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(1.20) !8AB53@5H=>ABL A@54AB20 87AB02;ONI0O ?>3@5H=>AB8 !, >AB0NI0OAO ?>AB>O==>9 (?@8 =5879 87<5@O59 25;8G8=5) 8;8 87=>. !;CG09=0O (F5=B@8@>20==0O) ?>3@5H=>ABL A@54AB20 87AB02;ONI0O ?>3@5H=>AB8 !, 87<5=ONI0OAO A;CG09=K1@07>< 8 85 <0B55 >6840=85.  ?>=OB8O< A8AB53@5H=>ABL A@54AB20 87;=>ABLN ?@8<5=8>1@065=8O, 87;>65==K5 2KH5 2 @0745;5 1.1.2, 8 D>@B>@KE A;54C5B 703@5H=>ABL 873@5H=>ABL A@54AB20 873@5H=>ABL A@54AB20 87 ?>3@5H=>ABL !, ?@8<5=O53> 4;O 87<5@5=8O =5879 (2 ?@>F5AA5 879 25;8G8=K. 8=03@5H=>ABL A@54AB20 87 A>AB02;ONI0O ?>3@5H=>AB8 !, 2K720==0O 87<5=5=85< 87<5@O59 D878G5A:>9 25;8G8=K 2 ?@>F5AA5 87=OB8O, ?@82545==K5 2 :;0AA8D8:0F88 @8A. 1.2, 1C4CB @0AAB@5=K =865. 1.2.3. >3@5H=>AB8 871@07>20B5;59. 0AAB@5==0O :;0AA8D8:0F8O ?>3@5H=>AB59 A@54AB2 87<5@5=89 ?@8<5=8<0 8 4;O 871@07>20B5;59 (). 4=0:> 4;O =8E, :@>3>, H8@>:> 8A?>;L7CNBAO 5I5 420 ?>=OB8O: ?>3@5H=>ABL , ?@82545==0O :> 2E>4C (?>3@5H=>ABL ?> 2E>4C), 8 ?>3@5H=>ABL , ?@82545==0O : 2KE>4C (?>3@5H=>ABL ?> 2KE>4C). =D>@1 MB8E ?>3@5H=>ABOE =5>1E>48<0 4;O @0AG5B0 ;>38G5A:8E E0@0:B5@8AB8: A@54AB2 87AB02 :>B>@KE 2E>4OB 871@07>20B5;8. $C=:F859 ?@5>1@07>20=8O 873> ?@5>1@07>20B5;O =07K20NB 7028A8ABL @<0B82=K<8 ?0@0<5B@04=>3> 8 2KE>4=>3> A83=0;>2 879 8=D>@<0F88.  :0G5AB25 ?@8<5@0 @0AAB@84=K4=K< A83=0;0B>@>3> O2;ONBAO M;5:B@8G5A:85 =0?@O65=8O. =D>@<0B82=K< ?0@045  O2;O5BAO 459AB2CNI55 7=0G5=85 MB>3> =0?@O65=8O, 0 8=D>@<0B82=K< ?0@045  G0AB>B0 2KE>4=>3> =0?@O65=8O. $C=:F8O ?@5>1@07>20=8O B0:>3>   MB> 7028A8ABL <564C 459AB2CNI8< 7=0G5=85 2E>45 8 G0AB>B>9 =0?@O65=8O =0 2KE>45. 25451>7=0G5=8O: x  2E>4=0O 25;8G8=0  (8AB8==>5 7=0G5=85 8=D>@3> ?0@04=>3> A83=0;0), y  2KE>4=0O 25;8G8=0 , Æ(x)  @50;L=0O DC=:F8O ?@5>1@07>20=8O , Æ=(x)  =>1@07>20=8O. > >?@545;5=8N ”2KE(x) = Æ(x)  Æ=(x), (1.21) 345 ”2KE(x)  01A>;NB=0O ?>3@5H=>ABL  ?> 2KE>4C. >3@5H=>ABL  6=> ?@825AB8 : 53> 2E>4C: ”2E(x) = ¨=[Æ(x)]  x, (1.22) 345 ”2E(x)  01A>;NB=0O ?>3@5H=>ABL  ?> 2E>4C, 0 ¨=  DC=:F8O, >1@0B=0O DC=:F88 Æ=. @82545==K5 >?@545;5=8O 01A>;NB=KE ?>3@5H=>AB59  ?> 2E>4C 8 2KE>4C 8;;NAB@8@C5B @8A. 1.3. 1A>;NB=CN ?>3@5H=>ABL  ?> 2E>4C 6=> 8=B5@?@5B8@>20BL A;54CNI81@07>;>68  8A?>;L7C5BAO 4;O 879 25;8G8=K x. 0 2KE>45  2:;NG5= B>G=K9 ?@81>@, 874=CN 25;8G8=C y A ?@5=51@568 9 ?>3@5H=>ABLN. =0O 7=0G5=85 y = Æ=(x), M:A?5@8@ =0E>48B @57C;LB0B 874=>9 25;8G8=K ?> 8725AB=>9 59 DC=:F88 ?@5>1@07>20=8O X = ¨=(y) = ¨=[Æ(x)]. "0:81@07>5 ?> D>@<C;5 (1.22) 7=0G5=85 ”2E(x) 6=> @0AAAB02;ONICN ?>3@5H=>AB8, 2=>A8<CN  2 @57C;LB0B 874=>9 25;8G8=K x.   A;8 Æ(x) 8 Æ=(x)  DC=:F88, ?@>872>4=K5 :>B>@KE 87<5=ONBAO  8 ?;02=>, B>  EMBED Equation.3  . (1.23) A;8 Æ=(x)  ?@O D>@;55 C?@>I05BAO. 0?@8<5@, 5A;8   87<8=0;L=KMDD8F85=B> 53> ?>3@5H=>AB8, ?@82545==K5 :> 2E>4C 8 2KE>4C, A2O70=K 1>9 ?@>ABK>B=>H5=85<: ”2KE = = ”2E . (1.24) 1.2.4. 448B82=0O, AB02;ONI85 ?>3@5H=>AB8. 0==K5 A>AB02;ONI85 ?>3@5H=>AB8 E0@0:B5@=K :0: 4;O A@54AB2 87<5@5=89, B0: 8 4;O 871@07>20B5;59. 1KG=> >?@545;ONB 0448B82=CN, 3@5H=>AB8 :0: A>AB02;ONI85 01A>;NB=>9 A8AB59 ?>3@5H=>AB8 ”(x), A>>B25BAB25==> =5 7028AOICN >B 87<5@O59 25;8G8=K x, 7028AOICN >B x ;8=59=> 8 7028AOICN >B x =5 ;8=59=>. 5;8=59=CN A>AB02;ONICN ?>3@5H=>AB8 ?@8 : 87<5@8B5;L=K1@07>20B5;O9 =>9 DC=:F859 ?@5>1@07>20=8O =07K20NB ?>3@5H=>ABLN ;8=59=>AB8. 4=0:> B0:>5 >?@545;5=85 =5 ?>72>;O5B >4=>7=0G=> 2K45;8BL MB8 A>AB02;ONI85 87 @50;L=> =01;N4059 7028A8AB8 ”(x), ?@8B>@>9 ?@82545= =0 @8A. 1.40. 59AB28B5;L=>, 2 :0G5AB25 A>AB02;ONI59 ?>3@5H=>AB8 ”(x), =0?@8B x, 6=> ?@8=OBL ;N1>5 7=0G5=85 ?>3@5H=>AB8. !CI5AB2CNB @07;8G=K5 ?>4E>4K : >?@545;5=8N C:070==KE A>AB02;ONI8E ?>3@5H=>AB8. 865 ?@82545= >48= 87 ?@8=OBKE ?>4E>4>2. > >?@545;5=8N ”(x) = ”0 + ”;NB=0O ?>3@5H=>ABL, ”0  0448B82=0O A>AB02;ONI0O MB>9 ?>3@5H=>AB8 (0448B82=0O ?>3@5H=>ABL), ”<  AB02;ONI0O ?>3@5H=>AB8 (3@5H=>ABL), ”=  =5;8=59=0O A>AB02;ONI0O ?>3@5H=>AB8 (?>3@5H=>ABL ;8=59=>AB8, =5;8=59=>ABL). 1KG=> AG8B0NB, GB> ”0 = ”(x0), (1.26) 345 x0  7=0G5=85 87<5@O59 25;8G8=K, ;560I55 2=CB@8 480?07>=0 87AB8, 5A;8 MB>B 8=B5@20; A>45@68B B>G:C 0, B> 2K18@0NB x0 = 0. ">340 ”0 = ”(0). (1.27) 0 @8A. 1.41 ?@82545= 3@0D8: 7028A8AB8 ”(x)  ”0 = ”B 87<5@O59 25;8G8=K x. C;LB8?;8:0B82=0O A>AB02;ONI0O ?>3@5H=>AB8 ?> >?@545;5=8N 7028A8B >B x ;8=59=>. !>>B25BAB2CNICN ?@O1KG=> ?@>2>4OB G5@57 B>G:8 [x0; ”(x0)] 8 [x2; ”(x2)]. ">340  EMBED Equation.3 . (1.28)  G0AB=>  EMBED Equation.3  (1.29) 5;8=59=0O A>AB02;ONI0O ?>3@5H=>AB8 ”= >?@545;O5BAO 87 (1.25) A CG5B> ?>:070=> =0 @8A. 1.42.  1.2.5. A=>2=0O 8 4>?>;=8B5;L=K5 ?>3@5H=>AB8. $878G5A:0O 25;8G8=0, =5 87<5@O5<0O 40==K< 87 >:07K20NI0O 2;8O=85 =0 @57C;LB0BK 879 25;8G8=>9. @8<5@K 2;8ONI8E 25;8G8=: B5ABL >:@C60NI53> 2>74CE0, =0?@O65=85 8 G0AB>B0 ?8B0NI59 A5B8, 0BAD5@=>5 402;5=85.  2;8ONI8< 25;8G8=0B=>AOB B0:65 =58=D>@<0B82=K5 ?0@0<5B@K 872. 0?@8;LB<5B@0, 87 459AB2CNI55 7=0G5=85 =0?@O65=8O (=0?@O65=85  87@<0B82=K9 ?0@0@<0B82=K<8 ?0@0<5B@0B0 8 :>MDD8F85=B 03> =0?@O65=8O.  B5E=8G5A:>9 4>:C=:@5B=K5 @07=>284=>AB8 A@54AB2 87@@G85 >1;0AB8 7=0G5=89 2;8ONI8E 25;8G8=, 0 B0:65 =>@G85 CA;>28O 87<5@5=89. 0?@89 4>:C<5=B0F88 65B 1KBL C:070=>: ;8ONI0O 25;8G8=0: B5:@C60NI53> 2>74CE0. >@5 7=0G5=85 2;8ONI59 25;8G8=K: 20 °!. >@1;0ABL 7=0G5=89 2;8ONI59 25;8G8=K: >B +18 4> +22 °!. 01>G0O >1;0ABL 7=0G5=89 2;8ONI59 25;8G8=K: >B +5 4> +40 °!. >3@5H=>ABL A@54AB20 87<5@5=89, ?@8<5=O53> 2 =>@28OE, =07K205BAO >A=>2=>9. !>AB02;ONI0O ?>3@5H=>AB8 A@54AB20 87B:;>=5=854=>9 87 2;8ONI8E 25;8G8= >B =>@3> 7=0G5=8O 8;8 2KE>40 55 70 ?@545;K =>@9 >1;0AB8 7=0G5=89, =07K205BAO 4>?>;=8B5;L=>9.  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