A Model for Signature Verification Trevor Hastie and Eyal Kishon ...

2 downloads 0 Views 544KB Size Report
Feb 5, 1992 - Trevor Hastie and Eyal Kishon. AT&T Bell Laboratories,. 600 Mountain Ave. Murray Hill, NJ 07974. Malcolm Clark. Monash University. Clayton ...
     !#"%$& ')(+* FH,.GJ-/(%IK02GM1/3 LO46NQ57* PBPS1.R8:T.9WX=?TZ1.Y+@V?W\A[BNQ5B3D]_CE^ -/8 `b .dfa?W\W+acTjigb kV?df[lPBe!P7YD^TZmegn Fa!o.h?p?N oZq rV?seE1.TZ@B]XtD|~-/@v}uxefwy[zh?@zN_1.W\(+]X{ [zYi  P€TjiY+b V?e ^f„f1/[B3…‚ -/Y+8gV?W\†[€T)1.^8 F%df]ƒY+WXT.PB[BT ‡ N_ˆf T.Y+W\T.YXe)‰ŠŒ‘V?NQW\e’“Y‹}‹V.ŒŽefH[lh.PBN_NQW\‚Q]XY+[lW\Y[Bi.‚_^T.PS HF ef?[lefN_NQWX[Be) p.q!”?a!• – NQUfWXdETZW\i • ^ — p?p!˜ ™Jšf›\œƒDž Ÿ¡œ ¤ © ¥¨¹ £ª¨¢ £ƒ§¨¥X«·°²Á £JÂ묤 ¯ © ¥7¹ ¦ ¥Ë¥S¤.½ °²¦Q¹ §¨¦…ªÃ£J³…¸ £ƒ©2¦ ¯ÄªË§‘¥¨ª#£X«¬©D³ ­&ª7¦ £ƒ«¬¶Q¸_§6ª¨¸ ª¨«®«®«¬­ƒ­ƒÅƒ© © £\¯±¯l§ Áð²ª7ÂÃÆ/¦j©D¹ ³ ª¥Ã£ƒ¯±¥7°²£ƒ´µ¤.¦Q¦j£\¥>³ ©¡£ƒ§¨ª¨¯«·£\¶Q³%­ƒ¸/¦ ©D§¨¸/«·ª7§¨¶Q¹ «®¸/§‘¥7ª#©D£O§ª7ºQ¹ ¦¡£ƒ¥¨´±¥7£X«¼©K§Ç».½j­ƒÌΩD̓¿Ïª7ª¨«·¦QÐ?Æ ¸¾Ñ·£KÒDÌν_ȨÍ˦D¿¾ÉS§¨«¬­&¶ ¸ ¦Q¸/£ƒ°O¥#©¡Ê ÀÀ ª7«¬¸2¹ ¥¨£\£Ž©Q´µ­#¦QÆK¥ ¥¨£X£\© ¸/­#³…Æ«·ª¨«·«¬¸/¦ ³ ¸2«·ºj¦ «®´f³…¹/ª¨Æ ©¡«®¯B§ÃÓ/© ª¨£ƒ¸/°²³¤ §¨¯®£ƒ©DºQª7£ƒ£ ¥#ÁŽ©¡¯ZÕÇ´zÆ © £\­&§¨ª¨£¦ ¥#ºD§ ©¡ÉS¥7«¬Æ ©¡«®ª¨­#«¬Æ%¦ ¸/© §Ë¯·¬«·¦D¸ZÉÔ­&¯¬¹/´µ¦ ³…¥Ç£ºDª7©¡Æ ¥7£J«®©DÖBª¨Ð/«¬¦ Í#¸ZÍ7ק ¦ ¥7¦¡´.ª#ÉS©Dª¨¥7«¬«¼¦ ª7«·¸%¸/¶/©¡Ó ¸/©Q³§E§¨É Æ £\£\¯·© Z¥\© Á±§EÕǧ¨¯·Æ/¦D£HÉS£\¯¬¿§6ª¨ºD«¬°²©¡¥7©¡¿jª¨«·£X¸ ³‹¶Hª7©¡£ƒØ²°²¸/¤ £Ç¯®©Dª¨ª7¥#£H©¡¸/¥¨£\§6´µ¤ ¦ ¥¨¥7£X°§6£\©D¸_ª¨ª7«¬¦ § ¸Zª¨§)Æ/£K§¨¹/È6­#°²Æ£\© © §E¸/§¨ÊO«¬Åƒ¦¡£ ´ Ó ´z©2©Q¹/­§7© ª¨©¡¸Q¦Q°²ª7¥7«¼§ ¤ ª#©D¯¬­ƒ£Jª7© «·¸‹ºQ¦ ´S£Ã½.§¨°²£y«¬¶ ¹/£\¸/©Q§6©¡£X§6¹/ª¨³¹ ¥¨ª7£X¥7¦>£\§S§y£X©¡§‘´µ¥7¥7ª#£Ã¦ ©¡£X°Ù½ §¨¯¬§¨« §¨£ƒ© Ƹ_¸Úª¨§¨«®«·£ƒ©¡¸/ºQ¯?³ £ƒ´µ«·¥#¦Qºj©¡¥S«®¯.³…¥¨°²¹/£\©¡¯·£\«®¯B©¡© ÓE½/§¨©¡¹ ¯·£H¸/¥7£\³Ú§¨§ «·¶Qª¨¦¡¸/Æ ´Ë©D£Ȩª7ºD¹ º+©¡© ¥¨¥7£Ž¥¨«¬«®© ©Dº ¸/ª7£\«·¥¨­&¦Q«·£X»Z¸/Ê §H­\Á©D«¬ÕǪ¨¸Ú«¬Æ/¦ ª¨¸Ä£\Æ/§¨Á ££ Û Ü ÝÞßfà á%âã2ä ß±åƒáÞ æ7è&çgêvñ çÚè&éí…êµçëõ ìÄíjú…ìfîDïƒîDê®ïJûòDðŽíjî2è&êµìñ ç¾ïƒñ…üZì)ýñ ë&ò+îñ ô2íîDéï êµ%òƒé~íjïƒêµîOëë&û êzô2?î¡êµõgóµíjïSöBñ…üÄïK÷í…èÃç“ç!ñ…êzçèyõêµõ!êvú?î¡êµçZõè&÷êµòDí…í…ó‘óÎþ þ Ãí…é!òƒîOé ôKè&ñ?êµô2õ!î¡î óÄé!êµçZî¾ú…ñ ë&êvóvø ú…çî¡ëë éñ !çî>èî¡ï\í…í…ò\ò+é î¡ëÃñ?ñ òD÷òDèÃí…ë&è&êvéñ êzç±ëþ èî¡ôKé!ìÄî¡ózíjëîcèî ú_.íjç!ïƒñ…êzèŽíjè&î êv!ñ í…çò+ëè&óvêzý2çòDüÄóµ÷÷!èÃõ!îÚð êvè&è&éé îŠë&ëô2ìfí…îDóµî¡óõsëèñ…ñ.öò\éð í…ïƒëêvè&è&êµêµò>ç!øújíjyïƒí…êµíjë è&êvðÃñ î¡çóµë ó 

























…í ëJéë&êzóvóvñQîð è&óvé!ýïƒí…ç!ø…î¡ë  ! é D î & ï  î µ ê ë … í c ç î .  è ¡ î  ç ƒ ë v ê … ú  î µ ó µ ê  è D î ƒ ï j í & è ! ÷ & ï  î   ñ ç … í ! ÷  è   ñ 2 ô j í & è µ ê  ò & ë v ê   ø  ç j í & è  ÷ & ï J î … ú D î ƒ ï ® ê ) û D ò j í & è v ê   ñ c ç … í  ç õ ðïƒêvèîDïé!î‹êzõ!ô2î¡ç/îDè&è&êvé!ûñ.òDõíjñ è&êvóvñ ñ…ç ø…ý¾üZýÚölñ…ïOò+ñ õ!ôKý.ìçÄ÷!í…ô2èîDïêµòë&ëêvîDø î çÄíjè&÷!ï&îJ öBú…ñ…îDï ïƒêvíKûòDï&íjî¡ò+è&êvî¡ñ çZçí…÷óEëêµî²ëŽöBï&÷ÄîDçìÄò+ï&è&î¡êvëñ î¡ççZëŽèî¡èõÚñKí…ï&îDëìíïƒî¡öBë÷Äî¡çç/ò+èè&êví…ñ ç¾ç î¡ñ…çZö:è&è&êvï&êµô2îJëƒî êvø í…ççíjõ¾è&÷!è&ï&é!î…î²þ ú_>í…îDózï&÷!îî¡ëyè&é!ñ…î ö è&é!îOö€÷çò+è&êvñ ç íjèyõÄê )îDïƒî¡ç/èŽè&êµôKî>ì)ñ êzç/è&ëŽíjï&î²ò+ñ çë&êµõ!îDïƒî¡õèñüfî è&é!îOöBî¡íjè&÷!ï&î¡ëDþ ôKë&êµñ îDçè&éí…ñ.ó:õìë íjïƒè&í…éôKíjèÇîDë&è÷îDïƒô2ëOôñ…ï²íjïƒölêî¡DîíjËè&è&÷éï&îÃî¡ëDñ…þ ïƒêµø êµé!çî¡í…ë&ó.îë&ìÄêvø íjçï\í…í…ó/ôKüZîDý‹èîDíOïƒë²ç.÷ï&ô‹îDìüfïƒîDî¡ï ëî¡ñ…ç/öÄèOóvñQè&ðHé!îù6õë&êµêvôKø çî¡ç!í_ùù è&÷!ïƒîölñ…ïè&éîìÄ÷!ï&ìfñ ëî²ñ…öÇï&îDìï&î¡ë&î¡ç/è&íjè&êvñ çcí…çõÚï&î¡ò+ñ…ø çêµè&êvñ çEþ ø…î¡ç!ÿ îD>ïƒçíjèSî¡î¡õ íç!ñ…ëü.ï\î ýŠôK.÷!í¾ñ î¡÷öBçëcñ…ò+ïƒîç.ò+î+÷ñ…ù6ôö ëî¡üfçÄîDë&ïŠêvõè&êvê ñ…ú…)ö2îKîDï&ë&ìfî¡êµø çZî¡ççEèíjþ öBè&î¡?÷!íjñ ï&è&î~÷!ôKï&îKölî¡î¡ëOíjìÄíjè&íj÷!ï&ìfîïƒîDî¡ïƒ÷Äë ë²ëî¡éÄéõ í¡í¡Äú…ú…î“õ!î îDí…ü)ï\êvóµîDú…ëî¡ñÚî¡ç õï\ô2í…çíjõî¡õ î ?í…í…ë>ô2ölî¡ìÄíjóvîè&÷!ïƒî¡ë>í èïƒ ÷÷çë&òDî¡íjõ¾èî¡è&õ é!îëîDûÄèOïƒñ…ë&èö èú…ïƒîDí…ïƒçê®óvûñQëðHòDöBñ…íjù‘ïƒè&ölôÚïƒêvñ î ç þZ÷!yèî¡ñèOçÄè&ò+ûÄé!ý ïƒîOëò+èOè6ñ.ðŽêvî è>ñ2ëëîDòDèî¡êvîDî¡ôìÄçZëŽè&ë>ëñ…ú…ö ñ…îDöHïƒóµñ ýcè&ðHé!íjù6î2èóvîDèìfïƒú…í…ñ î¡ò+ðŽó)è&öBîDêvî¡ú…ï%íjîKè&ë&÷!ì)èñ¾ï&î¡î²ò+ï&èõ!î¡ï\õîDíÚè÷Äî¡ñ…ò+ò+üî‹è&è&êvè&ñ í…é!çêµç!î%!î¡öBè&õ~ñ í…óµë óv÷cñQë&ðÃêµñ…çî¡öÃø¾õ ë&êvíü.ø ýçíjëè&ñ í…÷!ôKóµë&ïƒé îî ëë&è&êµôKí…çìÄõózê®íjûïƒòDõŠíjè&ôKêvñ îDç è&é!êzñ?ë‹õÚè&éñ…íjöSè%öBî¡è&íjé!è&î ÷!ï&ñ î+ú…ù‘ú…îDïƒî¡í…ò+ózèóyñ…ïï&î¡ò+ë&ñ ÷ôKóvèìÄêµíjë‹ïƒêzñ ëçÄñ óvçEý þ í…ë%é!ø…îJñZìñ?ï\õ êµò+í…îëñ è&ç!éî‹î ìöBí¡î¡ý?íjëè&÷!öBñ…ï&î¡ï ëKè&éëî+êµëù óvî¡ò+èî¡õEþ æ¨è%êµëõÄê òD÷óvè‹èñcûçÄõgí ëîDèñ…öHöBî¡íjè&÷!ï&î¡ë%è&éíjèí…õ!î .÷íjèî¡óvýgõî¡ë&ò+ïƒêvüfîí…óµó 































 





















 



























 !#"%$



&

(

'



*)

'





 ,+ -#.%$



0/#/

1)

2.



43

5

/ 

0

 ;

6,798:#%$





5

=






è&ëîDé!è îK>êµè&ôKéìfîDï&ñ…îÔï&è&êµí…ë çZè>è&é!í…î ëìfí…î¡õÄò+õè&ëOêvè&ñ…êvñ öËçè&í…é!ó>î%ìüfï&î¡ñ…éüí¡óvî¡ú?ô êvñ…ïOñ…ñ…ö%öËí…í¾ë&ë&ë&êµêvôø çêµóµíjíjè&è&÷êµç!ï&øgî…þ è&é!î¡êvú…ëî î¡ç ölî¡ë&íj÷è&òƒ÷é ï&î¡í ëÚêµóµçZíjèï&ñ ø…î í òDêvèóµî¡í…õŠë&ë&ê®êzû)çŠòDë&íjò+è&ñ…êvñ ìfçñ…í…ö çÄø…õ!îDðñ ïƒôKêvè&îDêzç!èïƒø êµò‹ ô%ë&é÷íjòƒìféJîJózê …í…îçí…ëìfóvý?îDë&î¡êµòƒëDéþ jêµëfè&êµô2îõ!îDìfî¡çõ!î¡çZèDþ  ñ è6ðŽñ>ë&êvø çÄíjè&÷!ï&î¡ëEð êzóµó éü)í¡î%ú…óµîêµç!î î¡?íjí…ï ò+þ è&óvý¾êµôKè&é!îîðŽë&í…íjôKïƒìÄîJêµç!è&øêµôí…êµózç!óvñ øð ìÄë>íjñ èèç!îDî%ïƒç èñ¾í…ø…çîDõÚèOíè&é!ìfî¡ëñ î‹êµç/è&è#êµù‘ô2èñjêµù‘ç!ìføKñ êµõçZê è²)îDò+ï&ñ…î¡ï&çÄï&ò+î¡î¡ëìfëHñ ð çêµõ!óµófî¡ç!çÄñ…ò+îè ü)è&é!îDî¡è¨ðÃêvïKîDè&î¡êµç ô2è¨êzç!ðÃøŠñ ìë&íjêvø èçèîDí…ïƒózçë2ëDðþ éÿ²êzòƒ÷!é ï2êzô2ë2ñ.ï&î¡õ!óµî¡íjóHè&êµ÷Äú…ëî¡î¡óvýë êµçëî¡çëƒêvèè&ñ~êvú…îÚô2èíjñ è&òƒéë&ô2è&í…é!óµîç ë&êvø çíjè&÷!Sïƒí…î¡çëDõ þ:æ#çJ õ! ñ  êµç øy ë&ñè&é!îDðyý²í…êµë>ç/è÷Äïƒëñ.î¡õõc÷Äò+èñ î¡õô2ç!íjñ è&çòƒóµé êµçè&î¡é!íjîï ðè&õé!êµéëîHèêµò\ñ…ñ…éçêvø õñ çÄçíjë&óvè&ýÚé!÷!î¡èï&íjñ¾î…ï¡þ þ üfîò+é!ñ î¡ôëî ù ìÄú_í…íjóµï&êzî¡õõ“íjèèîñÔí è&é!ç!î îDð èî¡ë&ôKêµø ìÄçóµíjíjè&è÷!îÚï&ë&î%êvø í…çÄë>íjíjè&ï&÷!î%ï&î…÷þ ëî¡õcé!èî¾ñë&ûÄí…è>ôKè&îÚé!îëîDô2èñ.ñ…õ!ö>î¡èó±î¡èòƒñ éçè&é!ê Zî÷!èî¡ïƒëí…êµíjçï&êzîÚç!ø2÷ë&ë&î¡êvø õgçèí_ñ ù è&÷!ï&î¡ë êvè&ëHë&ì)îDî¡õcë&êvø çí…óEêµëyè&êzôKî+ù‘ðŽíjïƒì)î¡õcíjø í…êµçëèè&éîï&îDölîDïƒî¡çò+î êvèêzëHëîDø ôKî¡çZèî¡õcêµçZèñóvîDèèîDïƒë î¡í…í…ëHò\ìfé ñ óµë&îDëƒèêvèüÄîDóvïyî…þ êzëÃí çî¡óvýèïƒí…çëöBñ…ïƒôKî¡õ èñ%ôíjè&òƒé¾è&é!îOèî¡ôKìÄóµíjèîOóvîDèèîDïHí…ëŽðÃî¡óµó è&ñ Ëé!ú…ý.îJîDìÄï&õ!êµð òDîDí…éú?óµî¡êµóµóµíjýsô2è&êví~êµñ ç!çø>öBëyñ…îDï&è&ú.ø…éêzîDíjõ!ïî¡çòDí…í…ò+òDîyç òD÷íjüfôø îí…÷Äêµóµçêµíjõ!ëèî¡èÇîJçZí…è&íj÷!ê®èûÄè&é!î¡î¡õî¡í…çZòƒécè&íjêµè òDñ…êvö è¨è&ý…éè&þ éî ÇîJè&êvêzëø ôKè÷!îDî+ïƒìÄù‘î ëHðŽñ íj÷!ë&ïƒé!ìÄè&ózñQêµêµç!ðç!ø î¡ë:õ¾è&ëéè&íjíjï&üfø…îDñ îŽî ú…ëƒîJêví…ø ìóvçè&ïƒé!íjñ.è&ñ õ÷!÷!÷Äï&ø ò+î¡é îë 

1)

*)







 








" ñ…öSð>*é êµòƒéŠ‹èêµëOï\í…í2êµçöBêµñ…ç!ï&øø…îDë&ï&êvø ý…çÄþ íj?è&÷!÷!ìfï&î¡îDëDïƒþêµôKìfé!ñ îDëïƒî¡î²õ êzëŽñ çí òDóvî¡íjï>éô2êµë%êzë&ô2ìÄíjíjìfè&îDòƒïKécêµêµë%ç¾ñ…è&ï&é!ø îJí…òDçí…ê Dîë¡îõñ…ö í…ëKè&é!ölî‹ñ ózölóvñ…ñ ï&ð ø…ë¡îDþïƒý…þ.î¡ò+è&êvñ ç õ!î¡ë&ò+ï\êvüfî¡ëñ ÷ïë&èñ.ò\éí…ëè&êµò ïƒë&êµç êvêvø è&éçè&éô íjêµè&ë²÷!öBñ…ïƒëïÇîJî¡ò+ûÄôKè&èêvè&ñ ñ.êµçõç!:î¡ø²ó ð !è&é!í…êvè&î>çé õ ôKè&.é!ñ.î¡î2õò+î¡è&éóÎêvþñ…ñ ì)Ôç îKî è&õéø î¡êvíjú…óµèêvî¡üfëêvè²îDíKïƒï&íjî¡ëèèí…î¡îDõóvìóvè&êvé!è&ñ éÔ÷!è&ø êµé ôKè&î é!%î2è&é!ò\é!î ñ è&êµêµò+ôKî2îñ…öŽè&í è&…é!î¡îKç ìÄí…í_ëù è&è6ðŽé!îcñcë&õêvêø fçÄîDíjï&è&î¡÷!çZï&èOîñ ñ…÷!öÃèDîþ ?í…?ò+êµè&çóµò+ý î¾è&è&éé!îîcëƒè&í…êµôKô2î2êµç!ë&øÔêvø êµçëíjè&óµê ÷…ï&î¡î óvý~±êvèèñgêµëüf÷îëyë&í…ìêµçø ï&õñ?çò+íjî¡óvè&ñ.ë&÷!ëòDï&í…î¡êzózë ëSóvý ü.Žýêzçsè&é!óvî>ñ?ëƒòDí…íjôKè&êvñ î ç ðyï\ë&êvòDèîDí…ïËóvîŠíjï&í…î çÄçõñ…ñ…èÃïƒêµêvõ!î¡î¡çZçZè&íjè&êµè&òDêví…ñ ó!çEüþ ÷!èSð ìÄêµóµóµó!í…õÄ÷êë&)êµüÄîDóvï î #&



3

*)









*)









    






Dî ï&î Ãè&é!î¾!ôKç!ñ îDç!î¡õ!ñ…èî¡ñ õç!èîÚñö€ò+÷ñ ççZò+ú…è&îDêvñ ï&èÃç öBï&ñ ô è&õ!é!î+îûè&ç!êµî¡ôKë%î è&ìÄé!íjî¾ïƒèí…ïƒôKí…çÄîDèëïƒölñ…ê ¡íï\jô2è&êvíjñ è&ç2êvñ ñ…ç öEè&?é!ç!î ñ ï&ð>î¡ò+ç“ñ…ïƒí…õ!ëKî¡õí ï&ölë&ï&î¡êvø ñ óµíjçô èíjî¡è&ñ õ ÷!çïƒèîKîñï&èè&î¡ñéçîO÷õçëêvè&ìfêvêµè&îDñ ëyî¡çcõñ…öÇèíjñÚè&èÃé!è&ðîJé!îKéÄ÷Äêµçç!òƒêvé î ú…?îDè&è ïƒé!:ë&î>í…í…ófëƒçêvìõÔø íjçëƒïƒíjé!í…è&ôKñ ÷!÷ï&îDîOóµèõ îDêµïëí…ðóµ ëþñÚïƒêvèüfèéî¡î%çêzëyï&?íîDè&…ø êµëyôKíjïƒë&î+õ!÷ù‘î¡ðyòƒõÔé íjï&í…êvèÃìò²îyõ!ðè&î¡é!ïƒç!îHêµñ…èï&îDèî¡ïî‹í…êµè&õëHéîDô2îJïSölîDí…ï&ï&óvñ î…ï&ôñ…þ ïƒë>éÄêµçò+ð ñ ïƒçÄêvë&è&êµêµëç!èø¾î¡çëò+ìfý îDî¡ñ õ ú…îDð ï%êµózõó ê fò\éîDï&í…î¡ç!çZø…èî2ï&öBîDï&ø ñ êvô ñ çñ ë²ç!ñ…î öyë&è&êvé!ø î2çíjë&è&êµø ÷!çïƒî%íjè&è÷!ñcï&î è& èé!&î2é!ç!îKî öB?÷Äè ç:ò+í…è&ëJêvñ ðç êzóµó ï&î î¡ò+è&ëHè&é!î¡ëî‹ë&ì)îDî¡õ 











 



 

 





 





 





 









 



        =





 !





/



Dþ þDþ þDþDþ ð é!îDèï&ñîJî öBZñ…÷ï êµú_í…óvî¡çZèHújí…þDóµ÷!þDþî¡ëHñ…ö è&è&é!é!î‹î‹ôK÷çÄñ ç!êvú…ñ…îDèïƒñ ë&çí…î‹ó)ìÄö€÷íjçïƒí…ò+ô2è&êvñ îDçèîDë ï  þ ò+ñ çZú…îDï&è>è&éîJè&êµôKî¡ë  

  









 > 







 > 





 





 > 





   !

ðèñ êvè&újé!íjñ ï&é!÷!ýéò+î¡ñ…ëîï&ï&î¡ë&ì)ñ üfçÄñ õ!êµóµî¡ëKçõò+îñ ð üfç îDè6ðŽèñgîDî¡î¡çÔëè&è6íjðŽüÄññ…è²ñ çóvýcêµë ìÄêvêµèçíjõóvïƒñ?êµí…òDòDôKíjíjèè&îDî êvèñ ïƒüÄçõü)îDñ î>ì)êµçZî¡÷è&çÄëë õÚîDö€ñ…÷ñ ö²çï&êµîKçZè&êµèö€ôKñÚ÷î‹çóvñ…ò+ìø è&íjêµêµñ òDïƒí…çí…ó ë²ôKìÄñ…îDêvöÃèî¡ïƒò+è¨ê î¡ðáíëjñ ±è&êµêvë&ñ ï&êµçï&ô2î¡ë ëêzÄìfóµíjñ î¡ïƒçò+óvî%è&ýÚêvú…ë&ë&éîéñ íjñ…÷ìföÃóµî¡õÚêvõÔè&ë²üfòDîñ…÷!ï\ïƒíjêvú…î¡üî¡ç/óvëî‹è&:íjèè&î¡ñ êµí…ñ ò\î çEé~.þ èôKï\Žýí…î¡Šò+í…èOô2ëƒè&÷!éíjï&î‹è&î¡ò\õÔè&éêµêµ÷ôKç!ë#øî ù ò+í2ñ…ô2ï&ï&íjî¡è&ëìfòƒéÄñ êµçç!õ!ø!î¡þ çÄò+î¡ëHñ…ïè&êµôKî+ù‘ðyíjï&ì 







 







 



20 10 0 -20

-10

Curvature, 1/cm

. . . . . . .. . .. . . ... . . . .. . .... . ... . .. . . .. . ... . . . . . ...... . . . .... . . .. .... . .. . .. ... . . . . . . ... .. ... .. . . .... . .... . . ... ... . . . .. . . .... ... .. . . . . . ..... . . . . . .. . ... ... ...... . .. . .... . . . . ............... . .. . . ... . .. .. . . . ............. ........ ... . .... ... . . .. ....................... .... .. . . ................... ........ ... .. . .. . . . .................. .. .. .. . . ..... .. ........ ....................... ... .. . .. . .. . . . . . . . .................................. .... . . . ...... ...... . .. .. ... . .... .............. .. . .. ....... ........... .... . . ......................................................... ....... . .. ... .... ............ ..... . . . . .. . . . .... ... .. Constant Centripetal Acceleration Contour, cm/s/s .. . ............................................................. ......... . ......... .. ............. .......... .. . . ................................................................................................ . . . ... .... .............................................. ... . ................................................. ........ ... ... . 800 . .... ......................................................... .. ... . 700 .......... ............................ .. . .......................... ..................................... 600 .......................................................................................... .. . ............................................. .............................. 500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..........................................................400 ......... .............................................. ................ . ................................. . . .. ..... . .. . . . . . . . . . .. . . . . . . . . . .. . ..... . . . . . . .... . . . . . .. .. . . . . . .................... . . . . .. . . . . .. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . ..... . . . . . . . ... . . . . . . . . . . .. . . . . . . . . ....................................... ....... . . . . . ......... .... ........... ... ..... ................ ........ ............................................................................................................................ .............................. ............ .. . ........... .............. ........... ........................... ................. ............ ........ ............ ............. ........... ......... ................................ ... ......... ..... ............. ............................................................................................................. ......... ............................ .. ................ . ........... ....... ..... . . . ....... . . . . ..... .......... . . . . ........ . . .............. . . . ..... . . . ......... ..... . ......... . .................... . . . . . . ......... .......... ......... ..................... .... ........................... ....... . . . ..... . . . . ......... . ............ . . . . . . ................. . . . . .. . ....... .... ........................ ......... ...... ............................... .............. ............ ..................... ............. ............... ........... ..................................................................................................................................... ....... ... . .......... ..... ....... ........................................................................................ ..... ......... ... ...................... .......... .................................... ................................. ....... .... . . . .. ..... .. .... ......................... ........ ............... ... .............. ................................ ........... ..... ........................ .................................................. .......... ......... . ............... . ........ . . . . ..... ..................................................... ............................................ . . . . . . . ........ . . . . . . . .. ........... . ............. . . . . . . . . . . . . . . . . . . . . . . . . . . .. ......... ... ... ... ....... ........ ............ ................ ........... .............................. ......... ................... .......................... . .. .............................................. .. .................................................................. . . . . . . . . ................. .. .... .... .. .. ... . . . .. . ... . . . . .... . ..... ............ ........................... . ........ ................................. ... . .. . . . .. . . . .. . .. ... .... . . . . . . . . .. . . . . . . . .. . . . . ... . . . ........... ........................ .. .... . ......... ................... ........................... ............ .......... .. ...... . ..... .. . . .. .......... ........................ .. ........ .... .......... . . ....... .............. . ..... .... . . . . .... .. . .... ........................................................... ................. ... ............. ...... ... ... ... -400 -500 .. . . . . . . . . . . . . . . . . . . . . . . .. .. . .. . . . .. . ......................................... ....................... ... .. ........... . -600 . . . .................. . . .. . ... . .... . . .. . . -700 . . . . . . . . .. . . . . . . . . . . ..... ... ......................... ...... -800 ... ................ .... ... . . .. . . . ... . ................ ............................. .... . . . . . . . .. .... ............. .. .. .. . .. . .. ... . .. . . . .. ...... ................ . ..... ... . . ............................. .... .... .. . .. ....... .. . . . ........ . .. .. . ............ ...... . . . . . .. ........... .... .. ......... .............. . ... . ...... .... . .. ... ..... ... .. .. . .. ........... . 0 5 10 15 20 25 30 . ... . .... . ..... . .. ... . . .. Speed, cm/s . .. . .... . .. ... .. .. . ..... ... .. .. . . ...... . / . & . . . . .......





 

 



  





 

. .  .. .. ..... . . . . . . . . .

.. . 

 3   

 

. .. ... . . . .......... . . . ... ... . .... .. ... . . ....... . .  . . . . ... . . .. . . . .. .  . . . ..... .  .. . .... .  .. .  ...... 

 . . ......  . .. .. .. .. .  . . . . .. .. ... .  / .. . . . .. . ... ... . . .. ...... . .. . . . ..  . . . . 3 / > . .. .. . ... .... .. .... . . . .. . . . ..  . . .. . . . . . . . .. .. . . . .. .. . ... . .. . .. . .. .. . .

êµø ÷!ï&î ,   ,   ?÷!ïƒî¡ ë&é O* ñ ý í…ó (   2 %7 . -,    ölêvéè:ï&êvñ ø êµë:ô é¾üÄòDè&í…÷!é!ëï&î¡îújõJë&íjô2ñ è&÷!ç%ñZï&ëñ…î î¡è&?ò+é!ð ñ î¡çéõÚõêzòƒëƒõ!é¾êvø îDçíjïƒï&íjêvújîè&íj÷!è&è&ï&é!êvîOú…îîËòDíj÷!êzï&ç!ï&î¡ölú…í…ñ…î¡ëHï\ëDô2þñ…öÇíjè&êµéçZêvñ êµèëŽç îDï&_êµî¡ëŽõ!ëî¡ëèyìfëìÄöBî¡ñ…êvòDïèêµîËí…ëóµè&îDóvé!ø ýKîËôKèö€ïƒî¡í…÷çZò+îOè&è:íjíjè&è&ï&éêvñ ñ íj÷ÄçEè çþ êvè:õêµìfë éñ î²õ!êµîDë&çZïƒì)è&êvëŽú…îDî¡î¡ñ…õõ ö öBí…÷ççÄõ“ò+è&ü)êvñ î¡çéÄí¡Çú…ñ î¡ç“ë2è&êµç“é!î í ñ…ôKè&éñ…îDï&ïîÚéÄëí…è&çíjõüÄóµSî êµçZö€í…ú…ë&ñ éóvú…êµñ î¡çEëþ ûÄïƒëèé!î¾ïƒíjëè&ìfé!îDîDî¡ïõ~è&éö€÷í…çç“ò+è&ëêµî¡ñ ò+ç~ñ çñ…õ öOõ!í îDë&ïƒêvêvø újçíjè&íjêvè&ú…÷!î¡ïƒë î èñ…î¡öJçéõêvëJø ésèñŠòDé÷!í¡ïƒú_ú…íjî è&÷!í…çgïƒîcêµçZò+ú…ñ…îDï&ï&ïƒî¡ëî2ëìfïƒñ î¡çóµíjõsè&êvèñ ñ~çë&ìféÄñ êvìêµçZè&ð ëKêvè&ñ…é öJè&óvé!ñQð îòDë÷ìfï&îDú_î¡íjõEè&þ÷ï&îÇ êvø ë&÷!÷Äï&òƒîé “è&éÄë&íjé!èJñQìfð ñ ëêµç/í…è&ç ë î ?êµø í…÷!ôKï&ìî óvî2.þ>ñ…öŽæ7èOè&éë&îDêµëJî¡ô2êµçZëOú…è&îDé!ïƒëî¡îKçcïƒè&î¡éÄóµíjíjè&èOêvñ ðŽçîë&éÄòDêví…ì ç öl÷Äñ…ïëî%è&é!ë&ì)îîDëî¡ìfõ îDî¡í…õÔë²í í…çëƒõ ÷!ï&òDï&÷ñ…ø ï&ú_íjíjèî%è&÷ölï&ñ…îï²ë&è&êvé!ø îçÄí…ôKóµë²ñ…ï&ñ…î ö êè&µç/é!újî íjïƒëìêµí…óµçZêµç!èî%üÄï&÷îDèËìç!ï&î¡ñ ë&êµëî¡ýKç/è&òDíj÷!è&ïƒêvñ ú_ç~íjè&÷!ñ…öHïƒî…êvþè&ë‹ñ…ò+ñ.ïŽñ…î¡ïƒí…õò\êzé¾çíjë&èêvø î¡çëJíj÷è&ç÷!êµïƒölîñ…ïƒè&ôé!î>óvýcë&ì)êµçÔîDî¡è&õ êzôKêµëËî…ëƒþ í…ôK?î¡ìÄò+óvè&î¡êvõñ ç ölï&ñ !ô þ ø òD÷!êvú…ï&î¡újë íjè&íg÷!ï&ôKîñ…öBñ…ï&îcï è&ï\êµêvôKø…ñ…îï&ñ ðy÷íjë ï&ìÄ&÷êzç!ëø!è&êvþ ûòDíjè&êvñ ç öBñ…ï ÷ë&êzç!øÔè&é!îcëìfîDî¡õ ë&êvø çí…óyïƒíjè&éîDïè&éí…ç 







0.0

0.4

Speed

0.8

Two speed Signals Superimposed

0

100

200

300

400

Time

0.0

0.4

Speed

0.8

Two speed Signals Superimposed after Time-warping

0

100

200

300

400

Time

ê µø ÷!ï&î     -  *#     %7 ,  %*  % #          "     %  6   " 7  *   *   7  &%    

 &









 

 















 

























 

 



 





 





 













 























  

































 













 



















 

ò+ñ…é!ï&îcï&î¡ëç!ìfî ñ ?çèõëêzèç!îDøì ðŽêµëKñ…ïƒèõñ“ëŽ÷öBï&ëñ îñ ç  î¡í…òƒéÔ òDí…Eç í…üfçîõ êµêµõëOî¡ç/é!è&î¡ê®í¡ûú?î¡êµõEóvýòDìóvñ êvî¡ë&ò+î îÃêµñ…çÄöëí>ìfî¡è¨ýZò+è&ìêvêµñ òDç í…ó?ë&ò+é!ñ…ñQï&ð ï&î¡ë%ëìfè&éñ íjçèõ!î¡êvèçÄò+êµîë ìÄç!î¡êvî¡ò+ò+î¡îDë&ð ë&íjêµïƒë&êzîyóvý‹ózêµç!è&é!î¡íjî>ï¡ë&þ í…ËôKí…î òƒéç.÷ëôìfîDü)î¡îDõKï þ ë&êvHø çðŽí…ñJó?ñ…êµë ïËï&ôKîDìñ…ïƒïƒî¡îëí…î¡ç/õ èî¡í…õKò+î¡íjçZèÃèËíOìfñ ë&îDêµçZèSè&ñ…ëÇöñ è&çKêµô2ñ îŽç!î>ìfñ ë&êvêµø çZçè&ë íj è&ç!÷!ñ…ïƒîè ôè&2é!í¡îŠýŠëü)ñ ô2îîDölñ è&÷ÄêµôKçõcî¡ë èñÚíjò+è2ñ…ï&ï&ïƒîDî¡ø ëêvìfñ çñ çë õòDí…ñ ó ç í…è&çÄé!õ îñ…é!è&ñ…éïƒîDê Dñï  fç/ð è&í…éóêµò\õÄécêvï&î î¡?ò+ìÄè&êvóµñ í…çêµçÄë¡ë þ Ëñ…ö í…è&òƒé!égî²ñ…è&öÃêµô2è&éîOî újí…óµ÷!î¡ëŽöBò+ñ…ñ…ïHï&è&ï&é!î¡ëî²ìfï&ñ îDçìõï&î¡î¡ë&çî¡ò+ç/îKè&íjòDè&÷!êvï&ú…ú…îî¡ëJë&êvø êµë²çíjë&êzè&ô2÷!ïƒêµîóµíj.ïƒí…óµýÚçõ¾ìÄóvî¡ñ…í…èò\èéçõè&êzêvç!î¡ëDøJþ è&!êµôKñ…ïyî¡ëŽî¡í…öBòƒñ…é ïyî¡è&êµí…ôKòƒéÚî>ñ…ì)ö±ñ è&êzç/éèî>ñ…ñ…öfè&è&é!é!îDî>ï ï&îDìï&î¡ë&ë&î¡ì)ç/è&îDíjî¡è&õ êvú…òDî²÷!ï&ëú…ìfî¡îDë î¡õ òD÷òDï&í…ú…ç¾î üf î Zï&î¡è&í…é!õ î ñë&텾ôKöBï&ìÄñ óvôî¡õè&ölé!ïƒñ î¡ë&ô îë&ë&ôKêµø çñ.ñ…íjè&è&é!÷!î¡ï&îõ2ò+ñ…íjï&è ï&î¡ë&ì)Žñ è&çÄêµôKõ!î¡î¡çë ò+.îHðŽòDî ÷!ø…ï&îDú…è î¡ëDþÇyæ7öÄò+è&ñ…é!ï&îDï&î¡ïƒîëìfíjñ ï&çî õÄêµç!Søë&ì)è&êµîDôKî¡õî>ìfújí…ñ óµêµ÷!ç/î¡è&ëë ölè&ï&é!ñ î ôMî¡í…ò\é 



&

















3

0


























ú…íjîcë è&êvêzú…è&ëKéîŠîëòDîD÷!ø ìfï&ôKñ ú…êµî¡î¾çZçZè&ölèë ñ…î¡ïõñ…öè&íjé!ëè2îîDø ï&" ôKîDø î¡êµçZñ çè&*íjŠëKè&êvñ…ðŽñ öçñ…ïƒóvñ õEüð þ í…ëî¡ëìfõ é!îDîÚî¡ñ õ ç óvñQðÃè&ééîDêvî ïø éë&ë&ì)ì)òDîDîD÷!î¡î¡ïõõ ù è&é!ï&î¡ë&é!ñ ózõ êzëHòƒé!ñ ëî¡çóµêzêµçèêµè&ô2óvîJí%ëìÄüfíjî¡óvè&ñ êµí…ð ó ò+ëìÄñ çí…ò+ëîî….þ ÷!Ôî¡çî¾ò+î éyí¡ë&ú…êµî¾çò+êµî¾ôKìü.ý~óvî¡ôKõ!î+î¡ûçZçÄèî¡êvè&õgêvñ ícç~õì)ý.ñ çêzí…ç/ôè&ëêµò2ñ…öOôKóvñ ñ?ð õê®ûëòDìfíjîDè&î¡êµõñ çÔíjï&èîéêµòƒ éŠòƒé!î¡ò è&.é!ëï&î¡êµöÇë&é!í…ñ çZózýcõ !êç!vîDö ð ëñKóvñ?è&òDéí…îó è&ô2é!ï&êzçî¡ë&êµô2é!ñ íKózõÚíjï&êµîëHêµõçêµò+ëƒï&ò+î¡ñ ô2ú…îDî¡ï&ç/î¡èõŠî¡õÚüfîDèè6ñ ðŽîD)î¡çŠè&í…éçî õÚè&é!î ëè&èé!îDîìÚëêµîDëŽø ô2ï&îDî¡ìfç/î¡è&íjíjèè&î¡êvõEñ þSçŠæ7ìç ï&ìñ?ïƒò+í…î¡ë&ò+ë>è&êzò+êµëî>ôKè&éñ…êzï&ëËî%ï&î¡ëè&ëƒíj÷üÄóvè&óvëŽî…þ êµçè&é!éîJï&î¡óµñ ë&é!ðŽñ îDóµï>õÄëìÄí…üfçîDî¡è6ðŽó±êµîDç¾î¡ç ûÄø ÷ï&î ë&Äéí…ñ ðçõ ë è&í…é!ë îcë&ëî¡îDóvø özôKù6ë&îDî¡ø çZôKè&ëKî¡ç/è&é!è&íjî¡è&ôêµñ ëçî¡óvú…î¡êµëç yè&ëé!îDî ìÄíjëïƒìfíjîDèî¡î¡òƒõ é~üZï&ý î¡ò+ëñ…ñ ø ôKçêvîÚè&êµñ ð>ç~éêvóµèêµîÚèîDïƒëíjìÄè&í…÷!ò+ï&î…î þ éÄêµëKêµë þ ?ç!ÿ²ñ çð ò+ç î è&í…é!÷!îèñ ëô2îDø íjô2è&êµî¡òDç/í…è&óµóµíjý¾è&êvõñ î+ç ûéç!í…î¡õ¾ë>üföBñ…îDï>î¡çöBë&ñ…êµïOø çè&é!íjè&î‹÷!ï&ï&îDî¡ìÄëHï&üfî¡ëî¡î¡òDçZí…è&÷íjë&è&îJêvú…ñ…î%öÇëƒè&êvé!ø îJçíjò+ñ…è&÷!ï&ï&ï&î¡î ë)ìfêvèñ ç?êµëù õ!ë&êµî¡ç!çø ò+óvî¡îëDóvþ îDèÔèîDî%ï\ë ï&îDüÄölîD÷!ï>èHèè&ñéÄî¡êµëHí…ò\êµëHéŠç!ñ…ñ…öÇè è&é!í2î%ï&î ëZîDø ÷ÄôKêvï&î¡î¡ôKçZè&î¡ë>çZí…èDëþ fêµçë&êvø çÄíjè&÷!ï&î¡ë !è&é!î¡ë&îJô2íjììÄêµçø ëHíjï&îJè&é!î¡çÚî¡ë&è&êµô2íjèî¡ëñ…ö þ " " "   é  î & ï D î l ö D î ƒ ï ¡ î  ç + ò ‹ î & ë v ê   ø Ä ç j í & è ! ÷ & ï J î µ ê  ë & ë D î   ø K ô ¡ î / ç  è ¡ î Š õ j í  è f ì   ñ µ ê Z ç & è H ë … ñ ö óvóµñQêzë&ð é!î¡ë&õ¾ì)îDêµçÚî¡õ ëèêµîDçZì èñ%íí…ëîóµóf.è&÷!é!î¡î‹çò+ë&îOêµø ñ…çö íjè&÷!ï&î¡ëXíjþ ïƒ>îJëƒë&êµêµç!ô2ø‹êµózè&íjéïƒîOóvý2ò+ñ…ëîDï&ø ïƒî¡ôKëìfî¡çZñ èçî¡õ!õEî¡þ çò+î¡ëÃî¡ëè&íjü!ù "   é z ê ë  ë  è D î ì + ò   ñ 2 ô Ä ì ! ÷  è ¡ î ¾ ë & è ! é î  è ¡ î K ô Ä ì z ó j í  è $î ' í…çÄõ è&é!î ìÄêvî¡ò+îDð êµë&î ò+ñ çë&è&í…ç/è ö€÷çò+è&êvñ çÄë   í…çõ  öBñ…ï2î¡í…òƒ é ë&êvø çíjè&÷!ïƒî…þ ñ…ïúj í…óµ÷!î¡ëñ…ö  ò+ñ…ïù ï&î¡ë&ì)ñ çÄõêµç!øŠèñÔè&é!î è&é óvîDèèîDï  í…çõ þ éî

























>



" 

 



 

  









 



  ! #" 

&%(' )* 

$



 



.









  ,+



 

  ' *- 

.

  0

'









 



/.





 

 



$ 





"





(' 





 







ï&î¡ëƒþ êµõ÷í…óµëölï&ñ ô è&é!îí ç!îKí ú…îDïƒíjø êµç!øÚêµç ëèîDì íjï&îè&éî%ïƒî¡ô2í…êµçõ!îDï>èîDïƒô2ë 



















 

µè&ê ë2êµôKé!ë&î ôKî¡çgñ.ðŽñ…íè&éî¡îëè&óµíjíjüÄï&ózø…êµîë&é!ëî¡ìfõEîDþ î¡õcËý.õÄìÄêµë&êµò+òDï&í…îDóµóµìÄý¾í…çÄí ò+öBý ñ…ï&ïƒø…îDîDì)ï&ñ…ýcïƒèòDî¡í…õcç ü.üfýÚîè&êzé!õ!î‹î¡ç/è&è&êzôKêvûÄî‹î¡õcðyíjíjè²ï&ìÄè&êµéçêµø ë ìèïƒï&í…ñ?çò+ëî¡öBõñ…÷!ïƒôKï&î…î¡þ¾õæ7èöyñçô2ñ…è íj è&òƒè&éé!î è&é!ç!îŽîDèð î¡ôKëƒêvìÄø ózçíjíjèè&î ÷! ï&í…î çõêµë‹óvî¡ëí…îDø ëèÇô2ë î¡Zç/÷Äèíjî¡ï&õ îÃÇõè&êzé!ëî è&í…óvçîDò+èî¡èîDëÇïƒíjë%ï&îyíjï&ò+î ñ ôKí çìÄ÷!!èî¡î¡óvõý ñ èñ ç2è&íéóvî îDèèîDë&ïêµüÄô2í…êµëƒózíjêµë ï ü)õîDêµè¨ëðÃè&í…îDçÄî¡ò+ç2î¡è&ë é!öBîHñ…ï²è6ðŽè&é!ñ!îþ ñ…ï\é!êvî¡ø ëêµçîHí…õó êzëë&è&êví…ø ççò+íjîè&÷!ëïƒè&î¡íjë è&êµöBë&ï&è&ñ êµòDô ëSòDè&í…é!çKîüfèî¡îHô2ò+ñ ìÄôKóµíjìÄèî…íjþ²ï&î¡æ¨õ è êµëëìfîDî î¡?õ &





'

       



'  



$





òèDñK÷!Dî ï&ï&è&újîé!íjîOè&÷!òDï&÷î²ï&ú…íjîèŽêµë íjí%èŽí~ìfè&ñ ç!éÄêµñ…íjçZï\èŽèÃô2ìfêµëÃí…ñ óêµí…çZóµú…èëî¡ñ%.ò+è&ø èéñ…êvíjú…ï

êµ ø ÷!ï&î        ?÷%ï& î¡ë& é 9² ñ ý   í…ó ë       *     % ,     % 9  !       % )     % 9 #  *%    % # )      ,  ,  %    :    87 &    #  %* #   6%7 -, %      ñQðÃîDú…îDï î¡ôKìêvïƒêµòDí…ó îDú.êzõ!î¡çò+î ±í…ëî !éêvüÄêµèî¡õŠêµçŠûÄø ÷ï&î :ë&÷!ø…ø…î¡ëè&ë²è&éÄíjèölñ…ï " &











 

(







































  





































> .

























 



/

















 



 



 

























 



 







 











 















   





3





 

  





            =    

  =















    











 



&ïï&ë&î¡î¡êvø óµóµíjíjçèè&íjî¡êvè&ñ õ ÷!çïƒëƒî¡éòDë êv÷!ZìÄïƒìëOú_íjíjð ïƒè&í…êv÷!è&ôKïƒéÔî îDèë&éïƒì)ê í…îDDîëÚî¡¡õÔõ ísü.êzç ë&ý2êvø ûÄðç ø ïƒ÷!êµè&ï&ð êµî ç!éøJêzòƒè&éþ êµô2í…î òDé.ò+êµëñ ë²ìf÷ô2îDçZî¡è&í õ ëò+ö€è&÷!êµñ ï&è&çÚé!îDñ…ï ö é!ç!îDñ…ï&ïƒî…ô2þ í…óí…éòDî¡ò+ç î¡óµîDðŽïƒîíjè&ëêvñ ð ç êzç!êµøñ õú…îDê fïîDè&ï&éî¡îOçò+èîHï\í…üfçîDëè6öBðŽñ…ïƒîDô2î¡çíjè&è&êvéñ îç è6ìÄðŽíjñ%è&éÚëƒêvø êµç çí…è&óµé!ë î ëƒòD÷í…òƒëé î ñ…ñ…ö:öËõñ…ïƒêµë&õ!ò+îDïƒïƒîDî¡èõcî è&ìÄêµí…ôKêµïƒî²ë ÷ñ…çöÃêµè&ò+ëDñ…þ ï&ï&î¡é!ëìfî ñ èçïƒõí…çÄêzç!ëø2ölñ…è&ï\êµô2ôKíjîè&êvêµñ çç ë&è&ìÄí…íjçè&ò+é î¡.ë>ð êzçcéêµè&ò\é!é î%êµëÃè6ðŽë&êµñÚôKö€ì÷óvçýKò+íè&êvñ ëîç.ë ÷!î¡ô2çí ò+ý î î¡ô2í…êµë&çêµóvêµýôêüfDîîc¡õEõ!þ îDèîDïƒôêµç!î¡õsêµç í õ!ý?çí…ô2êµòÚö€í…ë&éêµñ çsëñ è&éíjè è&é!îcø óµñ…üÄí…ó ôKî¡í…ëƒ÷!ï&îcêµë è&èñé!îûÄæ7ðÃèçcñ…ígëï\ìfõ ìîDî¡ï&î¡òƒéÚõ! îDï&èî¡îDò+ï\ñ…ô2ø êµçÄç! %>êvî¡è&õêvêµñ ç çÚïƒè&îDéí…ölîDêµëëHý?ï&î¡ô2ò+çÄñ ôKò+çZîcèîDî èë&.ïƒêvø è>êzò çôKí… ó‘î¡þ í…ç>ëyñ è&éðŽéí…íjîDëèHú…ü)îDñ ï îDç!î¡îJç¾ðŽëƒè&îŠêvéø çéîJí…í ôKú…ófîŠîDêµëyè&ò\é!üfé!ñ?î¡ñ õÚêµëç!î¡ñ…ø%ç ö ðŽò\èé!íjñ~ïƒñ ì)êµ÷ò+î¡ëî õ î ëëý.èï&ôîDè&ôKòƒéÄîDêµèç!ïƒøêµò í… çÄõ ò+ñ ôKöBñ…ìÄïï&î¡ñ ë&÷!ë&êvïñ çðÃñ…ñ…ïöE)è&þé!î .è¨ý?ðÃô2ñKôKë&êµîDø èçïƒêzí…ò óµëS üfî¡êµç!øí…ò+ózñ óvôKñ ð ìÄë%íjï&öBî¡ñ…õ ïK.èë&&êµé!ô%î²÷ô2óvè&í…íjìç!îDìÄñ êzç!÷ø ë ñ…ñ…üè&é!è&îDí…ï¡êµç!þ î¡õ

3

 



  







3



  





 



èè&ïƒé!í…ñ çÄ÷ëø öléëï%î¡í çZî¡è>ô2í…òƒè&íjé~éèî%ïƒï&ê ñQóvîDð Eèèí…ñ…îDçïJöyõŠè&í…é!ï&ëîDî íìêµï&çö€î¡÷õëçî¡êvú?çZò+è&êµè&õêvëOñ ÷ÄçEè&í…é!þ ó îóvîDí¡èú…èëƒîDîDêµïƒôKï\íjë ìÄø…î2óvî%jóvþ¾ëîDñ èèæ7óµ÷!îDçgïJè&êµìñ íjïƒçëƒêzëôKë&ñZôKñ…è&ñ.é±ñ…þè&é ÿEêvç!èOî ô2òDí¡í…ýcç éÄêµô2íjìì)ìfñ î¡ë&ç î ï&íêµëñ ÷è&ë&é!ôKø î>éñ.ç!êµñ…çZî¡è&èë&éîDë>ç!ø…ìfî¡ïƒíjëƒî¡ëèçî¡í…ìfõ óvè6î¡?ýÚçëî¡í…ñ…ò+óµöËè6ñ ýsçè&é!õ!ñ îù6ç ë öBZñ…è&÷Äïƒé!íjô îÔï&î¡ò+õ?ïƒèù6êvïõ!èîDîDï\ïƒêvêµñ ú_çíj>è&êvú…þ î>ô2²çíjü.íjèýè&ïƒ÷!ê Kïƒí…í…ò+õó ñ…õï&òDêzï&ç!í…î¡çø“ëõìfí êµñ õÄçíj.õÄè÷îêµí…ç!õ!öBøñ…ïƒïèíjñè&êzíò ë&ò+ô2ñ…ï&ñZïƒî¡ñ…ëè&ìféñ êzç!çøõêµëç!ìÄø óµêµçèñOî…þ:è&éæ#çîŽè¨è&ðÃéêµñJëSëƒòDô2í…ëí…îóµóvè&î¡éëè î î¡ëêvñ ø…óµî¡÷!çZè&ú_êµñ í…ç%óµ÷êzî¡ëëÇí²ñ…üÄö í…ë& êµëÇöB ñ…ïè&é!îHþ æ#î¡ç%êµø…ìî¡çïƒí…ëò+ìÄè&í…êµò+ò+îî ñ í…÷!õïÚõÄêvè&÷êvçÄñ ò+çñ í…çó±ëò+èñ ïƒçÄí…êµëçèïƒî¡í…õ êµçZëèDñ þ‹óz÷!ÿOè&êvöñ ò+çñ ë ÷!ïƒíjëï&î%î è&ë&é!ôKîñ.ë&ñ…êµôKè&é ìóvî¡îDç!ï ñ üÄ÷!÷ø è>éóvî¡ç!ë&ñ…ë>è¾î¡èóvîDñø í…ï&îçZ.è÷ëêvñ ïƒóµîc÷!è&è&êvéñ êµç ë êµëyèññ çò+î‹íjø í…êµçŠë&ôKñ.ñ…è&éÚè&é!îJò+ñ óµ÷ôçëyñ…ö þ Oô2óvíjè&èé!ï\ñ ê ÷!ø ésè&é!î‹ñ ÷!ìÄï ï&ñ…í üÄú…óvîDî¡ïƒô íjø…óvî î¡çï&õî Zë÷Äêµè&êvï&ëî¡î¡ë2óvöSí…çç íjè&î¡÷!êvïƒø…í…î¡ózçóvý¾õ!î¡èò+ñ ñ ôKí ìfë&êµñ ôKë&êµìÄè&êvózñ ê®ûÄçî¡õÚñ…öJêvèí…îDçïƒíjè&êµú…î( ëñjù óµ÷ô2è&íjêvñ èçEï\ê þ æ¨èîDè6ïƒý.íjìÄè&êµêµòDú…í…îJóµóµí…ýÔóvø…ñ…ñ…ì)ïƒîDêvè&ï\éíjôèî ëÃü.öBýñ…ïyï&ûîDìfçî¡õÄíjêµç!èî¡ø‹õî¡óvýêµø…î¡íjç?ìÄù6ìÄë&óv÷!ý?üÄêµç!ë&ìÄøÚí…è&ò+é!î¡ëyî¾ñ…ô2ö íjí…èç¾ïƒê ñ…ìfèîDñ ïƒíjè&èé!ñ…îï òDêµë ÷!ïƒï&î¡(ç/è ø ÷!î¡êµèë&ë êµ)ëHölè&ñ é!ózóvî%ñ ðŽë&÷î¡ôÙõcü.ñ…ýêµòò+êµîë í…çõ¾ïƒî¡ë&÷óvè&ëêzçÚíKõ!ïƒí…ô2íjè&êµòë&ì)îDî¡õÄ÷!ìíjè&óv÷!è&éï&î¡ñ ë ÷!Sø è&é“í …è&î¡é!çsî¾ölï&ï&î¡ñ ë&ô ÷óvè&í ë ëîD&é!ïƒë2ñ ÷ð óµõgêzóµóËüfüfîî