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Asymptotics of First-Passage Percolation on 1-Dimensional Graphs

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(39) ]t™;EEDZ B \Z ›˜.Y ¢k< B ™0;] œš"E; š^žš*£B™›˜Iœš ™<š 9 š = ; ]tš Ÿž›˜y¢ ™<a B ™ šF˜!Z  B  3 + o  p : I j ˜ž  $S ¥ ; ™ ;];œ‚šE;Žš"^ š£™_< B ™  B  3 + o  p : ; ]\˜!Z™_<š˜ ›£š_ / 4   B ¤£ B £%; ] = fd]_]e;Ž˜ž¤ < B ]œš_š_¤#Ÿ ˜.;Ž¤Ÿ%˜ž¤¢k<š_™<š™ ˜š .%9‚š = ™™<š] B Y šˆœ‚š< B ^ ; ˜Pf ; ¤ <D;ŽŸ.<š_ £D;Y š_¤/]e;Ž˜ž¤d]Ho ] š_šHKDš_¢kY B ¤ B ¤£ m ; B oeLS.SO.p.lFš_¤/ B Y ;Ž¤D;‚š ™ B E7I+o}¥r¦ ¦.Xp Z ˜ a]<˜ t™F š#]efD Y š# ]_p1I€KD˜r™aYf = <-;] 6 ¤˜y¢ ¤ )œDf™Z ˜ 3$VS2¥ K š¢kY B ¤ B ¤£ m ; B oeLS.SO.p < B ^ š]<˜y¢ ¤ df¤£"š_&¤ B ™_f B E = ˜ž¤£%; ™;Ž˜ž¤/] ˜ž¤%™_<š9 B ]_] B ŸžšI™;Y š] ™_< B ™ ™_<š_›š ;] B = ˜ž¤d]t™ B ¤ ™  >N¦ ]f = <\™< B ™  B  3 + o  p : ' E ˜ R Ÿ /2 Z ˜  B ERE /' L.I ba<š] B Y šqE ˜y¢Fš_œ˜.f¤£#¢ B ] Z ˜.f¤£ ;Ž¤£"š"9š_¤‚£"š_¤:™E:Uœ: m š1Q Y B ¤:™_E š B ¤£ m š š#]oLSPS!h pn %;Ž¤ ™_<š = B ]tš7˜!Z 7š .%9˜ž¤š¤:™; B E39 B ]] B Ÿ šD™_;Y š]I J ¤™_<D;] 9 B 9‚šg¢Fš = ˜ž¤/]e;!£"š_N] ™Qs9 B ]] B Ÿ š 9š_ = ˜PE B ™;Ž˜ž¤˜ž¤ { mm_{ q‚x}kpvr€(€

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(78) œšH;Ž¤ˆš"; ™<š ˜!Z™_<šH]t™ B ™›š] ¦ dL  ž˜  ¥%I ¡:™ B ™ šD¦; ] ™›˜Bœš = ˜ ¤d]e;!£"š š*£ B ]0<š B E ™< :ž  B ¤£\™<š ] ™ B ™›š]iL B ¤£¥ B ]r;Ž¤%Z š = ™ š£œ:\˜ž¤šB˜!Z ™ ¢F˜q; ¤%Z š = ™_; ˜ ¤d]"IrFD¤ ;Ž¤%Z š = ™ š£ ^ š_ ™ š7. ]t™ B :%] ;Ž¤ ; ™_];Ž¤%Z š = ™ š*£ ]t™ B ™ š Z ˜ž›š"^ š_#Iš_™B˜ž¤š ^žšt™›š7. B ¤£ B ¤˜r™_<š_ œš ; ¤D; ™; B EE: ; ¤DZ š = ™›š£œ :‚; ¤%Z š = ™_; ˜ ¤>L B ¤£U¥" ›š]9‚š = ™_;^ š"E:.Iiba<š ; ¤DZ š = ™_; ˜ ¤d] š^ž˜.E^žš B ¤£ B ^ š_ ™ 7š . ;Ž¤>]t™ B ™ š L\˜žˆ¥‚;Ž¤%Z š = ™_] B 0£ / B = š_¤:™ ^ š_ ™; = š#]i;Ž¤>]t™ B ™›š\¦ B Z(™ š_ B ¤š7.%9˜ž¤š¤ ™_; B EE:£%; ] ™›;ŽœDf"™›š£™_;Y š ¢k; ™<w B ™›š " ˜  4  ›š]9š = ™_;^ š"E:.I ba<D; ]Ÿ š_¤š B E; _š#] ™_<šˆ˜ž¤š"Q}™: 9š V ; = < B ›£d]t˜ ¤ Y ˜"£"š"E„ ¢k<D; = < ;]7š  fd;^ B EŽš_¤:™7™ ˜ ]t™eQT9 B ]_] B ŸžšC9‚š = ˜.E B ™;Ž˜ž¤\¢k; ™<%7š .%9˜ž¤š¤ ™_; B EE: £%; ]t™ _; œDf™ š£c9 B ]] B Ÿ šD™_;Y š#]"I ba<š ™ ¢ ˜.Q}™: 9š V ; = < B £D] ˜ž¤ Y ˜"£"š"E ¢ B ]i;Ž¤ ™› ˜"£%f = š£œ: B — ŸžŸ] ™› ˜P— Y B ¤‚£ m šY B ¤:™EŽš oeLSPSž§Pp1I0ba<š  fš]t™;Ž˜ž¤;™<š: = ˜ž¤d];Ž£š_›š£;¢ B ] ¢k<š ™_<š_ œ˜r™_<c;Ž¤%Z š = Q ™_; ˜ ¤d] ¢k;EE"Ÿ  ˜y¢#™›˜; ¤%Z š = ™ ;Ž]¤ ¤D; ™ šE: Y B ¤ :i^žšt™_; = š] ¢k; ™< 9‚˜]e; ™;^žš 9›˜žœ B œD;E; ™:.I @ š_¤˜ž™ šœ : 5™_<šš"^ š_¤:™ ™< B ™ œ˜r™_< ; ¤%Z š = ™_; ˜ ¤d] Ÿž›˜y¢ ;Ž¤£"š7‚¤D; ™›š"E:.Iba<š": = ˜ž¤%Q / š = ™f š*£ ™_< B ™ qo C3 p > ¦ ; Z B ¤£;˜ž¤dE: ;Z " S 4 B — ŸžŸ] ™› ˜P— Y B ¤£ m š"Y B ¤:™_E šoeLSPSž§Pp 9 ˜R^ š£;™< B ™ S 4;Y 9DE;Žš)] qo C0p >2¦ Z ˜ J $ S ¥%I\ba<D; ] ¢ B ] E B ™›š_ Ÿ š_¤š B E; _š*£a™ ˜i<D;ŽŸ.<š_£%" ;Y š_¤d];Ž˜ž¤d]Co š B = <ˆ˜!Z – B ›š ™ B ¤£ [ B  = < B ¤£'o„¥r¦ ¦PO.p D˜4Y B ¤>o„¥r¦ ¦PO B p  @ š; / Z š¤ B ¤£ B — Ÿ ŸP]t™  ˜.— Y o}¥r¦ ¦U.p 9›š] š_¤:™] B £%\; 4š š¤ ™9 ˜)˜.Z_p I\ba< š  ˜ž¤DE:;Z  9 B t™ ; ] ¤˜ž™ :žš_™ Z fDEE: 9›˜R^žš£co ] š_š @ š"; / Z š_¤ B ¤£ B — Ÿ ŸP]t™  ˜.— Y o}¥ž¦ž¦ §PpZ ˜ž B ]f^ š":ˆ˜.Z™_<š š"E!£dp1I j ¤ š]_] š_¤:™; B EE:-L1Qƒ£%;YŒš¤d]; ˜ ¤ B E%9š__; ˜"£%; = Ÿž B 9d<d]

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(82). pD> ¦& Z ˜  B EE "  4 f¤dE š#]]ˆ˜ ¤š ; ¤DZ š = ™_; ˜ ¤ ;]Œ™›;^ ; B EE:œDEŽ˜ = 6 š £Pœ :#™<š˜ž™<š B EŽ š B £%: Z ›˜.Y?™<š ]t™ B t™#I F = E ˜]tšE:; šE B ™ š*£ 9 ˜ œDEŽš"Y = ˜ž¤ = š_›¤d] ™_<š x„‡ {{aotsBk(q*s {›~_x„kpoyq  ™ ˜ œ‚šŒ£"š1Q ¤š£3I 8 ˜ž¤/]e;!£"š_R _]t™eQT9 B ]] B Ÿ š9š_ = ˜.E B ™_; ˜ ¤ ˜ž%¤ [ ¢k; ™< B ]; ¤Ÿ.EŽšk; ¤%Z š = ™›š£ ^žšeQ ™›š7. B ™ ™<šI˜ž_;ŽŸ.;Ž¤  B ¤£ B 9 B ]_] B Ÿžš ™_;Y š7£%;]t™ _;ŽœDf"™;Ž˜ž¤ "!g¢k; ™_<˜.f™ B ™ ˜.Yq]I€š ™  o%H pœš™_<šY ;Ž¤D;Y ; ";Ž¤Ÿ9 B ™<-o B ]_]efdY ;Ž¤Ÿ ]ef = <a7š .%; ] ™]_p˜!Z + %o H p  !;sI šPI   ™_<š9 B ™< B E ˜ ¤Ÿ¢k<D; = <LHgŸž˜ž™;Ž¤%Z š = ™ š£ I\ba<š_¤  ;] £"š7‚¤š£ B ] ™<š ™ ›š_š  S 2  o%H p ]9 B ¤¤D; ¤Ÿ [   ¢k<D; = <ˆ¢ š ›š1Z š ™ ˜ B ] ™<š ™› šš ˜!Z; ¤DZ š = ™_; ˜ ¤ o ] š_š j ;ŽŸ.f›šD¥" !9 B Ÿžš L ¥ Z ˜  B ›š B E;  B ™;Ž˜ž¤ ˜ ¤L™_<š o} ¥ ›¥.p Q}™_fœš#p I ba<š  fš#] ™_; ˜ ¤ B œ‚˜Pf"™  ™< B ™r;]F›š1Q E B ™›š£%™›˜ˆ™<šB™ ¢ ˜.Q}™: 9š V ; = < B £D]t˜ ¤ YŒ˜"£"šE = ˜ž¤ = š_›¤d] ™<šg¤ fDYgœš_&˜!Z0;Ž]¤ ¤D; ™ š ] š"EZ,Q B ^ ˜.;!£%;Ž¤Ÿ-9 B ™</]; ¤  ]t™ B t™›š£ B ™™<šŒ˜ ;ŽŸ.;Ž¤ £š_¤˜ž™ š£œ. : o  p I J Z :ž˜Pf B B B ¢k; ]e<  ™_<D; ]š  f E ] ™<šD¤ fDYgœš_F˜!ZG] ˜!Q = EEŽš£a™›˜.9˜.EŽ˜žŸ.; = Eš_¤‚£D]˜.Z  I0K š_¢kY B ¤ qo

(83). . . S.  .

(84) oL#S.SPOPp = ˜ž¤/ š = ™_f š*£L™_< B ™. o  Rp S AQ B EY ˜] ™r]f šE: . B ¤£<š 9›˜R^žš*£ ™<D; ]af¤£š_r] ˜.Y š9DE B fd]; œDEŽšž "œdf"™r] ™_;EE3f¤D9›˜R^žš¤  B ]_]efdY 9™;Ž˜ž¤ ˜ž¤ˆ™_<š B ]:Y 9"™›˜r™_; = ]e< B 9š M   I F _]t™ o7]eY B EE,p]t™ š9L™›˜y¢ B ›£D] ™<D; ] = ˜ ¤/ š = ™f›š ¢ B ] Y B £š œ : B — ŸžŸP]t™  ˜.— Y B ¤‚£ m š"Y B ¤:™_E š oLSPSž§p I j ˜ž$ S2¥ B ¤£Bš7.%9‚˜ ¤š_¤:™_; B E 9 B ]_] B Ÿžš ™;YŒš £%; ]t™ _; œDf™;Ž˜ž¤ y™_<š": = ˜.fDE!£Z  ˜PYT™<š 9‚˜]];ŽœDE š = ˜)š . ; ]t™ š_¤ = šF˜!Z™ ¢F˜ ; ¤DZ š = ™_; ˜ ¤d]a;Ž¤;™_<š7™ ¢F˜!Q„™:9š V ; = < B £D] ˜ž¤Y ˜"£"šE = ˜ ¤ = Ef£"šI™< B ™ qo o  D p ' ¥.Dp > ¦  ¦.N!h  ba<D; ] ¢ B ]aE B ™ š_k;Y 9›˜R^žš£L™ ˜ o  Dp ' ¥ $  B EY ˜P]t™k]f›š"E: Z ˜ž $ S ¥Uœ : ˜ 4Y B ¤ o„¥r¦ž¦Oyœ/p   B ¤£ ; ¤ <d; ŸP<š_ £D;Y š_¤/]e;Ž˜ž¤d]Lœ: – ˜.f š  š  o}¥ž¦ž¦U.p IKD˜r™›šg™_< B ™ B `¦ ^LE B ¢ B ¤ B E ˜ Ÿž˜Pfd] ™›˜cba<š_˜ž›š"Y LPI UL˜ž¤ 0&¢F˜.fDE!£ ;Ž¤ 9 B  ™; = fdE B  ;Y 9DE:L™< B ™ qo o  pRS :Dp& *¦&"L Z ˜ž B EE : '¦DI [ ˜P]t™\˜.Zg™_<š š#]efDE ™_]c9›˜R^žš*£ ;Ž¤2™_<D;]c9 B 9‚š Y B 6 š fd] šU˜.Z B  šŸžš_¤š_ B Q  ™;^žšˆœš"< B ^ ;Ž˜.fB™< B ™ B _;] š] Z ˜ =] ™Qs9 B ]_] B Ÿžš 9‚š = ˜.E B ™_; ˜ ¤˜ ¤#š]_]tš¤ ™_; B EE:)L"Q £%;YŒš¤d]; ˜ ¤ B E9š__; ˜"£%; = Ÿž B 9D</]"I 1 ; ™_< B ›š_Ÿ š_¤š B ™;^žš&œ‚š< B ^ ; ˜Pf ¢ šY š B ¤c;Ž¤ ™<D; ] = B ] šD™_< B ™ ™_<š_›š ;] B ] š  fš¤ = V š   7  7 " ]f = <;™< B ™ . , + %S +  50n  #! " +  5  +    7 ". B ¤ £U + 

(85) 5  +   7 " Z ˜ž_Yq] B ¤ ;sI ;7I £3I ] š  fš_¤ = š.I FH]7¢Fša¢k;EE ] š_š   B £%; ›š = ™ = ˜ ¤d]tš  fš_¤ = š7˜!Z™_<D; ] œ‚š< B ^ ; ˜Pfk; ] ™< B ™ ™<š ;Ž¤]dY B ;Ž¤ oL.IL#p  GoLPI ¥Pp B ¤£ oLPI Np B ›š;Ž¤)Z B = ™qY ; ¤d;Y B o = ZI V šY B  6 ¥DI §p I J ™ Z f ™<š_ Z ˜.EEŽ˜y¢r]Z ›˜.Y ™_<D; ] œ‚š"Q < B ^ ; ˜Pf&™< B ™7˜ ¤ B ¤ :š]_]tš¤ ™_; B EE: L1Qƒ£%;Y š_¤d]; ˜ ¤ B E\9š__; ˜"£%; = Ÿž B 9D<

(86)  GZ ˜žI™<š ™ ›š_š7˜!Z€; ¤DZ š = ™_; ˜ ¤  \¢ š< B ^ š Go   pES2¥] B EY ˜P]t™r]ef›š"E:  oLPI Sp J ¤ V š"Y B  6 ¥%I SD¢Fš ¢k;EE"Ÿ.;^žš B ¤ B ›Ÿ.fDY š¤ ™€Z ˜ž ™_<D; ]"I\F Ÿ B ;Ž¤ rœ˜r™< Z ˜ž ™_<šF™ ¢ ˜.Q ™: 9‚š V ; = < B £D] ˜ž¤ Y ˜"£"š"E B ¤£7™<š ™› šš ˜.Zd;Ž¤%Z š = ™;Ž˜ž¤g¢Fša]tšš<˜y¢#™_<šFœ‚š< B ^ ; ˜Pf ˜!RZ ‚_]t™eQT9 B ]_] B Ÿžš9‚š = ˜.E B ™;Ž˜ž¤w˜ž¤wš#]] š_¤:™_; B EE: L1Qƒ£%;Y š¤d]e;Ž˜ž¤ B E€9‚š;Ž˜"£%; = Ÿž B 9d<d] £%\; 4šaZ  ˜PYV¢k< B ™a; ] œš"E; š^žš*£L™›˜ˆœ‚š7™_<š = B ]tš ; ¤ <D;ŽŸ.<š_ £%;Y š_¤d]; ˜ ¤d]I . L¦.

(87) ¡)š = ™_; ˜ ¤¥ ; ]L£"š£D; = B ™ š*£™›˜š7.%9DEŽ˜ž_; ¤ŸU™_<š% šŸžš_¤š_ B ™;^žš\œš"< B ^ ;Ž˜.f B ¤‚£ 9›˜R^ ;Ž£šD™_<š š#]efdE ™] ¢Fš7¤š_š*£ Z ˜  ™<š Z ˜PEEŽ˜y¢k; ¤Ÿ ] š = ™;Ž˜ž¤d]I0ba<š_˜  šY ] LPI ¥ +LPI X B ¤£ LPI h‚  B ] ¢Fš"EE B ] 8 ˜ž›˜.EE B :cL.I O B  šC9 ˜R^ š£ ;Ž¤\¡)š = ™_; ˜ ¤-XDI J ¤%¡)š = ™;Ž˜ž¤ hŒ¢ š 9›˜R^žš m  ˜P9‚˜]e; ™;Ž˜ž¤ L.I NDI J ¤%™<š¤ B E ¡)š = ™;Ž˜ž¤ Og™<š = ˜.fD9dE;Ž¤Ÿ ˜!Z m ›˜.9˜P]; ™_; ˜ ¤ LPI § ; ] = ˜ž¤d]t™ _f = ™ š£ P;Ž¤q; ™] = ˜ž¤:™;Ž¤ f˜.f/] B ¤£ ; ™_]F£%; ] =  š_™ šr^ š_]e;Ž˜ž¤GI ba<šD ¦ ^+LkE B ¢ ba<š˜ž›š"Y L.I„U-;] B E] ˜£"š__;^žš£ B ¤£™<š = ˜.f¤:™›š_›7š . B Y 9DEŽš ˜!ZF™<š ¦ ^+L E B ¢Z˜ ¤ ™› šš]a; ]k9›š] š_¤:™ š*£ B ™F™_<š ^žš: š_¤£\˜!Z™<D; ]r] š = ™;Ž˜ž¤ B ¤£c9 B 9‚šI.     )

(88)   O 

(89)  1UšB¢k;EE £%; ›š = ™C]9‚š = ; B E ;Ž¤:™ š_›š]t™ ™›˜ _]t™eQT9 B ]] B Ÿ šC9š_ = ˜PE B ™;Ž˜ž¤%˜ž¤\™<šoZ@Y$ pTQ ™_fœ‚šPI ba<šioZ@Y $ pTQ„™fœšr; ] š#]] š_¤:™; B EE: L1Qƒ£%;YŒš¤d]; ˜ ¤ B E„  B ¤‚£a›š = B EE)™< B ™¢Fšr] B : ™_< B ™ B ^ š_ ™ š . ; ] B ™ €Ž{ ly{ € />;Zk; ™]=]t™ = ˜)˜ž£%;Ž¤ B ™›šˆš  f B E ]/0IG1šL¢k;EE B E ] ˜ £%; ]t™;Ž¤Ÿ.fD; ]<™<š ]tš_™&˜.Z\^ š_ ™; = š#][  *¦ `!#"  B ¤£% š"Z š_D™ ˜Lš B = < ]f = < ^žšt™›š7. B ] B ^žšt™›š7. B ™ z{_k 6*z"x*{_‡ o I0FC] ¢ š ¢k;EE/] š_šž r™<š 6 š":i;!£"š B ˜!Z™<D; ]09 B 9‚š B _;] š] ¤ B ™f B EE:iZ ˜žR _]t™eQT9 B ]] B Ÿ š9š_ = ˜.E B ™_; ˜ ¤ ¢k; ™_<Œš .%9‚˜ ¤š_¤:™; B Ed9 B ]_] B ŸžšF™;Y š]I J ¤ ¡)š = ™_; ˜ ¤¥%ILž ‚¢ šB£"šY ˜ž¤d]t™  B ™›š™<D; ]r;!£"š B ˜ž¤%™_<š-o„¥]› ¥PpTQ„™fœš.I J ¤w¡"š = ™_; ˜ ¤w¥%I ¥"  ¢Fš] š_ši<˜y¢5™_<š] ši;!£"š B ] š7). ™›š_¤£\™›˜LŸžš¤š_ B E 9 B ]_] B ŸžšI™;Y š]I j ;Ž¤ B EE:ž ¢ šfd]tš ¡)š = ™_; ˜ ¤2¥%I X Z ˜ ˆ™<š ]t˜PYŒš¢k< B ™ˆ™›š = <¤d; = B ErY ˜"£%;\ = B ™;Ž˜ž¤d] ¤šš£"š*£ ™ ˜ B £ B 9"™ ™_<š] š ;Ž£"š B ]D™ ˜  ] ™Qs9 B ]] B Ÿ ši9š_ = ˜.E B ™_; ˜ ¤˜ž¤ B ¤ :š]_]tš¤:™; B EE: L1Qƒ£%;Y š_¤d]; ˜ ¤ B E 9š__; ˜"£%; = Ÿ  B 9D<  B ]£š7 ¤š*£q;Ž¤ @ š  ¤D; ™;Ž˜ž¤\¥DI h/I_U 1 šH<˜.9šr; ¤L™<D; ]¢ B :B™_< B ™F¢ š B = <D; š^žš7Ÿž›š B ™ š = E B  ; ™:ˆ˜!Z\9›š] š_¤:™ B ™;Ž˜ž¤ I.  !#"$&%('*) +)-,.,/)-01"2%3'*45"$,.  š ™™_<š š£Ÿžš]˜!Z:™<šCo}¥]¥.p Q}™_fœ‚šœ‚š š  fD;9d9‚š*£¢k; ™_< ;7I ;sI £3Iš7.%9˜ž¤š¤ ™_; B E!9 B ]] B Ÿ š ™_;Y š]02 0E‚  B ¤£ E š_™Fœ˜r™_<^žšt™_; = š] B ™aE š^žš"E _š ˜gœ‚š ; ¤d; ™_; B EE: ; ¤%Z š = ™›š£3I FF™ B ¤:&.)š*£B™_;Y š Qn rŸP;^ š_¤g™<ša;Ž¤%Z š = ™ š£ = ˜.Y 9‚˜ ¤š_¤:™ M N  rš B = <aš£"Ÿ šF¢k; ™<Œš7. B = ™E: ˜ ¤š7š_¤£%9˜.;Ž¤:™r; ¤;™<š ;Ž¤%Z š = ™ š*£ = ˜.Y 9˜ž¤š¤:™a; ] š  f B EE:qE; 6 š"E:ˆ™ ˜ œš 9 B ]_]tš*£Lœ : ™_<š;Ž¤%Z š = ™;Ž˜ž¤¤š7.)™I‚ba<D; ]i; ] B £D; ›š = ™ = ˜ ¤d]tš  fš_¤ = šˆ˜!Z ™_<š E B = 6 Q„˜.Z,QsY šYŒ˜ : 9›˜.9š_ ™:\˜!Z ™<šg7š .%9‚˜ ¤š_¤:™_; B E£%; ] ™›;ŽœDf"™_; ˜ ¤ I 1 ; ™< 9›˜žœ B œD;E; ™:\˜ž¤š   B ™ ]t˜PYŒš EŽš"^ š"3E 6) :œ‚˜ž™< ^žšt™_; = š] ¢k;EEœš = ˜.Y šk;Ž¤%Z š = ™ š£Œœš1Z ˜  š B ¤:^žš_ ™ š . B ™ EŽš"^ š"E(6 n L.I @ š_¤˜ž™ šBœ :  ™<=š ‚_]t™rE š^žšEZ ˜ž ¢k<D; = <\™<D; ]k< B 9D9š_¤d]  B ¤‚£-EŽš ™   £"š¤˜r™›š7™<š ™_;Y š.I l :Œ™<šCE B = 6 Q ˜!Z,QTYŒšY ˜ž_:i9›˜.9š_ ™:ž  ™<š&™;Y šC; ™™ B 6 š#] Z ˜  ™_<šC;Ž¤%Z š = ™;Ž˜ž¤ Z ›˜.Ye™_<D; ]kY ˜.Y š_¤:™ ™ ˜ ›š B = 8 < 7 E š^žšE]Z f ™<šk< B ]F™_<š ] B Y š7£D;]t™ _; œdf"™;Ž˜ž¤ B ] B 6 ™_<š7™;Y ši; ™ ¢F˜.fdEŽ£ ™ šI™ ˜ ›š B = <-E š^žš9E 7 D;sI š.IŽ . +.  ?5. . . LPL. S +5 . o}¥%IL#p.

(90) J ¤ Z B = ™  B ™;Ž¤]¤D; ™ šE: Y B ¤ :EŽš"^ š"E ]_  œ‚˜ž™<q^žšt™_; = š] ¢k;EEœšr; ¤DZ š = ™›š£ œš1Z ˜  š B ¤ : ž^ št™›š7. B ™0<D;ŽŸ.<š\E š^žš"E ]II1Uša] š_š ™< B ™ ™<ša9›˜ = š#]]€<˜PEŽ£D] = š_ ™ B ;Ž¤g›š_Ÿ š_¤š B ™;^žš 9›˜.9š_ ™;Žš]I_1 < B ™ ¢ šY š B ¤;œ :ˆ™_<D; ]a;]F™_< B ™r;Z ¢FšI š9‚š B ™ ™<š B  ŸPfDY š_¤:™ )¢Fš   .   

(91). j Ž; Ÿ.f š%¥%W-F ›š B E; B ™;Ž˜ž¤#˜!Z&™<š ]9 š B £P˜!Z B ¤);Ž¤%Z š = ™;Ž˜ž¤P˜ ¤™_<š o}¥]¥.p Q}™_fœ‚šPI ba<šœ ˜ 6 š_¤ E;Ž¤š]c;Ž¤£%; = B ™ š E š^žš"E ] B ™%¢k<D; = <2œ‚˜ž™< ^žš_ ™; = š#] ¢k;EE œš = ˜.Y š‚; ¤DZ š = ™›š£œš1Z ˜  š B ¤:)^žš_ ™ š . B <š B £ I ba<š ™<D; = 6 E; ¤š = ˜ž¤d]t™; ™f™ š] ™<š7™› ššI˜.Z ;Ž¤%Z š = ™;Ž˜ž¤ I Ÿžš¤š_ B ™›š B ] š  fš¤ = šˆ˜.ZF›š_Ÿ š_¤š B ™;^žš E š^žšE]V  7d7 " o ] š_š j ; ŸPf›š ¥.pn ¢k; ™_< = ˜  ›š]9‚˜ ¤£%;Ž¤Ÿ] š  fš¤ = šI˜!ZG;Ž¤d]t™ B ¤ ™]0     7  D]ef = < ™< B ™io}¥%IL#p<˜PEŽ£D]I0ba<D; ] ;]GY B £"š09›š = ;] š ;Ž¤išY Y B ¥DI ¥DI V š"Z š_™›˜ ™<š9 " B  ™˜!Z)™_<š Ÿž B 9d<Iœš ™ ¢Fš_š¤ E š^žšE  7 B ¤£  7@? " B ] B †vyxƒ~z IB¡ ;Ž¤ = šg™<š 9 B ]_] B Ÿžš7™_;Y š#] B  š;7I ;7I £3IŽ ™<š ]tš  fš_¤ = š ˜!ZaE š¤Ÿr™_<d]B˜.Z B 9 B ™ = <U¢k;EEœš ;7I ;sI £3IŽ  B ]¢Fš"EE B ]S  

(92) 5 R    ™<š]tš  fš_¤ = š ˜!ZI™;Y š]q; ™L™ B 6 š#]Œ™ ˜ 9 B ]] B 9 B ™ = < I J ¤ 9 B  ™; = fDE B *  ™_<š*/ ™_< ›š_Ÿ š_¤š B ™;^žš . . E š^žšE B ¤£ˆ™_<š&™;YŒš B ™ ¢k<d; = <-; ™k; ] ›š B = <š£ Y B :ˆœšI¢ ; ™t™›š_¤ B ]a]efdY ]F˜.ZG;7I ;sI £3I  B ¤£"˜PY ^ B ; B œdE š#]_ %;sI šPI   . , S. ,!"  7.  7@?. . " .  7. B ¤£. . %S . ,!"  7. .   

(93) 5 (  . . ¢k<š_›š   S ¦ B ¤‚£   S ¦DI ba< fd]_ ; ™ ; ]&š B ]:\™ ˜ ]tššB™_< B ™ = E B ]_]e; = B E›š]fDE ™_]  ]ef = < B ]F™<šE B ¢ ˜!Z0E B  Ÿ š&¤ fDYaœ‚š_]o = ZI+šY Y B XdILpn  = š_¤:™  B E3E;Y ; ™ ™<š_˜ž›š"Y o = ZIš"Y Y B XdI ¥Pp B ¤£™<š E B ¢S˜.Z ™<š ; ™›š_ B ™›š£‚EŽ˜žŸ B _; ™_<DY o = ZI3šY Y B XDI XPp   B 9D9dE;Žš] ™›˜     ™<šr9 B ]_] B ŸžšF™;Y š ™ ˜™_<š /™_<ˆ šŸžš_¤š_ B ™;Ž˜ž¤GIGFH] B 9 B  ™ ˜!Z˜Pf Y B ;Ž¤w›š]fDE ™]_ ¢Fša š .%9 B ¤£™<D; ]CZ f ™<š&™›˜-;Ž¤ ^ž˜PE^ š +#,  ™<š 9 B ]] B Ÿ š™;Y ša™›˜ E š^žš#E /0I ba<D;]a; ] B EE£"˜ ¤š; ¤¡)š = ™_; ˜ ¤ X.  . . ' , % ) ,/,/)-01" " !+ ) %3' ! ! ) % " . . . .  š_™ fd]I¤˜y¢ Z ˜ = fd]I˜ž¤™_<š‚oZ*$p Q}™_fœša¢k; ™<UŸžš¤š_ B E 9 B ]_] B Ÿžš™_;Y š#]"I=1 <š¤ ¢ š  š"Z š_a™ ˜ B ¤#š£"Ÿ š vrx ]t˜PY šEŽš"^žšEE/   ¢FšY š B ¤ B ¤#š*£"Ÿžš = ˜ ¤¤š = ™;Ž¤Ÿ™ ¢F˜ ^žšt™_; = š] B ™E š^žšE&/0I1 <š_¤ˆ¢Fš ›š1Z š ™ ˜ B ¤ˆš£Ÿžš 5{_x - {{_q EŽš"^ š"E ]2/ B ¤£%/ n7U  ¢ š Y š B ¤ B ¤š£"Ÿ š = ˜ž¤¤š = ™;Ž¤Ÿ%™ ¢ ˜ ^ š_ ™; = š] B ™ B ¤ :w˜.Z™<š E š^žšE]qo7] B YŒšˆ˜ . L*¥.

(94) £%;\4š_›š_¤:™p /2 /n L  7Y/-n 7 I31 <š¤¢ šg š"Z š_ ™›˜ B ¤š*£"Ÿžš vrx <š; ŸP< ™ _š_›˜  ¢Fš Y š B ¤;™< B ™ œ˜r™< ; ™_] š¤£%9˜.;Ž¤:™_] B ›š B ™k<š; ŸP< ™š_›˜dI š ™ œš B 9˜P]; ™_;^ šH;Ž¤ ™›š_Ÿ š_ B ¤£;£"š_¤˜r™ š&™<š ] š ™ ˜!Zš*£"Ÿžš#]Fœ‚š_™ ¢ šš_¤EŽš"^ š"E / B ¤£ /nP¥ œ : , I @ š ¤š7™<ši]efœ/]tš_™  , ˜.Z , B ]   , W SP21 & , W 1;] B ™r<š";ŽŸ.<:™ _š ˜‚  B ™kEŽš"^žšE#/  ˜ž B ™rE š^žš"E#/ nN¥ ?d o}¥%I ¥.p @ 7š ¤š 7! W S ;Ž¤%Z ' ¦ W "!3  ¦   : >N¦  o}¥%I XPp. ! W S ]fD9 ' ¦ W  ! 3   A>p : > ¦  KD˜r™ š™< B ™ ¦ P7! = !$P A’  ¢k<š_›š\™<š ]t™ _; = ™ ;Ž¤š  f B E; ™:)<˜PEŽ£d] Z ˜ž 9 B ]] B Ÿ šŒ™;YŒš;£%;]t™ _;ŽœDf"™;Ž˜ž¤/]™< B ™g£"˜¤˜r™ = ˜ ¤ = š¤:™  B ™ š B EEY B ]] B ™ B ]; ¤ŸPE š 9˜.;Ž¤:™I j ˜ž = ˜ž¤/] ™ B ¤:™_] Q B ¤£Q ]f = <™_< B ™ 7 ! = Q = Q = ! £"š ¤šg™<š ›š_Ÿ š_¤š B ™;^žšIš"^žš¤:™ . . . . . . . , W S

(95)   P Q  1S&  , b;^ ; B E E: qo , pD>¦DI .

(96). . .   ' Q    ;1S& ,   , . o}¥%I hp.

(97).    .  .  !. j ; ŸPf›š XDWrba<š-o X&›¥PpTQ„™fœšaœš ™ ¢Fš_š¤ EŽš"^žšE_/ B ¤£:/-n¥ I J Z , ˜ ="= f_] F™<š™<D; = 6 š*£"Ÿžš#] B ›š   fD; = 6   B ¤£N™<š™<D;Ž¤’š*£"Ÿžš#] B ›š  ]EŽ˜y¢ DI @ š_¤˜ž™ šœ :   W S Y B . / '¦ W " H &* B ™kE š^žšE /7™<š Z ft™_<š]t™r; ¤d; ™_; B EE: ;Ž¤%Z š = ™ š*£ E š^žš"E„  B ¤‚£ œ : H  , ™<š ^žš_ ™ š . o /2› ¦   7›¦Pp1I b U    { x Q vrq  Q 5{L~oyqmnx vrqx}mBm ~›zwx zvyx 7 ! = Q = Q = ! / z{_qUx(z{ ‡ {Œ{žk!mnx}mvrq &$#  m ~›zx(zvyxs oy‡avr€(€ / '    k s  , o~~ "‡m  x(z{ q + o H  , ?&%pRS + , ?% vyq  + o%H pRS + o H  , ?&% p n + o H  , ?&%N3H p

(98). . . . . . s or‡a{vž~zly{ ‡nxƒ{. H.

(99). vyxF€ {_l _{ €  / nP¥. /. L#X. .

References

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