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B@5BL59 3;025 @0AA<0B@820NBAO AE5<K @>B>@>2 A 4>?>;=8B5;L=K<8 C?@C38<8 A2O7O<8, :>B>@K5 2 @07;8G=KE 2840E 2A5340 2E>4OB 2 A>AB02 B5E=>;>38G5A:8E @>B>@>2. !=0G0;0 87CG0;0AL ?@>AB59H0O <>45;L @>B>@0 B0:>3> B8?0, >B;8G0NI0OAO >B AE5<K, 87>1@065==>9 =0 @8A.1, B>;L:> =0;8G85< >4=>9 4>?>;=8B5;L=>9 C?@C3>9 A2O78. !>>B25BAB25==> C@02=5=8O 42865=8O (9) 4;O 40==>3> A;CG0O >B;8G0NBAO >B C@02=5=89 (5), (6) B>;L:> G;5=0<8, A>45@60I8<8 :>MDD8F85=BK 45<?D8@>20=8O  EMBED Equation.3  8 65AB:>AB8  EMBED Equation.3 :  EMBED Equation.3  (9) ( EMBED Equation.3 - @0AAB>O=85 >B >?>@K  4> B>G:8 :@5?;5=8O C?@C3>9 A2O78.). 5H5=85 A8AB5<K (9) ?>:070;>, GB> 2 A;CG05  EMBED Equation.3  ?@5F5AA8>==>5 42865=85 @>B>@0 ?@8 =0;8G88 C?@C3>9 A2O78 A>>B25BAB2C5B ?@O<>9 ?@5F5AA88, B> 5ABL O2;O5BAO B0:8< 65, :0: 8 ?@8 >BACBAB288 C?@C38E A2O759. 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EMBED Equation.3  (10)  57C;LB0BK G8A;5==>3> @5H5=8O C@02=5=89 (9, 10), ?>;CG5==K5 ?@8 A:>@>AB8 2@0I5=8O @>B>@0  EMBED Equation.3 , ?@54AB02;5=K =0 @8A.2. !@02=5=85 40==KE 3@0D8:>2 ?>:07K205B, GB> 4065 2 A;CG05 >B=>A8B5;L=> =87:>9 C3;>2>9 A:>@>AB8 8 1>;LH8E =0G0;L=KE >B:;>=5=8OE @>B>@0 >B;8G8O <564C @5H5=8O<8 =5;8=59=>9 8 ;8=59=>9 A8AB5< C@02=5=89 A ?@0:B8G5A:>9 B>G:8 7@5=8O <>6=> AG8B0BL =57=0G8<K<8. 0==K9 2K2>4 405B >A=>20=85 2 40;L=59H5< ?@8 8AA;54>20=88 @50;L=KE :>=AB@C:F89 B5:AB8;L=KE @>B>@>2 >3@0=8G820BLAO ;8=59=K<8 <0B5<0B8G5A:8<8 <>45;O<8, 4>?CAB8<>ABL G53> 4>?>;=8B5;L=> ?>4B25@6405BAO 0=0;87>< 48=0<8G5A:>9 <>45;8 25@5B5=0 "-45-IV, 87>1@065==>9 =0 @8A.3. -B0 <>45;L >B>1@0605B 25@B8:0;L=>5 25@5B5=> A :0BCH:>9 8 ?0:>2:>9, ?@54AB02;5==K<8 2 2845 65AB:>3> 8=5@F8>==>3> 48A:0 1, ?@8:@5?;5==>3> : 65AB:><C H?8=45;N 2, :>B>@K9 2@0I05BAO 2 C?@C38E >?>@0E 3, 4 #@02=5=8O 42865=8O 25@5B5=0 4;O 40==>9 <>45;8 1K;8 ?>;CG5=K 2 A;54CNI5< 2845:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  (11)  EMBED Equation.3  #@02=5=8O (11) >?8AK20NB :0: AB0F8>=0@=>5, B0: 8 =5AB0F8>=0@=>5 42865=85 @>B>@0. 0?@8<5@, 704020O 70:>= 2@0I0B5;L=>3> 42865=8O @>B>@0 A ?>;>68B5;L=K<8 7=0G5=8O<8 CA:>@5=89, <>6=> 87CG0BL ?@>F5AAK @073>=0 25@5B5=0 8 AB@>8BL @57>=0=A=K5 :@82K5, A ?><>ILN :>B>@KE >?@545;OBL :@8B8G5A:85 A:>@>AB8 2@0I5=8O. 57C;LB0BK G8A;5==>3> 0=0;870 @57>=0=A=KE :@82KE ?@54AB02;5=K =0 @8A. 4-1, 345 O2=> ?@>A<0B@820NBAO 420 ?8:0: ?@8 G0AB>B0E 2@0I5=8O  EMBED Equation.3  8  EMBED Equation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quation.3  CAB0=>2;5= 2 C?@C38E >?>@0E  8 , :>MDD8F85=BK 65AB:>AB8 :>B>@KE 2 =0?@02;5=8OE  EMBED Equation.3  >1>7=0G5=K G5@57:  EMBED Equation.3 . ( >1I5< A;CG05 65AB:>AB8 2 =0?@02;5=8OE  EMBED Equation.3  @07;8G=K.). >B>@ 1 ?@82>48BAO 2> 2@0I5=85 ?>A@54AB2>< 1;>G:0 2 8 @5<5==>3> ?@82>40 3, 65AB:>ABL :>B>@>3> 2 =0?@02;5=88 >A8  EMBED Equation.3  >1>7=0G5=0 G5@57  EMBED Equation.3 .  B>G:5  EMBED Equation.3  : @>B>@C 1 A ?><>ILN AD5@8G5A:>3> H0@=8@0 8 C?@C3>3> M;5<5=B0 4 A C3;>2>9 65AB:>ABLN  EMBED Equation.3  ?>4A>548=5= @01>G89 @>B>@ 5 A 8=5@F8>==K< 48A:>< 6. (B<5B8<, GB> 2 @01>B5 8AA;54>20;8AL B0:65 <>45;8 A C?@C38< :@5?;5=85< 48A:0 6 : @>B>@C 5.). 2865=85 40==>9 @>B>@=>9 A8AB5<K >?@545;O5BAO :>>@48=0B0<8 F5=B@0 <0AA ?@82>4=>3> @>B>@0  EMBED Equation.3  EMBED Equation.3 , C3;0<8 ?>2>@>B0 >A8 MB>3> @>B>@0  EMBED Equation.3  2>:@C3 53> F5=B@0 <0AA 8 C3;0<8 ?>2>@>B0 >A8 @01>G53> @>B>@0  EMBED Equation.3  2>:@C3 B>G:8  EMBED Equation.3 . >>@48=0BK 107>2KE B>G5: @>B>@0 >?@545;ONBAO @025=AB20<8:  EMBED Equation.3  (12) ! 8A?>;L7>20=85< C@02=5=8O 03@0=60 1K;0 ?>;CG5=0 A;54CNI0O A8AB5<0, A>AB>OI0O 87 H5AB8 48DD5@5=F80;L=KE C@02=5=89 42865=8O @>B>@0 ?@O48;L=>9 :0<5@K:  EMBED Equation.3  (13)  EMBED Equation.3  (14) 0==0O A8AB5<0 C@02=5=89 >15A?5G8205B 2>7<>6=>ABL 2A5AB>@>==53> 0=0;870 42865=8O @>B>@0. =0 ?>72>;O5B 8AA;54>20BL ?@>F5AAK @073>=0 8 2K1530, E0@0:B5@ 7028A8<>AB8 42865=8O ?@82>4=>3> 8 @01>G53> @>B>@>2 >B 35><5B@8G5A:8E, :8=5<0B8G5A:8E 8 D878G5A:8E ?0@0<5B@>2 @>B>@=>9 A8AB5<K, >?@545;OBL CA8;8O 2 >?>@0E ?@82>4=>3> @>B>@0, <><5=B 2 C?@C3>< AD5@8G5A:>< H0@=8@5, 0 B0:65 :@8B8G5A:85 A:>@>AB8 @>B>@=>9 A8AB5<K. ! ?@0:B8G5A:>9 B>G:8 7@5=8O =081>;55 206=K< O2;O5BAO 87CG5=85 2>7<>6=>AB8 @073@C7:8 >?>@ ?@82>4=>3> @>B>@0 >B 2>7459AB28O 2KA>:>G0AB>B=KE =03@C7>:, 2>7=8:0NI8E 2A;54AB285 =5C@02=>25H5==>AB8 @01>G53> @>B>@0. -B>B 2>?@>A 87CG0;AO =0 ?@8<5@5 @>B>@=>9 A8AB5<K A> A;54CNI8<8 7=0G5=8O<8 >A=>2=KE ?0@0<5B@>2:  EMBED Equation.3   ?@>F5AA5 0=0;870 @0AA<0B@820;8AL 420 20@80=B0 :>=AB@C:F89 @>B>@=>9 A8AB5<K: 1  ?@82>4=>9 8 @01>G89 @>B>@K 2K?>;=5=K :0: 548=>5 F5;>5 ( EMBED Equation.3 ), 2 - ?@82>4=>9 8 @01>G89 @>B>@K A>548=5=K <564C A>1>9 C?@C3>9 A2O7LN A C3;>2>9 65AB:>ABLN  EMBED Equation.3 . 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