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ABC? 8AC=CB0 ;0C7VCA>< 3V?>B570 ?@> <>6;82VABL B5?;>2>W A<5@BV A5A2VBC (1865), 0 B0:>6 E81=V CO2;5==O ?@> =5V=20@V0=B=VABL @V2=O=L B5@<>48=0<V:8 I>4> @5;OB82VABAL:8E ?5@5B2>@5=L ?@8725;8 4> ?><8;:>2>3> 28A=>2:C ?@> =5?@840B=VABL <5B>4V2 B5@<>48=0<V:8 4> 0=0;V7C 52>;NFV9=8E ?@>F5AV2 C <530A2VBV. 0@07V 6 2V4><>, I> >AB83=CB8 70 1C4L-O:89 O: 7023>4=> 25;8:89, ?@>B5, :V=F5289 ?@><V6>: G0AC A5A2VB ?@8=F8?>2> =5 <>65. >2=><C >E>;>465==N @5G>28=8 ?5@5H:>460T A0<>CB2>@5==O =5N ?@>AB>@>2> =5>4=>@V4=8E B5@<>48=0<VG=8E AB0=V2 V 2V4?>2V4=8E W< 3@02VB0FV9=8E ?>;V2. 5>1<565=>3> @>ABC 5=B@>?VW C A5A2VBV ?5@5H:>460T A0<>CB2>@5==O 2 =L><C B0:>6 V @V7=8E AB@C:BC@=8E >48=8FL, A:;04=VABL O:8E 7@>AB0T 7 :>6=8< =>28< VT@0@EVG=8< @V2=5< A0<>CB2>@5==O ?@8@>4=8E >1'T:BV2, I> A:;040NBLAO 7 =8E. 5;OB82VABAL:5 6 C7030;L=5==O B5@<>48=0<V:8 7 V=20@V0=B=>N 01A>;NB=>N B5<?5@0BC@>N @>73;O40TBLAO 70@07 O: WW =091V;LH ?@89=OB=5 C7030;L=5==O [Van Kampen, 1968; 070@>2, 1964; 1991]. "5@<>48=0<V:0 2 BV9 G8 V=HV9 <V@V 70;CG0;0AO 4> 0=0;V7C ?@>F5AV2 D>@<C20==O <530A:>?VG=8E >1'T:BV2 A5A2VBC V @0=VH5 [=B>=>2, 1962; Lynden-Bell & Kalnajs, 1972; >;OG5=:>, $@84<0=, 1976; 1984; Saslaw, 1968; 1969; 1970; 1985; Binney & Tremaine, 1987]. A>1;82> A;V4 284V;8B8 4>A;V465==O 7 3@02VB0FV9=>W ?;07<8 [Binney & Tremaine, 1987; Binney, 1993] V =0 >A=>2V :V=5B8G=>W B5>@VW @>7@V465=8E 307V2 [40=>2, >;4C38=, 1998], 0 B0:>6 B5>@VN ?@>AB>@>2>-G0A>2>W 52>;NFVW =5@V2=>206=8E B5@<>48=0<VG=8E A8AB5< [;5<A:>9, >?;K:, 1995]. AB0==V< 65 G0A>< =0 >A=>2V 0=0;V7C ?@>F5AV2 A0<>CB2>@5==O 2 =5@V2=>206=8E A8AB5<0E [@83>68=, 8:>;8A, 1977; 1979; @83>68=, 1985] V 1V;LH H8@>:>3> 28:>@8AB0==O <5B>4V2 AB0B8AB8G=>W DV78:8 B5@<>48=0<V:0 A0<>3@02VBCNG8E A8AB5< 4>AO3;0 4>A8BL B0:8 VAB>B=8E CA?VEV2 [Chavanis, 2002; 2005; Katz, 2003]. 4=0: B5@<>48=0<VG=89 V 3@02VB0FV9=89 >?8A8 ?@>F5AV2 A0<>CB2>@5==O 0AB@>=><VG=8E >1'T:BV2 A5A2VBC 2A5 6 I5 =5 ?>T4=0;8AO >@30=VG=> <V6 A>1>N. 5O:V 02B>@8 [Gogberashvili & Kanatchikov, 2010] 2A5 I5 ?@>4>26CNBL ?>HC: 1V;LH 203><8E ACB> B5@<>48=0<VG=8E ?@8G8=, 2V4?>2V40;L=8E O: 70 :@828=C, B0: V 70 DV78G=C =5>4=>@V4=VABL 2;0A=8E ?@>AB>@V2 @5G>28=8. =HV 6 02B>@8 [Jacobson, 1995; Verlinde, 2010] >B>B>6=NNBL A8;C BO6V==O 7 5=B@>?V9=>N A8;>N =5 BV;L:8 =0 >A=>2V B5@<>48=0<V:8, 0 =02VBL V =0 >A=>2V =5728G09=8E 2;0AB82>AB59 =5@50;L=8E G>@=8E 4V@ (70 O:V 2 0AB@>=><VG=8E A?>AB5@565==OE ?@89<0NBL =04728G09=> <0A82=V =59B@>==V 7V@:8, I> 2>;>4VNBL O: B>?>;>3VTN ?>@>6=8AB>3> BV;0 2 D>=>2><C 52:;V4>2><C ?@>AB>@V [Zeldovich & Grischuk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a; 2009: 75; 2009a; 2010: 64; 2010a: 38; 0=8;LG5=:>, 2020: 5]. "5@<>48=0<VG=V AB0=8 @5G>28=8, I> @>73;O40NBLAO C 7030;L=V9 B5>@VW 2V4=>A=>ABV ("), T A0<>=02545=8<8 @5G>28=>N WW ?@>AB>@>2> =5>4=>@V4=8<8 AB0=0<8. &5 ?>2'O7CTBLAO 7 =0O2=VABN C @5G>28=V 3@02VB0FV9=>3> ?>;O, I> 2V4?>2V40T 70 ?@>AB>@>2C =5>4=>@V4=VABL B5<?V2 2V41C20==O 2=CB@VH=L>0B><=8E DV78G=8E ?@>F5AV2 C =V9 0, >B>6, V =02>48BL =5 BV;L:8 :@828=C, 0 V DV78G=C =5>4=>@V4=VABL 2;0A=>3> ?@>AB>@C @5G>28=8 [0=K;LG5=:>, 1994a; 2004: 35; 2008b: 45].  6>@AB:8E A8AB5<0E 2V4;V:C ?@>AB>@>28E :>>@48=0B B0 G0AC (!) FO DV78G=0 =5>4=>@V4=VABL ?@>AB>@C ?@>O2;OTBLAO C 283;O4V =5>4=0:>2>ABV 2 @V7=8E 9>3> B>G:0E B0:>W ?@8E>20=>W B5@<>48=0<VG=>W 2;0AB82>ABV (?0@0<5B@0) @5G>28=8, O: :>>@48=0B=0 H284:VABL A2VB;0  EMBED Equation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b; 2008: 4], 7=0G5==O :>>@48=0B=>W H284:>ABV A2VB;0 =0A?@024V T =5 20:CC<=8<8, 0 3@02V10@8G=8<8 7=0G5==O<8. >=8 287=0G0NBLAO 7=0G5==O<8 B5@<>48=0<VG=8E ?0@0<5B@V2 V450;L=>W @V48=8 7 B>G=VABN 4> :0;V1@C20;L=>3> :>5DVFVT=B0, ;8H5 O:89 V <>65 @>73;O40B8AO O: ?A524>20:CC<=5 7=0G5==O :>>@48=0B=>W H284:>ABV A2VB;0. @8 =0O2=>ABV O: <5E0=VG=>W, B0: V B5?;>2>W @V2=>2038 C V450;L=V9 @V48=V F5 ?A524>20:CC<=5 7=0G5==O :>>@48=0B=>W H284:>ABV A2VB;0 >4=0:>25 2 <560E CAVTW @V48=8, I> A0<>CB2>@8;0 A2V9 ?@>AB>@>2> =5>4=>@V4=89 @V2=>206=89 AB0= B0 2V4?>2V4=5 9><C 3@02VB0FV9=5 ?>;5 [0=K;LG5=:>, 2005b; 2008: 4]. &5 4>72>;OT @>73;O40B8 9>3> ;8H5 O: :0;V1@C20;L=89 ?0@0<5B@, I> ?>2'O7CT ?><V6 A>1>N ?@>AB>@>2C B0 G0A>2C <5B@8:8 V T ?@8=F8?>2> =5A?>AB5@56;828< O: C 3@02V:20=B>28E 2;0A=8E ! 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"><C-B> 2 -! >1'T< 2AL>3> A5A2VBC  EMBED Equation.3  ?@8=F8?>2> <>65 1CB8 V :V=F528<. 465 2 =V9, E>G0 V A?>AB5@V30NBLAO =02VBL V =5A:V=G5==> 40;5:V >1'T:B8 !! , 2A5 6 =5A:V=G5==> 25;8:0 :V;L:VABL 0AB@>=><VG=8E >1'T:BV2 A5A2VBC <VAB8BLAO 70 <560<8 ?@>AB>@>2>-G0A>2>3> :>=B8=CC<C (') 3@02VB5@<>48=0<VG=> ?>2'O70=>W @5G>28=8. , >B65, 2V4?>2V4=> 4> @V2=O==O AB0=C V450;L=>3> 307C B8A: C -! =5 <>65 ?@89<0B8 =5 BV;L:8 =5A:V=G5==> 25;8:5, 0;5 V =C;L>25 7=0G5==O:  EMBED Equation.3 .  >3;O4C 6 =0 B>9 D0:B, I> 2AV<0 ?@8;040<8 28:>=CNBLAO 7>2AV< =5 01A>;NB=V, 0 ;8H5 2V4=>A=V 28<V@N20==O B8A:C:  EMBED Equation.3 , @V2=O==O <5E0=VG=>W @V2=>2038 @5G>28=8 2 3@02VB0FV9=><C ?>;V ?>28==> <0B8 B0:89 283;O4:  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3   E>G0 V O: 7023>4=> <0;5 0;5, 2A5 6, :V=F525 7=0G5==O B8A:C =0 ?>25@E=V :><?0:B=>3> DV78G=>3> BV;0, I> <VAB8BLAO 2 C<>2=> ?>@>6=L><C ?@>AB>@V;  EMBED Equation.3  V  EMBED Equation.3   IV;L=VABL 2V4?>2V4=> 3@02VB0FV9=>W <0A8 A?>:>N @5G>28=8 V 2;0A=>3> 7=0G5==O WW <0A8;  EMBED Equation.3   :>>@48=0B=0 H284:VABL A2VB;0 " [Q;;5@, 1972]; c  AB0;0 H284:>ABV A2VB;0 (4V9A=> <5B@8G=0 ?A524>20:CC<=0 H284:VABL A2VB;0). ">4V =02VBL 70 =C;L>2>W IV;L=>ABV <0A8 ( EMBED Equation.3 ) @04V0;L=89 @>7?>4V; B8A:C 2 C<>2=> ?>@>6=L><C ?@>AB>@V, I> T =02:>;8H=V< 4;O BV;0, D>@<0;L=> AB@>3> 2V4?>2V40T @04V0;L=><C @>7?>4V;C 2 =L><C :>>@48=0B=>W H284:>ABV A2VB;0 ":  EMBED Equation.3 ,  EMBED Equation.3  (1). @8 FL><C ?@03=5==O :>>@48=0B=>W H284:>ABV A2VB;0 4> =C;O C @07V =01;865==O 4> DV:B82=>W A8=3C;O@=>W ?>25@E=V ?A524>>1@VN 2848<>ABV 2V4?>2V40T ?@03=5==N B8A:C 4> =5A:V=G5==>ABV, O: F5 <0T <VAF5 V C @07V =01;865==O 4> 4V9A=>W A8=3C;O@=>W ?>25@E=V, I> 2V4>:@5<;NT 7>2=VH=N @5G>28=C 2V4 2=CB@VH=L>W 0=B8@5G>28=8 2 =04728G09=> <0A82=8E =59B@>==8E 7V@:0E [0=K;LG5=:>, 2004: 35; 2005; 2005b; 2008: 4; 2008: 19; 2008a; 2008b: 45].  F5, 728G09=> 6, ?V4B25@46CT <>6;82VABL 28:>@8AB0==O 2 O:>ABV 3@04VT=B0 3@02VB0FV9=>3> ?>;O 3@04VT=B0 B8A:C 2 @5G>28=V V :>A<>AD5@V. 465 =5 28:;8:0=89 5;5:B@><03=VB=>N 270T<>4VTN <>;5:C; B8A: 2 @5G>28=V V 2 :>A<>AD5@V <0T, A0<5, 3@02VB0FV9=C ?@8@>4C. #<>2=> ?>@>6=V9 ?@>ABV@, I> >B>GCT B0:C :><?0:B=C @5G>28=C, =0A?@024V 6 =V:>;8 =5 1C2 ?>@>6=V< C A5A2VBV V =V:>;8 =5 AB0=5 01A>;NB=> ?>@>6=V<. 02VBL A0<89 =0428A>:89 :>A<VG=89 20:CC< B@510 @>73;O40B8 O: =04728G09=> A8;L=> @>7@V465=C 307>?8;>2C =5:>35@5=B=C @5G>28=C, I> ?V4:>@NTBLAO 70:>=0< B5@<>48=0<V:8 0=0;>3VG=> V450;L=><C 307C =5270T<>4VNG8E <>;5:C;. 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quation.3  V 4>268=0 E28;V  EMBED Equation.3  45 @>9;O @CE><>3> BV;0. 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B>4V, =572060NG8 =0 7<5=H5==O 3@0=8G=> <>6;82>W H284:>ABV @CEC @5G>28=8 (0;LB5@=0B82=>W :>>@48=0B=V9 H284:>ABV A2VB;0 "), G0AB>B0 >4=>3> V B>3> 6 5<VAV9=>3> 28?@><V=N20==O, 2>G5284L, 1C45 >4=0:>2>N 2 <560E 2AVTW >4=>@V4=>W D>B>AD5@=>W @5G>28=8, I> ?5@51C20T 2 ?@>AB>@>2> =5>4=>@V4=><C @V2=>206=><C B5@<>48=0<VG=><C AB0=V (O: 2 T-!, B0: V 2 1C4L-O:V9 -!). $0:B8G=> ACB> 3@02VB0FV9=5 7<5=H5==O V ACB> B5@<>48=0<VG=5 71V;LH5==O G0AB>B8 5<VAV9=>3> 28?@><V=N20==O @5G>28=8 =50:B82=8E 7V@>:, I> :207V@V2=>206=> >AB830NBL, 270T<=> :><?5=ACNBLAO. , >B65, 3@02VB5@<>48=0<VG=89 7AC2 G0AB>B8 FL>3> 5<VAV9=>3> 28?@><V=N20==O T 2V4ACB=V<.  F5 >7=0G0T, I> @>7H8@5==O A?5:B@0;L=8E ;V=V9 5<VAV9=>3> 28?@><V=N20==O <>65 1CB8 ;8H5 4>??;5@V2AL:8<, B>1B> 28:;8:0=8< ;8H5 B5?;>28<8 :>;820==O<8 <>;5:C; @5G>28=8.  F5 ?V4B25@46CTBLAO 2V4ACB=VABN O: 3@02VB0FV9=>3>, B0: V B5@<>48=0<VG=>3> @>7<8BBO A?5:B@0;L=8E ;V=V9 C 71C465=8E 0B><V2 E>;>4=>3> @>7@V465=>3> 30;0:B8G=>3> A5@54>28I0 =02VBL ?@8 7=0G5==OE WE 3>;>2=8E :20=B>28E G8A5;  EMBED Equation.3  ( EMBED Equation.3 ) [!>@>G5=:>, !0;><>=>28G, 1987; >@4>=, !>@>G5=:>, 2003] . B65 ACBBT289 =54>??;5@V2AL:89 G5@2>=89 7AC2 A?5:B@C 5<VAV9=>3> 28?@><V=N20==O <>65 <0B8 <VAF5 ;8H5 C B8E 0AB@>=><VG=8E >1'T:BV2, I> =5 <0NBL B25@4>3> O4@0, @V4:0 G8 307>?>4V1=0 >4=>@V4=0 @5G>28=0 O:8E ?5@51C20T 2 =5@V2=>206=><C B5@<>48=0<VG=><C AB0=V.  287=0G0B8AO 2>=> 1C45 A0<5 B5@<>48=0<VG=8<8 ?0@0<5B@0<8 @5G>28=8, 0 06 =VO: =5 7=0G5==O<8 3@0=8G=> <>6;82>W <0:A8<0;L=>W H284:>ABV @CEC @5G>28=8 V 2V4?>2V4=>3> W9 3@02VB0FV9=>3> ?>B5=FV0;C. @>B5 C " B0:V 0AB@>=><VG=V >1'T:B8 27030;V =5 @>73;O40NBLAO, B0: O: C B5=7>@V 5=5@3VW-V<?C;LAC @07>< 7V IV;L=VABN V=5@B=>W 2V;L=>W 5=5@3VW A?>:>N @5G>28=8  EMBED Equation.3  28:>@8AB>2CTBLAO IV;L=VABL 3V1@84=>W 5=B0;L?VW 70<VABL IV;L=>ABV >@48=0@=>W 2=CB@VH=L>W 5=5@3VW A?>:>N @5G>28=8  EMBED Equation.3  (45  EMBED Equation.3   2;0A=5 7=0G5==O <0A8 >4=>3> <>;O @5G>28=8,  EMBED Equation.3   2;0A=5 7=0G5==O IV;L=>ABV WW <0A8). "0:8< G8=><, 2AV DV78G=V 2;0AB82>ABV B0:>W @5G>28=8 =5 70;560BL 2V4 3@02VB0FV9=>3> ?>;O, I> D>@<CTBLAO WW 2=CB@VH=L>O45@=8<8 E0@0:B5@8AB8:0<8. @02VB0FV9=5 ?>;5 A0<5 ?@>O2;OTBLAO 2 =0O2=>ABV ?@>AB>@>28E 3@04VT=BV2 O: B5@<>48=0<VG=8E ?0@0<5B@V2 B0 ?>B5=FV0;V2, B0: V 2AVE V=H8E 2V4><8E ?0@0<5B@V2 V E0@0:B5@8AB8: ACFV;L=>W >4=>@V4=>W @5G>28=8. AL G><C 2 ", O: V 2 :;0A8G=V9 B5@<>48=0<VFV, 4;O >?8AC ?@>AB>@>2> =5>4=>@V4=>3> :207V@V2=>206=>3> B5@<>48=0<VG=>3> AB0=C @V4:>W G8 307>?>4V1=>W ACFV;L=>W >4=>@V4=>W @5G>28=8 4>A8BL 28:>@8AB0==O ;8H5 42>E =570;56=8E ?0@0<5B@V2.  " 6 28:>@8AB>2CNBLAO B@8 =570;56=V ?0@0<5B@8. @8 FL><C 22060TBLAO, I> DV78G=V 2;0AB82>ABV >4=VTW V B>W 6 B0:>W @5G>28=8 ?@8 >4=0:>28E 7=0G5==OE 42>E WW B5@<>48=0<VG=8E ?0@0<5B@V2 70;560BL I5 9 2V4 25;8G8=8 :>>@48=0B=>W H284:>ABV A2VB;0 2 =V9. # 72'O7:C 7 F8< ACB> B5@<>48=0<VG=89 G5@2>=89 7AC2 28?@><V=N20==O C D>B>AD5@=><C H0@V ACFV;L=>W >4=>@V4=>W @V4:>W G8 307>?>4V1=>W @5G>28=8, I> ?5@51C20T 2 AB0=V B5@<>48=0<VG=>W :207V@V2=>2038, V @>73;O40TBLAO 2 " O: 3@02VB0FV9=89. %>G0, 728G09=> 6, C 7030;L=><C 28?04:C 2V= V T 3@02VB0FV9=>-B5@<>48=0<VG=8<. 572060NG8 =0 4>A8BL 25;8:C H284:VABL @CEC !>=OG=>W A8AB5<8 C A5A2VBV (1;87L:> 370 :</A5:) 2 V7>B@>?=8E A5@54>28I0E 2V4ACB=O 0=V7>B@>?VO, A0<5, @50;L=>W H284:>ABV A2VB;0 2 =8E, 0 7>2AV< =5 C<>2=>W :>>@48=0B=>W H284:>ABV A2VB;0 C 3V?>B5B8G=><C 01A>;NB=><C 20:CC<V. , >B65, @5G>28=0, 040?BCNG8AL 4> A2>TW H284:>ABV @CEC, =5 BV;L:8 7<5=HCT A2>W @>7<V@8, 0;5 V, :>=D>@<=>-:0;V1@C20;L=> 45D>@<CNG8AL [0=K;LG5=:>, 1994, 1994a], =02>48BL 0=V7>B@>?VN A2>WE DV78G=8E 2;0AB82>AB59 (V 2 ?5@HC G5@3C A2>3> ?>:07=8:0 70;><;5==O 28?@><V=N20==O [0=K;LG5=:>, 2009: 79]) 2 !, 2 O:V9 2>=> @CE0TBLAO.  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"><C-B> " V 4>?CA:0T <>6;82VABL @>71V6=>ABV 7=0G5=L 3@02VB0FV9=8E ?>B5=FV0;V2 (I> D>@<CNBLAO =0 >A=>2V 3@0=8G=>W H284:>ABV @CEC @5G>28=8) =0 <56V A5@54>28I V =02VBL D07 >4=>W V B>W 6 @5G>28=8. 4=0: 70 4>?><>3>N 2V4?>2V4=8E :0;V1@C20;L=8E :>5DVFVT=BV2 =5>4=0:>2V C @V7=8E @5G>28= (V WE D07>28E AB0=V2) O: 2=CB@VO45@=V, B0: V B5@<>48=0<VG=V ?>B5=FV0;8, I> 28:>@8AB>2CNBLAO 2 ;>30@8D<VG=><C 3@02VB0FV9=><C ?>B5=FV0;V, 2A5 6 B0:8 <>6=0 ?@825AB8 4> O:>3>AL T48=>3> ?0@0<5B@0 ;>30@8D<VG=>3> 3@02VB0FV9=>3> ?>B5=FV0;C (?>4V1=> 28:>@8AB0==N 2 " C<>2=>W :>>@48=0B=>W H284:>ABV A2VB;0 2 3V?>B5B8G=><C 01A>;NB=><C 20:CC<V, =0 >A=>2V O:>W V D>@<CTBLAO ?@>AB>@>289 @>7?>4V; ;>30@8D<VG=8E 3@02VB0FV9=8E ?>B5=FV0;V2). "0:8< C=V25@A0;L=8< ?0@0<5B@>< <>65 1CB8, =0?@8:;04, 3@0=8G=0 H284:VABL A?V;L=>3> @CEC 2AVE "-?>2'O70=8E @5G>28=, ?@8 O:V9 2AV FV @5G>28=8 I5 T 740B=8<8 CB2>@N20B8 7030;L=V :>;5:B82=V 3@02VB5@<>48=0<VG=V <V:@>AB0=8 V11A0.  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" 4>?CA:0T 28:>@8AB0==O 2 O:>ABV 3@02VB0FV9=>3> ?>B5=FV0;C =5 BV;L:8 ;>30@8D<0 3@0=8G=>W H284:>ABV @CEC @5G>28=8 01> ;>30@8D<0 WW 2V;L=>W 5=5@3VW V11A0, >15@=5=> ?@>?>@FV9=>W FV9 H284:>ABV. @02VB0FV9=89 ?>B5=FV0; 2 =V9 <>65 1CB8 AD>@<>20=89 V =0 >A=>2V ;>30@8D<C DC=:FVW 2V4 2=CB@VH=L>3> <0AHB01=>3> G8==8:0 @5G>28=8 [0=K;LG5=:>, 2008: 19; 2008a; 2009a; 0=8;LG5=:>, 2020: 5] V 2V4 ?>:07=8:0 70;><;5==O =5N 28?@><V=N20==O (G8 @50;L=>W H284:>ABV ?>H8@5==O 2 =V9 28?@><V=N20==O  EMBED Equation.3 ) =0 AB0=40@B=V9 01> 6 =0 >1@0=V9 G0AB>BV 2V4?>2V4=>W 9><C 5;5:B@><03=VB=>W E28;V. 024O:8 FL><C ACB> 3@02VB0FV9=89 G5@2>=89 7AC2 4>268=8 E28;V 28?@><V=N20==O  EMBED Equation.3  <>65 1CB8 287=0G5=>, 28E>4OG8 7 B>3>, I>:  EMBED Equation.3 , 45:  EMBED Equation.3   ?>:07=8: 70;><;5==O @5G>28=8 ACFV;L=>3> O4@0 0AB@>=><VG=>3> BV;0 =0 :>@4>=V 7 H0@>< V=H>W @5G>28=8 01> V=H>W D078 FVTW 6 @5G>28=8, I> ?>:@820T 9>3>;  EMBED Equation.3   ?>:07=8: 70;><;5==O =86=L>3> H0@C 0B<>AD5@8 (D>B>AD5@8);  EMBED Equation.3  V  EMBED Equation.3  ?>:07=8:8 70;><;5==O ?@><V6=>3> H0@C @5G>28=8 2V4?>2V4=> =0 25@E=V9 V =86=V9 9>3> <560E; k  :V;L:VABL ?@><V6=8E H0@V2 @5G>28=8. 6. =5@B=0 2=CB@VH=L>O45@=0 5=5@3VO @5G>28=8 1A>;NB=0 B5<?5@0BC@0 T V=B5=A82=8< ?0@0<5B@><, I> E0@0:B5@87CT @V25=L ;8H5 B5?;>2>W 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3 , 4> O:>W 2V4=>A8BLAO V ?>B5=FV9=0 5=5@3VO <V60B><=8E B0 <V6<>;5:C;O@=8E 72'O7:V2 C @5G>28=V. =20@V0=B=VABL CAVE B5@<>48=0<VG=8E ?0@0<5B@V2 B0 E0@0:B5@8AB8: @5G>28=8 2V4=>A=> ?5@5B2>@5==O G0AC 2:07CT =0 B5, I> 2AV 2>=8 ?>28==V 1CB8 V @5;OB82VABAL:V V=20@V0=B=8<8. "><C B5<?5@0BC@8 D07>28E ?5@5E>4V2 ?>28==V 7>AB020B8AO 2=CB@VH=V<8 2;0AB82>ABO<8 V @5G>28=8, I> @CE0TBLAO.  F5 >7=0G0T, I> 7<V=0 7=0G5=L B5@<>48=0<VG=8E ?0@0<5B@V2 B0 E0@0:B5@8AB8: @5G>28=8 ?>28==0 =5 =0?@O<C, 0 ;8H5 ?>A5@54=L> 2V41820B8AO =0 7<V=V WW V=5@B=>W 2V;L=>W 5=5@3VW. , >B65, =5EV<VG=0 2=CB@VH=O ?>B5=FV9=0 5=5@3VO <V60B><=8E B0 <V6<>;5:C;O@=8E 72'O7:V2 <>65 ?5@5E>48B8 C :V=5B8G=C 5=5@3VN ;8H5 E0>B8G=>3>, 0 =5 A?@O<>20=>3> @CEC <>;5:C; @5G>28=8. B65, 5:2V20;5=B=>N V=5@B=V9 <0AV A?>:>N  EMBED Equation.3  <>65 1CB8 =5 ?>2=0  EMBED Equation.3  V =5 >@48=0@=0 2=CB@VH=O 5=5@3VO A?>:>N  EMBED Equation.3  @5G>28=8, 0 ;8H5 V=5@B=0 2V;L=0 5=5@3VO A?>:>N @5G>28=8  EMBED Equation.3 . 48B82=0 :><?5=A0FVO  EMBED Equation.3  <C;LB8?;V:0B82=>3> ?@54AB02;5==O 2=CB@VH=L>W 5=5@3VW U @5G>28=8 T ?@>AB>@>2> >4=>@V4=>N V, >B65, =5 70;568BL 2V4 =0?@C65=>ABV 3@02VB0FV9=>3> ?>;O. # :;0A8G=V9 B5@<>48=0<VFV 22060TBLAO, I> 2=CB@VH=L>O45@=0 5=5@3VO C B5@<>48=0<VG=8E ?@>F5A0E =5 7<V=NTBLAO. 0A?@024V 6 F5 =5 7>2AV< B0:. @8 04V010B=><C 7@>AB0==V B8A:C C 307V G0AB8=0 9>3> ?>B5=FV9=>W 2=CB@VH=L>O45@=>W 5=5@3VW ?5@5E>48BL O: 2 5=5@3VN E0>B8G=>3> AB0=C 9>3> =C:;>=V2, B0: V C ?>B5=FV9=C 5=5@3VN =0?@C65=>3> AB0=C @5G>28=8 CB@8<CNG>3> 9>3> 10;>=C [0=K;LG5=:>, 2008: 19; 2008a]. @8 =03@V20==V 6 AB8A=5=>3> 307C B56 2V41C20TBLAO 282V;L=5==O 2=CB@VH=L>O45@=>W ?>B5=FV9=>W 5=5@3VW, O:0 1C;0 70?0A5=0 2 45D>@<>20=><C :>@?CAV 10;>=0, I> ?5@51C20T 2 =0?@C65=><C AB0=V. # ?@>F5AV =03@V20==O B25@4>3> BV;0 2>=> 2V;L=> @>7H8@NTBLAO V ?@8 FL><C 2V41C20TBLAO 7=865==O G0AB>B8 270T<>4VW V 9>3> =C:;>=V2 [0=K;LG5=:>, 2004: 35; 2008: 19; 2008a; 2008b: 45].  B8< A0<8< 2V41C20TBLAO V A?>2V;L=5==O 9>3> 3@02V:20=B>2>3> G0AC, 0=0;>3VG=> B><C, O: F5 2V41C20TBLAO ?@8 =52V;L=><C @CAV BV;0. 4=0: ?@8@VAB B5?;>2>W 5=5@3VW BV;0, O:89 AC?@>2>46CTBLAO ?V428I5==O< 9>3> B5?;>2>W B5<?5@0BC@8 ", ;8H5 2 =57=0G=V9 <V@V :><?5=ACTBLAO A?04>< 9>3> 2=CB@VH=L>O45@=>W 5=5@3VW 2=0A;V4>: 7=865==O O: 2=CB@VH=L>O45@=>W 5=B@>?VW  EMBED Equation.3 , I> 2V4?>2V40T >4=><C <>;N @5G>28=8, B0: V 2=CB@VH=L>O45@=V9 B5<?5@0BC@8 EMBED Equation.3 . "><C-B> V =5 240TBLAO 28:@8B8 ACBBT2C 70;56=VABL <>;O@=>W 3@02VB0FV9=>W <0A8 @5G>28=8 2V4 B5?;>2>W A:;04>2>W WW 2=CB@VH=L>W 5=5@3VW, =572060NG8 =0 =0O2=VABL 270T<=>W :>@5;OFVW <V6 V=5@B=>N 2V;L=>N 5=5@3VTN E V B5@<>48=0<VG=>N 2V;L=>N 5=5@3VTN V11A0 G @5G>28=8. # ?@>F5AV 6 >E>;>465==O BV;0 =57=0G=0 G0AB8=0 9>3> B5@<>48=0<VG=>W 2=CB@VH=L>W 5=5@3VW 28B@0G0TBLAO =0 ?>?>2=5==O 2=CB@VH=L>O45@=>W V=5@B=>W 2V;L=>W 5=5@3VW. =0;>3VG=5 7=865==O G0AB>B8 270T<>4V9 =C:;>=V2 V 2V4?>2V4=5 9><C 282V;L=5==O 2=CB@VH=L>O45@=>W 5=5@3VW 2V41C20TBLAO V 2 5:A?5@8<5=B0E 7 3V@>A:>?><, I> >15@B0TBLAO. 7. #7030;L=5=V @V2=O==O " >73;O=CB89 BCB D>@<0;V7< =091V;LH ?@89=OB=89 4;O 30;0:B8G=8E 3@02VB0FV9=8E ?>;V2 25;8:>W AC:C?=>ABV 0AB@>=><VG=8E >1'T:BV2, I> ?5@51C20NBL C :>A<VG=><C 20:CC<V V CB@8<CNBLAO =0 A2>WE B@0T:B>@VOE @CEC ;8H5 2V4F5=B@>28<8 ?A524>A8;0<8. ;O ACFV;L=>W 6 @5G>28=8, I> G8=8BL >?V@ 3@02VB0FV9=><C A0<>AB8A:0==N 7024O:8 =0O2=>ABV 2 =V9 2=CB@VH=L>3> B8A:C, =5>1EV4=> 2@0E>2C20B8 B0:>6 V WW B5@<>48=0<VG=V 2;0AB82>ABV, >?8AC20=V @V2=O==O<8 B5@<>48=0<V:8. =5@B=0 2V;L=0 5=5@3VO ?>28==0 2V4>1@060B8AO 2 C7030;L=5=8E 48D5@5=FV9=8E @V2=O==OE B5@<>48=0<V:8 =5 ;8H5 70 4>?><>3>N <C;LB8?;V:0B82=>3> ?0@0<5B@0 ?@O<>W 4VW  EMBED Equation.3 , ?@>?>@FV9=>3> 3@0=8G=><C 7=0G5==N <VAF52>W 3@C?>2>W H284:>ABV @CEC @5G>28=8  EMBED Equation.3  C !!  0, >B65, V D0:B8G=> B>B>6=V9 W9 :>>@48=0B=V9 ?A524>20:CC<=V9 H284:>ABV A2VB;0 " C !!  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V4?>2V4=> 4> FL>3> B5<? :20=B>28E ?@>F5AV2 2=CB@VH=L>O45@=>W 270T<>4VW =C:;>=V2 @5G>28=8 <>6;82> >E0@0:B5@87C20B8 C 3;>10;L=V9 T-! 2V4=>A=>N A5@54=L>AB0B8AB8G=>N G0AB>B>N  EMBED Equation.3  FVTW 270T<>4VW, ?@>?>@FV9=>N 3@0=8G=><C 7=0G5==N <VAF52>W 3@C?>2>W H284:>ABV @CEC @5G>28=8  EMBED Equation.3  C T-! 0, >B65, V D0:B8G=> B>B>6=V9 W9 ?A524>20:CC<=V9 :>>@48=0B=V9 H284:>ABV A2VB;0 " C T-!  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V4?>2V4=5 3@02VB0FV9=><C ?>B5=FV0;C 1V;LH 28A>:5 7=0G5==O A2>TW 2=CB@VH=L>W 5=5@3VW @5G>28=0 ?@89<5 ;8H5 2 AB0=V A?>:>N, :>;8 ?@8945 2 B5@<>48=0<VG=0 @V2=>2030 7 =02:>;8H=V< A5@54>28I5<. @>AB0==N 2=CB@VH=L>W 5=5@3VW @5G>28=8 ?@8 =01;865==V WW 4> F5=B@C BO6V==O 2V4?>2V40T V 52>;NFV9=5 WW 7@>AB0==O 2 !! . ;5 B0: O: C !! :  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , B>:  EMBED Equation.3  V, >B65, 2 ! A2VBC ;N459 52>;NFV9=5 7@>AB0==O 2=CB@VH=L>W 5=5@3VW T ?@8=F8?>2> =5A?>AB5@56;828<. "CB:  EMBED Equation.3   AB0;0 %011;0, I> 2AB0=>2;NT H284:VABL 52>;NFV9=>3> @>7H8@5==O A5A2VBC,   :>A<>;>3VG=89 G0A, I> 2V4;VGCTBLAO C !!  70 <5B@8G=> >4=>@V4=>N H:0;>N ( EMBED Equation.3 ), z  4>??;5@V2AL:89 G5@2>=89 7AC2 4>268=8 E28;V 28?@><V=N20==O 2V4 0AB@>=><VG=>3> >1'T:B0, E0@0:B5@8AB8:8 O:>3> 287=0GCNBLAO. 4=0: 2 !!  70 70:>=>< %011;0 7<V=NNBLAO O: <>;O@=0 2=CB@VH=O 5=5@3VO  EMBED Equation.3 , B0: V <>;O@=0 V=5@B=0 2V;L=0 5=5@3VO  EMBED Equation.3  0, >B>6, V 5:2V20;5=B=0 W9 <>;O@=0 V=5@B=0 <0A0  EMBED Equation.3 :  EMBED Equation.3 ,  EMBED Equation.3 . "0 9 =5 BV;L:8 A0<0 <>;O@=0 V=5@B=0 <0A0 2 (1+z) @07, 0 9 WW :>=F5=B@0FVO C 2;0A=><C ?@>AB>@V @5G>28=8 2 (1+z)3 @07V2 1C;0 1V;LH5 2 B>9 40;5:89 G0A [0=K;LG5=:>, 2008: 106].  F5 >7=0G0T, I> ?>B@510 2 B5<=V9 =510@V>==V9 <0B5@VW <>65 28O28B8AO CO2=>N. $V78G=89 ?@>ABV@, I> 6>@AB:> ?>2'O70=89 7 E>;>=CG8< BV;><, A0<>AB8A:0TBLAO ?@8 FL><C =5 BV;L:8 C !! , 0 9 C 2;0A=><C <5B@8G=><C ?@>AB>@V BV;0, I> 2>;>4VT =56>@AB:>N 2;0A=>N ! [0=K;LG5=:>, 1994: 52]:  EMBED Equation.3 ,  EMBED Equation.3 , 45:   @04V0;L=0 :>>@48=0B0, I> 2V4@0E>2CTBLAO ?> 6>@AB:> ?>2'O70=V9 7 BV;>< :>>@48=0B=V9 AVBFV =5 2 <5B@8G=><C, 0 C DV78G=><C ?@>AB>@V ?>ABC?>2> >AB830NG>3> BV;0,  EMBED Equation.3   ?0@0<5B@, I> E0@0:B5@87CT H284:VABL A?>AB5@56;82>3> A:>@>G5==O @>7<V@V2 >AB830NG>3> BV;0.  B0: O:  EMBED Equation.3 , B> C A:V;L:8 @07V2 71V;LH8BLAO >@48=0@=0 2=CB@VH=O 5=5@3VO, C ABV;L:8 6 @07V2 7<5=H8BLAO V=5@B=0 2V;L=0 5=5@3VO V 2V4?>2V4=0 W9 V=5@B=0 <0A0 @5G>28=8. @02VB0FV9=0 6 <0A0 =5 1C45 71V;LHC20B8AO ?@>?>@FV9=> 71V;LH5==N >@48=0@=>W 2=CB@VH=L>W 5=5@3VW G5@57 ?>@CH5==O B5@<>48=0<VG=>W @V2=>2038 =03@VB>W @5G>28=8 7 =02:>;8H=V< A5@54>28I5<.  2>=0, =02?0:8, 1C45 7<5=HC20B8AO @07>< 7 V=5@B=>N <0A>N, B0: O: 70 2;0A=8< 3>48==8:>< 5:A?5@8<5=B0B>@0 FV <0A8 ?>28==V 1CB8 @V2=V >4=0 >4=V9.  F5 4>1@5 C73>46CTBLAO 7 @57C;LB0B0<8 5:A?5@8<5=BV2, B0: O: C 1030BL>E =03@VB8E <5B0;528E BV; 2A5 6 240TBLAO 28O28B8 7<5=H5==O WE <0A8 [-9=HB59=, =D5;L4, 1938; 1965; Chen & Cook, 1993; <8B@852, 2005]. "0:8< G8=><, :>@5;OFVO B5@<>48=0<VG=8E E0@0:B5@8AB8: @5G>28=8 7 9>3> 2=CB@VH=L>O45@=8<8 3@02VB5@<>48=0<VG=8<8 E0@0:B5@8AB8:0<8 <0T <VAF5 ;8H5 C ACFV;L=>W >4=>@V4=>W @5G>28=8, I> ?5@51C20T 2 :207V@V2=>206=><C AB0=V 0, >B65, V 2 B5@<>48=0<VG=V9 @V2=>207V 7 =02:>;8H=V< A5@54>28I5<. "><C 28:>@8AB0==O 2 @V2=O==OE 3@02VB0FV9=>3> ?>;O 70<VABL 2=CB@VH=L>O45@=8E E0@0:B5@8AB8: 7>2=VH=L>O45@=8E B5@<>48=0<VG=8E E0@0:B5@8AB8: @5G>28=8 ?@8=F8?>2> =5<>6;82> 70 2V4ACB=>ABV :>@5;OFVW <V6 =8<8. 0O2=VABL :>@5;OFVW 7-?><V6 =8<8 C :207V@V2=>206=><C AB0=V @5G>28=8 2AB0=>2;5=0 ">;<5=>< [">;<5=, 1969] C 283;O4V ?@>AB>@>2>W >4=>@V4=>ABV ?0@0<5B@0  EMBED Equation.3 . /:I> :>>@48=0B=0 ?A524>20:CC<=0 H284:VABL A2VB;0  EMBED Equation.3  E0@0:B5@87CT H284:VABL ?@>BV:0==O 2=CB@VH=L>O45@=8E 3@02V20=B>28E ?@>F5AV2, B> 01A>;NB=0 B5<?5@0BC@0 " E0@0:B5@87CT H284:VABL ?@>BV:0==O ?>70O45@=8E B5@<>48=0<VG=8E ?@>F5AV2. , >B65, C :207V@V2=>206=><C AB0=V @5G>28=8, G8< ?>2V;L=VH5 ?@>BV:0NBL C =V9 2=CB@VH=L>O45@=V ?@>F5A8, B8< H284H5 ?@>BV:0NBL C =V9 ?>70O45@=V ?@>F5A8. "><C ?>@O4 7 3@02V:20=B>28< 2;0A=8< G0A><, 2 O:><C 2;0A=5 7=0G5==O ?A524>20:CC<=>W H284:>ABV A2VB;0  EMBED Equation.3  T V=20@V0=B=8< ?0@0<5B@><, 4>FV;L=> @>73;O40B8 V B5@<>48=0<VG=89 2;0A=89 G0A, 2 O:><C 3@02VB5@<>48=0<VG=5 2;0A=5 7=0G5==O B5<?5@0BC@8  EMBED Equation.3  T V=20@V0=B>< 2 <560E 2AVTW "-?>2'O70=>W >4=>@V4=>W @5G>28=8, I> 7=0E>48BLAO 2 :207V@V2=>206=><C AB0=V.  V=5@B=0 2V;L=0 5=5@3VO, V 2V;L=0 5=5@3VO V11A0 4>AO30NBL A2>3> <V=V<C<C A0<5 C F5=B@V BO6V==O 0AB@>=><VG=>3> BV;0. 4=0:, =572060NG8 =0 F5, ?@8 =01;865==V 4> F5=B@C BO6V==O :>>@48=0B=0 H284:VABL A2VB;0 ?@03=5 A2>3> <V=V<C<C, 0 B5<?5@0BC@0 @5G>28=8, =02?0:8, A2>3> <0:A8<C<C. "><C V=B5=A82=V ?0@0<5B@8 @5G>28=8 (WW B5<?5@0BC@C B0 2V4?>2V4=C W9 :>>@48=0B=C H284:VABL A2VB;0) 287=0G0NBL B0:V E0@0:B5@8AB8:8 @5G>28=8 O: IV;L=VABL <C;LB8?;V:0B82=>W A:;04>2>W WW 2V;L=>W 5=5@3VW V11A0  EMBED Equation.3  B0 IV;L=VABL WW ?>2=>W 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3 . @828=C 6 2;0A=>3> ?@>AB>@C @5G>28=8 287=0G0NBL 3CAB8=0 <C;LB8?;V:0B82=>W A:;04>2>W WW ?>2=>W 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3  (V 2V4?>2V4=>W W9 3@02VB0FV9=>W <0A8) B0 3CAB8=0 WW V=5@B=>W 2V;L=>W 5=5@3VW  EMBED Equation.3  (V 2V4?>2V4=>W W9 V=5@B=>W <0A8). @>AB>@>2> =5>4=>@V4=89 @V2=>206=89 "-AB0= @V4:>W G8 307>?>4V1=>W @5G>28=8 <0T <VAF5 ?@8 4>B@8<0==V =0ABC?=>3> C<>28:  EMBED Equation.3 . 0 C<>28 V7>B@>?VW @04V0;L=>3> @>7?>4V;C DV78G=8E ?0@0<5B@V2 V E0@0:B5@8AB8: >4=>@V4=>W @5G>28=8 0AB@>=><VG=>3> >1'T:B0 2>=0 <>65 1CB8 ?@54AB02;5=0 2 =0ABC?=><C 283;O4V:  EMBED Equation.3 . ;O @04V0;L=>3> 01> 6 28A>B=>3> 1030B>H0@>2>3> @>7?>4V;C =5>4=>@V4=>W @5G>28=8 FO C<>20 28:>=CTBLAO ?>H0@>2>, B5@?;OG8 @>7@82 =0 <56V 42>E A5@54>28I:  EMBED Equation.3 , 45 (k+1)  ?>@O4:>289 =><5@ <5=H IV;L=>3> V, >B65, 1V;LH 2V440;5=>3> 2V4 F5=B@C 3@02VB0FVW H0@C @5G>28=8. # @V2=O==OE 3@02VB0FV9=>3> ?>;O " D0:B8G=> 28:>@8AB>2CTBLAO 3V1@84=0 B5@<>48=0<VG=0 5=B0;L?VO  EMBED Equation.3  ( EMBED Equation.3 ), I> @C=BCTBLAO =0 70<V=V IV;L=>ABV 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3  IV;L=VABN V=5@B=>W 2V;L=>W 5=5@3VW  EMBED Equation.3 .  ?@8 FL><C @V2=>206=89 AB0= V450;L=>W @V48=8 2 " 4>AO30TBLAO ;8H5 ?@8 A?V;L=V9 2V4ACB=>ABV @04V0;L=8E 3@04VT=BV2 C 2;0A=><C 3@02V:20=B>2><C G0AV @5G>28=8 =5 BV;L:8 3@02VB5@<>48=0<VG=>3> 2;0A=>3> 7=0G5==O B5<?5@0BC@8  EMBED Equation.3 , 0 V WW 3@02VB5@<>48=0<VG=>3> 2;0A=>3> 7=0G5==O 5=B0;L?VW  EMBED Equation.3  B0 5=B@>?VW  EMBED Equation.3  [">;<5=, 1969; 0=K;LG5=:>, 2008: 4; 2008a; 0=8;LG5=:>, 2020: 5]. &V C<>28 704>2>;L=ONBL 1V;LH 7030;L=V9 C<>2V @V2=>206=>3> AB0=C @V48= V 307V2  ?@>AB>@>2V9 >4=>@V4=>ABV 3@02VB5@<>48=0<VG=>3> 2;0A=>3> 7=0G5==O 2V;L=>W 5=5@3VW V11A0:  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 . 2V4A8:  EMBED Equation.3 ,  EMBED Equation.3 , 0 70 C<>28  EMBED Equation.3  B0 70<V=8 IV;L=>ABV 2=CB@VH=L>W 5=5@3VW IV;L=VABN V=5@B=>W 2V;L=>W 5=5@3VW A?>:>N  EMBED Equation.3  <>3;0 1 28:>@8AB>2C20B8AO 2 " V 70;56=VABL:  EMBED Equation.3 . 4=0: 65, 2 B5=7>@V 5=5@3VW-V<?C;LAC " =0A?@024V 28:>@8AB>2CNBLAO =5 :>>@48=0B=V, 0 2;0A=V 7=0G5==O IV;L=>ABV <0A8  EMBED Equation.3  V B8A:C  EMBED Equation.3  [Q;;5@, 1972]. 0 ?V4AB02V 6 FL>3> V 28:>@8AB>2CTBLAO 2 =V9 70;56=VABL, I> 2V4?>2V40T =5 :>>@48=0B=><C, 0 2;0A=><C 7=0G5==N  EMBED Equation.3  V=5@B=>W 2V;L=>W 5=5@3VW A?>:>N @5G>28=8 (45  EMBED Equation.3 ):  EMBED Equation.3 , (2) V2=>206=V "-AB0=8 @5G>28=8, ?@8 O:8E 7>2=VH=V9 3@02VB0FV9=89 B8A: 25@E=VE H0@V2 @5G>28=8 2@V2=>206CTBLAO =5 ;8H5 2=CB@VH=V< B8A:>< C @5G>28=V, 0 9 @04V0FV9=8< (B5?;>28<) B8A:>< ( EMBED Equation.3 ), 2 ", =0 2V4<V=C 2V4 ", 27030;V =5 @>73;O40NBLAO. , >B65, " =5 BV;L:8 1V;LH A?@>I5=> 2V4>1@060T DV78G=C @50;L=VABL, 0 V AB>ACTBLAO ;8H5 4> @V2=>206=8E AB0=V2 3@0=8G=> >AB83;>W >4=>@V4=>W @5G>28=8 ( EMBED Equation.3 ). "><C 2V4>1@065==O DV78G=>W @50;L=>ABV 2 " A;V4 @>73;O40B8 ;8H5 O: >:@5<89 28?04>: WW 2V4>1@065==O C ". =CB@VH=O 5=5@3VO U @50;L=8E 307V2 V @V48= 70;568BL 2V4 1030BL>E ?0@ WE V=B5=A82=8E ( EMBED Equation.3 ) V 5:AB5=A82=8E ( EMBED Equation.3 ) B5@<>48=0<VG=8E ?0@0<5B@V2. 4=0: 2>=0 <>65 1CB8 28@065=0 V C 283;O4V AC<8 2=CB@VH=L>W 5=5@3VW 3V?>B5B8G=>3> V450;L=>3> 307C (@V48=8)  EMBED Equation.3  V 4>1CB:C @57C;LBCNG>3> V=B5=A82=>3> ( EMBED Equation.3 ) V 5:AB5=A82=>3> ( EMBED Equation.3 ) B5@<>48=0<VG=8E ?0@0<5B@V2:  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . ;O 307V2:  EMBED Equation.3 ,  EMBED Equation.3   2V@V0;L=V :>5DVFVT=B8, I> 70;56=V O: 2V4 B5<?5@0BC@8, B0: V 2V4 V=482V4C0;L=8E 2;0AB82>AB59 307C [070@>2, 1964; 1991],  EMBED Equation.3   C=V25@A0;L=0 307>20 AB0;0, 0  EMBED Equation.3   ?@>AB>@>289 B5@<>48=0<VG=89 ?0@0<5B@ @5G>28=8, I> =5 7<V=NTBLAO C ?@>AB>@V 70 C<>2 :207V@V2=>206=>3> >AB830==O @5G>28=8 (B>1B> T >4=0:>28< =0 1C4L-O:V9 @04V0;L=V9 2V4AB0=V r 2V4 F5=B@C BO6V==O C AC?CB=V9 W9 A8AB5<V 2V4;V:C ?@>AB>@>28E :>>@48=0B B0 G0AC t).  A0<5 FO =57<V==VABL C ?@>AB>@V  EMBED Equation.3  V T 2V4?>2V40;L=>N 70 1;87L:VABL 4> 2;0AB82>AB59 3V?>B5B8G=>3> V450;L=>3> 307C 2;0AB82>AB59 :207V@V2=>206=> E>;>=CG8E @50;L=8E 307V2. @8 FL><C V450;L=0 A:;04>20  EMBED Equation.3  2=CB@VH=L>W 5=5@3VW T B>B>6=>N 2V;L=V9 5=5@3VW 5;L<3>;LFO  EMBED Equation.3 , 0 V450;L=0 A:;04>20  EMBED Equation.3  5=B0;L?VW T B>B>6=>N 2V;L=V9 5=5@3VW V11A0 G:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . &5, 728G09=> 6, >1C<>2;5=> 2V4ACB=VABN O: C V450;L=>3> 307C, B0: V C V450;L=>W @V48=8 ?>2'O70=>W 5=5@3VW ( EMBED Equation.3 ) G5@57 2V4ACB=VABL 5;5:B@><03=VB=>3> 270T<>4VW WE <>;5:C; V 0B><V2. !0<>CB2>@5==O 2 @5G>28=V VT@0@EVG=> CA:;04=5=8E 270T<>4V9 B0 270T<>72'O7:V2 V ?@>O2;OTBLAO 2 ?@03=5==V 4> <V=V<C<C 2V;L=8E 5=5@3V9 5;L<3>;LFO B0 V11A0. 86=V H0@8 @5G>28=8, I> =020=B065=V WW 25@E=V<8 H0@0<8, CB2>@NNBL @>7H8@5=C A8AB5<C. =5@3VO B0:>W @>7H8@5=>W A8AB5<8 [070@>2, 1964; 1991], I> A:;040TBLAO 7V 2AVTW "-?>2'O70=>W @5G>28=8, 4V9A=> T 5:2V20;5=B=>N 5=B0;L?VW. > B>3> 6, O: 1C45 ?>:070=> 40;V, ?0@0<5B@  EMBED Equation.3  (=0 2V4<V=C 2V4 ?0@0<5B@0  EMBED Equation.3 ) ?@89<0T >4=0:>25 7=0G5==O C 2AL><C ?@>AB>@V, 70?>2=5=><C :207V@V2=>206=> E>;>=CG>N >4=>@V4=>N @5G>28=>N ( EMBED Equation.3 . B><C-B> 5=5@3VO V11A0 ?>2>48BLAO O: W9 V =0;568BL, ;8H5 7<V=NNG8AL C ?@>AB>@V 274>26 @04V0;L=>W :>>@48=0B8 r @07>< 7 3@02VB0FV9=8< ?>B5=FV0;><. , 7<V=NNG8AL @07>< 7 3@02VB0FV9=8< ?>B5=FV0;>< ?@>BO3>< G0AC 2>=0 2545 A515 O: <C;LB8?;V:0B82=0 A:;04>20 5=B0;L?VW (O: 5=5@3VO @>7H8@5=>W A8AB5<8). A5 F5 FV;:>< ;>3VG=> V 2V4>1@065=> 2 AB0B8G=8E @V2=O==OE 3@02VB0FV9=>3> ?>;O ". 4=0: 65 C 48=0<VFV G>B8@L>E-V<?C;LA ?>28==0 CB2>@N20B8 7>2AV< =5 5=B0;L?VO, 0 >@48=0@=0 2=CB@VH=O 5=5@3VO @5G>28=8. 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B5>@5B8G=> <>6;825 27030;V, 0 =5 2 :>=:@5B=8E C<>20E 28:>@8AB0==O, ?>2=5 7=0G5==O <C;LB8?;V:0B82=>W WW A:;04>2>W =5 <0T >A>1;82>W 206;82>ABV.  V=H>3> 1>:C, ?>2=0 2=CB@VH=O 5=5@3VO @5G>28=8 2 <5E0=VFV V 2 B5>@VOE BO6V==O T 7>2AV< =5 4>AO3=CB8<, 0 ?@8=F8?>2> 4>AO6=8< C ?52=8E C<>20E WW 7=0G5==O<, :>;8 @5G>28=0 WW >B@8<0T 7 =02:>;8H=L>3> A5@54>28I0 ?VA;O ?@8E>4C 2 B5@<>48=0<VG=C :207V@V2=>203C 7 =8<. /: 1C45 ?>:070=> 40;V, 3@02VB0FV9=>-<5E0=VG=0 ?>2=0 2=CB@VH=O 5=5@3VW A?>:>N @5G>28=8  EMBED Equation.3  B>B>6=0 2 B8E 65 A0<8E @50;L=8E C<>20E <C;LB8?;V:0B82=V9 A:;04>2V9  EMBED Equation.3  WW B5@<>48=0<VG=>W ?>2=>W 5=5@3VW, 1> >1842V 2>=8 >?8ACNBLAO V45=B8G=8<8 <0B5<0B8G=8<8 28@070<8. @>B5 FV B>B>6=V ?>2=V 5=5@3VW @5G>28=8, O: V WE A:;04>2V 2V;L=V 5=5@3VW, ?@>O2;ONBL A515 =5>4=0:>2> C @V7=8E DV78G=8E ?@>F5A0E. @8 :207V@V2=>206=><C A0<>AB8A:0==V >AB830NG>W @5G>28=8 7<5=H5==O WW V=5@B=>W 2V;L=>W 5=5@3VW AC?@>2>46CTBLAO =5 71V;LH5==O< H284:>ABV WW @CEC (=0 2V4<V=C 2V4 WW 2V;L=>3> ?04V==O C 3@02VB0FV9=><C ?>;V), 0 =02?0:8 30;L<C20==O< 9>3>. "><C 2=CB@VH=L>O45@=0 2V;L=0 5=5@3VO, I> 282V;L=OTBLAO, ?5@5E>48BL =5 2 :V=5B8G=C 5=5@3VN, 0 2 5=5@3VN B5?;>2>3> 28?@><V=N20==O.  BCB 7<5=H5==O V=5@B=>W 2V;L=>W 5=5@3VW A?>:>N  EMBED Equation.3 , O: V 7<5=H5==O 2V;L=>W 5=5@3VW V11A0, 287=0G0TBLAO ?@8@>AB0<8 ;8H5 V=B5=A82=8E ?0@0<5B@V2 @5G>28=8 V C B><C G8A;V 7<5=H5==O< H284:>ABV WW @CEC. @8 2V;L=><C ?04V==V @5G>28=8 2 3@02VB0FV9=><C ?>;V (I> ?@8=F8?>2> =5 AC?@>2>46CTBLAO 7<V=>N WW B5@<>48=0<VG=>3> AB0=C) 7<5=H5==O WW V=5@B=>W 2V;L=>W 5=5@3VW @V2=>7=0G=> 7<5=H5==N WW ?>2=>W 2=CB@VH=L>W 5=5@3VW A?>:>N.  B><C 7<5=H5==O V=5@B=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8 2 FL><C 28?04:C 287=0G0TBLAO ?@8@>AB>< 7>2AV< =5 V=B5=A82=>3>, 0 5:AB5=A82=>3> ?0@0<5B@0, 0 A0<5, WW V<?C;LAC. > B>3> 6 ?@8 @CAV @5G>28=8 5;V?B8G=>N >@1VB>N 7<V=0 WW V=5@B=>W 2V;L=>W 5=5@3VW =5 AC?@>2>46CTBLAO 7<V=>N WW B5@<>48=0<VG=>3> AB0=C. 465 7<V=0 :>>@48=0B=>W H284:>ABV A2VB;0 274>26 B@0T:B>@VW >@1VB8, O: V <>6;825 7<5=H5==O G0AB>B8 270T<>4VW 5;5<5=B0@=8E G0AB8=>: @CE>< @5G>28=8, ?>2=VABN :><?5=ACTBLAO @5;OB82VABAL:8< A:>@>G5==O< 2V4AB0=59 270T<>4VW. "><C ?@8 B0:><C @CAV @5G>28=8 70 V=5@FVTN =5 BV;L:8 =5 28=8:0T C?>2V;L=5==O ?;8=C WW 2;0A=>3> G0AC, 0 V 2V4ACB=O :>@5;OFVO <V6 2=CB@VH=L>O45@=8<8 V ?>70O45@=8<8 DV78G=8<8 E0@0:B5@8AB8:0<8 @5G>28=8. , >B65, 2 FL><C 28?04:C D>@<C20==O B5=7>@0 5=5@3VW-V<?C;LAC @5G>28=8 =0 ?V4AB02V WW ?>70O45@=8E B5@<>48=0<VG=8E E0@0:B5@8AB8: ?@8=F8?>2> =5<>6;82>. V= <>65 1CB8 AD>@<>20=8< =0 ?V4AB02V ;8H5 2=CB@VH=L>O45@=8E E0@0:B5@8AB8: @5G>28=8. 8<>2V;L=0 7<V=0 "-AB0=C :>35@5=B=>W @5G>28=8 0, >B65, V WW 2V;L=5 ?04V==O <>6;82V BV;L:8 B>4V, :>;8 2>=8 AC?@>2>46CNBLAO 157?5@5@2=8< 7<5=H5==O<  EMBED Equation.3 , 0 B8< A0<8<,  V V=5@B=>W <0A8 @5G>28=8 2 AB0=V A?>:>N. "0: O: ?@8 2V;L=><C ?04V==V @5G>28=8 C 3@02VB0FV9=><C ?>;V 28B@0G0TBLAO V=5@B=0 2V;L=0 5=5@3VO, B> A0<5 WW ?@8@>AB8 ?>28==V 287=0G0B8AO ?@8@>AB0<8 5:AB5=A82=8E 2=CB@VH=VE ?0@0<5B@V2  EMBED Equation.3  B0  EMBED Equation.3 . V4?>2V4=> 4> FL>3> 2 ?@>F5AV 2V;L=>3> ?04V==O @5G>28=8 ( EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ) <0T <VAF5 52>;NFV9=>-3@02VB0FV9=5 7@>AB0==O 2=CB@VH=L>O45@=>W 5=B@>?VW ( EMBED Equation.3 ), AC?@>2>46C20=5 2 O:>ABV G0AB:>2>W :><?5=A0FVW 2?;82C WW 7@>AB0==O 71V;LH5==O< <>;O@=>3> 7=0G5==O 2=CB@VH=L>O45@=>3> >1'T<C ( EMBED Equation.3 ), V, O: =0A;V4>: FL>3>, 282V;L=5==O V=5@B=>W 2V;L=>W 5=5@3VW  EMBED Equation.3  7 ?5@5B2>@5==O< WW 2 :V=5B8G=C 5=5@3VN A?@O<>20=>3> @CEC @5G>28=8:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . "0:8< G8=><, 2 ?@>F5AV 2V;L=>3> ?04V==O BV;0 2 3@02VB0FV9=><C ?>;V 2V41C20TBLAO 52>;NFV9=>-3@02VB0FV9=5 7@>AB0==O 2=CB@VH=L>O45@=V9 5=B@>?VW, O: F5 <0T <VAF5 V 2 B5>@VW 5=B@>?V9=>W 3@02VB0FVW [Verlinde, 2010; Gogberashvili & Kanatchikov, 2010]. &5-B> V 70157?5GCT 71V;LH5==O 2=CB@VH=L>W 5=5@3VW 2AVTW 3@02VB5@<>48=0<VG=> ?>2'O70=>W @5G>28=8 ?VA;O 2V4=>2;5==O WW <5E0=VG=>W @V2=>2038, 0 B8< A0<8< V 30@0=BCT WW =5A:V=G5==> 4>235 VA=C20==O C A5A2VBV. 8. 5B>B>6=VABL V=5@B=>W V 3@02VB0FV9=>W <0A # :;0A8G=V9 <5E0=VFV V 2 !" 0=0;>3>< 2V;L=8E 5=5@3V9 5;L<3>;LFO V V11A0, I> ?@03=CBL 4> <V=V<C<C 2 B5@<>48=0<VG=8E ?@>F5A0E, D0:B8G=> T V=5@B=0 2V;L=0 5=5@3VO A?>:>N  EMBED Equation.3 , O:0 ?@03=5 4> <V=V<C<C V ?5@5B2>@NTBLAO 2 :V=5B8G=C 5=5@3VN 2 ?@>F5AV ?04V==O @5G>28=8 2 3@02VB0FV9=><C ?>;V. 024O:8 7<5=H5==N V=5@B=>W <0A8 A?>:>N  EMBED Equation.3  @5G>28=8 2 ?@>F5AV WW 2V;L=>3> ?04V==O V 70157?5GCTBLAO ?@8 FL><C 715@565==O 30<V;LB>=V0=0  EMBED Equation.3  WW V=5@B=>W 2V;L=>W 5=5@3VW A?>:>N.  2V4 ;03@0=6V0=0  EMBED Equation.3  A0<5 V=5@B=>W 2V;L=>W 5=5@3VW @5G>28=8 T ?>EV4=8< WW 30<V;LB>=V2 V<?C;LA  EMBED Equation.3  ( EMBED Equation.3 ), I> T ?@>?>@FV9=8< 3@02VB0FV9=V9 <0AV  EMBED Equation.3 . 5;8G8=0 6 V<?C;LAC @5G>28=8 2V4?>2V4=> 4> B5>@5<8 L>B5@ [QB5@, 1918] V 4> ?@8=F8?C =5287=0G5=>AB59 5975=15@30 T V=20@V0=B=>N I>4> ?5@5B2>@5==O G0AC E0@0:B5@8AB8:>N @5G>28=8, I> @CE0TBLAO, V, >B65, T >4=0:>2>N 4;O 2AVE A?>AB5@V30GV2, =572060NG8 =0 @V7=V B5<?8 E>4C WE 3@02V:20=B>28E 3>48==8:V2. >>@48=0B=0 ?A524>20:CC<=0 H284:>ABV A2VB;0 vcj(r)=cbj1/2 287=0GCTBLAO 4;O :>=:@5B=>W B>G:8 j 2 C=VDV:>20=><C (4;O 2AVTW 3@02VB5@<>48=0<VG=> ?>2'O70=>W @5G>28=8 5<;V) 0AB@>=><VG=><C G0AV tE. >=0 T B>B>6=>N 3@0=8G=V9 H284:>ABV @CEC @5;OB82VABAL:>W 3@02VB5@<>48=0<V:8 ( ") [0=K;LG5=:>, 2009: 20/2; 2010: 38; 0=8;LG5=:>, 2020: 5; 2021] V WW 25;8G8=0 70;568BL 2V4 @04V0;L=>W :>>@48=0B8 (20@FH8;L40 r FVTW B>G:8. >=0 7<5=HCTBLAO 2 "-! @07>< 7 =01;865==O< O: 4> ?A524>>1@VN, B0: V 4> F5=B@C BO6V==O.  3@02V:20=B>25 7=0G5==O :>>@48=0B=>W H284:>ABV A2VB;0:  EMBED Equation.3   EMBED Equation.3  T 70;56=8< B0:>6 V 2V4 :>>@48=0B=>W H284:>ABV A2VB;0 vci 2 B>GFV i 48A;>:0FVW @50;L=>3> 01> 6 ?5@5410GC20=>3> A?>AB5@V30G0, 45  EMBED Equation.3  V  EMBED Equation.3   7=0G5==O :>>@48=0B=>W H284:>ABV A2VB;0 C 2;0A=V9 F5=B@8G=V9 ic!0 ?5@5410GC20=>3> A?>AB5@V30G0. @8 FL><C 70 2;0A=8< 3@02V:20=B>28< 3>48==8:>< H284:VABL A2VB;0 T ?@>AB>@>2>-B5<?>@0;L=8< V=20@V0=B>< (:0;V1@C20;L=>-V=20@V0=B=>N V ;>@5=F-V=20@V0=B=>N :>=AB0=B>N). W 2;0A=5 7=0G5==O 2 1C4L-O:V9 B>GFV ?@>AB>@C 4>@V2=NT AB0;V9 H284:>ABV A2VB;0:  EMBED Equation.3  "0: O: V<?C;LA  EMBED Equation.3  @5G>28=8 T =570;56=8< 2V4 B5<?C ?5@51V3C 3@02V:20=B>2>3> G0AC ti, =5>4=0:>2>3> 2 B>G:0E 7 @V7=8< 3@02VB0FV9=8< ?>B5=FV0;><, :>>@48=0B=V 7=0G5==O V=5@B=>W B0 3@02VB0FV9=>W <0A 1C4CBL 28@060B8AO G5@57 WW 2;0A=5 7=0G5==O  EMBED Equation.3  B0:8< G8=><  EMBED Equation.3 ,  EMBED Equation.3 .  WE 3@02V:20=B>2V 7=0G5==O 1C4CBL B0:8<8:  EMBED Equation.3 ,  EMBED Equation.3 . >G5284L, C 3@02VB0FV9=><C ?>;V C<>2=5 2;0A=5 7=0G5==O <0A8 A?>:>N  EMBED Equation.3  <>65 1CB8 >4=0:>28< C >4=>@V4=>W @5G>28=8 ;8H5 70 =0O2=>ABV WW B5@<>48=0<VG=>W :207V@V2=>2038. /: ?>:0702 ">;<5= [">;<5=, 1969] V O: F5 28?;820T V 7 2=CB@VH=L>3> @>72'O7:C (20@FH8;L40 @V2=O=L 3@02VB0FV9=>3> ?>;O 4;O =5AB8A;82>W V450;L=>W @V48=8 [Q;;5@, 1972], 3@02VB0FV9=V A8;8 2 =V9 T ?@>?>@FV9=8<8 >@48=0@=V9 5=B0;L?VW  EMBED Equation.3  ( EMBED Equation.3 ), I> =5 7<5=HCTBLAO =0 2V4<V=C 2V4 V=5@B=>W 2V;L=>W 5=5@3VW , 0 =02?0:8, 7@>AB0T @07>< 7 =01;865==O< 4> F5=B@C BO6V==O.  B0: O: 4;O :207V@V2=>206=> E>;>=CG>W @5G>28=8  EMBED Equation.3 , B> >15@=5=> ?@>?>@FV9=>N :>>@48=0B=V9 H284:>ABV A2VB;0 T V >@48=0@=0 2=CB@VH=O 5=5@3VO A?>:>N  EMBED Equation.3  ( EMBED Equation.3 ) @5G>28=8, 45 p  B8A:, V  <>;O@=89 >1 T<, 0  EMBED Equation.3   048B82=0 :><?5=A0FVO <C;LB8?;V:0B82=>3> 7<5=H5==O C ?;8=V G0AC <C;LB8?;V:0B82=>W A:;04>2>W  EMBED Equation.3  2=CB@VH=L>W 5=5@3VW  EMBED Equation.3 . , >B65, FV;:>< 2>G5284L, I> V=5@B=0 <0A0 @5G>28=8, I> @CE0TBLAO, T C<>2=> 5:2V20;5=B=>N WW 3@02VB0FV9=V9 <0AV ;8H5 70 2;0A=8< 3>48==8:>< B>G:8, 7 O:>W @5G>28=0 ?>G0;0 @CE0B8AO 70 V=5@FVTN, ?@8 :>@83C20==V 7=0G5==O 3@02VB0FV9=>W AB0;>W, I> 4;O F5=B@8G=>W 01> 6 4;O ?A524>F5=B@8G=>W 2;0A=>W ! @5G>28=8 70157?5GCT C<>2=C 2V4ACB=VABL C @5G>28=8 ?>2'O70=>W 5=5@3VW.  F5 A?@8G8=5=5 5:2V20;5=B=VABN V=5@B=>W <0A8 @5G>28=8 30<V;LB>=V0=C WW V=5@B=>W 2V;L=>W 5=5@3VW, B>4V O: 3@02VB0FV9=0 <0A0 @5G>28=8 T 5:2V20;5=B=>N ;03@0=6V0=C WW >@48=0@=>W 2=CB@VH=L>W 5=5@3VW.  A?V22V4=>H5==O F8E <0A T =57<V==8< 7024O:8 715@565==N C G0AV O: 30<V;LB>=V0=0 V=5@B=>W 2V;L=>W 5=5@3VW, B0: V ;03@0=6V0=0 >@48=0@=>W 2=CB@VH=L>W 5=5@3VW 3@02V:20=B>28E 3>48==8:V2 A?>AB5@56C20=>W @5G>28=8 V A?>AB5@V30G0, I> @CE0NBLAO 70 V=5@FVTN:  EMBED Equation.3 , 45:  EMBED Equation.3   7=0G5==O 3@0=8G=>W H284:>ABV @CEC @5G>28=8 2 B>G:0E WW 3V?>B5B8G=>3> A?>:>N 2V4=>A=> 3V?>B5B8G=>3> A?>AB5@V30G0 @CEC. 28G09=>, <>6=0 1C;> 1 ?@8?CAB8B8, I> B0:5 ?>=OBBO O: 30<V;LB>=V0= 4;O ", 0 B8< 1V;LH5 V 4;O " T =04<V@=8<. 465 2 =8E <0T <VAF5 715@565==O ;03@0=6V0=0 >@48=0@=>W 2=CB@VH=L>W 5=5@3VW, V ?@03=5==O 4> <V=V<C<C ;03@0=6V0=0 V=5@B=>W 2V;L=>W 5=5@3VW @5G>28=8. 4=0: 65, 28:>@8AB0==O BV;L:8 ;03@0=6V0=0 =5 4>72>;8BL 2V4>1@060B8 4V9A=VABL 70 4>?><>3>N ;>:0;L=>3> ?A524>52:;V4>20 ?@>AB>@C-G0AC. "0 V 7<5=H5==O 2  EMBED Equation.3  @07 =5>1EV4=>W A5@54=L>W IV;L=>ABV V=5@B=>W <0A8 0AB@>=><VG=8E >1'T:BV2 2 30;0:B8FV =5 1C45 70157?5G5=5. "><C-B> V 4>2545BLAO ?>:;040B8AO A0<5 =0 FN 3V?>B57C. "0:>6 <>6;82>, I> <0AC A;V4 @>73;O40B8 ;8H5 O: <V@C :V;L:>ABV @5G>28=8, 0 V=5@B=V V 3@02VB0FV9=V 2;0AB82>ABV @5G>28=8 E0@0:B5@87C20B8 2V4?>2V4=> 30<V;LB>=V0=>< V=5@B=>W 2V;L=>W 5=5@3VW V ;03@0=6V0=>< >@48=0@=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8. 9. @02VB5<?>@0;L=0O V=20@V0=B=VABL 4V9A=> <5B@8G=8E 7=0G5=L <5E0=VG=8E V B5@<>48=0<VG=8E ?0@0<5B@V2 @5G>28=8 0 2V4<V=C 2V4 V<?C;LAC 4VNGV =0 @5G>28=C A8;8, O: V 2AV 2848 WW 5=5@3V9, D>@<0;L=> 70;560BL 2V4 B5<?C E>4C WW 3@02V:20=B>28E 3>48==8:V2. @8 ?5@5E>4V 2V4 T48=>3> 3@02VB5@<>48=0<VG=>3> (0AB@>=><VG=>3>) G0AC 4> 3@02V:20=B>28E 2;0A=8E G0AV2 @5G>28=8 25;8G8=8 F8E A8;, O: V =5 2V4F5=B@>20=V 7=0G5==O 2AVE 5=5@3V9, 71V;LHCNBLAO 2  EMBED Equation.3  @07. # 2;0A=V9 ! B>G:8 r, 7 O:>W @5G>28=0 ?>G0;0 ?040B8:  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 , 0 ?@82545=V 4> 2;0A=>3> 7=0G5==O 3@02VB0FV9=>W AB0;>W (2V4F5=B@>20=V) 7=0G5==O 30<V;LB>=V0=0 V=5@B=>W 2V;L=>W 5=5@3VW V ;03@0=6V0=0 >@48=0@=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8 2 WW ?A524>F5=B@8G=V9 rc!0 1C4CBL B0:8<8:  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3   4V9A=> <5B@8G=5 7=0G5==O H284:>ABV @CEC @5G>28=8 [0=K;LG5=:>, 2006: 27; 2008: 60; 2021]; v  :>>@48=0B=0 H284:VABL @CEC @5G>28=8 2 D>=>2><C @53C;O@=><C ?@>AB>@V, O:0 =5 2@0E>2CT 9>3> ;>:0;L=C :V=5<0B8G=C :@828=C, I> 2=>A8BLAO A0<8< @CE>< @5G>28=8;  EMBED Equation.3  V  EMBED Equation.3   4V9A=> <5B@8G=V 7=0G5==O ?@8A:>@5=L 2V;L=>3> ?04V==O BV;0 2V4?>2V4=> C 2;0A=><C 3@02V:20=B>2><C G0AV B>G:8 r B0 2 3@02VB5@<>48=0<VG=><C G0AV (A2VB>2><C G0AV " [Q;;5@, 1972]);  EMBED Equation.3  V  EMBED Equation.3   3@02VB0FV9=5 ?@8A:>@5==O 2 B>GFV r 2V4?>2V4=> 70 WW 2;0A=8< 3@02V:20=B>28< 3>48==8:>< B0 2 3@02VB5@<>48=0<VG=><C G0AV;  EMBED Equation.3   :>>@48=0B=5 ?@8A:>@5==O @CEC @5G>28=8 2 D>=>2><C @53C;O@=><C ?@>AB>@V;  EMBED Equation.3 , 1>  EMBED Equation.3 ;  EMBED Equation.3 , B0: O:  EMBED Equation.3 ;  EMBED Equation.3   3@0=8G=0 H284:VABL @CEC @5G>28=8 2 1C4L-O:V9 B>GFV C 2;0A=><C 3@02V:20=B>2><C G0AV B>G:8 r;  EMBED Equation.3   7=0G5==O 3@02VB0FV9=>W AB0;>W 70 2;0A=8< 3>48==8:>< B>G:8 r;  EMBED Equation.3   7=0G5==O ?@8@>ABC 2;0A=>3> 3@02V:20=B>2>3> G0AC B>G:8 r. "0:8< G8=><, 70 3@02V:20=B>28< 3>48==8:>< 1C4L-O:>W B>G:8 i V=5@B=0 V 3@02VB0FV9=0 <0A8 A?>:>N @5G>28=8 1C4CBL 287=0G0B8AO 2 B0:89 A?>AV1:  EMBED Equation.3 ,  EMBED Equation.3  4=0: 65, 70 4>?><>3>N @>73;O=CB8E BCB ?5@5B2>@5=L 74V9A=NTBLAO ?5@5EV4 ;8H5 4> =>28E :>>@48=0B=8E, 0 7>2AV< =5 4> <5B@8G=8E 7=0G5=L V=5@B=>W V 3@02VB0FV9=>W <0A.  FV 7=0G5==O <0A 2 ?A524>F5=B@8G=V9 rc!0 =5 2V4?>2V40NBL @50;L=8< 7=0G5==O< 2=CB@VH=L>W 5=5@3VW @5G>28=8 V WW B5@<>48=0<VG=8< AB0=0< 27030;V.  V=5@B=0 ?>2'O70=0 5=5@3VO 2 =>2><C F5=B@V :>>@48=0B 27030;V 2V4ACB=O. "><C-B>, 2>=8 V =5 <>6CBL @>73;O40B8AO O: 4V9A=> <5B@8G=V 7=0G5==O V=5@B=>W V 3@02VB0FV9=>W <0A. /: 10G8<>, ?A524>A8;0 V=5@FVW 71V;LH8;0AO 70 @0EC=>: 7@>AB0==O 2  EMBED Equation.3  @07 V=5@B=>W 2V;L=>W 5=5@3VW G8 5:2V20;5=B=>W W9 V=5@B=>W <0A8. 5B@8G=5 7=0G5==O ?@8A:>@5==O 2V;L=>3> ?04V==O BV;0, O: V <5B@8G=5 7=0G5==O H284:>ABV 9>3> ?04V==O =5 7<V=8;8AO. V2=O==O 2V;L=>3> ?04V==O @5G>28=8  EMBED Equation.3 , O: V 1C4L-O:8E V=H8E WW @CEV2, >4=0:>2> D>@<C;NNBLAO 7 28:>@8AB0==O< 1C4L-O:8E 3@02V:20=B>28E 3>48==8:V2. 465 2 =8E 28:>@8AB>2CNBLAO 7>2AV< =5 01A>;NB=V, 0 ;8H5 2V4=>A=V 7=0G5==O ?0@0<5B@V2 @CEC. ">1B> 3@02V:20=B>289 3>48==8: @5G>28=8 ;8H5 ?@8E>20=> 2?;820T =0 WW <0AC V =5 ?>7=0G0TBLAO =0 4V9A=> <5B@8G=8E 7=0G5==OE ?0@0<5B@V2 @CEC @5G>28=8, O:V 7>2AV< =5 70;560BL 2V4 B5<?C E>4C 3@02V:20=B>28E 3>48==8:V2.  F5, 728G09=> 6, >1C<>2;5=> B8<, I> :20=B>20 7<V=0 :>;5:B82=>3> <V:@>AB0=C 2AVTW 3@02VB5@<>48=0<VG=> ?>2'O70=>W @5G>28=8 2V41C20TBLAO >4=>G0A=> V, >B65, 7 >4=VTN V BVTN 6 G0AB>B>N.  B><C-B> F5 2A5 T FV;:>< ;>3VG=8<. @0=8G=0 H284:VABL @CEC @5G>28=8  EMBED Equation.3 , O: V B>B>6=0 W9 :>>@48=0B=0 H284:VABL A2VB;0 ", T ?@8E>20=8< <5E0=VG=8< V B5@<>48=0<VG=8< ?0@0<5B@>< V 265 2@0E>20=0 2 28:>@8AB>2C20=8E =0 ?@0:B8FV WW ?0@0<5B@0E V E0@0:B5@8AB8:0E. , B><C-B>, 2>=0 ?@8=F8?>2> =5 <>65 I5 V O2=> 2?;820B8 =0 1V;LHVABL <5E0=VG=8E V B5@<>48=0<VG=8E ?0@0<5B@V2 @5G>28=8. W 7=0G5==O E0@0:B5@87CT ;8H5 2V4<V=C <C;LB8?;V:0B82=>W A:;04>2>W B5@<>48=0<VG=>W 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3  2 @V7=8E B>G:0E 3@02VB0FV9=>3> ?>;O G5@57 B5, I> @5G>28=0 2 =8E ?5@51C20T 2 =5>4=0:>28E B5@<>48=0<VG=8E AB0=0E. @8 FL><C <V=V<0;L=> <>6;825 7=0G5==O B5@<>48=0<VG=>W 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3  ( EMBED Equation.3 ) T, O: V V=HV B5@<>48=0<VG=V ?0@0<5B@8, 2;0A=>N E0@0:B5@8AB8:>N @5G>28=8. > B>3> 6 <C;LB8?;V:0B82=0 A:;04>20 B5@<>48=0<VG=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8 B>B>6=0 WW <5E0=VG=V9 >@48=0@=V9 2=CB@VH=V9 5=5@3VW ( EMBED Equation.3 ) V B><C-B>, O: V 2>=0, ?@8=F8?>2> =5 <>65 70;560B8 2V4 B5<?C ?;8=C G0AC 70 3@02V:20=B>28< 3>48==8:>< A?>AB5@V30G0 (728G09=> 6, O:I> B5<? WE E>4C 2V4:0;V1@>20=> 70 B5<?>< E>4C T48=>3> 3@02VB5@<>48=0<VG=>3> G0AC 2AVTW 3@02VB5@<>48=0<VG=> ?>2'O70=>W @5G>28=8). , >B65, =5 70;560BL 2V4 =L>3> V 2AV V=HV B5@<>48=0<VG=V ?>B5=FV0;8.  B8< 1V;LH5 =5 70;560BL 2V4 =L>3> =5 BV;L:8 5:AB5=A82=V, 0 9 V=B5=A82=V B5@<>48=0<VG=V ?0@0<5B@8 @5G>28=8. "0:8< G8=><, 28:>@8AB0==O D>@<0;V7<C 3@02V:20=B>2>3> G0AC 4>72>;OT 74V9A=N20B8 ;8H5 2V4=>A=V 28<V@N20==O <5E0=VG=8E V B5@<>48=0<VG=8E ?0@0<5B@V2 B0 E0@0:B5@8AB8: @5G>28=8. ;O B>3> 6, I>1 =0 ?V4AB02V =L>3> <>6=0 1C;> 287=0G8B8 WE 4V9A=V <5B@8G=V 7=0G5==O C A?>AB5@56C20=>W @5G>28=8 =5>1EV4=> I5 7=0B8  O:8< WE 7=0G5==O< 2V4?>2V40T ?>:070==O 3@02V:20=B>2>3> 3>48==8:0 A?>AB5@V30G0.  BV;L:8 2 FL><C 28?04:C A?>AB5@56C20=V 7=0G5==O <5E0=VG=8E V B5@<>48=0<VG=8E ?0@0<5B@V2 @5G>28=8 1C4CBL >4=0:>28<8 4;O 2AVE A?>AB5@V30GV2. "0:, =0?@8:;04, 7 >3;O4C =0 B5, I> 4;O :207V@V2=>206=> E>;>=CG8E 307V2 V =09?@>ABVH8E @V48=:  EMBED Equation.3  ( EMBED Equation.3 ),  EMBED Equation.3  ( EMBED Equation.3 ),  EMBED Equation.3  ( EMBED Equation.3 ),  EMBED Equation.3  ( EMBED Equation.3 ), >B@8<0T<> 4V9A=V <5B@8G=V 7=0G5==O (I> A?>AB5@V30NBLAO 70 3@02V:20=B>28< 3>48==8:>< B>G:8 i 2 B>GFV j) B0:8E E0@0:B5@8AB8: @5G>28=8 O: 3@02VB0FV9=0 <0A0, 2=CB@VH=O 5=5@3VO, B5@<>48=0<VG=0 5=B0;L?VO V B5<?5@0BC@0, O:V T B>B>6=8<8 WE :>>@48=0B=8< 7=0G5==O< 2 "-!:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . 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H284:>ABV V ?@8A:>@5==O >1'T:BV2 70;8H8;8AO B0:8<8 6, O: V 2 3@02VB5@<>48=0<VG=><C (0AB@>=><VG=><C) G0AV. @8 FL><C C 2;0A=><C 3@02V:20=B>2><C G0AV 1C4L-O:>W 4>2V;L=>W B>G:8 i A?V22V4=>H5==O 7=0G5=L V=5@B=>W 2V;L=>W 5=5@3VW V >@48=0@=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8 (0, >B65, V 5:2V20;5=B=8E W< <0A) 70;8H0TBLAO B0:8< 65  EMBED Equation.3 , O: V 2 7030;L=><C 4;O 2AVTW 3@02VB5@<>48=0<VG=> ?>2'O70=>3> @5G>28=8 3@02VB5@<>48=0<VG=><C G0AV. 465:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3  V  EMBED Equation.3 ,  EMBED Equation.3   2V4?>2V4=> ?@8A:>@5==O @CEC V 3@02VB0FV9=V ?@8A:>@5==O 2 3@02V:20=B>2><C G0AV B>G:8 i B0 2 7030;L=><C 4;O 2AVTW 3@02VB5@<>48=0<VG=> ?>2'O70=>W @5G>28=8 3@02VB5@<>48=0<VG=><C G0AV;  EMBED Equation.3   5:2V20;5=B=5 7=0G5==O 3@02VB0FV9=>W AB0;>W. 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"><C-B>, 70 28=OB:>< V=5@B=>W 2V;L=>W 5=5@3VW V 5:2V20;5=B=>W W9 V=5@B=>W <0A8 2AV V=HV 4V9A=> <5B@8G=V <5E0=VG=V B0 B5@<>48=0<VG=V ?0@0<5B@8 B0 E0@0:B5@8AB8:8 @5G>28=8 =5 70;560BL 2V4 ?>:070=L 3@02V:20=B>28E 3>48==8:V2 V, >B65, T B5<?>@0;L=> V=20@V0=B=8<8.  <560E 0B<>AD5@8 V :>A<>AD5@8 5<;V F5 5:2V20;5=B=5 7=0G5==O 3@02VB0FV9=>W AB0;>W =5ACBBT2> 70;568BL 2V4 28A>B8 =04 WW ?>25@E=5N.  >AL =0 :@0N !>=OG=>W A8AB5<8 A0<5 2>=> V <>3;> ?@8725AB8 4> 0=><0;L=>3> @CEC :>A<VG=8E 0?0@0BV2 V>=5@ [Anderson et al., 2002; Masreliez, 2005; Jacobson, 2009]. /:I> 6 <8 703;818<>AO 2 40;5:89 :>A<VG=89 ?@>ABV@, 45  EMBED Equation.3  T <0:A8<0;L=> <>6;828< 7=0G5==O< 3@0=8G=>W H284:>ABV @CEC @5G>28=8 2 :>A<>AD5@V, B> >B@8<0T<> 4>A8BL ACBBT2C 2V4<V==VABL 3@02VB0FV9=>W AB0;>W 2V4 WW 7=0G5==O =0 5<;V. > B>3> 6 4;O 40;5:8E 30;0:B8: F5 1C4CBL 265 =5 ?A524>F5=B@8G=V, 0 @50;L=V F5=B@8G=V 30;0:B8G=V !. 10. V2=O==O 3@02VB0FV9=>3> ?>;O " >G5284L, 2 B5=7>@V 5=5@3VW-V<?C;LAC @V2=O=L 3@02VB0FV9=>3> ?>;O " A;V4 28:>@8AB>2C20B8 70<VABL ;>@5=F-V=20@V0=B=8E B5@<>48=0<VG=8E E0@0:B5@8AB8: @5G>28=8 WW ;>@5=F-=5V=20@V0=B=V 2=CB@VH=L>O45@=V "-E0@0:B5@8AB8:8. ;O ?>ABC?>2> :207V@V2=>206=> E>;>=CG>W @5G>28=8 2 =8E 70<VABL IV;L=>ABV 5=B0;L?VW ?>28==0 1CB8 28:>@8AB0=0 IV;L=VABL >@48=0@=>W 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3 . # !!  =5=C;L>2V :><?>=5=B8 <5B@8G=>3> B5=7>@0 <0NBL B0:89 283;O4: EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3. V4?>2V4=> 4> FL>3> @V2=O==O 3@02VB0FV9=>3> ?>;O 4;O >4=>@V4=>W @5G>28=8 [0=K;LG5=:>, 2004: 35; 2008b: 45; 2009; 0=8;LG5=:>, 2020: 5]: EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 (3) C ?A524>52:;V4>2><C ?@>AB>@V V=:>2AL:>3> !!  C 7030;L=><C 28?04:C 1C4CBL <0B8 =0ABC?=89 283;O4: EMBED Equation.3 EMBED Equation.3 EMBED Equation.3, EMBED Equation.3EMBED Equation.3, EMBED Equation.3 EMBED Equation.3  EMBED Equation.3   EMBED Equation.3 , EMBED Equation.3 EMBED Equation.3 EMBED Equation.3, 45:  EMBED Equation.3  B0  EMBED Equation.3   2V4?>2V4=> <C;LB8?;V:0B82=0 A:;04>20 ?>2=>W 5=5@3VW (>@48=0@=0 2=CB@VH=O 5=5@3VO) V V=5@B=0 2V;L=0 5=5@3VO @5G>28=8;  EMBED Equation.3   :>A<>;>3VG=0 AB0;0;  EMBED Equation.3 ;  EMBED Equation.3  V  EMBED Equation.3   H284:>ABV @04V0;L=>3> @CEC <V:@>>1'T:BV2 @5G>28=8 2 !! , I> 287=0G0NBLAO C :>A<>;>3VG=><C G0AV  2V4?>2V4=> 70 T48=8< AB0=40@B>< 4>268=8 V 70 WE 2;0A=8<8 AB0=40@B0<8 4>268=8; EMBED Equation.3  2V4=>A=0 H284:VABL @04V0;L=>3> @CEC <V:@>>1'T:BV2 @5G>28=8; EMBED Equation.3 V  EMBED Equation.3   3@0=8G=V H284:>ABV @CEC <V:@>>1'T:BV2 @5G>28=8 2V4?>2V4=> C :>A<>;>3VG=><C G0AV V C 2;0A=><C G0AV @5G>28=8; EMBED Equation.3 V  EMBED Equation.3   G0AB>B8 2=CB@VH=L>O45@=>W 270T<>4VW 2V4?>2V4=> C :>A<>;>3VG=><C G0AV V C 2;0A=><C G0AV @5G>28=8.  C<>2=> ?>@>6=L><C ?@>AB>@V:  EMBED Equation.3 ,  EMBED Equation.3 , 0 @04V0;L=V :>>@48=0B8 2 !!  V C 2;0A=V9 ! @5G>28=8 ?>2'O70=V <V6 A>1>N 1V;LH ?@>AB8<8 70;56=>ABO<8:  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3 . V4?>2V4=> 4> F8E @>72'O7:V2 @V2=O=L 4;O 6>@AB:>W 2;0A=>W ! @5G>28=8 (EMBED Equation.3, EMBED Equation.3 287=0G0T<> 70 <5B@8G=> >4=>@V4=>N H:0;>N :>A<>;>3VG=>3> G0AC ( (EMBED Equation.3 ?@8 EMBED Equation.3) =0ABC?=V 70;56=>ABV: EMBED Equation.3, EMBED Equation.3. 2V4:8: EMBED Equation.3 EMBED Equation.3 EMBED Equation.3, EMBED Equation.3, EMBED Equation.3, EMBED Equation.3, EMBED Equation.3, EMBED Equation.3 EMBED Equation.3, 45: EMBED Equation.3 4;O >1;0ABV DC=40<5=B0;L=>3> ?@>AB>@C !!  EMBED Equation.3, 2 O:V9 EMBED Equation.3, V  EMBED Equation.3  4;O >1;0ABV EMBED Equation.3, 2 O:V9 EMBED Equation.3. /: 10G8<>, C :>A<>;>3VG=><C G0AV, I> 2V4;VGCTBLAO 2 !! , 2V4ACB=O =5 BV;L:8 3@02VB0FV9=0, 0 V @5;OB82VABAL:0 0=V7>B@>?VO A:>@>G5==O @>7<V@V2 <V:@>>1'T:BV2 @5G>28=8 C WW DC=40<5=B0;L=><C ?@>AB>@V.  28=8:0T 2>=0 ;8H5 G5@57 =54>45@60==O :>A<>;>3VG=>W >4=>G0A=>ABV ?>4V9, 2V4?>2V4=8E >4=><C V B><C 6 :>;5:B82=><C <V:@>AB0=C @5G>28=8, C @07V 28:>@8AB0==O 2 FL><C D>=>2><C 52:;V4>2><C ?@>AB>@V AC?CB=L>3> 2;0A=>3> G0AC @5G>28=8, I> A0<>AB8A:0TBLAO. 465 2 C<>2=> ?>@>6=L><C ?@>AB>@V (EMBED Equation.3, EMBED Equation.3): EMBED Equation.3, EMBED Equation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quation.3 , 45: NDn=1,5(tpBn)-2=3chmn-2/G=0,9998851040  =59B@>==5 25;8:5 G8A;> V@0:0, HE=62,29548 :</A?:; =e2/c'  AB0;0 B>=:>W AB@C:BC@8, Bn=mnc2/2' =2,2718591023 [c-1]  G0AB>B0 E28;V 45 @>9;O =59B@>=0, tp=(c-5'G)1/2  ?;0=:V2AL:89 G0A, '=h/2  AB0;0 ;0=:0-V@0:0, G  3@02VB0FV9=0 AB0;0 LNB>=0, e  5;5:B@8G=89 70@O4 ?@>B>=0 V 5;5:B@>=0, mn  <0A0 =59B@>=0 [0=8;LG5=:>, 2020: 85; 2021; Danylchenko, 2021a: 29]. ;5 V 7=0G5==O AB0;>W %011;0 (?@8 =1,3545710-52 <-2) HE=(4/8NDH)BH=62,16420 :</A?:, I> T 2V4?>2V4=8< G0AB>BV E28;V 45 @>9;O 0B><0 2>4=N BH=mHc2/2'=2,2702621023 [c-1] (mH=1,6737510-27 [:3], NDH=1,5(tpBH)-2=1,0012921040), ;8H5 4;O <0;8E 48AB0=FV9 70157?5GCT =57=0G=> 3V@HC 2V4?>2V4=VABL 40=8< 3@0DVG=>W 5:AB@0?>;OFVW @57C;LB0BV2 0AB@>=><VG=8E A?>AB5@565=L. >6;82>, 2>4=525 7=0G5==O AB0;0 %011;0 ?@89=O;0 ;8H5 ?VA;O A?>=B0==>3> ?5@5B2>@5==O :20@:>2>3> 01> 6 =59B@>==>3> A5@54>28I0 A5A2VBC 2 2>4=525. %>G0, 728G09=> 6, 4> FL>3> V =5 <>6;82> 1C;> <5B@8G=> E0@0:B5@87C20B8 WW ACFV;L=C ?@>B>@5G>28=C 0, >B65, V 1573;C74> 1C;> 1 E0@0:B5@87C20B8 WW V =59B@>==>N AB0;>N %011;0. "><C-B> >AB0B>G=89 281V@ >4=>3> 7 F8E 42>E 1;87L:8E 7=0G5=L AB0;>W %011;0 <>65 1CB8 7@>1;5=89 =0 ?V4AB02V ;8H5 1V;LH B>G=8E @57C;LB0BV2 0AB@>=><VG=8E A?>AB5@565=L. >G5284L, ?5@5410GC20=0 ?>B@510 =0O2=>ABV C A5A2VBV B5<=>W 5=5@3VW @C=BCTBLAO =5 BV;L:8 =0 2@0EC20==V CO2=>3> (?>ABC;L>20=>3> B>B>6=VABN B5@V=3B>=0 [Etherington, 1933] DV:B82=>3>) C?>2V;L=5==O ?;8=C G0AC =0 0AB@>=><VG=8E >1'T:B0E, I> 2V440;ONBLAO 2V4 A?>AB5@V30G0, 0;5 V =0 1060==V <0B8 ;V=V9=C 70;56=VABL G5@2>=>3> 7AC2C A?5:B@0 28?@><V=N20==O z 2V4 =5:>@83>20=>W A2VB8<VA=>W 2V4AB0=V DL 4> =8E. 0A?@024V 6 73V4=> " [0=K;LG5=:>, 2008: 102; 2008b: 45; 96; 0=8;LG5=:>, 2020: 85; 2021] ;V=V9=V 70;56=>ABV G5@2>=>3> 7AC2C <0NBL <VAF5 ;8H5 2V4 ?>?5@5G=>W AC?CB=L>W 2V4AB0=V DM:  EMBED Equation.3  2V4 2V4AB0=V 70 :CB>28< 4V0<5B@>< DA:  EMBED Equation.3  > B>3> 6 ?5@5410GC20=0 B5<=0 5=5@3VO 7>2AV< V =5 <>3;0 1 1CB8 O:>NAL DV78G=>N ACB=VABN. >=0 <>3;0 1 1CB8 ;8H5 ?@>O2>< 2AN48ACI>3> =530B82=>3> 72>@>B=>3> 72'O7:C. 0 4>?><>3>N FL>3> 72>@>B=>3> 72'O7:C 74V9A=N20;>AO 1 30;L<C20==O 52>;NFV9=>3> A0<>AB8A:0==O @5G>28=8 2 !! . , B8< A0<8<, V 30;L<C20;>AO 1 52>;NFV9=5 7<5=H5==O H284:>ABV A2VB;0 2 =V9 ?> ('.  F5 30;L<C20==O, 728G09=> 6, <0;> 1 1CB8 B8< 1V;LH8<, G8< <5=H8< 1C;> 1 C "-! =52;0A=5 (3@02VB5@<>48=0<VG=5) 7=0G5==O H284:>ABV A2VB;0 2 :>A<>AD5@V uvcos. ;5 2A5 6 FV;:>< <>6;82>, I> ?0@0<5B@ %011;0 4V9A=> T =57<V==>N 2 G0AV :>=AB0=B>N, O: BCB V 4>25;>AO ?5@5:>=0B8AO 2 FL><C.  =02VBL ?>4V1=> 2;0A=><C 7=0G5==N H284:>ABV A2VB;0 2V= <>65 1CB8 V ?@>AB>@>2>-B5<?>@0;L=8< V=20@V0=B><.  >B@8<0=8E @>72'O7:0E @V2=O=L V=B53@C20==O IV;L=>ABV 5:2V20;5=B=>W >@48=0@=V9 2=CB@VH=V9 5=5@3VW 3@02VB0FV9=>W <0A8 EMBED Equation.3 B0 IV;L=>ABV 5:2V20;5=B=>W V=5@B=V9 2V;L=V9 5=5@3VW V=5@B=>W <0A8 EMBED Equation.3 ?@>2>48BLAO 70 WE 7=0G5==O<8, A?>AB5@56C20=8<8 7 28:>@8AB0==O< >4=>3> V B>3> 6 3>48==8:0, 0 7>2AV< =5 70 2;0A=8<8 7=0G5==O<8 IV;L=>ABV <0A8 EMBED Equation.3 B0 B8A:C EMBED Equation.3, I> >B@8<CNBLAO 70 @V7=8<8 2;0A=8<8 3>48==8:0<8, O: F5 ?@89=OB> 2 " [Q;;5@, 1972].  CAL><C V=H><C FV @>72'O7:8 D>@<0;L=> 2V4?>2V40NBL @>72'O7:0< " 4;O 3@0=8G=> >AB83;>W @5G>28=8 (EMBED Equation.3), I> ?5@51C20T 2 AB0=V <5E0=VG=>W @V2=>2038 [0=K;LG5=:>, 2005b; 2008: 4]: EMBED Equation.3. # FL><C 28?04:C <0T <VAF5 4>B@8<0==O =5 BV;L:8 C<>2 BV;L:8 C<>2 ">;<5=0 4;O B5@<>48=0<VG=8E ?0@0<5B@V2 @5G>28=8 2 WW 2;0A=><C 3@02V:20=B>2><C G0AV EMBED Equation.3 V EMBED Equation.3, 0 9 28:>@8AB0=>W 2 >B@8<0=8E @>72'O7:0E C<>28 EMBED Equation.3:  EMBED Equation.3 . 024O:8 270T<=V9 ?@>?>@FV9=>ABV  EMBED Equation.3  B0  EMBED Equation.3  ( EMBED Equation.3 ) ' @5G>28=8, >B@8<0=89 =0 >A=>2V 0=0;V7C ?@>AB>@>2>3> @>7?>4V;C ;>@5=F-=5V=20@V0=B=8E 2=CB@VH=L>O45@=8E " E0@0:B5@8AB8: @5G>28=8, T V45=B8G=8< ', I> >B@8<CTBLAO 2 " ?@8 V3=>@C20==V O: ;>@5=F-V=20@V0=B=>ABV, B0: V 3@02VB0FV9=>-B5<?>@0;L=>W =5?5@5B2>@N20=>ABV B5@<>48=0<VG=8E ?0@0<5B@V2 V E0@0:B5@8AB8: @5G>28=8. 0@B> B0:>6 2V47=0G8B8, I> 73V4=> O: 7 ", B0: V 7 " V450;L=89 307 (EMBED Equation.3) ?@8=F8?>2> =5 <>65 2>;>4VB8 3@02VB0FV9=8< ?>;5<. >;O@=0 5=5@3VO V450;L=>3> 307C 0, >B65, V :>>@48=0B=0 H284:VABL A2VB;0 2 =L><C, T >4=0:>28<8 C 2AL><C 709<0=><C F8< 307>< ?@>AB>@V: EMBED Equation.3, EMBED Equation.3.  F5 6 >7=0G0T, I> O28I5 3@02VB0FVW ?>2'O70=> 7 5;5:B@><03=VB=>N 270T<>4VTN <>;5:C; @5G>28=8 V, >B65, <0T ACB> 5;5:B@><03=VB=C ?@8@>4C. 11. V2=O==O 3@02VB0FV9=>3> ?>;O 30;0:B8:8 >;8 ?>>48=>:V >1'T:B8 V WE AC:C?=>ABV CB2>@NNBL 25;8:89 :>;5:B82, WE AC<0@=0 <0A0 <>65 VAB>B=> ?5@528IC20B8 <0AC F5=B@0;L=>3> 0AB@>=><VG=>3> BV;0 (=04<0A82=>W =59B@>==>W 7V@:8 01> 6 :2070@0). "O6V==O 0AB@>=><VG=8E 265 VAB>B=> A?>B2>@8B8 2AB0=>2;5=V 5?;5@>< 70:>=8 @CEC 4;O ?5@8D5@V9=8E ?>>48=>:8E 0AB@>=><VG=8E >1'T:BV2. , B><C-B>, 73V4=> 7 0AB@>=><VG=8<8 A?>AB5@565==O<8 4;O 70?>1V30==O A?V;L=>3> :>;0?AC 2AVTW @5G>28=8 30;0:B8:8 V ?>B@V1=V =0 1030B> 1V;LHV H284:>ABV >15@B0==O >1'T:BV2 2=CB@VH=VE AD5@8G=8E H0@V2 30;0:B8:8 <>65 28O28B8AO 7=0G=> A8;L=VH8<, =V6 BO6V==O F5=B@0;L=>3> BV;0 30;0:B8:8.  B>4V WE :>;5:B82=89 3@02VB0FV9=89 2?;82 <>65 v WW ?5@8D5@V9=8E 0AB@>=><VG=8E >1'T:BV2, =V6 H284:>ABV >15@B0==O >:@5<8E ?5@8D5@V9=8E 0AB@>=><VG=8E >1'T:BV2, I> M =5>1EV4=8<8 4;O 70?>1V30==O A0<>ABV9=>3> ?04V==O WE =0 F5=B@0;L=5 0AB@>=><VG=5 BV;>. @8 FL><C :204@0B 4V9A=> <5B@8G=>3> 7=0G5==O EMBED Equation.3 ;V=V9=>W H284:>ABV v >@1VB0;L=>3> >15@B0==O 0AB@>=><VG=8E >1'T:BV2 30;0:B8:8, I> 7=0E>48BLAO 7 C<>28 4>@V2=N20==O 2V4F5=B@>2>W ?A524>A8;8 V=5@FVW Fin=Hv2c-2a-1/2/r ?A524>A8;V BO6V==O Fgr=Lc-2a-1/2d(lnvc/c)/dr:  EMBED Equation.3  25;L<8 A;01:> 70;568BL 2V4 r>>re G5@57 <0;VABL O: B8A:C p 2 :>A<>AD5@V 30;0:B8:8, B0: V :>A<>;>3VG=>W AB0;>W . "CB 30;0:B8G=5 7=0G5==O :>>@48=0B=>W H284:>ABV A2VB;0 vc=Ab1/2, ;03@0=6V0= V 30<V;LB>=V0=: EMBED Equation.3, EMBED Equation.3 28@065=V G5@57 ?0@0<5B@8 EMBED Equation.3, b B0 a @V2=O=L 3@02VB0FV9=>3> ?>;O ": EMBED Equation.3, EMBED Equation.3. 4=0: 65, 70<VABL 2;0A=8E 7=0G5=L IV;L=>ABV <0A8 EMBED Equation.3 V B8A:C EMBED Equation.3 [Q;;5@, 1972] 2 B5=7>@V 5=5@3VW-V<?C;LAC 28:>@8AB0=V :>>@48=0B=V 3@02VB0FV9=V WE 7=0G5==O EMBED Equation.3 B0 EMBED Equation.3 (EMBED Equation.3). &5 ?>2'O70=> 7 B5<?>@0;L=>N V=20@V0=B=VABN 4V9A=> <5B@8G=8E <5E0=VG=8E V B5@<>48=0<VG=8E ?0@0<5B@V2 V E0@0:B5@8AB8: @5G>28=8. "0 9 =5AB0G0 <0A8 C A5A2VBV 2:07CT =0 B5, I> =5 BV;L:8 2 ", 0;5 V 2 " B5=7>@ 5=5@3VW-V<?C;LAC ?>28=5= @C=BC20B8AO =0 >@48=0@=V9 2=CB@VH=V9 5=5@3VW @5G>28=8, I> 2:;NG0T 4> A515 =5 BV;L:8 V=5@B=C 2V;L=C 5=5@3VN, 0 V ?>2'O70=C 5=5@3VN @5G>28=8. /:I> =5 725@B0B8 C203C =0 <VAF52V >A>1;82>ABV @>7?>4V;C A5@54=L>W IV;L=>ABV V=5@B=>W <0A8 2 30;0:B8:0E V, >B65, @>73;O40B8 ;8H5 7030;L=C B5=45=FVN B8?>2>W 70;56=>ABV H284:>ABV >@1VB0;L=>3> @CEC WE >1'T:BV2 2V4 @04V0;L=>W 2V4AB0=V 4> F5=B@C 30;0:B8:8, B> W< <>6=0 1C45 7VAB028B8 =0ABC?=C 70;56=VABL FVTW H284:>ABV 2V4 ?0@0<5B@0 b, 0 B8< A0<8< V 2V4 @04V0;L=>W 2V4AB0=V r [Danylchenko, 2021a: 33]:  EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 , EMBED Equation.3, EMBED Equation.3, 0: EMBED Equation.3  @04VCA C<>2=>3> ?CE:>3> O4@0 30;0:B8:8, =0 ?>25@E=V O:>3> :>@83>20=5 7=0G5==O >@1VB0;L=>W H284:>ABV @CEC EMBED Equation.3 >1'T:BV2 <>65 ?@89<0B8 <0:A8<0;L=> <>6;825 7=0G5==O EMBED Equation.3 [0=8;LG5=:>, 2020: 85; 2021]. 0 C<>28, I> EMBED Equation.3 ?>70 ?CE:>3> O4@0 30;0:B8:8, EMBED Equation.3 ?@89<0T <V=V<0;L=5 A2>T 7=0G5==O EMBED Equation.3 ?@8 EMBED Equation.3. # FL><C 28?04:C ?@8 EMBED Equation.3 (EMBED Equation.3, EMBED Equation.3) ;V=V9=V H284:>ABV >15@B0==O >1'T:BV2 30;0:B8:8 V @04V0;L=V 2V4AB0=V 4> =8E 1C4CBL B0:8<8:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 . @8 FL><C 1V;LH 1V;LH><C 7=0G5==N ?>:07=8:0 n IV;L=>ABV ?CE:>3> O4@0 2V4?>2V40T V 1V;LH5 7=0G5==O kb =0 >4=8E V B8E 65 25;8:8E @04V0;L=8E 2V4AB0=OE. ;5 ;8H5 ?@8 =04728G09=> 25;8:8E 7=0G5==OE EMBED Equation.3 <0T <VAF5 VAB>B=> <5=H0 A5@54=O IV;L=VABL @5G>28=8 70 <560<8 ?CE:>3> O4@0 30;0:B8:8.  B><C-B> 70;56=VABL 2V4 @04V0;L=>W 2V4AB0=V >@1VB0;L=8E H284:>AB59 WW >1'T:BV2 V <>65 1CB8 1;87L:>N 4> :5?;5@>2>W.  B><C-B> 70;56=VABL 2V4 @04V0;L=>W 2V4AB0=V >@1VB0;L=8E H284:>AB59 WW >1'T:BV2 V <>65 1CB8 1;87L:>N 4> :5?;5@>2>W. "0: ?@8 n=240 (kbn=16,780) >@1VB0;L=0 H284:VABL ?5@8D5@V9=8E >1'T:BV2 30;0:B8:8 265 <5=H5 ?>;>28=8 <0:A8<0;L=>W H284:>ABV (?@8 rp/re=20 EMBED Equation.3), 0 ?@8 n=245 (EMBED Equation.3=535) 2>=0 265 7=0G=> <5=H5 <0:A8<0;L=>W H284:>ABV (EMBED Equation.3). 4=0: 65, =5 BV;L:8 2 A;01:8E 3@02VB0FV9=8E ?>;OE (n<<234, EMBED Equation.3<<1,1391), 0;5 =02VBL 2 4>A8BL B0:8 A8;L=><C 3@02VB0FV9=><C ?>;V (n=234, EMBED Equation.3<1,1391, kbp=1,00000000000758) >@1VB0;L=V H284:>ABV WE ?>70O45@=8E >1'T:BV2 1C4CBL 4C65 1;87L:8<8 4> <0:A8<0;L=>3> 7=0G5==O EMBED Equation.3 :</A5: =0 4>A8BL B0:8 25;8:8E @04V0;L=8E 2V4AB0=OE EMBED Equation.3:  EMBED Equation.3 . @0:B8G=> 5:2V20;5=B=>N FV9 ! A?>AB5@56C20=>W 30;0:B8:8 T WW 2;0A=0 "-!0, 2 O:V9 ?@8 bre0=1, EMBED Equation.3 B0 EMBED Equation.3:  EMBED Equation.3  (EMBED Equation.3),  EMBED Equation.3 . =20@V0=B0<8 B0:>3> ?5@5B2>@5==O T =5 BV;L:8 ;03@0=6V0= >@48=0@=>W 2=CB@VH=L>W 5=5@3VW V 5:2V20;5=B=0 9><C 3@02VB0FV9=0 <0A0 @5G>28=8, 0 9 =0ABC?=V A?V22V4=>H5==O: EMBED Equation.3, EMBED Equation.3 [EMBED Equation.3]. &5, 728G09=> 6, T ?>2'O70=8< O: 7 B8<, I> 25;8:V 3@04VT=B8 3@02VB0FV9=>3> ?>;O =0 ?5@8D5@VW B0:8E 30;0:B8: D>@<CNBLAO 7>2AV< =5 WE O4@0<8, 0 CAVTN 25;8:>N AC:C?=VABN WE >1'T:BV2, B0: V 7V 7=0G=> <5=H8< :>>@48=0B=8< 7=0G5==O< 30<V;LB>=V0=0 V=5@B=>W 2V;L=>W 5=5@3VW @5G>28=8 2 ?>@V2=O==V 7 :>>@48=0B=8< 7=0G5==O< ;03@0=6V0=0 WW >@48=0@=>W 2=CB@VH=L>W 5=5@3VW ?@8 bre=2,253110-6 (EMBED Equation.3). ">4V 7 C@0EC20==O< 7=5206;82>W <0;>ABV O: :>A<>;>3VG=>W AB0;>W, B0: V B8A:C 2 :>A<>AD5@V 30;0:B8:8 2 " <0B8<5 <VAF5 =0ABC?=89 B8?>289 @04V0;L=89 @>7?>4V; A5@54=L>W IV;L=>ABV 3@02VB0FV9=>W <0A8 @5G>28=8 2 30;0:B8FV:  EMBED Equation.3   EMBED Equation.3 , 45 EMBED Equation.3  3@02VB0FV9=0 AB0;0 LNB>=0, 2;0A=V 30;0:B8G=V 7=0G5==O EMBED Equation.3 O:>W (70 3V?>B57>N V@0:0 [8@0:, 1978]) 2 40;5:><C :>A<>;>3VG=>W <8=C;><C, <>6;82>, 1C;8 7=0G=> 1V;LH8<8, =V6 70@07, G5@57 4C65 25;8:C A5@54=N IV;L=VABL @5G>28=8 C A5A2VBV [0=8;LG5=:>, 2021], 0:  EMBED Equation.3 . "0:8< G8=><, 73V4=> 7 ", G8< 1V;LH5 ?>:07=8: n V G8< <5=H5 7=0G5==O ?0@0<5B@0 be, B8< <5=H5 V <V=V<0;L=> 4>?CAB8<5 7=0G5==O A5@54=L>W IV;L=>ABV 3@02VB0FV9=>W <0A8 @5G>28=8 =0 :@0N 30;0:B8:8. 4=0: 65 ?@8 EMBED Equation.3 :</A5:, re=5 :?:, rp/re=20, n=234 B0 be=1,1265610-6 (EMBED Equation.3=1,1391) B>G=5 7=0G5==O IV;L=>ABV 3@02VB0FV9=>W <0A8 [gr0p]"=1,4 10-29 :3/<3 T =5 1V;LH5 =V6 =0 1% <5=H>N WW ?@81;87=>3> 7=0G5==O. , >B65, G5@57 EMBED Equation.3 A5@54=O IV;L=VABL 3@02VB0FV9=>W <0A8 @5G>28=8 =0 :@0N 30;0:B8:8 4>A8BL A;01> 70;568BL 2 " 2V4 ?>:07=8:0 n IV;L=>ABV ?CE:>3> O4@0 30;0:B8:8. !0<5 7024O:8 7<5=H5==N EMBED Equation.3 @07>< 7 =01;865==O< 4> ?A524>>1@VN ?>4V9 <V=V<0;L=> <>6;825 7=0G5==O A5@54=L>W IV;L=>ABV V=5@B=>W <0A8 @5G>28=8 =0 :@0N 30;0:B8:8 <>65 1CB8 ACBBT2> 7<5=H5=>.  F5 2A5 4>1@5 C73>46CTBLAO 7 70;56=VABN 7=0G5==O 3@02VB0FV9=>W AB0;>W 2V4 B5<?C E>4C 3@02V:20=B>28E 3>48==8:V2, 70 O:8<8 2>=0 287=0G0TBLAO. # F5=B@8G=V9 2;0A=V9 "-!g0 (ec!0g) 30;0:B8:8 <>65 1CB8 7VAB02;5=0 WW >1'T:B0< =0ABC?=0 70;56=VABL WE >@1VB0;L=>W H284:>ABV 2V4 ?0@0<5B@0 b 0, >B65, V 2V4 @04V0;L=>W 2V4AB0=V r 4> =8E [0=8;LG5=:>, 2020: 85; 2021; Danylchenko, 2021: 33]:  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 . @8 FL><C 2V4?>2V4=> 4> 70;56=>ABV EMBED Equation.3 C 2;0A=V9 T-!0 30;0:B8:8 4V9A=> <0T <VAF5 1V;LH A8;L=5 3@02VB0FV9=5 ?>;5, =V6 2 ! 40;5:>3> 7>2=VH=L>3> A?>AB5@V30G0: EMBED Equation.3, 45: EMBED Equation.3 G5@57 =570;56=VABL ;03@0=6V0=0 >@48=0@=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8, I> @CE0TBLAO 70 V=5@FVTN, 2V4 30;0:B8G=8E B5<?V2 ?;8=C 3@02VB5@<>48=0<VG=>3> (0AB@>=><VG=>3>) G0AC [0=8;LG5=:>, 2021; Danylchenko, 2021: 37]. 2>@>B=8<8 6 ?5@5B2>@5==O<8, 728G09=> 6, <>6=0 ?5@59B8 4> A?>AB5@565==O >1'T:BV2 30;0:B8:8 7V 715@565==O< ;03@0=6V0=0 >@48=0@=>W 2=CB@VH=L>W 5=5@3VW WE @5G>28=8 7 B>G>: 7 V=H8<8 3@02VB0FV9=8<8 ?>B5=FV0;0<8, ?@8 O:8E <0NBL <VAF5 265 V=HV 7=0G5==O WE ?0@0<5B@V2 b V br. &5 2:07CT =0 B@0=A?>78FV9=C 3@02VB0FV9=C =570;56=VABL ;03@0=6V0=0 >@48=0@=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8, I> @CE0TBLAO 70 V=5@FVTN, 2V4 3@02VB0FV9=8E ?>B5=FV0;V2 2 B>G:0E 48A;>:0FVW A?>AB5@V30GV2, I> B56 @CE0NBLAO 70 V=5@FVTN, 0, >B65, V 2V4 B5<?V2 ?;8=C WE 3@02V:20=B>2>3> G0AC. >G5284L, 7=0G=5 C?>2V;L=5==O B5<?C ?;8=C G0AC, I> A?>AB5@V30TBLAO C 40;5:8E 30;0:B8: (G5@57 be=1,1265610-6), <>65 @>73;O40B8AO O: 52>;NFV9=>-3@02VB0FV9=5 O28I5, O:5 C73>465=5 7 ;V=V9=>N E011;>2>N 70;56=VABN G5@2>=>3> 7AC2C 4>268=8 E28;V 28?@><V=N20==O V ACBBT2> 2V4@V7=OTBLAO 2V4 =5W ;8H5 C :2070@V2, I> <0NBL 4C65 A8;L=5 3@02VB0FV9=5 ?>;5. /:I> 7=0G5==O @04VCA0 re ?>25@E=V ?CE:>3> O4@0 30;0:B8:8 T <V=V<0;L=> <>6;828< C 475@:0;L=> A8<5B@8G=V9 :>=DV3C@0FVW 2;0A=>3> ?@>AB>@C 30;0:B8:8, B> F5 WW O4@> D0:B8G=> 1C45 ?CE:8< :2070@><. , >B65, 2AV 7V@:8 ?CE:>3> O4@0 30;0:B8:8 1C4CBL A:;040B8AO ;8H5 7 0=B8@5G>28=8. >72'O7>: @V2=O=L 3@02VB0FV9=>3> ?>;O " C D>=>2><C 52:;V4>2><C ?@>AB>@V [0=K;LG5=:>, 2005; 2008: 45; 2008: 96; 0=8;LG5=:>, 2020: 5; 2021] ?V4B25@46CT ?@8=F8?>2C <>6;82VABL B0:>W ?CE:>W AB@C:BC@8 9>3>. 024O:8 =87L:V9 =0?@C65=>ABV 3@02VB0FV9=>3> ?>;O 70 <560<8 ?CE:8E O45@ 30;0:B8: WE 4V9A=> <>6=0 @>73;O40B8 O: >AB@V2=V A5A2VB8 [Gordon, 1969, Weinberg, 2010; Koberlein, 2013] (=5V7>;L>20=V >AB@V2=V A8AB5<8 [Q;;5@, 1972]), I> <0NBL V=482V4C0;L=V 2;0A=V 7=0G5==O 3@02VB0FV9=>W AB0;>W: EMBED Equation.3. >73;O=5<> @CE >1'T:BV2 B0:>W 30;0:B8:8 7 28:>@8AB0==O< <5B@8G=> >4=>@V4=>W H:0;8 :>A<>;>3VG=>3> G0AC, 70 O:>N G0AB>B0 28?@><V=N20==O WW 7V@>: =5 7<V=NTBLAO 2 G0AV, 0 G5@2>=89 7AC2 9>3> 4>268= E28;L 28=8:0T 2=0A;V4>: 52>;NFV9=>3> 7<5=H5==O H284:>ABV A2VB;0 2 AC?CB=V9 @>7H8@=><C A5A2VBC !. 0 A8=E@>==8<8 7 =5N H:0;0<8 2;0A=8E G0AV2 2 !obs 40;5:>3> A?>AB5@V30G0 (zdop>0, brdop=(1+zdop)-2, min0(z)=mgr0(z)(1+zdop)-2, r, G) V 2 AC?CB=V9 30;0:B8FV !g0 (z0=0, br=1, min0(z0)=mgr0(z0), R=r(1+zdop), Gg0dop=G(1+zdop)2) >B@8<0T<> =0ABC?=V A?V22V4=>H5==O 2 F8E ! ?A524>A8; BO6V==O V V=5@FVW: EMBED Equation.3EMBED Equation.3, EMBED Equation.3 EMBED Equation.3, 45: EMBED Equation.3; EMBED Equation.3 8 EMBED Equation.3  @04VCA8 >@1VB >1'T:BV2 30;0:B8:8 2V4?>2V4=> 2 !g0 V 2 !obs;  B0   0?5@BC@=V :CB8 @04VCAV2 >@1VB >1'T:BV2 30;0:B8:8 2V4?>2V4=> 2 !!  V 2 !obs; 0 8   :CB>2V H284:>ABV >15@B0==O >1'T:BV2 30;0:B8:8 2V4?>2V4=> 2 !g0 V 2 !obs. ;O B>3> 6, I>1 2V4F5=B@>2V ?A524>A8;8 V=5@FVW :><?5=AC20;8 ?A524>A8;8 BO6V==O V ?>28==V 2V4?>2V4=> 4> FL>3> 28:>=C20B8AO C<>28: EMBED Equation.3EMBED Equation.3, EMBED Equation.3EMBED Equation.3 45: EMBED Equation.3; EMBED Equation.3; EMBED Equation.3; EMBED Equation.3; EMBED Equation.3  7=0G5==O :>>@48=0B=>W H284:>ABV A2VB;0 2 :>A<>AD5@V; EMBED Equation.3 V EMBED Equation.3  2V4?>2V4=> 4>??;5@V2AL:89 V 3@02VB0FV9=89 G5@2>=89 7AC2 A?5:B@C 28?@><V=N20==O 40;5:8E 30;0:B8:; EMBED Equation.3 V EMBED Equation.3 ;V=V9=V H284:>ABV >15@B0==O >1'T:BV2 30;0:B8:8 2V4?>2V4=> 2 !g0 V 2 !obs. ">1B> ?5@5206=> A0<5 G5@57 V3=>@C20==O ACBBT2> 1V;LH>3> 7=0G5==O 3@02VB0FV9=>W AB0;>W 2 40;5:><C :>A<>;>3VG=>W <8=C;><C V 28=8:0T CO2=0 ?>B@510 1V;LH>W <0A8 EMBED Equation.3 0, >B65, V DV:B82=>W B5<=>W <0B5@VW. !?>AB5@56C20=V @04VCA8 >@1VB >1'T:BV2 30;0:B8:8 =5 2V4@V7=ONBLAO 2V4 2;0A=8E WE 7=0G5=L 0 ;8H5 ?@8 2V4ACB=>ABV 3@02VB0FV9=>3> C?>2V;L=5==O 2;0A=>3> G0AC >1'T:BV2 30;0:B8:8 :>A<>AD5@>N, I> WE >B>GCT: EMBED Equation.3 01> 6 C @07V 2@0EC20==O C 2;0A=><C 7=0G5==V 3@02VB0FV9=>W AB0;>W B0:>6 V 3@02VB0FV9=>3> C?>2V;L=5==O ?;8=C G0AC (EMBED Equation.3). A5 F5 4>1@5 C73>46CTBLAO V 7 B5>@VTN @>7<V@=>AB59. 091V;LH 7=0G=8< D0:B>< T 2V4ACB=VABL @5;OB82VABAL:>3> C?>2V;L=5==O 2;0A=>3> G0AC 30;0:B8: 73V4=> 7 >B@8<0=8<8 ?5@5B2>@5==O<8.  F5 ?V4B25@46CT 2V4?>2V4=VABL 30;0:B8: A0<5 :>=D>@<=>-;>@5=F>28< ?5@5B2>@5==O< ?@8@>ABV2 <5B@8G=8E 2V4@V7:V2 V <5B@8G=>3> G0AC [0=8;LG5=:>, 2021]. "0: O: 30;0:B8:8 2 ! A2VBC ;N459 ?040NBL =0 ?A524>>1@V9 <8=C;>3> 70 V=5@FVTN, B> 73V4=> 7 F8<8 :>=D>@<=8<8 @5;OB82VABAL:8<8 ?5@5B2>@5==O<8 =VO:>3> @5;OB82VABAL:>3> C?>2V;L=5==O ?;8=C WE G0AC ?@8=F8?>2> V =5 ?>28==> 1CB8. #?>2V;L=5==O 6 ?;8=C WE 2;0A=>3> G0AC <>3;> 1CB8 2 :>A<>;>3VG=><C <8=C;><C ;8H5 3@02VB0FV9=8< 2=0A;V4>: 25;8:>W IV;L=>ABV B>4V 307>?8;>2>W @5G>28=8, 2 O:C 2>=8 1C;8 70=C@5=V. ;O =091;86G8E 30;0:B8:, O:V, O: V =0H0, ?5@51C20NBL C :>A<VG=><C 20:CC<V, <>6=0 ?@89=OB8, I> :CB>20 H284:VABL A?>AB5@56C20=>3> >@1VB0;L=>3> @CEC WE >1'T:BV2 1C;0 B>4V =5 ACBBT2> <5=H>N, =V6 V 70@07 (EMBED Equation.3). , >B65, @04VCA8 >@1VB WE >1'T:BV2 2 !!  ?@0:B8G=> =5 7<5=H8;8AO 7 B>3> 40;5:>3> G0AC (EMBED Equation.3). , >B65, A0<V 30;0:B8:8, O: V WE 52>;NFV9=> E>;>=CGV 7V@:8, <0NBL 2 !!  =56>@AB:V !. 04V0;L=V 2V4AB0=V 4> WE=VE 7V@>: EMBED Equation.3 C !!  52>;NFV9=> 7<5=HCNBLAO 70 72>@>B=8< 70:>=>< %011;0 G5@57 52>;NFV9=5 7<5=H5==O 2 !!  3@02VB0FV9=>W AB0;>W EMBED Equation.3. "0:8< G8=><, 2 !!  >1'T:B8 30;0:B8: =0A?@024V @CE0NBLAO 7>2AV< =5 70<:=5=8<8, 0 A?V@0;L=8<8 >@1VB0<8. , >B65, F5 4>1@5 C73>46CTBLAO 7V A?V@0;L=>E28;L>2>N ?@8@>4>N @5G>28=8 V A5A2VBC 2 FV;><C [0=K;LG5=:>, 2004a: 35; 2004b: 44; 2008: 45; 2014: 21]. 28G09=> 6, :0;V1@C20;L=8< ?5@5B2>@5==O< H:0;8 :>A<>;>3VG=>3> G0AC [0=K;LG5=:>, 2008a: 106] <>6=0 70157?5G8B8 =57<V==VABL 3@02VB0FV9=>W AB0;>W 2 !!  [0=K;LG5=:>, 1994: 52]. 4=0: >1'T:B8 30;0:B8: 2A5 >4=> 1C4CBL @CE0B8AO 2 !!  A?V@0;L=8<8 >@1VB0<8. # " 6 (7 C@0EC20==O< 7=5206;82>W <0;>ABV ;8H5 :>A<>;>3VG=>W AB0;>W) <0T <VAF5 7>2AV< V=H89 B8?>289 @04V0;L=89 @>7?>4V; A5@54=L>W IV;L=>ABV V=5@B=>W <0A8 @5G>28=8 2 30;0:B8FV [Danylchenko, 2021a: 33]:  EMBED Equation.3 , 73V4=> 7 O:8< 2>=0 AB0T =5A:V=G5==> <0;>N. @8 FL><C =5>1<565=><C ?04V==N 4> =C;O A5@54=L>W IV;L=>ABV <0A8 @5G>28=8 =0 :@0N 30;0:B8:8 ?5@5H:>460T ?@03=5==O 4> >48=8FV =5 BV;L:8 ?0@0<5B@0 a, 0;5 V ?0@0<5B@0 b. "><C-B> 2 ", =0 2V4<V=C 2V4 ", ?@8=F8?>2> =5 <>65 1CB8 45DVF8BC 10@V>==>W <0A8 =5 BV;L:8 2 F5=B@V, 0 V =0 :@0N 30;0:B8:8.  F5 ?>2'O70=> A0<5 7 B8<, I> B5=7>@ 5=5@3VW-V<?C;LAC " T AD>@<>20=8< =0 >A=>2V >@48=0@=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8 V 2V4?>2V40T (=0 2V4<V=C 2V4 B5=7>@0 5=5@3VW-V<?C;LAC ") 7>2AV< =5 3@0=8G=> >AB83;V9 @5G>28=V, 0 =5A:V=G5==> 4>23> E>;>=CGV9 @5G>28=V 0AB@>=><VG=8E >1'T:BV2 30;0:B8:8.  >3;O4C =0 B5, I> 2 :>A<>AD5@V ?@8 1;87L:8E 4> >48=8FV 7=0G5==OE EMBED Equation.3 =0 ?5@8D5@VW 30;0:B8:8 ap-1H"1-bp V, >B65, ap=1,0000011197320368 (?@8 EMBED Equation.3, bp=0,99999888026796323), 287=0G8<> 4;O EMBED Equation.3, n=215 B0 B8E 65 V=H8E 28EV4=8E 40=8E <0:A8<0;L=> 4>?CAB8<5 7=0G5==O A5@54=L>W IV;L=>ABV <0A8 @5G>28=8 =0 :@0N 30;0:B8:8: [gr0p] "=5 10-26 :3/<3. %>G0, 728G09=> 6, ?@8 7=0G5==V be, I> 70157?5GCT lim<10-15, <>65 <0B8 <VAF5 2 " V ?@8 bre=1 7=0G=> <5=H0 A5@54=O IV;L=VABL <0A8 @5G>28=8 =0 :@0N 30;0:B8:8. > ?@8 n=1 (EMBED Equation.3 :</A5:) V B><C 6 7=0G5==V lim=10-15 (be=0,99999606363264543, bp=0,999999436721227408) [gr0p]R"=1,4 10-27 :3/<3. /:I> 6 ?@8 n=1, apH"1 B0 lim=10-15 1C45 <0B8 <VAF5 B0:>6 V EMBED Equation.3, B> 27030;V >B@8<0T<> [gr0p] "H"1,2410-38 :3/<3. /: 10G8<>, 2 ", =0 2V4<V=C 2V4 ", ?>:07=8: EMBED Equation.3 ACBBT2> (<0965 2 36 @07V2) 725;8GCT 4>?CAB8<5 A5@54=T 7=0G5==O IV;L=>ABV V=5@B=>W <0A8 @5G>28=8 =0 :@0N 30;0:B8:8. 4=0: 2=0A;V4>: 270T<=>W 70;56=>ABV 20@V9>20=8E ?0@0<5B@V2 n, be V ae (ap), I> 2AB0=>2;NTBLAO ?@8=F8?0<8 4>FV;L=>ABV V 2V4?>2V4=8<8 W< =530B82=8<8 72>@>B=8<8 72'O7:0<8, 71V;LH5==O EMBED Equation.3 =0A?@024V 1C45 ACBBT2> <5=H8<. 465 28:;8:0=5 EMBED Equation.3 71V;LH5==O 7=0G5==O EMBED Equation.3 =0 ?5@8D5@VW 30;0:B8:8 <>65 G0AB:>2> :><?5=AC20B8AO 9>3> 7=865==O< 7024O:8 7<5=H5==N 25;8G8=8 lim. =0A;V4>: O: 52>;NFV9=>3> 7<5=H5==O A5@54=L>W IV;L=>ABV @5G>28=8 C A5A2VBV, B0: V ?>ABC?>2>3> >E>;>465==O O45@ 30;0:B8: WE ?0@0<5B@8 n, be (bp) V ae (ap) ?>ABC?>2> 7<V=NNBLAO. &5 ?@>O2;OTBLAO C 283;O4V ?>ABC?>2>3> 2V440;5==O 0AB@>=><VG=8E >1'T:BV2 2V4 F5=B@C 30;0:B8:8. (284:>ABV ?>ABC?>2>W 7<V=8 F8E ?0@0<5B@V2 C @V7=8E 30;0:B8: T =5>4=0:>28<8, I> <>65 28O2;OB8AO 2 =5>4=0:>2>ABV 30;0:B8G=8E 7=0G5=L AB0;>W %011;0. 4=0: 2V4<V==VABL 30;0:B8G=8E 7=0G5=L 2V4 3;>10;L=>3> 7=0G5==O AB0;>W %011;0, 2V4?>2V4=>3> ;8H5 ?@>F5AC 52>;NFV9=>3> @>7H8@5==O A5A2VBC, 2 ACG0A=C 5?>EC T 7=5206;82> <0;8<. %>G0 2 40;5:><C :>A<>;>3VG=><C <8=C;><C 2>=0 <>3;0 1CB8 V 1V;LH 7=0G=>N G5@57 25;8:V 7=0G5==O A5@54=L>W IV;L=>ABV @5G>28=8 C A5A2VBV, 0 B8< A0<8< V G5@57 <5=HV 7=0G5==O ?0@0<5B@0 b (0, >B65, V G5@57 <5=HV 7=0G5==O :>>@48=0B=>W H284:>ABV A2VB;0, I> 7040NBLAO F8< ?0@0<5B@><) C :>A<>AD5@V A5A2VBC. 0@07 65 2>=> T 1V;LH 7=0G=8< ;8H5 2 =56>@AB:8E ! [0=K;LG5=:>, 1994: 52] 0AB@>=><VG=8E BV;, I> ?>ABC?>2> >AB830NBL. 04V0;L=V9 @>7?>4V; ?0@0<5B@0 a ?@8 bre=1 287=0G0TBLAO @>72'O7:>< 48D5@5=FV9=>3> @V2=O==O:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 , 0, 2@0E>2CNG8, I> EMBED Equation.3, 0 EMBED Equation.3,  B0:>6 V @V2=O==O:  EMBED Equation.3   EMBED Equation.3 . 12. #<>20 V=20@V0=B=>ABV B5@<>48=0<VG=8E ?>B5=FV0;V2 V ?0@0<5B@V2 I>4> @5;OB82VABAL:8E ?5@5B2>@5=L "5@<>48=0<VG=V ?>B5=FV0;8 V ?0@0<5B@8 @5G>28=8, O: V B5<?5@0BC@8 WW D07>28E ?5@5E>4V2, T ACB> 2=CB@VH=V<8 2;0AB82>ABO<8 @5G>28=8 [070@>2, 1964; Van Kampen, 1968] V B><C ?@8=F8?>2> =5 ?>28==V 7<V=N20B8AO ?@8 @5;OB82VABAL:8E ?5@5B2>@5==OE ?@8@>ABV2 ?@>AB>@>28E :>>@48=0B V G0AC. 0 F5 2:07CT V =0O2=VABL 42>E 01A>;NB=> ?@>B8;56=8E @5;OB82VABAL:8E C7030;L=5=L B5@<>48=0<V:8 [Marea, et al., 2010; 2017], 2V4?>2V4=> 4> >4=>3> 7 O:8E [Hasenhrl, 1907; Mosengeil, 1907; Planck, 1907, 1908] @5G>28=0, I> @CE0TBLAO E>;>4=VH5 =5@CE><>W, 0 73V4=> 7 V=H8< [Ott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quation.3  @07V2 1V;LH>N, =V6 70 5B0;>=>< 4>268=8 (<5B@><) A?>AB5@V30G0.  G0A, 70 O:89 BV;> 7@>18BL ?>2=89 >15@B, 70 9>3> 2;0A=8< 3>48==8:>< <0T 1CB8 2 B0:C 6 :V;L:VABL @07V2 <5=H8<, =V6 70 3>48==8:>< FL>3> A?>AB5@V30G0. , >B65, =0 4C<:C 7>2=VH=L>3> A?>AB5@V30G0 H284:VABL >@1VB0;L=>3> @CEC BV;0 2 9>3> 2;0A=V9 ! ?>28==0 1CB8 2  EMBED Equation.3  @07V2 1V;LH>N, =V6 WW 7=0G5==O, I> @5TAB@CTBLAO 157?>A5@54=L> A0<8< 7>2=VH=V< A?>AB5@V30G5<. 5@5B2>@5==O 6 >@5=F0 F5 =5 70157?5GCNBL, 1> 73V4=> 7 =8<8 H284:VABL @CEC BV;0 2 9>3> 2;0A=V9 ! T B0:>N 6, O: V 2 !out 7>2=VH=L>3> A?>AB5@V30G0. @8@>AB8 :>>@48=0B=>3> G0AC V ?@>AB>@>28E :>>@48=0B <>6CBL 1CB8 28@065=V =5 BV;L:8 2 G>B8@828<V@=><C ?A524>52:;V4>2><C ?@>AB>@V V=:>2AL:>3>, 0 V 2 ?>4V1=><C 4> =L>3> G>B8@828<V@=><C 3V?5@1>;VG=><C ?@>AB>@V [Q;;5@, 1972; #30@>2, 1977]. >73;O=5<> A?>G0B:C @CE C74>26 >4=>3> =0?@O<:C. V4?>2V4=> 4> ?5@5B2>@5=L >@5=F0 1C45<> <0B8:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . @8  EMBED Equation.3  ( EMBED Equation.3 ):  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . , >B65, C 2;0A=><C G0AV  EMBED Equation.3  BV;0, I> @CE0TBLAO, H284:VABL 9>3> @CEC T 1V;LH>N =V6 70 A?>AB5@565==O<8 7V AB>@>==VE !, I> 728G09=> 6 ?>2'O70=5 7 C?>2V;L=5==O< 2;0A=>3> G0AC @CE><>3> BV;0 2 !". 024O:8 V=20@V0=B=>ABV 4> @5;OB82VABAL:8E ?5@5B2>@5=L ?>4V1=>3> G0AC V=B5@20;C (B>B>6=><C 2;0A=><C G0AC @5G>28=8, I> @CE0TBLAO) 9>3> <>6=0 1C;> 1 28:>@8AB>2C20B8 2 O:>ABV T48=>3> C=V25@A0;L=>3> (:>A<>;>3VG=>3>) G0AC, O:18 E>G0 1 C @5G>28=8, I> @CE0TBLAO 70 V=5@FVTN, 1C;> 1 2V4ACB=V< C?>2V;L=5==O WW 2;0A=>3> G0AC. "0 9 4;O 70157?5G5==O V=20@V0=B=>ABV 4> @5;OB82VABAL:8E ?5@5B2>@5=L B5@<>48=0<VG=8E ?0@0<5B@V2 V ?>B5=FV0;V2 =5>1EV4=0 V=20@V0=B=VABL 4> @5;OB82VABAL:8< ?5@5B2>@5=L, A0<5, G0AC @5G>28=8, I> @CE0TBLAO 70 V=5@FVTN.  F5, 2>G5284L, <>6CBL 70157?5G8B8 ;8H5 :>=D>@<=V ?5@5B2>@5==O >@5=F0. 465 :>=D>@<=5 ?5@5B2>@5==O ?@8@>ABV2 G0AC V :>>@48=0B =5 2?;820T =0 D>@<C ?5@5B2>@5=L ?@>5:FV9 H284:>AB59 V B><C T FV;:>< ?@8?CAB8<8<. # 7030;L=><C 28?04:C >@5=F>2V ?5@5B2>@5==O O: ?@8@>ABV2 G0AC V :>>@48=0B, B0: V ?@>5:FV9 H284:>AB59 @CEC ?@8 ?5@5E>4V 2V4 !out 4> !0 ( EMBED Equation.3 ) 1C4CBL =0ABC?=8<8:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 .  7 C@0EC20==O<, I>  EMBED Equation.3 , >B@8<0T<>  EMBED Equation.3 .  2V4?>2V4=> 4> FL>3> B0 73V4=> 7 ?5@5B2>@5==O< B@83>=><5B@8G=8E DC=:FV9 :CBV2 [-9=HB59=, 1905; Q;;5@, 1972; 09AA:>?D, 1972] <0B8<5<>:  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 , ( EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ). "0: O: 3V?5@1>;VG=89 :>A8=CA =5 <>65 4>@V2=N20B8 =C;N, B> ?@8@VAB G0AC 2 !out <>65 4>@V2=N20B8 =C;N ;8H5 ?@8 @V2=>ABV =C;N ?@8@>ABC V=B5@20;C s.  F5 6 2V4?>2V40T BV;L:8 A2VB>28< ;V=VO< 28?@><V=N20==O 2 3V?>B5B8G=><C 01A>;NB=><C 20:CC<V. > B>3> 6 ?@8  EMBED Equation.3  V  EMBED Equation.3  B0:>6 V  EMBED Equation.3 . "><C B> =V ?@> O:89 A8=E@>==89 28<V@ 2 !out 4>268=8 BV;0, I> @CE0TBLAO, =5 <>65 1CB8 9 <>28. , >B65, A8=E@>==5 DV:AC20==O :>>@48=0B 2V440;5=8E >48= 2V4 >4=>3> >1'T:BV2 @CE><>3> BV;0 ?@8=F8?>2> =5 <>6;82>. A8=E@>==5 6 DV:AC20==O [Cavalleri, Salgarelli, 1969] WE :>>@48=0B 2 !out, 2>G5284L, <0T 2V4?>2V40B8 >4=><C V B><C 6 :>;5:B82=><C 3@02VB5@<>48=0<VG=><C (?@>AB>@>2>-G0A>2><C) <V:@>AB0=C V11A0 2AVTW @5G>28=8 @CE><>3> BV;0. "0: O: 2V4?>2V4=89 9><C D@>=B 2;0A=>3> G0AC BV;0, I> @CE0TBLAO, ?>H8@NTBLAO 2 !out 7V H284:VABN  EMBED Equation.3  [0=K;LG5=:>, 1994: 5, 2008b], B> ?@8  EMBED Equation.3  >B@8<0T<>:  EMBED Equation.3 . , >B65, 73V4=> 7 ?5@5B2>@5==O<8 >@5=F0 <0B8<5 <VAF5 7>2AV< =5 A:>@>G5==O, 0 =02?0:8 71V;LH5==O ?>74>26=L>3> :>>@48=0B=>3> @>7<V@C BV;0, I> @CE0TBLAO.  ;8H5 ?@8 B0:><C 7@>AB0==V :>>@48=0B=>W 4>268=8 BV;0, I> @CE0TBLAO, ?5@5B2>@5==O >@5=F0 V =5 ?@872>4OBL 4> ?0@0;>3V7<C 70<:=CB>W B@0T:B>@VW, 1> C A:V;L:8 @07V2 7<5=H82AO G0A WW ?@>E>465==O 2 ABV;L:8 6 @07V2 V 7<5=H5=0 :>>@48=0B=0 4>268=0 ?@>945=>3> H;OEC A?>AB5@V30G5<, I> ?>:>WBLAO 2 !0. %>G0 ?> 2V4=>H5==N 4> @CEC !out 2 9>3> !0 V A:;040TBLAO ?0@04>:A0;L=0 4C<:0, I> @C=BCTBLAO =0 >B>B>6=5==V 2 !" ?@8@>ABV2 :>>@48=0B V ?@8@>ABV2 <5B@8G=8E 2V4@V7:V2. 465 :>65= 7 42>E A?>AB5@V30GV2 22060T, I> C?>2V;L=5==O B5GVW G0AC V ?>4>265==O @CE><>3> BV;0 2V4=>AOBLAO 4> ?@>B8;56=>W !. V@:C20==O ?@> B5, I> 70<VABL @5;OB82VABAL:>3> A:>@>G5==O ?>74>26=L>3> @>7<V@C BV;0, I> @CE0TBLAO, <>65 <0B8 <VAF5 9>3> 71V;LH5==O, 28A;>2;N20;8AO =5>4=0@>7>2> [Arzelies, 1965; Rohrlich, 1966; !B@5;LF>2, 1988, 1991]. 4=0: F5 <>65 <0B8 <VAF5 ;8H5 C BV;, I> @CE0NBLAO ?@8<CA>2> ?@8A:>@5=>, 0 =5 70 V=5@FVTN. # BV; 65, I> @CE0NBLAO 70 V=5@FVTN, 2A5 6 B0:8 <0T <0B8 <VAF5 A:>@>G5==O WE @>7<V@V2 C D>=>2><C 52:;V4>2><C ?@>AB>@V A?>AB5@V30G0.  >3;O4C =0 =5>1EV4=VABL 4>B@8<0==O 7030;L=>W :>20@V0=B=>ABV @V2=O=L DV78:8 7<V=0 <5B@8G=8E @>7<V@V2 @5G>28=8, I> @CE0TBLAO, C 2;0A=><C ;>:0;L=> 28:@82;5=><C ?@>AB>@V A?>AB5@V30G0, 728G09=>, ?@8=F8?>2> 1C45 2V4ACB=L>N [Terrell, 1959; 0=K;LG5=:>, 2009: 75, 2010: 64].  F5 >7=0G0T, I> ?5@5B2>@5==O >@5=F0 T ?5@5B2>@5==O<8 ?@8@>ABV2 ;8H5 ?@>AB>@>28E :>>@48=0B V :>>@48=0B=>3> G0AC, 0 7>2AV< =5 <5B@8G=8E ?@>AB>@>28E 2V4@V7:V2 V <5B@8G=8E V=B5@20;V2 G0AC. , >B65, <0B@8FN ?5@5B2>@5=L ?@8@>ABV2 :>>@48=0B [Q;;5@, 1972; #30@>2, 1977], I5 =5>1EV4=> ?5@5<=>68B8 7 <0B@8F5N ?5@5E>4C 4> ?@8@>ABV2 <5B@8G=8E 2V4@V7:V2. &O <0B@8FO ?>28==0 1CB8 ?>4V1=>N 4> <0B@8FV <5B@8G=>3> B5=7>@0 " V, 728G09=> 6, ?>28==0 2:;NG0B8 2 A515 =5 BV;L:8 ?>:07=8:8 ;>:0;L=>W :@828=8 G0AC (7=0G5==O ;>:0;L=8E :>>@48=0B=8E H284:>AB59 A2VB;0  EMBED Equation.3 ), 0;5 V ?@O<V 01> 6 72>@>B=V ?>:07=8:8 ;>:0;L=>W :@828=8 ?@>AB>@C:  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3  V  EMBED Equation.3   ?@8@>AB8 2V4?>2V4=> ?@>AB>@>2> =5>4=>@V4=>3> :>>@48=0B=>3> (3@02V:20=B>2>3>) G0AC 2 D>=>2><C ?A524>52:;V4>2><C ' V 28:@82;5=>3> T48=>3> (3@02VB5@<>48=0<VG=>3>) G0AC 2AVTW 3@02VB5@<>48=0<VG=> ?>2'O70=>W @5G>28=8;  EMBED Equation.3  V  EMBED Equation.3   ?@8@>AB8 ?@>AB>@>28E 2V4@V7:V2 2V4?>2V4=> C D>=>2><C 52:;V4>2><C ?@>AB>@V V C ;>:0;L=> 28:@82;5=><C 2;0A=><C ?@>AB>@V @5G>28=8;  EMBED Equation.3  V  EMBED Equation.3 ,  EMBED Equation.3   2V4?>2V4=> :>>@48=0B=0 H284:VABL A2VB;0, 0 B0:>6 ?@O<5 V 72>@>B=5 7=0G5==O ?>:07=8:V2 :@828=8 ?@>AB>@C 2 3V?>B5B8G=V9 B>GFV !out, 2 O:V9 @5G>28=0 <>3;0 1 ?5@51C20B8 2 AB0=V A?>:>N. @8 FL><C, O: V 2 C<>2=> ?>@>6=L><C ?@>AB>@V 2 ",  EMBED Equation.3 .  C 30;0:B8:, I> 4C65 H284:> 2V440;ONBLAO 2V4 A?>AB5@V30G0, ;>:0;L=V 2V4E8;5==O :>>@48=0B=>W H284:>ABV A2VB;0 V :@828=8 ?@>AB>@C T 7=5206;82> <0;8<8 ( EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ). 4=0: 65, FV ?>:07=8:8, I> <0NBL =5>4=0:>2V 7=0G5==O 2 @V7=8E !, FV;:>< <>6CBL 1CB8 2:;NG5=V V 157?>A5@54=L> 2 A0<V <>45@=V7>20=V ?5@5B2>@5==O >@5=F0. "0:8< G8=><, 2V4?>2V4=> 4> ?@8@>ABC <5B@8G=>3> 2V4@V7:0  EMBED Equation.3  4V9A=> <5B@8G=0 H284:VABL @CEC BV;0 70 V=5@FVTN 2 T48=><C 3@02VB5@<>48=0<VG=><C G0AV (A2VB>2><C G0AV " [Q;;5@, 1972]) !out D0:B8G=> 4>@V2=NT WW 2;0A=><C 7=0G5==N 2 ! BV;0, I> @CE0TBLAO [0=K;LG5=:>, 2006: 27; 2008: 60; 0=8;LG5=:>, 2021]:  EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3 ;  EMBED Equation.3   H284:VABL @CEC >1'T:B0 2 D>=>2><C @53C;O@=><C ?@>AB>@V !out, I> =5 2@0E>2CT ;>:0;L=>W :@828=8, O:0 2=>A8BLAO O: =02:>;8H=V<8 0AB@>=><VG=8<8 >1'T:B0<8, B0: V A0<8< @CE><8< BV;><.  F5 >7=0G0T, I> @CE>< 70 V=5@FVTN ;>:0;L=> :><?5=ACTBLAO =5 BV;L:8 7<5=H5==O :>>@48=0B=>W H284:>ABV A2VB;0, 0;5 V 7@>AB0==O :@828=8 2;0A=>3> ?@>AB>@C !out. >G5284L, 3@02VB0FV9=0 :@828=0 @53C;O@=>3> ?@>AB>@C (3@02VB0FV9=5 7<5=H5==O ?>74>26=L>3> @>7<V@C 2V;L=> ?040NG>3> BV;0 2 D>=>2><C 52:;V4>2><C ?@>AB>@V) ?>2=VABN :><?5=ACTBLAO ;>:0;L=>N :@828=>N FL>3> ?@>AB>@C, I> 28=8:0T 2=0A;V4>: 71V;LH5==O H284:>ABV @CEC BV;0 70 V=5@FVTN 2 3@02VB0FV9=><C ?>;V. , >B65, O: ;>:0;L=0 :>>@48=0B=0 H284:VABL A2VB;0, B0: V ?>:07=8:8 ;>:0;L=>W :@8287=8 ?@>AB>@C 2 B>GFV <8BBT2>W 48A;>:0FVW BV;0, I> @CE0TBLAO 70 V=5@FVTN, 2V4?>2V40NBL 2 9>3> 2;0A=V9 ! WE 7=0G5==O<  EMBED Equation.3 ,  EMBED Equation.3  C 3V?>B5B8G=V9 B>GFV ?>G0B:C A0<>ABV9=>3> @CEC BV;0, 0 7>2AV< =5 @53C;O@=8< WE 7=0G5==O< 2 B>G:0E <8BBT2>W 9>3> 48A;>:0FVW 2 !out. 0 ?V4AB02V 7<V=8 A0<5 FVTW VAB8==>W <5B@8G=>W H284:>ABV @CEC BV;0 L>;;5@ V >B@8<02 ?@8A:>@5==O @CEC BV;0  EMBED Equation.3  [Q;;5@, 1972; 0=K;LG5=:>, 1994: 5, 2008b: 3]. 3V4=> 4> FL>3> 30<V;LB>=V0= V=5@B=>W 2V;L=>W 5=5@3VW V ;03@0=6V0= >@48=0@=>W 2=CB@VH=L>W 5=5@3VW, 0 B0:>6 30<V;LB>=V2 V ;03@0=6V2 V<?C;LA8 BV;0, I> @CE0TBLAO 70 V=5@FVTN, 2V4?>2V4=> 4>@V2=NNBL [Danylchenko, 2021a: 37]:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 , 0:  EMBED Equation.3 . >@5=F-V=20@V0=B=VABL H284:>ABV A2VB;0 ?@8=F8?>2> <0T <VAF5 ;8H5 2 B>GFV 48A;>:0FVW 3>48==8:0 [0=K;LG5=:>, 1994: 10, 2008b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quation.3 , 2V;L=5 ?04V==O 40;5:8E 30;0:B8: =0 ?A524>>1@V9 ?>4V9 A5A2VBC AC?@>2>46CTBLAO 2V4?>2V4=8< H284:>ABV WE @CEC 3@02VB0FV9=8< ?>;5<, I> 7040TBLAO @>7?>4V;>< :>>@48=0B=>W H284:>ABV A2VB;0:  EMBED Equation.3 . >4V1=89 65 ;>:0;L=89 3@02VB0FV9=89 2?;82 =0 <5B@8:C ?@>AB>@C-G0AC, >G5284=>, <>65 2V4B2>@N20B8AL 1C4L-O:8< @CE>< @5G>28=8 70 V=5@FVTN.  " 70<VABL ?5@5B2>@5=L H284:>AB59 @CEC, I> 287=0G0NBLAO 2 B>GFV i 70 3@02V:20=B>28< 3>48==8:>< A?>AB5@V30G0, ?5@5B2>@NNBLAO 70 ?@028;0<8 >@5=F0 =0A?@024V WE 3@02VB5@<>48=0<VG=V 7=0G5==O  EMBED Equation.3 , =>@<>20=V :>>@48=0B=>N H284:VABN A2VB;0 V B><C =570;56=V 2V4 ?>:070=L 1C4L-O:8E :>=:@5B=8E 3@02V:20=B>28E 3>48==8:V2. >=8, E>G0 V 2@0E>2CNBL :@828=C ?@>AB>@C A?>AB5@V30G0, 0;5 2A5 6, V3=>@CNBL <>6;82VABL WW 7<V=8 @CE><8< BV;><, I> V ?@872>48BL 4> CO2=>W A?>AB5@56;82>ABV @5;OB82VABAL:>W 45D>@<0FVW FL>3> @CE><>3> BV;0. "8< A0<8< D0:B8G=> 74V9A=NTBLAO ?5@5EV4 2V4 28:>@8AB0==O ;>:0;L=>3> 3@02V:20=B>2>3> 3>48==8:0 1C4L-O:>3> A?>AB5@V30G0 4> 28:>@8AB0==O =570;56=>3> 2V4 9>3> ?>:070=L T48=>3> 3@02VB5@<>48=0<VG=>3> (7030;L=>?;0=5B0@=>3>) G0AC  EMBED Equation.3  2AVTW "-?>2'O70=>W @5G>28=8.  F5 FV;:>< ;>3VG=>. 465 =0 2V4<V=C 2V4 3@02V:20=B>28E G0AV2 48A:@5B=0 7<V=0 :>;5:B82=>3> 3@02VB5@<>48=0<VG=>3> AB0=C @5G>28=8 2V41C20TBLAO 7 >4=>N V B>N 6 G0AB>B>N C 2AL><C ?@>AB>@V, 709<0=><C "-?>2'O70=>N @5G>28=>N. !0<5 FV9 48A:@5B=V9 7<V=8 V 2V4?>2V40T T48=89 3@02VB5@<>48=0<VG=89 G0A, I> <0T 3@02VB0FV9=C :@828=C. > B>3> 6 ?@8 ?5@5E>4V 2V4 !!  4> ! A?>AB5@V30G0 2 " 28:>@8AB>2CNBLAO V :>=D>@<=V >@5=F>2V ?5@5B2>@5==O, I> 4>72>;ONBL =0 2V4<V=C 2V4 ACB> >@5=F>28E 1V;LH 045:20B=> 2V4>1@060B8 DV78G=C @50;L=VABL. "><C-B> =02VBL V 70 C<>2=>W 2V4ACB=>ABV 3@02VB0FV9=>3> ?>;O 70<VABL 728G09=8E >@5=F>28E 2A5 6 B0:8 ?>28==V 28:>@8AB>2C20B8AO V 2 " :>=D>@<=V 3@02VB0FV9=>-;>@5=F>2V ?5@5B2>@5==O [0=K;LG5=:>, 1994: 22] O: ?@8@>ABV2 :>>@48=0B B0 G0AC, B0: V H284:>AB59 @CEC @5G>28=8. /:I> BV;> @CE0TBLAO 7V H284:VABN  EMBED Equation.3  V 7 C@0EC20==O< FL>3> 3@0=8G=0 H284:VABL 9>3> 2 =0?@O<:C @CEC 2 D>=>2><C @53C;O@=><C ?@>AB>@V !out 7>2=VH=L>3> A?>AB5@V30G0 4>@V2=NT  EMBED Equation.3 , B> 2 AC?CB=V9 9><C !0 V 2 !out ?@8@>AB8 :>>@48=0B (0 B8< A0<8< V <5B@8G=8E 2V4@V7:V2) 9>3> @CE><8E >1'T:BV2 V G0AC 1C4CBL =0ABC?=8<8 [Danylchenko, 2021a: 37]:  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3  ( EMBED Equation.3 );  EMBED Equation.3 ;  EMBED Equation.3 ,  EMBED Equation.3  ( EMBED Equation.3 ,  EMBED Equation.3 );  EMBED Equation.3  V  EMBED Equation.3   7=0G5==O 3@0=8G=>W H284:>ABV @CEC 2 D>=>2><C @53C;O@=><C ?@>AB>@V V >@5=F>20 A:>@>G5==O @>7<V@V2 2 @53C;O@=><C ?@>AB>@V !out @CE><>3> >1'T:B0 (@5G>28=8) m;  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  B0  EMBED Equation.3   7=0G5==O 3@0=8G=>W H284:>ABV @CEC V >@5=F>25 A:>@>G5==O @>7<V@V2 2 @53C;O@=><C ?@>AB>@V !0 2V4?>2V4=> =5@CE><>3> V @CE><>3> >1'T:BV2;  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   ?@8@>AB8 ?@>5:FV9 <5B@8G=>3> 2V4@V7:C >1'T:B0, I> @CE0TBLAO, 2 !0, 0  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   ?@8@>AB8 :>>@48=0B FL>3> >1'T:BC 2 !out A?>AB5@V30G0 @CEC 2AL>3> BV;0 V 9>3> >1'T:BV2;  EMBED Equation.3  V  EMBED Equation.3 ,  EMBED Equation.3   @50;L=0 V 3@0=8G=V H284:>ABV @CEC >1'T:B0 m 2 !out;  EMBED Equation.3  V  EMBED Equation.3   2A51VG=5 A:>@>G5==O @>7<V@V2 @CE><>3> BV;0 2 D>=>2><C @53C;O@=><C ?@>AB>@V 2V4?>2V4=> 2 !out V 2 !0;  EMBED Equation.3  8  EMBED Equation.3   DC=:FVW 2V4 ?@8A:>@5==O G ?@8<CA>2>3> @CEC;  EMBED Equation.3   ?0@0<5B@, I> E0@0:B5@87CT :@828=C 2;0A=>3> ?@>AB>@C A?>AB5@V30G0 2 ?5@2VA=><C AB0=V A?>:>N BV;0, I> @CE0TBLAO;  EMBED Equation.3  V  EMBED Equation.3   :V=5<0B8G=V <0AHB01=V G8==8:8 @CE><>3> BV;0 2 !out V 2 !0;  EMBED Equation.3   ABC?V=L A:>@>G5==O @>7<V@V2 @CE><>3> BV;0 2 D>=>2><C @53C;O@=><C ?@>AB>@V. V4?>2V4=> 4> FL>3> ?5@5B2>@5==O ?@>5:FV9 H284:>AB59 @CEC 1C4CBL B0:8<8 [Danylchenko, 2021a: 37]:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 45 A?@026=V H284:>ABV @CEC O: A?>AB5@56C20=>3> >1'T:B0, B0: V !0 2V4?>2V4=> 1C4CBL B0:8<8:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  V  EMBED Equation.3 . @8  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  ( EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ) B0  EMBED Equation.3  (I> 2V4?>2V40T >4=><C V B><C 6 :>;5:B82=><C ?@>AB>@>2>-G0A>2><C <V:@>AB0=C V11A0 2AVTW @5G>28=8, I> @CE0TBLAO 7V H284:VABN  EMBED Equation.3 ) <0T<> @5;OB82VABAL:C V=20@V0=B=VABL ?>74>26=VE <5B@8G=8E @>7<V@V2 BV;0, I> @CE0TBLAO ( EMBED Equation.3 ), ?@8G><C =570;56=> 2V4 7=0G5=L ?>:07=8:0 p. 024O:8 6 V7>B@>?VW :V=5<0B8G=>3> A0<>AB8A:0==O @>7<V@V2 BV;0, I> @CE0TBLAO 2 D>=>2><C @53C;O@=><C ?@>AB>@V, @5;OB82VABAL:V V=20@V0=B=8<8 B0:>6 1C4CBL V ?>?5@5G=V <5B@8G=V 2V4@V7:8.  F5, 728G09=> 6, 2V4?>2V40T ?@89=OB><C 2 " ?@8=F8?C =5A?>AB5@56;82>ABV 45D>@<0FVW @5G>28=8 =0 @V2=V WW <V:@>>1'T:BV2 (D0:B8G=> ?@8=F8?C <5B@8G=>W >4=>@V4=>ABV ?@>AB>@C A?>AB5@V30G0 @CEC @5G>28=8) . 5@V2=VABL 65 ?@8@>ABV2 ?>?5@5G=8E <5B@8G=8E 2V4@V7:V2 2 @V7=8E ! ?@8 >4=><C V B><C 6 @5;OB82VABAL:V V=20@V0=B=><C 71V;LH5==V <5B@8G=>3> G0AC 28:;8:0=0 2V4<V==VABN 2 =8E ?>?5@5G=8E A:;04>28E H284:>AB59 @CEC. 3V4=> ?@8@>AB0< G0AC  EMBED Equation.3  V  EMBED Equation.3  ( EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  V  EMBED Equation.3 ) V :>=D>@<=>3> V=B5@20;C ?@8 @CAV BV;0 70 V=5@FVTN ( EMBED Equation.3 ) [Danylchenko, 2021a]:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  <0T <VAF5 =5 BV;L:8 =57<V==VABL B5<?C 3>48==8:0, I> @CE0TBLAO 70 V=5@FVTN, 0;5 V V=20@V0=B=VABL I>4> @5;OB82VABAL:8E ?5@5B2>@5=L T48=>3> 2A5;5=AL:>3> 3@02VB5@<>48=0<VG=>3> G0AC, I> 2V4;VGCTBLAO =8<, ( EMBED Equation.3 ). &5, 728G09=> 6, <>65 2V4?>2V40B8 ;8H5 <8<>2V;L=><C @CEC (@CEC 70 V=5@FVTN G8 E0>B8G=><C @CEC) 1C4L-O:8E >1'T:BV2.  C<>28 715@565==O 2 !0 30<V;LB>=V0=0 BV;0, I> 2V;L=> ?040T, 28?;820T, I>  EMBED Equation.3 . # @07V 6 ?@8<CA>2>3> @CEC (?@8  EMBED Equation.3  V  EMBED Equation.3 ,  EMBED Equation.3 ), 4V9A=>, <>65 <0B8 <VAF5 C?>2V;L=5==O 2;0A=>3> G0AC >1'T:BV2, I> ?@8A:>@5=> @CE0NBLAO. &5 ?V4B25@46CTBLAO, =0?@8:;04, 71V;LH5==O< B@820;>ABV 68BBO =5AB01V;L=8E <V:@>>1'T:BV2, I> CB2>@NNBLAO 2 5:A?5@8<5=B0E =0 ?@8A:>@N20G0E. "5<? ?;8=C :>>@48=0B=>3> (3@02V:20=B>2>3>) G0AC  EMBED Equation.3 , I> T ?@>AB>@>2> =5>4=>@V4=8< 2 3@02VB0FV9=><C ?>;V, 728G09=> 6, 7<V=NTBLAO 274>26 B@0T:B>@VW @CEC 70 V=5@FVTN >1'T:BV2. 4=0: 65 @CE>< 70 V=5@FVTN ?>2=VABN :><?5=ACTBLAO 2?;82 3@02VB0FV9=>3> ?>;O =0 EV4 3@02V:20=B>2>3> 3>48==8:0, ?>4V1=> 4> ?>2=>W :><?5=A0FVW V A?@8G8=5=8E =8< 65 A8; BO6V==O. !0<V 6 7<5=H5=V 3@02VB0FV9=8< ?>;5< 3@0=8G=V H284:>ABV @CEC @5G>28=8 <>6CBL 1CB8 28@065=V 2 !0 G5@57 WW 4V9A=C H284:VABL @CEC  EMBED Equation.3  V H284:VABL @CEC 2 D>=>2><C @53C;O@=><C ?@>AB>@V  EMBED Equation.3  =0ABC?=8< G8=><:  EMBED Equation.3  ( EMBED Equation.3 ). E 7=0G5==O 70 3V?>B5B8G=>W 2V4ACB=>ABV 3@02VB0FV9=>3> ?>;O ( EMBED Equation.3 ,  EMBED Equation.3 ) 1C4CBL 287=0G0B8AO 70;56=VABN, I> 70157?5GCT ;>@5=F-V=20@V0=B=VABL B5@<>48=0<VG=8E ?>B5=FV0;V2 V ?0@0<5B@V2, V 2 FL><C 28?04:C:  EMBED Equation.3 . , >B65, FV;:>< <>6;82>, I> C @07V 1C4L-O:>3> A0<>2V;L=>3> (=5 ?@8<CA>2>N) @CEC =VO:>3> C?>2V;L=5==O E>4C 3>48==8:V2 =0A?@024V =5 ?>28==> 1CB8. 465 @CE, =02?0:8, =02VBL :><?5=ACT 3@02VB0FV9=5 C?>2V;L=5==O ?;8=C G0AC. > B>3> 6 ?@8 B0:><C @CAV 2V4ACB=O V 45:;0@>20=5 2 !" =54>B@8<0==O >4=>G0A=>ABV @V7=><VAF528E ?>4V9 2 ! BV;0, I> @CE0TBLAO, O:V T >4=>G0A=8<8 2 ! A?>AB5@V30G0. %>G0, 728G09=> 6, F5 <>65 AB>AC20B8AO ;8H5 V=5@FV9=>3> @CEC BV;0 2 =02:>;8H=L><C 2A5;5=AL:><C 3@02VB0FV9=><C ?>;V, :>;8 O: ACB> >@5=F>25 C?>2V;L=5==O ?;8=C G0AC C AC?CB=V9 BV;C, I> @CE0TBLAO, !0, B0: V C?>2V;L=5==O, =02545=5 3@02VB0FV9=8< ?>;5<, ?>2=VABN :><?5=ACNBLAO 2A51VG=8< V7>B@>?=8< A0<>AB8A:0==O< FL>3> BV;0 2 !out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quation.3  ( EMBED Equation.3 ), 0 V 28:;8:0T 2 @53C;O@=><C ?@>AB>@V !out @5;OB82VABAL:5 (:V=5<0B8G=5) A0<>AB8A:0==O WW O: 2 ?>74>26=L><C, B0: V 2 ?>?5@5G=8E =0?@O<:0E [0=K;LG5=:>, 2009: 79]. V4?>2V4=> 4> FL>3> B5<? ?;8=C <5B@8G=>3> G0AC BV;, I> @CE0NBLAO 70 V=5@FVTN, T =57<V==8< V @5;OB82VABAL:V V=20@V0=B=8<, 0 4;O ?5@5B2>@5==O ?@8@>ABV2 O: <5B@8G=8E 2V4@V7:V2 ( EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ), B0: V :>>@48=0B ( EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ) <0B8<5<> B0:V 28@078:  EMBED Equation.3 ,  EMBED Equation.3  ( EMBED Equation.3 ;  EMBED Equation.3 ),  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3   EMBED Equation.3  ( EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3 ,  EMBED Equation.3 ),  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3  V  EMBED Equation.3   ?@8@>AB8 :>>@48=0B, 2V4?>2V4=V ?@>AB>@>2><C ?5@5E>4C 4> V=H>3> >1'T:B0 j, @5G>28=0 O:>3> ?5@51C20T 2 >4=><C V B><C 6 :>;5:B82=><C ?@>AB>@>2>-G0A>2><C <V:@>AB0=V, I> 9 @5G>28=0 ?>G0B:>2>3> >1'T:B0 i (B>4V O: ?@8@>AB8  EMBED Equation.3  V  EMBED Equation.3  2V4?>2V40NBL 7<V=V 2 G0AV ?@>AB>@>2>3> ?>;>65==O >4=>3> V B>3> 6 >1'T:B0 m). ">4V O: B5=7>@ 5=5@3VW-V<?C;LAC, I> AD>@<>20=89 2 " =0 >A=>2V ACB> >@5=F>28E ?5@5B2>@5=L ?@8@>ABV2 :>>@48=0B B0 G0AC, B> <5B@8G=89 B5=7>@ D0:B8G=> T AD>@<>20=8< =0 >A=>2V WE :>=D>@<=8E 3@02VB0FV9=>-;>@5=F>28E ?5@5B2>@5=L. , A0<5, :>=D>@<=5 A0<>AB8A:0==O 2 D>=>2><C 52:;V4>2><C ?@>AB>@V !!  30;0:B8:, I> H284:> 2V440;ONBLAO 2V4 A?>AB5@V30G0, (V WE 0AB@>=><VG=8E >1'T:BV2) V T 2V4?>2V40;L=8< O: 70 :@828=C 2;0A=>3> ?@>AB>@C A?>AB5@V30G0, B0: V 70 >E>?;5==O 2AL>3> FL>3> =5A:V=G5==>3> ?@>AB>@C DV:B82=>N AD5@>N ?A524>>1@VN ?>4V9 ?@8 7=0G5==V :>A<>;>3VG=>W AB0;>W  EMBED Equation.3 . 0 AD5@V ?A524>>1@VN, 728G09=> 6, 28O2;OTBLAO :>=D>@<=VABL =5A:V=G5==>ABV =5 BV;L:8 :>A<>;>3VG=>3> <8=C;>3>, 0 9 ?@>AB>@C (?>4V; >4=VTW =5A:V=G5==>ABV =0 V=HC 4>72>;OT ?>71CB8AO 2V4 >1>E) [5=@>C7, 1968]. '5@57 V7>B@>?=VABL :>>@48=0B=>W H284:>ABV A2VB;0 2 " ;>@5=F-V=20@V0=B=8<8 2 =V9 <>6CBL 1CB8 B5@<>48=0<VG=V ?>B5=FV0;8 V ?0@0<5B@8 ;8H5 0AB@>=><VG=8E >1'T:BV2, I> C<>2=> ?>:>OBLAO 2 !! . 465 BV;L:8 2>=8 ?040NBL 70 V=5@FVTN =0 ?A524>>1@V9 ?>4V9 A5A2VBC, 715@V30NG8 ?@8 FL><C 7=0G5==O 30<V;LB>=V0=0 V=5@B=>W 2V;L=>W 5=5@3VW A?>:>N V ;03@0=6V0=0 >@48=0@=>W 5=5@3VW A?>:>N, 0 B8< A0<8< V ?>2=>W 5=5@3VW A2>TW @5G>28=8. # ! 6 1C4L-O:>3> A?>AB5@V30G0 :>>@48=0B=V @>7<V@8 F8E >1'T:BV2 2 <><5=B 28?CA:0==O =8<8 28?@><V=N20==O :>=D>@<=> 7<5=H5=V 2 ?>?5@5G=><C ?5@5@V7V 1V;LH5, =V6 F5 ?>B@V1=> 4;O 2V4ACB=>ABV C?>2V;L=5==O B5GVW WE 2;0A=>3> G0AC. 465 73V4=> " WE ?>?5@5G=89 :>>@48=0B=89 <0AHB01=89 G8==8:  EMBED Equation.3  D>@<0;L=> ?5@528ICT A2>T ?>@>3>25 7=0G5==O, ?VA;O O:>3> 70<VABL C?>2V;L=5==O ?>28==> 1CB8 ?@8A:>@5==O A?>AB5@56C20=>3> B5<?C ?;8=C 2;0A=>3> G0AC @CE><>3> BV;0 [0=K;LG5=:>, 2008: 106]:  EMBED Equation.3  ( EMBED Equation.3 ), 45:  EMBED Equation.3 ;  EMBED Equation.3   H284:VABL ?@><5=52>3> @CEC 40;5:>W 30;0:B8:8 =0 <><5=B 28?CA:0==O 28?@><V=N20==O =5N;  EMBED Equation.3   ?>?5@5G=0 AC?CB=O 2V4AB0=L (transverse comoving distance) 4> 30;0:B8:8 2 !! ;  EMBED Equation.3   2V4AB0=L 70 :CB>28< 4V0<5B@>< (angular diameter distance) 2 ! A?>AB5@V30G0 =0 <><5=B 28?CA:0==O 28?@><V=N20==O 30;0:B8:>N; z  G5@2>=89 7AC2 4>268=8 E28;V 28?@><V=N20==O 2V4 7V@>: 30;0:B8:8. 3V4=> ?@8@>ABC V=B5@20;C [Danylchenko, 2021a: 26]:  EMBED Equation.3  ?@8:  EMBED Equation.3 ,  EMBED Equation.3  B0  EMBED Equation.3  1C45 <0B8 <VAF5  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 0:  EMBED Equation.3   EMBED Equation.3 . , >B65, C?>2V;L=5==O 2;0A=>3> G0AC 0AB@>=><VG=8E >1'T:BV2 40;5:8E 30;0:B8:, I> 2V440;ONBLAO 2V4 A?>AB5@V30G0, T 2V4ACB=V< O: 2 :>=D>@<=> ?5@5B2>@5=><C :>>@48=0B=><C G0AV t ! A?>AB5@V30G0, B0: V B8< 1V;LH5 70 @50;L=8< 9>3> 3>48==8:><, I> 2V4;VGCT C=V25@A0;L=89 3@02VB5@<>48=0<VG=89 G0A  EMBED Equation.3 . ">1B> 73V4=> D>@<0;V7<C " <0T <VAF5 =5 C?>2V;L=5==O, 0 =02?0:8 ?@8A:>@5==O B5<?C ?;8=C 2;0A=>3> G0AC 40;5:8E 30;0:B8: 70 3>48==8:>< A?>AB5@V30G0:  EMBED Equation.3 . 4=0:, O:I> 2V;L=8< ?04V==O< 40;5:8E 30;0:B8: =0 ?A524>>1@V9 ?>4V9 2AL>3> ;8H5 ?>2=VABN :><?5=ACTBLAO 3@02VB0FV9=5 C?>2V;L=5==O ?;8=C WE G0AC, B> =0A?@024V =VO:>3> =V ?@8A:>@5==O, =V C?>2V;L=5==O B5GVW T48=>3> 3@02VB5@<>48=0<VG=>3> (=5 :>>@48=0B=>3>) G0AC F8E 30;0:B8: ?@8=F8?>2> =5 ?>28==> 1CB8. "><C-B> B>B>6=VABL B5@V=3B>=0  EMBED Equation.3  [Etherington, 1933], I> 2@0E>2CT ?><8;:>25 7<5=H5==O 2  EMBED Equation.3  @07 :V;L:>ABV :20=BV2 5=5@3VW, 28?CI5=8E @CE><8< 0AB@>=><VG=8< >1'T:B>< (=0 >A=>2V ?><8;:>2>3> CO2;5==O ?@> C?>2V;L=5==O ?;8=C 9>3> 2;0A=>3> G0AC), =0A?@024V T ?0@0;>3V7<><. , 728G09=> 6, 2>=0 ?>28==0 1CB8 70<V=5=>N B>B>6=VABN  EMBED Equation.3 , 73V4=> 7 O:>N ;V=V9=0 70;56=VABL %011;0  EMBED Equation.3  AB@>3> 4>B@8<CTBLAO V ?@8G><C, A0<5, 4;O <5B@8G=>W 2V4AB0=V  EMBED Equation.3 , 0 7>2AV< =5 4;O D>B><5B@8G=>W 2V4AB0=V (luminosity distance)  EMBED Equation.3  [0=8;LG5=:>, 2020: 85; Danylchenko, 2021a: 26].  F5 >7=0G0T, I> DV:B82=0 B5<=0 5=5@3VO 4;O A5A2VBC 7>2AV< =5 ?>B@V1=0 [0=8;LG5=:>, 2020: 85; 2021; Danylchenko, 2021a: 29]. # <><5=B 65 @5TAB@0FVW 28?@><V=N20==O (:>;8 0AB@>=><VG=89 >1'T:B, I> 28?CAB82 9>3> <>65 265 V =5 VA=C20B8) ?@>3=>7>20=89 2 " <0AHB01=89 G8==8: 7=86CTBLAO 4> 7=0G5==O  EMBED Equation.3 . "><C-B>, 4V9A=>, V ?@>3=>7CTBLAO CO2=5 C?>2V;L=5==O B5<?C ?;8=C 2;0A=>3> G0AC FL>3> 0AB@>=><VG=>3> >1'T:B0 2  EMBED Equation.3  @07. 4=0: 65 F5 CO2=5 C?>2V;L=5==O AB@>3> 2V4?>2V40T 7=0G5==N :>>@48=0B=>W H284:>ABV A2VB;0  EMBED Equation.3  2 <VAFV >GV:C20=>W =8=VH=L>W 48A;>:0FVW 0AB@>=><VG=>3> >1'T:B0. , >B65, 2>=> <>65 1CB8 7>2AV< =5 :V=5<0B8G=8<, 0 ACB> 3@02VB0FV9=8< 5D5:B><, >1C<>2;5=8< ?@03=5==O< :>>@48=0B=>W H284:>ABV A2VB;0 4> =C;O ?@8 =01;865==V 4> ?A524>>1@VN ?>4V9.  F5 <0T <VAF5 7024O:8 :>=D>@<=>-;>@5=F>28< ?5@5B2>@5==O< ?@8@>ABV2 :>>@48=0B B0 G0AC, O:V 70157?5GCNBL @5;OB82VABAL:C V=20@V0=B=VABL O: 30<V;LB>=V0=0 BV;0, I> @CE0TBLAO 70 V=5@FVTN, B0: V 2AVE B5@<>48=0<VG=8E ?>B5=FV0;V2 V ?0@0<5B@V2 9>3> @5G>28=8 ?@8 7=0G5==OE :V=5<0B8G=>3> ( EMBED Equation.3 ) V :>>@48=0B=>3> ( EMBED Equation.3 ) <0AHB01=8E G8==8:V2:  EMBED Equation.3 ,  EMBED Equation.3 . V4?>2V4=> 4> FL>3> 52>;NFV9=89 ?@>F5A A0<>AB8A:0==O ?@8B0<0==8E @5G>28=V A?V@0;L=>E28;L>28E CB2>@5=L D0:B8G=> D>@<CT C A5A2VBV 3;>10;L=C 3@02VB0FV9=>-52>;NFV9=C 3@04VT=B=C ;V=7C () 7 3@02VB0FV9=>->?B8G=>W A8;>N:  EMBED Equation.3 , 45:  EMBED Equation.3   ;>:0;L=5 7=0G5==O D>:CA=>W 2V4AB0=V ;  EMBED Equation.3   ?>2=0 D>:CA=0 2V4AB0=L  (@04VCA ?A524>>1@VN ?>4V9 A5A2VBC);  EMBED Equation.3  B0  EMBED Equation.3   @04V0;L=V 2V4AB0=V 4> 30;0:B8:8 2V4?>2V4=> 2 !!  V 2 ! A?>AB5@V30G0 2 <><5=B @5TAB@0FVW =8< 28?@><V=N20==O 2V4 30;0:B8:8. 4=0: 65, G5@2>=89 7AC2 z A?5:B@C 28?@><V=N20==O 7V@>: 40;5:>W 30;0:B8:8 287=0G0TBLAO 7>2AV< =5 WW :>>@48=0B=8< @04VCA>< (20@FH8;L40  EMBED Equation.3  V =5  EMBED Equation.3 , 1> =0 2V4<V=C 2V4 ?>?5@5G=>W AC?CB=L>W 2V4AB0=V 4> 30;0:B8:8 2 !!   EMBED Equation.3 , 2V4?>2V4=>W 30;0:B8FV 25AL G0A C ?@>F5AV ?>H8@5==O WW :20=B0 28?@><V=N20==O, 2V4AB0=L 70 :CB>28< 4V0<5B@><  EMBED Equation.3  0, >B65, V  EMBED Equation.3  <0NBL 2V4?>2V40B8 <><5=BC 28?CA:0==O 28?@><V=N20==O 30;0:B8:>N. >72 O7>: (20@FH8;L40 @V2=O=L 3@02VB0FV9=>3> ?>;O " A?@02;OT ><0=;825 2@065==O, I> ?@>ABV@, O:89 >B>GCT 40;5:V 30;0:B8:8, 2V440;OTBLAO 2V4 A?>AB5@V30G0 @07>< 7 =8<8. , >B65, 240;8=V 2V4 A?>AB5@V30G0 ! @>72 O7:C (20@FH8;L40 <>65 A?@89<0B8AO O: =56>@AB:5 ?@>4>265==O 6>@AB:>W ! =0H>W 30;0:B8:8. 4=0: 715@565==O 5=5@3VW 30;0:B8:, I> 2V440;ONBLAO 70 V=5@FVTN, A?@>AB>2CT F5 2@065==O, 1> 2 =56>@AB:8E ! 70:>= 715@565==O 5=5@3VW BV;, I> @CE0NBLAO 70 V=5@FVTN ?@8=F8?>2> =5 <>65 4>B@8<C20B8AO [0=K;LG5=:>, 1994: 52]. "><C-B> ! @>72 O7:C (20@FH8;L40 T 6>@AB:>N =0 2AL><C A2>T<C ?@>BO7V. , >B65, =0 :@828=C WW 6>@AB:>3> @53C;O@=>3> ?@>AB>@C ?>28==0 =0:;040B8AO I5 9 ;>:0;L=0 :V=5<0B8G=0 :@828=0 ?@>AB>@C, 70?>2=5=>3> @5G>28=>N, I> @CE0TBLAO. "8< A0<8<, O: V 2 ?@>AB>@V, I> =5 <0T :@828=8:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . @0E>2CNG8 I>  EMBED Equation.3 , 0:  EMBED Equation.3 , <>6=0 7=09B8 G0A  EMBED Equation.3 , 70 O:89 28?@><V=N20==O 30;0:B8:8 4>AO3=5 A?>AB5@V30G0, 0 A0<0 30;0:B8:0 709<5 ?>;>65==O, I> T >4=>G0A=8< 7 FVTN ?>4VTN:  EMBED Equation.3 ,  EMBED Equation.3 . 2V4A8, 2@0E>2CNG8, I>,  EMBED Equation.3 , 287=0G0T<>:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . V4?>2V4=C :;0A8G=V9 D>B><5B@8G=V9 70;56=>ABV ?>?5@5G=C AC?CB=N 2V4AB0=L 4> 40;5:>3> 0AB@>=><VG=>3> >1'T:B0, I> C<>2=> ?>:>WBLAO, O: V A?>AB5@V30G, 2 !! , <>6=0 B0:>6 287=0G8B8 V 7 C<>28 V=20@V0=B=>ABV 4> ?5@5B2>@5=L :>>@48=0B 4V0<5B@0 0?5@BC@8:  EMBED Equation.3  @5TAB@C20;L=>3> ?@8;04C [0=K;LG5=:>, 2008: 106]:  EMBED Equation.3 , 45 2V4?>2V4=> 4> @5;OB82VABAL:8E ?5@5B2>@5=L B@83>=><5B@8G=8E DC=:FV9 :CBV2 [-9=HB59=, 1905; Q;;5@, 1972]:  EMBED Equation.3  ( EMBED Equation.3 ), 0  EMBED Equation.3 ;  EMBED Equation.3   @04VCA ?A524>>1@VN ?>4V9, =0 O:><C 7=0G5==O 3@0=8G=>W H284:>ABV @CEC  EMBED Equation.3  4>@V2=NT =C;N [0=K;LG5=:>, 2004: 35; 20050: 95; 2008: 95]. /: 10G8<>, 3;>10;L=0 3@02VB0FV9=0 ;V=70, I> AD>@<>20=0 C74>26 A2VB>2>W ;V=VW 28?@><V=N20==O, 265 =5 T 3@04VT=B=>N, 1> <0T AB0;C C 2AL><C ?@>AB>@V 3@02VB0FV9=>->?B8G=C A8;C:  EMBED Equation.3 . V4?>2V4=> 4> FL>3> ?@>?>@FV9=VABL G5@2>=>3> 7AC2C 4>268=8 E28;V 28?@><V=N20==O  EMBED Equation.3  ?>?5@5G=V9 AC?CB=V9 2V4AB0=V 4> 30;0:B8:8 2 !!   EMBED Equation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b: 96]:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 . !0<5 WE :>=D>@<=V ?5@5B2>@5==O ?@8  EMBED Equation.3  B0 3@02VB0FV9=><C @04VCAV  EMBED Equation.3  2 FL><C ?@>AB>@V V T 5:2V20;5=B=8<8 =5V7>B@>?=8< :>>@48=0B0< (20@FH8;L40 [Q;;5@, 1972; 87=5@, ">@=, #8;5@, 1973]. "CB:  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3   157?5@5@2=> 7<5=HC20=5 7=0G5==O 2 C<>2=> ?>@>6=L><C D>=>2><C ?@>AB>@V 3@02VB0FV9=>3> @04VCA0  EMBED Equation.3  0AB@>=><VG=>3> BV;0;  EMBED Equation.3  ( EMBED Equation.3 ) 4;O 7>2=VH=L>W G0AB8=8 ?@>AB>@C, I> <VAB8BL @5G>28=C, V  EMBED Equation.3  ( EMBED Equation.3 ) 4;O 2=CB@VH=L>W G0AB8=8 ?@>AB>@C, I> <VAB8BL 0=B8@5G>28=C C =04728G09=> <0A82=>3> ?>@>6=8AB>3> 0AB@>=><VG=>3> BV;0. V4?>2V4=> 4> FL>3> 70;56=VABL G5@2>=>3> 7AC2C 4>268=8 E28;V 28?@><V=N20==O 2V4 ?>?5@5G=>W AC?CB=L>W 2V4AB0=V  EMBED Equation.3  1C45 =0ABC?=>N:  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . "0: O: 240;8=V 2V4 465@5;0 3@02VB0FV9=>3> ?>;O  EMBED Equation.3 , 0  EMBED Equation.3 , B> 4;O >4=>3> V B>3> 6 <><5=BC :>A<>;>3VG=>3> G0AC 1C4CBL 28:>=C20B8AO B0:>6 C<>28  EMBED Equation.3 ,  EMBED Equation.3 . "><C 240;8=V ?@>AB>@>2V :>>@48=0B8 (20@FH8;L40 @07>< 7 C=V25@A0;L=8< :>A<>;>3VG=8< G0A>< B56 CB2>@NNBL A8AB5<C V7>B@>?=8E :>>@48=0B.  B0: O: ?;0=5B0 5<;O >15@B0TBLAO =02:>;> !>=FO V A2>TW >AV ;8H5 70 V=5@FVTN, B> C?>2V;L=5==O B5<?C ?;8=C WW 2;0A=>3> G0AC ?@8=F8?>2> =5 <>65 1CB8, O: V C 2AVE V=H8E 0AB@>=><VG=8E >1'T:BV2, I> @CE0NBLAO 70 V=5@FVTN. "><C-B> WW 3@02VB5@<>48=0<VG=89 (0AB@>=><VG=89) G0A D0:B8G=> T B>B>6=8< C=V25@A0;L=><C (01A>;NB=><C) :>A<>;>3VG=><C G0AC.  B>4V AB0T FV;:>< 7@>7C<V;>N <0965 AB@>30 2V4?>2V4=VABL 40;5:8E 30;0:B8: O: 70:>=C %011;0, B0: V 3;>10;L=V9 3@02VB0FV9=>->?B8G=V9 ;V=7V, =5 72060NG8 =0 =5V7>B@>?=VABL :>>@48=0B 2;0A=>W ! 5<;V. >6=0, 728G09=> 6, 4>?CAB8B8, I> @>72'O7>: @V2=O=L 3@02VB0FV9=>3> ?>;O <0T 287=0G0B8AO 2 V7>B@>?=8E 45:0@B>28E :>>@48=0B0E V ;8H5 ?VA;O FL>3> ?5@5B2>@N20B8AO 2 AD5@8G=C A8AB5<C :>>@48=0B. 4=0: 65, B0:89 @>72 O7>: @V2=O=L 2 V7>B@>?=8E 45:0@B>28E :>>@48=0B0E [@0<5@ B0 V=HV, 1980] =VG8< =5 2V4@V7=OTBLAO 2V4 @>72'O7:C 2 V7>B@>?=8E AD5@8G=8E :>>@48=0B0E, 2V4?>2V4=8E D>=>2><C 52:;V4>2C ?@>AB>@C V :>A<>;>3VG=><C G0AC !! . # !!  30;0:B8:8 T <0965 =5@CE><8<8 (74V9A=NNBL ;8H5 <0;V ?5:C;O@=V @CE8).  B><C C 2V4?>2V4=8E FL><C @>72 O7:C @V2=O==OE 3@02VB0FV9=>3> ?>;O (3) :>A<>;>3VG=0 AB0;0  2V4?>2V40;L=0 7>2AV< =5 70 ?@><5=5289 @CE 30;0:B8:, 0 70 52>;NFV9=5 7<5=H5==O ?@>AB>@>2> =5>4=>@V4=8E 5B0;>=V2 4>268=8 2 52:;V4>2><C ?@>AB>@V !!  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 EMBED Equation.3   <8BBT25 7=0G5==O @50;V7>20=>W 70 4>?><>3>N 2V4 T<=8E 72>@>B=8E 72'O7:V2 G0AB:>2>W 048B82=>W :><?5=A0FVW <C;LB8?;V:0B82=>3> ?@54AB02;5==O B5@<>48=0<VG=8E ?>B5=FV0;V2 <V:@>AB0=C @5G>28=8 (<C;LB8?;V:0B82=>3> 7<5=H5==O WW 2V;L=8E 5=5@3V9 ?@>BO3>< G0AC);  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   =>@<>20=V 7=0G5==O B5@<>48=0<VG=8E ?0@0<5B@V2 (B8A:C, <>;O@=>3> >1'T<C, B5<?5@0BC@8 V 5=B@>?VW) <8BBT28E <V:@>AB0=V2 V11A0 @5G>28=8;  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  EMBED Equation.3 ,  EMBED Equation.3  EMBED Equation.3 ; k,  EMBED Equation.3 , m  ?@8E>20=V 7<V==V, I> T ?>:07=8:0<8 2?;82C ?0@0<5B@V2  EMBED Equation.3  B0  EMBED Equation.3  =0 ?0@0<5B@8 B5@<>48=0<VG=8E <V:@>AB0=V2 ;0B5=B=> :>35@5=B=>W @5G>28=8;  EMBED Equation.3 , 0: n  ?@8E>20=0 7<V==0, I> T ?>:07=8:>< 25;8G8= <8BBT28E <V:@>D;C:BC0FV9 7=0G5=L B8A:C V <>;O@=>3> >1'T<C 70 C<>2  EMBED Equation.3  B0 =5 01A>;NB=> 6>@AB:>3> CB@8<0==O 709<0=>3> 307>< AB0;>3> >1'T<C. <V==V k,  EMBED Equation.3 , m, B0 n E0@0:B5@87CNBL <8BBT2V :>;5:B82=V <V:@>AB0=8 (:20=B>2V 3>;>3@0<8) 2AVTW "-?>2'O70=>W @5G>28=8 V ?>4V1=> 4> E28;L>28E DC=:FV9 :20=B>2>W <5E0=V:8 T 740B=8<8 ?@89<0B8 7 ?52=>N 9<>2V@=VABN 1C4L-O:V 4>2V;L=V <8BBT2V 7=0G5==O. <>2V@=VABL 65 ?@89=OBBO @5G>28=>N 2V4?>2V4=>W :>=:@5B=V9 :><?>78FVW WE 7=0G5=L <8BBT2>W 5=5@3VW <V:@>AB0=C V11A0, 2>G5284L, >?8ACTBLAO :0=>=VG=8< @>7?>4V;>< V11A0. 0@0<5B@0< B5@<>48=0<VG=>3> <0:@>AB0=C @5G>28=8 2V4?>2V40NBL :>=:@5B=V <0B5<0B8G=V >GV:C20==O  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  F8E 7<V==8E, I> T 70;56=8<8 2V4 ?0@0<5B@0  EMBED Equation.3 . >@<>20=V 7=0G5==O B5@<>48=0<VG=8E ?0@0<5B@V2 <V:@>AB0=V2 @5G>28=8 ?>2'O70=V ?><V6 A>1>N =0ABC?=8<8 70;56=>ABO<8:  EMBED Equation.3  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 . /: V A;V4 1C;> >GV:C20B8 FL>3>, 2AV <8BBT2V B5@<>48=0<VG=V ?>B5=FV0;8 4>AO30NBL A2>3> <V=V<C<C =570;56=> =5 BV;L:8 2V4 7=0G5=L 7<V==8E k,  EMBED Equation.3 , m, n, 0 V 2V4 7=0G5==O ?@>AB>@>2>3> 307>2>3> (@V48==>3>) ?0@0<5B@0  EMBED Equation.3 :  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 .  4> B>3> 6 7<V=0 2 ?@>AB>@V O2=8E ?0@0<5B@V2 E>;>=CG>W @5G>28=8 =5<8=CG5 AC?@>2>46CTBLAO 7<V=>N V WW ?@8E>20=8E B5@<>48=0<VG=8E ?0@0<5B@V2  EMBED Equation.3  B0  EMBED Equation.3 :  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3  T ?@8@>AB>< <5B@8G=>W @04V0;L=>W 2V4AB0=V. "0:>6, G8< 40;V @5G>28=0 @>7B0H>20=0 2V4 F5=B@C BO6V==O, B8< <5=H>N T WW 2=CB@VH=O 5=5@3VO. "><C-B> =0 2V4<V=C 2V4 V=5@B=>W 2V;L=>W 5=5@3VW (I> =02?0:8 T B8< 1V;LH>N, G8< 40;V @5G>28=0 @>7B0H>20=0 2V4 F5=B@C BO6V==O) B5?;>20 5=5@3VO V ?>2>48BLAO ?>4V1=> 2V4'T<=V9 <0AV.  F5 ?V4B25@46CTBLAO 1030BL<0 4>A;V465==O<8 2?;82C =03@V2C @5G>28=8 =0 WW 203C [-9=HB59=, =D5;L4, 1938; 1965; Chen & Cook, 1993; <8B@852, 2005].  A0<5 C<>20 ?@>AB>@>2>W >4=>@V4=>ABV VT@0@EVG=>W A:;04=>ABV "-?>2'O70=>W @5G>28=8  EMBED Equation.3  V 287=0G0T ?@>AB>@>289 @>7?>4V; AC:C?=>AB59 B5@<>48=0<VG=8E ?0@0<5B@V2 :207V@V2=>206=> E>;>=CG>3> 307C. 28G09=> 6, :>6=0 @5G>28=0 <0T A2>W 7=0G5==O<8 3@02VB0FV9=8E ?>B5=FV0;V2, 1> 7030;L=5 4;O 2AVTW "-?>2'O70=>W @5G>28=8 3@02VB0FV9=5 ?>;5 D>@<CT ;8H5 WE 3@04VT=B8 2 ?@>AB>@V. 4=0: 65, 4;O B>3> I>1 B5@<>48=0<VG=V ?0@0<5B@8 2AVE V=482V4C0;L=8E B5@<>48=0<VG=8E  F8E @5G>28= 1C;8 C73>465=V 7 ?0@0<5B@0<8 a V b @>72'O7:C (20@FH8;L40 7030;L=>3> 4;O =8E 3@02VB0FV9=>3> ?>;O, ?>28==V 28:>=C20B8AO ?52=V C<>28. 3V4=> 7 >B@8<0=8<8 28@070<8 4;O B5@<>48=0<VG=8E ?>B5=FV0;V2 5:2V20;5=B=0 ?A524>20:CC<=V9 :>>@48=0B=V9 H284:>ABV A2VB;0  EMBED Equation.3  " 3@0=8G=0 H284:VABL @CEC @5G>28=8  EMBED Equation.3  T ?@8E>20=8< B5@<>48=0<VG=8< ?0@0<5B@><. @8 FL><C 2AB0=>2;5=0 2 " ">;<5=>< [">;<5=, 1969; 1974] C<>20 <5E0=VG=>W @V2=>2038 3@0=8G=> >AB83;>W @5G>28=8:  EMBED Equation.3  (4) <>3;0 1 28:>=C20B8AO C @50;L=8E 307V2 V @V48= ;8H5 7024O:8 <>6;82>ABV A0<>70157?5G5==O @5G>28=>N >?B8<0;L=>3> 7=0G5==O <0B5<0B8G=>3> >GV:C20==O A2>TW ?@8E>20=>W 7<V==>W  EMBED Equation.3 :  EMBED Equation.3 . =0;>3VG=>, 4>40B:>20 C<>20  EMBED Equation.3  V ?>EV4=0 2V4 =5W C<>20:  EMBED Equation.3  4;O 3@0=8G=> >AB83;>W @5G>28=8 <>3;8 1 28:>=C20B8AO ?@8 2V4?>2V4=8E W< 7=0G5==OE <0B5<0B8G=>3> >GV:C20==O ?@8E>20=>W 7<V==>W  EMBED Equation.3 :  EMBED Equation.3 . @>B5, ?@8 2AL><C FL><C =>@<0;V7>20=5 7=0G5==O 5=B0;L?VW  EMBED Equation.3 :  EMBED Equation.3 , 1>  EMBED Equation.3 .  F5 265 =5 2V4?>2V40T @V2=O==O< 3@02VB0FV9=>3> ?>;O " [0=K;LG5=:>, 2008: 19; 2008a], 73V4=> 7 O:8<8 [">;<5=, 1969; 1974]:  EMBED Equation.3 , 45:  EMBED Equation.3 . > B>3> 6 V ?@>AB>@>20 =5>4=>@V4=VABL ?@8E>20=8E ?0@0<5B@V2  EMBED Equation.3  B0  EMBED Equation.3  =5 2V4?>2V40T :>=F5?FVW A0<>CB2>@5==O @5G>28=>N T48=>3> :>;5:B82=>3> B5@<>48=0<VG=>3> <V:@>AB0=C V11A0 7 >4=0:>28<8 C 2AL><C ?@>AB>@V ?@8E>20=8<8 7<V==8<8 k,  EMBED Equation.3 , m B0 n. "><C-B>, ?5@51C20B8 2 <5E0=VG=><C @V2=>206=><C AB0=V 2 " <>6CBL BV;L:8 3@0=8G=> >AB83;V 3V?>B5B8G=V AC1AB0=FVW  @5G>28=0 01A>;NB=> B25@48E BV;, V450;L=89 307 B0 V450;L=0 @V48=0, ;8H5 C O:8E  EMBED Equation.3  0, B8< A0<8<, O:  EMBED Equation.3 , B0: V  EMBED Equation.3 . 0 F5 2:07CT V 2V4ACB=VABL 2 " 4VNG>W =0 ?@>1=5 BV;> A8;8 @04V0FV9=>3> (5;5:B@><03=VB=>3>) >?>@C ?04V==N 9>3> 2 3@02VB0FV9=><C ?>;V.  EMBED Equation.3  G5@57  EMBED Equation.3 , 45  EMBED Equation.3   30<V;LB>=V0= ?@>1=>3> BV;0, I> 2V;L=> ?040T 2 3@02VB0FV9=><C ?>;V. ;5 6, B0:V 3V?>B5B8G=V 3@0=8G=> >AB83;V AC1AB0=FVW ?@8=F8?>2> =5 T A?@><>6=8<8 AD>@<C20B8 A2V9 ?@>AB>@>2> =5>4=>@V4=89 B5@<>48=0<VG=89 AB0= V, B8< A0<8<, CB2>@8B8 2V4?>2V4=5 9><C 3@02VB0FV9=5 ?>;5. @8G8=>N FL>3> T 2V4ACB=VABL 5;5:B@><03=VB=>3> 270T<>4VW WE <>;5:C;.  F5, 728G09=> 6, >4=5 7 >A=>2=8E 2=CB@VH=VE ?@>B8@VG 28:>@8AB>2C20=>3> 2 @V2=O==OE 3@02VB0FV9=>3> ?>;O " A?@>I5=>3> 2V4>1@065==O B5@<>48=0<VG=8E 2;0AB82>AB59 @5G>28=8. 50;L=>N 6 @5G>28=>N 2 " <>65 1CB8 ;8H5 ?>ABC?>2> (:207V@V2=>206=>) E>;>=CG0 @5G>28=0, C O:>W  EMBED Equation.3  70  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3  V  EMBED Equation.3 .  F5 FV;:>< T <>6;828< A0<5 C @07V =0ABC?=>W 70;56=>ABV ?0@0<5B@0  EMBED Equation.3  O: 2V4 >@5=F>20 A:>@>G5==O @>7<V@V2 E>;>=CG>W @5G>28=8  EMBED Equation.3 , 7=0G5=L :>>@48=0B=>W H284:>ABV A2VB;0  EMBED Equation.3  V ?>:07=8:0 70;><;5==O A2VB;0 @5G>28=>N  EMBED Equation.3 , B0: V 2V4 <0B5<0B8G=>3> >GV:C20==O 25;8G8=8 ?@8E>20=>W 7<V==>W  EMBED Equation.3  307C:  EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   7=0G5==O ?0@0<5B@V2 @5G>28=8 C <8BL G0AC  EMBED Equation.3 . @>B5, F5 T <>6;828< ;8H5 ?@8 28:>@8AB0==V 2 @V2=O==OE 3@02VB0FV9=>3> ?>;O " =5AB01V;L=>W 5=B@>?VW.  2 FL><C 28?04:C ?@>AB>@>2> >4=>@V4=8< 70<VABL 5=B@>?VW T ?0@0<5B@  EMBED Equation.3 , I> E0@0:B5@87CT >4=0:>2VABL VT@0@EVG=>W A:;04=>ABV @5G>28=8 C 2AL><C 709<0=><C =5N ?@>AB>@V. #<>28 <5E0=VG=>W B0 B5?;>2>W :207V@V2=>2038 <VABOBLAO 2 A0<8E 70;56=>ABOE B5@<>48=0<VG=8E ?>B5=FV0;V2 2V4 B5@<>48=0<VG=8E ?0@0<5B@V2 :207V@V2=>206=> E>;>=CG>W @5G>28=8. ;O 5=5@3VW @>7H8@5=>W A8AB5<8, O:>W T 5=B0;L?VO [070@>2, 1964], 1C45<> <0B8:  EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3  ( EMBED Equation.3 );  EMBED Equation.3   >@48=0@=0 2=CB@VH=O 5=5@3VO @5G>28=8, B>B>6=0 <C;LB8?;V:0B82=V9 A:;04>2V9  EMBED Equation.3  WW ?>2=>W 5=5@3VW U;  EMBED Equation.3   <0B5<0B8G=5 >GV:C20==O G0AB:>2>W 048B82=>W :><?5=A0FVW <C;LB8?;V:0B82=>3> ?@54AB02;5==O B5@<>48=0<VG=8E ?>B5=FV0;V2 @5G>28=8;  EMBED Equation.3   IV;L=VABL 30<V;LB>=V0=0 E>;>=CG>W @5G>28=8;  EMBED Equation.3   IV;L=VABL WW 3@02VB0FV9=>W <0A8;  EMBED Equation.3 ,  EMBED Equation.3 .  B><C C<>28 <5E0=VG=>W B0 B5?;>2>W :207V@V2=>2038 4;O E>;>=CG>W @5G>28=8 2V4?>2V4=> 1C4CBL B0:8<8:  EMBED Equation.3  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 . (5) @8  EMBED Equation.3  ( EMBED Equation.3 ,  EMBED Equation.3 ) >B@8<0T<> C<>2C <5E0=VG=>W @V2=>2038 4;O 3@0=8G=> >AB83;>W @5G>28=8 ". V4ACB=VABL C 28:>@8AB>2C20=V9 2 " C<>2V <5E0=VG=>W @V2=>2038 (2) ?0@0<5B@0  EMBED Equation.3  ?>2'O70=5 7 70AB>AC20==O< WW ;8H5 4> AB0B8G=8E AB0=V2 @5G>28=8. > B>3> 6 2 " <0T <VAF5 28:>@8AB0==O C 28@07V 4;O 5=B0;L?VW @5G>28=8 V=5@B=>W 2V;L=>W 5=5@3VW  EMBED Equation.3  70<VABL WW ?>2=>W 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3 , 0 B0:>6 V V3=>@C20==O ;>@5=F-V=20@V0=B=>ABV B5@<>48=0<VG=8E ?0@0<5B@V2 V ?>B5=FV0;V2 [070@>2, 1964, 1991; Van Kampen, 1968]. 3=>@CTBLAO 2 " V 5:2V20;5=B=VABL 2;0A=>3> 7=0G5==O <0A8  EMBED Equation.3  @5G>28=8 2;0A=><C 7=0G5==N WW >@48=0@=>W 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3 , I> 287=0G0TBLAO 70 2;0A=8< 3@02V:20=B>28< 3>48==8:>< @5G>28=8 2 B>GFV i WW ?5@51C20==O.  B8< A0<8< V3=>@CTBLAO V V=20@V0=B=VABL I>4> 3@02VB5<?>@0;L=8E ?5@5B2>@5=L 2AVE B5@<>48=0<VG=8E ?>B5=FV0;V2 V ?0@0<5B@V2, O:V T 2;0A=8<8 7=0G5==O<8 2V4?>2V4=8E 2;0AB82>AB59 @5G>28=8. "0:8< G8=><, 2 AB0=V AB@>3>W <5E0=VG=>W @V2=>2038 ( EMBED Equation.3 ) A8;8 BO6V==O T ?@>?>@FV9=8<8 7>2AV< =5 V=5@B=V9 2V;L=V9 5=5@3VW , 0 <C;LB8?;V:0B82=V9 A:;04>2V9 5=B0;L?VW  EMBED Equation.3 .  F5, 728G09=> 6, 28?;820T V 7 @>72'O7:V2 @V2=O=L 3@02VB0FV9=>3> ?>;O " 4;O @5G>28=8, I> ?5@51C20T C AB0=V <5E0=VG=>W @V2=>2038. /: ?>:0702 ">;<5= [">;<5=, 1969] V O: F5 >B@8<0=> C 2=CB@VH=L><C @>72'O7:C (20@FH8;L40 4;O =5AB8A;82>W V450;L=>W @V48=8 [Q;;5@, 1972], 3@02VB0FV9=V A8;8 2 =L><C T ?@>?>@FV9=8<8 5=B0;L?VW, I> =5 7<5=HCTBLAO =0 2V4<V=C 2V4 V=5@B=>W 2V;L=>W 5=5@3VW , 0 =02?0:8, 7@>AB0T 7 =01;865==O< 4> F5=B@C BO6V==O. 3=>@C20==O 6 2AL>3> FL>3> V ?@872>48BL 4> CO2=>W ?>B@518 C A5A2VBV B5<=>W =510@V>==>W <0B5@VW. >G5284L, ?@>AB>@>2V9 >4=>@V4=>ABV VT@0@EVG=>W A:;04=>ABV @5G>28=8 ( EMBED Equation.3 ) 2V4?>2V40T V ?@>AB>@>20 >4=>@V4=VABL 4>1CB:C V=5@B=>W 2V;L=>W 5=5@3VW V <C;LB8?;V:0B82=>W A:;04>2>W ?>2=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8  EMBED Equation.3 , O:0 <0T <VAF5 =5 BV;L:8 C 3@0=8G=> >AB83;>W @5G>28=8 ", 0 9 C :207V@V2=>206=> E>;>=CG>W @5G>28=8. @8 FL><C V=5@B=0 2V;L=0 5=5@3VO >4=>3> <>;O @5G>28=8, I> @CE0TBLAO 2 ?@>F5AV A2>3> >E>;>465==O<, T B>B>6=>N 30<V;LB>=V0=C  EMBED Equation.3  V=5@B=>W 2V;L=>W 5=5@3VW A?>:>N @5G>28=8  EMBED Equation.3 . ">4V O: <C;LB8?;V:0B82=0 A:;04>20 WW ?>2=>W 2=CB@VH=L>W 5=5@3VW, O:0 7040TBLAO 2;0A=8< 7=0G5==O< WW <>;O@=>W <0A8  EMBED Equation.3 , D0:B8G=> T B>B>6=>N 30<V;LB>=V0=C  EMBED Equation.3  >@48=0@=>W 2=CB@VH=L>W 5=5@3VW >AB83;>W @5G>28=8  EMBED Equation.3 . V4?>2V4=C  EMBED Equation.3  ?>2=C 2=CB@VH=N 5=5@3VN  EMBED Equation.3  2?02H0 @5G>28=0 ?>B5=FV9=> A?@><>6=0 =0:>?8G8B8 ;8H5 >?VA;O 4>AO3=5==O @V2=>206=>3> AB0=C A?>:>N 7024O:8 B5?;>>1<V=C 7 =02:>;8H=V< A5@54>28I5<.  A0<5 G5@57 V=20@V0=B=VABL 3@0=8G=>W H284:>ABV @CEC @5G>28=8 2 AC?CB=V9 W9 !  EMBED Equation.3  I>4> ?5@5B2>@5==O ?@>AB>@>28E :>>@48=0B B0 G0AC :>=D>@<=>-3@02VB0FV9=> ;>@5=F-V=20@V0=B=8<8 T =5 BV;L:8 30<V;LB>=V0=  EMBED Equation.3  V ;03@0=6V0=  EMBED Equation.3 , 0 V ?>2=0 2=CB@VH=O 5=5@3VO @5G>28=8 U 0, >B>6, V O: 2AV V=HV B5@<>48=0<VG=V ?>B5=FV0;8, B0: V 2AV B5@<>48=0<VG=V ?0@0<5B@8 1C4L-O:>W @5G>28=8. "0: O: V=B53@C20==O 70 ?0@0<5B@><  EMBED Equation.3  2V41C20TBLAO C ?@>AB>@V, B> G5@57  EMBED Equation.3  ?@>AB>@>20 048B82=0 :><?5=A0FVO  EMBED Equation.3  C :207V@V2=>206=> E>;>=CG>W @5G>28=8 =5 BV;L:8 T AB0;>N, 0 V <>65 1CB8 O: 7023>4=> <0;>N.  F5, 2>G5284L, <0T <VAF5 =5 BV;L:8 40;5:> 2V4 465@5; 28?@><V=N20==O 2 <>;5:C;O@=8E E<0@0E E>;>4=>3> =5V>=V7>20=>3> 307C, 0 V 2 A8;L=> @>7@V465=V9 E>;>4=V9 ?;07<V :>A<>AD5@8, =572060NG8 =02VBL =0 WW ?5@5206=> =5@V2=>206=89 B5@<>48=0<VG=89 AB0=. 465, =0 2V4<V=C 2V4 C<>28 :207V@V2=>206=>ABV >AB830==O  EMBED Equation.3 , C<>20 ?@>AB>@>2>W >4=>@V4=>ABV VT@0@EVG=>W A:;04=>ABV  EMBED Equation.3  4;O FVTW ?;07<8, B56 <>65 28:>=C20B8AO. , >B65, =5 BV;L:8 C :207V@V2=>206=> E>;>=CGV9 @5G>28=V, 0 V 2 :>A<>AD5@V  EMBED Equation.3  <>65 1CB8 7=5206;82> <0;>N ( EMBED Equation.3 ). 4=0:, O:>N 1 <0;>N V =5 1C;0 ?@>AB>@>20 048B82=0 :><?5=A0FVO  EMBED Equation.3 , ?>2=0 2=CB@VH=O 5=5@3VO @5G>28=8 ?@8=F8?>2> =5 <>65 1CB8 <5=H>N WW A:;04>2>W  V=5@B=>W 2V;L=>W 5=5@3VW E, 1>:  EMBED Equation.3 . 024O:8 6 <0;>ABV  EMBED Equation.3  =5 BV;L:8 ;>30@8D<8>@48=0@=>W 2=CB@VH=L>W 5=5@3VW, 0 V ;>30@8D<8 ?>2=>W 2=CB@VH=L>W 5=5@3VW B0 5=B0;L?VW <>6CBL 1CB8 28:>@8AB0=V 2 O:>ABV 3@02VB0FV9=>3> ?>B5=FV0;C:  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3  T :>5DVFVT=B>< A?@>B82C @5G>28=8 A5@54>28I0 ?04V==N BV; C 3@02VB0FV9=><C ?>;V. , >B65, A0<>CB2>@5==O @5G>28=>N A2>3> ?@>AB>@>2> =5>4=>@V4=>3> B5@<>48=0<VG=>3> AB0=C V T 2V4?>2V40;L=8< 70 28=8:=5==O 2 =V9 3@02VB0FV9=>3> ?>;O. "0: O::  EMBED Equation.3   EMBED Equation.3  28@060TBLAO =5 BV;L:8 G5@57 AB0;V (2:;NG0NG8 V  EMBED Equation.3 , I> E0@0:B5@87CT :207V@V2=>206=VABL ?@>F5AC E>;>4V==O @5G>28=8 ?@>BO3>< 2AL>3> G0AC), 0 V G5@57 H284:VABL A2VB;0 2 @5G>28=V  EMBED Equation.3 , 3@0=8G=C H284:VABL @CEC  EMBED Equation.3  V >@5=F>25 A:>@>G5==O @>7<V@V2 @5G>28=8, I> @CE0TBLAO 2 ?@>F5AV A2>3> :207V@V2=>206=>3> >AB830==O  EMBED Equation.3  ( EMBED Equation.3 ), B> ;8H5 G5@57 =8E V <>6CBL 1CB8 28@065=V C G0A>2><C (G5@57  EMBED Equation.3 ) G8 ?@>AB>@>2><C (G5@57  EMBED Equation.3 ) 283;O4V <8BBT2V 7=0G5==O 2AVE >A=>2=8E B5@<>48=0<VG=8E ?0@0<5B@V2 V ?>B5=FV0;V2 "-?>2'O70=>3> 307C:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3  T 3@0=8G=>N H284:VABN @CEC :207V@V2=>206=> E>;>=CG>W @5G>28=8 C AC?CB=V9 W9 ! (B>1B> C 2;0A=><C WW ?@>AB>@>2>-G0A>2><C :>=B8=CC<V ('), 2 O:><C T 2V4ACB=V< @04V0;L=89 @CE WW <>;5:C;);  EMBED Equation.3  T <8BBT28< 7=0G5==O< G0AB:>2>W 048B82=>W :><?5=A0FVW <C;LB8?;V:0B82=>3> ?@54AB02;5==O B5@<>48=0<VG=8E ?>B5=FV0;V2 <V:@>AB0=C @5G>28=8 (<C;LB8?;V:0B82=>3> 725;8G5==O ?>2 O70=>W 5=5@3VW 7 =01;865==O< 4> F5=B@C BO6V==O);  EMBED Equation.3  T <8BBT28< 7=0G5==O< 5=5@3VW V11A0 G, ?>4V1=>W 4> ;03@0=6V0=C, I> =52?8==> ?@03=5 4> A2>3> <V=V<C<C. /: 10G8<>, 7024O:8  EMBED Equation.3  70 C<>28 :207V@V2=>206=>3> >AB830==O >4=>@V4=>W @5G>28=8 3@02VB0FV9=V 7<V=8 2 G0AV WW 2V;L=8E 5=5@3V9 5;L<3>;LFO V V11A0 2V41C20NBLAO ?>4V1=> 7<V=0< C ?@>AB>@V <C;LB8?;V:0B82=8E A:;04>28E 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3  V 5=B0;L?VW  EMBED Equation.3  2V4?>2V4=>.  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"><C 3V?>B5B8G=V V450;L=89 307 B0 V450;L=0 @V48=0 V T ?@8=F8?>2> =5A?@><>6=8<8 =0 A0<>CB2>@5==O A2>3> 3@02VB0FV9=>3> ?>;O. /: 10G8<>, BCB <0T <VAF5 70;56=VABL 2V4  EMBED Equation.3  (0, >B65, V 2V4  EMBED Equation.3  B0  EMBED Equation.3 ) ?@>AB>@>2>3> @>7?>4V;C AC:C?=>ABV A0<5 2;0A=8E 7=0G5=L F8E B5@<>48=0<VG=8E ?0@0<5B@V2 B0 ?>B5=FV0;V2, 0 7>2AV< =5 WE 7=0G5=L, I> A?>AB5@V30NBLAO 70 V=H8<8 3>48==8:0<8 V V=H8<8 5B0;>=0<8 4>268=8.  1C;> 1 7>2AV< =5 ;>3VG=8<, O:18  EMBED Equation.3  V  EMBED Equation.3  =5 2?;820;8 =0 ?@>AB>@>289 @>7?>4V; AC:C?=>AB59 2;0A=8E 7=0G5=L >A=>2=8E B5@<>48=0<VG=8E ?0@0<5B@V2 @5G>28=8. "0: I>, F5 06 =VO: =5 AC?5@5G8BL V=20@V0=B=>ABV B5@<>48=0<VG=8E ?0@0<5B@V2 V ?>B5=FV0;V2 @5G>28=8 I>4> ?@>AB>@>2>-G0A>28E ?5@5B2>@5=L [0=K;LG5=:>, 2008: 19]. , =02?0:8, F5 ;8H5 ?V4B25@46CT B>9 D0:B, I> 3@0=8G=0 H284:VABL @CEC @5G>28=8  EMBED Equation.3 , O: V  EMBED Equation.3 , T A0<5 WW 2=CB@VH=V< ?@8E>20=8< ?0@0<5B@><, 0 =5 =570;56=8< 2V4 :>=:@5B=>3> 3@02VB5@<>48=0<VG=>3> AB0=C @5G>28=8 7>2=VH=V< 3@02VB0FV9=8< ?0@0<5B@><. 14. "5@<>48=0<VG=V B0 V=HV DV78G=V E0@0:B5@8AB8:8 @5G>28=8 0 C<>28 ">;<5=0 (4) B0 ?@8  EMBED Equation.3  ?0@0<5B@  EMBED Equation.3  ?>28=5= 1CB8 =57<V==8< =5 ;8H5 C ?@>AB>@V, 0 V 2 G0AV.  F5 <>65 2V4?>2V40B8 @5G>28=V, I> >AB830T ( EMBED Equation.3 ) 0=><0;L=> V G5@57  EMBED Equation.3  <0T A0<5 B0:V B5@<>48=0<VG=V ?0@0<5B@8:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3  V  EMBED Equation.3  T :@8B8G=8<8 7=0G5==O<8 ?0@0<5B@V2 =0 <56V @>74V;C D07 @5G>28=8 G8 7 V=H>N @5G>28=>N. >:07=8: 70;><;5==O 28?@><V=N20==O B0:>N @5G>28=>N:  EMBED Equation.3  70;568BL =5 ;8H5 2V4 7=0G5=L WW E0@0:B5@=8E ?0@0<5B@V2  EMBED Equation.3  V  EMBED Equation.3  B0 2V4 3@0=8G=>W H284:>ABV WW @CEC  EMBED Equation.3 , 0 V 2V4 ?0@0<5B@V2  EMBED Equation.3 ,  EMBED Equation.3  B0  EMBED Equation.3 , I> 7<V=NNBLAO C G0AV @07>< 7 >AB830==O< @5G>28=8. >G5284L, C ?@>F5AV :207V@V2=>206=>3> >AB830==O @5G>28=8 <0T <VAF5 AB01V;L=VABL 25;8G8=8 V=B5=A82=>3> ?0@0<5B@0  EMBED Equation.3 . :A?5@8<5=B0;L=> 7=09H>2H8 9>3> CA5@54=5=5 7=0G5==O =0 ?>G0B:C 4>A;V46C20==O @5G>28=8 01> 6 28<V@O2H8 ?@8@>AB8 B5@<>48=0<VG=8E ?0@0<5B@V2:  EMBED Equation.3 , <>6;82> 287=0G8B8 V WW 5=B@>?VN:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3  B0  EMBED Equation.3   <0B5<0B8G=V >GV:C20==O 7=0G5=L DC=:FV9 2V4 ?@8E>20=8E 7<V==8E k,  EMBED Equation.3 , m, n, I> 28?04:>2> 7<V=NNBLAO V T AB@>3> AB0;8<8 25;8G8=0<8 ?@>BO3>< 2AL>3> =5B@820;>3> G0AC VA=C20==O 1C4L-O:>3> B5@<>48=0<VG=>3> <V:@>AB0=C V11A0. 4=0: 65, 7=0NG8  EMBED Equation.3  V  EMBED Equation.3 , 0 B0:>6, 287=0G82H8 ;8H5 <>;O@=89 >1'T< :207V@V2=>206=> E>;>=CG>3> 307C V B8A: 2 =L><C, <>6=0 7=09B8 BV;L:8 9>3> ?>2'O70=C 5=5@3VN:  EMBED Equation.3 . (6) ;O B>3> 6, I>1 <>6=0 1C;> 7=09B8 5=B@>?VN, 0 B8< A0<8< V 7=0G5==O ?0@0<5B@0  EMBED Equation.3 , ?>B@V1=> I5 28<V@OB8 V B5<?5@0BC@C 307C. >G5284L, ?0@0<5B@8  EMBED Equation.3  V  EMBED Equation.3  @V2=O==O AB0=C 307C (6) <>6CBL 1CB8 287=0G5=V V 5:A?5@8<5=B0;L=> 2 ?@>F5AV :>=B@>;L>20=>W 7<V=8 O: 9>3> ?>2'O70=>W 5=5@3VW, B0: V 2AVE 9>3> B5@<>48=0<VG=8E ?0@0<5B@V2. >A;V465==O 6 V V=H8E B5@<>48=0<VG=8E 2;0AB82>AB59 @5G>28=8 A;V4 ?@>2>48B8 7 28:>@8AB0==O< 70;56=>AB59 WW B5@<>48=0<VG=8E ?>B5=FV0;V2 2V4 B5@<>48=0<VG=8E ?0@0<5B@V2, I> 2@0E>2CNBL <V=;82VABL ?0@0<5B@0  EMBED Equation.3  C ?@>F5AV WE ?@>2545==O ( EMBED Equation.3 ). ;O 287=0G5==O O: B5@<VG=8E :>5DVFVT=BV2 @>7H8@5==O  EMBED Equation.3  B0 B8A:C  EMBED Equation.3 , B0: V <>4C;O ?@C6=>ABV  EMBED Equation.3  307C G8 @V48=8 4>A8BL 7=0B8 ;8H5 B5@<VG=5 @V2=O==O AB0=C (?0@0<5B@  EMBED Equation.3 ):  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . ;O 287=0G5==O 6 WE B5?;>T<=>AB59 70 AB0;8< >1'T<>< 01> B8A:>< 0, B8< A0<8<, V 2AVE WE B5@<>48=0<VG=8E ?>B5=FV0;V2 =5>1EV4=> 7=0B8, :@V<  EMBED Equation.3  B0 :@8B8G=8E D07>28E 7=0G5=L B8A:C  EMBED Equation.3  V <C;LB8?;V:0B82=>W A:;04>2>W 2=CB@VH=L>W 5=5@3VW  EMBED Equation.3 , I5 9 <0B5<0B8G=5 >GV:C20==O  EMBED Equation.3  7=0G5==O ?@8E>20=>W 7<V==>W  EMBED Equation.3 :  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 0 ?V4AB02V 6 B5<?5@0BC@=8E 70;56=>AB59 B5?;>T<=>AB59 ?@8 AB0;><C >1'T<V G8 B8A:C <>65 1CB8 287=0G5=8< V <0B5<0B8G=5 >GV:C20==O 70;56=>AB59 F8E DC=:FV9 2V4 V=482V4C0;L=8E ?0@0<5B@V2  EMBED Equation.3  8  EMBED Equation.3  0, >B65, V 2V4 1C4L-O:>W ?0@8 >A=>2=8E B5@<>48=0<VG=8E ?0@0<5B@V2:  EMBED Equation.3 . 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V;LH B>G=><C ?5@H><C B5@<VG=><C @V2=O==N VB5@VGV, I> 28:>@8AB>2CT 5:A?>=5=BC 7 F8< 65 ?0@0<5B@><  EMBED Equation.3 , 2V4?>2V40NBL:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 . >G5284L, V 5:A?5@8<5=B0;L=> 287=0G5=V B5?;>T<=>ABV 307V2 <>6=0 ?@54AB028B8 O: DC=:FVW ;8H5 2V4  EMBED Equation.3  B0  EMBED Equation.3 . @8E>20=V 7<V==V  EMBED Equation.3  V  EMBED Equation.3  T AB0;8<8 25;8G8=0<8 2 1C4L-O:C <8BL G0AC, 2V4?>2V4=C :>=:@5B=><C :>;5:B82=><C <V:@>AB0=C V11A0 2AVTW "-?>2'O70=>W @5G>28=8. , >B65, ?>EV4=V 2V4 =8E 70 1C4L-O:8< B5@<>48=0<VG=8< ?0@0<5B@>< 4>@V2=NNBL =C;N. &5 6 AB>ACTBLAO V <0B5<0B8G=8E >GV:C20=L F8E ?@8E>20=8E 7<V==8E  EMBED Equation.3  V  EMBED Equation.3 , =572060NG8 =0 70;56=VABL WE 7=0G5=L 2V4 V=H8E B5@<>48=0<VG=8E ?0@0<5B@V2 @5G>28=8. 15. >72 O7>: @V2=O=L 3@02VB0FV9=>3> ?>;O 3@0=8G=> >AB83;8E B0 :20=B>2> :207V@V2=>206=> E>;>=CG8E 307V2 # 72'O7:C 7 CB2>@5==O< CAVTN 3@02VB5@<>48=0<VG=> ?>2'O70=>N @5G>28=>N :>;5:B82=8E ?@>AB>@>2>-G0A>28E <V:@>AB0=V2 (<V:@>AB0=V2 V11A0) ?@>AB>@>25 V=B53@C20==O @V2=O=L 3@02VB0FV9=>3> ?>;O <0T DV78G=89 A5=A ;8H5 4;O :>=:@5B=>3> <><5=BC 2;0A=>3> G0AC @5G>28=8 B0 2 =52V4@82=><C 2V4 =5W 2;0A=><C DV78G=><C ?@>AB>@V. !0<5 :0@48=0;L=0 2V4ACB=VABL 2 V=B53@>20=8E @V2=O==OE H284:>ABV @CEC @5G>28=8 @>18BL =50:BC0;L=>N ?@>1;5<C @5;OB82VABAL:>W V=20@V0=B=>ABV B5@<>48=0<VG=8E ?0@0<5B@V2 V ?>B5=FV0;V2 @5G>28=8. A:V;L:8 2 :207V@V2=>206=> E>;>=CG8E A:C?G5==OE >4=>@V4=>3> 307C DC=:FVW G0AC  EMBED Equation.3  V 6>@AB:> ?>2'O70=>W 7 E>;>=CG8< 307>< @04V0;L=>W :>>@48=0B8  EMBED Equation.3  ( EMBED Equation.3 ) 28:>=CNBL 2V4?>2V4=> G0AC ?>4V1=89 307>289 ?0@0<5B@  EMBED Equation.3  V ?>:07=8: VT@0@EVG=>W A:;04=>ABV 307C  EMBED Equation.3 , B> ?@>AB>@>25 V=B53@C20==O @V2=O=L 9>3> 3@02VB5@<>48=0<VG=>3> AB0=C A;V4 ?@>2>48B8 4;O >4=>3> V B>3> 6 7=0G5==O ?0@0<5B@0, 0 V=B53@C20==O 2 G0AV 2V4?>2V4=> ?@8 >4=0:>2><C 7=0G5==V ?>:07=8:0 VT@0@EVG=>W A:;04=>ABV 1C4L-O:>3> :>=:@5B=>3> <V:@>>1'T<C 307C.  >3;O4C =0 F5 A:C?G5==O< :207V@V2=>206=> E>;>=CG>3> 307C <>65 1CB8 7VAB02;5=0 C " B5@<>48=0<VG=0 !, I> T FV;:>< 2V4?>2V4=>N ?0@0<5B@0< (20@FH8;L40 @V2=O=L 3@02VB0FV9=>3> ?>;O. 8E>4OG8 7 B>3>, I> 4;O :207V@V2=>206=> E>;>=CG8E 307V2 (EMBED Equation.3 ( EMBED Equation.3 ), B> 4;O =8E O: C ", B0: V 2 " <0B8<5<>:  EMBED Equation.3 . 2V4:8:  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 ;  EMBED Equation.3 ;  EMBED Equation.3  (2V4?>2V4=> 4> 70:>=C >9;O-0@V>BB0 [0=4A15@3, 1948]);  EMBED Equation.3 ;  EMBED Equation.3   3@0=8G=5 7=0G5==O IV;L=>ABV 3@02VB0FV9=>W <0A8 307C. >G5284L, A:C?G5==O :207V@V2=>206=> E>;>=CG>3> 307C <0NBL B0:>6 V ?@>AB>@>2C >4=>@V4=VABL 3@02VB5@<>48=0<VG=>3> 2;0A=>3> 7=0G5==O O: <C;LB8?;V:0B82=>W A:;04>2>W, B0: V ?>2=>W 2V;L=>W 5=5@3VW V11A0  EMBED Equation.3  (?>4V1=> 4> ?@>AB>@>2>W >4=>@V4=>ABV 3@02VB5@<>48=0<VG=>3> 2;0A=>3> 7=0G5==O 5=B0;L?VW  EMBED Equation.3  3@0=8G=> >AB83;>W @5G>28=8, O: F5 ?>:0702 ">;<5=): EMBED Equation.3EMBED Equation.3, 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . "><C:  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ;  EMBED Equation.3  V  EMBED Equation.3   <0B5<0B8G=V >GV:C20==O ?@8  EMBED Equation.3  2V4?>2V4=> IV;L=>ABV <0A8 V @V7=8FV IV;L=>AB59 5=5@3VW V11A0 B0 <0A8 307C;  EMBED Equation.3 . '5@57 @5;OB82VABAL:C V=20@V0=B=VABL B5@<>48=0<VG=8E ?0@0<5B@V2 V E0@0:B5@8AB8: @5G>28=8 @V2=O==O 3@02VB0FV9=>3> ?>;O 4;O :207V@V2=>206=> E>;>=CG>3> 307C <>6CBL 1CB8 7040=V ;8H5 C AC?CB=V9 9><C ! 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"0: O: C F5=B@0;L=V9 7>=V A:C?G5==O 307C ( EMBED Equation.3 ):  EMBED Equation.3 , B> 287=0G8<> =0 =5W =01;865=89 @>72'O7>: 48D5@5=FV0;L=>3> @V2=O==O  EMBED Equation.3 :  EMBED Equation.3   EMBED Equation.3 . 2V4A8:  EMBED Equation.3 ,  EMBED Equation.3 , 45:  EMBED Equation.3 , 0 ?0@0<5B@ z 287=0G0TBLAO 7 @V2=O==O:  EMBED Equation.3 . B@8<0=5 48D5@5=FV0;L=5 @V2=O==O T :20=B>28< @V2=O==O< 3@02VB0FV9=>3> (3@02VB5@<>48=0<VG=>3>) ?>;O, >A:V;L:8 9>3> @>72'O7:0<8 T ABC?5=52V DC=:FVW, ?>:07=8:8 ABC?5=O ( EMBED Equation.3 ) O:8E <>6CBL ?@89<0B8 ;8H5 FV;V 01> =0?V2FV;V 7=0G5==O [@KG:>2, 1986]:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3 . "0:8< G8=><, :20=B>289 ?5@5EV4 E>;>=CG>W @5G>28=8 4> A2>3> =>2>3> :207V@V2=>206=>3> AB0=C AC?@>2>46CTBLAO ?V428I5==O< =0 >48= :@>: ?>:07=8:V2 ABC?5=O 2AVE :><?>=5=BV2 ABC?5=52>3> @V2=O==O 3@02VB0FV9=>3> ?>;O:  EMBED Equation.3   EMBED Equation.3 , 45:  EMBED Equation.3 ,  EMBED Equation.3 . B65, C 3@0=8G=> >AB83;><C AB0=V @5G>28=8 ( EMBED Equation.3 ) ?0@0<5B@  EMBED Equation.3  4>AO30T <V=V<0;L=> <>6;82>3> A2>3> 7=0G5==O, I> 4>@V2=NT >48=8FV. "><C: EMBED Equation.3 . 0 <0;8E 7=0G5=L ?>:07=8:V2 ABC?5=52>W DC=:FVW E>;>=CG5 A:C?G5==O 307C A:840T A2>N 5=5@3VN 25;8:8<8 ?>@FVO<8. 4=0: FV ?>@FVW 5=5@3VW 28?@><V=N20==O 7 :>6=8< =>28< ?@89=OB8< 3@02VB5@<>48=0<VG=8< AB0=>< AB0NBL 2A5 <5=H5 V <5=H5. "0: I> A:C?G5==O 307C <>65 >AB830B8 =5A:V=G5==> 4>23>. ">G=89 @>72'O7>: FL>3> 48D5@5=FV0;L=>3> @V2=O==O ?@8  EMBED Equation.3  <0T =0ABC?=89 283;O4:  EMBED Equation.3 , 45:  EMBED Equation.3  V  EMBED Equation.3   5D5:B82=V 7=0G5==O @04V0;L=>W 2V4AB0=V, 7=0G=> <5=HV, =V6 @50;L=V, =0 25;8:8E 2V4AB0=OE 2V4 F5=B@C BO6V==O. >6;82>, I> V F5 28:;8:0T 5D5:B A8;L=VH>3> 3@02VB0FV9=>3> ?>;O, =V6 70 B5>@VTN BO6V==O LNB>=0, 0 B8< A0<8< V E81=C ?>B@51C C A5A2VBV B5<=>W =510@V>==>W <0B5@VW. ;O 3@0=8G=> >AB83;8E 307V2, C O:8E EMBED Equation.3 ( EMBED Equation.3 , EMBED Equation.3 ), 0  EMBED Equation.3  (2V4?>2V4=> 4> 70:>=C >9;O-0@V>BB0 [0=4A15@3, 1948]), O: 2 ", B0: V 2 " 1C45<> <0B8:  EMBED Equation.3 . 2V4A8:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 . 4=0: 65 4;O @50;L=8E 307V2: EMBED Equation.3, EMBED Equation.3, 45:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , 0: EMBED Equation.3 EMBED Equation.3  <>;O@=89 >1'T<, B>G=5 7=0G5==O O:>3> <>65 1CB8 G8A5;L=> 287=0G5=> 7 C<>28  EMBED Equation.3 . , >B65, 3@0=8G=> >AB83;8< 307>< <>65 1CB8 ;8H5 28@>465=89 307, C O:>3>  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  ( EMBED Equation.3 ),  EMBED Equation.3 . ;O B0:>3> 3@0=8G=> >AB83;>3> 28@>465=>3> 307C ( EMBED Equation.3 ,  EMBED Equation.3 ) >B@8<0=5 V=B53@0;L=5 @V2=O==O ?@89<5 =0ABC?=89 283;O4: EMBED Equation.3. >G5284L, F5 307 <V:@>>1'T:BV2 @5G>28=8, I> =5 270T<>4VNBL 5;5:B@><03=VB=>, 1> 2V= 1030B> 2 G><C T ?>4V1=8< 4> V450;L=>3> 307C.  28@>465==O 9>3> <>3;> AB0B8AO ;8H5 ?VA;O B>3>, O: 265 AD>@<C20;>AO 307>25 A:C?G5==O. &V;:>< <>6;82>, I> F5 A0<5 =59B@>==89 307, I> :>=45=AC202AO 2 =59B@>==C @V48=C [0=K;LG5=:>, 2004: 35; 2008b: 45]. ;O 3@0=8G=> >AB83;8E 307V2 B0:0 ?@>1;5<0 =5 VA=CT. 465 ?@8 1C4L-O:><C 7=0G5==V 307>2>3> ?0@0<5B@0  EMBED Equation.3  (=570;56=>3> 2V4 ?0@0<5B@V2 @V2=O==O 3@02VB0FV9=>3> ?>;O) <>6=0 70157?5G8B8 4;O :>6=>3> :>=:@5B=>3> 307C =5>1EV4=C :><1V=0FVN 7=0G5=L 2AVE G>B8@L>E 9>3> B5@<>48=0<VG=8E ?0@0<5B@V2 (p, V, T, S) 287=0G5==O< 2V4?>2V4=>W O: W9, B0: V  EMBED Equation.3  (0, >B65, V ?>?@02:0<  EMBED Equation.3  B0  EMBED Equation.3 ) :><1V=0FVW <0B5<0B8G=8E >GV:C20=L G>B8@L>E ?@8E>20=8E B5@<>48=0<VG=8E ?0@0<5B@V2 k, l, m B0 n. /:I> 6 ?@>0=0;V7C20B8 AC:C?=>ABV 270T<>2V4?>2V4=8E :><1V=0FV9 O2=8E B0 ?@8E>20=8E B5@<>48=0<VG=8E ?0@0<5B@V2, B> =0 >A=>2V FL>3> <>6CBL 1CB8 287=0G5=V V=482V4C0;L=V AB0;V 307C  EMBED Equation.3 ,  EMBED Equation.3  V  EMBED Equation.3 . @8 FL><C, 728G09=> 6, A;V4 2@0E>2C20B8, I> ?>?@02:8  EMBED Equation.3  V  EMBED Equation.3  ;8H5 ?@81;87=> 2V4>1@060NBL 2;0AB82>ABV @50;L=8E 307V2 C =5H8@>:8E 4V0?07>=0E 2V4ABC?V2 2V4 AB0=40@B=8E 7=0G5=L B8A:C V B5<?5@0BC@8:  EMBED Equation.3 . 4=0: 65 28:>@8AB0==O C G>B8@8V<?C;LAV " 5=B0;L?VW 70<VABL 2V;L=>W 5=5@3VW V11A0 AB028BL ?V4 AC<=V2 2V4?>2V4=VABL 9>3> =56>@AB:V9 ! :207V@V2=>206=> E>;>=CG>W @5G>28=8. "0 9, O: =0< 265 4>25;>AO ?5@5:>=0B8AO, I> B5@<>48=0<VG=V ?0@0<5B@8 @5G>28=8 ?>-@V7=><C ?>2>4OBLAO, 7<V=NNG8AL C G0AV B0 2 ?@>AB>@V. /:I> 4;O @50;L=8E 307V2 2 >4=><VA=8E 5:A?5@8<5=B0E 4>2>48BLAO 22>48B8 048B82=V ?>?@02:8 =0 <>;O@=89 >1'T< V B0: A0<> 5:AB5=A82=89 ?0@0<5B@  EMBED Equation.3 , B> G5@57  EMBED Equation.3  ?>?@02:8 4;O @50;L=8E 307V2, I> <VABOBLAO =0 @V7=8E @04V0;L=8E 2V4AB0=OE 2V4 F5=B@C BO6V==O, <>6;82>, ?>B@V1=> 1C45 22>48B8 4;O V=B5=A82=>3> ?0@0<5B@0  EMBED Equation.3  B0 V=H8E V=B5=A82=8E B5@<>48=0<VG=8E ?0@0<5B@V2. @8 FL><C FV ?>?@02:8 <>6CBL 1CB8 =5 048B82=8<8, 0 <C;LB8?;V:0B82=8<8. > B>3> 6, G5@57 @5;OB82VABAL:C V=20@V0=B=VABL B5@<>48=0<VG=8E ?0@0<5B@V2 V E0@0:B5@8AB8: @5G>28=8 @V2=O==O 3@02VB0FV9=>3> ?>;O 4;O 1C4L-O:8E :207V@V2=>206=> E>;>=CG8E 0AB@>=><VG=8E >1'T:BV2, I> @CE0NBLAO >@1VB0<8 =02:>;> 30;0:B8G=8E F5=B@V2 BO6V==O 7V H284:>ABO<8 v, <>6CBL 1CB8 AD>@<>20=V ;8H5 =0 >A=>2V @5;OB82VABAL:V =5V=20@V0=B=8E 2=CB@VH=L>O45@=8E "-?0@0<5B@V2. 4=0: 284 F8E @V2=O=L 1030B> 2 G><C T D>@<0;L=> ?>4V1=8< 4> @V2=O=L 3@02VB0FV9=>3> ?>;O, I> @C=BCNBLAO =0 B5@<>48=0<VG=8E ?0@0<5B@0E @5G>28=8: EMBED Equation.3,EMBED Equation.3EMBED Equation.3, 45:  EMBED Equation.3   7=0G5==O 2 " 3@02VB0FV9=>3> @04VCA0 @5G>28=8, I> >E>?;5=0 AD5@>N 7 @04VCA>< r. 2V4:8 0=0;>3VG=> >B@8<CT<> @04V0;L=V @>7?>4V;8 7=0G5=L ?0@0<5B@V2 b B0 a: EMBED Equation.3 EMBED Equation.3. 16. >@V2=O==O 2V4>1@065==O DV78G=>W @50;L=>ABV 2 " V 2 " 0@48=0;L=0 2V4<V==VABL " 2V4 " ?>;O30T C 28:>@8AB0==V 2 B5=7>@V 5=5@3VW-V<?C;LAC ?>70O45@=8E B5@<>48=0<VG=8E E0@0:B5@8AB8: @5G>28=8 4;O >?8AC BV;L:8 WW :207V@V2=>206=>3> @CEC, ;8H5 70 O:>3> V <0T <VAF5 270T<=0 :>@5;OFVO ?>70O45@=8E B0 2=CB@VH=L>O45@=8E E0@0:B5@8AB8: @5G>28=8. ;O >?8AC 6 @CEC 70 V=5@FVTN 2 " 28:>@8AB>2CNBLAO BV;L:8 3V?>B5B8G=V 2=CB@VH=L>O45@=V 3@02VB5@<>48=0<VG=V E0@0:B5@8AB8:8 @5G>28=8. 0 =5>1EV4=VABL FL>3> 2:07CT =570;56=VABL @CEC 0AB@>=><VG=8E >1'T:BV2 70 A2>W<8 AB0FV>=0@=8<8 >@1VB0<8 2V4 B5@<>48=0<VG=8E 2;0AB82>AB59 WE=L>W @5G>28=8 0, >B65, V 2V4ACB=VABL 2V4?>2V4=>W FL><C @CEC :>@5;OFVW 2=CB@VH=L>O45@=8E 3@02VB5@<>48=0<VG=8E E0@0:B5@8AB8: V7 ?>70O45@=8<8 B5@<>48=0<VG=8<8 E0@0:B5@8AB8:0<8 @5G>28=8. !0<5 F5 V 4>72>;OT ?@8=F8?>2> C=8:=CB8 ?>B@518 C A5A2VBV =510@V>==>W B5<=>W <0B5@VW. # 0AB@>=><VG=8E BV;, >4=>@V4=0 =09?@>ABVH0 @V4:0 G8 307>?>4V1=0 @5G>28=0 O:8E ?5@51C20T C AB0=V O: <5E0=VG=>W, B0: V B5?;>2>W @V2=>2038, G0AB>B8 270T<>4VW  EMBED Equation.3  V  EMBED Equation.3  AB@>3> 287=0G0NBLAO 7=0G5==O<8 B8A:C V B5<?5@0BC@8 2 @5G>28=V. # B25@48E B0 C @V4:8E 0AB@>=><VG=8E BV;, 0 B0:>6 V C 307>?>4V1=>W @5G>28=8, I> ?>:@820T WE 01> =5 ?5@51C20T C AB0=V B5@<>48=0<VG=>W @V2=>2038, 2>=8 <>6CBL 70;560B8 B0:>6 V 2V4 25;8G8=8 3@02VB0FV9=>3> 28?5@5465==O 52>;NFV9=>3> 7=865==O WE 2=CB@VH=L>O45@=>W 5=5@3VW. , >B65, O:I> C ACFV;L=>W >4=>@V4=>W 307>?>4V1=>W @5G>28=8 =54>??;5@V2AL:89 G5@2>=89 7AC2 A?5:B@C 28?@><V=N20==O T =5<>218 AC2>@> B5@<>48=0<VG=8<, B> C ?>H0@>2> >4=>@V4=>W 307>?>4V1=>W @5G>28=8, I> ?>:@820T B25@45 01> @V4:5 O4@>, 2V= 265 T 3@02VB0FV9=>-B5@<>48=0<VG=8<.  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"><C-B>, V3=>@CTBLAO V =0O2=VABL 2=CB@VH=L>3> <0AHB01=>3> G8==8:0 C @5G>28=8. 0 F5 2:07CT 28:>@8AB0==O 2 " 2 O:>ABV 3@02VB0FV9=>3> ?>B5=FV0;C DC=:FVW =5 2V4 G0AB>B8 270T<>4VW, 0 2V4 7030;L=>W 4;O 2AVE @5G>28= ?A524>20:CC<=>W :>>@48=0B=>W H284:>ABV A2VB;0. # 2;0A=8E ?@>AB>@0E, I> ?@8B0<0==V @5G>28=0<, 7<V=8 2V4AB0=59 5;5:B@><03=VB=>W 270T<>4VW ?@8=F8?>2> =5 A?>AB5@V30NBLAO C ". @0E>2CTBLAO ;8H5 ?@8ACB=O C D>=>2><C 52:;V4>2><C ?@>AB>@V ?@>AB>@>20 =5>4=>@V4=VABL 7=0G5=L FVTW 2V4AB0=V C >4=>@V4=>W @5G>28=8 (0, >B>6, V 7=0G5=L WW 7>2=VH=L>3> <0AHB01=>3> G8==8:0), I> ?@872>48BL 4> :@828=8 2;0A=>3> ?@>AB>@C @5G>28=8. 0 F5 2:07CT 28:>@8AB0==O 2 " 2 O:>ABV 3@02VB0FV9=>3> ?>B5=FV0;C DC=:FVW =5 2V4 G0AB>B8 270T<>4VW, 0 2V4 7030;L=>W 4;O 2AVE @5G>28= :>>@48=0B=>W ?A524>20:CC<=>W (3@02V10@8G=>W) H284:>ABV A2VB;0. @8 04V010B=><C 7@>AB0==V B8A:C C 307V @>7<V@ 9>3> :20=B>2>3> 5B0;>=C 4>268=8 2A5-B0:8 7<5=HCTBLAO C "-! A2VBC ;N459, I> >4=0: ?@>O2;OTBLAO ;8H5 2 2V4?>2V4=><C 71V;LH5==V 2=CB@VH=L>3> <0AHB01=>3> G8==8:0  EMBED Equation.3  V, B><C, =5 ?@872>48BL 4> 7<V=8 :@828=8 ?@>AB>@C, 70?>2=5=>3> 307><. '5@57 F5 B0 G5@57 ?@8B0<0==C " ?@8=F8?>2C =5A?>AB5@56;82VABL 7<V=N20=>ABV 2V4AB0=59 270T<>4VW <V:@>>1'T:BV2 @5G>28=8, I> 287=0GCNBL C " @>7<V@ WW :20=B>2>3> 5B0;>=C 4>268=8, 1C45 71V;LHC20B8AO 2V4?>2V4=5 FL><C 307C 3@02V:20=B>25 7=0G5==O <5B@8G=>W T<=>ABV 10;>=C, I> 2<VICT 307. "0:8< G8=><, 7024O:8 =0O2=>ABV 2V4'T<=>3> 72>@>B=>3> 72'O7:C [0=K;LG5=:>, 1994a; 2005c; 2008: 19; 2008a] 3@02V:20=B>25 <5B@8G=5 7=0G5==O <>;O@=>3> >1'T<C 307C 1C45 7<5=HC20B8AO =5 B0: H284:>, O: B5@<>48=0<VG=5 <5B@8G=5 7=0G5==O 9>3> <>;O@=>3> >1'T<C. "0:5 3@02VB0FV9=5 A:>@>G5==O @>7<V@C :20=B>2>3> 5B0;>=C 4>268=8, I> 2V41C20TBLAO =0 @V2=V <V:@>>1'T:BV2 @5G>28=8, T 0=0;>3VG=8< CO2=><C @5;OB82VABAL:><C A:>@>G5==N @>7<V@C 5B0;>=C 4>268=8 C74>26 =0?@O<:C @CEC @5G>28=8. 4=0: G5@57 =0O2=VABL C :>6=>W @5G>28=8 2;0A=>W <5B@8:8 ?@>AB>@C 2 WW 3@02V:20=B>2V9 ! =5 <>6;82> 225AB8 4;O 2AVE B0:8E ! T48=89 ?@>ABV@ [0=K;LG5=:>, 2008: 19; 2008a]. "><C C A2VBV ;N459 B0 2 " 28:>@8AB>2CTBLAO 7>2AV< =5 3@02V:20=B>25, 0 B5@<>48=0<VG=5 <5B@8G=5 7=0G5==O <>;O@=>3> >1'T<C @5G>28=8. =0;>3VG=> :20=B>28< 3>48==8:0<, :20=B>2V V, 27030;V, 1C4L-O:V @5G>28==V 5B0;>=8 4>268=8 <>6;82> 28:>@8AB>2C20B8 C T-! 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F5 2V4=>A8BLAO V 4> 7H820==O WE B0:>6 7 DV:B82=8<8 @>72'O7:0<8 4;O DV78G=> =5@50;L=>3> 01A>;NB=> ?>@>6=L>3> ?@>AB>@C (?@>AB>@>2> =5>4=>@V4=>3> ?A524>20:CC<C) [0=K;LG5=:>, 2008: 19; 2008a]. "0:8< G8=><, 48D5@5=FV0;L=V @V2=O==O 3@02VB0FV9=>3> ?>;O " 287=0G0NBL >4=>7=0G=> ;8H5 3@04VT=B8 ?>B5=FV0;V2 (0 =5 A0<V ?>B5=FV0;8 3@02VB0FV9=>3> ?>;O, I> <>6CBL 1CB8 :0;V1@C20;L=> ?5@5B2>@5=8<8). 4=0: 2 =5 ?>@>6=L><C ?@>AB>@V 2>=8 2A5 6 ?@8=F8?>2> 4>72>;ONBL ?5@59B8 2V4  EMBED Equation.3  4>  EMBED Equation.3 ,  EMBED Equation.3  B0  EMBED Equation.3 . , >B65, FV ?@>1;5<8 C " <>6CBL 1CB8 @>72'O70=8<8. ;O FL>3> =5>1EV4=> V 4>AB0B=L> 287=0G8B8 7 @V2=O=L B5@<>48=0<V:8 7=0G5==O  EMBED Equation.3  B0  EMBED Equation.3  ;8H5 2 1C4L-O:V9 >4=V9 B>GFV @5G>28=8, I> ?5@51C20T C @V2=>206=><C " AB0=V. ">4V ?@>AB>@>2V @>7?>4V;8  EMBED Equation.3  B0  EMBED Equation.3  2 1C4L-O:V9 @5G>28=V <>6CBL 1CB8 287=0G5=V 70 4>?><>3>N @VH5=L @V2=O=L ". ;O FL>3> 7=04>18BLAO 28:>@8AB0==O 2V4?>2V4=>3>  EMBED Equation.3  B0  EMBED Equation.3  7=0G5==O :>>@48=0B=>W H284:>ABV A2VB;0  EMBED Equation.3 , 0 B0:>6 V 2V4><>W 70;56=>ABV  EMBED Equation.3  2V4  EMBED Equation.3  01> 6 2V4 2V4?>2V4=8E  EMBED Equation.3  B5@<>48=0<VG=8E ?0@0<5B@V2 @5G>28=8. <5=H5==O 4>268= 5;5:B@>==8E >@1VB 2 0B><0E 0, >B65, V 4>268= E28;L 5<VAV9=8E 28?@><V=N20=L C D>B>AD5@V 307C, I> :207V@V2=>206=> AB8A:0TBLAO, <0965 ?>2=VABN :><?5=ACTBLAO 7<5=H5==O< H284:>ABV ?>H8@5==O 28?@><V=N20==O 2 =L><C. &5 ?@>O2;OTBLAO 2 ?@0:B8G=V9 =570;56=>ABV 2V4 B5@<>48=0<VG=8E ?0@0<5B@V2 @5G>28=8 G0AB>B 5<VAV9=>3> 28?@><V=N20==O 0, >B65, V 2 7=5206;82> <0;><C CH8@5==V A?5:B@0;L=8E ;V=V9. 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F5 4>1@5 C73>46CTBLAO 7 B8<, I> 3@02VB0FV9=5 ?>;5 D>@<CT BV;L:8 3@04VT=B8 ?0@0<5B@V2 V E0@0:B5@8AB8: @5G>28=8 V 2V4?>2V4=>3> W< 3@02VB0FV9=>3> ?>B5=FV0;C, 7=0G5==O O:>3> <>65 7<V=N20B8AO ;8H5 @07>< 7V 7<V=>N WW ?0@0<5B@V2 V E0@0:B5@8AB8:. "><C-B>, 70 28=OB:>< V=5@B=>W 2V;L=>W 5=5@3VW V 5:2V20;5=B=>W W9 V=5@B=>W <0A8 2AV V=HV 4V9A=> <5B@8G=V <5E0=VG=V B0 B5@<>48=0<VG=V ?0@0<5B@8 B0 E0@0:B5@8AB8:8 @5G>28=8 =5 70;560BL 2V4 ?>:070=L 3@02V:20=B>28E 3>48==8:V2 V, >B65, T B5<?>@0;L=> V=20@V0=B=8<8. "5@<>48=0<VG=0 2=CB@VH=O 5=5@3VO, I> A:;040TBLAO 7 ;03@0=6V0=0 728G09=>W 2=CB@VH=L>W 5=5@3VW A?>:>N (<C;LB8?;V:0B82=>W A:;04>2>W) B0 048B82=>W :><?5=A0FVW <C;LB8?;V:0B82=>3> WW ?@54AB02;5==O, D0:B8G=> T ?>2=>N 5=5@3VTN @5G>28=8, 1> 2:;NG0T 2 A515 =02VBL 282V;L=5=C :V=5B8G=C 5=5@3VN WW @CEC. "5@<>48=0<VG=0 2=CB@VH=O 5=5@3VO @5G>28=8 T >4=0:>2>N 2 CAVE ! BV;, I> @CE0NBLAO 2V4=>A=> =5W 70 V=5@FVTN.  A0<5 F5 T 70?>@C:>N ;>@5=F-V=20@V0=B=>ABV 2AVE B5@<>48=0<VG=8E ?>B5=FV0;V2 V ?0@0<5B@V2 @5G>28=8. "0: O: @CE @5G>28=8 AC?@>2>46CTBLAO 2A51VG=8< :>=D>@<=>-:0;V1@C20;L=8< A0<>A:>@>G5==O< WW @>7<V@V2 C D>=>2><C 52:;V4>2><C ?@>AB>@V A5A2VBC, B> ?;8= 2;0A=>3> G0AC BV;0, I> @CE0TBLAO 70 V=5@FVTN, 7>2AV< =5 A?>2V;L=NTBLAO, 0 =02?0:8 70;8H0TBLAO =57<V==8<, =572060NG8 =0 =0O2=VABL 3@02VB0FV9=>3> 7=865==O B5<?C ?;8=C 2;0A=>3> G0AC C =02:>;8H=VE =5@CE><8E >1'T:BV2. $0:B8G=> @CE @5G>28=8, O: V WW 3@02VB0FV9=5 A0<>AB8A:0==O C D>=>2><C 52:;V4>2><C ?@>AB>@V A5A2VBC, ?@872>48BL 4> 28?5@5465==O =5N =5A?>AB5@56;82>3> 2 A2VBV ;N459 52>;NFV9=>3> A0<>AB8A:0==O C A5A2VBV C<>2=>W =5@CE><>W @5G>28=8. "><C-B> 282V;L=5==O :V=5B8G=>W 5=5@3VW V AC?@>2>46CTBLAO 702648 7<5=H5==O< O: 3@0=8G=>W H284:>ABV @CEC @5G>28=8 (B>B>6=>W :>>@48=0B=V9 H284:>ABV A2VB;0 @5G>28=8 2 "), B0: V WW V=5@B=>W 2V;L=>W 5=5@3VW. # @V7=8E DV78G=8E ?@>F5A0E =5>4=0:>2> 72'O7CTBLAO 2=CB@VH=O 5=5@3VO @5G>28=8.  B><C-B> <8 <0T<> 2 =8E V @V7=><0=VB=V 2V;L=V 5=5@3VW. 8:;8:0=0 @CE>< @5G>28=8 70 V=5@FVTN 7<V=0 WW V=5@B=>W 2V;L=>W 5=5@3VW, O: V WW 52>;NFV9=5 7<5=H5==O 2 !! , 157?>A5@54=L> =5 2?;820T =0 B5@<>48=0<VG=V ?0@0<5B@8 @5G>28=8, I> 7<V=NNBLAO BV;L:8 2 B5@<>48=0<VG=8E ?@>F5A0E.  B><C-B> 2>=0 T ?@8=F8?>2> =5A?>AB5@56;82>N C 2;0A=8E ! @5G>28=8, 0=0;>3VG=> =5A?>AB5@56;82>ABV 2 =8E O: 52>;NFV9=>3> B0: V A?@8G8=5=>3> @CE>< 7<5=H5==O <>;O@=>3> >1'T<C @5G>28=8 2 AC?CB=V9 @>7H8@=><C A5A2VBC !. 5A?>AB5@56;828< 157?>A5@54=L> C 2;0A=8E ! @5G>28=8 T V 3@02VB0FV9=5 7<5=H5==O <>;O@=>3> >1'T<C @5G>28=8 @07>< 7 =01;865==O< 4> F5=B@C BO6V==O. ;5 6 70 =0O2=VABL 9>3> 2 52:;V4>2><C ?@>AB>@V !!  2A5 6 B0:8 <>6;82> AC48B8 G5@57 =0O2=VABL 3@02VB0FV9=>W :@828=8 2;0A=>3> ?@>AB>@C @5G>28=8. "0 9 ?@> =0O2=VABL 52>;NFV9=>3> A0<>AB8A:0==O @5G>28=8 <8 B0:>6 <>65<> AC48B8 >?>A5@54:>20=> 7024O:8 =0O2=>ABV =5 BV;L:8 ?@>F5AC @>7H8@5==O A5A2VBC 2 ! A2VBC ;N459 0;5 V 2V4?>2V4=>W 9><C 3;>10;L=>W 3@02VB0FV9=>-52>;NFV9=>W 3@04VT=B=>W ;V=78 (). > B>3> 6 =5 BV;L:8 52>;NFV9=0, 0 9 3@02VB0FV9=0 V :V=5<0B8G=0 45D>@<0FVW <V:@>>1'T:BV2 @5G>28=8 2 D>=>28E ?@>AB>@0E (D>@<CNGV ) T V7>B@>?=8<8.  B><C 2 ", O: ?@028;>, 28:>@8AB>2CNBLAO ;8H5 V7>B@>?=V :>>@48=0B8. 2>;NFV9=89 ?@>F5A A0<>AB8A:0==O 2V4?>2V4=8E @5G>28=V A?V@0;L=>E28;L>28E CB2>@5=L D>@<CT C A5A2VBV 7>2AV< =5 728G09=C, 0 A0<5 3@04VT=B=C 3;>10;L=C 3@02VB0FV9=C ;V=7C [0=K;LG5=:>, 2009a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http://pavlo-danylchenko.narod.ru/docs/Ketm.pdf" http://pavlo-danylchenko.narod.ru/docs/Ketm.pdf. 0=K;LG5=:>, 02;>: 1994, 0;81@>2>G=>5 >1>A=>20=85 A?5F80;L=>9 B5>@88 >B=>A8B5;L=>AB8. 0;81@>2>G=>-M2>;NF8>==0O B5>@8O <8@>740=8O, 1, V==8FO, 10-21.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/Ketm.pdf" http://pavlo-danylchenko.narod.ru/docs/Ketm.pdf. 0=K;LG5=:>, 02;>: 1994, A524>8=5@F80;L=> A68<0NI85AO A8AB5<K >BAG5B0 :>>@48=0B 8 2@5<5=8. 0;81@>2>G=>-M2>;NF8>==0O B5>@8O <8@>740=8O, 1, V==8FO, 22-51.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/Ketm.pdf" http://pavlo-danylchenko.narod.ru/docs/Ketm.pdf. 0=K;LG5=:>, 02;>: 1994, 565AB:85 A8AB5<K >BAG5B0 :>>@48=0B 8 2@5<5=8, A68<0NI85AO 2 ?@>AB@0=AB25 8=:>2A:>3>. 0;81@>2>G=>-M2>;NF8>==0O B5>@8O <8@>740=8O, 1, V==8FO, 52-77.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/Ketm.pdf" http://pavlo-danylchenko.narod.ru/docs/Ketm.pdf. 0=K;LG5=:>, 02;>: 1994a, A=>2K :0;81@>2>G=>-M2>;NF8>==>9 B5>@88 8@>740=8O. V==8FO (1994); 8W2: V" (2005),  HYPERLINK "http://n-t.org/tp/ns/ke.htm" http://n-t.org/tp/ns/ke.htm; V==8FO (2006). HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/Osnovy_Rus.html"http://pavlo-danylchenko.narod.ru/docs/Osnovy_Rus.html. 0=K;LG5=:>, 02;>: 2004, @8@>40 @5;OB828ABA:>3> A>:@0I5=8O 4;8=K. 0;81@>2>G=>-M2>;NF8>==0O 8=B5@?@5B0F8O !" 8 ". V==8FO: . ;0AN:, 3-16. 0=K;LG5=:>, 02;>: 2004,  2>7<>6=>ABOE D878G5A:>9 =5@50;87C5<>AB8 :>A<>;>38G5A:>9 8 3@028B0F8>==>9 A8=3C;O@=>AB59 2 >1I59 B5>@88 >B=>A8B5;L=>AB8. 0;81@>2>G=>-M2>;NF8>==0O 8=B5@?@5B0F8O !" 8 ". V==8FO: . ;0AN:, 35-81; V==8FO: >20 :=830, 2008b, 45-95.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/Possibilities_Rus.html" http://pavlo-danylchenko.narod.ru/docs/Possibilities_Rus.html. 0=K;LG5=:>, 02;>: 2004, $5=><5=>;>38G5A:>5 >1>A=>20=85 D>@<K ;8=59=>3> M;5<5=B0 H20@FH8;L4>20 @5H5=8O C@02=5=89 3@028B0F8>==>3> ?>;O ". 0;81@>2>G=>-M2>;NF8>==0O 8=B5@?@5B0F8O !" 8 ". V==8FO: . ;0AN:, 82-98; V==8FO: >20 :=830, 2008b, 96-112. http://pavlo-danylchenko.narod.ru/docs/Schwarzschild_Rus.html. 0=K;LG5=:>, 02;>: 2004b, !?8@0;L=>2>;=>20O ?@8@>40 M;5<5=B0@=KE G0AB8F. 0B5@80;K 564C=0@>4=>9 =0CG=>9 :>=D5@5=F88  . . 20=5=:>  2K40NI89AO D878:-B5>@5B8:, ?5403>3 / @54. .. C45=:>. >;B020: #, 44-55.  HYPERLINK "http://www.sciteclibrary.ru/rus/catalog/pages/8276.html" http://www.sciteclibrary.ru/rus/catalog/pages/8276.html. 0=K;LG5=:>, 02;>: 2005, 5>1KG=0O B>?>;>38O G@572KG09=> <0AA82=KE =59B@>==KE 72574 8 :2070@>2. "578AK 4>:;04>2 =0 XXII :>=D5@5=F88 :BC0;L=K5 ?@>1;5<K 2=530;0:B8G5A:>9 0AB@>=><88, CI8=>, 16-18 8N;O 2005.  HYPERLINK "http://prao.ru/conf/22_conf/rus/thesis.html" http://prao.ru/conf/22_conf/rus/thesis.html; 8W2: V".  HYPERLINK "http://n-t.ru/tp/ng/nt.htm" http://n-t.ru/tp/ng/nt.htm. 0=K;LG5=:>, 02;>: 2005a, $878G5A:0O ACI=>ABL A8=3C;O@=>AB59 2 H20@FH8;L4>2>< @5H5=88 C@02=5=89 3@028B0F8>==>3> ?>;O >1I59 B5>@88 >B=>A8B5;L=>AB8. Sententiae, A?5F2K?CA: 1 $V;>A>DVO V :>A<>;>3VO, V==8FO: # !#-V==8FO, 95-104.  HYPERLINK "http://www.bazaluk.com/journals/journal/3.html" http://www.bazaluk.com/journals/journal/3.html. 0=K;LG5=:>, 02;>: 2005b, !>2<5AB=>5 @5H5=85 C@02=5=89 3@028B0F8>==>3> ?>;O " 8 B5@<>48=0<8:8 4;O 8450;L=>9 684:>AB8 2 A>AB>O=88 B5?;>2>3> @02=>25A8O. "57. 4>:;. XII-9 >AA89A:>9 3@028B0F8>==>9 :>=D. 20-26 8N=O, @54. 3=0BL52 ..., 070=L: , 39-40. 0=K;LG5=:>, 02;>: 2006, 5;OB828ABA:0O B5@<>48=0<8:0 A >@5=F-8=20@80=B=K<8 M:AB5=A82=K< >1J5<><. Sententiae, A?5F2K?CA: 2 $V;>A>DVO V :>A<>;>3VO, V==8FO: # !#-V==8FO, 27-41.  HYPERLINK "http://www.bazaluk.com/journals/journal/6.html" http://www.bazaluk.com/journals/journal/6.html. 0=K;LG5=:>, 02;>: 2008, !>2<5AB=>5 @5H5=85 C@02=5=89 3@028B0F8>==>3> ?>;O " 8 B5@<>48=0<8:8 4;O 8450;L=>9 684:>AB8 2 A>AB>O=88 55 B5?;>2>3> @02=>25A8O. 2545=85 2 @5;OB828ABA:CN 3@028B5@<>48=0<8:C. V==8FO: >20 :=830, 4-18. HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/UnitedSolution_Rus.html"http://pavlo-danylchenko.narod.ru/docs/UnitedSolution_Rus.html. 0=K;LG5=:>, 02;>: 2008,  548=>9 ?@8@>45 B5@<>48=0<8G5A:8E 8 3@028B0F8>==KE A2>9AB2 25I5AB20. 2545=85 2 @5;OB828ABA:CN 3@028B5@<>48=0<8:C. V==8FO: >20 :=830, 19-59.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/UnitedNature.html" http://pavlo-danylchenko.narod.ru/docs/UnitedNature.html. 0=K;LG5=:>, 02;>: 2008, 5;OB828ABA:>5 >1>1I5=85 B5@<>48=0<8:8 A> AB@>3> M:AB5=A82=K< <>;O@=K< >1J5<><. 2545=85 2 @5;OB828ABA:CN 3@028B5@<>48=0<8:C. V==8FO: >20 :=830, 60.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/RelativisticGeneralization_Rus.html" http://pavlo-danylchenko.narod.ru/docs/RelativisticGeneralization_Rus.html. 0=K;LG5=:>, 02;>: 2008, 5G=0 ;8 A5;5==0O? 2545=85 2 @5;OB828ABA:CN 3@028B5@<>48=0<8:C. V==8FO: >20 :=830, 95-105.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/RelativThermodIntro.pdf" http://pavlo-danylchenko.narod.ru/docs/RelativThermodIntro.pdf. 0=K;LG5=:>, 02;>: 2008, 5;OB828ABA:85 7=0G5=8O @0480;L=KE :>>@48=0B 40;5:8E 0AB@>=><8G5A:8E >1J5:B>2 @0AH8@ONI59AO A5;5==>9. 2545=85 2 @5;OB828ABA:CN 3@028B5@<>48=0<8:C. V==8FO: >20 :=830, 106-128.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/RelativisticValues.html" http://pavlo-danylchenko.narod.ru/docs/RelativisticValues.html. 0=K;LG5=:>, 02;>: 2008a,  548=>9 ?@8@>45 B5@<>48=0<8G5A:8E 8 3@028B0F8>==KE A2>9AB2 25I5AB20. "578AK 4>:;04>2 =0 RUSGRAV-13, 23  28 8N=O. >A:20: #, 109 0=K;LG5=:>, 02;>: 2008b, 5;OB828ABA:>5 A>:@0I5=85 4;8=K 8 3@028B0F8>==K5 2>;=K. !25@EA25B>20O A:>@>ABL @0A?@>AB@0=5=8O. 0;81@>2>G=>-M2>;NF8>==0O 8=B5@?@5B0F8O !" 8 ". V==8FO: >20 :=830, 3-23. http://pavlo-danylchenko.narod.ru/docs/rsd.html. 0=K;LG5=:>, 02;>: 2008b, 0;81@>2>G=0O 8=B5@?@5B0F8O !". 0;81@>2>G=>-M2>;NF8>==0O 8=B5@?@5B0F8O !" 8 ". V==8FO: >20 :=830, 24-37.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/Foundations_Rus.html" http://pavlo-danylchenko.narod.ru/docs/Foundations_Rus.html. 0=K;LG5=:>, 02;>: 2009, A=>2K @5;OB828ABA:>9 3@028B5@<>48=0<8:8. 0B5@V0;8 2A5C:@0W=AL:>3> A5<V=0@C V7 B5>@5B8G=>W B0 <0B5<0B8G=>W DV78:8. > 80-@VGGO ?@>D. ..!2V478=AL:>3>, "$ 2009. CFL:, 27 ;NB>3>  1 15@57=O, CFL:: 560 >;8=AL:89 C=V2., 75-79.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/SvidzinskySeminar.pdf" http://pavlo-danylchenko.narod.ru/docs/SvidzinskySeminar.pdf. 0=K;LG5=:>, 02;>: 2009, 1>1I5==K5 @5;OB828ABA:85 ?@5>1@07>20=8O. 0B5@V0;8 2A5C:@0W=AL:>3> A5<V=0@C V7 B5>@5B8G=>W B0 <0B5<0B8G=>W DV78:8. > 80-@VGGO ?@>D. ..!2V478=AL:>3>, "$ 2009. CFL:, 27 ;NB>3>  1 15@57=O, CFL:: 560 >;8=AL:89 C=V2., 79.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/GeneralizedTransformations.htm" http://pavlo-danylchenko.narod.ru/docs/GeneralizedTransformations.htm. 0=K;LG5=:>, 02;>: 2009a, ;>10;L=0O 3@028B0F8>==>->?B8G5A:0O 3@0485=B=0O ;8=70 2 @0AH8@ONI59AO A5;5==>9. @>3@0<<0 8 B578AK 4>:;04>2 IV-9 0<>2A:>9 <564C=0@>4=>9 :>=D5@5=F88 2 45AA5. 17-23.08.2009,20/1.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/GravitationalLense.htm" http://pavlo-danylchenko.narod.ru/docs/GravitationalLense.htm. 0=K;LG5=:>, 02;>: 2009a, A=>2K @5;OB828ABA:>9 3@028B5@<>48=0<8:8. @>3@0<<0 8 B578AK 4>:;04>2 IV-9 0<>2A:>9 <564C=0@>4=>9 :>=D5@5=F88 2 45AA5. 17-23.08.2009, !. 20/2.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/Gravithermodynamics.pdf" http://pavlo-danylchenko.narod.ru/docs/Gravithermodynamics.pdf. 0=K;LG5=:>, 02;>: 2010, A=>2K @5;OB828ABA:>9 3@028B5@<>48=0<8:8. 0C:. 2VA=8: >;8=AL:>3> C=V2., 6, 64-71.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/VisnykVolyn.pdf" http://pavlo-danylchenko.narod.ru/docs/VisnykVolyn.pdf. 0=K;LG5=:>, 02;>: 2010a, A=>2K @5;OB828ABA:>9 3@028B5@<>48=0<8:8. $V;>A>DVO V :>A<>;>3VO 2010, >;B020: >;B02AL:89 ;VB5@0B>@, 9, 38-50,  HYPERLINK "http://ispcjournal.org/journals/2010/2010-5.pdf" http://ispcjournal.org/journals/2010/2010-5.pdf. 0=K;LG5=:>, 02;>: 2014, !?8@0;L=>2>;=>20O <>45;L A5;5==>9. 0B5@V0;8 2A5C:@0W=AL:>3> A5<V=0@C V7 B5>@5B8G=>W B0 <0B5<0B8G=>W DV78:8. > 85-@VGGO ?@>D. ..!2V478=AL:>3>, "$ 2014. CFL:, 27 ;NB>3>  1 15@57=O, CFL:: 560-@C: >;8=AL:89 C=V2., 21-26.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/spiralwaveuniverse.html" http://pavlo-danylchenko.narod.ru/docs/spiralwaveuniverse.html. 0=8;LG5=:>, 02;>: 2020, A=>28 @5;OB82VABAL:>W 3@02VB5@<>48=0<V:8. A=>28 B0 =0A;V4:8 @5;OB82VABAL:>W 3@02VB5@<>48=0<V:8. V==8FO: >20 :=830, 5-84.  HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/FoundationRGTDUkr.pdf" http://pavlo-danylchenko.narod.ru/docs/FoundationRGTDUkr.pdf. 0=8;LG5=:>, 02;>: 2020, "5>@5B8G=V ><0=8 V D0=B><=V ACB=>ABV 2 0AB@>=><VW, :>A<>;>3VW B0 DV78FV. A=>28 B0 =0A;V4:8 @5;OB82VABAL:>W 3@02VB5@<>48=0<V:8. V==8FO: >20 :=830, 85-128,  HYPERLINK "https://elibrary.com.ua/m/book//download/34/3755" https://elibrary.com.ua/m/book//download/34/3755. 0=8;LG5=:>, 02;>: 2021, "5>@5B8G=V ><0=8 V D0=B><=V ACB=>ABV 2 0AB@>=><VW, :>A<>;>3VW B0 DV78FV. 3-T V=B5@=5B-2840==O, V==8FO.  HYPERLINK "https://elibrary.com.ua/m/articles//download/11790/3779" https://elibrary.com.ua/m/articles//download/11790/3779. <8B@852, ;5:A0=4@: 2005, #?@02;O5<0O 3@028B0F8O. .: >2K9 F5=B@.  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Van Kampen, N.G.: 1968, Relativistic Thermodynamics of Moving Systems. Phys. Rev., 173, 295-301. Verlinde, Erik: 2010, On the Origin of Gravity and the Laws of Newton.  HYPERLINK "https://arxiv.org/abs/1001.0785" https://arxiv.org/abs/1001.0785. Weinberg, David H.: 2010, From the Big Bang to Island Universe: Anatomy of a Collaboration. Ohio State University Department of Astronomy. June 2010, Narrative, edited by J. Phelan.  HYPERLINK "https://arxiv.org/pdf/1006.1013.pdf" https://arxiv.org/pdf/1006.1013.pdf. Abstracts FOUNDATIONS OF RELATIVISTIC GRAVITHERMODYNAMICS The cardinal difference between relativistic gravithermodynamics (RGTD) and general relativity (GR) is that in RGTD the extranuclear thermodynamic characteristics of matter are used in the tensor of energy-momentum to describe only its quasiequilibrium motion. For the description of the inertial motion in RGTD only the hypothetical intranuclear gravithermodynamic characteristics of matter are used. Exactly this fact allows avoid the necessity of nonbarionic dark matter in the Universe in principle. Evolutionary self-contraction of microobjects of lower layers of gravithermodynamically bonded matter outpaces the similar self-contraction of its upper layers. This is the exact reason of the curvature of intrinsic space of matter. That is why gravitational field itself should be primarily considered as the field of spatial inhomogeneity of evolutionary decreasing of the size of matter microobjects in the background Euclidean space of expanding Universe. In correspondence to this the gravitational field itself is the field of spatial inhomogeneity of gravithermodynamic state of dense matter of compact astronomical objects, as well as of strongly rarefied gas-dust matter of space vacuum. And, therefore, the gravitational field fundamentally cannot exist without matter. That is why it is not an independent form of matter. It is shown that equations of the gravitational field of GR should be considered as equations of spatially inhomogeneous gravithermodynamic state of only utterly cooled down matter. This matter can only be the hypothetical substances such as ideal gas, ideal liquid and the matter of absolutely solid body. The real matter will be inevitably cooling down for infinite time and never will reach the state that is described by the equations of gravitational field of the GR. Only conditional identity of inertial mass of moving matter to its gravitational mass only by gravity-quantum clock, which is located in the point, from which the matter started its inertial motion, and due to the usage of corrected value of gravitational constant in its pseudo-centric intrinsic frame of reference of spatial coordinates and time, is justified. This is related to the equivalence of inertial mass of matter to the Hamiltonian of its inert free energy, while the gravitational mass of matter is equivalent to the Lagrangian of its ordinary internal energy. It was proved that total energy of matter of inertially moving body is equal in all global gravithermodynamic frames of references of spatial coordinates and time (GT-FR) that are also inertially moving relatively to matter. The temporal invariance of not only the momentum but also of Lagrangian of ordinary internal energy and of equivalent to it gravitational mass of matter is justified. And that is precisely why there is the temporal invariance and a conform Lorentz-invariance of thermodynamic potentials and parameters in examined modification of transformations of the special theory of relativity (SR). Conformal relativistic transformations of increments of metrical spatial segments and metrical temporal intervals (instead of increments of coordinates and coordinate time of SR) were received. Exactly this fact allows avoid not only the twins paradox when twins are inertially moving but also the necessity of the dark energy in the Universe. It is also shown that the tensor of energy-momentum of matter (right side of the gravitational field equation) should be formed not being based on external thermodynamic parameters, but being based exactly on the intranuclear gravithermodynamic parameters. In this case the observed motion of astronomical objects of the galaxies is provided at arbitrary small density of mass of the matter on their periphery and, consequently, the presence of dark non-baryonic matter in the Universe is unnecessary. Of course, bodies free fall in gravitational field is an original realization of their tendency to increase the evolutionary self-contraction of microobjects of their matter, and the realization of the tendency of the whole gravitationally bonded inhomogeneous matter to the minimum of the integral values of its inert free energy and thermodynamic Gibbs free energy. It is shown that in case of bodies free fall the gravitational deceleration of the rate of their intrinsic time is completely compensated by the motion due to isotropic all-round conformal gauge self-contraction of the size of falling bodies in the background Euclidean space of the Universe. Clocks that fall free are inertially moving and, therefore, continue to count time at the same rate as when they were in the state of rest. Similarly, the rate of time of astronomical body is not changed in the process of its motion in elliptical orbit. The dilatation of intrinsic time of distant galaxies is also absent, which points on the fact that Etherington identity does not correspond to reality. The fact that Hubble s redshift is linearly dependent on transversal comoving distance instead of luminosity distance is justified. It is shown that mentioned above fact corresponds to astronomical observations. According to this the presence of dark energy in the Universe is also unnecessary. For the collective gravithermodynamic Gibbs microstates the connection between all thermodynamic potentials and parameters of matter have been found. This connection is realized with the help of several wave functions that can take arbitrary values with certain probability. The quantum equation of gravitational field have been found, the solutions of which set the spatial distribution of gravitational radius of matter in its every new gravithermodynamic state with the polynomial function with the next more high degree. The indicator of the degree of this function of continuously cooling down matter can successively take only integer and semi-integer values. That is why the process of cooling down of the whole RGTD-bonded matter is the quantum process that is caused by its spontaneous transition to the polynomial function with more high value of degree and, therefore, to the next quantum collective state. Keywords: gravithermodynamics, thermodynamics, gravity, gravitation, GR, SR, vacuum, inert free energy, Gibbs free energy, field, evolutionary and gravitational conformal gauge self-deformation, all-round isotropic conformal gauge self-contraction of moving matter, collective space-time microstate, Gibbs microstate, Lorentz conformal transformations, the principle of unobservability of the kinematic and gravitational self-contraction of the size of matter, limit velocity of matter, coordinate velocity of light, internal scale factor, hidden variables, wave functions, quantum gravity, spiral waves, micro-object, outer space, background regular space, photosphere, redshift, quasar, supernova. 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"><C 7<5=H5==O 2038 3V@>A:>?0, <>6;82>, 28:;8:0=> BVTN 6 ?@8G8=>N, I> V 7<5=H5==O 2038 =03@VB8E BV;.  FVTN ?@8G8=>N, >G5284=>, T ?@>?>@FV9=VABL A8;8 BO6V==O 7>2AV< =5 30<V;LB>=V0=C, 0 ;03@0=6V0=C >@48=0@=>W 2=CB@VH=L>W 5=5@3VW @5G>28=8 @>B>@0, I> >15@B0TBLAO.  024O:8 157?5@5@2=><C :0;V1@C20==N ?>74>26=L>3> (@04V0;L=>3>) 5B0;>=0 4>268=8 2 !!  70 9>3> @>7<V@>< 2 "-! =0 ?>25@E=V BV;0 ( EMBED Equation.3 ) =0 =V9 702648  EMBED Equation.3 .  G5@57 @5;OB82VABAL:5 =54>B@8<0==O >4=>G0A=>ABV ?>4V9 2 :>A<>;>3VG=><C G0AV, I> 2V4@0E>2CTBLAO 2 !! , 7 >4=>G0A=8<8 ?>4VO<8 2 "-! 2AV 2=CB@VH=V >1'T:B8 BV;0 =0;560BL 4> :>A<>;>3VG=>3> <091CB=L>3>. 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C"+H#%]p#>Bܤ9(Dt|kkoe𹠱N!`B^F&&\ {: `g!0`cdDd dhh  s *A? ?3"`?+2xYL1<&d `!|xYL1<&@^ |Jxcdd``ed``baV d,FYzP1n:&B@?b 8 ㆪaM,,He`H @201d++&1"+|-_̑Nh8WTvVJy 3Dф \w2@penR~'9pb.#ܽU, .bHyXA&cF1@Hb#($pAS8= g+KRs^ePdk[> 1煖oDd Thh  s *A? ?3"`?,2R mnLj_A@w.g `!& mnLj_A@w @XJ|xcdd``> @c112BYL%bpu @c112BYL%bpu !0kT  ep ]0؝rgpenR~C '9p4ĝpw ̀3_ J\ Hsr3| X G>pp!|/ \ #t]ao>{(H_\5l> |,@RNCf=pnFvF30_?q7`g@Kv0o(adbR ,.IeC Dl,Āf`~fDd ,hh  s *A? ?3"`?/2S":ʳJ䆭=/Bn `!'":ʳJ䆭=@|xcdd``> @c112BYL%bpuW0$& \Jqar-ʼ zJՙ]ç{JZVhqFv:v|peyŵm&#x\,I'h|y[pie_yPc~ROe&mⓚ/Io /:"6>D%2ş|h~Q}7{OxT*J=1[*Lv}xv)Qsgef~1f$0XtC'nآY~T]%j-|h?P@̓Aiï⑩ly%IK1 7E o{*CZFDd @hh  s *A? ?3"`?22RBZ>+jt .u `!&BZ>+jt @ |xcdd``> @c112BYL%bpu @c112BYL%bpu 1,LDd @hh  s *A? ?3"`?42Rg-oXk zT[@.y `!&g-oXk zT[@@ |xcdd``> @c112BYL%bpu @c112BYL%bpusi#`~g#71dBA%\`2M%F&&\ s: `g!!v120e6NDd @hh  s *A? ?3"`?62Rju3 Si3.} `!&ju3 Si3@ |xcdd``> @c112BYL%bpu v lb FMicrosoft Equation 3.0 DS Equation Equation.39qp@he N E =r/Re" EOle ICompObjJfObjInfoLEquation Native M\_1665382208zFIIOle OCompObjPfObjInfo R FMicrosoft Equation 3.0 DS Equation Equation.39qp#e4  E >1 FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native S?_1663931479#FIIOle TCompObj"$UfObjInfo%WEquation Native X:_1663931436(FKIKIOle YTg m cr FMicrosoft Equation 3.0 DS Equation Equation.39qT"e v lcr FMicrosoft Equation 3.0 DS EqCompObj')ZfObjInfo*\Equation Native ]>_1626364111-FKIKIOle ^CompObj,._fObjInfo/aEquation Native b>uation Equation.39q"hh T Ncr FMicrosoft Equation 3.0 DS Equation Equation.39q"w\ p Ncr_1626364185+@2FIIOle cCompObj13dfObjInfo4fEquation Native g>_16654783547FIIOle hCompObj68if FMicrosoft Equation 3.0 DS Equation Equation.39qm f G =q N N RE = m v l /c=v l /v lcr d" mObjInfo9kEquation Native l_1626612535<FIIOle p FMicrosoft Equation 3.0 DS Equation Equation.39qxh v l FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj;=qfObjInfo>sEquation Native t6_1626612698:AFIIOle uCompObj@BvfObjInfoCxEquation Native yh07$ v cv =v cbv N RE a"v l FMicrosoft Equation 3.0 DS Equation Equation.39q_1624337808-FFIIOle |CompObjEG}fObjInfoHEquation Native 6_1626075912KFIIOle CompObjJLf`(\ f G FMicrosoft Equation 3.0 DS Equation Equation.39q^B v cv FMicrosoft Equation 3.0 DS EqObjInfoMEquation Native :_1626115351H9PFIIOle CompObjOQfObjInfoREquation Native 6_1707677270UFIIuation Equation.39q_dl F G FMicrosoft Equation 3.0 DS Equation Equation.39q gd =E 0 (Ole CompObjTVfObjInfoWEquation Native &1"v 2 v  ecv "2 ) "1/2 =m  ein  c 2 =m  ein0  c 2 (1"v 2 v  ecv "2 ) "1/2 =m 00 cv  ecv  (1"v 2 v  ecv "2 ) "1/2 =const(2r)_1687865302gZFIIOle CompObjY[fObjInfo\ FMicrosoft Equation 3.0 DS Equation Equation.39qo7t E 0 FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native 6_1687880487b _FIIOle CompObj^`fObjInfoaEquation Native :_1687862130YXdFIIOle oX< m in FMicrosoft Equation 3.0 DS Equation Equation.39qod [F G ] GR =f G d(/vCompObjcefObjInfofEquation Native _1687865091iFII cv )d2r="dlnv cv d2r="dlnm in0 d2r="dlnE 0 d2r=HdlnW 0 d2r FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjhjfObjInfokEquation Native 6oj4 W 0 FMicrosoft Equation 3.0 DS Equation Equation.39qb [F G ] RGTD =1f g _1687260925nFIIOle CompObjmofObjInfopEquation Native _1707238924sFIIOle CompObjrtfd(Lf G )d2r="Ldlnf G d2r=Ldlnm gr0 d2r="LdlnE 0 d2r=LdlnW 0 d2r FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfouEquation Native _1707238995qxFIIOle wj L=W 0 (1"v 2 v l"2 ) 1/2 =m gr c 2 =m gr0 c 2 (1"v 2 v l"2 ) 1/2 =m 00 (c 3 /v l )(1"v 2 v l"2 ) 1/2 = FMicrosoft Equation 3.0 DS Equation Equation.39qwhئk =m cr c 4 v l"2 f g (1"v 2 v l"2 ) CompObjwyfObjInfozEquation Native _1686262523}FII1/2 =m cr ( m2 c 2 /f g )(1"v 2 v l"2 ) 1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObj|~fObjInfoEquation Native Q5Hm L=const(2r) FMicrosoft Equation 3.0 DS Equation Equation.39q84 f G =N RE q N =m in0_1707677793FIIOle CompObjfObjInfoEquation Native _1687260992lFIIOle CompObjf m cr =E 0 E 0cr =W 0 "S N T N +V N p N W 0cr "S Ncr T Ncr +V Ncr p Ncr FMicrosoft Equation 3.0 DS Equation Equation.39q"b m in0 FMicrosoft Equation 3.0 DS Equation Equation.39qi, m crObjInfoEquation Native >_1625848004jFIIOle CompObjfObjInfoEquation Native :_1665745917FIIOle CompObjfObjInfoEquation Native  FMicrosoft Equation 3.0 DS Equation Equation.39q|l W 0cr =m cr c 2 +S Ncr T Ncr "V Ncr p Ncr_1707677482FIIOle CompObjfObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39qO8: W 0 =m gr0 c 2 = FMicrosoft Equation 3.0 DS EqEquation Native k_1707677560FIIOle CompObjf    !"#$%&),-./014789:;<=@CDEFGHILOPQRSTUVWX[^_`abcdehklmnopqruxyz{|}~uation Equation.39q,l =E 0 +S N T N "V N p N = m2 m cr c 2 q N N RE = m m 00 c 2 q N" N RE" =mObjInfoEquation Native 0_1707240015FIIOle   cr c 2  1"p Ncr"2 p N2 +T Ncr"2 T N2 = FMicrosoft Equation 3.0 DS Equation Equation.39qw6r =m 00CompObj fObjInfoEquation Native R_1707240270pFII M    2 c 4  m 002 c 4 +p Ncr2 V N2 "T Ncr2 S N2 =m 002 c 4 E 0 =m 002 c 4 p N p Ncr2 V N =m 002 c 4 T N T Ncr2 S N = FMicrosoft Equation 3.0 DS Equation Equation.39qwJ_ =m 002 c 4  1"p Ncr"2 p N2 m 002 cOle CompObjfObjInfoEquation Native f 4 "T Ncr2 S N2 =m cr2 c 4  1+T Ncr"2 T N2 m 002 c 4 +p Ncr2 V N2 =m 002 c 2 f N" N RE"_1665746194/FIIOle 'CompObj(fObjInfo* FMicrosoft Equation 3.0 DS Equation Equation.39q|<l W 0 (q N ,N RE )=E 0 (q N ,N RE )+S N (q N ,N RE )T N (q N )"V N Equation Native +_1665746232FIIOle 2CompObj3f(N RE )p N (q N ,N RE ) FMicrosoft Equation 3.0 DS Equation Equation.39q|P| W 0 (q N" ,N RE" )=E ObjInfo5Equation Native 6_1707240940FIIOle >0 (q N" ,N RE" )+S N (q N" )T N (q N" ,N RE" )"V N (q N" ,N RE" )p N (N RE" ) FMicrosoft Equation 3.0 DS EqCompObj?fObjInfoAEquation Native B_1707241087FIIuation Equation.39qw4j E 0 =m 00 c 2 q N N RE =m 00 c 2 q N" N RE" = m 002 c 4 +p Ncr2 V N2 "T Ncr2 S N2 =p Ncr2 V N /p N = FMicrosoft Equation 3.0 DS Equation Equation.39qw}\ =T Ncr2 S N T N =mOle JCompObjKfObjInfoMEquation Native N 00 c 2  1"p Ncr"2 p N2 +T Ncr"2 T N2 = m 002 c 4 "T Ncr2 S N2 1"p Ncr"2 p N2 = m 002 c 4 +p Ncr2 V N2 1+T Ncr"2 T N2 FMicrosoft Equation 3.0 DS Equation Equation.39qw"H F N0 =E 0 "p N V N =m 00 c 2 [ m2_1707241470FIIOle YCompObjZfObjInfo\Equation Native ]>_1707678346FIIOle fCompObjgf "( m2 "q N2 )N RE2 ]q N N RE =m 00 c 2 q N"  m N RE" =V N (p Ncr2 "p N2 )p N = FMicrosoft Equation 3.0 DS Equation Equation.39qrLc = (m 002 c 4 "T Ncr2 S N2 )(1"p Ncr"2 p N2 )  =m 002 c 4 "T Ncr2 S N2  m 002 cObjInfoiEquation Native j _1707678113FIIOle s 4 +p Ncr2 V N2 "T Ncr2 S N2 = FMicrosoft Equation 3.0 DS Equation Equation.39q?b =(m 0CompObjtfObjInfovEquation Native w[_1707242164FII02 c 4 "T Ncr2 S N2 )T N T Ncr2 S N =m 00 c 2 (1"p Ncr"2 p N2 ) 1"p Ncr"2 p N2 +T Ncr"2 T N2 =m 002 c 4 "p Ncr2 V N2 T Ncr"2 T N2  (m 002 c 4 +p Ncr2 V N2 )(1+T Ncr"2 T N2 )  FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjfObjInfoEquation Native +wXg H N0 =E 0 +T N S N =m 00 c 2  m N RE q N =m 00 c 2 [ m2 "q N"2 (1"N I"2 )]q N" N I" =S N (T Ncr2 +T N2 )T N = FMicrosoft Equation 3.0 DS Equation Equation.39qwi = (m 002 c 4 +p Ncr2 _1707242401FIIOle CompObjfObjInfoEquation Native _1707242355FIIOle CompObjfV N2 )(1+T Ncr"2 T N2 )  =(m 002 c 4 +p Ncr2 V N2 )p Ncr2 (V N /p N )=m 00 c 2 (1+T Ncr"2 T N2 ) 1"p Ncr"2 p N2 +T Ncr"2 T N2 = FMicrosoft Equation 3.0 DS Equation Equation.39qwh =m 002 c 4 +p Ncr2 VObjInfoEquation Native _1707243203yFIKIOle  N2  m 002 c 4 +p Ncr2 V N2 "T Ncr2 S N2 =m 002 c 4 "T Ncr2 S N2 p Ncr"2 p N2  (m 002 c 4 "T Ncr2 S N2 )(1"p Ncr"2 p N2 )  FMicrosoft Equation 3.0 DS Equation Equation.39qwte S N =m 00 c 2 N RE  m T Ncr   mh  s *A? ?3"`?72=8l0ت `!=8l0تd @|sxcdd`` @c112BYL%bpu`b3@penR~{s> zV0nFK|1 +=N\N`Fv0oȣg+KRs@2u(2tA4B ~bDd @hh  s *A? ?3"`?82RBZ>+jt . `!&BZ>+jt @ |xcdd``> @c112BYL%bpu @c112BYL%bpu  Bܤ5\s> ^FXAF7b`wb".b_=.p Ɲ;&021)W2ePdh- I8Dd Th  s *A? ?3"`?;2|JZhscX `!PJZhsc@  XJxcdd`` @c112BYL%bpu 1aDd hhb  c $A? ?3"`?<2Qd~s":+S--> `!%d~s":+S-@@||xcdd``> @c112BYL%bpudKrF&&\ @ ] @28LDd Thb  c $A? ?3"`?=2ZJOa}>JR&_c6E `!.JOa}>JR&_c @XJ|xcdd``> 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FMicrosoft Equation 3.0 DS Equation Equation.39qw#; =m 00 c 2 T Ncr"2 T N  1"p Ncr"2 p N2 +T Ncr"2 T N2 =T N T Ncr  m 002 c 4 +p Ncr2 V N2 T Ncr2 +T N2 =p Ncr2 V N T Ncr p N  p N2 p Ncr2 1+m 002 c 4 p Ncr2 V N2 ()"1  FMicrosoft Equation 3.0 DS Equation Equation.39qp)d4 T N =T Ncr   m2 "q N2 q N =T Nc_1707756638m|FKIKIOle CompObjfObjInfoEquation Native E_1707757559FKIKIOle CompObjfr   m2 "(q N" ) 2 q N" N RE" =cT Ncr v l  1"v l2 c 2 (N RE" ) 2 =T cr2 S N E= FMicrosoft Equation 3.0 DS Equation Equation.39qpsHr4 =T  ecr  e2 S  eN   m 00 e2 c  e4 +p  eNcr  e2 V  eN  e2 "T  eNcr  e2 S  eN  e2 ObjInfoEquation Native _1707244080FKIKIOle  =T  eNcr  e2 S  eN   1"p  eNcr " e2 p  eN  e2 m 00 e2 c  e4 "T  eNcr  e2 S  eN  e2  =T  eNcr   p  eN  e2 p  eNcr  e2 1+m 00 e2 c  e4 p  eNcr  e2 V  eN  e2 ()"1  FMicrosoft Equation 3.0 DS Equation Equation.39qwDPe V N =m 00 c 2 p NcrCompObjfObjInfoEquation Native `_1707680111FKIKI  N RE2 "1  =m 00 c 2 q N"  m p Ncr  (N RE" ) 2 "1  =m 00 c 2 p N p Ncr2  1"p Ncr"2 p N2 +T Ncr"2 T N2 =Ole CompObjfObjInfoEquation Native       !$'()*+,-./256789<?@CFGHIJKNSX]bglqtwz{| FMicrosoft Equation 3.0 DS Equation Equation.39q= =m 00 cv  el  e" p  eNcr   1"(N  eRE  e" )  e"2  =Ep  eN  p  eNcr  e2 =p  eN  p  eNcr   m 00 e2 c  e4 "T  eNcr  e2 S  eN  e2 p  eNcr  e2 "p  eN  e2  =T  eNcr  e2 S  eN  p  eNcr  T  eN   1+T  eN  e2 T  eNcr  e2 1"m 00 e2 c  e4 T  eNcr  e2 S  eN  e2 ()  FMicrosoft Equation 3.0 DS Equation Equation.39q_1707244301FKIKIOle CompObjfObjInfoEquation Native U_1707244149FKIKIOle "CompObj#fw9et p N =p Ncr  m  N RE2 "1  q N N RE =p Ncr  1"(N RE" ) "2 =p Ncr2 V N E=p Ncr2 V N  m 002 c 4 +p Ncr2 V N2 "T Ncr2 S N2 = FMicrosoft Equation 3.0 DS Equation Equation.39qwSH>, =cp Ncr v l  N RE2 ObjInfo%Equation Native &o_1687263040FKIKIOle 0"1  =p Ncr2 V N  1+T Ncr"2 T N2 m 002 c 4 +p Ncr2 V N2 =p Ncr  1+T N2 T Ncr2 1"m 002 c 4 T Ncr2 S N2 ()  FMicrosoft Equation 3.0 DS Equation Equation.39q.z|h q N" =  m2 "N RE2 ( m2 "q N2 )  = m  1"m 00"2 c                    E    ! # " $ & % ' ) ( * + , - . / 0 1 2 4 3 5 7 6 8 : 9 ; < = ? > @ B A C F D G H I K J N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~  CompObj1fObjInfo3Equation Native 4J_1707680587  FKIKI "4 T Ncr2 S N2 FMicrosoft Equation 3.0 DS Equation Equation.39qeg4 N RE" =r/(R "  E" )=Ole :CompObj ;fObjInfo =Equation Native > FMicrosoft Equation 3.0 DS Equation Equation.39qu`wl =q N N RE /q N" =q N N RE [ m2 "N _1707680797FKIKIOle ACompObj BfObjInfoDEquation Native E_1642501750FKIKIOle LCompObjMfRE2 ( m2 "q N2 )] "1/2 =(1"p Ncr"2 p N2 ) "1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoOEquation Native P;_16654821705>FKIKIOle Q@>t  E" FMicrosoft Equation 3.0 DS Equation Equation.39q0|< q N FMicrosoft Equation 3.0 DS EqCompObjRfObjInfoTEquation Native U6_1642501630VFKIKIOle VCompObjWfObjInfoYEquation Native Z:uation Equation.39q|C N RE FMicrosoft Equation 3.0 DS Equation Equation.39qл,j  E_1642501832C"FKIKIOle [CompObj!#\fObjInfo$^Equation Native _7_1315756181|D'FKIKIOle `CompObj&(af FMicrosoft Equation 3.0 DS Equation Equation.39q II m cr FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo)cEquation Native d<_1626364266,FKIKIOle eCompObj+-ffObjInfo.hEquation Native i>_1665746723a1FKII"w\ p Ncr FMicrosoft Equation 3.0 DS Equation Equation.39q|"P= W 0crOle jCompObj02kfObjInfo3mEquation Native n>_16260978606FIIOle oCompObj57pfObjInfo8r FMicrosoft Equation 3.0 DS Equation Equation.39q_?*d  E =const() FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native s[_1626299297;FIIOle uCompObj:<vfObjInfo=xEquation Native y_1665483270CD@FIIOle }b8 N Eb =N E expH E " 0 ()[]=N E /(1+z) FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj?A~fObjInfoBEquation Native _1665483215EFIIk q Nb =q N exp"H E (" 0 )[]=q N (1+z) FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjDFfObjInfoGEquation Native (j f G =q Nb N Eb =q N N E =const() FMicrosoft Equation 3.0 DS Equation Equation.39q_16261011594MJFIIOle CompObjIKfObjInfoLEquation Native 6_1626101348OFIIOle CompObjNPf_P[ H E FMicrosoft Equation 3.0 DS Equation Equation.39q_. d=dt FMicrosoft Equation 3.0 DS EqObjInfoQEquation Native 9_1682273702TFIIOle CompObjSUfObjInfoVEquation Native :_1682273843YFIIuation Equation.39qj W 0b FMicrosoft Equation 3.0 DS Equation Equation.39q \ E 0bOle CompObjXZfObjInfo[Equation Native :_1682273905^FIIOle CompObj]_fObjInfo` FMicrosoft Equation 3.0 DS Equation Equation.39q"Hl m inb FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native >_1665747111cFIIOle CompObjbdfObjInfoeEquation Native _1687263161hFIIOle |l W 0b =W 0 N b =W 0 N E expH E (" 0 )[]=W 0 N E /(1+z) FMicrosoft Equation 3.0 DS EqCompObjgifObjInfojEquation Native n_1631111193pmFIIuation Equation.39qRjt E 0b =m in0b c 2 =E 0 /N Eb =(E 0 /N E )exp"H E (" 0 )[]=(E 0 /N E )(1+z)Ole CompObjlnfObjInfooEquation Native  FMicrosoft Equation 3.0 DS Equation Equation.39qtl R=exp"(H E +H T )(" 0 )[]_1631111192 rFIIOle CompObjqsfObjInfot FMicrosoft Equation 3.0 DS Equation Equation.39qthm r=exp"H T (t"t 0 )[] FMicrosoft Equation 3.0 DS EqEquation Native _1707758698wFIIOle CompObjvxfuation Equation.39qphjd H  e T  FMicrosoft Equation 3.0 DS Equation Equation.39qZj EW=m 00ObjInfoyEquation Native ;_1687263266|FIIOle CompObj{}fObjInfo~Equation Native v_1687263587zF-I-I2 c 4 =const FMicrosoft Equation 3.0 DS Equation Equation.39qiȷi T 00 =Tv cv /c=const(r)Ole CompObjfObjInfoEquation Native _1705145061:FI-IOle CompObjfObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39qh v cv FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native :_1705145895 F-I-IOle CompObjfObjInfoEquation Native M_1705146258F-I-IOle 1`m c=const(r) FMicrosoft Equation 3.0 DS Equation Equation.39qCf T 00 =cCompObjfObjInfoEquation Native __1705484284F-I-Ionst(r) FMicrosoft Equation 3.0 DS Equation Equation.39qwph G 0 FMicrosoft Equation 3.0 DS EqOle CompObjfObjInfoEquation Native 6_1705483933F-I-IOle CompObjfObjInfouation Equation.39qwjt W 0 FMicrosoft Equation 3.0 DS Equation Equation.39qw0d U 0 a"WEquation Native 6_1705483762F-I-IOle CompObjfObjInfoEquation Native L_1705484340F-I-IOle  0 FMicrosoft Equation 3.0 DS Equation Equation.39qw{\ E 0 FMicrosoft Equation 3.0 DS EqCompObjfObjInfoEquation Native 6_16648339619F-I-IOle CompObjfObjInfoEquation Native    #(+,/2369<?@ADGHILORUVWXY\_`cfilorstux}uation Equation.39qlh8.t W j =(f Gi /f Gj )W i FMicrosoft Equation 3.0 DS Equation Equation.39q_1705147706F-I-IOle CompObjfObjInfozl W 00" =f G (r)W(r)=const(r) FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native  _1705147751F-I-IOle  CompObj fObjInfoEquation Native _1665747579? 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" # $ ' * + , - . / 0 1 2 3 4 5 8 ; < = > ? @ A B E H I J K L M N O P S V W X Y \ a d e f g j m n o r u x }  FMicrosoft Equation 3.0 DS Equation Equation.39qp=h4 p=p  e00  / b  FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoa Equation Native  Y_1687547438dFL/IL/IOle  CompObjce fObjInfof Equation Native  _1707330035liFL/IЖ1IPg p/ gr0 =p 00 / 00 =const(r) FMicrosoft Equation 3.0 DS Equation Equation.39qOle  CompObjhj fObjInfok Equation Native  s(l 2v= 2LH e (b/b e ) n HL e [1+(b/b e ) 2n ]  2v e = 2b re (b/b e ) n b r [1+(b/b e ) 2n ]  2v e =_1707329984nFЖ1IЖ1IOle  CompObjmo fObjInfop  FMicrosoft Equation 3.0 DS Equation Equation.39qst = 2(b/b e ) n b r [1+(b/b e ) 2n ]  2v  max =c1bEquation Native  *_1707690272&6sFЖ1IЖ1IOle % CompObjrt& f+(c 2 b e "2v e2 )[1+(b/b e ) 2n ]22v e2 b e (b/b e ) n"1 {} "1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfou( Equation Native ) _1707690327xFЖ1IЖ1IOle 6 ogd b=b  ee  2v  max c2vv  elr  () 2  2v  max c2vv  elr  () 4 "1  [] ,  1/ en =b  ee  2nv  ee 2 v  elre 2 c 4 lnrr  ee  + 1+2nv  ee 2 v  elre 2 c 4 lnrr  ee  () 2 [] ,  1/ en FMicrosoft Equation 3.0 DS EqCompObjwy7 fObjInfoz9 Equation Native : $_1687982498}FЖ1IЖ1Iuation Equation.39qo3\ r=r e expc 4 2n (2vv lr ) "4 "(2v e v lre ) "4 []=r e expc 2 2v  max"2 4nbb e () n "b e b() n []  {} FMicrosoft Equation 3.0 DS Equation Equation.39qtCL b r =Ole C CompObj|~D fObjInfoF Equation Native G _b1"2v 2 c "2 /b=b+22v  max2 (b/b e ) n"1 c 2 b e [1+(b/b e ) 2n ]=b+22v e2 (b/b e ) n"1 (c 2 "2v e2 /b e )[1+(b/b e ) 2n ] FMicrosoft Equation 3.0 DS Equation Equation.39qt`+ b re =b e +2v e2 c 2 "2v e2 /b e _1687982551FЖ1I4IOle Q CompObjR fObjInfoT Equation Native U 8_1665682900 F4I4IOle Z CompObj[ f=c 2 b e2 c 2 b e "2v e2 FMicrosoft Equation 3.0 DS Equation Equation.39qfPq\ r eObjInfo] Equation Native ^ 6_1687982609F4I4IOle _ CompObj` fObjInfob Equation Native c 9_1687982676F4I4I   2 ! "$#%&')(*,+.-0/13456789:;<=>@?ABCFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ FMicrosoft Equation 3.0 DS Equation Equation.39qt 2v =b r1/2 2v=v lr 2v/c={[(b e /b) n +(b/b e ) n ]/2} "1/2 2v  maxOle h CompObji fObjInfok Equation Native l  FMicrosoft Equation 3.0 DS Equation Equation.39qt4g 2v  max =b re1/2 2v e (b e )=v lre 2v e /c_1687983013F4I4IOle p CompObjq fObjInfos  FMicrosoft Equation 3.0 DS Equation Equation.39qt5lt 2vH"const(b) FMicrosoft Equation 3.0 DS EqEquation Native t Q_1685199733F4Ix6IOle v CompObjw fuation Equation.39q[t b r FMicrosoft Equation 3.0 DS Equation Equation.39qt[Xm b rminObjInfoy Equation Native z 7_1687983043Fx6Ix6IOle { CompObj| fObjInfo~ Equation Native  w_1687983070Fx6Ix6I =42v 2 c "2 FMicrosoft Equation 3.0 DS Equation Equation.39qt@4 b=22v 2 c "2Ole  CompObj fObjInfo Equation Native  \_1687983098Fx6Ix6IOle  CompObj fObjInfo  FMicrosoft Equation 3.0 DS Equation Equation.39qtS b e =22v e2 c "2 FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native  o_1687983130Fx6Ix6IOle  CompObj fObjInfo Equation Native  s_1687983155Fx6I8IOle  tWn b re =42v e2 c "2 FMicrosoft Equation 3.0 DS Equation Equation.39qtR| 2v  maxCompObj fObjInfo Equation Native  n_1687983393F8I8I =22v e2 /c FMicrosoft Equation 3.0 DS Equation Equation.39qt8:d 2v=22v e  k bn"1 1+2k bn"2 +k b2nOle  CompObj fObjInfo Equation Native   FMicrosoft Equation 3.0 DS Equation Equation.39qt\0De 2v =22v e2 c 2k bn 1+k b2n =c4n_1687983438F8I8IOle  CompObj fObjInfo Equation Native  x_1687983473F8I8IOle  CompObj f 2 ln 2 rr e ()+c 8 162v e8 [] "1/4 FMicrosoft Equation 3.0 DS Equation Equation.39qt`  r  =r ObjInfo Equation Native  _1707331286F8I8IOle  e exp[c 4 2v e"4 (k bn "k b"n )/16n] FMicrosoft Equation 3.0 DS Equation Equation.39qsg4 k b =b/CompObj fObjInfo Equation Native  _1685876402^F8I3;Ib e = 1+64n 2 2v e8 c "8 ln 2 (r/r e )  +8n2v e4 c "4 ln(r/r e )[]   1/n FMicrosoft Equation 3.0 DS EqOle  CompObj fObjInfo Equation Native  Fuation Equation.39q*h> n>>2 34 FMicrosoft Equation 3.0 DS Equation Equation.39q_1687983771F3;I3;IOle  CompObj fObjInfo Equation Native  h_1707331810gF}=I}=IOle  CompObj ftLptz 2v p =0,4612v e FMicrosoft Equation 3.0 DS Equation Equation.39qsl k bnObjInfo Equation Native  ;_1687983649F3;I3;IOle  CompObj fObjInfo Equation Native  h_1707331744FGIGI FMicrosoft Equation 3.0 DS Equation Equation.39qtLqT 2v p =0,0862v e FMicrosoft Equation 3.0 DS Equation Equation.39qOle  CompObj fObjInfo Equation Native  ;sl k bn FMicrosoft Equation 3.0 DS Equation Equation.39qt/o 2v e <225_1687983824F}=I}=IOle  CompObj fObjInfo Equation Native  K_1665681981F}=I}=IOle  CompObj f FMicrosoft Equation 3.0 DS Equation Equation.39qf/e r/r e <20ObjInfo RichEditFlags Equation Native  K_1687984001F}=I}=IOle  CompObj fObjInfo Equation Native   FMicrosoft Equation 3.0 DS Equation Equation.39qtPh 2v=2v e "2v=2v e "(c 2 /22v e )2 35 ln(r/r e )[] 2 +c 8 /162v e8 {} "1/4 d"  0,95  [km/s] FMicrosoft Equation 3.0 DS Equation Equation.39qs? b e0 =0,5+(0,25"2v e2 _1707332813F}=I}=IOle  CompObj fObjInfo Equation Native  _1687984429F}=I?IOle  CompObj fc "2 ) 1/2 H"0,99999943672 FMicrosoft Equation 3.0 DS Equation Equation.39qtl n 0 =b r n=4(2v e /c)ObjInfo Equation Native  4_1707332272F?I?IOle                ! $ ' ( + . / 2 5 6 9 < ? B C D E H K L M N O P Q R S T W [ ^ a b c f i j k l m n o p q r s v y | 2 n=2 36 (2v e /c) 2 =38708,24438H"2 15,24 FMicrosoft Equation 3.0 DS Equation Equation.39qshjt k bp0 =CompObj fObjInfo Equation Native  3_1685620705{F?I?Ib p0 b e0 = 1+2 32,48 2v e4 c 4 ln 2 r p r e ()  +2 16,24 2v e2 c 2 lnr p r e [] 115,24 =1,000003366Ole  CompObj fObjInfo Equation Native   FMicrosoft Equation 3.0 DS Equation Equation.39q(-d k bp0n =1,1391,  n 0 =2 15,24_1687984776@ F?I?IOle  CompObj   fObjInfo   FMicrosoft Equation 3.0 DS Equation Equation.39qth|j 2v=2v e "2v=2v e "c2 16,24 ln(r/r e )[] 2 +(c/2v e ) 4 {} "1/4Equation Native  _1687985056F?I_BIOle " CompObj# f d"  0,95  [km/s] FMicrosoft Equation 3.0 DS Equation Equation.39qtu=l 2v 0 /2v e0 =2v/2v e ObjInfo% Equation Native & _1685660365FIIIIOle ) =inv FMicrosoft Equation 3.0 DS Equation Equation.39qsmm n 0 lnk b0 =nlnk b =invCompObj* fObjInfo, Equation Native - _1685660614F_BI_BIOle 0 CompObj1 fObjInfo3 Equation Native 4  FMicrosoft Equation 3.0 DS Equation Equation.39qsl8}m n 0 (k b0 "1)H"n(k b "1)_1685432560:F_BI_BIOle 7 CompObj8 fObjInfo :  FMicrosoft Equation 3.0 DS Equation Equation.39q](l 2v  max =0,3377  km/s FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native ; y_1707333194 #F_BI_BIOle = CompObj"$> fE)+";3ja +,(1O:oK!w`OS gBs;021)W2lԡ[> 1,S;nDd ,b  c $A? ?3"`?r2mψ& @ `!mψ& @T!4hZxڝMhAwV[7Q\7ŋATT i0 zkZ`"(xOz""xRI:ovwȋbo߾qma 3w]WF؀-|ΦnW2_3Eu0n.J"c+naPq0Jy\7OexQ#yl~OZ ЎwAo,?f(ӔGQG̖V>f )j{X> ZdE xyb?bt8G2SBFTW|7BN2Ͼ=o}f*k&zTq)OmGW?)%gd],CUCwmqGW'$Z=\~Pq&% =5u i;fw[qLNҴa9 $'s{9<{NRB:?gsKv%9}=`eZ6Vgw'qdZZ\'#gcݿuyGˋɿ} Jz896,cY 󤑂5)*Dd hhb  c $A? ?3"`?s2hNjpET D, `!<NjpET @@|| xcdd``> @c112BYL%bpu @c112BYL%bpu*=n/m](NSjmG!1~?Ʉ8{ܙĜk;cOg??Մ Py;|`9xx-gX|Lf *[=MeC]lVwdƯDd $'b  c $A? ?3"`?v2/! 0=b^&  `!/! 0=b^&HD hlxڝR=KP=C,A!EAAm!bljAb.D):(W-j…sn=ޗǐSx, 1($g:RԤK;Ѭ= DB4nym`ZFdP0Ͼc)1f@Xi֮rҶYi5K}+Rܮ-Bnoҥ߫^-1'k T{,:ֲDe5: !?3.bA"/i_Cΐa_0/7] jq\%ysYG G9.T4$<2bX?|b @n `/SDd  |b  c $A? ?3"`?w2al쒩Ą v  `!al쒩Ą @`0xcdd``~ @c112BYL%bpu~?х40UVT~#3#oF {`r ~Bnb/?{Խ\ԕW\-0@penR~+#6ts;'|_'L,Hqr3NRA9sAs8ԏ ;Ĥ\Y\pdP"CX,ĀGf~gYDd  b  c $A? ?3"`?x28 hs~+ޱ `!  hs~+ޱR@h $8xڥUKOQ>-mgh)-W*Q1EB|C jbcNecB,qc a4r>m`afw9v@(~Ee!!E^ }kFd:Γ!<8QV4Cq[<a_(+m8ȭ8ҷZ!GQO(ːzM 0ҧ,9JC,4K+ cJ@@L5|SW=1|i +1__P. vߓ06e\Yb~hHY{FȌK=ٺýq%o2-Gc}|Ӻzi}*6G|\x9q/ 񏑟G'昧-;"~WmQ)ߑ`J_ %+`~yt$n 9YzbN 4qXl A%2`y%w@=(cxΒfleztGţYyUh,v@"RВ:tv7@]T!?bY0[1 ؆]Yۡ5kHUk]>{mOdYg ?͛sP.=.Xd @54xF6I +|@}u*OU/':\z4kG|iñ!],vZބICkNwoau0zhVGr8薤/TQ{mx@'|*iwM"#Kv,/ipRJ}q%^zihrD[e{/U' =A'5)棖 Ti6'g2 R/n_Jyx?x~3 1~/ηF_ks\ႇp+;W Miy8d|6 4|X'ϢbDϢ}A 52nD|XRyFR9Ts9&VLX_SU>ze} ox%mS١2Bj'4+nɹv'm#i1~x̀|Os}}\ x"$,f0AȻBTSub\+Dd 8<*b  c $A? ?3"`?z2uoֵ}ҨM)Qf `!Ioֵ}ҨM) ,hDv xڥ]h\EϝMl$m>6Mc[[ACLM *n&nRZ_ "Hi!i1 >Q4 Rր1yPJMS\̙ {g=sr=/4!FEQ3"Ŷ棒+~ϻI>ݫ\o"&7R~EXXiSWW齴 y'$ ttTfLX>f@/ng)glO\9hk pjIdȷy}Yc~Ż:Dj;#K9A^h|f. =S~9c ߦ.E' ?|]>Α=r:^.ŗsq_)rwYhݯu;1l6G{p娸\Rm :Jo*BY~;UP 1p)m#Ԍ5C }P6xh3z[5[Vec_D@'hM~Me F|HƋm%,m/K-[U]bIo~c*C Nѓۋ}c5|lCuEOkK~#G)[gJ׵MxAͧG)G5Iv6% GBgUC9AU*gM]0^RV)*xFOX2JzT?@T~ح_MuϨ|? 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Equation Native 12 (a"1)42v e2 b en b n+1 (1"b)[(b 2n +b e2n )"22v e2 c "2 b en b n ]"(b 2n +b e2n )+22v e2 c "2 b en b n"1 (1"b)(1"b)[(b 2n +b e2n )"22v e2 c "2 b en b n ]+ FMicrosoft Equation 3.0 DS Equation Equation.39qopb +1ad_1707692361B FPfIPfIOle CompObjA C fObjInfoD Equation Native ;_1669391527 J G FPfIPfIOle (CompObjF H )fadbH"c 2 (b 2n +b e2n )(a"1)42v e2 b en b n+1 (1"b)"1(1"b)=1adadb+c 2 (a"1)22v 2 b(1"b)"1(1"b)+1adadb=0 FMicrosoft Equation 3.0 DS Equation Equation.39qdg =(1"v 2 c "2 ) "1/2 FMicrosoft Equation 3.0 DS EqObjInfoI +Equation Native ,_1669392334L FPfIPhIOle .CompObjK M /fObjInfoN 1Equation Native 26_1707764140 | Q FPhIPhIuation Equation.39qj  2 FMicrosoft Equation 3.0 DS Equation Equation.39qp'= cd2t=chOle 3CompObjP R 4fObjInfoS 6Equation Native 7C(  et  " t e0  )ds=1"vv 0 c "2  (1"v 2 c "2 )(1"v 02 c "2 )  ds=ch( t " t0 )ch t cdt= 1"v 2 c "2 1"2v 2 c "2 cdt FMicrosoft Equation 3.0 DS Equation Equation.39qjt d2l=sh( t " t0 )ds=(v"v 0 )/c (1"v_1672592976 V FPhIPhIOle ACompObjU W BfObjInfoX DEquation Native E8_1672593537m [ FPhI@jIOle NCompObjZ \ Of 2 c "2 )(1"v 02 c "2 )  ds=sh( t " t0 )sh t dl=2vv 1"v 2 c "2 1"2v 2 c "2 dl FMicrosoft Equation 3.0 DS Equation Equation.39qF j 2v=d2ld2t=c  th( t " t0 )=v"v 0 1"vv 0 c "2 =th( t " t0 )th t vObjInfo] QEquation Native Rb_1707382768` F@jI@jIOle X FMicrosoft Equation 3.0 DS Equation Equation.39q(; ds=cd  2t = 1"2v 2 c "2 d2t= 1"v 2 c "2 dt=invCompObj_ a YfObjInfob [Equation Native \_1672594555Y h e F@jI@jIOle `CompObjd f afObjInfog cEquation Native d FMicrosoft Equation 3.0 DS Equation Equation.39q`td sh t =(v/c)(1"v 2 c "2 ) "1/2_1672594752j F@jI@jIOle gCompObji k hfObjInfol j FMicrosoft Equation 3.0 DS Equation Equation.39qx e ch t =(1"v 2 c "2 ) "1/2 FMicrosoft Equation 3.0 DS EqEquation Native k_1672594436o F@jI@@mIOle nCompObjn p ofuation Equation.39q3 th t =v/c FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoq qEquation Native rO_1672594928c t F@@mI@@mIOle tCompObjs u ufObjInfov wEquation Native xC_1672594991y F@@mI@@mI'P>  t0 =0 FMicrosoft Equation 3.0 DS Equation Equation.39q#g v 0 =0Ole zCompObjx z {fObjInfo{ }Equation Native ~?_1707764581~ F@@mI@@mIOle CompObj}  fObjInfo  FMicrosoft Equation 3.0 DS Equation Equation.39qp`; cd,  2t=cd,  t=ch  et  ds=c(1"v 2 c "2 ) "1/2 d2t Equation Native _1707764753O F@oI@oIOle CompObj f FMicrosoft Equation 3.0 DS Equation Equation.39qp f dt/d,  2t =ch  et  =(1"v 2 c "2 ) "1/2 FMicrosoft Equation 3.0 DS EqObjInfo Equation Native _1707764785 F@oI@oIOle CompObj fObjInfo Equation Native _1707765516 F@oI@oIuation Equation.39qpf d2l=dl=sh  et  ds=v(1"v 2 c "2 ) "1/2 d,  2t  FMicrosoft Equation 3.0 DS EqOle CompObj fObjInfo Equation Native uation Equation.39qpkt dl/d,  2t =c  sh  et  =v(1"v 2 c "2 ) "1/2 FMicrosoft Equation 3.0 DS Eq_1678448782  F@oI0qIOle CompObj fObjInfo uation Equation.39qzضr 2t  FMicrosoft Equation 3.0 DS Equation Equation.39qo+  t0 (vEquation Native -_1671999836s f F0qI0qIOle CompObj fObjInfo Equation Native _1672660858 F0qI0qIOle  0 )=arth(v 0 /c) FMicrosoft Equation 3.0 DS Equation Equation.39q0d d2t=dt"v 0 c "2 dx 1CompObj fObjInfo Equation Native  _1672660857r F0qI0qI"v 02 c "2 = 1"v 2 c "2 1"2v 2 c "2 dt=ch( t " t0 )ch t dt=ch( t " t0 )cds txOle CompObj fObjInfo Equation Native  FMicrosoft Equation 3.0 DS Equation Equation.39qX\ d2x=dx"v 0 dt 1"v 02 c "2 =2v x v x  1"v 2 c "2 1"2v 2 c "2 dx=sh( t " t0 )sh t dx=sh( t " t0 )ds tx FMicrosoft Equation 3.0 DS Equation Equation.39q_1672607160w F0ltI0ltIOle CompObj fObjInfo Equation Native =_1672607360 F0ltI vIOle CompObj f!!j d2y=dy FMicrosoft Equation 3.0 DS Equation Equation.39q!Xf d2z=dz FMicrosoft Equation 3.0 DS EqObjInfo Equation Native =_1672608336 F vI vIOle 8CompObj fObjInfo Equation Native u_1707767308 F vI vIuation Equation.39qY`4 2v x =v x "v 0 1"v x v 0 c "2 =v x th( t " t0 )th t =c  th( t " t0 )Ole CompObj fObjInfo Equation Native  FMicrosoft Equation 3.0 DS Equation Equation.39qp*d 2v  ey  =v  ey   1"v 02 c "2 1"v  ex  v 0 c "2 =v  ey   1"2v 2 c "2 1"v 2 c "2 =v  ey  ch  et  ch(  et  "  et 0 ) FMicrosoft Equation 3.0 DS Equation Equation.39q_1707766972 F vI vIOle CompObj fObjInfo p0l 2v  ez  =v  ey   1"v  e0 2 c "2 1"v  ex  v  e0  c "2 =v  ez   1"2v 2 c "2 1"v 2 c "2 =v  ez  ch  et  Equation Native  _1672660743 F 'yI 'yIOle CompObj fch(  et  "  et0  ) FMicrosoft Equation 3.0 DS Equation Equation.39q< ds tx = c 2 (d2t) 2 "ObjInfo Equation Native _1707766742 F 'yI 'yIOle (d2x) 2 = c 2 (dt) 2 "(dx) 2 =inv FMicrosoft Equation 3.0 DS Equation Equation.39qp>0k dtd2tCompObj fObjInfo Equation Native Z_1672661714 F 'yI 'yI  !$'(),/012589:;>ABCDEFGJMNOPQRUXYZ[\]^adefghilopqrstwz{|}~=2v  ey  v  ey  =2v  ez  v  ez  = 1"2v  ex  e2 c " e2 1"v  ex  e2 c " e2  = 1"2v  e2 c " e2 1"v  e2 c " e2  =ch  et  ch(  et  "  et0  ) FMicrosoft Equation 3.0 DS Equation Equation.39qf cd2t=ccos" x cth( t " t0 )d2lCn?N>rGV9uTþ|r>y_Ju22똄:/ wr"e3~mdD@k1!\<.Et@~lPe)lDd T"b E c $AE? 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F {I {IOle "" t0 )"1] "1/2 ds= FMicrosoft Equation 3.0 DS Equation Equation.39qo`db =[1"sec 2 " x th 2 (CompObj #fObjInfo %Equation Native &_1672663618 F {I}I t " t0 )] "1/2 ds FMicrosoft Equation 3.0 DS Equation Equation.39qo d2x=cos" x [cos 2 " Ole *CompObj +fObjInfo -Equation Native .x cth 2 ( t " t0 )"1] "1/2 ds FMicrosoft Equation 3.0 DS Equation Equation.39qc d2y=cos"_1707383079 F}I}IOle 3CompObj 4fObjInfo 6Equation Native 7_1707383596 F}I}IOle <CompObj =f y [cos 2 " x cth 2 ( t " t0 )"1] "1/2 ds FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo ?Equation Native @_1707751986 F}I}IOle Hh d2ldl=cos x sh( t " t0 )cos" x sh t = cos 2  x cth 2  t "1cos 2 " x cth 2 ( t " t0 )"1  = l FMicrosoft Equation 3.0 DS Equation Equation.39qprPlf d2tdt=ch(  et  "  et0  )ch  et  =cos"  ex  cth(  eCompObj IfObjInfo KEquation Native L_1707752046 FSISIt  "  et0  )cos  ex  cth  et    el  FMicrosoft Equation 3.0 DS Equation Equation.39qpyt d2xdxOle SCompObj TfObjInfo VEquation Native W=cos"  ex  cos  ex    el  = cth  e2   et  "sec  e2   ex  cth  e2 (  et  " t e0  )"sec  e2 "  ex  =  ex _1707383335 FSISIOle _CompObj `fObjInfo b FMicrosoft Equation 3.0 DS Equation Equation.39qpul d2ydy=cos" y cos x sh( t " t0 )cos y cos" x sh t =cos"Equation Native c_1672673194 + FSISIOle jCompObj kf y cos y  l =1 FMicrosoft Equation 3.0 DS Equation Equation.39qpl4 d2zdz=cos" z cos ObjInfo mEquation Native n_1707383483 FSIIOle ux sh( t " t0 )cos z cos" x sh t =cos" z cos z  l =1 FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj  vfObjInfo xEquation Native yV_1707766204 FII:Mli sin" x =sech( t " t0 )=sin x ch t ch( t " t0 )=sin x  1"2v 2 c "2 1"v 2 c "2 =sin x  1"v 02 c "2 1"(v 0 /c)cos x FMicrosoft Equation 3.0 DS Equation Equation.39qpj cos"  eOle CompObj  fObjInfo Equation Native :x  =th(  et  "  et0  )=cos  ex  "v  e0  /c1"(v  e0  /c)cos  ex  FMicrosoft Equation 3.0 DS Equation Equation.39q_1672765339T  FIIOle CompObj fObjInfo Equation Native ~_1672765463 FIIOle CompObj  fb`h4 cos" y =cos y / l FMicrosoft Equation 3.0 DS Equation Equation.39qb?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwz|{}~Ole CompObj, . fObjInfo/ Equation Native `Dl th t =cos x FMicrosoft Equation 3.0 DS Equation Equation.39qzt dt=0_1670409367] 2 FȉI9IOle CompObj1 3 fObjInfo4 Equation Native 5_1670409312b 7 F9I9IOle CompObj6 8 f FMicrosoft Equation 3.0 DS Equation Equation.39qzt ds=0 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo9 Equation Native 5_1670409404< F9I9IOle CompObj; = fObjInfo> Equation Native 5_1670273141 A F9I𪎩Iz;e dx=0 FMicrosoft Equation 3.0 DS Equation Equation.39qJe v t0 =c 2 /v 0Ole CompObj@ B fObjInfoC Equation Native f_1672517390F F𪎩I𪎩IOle CompObjE G fObjInfoH  FMicrosoft Equation 3.0 DS Equation Equation.39qhj4 dt ij =v 0 c "2 dx ij FMicrosoft Equation 3.0 DS EqEquation Native _1707693226 K F𪎩I𪎩IOle CompObjJ L fuation Equation.39qo`=4 d2x ij =(1"v 02 c "2 ) "1/2 (dx ij "v 0 dt ij )= 1"v 02 c "2 dx ij =sech t0 dx ObjInfoM Equation Native _1670360335P F𪎩IIOle ij =th t0 ds ij FMicrosoft Equation 3.0 DS Equation Equation.39qwj v cv =c(dt/d2t)=v cvr CompObjO Q fObjInfoR Equation Native _1671400608( X U FII(1"v 2 v cv"2 ) 1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qxg =d2x/dx=1/=c/v cv =Ole CompObjT V fObjInfoW Equation Native  r (1"v 2 v cv"2 ) "1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qxxh =dx/d2x=v cv /c= r (_1671400653Z FIeIOle CompObjY [ fObjInfo\ Equation Native _1670361003g 5 _ FeIeIOle CompObj^ ` f #(+.149>ABEHIJKLORSTUX[^abcdglqtux{|}~1"v 2 v cv"2 ) 1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qw09t dtObjInfoa Equation Native -_1670361029d FeIeIOle CompObjc e fObjInfof Equation Native  1_1670360706N l i FeI֕I FMicrosoft Equation 3.0 DS Equation Equation.39qwx|j d2t FMicrosoft Equation 3.0 DS Equation Equation.39qOle  CompObjh j fObjInfok Equation Native -wXi dx FMicrosoft Equation 3.0 DS Equation Equation.39qwx4j d2x FMicrosoft Equation 3.0 DS Eq_1670360762n F֕I֕IOle CompObjm o fObjInfop Equation Native 1_16714007105s F֕I֕IOle CompObjr t fuation Equation.39qxZP\d v cvr =c r =c/ r FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfou Equation Native v_1671400743x F֕I IOle CompObjw y fObjInfoz Equation Native  6_1671400761v } F I Ix,q  r FMicrosoft Equation 3.0 DS Equation Equation.39qx4  r FMicrosoft Equation 3.0 DS EqOle !CompObj| ~ "fObjInfo $Equation Native %6_1671400790 F I IOle &CompObj 'fObjInfo )uation Equation.39qx_  v cv =v cvr / r =c FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native *{_1670425714: F I IOle ,CompObj -fObjInfo /Equation Native 0G_1671400851{ FБIБIOle 2z+(8 v cvr H"c FMicrosoft Equation 3.0 DS Equation Equation.39qx#}g  r H"1CompObj 3fObjInfo 5Equation Native 6?_1671400879 FБIБIOle 7CompObj 8fObjInfo :Equation Native ;? 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KA?H1Z00< UXRY7S?&meabM-VK-WMc8sE VZʙ 4AHq50:0t&Ww@J 3xp{00\nP@penR~'ל9pb.#9L #l˰ \Ewo8*ʸ!F= adbR ,.Ieԡ[> 1,puQDd |%h  s *A? ?3"`?2.&hm w+ŅqZ `!i.ObjInfo hEquation Native i6_1671401051 y FLIIOle jx  r FMicrosoft Equation 3.0 DS Equation Equation.39qx!  rCompObj kfObjInfo mEquation Native n6_16705355560 o FIIOle oCompObj pfObjInfo rEquation Native s FMicrosoft Equation 3.0 DS Equation Equation.39qui G=d2v/d2t=(1"v 2 v cv"2 ) "3/2 dv/d2t FMicrosoft Equation 3.0 DS Eq_1682067387 FIIOle vCompObj wfObjInfo yuation Equation.39q gt H=E 0 =m 0 cv cv (1"v 2 v cv"2 ) "1/2 =m 0 cv cvr =const(t)Equation Native z&_1682067408 FIIOle CompObj f( FMicrosoft Equation 3.0 DS Equation Equation.39q.Xi L=W 0 /=m 0 c 3 (1"v 2 v cv"2 ) 1/2 /v cv =m 0 c 3 /v cvr =const(ObjInfo Equation Native J_1682067494 } FIIOle t) FMicrosoft Equation 3.0 DS Equation Equation.39q`xt P H =m 0 2v=m 0 vc/v cv =m 0 vc/v CompObj fObjInfo Equation Native _1707693646I FIIcvr (1"v 2 v cv"2 )=2m 0 vc/v cvr (1+ 1"4v 2 v cvr"2 ) FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObj fObjInfo Equation Native 1owl P L =m 0 2v=m 0 vc/v cv =(m 0 vc/v cvr )(1"v 2 v cv"2 ) "1/2 = FMicrosoft Equation 3.0 DS Equation Equation.39q_1707693537 FxIxIOle CompObj fObjInfo o8jt =(m 0 vc/v cvr )1+ 1"4v 2 v cvr"2 ()/2[] "1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native _1682067537 FxIxIOle CompObj fObjInfo Equation Native _1707385170, / FxIxIOle ; v cv"2 H 2 "P H2 =v cv2 c "4 L 2 +P L2 =m 02 c 2 FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj fObjInfo Equation Native ]_1707768842 F騩I騩IAit =3c "2 H E2 FMicrosoft Equation 3.0 DS Equation Equation.39qpkt v  ecv  Ole CompObj fObjInfo Equation Native  =c(1"v 2 v  ecv "2 ) 1/2 =c (1+ 1"4v 2 c "2 )/2  FMicrosoft Equation 3.0 DS Equation Equation.39q_1670918412 F騩I騩IOle CompObj fObjInfo Equation Native _1670449354 F騩I騩IOle CompObj f|/d 2v=d2x/d2t=, i vc  /, i v cv FMicrosoft Equation 3.0 DS Equation Equation.39qz?j4 2t=(c/vObjInfo Equation Native [_1665921327 F3I3IOle  cv )t FMicrosoft Equation 3.0 DS Equation Equation.39qu< v 0 FMicrosoft Equation 3.0 DS EqCompObj fObjInfo Equation Native 6_1671480744 F3I3IOle CompObj fObjInfo Equation Native uation Equation.39q}ed v l0 =v lr0  01"p =v lr0 (1"v 02 v l0"2 ) (p"1)/2_1707386540 F3IIOle CompObj fObjInfo  FMicrosoft Equation 3.0 DS Equation Equation.39qWi 2N C cd2t=2v l d2t (1"2v 2 c "2 ) p =2v lG d2t 1"2v 2 c "2Equation Native s_1707386583  FIIOle CompObj f =ch( t " t0 )2v lG d2t=N C cdt"(v 0 /v l0 )dx m  1"v 02 v l0"2 = FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo Equation Native _1671823526  FIIOle { =v l d2t"(2v 0 /c)d2x m  (1"2v 02 c "2 )(1"2vc "2 ) p =v lG d2t"(2v 0 /c) G d2x m  (1"2v 02 c "2 )(1"2v 2 c "2 )  =v lG d2t 1"2v 2 c "2 FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj  fObjInfo Equation Native _1672422650 FIId 2v lG d2t=v lG d2t=ds FMicrosoft Equation 3.0 DS Equation Equation.39qufd " G d2x m =th" t dsOle CompObj fObjInfo Equation Native 3      #&'(),/012369:;<=>?BEFGHIJKLMPSTUVWXYZ[^abcdefgjmnopqtwxyz}=th( t " t0 )2v lG d2t=(2v/c)2v lG d2t FMicrosoft Equation 3.0 DS Equation Equation.39qu(q 2N C d2x_1707388242  FIIOle CompObj  fObjInfo Equation Native _1707388124 F_I_IOle CompObj  f m ="d2x m  (1"2v 2 c "2 ) p =" G d2x m  1"2v 2 c "2 =ch( t " t0 )" G d2x m =N C dx m "(v 0 /v l0 )cdt 1"v 02 v l0"2 = FMicrosoft Equation 3.0 DS Equation Equation.39q~Hed =d2x m "(2v 0 /c)v ObjInfo Equation Native _1672423299 D  F_I_IOle !l d2t (1"2v 02 c "2 )(1"2v 2 c "2 ) p = G d2x m "(2v 0 /c)v lG d2t (1"2v 02 c "2 )(1"2v 2 c "2 )  =sh( t " t0 )v lG d2t FMicrosoft Equation 3.0 DS Equation Equation.39qu et " G v lG d2x m d2t=" G 2v lGCompObj  "fObjInfo $Equation Native %<_1707388351 F_IдI d2x m d2t=th" t =2vc FMicrosoft Equation 3.0 DS Equation Equation.39qCe4 2N C d2y m ="d2y mOle *CompObj  +fObjInfo -Equation Native ._  (1"2v 2 c "2 ) p =" G d2y m  1"2v 2 c "2 = FMicrosoft Equation 3.0 DS Equation Equation.39q_1707388480 4 " FдIдIOle 4CompObj! # 5fObjInfo$ 7Equation Native 8_1672769651' FдIдIOle @CompObj& ( Afl =ch( t " t0 )" G d2y m =N C dy m =d2y m  (1"2v 2 c "2 ) p = G d2y m  1"2v 2 c "2 =ch t  G d2y m FMicrosoft Equation 3.0 DS Equation Equation.39q<h " G d2y m =ch t ch( t " t0 ) G d2y m = 1"2vObjInfo) CEquation Native DX_1672769836 < , FдIIOle N 2 c "2 1"2v 2 c "2  G d2y m = 1"2v 02 c "2 1"2v 0 2v x c "2  G d2y m FMicrosoft Equation 3.0 DS EqCompObj+ - OfObjInfo. QEquation Native RX_1707388707 W 1 FIIuation Equation.39q<8|< " G d2z m =ch t ch( t " t0 ) G d2z m = 1"2v 2 c "2 1"2v 2 c "2  G d2z m = 1"2v 02 c "2 1"2v 0 2v x c "2  G d2z m FMicrosoft Equation 3.0 DS Equation Equation.39qOle \CompObj0 2 ]fObjInfo3 _Equation Native `|j 2N C d2z m ="d2z m  (1"2v 2 c "2 ) p =" G d2z m  1"2v 2 c "2 =ch( t " t0 )" G d2z m =N C dz m =_17073886356 FIIOle hCompObj5 7 ifObjInfo8 k FMicrosoft Equation 3.0 DS Equation Equation.39q2gt =d2z m  (1"2v 2 c "2 ) p = G d2z m  1"2v 2 cEquation Native lN_1707388770; FIIOle rCompObj: < sf "2 =ch t d2z m FMicrosoft Equation 3.0 DS Equation Equation.39qSd N C cdt=v l d2t (1"2vObjInfo= uEquation Native v/_17073889659 \ @ FIIOle { 2 c "2 ) p =v lG d2t 1"2v 2 c "2 = FMicrosoft Equation 3.0 DS Equation Equation.39qqgt =ch(" CompObj? A |fObjInfoB ~Equation Native _1671827232E FIIt "" t0 )v lG d2t=2N C cd2t"(2v 0 /2v l0 )d2x m  1"2v 02 2v l0"2 =2v l d2t"(2v 0 /c)"d2x m  (1"2v 02 c "2 )(1"2v 2 c "2 ) p = FMicrosoft Equation 3.0 DS Equation Equation.39qf =2v lG d2t"(2v 0 /cOle CompObjD F fObjInfoG Equation Native )" G d2x m  (1"2v 02 c "2 )(1"2v 2 c "2 )  =2v lG d2t 1"2v 2 c "2 FMicrosoft Equation 3.0 DS Equation Equation.39q_1671827355C R J FIIOle CompObjI K fObjInfoL d> Y FpFIpFIl d2x=th t ds=th(" t "" t0 )v lG d2t FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjX Z fObjInfo[ Equation Native hLj N C dx m =d2x m  (1"2v 2 c "2 ) p = G d2x m  1"2v 2 c "2 =ch t  G d2x m =2N C d2x m "(2v 0 /2v l0 )cd2t 1"2v 02 2v l0"2 = FMicrosoft Equation 3.0 DS Equation Equation.39qi ="d2x m "(2v 02 /c_1707389286^ FpFIpFIOle CompObj] _ fObjInfo` Equation Native _1671051057 k c FpIpIOle CompObjb d f)2v l d2t (1"2v 02 c "2 )(1"2v 2 c "2 ) p =" G d2x m "(2v 0 /c)2v lG d2t (1"2v 02 c "2 )(1"2v 2 c "2 )  =sh(" t "" t0 )2v lG d2t FMicrosoft Equation 3.0 DS Equation Equation.39qu8!d 2v 0 ="v 0     ~ !#"$%&)'*Q+,.-/0132456879:;=<>@?ACBDEFHGIKJLMNOPRSrUTVWXZY[\]_^a`bcdefhgijklmnopqtsuwvxy{z|&hm w+Ņ`)07xڝAOALKVX5YLl0/OД#.RͶ=cԓLD.z~ɞT`4,3ow'}$6}yoy0"?8 14Zb\FXXr`0 kU@V'ga R&(n-SV˼ӨWa^kG ֤6׉Qq'Lq'g%_Qbw=_@\vWNuΐlevV`H.(^9A5ʥ}ϘvE~̡}TدB}^:|soȻK__)({dG=rY2V<9D_ <6H/l%(Q^Jn*^Co0Z;k'ݫvLk/y.{J3Sg)Gf*W̉vs ^EnME;iO&(ƺ G9XgoE.CvG܇:ޙxq5ٸ-igiա#X1yEswc#Dd T=h o s *Ao? ?3"`?n2gu%vzU.{@C `!;u%vzU.{@ XJ xcdd``> @c112BYL%bpu 1,!YL`#Dd T=h p s *Ap? ?3"`?o2gJ-ޓI~NC `!;J-ޓI~N HXJ xcdd``> @c112BYL%bpu 1,0N^Dd |h q s *Aq? ?3"`?p2Cg3H { `!g3H {ڪ@`0xcdd``eb``baV d,FYzP1n:&A! 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KA?H1Z ㆪaM,,He`I? 01d++&1"+|-J[T T0^`+A|J 3DxdK%Oݙ@|8߇įpO;4ݡTL@(\ 1.s> `VrAc `@RJ#g+KRsVePdh- 8Dd Th M s *A#? ?3"`?2|`g!]{%lXQx `!P`g!]{%l` PXJxcdd`` @c112BYL%bpu 1%e0RDd t|A:b H c $A? ?3"`?2k}y6jbCxz `!pk}y6jbC `@00>xcdd`` @c112BYL%bpuv'\F @FVb 6o,<|^f~,b`+$37X/\!(?71H.`t7n IP{1f 83/G#%h _,MUQe9Q1ʛ0@!!🼐@/ >7ҀJ'yPQQ5'l|%VT~@Q&;%bƸ4,xxIAp%AAx/`=)¨|QA?ί  8 %B~pWfTjy鈑27' ?gW87 -e(8BKGv0oȠ3LLJ% 7A2u(2tA4B a *Dd  hb I c $A? ?3"`?2ig-lXଙZ'zOE} `!=g-lXଙZ'zOd'P=8 xڥMHTQ=83N83淌gJ&Ba ֐攆HiѪ]H!dm"iBi(Zq1PTQL˻_9νyZNPۉt:ͭR`˖qnbZvA"=Q0Gd1n8=1~9J㈃bh  1OVo|#o㱞u~7;xX¤$r5IZ;齱C^7nYI@vobg淩]B#2c].Ù]agYCw"[ru&a58o+fObjInfo@Equation Native Aa_1707400620@fFp鈪IpZIE\k =N  eC  e2 [(1"r  ege  /r)c  e2 "H  eE  e2 r  e2 ](d2t)  e2 "[(1"r  ege  /r)c  e2 "H  eE  e2 r  e2 ] " e1 (dr)  e2 "r  e2 [(d)  e2 +sin  e2 (d)  e2 ]{}= FMicrosoft Equation 3.0 DS Equation Equation.39q)k =[2v lbOle KCompObjLfObjInfoNEquation Native OE2 /(1"2v b2 2v lb"2 )](d) 2 =[v l2 /(1"v 2 v l"2 )](d2t) 2 FMicrosoft Equation 3.0 DS Equation Equation.39q_1677353637FpZIpZIOle UCompObjVfObjInfoX#h R=R k FMicrosoft Equation 3.0 DS Equation Equation.39qFPi R gek =r ge /4Equation Native Y?_1677352786FpZIpˍIOle ZCompObj[fObjInfo]Equation Native ^b_1677327475!FpˍIpˍIOle ` FMicrosoft Equation 3.0 DS Equation Equation.39q:d R=R ge r1+ 1"r ge /r  () 2 /r geCompObjafObjInfocEquation Native d_1677327621FpˍI`IOle gCompObjhfObjInfojEquation Native k FMicrosoft Equation 3.0 DS Equation Equation.39qj4 r=r ge R+R ge () 2 /4RR ge FMicrosoft Equation 3.0 DS Eq_1678032266 F`I`IOle nCompObj  ofObjInfo quation Equation.39qr=t N E =1/N  =r/R=r ge R+R ge () 2 /4R ge R 2 =41+ 1"r ge /r  () "2 expH E "Equation Native r_1707738729gF`I`IOle yCompObjzf k ()[] FMicrosoft Equation 3.0 DS Equation Equation.39q(1 v  elb  =4cR  ege  R  e2 R"R  ege  ()/r  eObjInfo|Equation Native }_1690292357F`IPДIOle ge  R+R  ege  ()  e3 =cR  e2 (R"R  ege  )(R+R  ege  ) " e3 exp["H  eE  ("  ek  )] FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjfObjInfoEquation Native _1677352358+FPДIPДI| j f Gb =2v lb /c=R"R ge ()/R+R ge ()=(1"r g /r) 1/2 FMicrosoft Equation 3.0 DS EqOle CompObjfObjInfoEquation Native uation Equation.39qkd R ge =(r ge /4)exp"H E " k ()[] FMicrosoft Equation 3.0 DS Equation Equation.39q_1677328070&FPДIPAIOle CompObjfObjInfo t r ge FMicrosoft Equation 3.0 DS Equation Equation.39ql =1Equation Native :_1677351742X#FPAIPAIOle CompObj"$fObjInfo%Equation Native 1_16773292690(FPAIPIOle CompObj')fObjInfo*Equation Native B_1677351794-FPIPI FMicrosoft Equation 3.0 DS Equation Equation.39q&x8 R>R ge FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObj,.fObjInfo/Equation Native 5@l ="1 FMicrosoft Equation 3.0 DS Equation Equation.39q&lf R<R ge_16773294182FPI@IOle CompObj13fObjInfo4Equation Native B_1676974823{7F@I@IOle CompObj68f FMicrosoft Equation 3.0 DS Equation Equation.39q#j D M a"R FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo9Equation Native ?_1690290769D<F@I@mIOle CompObj;=fObjInfo>Equation Native _1677527160]NAF@mI@mI|ug H E c(R+R ge ) 3 dRR 2 (R"R ge ) R4R  ege  +" =H E c(R+R ge ) 3 v lb dR 2 (R"R ge )  e@   e0   e@   ek  +" =1"exp("H E  0 )=1" k  0 =" 0 FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObj@BfObjInfoCEquation Native qnu z= 0 =H E cR+r ge2 16R+r ge ln(R"r ge /4) 2 R[]"r ge (1,0625+2ln1,5){}_1690290833FF@ޠI@ޠIOle CompObjEGfObjInfoH FMicrosoft Equation 3.0 DS Equation Equation.39q|+HHL v lbk =c FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native G_1690290867KF@ޠI0(IOle CompObjJLfObjInfoMEquation Native _1677528099SPF0(I0(IOle ||d v lb =cR 2 (R"R ge )(R+R ge ) "3 exp[H E (" k )]/0,384 FMicrosoft Equation 3.0 DS EqCompObjOQfObjInfoREquation Native ]_1677528255UF0(I0Iuation Equation.39qqAXxi  0 d"d" k =0 FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjTVfObjInfoWEquation Native qqhr  k / 0 =exp("H E  0 ) FMicrosoft Equation 3.0 DS Equation Equation.39q/x= r ge /r_1677391221?ZF0I0IOle CompObjY[fObjInfo\Equation Native K_1677391284b_F0I 㧪IOle CompObj^`fH"0 FMicrosoft Equation 3.0 DS Equation Equation.39qoi RH"rexp"H E " k ()[]ObjInfoaEquation Native _1677391331dF 㧪I 㧪IOle  FMicrosoft Equation 3.0 DS Equation Equation.39q- dR/drH"R/r FMicrosoft Equation 3.0 DS EqCompObjcefObjInfofEquation Native I_1707740780iF 㧪I TIOle CompObjhjfObjInfokEquation Native   !$%&'(+0369:;>ADGHIJKLMPSTUVWX[`cdehknqruxyz{~uation Equation.39qi exp2H  eE  ("  ek  )[]{(dR)  e2 +R  e2 [(d)  e2 +sin  e2 (d)  e2 ]}H"(dr)  e2 +r  e2 [()  e2 +sin  e2 (d)  e2 ] FMicrosoft Equation 3.0 DS Equation Equation.39qsl`k G  =2v li2 dln2v l /d2_1667926075 nF TI TIOle  CompObjmo fObjInfop Equation Native _1667922795sF ŬI ŬIOle CompObjrtfx FMicrosoft Equation 3.0 DS Equation Equation.39qs7 2v l FMicrosoft Equation 3.0 DS EqObjInfouEquation Native :_16769679835xF ŬIIOle CompObjwyfObjInfozEquation Native _1676968014}FIIuation Equation.39qxl N Ci =2v li2 v li"2 =(1"v 02 v li"2 ) "1 `"const(2x)Ole CompObj|~ fObjInfo"Equation Native #_ FMicrosoft Equation 3.0 DS Equation Equation.39qC8\s 2v lj =2v li (1+G i v li"2 2x ij /N Ci )=2v li (1+G i 2v li"2 2x ij )=inv FMicrosoft Equation 3.0 DS Equation Equation.39qs7 x ij FMicrosoft Equation 3.0 DS Eq_1667923347qFIIOle )CompObj*fObjInfo,Equation Native -:_1668289169FIIOle .CompObj/fuation Equation.39quK(q va"v 0 =const(2x) FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo1Equation Native 2g_16682899913 FIIOle 4     [\ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ]^_a`bdcefghikjlnmoqprtsuwvxyz|{}~CompObj5fObjInfo7Equation Native 8_1667925065FI;Iuhj v li =2v li  1+ 1"4v 02 2v li"2 ()/2  `"const(2x) FMicrosoft Equation 3.0 DS Equation Equation.39qOle <CompObj=fObjInfo?Equation Native @Us98Lk 2t=const(2x) FMicrosoft Equation 3.0 DS Equation Equation.39qh$ 1G j =2v li2 c 2 _1707381397^ F;I;IOle BCompObjCfObjInfoEEquation Native F_1707381370F;IIOle NCompObjOfG i2 d2v j d2t j =v li2 2v lj G i2 d(2v/2v lj )d2t=1G i +2x ij v li2 N Ci = FMicrosoft Equation 3.0 DS Equation Equation.39qrH =1G i +2x ij v li"2 (1"v 2 v li"2 )=1G i +2x ij 2v li"2 =2v lj G i 2v li =ObjInfoQEquation Native R_1668335392FIIOle Yinv FMicrosoft Equation 3.0 DS Equation Equation.39qi  2v FMicrosoft Equation 3.0 DS EqCompObjZfObjInfo\Equation Native ]-_1676967913FIIOle ^CompObj_fObjInfoaEquation Native buation Equation.39q4j N Ci =(2v li /v li ) 2 =(1"v 02 v li"2 ) "1 FMicrosoft Equation 3.0 DS Eq_1690309584FIIOle fCompObjgfObjInfoiuation Equation.39q|Wit m in =m 00 v l /c FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native js_1687035603"FfIfIOle lCompObjmfObjInfooEquation Native p_1690307723FfI׿IOle su} #l Ha"E=m in0 c 2 =m 00 cv l  FMicrosoft Equation 3.0 DS Equation Equation.39q|8=d U=W+U aCompObjtfObjInfovEquation Native w_1689355698F׿I!ªId =m gr0 c 2  m +U ad =m 00 c 3  m /v l +U ad FMicrosoft Equation 3.0 DS Equation Equation.39qOle |CompObj}fObjInfoEquation Native xgd f G =q N N RE = m v l /cd" m FMicrosoft Equation 3.0 DS Equation Equation.39qd(h_ f I =_1665522758F!ªI!ªIOle 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Equation Native  @_1661450703<1FII FMicrosoft Equation 3.0 DS Equation Equation.39q$HIpI l cr FMicrosoft Equation 3.0 DS Equation Equation.39qOle  CompObj02 fObjInfo3Equation Native 6D hd n m FMicrosoft Equation 3.0 DS Equation Equation.39qw@< U cr FMicrosoft Equation 3.0 DS Eq_16299324136FIIOle CompObj57fObjInfo8Equation Native :_1664899786;FIGIOle CompObj:<fuation Equation.39q[i G cr FMicrosoft Equation 3.0 DS Equation Equation.39qfft T crObjInfo=Equation Native :_1627228080t@FGIGIOle CompObj?AfObjInfoBEquation Native :_1628198620EFIIOle  CompObjDF!fObjInfoG#Equation Native $: FMicrosoft Equation 3.0 DS Equation Equation.39qtPlP p cr FMicrosoft Equation 3.0 DS Equation Equation.39q_1631366923MJFI)IOle %CompObjIK&fObjInfoL(cP.t q M =v cm /c=1/n m <1 FMicrosoft Equation 3.0 DS Equation Equation.39q h N IEquation Native )_1631368369oOFpsIpsIOle +CompObjNP,fObjInfoQ.Equation Native /6_1626878674>TF ֦I ֦IOle 0 FMicrosoft Equation 3.0 DS Equation Equation.39q`x: f I FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjSU1fObjInfoV3Equation Native 46_1631368402HYF6I6IOle 5CompObjXZ6fObjInfo[8Equation Native 960Ll q M FMicrosoft Equation 3.0 DS Equation Equation.39qprhd 2G(q  eM  ,N  eI  e, 2R  eT_1707772971^FpIpIOle :CompObj]_;fObjInfo`=Equation Native >_1707773062\cFpI`.IOle ACompObjbdBf  )= FMicrosoft Equation 3.0 DS Equation Equation.39qp =2U(q  eM  ,N  eI  ,2R  eT  )"2S(q  eM  ,N  eObjInfoeDEquation Native E_1707403752hF`.I`.IOle MI  ,2R  eT  )2T(q  eM  ,N  eI  ,2R  eT  )+2V(q  eM  ,N  eI  )2p(q  eM  ,N  eI  ) FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjgiNfObjInfojPEquation Native Q'_1707404523mF`.I`I f 2S=""2G/"2T() 2p =""2F T /"2T() 2V =( ST / pV )2R T (2S ) FMicrosoft Equation 3.0 DS EqOle VCompObjlnWfObjInfooYEquation Native Zuation Equation.39ql 2T="2H T /"2S() 2p ="2U/"2S() 2V =( pV U cr /2R T )(2T )=c m  pV U cr /v l 2R T = pV 2U 0 /2R T FMicrosoft Equation 3.0 DS Equation Equation.39qe 2V="2H T /"2p() 2S =_1707160535lJrF`I`IOle bCompObjqscfObjInfoteEquation Native f_1707160751wF`I`IOle kCompObjvxlf"2G/"2p() 2T =(U cr /p l )(2V ) FMicrosoft Equation 3.0 DS Equation Equation.39qe 2p=""2UObjInfoynEquation Native o_1665297828|F`IPZIOle t/"2V() 2S =""2F T /"2V() 2T = pV p l (2p ) FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj{}ufObjInfo~wEquation Native xO_1707081319qFPZIPZI^3Pk 2U=2U 0 +2U ad =2R T 2T pV +2T2S2R T e 2R e  eT0   e 2R e  eT  +" d2R T =2p2V pV + ST (2T )(2S )d2R T 2R T e 2R e  eT0   e 2R e  eT  +" = FMicrosoft Equation 3.0 DS Equation Equation.39q<`. =U cr q M N I + ST Ole CompObjfObjInfoEquation Native X(q M N I /2R T )ln(q MCourier New e ~l N I )d2R T e 2R e  eT0   e 2R   eT  +" []=2a  2T/ pV +2A  d2a  e 2a   e0   e 2a e  e  +" =_1665297830FPIPIOle CompObjfObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39q^xĚ =U cr p l 2VU cr () " e@ pV exp pV 2S2R T Equation Native _1707742634  FPIP<IOle CompObjf()+ pV p l 2VU cr ()  e 2R e  eT0   e 2R e  eT  +"  " e    epV  exp pV 2S2R T ()2S2R T2 d2R T []= FMicrosoft Equation 3.0 DS Equation Equation.39qpjt =U  ecr  2p  epV  p  el  ()  e pV eH e  exp  epV  2S  eH  2R  eObjInfoEquation Native ;_1707741942FP<IP<IOle T  ()+  epV  2p  epV  p  el  ()  e 2R   eT0   e 2R   eT  +"   e pV eH e  exp  epV  2S  eH  2R  eT  ()2S2R  eT  e2 d2R  eT  []= FMicrosoft Equation 3.0 DS Equation Equation.39qe4 =2R T 2T+ H ln2R T 2TU cr  pV ()" pV lnCompObjfObjInfoEquation Native _1707742851FP<I@I2pp l  pV ()[]  e 2R e  eT0   e 2R e  eT  +" 2Td2R T {}1 pV = FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjfObjInfoEquation Native "`|Lk =U  ecr  (2T )+  eST  (2T )(2S )  e 2R   eT0   e 2R e  eT  +" d2R  eT  2R  eT  []=1  epV  2R  eT  2T+ln2R  eT  2T  epV  U  ecr  ()+  epV  lnp  el  2VU  ecr  ()[]  e 2R e  eT0   e 2R e  eT  +" 2Td2R  eT  {} FMicrosoft Equation 3.0 DS Equation Equation.39q_1665297834F@I@IOle CompObjfObjInfo^w6 2F T =2U"2S2T=U cr (2T )" ST 2R T d(2T )(2S )2R T ()  e [(2S )(2T )/2R   eT  e ] e  e0  ( e 2T )(2S )/2R   eT  Equation Native _1665297835F@I@IOle CompObjf+" []=2F T0 +2S2T2R T d2R T e 2R   eT0   e 2R   eT  +" = FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEquation Native _1707743334 F@I0AIOle ^fT =U cr [1"ln(2T )" pV ln(2V )](2T )+ln(2T )+ pV ln(2V )[]  e 2R   eT0   e 2R e  eT  +" [(2T )/2R T ]d2R T {}=CompObjfObjInfoEquation Native _1707743547F0AI0AI FMicrosoft Equation 3.0 DS Equation Equation.39qh$k =1  epV  2R  eT  2T1"ln2R  eT  2T  epV  U  e cr  ()"  epV  lnp  el  2VU  ecr  ()[]+ln2R  eT  2T  epV  ()+  epV  lnp  el  2VU  ecr  ()[]  e 2R e  eT0   e 2R e  eT  +" 2Td2R  eT  {}d #    ! $"&F%')(*,+.-/0132465789:;=<?>A@CBDEGHJIKLMNOPQRSTUVWXZY\[]_^`baefghijklmnopqrstuvwxyz{|}~ Ӂ/G  ZzpKвCʠg+KRsnePdh-Ä, 1,|MDd Lhb  c $A? 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"Pm_RjiꥵUc4f&3ۤX7f7`@~(Q#aŨWȹbWBXc-)CU(ϝQ14_^#Bҧ{?FEkrG$~藱gϮ;xu\<ş9-`u:خlltEY]3$e,Y43Wȏܞʨ|ïr{Owb]1J].79.M(ԴMe&LJ&gYtR- | +<ۺGf5B}wvͫ:h+)[ek%gjMG'#} J+A[s 6ov~DZ/za'w>]aeoZTd/H^uLƶЗD{l}((ar%NyƎ*9StW}mo Tu:P8`'Lz~ʲOĹ>x*>C%;wY4$Wos̜"( M*!bo#,գ+~j&syqZ$|=}*I4wvsSx2 Q;Z(}_XKhbT@e7|oj>Yp2 YD2WQijbd<'8Jtlr|qp!ReG^,yS18܊9(zg 爛g(INw~M^j[Vr||C4׌/|yPCg 7Otw/t(1jIu'<<y&QyF:'T/nޠ$WE h )0^or;&7-"OyE4<#&.uqר1sOCռiR>!1VI\QJDX}/LWRnUI|\sk)-#̧*G .77|~Le,G`[9b$KY=y\rǗy|5csgN9\~$q4օ 5oԺ Tn7۶׷,5NYCnrEKOwљ{Ӹ%,ǖx.3zH_ 8ݐqU"P7?a?hDdF  3 A?"?2Uxī33v"~1{ `!)xī33v"~l$8xڭMLAv)]@ "JA41&@zd0*H)hB((.6DŃ!~hbrADLv646_{f>A5K÷R6RP6JHim=P Y ~x g.b"S CV ܿе/$)?KW xdmxS?sephޅyHoQo$ޢ?ʭy~sUӽu.]]0݈:H4[6/x0l0#>ڼxR[@BO6/ =Zޙ Nen($(8qzrޟwjH|g,%znB21<%`.ss/#gSB!&ov3G͔mWsO'1 zPBt=I&xE;,mYWJ%$"hw q"W֬ʚM;J?@ABCDGJKLMNOPQRSTWZ[\]^_`adghijklmnopqrsvyz{|}~ +" = H 2R T 2T pV +2T2S2R T e 2R e  eT e0   e 2R   eT  +" d2R T = FMicrosoft Equation 3.0 DS Equation Equation.39q_1707773187F0 I0 IOle CompObjfObjInfop$id =U cr { H (2T )+ ST [(2T )(2S )/2R T ]d2R T e 2R e  eT e0   e 2R e  eT  +" }= FMicrosoft Equation 3.0 DS EqEquation Native  @_1707774451aF0 I0# IOle CompObjfuation Equation.39qpR{\ =U  e cr    e H  2p  e pV  p  e l  ()  e  e@ e pV e@ e H exp  e pV  2S  e H  2R  e T  ()+ObjInfoEquation Native n_1707406059F0# I0# IOle    e pV  2p  e pV  p  e l  ()  e@2R e  e T e0   e@2R e  e T  +"  e@   e pV   e@   e H  exp  e pV  2S  e H  2R  e T  ()2S2R  e T  e 2 d2R  e T  []= FMicrosoft Equation 3.0 DS Equation Equation.39q = H  pV 2R T 2T+ln2R T 2T pV U cr ()"CompObj!fObjInfo#Equation Native $_1707406207F0# I mI pV  H ln2p pV p l ()[]  e 2R   eT0   e 2R e  eT  +" 2Td2R T {}= FMicrosoft Equation 3.0 DS Equation Equation.39qOle -CompObj.fObjInfo0Equation Native 1l =1 pV  H 2R T 2T+ln2R T 2T pV U cr ()+ pV lnp l 2VU cr ()[]  e 2R   eT0   e 2R e  eT  +" 2Td2R T {}= FMicrosoft Equation 3.0 DS Equation Equation.39q @l =c m U cr  H v l + ST lnc_1707406143F mI mIOle 9CompObj:fObjInfo<Equation Native =_1707775004F I IOle ECompObjFf m v l ()"(Courier New e~l " e`1 )lnn m []  e 2R   eT0   e 2R e  eT  +" d2R T 2R T v l {} FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoHEquation Native I_1707775220F I OIOle Upe 2G=2H  eT  "2S2T=U   ecr     eH  (2T )"  eST  2R  eT  d(2S )(2T )2R  eT  ()  e [(2S )(2T )/2R   eT  e ]   e0   e (2S )(2T )/2R e  eT  +" []=2G 0 +2S2T2R  eT  e 2R e  eT e0   e 2R   eT  +" d2R  eT  = FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjVfObjInfoXEquation Native Y _1707808124F OI OIpjt = H U cr 1"ln(2T )+ pV  H ln(2p )[](2T )+ln(2T )" pV  H ln(2p )[]  e 2R e  eT e0   e 2R   eT  +" (2T )2R T d2R T {}= FMicrosoft Equation 3.0 DS Equation Equation.39q~Kcd =2H  eT0  "2R  eT  d2A  eOle bCompObjcfObjInfoeEquation Native fg  e 2A e  e0   e 2A e  e  +" =  eH  2a  e  2T  epV  "2a  e  d2A  e  e 2A e  e0   e 2A e  e  +" =  eH  2R  eT  2T  epV  1"ln2R  eT  2T  epv  U  ecr  ()+  epV    eH  ln2p  epV  p  el  ()[]+ FMicrosoft Equation 3.0 DS Equation Equation.39q_1707809206F OIIOle tCompObjufObjInfowEquation Native x_1682535178FI IOle CompObjf~H +  eH    epV  ln2R  eT  2T  epV  U  ecr  ()"ln2p  epV  p  el  ()[]2Td2R  eT  e 2R e  eT0   e 2R e  eT  +" =U  ecr  f  eI  [1+  epV  "  eST  ln(f  eI Courier New Baltic e@~l N  eI 1 e" e@~l )]+2U  ead  = FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEquation Native _17078096732F I IOle 8< =c m U cr  H v l "2R T d ST 2R T v l lnc m v l ()"(Courier New e~l " e`1 )lnn m []()  e 2A   e0   e 2A e  e  +" {}= FMicrosoft Equation 3.0 DS Equation Equation.39q~дi =c  em  U  ecr    eST  v  el    eH  CompObjfObjInfoEquation Native _1632943620F ITI  eST  "lnc  em  v  el  ()+(Courier New e}l " e`1 )lnn  em  []+v  el  lnc  em  v  el  ()"( e}l " e`1 )lnn  em  []d2R  eT  2R  eT  v  el  e 2R e  eT0   e 2R   eT  +" {} FMicrosoft Equation 3.0 DS Equation Equation.39qkHed 2U 0 =(2T )U crOle CompObjfObjInfoEquation Native d_1632943644FTITIOle CompObjfObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39qkNh 2H T0 = H 2U 0 FMicrosoft Equation 3.0 DS EqEquation Native j_1664992101FIIOle CompObjfuation Equation.39q[J8ht 2G 0 = G 2U 0 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEquation Native f_1632943714FI6IOle CompObjfObjInfoEquation Native >_1630062353F6I6Ik"i 2F T0 FMicrosoft Equation 3.0 DS Equation Equation.39qji N I FMicrosoft Equation 3.0 DS EqOle CompObjfObjInfoEquation Native 6_1707809303F!I!IOle CompObjfObjInfouation Equation.39q~9l 2U  ead  =2A  ei  d2a  ei  e 2a e  ei e0   e 2a e  ei  +" =2A  e  d2a  e  e 2a e  e0   e 2a   e  +" =Equation Native U_1662191669F!I#IOle CompObjf(2T2S/2R  eT  )d2R  eT  e 2R e  eT0   e 2R   eT  +"  ei=2  en " >0 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEquation Native h_1662191932F#I#IOle [LX8d 2A  =2T2S/2R T FMicrosoft Equation 3.0 DS Equation Equation.39q[Yf 2a  a"2R T =2p2V/2TCompObj fObjInfo Equation Native u_1705266746 Fa&Ia&IOle CompObj fObjInfoEquation Native  FMicrosoft Equation 3.0 DS Equation Equation.39qY: (2p )=q M1+1/k N I1+m =q M1/k"m f I1+m =f I1+1/k N Im"1/k =(v l /c m ) " e    eH  / e    epV  exp("S/R T ) FMicrosoft Equation 3.0 DS Equation Equation.39q_1705266284Fa&I(IOle CompObjfObjInfoEquation Native _1689371997F(I(IOle CompObjfYhd (2V )=q M"1/k N I"m =q Mm"1/k f I"m =f I"1/k N I1/k"m =(v l /c m ) 1/ e    epV  exp(S/R T ) FMicrosoft Equation 3.0 DS Equation Equation.39q?H/t (2T )=(2p )(2V )=q M N I =f I = m /f G = m c/v cv a" m c/v l = m bObjInfoEquation Native [_1689514288F+I+IOle  "1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qvj (2S )=ln(q MCourier New e ~l N I )=ln(f ICourier New Greek e }lCompObjfObjInfoEquation Native _1682535377)!F+If-I   !"#&)*+,-.1456789:=@ABCDEFGJORUZ]`cfknqtwz} N 1" e }l ) FMicrosoft Equation 3.0 DS Equation Equation.39qvsf  ST =km" e`1 kCourier New e~l m" e`1 >0Ole CompObj "fObjInfo#Equation Native _1682535417&Ff-If-IOle CompObj%' fObjInfo(  FMicrosoft Equation 3.0 DS Equation Equation.39qh  pV =k(Courier New e~l " e`1 )k e~l m" e`1 >0Equation Native  _1682535982$[+Ff-I/IOle CompObj*,f FMicrosoft Equation 3.0 DS Equation Equation.39q(\  H =H T0 U 0 =1+ pV =k(Courier New e~l m+ e~l " e`1 )" e`1 k e~l m" e`1ObjInfo-Equation Native _1707406805kB0F/IH2IOle  FMicrosoft Equation 3.0 DS Equation Equation.39qe  G =2G 0 2U 0 =1+ pV " ST ln(q MCourier New e ~l N I )=CompObj/1fObjInfo2Equation Native _17074068245FH2IH2I H "Courier New Baltic e}l (km"1)k e}l m"1lnq M "km"1k e}l m"1lnN I = FMicrosoft Equation 3.0 DS Equation Equation.39qOle $CompObj46%fObjInfo7'Equation Native (|e =k(Courier New e~l m+ e~l " e`1 )" e`1 k e~l m" e`1 "~l(km" e`1 )k e~l m" e`1 lnf I +(km" e`1)(Courier New Baltic e}l e`"1) k e~l m" e`1 lnN I_17074068933=:FH2I4IOle /CompObj9;0fObjInfo<2 FMicrosoft Equation 3.0 DS Equation Equation.39qb  GR =2G2U 0 = e`1 + pV " ST (2T )2R T d2A  e 2A e  e0   e 2A   e  Equation Native 3_1707406980?F4I7IOle ;CompObj>@<f+" =k(Courier New e~l m+ e~l " e`1 )" e`1 k e~l m" e`1 " FMicrosoft Equation 3.0 DS Equation Equation.39q0x "  kmObjInfoA>Equation Native ?_17074094018~DF7I7IOle H" e`1 (kCourier New e~l m" e`1 )q M N I 2R T dq M N I ln(q M e ~l N I )2R T []  e [(2S }(2T )/2R e  eT  e ] e  e0   e (2S )(2T )/2R e  eT  +" FMicrosoft Equation 3.0 DS Equation Equation.39q =t Courier New e~l FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjCEIfObjInfoFKEquation Native L<_1688805872IF7It9IOle MCompObjHJNfObjInfoKPEquation Native QTo8x9 q M =1/n m FMicrosoft Equation 3.0 DS Equation Equation.39qji N I_1630062410eNFt9It9IOle SCompObjMOTfObjInfoPVEquation Native W6_1680098982SF;I;IOle XCompObjRTYf FMicrosoft Equation 3.0 DS Equation Equation.39q{8p7 p l =np cr FMicrosoft Equation 3.0 DS EqObjInfoU[Equation Native \T_1632944390XF;I/>IOle ^CompObjWY_fObjInfoZaEquation Native bM_1682536532]FߪIPIuation Equation.39qk1hd 2p2V=const FMicrosoft Equation 3.0 DS Equation Equation.39qdK~M#@; `!3+*]m&qK~M#@ -FxڭMlGgfwlvHL h0% 90P1)1Q K/-p!+mzDh!Ђ!qwK ֚ߛyyRR@1!cIS#FQ\:M b%WDI^,&6٣}m^kdMK׎Td[?0ӾbC1P1bʶR6_= )[]V*ۼZqav`vEl{zW!-kr]'vbDľ4O/94 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.e_1664568511m[FI"IOle 0CompObjZ\1f FMicrosoft Equation 3.0 DS Equation Equation.39qk R T FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo]3Equation Native 46_1664568535`F"I"IOle 5CompObj_a6fObjInfob8Equation Native 9u_1664567788eF0I0IY8l R T =R T0 =const(r) FMicrosoft Equation 3.0 DS Equation Equation.39q@/ U adOle ;CompObjdf<fObjInfog>Equation Native ?:_1664568640jFIIOle @CompObjikAfObjInfolC FMicrosoft Equation 3.0 DS Equation Equation.39q?hv\ A  =const(t) FMicrosoft Equation 3.0 DS EqEquation Native D[_1664568598^hoFINIOle FCompObjnpGfuation Equation.39q?5\ R T =const(r) FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoqIEquation Native J[_1663236623!tFNINIOle LCompObjsuMfObjInfovOEquation Native P?_1664385952yFNIIv#X.t  a H"1 FMicrosoft Equation 3.0 DS Equation Equation.39q^.d U ad FMicrosoft Equation 3.0 DS EqOle QCompObjxzRfObjInfo{TEquation Native U:_1690320804T~FI0IOle VCompObj}WfObjInfoYuation Equation.39qr&id U=U 0 +U ad >U 0 =Ec 2 v l"2 = m m in0 c 4 v l"2 =m gr0 c 2  mEquation Native ZB_1664968810tF0I0IOle `CompObjaf FMicrosoft Equation 3.0 DS Equation Equation.39q@k grad=c 2 gradlnWH"c 2 gradlnUObjInfocEquation Native d_1707418021FzIzIOle gCompObjhfObjInfojEquation Native k_1707418074FzII FMicrosoft Equation 3.0 DS Equation Equation.39qqeh grad=c 2 gradlnH T0 H" FMicrosoft Equation 3.0 DS EqOle nCompObjofObjInfoqEquation Native r?uation Equation.39qq#xi H"c 2 gradlnH T ="c 2 gradln(v lc /c)="c 2 grad[ln(v l /c)"ln m ]_1664384671wFI5IOle wCompObjxfObjInfoz FMicrosoft Equation 3.0 DS Equation Equation.39q^`'t =1/[1+U ad /U cr  m0 c(1+" pV )] FMicrosoft Equation 3.0 DS EqEquation Native {_1707418157F5I5IOle ~CompObjfuation Equation.39qqj R T =TS/A  =U cr " ST q M N I ln(q M2l N I )/A  =ObjInfoEquation Native _1707418499lFIIOle CompObjfObjInfoEquation Native J_1664487825`cFII FMicrosoft Equation 3.0 DS Equation Equation.39qq.`zl =U cr " ST c m [ln m "ln(v l /c)"(1"2l)ln(v cm /c)]/A  v l `"R T0 FMicrosoft Equation 3.0 DS Equation Equation.39q?f A  =const(t)Ole CompObjfObjInfoEquation Native [_1632949008FIaIOle CompObjfObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39qk`ul v cm FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native :_1632948930FaIIOle CompObjfObjInfoEquation Native 6_1633015976FIIOle kpcܜ v l FMicrosoft Equation 3.0 DS Equation Equation.39qo?0>  m `"const(r)CompObjfObjInfoEquation Native [_1690321036FC IC IOle CompObjfObjInfoEquation Native  FMicrosoft Equation 3.0 DS Equation Equation.39qrkX.t  m = m0  m `"const(r) FMicrosoft Equation 3.0 DS Eq_1633537908FC I IOle CompObjfObjInfouation Equation.39q~cd A  FMicrosoft Equation 3.0 DS Equation Equation.39q~0cd a  a"REquation Native 6_1633537929F IIOle CompObjfObjInfoEquation Native L_1682540070FIIOle  T FMicrosoft Equation 3.0 DS Equation Equation.39q i 2T=2A   pV  ST (Courier New e~l lnq M +lnNCompObjfObjInfoEquation Native _1666876779FIHI I )=2A   pV  ST [ln m0 "ln(v lc /c)+( e~l " e`1 )ln(v cm /c)]= FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjfObjInfoEquation Native Nu2f =U cr  pV q M N I 2R T =U cr  pV c m0 2R T v lc =2p2V2R T =U cr  pV 2R T U cr p l 2Vexp2S2R T ()[]  e@ pV e@ = FMicrosoft Equation 3.0 DS Equation Equation.39q~l =  epV _1707813158FHIIOle CompObjfObjInfoEquation Native _1707418911FI*IOle CompObjf 2A  e  ln2pp  el    epV  ()+(1+  epV  )lnp  el  2VU  ecr  ()[] e@  e@"1 =U  ecr    epV  2R T 2pp  el    epV  exp2S2R  eT  ()[]  e@  epV  e@1+   epV  FMicrosoft Equation 3.0 DS Equation Equation.39qq^4 2S=(U cr  ST2 / pV 2ObjInfoEquation Native _1707419793 F*I*IOle A  )q M N I (Courier New Baltic e}l elnq  M +lnN I ) 2 =2R T ( ST / pV )( e}l lnq M +lnN I )= FMicrosoft Equation 3.0 DS EqCompObjfObjInfoEquation Native _1690321300@FtItIuation Equation.39qqiB_ =U cr c m0  ST2 [ln m0 "ln(v lc /c)+(Courier New Baltic e}l "1)ln(v cm /c)] 2 / pV 2A  v lc = FMicrosoft Equation 3.0 DS Equation Equation.39qr0p/ =( ST 2R T / pV )[ln m0 +ln m "lnOle CompObjfObjInfoEquation Native L      !"#$'*+,-./014789:;<=>?BEFGHIJMPQRSTUVWX[^_`abcdefgjmnopqrstwz{|}~(v l /c)+(Courier New e~l " e`1 )ln(v cm /c)]= FMicrosoft Equation 3.0 DS Equation Equation.39q~_`d =U cr_1707812577KvFtIIOle CompObjfObjInfoEquation Native {_1663153504FIVIOle CompObjf  pV 2A  2T 2 2pp l  pV exp2A  2T()[]  e    epV  e /   eH  =U cr  pV 2A  2T 2 U cr p l 2Vexp2A  2T()[]  e  e  epV  = FMicrosoft Equation 3.0 DS Equation Equation.39qvc =( pV"2 2p2V/2A  )[ln(2p/p l  pV )ObjInfoEquation Native -_1690321432FVIp IOle + H ln(2Vp l /U cr )] 2 FMicrosoft Equation 3.0 DS Equation Equation.39qrb 2p=p l  pV q M1+1/k CompObjfObjInfoEquation Native _1687034564;Fp Ip IN I1+m =p l  pV c m0  m v l () 1+m cv cm () m"1/k =2R T 2T2V= FMicrosoft Equation 3.0 DS Equation Equation.39qOle %CompObj&fObjInfo(Equation Native )6uP` =p l  pV U cr p l 2V()  e@1+ pV exp pV 2A  2T()=p l  pV 2R T 2TU cr  pV ()  e 1+1/   epV  exp e@" 2S2R T () e@= FMicrosoft Equation 3.0 DS Equation Equation.39qo,ԧ =p l  pV 2S2T 2 U_1663745615Fp#Ip#IOle 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Yv] `=8N.Dd hb H c $AF? ?3"`?G2RlDDY3nUD. `!&lDDY3nUD@|xcdd``> @c112BYL%bpu梻Qdna4pS 8i@F&&\X @ ]` bg!t?0NDd lb J c $AH? ?3"`?I2bo߰7? `!bo߰7h Xh@2xڝR=KAK $D h!`ikP$9ml"$,B쵰S V)Dh๳{9CH ]c͛ahU&>0t"tleȘ1m[flȹ٤/`BEVqi`)eT&OTt<"bLi"9R6 g½oqcHx@"9HVLn`ӷp({ms2IP2Ww޺EWH'?6]6^sv#m.fe'\s C {haW  ;;ʅ%}]SCHV be0t&a/Dd \ bOle ]#CompObjHJ^#fObjInfoK`#Equation Native a#U9sh dR T "T() p =R UT (1+2)exp(")"R T T1"a m exp(")/(pV 2 )[]=R T R UT (1+2)exp(")"R T []TR T "R UT exp(")[]=R T T FMicrosoft Equation 3.0 DS Equation Equation.39qet\ "R T_1630687155jQNF I IOle k#CompObjMOl#fObjInfoPn#Equation Native o#_1630845222SF IiIOle r#CompObjRTs#f "T() V =R T T FMicrosoft Equation 3.0 DS Equation Equation.39q\~bt C V =(1+)R T " pVObjInfoUu#Equation Native v#_1663367677[XFiIIOle y# +  S FMicrosoft Equation 3.0 DS Equation Equation.39qxl C p =(1+)(1+" pV )R T " pV +SCompObjWYz#fObjInfoZ|#Equation Native }#_1663367810]FIKIOle #CompObj\^#fObjInfo_#Equation Native ########################################################$0 FMicrosoft Equation 3.0 DS Equation Equation.39ql C p "C V =[(1+)(1+1/" pV )"(1+)/" pV ]+(")S_1707674863bFKIKIOle #CompObjac#fObjInfod# FMicrosoft Equation 3.0 DS Equation Equation.39qg " pV =(")R T C V "C p +(1+)R T =Equation Native #_1707674916`gFKIIOle #CompObjfh#f FMicrosoft Equation 3.0 DS Equation Equation.39qHo =R T (1+)R UT (1+)exp(")"R T []R UT (1+2)C VObjInfoi#Equation Native #_1630685992olFIIOle # + 2 C p +(1+)R T []exp(")"R T (C V +C p ) FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjkm#fObjInfon#Equation Native #6_1630686026qFIOIeb$ R T FMicrosoft Equation 3.0 DS Equation Equation.39qe 0d  FMicrosoft Equation 3.0 DS EqOle #CompObjpr#fObjInfos#Equation Native #)_1631825868Z~vFOIIOle #CompObjuw#fObjInfox#uation Equation.39q+d  ST FMicrosoft Equation 3.0 DS Equation Equation.39q|\  pVEquation Native #:_1631567787{FI1"IOle #CompObjz|#fObjInfo}#Equation Native #:_1631826007F1"I1"IOle # FMicrosoft Equation 3.0 DS Equation Equation.39q"=t " ST FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj#fObjInfo#Equation Native #>_1631567876F{$I{$IOle #CompObj#fObjInfo#Equation Native #>|"7$?$B$G$L$P$Q$R$U$Y$Z$[$\$]$^$a$d$e$f$i$l$o$r$u$x$y$|$$$2m+1)"(2k+1)2k(2l"1)lnTT w (R T )() FMicrosoft Equation 3.0 DS Equation Equation.39qpjt S/R T =CompObj$fObjInfo$Equation Native $0_1705355727!FpI(" H /" pV )ln(R T T/U cr )"ln(p/p l )"ln" pV /" pV FMicrosoft Equation 3.0 DS Equation Equation.39qOle  $CompObj $fObjInfo$Equation Native $[j?h;d pexpSR T ()="p w expS w R T ()  bb w () " e "   eH   e 2"   epV  =" pV " l c 2 bb l () e   e   e 2k2l(1+2m)"(1+2k)  e 22k(1"2l) FMicrosoft Equation 3.0 DS Equation Equation.39qp,t " H =H 0 /U 0 =1+" _1705410167F>I>IOle $CompObj$fObjInfo$Equation Native $_1689871711F+AI+AIOle !$CompObj"$fpV FMicrosoft Equation 3.0 DS Equation Equation.39qniܜ " pV (R T )2n(R T )=(p 00 /p cr )expObjInfo$$Equation Native %$_1690491128FuCIuCIOle )$(S 00 /R T ) FMicrosoft Equation 3.0 DS Equation Equation.39qri " pV =pV/U 0 =p/ gr0 =2k(2l"1)/(2k2lCompObj*$fObjInfo,$Equation Native -$_1690491865FuCIEI2m"1)=const(r) FMicrosoft Equation 3.0 DS Equation Equation.39qr+t " ST =ST/(2S )U 0 =(2k2m"1)/(2k2l2m"1)Ole 1$CompObj2$fObjInfo4$Equation Native 5$=const(r) FMicrosoft Equation 3.0 DS Equation Equation.39qtPe " l =p cr c "2 2n/" pV_1705955474DFEIWHIOle 9$CompObj:$fObjInfo<$Equation Native =$_1705247535FWHIJIOle @$CompObjA$f FMicrosoft Equation 3.0 DS Equation Equation.39qY#Xhd G 00" FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoC$Equation Native D$?_1705247386FJIMIOle E$CompObjF$fObjInfoH$Equation Native I$?_1707673953+FMIOIY#gt H 00" FMicrosoft Equation 3.0 DS Equation Equation.39qit G 00" Ole J$CompObjK$fObjInfoM$RichEditFlagsN$ Equation Native O$_1707673985FOIpQIOle S$CompObjT$f=(v lc /c)G=(v lc /c)[U 0 +U ad +pV"TS]= FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoV$RichEditFlagsW$ Equation Native X$_1705261882FpQIpQIw|j =U cr  m0 [1+" pV "" TS ln(f I2l N I1"2l )]=U 00 [1+" pV (1"S/R T )]=const(r,A  )Ole _$CompObj`$fObjInfob$Equation Native c$ FMicrosoft Equation 3.0 DS Equation Equation.39qY(9 N I =f I"2l/(1"2l) exp[S" pV /" ST R T (1"2l)]_1705403568]NFp>TIp>TIOle g$CompObjh$fObjInfoj$ FMicrosoft Equation 3.0 DS Equation Equation.39q?Xtl R T =const(r) FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native k$[_1705316983F`VI`VIOle m$CompObjn$fObjInfop$Equation Native q$C_1705318617F`VI`XIOle s$'Hj U ad =0 FMicrosoft Equation 3.0 DS Equation Equation.39qHj v lc = CompObjt$fObjInfov$Equation Native w$_1707472745&F`XI`j[Ib  c=v l / m =c m0 /f I FMicrosoft Equation 3.0 DS Equation Equation.39qf V=(U cr /2p l )f I"1/2Ole z$CompObj{$fObjInfo}$Equation Native ~$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%k N I(1"2k2m)/2k = FMicrosoft Equation 3.0 DS Equation Equation.39qxv =(U cr /2np cr )(b m0_1707472803 F`j[IP]IOle $CompObj  $fObjInfo $Equation Native $_17074729410FP]IP%`IOle $CompObj$f"2 )  e 1/2"   epV  exp(S/R T )=(V 00 /2n)exp(S/R T )b  e 1/2"   epV  FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo$Equation Native $_1707472966FP%`IPbIOle $Pf p=2p l " pV f I(1+2k)/2k N I(2k2m"1)/2k =p cr 2n" pV (b m0"2 ) " e "   eH  / e 2"   epV  exp("S/R T )= FMicrosoft Equation 3.0 DS Equation Equation.39q =p 00 2n" pV exp("S/R T )b " e "   eH CompObj$fObjInfo$Equation Native $_1705332286FPbIPbI e /2"   epV  FMicrosoft Equation 3.0 DS Equation Equation.39qj&>t T=" pV U cr f I /R T =( m0 U cr "Ole $CompObj$fObjInfo$Equation Native $B pV /R T )b "1/2 =T 00 b "1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qjn U 0 =_1705338021SF@dI@dIOle $CompObj$fObjInfo $Equation Native $,_1705333296:#F@QgI@QgIOle $CompObj"$$f m0 U cr b "1/2 =(T 00 R T /" pV )b "1/2 =U 00 b "1/2 FMicrosoft Equation 3.0 DS Equation Equation.39q      !#"%$'&)(*+,.-/12R3456879:;<=>?A@BCDEFGIHKJLMONPQSTtVUXWZY[\]^_`abcdefghijkmlnoqpsrvuxwyz|{} K c $AI? ?3"`?J2yׯ F+ip,U `!Mׯ F+ip, ` "!dxڥkA߼idiI"*I 'Av /MpE\zГ'" BA/ 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r g (r)=r(1"1/a b )=(1_1705411565F얭I]IOle %CompObj%fObjInfo%Equation Native %_1689192031F]IΛIOle %CompObj%f"r 02 /3)r 0 +" l c 2 b l e (1+"   epV  e )/2"   epV  b  e "(1+"   epV  e )/2"   epV  r 2 dr r 0 r +" FMicrosoft Equation 3.0 DS Equation Equation.39qx"l re"r 0 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo%Equation Native %>_1689191309FΛIIOle %CompObj%fObjInfo%Equation Native %G_1707672739FIIx+@m 1/a 0 =0 FMicrosoft Equation 3.0 DS Equation Equation.39q8ht b=" pV  m0 U cr ROle %CompObj%fObjInfo%Equation Native %5 T T() 2 =2k(1"2l)1"2k2l2m() 2 U 00 R T T() 2 =2r g " c c 2 r 2 () " e 2" e  epV  e /"   eH _1707474957FIӢIOle %CompObj%fObjInfo% FMicrosoft Equation 3.0 DS Equation Equation.39qLa "2( pV / H )(r2r g /2r g "2)(1"r g /r"r 2 /3)"r g /r+2r 2 /3="Equation Native %h_1707672800FӢIDIOle %CompObj%f pT 2r g FMicrosoft Equation 3.0 DS Equation Equation.39q@l 2r g r(r"r g "r 3 /3)+" H " pTObjInfo%Equation Native %\_1707672852FDIIOle % 2r g2 2" pV r(r"r g "r 3 /3) 2 " FMicrosoft Equation 3.0 DS Equation Equation.39ql "22r CompObj%fObjInfo%Equation Native %_1707670661/FIIg r 2 (r"r g "r 3 /3) 2 +(1+" pV )(r g "2r 3 /3)2r g 2" pV (r"r g "r 3 /3) 2 =0 FMicrosoft Equation 3.0 DS EqOle %CompObj%fObjInfo%Equation Native %uation Equation.39q`dd 2u"ru 2 /n+"/=2u"(1"" H " pT /2" pV )ru 2 /+ FMicrosoft Equation 3.0 DS Eq_1707670694FIIOle %CompObj%fObjInfo%uation Equation.39q'|g +2r g r "2 (r g "2r 3 /3)(r"r g "r 3 /3) "2 (1+3" pV )/2" pV =0Equation Native %C_1706466205FpIpIOle %CompObj%f FMicrosoft Equation 3.0 DS Equation Equation.39q4q u==2r g /r(r"r g "r 3 /3)ObjInfo%Equation Native %_1706466777FᮭIᮭIOle %CompObj%fObjInfo%Equation Native %_1707672512FᮭI+I FMicrosoft Equation 3.0 DS Equation Equation.39qs =2r g /r(r"r g "r 3 /3) FMicrosoft Equation 3.0 DS EqOle %CompObj%fObjInfo%Equation Native %uation Equation.39qkd n=2"  epV  2"  epV  ""  eH  "  epT  =2(1+S/R   eT   )""  epV  (1"S/R  eT  )=2pVU 0 (pV+ST)U 0 "(pV"ST)pV FMicrosoft Equation 3.0 DS Equation Equation.39qgd 2u="+"=2r g r(r"_1707475590F+IIOle %CompObj%fObjInfo%Equation Native %_1707475626FIp浭IOle %CompObj%fr g "r 3 /3)"2r g (1"2r g "r 2 )r(r"r g "r 3 /3) 2 "2r g r 2 (r"r g "r 3 /3)+ FMicrosoft Equation 3.0 DS Eq&&&& & & &&&&&&&&&&!&$&%&&&'&(&)&*&+&.&1&4&7&8&9&:&;&<&?&B&C&D&E&F&I&L&M&N&Q&T&U&X&[&\&]&`&c&d&e&f&i&l&m&p&s&t&u&v&w&x&y&z&{&|&}&&uation Equation.39qti +2r g "r(r"r g "r 3 /3)=r 2 n FMicrosoft Equation 3.0 DS EqObjInfo&Equation Native &_1706467405Fp浭IpWIOle &CompObj&fObjInfo &Equation Native  &_1706468564FpWIpȺIuation Equation.39q< "=(1+3" pV )(r g "2r 3 /3)2" pV r(r"r g "r 3 /3)Ole &CompObj&fObjInfo&Equation Native & FMicrosoft Equation 3.0 DS Equation Equation.39qli "=r 2 n""=r 2 n"(1+3" pV )(r g "2r 3 /3)2" pV r 2 (r"r g "r 3 /3) 2 2r g FMicrosoft Equation 3.0 DS Equation Equation.39qHd H"1_1706471631FpȺI`IOle &CompObj&fObjInfo&Equation Native &1_1706471731F`I`IOle &CompObj &f 0ͤ KXB2sSRsNl\~rfF\"AZ*a|0_(B LGE@^00'`>H.\TR׳7faDүdC£y?W~P{.2u0^dw`< k`& Ma`(c8x?ׅ *ߔ{9pۋx*$#n/#տ狂LH3_PsAp&粡oeA5OG7Fҏy>P:/f'ӘAEX“5l&>`NIE0~2_Y-U%8@v0oȁg+KRs~aPdk[> 13X?fDd $h h s *Ae? ?3"`?g2b5??bG> `!65??bG #xڥ=LP^>Q!ӡ* ]  @ȪTuR#0СS+y%{wB( wg CJ}y@ tD` DB.[CRqi#vrz@ dGZr)?& ])T0]lQQ 0Vyݜ*š GzC.sU@T 褼Q;]aϙG|6?sKo3Qo =po T#zE__q} XȄ{)gmtgVimԛcg;uJAWq=Bu6z:=Y9G~l%UTx:1x'n5rs4Ǖc<=}*(U5j=E4<ܖe|'AlWudΐf`N OfZقȌ>VF8cBDd <2h i s *Af? ?3"`?h2LdN=-A{$Fb `!ZLdN=-A{$Fz,(xڥkQg&&uSkVjmKR  rPzPzABleJ?AzA#/}7o,cW}rX" d""Ma9yW~-Š+gF09#9rl>)rn97E<WZ5ZUW[Kwͳϝͽަ|ڣhTH:Myy晄=1q}2O+vgTۖ?m禮{ⵁs\Vz~Ru %&8=/Sy{A/CMȯS붂 ^znq^8-1Η̘C{ݴz8AK\Vx?n?,^]y_^ G/_Q?Ju%>{ u'X `!3YQ(QcjD>{ u "@04"xڥOHQ7:鸫 s)%Fb͍.{0t :Ţ:ءKPa =z ,$4 fyg~o@5IW5bV*:F҅0鋷PU-4C^Ыԩ Aj09]X$@w`?*6"]S8Uލ܋Ƚ[Jz6qj[.uˌ\0@׷0{>^s?&K"6S1Xa\QsU3ʞa˻b]Gރ51ZqHͥ`G"yىxHnpx><#JR v;N'p>ccaYSxɝxTz61i~LFqHvK49=d!7n'un{no>}Z hV(Γ:Wvx;%qvxZ;TKOZo']q7S':ȸ[z'?֬ƿl.uROTa]t4o=L[c 9sr(EOkNq_g}UwiYVP%Ӊ8xCvaF%if~%C~t x]=f3o?y&\ }|6ӬN   hK|h^nDd _h k s *Ah? ?3"`?j2O!S57Pg_ `!O!S57Pg,  0Txcdd``cf``baV d,FYzP1n:&fy! 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Ĭ&{:xQ&b x8xڥ+DQ=yLFX E$&VJ!j!5(-%P6@#=w,{ LO'}^Lt-ḏڶ-6Vi??.VcI9TM|&C8>~Z'v_QE'ܕ85 aMw2 ?T@N'⫑x:2JL%9}#Vd%grvE&-Ň,ƉW,|O<܃yuUoQ6dY#w]Ĭtj `ݧЏ:~ʻyXz>U3XY w~y[h:._˺5}B&Yy2)ETّk>۪yK}͗F>g[,F._,A(tJo!Ǭյxr7:ؐ;~A GDd 8 Hb  c $A? ?3"`?2M,2Hy5m `!eM,2Hy5B@"3xڥ=hA{{ݻi!AL!b^BbM8"K%! gIaLaF`(BX-IbNF!̛a.߼y0.u|1\,BRlƣz.ceiu2uz !/xGXbrldrmP8]b0*j[u sr?בs'եjxu>9/o(}o۪_*j kFOYs̾*qݶLqU}싪C?\gя|W9Liŝz~G|ۖ}[(+usL͏7Szs;a!5ZT~W5TTf[T>0){\nC_T,ƺ騹?k\ 4;}uꮈ}瓔 ~#x-&{>]9e} Q>~l`@ oOyx]O}93O>l%,qTKhNџLG^:*xm{<-󈜷gRr|va._3g{}cψdTfl!6kP*d&5d&ҳ͂&F聽GB:ӥBizy@_C[qh s:5Dd @h  s *An? ?3"`?2yIz ZC׉7\ U `!MIz ZC׉7\ @C xcdd`` @c112BYL FMicrosoft Equation 3.0 DS Equation Equation.39qh r 2 n=(1" H  pT /2 pV )2r g2 r(r"r g "r 3 /3) 2 >>(1+3"ObjInfo"&Equation Native #&2_1706472372F`I`IOle ,& pV )(r g "2r 3 /3)2" pV r 2 (r"r g "r 3 /3) 2 2r g FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj-&fObjInfo/&Equation Native 0&V_1707477197 F`IP>ĭI:+d "=r" 2 /n FMicrosoft Equation 3.0 DS Equation Equation.39qwi 2n(1/" 0 "1/")=2n[(1Ole 2&CompObj3&fObjInfo5&Equation Native 6&"r g0 /r 0 "r 02 /3)r 02 /2r g0 "(1"r g /r"r 2 /3)r 2 /2r g ]= FMicrosoft Equation 3.0 DS Equation Equation.39q_1707670147FP>ĭIP>ĭIOle =&CompObj>&fObjInfo@&Pi =(2n/ c c 2 )(1/a 0 b 0 e    eH  e /2   epV  "1/ab  e    eH  e /2   epV  )=r 2 "r 02Equation Native A&l_1707475927 FPƭIPƭIOle G&CompObjH&f FMicrosoft Equation 3.0 DS Equation Equation.39qht 2r g =2n(rr g "r 2 +r 4 /3)/(r 2 " 02 )ObjInfoJ&Equation Native K&_1706531327F@ȭI@ȭIOle O&CompObjP&fObjInfoR&Equation Native S&_1706531583 F@ȭI@j˭I FMicrosoft Equation 3.0 DS Equation Equation.39qnjtg r g =(r 2 " 02 ) n /z FMicrosoft Equation 3.0 DS EqOle V&CompObj W&fObjInfo Y&Equation Native Z&uation Equation.39qnM h  02 =r 02 "2n(r 0 /2r g0 )(r 0 "r g0 "r 03 /3) FMicrosoft Equation 3.0 DS Eq_1707476143F@j˭I@ͭIOle ^&CompObj _&fObjInfoa&uation Equation.39qg "d(1/z)/dr=2zz "2 =2n(r 2 "r 4 /3)(r 2 " 02 ) "(n+1)Equation Native b& _1706558505RWF@ͭI0%ЭIOle g&CompObjh&f FMicrosoft Equation 3.0 DS Equation Equation.39q|hd n=3/2,  2,  5/2,  3  ...  " FMicrosoft Equation 3.0 DS EqObjInfoj&Equation Native k&_1707666943F0%ЭI0ҭIOle n&CompObjo&fObjInfoq&Equation Native r&_1707667016%F0ҭI0խIuation Equation.39qi r  eg  =(r  e2 " 0 e2 )  en 1z 0 "2nr  e2 "r  e4 /3(r  e2 " 0 e2 )  en +1 dr  er   e0   er +" []=(r  e2 " 0 e2 )  en 1z 0 "2n"/3(r  e2 " 0 e2 )  en "1 (  er   e0   er +" [+ FMicrosoft Equation 3.0 DS EqOle ~&CompObj&fObjInfo&Equation Native &h&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'uation Equation.39qLlj +1(r  e2 " 0 e2 )  en " 0 e2 1+ 0 e2 /3(r  e2 " 0 e2 )  en +1 )dr1]="nr(r  e2 " 0 e2 )  e2 (n"1)/3"(n"2)(r" 0 )(n"1)(n"2) 0 e2 " FMicrosoft Equation 3.0 DS Equation Equation.39q_1707665085,"F0խI Q׭IOle &CompObj!#&fObjInfo$&Equation Native &w_1707668208'F Q׭I ٭IOle &CompObj&(&f[l ="(1+ 02 /3)+(r 2 " 02 ) n 1z 0 +nr 0 [(n"1)/3"(n"2)(r 0 " 0 ](n"1)(n"2) 02 (r 02 " 02 ) n"2 +1+ 02 /3(r 02 " 02 ) n {}+ FMicrosoft Equation 3.0 DS Equation Equation.39qf +(r  e2 " 0 e2 )  e n ObjInfo)&Equation Native &_1707669409,F ٭I ܭIOle &n 0 e2 "(2n"5)/3(n"2)(r  e2 " 0 e2 )  en"2 +2n"3(n"1)(r  e2 " 0 e2 )  en" 1 " 0 e2 (2n"1)(1+ 0 e2 /3)n(r  e2 " 0 e2 )  en+ 1 []dr  er   e0   er +" {}= FMicrosoft Equation 3.0 DS Equation Equation.39q@dh =1 0 e2 ("1)  eCompObj+-&fObjInfo.&Equation Native &_170766990641F ܭI}ޭIk [(2n"3)...(2n"2k"1)]r  e3 "[(2n"5)...(2n"2k"3)]r  e5 /32  ek [(n"1)(n"2)...(n"k)] 0 e2k ( 0 e2 "r  e2 )  e"k  ek=1  en"1 " []{}  e@r e  e0   e@r + FMicrosoft Equation 3.0 DS Equation Equation.39q2= +(r 2 " 02 ) n zOle &CompObj02&fObjInfo3&Equation Native &N 0 +1 02 (r 3 "r 5 /3)+[]{}  e@r e  e0   e@r + FMicrosoft Equation 3.0 DS Equation Equation.39q_170766985196F}ޭIIOle &CompObj57&fObjInfo8&Equation Native &_1707669759;FIIOle &CompObj:<&fhtdf +2n(r 2 " 02 ) n ("1) n+2  01"2n (2n"3)...32 n n!r 0 "12lnr+ 0 r" 0 ()[]    e@r e  e0   e@r " FMicrosoft Equation 3.0 DS Equation Equation.39qe "2n(r 2 " 02 ) n ("1) n+2  03"2n (2n"5)...33"ObjInfo=&Equation Native &:_1707652480H7@F8I8IOle &2 n n!r 3 3 03 +r 0 "12lnr+ 0 r" 0 ()[]    e@r e  e0   e@r FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj?A&fObjInfoB&Equation Native &5_1707652508~EFIIi n+1= FMicrosoft Equation 3.0 DS Equation Equation.39qXl =(3+S  en  /R  eTn  )""Ole &CompObjDF&fObjInfoG&Equation Native &  epVn  (1"S  en  /R  eTn  )(1+S  en  /R  eTn  )""  epVn  (1"S  en  /R  eTn  )=2(1+S  e(n+1)  /R  eT(n+1)  )""  epV(n+1)  (1"S ( en+1)  /R  eT(n+1 ) ) FMicrosoft Equation 3.0 DS Equation Equation.39q#<d "  epV(n+1)  ="  epVn  (1"S  en  /R  eTn_1707643152MJFIIOle &CompObjIK&fObjInfoL&Equation Native &?_1707647849OFcIcIOle &CompObjNP&f  )2""  epVn  (1"S  en  /R  eTn  ) FMicrosoft Equation 3.0 DS Equation Equation.39qXj S ( en+1)  R  eT(n+1)  ObjInfoQ&Equation Native &_1706547175TFvIvIOle '''''' '''''''!'"'#'$'%'&'''(')','/'2'5'8';'<'?'B'C'F'I'J'K'L'M'P'S'T'U'X'['\'_'b'c'd'g'j'k'l'o'r's't'u'v'w'z'~'''=("  epVn  "1)(1"S  en  /R  eTn  )(3+S  en  /R  eTn  )""  epVn  (1"S  en  /R  eTn  ) FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjSU'fObjInfoV'Equation Native  '1_1706865525aYFII|h S=0 FMicrosoft Equation 3.0 DS Equation Equation.39qDf " pV =pV/U 0Ole  'CompObjXZ 'fObjInfo[ 'Equation Native '`_1706865701k^FIIOle 'CompObj]_'fObjInfo`' FMicrosoft Equation 3.0 DS Equation Equation.39q&j pVe"U 0 FMicrosoft Equation 3.0 DS EqEquation Native 'B_1706714840cFIIOle 'CompObjbd'fuation Equation.39q+6d 1/a 0 =0 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoe'Equation Native 'G_1706892996uhFIJIOle '     `b!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_acdegfihjkmlnoprqstuwvxyz|{}~CompObjgi'fObjInfoj'Equation Native  'B_1706893407fpmFJIлIq&gd 1u=b  e "   eH  e /2"   epV  " c c 2 a="r 2 "r 02 2n+1+3" pV 2" pV r g "2r 3 /32r gr 0 r +" dr=r eff2 "r 0eff2 2n FMicrosoft Equation 3.0 DS Equation Equation.39qq+ r eff <rOle *'CompObjln+'fObjInfoo-'Equation Native .'G_1706893522rFлI,IOle 0'CompObjqs1'fObjInfot3' FMicrosoft Equation 3.0 DS Equation Equation.39qq<bl r 0eff <r 0 FMicrosoft Equation 3.0 DS EqEquation Native 4'X_1706866037wFvIIOle 6'CompObjvx7'fuation Equation.39qb " pS =" pV =p/ gr0 =2k=1/2m=1 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoy9'Equation Native :'_1689165503G|FI1IOle ='CompObj{}>'fObjInfo~@'Equation Native A'_1706896130\xF1IIj\  gr0 / gr0cr =p/p cr FMicrosoft Equation 3.0 DS Equation Equation.39qOle D'CompObjE'fObjInfoG'Equation Native H'\q@hd 1pdpdr="1+1" pV ()2b2b="1+12k()2v cv v cv =22v cv v cv FMicrosoft Equation 3.0 DS Eq_1706896802FIIOle N'CompObjO'fObjInfoQ'uation Equation.39qq85 p=p 00 2n/b=p 0 b l /b=" l c 2 b l /b FMicrosoft Equation 3.0 DS EqEquation Native R'_1706896596FI] IOle V'CompObjW'fuation Equation.39qqd p 0 =" l c 2 =2p l =p cr 2n FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoY'Equation Native Z'_1706896662F] I IOle ]'CompObj^'fObjInfo`'Equation Native a'_1706896714F I?IqP$e  gr0 =m gr0 /V=(m 00 /V)b "1/2 =" l b l /b FMicrosoft Equation 3.0 DS Equation Equation.39qOle e'CompObjf'fObjInfoh'Equation Native i'q V=V 00 b e   e 1/2 =(m l /" l )(b/b l )  e 1/2 FMicrosoft Equation 3.0 DS Equation Equation.39q_1689157819F?IIOle m'CompObjn'fObjInfop'e  gr0 =m gr0 V(v cv )=m 00  b  V(b)H"m 00 (R T "R UT ) b  b m R T "(a m /T 00 ) b  []Equation Native q'_1689178953zFIIOle x'CompObjy'f FMicrosoft Equation 3.0 DS Equation Equation.39qt8l p=" pV  gr0 =" pV m 00  b  V(b)H"ObjInfo{'RichEditFlags|' Equation Native }'_1689163817F@e4I@e4I''''''''''''''''''''''''''''''''''''''''''''''''''''''''''" pV m 00 (R T "R UT )b m R T "(a m /T 00 ) b  [] b  FMicrosoft Equation 3.0 DS Equation Equation.39qOle 'CompObj'fObjInfo'Equation Native 'oS8f R T =pV/T=const(r) FMicrosoft Equation 3.0 DS Equation Equation.39qtf T 00 =Tv cv /c=T b  =c%bpu@$sU0(Ăd'4ns2͕aU .pȁ v0o(021)W2\ԡ"|b@3X?5d\Dd Hb  c $Ao? ?3"`?2Zhy01<]6= `!.hy01<] @."xڥMhAN+M !ԃ EDE(ZHbb[KxPPb{AAi=xEPVࡗ(*cw Ae͛7o"07}A塏Fi!y :}r\ Dh+-zȳৼL[s5| T)cp`'*?PV$|JZnC/sn[/ Jl&=JGN 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~http://pavlo-danylchenko.narod.ru/docs/Gravithermodynamics.pdfQDyK 7http://pavlo-danylchenko.narod.ru/docs/VisnykVolyn.pdfyK nhttp://pavlo-danylchenko.narod.ru/docs/VisnykVolyn.pdf5DyK 0http://ispcjournal.org/journals/2010/2010-5.pdfyK `http://ispcjournal.org/journals/2010/2010-5.pdfqDyK ?http://pavlo-danylchenko.narod.ru/docs/spiralwaveuniverse.htmlyK ~http://pavlo-danylchenko.narod.ru/docs/spiralwaveuniverse.htmliDyK =http://pavlo-danylchenko.narod.ru/docs/FoundationRGTDUkr.pdfyK zhttp://pavlo-danylchenko.narod.ru/docs/FoundationRGTDUkr.pdf9DyK 1https://elibrary.com.ua/m/book//download/34/3755yK bhttps://elibrary.com.ua/m/book//download/34/3755UDyK 8https://elibrary.com.ua/m/articles//download/11790/3779yK phttps://elibrary.com.ua/m/articles//download/11790/3779DyK *http://bourabai.kz/aldmitriev/gravity.htmyK Thttp://bourabai.kz/aldmitriev/gravity.htm!DyK +https://scask.ru/a_book_phis_t1.php?id=232yK Vhttps://scask.ru/a_book_phis_t1.php?id=232DyK Phttps://inis.iaea.org/collection/NCLCollectionStore/_Public/19/101/19101809.pdfyK https://inis.iaea.org/collection/NCLCollectionStore/_Public/19/101/19101809.pdfDyK Qhttp://www1.jinr.ru/publish/Archive/Pepan/1991-v22/v-22-5/pdf_obzory/v22p5_3.pdfyK http://www1.jinr.ru/publish/Archive/Pepan/1991-v22/v-22-5/pdf_obzory/v22p5_3.pdfDyK Dhttps://iopscience.iop.org/article/10.1088/0004-6256/137/5/4322/pdfyK https://iopscience.iop.org/article/10.1088/0004-6256/137/5/4322/pdfDyK )https://doi.org/10.1017/CBO9780511563966yK Rhttps://doi.org/10.1017/CBO9780511563966UDyK 8https://elibrary.com.ua/m/articles//download/11893/3765yK phttps://elibrary.com.ua/m/articles//download/11893/3765UDyK 8https://elibrary.com.ua/m/articles//download/11906/3768yK phttps://elibrary.com.ua/m/articles//download/11906/3768UDyK 8https://elibrary.com.ua/m/articles//download/11907/3769yK phttps://elibrary.com.ua/m/articles//download/11907/3769UDyK 8https://elibrary.com.ua/m/articles//download/11905/3767yK phttps://elibrary.com.ua/m/articles//download/11905/3767DyK 'https://era.ed.ac.uk/handle/1842/32130yK Nhttps://era.ed.ac.uk/handle/1842/32130DyK  https://arxiv.org/abs/1012.5914yK @https://arxiv.org/abs/1012.5914}DyK Bhttps://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.19043201206yK https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.19043201206DyK $https://arxiv.org/abs/gr-qc/9504004yK Hhttps://arxiv.org/abs/gr-qc/9504004DyK Dhttps://iopscience.iop.org/article/10.1088/0004-6256/137/5/4322/pdfyK https://iopscience.iop.org/article/10.1088/0004-6256/137/5/4322/pdf9DyK 1https://briankoberlein.com/post/island-universe/yK bhttps://briankoberlein.com/post/island-universe/DyK !https://arxiv.org/abs/1606.02127yK Bhttps://arxiv.org/abs/1606.02127qDyK ?https://onlinelibrary.wiley.com/doi/pdf/10.1002/prop.201700018yK ~https://onlinelibrary.wiley.com/doi/pdf/10.1002/prop.2017000185DyK 0http://estfound.org/downloads/pioneer_paper.pdfyK `http://estfound.org/downloads/pioneer_paper.pdfyDyK 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