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Minkowski Measure of Asymmetry and Minkowski Distance for Convex Bodies

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(19) K<=7< 75B 69 HF5798 657? HC H<9 95F@M (=B?CK G?=G D5D9F 13 =B 

(20) 5B8 H<9 (=B?CKG?= 8=GH5B79 69HK99B 7CBJ9L 6C8=9G

(21) K<=7< =G H<9 ;9B9F5@=N5H=CB C: H<9 K9@@ ?BCKB 5B57< (5NIF 8=GH5B79 69HK99B 79BHF5@@M GMAA9HF=7 7CBJ9L 6C8=9G CF 5B57< GD579G  .<9 GHI8M C: H<9G9 HKC GI6>97HG 5B8 H<9=F F9@5H=CBG G<CI@8 69 5 D5FH C: 7CBJ9L=HM =B B=H9 8=A9BG=CB5@ 5B9 GD579G .<9 7CBH9BH C: H<=G H<9G=G =G 5FF5B;98 =B H<9 :C@@CK=B; K5M $B -97H=CB  K9 ;=J9 GCA9 657?;FCIB8G HC H<9 F9GI@HG =B H<9 H<9G=G $B -97H=CB  K9 ;=J9 GCA9 DF9@=A=B5FM 89B=H=CBG 5B8 F9GI@HG $B H<9 :C@@CK=B;  G97H=CBG K9 DF9G9BH H<9 A5=B F9GI@HG :FCA H<9 +5D9F $

(22) $$

(23) $$$ 5B8 $/ F9GD97H=J9@M 

(24)  

(25) $B H<=G G97H=CB K9 ;=J9 5 657?;FCIB8 HC A95GIF9G C: 5GMAA9HFM CF GMAA9HFM 5B8 HC (=B?CKG?= CF 5B57< (5NIF 8=GH5B79G .<9B :C@ @CKG 5 6F=9: 89G7F=DH=CB C: CIF KCF?  %&-*3160' 51 /(%463(4 1) %49//(539 $B 

(26) ACH=J5H98 6M AI7< DF9J=CIG KCF?

(27)  "FOIB65IA DFCDCG98

(28) =B <=G K9@@ ?BCKB D5D9F 13

(29) H<9 7CB79DH C: A95GIF9G C: 5GMAA9HFM CF GMAA9HFM :CF 7CBJ9L 6C8=9G =B B=H9 8=A9BG=CB5@ GD579G  A95GIF9 C: 5GMAA9HFM =G 5 BCB B9;5H=J9 F95@ J5@I98 :IB7H=CB 89B98 CB H<9 :5A=@M C: 5@@ 7CB J9L 6C8=9G C: 5 B=H9 8=A9BG=CB5@ 5B9 GD579

(30) K<=7< G5H=G9G GCA9 588=H=CB5@ 7CB8=H=CBG

(31) 9;

(32) H<9 6=;;9F H<9 A95GIF9 =G

(33) H<9 2ACF9 5GMA A9HF=7 H<9 7CBJ9L 6C8M G<CI@8 69

(34) 5B8 GC 75B 69 IG98 HC 89G7F=69 <CK.  *#*) + * "))*%$  

(35)        / -%() $ &()) ?>E5G B5CB "51BDA5 ?6 1BH==5CAH "9>;?FB;9 =51BDA5 ?6 BH==5CAH >5 B@135 >5 6D>3C9?> "9>;?FB;9 49BC1>35 1>138"1IDA 49BC1>35 .

(36) :5F 5 7CBJ9L 6C8M =G :FCA 5 79BHF5@@M GMAA9HF=7 CB9 CF <CK 7@CG9 HC 5 GD97=98 CB9

(37) 9;

(38) H<9 G=AD@9L (5BM A95GIF9G C: 5GMAA9HFM 5FCG9 :FCA 9LHF9A5@ DFC6@9AG =B ;9 CA9HFM CF CH<9F 6F5B7<9G C: A5H<9A5H=7G G99 1313

(39) 1313

(40) 13

(41) 13

(42) 13

(43) 13

(44) 13

(45) 13

(46) 13  9:CF9 "FOIB65IAG 13 A5BM C: H<9A K9F9 8=G7CJ9F98

(47) 5B8 :CF;CHH9B 5B8 F98=G7CJ9F98

(48) 5;5=B 5B8 5;5=B : H9F 13 A5H<9A5H=7=5BG GH5FH98 HC :C7IG 9=H<9F CB GHI8M=B; H<9 GD9 7=5@ DFCD9FH=9G C: H<9 ?BCKB CB9G CF CB B8=B; B9K CB9G 5B8 5DD@= 75H=CBG

(49) 9;

(50) ;9CA9HF=75@ =B9EI5@=H=9G G99 13

(51) 13

(52) 1313

(53) 13

(54) 13

(55) 1313

(56) 13  $B F979BH M95FG GCA9 A95GIF9G C: CH<9F ?=B8G C: GMAA9 HFM <5J9 699B DFCDCG98 5B8 GHI8=98 GI7< 5G A95GIF9G C: FCH5H=CB GMA A9HFM

(57) <MD9FD@5B9 F997H=CB 5GMAA9HFM 9H7 G99 1313

(58) 13

(59) 13

(60) 13

(61) 13 13  ACB; 5@@ ?BCKB A95GIF9G C: 5GMAA9HFM

(62) H<9 FGH 5B8 DFC656@M H<9 ACGH =ADCFH5BH CB9 =G H<9 GC 75@@98 (=B?CKG?= A95GIF9 G99 -97H=CB 

(63) K<=7< 7<5F57H9F=N9G H<9 G=AD@9L 5G H<9 ACGH 5GMAA9HF=7 7CBJ9L 6C8=9G .<=G A95GIF9 <5G 699B GHI8=98 :CF CJ9F 5 79BHIFM

(64) 5B8 A5BM =ADCFH5BH DFCD9FH=9G <5J9 699B :CIB8 CIH

(65) 6IH H<9F9 5F9 GH=@@ GCA9 DFC6@9AG @9:H

(66) :CF =BGH5B79

(67) H<9 GC 75@@98 GH56=@=HM DFC6@9A

(68) =9

(69) 9GH=A5H=B; H<9 89J= 5H=CB C: 5 7CBJ9L 6C8M :FCA H<9 G=AD@9L =: =HG (=B?CKG?= A95GIF9 =G 7@CG9 HC =HG A5L=A5@ J5@I9  %&-*3160' 51 ,0-184-, ',45%0&( $B  ! %C<B DFCJ98 =B H<9 K9@@ ?BCKB D5D9F 13 H<5H 9J9FM & 8=A9BG=CB5@ 7CBJ9L 6C8M  =G 7CBH5=B98 =B 5B IB=EI9 9@@=DGC=8  C: A=B=A5@ JC@IA9 B8 <9 5@GC DFCJ98 H<5H =:  =G 79BHF5@@M GMAA9HF=7

(70) H<9B     <C@8G

(71) 5B8     CH<9FK=G9

(72) K<9F9 H<9 <CA9H<9H=7 79BH9F =G H<9 79BH9F C:   7CBG9EI9B79 C: H<=G =G H<5H =:  =G 5B & 8=A9BG=CB5@ 5B57<  GD579

(73) H<9B H<9 5B57< (5NIF 8=GH5B79   $  & 5B8 G=B79 H<9 5B57< (5NIF 8=GH5B79 =G GI6AI@H=D@=75H=J9 =H :C@@CKG H<5H :CF 5F6=HF5FM & 8=A9BG=CB5@ 5B57< GD579G  5B8 

(74)     & 9B=B; =B 5 B5HIF5@ K5M G99 -97H=CB  5 8=GH5B79   

(75) 75@@98 H<9 (=B?CKG?= 8=GH5B79

(76) 69HK99B 5F6=HF5FM 7CBJ9L 6C8=9G  

(77) K<=7< F98I79G HC H<9 5B57< (5NIF 8=GH5B79 :CF GMAA9HF=7 CB9G

(78) K9 75B 95G=@M 89F=J9 H<5H     & :CF 5F6=HF5FM 7CBJ9L 6C8=9G  5B8  :H9F ! %C<BG KCF?

(79) AI7< 5HH9BH=CB <5G 699B D5M98 HC H<=G ?=B8 C: DFC6@9A

(80) 9=H<9F HC ;9H GCA9 ACF9 DF97=G9 9GH=A5H9G C: H<9 GIDF9 AIA C: (=B?CKG?= 8=GH5B79G CF HC =BH9FDF9H %C<BG F9GI@H =B GCA9 CH<9F K5MG HCC A5BM F9:9F9B79G HC A9BH=CB <9F9

(81) G99 13

(82) 13

(83) 1313

(84) 13

(85) 1313 5B8 H<9 7CFF9GDCB8=B; F9:9F9B79G  ACB; H<9A

(86) , '9K=GG 13 =B  ;5J9 5B CD9F5HCF J9FG=CB 5B8 5 B9K DFCC: :CF .

(87) H<9 GMAA9HF=7 75G9 C: %C<B

(88) G F9GI@H $B H<9 F9A5F?56@9 D5D9F 13

(89)  "@IG?=B IG98 5 DFC656=@=GH=7 A9H<C8 G<CK=B; H<5H :CF 5BM & H<9F9 9L=GH GMAA9HF=7 & 8=A9BG=CB5@ 7CBJ9L 6C8=9G  5B8  GI7< H<5H     &

(90) K<9F9   =G 5 IB=J9FG5@ BIA69F ( '5GG5? 13 =B  G<CK98 H<5H     &  =: CB9 C:  5B8  =G 79BHF5@@M GMAA9H F=7 (CF9 F979BH@M

(91) ( ,I89@GCB DFCJ98 =B 13

(92) 6M IG=B; H<9 8=9F9B79  6C8M 9GH=A5H9

(93) H<5H     &  @C; & K<9F9  5F9 IB=J9FG5@ 7CBGH5BHG )CK =H =G GH=@@ 5B CD9B DFC6@9A HC B8 H<9 DF97=G9 GIDF9AIA C:   .  3,() 1) 5+( 3(46.54 $B H<9 FGH HKC D5D9FG K9 F9@5H9 H<9 (=B?CKG?= 8=GH5B79 HC H<9 (=B?CKG?= A95GIF9 C: 5GMAA9HFM 6M ;=J=B; HKC 9GH=A5H9G :CF H<9 (=B?CKG?= 8=GH5B79 69HK99B 7CBJ9L 6C8=9G =B H9FAG C: (=B?CKG?= A95GIF9G G99 -97H=CB  5B8 

(94) K<=7< A5H7< H<9 =BHI=H=CB H<5H H<9 (=B?CKG?= 8=GH5B79 G<CI@8 69 GA5@@9F =: HKC 7CBJ9L 6C8=9G 6CH< <5J9 GA5@@9F A95GIF9G C: 5GMAA9HFM .<9 FGH 9GH=A5H9 =G 65G98 CB 5 ;9B9F5@=N5H=CB C: 5 @9AA5 C: '9K=G CB H<9 HF579 85I@=HM C: CD9F5HCF BCFAG .<9 G97CB8 =G 5 ;9B9F5@=N5H=CB C: '5GG5?G A9H<C8 IG98 =B 13 .<9G9 HKC 9GH=A5H9G F97CJ9F %C<BG 5B8 '5GG5?G F9GI@HG

(95) 6IH BCH H<9 69GH ?BCKB F9GI@H C: ,I89@GCBG +5D9F $$$ 5B8 $/ :C7IG CB H<9 (=B?CKG?= A95GIF9 =HG9@: $B +5D9F $$$ G99 -97H=CB 

(96) K9 8=G7IGG 5B8 89H9FA=B9 H<9 (=B?CKG?= A95GIF9G :CF 7CBJ9L <I@@G C: 5 DC=BH 5B8 GCA9 G9HG :CF K<=7< H<9 A95GIF9G C: 5GMAA9HFM 5F9 ?BCKB -CA9 B=79 DFCD9FH=9G C: (=B?CKG?= A95GIF9G 5F9 :CIB8 K<=7< A=;<H =B8=75H9 GCA9 =BH9F9GH=B; DFCD9FH=9G C: 7CBJ9L 6C8=9G .<9 @5GH +5D9F $/ G99 -97H=CB  =G 56CIH H<9 GH56=@=HM DFC6@9A :CF H<9 (=B?CKG?= A95GIF9

(97) =B K<=7< K9 ;5J9 9GG9BH=5@@M 5 69GH 9GH=A5H9 :CF H<9 8=GH5B79 C: 5 7CBJ9L 6C8M HC H<9 G=AD@9L  

(98)   #9F9 K9 K=@@ ;=J9 GCA9 DF9@=A=B5FM 89B=H=CBG 5B8 F9GI@HG -=B79 H<9 A95GIF9G C: 5GMAA9HFM 5B8 H<9 (=B?CKG?= 8=GH5B79 5F9 5B9 7CB79DHG

(99) K9 FGH DFCJ=89 GCA9 65G=7 :57HG 56CIH 5B9 GD579G 5B8 5B9 :IB7H=CBG .<9B :C@@CK H<9 89B=H=CB C: (=B?CKG?= 8=GH5B79 5B8 GCA9 ?BCKB F9GI@HG $B H<9 H<=F8 GI6G97H=CB K9 ;=J9 H<9 89B=H=CBG C: (=B?CKG?= 5B8 ;9B9F5@ A95GIF9G C: 5GMAA9HFM :CF 7CBJ9L 6C8=9G 5B8 GCA9 ?BCKB F9GI@HG 56CIH H<9 (=B?CKG?= A95GIF9  0( 42%&(4 %0' %0( )60&5,104 09 K=@@ 5GGIA9 ?BCK@ 98;9 C: H<9 65G=7 G9HG 5B8 ;9CA9HFM BCH5H=CBG !CF 89H5=@G

(100) G99

(101) 9;

(102) , -7<B9=89F 13 .

(103) 'CCG9@M GD95?=B;

(104) 5B 5B9 GD579 =G 5 @=B95F GD579 K=H<CIH CF=;=B

(105) =9

(106) BC DC=BH =G 8=GH=B7H

(107) GC CB@M GC 75@@98 5B9 7CA6=B5H=CBG 5F9 5@@CK98 (0,5,10  B 5B9 GD579 =G 5 G9H  C: DC=BHG 5GGC7=5H98 K=H< 5 J97HCF GD579  5B8 HKC CD9F5H=CBG  

(108) 

(109)  :FCA    HC 

(110) 89BCH98 6M / 0 :CF 5@@ / 0  

(111)  :FCA   HC 

(112) 89BCH98 6M / 6 :CF 5@@ /  6  K<=7< G5H=G:M " / 6 7  / 6 7 :CF 5@@ /  6 7 . "" / 6  / = 6   :CF 5@@ / . """ 0  / 0 / :CF 5@@ / 0  K<9F9 K9 IG9 H<9 G5A9 BCH5H=CB   5G :CF H<9 588=H=CB C: J97HCFG .<9 & 7CCF8=B5H9 GD579  =G 5 HMD=75@ 5B9 GD579 K=H< =HG9@: 5G H<9 5GGC7=5H98 J97HCF GD579 5B8 H<9 IGI5@ CD9F5H=CBG  !CF 5BM /  5B8 /    /         K=H<       

(113) 6M 89B=H=CB

(114) =H =G 95GM HC G<CK H<5H H<9 DC=BH /    / / 

(115) K<=7< =G H<9 GIA C: 5 DC=BH =B 5B8 5 J97HCF =B 

(116) =G =B89D9B89BH C: / -C K9 89BCH9 H<=G DC=BH 6M     /

(117) 75@@98 5B 5B9 7CA6=B5H=CB C: /    / 09 89BCH9

(118) :CF 5BM / /  1/ / 3  /   /       5B8  / /  /   /      $: H<9F9 9L=GH /    /  GI7< H<5H        /       H<9B  =G 75@@98 B=H9 8=A9BG=CB5@ .<9 GA5@@9GH % GI7< H<5H H<=G <C@8G =G 75@@98 H<9 8=A9BG=CB C: 

(119) 89BCH98 6M 8=A  $H =G 95GM HC G99 H<5H 8=A   8=A   09 K=@@ 7CBG=89F CB@M B=H9 8=A9BG=CB5@ 5B9 GD579G =B H<=G H<9G=G -C :FCA BCK CB K9 K=@@ 5@K5MG 5GGIA9 8=A   & &  .  A5D     (0,5,10  '9H   69 HKC 5B9 GD579G    =G 75@@98 5B9 =: :CF 5BM #

(120)      K=H<      5B8 /    /  

(121) .  .     /     /.  .  . $B D5FH=7I@5F

(122) =:     =G 75@@98 5B 5B9 :IB7H=CB CB   09 C:H9B IG9  9H7 HC 89BCH9 5B9 :IB7H=CBG 9BCH9 6M  H<9 :5A=@M C: 5@@ 5B9 A5DG :FCA  HC 

(123) 6M  H<9 :5A=@M C: 5@@ 5B9 :IB7H=CBG CB  $H =G 95GM HC G99 H<5H  697CA9G 5 @=B95F GD579 IB89F H<9 IGI5@ 588=H=CB 5B8 G75@5F AI@H=D@=75H=CB C: :IB7H=CBG  =G 75@@98 H<9 5B9 8I5@ GD579 C:  .

(124) 31214,5,10  '  !      !   !#!    !    !' % $   /    /    %    "! "  # !     "! " !"" #"    @95F@M 8=A    8=A   8=A   M H<=G DFCDCG=H=CB

(125) =B H<9 :C@@CK=B;

(126) =: B979GG5FM K9 K=@@ 26CFFCK :FCA B=H9 8=A9BG=CB5@ @=B95F GD579G GCA9 B5HIF5@@M 89B98 BCH5H=CBG :CF GI6G9HG

(127) GI7< 5G =BH9F=CF

(128) 6CIB85FM 9H7

(129) 5B8 5@GC H<9 BCH5H=CBG C: 8=GH5B79 CF A9HF=7 9H7 (0,5,10   GI6G9H    =G 75@@98 7CBJ9L =: :CF 5BM #

(130)  /    /  5B8          K=H<      K9 <5J9    /   7CAD57H 7CBJ9L G9H K=H< BCB 9ADHM =BH9F=CF =G 75@@98 5B & 8=A9BG=CB5@ 7CBJ9L 6C8M  7CBJ9L 6C8M C: H<9 :CFA '&. /    / :CF GCA9 /    /  =G 75@@98 5B & 8=A9BG=CB5@ G=AD@9L

(131) K<9F9 '&. 89BCH9G H<9 7CB J9L <I@@  7CBJ9L 6C8M  =G 75@@98 79BHF5@@M GMAA9HF=7 =: H<9F9 =G  "&,  GI7< H<5H :CF 5BM 7<CF8 1/ / 3

(132) / /  H<9 6CIB85FM C: 

(133) D5GG=B; H<FCI;< 

(134)    /  /  =G 75@@98 H<9 79BH9F C:  "=J9B 5B & 8=A9BG=CB5@ 5B9 GD579 

(135) K9 89BCH9 6M    . H<9 :5A=@M C: 5@@ & 8=A9BG=CB5@ 7CBJ9L 6C8=9G C: . (0,5,10   !CF  

(136) K9 89B9         1 3     .        1 3    . $H =G 95GM HC G99 H<5H               5B8    '&.      ,0-184-, ',45%0&( .C 89G7F=69 <CK 7@CG9 HKC 7CBJ9L 6C8=9G 5F9 HC 957< CH<9F

(137) G9J9F5@ 8=9BF9BH 8=GH5B79G 69HK99B 7CBJ9L 6C8=9G <5J9 699B =BHFC8I798 ACB; H<9A H<9 :C@@CK=B; (=B?CKG?= 8=GH5B79 <5G H<9 58J5BH5;9 H<5H =H =G 5B9 =BJ5F=5BH $H =G 5 B5HIF5@ ;9B9F5@=N5 H=CB C: H<9 5B57< (5NIF 8=GH5B79 09 8CBH ?BCK K<9B =H K5G FGH =BHFC8I798 !CF 5 L98 /  5B8  

(138) K9 89BCH9 6M ' /   H<9 5B9 A5D 89B98 6M ' /  /    / /. . / .

(139) B8 :CF G=AD@=7=HM

(140) K9 89BCH9

(141) :CF 5BM   

(142)    ' /  /  /  (0,5,10   !CF   

(143) H<9 (=B?CKG?= 8=GH5B79   . 69HK99B  5B8  =G 89B98 6M     =B:             K<9F9 H<9 =BAIA =G H5?9B CJ9F 5@@ /  5B8 5@@ BCBG=B;I@5F    (/%3-  -HF=7H@M GD95?=B;

(144) G=B79 H<9 (=B?CKG?= A95GIF9 =G 5B9 =BJ5F=5BH

(145) B5A9@M   .  .     :CF 5@@ BCBG=;I@5F   5B8   

(146)    CF ACF9 DF97=G9@M @C;   . =G 57HI5@@M 5 8=GH5B79 89B98 CB H<9 G9H 

(147) 

(148) K<9F9 2 =G H<9 5B9 9EI=J5@9B79 F9@5H=CB 89B98 CB 

(149) =9

(150)    = H<9F9 =G 5 BCBG=B;I@5F   GI7< H<5H    .    =G 5@GC C:H9B 75@@98 H<9 5B57< (5NIF 8=GH5B79

(151) 5B9 8=G H5B79 9H7 $H =G 95GM HC G99 H<5H    F98I79G HC H<9 5B57< (5NIF 8=GH5B79 =: 6CH<  5B8  5F9 GMAA9HF=7 B8 =H 75B 5@GC 69 95G=@M 7<97?98 H<5H      =    5B8       .           . ACB; 57<=9J9A9BHG CB H<9 9GH=A5H9 C: H<9 GIDF9AIA C: H<9 (=B?CK G?= A95GIF9

(152) H<9 :C@@CK=B;G 5F9 CIHGH5B8=B; +(13(/  1+0  

(153)   !  !   ! !'"  "     & " %!     & !#"'  "      !'"  "     &      &    +(13(/  %44%- 

(154)       ! " ' !' "  "     &  . +(13(/  6'(.410      &  @C; &  '   %     #$ ! !""!. +(13(/  .64-,0 .   & "  &!" !'"     !# ""     & %   !  #$ ! !"" 09 KCI@8 @=?9 HC DC=BH CIH H<5H H<9 A9H<C8G IG98 HC C6H5=B H<9 56CJ9 F9GI@HG 5F9 7CAD@9H9@M 8=9F9BH  (%463( 1) %49//(539 $B 13  "FO IB65IA =BHFC8I798 5 ;9B9F5@ 89B=H=CB C: A95GIF9G C: GMAA9HFM :CF 7CBJ9L 6C8=9G $B H<=G H<9G=G

(155) K9 K=@@ GHI8M H<9 A95GIF9G C: 5GMAA9HFM =BGH958 $H =G 95GM HC .

(156) HF5BG:CFA 5 GMAA9HFM A95GIF9 =BHC 5B 5GMAA9HFM A95GIF9 5B8 J9FG9 J=G5 -=A=@5F HC "FO IB65IAG 89B=H=CB C: A95GIF9G C: GMAA9HFM

(157) K9 ;=J9 H<9 :C@@CK=B; (0,5,10    :IB7H=CB     1 &3 =G 75@@98 5B 5B9 =BJ5F=5BH A95GIF9 C: 5GMAA9HFM =: =H G5H=G9G "      . :CF 5BM   5B8 5BM BCBG=B;I@5F    ""     =  =G GMAA9HF=7

(158)    & =:  =G 5B B 8=A9BG=CB5@ G=AD@9L """   =G 7CBH=BICIG CB  :CF

(159) 9;

(160) H<9 (=B?CKG?= 8=GH5B79    =G 5@GC 75@@98 H<9 A95GIF9 C: 5GMAA9HFM C:  (/%3-  *B9 A5M IG9 5BM =BH9FJ5@ 1 3   

(161) =BGH958 C: 1 &3 (5BM A95GIF9G C: 5GMAA9HFM <5J9 699B :CIB8 #CK9J9F K9 7CB G=89F A5=B@M H<9 (=B?CKG?= A95GIF9 <9F9 .<9 :C@@CK=B; =G H<9 CF=;=B5@ 89B=H=CB C: H<9 (=B?CKG?= A95GIF9 (0,5,10 

(162)  '9H   !CF 5 L98 / "&,  5B8 5 <MD9FD@5B9 D@5B9  H<FCI;< /

(163) 89BCH9 6M   H<9 HKC GIDDCFH <MD9FD@5B9G D5F5@@9@ HC  '9H *  / 89BCH9 H<9 F5H=C

(164) BCH @9GG H<5B 

(165) =B K<=7<  8=J=89G H<9 8=GH5B79 69HK99B  5B8   09 KF=H9 * /  *  /  GID *  / .<9B H<9 (=B?CKG?= A95GIF9 +  C:  =G 89B98 6M +  . =B:. . * /. BM DC=BH  "&,  G5H=G:M=B; *   +  =G 75@@98 5 7F=H=75@ DC=BH C:  $H 75B 69 7<97?98 H<5H H<9 :C@@CK=B; 89B=H=CB =G 9EI=J5@9BH (0,5,10 

(166)   '9H   !CF 5 L98 / "&, 

(167) H<9 =BH9F=CF C: 

(168) 5B8 5 7<CF8 $  1( )3 H<FCI;< / K<9F9 ( ) 

(169) H<9 6CIB85FM C: 

(170) 89BCH9 6M  $ / H<9 F5H=C

(171) BCH @9GG H<5B 

(172) =B K<=7< / 8=J=89G H<9 8=GH5B79 69HK99B ( ) 09 KF=H9  /    /  GID  $ / .<9B 89B9 H<9 (=B?CKG?= A95GIF9 C: 5GMAA9HFM +  C:  5G +  . =B:. .  /. BM DC=BH  "&,  G5H=G:M=B; H<5H    +  =G 75@@98 5 7F=H=75@ DC=BH C:  $H 75B 69 G<CKB H<5H  /  * / :CF 5BM / "&,  B8 :FCA H<9 G97CB8 89B=H=CB

(173) =H =G 95GM HC G99 H<5H +  =G 5B9 =BJ5F=5BH .

(174) .<9 FGH =ADCFH5BH F9GI@H 7CB79FB=B; H<=G A95GIF9 =G H<9 :C@@CK=B; DFCJ98 6M )9IA5BB 13 :CF &  

(175) -O -GG 13

(176) #5AA9F 13

(177) &@99 13

(178) '9=7<HK9=GG 13 9H7 =B H<9 ;9B9F5@ 75G9  +(13(/  '     +   &  +      ! !'"  +   &   !  !& &@99 13 G<CKG 5@GC H<5H +  8=A

(179)   & K<9F9

(180)  89BCH9G H<9 7F=H=75@ G9H C: 

(181) =9

(182) H<9 G9H C: 5@@ 7F=H=75@ DC=BHG C: 

(183) :FCA K<=7< =H :C@@CKG H<5H  <5G 5 IB=EI9 7F=H=75@ DC=BH =: +  &  )9LH =G 5 A95GIF9 C: GMAA9HFM 9EI=J5@9BH HC H<9 (=B?CKG?= CB9 G99 13

(184) 13

(185) K<=7< 7CA9G B5HIF5@@M =B CIF G9HH=B; 5B8 HIFBG CIH HC 69 ACF9 DF57H=75@ (0,5,10   '9H   !CF 957< / "&, 

(186) K9 KF=H9  /    /  =B:  /.  . .<9B 89B9 +   GID  /.   . K<=7< =G 75@@98 H<9 + A95GIF9 C: GMAA9HFM C:   .  CF +    +  5B8 +  5F9 F9@5H98 6M +      CF ACF9 ;9B9F5@@M

(187) * /    CF  /   :CF 5@@ / "&,  -C  =G 5 (=B?CKG?= 7F=H=75@ DC=BH =  =G 5B + 7F=H=75@ DC=BH .<9 7CB75J=HM CB "&,  C: H<9 :IB7H=CB  / =G C6J=CIG G=B79 =H =G 5 GIDF9AIA C: 5B9 :IB7H=CBG -C =H =G C:H9B 95G=9F HC KCF? K=H< +  H<5B K=H< + .   

(188)  $B H<=G D5D9F K9 ;5J9 5B 9GH=A5H9 :CF H<9 (=B?CKG?= 8=GH5B79 69HK99B HKC 7CBJ9L 6C8=9G =B H9FAG C: H<9=F (=B?CKG?= A95GIF9G CB7F9H9@M

(189) K9 DFCJ98 +(13(/   '    % $  & +  +       .<=G H<9CF9A F97CJ9FG %C<BG F9GI@HG

(190) 5B8

(191) 5G :5F 5G K9 ?BCK

(192) K5G H<9 FGH 5HH9ADH HC F9@5H9 H<9G9 HKC =ADCFH5BH EI5BH=H=9G .<9 A5=B =895 HC F957< GI7< 5B 9GH=A5H9 =G HC IG9 2@=B95F A9H<C8 :CF H<9 5B9 DFC6@9AG CB7F9H9@M

(193) K9 FGH 9A698 H<9 5B9 GD579  =BHC H<9 @=B95F GD579     5G G<CKB =B +FCDCG=H=CB  .<9B :CF .

(194) 5BM      K9 89BCH9    '&.    K<9F9  =G H5?9B =B H<9 @=B95F GD579 

(195) K<=7< =G 7@95F@M 5 GMAA9HF=7 & . 8=A9BG=CB5@ 7CBJ9L 6C8M K=H< H<9 CF=;=B 5G =HG 79BH9F 5B8     '9H  89BCH9 H<9 5B57< GD579  K=H<   5G =HG IB=H 65@@ 09 89BCH9

(196) =B 

(197)   /   /    :CF 5BM   )CH=79 H<5H    09 89BCH9 6M    H<9 G9H C: 5@@ @=B95F A5DG :FCA  HC 

(198) 6M    H<9 G9H C: 5@@     GI7< H<5H    

(199) 5B8 6M        

(200) K<=7< =G 5 GI6GD579 C:     !CF 5BM   

(201) =H =G ?BCKB H<5H H<9F9 =G 5 HF579 8I5@=HM 2,*  69HK99B    5B8    57HI5@@M H<=G =G HFI9 :CF 5BM HKC B=H9 8=A9BG=CB5@ 5B57< GD579G

(202) G99 9; 13  -C ;=J9B 5 BCFA CB   

(203) H<9F9 =G HF579 8I5@ BCFA  CB     )CK G=B79    =G 5 GI6GD579 C:   

(204) K9 <5J9   .     

(205)             K<9F9           ,* .  .<IG K9 89B9 5 HF579 8I5@=HM 69HK99B    5B8   .  6M   ,* .  ,* 13.    .  89BCH9G H<9 7CG9H K=H<  5G 5 F9DF9G9BH5H=J9 B8 K9 89BCH9 K<9F9 13 6M  H<9 8I5@ BCFA CB   .  K=H< F9GD97H HC H<9 BCFA F9 GHF=7H98 CB   . 0=H< H<9G9 BCH5H=CBG

(206) FGH K9 <5J9 95G=@M H<9 :C@@CK=B; 31214,5,10       "  !     . !# ""             %     ! " #!#  "        .<9B K9 DFCJ98 H<9 :C@@CK=B; ;9B9F5@=G5H=CB C: '9K=G @9AA5 =B 13 !CF 7CBJ9B=9B79

(207) @9H   69 7F=H=75@ DC=BHG C:   F9GD97H=J9@M

(208) 5B8 7<CCG9 /    /  GI7< H<5H  /    / 5B8  /    / :CFA 65G9G C:   F9GD97H=J9@M .<9B K9 =89BH=:M @=B95F A5DG  =B    5B8    K=H< A5HF=79G =B 5 B5HIF5@ K5M +(13(/  "         '         ,       %"  &   "  &!"     1 3   .  !# ""     1 3              !'         .

(209) %   "! " ""'   +FCDCG=H=CB  5B8 .<9CF9A   G<CK H<5H K9 A5M IG9 @=B95F A5DG =BGH958 C: 5B9 A5DG =B CIF 75G9 .<9 :C@@CK=B; @9AA5G K=@@ G<CK <CK H<9 (=B?CKG?= A95GIF9G +  5B8 +  7CA9 =B (//%  "    "          

(210)   !    1 3   '   +   GID    

(211)   .      . #!# (//%  "     %"    %    ! "     "   " ! ,   ,  %   

(212)          !    " ! '    (//% 

(213)  "        ! " #!#  "    % ' ! ,       . " %    .

(214) 5B8 K=H< H<9 <9@D C: )CK H5?=B;    

(215) K<9F9     56CJ9 @9AA5G

(216) K9 75B DFCJ9 H<5H &      +  + .

(217)   .    

(218)  .<=G D5D9F ;=J9G 5BCH<9F 9GH=A5H9 :CF H<9 (=B?CKG?= 8=GH5B79 =B H9FAG C: H<9 (=B?CKG?= A95IGF9G .<9 A9H<C8 IG98 <9F9 =G =BGD=F98 6M '5GG5?G =895 =B 13 M ;9B9F5@=N=B; <=G A9H<C8

(219) K9 FGH DFCJ98 GCA9 ;9B9F5@ 9L=GH9B79 H<9CF9AG :CF 5 7@5GG C: JC@IA9 =B7F9G=B; 5B9 A5DG

(220) H<9B 5G 5B 5DD@=75H=CB C: H<9G9 H<9CF9AG

(221) K9 ;CH H<9 :C@@CK=B; 9GH=A5H9 +(13(/  "     % $ "     &  A=B+ . +   &     ""     &.   "      !'"  """     &      !  !. )CK =:  CF  =G GMAA9HF=7

(222) H<9B A=B+ . +     5B8 GC 6M "

(223)     &    &  &  .<IG " F97CJ9FG '5GG5?G F9GI@H B8 :CF ;9B9F5@  

(224) " G<CKG H<5H     &  & &  &  G :CF "". """

(225) 9J9B =: H<9M 5F9 ?BCKB %C<BG F9GI@HG

(226) K9 GH=@@ DF9G9BH H<9A <9F9 5G 5 D5FH C: H<9 H<9CF9A >IGH 6975IG9 K9 <5J9 5 IB=:CFA 5F;IA9BH :CF 5@@ H<9G9 H<F99 5GG9FH=CBG .C ;9H H<=G 9GH=A5H9

(227) K9 GH5FH98 K=H< DFCJ=B; H<9 :C@@CK=B; 9L=GH9B79 H<9CF9A .

(228) +(13(/  "    "%   ' !     !# "" "&,  ! "%     ' / /  ' !"$'  " !  !! "  '   !"$'  !" "  !"    / /   .  /      / .   . % ! "  "   " "  

(229)   & " "  &!"!  $# !     !# ""    '&. / / . .<9B 5 GCA9K<5H GHFCB;9F CB9 +(13(/  " / /    " ! !         !"!' ""   '&. / / 

(230)   & "  '     %"      "  &!"!  $# !     !# ""    '&. / /          )CK 7CA9G H<9 ?9M C6G9FJ5H=CB '9H   69 H<9 A5L=AIA JC@IA9 5B9 7CDM 7CBH5=B98 =B  C: 

(231) 5B8 

(232)   !CF 5BM / 

(233) @9H /     1 / 3 5B8 @9H   69 HKC D5F5@@9@ GIDDCFH <MD9FD@5B9G C:   K=H<  / $: :IFH<9F /      /

(234) H<9B K9 <5J9  / /   . *  * . CF   *   *.

(235)  

(236)   K<9F9 * 

(237)    + . 5B8  

(238)   K<=7< G<CKG K<M H<9 (=B?CK G?= A95GIF9 7CA9G =B 5B8

(239) K=H< H<9 <9@D C: .<9CF9A  5B8 GCA9 9@9A9BH5FM 7CADIH5H=CBG

(240) @958G HC H<9 9GH=A5H9 "  -=A=@5F 5F;IA9BH KCF?G :CF "" 5B8 """  .<9 :C@@CK=B; H<9CF9A =G 5@GC DFCJ98 =B H<9 D5D9F

(241) K<=7< 7CAFAG H<5H '5GG5?G 9GH=A5H9 75B BCH 69 9GG9BH=5@@M =ADFCJ98. +(13(/   "     ' / "&,    % "  /  =B:         .         + .  /  %   

(242)   "#    ! !'"  "  /       / "&, .   

(243)  $B H<=G D5D9F

(244) K9 7CBG=89F CB@M H<9 (=B?CKG?= A95GIF9 =HG9@: =B CF89F HC B8 GCA9 ACF9 DFCD9FH=9G 09 89H9FA=B98 H<9 (=B?CKG?= A95GIF9 C: 5GMAA9HFM :CF 7CBJ9L <I@@G C: 5 DC=BH 5B8 GCA9 G9HG :CF K<=7< H<9 .

(245) A95GIF9 C: 5GMAA9HFM =G ?BCKB !CF 7CBJ9B=9B79

(246) K9 GH5H9 H<9 F9GI@HG =B H<9 GD97=5@ 5B9 GD579    !CF 5BM GMAA9HF=7 7CBJ9L 6C8M   K=H< H<9 CF=;=B 5G =HG 79BH9F

(247) K9 89BCH9 6M        H<9 BCFA 89H9FA=B98 6M 

(248) =9

(249)  57HG 5G  5 IB=H 65@@ =B  B8 :CF 5BM / 

(250) K9 89BCH9  /.  '&. / .  5B8 KF=H9  /  +  /.  .<9B H<9 A5=B H<9CF9A =B H<9 D5D9F =G 5G :C@@CKG +(13(/   ' !'"  $& '   %" "   ! "! "  % $    /  "  /  A5L    !  ##  " " "".  ' /    /. /  A5L. /  / / . .<=G H<9CF9A <5G 5B =BH9F9GH=B; 7CFC@@5FM 56CIH H<9 @9J9@ G9HG C:  /. 131..%39    !'"    %" "   ! "! "  " %!   " # 4      /   /       " /   /      4    %       /   /     .  "" /   /            %  / "! " ##  " "   /.        G K5G HC 69 9LD97H98

(251) =: K9 7CBG=89F  /. :CF ;9B9F5@ 

(252) =H 697CA9G ACF9 7CAD@=75H98 -C =B H<9 G97CB8 D5FH C: H<=G D5D9F

(253) K9 7CBG=8 9F98 CB@M H<9 7CB9G 6M K<=7< K9 A95B H<9 7CBJ9L <I@@ C: GCA9 &  8=A9BG=CB5@ 7CBJ9L 6C8M 5B8 5 DC=BH CIHG=89 H<9 6C8M +F97=G9@M

(254) @9H    69 5 <MD9FD@5B9 5B8    69 5B & .    '&. / 

(255) 8=A9BG=CB5@ 7CBJ9L 6C8M !CF 5BM /  

(256) K9 G9H     .<9B K9 <5J9 K<=7< =G 75@@98 5 7CB9

(257) 5B8 89BCH9  /  +  +(13(/   ' /    /  +     "    $ "   /  /  %  /   " "! /     +  "! " %! !#   !'" '   %" !" " " &  !  !   /

(258)  . 09 KCI@8 @=?9 HC DC=BH CIH H<5H G9J9F5@ CH<9F A95GIF9G C: 5GMAA9HFM G<5F9 H<9 DFCD9FHM

(259) G<CKB =B .<9CF9A 

(260) C: H<9 (=B?CKG?= CB9G .

(261)   

(262)   $B H<=G @5GH D5D9F K9 K9F9 89JCH98 HC GC@J=B; H<9 GH56=@=HM DFC6@9A :CF H<9 (=B?CKG?= A95GIF9

(263) =9

(264) ;=J=B; 5B 9GH=A5H9 :CF H<9 89J=5H=CB C: 5 7CBJ9L 6C8M :FCA H<9 G=AD@9L =: H<9 7CFF9GDCB8=B; (=B?CKG?= A95GIF9 =G 7@CG9 HC H<9 A5L=AIA J5@I9 & 0<=@9 H<9 9GH=A5H9 :CF H<9 75G9 K<9B H<9 A95GIF9 =G 7@CG9 HC H<9 A=BAIA J5@I9  =G 95GM 5B8 =G DFC656@M 5@F958M ?BCKB .<9 B5@ F9GI@H K9 C6H5=B98 =B +5D9F $/ =G H<9 :C@@CK=B; +(13(/  "  

(265)  +   &   !     "  ! !&  % $. . .       &   *F ACF9 DF97=G9@M . +(13(/   "  

(266)  +   &   !      " "  &!"!  !&    ' !# " ' !   !# ""    & 

(267)      %   ! " ##  " "  . .<9 7CBGH5BH  &  A5M BCH 69 H<9 69GH

(268) 6IH =H =G 95GM HC ;=J9 9L5AD@9G G<CK=B; H<5H  75B BCH 69 F9D@5798 6M  :CF 5BM #  -C =B H<=G G9BG9 H<9 9GH=A5H9 ;=J9B <9F9 =G H<9 69GH CB9 .<9 HF=7? HC ;9H H<=G 9GH=A5H9 =G HC GHI8M H<9 + A95GIF9 =BGH958 C: H<9 (=B?CKG?= CB9 5G K9 A9BH=CB98 =B G97H=CB  B8 =H HIFBG CIH H<5H H<9 9L=GH9B79 C: GI7< 5 G=AD@9L =G 9EI=J5@9BH HC H<9 DCGG=6=@=HM C: 897CADCG=B; H<9 7CBGH5BH :IB7H=CB +  =BHC 5 7CBJ9L 7CA6=B5H=CB C: GCA9 GD97=5@ 5B9 :IB7H=CBG CB7F9H9@M

(269) ;=J9B   K9 89BCH9

(270) :CF 5BM  .          +   09 K=@@ G<CK H<5H IB89F GCA9 7CB8=H=CBG

(271) H<9 7CBGH5BH :IB7H=CB + . 75B 69 9LDF9GG98 5G 5 7CBJ9L 7CB6=B5H=CB C: 9L57H &  @=B95F =B89 D9B89BH 9@9A9BHG =B  . :FCA K<=7< .<9CF9A   =G 89F=J98 CIH !=FGH K9 DFCJ98 H<9 :C@@CK=B; @9AA5G 5B8 7CFC@@5F=9G (//%   '    % $ '&.     1+ .  +  3 . (//% 

(272)  +             %"       "  ' 

(273)        " .

(274) 131..%39   '    

(275)  % $ +  '&.  .  (//%   ' 

(276)  "  &!"             %"          !# "". +  .  .   .  . .<9B

(277) K9 G<CK H<5H H<9 7CB8=H=CB +    "  &  .  . 9BGIF9G H<5H 5@@  .  (//%  

(278)  +     +         !         %"      " " !"        ! # !            !  !& '9AA5  5B8  ;=J9 H<9 :C@@CK=B; 131..%39  "  

(279)  +    " "  &!"         %  " ## 

(280)   !# ""       ! #    !  !&             (//%   "    

(281)    +      "  ' &.   #"! .   .    %"         #   !&  % $. .  .  /    &  .  /      .  . 0=H< H<9 <9@D C: CFC@@5FM  5B8 '9AA5 

(282) K9 7CI@8 BCK DFCJ9        +(13(/  $  

(283)  +      " "  &!"!  !&    ' !# " ' !  !# ""   &    

(284)     . 0<=7< =G 57HI5@@M 5 GH56=@=HM H<9CF9A :CF H<9 + A95GIF9

(285) 5B8 :FCA K<=7< .<9CF9A   75B 69 95G=@M 89F=J98 .<9 :C@@CK=B; 9GH=A5H9 7CA9G :CFA .<9CF9A  =AA98=5H9@M 131..%39  "   

(286)  +   & . " & . . .       A5L& + . & +   %     &   . +  .

(287) 

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(289)   

(290)   /

(291) 0 5B93?E9C38 ( )+( % )/##*(/ % %$,. +(,)

(292)

(293)   !?>4?> "1C8 (?3     

(294)  / 0 5A>4  )) 1 +( 0/!") )/##*($ $( !%$,.( !1%(&( "1>DB3A9@C1 "1C8   

(295)

(296) 

(297)  /0 81;5A91>  (C59> (  $ * )/##*(/ % %$,. %) D<< =5A "1C8 (?3       /0 81;5A91>  (C59> (  )* %() %  %$,. %/ A38 "1C81B5<     /0 I5953839 B;11<1=?41 . (IF953 , (*(0*%$ % * )* % $*() %  %$,. %/ / )+&&%(* %$) .5IHCH #1D; ,HI (;?<H %54 , $@?<D "1C    

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(299)    

(300)   / 0 77<5BC?>   %# &(%&(*) % *($") ) .*(#" %$,. +(,)  !?>4?> "1C8 (?3  

(301) 

(302) 

(303)  /. 0 F1<4  (85@81A4  %(# ,*%( )&) %$))*$ % "))) % %$,. )*) "1C8 .      / 0 ;BCAJ?=   (*" )* %  %$,. %/ **" %A?:53C '5@?AC % /

(304) 0 A145<9I9 " *%$" %) ))%* -*  %$,. %/ %A?3 =5A "1C8 (?3   

(305)    / 0 AJ D>21D=  )+( % )/##*(/ % %$,. )*) ?>E5G9CH %A?35549>7B ?6 (H=@?B91 9> %DA5 "1C85=1C93B  =5A931> "1C8 (?395CH %A?E945>35. 

(306) 

(307)

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References

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