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V4?@8T<AB20 <>6CBL A0<>ABV9=> 74V9A=N20B8 ?5@5>FV=N20==O A2>WE >A=>2=8E D>=4V2 V @>7@0E>2C20B8 :>5DVFVT=B V=45:A0FVW, 0 <>6CBL 9>3> ?@>2>48B8 70 @>7?>@O465==O< >@30=V2 45@60=>W 2;048 B0 C?@02;V==O. ;O ?5@2VA=>W 9 2V4=>2;5=>W 20@B>ABV >A=>2=8E D>=4V2 VA=CT >FV=:0 70 ?>2=>N B0 70;8H:>2>N 20@BVABN. >2=0 20@BVABL >A=>2=8E D>=4V2 (!, 3@=.)  F5 20@BVABL C =>2><C, =57=>H5=><C AB0=V. 0 FVTN 20@BVABN >A=>2=V D>=48 2@0E>2CNBLAO =0 10;0=AV ?V4?@8T<AB20. 0;8H:>20 20@BVABL (!, 3@=.)  @50;L=0 20@BVABL >A=>2=8E D>=4V2, I5 =5 ?5@5=5A5=0 =0 20@BVABL 283>B>2;5=>W ?@>4C:FVW. 1G8A;NTBLAO 28@0EC20==O< 7=>AC >A=>2=8E D>=4V2 V7 ?>2=>W ?5@2VA=>W (?5@5>FV=5=>W) 20@B>ABV:  EMBED Equation.3 , (2.2) 45  EMBED Equation.3   AC<0 =0:>?8G5=>3> 7=>AC ?@>BO3>< 5:A?;C0B0FVW >A=>2=8E D>=4V2; 70AB>A>2CTBLAO O: 4> >:@5<>3> >1 T:B0, B0: V 4;O WE AC:C?=>ABV. V4=>2;5=0 20@BVABL 7 C@0EC20==O< 7=>AC ( EMBED Equation.3 , 3@=.):  EMBED Equation.3 . (2.3) V:2V40FV9=0 20@BVABL (!, 3@=.)  AC<0 3@>H>28E :>HBV2, O:C ?V4?@8T<AB2> >GV:CT >B@8<0B8 2V4 ;V:2V40FVW >A=>2=8E 70A>1V2 ?VA;O 70:V=G5==O AB@>:C WE :>@8A=>3> 28:>@8AB0==O, 70 28@0EC20==O< 28B@0B, ?>2 O70=8E V7 ;V:2V40FVTN. 287=0G0TBLAO >:@5<> ?> :>6=><C >1 T:BC. 0@BVABL, O:0 0<>@B87CTBLAO (!, 3@=.)  B0 20@BVABL, :>B@0 ?>28==0 1CB8 ?5@5=5A5=0 =0 28B@0B8 ?@>BO3>< CAL>3> AB@>:C :>@8ABC20==O >1 T:B>< >A=>2=8E D>=4V2; F5 ?5@2VA=0 01> ?5@5>FV=5=0 20@BVABL >A=>2=8E 70A>1V2 70 28@0EC20==O< WE ;V:2V40FV9=>W 20@B>ABV:  EMBED Equation.3 . (2.4) =>A V 0<>@B870FVO >A=>2=8E D>=4V2 A=>2=V D>=48 ?@>BO3>< A2>3> DC=:FV>=C20==O 707=0NBL DV78G=>3> A?@0FN20==O B0 <>@0;L=>3> AB0@V==O. >ABC?>20 2B@0B0 :>@8A=>ABV (A?>682G>W 20@B>ABV) ?V4 2?;82>< @V7=8E D0:B>@V2 =07820TBLAO 7=>A>< >A=>2=8E D>=4V2. =>A 1C20T DV78G=8< V <>@0;L=8<. $V78G=>3> 7=>AC >1 T:B8 >A=>2=8E D>=4V2 707=0NBL G5@57 A?@0FN20==O B0 ?V4 2?;82>< 7>2=VH=VE A8; (2VB@C, 4>IC, A=V3C B>I>). =0A;V4>: DV78G=>3> 7=>AC >A=>2=V D>=48 ?5@5AB0NBL 2V4?>2V40B8 28<>30<, O:V 4> =8E AB02;OBLAO. $0:B>@8, I> 2?;820NBL =0 DV78G=89 7=>A: O:VABL >A=>2=8E D>=4V2; C<>28 5:A?;C0B0FVW  ABC?V=L 7020=B065==O, O:VABL B5E=VG=>3> 4>3;O4C, @568< @>1>B8. $V78G=89 7=>A <>65 1CB8 CAC2=89 B0 =5CAC2=89. 5@H89 ;V:2V4>2CTBLAO H;OE>< ?@>2545==O @5<>=BV2, =5CAC2=89 ?@872>48BL 4> @C9=0FVW >A=>2=8E D>=4V2 V WE ;V:2V40FVW. >@0;L=5 7=>H5==O  7=5FV=5==O >A=>2=8E D>=4V2, 28:;8:0=5 745H52;5==O< 0=0;>3VG=8E (<>@0;L=89 7=>A ?5@H>3> @>4C) 01> ?>O2>N 1V;LH ACG0A=8E 27V@FV2 (<>@0;L=89 7=>A 4@C3>3> @>4C). >@0;L=89 7=>A 4@C3>3> @>4C G0AB:>2> CAC20TBLAO 70 @0EC=>: <>45@=V70FVW >A=>2=8E D>=4V2. $V78G=> 9 <>@0;L=> 7=>H5=V >A=>2=V D>=48 ?>B@51CNBL 70<V=8. >HB8 =0 2V4H:>4C20==O >A=>2=8E D>=4V2 =0:>?8GCNBLAO 70 @0EC=>: 0<>@B870FV9=8E 2V4@0EC20=L. <>@B870FVO >A=>2=8E D>=4V2  F5 ?>ABC?>25 2V4H:>4C20==O 28B@0B 2;0A=8:0 ?V4?@8T<AB20 =0 ?@8410==O 01> 22545==O 2 5:A?;C0B0FVN >A=>2=8E D>=4V2 H;OE>< =0@0EC20==O 0<>@B870FV9=8E 2V4@0EC20=L V 2V4=5A5==O WE =0 28B@0B8 28@>1=8FB20. >=OBBO 0<>@B870FVW 206;825 2 5:>=><VG=V9 =0CFV. 0@BVABL >A=>2=8E D>=4V2, I> 0<>@B87CTBLAO (!), @>7?>4V;OTBLAO ?@>BO3>< AB@>:C :>@8A=>3> 28:>@8AB0==O >1 T:B0 >A=>2=8E D>=4V2 C 283;O4V 0<>@B870FV9=8E 2V4@0EC20=L. # ?@0:B8FV 3>A?>40@N20==O <>6CBL 70AB>A>2C20B8AO @V7=V <5B>48 =0@0EC20==O 0<>@B870FVW. 0?@8:;04, <5B>4 @V2=><V@=>3> (?@O<>;V=V9=>3>) =0@0EC20==O: ?@8 28:>@8AB0==V <5B>4C ?V4?@8T<AB2> =0@0E>2CT V @>7?>4V;OT 0<>@B870FV9=V 2V4@0EC20==O @V2=8<8 I>@VG=8<8 G0AB8=0<8 ?@>BO3>< CAL>3> B5@<V=C 28:>@8AB0==O >1 T:B0. VG=0 AC<0 0<>@B870FVW 287=0G0TBLAO 4V;5==O< 20@B>ABV, I> 0<>@B87CTBLAO, =0 >GV:C20=89 B5@<V= 28:>@8AB0==O >1 T:B0 >A=>2=8E 70A>1V2:  EMBED Equation.3 , (2.5) 45  EMBED Equation.3   20@BVABL, I> 0<>@B87CTBLAO, 3@=.; "  B5@<V= :>@8A=>3> 28:>@8AB0==O >1 T:B0 >A=>2=8E D>=4V2, @>:8. A=>2=V ?@028;0 =0@0EC20==O 0<>@B870FVW 7 <5B>N CB@8<0==O ?>40B:C =0 ?@81CB>: ?V4?@8T<AB20 287=0G5=V 0:>=>< #:@0W=8  @> >?>40B:C20==O ?@81CB:C ?V4?@8T<AB2 . ;O FL>3> >A=>2=V D>=48 @>7?>4V;ONBL =0 G>B8@8 3@C?8. <>@B870FVO =0@0E>2CTBLAO I>:20@B0;L=> 70 =0ABC?=8<8 :20@B0;L=8<8 =>@<0<8: 1-H0 3@C?0  2%, 2-30 3@C?0  10%, 3-BO 3@C?0  6%, 4-B0 3@C?0  15 %. %0@0:B5@8AB8:0 =0O2=>ABV B0 AB0=C >A=>2=8E D>=4V2 0O2=VABL >A=>2=8E D>=4V2 E0@0:B5@87CTBLAO: <><5=B=8<8 ?>:07=8:0<8 =0 287=0G5=C 40BC (70;8H:>20 20@BVABL >A=>2=8E D>=4V2 ?V4?@8T<AB20 =0 1 AVG=O); A5@54=V<8 ?>:07=8:0<8 70 287=0G5=89 ?5@V>4 (AB>A>2=> >A=>2=8E D>=4V2 G0ABVH5 70 2A5 287=0G0NBL A5@54=L>@VG=C 20@BVABL >A=>2=8E D>=4V2). 5B>48 @>7@0EC=:C A5@54=L>@VG=>W 20@B>ABV >A=>2=8E D>=4V2 ( EMBED Equation.3 ): /:I> =5<0T <>6;82>ABV @>7@0E>2C20B8 F59 ?>:07=8: 1V;LH B>G=8< <5B>4><, >1G8A;NNBL 70 B0:>N D>@<C;>N:  EMBED Equation.3 , (2.6) 45  EMBED Equation.3 ,  EMBED Equation.3   2V4?>2V4=> 20@BVABL >A=>2=8E D>=4V2 =0 ?>G0B>: B0 :V=5FL 4>A;V46C20=>3> ?5@V>4C, 3@=.; /:I> 2V4><V 40=V ?@> 20@BVABL >A=>2=8E D>=4V2 70 >4=0:>2V ?@><V6:8 G0AC:  EMBED Equation.3 , (2.7) 45  EMBED Equation.3   20@BVABL >A=>2=8E D>=4V2 =0 ?>G0B>: V-3> ?5@V>4C, 3@=.; V  ?>@O4:>289 =><5@ 2V4B8=:C G0AC; n  :V;L:VABL 2V4B8=:V2 G0AC; /:I> 2V4><V 20@BVABL V G0A =04E>465==O B0 281CBBO >A=>2=8E 70A>1V2:  EMBED Equation.3 , (2.8) 45  EMBED Equation.3   20@BVABL V-3> >1 T:B0, I> =04V9H>2 ?@>BO3>< :0;5=40@=>3> @>:C, 3@=.;  EMBED Equation.3   :V;L:VABL ?>2=8E <VAOFV2 DC=:FV>=C20==O V-3> >1 T:B0, O:89 =04V9H>2 C :0;5=40@=><C @>FV;  EMBED Equation.3   20@BVABL j-3> >1 T:B0, I> 281C2 ?@>BO3>< :0;5=40@=>3> @>:C, 3@=.;  EMBED Equation.3   :V;L:VABL ?>2=8E <VAOFV2 DC=:FV>=C20==O j-3> >1 T:B0, O:89 281C2 C :0;5=40@=><C @>FV; n, m  2V4?>2V4=> :V;L:VABL >1 T:BV2, I> =04V9H;8 B0 281C;8 ?@>BO3>< :0;5=40@=>3> @>:C. "5E=VG=89 AB0= >A=>2=8E D>=4V2 E0@0:B5@87CNBL :>5DVFVT=B8 ?@840B=>ABV 9 7=>AC: >5DVFVT=B ?@840B=>ABV ( EMBED Equation.3 ) 287=0G0TBLAO 70 D>@<C;>N  EMBED Equation.3 , (2.9) 45  EMBED Equation.3   70;8H:>20 20@BVABL >A=>2=8E D>=4V2, 3@=.;  EMBED Equation.3   ?5@2VA=0 20@BVABL >A=>2=8E D>=4V2, 3@=. >5DVFVT=B 7=>AC ( EMBED Equation.3 ):  EMBED Equation.3 , (2.10) 45  EMBED Equation.3   AC<0 =0:>?8G5=>3> 7=>AC >A=>2=8E D>=4V2, 3@=. >:07=8:8 28:>@8AB0==O >A=>2=8E D>=4V2 D5:B82=VABL 28:>@8AB0==O >A=>2=8E D>=4V2 E0@0:B5@87CT A8AB5<0 C7030;L=NNG8E B0 G0AB:>28E ?>:07=8:V2. &O A8AB5<0 ?>1C4>20=0 =0 7VAB02;5==V >A=>2=8E @57C;LB0BV2 4VO;L=>ABV ?V4?@8T<AB20 70 ?52=89 ?5@V>4 (>1AO3C 284>1CB:C =0DB8, 307C, >1AO3C 28:>=0=8E @>1VB 7 5:A?;C0B0FV9=>3> V @>72V4C20;L=>3> 1C@V==O, 7V A?>@C465==O, @5<>=BC 9 45<>=B06C 1C@>28E 28H>:, ?@81CB:C B>I>) 7 =0O2=VABN >A=>2=8E D>=4V2. '0ABVH5 ?>:07=8:8 287=0G0NBL 70 @57C;LB0B0<8 @>:C. #7030;L=NNGV ?>:07=8:8: $>=4>2V440G0 ( EMBED Equation.3 ):  EMBED Equation.3 , (2.11) 45  EMBED Equation.3   >1AO3 28@>1=8FB20 ?V4?@8T<AB20 70 @V:;  EMBED Equation.3   A5@54=L>@VG=0 20@BVABL >A=>2=8E D>=4V2, 3@=. 0=89 ?>:07=8: T >A=>2=8< 4;O C7030;L=NNG>W >FV=:8 5D5:B82=>ABV 28:>@8AB0==O >A=>2=8E 28@>1=8G8E D>=4V2. :>=><VG=89 7<VAB ?>:07=8:0 @C=BCTBLAO =0 ?@8=F8?V 7VAB02;5==O >1AO3C 28@>1;5=>W ?@>4C:FVW 01> 28:>=0=8E @>1VB V7 AC:C?=>N 20@BVA=>N >FV=:>N 28:>@8AB0=8E 4;O 28@>1=8FB20 >A=>2=8E D>=4V2. $>=4>2V440G0 ?>:07CT, A:V;L:8 ?@>4C:FVW C 20@BVA=><C 28<V@V 2V440T =0< >4=0 3@82=O, 2:;045=0 2 >A=>2=V D>=48. 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A5@54=L>@VG=>W 20@B>ABV >A=>2=8E 28@>1=8G8E D>=4V2. # 284>1CB:C =0DB8 D>=4>2V440G0 287=0G0TBLAO @VG=8< >1AO3>< 284>1CB:C =0DB8 C B>==0E 01> C 3@>H>2><C 28@065==V =0 1 3@=. 20@B>ABV >A=>2=8E 28@>1=8G8E D>=4V2. # 307>284>1C2=V9 ?@><8A;>2>ABV ?>:07=8: D>=4>2V440GV @>7@0E>2CTBLAO O: 2V4=>H5==O 284>1CB>3> 307C 2 <5B@0E :C1VG=8E 4> A5@54=L>@VG=>W 20@B>ABV >A=>2=8E 28@>1=8G8E D>=4V2. >:07=8: D>=4>2V440GV C 3@>H>2><C 28@065==V 40T <>6;82VABL >FV=8B8 ABC?V=L 28:>@8AB0==O >A=>2=8E D>=4V2 7 C@0EC20==O< CAVTW ?@>4C:FVW, I> 28?CA:0TBLAO, 01> 2AVTW 28:>=0=>W @>1>B8.  B>9 A0<89 G0A D>=4>2V440G0 C =0BC@0;L=><C 28@065==V E0@0:B5@87CT 28:>@8AB0==O >A=>2=8E D>=4V2 BV;L:8 70 >A=>2=>N 4VO;L=VABN ?V4?@8T<AB20. 15@=5=8< 4> D>=4>2V440GV ?>:07=8:>< T D>=4>T<=VABL ( EMBED Equation.3 ):  EMBED Equation.3 . (2.12) $>=4>T<=VABL  F5 ?8B><89 ?>:07=8: ?>B@518 >A=>2=8E 28@>1=8G8E D>=4V2 4;O 70157?5G5==O 28:>=0==O >48=8FV @>1VB 01> 28@>1=8FB20 >48=8FV ?@>4C:FVW; ?>:07CT G0AB:C 20@B>ABV >A=>2=8E D>=4V2, O:V ?@8?040NBL =0 :>6=C 3@82=N 28@>1;5=>W ?@>4C:FVW. >6=0 287=0G0B8 ?>:07=8: D>=4>2V440GV V ?> 2V4=>H5==N 4> 20@B>ABV 0:B82=>W G0AB8=8 >A=>2=8E 28@>1=8G8E D>=4V2. $>=4>2V440G0 0:B82=>W G0AB8=8 D>=4V2 ( EMBED Equation.3 ):  EMBED Equation.3 , (2.13) 45  EMBED Equation.3   A5@54=O 20@BVABL 0:B82=>W G0AB8=8 >A=>2=8E D>=4V2 70 4>A;V46C20=89 @V:, 3@=. $>=4>@5=B015;L=VABL ( EMBED Equation.3 ):  EMBED Equation.3 , (2.14) 45    ?@81CB>:, >45@60=89 ?V4?@8T<AB2>< 70 4>A;V46C20=89 @V:, 3@=. $>=4>>71@>T=VABL ?@0FV @>1VB=8:V2 ( EMBED Equation.3 ):  EMBED Equation.3 , (2.15) 45  EMBED Equation.3   A5@54=L>>1;V:>20 G8A5;L=VABL @>1VB=8:V2 70 4>A;V46C20=89 @V:, G>;. >:07=8: D>=4>>71@>T=>ABV E0@0:B5@87CT @V25=L >71@>T=>ABV ?@0FV @>1VB=8:V2 70A>10<8 ?@0FV, ?>:07CT, A:V;L:8 3@825=L >A=>2=8E D>=4V2 ?@8?040T =0 >4=>3> @>1VB=8:0 ?V4?@8T<AB20. 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'0A =0:>?8G5==O @V48=8 70 C<>28 ?5@V>48G=>W 5:A?;C0B0FVW =0;568BL 4> @>1>G>3> G0AC. >5DVFVT=B 28:>@8AB0==O A25@4;>28= ( EMBED Equation.3 )  2V4=>H5==O AC<0@=>3> G0AC @>1>B8 A25@4;>28=, 28@065=>3> 2 A25@4;>28=>-<VAOFOE (A25@4;>28=>-4=OE 01> A25@4;>28=>-3>48=0E), 4> AC<0@=>3> :0;5=40@=>3> G0AC 5:A?;C0B0FV9=>3> D>=4C A25@4;>28=, 28@065=>3> C B8E A0<8E >48=8FOE:  EMBED Equation.3 . (2.16) >5DVFVT=B 5:A?;C0B0FVW A25@4;>28= ( EMBED Equation.3 )  F5 2V4=>H5==O AC<0@=>3> G0AC @>1>B8 A25@4;>28=, 28@065=>3> C A25@4;>28=>-<VAOFOE (A25@4;>28=>-4=OE 01> A25@4;>28=>-3>48=0E), 4> AC<0@=>3> :0;5=40@=>3> G0AC 70 4VNG8< D>=4>< A25@4;>28=, 28@065=>3> 2 B8E A0<8E >48=8FOE:  EMBED Equation.3 . (2.17) >5DVFVT=B 5:A?;C0B0FVW E0@0:B5@87CT ABC?V=L 28:>@8AB0==O C G0AV 4VNG8E A25@4;>28=, B>1B> =091V;LH 0:B82=>W G0AB8=8 D>=4C A25@4;>28=. =B5=A82=VABL 2V41>@C =0DB8 E0@0:B5@87CNBL 451VB8 A25@4;>28=. >7@V7=ONBL 451VB8 A5@54=L>4>1>2V 9 A5@54=L><VAOG=V. AB0==V 287=0G0NBL 70 2V4=>H5==O< 4> A25@4;>28=>-<VAOFV2 2V4?@0FL>20=8E B0 A25@4;>28=>-<VAOFV2, I> >1@0E>2CNBLAO 70 4VNG8< D>=4>< A25@4;>28=. !5@54=L>4>1>289 451VB A25@4;>28= (>4=VTW 01> 3@C?8  EMBED Equation.3 )  F5 A5@54=O :V;L:VABL =0DB8 (307C), 284>1CB0 70 4>1C 157?5@5@2=>W @>1>B8 A25@4;>28=8 (A25@4;>28=). V= 287=0G0TBLAO 2V4=>H5==O< 7030;L=>3> 284>1CB:C =0DB8 (307C) 4> G8A;0 A25@4;>28=>-4V1, 2V4?@0FL>20=8E A25@4;>28=>N (01> 3@C?>N A25@4;>28=) 70 >48= V B>9 A0<89 ?5@V>4 G0AC. '0A ?@>AB>N A25@4;>28=8 7 <5B>N =0:>?8G5==O @V48=8 70 C<>28 ?5@V>48G=>W 5:A?;C0B0FVW 2V4=>A8BLAO 4> @>1>G>3> G0AC. !5@54=L><VAOG=89 451VB =0 A25@4;>28=>-<VAOFL 2V4?@0FL>20=89 ( EMBED Equation.3 ) >1@0E>2CTBLAO 2V4=>H5==O< 7030;L=>3> 284>1CB:C =0DB8 (307C) 4> G8A;0 2V4?@0FL>20=8E A25@4;>28=>-<VAOFV2 (01> B8E, I> >1@0E>2C20;8AO 70 4VNG8< D>=4><) 70 B>9 65 G0A. A>1;82>ABV ?@8 287=0G5==V ?>:07=8:V2 5:AB5=A82=>3> 9 V=B5=A82=>3> 28:>@8AB0==O 1C@>2>W B5E=V:8, O:0 709<0T >A=>2=C ?8B><C 203C 2 7030;L=V9 20@B>ABV >A=>2=8E 28@>1=8G8E D>=4V2 1C@>28E ?V4?@8T<AB2: >5DVFVT=B 5:AB5=A82=>3> 28:>@8AB0==O 1C@>28E CAB0=>2>: ( EMBED Equation.3 ) 7=0E>4OBL B0::  EMBED Equation.3 , (2.18) 45  EMBED Equation.3  B0  EMBED Equation.3   G0A 709=OB>ABV 1C@>28E CAB0=>2>: 2V4?>2V4=> 2 1C@V==V 9 28?@>1C20==V;  EMBED Equation.3   :0;5=40@=89 G0A ?5@51C20==O 1C@>28E CAB0=>2>: =0 1C@>2><C ?V4?@8T<AB2V C 25@AB0B>-<VAOFOE, 25@AB0B>-4>10E, 25@AB0B>-3>48=0E. 5@AB0B>-<VAOFL  F5 C<>2=0 >48=8FO 28<V@N20==O G0AC 2 1C@V==V, I> 4>@V2=NT 30 25@AB0B>-4>10<, 01> 720 25@AB0B>-3>48=0<. =B5=A82=VABL @>1VB C 1C4V2=8FB2V A25@4;>28= 28<V@NNBL H284:>ABO<8 1C@V==O, O:V ?@89<0NBL 70 >A=>2C ?@8 287=0G5==V :>5DVFVT=B0 V=B5=A82=>3> 28:>@8AB0==O 1C@>28E CAB0=>2>:. 5E0=VG=0 H284:VABL ?@>E>4:8 ( EMBED Equation.3 , </3>4) 287=0G0TBLAO 4V;5==O< G8A;0 <5B@V2 ?@>E>4:8  EMBED Equation.3  ?> A25@4;>28=V ( 01> 3@C?V A25@4;>28=) =0 G0A <5E0=VG=>3> 1C@V==O  EMBED Equation.3  ( C 3>48=0E):  EMBED Equation.3 . (2.19) 5E0=VG=0 H284:VABL E0@0:B5@87CT V=B5=A82=VABL @C9=C20==O 3V@=8G8E ?>@V4. 59A>20 H284:VABL ?@>E>4:8 ( EMBED Equation.3 , </3>4) O2;OT A>1>N 2V4=>H5==O G8A;0 <5B@V2 ?@>E>4:8 ?> A25@4;>28=V (01> 3@C?V A25@4;>28=) 4> AC<0@=8E 70B@0B G0AC =0 <5E0=VG=5 1C@V==O  EMBED Equation.3  B0 A?CA:>-?V49><=V >?5@0FVW  EMBED Equation.3  ( C 3>48=0E)  EMBED Equation.3 . (2.20) 59A>20 H284:VABL E0@0:B5@87CT @07>< 7 V=B5=A82=VABN @C9=C20==O 3V@=8G8E ?>@V4 5D5:B82=VABL @>1VB 7V A?CA:C V ?V49><C 1C@>2>3> V=AB@C<5=BC. "5E=VG=0 H284:VABL 1C@V==O ( EMBED Equation.3 ) 287=0G0TBLAO 2V4=>H5==O< G8A;0 <5B@V2 ?@>E>4:8  EMBED Equation.3  ?> A25@4;>28=V (01> 3@C?V A25@4;>28=) 4> AC<0@=8E 28B@0B G0AC =0 28:>=0==O 2AL>3> :><?;5:AC B5E=VG=> =5>1EV4=8E 284V2 @>1VB  EMBED Equation.3 , 28@065=8E C 25@AB0B>-<VAOFOE:  EMBED Equation.3 . (2.21) "5E=VG=0 H284:VABL 1C@V==O E0@0:B5@87CT 5D5:B82=VABL ?@>2545==O 2AVE 284V2 @>1VB V7 1C@V==O A25@4;>28=: <5E0=VG=>3> 1C@V==O, A?CA:>-?V49><=8E >?5@0FV9, =0@>IC20==O V=AB@C<5=BC, :><?;5:AC 4>?><V6=8E @>1VB, :@V?;5==O A25@4;>28=, @5<>=B=8E @>1VB V @>1VB V7 70?>1V30==O CA:;04=5=L. ><5@FV9=0 H284:VABL 1C@V==O ( EMBED Equation.3 )  F5 2V4=>H5==O G8A;0 <5B@V2 ?@>E>4:8  EMBED Equation.3  ?> A25@4;>28=V (01> 3@C?V A25@4;>28=) 4> 7030;L=8E 70B@0B G0AC =0 1C@V==O  EMBED Equation.3 , 28@065=8E C 25@AB0B>-<VAOFOE:  EMBED Equation.3 . (2.22) ><5@FV9=0 H284:VABL T >4=8< V7 =09206;82VH8E ?>:07=8:V2. >=0 E0@0:B5@87CT =5 BV;L:8 5D5:B82=VABL B5E=VG=> =5>1EV4=8E 284V2 @>1VB, 0;5 40T >FV=:C ?>7028@>1=8G8< 28B@0B0< G0AC =0 CAC=5==O 020@VW, >@30=V70FV9=V ?@>AB>W B>I>. &8:;>20 H284:VABL 1C4V2=8FB20 A25@4;>28=8 ( EMBED Equation.3 ) 2V4>1@060T @57C;LB0B8 28:>@8AB>2C20==O G0AC ?> 2AL><C 28@>1=8G><C F8:;>2V. >=0 287=0G0TBLAO 2V4=>H5==O< G8A;0 <5B@V2 ?@>E>4:8  EMBED Equation.3  ?> A25@4;>28=V 01> 3@C?V A25@4;>28= 4> 7030;L=8E 70B@0B :0;5=40@=>3> G0AC ?> 2AL><C F8:;C 1C4V2=8FB20 .  EMBED Equation.3 . (2.23) 8E>4OG8 7V H284:>ABV 1C@V==O, :>5DVFVT=B V=B5=A82=>3> 28:>@8AB0==O 1C@>2>W  EMBED Equation.3  CAB0=>2:8 <>65 1CB8 ?@54AB02;5=89 O: 2V4=>H5==O A5@54=L>W :><5@FV9=>W H284:>ABV  EMBED Equation.3 4> <0:A8<0;L=> <>6;82>W C ?52=8E 28@>1=8G8E C<>20E  EMBED Equation.3 .  EMBED Equation.3 . (2.24) 0<VABL  EMBED Equation.3  <>6=0 28:>@8AB0B8 B5E=VG=C H284:VABL. >1CB>:  EMBED Equation.3  B0  EMBED Equation.3  40T 7030;L=5 CO2;5==O ?@> ABC?V=L 28:>@8AB0==O 1C@>28E CAB0=>2>:. >5DVFVT=B >15@B0==O 1C@>28E CAB0=>2>:  ?>:07=8:, I> E0@0:B5@87CT @V25=L 28@>1=8G>3> 28:>@8AB0==O 2 G0AV 1C@>28E CAB0=>2>:.  EMBED Equation.3 , (2.25) 45  EMBED Equation.3   G0A <>=B06=>-45<>=B06=8E @>1VB;  EMBED Equation.3   G0A ?V43>B>2G8E @>1VB 4> 1C@V==O;  EMBED Equation.3   G0A 1C@V==O V :@V?;5==O;  EMBED Equation.3   G0A 28?@>1C20==O;  EMBED Equation.3   G0A @5<>=B=8E @>1VB;  EMBED Equation.3   G0A ?5@51C20==O 1C@>28E CAB0=>2>: C @575@2V. 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FV=N20==O C 4=OE 70?0AC ?>:07CT, =0 A:V;L:8 4=V2 =>@<0;L=>W 157?5@51V9=>W @>1>B8 ?V4?@8T<AB2> <>65 70157?5G8B8 28@>1=8G89 ?@>F5A <0B5@V0;L=8<8 @5AC@A0<8. >7@V7=ONBL B0:V 2848 70?0AV2 C 4=OE: B@0=A?>@B=89; ?V43>B>2G89; ?>B>G=89; @575@2=89 (AB@0E>289). "@0=A?>@B=89 70?0A  =5 ?>28=5= ?5@528IC20B8 2 4=V2, >1>@>B=V :>HB8 2:;040NBLAO =0 ?5@V>4 V7 <><5=BC >?;0B8 28AB02;5=>3> ?>AB0G0;L=8:>< @0EC=:C 4> ?@81CBBO 20=B06C =0 A:;04. 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quation.3 , (3.1) 45  EMBED Equation.3 ,  EMBED Equation.3   2V4?>2V4=> 70;8H:8 >1>@>B=8E 70A>1V2 =0 ?>G0B>: B0 =0 :V=5FL 4>A;V46C20=>3> <VAOFO, 3@=.; - 70 :20@B0;  EMBED Equation.3 , (3.2) 45 V  =><5@ <VAOFO 4>A;V46C20=>3> :20@B0;C;  EMBED Equation.3   A5@54=L><VAOG=89 70;8H>: >1>@>B=8E 70A>1V2 V-3> <VAOFO 4>A;V46C20=>3> :20@B0;C; - 70 @V:  EMBED Equation.3 , (3.3) 45 V  =><5@ <VAOFO 4>A;V46C20=>3> @>:C;  EMBED Equation.3   A5@54=L><VAOG=89 70;8H>: >1>@>B=8E 70A>1V2 V-3> <VAOFO 4>A;V46C20=>3> @>:C. !CB=VABL >1>@>B=8E :>HBV2 B0 WE :@C3>>1V3 1>@>B=V 70A>18 74V9A=NNBL :@C3>>1V3, ?>A;V4>2=> ?@>E>4OG8 3@>H>2C, ?@>4C:B82=C, B>20@=C D>@<8:   "    "   . 0  AB04VW >1>@>B=V 70A>18 7<V=NNBL 3@>H>2C D>@<C =0 B>20@=C (3@>HV 28:>@8AB>2CNBLAO =0 703>BV2;N 28@>1=8G8E 70?0AV2); =0  AB04VW 945 ?@>F5A A?>6820==O ?@54<5BV2 ?@0FV C 28@>1=8FB2V V WE ?5@5B2>@5==O 2 3>B>2C ?@>4C:FVN (@>1>B8, ?>A;C38); =0  AB04VW >1>@>B=V 70A>18 C 283;O4V 3>B>2>W ?@>4C:FVW (@>1VB, ?>A;C3) 71V;LH5=>W 20@B>ABV 2ABC?0NBL C AD5@C >1V3C 9 =01C20NBL 7=>2C 3@>H>2>W D>@<8. 1V;LH5==O AC<8 3@>H59 C AD5@V 28@>1=8FB20 2V41C20TBLAO 70 @0EC=>: ?@0FV CG0A=8:V2 28@>1=8G8E ?@>F5AV2. #=0A;V4>: 157?5@5@2=>3> :@C3>>1V3C >1>@>B=V 70A>18 ?>ABV9=> B0 >4=>G0A=> 7=0E>4OBLAO =0 2AVE 9>3> AB04VOE. !C:C?=VABL 3@>H>28E :>HBV2 ?V4?@8T<AB20, =5>1EV4=8E 4;O D>@<C20==O 9 70157?5G5==O :@C3>>1V3C 28@>1=8G8E >1>@>B=8E D>=4V2 V D>=4V2 >1V3C, =07820NBL >1>@>B=8<8 :>HB0<8 ?V4?@8T<AB20. D5:B82=VABL 28:>@8AB0==O >1>@>B=8E 70A>1V2 # ?@>F5AV DC=:FV>=C20==O ?V4?@8T<AB20 702648 28=8:0T ?8B0==O ?@> >FV=N20==O 5D5:B82=>ABV 28:>@8AB0==O 28@>1=8G8E @5AC@AV2. D5:B82=VABL 28:>@8AB0==O >1>@>B=8E :>HBV2 E0@0:B5@87CTBLAO H284:VABN WE >15@B0==O, >1>@>B=VABN. 1>@>B=VABN =07820TBLAO >1>@>B >1>@>B=8E 70A>1V2, 28<V@O=89 C G0AV. :>=><VG=5 7=0G5==O >1>@>B=>ABV ?>;O30T 2 B><C, I> 2V4 =5W 70;568BL 25;8G8=0 =5>1EV4=8E ?V4?@8T<AB2C AC< 3@>H>28E :>HBV2 4;O 74V9A=5==O ?@>F5AC 28@>1=8FB20 V @50;V70FVW ?@>4C:FVW. >:07=8:0<8 >1>@>B=>ABV (5D5:B82=>ABV 28:>@8AB0==O) >1>@>B=8E 70A>1V2 T: :>5DVFVT=B >1>@>B=>ABV (); :>5DVFVT=B 7020=B065==O (70:@V?;5==O) (); B@820;VABL >4=>3> >1>@>BC 2 4=OE (). >5DVFVT=B >1>@>B=>ABV ( EMBED Equation.3 , >1.) ?>:07CT, A:V;L:8 >1>@>BV2 74V9A=NNBL >1>@>B=V :>HB8 70 4>A;V46C20=89 ?5@V>4.  EMBED Equation.3 , (3.4) 45  EMBED Equation.3   28@CG:0 2V4 @50;V70FVW ?@>4C:FVW (B>20@V2, @>1VB, ?>A;C3) 70 4>A;V46C20=89 ?5@V>4 (157  B0 0:F87C), 3@=.;  EMBED Equation.3   A5@54=V9 70;8H>: >1>@>B=8E 70A>1V2 70 B>9 65 ?5@V>4, 3@=. >5DVFVT=B 7020=B065==O (70:@V?;5==O) ( EMBED Equation.3 , 3@=./3@=.)  ?>:07=8:, >15@=5=89 ?>:07=8:C >1>@>B=>ABV; ?>:07CT, A:V;L:8 >1>@>B=8E :>HBV2 ?V4?@8T<AB20 ?@8?040T =0 >4=C 3@82=N @50;V7>20=>W ?@>4C:FVW.  EMBED Equation.3 . (3.5) "@820;VABL >4=>3> >1>@>BC ( EMBED Equation.3 , 4=V2) ?>:07CT B@820;VABL >4=>3> >1>@>BC >1>@>B=8E :>HBV2 C 4=OE V 287=0G0TBLAO B0::  EMBED Equation.3 , (3.6) 45 "  B@820;VABL ?5@V>4C, O:89 4>A;V46CTBLAO; ?@89<0TBLAO 30, 90, 360 4=V2 2V4?>2V4=> 4;O <VAOFO, :20@B0;C B0 @>:C. "@820;VABL >1>@>BC >1>@>B=8E 70A>1V2 2?;820T =0 ?>B@51C ?V4?@8T<AB20 2 >1>@>B=8E :>HB0E:  EMBED Equation.3 . (3.7) @8A:>@5==O >15@B0==O 9 A:>@>G5==O B@820;>ABV >1>@>BC 7<5=HCT ?>B@51C ?V4?@8T<AB20 2 >1>@>B=8E :>HB0E, V =02?0:8. # A8AB5<V ?>:07=8:V2 5D5:B82=>ABV 28:>@8AB0==O <0B5@V0;L=8E @5AC@AV2 F5=B@0;L=5 <VAF5 709<0T ?>:07=8: <0B5@V0;><VAB:>ABV. 030;L=C <0B5@V0;><VAB:VABL <>6=0 287=0G8B8:  EMBED Equation.3 , (3.8) 45  EMBED Equation.3   7030;L=0 AC<0 <0B5@V0;L=8E 70B@0B, 3@=.;   >1AO3 28@>1=8FB20 C 3@>H>2><C 28@065==V G8 C =0BC@0;L=8E >48=8FOE. >:07=8: ?>:07CT, A:V;L:8 2AL>3> <0B5@V0;L=8E 70B@0B ?@8?040T =0 >48=8FN 28@>1C 01> =0 1 3@82=N 283>B>2;5=>W ?@>4C:FVW, 28:>=0=8E @>1VB, =040=8E ?>A;C3. 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V 0 :20;VDV:0FVTN 20;VDV:0FVO  F5 AC:C?=VABL A?5FV0;L=8E 7=0=L V ?@0:B8G=8E =028G>:, I> 287=0G0NBL ABC?V=L ?V43>B>2;5=>ABV ?@0FV2=8:0 4> 28:>=0==O ?@>D5AV9=8E DC=:FV9 2V4?>2V4=>W A:;04=>ABV. V25=L :20;VDV:0FVW # E0@0:B5@87CTBLAO @V2=5< >A2VB8, 4>A2V4>< @>1>B8 =0 ?>A04V. V25=L :20;VDV:0FVW @>1VB=8:V2  @V2=5< A:;04=>ABV @>1VB, @V2=5< ?@>D5AV9=>W ?V43>B>2:8 B0 4>A2V4>< @>1>B8. V4=5A5==O :20;VDV:0FVW ?@0FV2=8:V2 4> ?52=>3> @V2=O 74V9A=NTBLAO ?V4?@8T<AB2>< A0<>ABV9=>. >=:@5B=89 @V25=L :20;VDV:0FVW 287=0G0TBLAO >2V4=8:>< :20;VDV:0FV9=8E E0@0:B5@8AB8: ?@>D5AV9 ?@0FV2=8:V2, 70B25@465=8< =0:07>< V=VAB5@AB20 ?@0FV B0 A>FV0;L=>W ?>;VB8:8 #:@0W=8 !24 2V416.02.98 @. A=CT @>7?>4V; ?5@A>=0;C ?V4?@8T<AB20 9 70 V=H8<8 >7=0:0<8: 70 2V:><, AB0BBN, AB065< B>I>. >7?>4V; ?@0FV2=8:V2 70 :;0A8DV:0FV9=8<8 3@C?0<8 A;C68BL >A=>2>N 4;O @>7@0EC=:V2 @V7=>3> @>4C AB@C:BC@, A?V22V4=>H5=L >:@5<>W :0B53>@VW ?@0FV2=8:V2 4> 7030;L=>W G8A5;L=>ABV ?5@A>=0;C ?V4?@8T<AB20 01> 4> V=H>W :;0A8DV:0FV9=>W 3@C?8. 87=0G5==O G8A5;L=>ABV ?5@A>=0;C V;L:VA=89 A:;04 ?5@A>=0;C ?V4?@8T<AB20 287=0G0TBLAO 70 40=8<8 :04@>2>3> >1;V:C, 2 O:><C 28>:@5<;NNBL: ?@0FV2=8:V2, I> 7=0E>4OBLAO 2 HB0BV ?V4?@8T<AB20 (B@C4>2V :=86:8 715@V30NBLAO C :04@>2V9 A;C61V, VA=CT =0:07 :5@V2=8:0 ?@> ?@89=OBBO =0 @>1>BC 7 ?>A8;0==O< =0 ?>A04C B0 AB02:C 70@>1VB=>W ?;0B8); AC<VA=8:V2, 7>2=VH=VE V 2=CB@VH=VE (C =0:07V ?@> ?@89=OBBO =0 @>1>BC 707=0G5=>, I> @>1>B8 1C4CBL 28:>=C20B8AO 70 AC<VA=8FB2><); ?@0FNNG8E 70 4>3>2>@0<8 F82V;L=>-?@02>2>3> E0@0:B5@C. >6=><C ?@0FV2=8:>2V, I> 7=0E>48BLAO C HB0BV ?V4?@8T<AB20, ?@8A2>NNBL B015;L=89 =><5@. >:07=8:8 :V;L:VA=>3> A:;04C E0@0:B5@87CNBLAO: <><5=B=8<8 ?>:07=8:0<8 =0 287=0G5=C 40BC; A5@54=V<8 ?>:07=8:0<8 70 287=0G5=89 ?5@V>4. ><5=B=V ?>:07=8:8: /2>G=0 G8A5;L=VABL  C:;NG0T 2AVE ?@0FV2=8:V2, I> 7 O28;8AO =0 @>1>BC =0 ?52=C 40BC. 1;V:>20 G8A5;L=VABL ( EMBED Equation.3 , G>;.)  C:;NG0T 2AVE ?@0FV2=8:V2, :>B@8E ?@89=OB> =0 @>1>BC B5@<V=>< =0 1 V 1V;LH5 4=V2 =570;56=> 2V4 B>3>, ?5@51C20NBL 2>=8 =0 @>1>BV, 7=0E>4OBLAO C 2V4?CAB:0E, 2V4@O465==OE, B8<G0A>2> =5?@0F5740B=V B>I>. &5 70@0E>20=V 4> HB0BC ?V4?@8T<AB20 ?@0FV2=8:8. > >1;V:>2>W G8A5;L=>ABV =5 2:;NG0NBL ?@0FNNG8E 70 4>3>2>@0<8 F82V;L=>-?@02>2>3> E0@0:B5@C, 70 7>2=VH=V< B0 2=CB@VH=V< AC<VA=8FB2><, ?@89=OB8E 4;O 28:>=0==O @07>28E @>1VB. !5@54=V ?>:07=8:8 70 4>A;V46C20=89 ?5@V>4 (<VAOFL, :20@B0;, @V:): !5@54=L>>1;V:>20 G8A5;L=VABL 70 ?5@V>4 ( EMBED Equation.3 , G>;.)  287=0G0TBLAO O: AC<0 A5@54=L><VAOG=8E G8A5;L=>AB59 ?@0FV2=8:V2 >1;V:>2>3> A:;04C ( EMBED Equation.3 , G>;.) 70 :>65= <VAOFL @>7@0EC=:>2>3> ?5@V>4C, ?>4V;5=0 =0 :V;L:VABL <VAOFV2 (m) C FL><C 6 ?5@V>4V.  EMBED Equation.3 , (4.1) 45 V  ?>@O4:>289 =><5@ <VAOFO, O:89 CE>48BL 4> @>7@0EC=:>2>3> ?5@V>4C. !5@54=L>>1;V:>20 G8A5;L=VABL ?@0FV2=8:V2 70 <VAOFL ( EMBED Equation.3 , G>;.)  287=0G0TBLAO H;OE>< ?V4AC<>2C20==O G8A5;L=>ABV ?@0FV2=8:V2 >1;V:>2>3> A:;04C 70 :>65= 45=L 72VB=>3> <VAOFO ( EMBED Equation.3 ), 2:;NG0NG8 28EV4=V 9 A2OB:>2V 4=V, B0 4V;5==O< >B@8<0=>W AC<8 =0 :V;L:VABL :0;5=40@=8E 4=V2 C FL><C <VAOFV (n).  EMBED Equation.3 , (4.2) 45 V  ?>@O4:>289 =><5@ :0;5=40@=>3> 4=O @>7@0EC=:>2>3> <VAOFO. >=OBBO ?@>4C:B82=>ABV ?@0FV. >:07=8:8 9 <5B>48 WW 28<V@N20==O 57C;LB0B82=VABL :>=:@5B=>W 682>W ?@0FV 287=0G0TBLAO ?@>4C:B82=VABN ?@0FV. @>4C:B82=VABL ?@0FV E0@0:B5@87CT WW 5D5:B82=VABL V ?>:07CT 740B=VABL ?@0FV2=8:V2 28?CA:0B8 ?52=C :V;L:VABL ?@>4C:FVW (@>1VB, ?>A;C3) 70 >48=8FN G0AC. V25=L ?@>4C:B82=>ABV ?@0FV E0@0:B5@87CTBLAO 42><0 ?>:07=8:0<8: ?@O<8<: 28@>1VB:>< ?@>4C:FVW 70 >48=8FN G0AC (); >15@=5=8<: B@C4><VAB:VABN ?@>4C:FVW (@>1VB, ?>A;C3) ("@). 8@>1VB>: ( EMBED Equation.3 )  ?>:07CT :V;L:VABL ?@>4C:FVW (@>1VB, ?>A;C3), I> 28@>1;5=0 >4=8< ?@0FV2=8:>< 70 >48=8FN G0AC (F5 =091V;LH ?>H8@5=89 B0 C=V25@A0;L=89 ?>:07=8:).  EMBED Equation.3 , (4.3) 45   >1AO3 28@>1=8FB20 70 ?52=89 ?5@V>4;  EMBED Equation.3 - 70B@0B8 682>W ?@0FV (:V;L:VABL ?@0FV2=8:V2 G8 70B@0G5=89 @>1>G89 G0A). "@C4><VAB:VABL >48=8FV ?@>4C:FVW (@>1VB, ?>A;C3) ("@)  >15@=5=89 4> 28@>1VB:C ?>:07=8:, ?>:07CT 70B@0B8 ?@0FV =0 283>B>2;5==O >48=8FV ?@>4C:FVW (@>1VB, ?>A;C3).  EMBED Equation.3 , (4.4) 45  EMBED Equation.3   70B@0B8 682>W ?@0FV, 28@065=V C 70B@0B0E @>1>G>3> G0AC, ;N4-3>4., ;N4-4=., ;N4-7<. 5B>48 287=0G5==O 28@>1VB:C: 0BC@0;L=89 <5B>4, :>;8 >1AO3 28@>1=8FB20 70 ?52=89 ?5@V>4 28<V@NTBLAO C =0BC@0;L=8E ?>:07=8:0E (C <5B@0E ?@>E>4:8, <3, B>==0E V B. 4). 5B>4 ?>:07>289, 0;5 =5 2@0E>2CT 45O:V >A>1;82>ABV: :0B53>@VN 3V@AL:8E ?>@V4 =0 1C@>28E @>1>B0E, ?@8@>4=V C<>28 5:A?;C0B0FVW ?>:;04V2 V B.?. >3> 4>FV;L=> 70AB>A>2C20B8 I>4> 1@8304 B0 ?V4?@8T<AB2, O:V 28?CA:0NBL >4=>@V4=C ?@>4C:FVN. 0@BVA=89 <5B>4, :>;8 >1AO3 28@>1=8FB20 28<V@NTBLAO C 3@>H>28E >48=8FOE. # 1C@V==V =0DB>28E V 307>28E A25@4;>28=  :>HB>@8A=0 20@BVABL 28:>=0=8E 1C@>28E @>1VB; ?@8 284>1CB:C =0DB8 9 307C  >1AO3 B>20@=>W (20;>2>W) ?@>4C:FVW 2 >?B>28E FV=0E ?V4?@8T<AB20; C 35>;>3>@>72V4FV  >1AO3 35>;>3>@>72V4C20;L=8E @>1VB, 28:>=0=8E 70 ?52=89 ?5@V>4 70 WE D0:B8G=>N 20@BVABN. 5B>4  C=V25@A0;L=89, ?@>B5 <0T @O4 =54>;V:V2, >A:V;L:8 ?>:07=8:8 20;>2>W, B>20@=>W ?@>4C:FVW, >1AO3C 28:>=0=8E @>1VB C:;NG0NBL V BC 20@BVABL , O:0 1C;0 AB2>@5=0 @0=VH5. &5 <0B5@V0;L=V 28B@0B8 (28B@0B8 ?0;820, 5;5:B@>5=5@3VW, <0B5@V0;V2) B0 0<>@B870FVO >A=>2=8E D>=4V2. # B0:><C @07V ?@>4C:B82=VABL 1C45 1V;LH>N B0<, 45 1V;LH <0B5@V0;>- 9 5=5@3><VAB:5 28@>1=8FB2>. 5B>4 ?>B@51CT 4>40B:>28E @>7@0EC=:V2 70 C<>2=> G8AB>N ?@>4C:FVTN. @V< B>3>, =5>1@C=B>20=5 ?V428I5==O FV=8 ?@872>48BL 4> DV:B82=>3> 7@>AB0==O ?@>4C:B82=>W ?@0FV. 1G8A;5==O ?>:07=8:0 28@>1VB:C 2 3@>H>28E >48=8FOE =5 4>72>;OT 2V4AB56C20B8 48=0<V:C ?@>4C:B82=>ABV ?@0FV =02VBL ?@8 =525;8:><C @V2=V V=D;OFVW. ;O FL>3> ?>B@V1=> 25AL G0A ?@>2>48B8 V=45:A0FVN 20@B>ABV >A=>2=8E D>=4V2, 70@?;0B8 B>I>, I> =5 702648 2V41820T @50;L=C A8BC0FVN, O:>N 1 4>A:>=0;>N =5 1C;0 A8AB5<0 V=45:A0FVW. 0 B@C4>28< <5B>4>< 4;O E0@0:B5@8AB8:8 >1AO3C 28@>1=8FB20 70AB>A>2CNBL =>@<8 B@C4>28E 28B@0B C =>@<>-3>48=0E (>1AO3 @>1VB C =0BC@0;L=8E ?>:07=8:0E <=>60BL =0 2V4?>2V4=V =>@<8 G0AC ). 54>;V:8  =54>AB0B=T >1@C=BC20==O =>@<, WE G0AB89 ?5@53;O4. (8@>:>3> 70AB>AC20==O <5B>4 =5 7=09H>2. 8B@0B8 682>W ?@0FV ?@8 @>7@0EC=:0E <>6CBL 28<V@N20B8AO 2 ;N48=>-3>48=0E, :>;8 287=0G0NBL A5@54=L>3>48==89 28@>1VB>:; C ;N48=>-4=OE (A5@54=L>45==89 28@>1VB>:); A5@54=L>>1;V:>2>N G8A5;L=VABN ?5@A>=0;C 70 2V4?>2V4=89 ?5@V>4. @>4C:B82=VABL ?@0FV ?>ABV9=> 7<V=NTBLAO ?V4 2?;82>< 1030BL>E D0:B>@V2. 0 @V25=L V 48=0<V:C ?@>4C:B82=>ABV ?@0FV 2?;820NBL: 1-H0 3@C?0  <0B5@V0;L=>-B5E=VG=V D0:B>@8: @V25=L B5E=VG=>W >71@>T=>ABV 28@>1=8FB20 (D>=4>>71@>T=VABL); 70AB>AC20==O 4>AO3=5=L =0C:8 V B5E=V:8; 5=5@3>>71@>T=VABL ?@0FV (:V;L:VABL :B-3>4 5=5@3VW, O:0 28B@0G0TBLAO =0 3>48=C ?@0FV). 2-30 3@C?0  >@30=V70FV9=V D0:B>@8: ?@8@>4=V, A0=VB0@=>-3V3VT=VG=V C<>28 ?@0FV; AB@C:BC@0 :04@V2 ?V4?@8T<AB20; V=B5=A82=VABL ?@0FV, :>B@0 28<V@NTBLAO 28B@0B0<8 DV78G=>W B0 @>7C<>2>W 5=5@3VW ;N48=8 70 >48=8FN @>1>G>3> G0AC (=>@<0;L=>N 22060TBLAO V=B5=A82=VABL, O:0 =5 28:;8:0T =530B82=>3> 2?;82C =0 >@30=V7< ;N48=8, 0 28B@0B8 5=5@3VW ?>2=VABN :><?5=ACNBLAO 70 @0EC=>: E0@GC20==O V 2V4?>G8=:C); 28:>@8AB0==O =><V=0;L=>3> D>=4C @>1>G>3> G0AC. 3-BO 3@C?0  A>FV0;L=>-5:>=><VG=V D0:B>@8: <0B5@V0;L=0 V <>@0;L=0 70FV:02;5=VABL ?@0FV2=8:V2; WE AB02;5==O 4> ?@0FV; 7030;L=89 :C;LBC@=>-B5E=VG=89 @V25=L ?5@A>=0;C, @V25=L ?@>D5AV9=>W ?V43>B>2:8 B0 :20;VDV:0FVW ?@0FV2=8:V2; ?A8E>;>3VG=89 :;V<0B C :>;5:B82V; 7<V=0 2;0A=>ABV =0 70A>18 ?@0FV. 5 >@<C20==O B0 >?;0B0 ?@0FV =0 ?V4?@8T<AB2V "@C4>289 ?@>F5A V 9>3> A:;04>2V G0AB8=8. 0B@0B8 @>1>G>3> G0AC 9 <5B>48 9>3> 282G5==O. >@<8 ?@0FV B0 WE :;0A8DV:0FVO. >=OBBO V 2848 70@>1VB=>W ?;0B8. 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"5E=>;>3VG=89 1V: ?>2 O70=89 V7 ?5@5B2>@5==O< ?@54<5BV2 ?@0FV 2 3>B>2C ?@>4C:FVN ?V4 2?;82>< ?52=>3> B5E=>;>3VG=>3> ?@>F5AC, O:8< ?5@5410G5=> ?>@O4>: B0 A?>A>18 28:>=0==O @>1VB. 7 B@C4>2>3> 1>:C 28@>1=8G89 ?@>F5A  F5 AC:C?=VABL 4V9 28:>=02FV2 V7 <5B>N 74V9A=5==O :><?;5:A=>3> B5E=>;>3VG=>3> ?@>F5AC. 18420 ?@>F5A8  V B5E=>;>3VG=89, V B@C4>289  =5@>7@82=> ?>2 O70=V. @8 =>@<C20==V ?@0FV 28@>1=8GV ?@>F5A8 4V;OBLAO =0 >?5@0FVW. 57?>A5@54=V< >1 T:B>< =>@<C20==O T >?5@0FVO, B><C B5E=>;>3VG=0 =>@<0 2AB0=>2;NTBLAO =0 :>6=C >?5@0FVN. B65, >?5@0FVO  F5 G0AB8=0 B5E=>;>3VG=>3> ?@>F5AC, O:0 28:>=CTBLAO >4=8< 01> 45:V;L:><0 @>1VB=8:0<8 =0 >4=><C @>1>G><C <VAFV V A:;040TBLAO 7 @O4C 4V9, A?@O<>20=8E =0 >1@>1;5==O >4=>3> G8 45:V;L:>E ?@54<5BV2 ?@0FV. # B8E 28?04:0E, :>;8 =5<>6;82> @>74V;8B8 28@>1=8G89 ?@>F5A =0 >?5@0FVW, I> @53C;O@=> ?>2B>@NNBLAO, >1 T:B>< =>@<C20==O <>65 1CB8 :><?;5:A >?5@0FV9. !BC?V=L ?>4V;C >?5@0FVW =0 A:;04>2V 5;5<5=B8 70;568BL 2V4 ?>B@V1=>W B>G=>ABV 0=0;V7C 70B@0B @>1>G>3> G0AC, =>@< V =>@<0B82V2. 0B@0B8 @>1>G>3> G0AC 9 <5B>48 9>3> 282G5==O @8 =>@<C20==V 206;828< T 282G5==O 70B@0B @>1>G>3> G0AC. V4 @>1>G8< G0A>< @>7C<VNBL CAB0=>2;5=C B@820;VABL @>1>G>W 7<V=8. >1>G89 G0A 28:>=02FO 4V;8BLAO =0: G0A @>1>B8, G0A ?5@5@2. '0A @>1>B8 ( EMBED Equation.3 )  28B@0G0TBLAO @>1VB=8:>< =0 74V9A=5==O 4V9, ?>2(O70=8E V7 28:>=0==O< 28@>1=8G8E 70240=L. V= ?>4V;OTBLAO =0: G0A ?@>4C:B82=>W @>1>B8; G0A @>1>B8, =5 ?5@5410G5=89 28:>=0==O< 28@>1=8G>3> 70240==O. '0A ?@>4C:B82=>W @>1>B8 (" ) C:;NG0T: 0) G0A ?V43>B>2G>-7025@H0;L=>W @>1>B8 (") 28B@0G0TBLAO @>1VB=8:>< =0 ?V43>B>2:C 4> @>1>B8, =0 ?>G0B:>25 >7=09><;5==O 7 @>1>B>N, =0 28:>=0==O 4V9, ?>2(O70=8E 7 WW 70:V=G5==O< (V=AB@C:B06, >7=09><;5==O 7 4>:C<5=B0<8, =0;03>465==O >1;04=0==O B>I>). A>1;82VABL ?V43>B>2G>-7025@H0;L=>3> G0AC 2 B><C, I> 2V= 28B@0G0TBLAO >48= @07 70 7<V=C 01> =0 ?0@BVN 28@>1V2; 1) G0A >?5@0B82=>W @>1>B8 (" ) 28B@0G0TBLAO =0 74V9A=5==O >A=>2=>W <5B8 >?5@0FVW V ?>2B>@NTBLAO 7 :>6=>N HBC:>N 28@>1C. !:;040TBLAO 7 >A=>2=>3>, :>;8 74V9A=NTBLAO 7<V=0 @5G>2>W D>@<8 ?@54<5BV2 ?@0FV, B0 4>?><V6=>3>, O:89 28B@0G0TBLAO =0 @V7=V ?@89><8, I> 70157?5GCNBL 28:>=0==O >A=>2=>W @>1>B8 (70<V@8, ?CA: >1;04=0==O B>I>); 2) G0A >1A;C3>2C20==O @>1>G>3> <VAFO ("!) 28B@0G0TBLAO =0 4>3;O4 70 @>1>G8< <VAF5< V =0 ?V4B@8<:C 9>3> C @>1>G><C AB0=V (70B>GC20==O V=AB@C<5=BC, =0;03>465==O 25@AB0B0, ?@818@0==O V=AB@C<5=BC B>I>). 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A=>2>N >@30=V70FVW >?;0B8 ?@0FV 2 #:@0W=V T B0@8D=0 A8AB5<0. "0@8D=0 A8AB5<0 >?;0B8 ?@0FV O2;OT A>1>N AC:C?=VABL =>@<0B82V2, 70 4>?><>3>N O:8E 74V9A=NTBLAO 48D5@5=FV0FVO V @53C;N20==O 70@?;0B8 @V7=8E 3@C? ?@0FV2=8:V2 70;56=> 2V4 WE :20;VDV:0FVW, A:;04=>ABV ?@0FV, ABC?5=O 2V4?>2V40;L=>ABV. >=0 2:;NG0T: B0@8D=V AVB:8; B0@8D=V AB02:8; AE5<8 ?>A04>28E >:;04V2; B0@8D=>-:20;VDV:0FV9=V E0@0:B5@8AB8:8. "0@8D=0 AVB:0  ?5@5;V: B0@8D=8E @>7@O4V2 ?@0FV2=8:V2 B0 2V4?>2V4=8E =8< B0@8D=8E :>5DVFVT=BV2. V4?@8T<AB20 A0<>ABV9=> D>@<CNBL B0@8D=V AVB:8, :@V< 45@602=8E. ;O 70AB>AC20==O <>65 1CB8 70?@>?>=>20=0 B0@8D=0 AVB:0, =02545=0 2 B01;8FV 5.1. "01;8FO 5.1  "0@8D=0 AVB:0 "0@8D=V @>7@O48VVV"0@8D=V :>5DVFVT=B81,01,141,31,481,681,9 >65= @>7@O4 B0@8D=>W AVB:8 <0T A2V9 :>5DVFVT=B, O:89 ?>:07CT, 2 A:V;L:8 @07V2 70@>1VB=0 ?;0B0 ?@0FV2=8:0 40=>3> @>7@O4C 28I5 2V4 >?;0B8 ?@0FV ?@0FV2=8:0 ?5@H>3> @>7@O4C 70 C<>28, I> 2>=8 2V4?@0FN20;8 >4=0:>289 G0A. V4=5A5==O 28:>=C20=8E @>1VB 4> 287=0G5=8E B0@8D=8E @>7@O4V2 B0 ?@8A2>T==O :20;VDV:0FV9=8E @>7@O4V2 @>1VB=8:0< 74V9A=NTBLAO 2;0A=8:>< 01> C?>2=>2065=8< =8< >@30=>< B0: A0<>, O: V ?>A04>2V >:;048 :5@V2=8:0<, ?@>D5AV>=0;0<, A?5FV0;VAB0< B0 A;C61>2FO<. $>@<C20==O B0@8D=>W AVB:8 74V9A=NTBLAO =0 >A=>2V: B0@8D=>W AB02:8 @>1VB=8:0 1-3> @>7@O4C, O:0 2AB0=>2;NTBLAO =5 =86G5 2V4 70:>=>402G> 287=0G5=>3> <V=V<0;L=>3> @V2=O ; <V6:20;VDV:0FV9=8E A?V22V4=>H5=L @>7<V@V2 B0@8D=8E AB02>: 73V4=> 7 @>7@O40<8 B0@8D=>W AVB:8. "0@8D=0 AB02:0  F5 =>@<0 >?;0B8 ?@0FV ?@0FV2=8:0 2V4?>2V4=>W A?5FV0;L=>ABV B0 :20;VDV:0FVW 70 >48=8FN G0AC. >48==0 B0@8D=0 AB02:0 ?@0FV2=8:0 V  3> @>7@O4C 287=0G0TBLAO B0::  EMBED Equation.3 , (5.2) 45  EMBED Equation.3   3>48==0 B0@8D=0 AB02:0 ?@0FV2=8:0 ?5@H>3> @>7@O4C, :>?.;  EMBED Equation.3   B0@8D=89 :>5DVFVT=B ?@0FV2=8:0 V-3> @>7@O4C.  EMBED Equation.3 , (5.3) 45  EMBED Equation.3   =><V=0;L=89 (<0:A8<0;L=> <>6;8289 70 ?52=89 @568< @>1>B8 ?V4?@8T<AB20) D>=4 @>1>G>3> G0AC 70 2V4?>2V4=89 ?5@V>4, 3>4.;  EMBED Equation.3   70@>1VB>: 1-3> ?@0FV2=8:0, =5 =86G89 2V4 @V2=O <V=V<0;L=>W 70@>1VB=>W ?;0B8, :>?. @028;L=0 B0@8DV:0FVO ?@0FV2=8:V2 <>6;820 ;8H5 ?@8 GVB:><C 287=0G5==V E0@0:B5@C 9 A:;04C @>1VB, 0 B0:>6 :>;0 ?8B0=L, 7=0=L B0 2<V=L, O:8<8 2>=8 ?>28==V 2>;>4VB8 73V4=> 7 ?@8A2>T=8< @>7@O4><. "0@8D=>-:20;VDV:0FV9=V E0@0:B5@8AB8:8 =02>4OBLAO C >2V4=8:>2V :20;VDV:0FV9=8E E0@0:B5@8AB8: ?@>D5AV9 ?@0FV2=8:V2, 70B25@465=><C =0:07>< V=VAB5@AB20 ?@0FV V A>FV0;L=>W ?>;VB8:8 #:@0W=8. ;O >@30=V70FVW >?;0B8 ?@0FV V=65=5@=>-B5E=VG=8E ?@0FV2=8:V2 B0 A;C61>2FV2 28:>@8AB>2CNBL AE5<8 ?>A04>28E >:;04V2. !E5<8 ?>A04>28E >:;04V2  F5 ?5@5;V: ?>A04 V 2V4?>2V4=8E W< ?>A04>28E >:;04V2, O:V 287=0G0NBLAO C 283;O4V 25@E=L>W 9 =86=L>W <56V ?>A04>2>3> >:;04C ?> :>6=V9 ?>A04V. "0: 720=0  28;:0 4>72>;OT 2AB0=>2;N20B8 >:;048 :>=:@5B=8< ?@0FV2=8:0< 7 C@0EC20==O< WE B5>@5B8G=>W ?V43>B>2:8, 4V;>28E O:>AB59, AB06C @>1>B8 V B.?. $>@<8 B0 A8AB5<8 >?;0B8 ?@0FV  #:@0W=V VA=CNBL 3 D>@<8 >?;0B8 ?@0FV: ?>3>48==0; 2V4@O4=0; 157B0@8D=0. 0 >A=>2C ?>3>48==>W D>@<8 ?>:;045=89 D0:B8G=> 2V4?@0FL>20=89 G0A ?@0FV2=8:><. 0 >A=>2C 2V4@O4=>W D>@<8  >1AO3 283>B>2;5=>W ?@>4C:FVW (@>1VB, ?>A;C3) 70 ?52=89 ?5@V>4.  >3>48==0 D>@<0 >?;0B8 ?@0FV B0 WW A8AB5<8: ) 0 ?@>AB>W ?>3>48==>W A8AB5<8 70@>1VB>: ?@0FV2=8:>2V V-3> @>7@O4C =0@0E>2CTBLAO 70 D0:B8G=> 2V4?@0FL>20=89 G0A  EMBED Equation.3 , (5.4) 45  EMBED Equation.3   D0:B8G=> 2V4?@0FL>20=89 G0A, 3>4.;  EMBED Equation.3   3>48==0 B0@8D=0 AB02:0 ?@0FV2=8:0 V-3> @>7@O4C. ) 0 ?>3>48==>-?@5<V0;L=>N A8AB5<>N, :@V< 70@>1VB:C 70 ?@>AB>N ?>3>48==>N A8AB5<>N, ?@0FV2=8:>2V 28?;0GCTBLAO ?@5<VO. #<>28 ?@5<VN20==O 287=0G0NBLAO @>7@>1;5=8< =0 ?V4?@8T<AB2V  >;>65==O< ?@> ?@5<VN20==O . >;>2=>N C<>2>N ?@5<VN20==O ?>28==> 1CB8 O:VA=5 28:>=0==O V ?5@528:>=0==O 28@>1=8G>3> 70240==O.  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A=>2>N T 2V4@O4=0 @>7FV=:0 ( EMBED Equation.3 ), O:0 2AB0=>2;NTBLAO =0 :>6=C >48=8FN ?@>4C:FVW (>48=8FN @>1>B8), 28E>4OG8 7 B0@8D=>W AB02:8 2V4?>2V4=>3> @>7@O4C B0 =>@< 28@>1VB:C 01> =>@<8 G0AC =0 40=C @>1>BC:  EMBED Equation.3 , (5.5) 45  EMBED Equation.3   7<V==0 B0@8D=0 AB02:0 ?@0FV2=8:0, O:0 2V4?>2V40T V-B><C @>7@O4C @>1>B8;  EMBED Equation.3   7<V==0 =>@<0 28@>1VB:C, >4., 01>  EMBED Equation.3 , (5.6) 45  EMBED Equation.3   3>48==0 B0@8D=0 AB02:0 ?@0FV2=8:0 V-3> @>7@O4C, :>?.;  EMBED Equation.3   =>@<0 G0AC =0 >48=8FN ?@>4C:FVW, 3>4. $0:B8G=89 70@>1VB>: 287=0G0TBLAO:  EMBED Equation.3 , (5.7) 45  EMBED Equation.3   D0:B8G=89 >1AO3 28:>=0=8E @>1VB ?> :>6=><C 284C ?@>4C:FVW, >4. ) 0 2V4@O4=>-?@5<V0;L=>W A8AB5<8  ?@0FV2=8:>2V 28?;0GCTBLAO ?@5<VO 70 28:>=0==O V ?5@528:>=0==O @0=VH5 2AB0=>2;5=8E :>=:@5B=8E :V;L:VA=8E B0 O:VA=8E ?>:07=8:V2 @>1>B8 ?>=04 70@>1VB>: 70 ?@O<>N 2V4@O4=>N A8AB5<>N. @5<VW 2AB0=>2;NNBLAO C 2V4A>B:0E.  EMBED Equation.3 , (5.8) 45  EMBED Equation.3   AC<0 ?@5<V0;L=8E 4>?;0B, 3@=.  EMBED Equation.3 , (5.9) 45  EMBED Equation.3   ?@>F5=B 4>?;0B 70 28:>=0==O ?;0=C;  EMBED Equation.3   ?@>F5=B 4>?;0B 70 :>65= 2V4A>B>: ?5@528:>=0==O ?;0=C;  EMBED Equation.3   ?@>F5=B ?5@528:>=0==O ?;0=C.  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AB0==V <>6CBL 1CB8 @50;V7>20=8<8 =0 AB>@>=C. >B>28< ?@>4C:B>< 287=0NBL B0:C ?@>4C:FVN, O:0 ?@>9H;0 28@>1=8G89 ?@>F5A, 2V4?>2V40T AB0=40@B0< 01> B5E=VG=8< C<>20< V ?5@5E>48BL 2 V=HV ?V4@>74V;8, =0 A:;04 3>B>2>W ?@>4C:FVW B0 ?@87=0G5=0 4;O A?>6820==O. 8<V@=8:8 >1AO3C ?@>4C:FVW >:07=8:8, O:V E0@0:B5@87CNBL >1AO3 28@>1;5=>W ?@>4C:FVW (@>1VB, ?>A;C3) 70 ?52=89 ?5@V>4 70;56=> 2V4 28<V@=8:V2 @>7?>4V;ONBLAO =0: =0BC@0;L=V  :>=:@5B=V DV78G=V >48=8FV (HBC:8, B>==8, <5B@8, <5B@8 :204@0B=V, :C1VG=V B>I>); C<>2=>-=0BC@0;L=V  70AB>A>2CNBLAO =0 ?V4?@8T<AB20E, :>B@V 28@>1;ONBL >48= 284 ?@>4C:FVW (@>1VB), 0;5 B0:89, I> @V7=8BLAO 70 A>@B=VABN, O:VABN B>I> (B>==8 C<>2=>3> =0;82C 4;O @V7=8E 70 :0;>@V9=VABN 284V2 ?0;820, ?@>E>4:0 C<>2=0, ?@>E>4:0 72545=0 V B. V=.); B@C4>2V  70 =>@<0<8 B@C4>28E 28B@0B C =>@<>-3>48=0E (>1AO3 @>1VB C =0BC@0;L=8E ?>:07=8:0E <=>60BL =0 2V4?>2V4=V =>@<8 G0AC); 20@BVA=V  C 3@>H>28E >48=8FOE. 0BC@0;L=V 28<V@=8:8 4>72>;ONBL C73>46C20B8 28@>1=8FB2> 9 ?@>406 ?@>4C:FVW 7 ?>B@510<8 @8=:C, 70157?5GCNBL ?>@V2=O==VABL >1AO3C 28?CA:C 70 @V7=V ?5@V>48, 0;5 =5 4>72>;ONBL 287=0G8B8 >1AO3 V AB@C:BC@C 28@>1=8FB20 =0 1030B>?@>DV;L=8E ?V4?@8T<AB20E, =5 40NBL <>6;82>ABV A?;0=C20B8 4>E>48 B0 ?@81CB>: ?V4?@8T<AB20 2V4 @50;V70FVW ?@>4C:FVW. &V ?@>1;5<8 @>72 O7CNBL 20@BVA=V 28<V@=8:8. 0BC@0;L=V ?>:07=8:8, O:V E0@0:B5@87CNBL @57C;LB0B8 @>1>B8 ?V4?@8T<AB2 =0DB>307>2>W 30;C7V: 1) ;O ?V4?@8T<AB2 B@C1>?@>2V4=>3> B@0=A?>@BC  1AO3 B@0=A?>@B>20=>3> 307C ( EMBED Equation.3 , B8A.<3)  ?>:07CT :V;L:VABL 307C, :>B@C ?>40=> A?>6820GC:  EMBED Equation.3 , (6.1) 45  EMBED Equation.3   >1AO3 =04E>465==O 307C 2 307>?@>2V4, B8A.<3;  EMBED Equation.3   28B@0B8 =0 2=CB@VH=V ?>B@518, B8A.<3;  EMBED Equation.3   25;8G8=0 B5E=>;>3VG=8E 2B@0B, B8A.<3. 1AO3 ?5@5:0GC20==O =0DB8 V =0DB>?@>4C:BV2 ( EMBED Equation.3 , B>==)  ?>:07CT :V;L:VABL ?5@5:0G0=>W =0DB8 70 ?52=89 ?5@V>4  EMBED Equation.3 , (6.2) 45  EMBED Equation.3   4>1>20 ?@>?CA:=0 740B=VABL B@C1>?@>2>4C, B>==;  EMBED Equation.3   G0A @>1>B8 B@C1>?@>2>4C, 4V1;  EMBED Equation.3   ?@8@>4=89 C1CB>: =0DB8 ?@8 B@0=A?>@BC20==V, B>==. 2) ;O ?V4?@8T<AB2, I> 28:>=CNBL 1C@>2V 9 35>;>3>@>72V4C20;L=V @>1>B8 F5  V;L:VABL A25@4;>28=, 70:V=G5=8E 1C4V2=8FB2><, HB.  C:;NG0NBL A25@4;>28=8, ?> O:8E 28:>=0=89 C25AL ?5@5410G5=89 :><?;5:A @>1VB. @>E>4:0 (H, <)  >A=>2=89 ?>:07=8:, I> E0@0:B5@87CT >1AO3 1C@>28E @>1VB C =0BC@0;L=V9 D>@<V. &5 2AV ?@>1C@5=V <5B@8 ?> 2AVE A25@4;>28=0E, ?@>1C@5=V 70 4>A;V46C20=89 ?5@V>4, 70 28=OB:>< 1C@V==O  4@C38< AB>21C@>< , I> O2;OT A>1>N 28?@02;5==O 1@0:C 2 1C@V==V. @>E>4:C ?>:07CNBL >:@5<> 70 <5B>N V A?>A>10<8 1C@V==O, >:@5<> 1C@V==O =0 =0DBC 9 307, 70 B8?0<8 4>;VB, V=B5@20;0<8, 2840<8 ?@82>40 B0 V=. @>E>4:0 =0 4>;>B> (H, <)  :V;L:VABL <5B@V2, ?@>1C@5=8E 4>;>B>< 4> ?>2=>3> 9>3> DV78G=>3> A?@0FN20==O. @>E>4:0 72545=0  AC<0 ?@>E>4>:, A:>@83>20=8E G5@57 A?V22V4=>H5==O H284:>AB59 1C@V==O, E0@0:B5@87CT >1AO3 @>1VB 1C@>2>3> ?V4?@8T<AB20 7 C@0EC20==O< @V7=8FV ?>:07=8:V2 70 <5B>N 1C@V==O  EMBED Equation.3 , (6.3)  EMBED Equation.3 , (6.4) 45  EMBED Equation.3 ,  EMBED Equation.3   ?@>E>4:0, 2V4?>2V4=> 72545=0 4> 5:A?;C0B0FV9=>3> 01> @>72V4C20;L=>3> 1C@V==O, <;  EMBED Equation.3   ?@>E>4:0 C @>72V4C20;L=><C B0 5:A?;C0B0FV9=><C 1C@V==V, <;  EMBED Equation.3   :><5@FV9=0 H284:VABL @>72V4C20;L=>3> 9 5:A?;C0B0FV9=>3> 1C@V==O, </25@AB0B>-<VA. @>E>4:0 C<>2=0  ?5@5@0E>20=0 ?@>E>4:0 2 C<>2=V <5B@8 G5@57 =>@<0B82=C B@C4><VAB:VABL 1C@V==O 1-3> DV78G=>3> <5B@0. >:07=8: 40T 7<>3C 70157?5G8B8 2V4=>A=5 7VAB02;5==O ?>:07=8:V2 ?> A25@4;>28=0E V 3@C?0E A25@4;>28= V7 @V7=>N B@C4><VAB:VABN 1C@V==O ?@8 0=0;VB8G=8E @>7@0EC=:0E. 0 >A=>2C C<>2=>3> <5B@0 15@5BLAO =>@<0B82=0 B@C4><VAB:VABL 1C@V==O >4=>3> DV78G=>3> <5B@0 2 ?52=><C V=B5@20;V , I> 9 ?@89<0TBLAO 70 5B0;>=. 5@5@0EC=>: 74V9A=NNBL 70 :>5DVFVT=B0<8, I> 287=0G0NBLAO ?> >:@5<8E V=B5@20;0E 3;818=. 3) ;O 307>- V =0DB>284>1C2=8E ?V4?@8T<AB2  0;0=A =0DB8 (307C): E0@0:B5@87CT 284>1CB>: ?0;820, 7 >4=>3> 1>:C, B0 9>3> 28:>@8AB0==O 9 @>7?>4V; <V6 A?>6820G0<8  7 4@C3>3>. ;O =0DB8  EMBED Equation.3 . (6.5) ;O 307C  EMBED Equation.3 , (6.6) 45  EMBED Equation.3 , EMBED Equation.3 - 70?0A8 =0DB8 2 @575@2C0@0E =0 ?>G0B>: V =0 :V=5FL @>7@0EC=:>2>3> ?5@V>4C;  EMBED Equation.3   >1AO3 284>1CB:C;  EMBED Equation.3   >1AO3 =04E>465==O 7V AB>@>=8;  EMBED Equation.3   >1AO3 74020==O A?>6820G52V;  EMBED Equation.3 , EMBED Equation.3 - =5B>20@=V B0 B>20@=V 28B@0B8 ?0;820. 1AO3 284>1CB:C =0DB8 01> ?@8@>4=>3> 307C <>6=0 @>7@0EC20B8 70 D>@<C;>N  EMBED Equation.3 , (6.7) 45  EMBED Equation.3   A5@54=L><VAOG=89 451VB A25@4;>28=, B>==;  EMBED Equation.3   >1AO3 @>1VB 7 5:A?;C0B0FVW A25@4;>28=, A25@4;.-<VA.;  EMBED Equation.3   :>5DVFVT=B 5:A?;C0B0FVW. 1AO3 284>1CB:C =0DB>2>3> 307C 287=0G0NBL 7 >1AO3C 284>1CB:C =0DB8  EMBED Equation.3 7 C@0EC20==O< 307>2>3> D0:B>@0  EMBED Equation.3  B0 :>5DVFVT=B0 CB8;V70FVW EMBED Equation.3 .  EMBED Equation.3 . (6.8) 07>289 D0:B>@  F5 A?V22V4=>H5==O >B@8<0=>3> 307C, ?@82545=>3> 4> 0B<>AD5@=>3> B8A:C V B5<?5@0BC@8  EMBED Equation.3 , B0 >1AO3C 284>1CB>W 70 B>9 A0<89 G0A =0DB8 ?@8 B><C 6 B8A:>2V 9 B5<?5@0BC@V. 84>1CB>: =0DB8, 307C B0 307>:>=45=A0BC @>7?>4V;OTBLAO =0 20;>289 V B>20@=89. 0;>289 284>1CB>: ( EMBED Equation.3 , B>==)  C25AL 284>1CB>: =0DB8, 307C 9 307>:>=45=A0BC. @8G><C 1 B8A. :C1. <5B@V2 307C ?@8 ?5@52545==V >48=8FL C 203>2V ?@8@V2=NTBLAO 4> 1 B>==8 =0DB8. 0;>289 284>1CB>: C:;NG0T B>20@=89 284>1CB>:  EMBED Equation.3  B0 =5B>20@=V 28B@0B8  EMBED Equation.3 , B>1B> 28B@0B8 =0 2;0A=V ?>B@518. ">20@=89 284>1CB>: ( EMBED Equation.3 , B>==) ?@87=0G5=89 4;O @50;V70FVW AB>@>==V< A?>6820G0<. 84>1CB>: =0DB8 V 307C 70;568BL ?5@54CAV< 2V4 :V;L:>ABV (D>=4C) A25@4;>28= =0 ?>G0B>: ?5@V>4C, 2V4 WW 7<V=8 B0 ABC?5=O 28:>@8AB0==O. A=>2=0 G0AB8=0 A25@4;>28= AB0=>28BL 5:A?;C0B0FV9=89 D>=4, I> 2:;NG0T 4VNGV V =54VNGV A25@4;>28=8. > 4VNG>3> D>=4C =0 :V=5FL <VAOFO 2V4=>AOBL A25@4;>28=8, O:V E>G0 1 45:V;L:0 3>48= DC=:FV>=C20;8 9 4020;8 ?@>4C:FVN C FL><C <VAOFV. > =54VNG>3> D>=4C =0;560BL B0:V A25@4;>28=8, :>B@V =5 ?@0FN20;8 1V;LH5 2V4 >4=>3> :0;5=40@=>3> <VAOFO. 1AO3 ?@>4C:FVW C 20@BVA=><C 28@07V =0 ?V4?@8T<AB20E =0DB>- 307>- 284>1C2=>W 30;C7V 287=0G0TBLAO ?>:07=8:0<8 B>20@=>W, 20;>2>W, @50;V7>20=>W, G8AB>W ?@>4C:FVW. > A:;04C B>20@=>W ?@>4C:FVW (", 3@=.) C:;NG0NBL 20@BVABL: - 3>B>2>W ?@>4C:FVW, 28?CI5=>W B0 ?V43>B>2;5=>W 4;O @50;V70FVW =0 AB>@>=C (?>70 <56V ?V4?@8T<AB20) 2 40=><C ?5@V>4V; - @>1VB ?@><8A;>2>3> E0@0:B5@C (=0?@8:;04: @5<>=B=8E @>1VB), 28:>=0=8E =0 70<>2;5==O 7V AB>@>=8 G8 A2>T<C :0?VB0;L=><C 1C4V2=8FB2C. > B>20@=>W ?@>4C:FVW =5 2:;NG0TBLAO 20@BVABL 2=CB@VH=L>702>4AL:>3> >1>@>BC (), B>1B> G0AB8=0 3>B>2>W ?@>4C:FVW, O:0 28:>@8AB>2CTBLAO 4;O ?>40;LH>3> ?@><8A;>2>3> ?5@5@>1;5==O 2 <560E >4=>3> ?V4?@8T<AB20. 0@BVABL 3>B>2>W ?@>4C:FVW, I> 2:;NG0TBLAO 4> B>20@=>W ?@>4C:FVW, 287=0G0TBLAO 70 D>@<C;>N  EMBED Equation.3 , 3@=., (6.9) 45  EMBED Equation.3   28?CA: ?@>4C:FVW V-3> 284C 2 =0BC@0;L=8E >48=8FOE;  EMBED Equation.3   3C@B>20 (>?B>20) FV=0 ?V4?@8T<AB20 =0 >48=8FN 28@>1C V-3> 284C (70 28@0EC20==O< ?>40B:C =0 4>40=C 20@BVABL, 0:F87C B0 V=H8E =5?@O<8E ?>40B:V2), 3@=.; ?  :V;L:VABL 284V2 ?@>4C:FVW, I> 28?CA:0TBLAO =0 ?V4?@8T<AB2V. ">20@=0 ?@>4C:FVO @>7@0E>2CTBLAO 2 4VNG8E 2V4?CA:=8E FV=0E ?V4?@8T<AB20 ( EMBED Equation.3 ), 0 B0:>6 C ?>@V2=O;L=8E FV=0E V B0@8D0E ( EMBED Equation.3 ). 5@H0 >FV=:0 4>72>;OT 2AB0=>28B8 4>EV4 B0 DV=0=A>2V @57C;LB0B8 ?V4?@8T<AB20 70 4>A;V46C20=89 ?5@V>4, V=H0  287=0G8B8 B5<?8 7@>AB0==O 9 7<V=8 C AB@C:BC@V 28@>1=8FB20.  EMBED Equation.3  @>7@0E>2CTBLAO =0 >A=>2V >?B>28E FV= ?V4?@8T<AB20, I> 4VNBL C 4>A;V46C20=><C ?5@V>4V. 0;>20 ?@>4C:FVO (, 3@=.)  CAO ?@>4C:FVO C 20@BVA=><C 28@07V =570;56=> 2V4 ABC?5=O 3>B>2=>ABV B0 <VAFO, 45 2>=0 1C45 A?>68B0. >:07=8: 20;>2>W ?@>4C:FVW, :@V< 5;5<5=BV2 B>20@=>W ?@>4C:FVW, 2:;NG0T B0:>6 7<V=C 70;8H:V2 =57025@H5=>3> 28@>1=8FB20 ?@>BO3>< @>7@0EC=:>2>3> ?5@V>4C  EMBED Equation.3 , (6.10) 45  EMBED Equation.3   70;8H:8 =57025@H5=>3> 28@>1=8FB20 =0 :V=5FL @>7@0EC=:>2>3> ?5@V>4C, 3@=.;  EMBED Equation.3   70;8H:8 =57025@H5=>3> 28@>1=8FB20 =0 ?>G0B>: @>7@0EC=:>2>3> ?5@V>4C, 3@=. 50;V7>20=0 ?@>4C:FVO ( , 3@=.)  F5 ?@>4C:FVO, O:0 2V420=B065=0 A?>6820G52V V 70 O:C =04V9H;8 :>HB8 =0 ?>B>G=89 @0EC=>: ?V4?@8T<AB20 - ?>AB0G0;L=8:0 01> <0NBL =04V9B8 C 707=0G5=89 B5@<V=. 1G8A;NTBLAO 70 D>@<C;>N  EMBED Equation.3 , (6.11) 45  EMBED Equation.3   70;8H:8 =5@50;V7>20=>W ?@>4C:FVW =0 ?>G0B>: @>7@0EC=:>2>3> ?5@V>4C, 3@=.;  EMBED Equation.3   70;8H:8 =5@50;V7>20=>W ?@>4C:FVW =0 :V=5FL @>7@0EC=:>2>3> ?5@V>4C, 3@=. ;O ?V4?@8T<AB2, I> 28:>=CNBL 1C@>2V V 35>;>3>@>72V4C20;L=V @>1>B8, >1AO3 1C@>28E B0 35>;>3>@>72V4C20;L=8E @>1VB AB0=>28BL, 3@=.:  EMBED Equation.3 , (6.12) 45  EMBED Equation.3   >1AO3 28@>1=8FB20 C =0BC@0;L=8E >48=8FOE;  EMBED Equation.3   :>HB>@8A=0 20@BVABL >48=8FV 1C@>28E B0 35>;>3>-@>72V4C20;L=8E @>1VB. 7 8@>1=8G0 ?>BC6=VABL ?V4?@8T<AB20 >=OBBO 28@>1=8G>W ?>BC6=>ABV, 2848 ?>BC6=>ABV. >BC6=VABL =0 ?>G0B>: @>:C. !5@54=O ?>BC6=VABL ?V4?@8T<AB2. 8:>@8AB0==O 28@>1=8G>W ?>BC6=>ABV. 8@>1=8G0 ?>BC6=VABL ?V4?@8T<AB20  <0:A8<0;L=> <>6;8289 >1AO3 28?CA:C ?@>4C:FVW ?5@5410G5=>W =><5=:;0BC@8 B0 0A>@B8<5=BC, 70 C<>28 =091V;LH ?>2=>3> 28:>@8AB0==O 28@>1=8G>3> >1;04=0==O V ?;>I 73V4=> V7 7040=8< @568<>< @>1>B8. 848 ?>BC6=>ABV ?V4?@8T<AB20: ?@>5:B=0; ?>B>G=0 (D0:B8G=> 4>AO3=CB0); @575@2=0. @>5:B=0 ?>BC6=VABL 287=0G0TBLAO C ?@>F5AV ?@>5:BC20==O, @5:>=AB@C:FVW 4VNG>3> 01> 1C4V2=8FB20 =>2>3> ?V4?@8T<AB20. >=0 22060TBLAO >?B8<0;L=>N. @>5:B=0 ?>BC6=VABL <0T 1CB8 4>AO3=CB0 ?@>BO3>< =>@<0B82=>3> B5@<V=C WW >A2>T==O. >B>G=0 28@>1=8G0 ?>BC6=VABL 287=0G0TBLAO ?5@V>48G=> C 72 O7:C 7V 7<V=>N C<>2 28@>1=8FB20 01> ?5@528I5==O< ?@>5:B=8E ?>:07=8:V2. @8 FL><C >1G8A;NNBL 2EV4=C (=0 ?>G0B>: @>:C), 28EV4=C (=0 :V=5FL @>:C) B0 A5@54=L>@VG=C ?>BC6=VABL ?V4?@8T<AB20. 575@2=0 ?>BC6=VABL D>@<CTBLAO V ?>ABV9=> VA=CT 2 5=5@35B8FV, 307>2V9 ?@><8A;>2>ABV 4;O ?>:@8BBO ?V:>28E =020=B065=L 2 5;5:B@>- 9 307>28E <5@560E; C B@0=A?>@BV  4;O >1A;C3>2C20==O 4>40B:>28E >1AO3V2 C 72 O7:C 7V 7<V=0<8 A57>=V2. 0 25;8G8=C 28@>1=8G>W ?>BC6=>ABV 2?;820NBL: :V;L:VABL >1;04=0==O; ?@>4C:B82=VABL >1;04=0==O; @568< @>1>B8 ?V4?@8T<AB20; :20;VDV:0FV9=89 @V25=L ?@0FV2=8:V2; AB@C:BC@0 >A=>2=8E D>=4V2. EV4=0 ?>BC6=VABL 287=0G0TBLAO =0 ?>G0B>: 4>A;V46C20=>3> ?5@V>4C (@>:C) =0 >A=>2V 40=8E ?@> =0O2=5 >1;04=0==O B0 V=HV 70A>18 28@>1=8FB20 =0 FN 40BC. 8EV4=0 ?>BC6=VABL CAB0=>2;NTBLAO =0 :V=5FL 4>A;V46C20=>3> ?5@V>4C (@>:C) 7 C@0EC20==O< @5:>=AB@C:FVW >1;04=0==O, 9>3> ?>?>2=5==O, 7<V=8 B5E=>;>3VW 28@>1=8FB20 B>I>.  EMBED Equation.3 , (7.1) 45  EMBED Equation.3   28EV4=0 28@>1=8G0 ?>BC6=VABL;  EMBED Equation.3   2EV4=0 28@>1=8G0 ?>BC6=VABL;  EMBED Equation.3   71V;LH5==O ?>BC6=>ABV 2=0A;V4>: :0?VB0;L=>3> 1C4V2=8FB20 V ?@8410==O 4>40B:>2>3> >1;04=0==O;  EMBED Equation.3   71V;LH5==O ?>BC6=>ABV 2 @57C;LB0BV <>45@=V70FVW 4VNG>3> >1;04=0==O, 24>A:>=0;5==O B5E=>;>3VW;  EMBED Equation.3   7<5=H5==O ?>BC6=>ABV 2=0A;V4>: ;V:2V40FVW >:@5<8E >1 T:BV2 ?V4?@8T<AB20 B0 ;V:2V40FVW >1;04=0==O. !5@54=L>@VG=0 ?>BC6=VABL 287=0G0TBLAO 7 C@0EC20==O< C2545=8E V 282545=8E 7 5:A?;C0B0FVW >A=>2=8E D>=4V2 ?@>BO3>< @>:C. 8@>1=8G0 ?>BC6=VABL @>7@0E>2CTBLAO 70 ?@>2V4=8<8 2840<8 ?@>4C:FVW ?V4?@8T<AB20. ;O 1C@>28E ?V4?@8T<AB2  F5 <0:A8<0;L=89 @VG=89 >1AO3 1C@>28E @>1VB, O:89 28@065=89 :V;L:VABN 70:V=G5=8E 1C4V2=8FB2>< A25@4;>28= V ?@>E>4:>N. !5@54=N ?>BC6=VABL 1C@>2>3> ?V4?@8T<AB20 (2 <5B@0E ?@>E>4:8) <>6=0 @>7@0EC20B8, 28:>@8AB>2CNG8 A5@54=L>A?8A:>2C :V;L:VABL 1C@>28E CAB0=>2>:, ?>:07=8: WE 5:AB5=A82=>3> 28:>@8AB0==O 9 =>@<0B82=C :><5@FV9=C H284:VABL, 70 D>@<C;>N  EMBED Equation.3 , (7.2) 45  EMBED Equation.3   A5@54=L>A?8A:>20 :V;L:VABL 1C@>28E CAB0=>2>:, HB.;  EMBED Equation.3   =>@<0B82=0 :><5@FV9=0 H284:VABL 1C@V==O, </25@AB0B>-<VA.;  EMBED Equation.3   ?>:07=8: 5:AB5=A82=>3> 28:>@8AB0==O 1C@>28E CAB0=>2>:. !5@54=L>A?8A:>20 :V;L:VABL 1C@>28E CAB0=>2>:  EMBED Equation.3 , (7.3) 45  EMBED Equation.3   :V;L:VABL 1C@>28E CAB0=>2>: =0 ?>G0B>: @>:C, HB.;  EMBED Equation.3   :V;L:VABL 1C@>28E CAB0=>2>: 2V4?>2V4=> B8E, O:V =04V9H;8 B0 281C;8 70 @V:, HB.;  EMBED Equation.3   :V;L:VABL ?>2=8E :0;5=40@=8E <VAOFV2 709=OB>ABV 1C@>28E CAB0=>2>: 2V4?>2V4=> B8E, I> =04V9H;8 9 281C;8 C 4>A;V46C20=><C @>FV. @8 284>1CB:C =0DB8 V 307C 4> 0:B82=>W G0AB8=8 >A=>2=8E D>=4V2, O:0 287=0G0T 28@>1=8GC ?>BC6=VABL =0DB>307>284>1C2=>3> ?V4?@8T<AB20, =0;568BL 5:A?;C0B0FV9=89 D>=4 A25@4;>28=. 8@>1=8G0 ?>BC6=VABL B0:>3> ?V4?@8T<AB20 2V41820T 284>1C2=V <>6;82>ABV 70:@V?;5=8E 70 =8< =0DB>28E 01> 307>28E A25@4;>28=. 8@>1=8G0 ?>BC6=VABL =0DB>307>284>1C2=>3> ?V4?@8T<AB20 4>@V2=NT AC<V @VG=8E ?@>5:B=8E =>@< 2V41>@C =0DB8 9 307C 70 2AV<0 ?@>4C:B82=8<8 ?;0AB0<8, O:V 5:A?;C0BCNBLAO ?V4?@8T<AB2><. EV4=0 ?>BC6=VABL ?V4?@8T<AB20:  EMBED Equation.3 , (7.4) 45  EMBED Equation.3   :V;L:VABL A25@4;>28= 4VNG>3> D>=4C =0 ?>G0B>: @>:C, HB.;  EMBED Equation.3   A5@54=L>4>1>289 451VB A25@4;>28=, B/4>1C;  EMBED Equation.3   :>5DVFVT=B 28:>@8AB0==O A25@4;>28=. 8EV4=C ?>BC6=VABL  EMBED Equation.3  287=0G0NBL 7 C@0EC20==O< 7=865==O ?@>4C:B82=>ABV 4VNG8E A25@4;>28=  EMBED Equation.3 V 71V;LH5==O ?>BC6=>ABV 70 @0EC=>: C2545==O =>28E A25@4;>28= 2V4 1C@V==O EMBED Equation.3  B0 AB0@8E 2V4 1574VO;L=>ABV  EMBED Equation.3 .  EMBED Equation.3 . (7.5) !5@54=N ?>BC6=VABL <>6=0 287=0G8B8:  EMBED Equation.3 . (7.6) 8:>@8AB0==O 28@>1=8G>W ?>BC6=>ABV >FV=NTBLAO 70 :>5DVFVT=B>< 28:>@8AB0==O ?>B>G=>W ?>BC6=>ABV ():  EMBED Equation.3 , (7.7) 45  EMBED Equation.3   >1AO3 28@>1=8FB20 70 4>A;V46C20=89 ?5@V>4;  EMBED Equation.3   A5@54=O 28@>1=8G0 ?>BC6=VABL 70 4>A;V46C20=89 ?5@V>4. 8 8B@0B8 ?V4?@8T<AB20. !>1V20@BVABL ?@>4C:FVW V WW 2848. &V=8 =0 ?@>4C:FVN 030;L=0 E0@0:B5@8AB8:0 28B@0B ?V4?@8T<AB20. ;0A8DV:0FVO 28B@0B. @C?C20==O 28B@0B 70 5:>=><VG=8<8 5;5<5=B0<8. !CB=VABL @>7?>4V;C 28B@0B =0 7<V==V B0 ?>ABV9=V. !CB=VABL @>7?>4V;C 28B@0B =0 ?@O<V 9 =5?@O<V. !:;04 7030;L=>28@>1=8G8E 28B@0B. >=OBBO A>1V20@B>ABV ?@>4C:FVW B0 WW 2848. 0;L:C;N20==O A>1V20@B>ABV ?@>4C:FVW. &V=8 =0 ?@>4C:FVN, =0?@O<8 V 465@5;0 7=865==O 70B@0B =0 28@>1=8FB2>. 030;L=0 E0@0:B5@8AB8:0 28B@0B ?V4?@8T<AB20. ;0A8DV:0FVO 28B@0B # ?@>F5AV D>@<C20==O >4=8E B0 28:>@8AB0==O V=H8E @5AC@AV2 ?V4?@8T<AB2> 74V9A=NT 28B@0B8. 0@BVABL 28:>@8AB0=8E 28@>1=8G8E 70?0AV2 (A8@>28=8, <0B5@V0;V2), 7=>AC >A=>2=8E D>=4V2 V =5<0B5@V0;L=8E 0:B82V2, >?;0B8 ?@0FV ?@0FV2=8:V2 D>@<CT 28B@0B8 I>4> 28@>1=8FB20 ?@>4C:FVW, =040==O ?>A;C3, 28:>=0==O @>1VB. B65, 28B@0B8  F5 28B@0G5=V @5AC@A8 C E>4V 4VO;L=>ABV ?V4?@8T<AB20, O:V 28:>@8AB>2CNBLAO 7 <5B>N >B@8<0==O ?@81CB:C 01> 704;O 4>AO3=5==O V=H>W <5B8. 65@5;>< ?>:@8BBO 28B@0B ?V4?@8T<AB20 T 9>3> 4>E>48. 0B@0B8, 74V9A=N20=V 157 1C4L-O:>W :><?5=A0FVW, 2V4=>AOBL 4> 2B@0B. 1AO3 28@>1=8FB20 ?>28=5= 1CB8 B0:8<, I>1 >B@8<0=89 4>EV4 ?VA;O @50;V70FVW 28@>1;5=>W ?@>4C:FVW (@>1VB, ?>A;C3) ?>:@8202 28B@0B8 ?V4?@8T<AB20, 9 C @57C;LB0BV 2>=> 1 >45@60;> ?@81CB>:. ">1B> 28@CG:0 2V4 @50;V70FVW 28@>1;5=>W ?@>4C:FVW = 28B@0B8 + ?@81CB>:. G5284=>, I> 28B@0B8 ?V4?@8T<AB20 @07>< 7 CAB0=>2;5=>N FV=>N =0 ?@>4C:FVN ACBBT2> ?>2 O70=V 7 >B@8<0=8< ?@81CB:><. #AV 28B@0B8, O:V 74V9A=NNBLAO ?V4?@8T<AB2><, @V7=OBLAO 70 E0@0:B5@><, 5:>=><VG=8< 7<VAB><, <VAF5<, ?5@V>4>< 28=8:=5==O B>I>, B><C WE <>6=0 :;0A8DV:C20B8 70 @V7=8<8 >7=0:0<8. "01;8FO 8.1  ;0A8DV:0FVO 28B@0B ?V4?@8T<AB20 7=0:08B@0B8@8<VB:81231 0 F5=B@0-<8 2V4?>2V-40;L=>ABV (<VAF5< 28=8:=5==O 28B@0B)@>1>G>3> <VAFO, F5EC, AB04VW, 28@>1=8FB20, A;C6188B@0B8 3@C?CNBL C @>7@V7V AB@C:BC@=8E ?V4@>74V;V2 2 0 2840<8 ?@>4C:FVW (@>1VB, ?>A;C3)=0 >:@5<V 2848 ?@>4C:FVW, @>1VB, ?>A;C3; =0 >4=>@07>2V 70<>2;5==O; =0 20;>2C; =0 B>20@=C; =0 @50;V7>20=C ?@>4C:FVW 8B@0B8 =0 :>=:@5B=89 >1 T:B 28B@0B3 0 2840<8 28B@0B28B@0B8 70 5:>=><VG=8<8 5;5<5=B0<8; 28B@0B8 70 AB0BBO<8 :0;L:C;OFVW V4 5;5<5=B0<8 28B@0B @>7C<VNBL 5:>=><VG=> >4=>@V4=V 2848 28B@0B. @C?C20==O 74V9A=NNBL 4;O >@30=V70FVW :>=B@>;N 70 @V2=5< 28B@0B C FV;><C ?> ?V4?@8T<AB2C. @C?C20==O 70 AB0BBO<8 :0;L:C;OFVW ?@87=0G5=5 4;O >@30=V70FVW 0=0;V7C B0 >1;V:C 28B@0B, :0;L:C;N-20==O A>1V20@B>ABV ?@>4C:FVW (@>1VB, ?>A;C3), 74V9A=NTBLAO 70 AB0BBO<8 :0;L:C;OFVW. 5@5;V: AB0B59 70;568BL 2V4 30;C752>W =0;56=>ABV ?V4?@8T<AB204 > 2V4=>H5==N 4> 28@>1-=8FB2028@>1=8GV, ?>7028@>1=8GV> 28@>1=8G8E 2V4=>AOBL CAV 28B@0B8, 157?>A5@54=L> ?>2 O70=V 7 283>B>2;5==O< ?@>4C:FVW (B>20@V2, @>1VB, ?>A;C3). >7028@>1=8GV 28B@0B8 ?>2 O70-=V 7 C?@02;V==O< ?V4?@8T<AB2>< B0 @50;V70FVTN ?@>4C:FVW B>I>. @>4>265==O B01;8FV 8.11235 0 A?>A>1>< ?5@5=5A5==O 20@B>ABV =0 ?@>4C:FVN?@O<V, =5?@O<V@O<V 28B@0B8 ?>2 O70=V 7 283>B>2;5==O< ?52=>3> 284C ?@>4C:FVW (B>20@V2, @>1VB, ?>A;C3). >=8 <>6CBL 1CB8 157?>A5@54=L> 2:;NG5=V 4> WE A>1V20@B>ABV. 5?@O<V 28B@0B8 =5 <>6CBL 1CB8 ?@O<> ?>2 O70=8<8 7 :>=:@5B=8< 284>< ?@>4C:FVW. 5?@O<V 28@>1=8GV 28B@0B8 <0NBL =072C 7030;L=>-28@>1=8G8E. 6 0 5:>=><VG=8< 7<VAB>< >A=>2=V, =0:;04=V 8B@0B8 3@C?CNBL 70 2V4=>H5==O< 4> B5E=>;>3VG=>3> ?@>F5AC: >A=>2=V 28B@0B8 157?>A5@54=L> ?>2 O70=V 7 B5E=>;>3VG=8< ?@>F5A>< 283>B>2;5==O ?@>4C:FVW; 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FV=:0 5D5:B82=>ABV :0?VB0;L=8E 2:;045=L # ?@0:B8FV 3>A?>40@N20==O 206;82> >FV=8B8 @57C;LB0B 1C4L-O:>3> 70E>4C. 57C;LB0B82=VABL V=25ABC20==O >FV=NTBLAO G5@57 5D5:B82=VABL (4>FV;L=VABL) 2:;045=L. 87=0G0TBLAO A?V22V4=>H5==O< <V6 :>@8A=8< @57C;LB0B>< 2V4 :0?VB0;L=8E 2:;045=L B0 28B@0B0<8, O:V 1C;8 A?@O<>20=V =0 WE @50;V70FVN V A?@8G8=8;8 F59 @57C;LB0B. )>4> @50;L=8E V=25AB8FV9 @>7@V7=ONBL: 01A>;NB=C 5D5:B82=VABL; ?>@V2=O;L=C 5D5:B82=VABL. 1A>;NB=0 5D5:B82=VABL ?>:07CT 7030;L=C 25;8G8=C 2V440GV :0?VB0;L=8E 28B@0B =0 B><C G8 V=H><C ?V4?@8T<AB2V. >@V2=O;L=0 5D5:B82=VABL 287=0G0TBLAO 70 C<>28 =0O2=>ABV 45:V;L:>E 20@V0=BV2 V=25AB8FV9=8E ?@>5:BV2, E0@0:B5@87CT ?5@52038 O:>3>AL ?@>5:BC. >:07=8:8 01A>;NB=>W V ?>@V2=O;L=>W 5D5:B82=>ABV 270T<>?>2 O70=V G5@57 A8AB5<C V=45:AV2, =>@<0B82=8E ?>:07=8:V2 B>I>. 1A>;NB=0 5D5:B82=VABL E0@0:B5@87CTBLAO B0:8<8 ?>:07=8:0<8: 1 >5DVFVT=B 5:>=><VG=>W 5D5:B82=>ABV :0?VB0;>2:;045=L ( EMBED Equation.3 ) 0) 4;O >:@5<8E ?@>5:BV2 01> 4;O :0?VB0;L=8E 28B@0B =0 4VNG8E ?V4?@8T<AB20E:  EMBED Equation.3 , (10.1) 45  EMBED Equation.3   @VG=89 >1AO3 28@>1=8FB20, 3@=.;  EMBED Equation.3   ?>2=0 A>1V20@BVABL @VG=>3> 28?CA:C ?@>4C:FVW (@>1VB, ?>A;C3), 3@=.;  EMBED Equation.3   @VG=89 ?@81CB>:, 3@=.;  EMBED Equation.3 - :0?VB0;L=V 2:;045==O =0 74V9A=5==O 70E>4C, 3@=.; 1) 4;O ?V4?@8T<AB2, O:8< CAB0=>2;NNBLAO 70240==O I>4> 7=865==O A>1V20@B>ABV:  EMBED Equation.3 , (10.2) 45  EMBED Equation.3 ,  EMBED Equation.3  ?>2=0 A>1V20@BVABL @VG=>3> 28?CA:C ?@>4C:FVW (@>1VB, ?>A;C3) 2V4?>2V4=> 4> V ?VA;O 74V9A=5==O :0?VB0;>2:;045=L, 3@=. >7@0EC=:>2V 7=0G5==O :>5DVFVT=BV2  EMBED Equation.3  ?>@V2=NNBL V7 =>@<0B82=8< :>5DVFVT=B><  , I> 2AB0=>2;NTBLAO =0 7030;L=>45@602=><C @V2=V 01> 30;C7528<8 =>@<0<8. "5?5@  EMBED Equation.3 . /:I>  EMBED Equation.3 , B> 2:;045==O :0?VB0;C 22060TBLAO 4>FV;L=8<. 2 !B@>: >:C?=>ABV :0?VB0;>2:;045=L ( EMBED Equation.3 , @>:V2)  EMBED Equation.3 . (10.3) >@V2=O;L=0 5D5:B82=VABL :0?VB0;>2:;045=L 287=0G0TBLAO G5@57 ?>:07=8: ?@82545=8E 28B@0B (Z):  EMBED Equation.3 , (10.4) 45  EMBED Equation.3   A>1V20@BVABL @VG=>3> 28?CA:C ?@>4C:FVW (@>1VB, ?>A;C3) 70 V-8< 20@V0=B>< :0?VB0;>2:;045=L, 3@=.;  EMBED Equation.3   :0?VB0;>2:;045==O 70 V-8< 20@V0=B><, 3@=. '0AB> ?>:07=8:  EMBED Equation.3  287=0G0TBLAO C @>7@0EC=:C =0 >48=8FN ?@>4C:FVW. &59 <5B>4 107CTBLAO =0 ?@8?CI5==V, I> :0?VB0;L=V 28B@0B8 74V9A=NNBLAO >4=>@07>2>. "><C, O:I> 2:;045==O C :0?VB0; 1C4CBL 74V9A=N20B8AL ?@>BO3>< 45:V;L:>E @>:V2, C@0E>2CNBL G8==8: G0AC  :>5DVFVT=B  EMBED Equation.3 . 0?VB0;L=V 28B@0B8 1V;LH ?V7=VE @>:V2 ?@82>4OBL 4> @>7@0EC=:>2>3> @>:C <=>65==O< =0 :>5DVFVT=B  EMBED Equation.3 .  EMBED Equation.3 , (10.5) 45  EMBED Equation.3   =>@<0B82 ?@82545==O (<>65 1CB8 ?@89=OB0 ?@>F5=B=0 AB02:0 10=:V2AL:>3> :@548BC 01> AB0;0 25;8G8=0  EMBED Equation.3 = 0,08);  EMBED Equation.3   ?5@V>4 ?@82545==O (t-89 @V:), B>1B> C ?5@H><C @>FV:  EMBED Equation.3 ; C 4@C3><C @>FV:  EMBED Equation.3 ; C B@5BL><C @>FV:  EMBED Equation.3 . ">4V  EMBED Equation.3 , 45  EMBED Equation.3   :0?VB0;L=V 28B@0B8 C t-<C @>FV WE >A2>T==O, 3@=.;  EMBED Equation.3   :>5DVFVT=B ?@82545==O 2V4?>2V4=>3> @>:C >A2>T==O V=25AB8FV9; "  7030;L=89 B5@<V= @50;V70FVW V=25AB8FV9=>3> ?@>5:BC, @>:V2. 11 :>=><VG=0 5D5:B82=VABL 4VO;L=>ABV ?V4?@8T<AB20 D5:B82=VABL 4VO;L=>ABV ?V4?@8T<AB20 O: 5:>=><VG=0 :0B53>@VO. !8AB5<0 ?>:07=8:V2 5:>=><VG=>W 5D5:B82=>ABV 28@>1=8FB20: C7030;L=NNGV ?>:07=8:8 B0 ?>:07=8:8 5D5:B82=>ABV 28:>@8AB0==O @5AC@AV2. C4L-O:V @57C;LB0B8 4VO;L=>ABV ?V4?@8T<AB20 1060=> >FV=8B8 7 B>G:8 7>@C >B@8<0=>3> 5D5:BC 2V4 28:>@8AB0==O :04@>2>3> ?>B5=FV0;C, <0B5@V0;L=8E, =5<0B5@V0;L=8E B0 DV=0=A>28E @5AC@AV2. >B@510 2 >FV=N20==V 5D5:B82=>ABV 4VO;L=>ABV 28=8:0T G5@57 =5>1EV4=VABL >45@60==O =091V;LH>3> ?@81CB:C 7 =09<5=H8<8 70B@0B0<8 @5AC@AV2. 87=0G8B8, =0A:V;L:8 5D5:B82=>N 1C;0 4VO;L=VABL C B><C G8 V=H><C ?5@V>4V, <>6=0, O:I> 28:>@8AB>2C20B8 =0ABC?=C <>45;L:  EMBED Equation.3 . !CB=VABL >FV=:8 ?>;O30T C 7VAB02;5==V >45@60=>3> 5:>=><VG=>3> 5D5:BC 7 28B@0B0<8 =0 9>3> 4>AO3=5==O. 57C;LB0B 28@>1=8FB20, O: =09206;82VHC A:;04>2C 287=0G5==O 5D5:B82=>ABV, =5 <>6=0 @>7C<VB8 >4=>7=0G=>. &5 <>65 1CB8 @57C;LB0B A0<>3> 28@>1=8FB20 01> :V=F5289 =0@>4=>3>A?>40@AL:89 @57C;LB0B @>1>B8 ?V4?@8T<AB20. AB0==V9 C@0E>2CT 7=0G8<VABL @57C;LB0BV2 @>1>B8 ?V4?@8T<AB20 4;O ACA?V;LAB20. 57C;LB0B 28@>1=8FB20 <>65 1CB8 28@065=89 O: C =0BC@0;L=V9, B0: V C 20@BVA=V9 D>@<0E. :>=><VG=V @57C;LB0B8 E0@0:B5@87CNBLAO @V7=8<8 20@BVA=8<8 ?>:07=8:0<8, O:V 287=0G0NBL ?@><V6=V B0 :V=F52V @57C;LB0B8 28@>1=8FB20. &5 ?@81CB>:, >1AO38 28@>1=8FB20 B>20@=>W, 20;>2>W, @50;V7>20=>W, G8AB>W ?@>4C:FVW, 5:>=><VO >:@5<8E 284V2 @5AC@AV2 01> 7030;L=0 5:>=><VO 2V4 7<5=H5==O A>1V20@B>ABV. !>FV0;L=89 5D5:B 28@060TBLAO C A:>@>G5==V @>1>G>3> B86=O, 71V;LH5==V @>1>G8E <VAFL, ?>;V?H5==O< C<>2 ?@0FV 9 B. V=. !>FV0;L=89 5D5:B 702648 <>65 1CB8 28<V@O=89 :V;L:VA=>. V7=><0=VBBO @57C;LB0BV2 28@>1=8FB20 ?@82>48BL 4> =0O2=>ABV @V7=8E 284V2 5D5:B82=>ABV 28@>1=8FB20. :>=><VG=C 5D5:B82=VABL 4VO;L=>ABV ?V4?@8T<AB20 ?@89=OB> >FV=N20B8 70 4>?><>3>N A8AB5<8 ?>:07=8:V2, O:0 2:;NG0T C7030;L=NNGV ?>:07=8:8 B0 G0AB:>2V ?>:07=8:8 5D5:B82=>ABV 28:>@8AB0==O >:@5<8E 284V2 @5AC@AV2.  #7030;L=NNGV ?>:07=8:8: . >:07=8:8 @5=B015;L=>ABV (?@81CB:>2>ABV) ?@>4C:FVW (@>1VB, ?>A;C3) E0@0:B5@87CNBL @V25=L 5D5:B82=>ABV (4>EV4=>ABV) 28B@0B =0 28@>1=8FB2> V 71CB. 5=B015;L=VABL ?@>4C:FVW, @>1VB 01> ?>A;C3 (R, %) 287=0G0TBLAO O: 2V4=>H5==O >B@8<0=>3> ?@81CB:C (@) 4> G8AB>3> 4>E>4C (') G8 ?>2=>W A>1V20@B>ABV ?@>4C:FVW, @>1VB 01> ?>A;C3 EMBED Equation.3   EMBED Equation.3 . (11.1) 5=B015;L=VABL 28@>1=8FB20 >:@5<>3> 28@>1C(>48=8FV ?@>4C:FVW) V-3> 284C ( EMBED Equation.3 , %):  EMBED Equation.3 , (11.2) 45  EMBED Equation.3   FV=0 V -3> 28@>1C (>48=8FV ?@>4C:FVW), 3@=.;  EMBED Equation.3   ?>2=0 A>1V20@BVABL V -3> 28@>1C, 3@=. 5=B015;L=VABL 28@>1=8FB20 ( EMBED Equation.3 , %) 287=0G0TBLAO 2V4=>H5==O< ?@81CB:C 4> A5@54=L>W 20@B>ABV >A=>2=8E D>=4V2  EMBED Equation.3  V >1>@>B=8E 70A>1V2  EMBED Equation.3  70 4>A;V46C20=89 ?5@V>4  EMBED Equation.3 ; (11.3) . V25=L 28B@0B =0 >48=8FN ?@>4C:FVW (@>1VB, ?>A;C3) ( EMBED Equation.3 , 3@=./3@=.) 287=0G0TBLAO 4V;5==O< AC<8 28B@0B =0 28@>1=8FB2> 9 @50;V70FVN ?@>4C:FVW ( EMBED Equation.3 ) =0 >1AO3 283>B>2;5=>W ?@>4C:FVW, @>1VB, ?>A;C3 (, 3@=.)  EMBED Equation.3 . (11.4)  '0AB:>2V ?>:07=8:8 (?>:07=8:8 5D5:B82=>ABV 28:>@8AB0==O @5AC@AV2) > G0AB:>28E ?>:07=8:V2 5:>=><VG=>W 5D5:B82=>ABV 4VO;L=>ABV ?V4?@8T<AB20 2V4=>AOBL ?>:07=8:8 5D5:B82=>ABV 28:>@8AB0==O ?5@A>=0;C (28@>1VB>: V7 @>7@0EC=:C =0 >4=>3> ?@0FNNG>3> B0 =0 >4=>3> @>1VB=8:0, B5<?8 WE 7@>AB0==O, B@C4><VAB:VABL >48=8FV ?@>4C:FVW, @>1VB, ?>A;C3 B>I>); >A=>2=8E 28@>1=8G8E D>=4V2 (7030;L=0 D>=4>2V440G0, D>=4>2V440G0 0:B82=>W G0AB8=8 >A=>2=8E D>=4V2, D>=4>@5=B015;L=VABL, D>=4>T<=VABL ?@>4C:FVW); >1>@>B=8E :>HBV2 (:>5DVFVT=B >1>@>BC, :>5DVFVT=B 7020=B065==O >1>@>B=8E 70A>1V2, B@820;VABL >4=>3> >1>@>BC >1>@>B=8E :>HBV2, 2V4=>A=5 282V;L=5==O 01> 4>40B:>25 70;CG5==O >1>@>B=8E :>HBV2); :0?VB0;L=8E 2:;045=L (01A>;NB=0 5D5:B82=VABL :0?VB0;>2:;045=L, B5@<V= >:C?=>ABV V=25AB8FV9). 12 :>=><VG=0 5D5:B82=VABL 28:>@8AB0==O =>2>W B5E=V:8 :>=><VG=0 5D5:B82=VABL B0 5:>=><VG=89 5D5:B 2V4 C?@>20465==O 70E>4V2. VG=89 5:>=><VG=89 5D5:B =>2>W B5E=V:8, =>28E B5E=>;>3VG=8E ?@>F5AV2, <5E0=V70FVW 9 02B><0B870FVW 28@>1=8FB20, 70A>1V2 >@30=V70FVW 28@>1=8FB20 V ?@0FV, =>28E 70A>1V2 ?@0FV 4>23>B@820;>3> 70AB>AC20==O, 2V4 28@>1=8FB20 B0 28:>@8AB0==O =>28E 01> 24>A:>=0;5=8E 70A>1V2 ?@0FV. VG=89 5:>=><VG=89 5D5:B 2V4 28@>1=8FB20 =>2>W ?@>4C:FVW ?>;V?H5=>W O:>ABV. 87=0G5==O 2?;82C 70E>4V2 =0 B5E=V:>-5:>=><VG=V ?>:07=8:8 ?V4?@8T<AB20. :>=><VG=0 5D5:B82=VABL B0 5:>=><VG=89 5D5:B 2V4 C?@>20465==O 70E>4V2 @8 @>73;O4V ?8B0==O 5:>=><VG=>W 5D5:B82=>ABV 28:>@8AB0==O =>2>W B5E=V:8 A;V4 @>7@V7=OB8 ?>=OBBO 5:>=><VG=>W 5D5:B82=>ABV B0 5:>=><VG=>3> 5D5:BC 2V4 C?@>20465==O B8E G8 V=H8E 70E>4V2. D5:B82=VABL  F5 2V4=>A=0 25;8G8=0, I> E0@0:B5@87CT @57C;LB0B82-=VABL 1C4L-O:8E 70B@0B. D5:B82=VABL B5E=VG=8E =>2>22545=L T 2V4=>H5==O< 5D5:BC 2V4 74V9A=5==O 70E>4V2 4> 70B@0B =0 =8E. D5:B  F5 @57C;LB0B 1C4L-O:>3> 70E>4C, O:89 G0ABVH5 28@060TBLAO ?52=>N 3@>H>2>N AC<>N. VG=89 5:>=><VG=89 5D5:B =>2>W B5E=V:8 (28=0E>4V2 B0 @0FV>=0;V70B>@AL:8E ?@>?>78FV9) 2V4>1@060T AC<0@=C 5:>=><VN 2AVE 28@>1=8G8E @5AC@AV2 (682>W ?@0FV, <0B5@V0;V2, :0?VB0;L=8E 2:;045=L), O:C >B@8<CT 3>A?>40@AB2> C @57C;LB0BV 28@>1=8FB20 9 28:>@8AB0==O =>2>W B5E=V:8. 87=0G5==O @VG=>3> 5:>=><VG=>3> 5D5:BC >A=>2CTBLAO =0 7VAB02;5==V ?@82545=8E 70B@0B ?> 107>2V9 V =>2V9 B5E=VFV. @82545=V 70B@0B8 >48=8FV ?@>4C:FVW (2 3@82=0E), B>1B> AC<0 A>1V20@B>ABV B0 =>@<0B82=>3> ?@81CB:C:  EMBED Equation.3 , (12.1) 45  EMBED Equation.3   A>1V20@BVABL >48=8FV ?@>4C:FVW (@5<>=BC), 3@=.;  EMBED Equation.3   =>@<0B82=89 :>5DVFVT=B 5D5:B82=>ABV :0?VB0;L=8E 2:;045=L ( EMBED Equation.3 );  EMBED Equation.3   ?8B><V :0?VB0;L=V 2:;045==O C 28@>1=8GV D>=48, 3@=. VG=89 5:>=><VG=89 5D5:B 2V4 70AB>AC20==O =>28E B5E=>;>3VG=8E ?@>F5AV2, <5E0=V70FVW B0 02B><0B870FVW 28@>1=8FB20, 70A>1V2 >@30=V70FVW 28@>1=8FB20 9 ?@0FV, I> 70157?5GCNBL 5:>=><VN 28@>1=8G8E @5AC@AV2 ?@8 28?CA:C >4=VTW V BVTW 6 ?@>4C:FVW, 287=0G0TBLAO 70 D>@<C;>N  EMBED Equation.3 , (12.2) 45  EMBED Equation.3   ?@82545=V 70B@0B8 >48=8FV ?@>4C:FVW (@>1VB), I> 28@>1;OTBLAO 70 4>?><>3>N 107>2>W B0 =>2>W B5E=V:8, 287=0G0NBLAO 70 D>@<C;>N 12.1;  EMBED Equation.3   @VG=89 >1AO3 28@>1=8FB20 ?@>4C:FVW (@>1VB) 70 4>?><>3>N =>2>W B5E=V:8 C @>7@0EC=:>2><C @>FV, =0BC@0;L=V >48=8FV. 8E>4OG8 7V 7<VABC ?@82545=8E 28B@0B, D>@<C;0 (12.2) <>65 1CB8 ?@54AB02;5=0 C =0ABC?=><C 283;O4V:  EMBED Equation.3 . (12.3) VG=89 5:>=><VG=89 5D5:B ?@8 28:>@8AB0==V =>28E 70A>1V2 ?@0FV 4>23>B@820;>3> 70AB>AC20==O (<0H8=8, >1;04=0==O, ?@8;048 B>I>) 7 ?>;V?H5=8<8 O:VA=8<8 E0@0:B5@8AB8:0<8 (?@>4C:B82=VABL, 4>23>2VG=VABL, 5:A?;C0B0FV9=V 70B@0B8 B>I>) 287=0G0NBL 70 D>@<C;>N  EMBED Equation.3 , (12.4) 45  EMBED Equation.3   ?@82545=V 28B@0B8 2V4?>2V4=> 107>2>3> B0 =>2>3> 70A>1C ?@0FV, 3@=.;  EMBED Equation.3   :>5DVFVT=B 7@>AB0==O ?@>4C:B82=>ABV >48=8FV =>2>3> 70A>1C ?@0FV ?>@V2=O=> 7 107>28<;  EMBED Equation.3   @VG=V >1AO38 ?@>4C:FVW, I> 28@>1;OTBLAO 70 4>?><>3>N 2V4?>2V4=> 107>2>3> B0 =>2>3> 70A>1C ?@0FV, =0BC@0;L=V >48=8FV;  EMBED Equation.3   :>5DVFVT=B 7<V=8 AB@>:C A;C618 =>2>3> 70A>1C ?@0FV ?>@V2=O=> 7 107>28<;  EMBED Equation.3   G0AB:8 2V4@0EC20=L =0 ?>2=5 2V4=>2;5==O (@5=>20FVN) 107>2>3> V =>2>3> 70A>1C ?@0FV. >7@0E>2CNBLAO O: 25;8G8=8, >15@=5=V AB@>:0< A;C618 70A>1V2 ?@0FV;  EMBED Equation.3   5:>=><VO A?>6820G0 =0 ?>B>G=8E 28B@0B0E, 5:A?;C0B0FVW V 2V4@0EC20==OE 2V4 AC?CB=VE :0?VB0;L=8E 2:;045=L 70 25AL B5@<V= =>2>3> 70A>1C ?@0FV ?>@V2=O=> 7 107>28<, 3@=.;  EMBED Equation.3   AC?CB=V :0?VB0;L=V 2:;045==O A?>6820G0 (157 C@0EC20==O 20@B>ABV 70A>1V2 ?@0FV) 2V4?>2V4=> ?@8 28:>@8AB0==V 107>2>3> B0 =>2>3> 70A>1C ?@0FV C @>7@0EC=:C =0 >1AO3 ?@>4C:FVW (@>1>B8), I> 28:>=CTBLAO 70 4>?><>3>N =>2>3> 70A>1C ?@0FV, 3@=.;  EMBED Equation.3   @VG=V 5:A?;C0B0FV9=V 70B@0B8 A?>6820G0 2V4?>2V4=> ?@8 28:>@8AB0==V =8< 107>2>3> 9 =>2>3> 70A>1C ?@0FV C @>7@0EC=:C =0 >1AO3 ?@>4C:FVW (@>1>B8 ), I> 28:>=CTBLAO 70 4>?><>3>N =>2>3> 70A>1C ?@0FV, 3@=. # F8E 70B@0B0E C@0E>2CNBL BV;L:8 G0AB8=C 0<>@B870FVW, ?@87=0G5=>W 4;O :0?VB0;L=>3> @5<>=BC 70A>1V2 ?@0FV, 0 B0:>6 0<>@B870FV9=V 2V4@0EC20==O ?> AC?CB=VE :0?VB0;L=8E 2:;045==OE A?>6820G0;  EMBED Equation.3   @VG=89 >1AO3 28@>1=8FB20 (28:>@8AB0==O) =>28E 70A>1V2 ?@0FV C @>7@0EC=:>2><C @>FV 2 =0BC@0;L=8E >48=8FOE. VG=89 5:>=><VG=89 5D5:B 2V4 28@>1=8FB20 V 28:>@8AB0==O =>28E 01> 24>A:>=0;5=8E ?@54<5BV2 ?@0FV (<0B5@V0;8, A8@>28=0, ?0;82>), 0 B0:>6 70A>1V2 ?@0FV V7 AB@>:>< A;C618 <5=H5 2V4 >4=>3> @>:C 287=0G0NBL 70 D>@<C;>N  EMBED Equation.3 , (12.5) 45  EMBED Equation.3   ?@82545=V 28B@0B8 2V4?>2V4=> 107>2>3> B0 =>2>3> ?@54<5BV2 ?@0FV, 3@=.;  EMBED Equation.3   ?8B><V 28B@0B8 2V4?>2V4=> 107>2>3> V =>2>3> ?@54<5BV2 ?@0FV 2 @>7@0EC=:C =0 >48=8FN ?@>4C:FVW (@>1>B8), I> 28?CA:0TBLAO A?>6820G5<, C =0BC@0;L=8E >48=8FOE;  EMBED Equation.3   28B@0B8 =0 >48=8FN ?@>4C:FVW (@>1>B8), I> 28?CA:0TBLAO, 2V4?>2V4=> 7 28:>@8AB0==O< 107>2>3> 9 =>2>3> ?@54<5BV2 ?@0FV;  EMBED Equation.3   AC?CB=V :0?VB0;L=V 2:;045==O A?>6820G0 2V4?>2V4=> ?@8 28:>@8AB0==V 107>2>3> B0 =>2>3> ?@54<5BV2 ?@0FV C @>7@0EC=:C =0 >48=8FN ?@>4C:FVW (@>1>B8), I> 28@>1;OTBLAO V7 70AB>AC20==O< 107>2>3> V =>2>3> ?@54<5BV2 ?@0FV, 3@=.;  EMBED Equation.3   @VG=89 >1AO3 28:>@8AB0==O =>2>3> ?@54<5B0 ?@0FV C @>7@0EC=:>2><C @>FV 2 =0BC@0;L=8E >48=8FOE. VG=89 5:>=><VG=89 5D5:B 2V4 28@>1=8FB20 =>2>W ?@>4C:FVW ?>;V?H5=>W O:>ABV <>6=0 287=0G8B8 70 D>@<C;>N  EMBED Equation.3 , (12.6) 45  EMBED Equation.3   >?5@0FV9=89 ?@81CB>: 2V4 @50;V70FVW =>2>W ?@>4C:FVW (?@8@VAB ?@81CB:C), 3@=.;  EMBED Equation.3   ?8B><V :0?VB0;L=V 2:;045==O =0 28@>1=8FB2> =>2>W ?@>4C:FVW (?8B><V 4>40B:>2V :0?VB0;L=V 2:;045==O ?>2 O70=V 7 ?>;V?H5==O< O:>ABV ?@>4C:FVW), 3@=.;  EMBED Equation.3   @VG=89 >1AO3 =>2>W ?@>4C:FVW ?>;V?H5=>W O:>ABV 2 @>7@0EC=:>2><C @>FV, =0BC@0;L=V >48=8FV. 0?VB0;L=V 2:;045==O, ?>B@V1=V 4;O 268BBO 70E>4C =0C:>2>-B5E=VG=>3> ?@>3@5AC , 287=0G0NBL :>HB>@8A=>-DV=0=A>28< @>7@0EC=:>< 01> 70 :>HB>@8A0<8 70 @>1>G8<8 :@5A;5==O<8, O:V 2:;NG0NBL: 20@BVABL =>2>3> >1;04=0==O 7 C@0EC20==O< 70B@0B =0 9>3> 4>AB02:C, 7020=B065==O, @>720=B065==O 9 A:;04C20==O; 20@BVABL <>=B06=8E V 45<>=B06=8E @>1VB, 28B@0B8 =0 B5E=VG=C ?5@5?V43>B>2:C , =0;03>465==O B0 >A2>T==O 28@>1=8FB20; 20@BVABL 1C4V25;L=8E @>1VB, ?>2 O70=8E V7 @5:>=AB@C:FVTN 1C4V25;L, DC=40<5=BV2 V <0940=G8:V2 4;O >1;04=0==O; 28B@0B8 =0 ?@>5:BC20==O 9 ?5@5428@>1=8GV 28B@0B8, ?>2 O70=V 7 =>2>N B5E=V:>N; 718B>: (-) 01> ?@81CB>: (+) 2V4 28@>1=8FB20 B0 @50;V70FVW ?@>4C:FVW, I> ?5@54CT @>7@0EC=:>2><C. @8 @>7@0EC=:C :0?VB0;L=8E 2:;045=L 20@BVABL >1;04=0==O, I> ?@841020TBLAO, 70A>1V2 <5E0=V70FVW 9 02B><0B870FVW 287=0G0NBL 70 ?@59A:C@0=B=8<8 FV=0<8, 0 70 C<>28 WE 2V4ACB=>ABV  70 4>3>2V@=8<8. 0@BVABL <>=B06=8E @>1VB @>7@0E>2CNBL >:@5<8<8 :>HB>@8A0<8 ?> 2840E @>1VB (=0 >A=>2V @>1>G8E :@5A;5=L), ?@8 C:@C?=5=8E @>7@0EC=:0E ?@89<0NBL C 2V4A>B:0E 4> 20@B>ABV >1;04=0==O. 0@BVABL 1C4V25;L=8E @>1VB B0:>6 287=0G0NBL H;OE>< A:;040==O :>HB>@8AV2, 0 ?@8 C:@C?=5=><C @>7@0EC=:>2V  28E>4OG8 7 >1AO3C @>1VB V 20@B>ABV WE >48=8FV. /:I> ?V4?@8T<AB2> ?5@5410G0T 70<V=C 4VNG>W 01> I5 ?@840B=>W 4> 70AB>AC20==O B5E=V:8, B> =54>0<>@B87>20=0 G0AB:0 20@B>ABV 70 28@0EC20==O< AC<8 <>6;82>W @50;V70FVW ?>28==0 1CB8 >:C?;5=0 5:>=><VTN C @57C;LB0BV 2?@>20465==O 70E>4C V B><C 4>40TBLAO 4> AC<8 ?>B@V1=8E :0?VB0;>2:;045=L. 54>0<>@B87>20=C G0AB:C >1;04=0==O, I> ;V:2V4>2CTBLAO (), <>6=0 287=0G8B8 70 D>@<C;>N  EMBED Equation.3 , (12.7) 45  EMBED Equation.3   20@BVABL >1;04=0==O, I> 0<>@B87CTBLAO, 3@=.;  EMBED Equation.3   @VG=0 =>@<0 0<>@B870FVW =0 @5=>20FVN;  EMBED Equation.3   B@820;VABL 5:A?;C0B0FVW >1;04=0==O, O:5 ;V:2V4>2CTBLAO, @>:8. !>1V20@BVABL ?@>4C:FVW 4> V ?VA;O 2?@>20465==O =>2>W B5E=V:8 287=0G0TBLAO =0 >A=>2V A:;040==O ?;0=>28E :0;L:C;OFV9. VG=89 5:>=><VG=89 5D5:B C @57C;LB0BV 268BBO 70E>4V2, I> 4>72>;ONBL ?V428I8B8 :V=F52C =0DB>2V440GC 01> V=B5=A8DV:C20B8 ?@>F5A 284>1CB:C:  EMBED Equation.3 , (12.8) 45  EMBED Equation.3   ?@82545=V 28B@0B8 =0 284>1CB>: 1 B =0DB8 2V4?>2V4=> 157 B0 V7 70AB>AC20==O< =>2>W B5E=V:8, 3@=.;  EMBED Equation.3   @VG=89 284>1CB>: =0DB8 70 20@V0=B0<8, I> 7VAB02;ONBLAO, B;  EMBED Equation.3   =>@<0B82 ?@82545=8E 28B@0B =0 1 B ?@8@>ABC 284>1CB:C =0DB8, 3@=. /:I> 2?@>20465==O =>28E <5B>4V2 2?;82C =0 ?>:;048 74V9A=NTBLAO 2 C<>20E C65 @>7@>1;N20=>3> @>4>28I0, B> @VG=89 5D5:B AB0=>28BL  EMBED Equation.3 , (12.9) 45  EMBED Equation.3   A>1V20@BVABL 284>1CB:C 1 B>==8 =0DB8 70 20@V0=B0<8, 3@=.;  EMBED Equation.3   4>40B:>2V :0?VB0;L=V 2:;045==O =0 2?@>20465==O =>2>W B5E=V:8, 3@=. "0:89 ?V4EV4 4> >FV=N20==O 2@0E>2CT 5:>=><VN 70E>4V2 4;O @>71C@5==O, >1;0HBC20==O V @>7@>1;5==O =>2>3> @>4>28I0 4;O 284>1CB:C 4>40B:>2>3> >1AO3C =0DB8  EMBED Equation.3 , 0 B0:>6 @57C;LB0B8 V=B5=A8DV:0FVW @>7@>1;5==O ?>:;04V2. ;O C<>2 1C@V==O >4=8< 7 >A=>2=8E ?>:07=8:V2 5D5:B82=>ABV =>2>W B5E=V:8 T A:>@>G5==O B@820;>ABV 1C4V2=8FB20 A25@4;>28=, ?V428I5==O O:>ABV WE 70:V=G5==O. >A?@>7@0EC=:>289 @VG=89 5:>=><VG=89 5D5:B 1C@>2>3> ?V4?@8T<AB20 ?@8 2?@>20465==V =>2>W B5E=V:8  EMBED Equation.3 , (12.10) 45  EMBED Equation.3   5D5:B =0 >4=C B8?>2C A25@4;>28=C  >48=8FN ?@>4C:FVW 1C@>2>3> ?V4?@8T<AB20, 3@=.;  EMBED Equation.3   :V;L:VABL A25@4;>28=, ?>1C4>20=8E ?@>BO3>< @>:C V7 70AB>AC20==O< =>2>W B5E=V:8.  EMBED Equation.3 , (12.11) 45 !  7<V=0 A>1V20@B>ABV 1C@V==O A25@4;>28=8 70 @0EC=>: C?@>20465==O =>2>W B5E=V:8, 3@=.;  EMBED Equation.3   =>@<0B82=89 :>5DVFVT=B 5D5:B82=>ABV =>2>W B5E=V:8 (0,15);  EMBED Equation.3   ?8B><V (=0 A25@4;>28=C) :0?VB0;L=V 2:;045==O ?> 20@V0=B0E 157 V 7 28:>@8AB0==O< =>2>W B5E=V:8, 3@=. 5;8G8=8  EMBED Equation.3  B0  EMBED Equation.3  70;560BL 2V4 B@820;>ABV 1C@V==O A25@4;>28=8. @8 >FV=N20==V 5D5:B82=>ABV =>2>W 1C@>2>W B5E=V:8 =5>1EV4=> 2@0E>2C20B8 4>40B:>289 5D5:B 70 @0EC=>: 4>AB@>:>2>3> 70:V=G5==O 1C4V2=8FB20 A25@4;>28=8 (22545==O WW 2 5:A?;C0B0FVN):  EMBED Equation.3 , (12.12), 45  EMBED Equation.3   :>HB>@8A=0 20@BVABL 1C4V2=8FB20 A25@4;>28=8, 3@=.;  EMBED Equation.3   :>5DVFVT=B, O:89 C@0E>2CT @V7=>B5@<V=>2VABL :0?VB0;L=8E 2:;045=L C 1C4V2=8FB2> A25@4;>28=8;  EMBED Equation.3   =>@<0B82=89 :>5DVFVT=B 5D5:B82=>ABV :0?VB0;L=8E 2:;045=L (0,12);  EMBED Equation.3   A:>@>G5==O B@820;>ABV 1C4V2=8FB20 A25@4;>28=8 70 @0EC=>: C?@>20465==O =>2>W B5E=V:8, @>:8. # A2>N G5@3C 7<V=0 B@820;>ABV 1C4V2=8FB20 >:@5<>W A25@4;>28=8  >48=8FV ?@>4C:FVW 1C@>2>3> ?V4?@8T<AB20:  EMBED Equation.3 , (12.13) 45  EMBED Equation.3   7<V=0 B@820;>ABV 2V4?>2V4=> 28H:>-<>=B06=8E @>1VB, 1C@V==O, :@V?;5==O V 28?@>1C20==O A25@4;>28=8, 3@=. <V=C B@820;>ABV 1C@V==O 9 :@V?;5==O A25@4;>28=8 <>6=0 287=0G8B8 70 4>?><>3>N :>=:@5B=8E ?>:07=8:V2, C B><C G8A;V ?>:07=8:V2 <5E0=VG=>3> 1C@V==O:  EMBED Equation.3 , (12.14) 45 ?> 20@V0=B0E h  A5@54=O ?@>E>4:0 =0 4>;>B>, <;  EMBED Equation.3   <5E0=VG=0 H284:VABL ?@>E>4:8, </3>4;  EMBED Equation.3   G8A;> 4>210=L (@59AV2 V=AB@C<5=BC);  EMBED Equation.3   A5@54=O B@820;VABL 2V4?>2V4=> A?CA:>-?V49><=8E >?5@0FV9 V ?V43>B>2G>-4>?><V6=8E @>1VB C @>7@0EC=:C =0 >4=5 4>210==O (@59A V=AB@C<5=BC), 3>4.;  EMBED Equation.3   B@820;VABL :@V?;5==O A25@4;>28=8, 3>4.;  EMBED Equation.3   V=HV 4>40B:>2V 70B@0B8 G0AC (01> 9>3> 5:>=><VO) C 72 O7:C 7 C?@>20465==O< =>2>W B5E=V:8, 3>4. (=0?@8:;04, A:>@>G5==O G0AC 020@V9, CA:;04=5=L, ?@>AB>N20=L B>I>). !:>@>G5==O B@820;>ABV 1C4V2=8FB20 >:@5<8E A25@4;>28= 70157?5GCT: 7=865==O WE A>1V20@B>ABV, >A:V;L:8 >A=>2=0 G0AB8=0 28B@0B C 1C@V==V 70;568BL 2V4 B@820;>ABV; A:>@>G5==O :0?VB0;L=8E 2:;045=L =0 1C@V==O; 7<5=H5==O >1AO3V2 :0?VB0;L=8E 2:;045=L, I> 7=0E>4OBLAO C =57025@H5=><C 28@>1=8FB2V; 7<5=H5==O 20@B>ABV 28@>1=8G8E D>=4V2 1C@>28E ?V4?@8T<AB2. 5O:V 70E>48, I> 26820NBLAO C ?@>F5AV 1C@V==O A25@4;>28=, 71V;LHCNBL 70B@0B8 =0 WE 1C4V2=8FB2>, 0;5 70157?5GCNBL 5D5:B C =0DB>307>284>1C20==V. 0?@8:;04, 28:>@8AB0==O A?5FV0;L=8E @>7G8=V2 4;O @>7:@8BBO ?@>4C:B82=8E 3>@87>=BV2 40T <>6;82VABL >B@8<0B8 ?V428I5=V ?>G0B:>2V 451VB8. !5@54=L>@VG=89 30;C75289 5D5:B C FL><C 28?04:>2V:  EMBED Equation.3 , (12.15) 45  EMBED Equation.3 B0   A5@54=L>4>1>2V 451VB8 A25@4;>28= ?@8 28:>@8AB0==V 728G09=>3> V A?5FV0;L=>3> ?@><820;L=>3> @>7G8=C, B;   :>5DVFVT=B 5:A?;C0B0FVW A25@4;>28=8; "  A5@54=V9 B5@<V= @>1>B8 =>2>W A25@4;>28=8 ?@>BO3>< @>:C, 4>@V2=NT 183 4>18;   A?5FV0;L=89 =>@<0B82;  EMBED Equation.3   71V;LH5==O 20@B>ABV 1C4V2=8FB20 A25@4;>28=8 70 @0EC=>: 70AB>AC-20==O A?5FV0;L=8E @>7G8=V2;  EMBED Equation.3   @VG=0 :V;L:VABL A25@4;>28=, =0 O:8E 7025@HCTBLAO 1C4V2=8FB2> 7 28:>@8AB0==O< =>2>W B5E=>;>3VW. 87=0G5==O 2?;82C 70E>4V2 =0 B5E=V:>-5:>=><VG=V ?>:07=8:8 ?V4?@8T<AB20 ;O 270T<>72 O7:C 5:>=><VG=>W 5D5:B82=>ABV =>2>W B5E=V:8 7 @5HB>N ?>:07=8:V2 A>FV0;L=>3> 9 5:>=><VG=>3> @>728B:C ?V4?@8T<AB20 70 :>6=8< V7 70E>4V2 <0NBL 1CB8 287=0G5=V: ?@8@VAB ?@81CB:C; 7=865==O A>1V20@B>ABV ?@>4C:FVW; 7@>AB0==O ?@>4C:B82=>ABV ?@0FV; 7<5=H5==O =>@< 28B@0B <0B5@V0;L=8E, 5=5@35B8G=8E B0 B@C4>28E @5AC@AV2. >A?@>7@0EC=:>289 5D5:B @8@VAB ?@81CB:C @>7@0E>2CNBL 70 D>@<C;>N  EMBED Equation.3 , (12.16) 45  EMBED Equation.3   >?B>20 FV=0 ?V4?@8T<AB20 70 >48=8FN ?@>4C:FVW, 3@=.;  EMBED Equation.3  B0  EMBED Equation.3   28?CA: ?@>4C:FVW ?VA;O 2?@>20465==O 70E>4C =0 >A=>2V =>2>W V 107>2>W B5E=V:8;  EMBED Equation.3  B0  EMBED Equation.3   A>1V20@BVABL 28@>1=8FB20 >48=8FV ?@>4C:FVW 2 t-<C @>FV 28:>@8AB0==O =>2>W B5E=V:8 9 C @>FV, I> ?5@54CT 2?@>20465==N =>2>W B5E=V:8, 3@=. ;0=>20 5:>=><VO A>1V20@B>ABV ( EMBED Equation.3 ) 287=0G0TBLAO <=>65==O< 7=865==O A>1V20@B>ABV >48=8FV ?@>4C:FVW =0 :V;L:VABL ?@>4C:FVW, O:C 1C45 28@>1;5=> 70 4>?><>3>N =>2>W B5E=V:8:  EMBED Equation.3 , (12.17) 45  EMBED Equation.3   >1AO3 28@>1=8FB20 ?@>4C:FVW 2 t-<C 70?;0=>20=><C @>FV. !C<0 ?;0=>2>W 5:>=><VW ?> 2AVE 70E>40E ?>:07CT 4>AO3=CB5 7=865==O A>1V20@B>ABV 2AVTW B>20@=>W ?@>4C:FVW C 70?;0=>20=><C @>FV. ?;82 C?@>20465==O =>2>W B5E=V:8 =0 ?;0=>2V 01> D0:B8G=V ?>:07=8:8 =0DB>307>284>1C2=8E V 1C@>28E ?V4?@8T<AB2 287=0G0NBL 7 C@0EC20==O< A?5F8DV:8 30;C7V. "0:, A>1V20@BVABL 284>1CB:C 1 B =0DB8 (3@=.) 70 20@V0=B>< V7 28:>@8AB0==O< =>2>W B5E=V:8:  EMBED Equation.3 , (12.18) 45  EMBED Equation.3   C<>2=> ?>ABV9=V 9 7<V==V 28B@0B8 2V4?>2V4=> C A:;04V A>1V20@B>ABV 1 B =0DB8 70 1078A=8< 20@V0=B>< ( EMBED Equation.3 );  EMBED Equation.3  B0  EMBED Equation.3   @VG=89 284>1CB>: =0DB8 ?> 20@V0=B0E 157 C?@>20465==O =>2>W B5E=V:8 V 7 =8<, B;  EMBED Equation.3   V=HV 4>40B:>2V 70B@0B8 B0 5:>=><VO :>HBV2, ?>2 O70=8E V7 70?@>20465==O< =>2>W B5E=V:8, 3@=. > 25;8G8=8  EMBED Equation.3  C:;NG0NBL, =0?@8:;04, 20@BVABL @5035=BV2 4;O 70:0GC20==O, 5;5:B@>5=5@3VW B>I>. <V=0 A>1V20@B>ABV 1C@V==O B8?>2>W A25@4;>28=8 70 @0EC=>: C?@>20465==O =>2>W B5E=V:8 AB0=>28BL  EMBED Equation.3 , (12.19) 45  EMBED Equation.3  B0  EMBED Equation.3   20@BVABL 1 3>48=8 1C@V==O (@>1>B8 1C@>2>W CAB0=>2:8) ?> 70B@0B0E, O:V 70;560BL 2V4 G0AC, 3@=.;  EMBED Equation.3  B0  EMBED Equation.3   B@820;VABL 1C@V==O V :@V?;5==O A25@4;>28=8, 3>4.;  EMBED Equation.3   V=HV 4>40B:>2V 28B@0B8 01> 5:>=><VO :>HBV2 70 @0EC=>: C?@>20465==O =>2>W B5E=V:8, 3@=.;  EMBED Equation.3   :>5DVFVT=B, O:89 C@0E>2CT @V25=L =5?@O<8E 28B@0B. 8B><V (=0 A25@4;>28=C) :0?VB0;L=V 2:;045==O (3@=.) 287=0G0NBL 70 D>@<C;0<8:  EMBED Equation.3 ; (12.20)  EMBED Equation.3 , (12.21) 45  EMBED Equation.3  B0  EMBED Equation.3   20@BVABL :><?;5:B=>W 1C@>2>W CAB0=>2:8 ?> 20@V0=B0E;  EMBED Equation.3  V  EMBED Equation.3   :>5DVFVT=B >15@B0==O 1C@>2>3> >1;04=0==O, O:89 70;568BL 2V4 H284:>ABV 1C@V==O;  EMBED Equation.3  B0  EMBED Equation.3   20@BVABL :><?;5:BC 1C@8;L=8E B@C1, 3@=.;  EMBED Equation.3  V  EMBED Equation.3   :>5DVFVT=B >15@B0==O :><?;5:BC 1C@8;L=8E B@C1 ( EMBED Equation.3 );  EMBED Equation.3   =>@<0B82 701V9=8E 4283C=V2 =0 1 A25@4;>28=C, I> 1C@8BLAO (5- 7 >48=8FL);  EMBED Equation.3  B0  EMBED Equation.3   20@BVABL >4=>3> 701V9=>3> 4283C=0, 3@=.;  EMBED Equation.3  V  EMBED Equation.3   B@820;VABL 1C@V==O B0 :@V?;5==O A25@4;>28=8 ?> 20@V0=B0E, 3>4. %0@0:B5@ 2?;82C 2?@>20465==O =>2>W B5E=V:8 =0 >48= V7 =09206;82VH8E B5E=V:>-5:>=><VG=8E ?>:07=8:V2  H284:VABL 1C@V==O  2AB0=>2;NNBL 70 D>@<C;0<8:  EMBED Equation.3 , (12.22)  EMBED Equation.3 , (12.23) 45  EMBED Equation.3  B0  EMBED Equation.3   ?;0=>20 :><5@FV9=0 H284:VABL 1C@V==O 2V4?>2V4=> 157 V 7 C@0EC20==O< C?@>20465==O =>2>W B5E=V:8, </25@AB.-<VA.;  EMBED Equation.3   @VG=89 ?;0=>289 >1AO3 ?@>E>4:8 ?V4?@8T<AB20, <;  EMBED Equation.3   70?;0=>20=89 G0A 1C@V==O 157 C@0EC20==O 2?@>20465==O =>2>W B5E=V:8, 25@AB.-<VA.;  EMBED Equation.3   :0;5=40@=89 G0A 1C@V==O, A:>@>G5=89 70 @0EC=>: 70AB>AC20==O >4=>3> V7 70E>4V2, 25@AB.-<VA. <V=C ?@>4C:B82=>ABV ?@0FV ( EMBED Equation.3 ) ?V4 2?;82>< 70E>4V2 4;O =>2>W B5E=V:8 9 >@30=V70FVW 28@>1=8FB20 287=0G0NBL H;OE>< @>7@0EC=:C 7<V=8 28@>1VB:C ?@>4C:FVW =0 >4=>3> ?@0FNNG>3> ?> 20@V0=B0E, O:V ?>@V2=NNBLAO. @8@VAB ?@>4C:B82=>ABV ?@0FV C 2V4A>B:0E  EMBED Equation.3 , (12.24) 45  EMBED Equation.3  B0 EMBED Equation.3   ?@>4C:B82=VABL ?@0FV >4=>3> ?@0FNNG>3> 4> V ?VA;O 2?@>20465==O 70E>4C;  EMBED Equation.3   ?@8@VAB >1AO3C 28@>1=8FB20 C @57C;LB0BV 2?@>20465==O 40=>3> 70E>4C;  EMBED Equation.3   ?@8@VAB ( ) 01> 7<5=H5==O (+) G8A5;L=>ABV C @57C;LB0BV 2?@>20465==O 40=>3> 70E>4C ( EMBED Equation.3 ), G>;.;  EMBED Equation.3  B0  EMBED Equation.3   G8A5;L=VABL ?@0FNNG8E 4> V ?VA;O 2?@>20465==O 70E>4C, G>;. # @>7@0EC=:0E 7<V=8 G8A5;L=>ABV ?@0FNNG8E A;V4 C@0E>2C20B8 WW ?@8@VAB 01> 7<5=H5==O =5 BV;L:8 70 B8<8 ?V4@>74V;0<8, 45 2?@>2046CTBLAO 70EV4, 0;5 9 C AC<V6=8E V7 =8<8 ?V4@>74V;0E. >20 B5E=V:0, I> 2?@>2046CTBLAO =0 ?V4?@8T<AB2V, ?>28==0 70157?5GC20B8 >B@8<0==O 3>A?@>7@0EC=:>2>3> 5D5:BC, :>B@89 @>7@0E>2CTBLAO O: @V7=8FO <V6 >B@8<0=8< ?@81CB:>< 2V4 C?@>20465==O 70E>4C ( EMBED Equation.3 ) B0 =>@<0B82=>N 25;8G8=>N ?@81CB:C ( EMBED Equation.3 ), O:0 70157?5GCTBLAO 4>40B:>28<8 :0?VB0;L=8<8 2:;045==O<8 ( EMBED Equation.3 ):  EMBED Equation.3 . (12.25) >A?@>7@0EC=:>289 5D5:B 287=0G0TBLAO O: 70 :>6=8< 70E>4><, B0: V 72545=89 ?> 2AVE 70E>40E:  EMBED Equation.3 , (12.26) 45  EMBED Equation.3   ?@8@VAB ?@81CB:C (7=865==O A>1V20@B>ABV) 2V4 CAVE 70E>4V2 4;O 2?@>20465==O =>2>W B5E=V:8 2 V-<C @>FV, 3@=.;  EMBED Equation.3   :0?VB0;L=V 2:;045==O =0 2AV 70E>48 4;O 2?@>20465==O =>2>W B5E=V:8 V-3> @>:C, 3@=. A:V;L:8 ?5@52038 =>2>W B5E=V:8 @50;V7CNBLAO ?@>BO3>< 45:V;L:>E @>:V2, 28=8:0T =5>1EV4=VABL 287=0G5==O ?>@O4 V7 @VG=8< 5:>=><VG=8< 5D5:B>< V=B53@0;L=>3> 5:>=><VG=>3> 5D5:BC, O:89 4>72>;OT >FV=8B8 @57C;LB0B8 =0C:>2>-B5E=VG=>3> ?@>3@5AC ("). A=>2=8< C7030;L=NNG8< ?>:07=8:>< :><?;5:A=>W >FV=:8 5D5:B82=>ABV =0C:>2>-B5E=VG=8E 70E>4V2 T ?>:07=8: 5:>=><VG=>3> 5D5:BC 2V4 70E>4C ", C O:><C 7=0E>4OBL 2V4>1@065==O G0AB:>2V ?>:07=8:8 5D5:B82=>ABV: ?@>4C:B82=VABL ?@0FV B0 D>=4>2V440G0, <0B5@V0;><VAB:VABL V 5=5@3><VAB:VABL 28@>1=8FB20, ?>:07=8:8 B5E=VG=>3> @V2=O 28@>1=8FB20 B0 O:>ABV ?@>4C:FVW. >:07=8: 5:>=><VG=>3> 5D5:BC  EMBED Equation.3  =0 2AVE 5B0?0E >FV=N20==O 70E>4V2 =0C:>2>-B5E=VG=>3> ?@>3@5AC 287=0G0NBL O: ?5@528I5==O 20@BVA=>W >FV=:8 @57C;LB0BV2  EMBED Equation.3  =04 AC:C?=8<8 28B@0B0<8  EMBED Equation.3  @5AC@AV2 70 25AL B5@<V= 74V9A=5==O 70E>4V2  EMBED Equation.3   EMBED Equation.3 . (12.27) >;8 74V9A=NNBL 20@BVA=C >FV=:C @57C;LB0BV2 V 28B@0B 70 ?52=8< 70E>4>< " <>6;82V 420 >A=>2=8E 20@V0=B8: 20@V0=B, :>;8 28:>@8AB0==O 70E>4C 4>72>;OT 71V;LH8B8 >1AO3 ?@>4C:FVW, I> 28@>1;OTBLAO (284>1CB:C =0DB8, 307C, :>=45=A0BC); 20@V0=B, :>;8 28:>@8AB0==O 70E>4C 7<V=NT B5E=V:>-5:>=><VG=V ?>:07=8:8 VA=CNG>3> 28@>1=8FB20 70 @0EC=>: 9>3> @5:>=AB@C:FVW, <>45@=V70FVW, 7<V=8 B5E=V:8 V B5E=>;>3V9 >:@5<8E 5;5<5=BV2 28@>1=8FB20, 24>A:>=0;5==O 9>3> >@30=V70FVW, C?@02;V==O B>I>. # ?5@H><C 28?04:>2V  EMBED Equation.3 O2;OT A>1>N ?@8@VAB 28@>1;5=>W ?@>4C:FVW, >FV=5=>W 2 >?B>28E FV=0E, 0  EMBED Equation.3  A:;040TBLAO 7 28B@0B =0 28@>1=8FB2> V 28:>@8AB0==O 4>40B:>2>W ?@>4C:FVW.  V=H><C 28?04:>2V, O:I> >1AO3 28?CI5=>W ?@>4C:FVW =5 7<V=NTBLAO,  EMBED Equation.3  28@060TBLAO 7<5=H5==O< 70B@0B =0 WW 28@>1=8FB2>, 0 ?@8 7<V=V >1AO3V2 28@>1=8FB20 25;8G8=0  EMBED Equation.3  C@0E>2CT 7<V=C 28B@0B V >1AO3V2 ?@>4C:FVW 2 >?B>28E FV=0E. 5;8G8=0  EMBED Equation.3  C FL><C 28?04:>2V O2;OT A>1>N 20@BVABL CAVE @5AC@AV2, 28:>@8AB0=8E =0 @50;V70FVN 70E>4V2 4;O ". >7@0EC=>: 5:>=><VG=>3> 5D5:BC 74V9A=NNBL 7 >1>2 O7:>28< 28:>@8AB0==O< <5B>4C ?@82545==O @V7=>G0A>28E 28B@0B B0 @57C;LB0BV2 4> T48=>3> 4;O 2AVE 20@V0=BV2 70E>4C <><5=BC  @>7@0EC=:>2>3> @>:C  EMBED Equation.3 . # O:>ABV @>7@0EC=:>2>3> @>:C 70AB>A>2CNBL =091V;LH @0==V9 V7 B8E, I> @>73;O40NBLAO, :0;5=40@=89 @V:, O:89 ?5@54CT ?>G0B:C 28?CA:C ?@>4C:FVW. 0@BVA=C >FV=:C @57C;LB0BV2 70 @>7@0EC=:>289 ?5@V>4  EMBED Equation.3  287=0G0NBL O:  EMBED Equation.3 , (12.28) 45  EMBED Equation.3   20@BVA=0 >FV=:0 @57C;LB0BV2 C t - @>FV @>7@0EC=:>2>3> ?5@V>4C, 3@=.;  EMBED Equation.3 , EMBED Equation.3   ?>G0B:>289 V :V=F5289 @V: @>7@0EC=:>2>3> ?5@V>4C ";  EMBED Equation.3   :>5DVFVT=B ?@82545==O 70 D0:B>@>< G0AC. # O:>ABV ?>G0B:>2>3> @>:C @>7@0EC=:>2>3> ?5@V>4C ?@89<0NBL @V: ?>G0B:C DV=0=AC20==O @>1VB V7 74V9A=5==O 70E>4C ". V=F528< @>:>< 22060NBL G0A C <><5=B 7025@H5==O 2AL>3> 68BBT2>3> F8:;C 70E>4C " (B5@<V= A;C618 70A>1V2 ?@0FV, B5@<V= <V6 AB@>:0<8 >=>2;5==O ?@>4C:FVW B>I>). >5DVFVT=B ?@82545==O 70 D0:B>@>< G0AC 4;O 1V;LH ?V7=VE @>:V2, =V6  EMBED Equation.3 , <>6=0 287=0G8B8 70 D>@<C;>N  EMBED Equation.3 , (12.29) 45  EMBED Equation.3   =>@<0B82 ?@82545==O (<>65 1CB8 ?@89=OB0 ?@>F5=B=0 AB02:0 10=:V2AL:>3> :@548BC 01> AB0;0 25;8G8=0  EMBED Equation.3 = 0,1);  EMBED Equation.3   ?5@V>4 ?@82545==O (t-89 @V:). >5DVFVT=B ?@82545==O 70 D0:B>@>< G0AC 4;O @>:V2, I> ?5@54CNBL @>7@0EC=:>2><C  EMBED Equation.3 , <>6=0 287=0G8B8 70 D>@<C;>N  EMBED Equation.3 . (12.30) 0@BVA=0 >FV=:0 @57C;LB0BV2 A:;040TBLAO 7 >A=>2=8E B0 AC?@>2V4=8E @57C;LB0BV2.  EMBED Equation.3 . (12.31) 0@BVA=C >FV=:C >A=>2=8E @57C;LB0BV2 287=0G0NBL 70 =0ABC?=8<8 D>@<C;0<8: 4;O =>28E 70A>1V2 ?@0FV B@820;>3> :>@8ABC20==O  EMBED Equation.3 ; (12.32) 4;O =>28E ?@54<5BV2 ?@0FV  EMBED Equation.3 , (12.33.) 45  EMBED Equation.3   FV=0 >48=8FV ?@>4C:FVW, O:0 28@>1;OTBLAO 70 4>?><>3>N =>2>3> 70A>1C 01> ?@54<5B0 ?@0FV C @>FV t, 3@=.;  EMBED Equation.3   >1AO3 70AB>AC20==O =>28E 70A>1V2 V ?@54<5BV2 ?@0FV C @>FV t, =0BC@0;L=V >48=8FV;  EMBED Equation.3   ?@>4C:B82=VABL 70A>1V2 ?@0FV C @>FV t, =0BC@0;L=V >48=8FV;  EMBED Equation.3   28B@0B8 ?@54<5BV2 ?@0FV =0 >48=8FN ?@>4C:FVW, O:0 28@>1;OTBLAO 7 WE 28:>@8AB0==O< C @>FV t, =0BC@0;L=V >48=8FV. 0@BVA=0 >FV=:0 AC?@>2V4=8E @57C;LB0BV2 <>65 2:;NG0B8 4>40B:>2V 5:>=><VG=V @57C;LB0B8 C @V7=8E AD5@0E =0@>4=>3> 3>A?>40@AB20 9 5:>=><VG=V >FV=:8 A>FV0;L=8E B0 5:>;>3VG=8E =0A;V4:V2 @50;V70FVW 70E>4V2 ". 0B@0B8 =0 74V9A=5==O 70E>4V2 " 287=0G0NBLAO =0ABC?=8< G8=><:  EMBED Equation.3 , (12.34) 45  EMBED Equation.3   28B@0B8 =0 28@>1=8FB2> ?@>4C:FVW 70 @>7@0EC=:>289 ?5@V>4, 3@=.;  EMBED Equation.3   28B@0B8 =0 28:>@8AB0==O ?@>4C:FVW 70 @>7@0EC=:>289 ?5@V>4, 3@=. @8 FL><C 28B@0B8 O: =0 28@>1=8FB2>, B0: V =0 28:>@8AB0==O ?@>4C:FVW (157 C@0EC20==O 28B@0B =0 ?@8410==O A0<>W ?@>4C:FVW) >1G8A;NNBLAO >4=0:>2>:  EMBED Equation.3 , (12.35) 45  EMBED Equation.3   @VG=V 70B@0B8 2AVE @5AC@AV2 C @>FV t, 3@=. VG=V 70B@0B8 2AVE @5AC@AV2 287=0G0NBL =0ABC?=8< G8=><:  EMBED Equation.3 , (12.36) 45  EMBED Equation.3   ?>B>G=V 28B@0B8 =0 28@>1=8FB2> (28:>@8AB0==O) ?@>4C:FVW C @>FV t 157 C@0EC20==O 0<>@B870FV9=8E 2V4@0EC20=L =0 @5=>20FVN, 3@=.;  EMBED Equation.3   >4=>G0A=V 28B@0B8 =0 28@>1=8FB2> (28:>@8AB0==O) C @>FV t, 3@=.;  EMBED Equation.3   70;8H:>20 20@BVABL (;V:2V40FV9=5 A0;L4>) >A=>2=8E D>=4V2, I> 281C20NBL C @>FV t, 3@=. > A:;04C ?>B>G=8E 2:;NG0NBLAO 28B@0B8, I> 2@0E>2CNBLAO 73V4=> 7 G8==8< =0 ?V4?@8T<AB20E ?>@O4:>< :0;L:C;N20==O A>1V20@B>ABV ?@>4C:FVW, 0 4> >4=>G0A=8E  :0?VB0;L=V 2:;045==O B0 V=HV 28B@0B8 :0?VB0;L=>3> E0@0:B5@C (=0 =0C:>2>-4>A;V4=V, :>=AB@C:B>@AL:>-B5E=>;>3VG=V 9 ?@>5:B=V @>1>B8, ?@8410==O CAB0B:C20==O, 9>3> B@0=A?>@BC20==O, <>=B06 V =0;03>465==O, A?>@C465==O =>28E 01> @5:>=AB@C:FVN 4VNG8E 1C4V25;L, A?>@C4 B0 ?5@54020;L=8E ?@8AB@>W2, ?>?>2=5==O >1>@>B=8E :>HBV2, :>B@5 ?>2 O70=5 7 @50;V70FVTN B5E=VG=>3> =>2>22545==O; :>HB8 ?>B@V1=V 4;O 70?>1V30==O =530B82=8< A>FV0;L=8<, 5:>;>3VG=8< 9 V=H8< =0A;V4:0<). VB5@0BC@0 >9:> .!., >=4@0B .., /@5<V9GC: .!. >2V4=8: 7 =0DB>307>2>W A?@028.  L2V2: !2VB, 1996.  620 A. >9G8: .. B0 V=. :>=><V:0 ?V4?@8T<AB20: 02G. ?>AV1=8:.  .: 0@025;0; L2V2: >289 A2VB  2000, 2001.  298 A. >9G8: .. :>=><V:0 ?V4?@8T<AB20: 02G. ?>AV1=8:.  .: BV:0, 2002.  480 A. :>=><V:0 ?V4?@8T<AB20: V4@CG=8: / 0 703. @54. !. $. >:@>?82=>3>.  .: #, 2001. 528 A. -:>=><8:0 8 AB0B8AB8:0 D8@< / >4 @54. !.. ;L5=:>2>9.  .: $8=0=AK 8 AB0B8AB8:0, 1996. 481 A. -:>=><8:0, >@30=870F8O 8 ?;0=8@>20=85 ?@>872>4AB20 =0 ?@54?@8OB8OE =5DBO=>9 8 307>2>9 ?@><KH;5==>AB8: #G51=8: / .$.(<0B>2, ...0;KH52 8 4@.  .: 54@0, 1990.  411 A. -:>=><8:0 ?@54?@8OB8O: #G51=8: 4;O 2C7>2 / ./. 2@0H:>2 8 4@.; ?>4 @54. ?@>D. ./. >@D8=:5;O, ?@>D. .. (20=40@0. 2-5 874., ?5@5@01. 8 4>?.  .: .", 1998. 742 A. I5=:> .., "5@5I5=:> !.. FV=:0 5:>=><VG=>W 5D5:B82=>ABV 28@>1=8FB20 V 70B@0B: 02G. ?>AV1=8:.  .: 8I0 H:., 1991. 173 A. C70= .. :>=><V:0 V >@30=V70FVO 35>;>3>@>72V4C20;L=>3> 28@>1=8FB20: 02G. ?>AV1=8:.  .:  5>?@>3=>7 , 2001.  302 A. ;0=8@>20=85 =0 ?@54?@8OB8OE =5DBO=>9 8 307>2>9 ?@><KH;5==>AB8: #G51=8: 4;O 2C7>2 / ..@5=F, .$.@N35<0= 8 4@.  .:54@0, 1989.  333 A.      HYPERLINK "http://globalteka.ru/" globalteka.ru - @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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