> ?><=>68B8 =><5@ :@0I>3> G8A;0 =0 ?>:07=8: AB5?5=O, 0 ?>BV< C B01;8FV >A=>2=8E @O4V2 :@0I8E G8A5; 7=09B8 7=0G5==O, I> 2V4?>2V40NBL >B@8<0=><C ?>@O4:>2><C =><5@C: 3,152, N3,15 EMBED Equation.3  = 2 EMBED Equation.3  = 40. ><5@C 40 2V4?>2V40T G8A;> 10, >B65, 3,152 EMBED Equation.3  10. 5>1EV4=> ?0<'OB0B8, I> >1G8A;5==O 70 4>?><>3>N ?>@O4:>28E =><5@V2 40NBL =525;8:C ?>E81:C, A?@8G8=5=C @>71V6=>ABO<8 <V6 B5>@5B8G=8<8 :@0I8<8 G8A;0<8 9 >:@C3;5=8<8 G;5=0<8 >A=>2=8E @O4V2: - ?>G8=0NG8 2V4 @O4C R10, C G8A;0E @O4V2 <VAB8BLAO G8A;> 3,15, I> ?@81;87=> 4>@V2=NT G8A;C  EMBED Equation.3 . 2V4A8 28?;820T, I> 4>268=0 :>;0 V ?;>I0 :>;0, O:I> WE 4V0<5B@8 G8A;0 :@0IV, B0:>6 <>6CBL 1CB8 28@065=V :@0I8<8 G8A;0<8. &5 <>65 1CB8 70AB>A>20=> V 4> :@C3>28E H284:>AB59, ?>25@E>=L V >1AO3V2 F8;V=4@V2; - G;5=8 >4=>3> @O4C, ?V4=5A5=V 4> :204@0B0, 40NBL 1V;LH @V4:89 @O4: =0?@8:;04, O:I> G;5=8 @O4C R10 (1; 1,25; 1,6; 2,0) ?V4=5AB8 4> :204@0B0, B> >45@68<> @O4 R5 (1; 1,6; 2,5; 4,0 ). 2 >@<0;L=V ;V=V9=V @>7<V@8 091V;LH0 :V;L:VABL G8A;>28E 7=0G5=L, I> 70AB>A>2CNBLAO C B5E=VFV, ?@8?040T =0 G0AB:C ;V=V9=8E @>7<V@V2. # 72'O7:C 7 4>?CI5=8<8 >:@C3;5==O<8 >:@5<8E :@0I8E G8A5; 28:>@8AB0==O !" 8032-84 4;O 281>@C ;V=V9=8E @>7<V@V2 =5 702648 @0FV>=0;L=5. 0?@8:;04, :>=AB@C:B>@ C @57C;LB0BV @>7@0EC=:C <VF=>ABV >45@602 7=0G5==O 4V0<5B@0 22,2 <<. V4?>2V4=> 4> !" 8032-84 :>=AB@C:B>@ <V3 18 27OB8 @>7<V@ 4V0<5B@0 22,4 01> 22 <<. "><C =0 107V @O4V2 :@0I8E G8A5; @>7@>1;5=V @O48 =>@<0;L=8E ;V=V9=8E @>7<V@V2 (!" 6636-69), I> T >1>2'O7:>28<8 4;O 2AVE 30;C759 ?@><8A;>2>ABV 9 2AB0=>2;5=V 2 4V0?07>=V 2V4 0,001 4> 20000 <<. # 4V0?07>=V 2V4 0,001 4> 0,009 =>@<0;L=V ;V=V9=V @>7<V@8 ?>1C4>20=V 70 0@8D<5B8G=8< @O4>< 7 @V7=8F5N 0,001. @8 FL><C 7 C@0EC20==O< AD>@<>20=>W ?@0:B8:8 :>=AB@CN20==O 70<VABL 45O:8E :@0I8E G8A5; 27OBV WE >:@C3;5=V 7=0G5==O . 02545=V 2 !" 6636-69 ;V=V9=V @>7<V@8 ?>4V;ONBLAO =0 ;V=V9=V @>7<V@8 >A=>2=>3> 70AB>AC20==O V 4>40B:>2V ;V=V9=V @>7<V@8. V=V9=V @>7<V@8 >A=>2=>3> 70AB>AC20==O 2 707=0G5=><C 28I5 V=B5@20;V ?>1C4>20=V =0 107V @O4V2 R5, R10, R20, R40 V ?>7=0G5=V R05, R010, R020, R040 (1C:20 0 >7=0G0T, I> @O4 <VAB8BL >:@C3;5=V G8A;0). >=B@>;L=V 70?8B0==O 1. /:V G8A;0 =07820NBLAO :@0I8<8? 2. >OA=VBL ?@8=F8? ?>1C4>28 @O4V2 70 0@8D<5B8G=>N ?@>3@5AVTN. 0254VBL ?@8:;048. 3. /:V ?5@52038 ?>1C4>28 @O4V2 70 0@8D<5B8G=>N ?@>3@5AVTN? 4. 0254VBL ?@8:;048 ?>7=0G5==O @O4V2 :@0I8E G8A5;. 5. 072VBL >A=>2=V B0 4>40B:>2V @O48 :@0I8E G8A5;. , 6. )> O2;ONBL A>1>N >A=>2=V, 281V@:>2V @O48? 7. /:89 ?@8=F8? ?>7=0G5==O 0@8D<5B8G=>3> :@0I>3> @O4C? 8. 072VBL >A=>2=V 2;0AB82>ABV :@0I8E G8A5;. 9. 3 O:>N <5B>N @>7@>1;5=V @O48 =>@<0;L=8E ;V=V9=8E @>7<V@V2? !?8A>: ;VB5@0BC@8 1.!B0=40@B870F8O 8 C?@02;5=89 :0G5AB2>< ?@>4C:F88: CG51=8: 4;O 2C7>2 / ?>4 @54, ?@>D. ..(20=40@0. - " .", 2000. - 487 A. 2."0=LW38= .. A=>28 AB0=40@B870F88 8 C?@02;5==O :0G5AB2>< ?@>4C:F88: CG51=>5 ?>A>1=5. - 2-5 874. - : 740B5;LAB2> AB0=40@B>2, 1989. - 208 A. 3.>7;>2A:89 .!. A=>28 AB0=40@B870F88, 4>?CA:8, ?>A04:8 8 B5E=8G5A:85 87<5@5=8O/ .!.>7;>2A:89, ..8=>3@04>2 : CG51=8:. - .: 0H8=>AB@>5=85, 1979. - 224 A. 4.5@=5@ !. !B0=40@B870F8O - >A=>2K 7:>=><8:8. - .: 740B5;LAB2> AB0=40@B>2, 1967. - 205 A. 5.A=>2K AB0=40@B870F88 / ?>4 @54. .. ":0G5=:>. - .: 740B5;LAB2> AB0=40@B>2, 1969. - 395 A. 6.!" 6636 - 69. A=>2=K5 =>@<K 2708<>70<5=O5<>AB8. >@<0;L=K5 ;8=59=K5 @07<5@K. 7.!" 8032 - 84. @54?>GB8B5;L=K5 G8A;0 8 @O4K ?@54?>GB8B5;L=KE G8A5;. "  (>1>2 O7:>289) 0240==O 1 >7H8D@C20B8 ?>7=0G5==O @O4V2 (2V4?>2V4=> 4> 70?@>?>=>20=>3> 20@V0=B0) 70 B01;8F5N .1. "01;8FO .1 0@80=B>7=0G5==O @O4C1R5(& ,10,& )2R10(2,5;& )3R10(1,0;& ;8,0)4R20(118,& )5R20/3(125,& )6R20/4(& ,40)7R40/4(& ,63)8 EMBED Equation.3  R10(& ;2,5)9 EMBED Equation.3  R40(400,& ,80) 10 EMBED Equation.3 5 0240==O 2 1G8A;8B8 ?;>IC ?;>A:8E 4=8I V 287=0G8B8 2V4?>2V4=VABL @O4C @575@2C0@V2, 4V0<5B@8 O:8E 281@0=V 70 B0:8<8 @O40<8 2V4?>2V4=> 4> 28:>=C20=>3> 20@V0=B0 70 B01;8F5N .2. "01;8FO .2 0@80=B>7=0G5==O @O4C1R5(1,6;& ;4)2R5(2,5;& ;6,3)3R10(1,0;& ;2,0)4R10(2,5;& ;5,0)5R20(1,25;& ;1,8)6R20(2,24;& ;3,15)7R20/3(1,25;& ;3,55)8R40(1,4;& ;1,7)9R40/2(1,0;& ;1,6) 10R40/3(1,25;& ;2,12) ;O 1V;LH>W =0>G=>ABV 40=V @>7@0EC=:V2 725AB8 2 B01;8G=C D>@<C (B01;8FO .3). "01;8FO .3 80<5B@ 4=8I0, < O4  EMBED Equation.3 ;>I0 4=8I0, <2 O4  EMBED Equation.3  EMBED Equation.3  0240==O  81@0B8 @O48 ?0@0<5B@V2 V V d F8;V=4@8G=8E ?0:C20;L=8E T<=>AB59 V 287=0G8B8 ?>@O4:>2V =><5@8 G;5=V2 F8E @O4V2 =0 >A=>2V 40=8E, =02545=8E C B01;8FV .4. 1 0;56=VABL, I> 287=0G0T 72'O7>: ?0@0<5B@V2, <0T B0:89 283;O4:  EMBED Equation.3  45 V ->1'T< ?0:C20;L=>W T<=>ABV, <3; h - 28A>B0 T<=>ABV, <; d - 4V0<5B@ T<=>ABV, <. 2 ;O 287=0G5==O ?>@O4:>28E =><5@V2 G;5=V2 @O4C BW V=B5@20;V2 7=0G5=L @O4C A:>@8AB0T<>AO 40=8<8, =02545=8<8 7 B01;8FV .4. 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