Probability distributions of lengths and angles | 10

ABSTRACT

Aë

[,é

ÝèY

ˆÛ

ß‚®æˆ

ÜÞÆ ÜÞ®æôß1

|~A0G[jCFHG_‚LlM;bJŒc"M;bCF‰PRACB;jﬁDHGFKJ˜X‰G7FKG[PdM1NCPdGFHNCG`XL>DHAJyDRB)DHLkJtDHLkP7BZe BZNBZel\JHLkJBZN`mqMﬁ`¡

G7ele>LlN0xmM;c9I&JHJHL>M1NDHFRB;PRQšPdM;bCN1DRJ7=|~A0LlJ[PRACBZj0DHG7F[LlJ[BZ^&M;bﬁDEDHA0G’DHA0GM;FKGdDHLkP7B;e(JtDKB)DKLlJtDHLkP7B;e

j0FHM1jGFtDKL>GJMZc‰DHFRB;PRQelG7N0x;DHACJB;NC`ÞM;FKL>GN1DRB)DKL>M1NCJ7= ?ÞGm`ﬁG7FKLl_;G”DHA0G,ÊyM1L>N‚Dµj0FKM;^CB;^0Lle>L>Dy\

`ﬁLlJtDHFKLl^0bﬁDHLlM;NJﬃMZcelG7NCxZDHAJŒBZNC`”M;FKL>GN‚DKB)DKL>M1NCJ9MZc&A0M;FKL>»M;N‚DKB;eﬁPdM;N0ICN0G`’DHFRB;PRQﬁJÎ-MZc&JHG7qL>¡

DHFRB;PRQﬁJLlN‚DHGFKJHGPdDHLlN0xrB”jCelB;N0G;Î0B;NC`OM;c(DKA0G7LlFj0FKMZÊyGPdDHLlM;NCJ‰M1N1DKM™B™j0ekBZNCG;Î0BZN`]`ﬁLkJKPdbCJKJ

JtM1q™G,Llqj0e>LkP7BZDHLlM;NCJ=

?ÞG,ICFRJyDWPdM1NCJHLl`ﬁGF~LlJHMZDKFHM1j0LlPelG7N0x;DHA`ﬁLkJyDKFHLl^0bﬁDKL>M1NCJ7ÎCXA0G7FKGDHFRB;PRQrelG7N0x;DHACJ`ﬁMrNCMZD

`ﬁG7j&G7NC`ÂM1NÂM1FHLlG7N‚DRB)DHLlM;N(=9…†NÂDKA0LlJOP7B;JHG;ÎŒ^&GPBZbCJHGšDHFRB;PRQﬁJrBZFKGFKB;NC`ﬁM1q™el\¤M;FKLlG7N‚DHG`sÎ

j0FHM1^CBZ^CL>elLœDy\`ﬁLkJyDKFHLl^0bﬁDKL>M1NCJ‹FKG7ekB)DKL>NCxDHM’DHFRB;PRQﬁJŒLlN1DKG7FRJtGPƒDKL>N0x”Bµj0ekBZN0G[`ﬁM’N0M;D‰`ﬁGjGNC`

M;NXA0LkPRAj0elB;N0GµL>D[LkJ7=v0FKM;qÀGPdDHLlM;Nõz={n™M;NX‰GµPdM1NCJHLl`ﬁGFEBZNCLlJHMZDKFHM1j0LlP,elG7NCxZDHAp`0LlJt¡

DHFKL>^0b0DHLlM;NCJÎCXA0GFHG,DKA0G’jCelB;N0GµMZcŒM1^CJtGFH_)BZDHLlM;N`ﬁMGJWqrBZDtDHGFÎ&PdM1NCPdGN1DKFKBZDHLlN0xM;NDKA0G

P7B;JHGmXA0GFHG]LœDLkJ”jBZFRBZele>Ge‹DHMŽBpjCFHLkJtqrBZDHLkPrcB;P7G;=ﬃhWele~MZcWDKA0GJHG]`ﬁLkJtDHFKL>^0b0DHLlM;NCJÎŒBZNC`

MZDHACG7FRJ7ÎﬁqrB-\O^&Gµ`ﬁGFHLl_;G`Oc"FKM;q¹DHA0GqrB;L>NFKGJHb0eœDWM;cﬃDHA0LkJWPRACB;jﬁDHGFÎ0G‚bCB)DKL>M1NÞü.z=l<a1ýdÎ

XA0LlPRAx1L>_1GJŒBc"M;FKq’bCelB[c"M;F‹DHA0GG7›j&GPdDHG`N‚bCq’^&G7F‹M;cDKFKB1PRQJ9DKACB)D‹LlN‚DHGFKJHGPdDB,j0elB;N0G

BZNC`ODHACBZDWACB-_;G,JHM;qGj0FKGJKPdFKL>^&G`]B)DtDKFHLl^0bﬁDKG;=

|:M’IC›ON0MZDRB)DKL>M1N*Îﬁv:Llx;bCFHGµz=l<JHA0M)XWJ˜DHACFHGGd¡†`ﬁL>qGNCJtLlM;NBZesPdMM;FR`ﬁLlNCB)DKGJÎ1XACG7FKGEDKA0G

OZ¡†B)›ﬁLkJ˜LkJjCB;FKB;e>elG7e&DKMDHA0G’P7FH\ﬁJtDKB;e>elM;x1FKB;j0A0LkP †R¡†B)›ﬁLkJBZNC`ODHA0G.ÑO;¡.j0elB;N0GLlJjBZFRBZele>Ge DHM

Bmj0FKLlJHqrB)DKLlP,cB1PdG1=&h DHFRB;PRQšMZc‹elG7N0x;DHA·íL>N‚DKG7FRJtGPƒDKJWDHA0G*ÑOZ¡.j0ekBZN0G1Î0XL>DHAõJHG7qL>¡2DKFKB1PRQ

e>GN0xZDKAmÓ B;NC`j0FKMZÊyGPdDHG`JtGq™L>¡ÇDHFRB;PRQWelG7N0x;DHA‹ì=-|~A0GBZNCx;elGŒ^G7DyX˜GG7NDHA0G˜j0FKMZÊyGPdDHLlM;N,MZc

DHA0G~DKFKB1PRQM;N‚DHMDHACGM;^CJHG7FK_)B)DHLlM;N”j0ekBZN0GBZN`’DKA0G•†R¡†B)›ﬁLkJ:LkJ‹`ﬁGN0MZDKG`”^\îíW=1¨[^CJHG7FK_;GFKJ

PdM;bCN1DsDKFKB1PRQﬁJsL>N‚DKG7FRJtGPƒDHLlN0xWBPRA0M‚JtGNBZFKGB~MZcDKA0G‹j0ekBZN0G1ÎB;NC`[DHA0G\qrB-\BZekJtMqGB1JtbCFHG

j0FHM;ÊyGPdDHG`JHG7qL>¡2DKFKB1PRQOelG7N0x;DHACJ‚ìmBZNC`šDKA0G”B;N0x;elG£íW=C….DLlJEjM‚JHJHL>^Ce>G1ÎC^0bﬁDACBZFR`ﬁGFÎCDHM

q™GB;JHb0FKGEDKA0GµB;PdDHbCB;e*JtGq™L>¡ÇDHFRB;PRQrelG7N0x;DHASÓ‰B;NC`]LœDRJWBZN0x1e>GµïDHM™DHA0GŽ†ƒ¡.BZ›LkJ=

§±23

ﬂﬂ‰7')0/¥*

‘

1Æ*

$Ž

‘

pC“ˆﬂ

‘

b0j0j&M1JHGDHACBZD’BZeleŒDHFRB;PRQﬁJ,ACB-_1GGd›0B;PdDHel\pDHACGmJHB;q™GrelG7NCxZDHA¤ít=(|~A0GrqGB;NÞelG7NCxZDHAŽÉ

G‚bCBZekJíŒBZN`mDKA0Gµ_)BZFKLlB;NCPdGÔ

LkJ»7GFHM=0hWe>DHA0M1b0x;AšDKA0LlJELlJWA0L>x1A0el\OLk`ﬁGB;e>LkJtG`sÎﬁL>DEj0FKMZ¡

_‚Lk`ﬁGJWBbCJHGdc"b0e:L>N‚DHbCLœDKL>_1G^CB;JHLlJc"M;FWb0N`ﬁG7FRJyDRBZNC`0L>N0xDKA0G’P7M;NCJHG‚b0GNCPdGJ~MZcŒJHB;q™jCe>LlN0x

^‚\rjCelB;N0GJHGPdDHLlM;N*=…†N]DHA0GB;^CJtGNCPdG[MZc9_-B;FHLkB)DKL>M1NmLlN]ekB)DKG7N‚D˜DKFKB1PRQe>GN0xZDKACJ7Î0B;N\™_)B;FHL>¡

B)DHLlM;N¤LlNJHG7qL>¡2DKFKB1PRQ·elG7N0x;DHACJ™BZNC`ˆj0FHM;ÊyGPdDHG`¤JHG7qL>¡2DKFKB1PRQ·elG7N0x;DHACJ’XL>ele‰^G`ﬁb0GODHM

DHA0GrFRBZNC`0M;qÀelMPB)DKL>M1NCJBZNC`õM;FKLlG7N‚DKBZDHLlM;NCJMZc‰DHFRB;PRQﬁJÎsBZelM;N0xšXLœDKAÞDHA0Grx1G7M;qG7DHFKLlPBZe

GdŸ GPƒDRJMZc:DHFKb0NCPB)DHLlM;NBZN`]jCFHM;ÊyGPƒDKL>M1N*=

È(GdD:FRBZN`ﬁM;qY_)BZFKLlB;^0e>GJ<

BZN`£<lï

`0G7N0M;DHG;ÎFKGJHjGPƒDHLl_;Ge>\1ÎdDKA0G˜JHG7qL>¡2DKFKB1PRQEelG7N0x;DHA

BZNC`Þj0FKMZÊyGPƒDHG`¤JtGqLœ¡ÇDHFRB;PRQpelG7NCxZDHA¤M;cWBšDHFRB;PRQ·LlN‚DHGFKJHGPdDHLlN0xpBj0ekBZN0G1=:‰GPBZbCJHGmBZele

G'GPÐ

<;<u Ł£W¨~hE‰…yÈ(…y|§‘®¯[…tﬁ|£…y~ëE|~…H¨¬¨vÈ(ž˜¬[¿,|U]h[¬E¯çh[¬[¿,È:ž˜

ñMò

÷ ø

ûüý

øŁþ ß

HJILKNM?OQPH9TLR`/_a'a7dﬂ\N`hbeNWj[Ce'šﬃ[0^”^fY?aN$`hbﬃnÇW-dfeXZg‡pv[0bnNWsYÇÍju ^![0w@`-x>W-dﬂeXZgopv[0bﬃnNWsYSÉ0uƒidfaFi+[ﬂXWj[ﬂ\

^[0w@`-x(W-dfeXZgpv[0bnNWsYu§a7d0`([0b?W(eNW-`>aNb eNbﬃnUpv[0^3aeNb\qcAuƒeNb\”WsY?[*eNbnUpv[ |Z[0W-~[Q[0b WsY;[zidﬂaUx

i'[QXW-`-aNb–afrEWsY?[<W-dfeXZgÇa7b WsY;[efd;xvipLeNb[<eNb\CWsY;[d;xe!šN`h^klY;[evd?xvi9pLe7b[*`h^ŽWsY;[’i9pLeNb[<afr

aU|^![0dZ{7eNW-`>a7bka7deZiAeNW-`hWj[@WsY`h^§`h^ eN^Q^QqAwm[ﬂ\.W(a*|Z[ezidZ`h^QwmeNW-`-X6r!eXZ[0u~$`hWsY*WsY;[Ëd?xe'šN`s^%iAeNdx

eNphpv[p9W(aŽWsY;[ Xd0}7^QW(eUphpLaQnNdfe0i?Y`>Xƒ™Uxje'šN`h^klY?[r0qAphp9pv[0bﬃnNWsYŽÍˆXQeNb;baNW%|Z[@aU|^![0dZ{N[ﬂ\*|Z[ﬂXQeNq^![@aNbp }

WsY?[z^0aUp `>\ˆiAeNd0W_`h^ˆ$`hWsY`hbEWsY;[ XdZ}7^ZW(eNp u_WsY?[•\UaNW-Wj[ﬂ\•iAeNdZW±Y?eN{'`hbﬃnŽ|Z[Q[0bmiAaUp `h^fY;[ﬂ\ŽeNeN}k

ﬀdﬂaNw

ÀeN^Zpv[0W-Wˆ[0W%eUpvkLuÁUÂÂ!Ã9k y

DHFRB;PRQﬁJŒACB-_1G~DHA0GEJKBZqGWelG7NCxZDHAmí(BZNC`FRBZNC`0M;q M1FHLlG7N‚DRB)DHLlM;N(Î)DHA0G`ﬁLkJyDKFHLl^0bﬁDKL>M1NCJ‹M;c2<

BZNC`£<`ï

BZFKGﬃDHACG‰JKBZqGŒc"M1F:BZN\j0ekBZN0G1=hWN`µ^&GP7B;bCJHGŒDHFRB;PRQﬁJ*PBZNµLlN‚DHG7FRJHGPƒD(DHA0G˜j0elB;N0G

c"FHM1q B]FRBZNCx;G’M;c‰`ﬁLkJtDKBZNPdGJ,B;NC`õBZDµBO_)BZFKLlGdDy\MZc~BZN0x1e>GJ7ÎsJHG7qL>¡2DKFKB1PRQšelG7NCxZDHAJBZNC`

j0FHM;ÊyGPdDHG`JHG7qL>¡2DKFKB1PRQOelG7N0x;DHACJ[P7B;N^M;DHAp_)BZFK\]c"FHM1q³‡DKM]ít=C?ÞG”JHA0M)Xº^&G7elM)XYDHACBZD

DHA0G[j0FHM1^CBZ^CL>elLœDy\r`ﬁLkJtDHFKL>^0b0DHLlM;NmM;c:<

LkJ"9ﬀ& )+='DºM)_1G7F‹DKA0LkJFRBZN0x1G;Î1XLœDKAOj0FKM;^CB;^0Lle>L>Dy\

`ﬁG7NCJHL>Dy\rc"b0NCPdDHLlM;N

ﬃ

ü(Ótýž

N ‡qoÓKoí ü.z=l<ý

BZNC`]qGBZN

É£ž÷žWì <£Kðž

|~A0G”_)B;FHLkBZNCP7G”M;c˜<

LkJ,í( -§ﬁ<TOBZNC`pDHA0GrPdMG7ârP7L>GN‚DM;c_)BZFKLlBZDHLlM;Nü"DHA0GrFRB)DKL>M]MZc‹DKA0G

JyDRBZNC`0B;FK``0G7_LlBZDHLlM;NDKMmDHACG’qGB;NýLkJWDKA0G7FKGdc"M1FHG”íF§

<T í§ZTpžû<§

a ¼®‡ﬂ n;€0ÎM;F

nZ€O=&…†N·DKA0LkJPB;JHG;Î&DHACG™`ﬁLkJtDHFKL>^0b0DHLlM;Nôü.z=l<ý[BZx1FHGGJ[XLœDKA·LlN1DKb0L>DHLlM;N*¸s^\pJH\‚qqGdDKFH\1Î

DHA0GmjCelB;N0GrMZcM;^JtGFH_)B)DKL>M1NõLkJµG‚bCBZele>\õe>LlQ;Ge>\·DHMpLlN‚DHGFKJHGPdD’BšDHFRB;PRQõB;NC`¤BZN\pj&M;LlN‚D

BZelM;N0x™LœDRJelG7N0x;DHA*=

hEÈ(ÈŽ|£WhE«§µšU[h(à[…y¬[¿ |UEž÷ﬁh[opžÈ(ž˜¬[¿,|U <1<-z

LlqL>ekBZFKel\µX˜GJHA0M)X¤DKACB)DŒDKA0G~j0FHM;ÊyGPdDHG`™JHG7qLœ¡ÇDHFRB;PRQelG7NCxZDHAÊ<

£‹ACB1JŒB*j='&(ﬁ;:A"9,Œﬁﬃ=

`ﬁLlJtDHFKLl^0bﬁDHLlM;NšXL>DHAj0FKM;^CB;^0Lle>L>Dy\m`ﬁG7NJtL>Dy\mc"b0NPƒDHLlM;N

ﬃ

£-üì)ý ž

í#Ì

<Å

N ‡poì°oÂí ü.z={T;ý

BZNC`]qGBZN

£Åž÷žWì <

£Kðž

|~A0G_)BZFKLkBZNCP7GMZcF<

£ﬃLkJﬃí( -§ﬁ<€WB;NC`L>DKJﬃPdMG7ârP7L>GN‚D:MZc_-B;FHLkB)DKL>M1NLlJ:DKA0G7FKGdc"M1FHGí§

<€

íF§)ažç<§

TP¼‡ﬂ{zﬁ<;ÎﬁM1FWzﬁ<yO=

|~A0LkJrj0FKM;^BZ^0Lle>L>Dy\ˆ`ﬁGNCJtL>Dy\ˆc"bCNCPƒDKL>M1NACB;JL>DKJrqrBZ›Llq’bCq MZcTv§ZíBZD!ìCžÒ‡¤BZNC`

`ﬁGP7FHGB;JHGJ~elL>N0GBZFKe>\ODHMr»G7FKMmB)Dì°žYíy=hçJtACM;FHDWj0FHM;ÊyGPdDHG`šelG7N0x;DHAì™XL>ele:B;FHLkJHG,c"FHM1q

DHFRB;PRQﬁJ9G7L>DHA0GF˜B)DBA0Llx;ArB;N0x;elG~DHM,DKA0Gj0ekBZN0GM1FŒc"FHM1q BZDHM;qrJ9c"b0FHDHACG7FB-X~B-\,c"FHM1qçDKA0G

j0elB;N0G;Î JHMmM;N0G™P7B;N·JtGG’LlN‚DHb0L>DHLl_;Ge>\XA\BrelB;FHx1Gµj0FKM;j&M;FHDHLlM;NM;c‹j0FHM;ÊyGPdDHG`pe>GN0xZDKACJ

q’bCJtD‰^&G,FHGelBZDHLl_;Ge>\rJHA0M;FHD=…†NOjBZFHDHLkPdb0ekBZFÎ‚DHA0GM;j&G7FRB)DKL>M1NOMZc(DHFKb0NCP7BZDHLlM;N]ACBZel_;GJ‹DKA0G

q™GBZNõDHFRB;PRQpelG7NCxZDHA(Î(BZNC`õDKFHb0NP7B)DKL>M1N·c"M1e>elM)X‰G`õ^‚\õj0FKMZÊyGPdDHLlM;NõFHG`ﬁbCPdGJDHA0GOq™GBZN

e>GN0xZDKAODKMrM;N0GDHACL>FR`šMZc:L>DKJWM;FKL>x1L>NCB;e _-B;e>bCG;=

|:M`ﬁG7FKL>_1GüÇz=l<ý9X‰GP7B;elP7b0elBZDHG‰DHACGDHA0GM;FKGdDKLlPBZeﬁj0FKM;j&M;FHDHLlM;N”MZc&DHFRB;PRQﬁJ9L>N‚DHGFKJHGPdDHLlN0x

BOb0NCLœDµBZFKGBOL>NõDHACG”j0ekBZNCG™M;cM;^JtGFH_)B)DKL>M1NpXA0M‚JtGJtGqLœ¡ÇDHFRB;PRQelG7N0x;DHACJ,BZFKG’x1FHGB)DKG7F

DHACB;NcÓƒÎ*c"M;F”BZN\·x1L>_1G7N Ó,L>NŽDKA0GmFRBZN0x1Gm‡ºª Óqªûít=*?ÞG]`ﬁMDKA0LlJ’^\ÞP7M;b0N‚DHLlN0xDKA0G

Gd›ﬁjGPƒDKG`Nb0q”^GF[M;cJtbCPRApDHFRB;PRQﬁJEB;NC`p`ﬁLl_Ll`ﬁLlN0x]^‚\šDKA0G™P7M;FKFHGJtj&M;N`ﬁL>NCxrGd›ﬁjGPƒDKG`

N‚bCq’^&G7FXA0G7NÇÓÅž®‡0= h JHLlq™LlekBZF,BZFKx;b0qG7N‚DELkJ[bCJtG`DHM]`ﬁG7FKL>_1G]ü.z={T;ýƒ=&|~A0GJHG”B;FHx1bﬁ¡

q™GN‚DKJ‰c"M;elelM)X÷c"FKM;q³«˜M)X~BZNŽüy<„‚z)„CÎﬁÈ*G7qqrBš<ýd=

?L>DHA0M1bﬁDe>M‚JHJ˜MZc:x;G7NCG7FRBZelLœDy\1Î1PdM1NCJHLl`ﬁGFDKFKB1PRQﬁJLlN‚DHG7FRJHGPƒDKL>NCxµDHACG@ÒÑ1¡.j0ekBZN0GLlN]v9L>x;¡

b0FHGpz={TÞBZNC`ôj0FKMZÊyGPƒDHLlM;NJ”M1N‚DHMõDHACBZDjCelB;N0G;=Œ….DrDKb0FHNJM;bﬁDDHAB)DDHA0GpPBZekPdb0ekB)DKL>M1NCJ

c"M;FDKA0G.ÒÑ1¡.j0ekBZN0GµB;FHGµJHLlq™jCe>GFWDHABZNDHACM1JHGc"M;FDKA0G.ÑO;¡ÇjCelB;N0G;=0hEelJHMCÎCc"M;FWFKGB1JtM1NCJMZc

Jt\qqGdDHFK\mX‰GµP7B;NšFKGJtDHFKLkPƒD½Q™DHMDKA0GµFRBZN0x1G‡#o¶Q#o

rŒÎCJtMDKA0G~ÊyM;LlN‚DEj0FKM;^CB;^0Lle>L>Dy\

`ﬁG7NCJHL>Dy\mMZcüRQSNRï ý~LlJ

JtLlNEïPN ‡poCQ#o

NÒ‡qoïŸo

v9Llx;b0FKGzﬁ= T”JHA0M)XWJ~B’jCB;FKB;e>elG7elG7jCL>j&G`]XLœDKA]bCN0LœDW^B;JHGB;FHGB]ü2JtACB1`ﬁG`ý‹DKACB)DLkJ~jCBZFH¡

BZele>Ge1DKMDHA0GzÒÑ1¡.j0ekBZN0GB;NC`’JHLl`0GJﬃjCB;FKB;e>elG7e‚DHMB[DHFRB;PRQXL>DHA™M;FKLlG7N‚DKBZDHLlM;N]ü¤QSNKï ýd=;|~A0G7N(Î

c"M;F’Óª®ítÎ&DHA0GelG7N0x;DHAÞMZc˜BšJtGqLœ¡ÇDHFRB;PRQLlN1DKG7FRJtGPƒDKL>N0xB]b0N0L>DB;FHGBmLlN·DKA0GÒﬀÑ‚¡.j0elB;N0G

XL>ele‹^&Grx;FKGB)DKG7F[DHACB;N Ó[L>c,ü2BZNC`ÞM1N0e>\·LœcKý,DHA0Gr^&MZDHDHM;qÐG7NC`ÞM;cDHACGDHFRB;PRQpLkJ,L>NÞDKA0G

jCBZFRBZele>Ge>Gj0LljG`s=‚|~ACLlJ‰jCB;FKB;e>elG7elG7j0Llj&G`mAB;J˜b0N0L>D~^B;JHG[BZFKGB”BZNC`OA0G7Llx;A‚Düíﬂ‹ÓtýﬁPdM‚JCï:Î

JtML>DWACB;J~_1M;elb0qG

ž üí ÓtýﬁP7M1JCï¨

hE`0B;jﬁDHLlN0x[DHA0GBZFKx;bCq™GN‚D9LlNr«˜ABZjﬁDKG7F‹TﬁÎZGPƒDHLlM;NTﬁ= a0Î-X‰G˜qrB-\FKG7x1B;FK`DHA0G~j&M1JHLœDKL>M1NCJ

MZcEDKA0G^M;DtDKM;q GNC`0JM;cEDHACGDHFRB;PRQﬁJB;JBŽŁﬃM;LkJHJHM;NˆjCFHMﬁPdGJHJ™XL>DHAFRB)DHGÖs=˜MÞDKA0G

Gd›ﬁjGPƒDKG`µNb0q”^GFﬃMZcCDKFKB1PRQﬁJ(XL>DHA’DHA0GL>FŒ^&MZDHDHM;qGNC`0JﬃLlNµDKA0LlJﬃjBZFRBZele>Ge>Gj0L>j&G`’LlJbÖ

BZNC`DKA0G™Gd›ﬁjGPƒDKG`pNb0q”^GF[XL>DHAõM;FKL>GN‚DKB)DKL>M1NˆüRQSNRï ýWLkJ

JHLlNEï Ö

ï@fQ0=sh[`0`ﬁLlN0x

DHA0GJtG˜Gd›ﬁjGPƒDKG`µNb0q”^GFKJ:c"M1F9B;e>e‚M;FKL>GN‚DKB)DKL>M1NCJ*x1L>_1GJ(DHA0G‰Gd›ﬁj&GPdDHG`’Nb0q’^&G7F9MZcJHG7qL>¡

DHFRB;PRQﬁJ‰XLœDKAšelG7NCxZDHAJ~x;FKGB)DKG7F‰DHABZNSÓƒÎ

›

&œN¤lÎ

ì Ù

ü>Ótý.ðAž

T–Ö

üí ÓtýﬁPdM‚JCïEJHLlNEï ï vQ

<;<€ Ł£W¨~hE‰…yÈ(…y|§‘®¯[…tﬁ|£…y~ëE|~…H¨¬¨vÈ(ž˜¬[¿,|U]h[¬E¯çh[¬[¿,È:ž˜

ﬀﬀﬁ ﬂﬃ"!ﬃ

ﬀ%&!(')ﬃ"!*ﬃ,+.-/!*ﬁ 0-1ﬂ

HJILKNM?OQP°9T “ùlY;[•iAaN^Q^Q`>|!pv[ziAaN^Q`hW-`>aNb?^.afrŽe<W-dfeXZgafrmpv[0bﬃnNWsY‚Í•eNb9\‚aNdZ`([0b;W(e7W-`>aNboÏRc

aﬀÐ’WsY?eNW

aNqApL\S`hb?Wj[0d0^[ﬂXW.eSqAb?`hWeNdQ[ﬂe a7bcWsY;[¨jexLi9pLeNb9[‚eNb\CnN`s{N[”dZ`h^[<W(a‡eS^![0w@`-x>W-dﬂeXZgopv[0bﬃnNWsY

nNdﬂ[ﬂeNWj[0dWsY?eNb@É+k$lY`h^%$`-phpﬃY?e0ii?[0b` rWsY;[z|QaNW-W(aNwÆ[0b9\’arˆWsY;[§W-dﬂeUXZg`s^%`hbEWsY?[6iAe7dﬂeUphpv[pv[ji;` i?[ﬂ\

$`hWsYE{7aUp qwm[ Ï>ÍÚÉﬂÐ\+='-—a_k

ﬀdﬂaNwÀe7^0pv[0W-W[0W%eUpvkvu~ÁUÂUÂ!Ã9k y

Öüí Ótý

Ł‹bﬁDHDHLlN0xEÓfž]‡µx1L>_1GJDHA0GGd›ﬁj&GPdDHG`mDHM;DKBZe&Nb0q’^&G7F~M;c(JtGq™L>¡ÇDHFRB;PRQﬁJŒDKM”^&G

Ö0íyÎﬁJHMµDKA0G

j0FHM1jM1FtDKL>M1NOXL>DHAelG7N0x;DHAx;FKGBZDHG7F‰DKACBZNCÓ˜LkJ

ü<

¥ Ótýlž

ì Ù

ü>Ótý†ðR§

ì Ù

ü‡‚ý.ðžç<Å Ó;§)íN ‡qo ÓËoí

¯EL>Ÿ&GFHGN‚DHLkB)DHLlN0xšXLœDKA·FKGJHjGPƒD[DHMCÓEBZNC`·PRACBZN0x1L>NCx]JHL>x1Npx;Ll_;GJDHACG”b0NCLœc"M1FHqÀj0FKM;^B)¡

^0L>elL>Dy\]`ﬁGNCJtL>Dy\rc"b0NPƒDHLlM;NŸﬃ

ü(Ótý~LlNšB;x;FKG7G7qGN1DXL>DHA¤üÇzﬁ=><-ýƒ=

|:MÞ`0G7FKL>_1GÞü.z={T;ýƒÎﬃM1^CJtGFH_1GmDKACB)DrX‰GšPBZNM1N0el\¤x;GdDmBõj0FKMZÊyGPdDHG`ˆelG7N0x;DHAx1FHGB)DKG7F

DHACB;Nì”LœcŒí)JHL>NEïb¥CìÎCLÇ= G;=lÎﬁc"M;F

BZFRP7JHL>N*üì–§Zí2ýËªï o

BZNC`õDHACLlJXLlele‹ACBZjCjGNÞL>c‰DHA0Gr^&MZDHDHM;qÒG7N`õM;cDKA0GrDHFRB;PRQLkJLlNÞDHA0GrjCB;FKB;e>elG7elG7jCL>j&G`

JtA0M)XNLlN v9Llx;b0FKGÞz={TﬁÎ˜XA0G7FKG°ì¬ž ÓﬁJHL>NEï:=‰…†NDHGFHqrJOMZcîìÎDKA0GÞ_;M;elb0qGpM;cDKA0LkJ

jCBZFRBZele>Ge>Gj0LljG`OLkJ

žçü2í¤ìf§ﬃJHL>NEï ýﬁP7M1J&ï

BZNC`^\ôDHA0G·JKBZqG·B;FHx1b0qG7N‚DOB;JO^G7c"M;FKG;ÎŒDKA0G·G7›ﬁjGPƒDHG`Nb0q’^&G7F]MZc’JHG7qLœ¡ÇDHFRB;PRQﬁJ

L>N‚DHGFKJHGPdDHLlN0xpBb0N0L>D”B;FHGB]LlNÞDHA0G‚ÒﬀÑ‚¡ÇjCelB;N0GDHACBZD’ACB-_1G™jCFHM;ÊyGPƒDKG`ÞelG7N0x;DHACJx1FHGB)DKG7F

DHACB;Nì”LlJ

ì Ù

£)üìZý.ð ž

TsÖ

8*9;: <

Í>=/?