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"01;8FO 1.1. 57C;LB0B8 28<V@N20==O 8<V@N20==O 0<?;VBC48 A83=0;C8<V@N20==O B@820;>ABV ?5@V>4C'0AB>B0 28<V@N20;L=>3> A83=0;C=0G5==O 70 >AF8;>3@0D>< >AF, =0G5==O 70 5;5:B@>==8< 2>;LB<5B@>< 52,   = (>AF -52) / 52 =0G5==O 70 >AF8;>3@0D>< t>AF, A=0G5==O 70 H:0;>N 35=5@0B>@0 t3, A  B =(t>AF -t3) / t3 >AF =1/">AF, :F 3 =1/"3,:F 57C;LB0B8, 7=0G5==O G0AB>B8 4>A;V46C20=>3> A83=0;C 70 H:0;>N 35=5@0B>@0, 0 B0:>6 @>7@0E>20=5 7=0G5==O ?5@V>4C 70?8A0B8 2 B01;. 1.1. 4. >2B>@VBL ?@>2545==O 4>A;V465==O 4;O =0ABC?=8E 70240=L 28:;040G0. 1@>1;5==O @57C;LB0BV2 0 >45@60=8<8 @57C;LB0B0<8 @>7@0EC20B8 2V4=>A=C ?>E81:C 28<V@N20==O  V B , 22060NG8 70 4V9A=V 7=0G5==O 28<V@N20;L=8E 25;8G8=, @57C;LB0B8 28<V@N20==O 0<?;VBC48, >B@8<0=V 5;5:B@>==8< 2>;LB<5B@>< 7-38 B0 70 H:0;>N 2V4;V:C G0AB>B8 28<V@N20;L=>3> 35=5@0B>@0 -112. @>18B8 28A=>2:8 I>4> 28<V@N20=L 0<?;VBC48 9 V=B5@20;V2 70 4>?><>3>N 40=>3> >AF8;>3@0D0, 7@CG=>ABV @>1>B8 7 =8<, ?5@5203 <5B>4V2, ?>:;045=8E 2 >A=>2C F8E 28<V@V2, ?>@V2=O=> 7 V=H8<8 2V4><8<8 <5B>40<8. 01>@0B>@=0 @>1>B0 ! 2 >A;V465==O E0@0:B5@8AB8: V ?0@0<5B@V2 1V?>;O@=>3> B@0=78AB>@0 5B0 @>1>B8: 7=OBBO 28EV4=>W B0 2EV4=>W E0@0:B5@8AB8: B@0=78AB>@0 V 287=0G5==O 70 E0@0:B5@8AB8:>N 9>3> ?0@0<5B@V2. "5>@5B8G=V 2V4><>ABV 0?V2?@>2V4=8:>289 1V?>;O@=89 B@0=78AB>@ O2;OT A>1>N 5;5:B@>==89 ?@8;04, 2 >A=>2V O:>3>  :@8AB0; V7 @V7=>N 70 284>< G5@3C20==O ?@>2V4=VABN, B>1B> =0?V2?@>2V4=8:>289 ?@8;04 V7 42><0 1;87L:> @>7<VI5=8<8 @-n  ?5@5E>40<8. @8 FL><C AB@C:BC@0 G5@3C20==O H0@V2 <>65 1CB8 01> @-n-@, 01> n-p-n (@8A. 2.1). !5@54=O 4V;O=:0 =07820TBLAO 107>N, 0 :@09=V  5<VB5@>< V :>;5:B>@><. V4?>2V4=V 4V;O=:0< 28E>48 B@0=78AB>@0 =07820NBLAO 107>28<8, 5<VB5@=8<8, :>;5:B>@=8<8. # @>1>BV B@0=78AB>@0 28:>@8AB>2CTBLAO ?@8=F8? C?@02;V==O ?>B>:>< =>AVW2 70@O4C 2 =0?V2?@>2V4=8:C ?@8 =0?@C7V 0,1  1 , I> ?@8:;0-40TBLAO 4> ?@O<>7<VI5=>3> 5<VB5@=>3> p-n  ?5@5E>4C. @8 FL><C =0 2V4<V=C 2V4 ;0<?8 40=89 B@0=78AB>@ T 5;5<5=B>< AB@C<>2>3> C?@02;V==O. >BV: =>AVW2 70@O4C 2V4 5<VB5@=>3> ?5@5E>4C <0965 ?>2=VABN, 70 28=OB:>< CB@0B =0 @5:><1V=0FVN 2 107>2V9 4V;O=FV, ?@>E>48BL 107>2C 4V;O=:C, 4>AO30T :>;5:B>@=>3> ?5@5E>4C V ?5@5=>A8BLAO A8;L=8< ?>;5< FL>3> ?5@5E>4C, AB2>@5=8< 7>2=VH=V< 465@5;><, C 4V;O=:C :>;5:B>@0. >BC6=VABL 28EV4=>3> A83=0;C 2 1030B> @07V2 <>65 ?5@528IC20B8 ?>BC6=VABL, :>B@0 28B@0G0TBLAO =0 C?@02;V==O 5<VB5@=8< ?5@5E>4><. 0;56=> 2V4 B>3>, O:89 5;5:B@>4 T 7030;L=8< 4;O 2EV4=8E V 28EV4=8E ;0=FN3V2, @>7@V7=ONBL B@8 A?>A>18 22V<:=5==O: V7 7030;L=>N 107>N  (@8A.2.2,0), V7 7030;L=8< 5<VB5@><  (@8A. 2.2,1), V7 7030;L=8< :>;5:B>@><  (@8A. 2.2,2). ;5:B@8G=V 2;0AB82>ABV B@0=78AB>@0 287=0G0NBLAO 2 >A=>2=><C 42><0 AV<59AB20<8 E0@0:B5@8AB8:: 2EV4=8<8 B0 28EV4=8<8. EV4=V E0@0:B5@8AB8:8, 73V4=> 7V AE5<>N 22V<:=5==O B@0=78AB>@0, ?>:07CNBL 70;56=VABL AB@C<C 2V4 =0?@C38 5<VB5@0 4;O AE5<8  G8 AB@C<C 1078 2V4 =0?@C38 1078 4;O AE5<8  V  ?@8 DV:A>20=8E 7=0G5==OE =0?@C38 :>;5:B>@0. EV4=V E0@0:B5@8AB8:8 45<>=AB@CNBL 70;56-=VABL AB@C<C :>;5:B>@0 2V4 =0?@C38 :>;5:B>@0 ?@8 DV:A>20=8E 7=0G5==OE AB@C<C 5<VB5@0 4;O AE5<8  B0 AB@C<C 1078 4;O AE5<8  V . V4;V: =0?@C3 ?@>2>48BLAO 2V4?>2V4=> 4> AE5<8 22V<:=5==O 2V4 7030;L=>3> 5;5:B@>40. 0 @8A.2.3 =02545=V ?@8:;048 2EV4=>W V 28EV4=>W E0@0:B5@8AB8: B@0=78AB>@0 4;O AE5<8 .  8A. 2.3 > 3>;>2=8E ?0@0<5B@V2, O:V E0@0:B5@87CNBL B@0=78AB>@, =0;560BL :>5DVFVT=B8 ?5@540GV 70 AB@C<>< 5<VB5@0  B0 AB@C<>< 1078 , I> 287=0G0NBL 7 C<>28  EMBED Equation.3 , U: 1 = const ;  EMBED Equation.3  , U: 5 = const. 5;8G8=8  V  2V4=>AOBLAO 4> ?5@28==8E ?0@0<5B@V2 B@0=78AB>@0 B0 ?>2 O70=V <V6 A>1>N  EMBED Equation.3 . ;O <0;8E A83=0;V2 B@0=78AB>@ <>65 1CB8 ?@54AB02;5=89 5:2V20;5=B=>N AE5<>N =0 >A=>2V DV78G=8E ?0@0<5B@V2. "0:, =0?@8:;04, ?@8 22V<:=5==V 70 AE5<>N  AE5<0 <0T 283;O4 (@8A. 2.4), 45 r5 , r: , r1 - 48D5@5=FV0;L=V >?>@8 5<VB5@0 V :>;5:B>@0, 0 B0:>6 >1 T<=89 >?V@ 1078 2V4?>2V4=>.  V?>;O@=89 B@0=78AB>@ <>65 1CB8 ?>40=89 B0:>6 C 283;O4V G>B8@8?>;NA=8:0 (@8A. 2.5). 2'O7>: <V6 2EV4=8<8 V 28EV4=8<8 25;8G8=0<8 G>B8@8?>;NA=8:0 <>65 1CB8 28@065=89 G5@57 h  ?0@0<5B@8 A8AB5<8 :5@C20==O U1 = h11 I1 + h12U2, I2 = h21 I1 + h22U2, 45 h11 = U1 /I1 ?@8 U2 = 0; h12 = U1 /U2 ?@8 I1 = 0; h21 = I2 /I1 ?@8 U2 = 0; h22 = I 2/U2 ?@8 I1 = 0. 5;8G8=0 h11 28<V@NTBLAO 2 ><0E B0 O2;OT A>1>N 2EV4=89 >?V@ G>B8@8?>;NA=8:0 ?@8 :>@>B:>70<:=5=><C 2E>4V, h12  157@>7<V@=0 25;8G8=0 V O2;OT A>1>N :>5DVFVT=B 72>@>B=>3> 72 O7:C 70 =0?@C3>N  ?@8 @>7V<:=5=><C 2E>4V, h21  B0:>6 157@>7<V@=0 25;8G8=0, 2>=0 287=0G0T :>5DVFVT=B ?5@540GV 70 AB@C<>< ?@8 :>@>B:>70<:=5=><C 28E>4V, 25;8G8=0 h22 28<V@NTBLAO 2 A8<5=A0E V O2;OT A>1>N 28EV4=C ?@>2V4=VABL G>B8@8-?>;NA=8:0 ?@8 @>7V<:=5=><C 2E>4V. ;O :>6=>W 7V AE5< 2:;NG5==O h  ?0@0<5B@8 <0NBL A2>T 7=0G5==O. 0 2EV4=8<8 V 28EV4=8<8 E0@0:B5@8AB8:0<8 h  ?0@0<5B@8 <>6CBL 1CB8 287=0G5=V 70 ?@8@>AB>< U1, U2, I1, I2, O: 284=> 7 @8A.2.1. !E5<V 22V<:=5==O B@0=78AB>@0  U1 2V4?>2V40T ?@8@VAB U51, U2 - @V7=8FO U:11  U:12, I1 - @V7=8FO I52  I51, I2  I:. $V78G=V ?0@0<5B@8 B0 h  ?0@0<5B@8 B@0=78AB>@0 O: G>B8@8?>;NA=8:0 ?>2 O70=V <V6 A>1>N ?52=8<8 A?V22V4=>H5==O<8 V, 7=0NG8 >4=C 7 3@C? ?0@0<5B@V2, 70 F8<8 A?V22V4=>H5==O<8 <>6=0 287=0G8B8 V=HC 3@C?C. "0:, 4;O AE5<8  ?0@0<5B@8 ?>2 O70=V =0ABC?=8<8 @V2=O==O<8: h111 = re+r1(1-), h211  EMBED Equation.3  -, h121 = r1 /r:, h221  EMBED Equation.3  1/r:. ;O AE5<8  h11e = r1 +re(1+), h21e  EMBED Equation.3  -, h12e  EMBED Equation.3 re /r:, h22e  EMBED Equation.3  1/r:. @8 @>1>BV B@0=78AB>@0 =0 ?V428I5=8E G0AB>B0E, :>;8 ?5@V>4 2EV4=>3> A83=0;C AB0T A?V2<V@=8< V7 G0A>< ?@>;L>BC 70@O4C G5@57 107C, :>5DVFVT=B ?5@540GV 70 AB@C<>< AB0T :><?;5:A=8<; BC G0AB>BC, =0 O:V9 :>5DVFVT=B8 ?5@540GV 70 AB@C<><  B0  AB0NBL C  EMBED Equation.3  @07V2 <5=H8<8, =07820NBL 3@0=8G=>N G0AB>B>N B@0=78AB>@0  V . 0 =5N AC4OBL ?@> G0AB>B=V 2;0AB82>ABV B@0=78AB>@0. '0AB>B=V 2;0AB82>ABV B@0=78AB>@0 287=0G0NBL B0:>6 T<=>ABV :>;5:B>@=>3> 9 5<VB5@=>3> ?5@5E>4V2 !: B0 !5. >@O4>: 28:>=0==O @>1>B8: 1. =OBBO E0@0:B5@8AB8: V >1G8A;5==O ?0@0<5B@V2 4;O AE5<8 . CG:8 @53C;N20==O @578AB>@V2 R1 B0 R2 CAB0=>28B8 4> C?>@C ?@>B8 3>48==8:>2>W AB@V;:8. V1@0B8 AE5<C 4;O 7=OBBO E0@0:B5@8AB8: =0 AB5=4V -4 (?0=5;L !1), O: ?>:070=> =0 @8A. 2.6. 2. V425AB8 4> AE5<8 =0?@C3C  EMBED Equation.3   2V4 465@5;0 ?>ABV9=>W =0?@C38. 3. 8<V@OB8 2EV4=C E0@0:B5@8AB8:C B@0=78AB>@0 1 = (U15) ?@8 U:5 = const:  8A. 2.6 0) CAB0=>28B8 =0?@C3C U:5 = 0 V, 7<V=NNG8 =0?@C3C U15, DV:AC20B8 AB@C< 1, 7@>182H8 6 - 8 2V4;V:V2. 0?@C3C 1078 281@0B8 ?@8 FL><C B0:, I>1 ?@>9B8 25AL 4V0?07>= AB@C<V2 2V4 0 4> <0:A8<0;L=>3>, 7040=>3> 28:;040G5<, 0 5:A?5@8<5=B0;L=V B>G:8 @>7B0HC20B8 @V2=><V@=> ?> >B@8<0=V9 :@82V9, @57C;LB0B8 70?8A0B8 2 B01;8FN 2.1; "01;8FO 2.1 U:5, >7=0G5==O 57C;LB0B8 28<V@N20=L0U15, 1, <-5U15, 1, <1) CAB0=>28B8 =0?@C3C U:5 = -5  V, ?V4B@8<CNG8 F5 7=0G5==O =57<V==8<, ?>2B>@8B8 28<V@N20==O =0?@C38 U15 B0 1, O: C ?>?5@54=L><C ?C=:BV. 4. =OB8 28EV4=C E0@0:B5@8AB8:C B@0=78AB>@0 4;O AE5<8  : = (U:5) ?@8 1 = const: 0) CAB0=>28B8 AB@C< 1078 1 = 1,0 <. V4B@8<CNG8 F5 7=0G5==O =57<V==8< V 7<V=NNG8 AB@81:0<8 =0?@C3C U:5, DV:AC20B8 =0?@C3C B0 AB@C< :>;5:B>@0 :. @>18B8 8-10 2V4;V:V2 C 4V0?07>=V =0?@C3, 7040=><C 28:;040G5<. 57C;LB0B8 70?8A0B8 2 B01;8FN 2.2; 1) ?>2B>@8B8 28<V@N20==O ?C=:BC (0) ?@8 AB@C<V 1078 1 = 2,5 <. 57C;LB0B8 70?8A0B8 2 B01;8FN 2.2; 2) 7@>18B8 BV 6 28<V@N20==O 4;O AB@C<C 1078 1 = 5,0 <. 57C;LB0B8 70?8A0B8 2 B01;8FN 2.2. 3) 7@>18B8 BV 6 28<V@N20==O 4;O AB@C<C 1078 1 = 7,5 <. 57C;LB0B8 70?8A0B8 2 B01;8FN 2.2. "01;8FO 2.2 1, <>7=0G5==O 57C;LB0B8 28<V@N20=L1,0U:5, :, <2,5U:5, :, <5,0U:5, :, <7,5U:5, :, < 1@>1;5==O @57C;LB0BV2 0 B01;8FO<8 2.1 V 2.2 ?>1C4C20B8 2EV4=V 9 28EV4=V E0@0:B5@8AB8:8 B@0=78AB>@V2. 87=0G8B8 =0 >A=>2V F8E 3@0DV:V2 7=0G5==O h  ?0@0<5B@V2 4;O 2V4?>2V4=8E AE5< C2V<:=5==O. >=B@>;L=V ?8B0==O 1. !D>@<C;N9B5 :>@>B:> ?@8=F8? @>1>B8 1V?>;O@=>3> B@0=78AB>@0. 2. # G><C >A>1;82VABL :5@C20==O AB@C<>< :>;5:B>@=>3> 1V?>;O@=>3> B@0=78AB>@0? 3. /: ?>7=0G0NBLAO =0?V2?@>2V4=8:>2V 1V?>;O@=V B@0=78AB>@8 V O:5 C<>2=5 ?>7=0G5==O F8E B@0=78AB>@V2, 28:>@8AB>2C20=8E C AE5<0E? 4. #:06VBL >A>1;82VABL C2V<:=5==O B@0=78AB>@V2 70 AE5<>N V7 7030;L=>N 107>N B0 70 AE5<>N V7 7030;L=8< 5<VB5@><. 5. /:C 70;56=VABL B@0=78AB>@0 287=0G0NBL 2EV4=V E0@0:B5@8AB8:8 ?@8 22V<:=5==V B@0=78AB>@V2 70 AE5<>N  V ? 6. >1@07VBL E0@0:B5@ 2EV4=8E E0@0:B5@8AB8: 4;O AE5< C2V<:=5==O  B0 . 7. /: 2?;820T 25;8G8=0 :>;5:B>@=>W =0?@C38 =0 ?>;>65==O :@82>W 2EV4=>W E0@0:B5@8AB8:8 B@0=78AB>@0? 8. /:C 70;56=VABL B@0=78AB>@0 287=0G0T 28EV4=0 E0@0:B5@8AB8:0 ?@8 22V<:=5==V B@0=78AB>@0 70 AE5<>N  V ? 9. >1@07VBL E0@0:B5@ 28EV4=8E E0@0:B5@8AB8: 4;O AE5< C2V<:=5==O B@0=78AB>@0  B0 . 10. /: 2?;820T 25;8G8=0 5<VB5@=>3> V 107>2>3> AB@C<C =0 ?>;>65==O :@828E 28EV4=8E E0@0:B5@8AB8: B@0=78AB>@0? 11. /:8<8 0=0;VB8G=8<8 28@070<8 <>6=0 287=0G8B8 :>;5:B>@=89 AB@C< B@0=78AB>@0? 12. /:V AE5<8 70<VI5==O 28:>@8AB>2CNBLAO ?@8 0=0;V7V B0 @>7@0EC=:C AE5< V7 B@0=78AB>@><? 13. 5@5@0EC9B5 9 >E0@0:B5@87C9B5 3@0=8G=> 4>?CAB8<V ?0@0<5B@8 B@0=78AB>@V2, =02545=V 2 4>2V4=8:0E. 14. /: 2?;820T B5<?5@0BC@0 =0 E0@0:B5@8AB8:8 V ?0@0<5B@8 B@0=78AB>@0? 15. /: ?V428I8B8 4>?CAB8<89 AB@C< :>;5:B>@0 B@0=78AB>@0? 16. /: ?>B@V1=> 1C;> 1 ?>1C4C20B8 AE5<C 28<V@N20==O 4;O 7=OBBO E0@0:B5@8AB8: G8 287=0G5==O ?0@0<5B@V2 B@0=78AB>@V2, I>1 =03@V20==O B@0=78AB>@0 2;0A=8< AB@C<>< ?V4 G0A ?@>2545==O 4>A;V4C =5 A?>B2>@N20;> @57C;LB0B8 28<V@N20==O? 17. /:V ?0@0<5B@8 V 28@078 E0@0:B5@87CNBL V=5@FV9=VABL 1V?>;O@=>3> B@0=78AB>@0? 18. /:V 4V0?07>=8 25;8G8= ?0@0<5B@V2 <0NBL ACG0A=V =87L:>G0AB>B=V, A5@54=L>G0AB>B=V 9 28A>:>G0AB>B=V B@0=78AB>@8, I> 28?CA:0NBLAO ?@><8A;>2VABN (:>5DVFVT=B8 ?5@540GV 70 AB@C<>< 1078, 4>?CAB8<V AB@C<8, 4>?CAB8<V ?>BC6=>ABV @>7AVN20==O, 4>?CAB8<V =0?@C38 <V6 :>;5:B>@>< V 5<VB5@><, 3@0=8G=V G0AB>B8, T<=>ABV :>;5:B>@=>3> ?5@5E>4C)? 19. 072VBL ?5@52038 B0 =54>;V:8 1V?>;O@=8E B@0=78AB>@V2 ?>@V2=O=> 7 ?>;L>28<8 B@0=78AB>@0<8. 01>@0B>@=0 @>1>B0 !3 !/ !%  //' 5B0 @>1>B8: 4>A;V465==O @V7=><0=VB=8E AE5< 28?@O<;5==O 7<V==>3> AB@C<C, ?>@V2=O==O ?>:07=8:V2 @>1>B8 F8E AE5<. 030;L=V 2V4><>ABV 8?@O<;OG5< =07820NBL ?@8AB@V9 4;O 157?>A5@54=L>3> ?5@5B2>@5==O 7<V==>3> AB@C<C 2 ?>ABV9=89. 8?@O<;OG C 7030;L=><C 28?04:C A:;040TBLAO 7 5;5:B@8G=8E 25=B8;V2, ?V4:;NG5=8E 70 ?52=>N AE5<>N, B0 4>40B:>28E ?@8AB@>W2 (B@0=AD>@<0B>@0, 5;5:B@8G=>3> DV;LB@0 V B. ?.).              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C;LACNG0 =0?@C30 =5 <0T ?5@V>48G=>3> 7=0:0, O: 7<V==0 =0?@C30, 0;5 ?5@V>48G=> 7<V=NTBLAO 70 25;8G8=>N. >=0 <>65 1CB8 ?@54AB02;5=0 O: U=U0+U7<V=, B>1B> AC<0 ?>ABV9=>W A:;04>2>W =0?@C38 U0 V =5A8=CA>W40;L=>W 7<V==>W =0?@C38 U7<V=. >ABV9=0 A:;04>20 ?@8 FL><C 2V4?>2V40T A5@54=L><C 7=0G5==N ?C;LACNG>W =0?@C38.  V=H>3> 1>:C, ?C;LACNG0 =0?@C30 O: ?5@V>48G=0 DC=:FVO <>65 1CB8 ?>40=0 C 283;O4V 30@<>=V9=>3> @O4C, B>1B> O: AC<0 ?>ABV9=>W A:;04>2>W B0 @O4C A8=CA>W40;L=8E =0?@C3 V7 A?04=>N, 70;56=> 2V4 ?>@O4:>2>3> =><5@0, 0<?;VBC4>N V 7@>AB0NG>N G0AB>B>N  EMBED Equation.3 . 1. ;O >4=>D07=8E >4=>?V2?5@V>4=8E AE5< 28?@O<;5==O  EMBED Equation.3  2. ;O >4=>D07=8E 42>?V2?5@V>4=8E AE5< 28?@O<;5==O  EMBED Equation.3  3. ;O B@8D07=8E >4=>?V2?5@V>4=8E AE5< 28?@O<;5==O  EMBED Equation.3  4. ;O B@8D07=8E 42>?V2?5@V>4=8E AE5< 28?@O<;5==O  EMBED Equation.3 , 45 =2f; f  G0AB>B0 28?@O<;5=>W =0?@C38, 2 =0H><C 28?04:C 50 F; Um <0:A8<0;L=5 7=0G5==O ?C;LACNG8E =0?@C3. <V==V A:;04>2V, I> 2E>4OBL C :@82V 28?@O<;5=>W =0?@C38, =07820NBL ?C;LA0FVO<8. E ?@89=OB> 287=0G0B8 70 =091V;LH>N @V7=8F5N <V6 <8BBT28<8 7=0G5==O<8 01> 70 2V4=>H5==O< 0<?;VBC48 =091V;LH 28@065=>W 30@<>=V9=>W A:;04>2>W 4> A5@54=L>3> 7=0G5==O =0?@C38 (?>ABV9=>W A:;04>2>W)  EMBED Equation.3 . &5 2V4=>H5==O =07820NBL :>5DVFVT=B>< ?C;LA0FV9. # B8E 28?04:0E, :>;8  EMBED Equation.3 , :>5DVFVT=B ?C;LA0FV9 <>6=0 28@078B8 O:  EMBED Equation.3 , 45 Umax i Umin  <0:A8<0;L=5 B0 <V=V<0;L=5 7=0G5==O 28?@O<;5=>W =0?@C38. ;O O:VA=>3> 28?@O<;5==O =5>1EV4=>, I>1 ?C;LA0FVO 1C;0 <V=V<0;L=>N. <VAB>< @>1>B8 T A?>AB5@565==O 70 D>@<>N 28?@O<;5=>W =0?@C38, @>7@0EC=>: >A=>2=8E ?>:07=8:V2 4;O :@828E V >B@8<0=8E =0?@C3. !?>AB5@565==O B0 7<V=0 =0?@C3 28:>=CTBLAO 2 40=><C 28?04:C 5;5:B@>==8< >AF8;>3@0D><, B><C ?5@54 ?>G0B:>< @>1>B8 =5>1EV4=> >7=09><8B8AO 7 V=AB@C:FVTN I>4> @>1>B8 7 >AF8;>3@0D>< (;01>@0B>@=0 @>1>B0 !1) V :5@C20B8AO =5N 2 ?@>F5AV 28<V@N20=L. V4 G0A 28<V@N20=L A;V4 >1>2 O7:>2> 725@B0B8 C203C =0 ?@028;L=VABL :0;V1@C20==O >AF8;>3@0D0, 0 B0:>6 A;V4:C20B8 70 ?@028;L=8< 2V4;V:>< 7=0G5=L Umax i Umin 2V4=>A=> =C;L>2>3> ?>;>65==O ?@><5=O. ;O 287=0G5==O ?>;>65==O =C;L>2>W ;V=VW =5>1EV4=> ?5@54 :>6=8< 28<V@N20==O< ?5@52V@OB8 @>7B0HC20==O ?@><5=O, O:5 2V4?>2V40T =C;N.  8A.3.2 >@O4>: 28:>=0==O @>1>B8 1) V1@0B8 AE5<C (@8A.3.2) =0 AB5=4V -4 (?0=5;L !5). 2) #2V<:=CB8 >AF8;>3@0D V 40B8 9><C ?@>3@VB8AO 5-7 E2. 3) V4 T4=0B8 >AF8;>3@0D =0 2EV4 28?@O<;ONG>W AE5<8 B0 70<V@OB8 25;8G8=C 2EV4=>W =0?@C38, 40=V 70?8A0B8. 4) V4 T4=0B8 >AF8;>3@0D 4> 28E>4C 28?@O<;ONG>W AE5<8 9 @>73;O=CB8 D>@<C >B@8<0=>W =0?@C38, 70<0;N20B8 E0@0:B5@ :@82>W, 70<V@OB8 <0:A8<0;L=5 B0 <V=V<0;L=5 <8BBT2V 7=0G5==O ?C;LACNG>W =0?@C38, 40=V 70?8A0B8. 5) 87=0G8B8 70 4>?><>3>N >AF8;>3@0D0 G0AB>BC ?C;LA0FVW 28?@O<;5=>W =0?@C38. @8 2AVE 28<V@0E ?5@5<8:0G >AF8;>3@0D0 9 @568< @>1>B8 2E>4C <0NBL AB>OB8 2 ?>;>65==V  EMBED Equation.3 . =OB8 >AF8;>3@0<8 :@828E D>@<8 =0?@C38 4;O 42>?V2?5@V>4=>3> @568<C @>1>B8 (70 4>?><>3>N ?5@5<8:0GV2 1 V 2), 0 B0:>6 V7 28:>@8AB0==O< V=4C:B82=>3> B0 T<=VA=8E DV;LB@V2 (?5@5<8:0GV 3, 4, 5). 1@>1;5==O >B@8<0=8E 40=8E 1) 1G8A;8B8 25;8G8=8 ?>ABV9=8E A:;04>28E B0 0<?;VBC48 =091V;LH 28@065=8E 30@<>=V:, 287=0G8B8 G0AB>BC F8E 30@<>=V: V :>5DVFVT=B8 ?C;LA0FVW. @8 >1G8A;5==V ?>ABV9=8E A:;04>28E, 0<?;VBC4 >A=>2=8E 30@<>=V: V :>5DVFVT=BV2 ?C;LA0FVW B C O:>ABV 0<?;VBC48 7<V==>W A:;04>2>W A;V4 1@0B8 <0:A8<0;L=89 :>5DVFVT=B, 0 2 O:>ABV ?>ABV9=>W A:;04>2>W G;5= @O4C, I> =5 70;568BL 2V4 G0AC (?5@H89 G;5=). '0AB>B0 f 287=0G0TBLAO 70 :>5DVFVT=B>< k ?@8 0@3C<5=BV t >A=>2=>W 30@<>=V:8 (fk=kf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ik. <V=0 :>;5:B>@=>3> AB@C<C AB2>@NT =0 >?>@V B0 :>;5:B>@V B@0=78AB>@0 7<V=C =0?@C38. >74V;N20;L=89 :>=45=A0B>@ !2 ?@>?CA:0T =0 RH BV;L:8 7<V==C A:;04>2C 28EV4=>3> AB@C<C. @8 2V4?>2V4=><C :>5DVFVT=BV ?5@540GV B@0=78AB>@0 ?> AB@C<C  B0 25;8G8=0E RK, RH, C2 =0?@C30 =0 =020=B065==V ?V4A8;N20G0 U28E 2 45:V;L:0 @07V2 ?5@528ICT 25;8G8=C 2EV4=>W =0?@C38 U2E. 0:A8<0;L=V :>5DVFVT=B8 ?V4A8;5==O B@0=78AB>@ <0T 4;O A5@54=VE G0AB>B; 28:>@8AB>2CNG8 DV78G=V ?0@0<5B@8 B@0=78AB>@0, 7=0G5==O :>5DVFVT=BV2 ?V4A8;5==O 40=>3> :0A:04C 4;O A5@54=VE G0AB>B <>6=0 287=0G8B8 B0:8< G8=><:  EMBED Equation.3  =0: <V=CA C =02545=V9 D>@<C;V 28@060T 7AC2 ?> D07V 28EV4=>W =0?@C38 ?V4A8;N20G0 2V4=>A=> 2EV4=>W =0 180.  EMBED Equation.3  45 Er, Rr   ! V 2=CB@VH=V9 >?V@ A83=0;C; r1,r5,r:  >?V@ B@0=78AB>@0 73V4=> 7 5:2V20;5=B=>N AE5<>N 70<VI5==O. EV4=89 >?V@ ?V4A8;N20;L=>3> :0A:04C R2E=R1||R2E=R1||[r1+(1+)r5 ]. 8EV4=89 >?V@  EMBED Equation.3 . 0 =87L:8E B0 28A>:8E G0AB>B0E :>5DVFVT=B ?V4A8;5==O 7=86CTBLAO V ?@8 45O:8E G0AB>B0E AB0T 1;87L:8< 4> =C;O. <5=H5==O :>5DVFVT=B0 ?V4A8;5==O =0 =87L:8E G0AB>B0E ?>OA=NTBLAO 71V;LH5==O< >?>@C @>74V;N20;L=8E :>=45=A0B>@V2 !1 V !2. 7 7<5=H5==O< G0AB>B8 2A5 1V;LH0 G0AB8=0 7<V==>W =0?@C38 2B@0G0TBLAO =0 >?>@0E @>74V;N20;L=8E :>=45=A0B>@V2. !?04 :>5DVFVT=BV2 ?V4A8;5==O =0 28A>:8E G0AB>B0E >1C<>2;5=89, ?>-?5@H5, 70;56=VABN :>5DVFVT=BV2 ?5@540GV 70 AB@C<><  V  2V4 G0AB>B8 B0, ?>-4@C35, =0O2=VABN T<=>AB59, 2;0AB828E A0<8< @ - ?  ?5@5E>40< B@V>40. 0;56=VABL <>4C;O :>5DVFVT=B0 ?V4A8;5==O 2V4 G0AB>B8 =07820NBL 0<?;VBC4=>-G0AB>B=>N E0@0:B5@8AB8:>N ?V4A8;5==O (@8A.4.2), 0 70;56=VABL D07>2>3> 7AC2C 28EV4=>W A8=CA>W48 =0?@C38 ?> 2V4=>H5==N 4> 2EV4=>W  D07>2>N E0@0:B5@8AB8:>N. V4=>H5==O <>4C;O :>5DVFVT=B0 ?V4A8;5==O =0 40=V9 G0AB>BV 4> <0:A8<C<C 7=0G5==O :>5DVFVT=B0 ?V4A8;5==O  EMBED Equation.3  =07820NBL :>5DVFVT=B>< G0AB>B=8E A?>B2>@5=L. =0G5==O G0AB>B, ?@8 O:8E :>5DVFVT=B8 A?>B2>@5=L AB0NBL @V2=8<8  EMBED Equation.3 , =>AOBL =072C 25@E=L>W B0 =86=L>W 3@0=8G=>W G0AB>B8 (?>7=0G0NBL f2 V f=), 0 @V7=8FN <V6 25@E=L>N B0 =86=L>N G0AB>B0<8 =07820NBL A<C3>N ?V4A8;5==O f = f2  f=.  >5DVFVT=B8 G0AB>B=8E A?>B2>@5=L =0 =86=VE G0AB>B=8E A?>B2>@5==OE <>6=0 @>73;O40B8 O: 4>1CB>: G0AB8E :>5DVFVT=BV2 A?>B2>@5==O ===1+=2, :>6=89 7 O:8E 287=0G0TBLAO 70 D>@<C;>N  EMBED Equation.3 , 45 =:  ?>ABV9=0 G0AC 4;O =87L:8E G0AB>B;  EMBED Equation.3  >5DVFVT=B ?V4A8;5==O 70 =0?@C3>N =0 =87L:8E G0AB>B0E <>65 1CB8 >1G8A;5=89 O:  EMBED Equation.3  030;L=89 :>5DVFVT=B G0AB>B=8E A?>B2>@5=L 4;O =87L:8E G0AB>B  EMBED Equation.3 . 0 28A>:8E G0AB>B0E 70;56=VABL :>5DVFVT=B0 ?V4A8;5==O 70 =0?@C3>N 2V4 G0AB>B8 <>65 1CB8 ?>40=0 C 283;O4V  EMBED Equation.3  45 2=+:  5:2V20;5=B=0 ?>ABV9=0 G0AC :0A:04C 2 >1;0ABV 28A>:8E G0AB>B;  EMBED Equation.3  :=!:(5)(rk(5)||R:||R=), 45 f2  3@0=8G=0 G0AB>B0 B@0=78AB>@0; !:(5), rk(5), R:, R=  ?0@0<5B@8, I> 2V4?>2V40NBL AE5<V 70<VI5==O :0A:04C (@8A.4.3).  >5DVFVT=B G0AB>B=8E A?>B2>@5=L =0 28A>:8E G0AB>B0E  EMBED Equation.3 . B65, 25@E=O 3@0=8G=0 G0AB>B0 :0A:04C, =0 O:V9 :>5DVFVT=B ?V4A8;5==O ?040T 2  EMBED Equation.3  @078,  EMBED Equation.3  <VAB>< @>1>B8 T 5:A?5@8<5=B0;L=5 7=OBBO 0<?;VBC4=>-G0AB>B=>W E0@0:B5@8AB8:8 ?V4A8;N20G0 B0 4>A;V465==O 2?;82C 25;8G8= !2, !28E, R= =0 E0@0:B5@ 0<?;VBC4=>-G0AB>B=>W E0@0:B5@8AB8:8 B@0=78AB>@=>3> :0A:04C ?V4A8;5==O.  O:>ABV 465@5;0 2EV4=>3> A83=0;C ?V4A8;N20G0 2 40=V9 @>1>BV 28:>@8AB>2CTBLAO 35=5@0B>@, 7<V=0 28EV4=>W =0?@C38 74V9A=NTBLAO >AF8;>3@0D>< 70 2:07V2:>N 28:;040G0 01> 5;5:B@>==8< 2>;LB<5B@><. 5@54 ?>G0B:>< @>1>B8 =5>1EV4=> >7=09><8B8AO 7 V=AB@C:FVTN I>4> @>1>B8 V7 F8<8 ?@8;040<8. >@O4>: 28:>=0==O @>1>B8 1. V1@0B8 AE5<C ;01>@0B>@=>W CAB0=>2:8 (=0 ?0=5;V !5, @8A.1): 0) ?V4:;NG8B8 4> <0:5B0 ?V4A8;N20G0 465@5;> 682;5==O ?>ABV9=>N =0?@C3>N  EMBED Equation.3  ; 1) ?V4:;NG8B8 4> 28E>4C ?V4A8;N20G0 35=5@0B>@ B8?C -112; 2) ?V4 T4=0B8 4> 28E>4C ?V4A8;N20G0 5;5:B@>==89 2>;LB<5B@ B8?C 7-38. 2. #2V<:=CB8 465@5;> ?>ABV9=>W =0?@C38, 35=5@0B>@, 2>;LB<5B@ G8 >AF8;>3@0D. 5=5@0B>@ ?@8 FL><C 2AB0=>2;NTBLAO =0 <V=V<0;L=5 28EV4=5 ?>;>65==O, 0 >AF8;>3@0D 01> 2>;LB<5B@  =0 <0:A8<0;L=C 3@0=8FN 28<V@N20=L. 3. =OB8 0<?;VBC4=>-G0AB>B=C E0@0:B5@8AB8:C ?V4A8;N20G0 ?@8 =>@<0;L=8E ?0@0<5B@0E R=, !1, !28E: KU=F(f): 0) ?>40B8 =0 2EV4 ?V4A8;N20G0 7040=C 28:;040G5< =0?@C3C A83=0;C; 1) ?V4B@8<C20B8 25;8G8=C 2EV4=>W =0?@C38 ?>ABV9=>N V, 7<V=NNG8 G0AB>BC 2V4 20 F 4> 200 F, 70<V@OB8 =0?@C3C =0 28E>4V U28E (27OB8 10-12 7=0G5=L G0AB>B8). 0=V 70?8A0B8 2 B01;8FN 4.1. 4. >A;V48B8 2?;82 =0 G0AB>B=C E0@0:B5@8AB8:C 7=0G5=L 25;8G8= !2, !5, R=: 0) 28:>=0B8 28<V@N20==O 70 ?C=:B>< 3 1 ?@8 22V<:=5=V9 (?0@0;5;L=> 4> :>=45=A0B>@0 !2) 4>40B:>2V9 T<=>ABV !2; "01;8FO 4.1 57C;LB0B8 28<V@N20==O B0 @>7@0EC=:V2 U2E=& .! 4>-A;V4C#<>28 4>A;V4Cf, F1!@2 !0 R=U28E, KU2!@2||!@2 C0 R=U28E, KU3!@2 !0||C28E R=U28E, KU4!@2 C0 R=|| R=U28E, KU 1) 28<:=CB8 4>40B:>2C T<=VABL !2 B0 ?@>25AB8 28<V@N20==O 70 ?C=:B>< 3 1 ?@8 2:;NG5=V9 4>40B:>2V9 T<=>ABV !28E ?0@0;5;L=> 28E>4C ?V4A8;N20G0; 2) 28<:=CB8 4>40B:>2C T<=VABL =0 28E>4V ?V4A8;N20G0 V 22V<:=CB8 70<VABL =5W 4>40B:>289 0:B82=89 >?V@ R=. 5@52V@8B8 28<V@8 73V4=> 7 ?C=:B>< 3 1. 0=V 70?8A0B8 2 B01;. 4.1. 1@>1;5==O @57C;LB0BV2 0 >A=>2V B01;. 4.1 ?>1C4C20B8 3@0DV:8 0<?;VBC4=>-G0AB>B=8E E0@0:B5@8AB8:, 287=0G8B8 4;O :>6=>W 7 =8E 25@E=V 9 =86=V 3@0=8G=V G0AB>B8 B0 A<C3C ?V4A8;5==O. @>0=0;V7C20B8 2?;82 =0 ?>:07=8:8 @>1>B8 ?V4A8;N20G0 70 =0?@C3>N 4;O A5@54=VE G0AB>B, >B@8<0=8E 5:A?5@8<5=B0;L=> 7 @>7@0EC=:>28< 7=0G5==O<. >=B@>;L=V ?8B0==O V 70240==O 1. #:06VBL, C G><C 2V4<V==VABL ?V4A8;N20==O 5;5:B@8G=8E A83=0;V2 2V4 ?V428I5==O =0?@C38 70 4>?><>3>N B@0=AD>@<0B>@0. 2. !D>@<C;N9B5 ?@8=F8? @>1>B8 B@0=78AB>@=>3> @578AB82=>3> ?V4A8;N-20;L=>3> :0A:04C. 3. >OA=VBL ?@87=0G5==O 5;5<5=BV2 AE5<8 4>A;V46C20=>3> ?V4A8;N20G0. 4. /:89 :>5DVFVT=B =07820TBLAO <0:A8<0;L=8< :>5DVFVT=B>< ?V4A8;5==O 70 =0?@C3>N, O: 28@078B8 70;56=VABL :>5DVFVT=B0 ?V4A8;5==O 70 =0?@C3>N 2V4 , R2E, R:, R=? 5. 0:@5A;VBL AE5<C 70<VI5==O 4;O 4>A;V46C20=>3> ?V4A8;N20G0. 6. )> O2;ONBL A>1>N 0<?;VBC4=>-G0AB>B=0 V D07>2>-G0AB>B=0 E0@0:B5@8AB8:8 ?V4A8;N20G0 B0 O:89 E0@0:B5@ 2>=8 <0NBL 4;O B@0=78AB>@=>3> @578AB82=>3> ?V4A8;N20G0? 7. )> @>7C<VNBL ?V4 25@E=L>N B0 =86=L>N 3@0=8G=8<8 G0AB>B0<8? 8. )> O2;OT A>1>N A<C30 ?V4A8;5==O? 9. V4 G>3> 70;568BL 7=865==O :>5DVFVT=B0 ?V4A8;5==O =0 =86=VE G0AB>B0E V G><C 4>@V2=NT =86=O 3@0=8G=0 G0AB>B0? 10. V4 G>3> 70;568BL 7=865==O :>5DVFVT=B0 ?V4A8;5==O =0 28A>:8E G0AB>B0E B0 G><C 4>@V2=NT 4;O 40=>3> ?V4A8;N20G0 25@E=O 3@0=8G=0 G0AB>B0? 11. /: 70;568BL G0AB>B=0 E0@0:B5@8AB8:0 1030B>:0A:04=>3> ?V4A8;N20G0 2V4 G0AB>B=8E E0@0:B5@8AB8: >:@5<8E :0A:04V2? 12. /:V T <>6;82>ABV ?@8 40=><C =020=B065==V ?V4A8;N20G0 ?V428I5==O <0:A8<0;L=>3> 7=0G5==O :>5DVFVT=B0 ?V4A8;5==O 70 =0?@C3>N? 13. /: 71V;LH8B8 25@E=N G0AB8=C 3@0=8G=>W G0AB>B8 ?V4A8;N20G0? 14. /: 7<5=H8B8 =86=N 3@0=8G=C G0AB>BC ?V4A8;N20G0? 15. /:0 E0@0:B5@8AB8:0 =07820TBLAO 0<?;VBC4=>N E0@0:B5@8AB8:>N ?V4A8;N20G0? 16. /:V ?@8G8=8 >1<56CNBL ;V=V9=C 4V;O=:C 0<?;VBC4=>W E0@0:B5@8AB8:8? 17. /:V ?@8G8=8 28:;8:0NBL A?>B2>@5==O ?V4A8;N20;L=>3> A83=0;C V O: ?V4V1@0B8 ?0@0<5B@8 ?V4A8;N20G0, I>1 703;CH8B8 <V=V<0;L=5 A?>B2>@5==O A83=0;C ?@8 ?V4A8;5==V? 18. 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"@0=78AB>@ V"2 70;8H0TBLAO 70:@8B8< (0 V"1  2V4:@8B8<), ?>:8 @>7@O48BLAO @>74V;>289 :>=45=A0B>@ !2, AB@C< @>7@O4C O:>3> G5@57 >?V@ R1 70:@820T B@0=78AB>@. >=45=A0B>@ !2 =0<030TBLAO ?5@570@O48B8AO, >A:V;L:8 ?VA;O 2V4:@820==O B@0=78AB>@0 V"2 B0 70:@820==O B@0=78AB>@0 !2 =0 ;0=FN3 :>=45=A0B>@0 !2 4VT V=H0 @V7=8FO ?>B5=FV0;V2. ;5 O: BV;L:8 B@0=78AB>@ V"2 ?>G=5 2V4:@820B8AO - 7=>2C 2ABC?0T 2 4VN ?>78B82=89 72>@>B=89 72'O7>: V 28=8:0T, O: @>73;O4C20;>AL 28I5, ;028=>- ?>4V1=89 ?@>F5A 2V4:@820==O B5?5@ C65 B@0=78AB>@0 V"2 B0 70:@820==O B@0=78AB>@0 V"1. # @57C;LB0BV @568< @>1>B8 AE5<8 <C;LB82V1@0B>@0 72>48BLAO 4> ?5@V>48G=>3> ?>G5@3>-2>3> 70:@820==O 9 2V4:@820==O B@0=78AB>@V2 V"1 B0 V"2. @8 FL><C, :>;8 B@0=78AB>@ 28O2;OTBLAO 2V4:@8B8<, 9>3> >?V@ =01030B> <5=H89, =V6 >?V@ @578AB>@0 R, ?>A;V4>2=> 2:;NG5=>3> 7 =8< C :>;5:B>@=><C ;0=FN7V, 0 =0?@C30 =0 B@0=78AB>@V <0965 @V2=0 =C;N, 2AO V=H0 =0?@C30 ?040T =0 :>;5:B>@=><C >?>@V @578AB>@0 R. >;8 6 B@0=78AB>@ 28O2;OTBLAO 70:@8B8<, B> 9>3> >?V@ =01030B> 1V;LH89, =V6 >?V@ R. &5 ?@82>48BL 4> <0965 ?@O<>:CB=>W D>@<8 :>;820=L =0?@C38 =0 :>;5:B>@V B@0=78AB>@V2 V 28=8:=5==O ?8;:>?>4V1=>W D>@<8 =0 WE 1070E, O: ?>:070=> =0 @8A. 5.3.  5@V>4 <C;LB82V1@0B>@0 (F8:; 9>3> @>1>B8) A:;040TBLAO V7 AC<8 B@820;>ABV V<?C;LAV2 B0 ?0C7 =0 :>;5:B>@0E B@0=78AB>@V2 01>, >A:V;L:8 B@820;VABL V<?C;LAC =0 :>;5:B>@V >4=>3> B@0=78AB>@0 @V2=0 ?0C7V V=H>3>, AC<V B@820;>ABV V<?C;LAV2 =0 :>;5:B>@0E B@0=78AB>@V2. T=tn1+tn2. "@820;VABL V<?C;LAC 2AB0=>2;NTBLAO ?5@V>4>< 70:@8B>3> AB0=C B@0=78AB>@0, O:89 C A2>N G5@3C 287=0G0TBLAO B@820;VABN @>7@O4C :>=45=A0B>@0, ?V4:;NG5=>3> 4> 1078.  5E09 C <><5=B, I> ?5@54CT ?5@5E>4C <C;LB82V1@0B>@0 2 =>289 AB0=, B@0=78AB>@ V"1 2V4:@8B89, 0 B@0=78AB>@ V"2 70:@8B89 (@8A. 5.2). 0?@C30, :>B@0 2V4?>2V40T ?@02V9 >1:;048=FV :>=45=A0B>@0 !4,  EMBED Equation.3 , 45 !  AB@C< 70:@8B>3> B@0=78AB>@0. 0?@C30, O:0 2V4?>2V40T ;V2V9 >1:;048=FV :>=45=A0B>@0 !4,  EMBED Equation.3 . B65, 2 <><5=B, I> ?5@54CT 70:@820==N B@0=78AB>@0 V"1, =0?@C30 =0 :>=45=A0B>@V !4 @V2=0 Uc4 H" E. VA;O 2V4:@820==O B@0=78AB>@0 V"2 (@8A.5.2) =0?@C30, O:0 2V4?>2V40T ?@02V9 >1:;048=FV :>=45=A0B>@0 !4, 28O28BLAO <0965 @V2=>N =C;N, B>1B> :>=45=A0B>@ !4 1C45 ?V4:;NG5=8< ?0@0;5;L=> 107V B@0=78AB>@0 V"1, ?@8G><C =0 107V 28O28BLAO ?>78B82=0 =0?@C30, I> 70:@820T B@0=78AB>@ V"1. ;5, 7 V=H>3> 1>:C, :>=45=A0B>@ 1C45 ?V4:;NG5=8< G5@57 >?V@ @578AB>@0 R2 4> =0?@C38  V, >A:V;L:8 2V= 70@O465=89 4> =0?@C38  7 ?@>B8;56=>N ?>;O@=VABN, 28<CH5=89 1C45 ?5@570@O460B8AO G5@57 >?V@ @578AB>@0 R2. >@O4>: 28:>=0==O @>1>B8: 8<V@OB8 70 4>?><>3>N >AF8;>3@0D0 ?5@V>4 :>;820=L "1 <C;LB82V1@0B>@0. 0B8A=CB8 :=>?:8 S1 B0 S2 V 70DV:AC20B8 =>25 7=0G5==O ?5@V>4C :>;820=L "2 <C;LB82V1@0B>@0. V4?CAB8B8 :=>?:C S1 B0 7=OB8 >AF8;>3@0<8 4;O 28?04:C =5A8<5B@8G=>3> <C;LB82V1@0B>@0. >7@0EC=:>25 7=0G5==O ?5@V>4C :>;820=L 287=0G0TBLAO V7 A?V22V4=>H5==O  EMBED Equation.3 , 45  EMBED Equation.3 ,  EMBED Equation.3  5:><5=4>20=0 ;VB5@0BC@0 >;>=B0T2AL:89 ..., !>A:>2 .. @><8A;>20 5;5:B@>=V:0 B0 <V:@>AE5<>B5E=V:0: B5>@VO V ?@0:B8:C<.  .: 0@025;0, 2003.  368 A. 0=0G52=89 .., !25@3C= ..$. 030;L=0 5;5:B@>B5E=V:0: B5>@VO V ?@0:B8:C<. - .: 0@025;0, 2003.  440 A. C45=:> .!., ><0H:> ./., "@8D>=N: .. @><8A;>20 5;5:B@>=V:0.  .: 81V4L, 1993.  432 A. LO:>=>2 .., 0:A8<GC: .., 5<=52 .., !<5@4>2 ... -=F8:;>?548O CAB@>9AB2 =0 ?>;52KE B@0=78AB>@0E.  .: !- , 2002.  512 A. 01@>48= ..!. @><KH;5==0O M;5:B@>=8:0.  .: KAH. H:>;0, 1982.  384A. C45=:> .!., !5=L:> .., '865=:> .. A=>2K ?@5>1@07>20B5;L=>9 B5E=8:8: #G51=8: 4;O 2C7>2.  .: KAH. H:>;0, 1980.  424 A. 5@0A8<>2 .., =O7L:>2 .., @0A=>?>;LA:89 .., !CE>@C:>2 .. A=>2K ?@><KH;5==>9 M;5:B@>=8:8: #G51=8: 4;O 2C7>2. - .: KAH. H:>;0, 1978.  336 A. 5@578=0 ".$., CA52 .., 0A;5==8:>2 .. 040G=8: ?> >1I59 M;5:B@>B5E=8:5 A >A=>20<8 M;5:B@>=8:8. - .: KAH. H:>;0, 1991.  380 A. ;C:5@ (.. @0:B8:C< ?> M;5:B@8G5A:8< 87<5@5=8O<. - .: >;>A, 1969.  244 A. #A0B5=:> !."., 0G5=N: ".., "5@5E>20 .. K?>;=5=85 M;5:B@8G5A:8E AE5< ?> !.- .: 740B5;LAB2> AB0=40@B>2, 1983.  325 A.      HYPERLINK "file:///E:\\87=5A\\!09B\\diplomrus.ru\\mydisser.com" mydisser.com - @0<>B=>5 8 :0G5AB25==>5 2K?>;=5=85 2A5E 284>2 =0CG=KE @01>B. !:84:8, >@838=0;L=>ABL, :>=B@>;L ?;0380B0, ?@O<>5 >1I5=85 A 02B>@><. 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