• Aucun résultat trouvé

Coefficients de restitution et efforts aux impacts : Revue et comparaison des estimations analytiques

N/A
N/A
Protected

Academic year: 2021

Partager "Coefficients de restitution et efforts aux impacts : Revue et comparaison des estimations analytiques"

Copied!
166
0
0

Texte intégral

(1)Coefficients de restitution et efforts aux impacts : Revue et comparaison des estimations analytiques Vincent Acary, Bernard Brogliato. To cite this version: Vincent Acary, Bernard Brogliato. Coefficients de restitution et efforts aux impacts : Revue et comparaison des estimations analytiques. [Rapport de recherche] RR-5401, INRIA. 2004, pp.162. �inria00070602�. HAL Id: inria-00070602 https://hal.inria.fr/inria-00070602 Submitted on 19 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Coefficients de restitution et efforts aux impacts. Revue et comparaison des estimations analytiques. Vincent Acary — Bernard Brogliato. N° 5401 Décembre 2004 Thème NUM. ISSN 0249-6399. apport de recherche.

(3)

(4)  

(5)    

(6)  !"#%$'&( )+*,$- .0/123  4 )+*3$#$ 

(7) 53 4 6 )7$8 

(8) %$9

(9) $: ; <=  . >,?A@BDCD@E'FBHGJILK MON CPIQ@RGSILT N IQUWVWXY?ZGJEQU [\^]_=`acbedgfihHjlknmo]_=`Lk pHq^_=rLsutwvDq^`Lk xOsuy{zn` m}| t~Sy{~ €}{~^~Sy{sum ‚^`ƒso`L„\ `s„\^`†pS‡ˆŠ‰P‹^ŒcfierL„`_9Ž su`Š‹P‹Š‰fŒLD~ {‘{`Qk ∗. †. ’“H”L•–—“™˜bcp^``Lkšmut›_œmotyPp"„y{sosu`Q„mu`=‚l`Qk8` žWy{sumok#Šq^Ÿ t_=~ P„mk8`Lkšm_¡y{mut›¢{rL`~ {s#£`‚lt›_=`p kut›y{pl¤ p `_=`pDm9‚l`Qk#knmosuq „ muq^so`Lk#¥3£w3suq^~^muq^so`kšyPq k8t_=~ P„mQ¦¨§6`ku`L„ yPp ‚©y{Žlzn`Q„mutª ‚l`„ `Qk8`Lkšmut›_=Šmut›y{p k8`Qknm £A« `Lkšmut›_=Šmut›y{p8~^sotyPsutJ‚lq„ yH` ¬„t`LpPm-‚^`}su`Qknmot­moqlmut›y{p=`Lp=ª®y{p „ mut›y{p‚l`Lk-‘{rLy{_=r mosut›`Lk`m ‚l`LkO~^suyP~^sotrmurLk ~ \Djlkut›vDq^`Qk‚l`Lk _œmorsot›{qlŸ¦Hbcp^`ƒ`Lkšmut›_=Šmut›y{p,Šp {£jDmot›vDq^`ƒsut›‘{yPq^so`q ku`c‚lq,„ yH` ¬„t`LpPm ‚l`8so`LkšmutmuqlmotyPp ~S`so_=` m=‚« `LpH¢DtwkoŠ‘{`Ls9‚l`Qk„LŠ£w„ q^£wk`m¡‚l`Qkkut_q^£wœmut›y{pJk#¯J{Ž^£`Qk‚^`Lk9kujlknmo]_=`Lk_9q £­mot­¤°„ yPsu~ kkšyPq^_=t›k ¥‚l`Lkƒ„ yPpDmusŠt›pPmo`Lkcq^p^t›£›ŠmursŠ£›`Lkc` m#¥'‚l`Qke„y{£›£twkutyPp k¦6± ` mumu`r muqJ‚l`¡Šq kokut~Sy{q^sƒŽ^qlm#‚l`¡~JyDkš`Lsc£›`Lk vDq^`QknmotyPp kRkuq^sO£›`Lk£›t_=tmu`Lk ‚l`Lk_=yl‚lrL£twkuŠmut›y{p kŽJ{kur`LkRkuq^sO£A« \DjH~SyŠmo\^]Lku` ‚l`ckuy{£›t›‚l`Qksut›‘{tw‚l`Qk²Š‚« t›_¡~J{„m `me‚l`¡„ yH` ¬„ t›`pDme‚^`su`Qknmot­moqlmut›y{p¨¦SƒŠp ke„ `sŠ~ ~JyPsšmc‚l`su`Q„\^`s„\^`P²^p^y{qJk p^y{qJk}~^soy{~SyPkuy{p kc‚« `žS`Q„¤ moq^`s9q^p^`so`¢Hq^`„ sotmutwvPq `‚l`£›,£›tmšmurLsoŠmuq^so`~Sy{sumoŠpDmkuq^s£A« `Qknmot_œmotyPp³Šp {£jDmutwvDq^`‚l`Lk` žWy{sumok‚l` „y{pDmoP„m#`pDmosu`kuy{£›t›‚^`Lk8` m¡‚lq³„ yH` ¬„ t›`pDm9‚l`'su`Qknmot­moqlmut›y{p³Šq^Ÿ©t›_¡~J{„mk¦´ep"sŠ~ ~J`L££›`s3£`Qk#\HjD~SyŠ¤ mo\^]Lku`Lke‘{rLp^rsŠ£›`Lke‚l`¡£›'_¡rQ„{p^t›vDq^`=‚l`Qkekuy{£›t›‚^`LkƒkšyPq^_=t›kƒŠqlŸ0t›_=~ {„ mokƒŠt›p kutvDq^`£›3‚lr¯ p^tmut›y{p©‚^q „yH` ¬„ t›`pDm#‚l`so`Lkšmutmuq^mut›y{p6¦¨´ep0~^sorLku`pDmo`s`pJkšq^tmu`¡£›`Lkƒ_=yH‚^]£›`Lkesu\^rLy{£›y{‘Pt›vDq^`Qk}q^p^tw‚lt›_=`p kutyPp^p^`L£›k ‚^` £wƒ£tmšmorsœmoq^su` µ¢œŠpDmO‚l` kL« ŠmšmoP„\^`sR¥ƒsŠ~^~S`£›`s£›`LkŽ Pkš`QkR‚l`£›emu\ ry{sot›`‚^`c¶·^¸P¹6ºl»šŒL¼{¼D{½ ¦L¾Op^¯ p6² yPp'sorLkuq^_=`s#£›`Lk‚ltžSrLsu`LpPmk surQkšq^£moŠmok vDq^tWsu`L£›ŠŸH`LpDm £›`Lk„ yPp ‚ltmut›y{p k ‚« Š~^~^£›tw„œmotyPp‚l`ƒ£w#mu\ ry{sot›`ƒ‚l` ¶¡·^¸P¹6ºe` m-rmu`pJ‚l`pDmL²P~ Šs £›¥8_=¿L_¡`P²Pkuy{p„\ {_¡~‚6« {~^~^£›t›„Lœmut›y{p¨¦D´ep` Ÿ^Š_=t›p^`sƒ£`QkO`ŸDmo`p kut›y{p kOvDq^` £A« y{p~S`qlmmosuyPq^¢{`Ls ‚^{p k-£w£tmšmorsœmuq su`ƒ„ y{pJ„ `sop {pPm £`Qk ‘PryP_¡rmusot`QkO`Lpku`c~S`p „\ {pDm `Lp'~ {sšmot›„q^£t›`s kuq^s£›`'„y{pDmoP„mt›p^t­mot›{£`L_=`pDm9£›tp^rLt›vDq^`P²¨~^q t›kkšq^s9£`'„y{_=~Sy{sumu`_=`LpPm9‚^`Lk_ŠmursotwŠqlŸÀ„ y{pJknmot­moq ŠpDmok £›`Lk kuy{£›tw‚l`Lk`Lp,„y{pDmoP„m#»®¢Htwku„yDrL£›Pknmot›„t­mor{²l~^£w{kšmutw„ tmurP²^`£w{kšmuyœ¢Htwku„y{~^£w{kšmutw„ tmurµ½¦ Á ÃQ” ÄÅ{ÆǓH”¡˜ÈdÈrL„LŠp^twvDq^`c‚lq„ y{pDm{„mQ²PdÈrQ„{p^t›vDq^`e‚l`Lk-_¡t›£›t`LqlŸ„ y{pDmotpHq kL²{kujHkšmu]L_=`LkO_q^£mut¤Z„y{so~ k² t›_=~ {„ mL²„ y{£›£›t›kutyPp6²6~S`s„ q kokutyPp6²6mo\^ryPsut›`‚l`'Éc`sumuÊ{²dÈyl‚l]£›`Lk9su\ ry{£›y{‘Pt›vDq^`Qk²rL£›Pknmot›„t­mor{²~^£›Pknmot›„t­mor{² ¢Htwku„yHr£w{kšmutw„ tmur{²HrL£›Pknmoyœ¢Dtwko„ y{~ £›Pknmot›„t­mor{²H` žWy{sum}‚l`„ yPpPm{„ mL²Dª®suy{mšmo`_=`pDmL² tp ‚^`pDmoŠmut›y{p ∗ †. ˮˮÌÌÍ6Í6ËÏËÏÎ"Î"Í6Í6ееѝѝҵҵӰӰÔÏÔÏÎÎÕ×Õ×Ö{Ö{ÓnÓnؚؚييÚJÚJÛÇÛÇÜÜÝÇÝÇÓnÓnÞÞßWßWˮˮÚSÚSààÚ^Ú^ÙLÙQáœñ åâ°ãQêãäoéåoã êò^æ^çwçwñèLêäoéóoôêë íLìQâšéâ°ã æêµóìQâšé â°ã íuîêµåQâoé ïDíuçwîðêåLïDçwðê. Unité de recherche INRIA Rhône-Alpes 655, avenue de l’Europe, 38334 Montbonnot Saint Ismier (France) Téléphone : +33 4 76 61 52 00 — Télécopie +33 4 76 61 52 52.

(10)  

(11) % /    

(12) 5$9

(13) '#  

(14) )+*3$9O . †   $9: / 2=    

(15) 3$:;¡  $:

(16)  L)7$8  .  ”Là ^Å{Ã{˜[\^twk so`~Sy{sum P‚^‚lso`Lkokš`QkOmo\^`ƒ~^suyPŽ^£›`_%yŠª¨mu\^`8Šp {£jDmot›„LŠ£S`Lkšmut›_=Šmut›y{pyŠª6mo\^`ƒª®y{s„ `Lk ŠpJ‚ mo\^` „yH` ¬„ t›`pDmso`Lkšmutmuq^mut›y{p9Šmt›_¡~J{„mk¦ ™„y{sosu`Q„m6`Qknmot_œmo`-y{ªlmu\^` ª®y{s„ `Qk¨œmt_=~ P„mk¨twk¨_=y{mut›¢µŠmu`Q‚ ŽHj#mo\^` ‚l`Lkut›‘{p¡yŠªSkšmusoq „ muq^so`LkL²œª®y{st›p kšmoŠpJ„ `{²  t­mo\mo\^` so`Lku~J`Q„mmuycªÇŠt›£q^so` „ sot­mo`sotyPp6¦  q^sumu\^`Lsu_=y{so`{² mo\^twk-`Qknmot_œmotyPp'y{ªª®y{s„ `Lk-t›k p^`L`L‚l`Q‚=muyy{ŽlmŠt›p'sot›‘{\Dm `Qknmot_œmo`cy{ª6mu\^`ƒ„ yH` ¬„t`LpPmyŠª6so`Lkšmutmuq^mut›y{p6¦ hlq „\'`Qknmot_œmo`Lk _ P`etm ~SyPkokutŽ^£›`emuy„ yPp kštw‚l`Ls so`£›t›{Ž^£›`e„ yP_=~^qlmoŠmut›y{p k{p ‚'kut_q^£wœmut›y{pJk y{ª¨_9q £­mot­¤ ŽSyl‚ljkujlknmo`_kRkuq^Žlzn`L„ mu`Q‚9moy#q^p^t›£›Šmu`Lso{£H„y{p kšmusŠt›pDmokR{p ‚„y{£›£twkutyPp k¦| jmu\ `  µjP²  `  t›££J„ y{pJkštw‚l`s mo\^`c£›t›_¡tmyŠªWmu\^`ƒ{kokšq _¡~^mut›y{p k-yŠª¨kujHkšmu`L_k-y{ªWsot›‘{tw‚=ŽJyl‚lt›`LkL²Ht_=~ P„m {p ‚„yD`¬„ t›`pDm-yŠª6so`Lkšmutmuq^mut›y{p6¦ °pÀmo\^`¯ skšm9~ ŠsumyŠªmo\^t›k9su`L~JyPsšmQ²  `  t›££ su`Q„Š£›£OŽ Pkštw„¡ªÇ{„ mok9y{p"mu\^`3dÈ`L„\JŠp^tw„k8y{ªt›_=~ {„ mŠpJ‚ „y{pDmoP„mQ¦  ªÏmo`smu\^twktpDmusoyl‚lq „ muy{sojƒ~ ŠsumL²Qmu\ ` q^p t›‚lt›_=`p kut›y{p {£Pso\^`yP£yP‘{tw„{£œ_¡yl‚l`L£›k  t›££HŽS`-so`¢Ht!`  `Q‚ {p ‚ „ sotmutw„ t›Ê`L‚6¦ [\ `p6"²  `  t›££8kšq _¡_{sut›Ê`,mo\^` _œznyPs'{kokuq^_=~lmut›y{p kyŠªÉ}`LsšmoÊ{« k'[\^`Ly{soj™ŠpJ‚ mo\^`t›s t›_¡~ £tw„Šmut›y{p k ª®yPs mo\^`„ yP_=~^qlmoŠmut›y{p3yŠªª®y{s„ `LkL#¦  ªÏmo`smu\ t›k ~ su`Qkš`LpPmœmotyPp'yŠª¢{`Lsu$j  `£›%£ Hp^y  p ªÇP„mk&²  '`  t£›£8~^so`Lku`pDm'mo\^`©¢œ{sut›y{q k` ŸHmo`p kutyPp kyŠªmo\^`"Éc`sumuÊÀ[\^`yPsuj moy™Ž^tw‚lt›_=`p kutyPp Š£8ŠpJ‚ „y{plª®yPsu_{£‘P`y{_=`musot`Qkƒ{p ‚ muy,yŠmo\^`s8_=`L„\ {p^tw„Š£R„y{p kšmutmuqlmot¢P`=£›( }k=»®~ £›Pknmot›„t­mnjP²6¢Ht›ko„ yH`£w{kšmutw„ tmnj{² `L£›Pknmoyœ¢Ht›ko„ yP~^£›Pknmot›„t­mnj^½ ¦ )*,+W.Ä -9/ 0”{˜©± yPpDmo{„ m dÈ`Q„\ Šp t›„Lk²l± y{pDmut›pHq^q^_%dÈ`L„\JŠp^tw„kL²Pt›_=~ {„ mL²ldÈq^£mut¤ZŽJyl‚ljkujlknmo`_k²H„ yP£­¤ £›twkšt›y{p6² t_=~^q^£wku`{²WÉ}`sumuÊP« kc[\^`yPsujP²^su\ `y{£›y{‘Pt›„LŠ£_=yl‚l`£A² `L£›Pknmot›„t­mnjP²^~^£w{kšmutw„ tmnj{²J¢Dtwko„ yH`£w{kšmutw„ tmnj{²^`L£›Pkn¤ moyœ¢Ht›ko„ yP~^£›Pknmot›„t­mnjP²l„ y{pDm{„m ª®y{s„ `Qk²Hª®sotw„mut›y{p¨²ltp ‚^`pDmoŠmut›y{p.

(17)  

(18)  

(19)          !"# $&%'! 

(20) (. 9

(21) 9

(22) ¡5$**"#¨3  +*3+*3. ,.-

(23) / !à œÂ 0•Ŋà 0Ç / ŒP¦Œ d0yŠmut›¢œœmotyPp k ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ŒP¦  ± yPpDmu`pHq,‚l`„ `8sŠ~^~Sy{sum}‚l`8su`Q„\^`s„\^`¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ŒP¦ ) €}`_=`s„ t›`_=`pDmk¦ ¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ • 6µÂ  Æ 7H– * 354 ÂJ” 0®à 0Ç / 0 ^¦Œ €cŠ~^~S`£wk}kuq^s £›¡_=rL„LŠp^twvDq^`#‚l`Lk „\ yH„Lk ‚^ŠpJk£`Qk}kšyP£tw‚l`Qk sot›‘{tw‚l`Lk¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ^¦ŒP¦Œ °pPmorso` m}‚l`#£w¡_¡rQ„{p^t›vDq^`#‚l`Qkt_=~ P„mk ¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ^¦ŒP¦  ± yD`¬„ t›`pDm}‚l`#su`Qknmot­moqlmut›y{p3` m}`žSyPsšmk ŠqlŸt_=~ P„mok ¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ^¦  x-suyPŽ^£rL_œmutwvDq^` ¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ” 0*H” *=< / µÃL” 0*0Å{ / !à  Ŋà 9 Á† 0:7HÆ *H”  / ^Æ +à 0;• *D$ ) ¦Œ d0yH‚^]£›`Lkso\^ryP£yP‘{twvPq `Lk q^p^tw‚lt›_¡`Lp kutyPp^p^`£wk¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ) ¦ŒP¦Œ ckokš`L_9Ž^£wŠ‘P`eso`LkokšyPsšm£›tp^rQŠt›su`8`m {_=y{sumutwkuku`q^s£›tp rLŠt›so`¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ) ¦ŒP¦  ckokš`L_9Ž^£wŠ‘P`eso`LkokšyPsšm£›tp^rQŠt›su`8`m {_=y{sumutwkuku`q^sp^yPp£›t›p^rL{tso` ¦8¦#¦8¦#¦#¦ƒ¦#¦ ) ¦ŒP¦ ) ckokš`L_9Ž^£wŠ‘P`eso`LkokšyPsšmp^yPpl¤A£›t›p^rL{tso`e`mcŠ_=y{sumutwkokš`Lq^s ¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ) ¦ŒP¦ ‰ ckokš`L_9Ž^£wŠ‘P`eso`LkokšyPsšmp^yPpl¤A£›t›p^rL{tso`e`m}~ œmotp ¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ) ¦ŒP¦ ˆ ± y{_=_=`pDmo{tso`Lk ‘{rLp^rsŠq^Ÿ'kšq^s £›`Lk_=yl‚l]L£`Qk}‚ltwku„su`mokL¦©¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ) ¦  d0yH‚^]£›`Lk „ yPpDmut›pDqJk ¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ à B*,µAà C,“HÆ là 0;• * ? ’ 6:6 *DÆY”=”L• 'Æ  Aà @“H/ 0 *0• Å{ / !à  Ŋ# ‰J¦Œ x-sut›p „ t›~ {£`Qk\DjH~SyŠmo\^]Lku`Lk Pkukuyl„ t›r`Lk{q3„y{pDmoP„m}‚l`É}`LsšmoÊ ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ‰J¦ŒP¦Œ c`Qku„sut›~lmut›y{p,‚l`Qk kšq^suªÇ{„`Lk`Lp3„y{pDmoP„m0¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ‰J¦ŒP¦  crª®y{so_=Šmut›y{p3` mc‚lrL~^£w{„ `L_=`pDm}‚l`Lk kuq^suªÇ{„ `Qk kšyPq k„\ Šso‘{`L_=`pDm—¦#¦8¦#¦#¦ƒ¦#¦ ‰J¦ŒP¦ ) ¾-knmot_Šmut›y{p !E%F  ‚l`8£›=~^so`LkokutyPp‚l`„y{pDmoP„m1¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ‰J¦  x-sut›p „ t›~S`#‘{rp rsŠ£‚l`#sorLkuy{£›qlmut›y{p3‚lq,~^suyPŽ^£›]_=`#‚l`É}`Lsšmoʦ#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ‰J¦ ) hly{£›qlmut›y{pȂlq3~^soy{Ž^£›]_=`#‚l`É}`LsšmoÊ#~JyPq^s q^pȄ yPpDmo{„ m t›p^tmutwŠ£›`_=`pDm}~Sy{p „ muq^`L£W¦#¦#¦ƒ¦#¦ ‰J¦ ) ¦Œ € rLkuy{£›qlmut›y{p,‚lq,~^soy{Ž^£›]_=`#œŸltwkšjH_=r mosutwvDq^`ƒ~JyPq^s}‚l`q^Ÿ3kuy{£›t›‚l`Qk‚l`#surL¢{yP£qlmotyPp k ‰J¦ ‰ €}rLkuy{£›qlmut›y{p,‚lq,~^soy{Ž^£›]_=`8~JyPq^s}‚l`LqlŸ3kuy{£›t›‚^`Lk ‚l`8~^soyŠ¯ £wk‘{rLp^rsŠq^Ÿ1¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ‰J¦ ˆ hly{£›qlmut›y{pȂlq3~^soy{Ž^£›]_=`#‚l`É}`LsšmoÊ#~JyPq^s q^pȄ yPpDmo{„ m t›p^tmutwŠ£›`_=`pDm}£›tp rtwvPq `%¦#¦#¦ƒ¦#¦ ‰J¦  hljDpDmo\^]Lku`#‚l`Lk ~ sut›p „ t›~ {qlŸ'sorLkuq^£­mœmk©¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ – 6 ^Ŋà 0*0*D:• OÀ”LÂSÆ 0 0*HE” 6-ÂS• ¡• / ÅP / à ^ŊPà 0 / 0®à 0 ^Æ *D– * / Eà 6- / ÅŠÄ H  6:6Æ 0YÅ là 0Ç /JI LÆ KM0ÇN ÃQ• *HÆ ˆ^¦Œ °_=~ P„mc„y{£›tp^rQŠt›su`8‚l`‚l`LqlŸku~^\^]Lsu`Qke¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ˆ^¦  °_=~ P„mc„y{£›tp^rQŠt›su`emusotw‚lt_=`Lp kšt›y{p p^`£‘Prp^rLso{£ ¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ˆ^¦ ) °_=~ P„m}Ž^tw‚lt›_=`p kutyPp^p^`L£6‚l`‚l`q^Ÿ3„ jH£›tpJ‚lsu`Qk#¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ˆ^¦ ‰ SO{£tw‚ltmur#~Sy{q^s £›`Lk}t_=~ P„mok ‚^`#£Y« \HjD~SyŠmo\^]Lku`#‚« r¢{yP£q^mut›y{p,vPqJ{kut­¤°knmœmot›vDq^`+¦8¦#¦#¦ƒ¦#¦ ˆ^¦ ‰J¦Œ }so‘{q^_=`pDmk\^`q^sotwknmot›vDq^`Qk ¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ˆ^¦ ‰J¦  b}p^`#rmuq ‚l`#‚lq3mo`_=~ k}‚l`#„y{pDmoP„m ` m}‚l`Qk _=yH‚^`Lk ‚l`8¢HtŽ soŠmut›y{p k ‚l`Qk kš~ \^]so`Lk ˆ^¦ ‰J¦ ) ± y{p „£q kut›y{p kÀ¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ÍÍ ÒT'UWV

(24) XY. ). 1.   2. 8. ¼ ¼ ŒQ‹ µŒ  ,>9. Œ) ŒL‰ Œ2 {‹ ^Œ P ). 3D?. Š‰ Pˆ {¼ G. ). . ) ). )=). . ). ¼. ) ?RQ. ‰D‹ ‰) ‰P‰ ‰P‰ ‰P‰ ‰D ‰D. . Œ.

(25) ‰. W!   ! . ^ˆ ¦ ˆ °p q^`pJ„ `‚lq3ª®soyŠmšmo`_=`pDm}kuq^s £Y« t›_¡~J{„mc‚^tso`L„ me¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ‰D ’“D”Q•Æ®Ã!^ÃL”}ÅPÂJ–N6ÆǓH– * / à D0 *H” I Æ Ã@“H 0 * 0*B*,µÃAC9Å{ / Å *  /  / ÃeÆ *H” J“HÂS–—“DÃ0 *H” 0*H”Å{ 6” * / Å{ / !à ^Å{à ?  ¦Œ c~^~^soyl„\^`8su`L£›Šmut›¢{`8r£w{kšmutwvDq^`8~JyPq^s £`#„y{pDmoP„m tp t­mot›{£`L_¡`LpDm}£t›p^rtwvDq^`#¦8¦#¦8¦#¦#¦ƒ¦#¦ ‰2  ¦ŒP¦Œ xyDkštmut›y{p,‚lq,~^soy{Ž^£›]_=`e¦#¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ‰2  ¦ŒP¦  b}p,` Ÿl`_=~^£›`#‚l`8musoy{twk „ jH£›tpJ‚lsu`Qk`p,„ yPpPm{„ mc¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ‰D¼  ¦ŒP¦ ) }p {£jlku`O~ Šs£w}_=r mo\^yl‚l` ‚l`Qk‚^r¢{`L£yP~^~S`_=`pDmok{kujH_=~lmuy{mutwvPq `Lk6`m£›`Lk¨mu`Q„\l¤ p^t›vDq^`Qk ‚l`#~S`sumuq^soŽ œmotyPp3PkšjH_=~lmoyŠmutwvDq^`{¦1¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ˆ{‹  ¦ŒP¦ ‰ }~^~^£›tw„œmotyPp k ¥=‚« Šqlmosu`Qk „{k~JŠsumutw„ q^£›t`Lsokc¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ˆ 2  ¦ŒP¦ ˆ }qlmosu`Qk ‚lr¢P`£›y{~^~S`_=`pDmk {kujD_=~lmoyŠmot›vDq^`Qk~^suyP~JyDkšrL`LkL¦-¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ D  ¦ŒP¦  }~^~^£›tw„œmotyPp3{qlŸ't›_=~ {„ mok}‚l`QktpJ‚l`pDmoŠmut›y{p k mosuyPq^¢{rL`LkL¦-¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ 2Š‹  ¦  ÉcjH~Jy{mu\^]Qkš`Qk‚^`Lk‚lr ª®yPsu_Šmut›y{p k~^£wŠp^`Qk`mRtp Jq^`p „` ‚^` £we‚^t_=`pJkšt›y{p9¯ p^t›`‚^`LkkšyP£tw‚l`Qk 2lŒ  ¦ ) ± yPpDmo{„ m `pDmuso`#kšyP£tw‚l`Lk „y{plª®yPsu_=`Qk,¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ 2œ‰  ¦ ) ¦Œ ± y{pDmoP„m}ŠsoŽ^so` œ{£rQku{‘{` yPq,ku~^\^]Lsu` œ„Lµ¢Dtmurƒkš~ \^rsot›vDq^`=¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ 2œ‰  ¦ ‰ d0r mu\ yH‚^`Lk pHq^_=rsotwvPq `Lk~Sy{q^s £›`#„ y{pDm{„m p^yPpl¤°É}`soÊ mot`Lp ¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ 2 G  ¦ ‰J¦Œ xOsut›p „t~S`#‘{rLp^rsŠ£¦#¦8¦#¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ 2 G  ¦ ‰J¦  }~^~^£›tw„œmotyPp3{qȄ y{pDm{„mp^yPp,Éc`sumuÊLt`Lpg¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ¼ Œ ’“D”Q•Æ®!à ^ÃL”'ÅPÂJJ– 6ÆY“D– * / à D0 *H” I Æ —Aà @“D 0 *'0* B*,µAà C©Å{ / Å *  /  / Ã,Æ *H”'ÅPÂJN– 6 / QÄ Ã *D– * / ÃQ” 0*H”– lÃQ“ 0 ^• O 0*H”=Å{  6$” * / Å{ / !à  Ŋà 8 3 2l¦Œ ¾OŸDmo`p kut›y{pȂlqȄ yPpPm{„ m ‚^`8Éc`sumuʁ{q3„y{_=~JyPsšmo`_=`pDm ¢Ht›ko„ yHrL£›Pknmot›vDq^`ƒ£t›p^rQŠt›su` ¦ƒ¦#¦ ¼D 2l¦ŒP¦Œ €}Š~^~S`£wk kuq^s £`„y{_=~Sy{sumu`_=`LpPm ¢Htwku„yDrL£›Pknmot›vDq^`ƒ£›tp^rQŠt›su` ¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ¼D 2l¦ŒP¦  ¾-knmot_Šmut›y{pȂl`8£Y« ` žWy{sumc‚l`#„ yPpDmo{„ m}‚ È¥£w¡¢Ht›ko„ yDkštmur³¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ ¼P 2l¦ŒP¦ ) ¾-knmot_Šmut›y{pȂlqȄ yH` ¬„t`LpPm}‚l`#so`Lkšmutmuq^mut›y{p3` mcŠ~ ~^£tw„Šmut›y{p,ŠqlŸt_=~ P„mok ¦#¦ GP‹ 2l¦  ¾OŸDmo`p kut›y{pȂlqȄ yPpPm{„ m ‚^`8Éc`sumuʁ{q3„y{_=~JyPsšmo`_=`pDm ~^£w{kšmutwvDq^`8~ ŠsuªÇŠtm ¦8¦#¦#¦ƒ¦#¦ GP¼ 2l¦ ^¦Œ ± y{pDmoP„m}‚l`#É}`LsšmoÊ#~JyPq^s q^pȄ yPsu~ k rL£›PknmoyŠ¤Z~^£›Pknmot›vDq^`ƒ~ {sšªÇ{t­m ¦8¦#¦8¦#¦#¦ƒ¦#¦ GP¼ 2l¦ ^¦  ± y{pDmusŠt›pDmu`Lk‚^{p k£›`‚l`_=t¤A`Qkš~ P„ ` ¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦ GP¼ 2l¦ ^¦ ) dÈyl‚l]£›`#‚« t›p ‚l`LpDmoœmotyPp,r£w{kšmuy{~ £›Pknmot›vDq^`ƒ`p3musoy{twk ~^\ Pkš`Qk¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒL‹Dˆ 2l¦ ^¦ ‰ ¾-knmot_Šmut›y{pȂlqȄ yH` ¬„t`LpPm}‚l`#so`Lkšmutmuq^mut›y{p3`p,r£w{kšmuyP~^£›Pknmot›„t­mor%¦#¦8¦#¦#¦ƒ¦#¦eŒ{ŒL‰ 2l¦ ^¦ ˆ °_¡~J{„m `LpPmosu`#‚l`LqlŸ3ku~^\^]Lsu`Qk9¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒ{Œ 2 2l¦ ^¦  °_¡~J{„m `LpPmosu`8q^pȄjD£›t›p ‚lso`ƒ`m}q^p,~^£wŠp ¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQ{‹ 2l¦ ) ¾OŸDmo`p kut›y{pȂlqȄ yPpPm{„ m ‚^`8Éc`sumuʁ{q3„y{_=~JyPsšmo`_=`pDm ¢Ht›ko„ yP~^£w{kšmutwvPq ` ¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQŠ‰ 2l¦ ) ¦Œ € `£wœmotyPp  y{s„ ` °p ‚l`LpPmœmotyPp'~Sy{q^s q^pȄy{_=~JyPsšmo`_=`pDm `p,£›y{t~^q t›koku{p „ `#¦#¦eŒQŠ‰ 2l¦ ) ¦  ¾-knmot_Šmut›y{pȂlqȄ yH` ¬„t`LpPm}‚l`#so`Lkšmutmuq^mut›y{p6² ¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQ{ 2l¦ ) ¦ ) ± y{_=_=`pDmo{tso`Lk ` m}¢œ{£tw‚^œmotyPp3‚^`LksorLkuq^£­mœmk ¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQ{¼ 4 0 / Å 06 Æ *H”=Å{ / ÅPÆǕA” 0Y / ” ,D3 4 œÂ  Æ 7D– * 0* ¡ÂJ•”QA” 0 / *H” ; *Pà *, œ•Aà 0 ,>? , 9¦Œ  y{p „ mut›y{p k~SyŠmo`pDmut›`£›£›`Lk}‚l`#| y{qJkukutp `Lkov` me± `sosoqlmut ¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒ‰JŒ 9¦   y{s„ `8p^yPsu_Š£›`8„ y{pJ„ `pDmosurL`8kuq^s q^p,`Qkš~ P„ `(¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒ‰D 9¦ ) x-su`QkukutyPpp y{so_={£`8Š~ ~^£twvDq^r`#kuq^s}q^p `8kuq^suªÇ{„`8„ts„ q £›{tso`©¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒ‰D¼

(26) . 1. . . . . . . . . . 8. . . . Ë®ÌÍ6ËÏÎ.

(27) ˆ.  

(28)  

(29)          !"# $&%'! 

(30) (. 9¦ ). ¦ Œ € r~ {sšmot­motyPp k ‚l`8~^so`Lkokšt›y{pJk p y{so_={£`QkœŸlt›kujH_=r musotwvPq `Lk ¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒ‰D¼ ¦ ± {k ‚l`8£w=~^su`Qkukut›y{p‚^`É}`sumuÊ ¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒ‰D¼ 9¦ ‰ x-su`QkukutyPpp y{so_={£`8Š~ ~^£twvDq^r`#kuq^s}q^p `8kuq^suªÇ{„`ƒ`L££›t›~lmutwvDq^`©¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQˆ^Œ 9¦ ‰J¦Œ(± {k ‚« q^pȂlr~ £›P„ `_=`LpPm q^p t­ª®yPsu_=`{² n = − 1 ¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQˆP 9¦ ‰J¦ ± {k ‚l`8£w=~^su`Qkukut›y{p‚^`É}`sumuÊP² n = 1 ¦#¦82¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQˆ ) 2 4 œÂ  Æ 7D– *  0 0:0Y– * / ” 0Ç /:/ *HÆ}>“ ;:• 0 ^Æ * / à ^• 6œÂ  Æ 7H– * 0* ÂS•”L” 0 / *HA” ; *Dà *,QÄ œ•ÃA0 ,DHH |ƒ¦›Œx-surQkš`LpPmœmotyPp3‚lq,~^soy{Ž £]L_¡` ¦8¦#¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQˆPˆ |ƒ¦×+hly{£›qlmut›y{pȂlq3~^soy{Ž^£›]_=`8‘{rLp^rsŠ£ ¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQˆ{ |ƒ¦ )  y{s„ `8p^yPsu_Š£›`8„ y{pJ„ `pDmosurL` ¦8¦#¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQˆ 2 |ƒ¦ ‰  y{s„ `ƒmo{p^‘{`LpDmut›`£›£`#„ yPp „ `LpDmusor` ¦#¦ƒ¦#¦8¦#¦8¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒQˆ G |ƒ¦×ˆ x-su`QkukutyPpsor~JŠsumut›`ep^yPsu_{£`8` m mŠp^‘P`pDmut›`£›£›` ¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒLP‹ |ƒ¦×ˆl¦›Œ crL~^£›P„ `L_¡`LpDmok` mc‚^r ª®y{so_œmotyPp k¥£wkuq^sšªÇP„ `©¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒL Œ |ƒ¦×ˆl¦× ± y{pDmusŠt›pDmu`Lk‚^{p k£›`‚l`_=t¤A`Qkš~ P„ ` ¦#¦#¦8¦#¦8¦#¦ƒ¦#¦8¦#¦#¦8¦#¦8¦#¦8¦#¦#¦ƒ¦#¦eŒL Œ . 9¦ ). . ÍÍ ÒT'UWV

(31) XY. . .

(32) . W!   ! . S

(33) ¨3- 

(34) .  

(35)  . . !"$#&%('#*)+#-, ./.0,12'#*,3#)34#5,3)34#. §-« yPŽlzn`L„ mutªe‚l`„`'mosoµ¢œ{t£A²¨`m¡~ {s9£w¥^²‚l`,„ `'sŠ~ ~JyPsšmQ²¨`Lkšm‚« `žS`Q„moq^`s¡q^p^`3su`L¢Hq^`„sutmutwvDq^`‚l` £w3£tmšmorsœmoq^su`¡~Sy{sumoŠpDmkuq^s8£Y« `Lkšmut›_œmut›y{pÀŠpJŠ£›jPmot›vDq^`=‚l`Qk8` žWy{sumok#‚l`„ yPpDmo{„ mƒ`LpDmuso`=kuy{£›tw‚l`Lkƒ` m9‚^q „yH` ¬„ t›`pDm}‚l`#so`LkšmutmuqlmotyPp3{qlŸ't›_¡~J{„mk¦ §-« `Qknmot_œmotyPp3{p Š£›jDmutwvDq^`#‚l`Lk `žSyPsšmk ŠqlŸt_=~ P„mok =‚l`LqlŸyPŽlzn`L„ mutªÇk~^sotp „t~JŠqlŸ¦^§6`#~ su`L_¡t›`s `Qknm£A« q^mut›£twkuŠmut›y{p ‚l`0„ `Qk¡`Lkšmut›_=Šmut›y{p k=~Sy{q sr¢œŠ£›q^`s=£›`Lk=`žSyPsšmk=_=ŠŸlt_q^_ ‚l`Ȅ yPpDmo{„ m‚^Šp k=q p Ž qlm¡‚l`3‚lt›_¡`Lp kutyPp^p^`_=`LpPm=‚l`LkknmosuqJ„muq su`Qk²¥È£› suq ~lmuq^so`~ {s9`ŸH`L_=~^£`P¦§¨`'ku`L„ yPp ‚Ày{Ž^zn`L„mot­ª}`Qknm £A« `Lkšmut›_=Šmut›y{p6² !#%R   ²-‚lq „ yH` ¬„ t›`pDm=‚l`so`Lkšmutmuq^mut›y{p—`Lp—ª®y{pJ„mut›y{p ‚l`Lk‘{rLy{_=r mosut›`Lk` m‚l`Qk9~^soyŠ¤ ~ sut›r morLk ~^\HjlkštwvDq^`Lk‚l`Qk_=ŠmurLsutwŠqlŸ¦H§6`#„ yH`¬„t`LpDm‚l`8so`LkšmutmuqlmotyPp`Qknm q^p,‚l`Qk ~JŠsŠ_=] mosu`Qk-£›`Lk~^£›q k t›_=~JyPsšmŠpDmok ‚^{p k £›kšt›_9q^£wœmotyPp‚l`Qk „y{£›£twkutyPp k ‚ Šp k £›`Lk kšjlkšmu]_=`Qk ‚^`ƒkuy{£›t›‚^`Lk sut›‘{tw‚l`LkL,¦ °£S~ su`Lp ‚`Lp „y{_=~lmo`#£`Qk}~^\^rLp^y{_=]Lp^`Lk}‚^t›kokšt›~ ŠmutªÇk}~S`p ‚^{pDmc£Y« t›_¡~J{„me`p,r¢œŠ£›q {pPm}£w‚ltwkokšt›~ œmotyPp,rp^`Lsu‘Pr mutwvDq^`{¦ hly{p3`Lkšmut›_=Šmut›y{p3p^rL„`Lkokštmu`#‚lyPp „8£A« rL¢µ{£qJœmut›y{p,‚l`8£w=~^q^twkukoŠp „`ƒ‚^`Lk `žSyPsšmk ‚l`#„ y{pDm{„m ~S`p ‚ ŠpDm}£` „\ yH„{¦^b}p^`#`Qknmot_Šmut›y{pȁŠp {£jDmot›vDq^`8sot‘Py{q^so`q ku`8‚lqȄ yH` ¬„ t›`pDm}‚l`#so`LkšmutmuqlmotyPp,~J`Lsu_=` mc‚6« `LpD¢Htwku{‘{`Ls ‚^`Lk-„LŠ£w„ q^£wkO`m ‚l`Qk kut_q^£wœmut›y{pJk¯JŠŽ £`Qk-‚l`Qk-kujHkšmu]L_=`Lk-‚^`ekuy{£›t›‚l`QkRsot‘Pt›‚l`Qk-kuy{q^_=twkO¥‚l`Qk „y{pDmusŠt›pDmu`Qk q p^t£wœmorsŠ£›`Lke` m¥3‚l`Lk8„ yP££›twkšt›y{p kL¦6± ` mšmo`=r muqJ‚l`{q kukut~JyPq^s8Ž^qlm‚l`=~JyDkš`Lse£›`Lk#vDq^`QknmotyPp kƒkšq^s8£›`Lk £›t›_¡tmu`Qk ‚^`Lk _¡yl‚lrL£twkoœmut›y{pJk-Ž PkšrL`Lk kšq^s £A« \HjH~Jy{mu\^]Qkš`ƒ‚l`ekuy{£›tw‚l`Lk-sut›‘{tw‚l`LkL²H‚« t›_=~ {„ m `m‚l`ƒ„ yH` ¬„t`LpPm ‚^`ƒso`Lkšmutmuq^mut›y{p6¦  £A« yPsut›‘{t›p^`{²W£›`=~^su`L_=t`Lsƒ_=y{mu`q s8‚^`=„`9mosoµ¢œ{t£r mŠtm#£`¡~^soy{Ž^£›]_=`=tpH¢P`skš`¡kšq^t›¢œŠpDm W£w3‚^r mu`Lsš¤ _=t›p œmotyPp ‚l`Qk}` žWy{sumokƒ‚l`¡„ y{pDm{„mƒ„ y{p p ŠtwkukoŠpDm}£w„ t›p^rL_=ŠmutwvDq^`9`me£w'„ t›p^rmutwvPq `‚« q^p kujlknmo]_=`‚l` kuy{£›tw‚l`Lkƒµ¢œŠpDme`m8{~^su]Qkct›_=~ {„ mL²WtA¦ `P¦²£›`Lke¢Ht­mo`Lkokš`Qke~ sur 3` m8~SyPkšm Dt›_=~ {„ mL²W£w‘{rLy{_=r mosut›`‚^`Lk8„ yPsu~ k `Lp „y{pDmoP„m=` m=£`Lq^sk=£yPt›k=‚l`Ȅ yP_=~JyPsšmo`_=`pDm=_¡rQ„{p^t›vDq^`P¦-± `3~ suyPŽ^£]L_=`3{~^~ Šs wm9mnjH~^twvDq^`_=`LpPm £›y{skovPq `9£A« yPp ¢{`Lqlm znq knmot­¯J`sQ² !%D    ²6q p"„LŠ£w„ q^£R‚l`¡_=rL„{p^twkš_=`Lk8‚l`Qk8kšyP£tw‚l`Lkƒsot‘Pt›‚^`Lkey ©vDq^` £A« y{p,kšyPq^\ Štmu`#‚lt›_=`p kut›y{p^p^`Ls}¥¡£›¡soq^~lmuq su`#q^p3_=rL„LŠp^twkš_=`¥¡~ {sšmots ‚« q^pȄ{£›„q^£6sot‘Pt›‚l`P¦ ± `mšmu`#rmuq ‚^`9¡~JyPq^s Ž^qlme‚^`‚lr‘DŠ‘{`Ls £›`Lk}~^sut›p „t~ {£`Qk`Lkšmut›_œmut›y{pJk Šp {£jDmutwvDq^`Lk „y{p „`sop ŠpDm£` „ yH` ¬„ t›`pDm‚l`'su`Qknmot­moqlmut›y{p³`m£›`Lk`žSyPsšmk#so`p „y{pDmusorLk#£›y{sk‚l`„\^yl„k#`LpPmosu`kšyP£tw‚l`LkL¦}¯ p ‚l`'‚^y{pl¤ p `s}q^p `9tw‚lr`~ £q kc~^sorL„ twku`‚lq „P‚lso`‚^Šp k}£`QvPq `£„` mumu`9rmuq ‚^`9kš`kštmuq^`P² p^yPq kc{££›y{pJk so{~^~S`£›`sc{q 6 l¦›Œ9£›`Lkƒ‘Pso{p ‚l`Lke£›t‘Pp^`Lk8‚l`¡£›_=rL„LŠp^twvDq^`¡‚^`Lk8kšyP£tw‚l`Qkcsot‘Pt›‚^`Lk8kšyPq^_=t›kƒŠq^Ÿ0t_=~ P„mokL¦¨± `L„tp y{q k ~S`so_=` mumus{q 6 l¦×‚l`#~^sorL„ twku`s £›¡~^soy{Ž^£›r_ŠmutwvPq `ƒ‚l`#„` mšmo`#r moq ‚l`{¦^§¨`#„ yH` ¬„ t›`pDm}‚l`8so`LkšmutmuqlmotyPp ~S`so_=` m‚l`mu`p ts„ yP_=~lmu`3‚l`Lk=‚ltžSrLsu`LpDmok¡~^\^rLp^y{_=]p `Lk¡‚lt›kokut~ ŠmutªÇk=vPq tku`'~ suyl‚lq^twku`pDm¡£›y{sk9‚6« q^p „\ yH„{¦{yPpso{~^~S`£›£`Lso#£›`Lk ‚lt›¢{`Lsok-~^\^rp y{_=]p^`QkO~^\Hjlkut›vDq^`Qk ‚ltwkokšt›~ œmot­ªÇk vDq^tkš`}~ suyl‚lq^twku`pDm {q'„ yPpPm{„ m Š¯ p'‚l`e~^sorL„ twku`s-£›`e‚^y{_Št›p^`e‚6« {~^~^£›t›„Lœmut›y{p‚l`Lk `Lkšmut›_œmut›y{pJk vDq^tS¢{yPpPm ¿ muso`e‚^y{p^p^rL`LkL¦l´ep‚ly{p^p `s `Lp kuq^t­mo`£w0‚lr ¯Jp^t­motyPp³rp^`Lsu‘Pr mot›vDq^`‚lq—„yH` ¬„ t›`pDm‚l`'su`Qknmot­moqlmut›y{p6¦R± ` mumu`'‚lr¯ p^tmut›y{p³p^yPq k~JŠs wm ¿muso`c£w9~ £q kznq ‚^t›„t`Lq kš`ƒ~Sy{q^s su`L~^sorLku`pDmu`Ls-£w‚ltwkokšt›~ œmotyPp'‚lq^`8Šq^Ÿ~^\^rp y{_=]p^`Qk-£›t›rLkŠqlŸ„y{_=~JyPsš¤ mo`_=`pDmktp^rL£›Pknmot›vDq^`Qk‚l`Lk_œmorsot›{qlŸ²H` m}„ `Q„ t6‚l`8_Šp^t›]so`ƒtp ‚^r~S`p ‚^{pDmu`#‚lqª®suy{mšmu`L_=`pDm ` m}‚l`8£› „tp r_œmot›vDq^`#‚lqȄ\^yl„Š¦J± `Qkso{~^~S`£wk kš`LsuyPpPm £A« yPŽlzn` m}‚lqȄ\ {~^tmuso` e`#~ Šsum£›=‚lr¯ p^tmut›y{p3rp^`Lsu‘Pr mutwvDq^`8‚lq3„yH` ¬„ t›`pDm}‚l`8su`Qknmot­moqlmut›y{p¨²^kšyPp'`Lkšmut›_œmotyPp3{p Š£›jDmutwvPq ` kL« Š~^~^q t`-kuq^s£Y« `Lkšmut›_œmotyPp~^sorLŠ£wŠŽ £`O‚l`Qk6mosoµ¢œ{qlŸƒsorL{£twkurLk~ {s¨£›`Lk` žWy{sumok‚l` „y{pDmoP„mL¦Š± `-~ suyPŽ^£]L_=` Ë®ÌÍ6ËÏÎ.

(36)  

(37)  

(38)          !"# $&%'! 

(39) ( 2. ‚^`£Y« `Lkšmut›_œmotyPp0‚l`Lke` žWy{sumok}{q „ yPpDmo{„ m}`Lkšmƒ‚lyPp „#q^pÈ~ suyPŽ^£]L_=`9„ £›r£›y{skuvDq^`#£A« yPp0¢{`Lqlmc`Qknmot_=`se£` „yH` ¬„ t›`pDm‚l`©su`Qknmot­moqlmut›y{p `m3‚lt›_=`p kut›y{p^p^`Ls'£›`Lkknmosuq „ muq^so`Lk'¥—£A« t›_=~ {„ mL¦ ƒŠpJk'£›`0~ {sšmot` ) ²-yPp ‚^y{p^p^`Lso—q^p {~J`Ls q ‚l`Qk‚ltžWrso`pDmok3_=yl‚l]£›`Lk3Šp {£jDmot›vDq^`Qk‚l`Qk3` žWy{sumok3‚l`"„y{pDmoP„m3`pDmuso`©‚l`LqlŸ kuy{£›tw‚l`LkL²¨vDq^t ~J`Lsu_=` mumu`LpPm=‚« r¢œŠ£›q^`s£`Qk`žSyPsšmk~S`p ‚^{pDm£A« t›_=~ {„ mL¦e`q^Ÿ³„£›Pkuku`Lk~^sut›p „t~ {£`Qk9‚l` _=yl‚l]L£`Qk kuy{pDm mus{‚ltmut›y{p p^`£›£`L_=`pDm q^mut›£twkšrL`Lk H£`Qk _=yl‚l]L£`Qk so\^rLy{£›y{‘{twvDq^`Lk q^p^tw‚lt›_=`p kutyPp^p^`L£›k8» 6&) ¦Œµ½ `m £›`Lk _=yl‚l]£›`Lk„y{pDmut›pHq ke» 6&) ¦×{½¦Ha}yPq k `Lkoku{t`LsuyPp k-‚^`ƒ‚lyPp^p^`Ls £›`Lkµ¢œŠpDmo{‘{`QkO` m£›`Lk tpJ„ y{pH¢Prp^t›`pDmok ‚^`8„\J{„ q p3Š¯ pȂl`8‘{q^tw‚l`s £›`#£›`L„mo`q^s}‚ Šp k ku`Lk „\^yPt­Ÿ¦ ƒŠp ke£w~ {sšmot`‰ ²Sp^y{q kesŠ~^~S`£›£`LsuyPp k £›`Lke~^sotp „t~JŠqlŸÈsorLkuq^£­mœmkc‚l`£›mu\^rLy{sot`¡‚lq „ yPpDmo{„ mƒ‚l` ¶¡·^¸P¹6º3»nŒL¼P¼PP½¦ °£k« Š‘Pt­mc‚lqÈ_=yl‚l]L£`9„y{pDmut›pHqÈ£`#~ £q kcsurL~ ŠpJ‚lqÈ~JyPq^s}`Qknmot_=`se£`Qk}`žSyPsšmk `p0‚l`LqlŸ „y{so~ ker£w{kšmutwvPq `Lke~JyPq^s8q^p©„y{pDmoP„mƒ„y{£›tp rLŠt›so`{²Stp^tmutwŠ£›`_=`LpPm8~Sy{p „ muq^`L£Ry{q0£›tp rtwvPq `{%¦ °£p^`=k« Š‘Pts ~J{kƒ‚^Šp k8„` mšmo`=~ Šsumut›`‚l`‚lyPp^p^`Lscmoy{q kƒ£›`Lk8‚lr mŠt›£›k8‚l`Qk8‚lr¢P`£›y{~^~S`_=`pDmke‚l`¶¡·^¸P¹º„ yPp „ `Lsup {pDm £›`Ȅ yPpPm{„ mL²R_Štwk=‚l`Èso{~^~S`£›`skš`Qk=\HjD~SyŠmo\^]Lku`Lkª®yPp ‚^Š_=`LpPmŠ£›`Lk=`m=~JŠs£w¥^²Okuy{p™„\JŠ_=~ ‚6« {~^~^£›t­¤ „LœmotyPp6¦a}y{qJke¢P`sosuyPp ke`pl¯ pÀ„ yP_=_¡`LpDm8t›£~J`Lqlm¿ mosu`=Š~ ~^£twvDq^r¥'£A« t_=~ P„m#`pDmuso`=‚l`qlŸ"kšyP£tw‚l`Lkƒ`Lp „y{pDmoP„mtp^tmutwŠ£›`_=`LpPm~Sy{p „ muq^`L£D`m„y{_=_=`pDmt£H~S`so_¡`m‚6« `Qknmot_=`s£›`Lk` žWy{sumokŠq¡„ yPpPm{„ m`p9ªÇŠtwku{pDm £A« \DjH~SyŠmo\^]Lku`#‚« q p,„\JŠso‘{`_=`LpPm vDq {kut¤ZkšmoŠmutwvPq `{¦ §¨`Lk~JŠsumut›`Lk#kuq^t¢œ{pPmo`Lk9surQkšq^_=`LpPm£›`Lk9‚lt­žWrso`pDmksorLkuq^£­mœmkvDq^tOso`£wœŸl`pDm£›`Lk„y{p ‚ltmut›y{pJk‚« Š~l¤ ~ £tw„Šmut›y{pȂl`9£w¡mu\ ry{sot›`9‚l`¶¡·^¸P¹º`mermu`pJ‚l`pDmL²J~ Šsc£›¥_=¿L_¡`P²Jkuy{p0„\ {_=~0‚« {~^~^£›t›„LœmotyPp6¦ ƒŠp k £w~JŠsumut›`¡ ²JyPp ` Ÿ^{_¡t›p^`£`Qke`ŸHmu`pJkšt›y{p kƒvDq^`¡£Y« y{p0~S`q^mƒmosuyPq^¢{`Lse‚^{p kƒ£›'£tmšmorsœmoq^su`¡„ yPp „ `Lsup {pDm £›`Lk¡‘Pry{_=rmusot`Qk9`Lp™ku`~S`p „\JŠpDm¡`Lp™~JŠsumutw„ q^£›t`Ls¡kuq^s=£›`3„y{pDmoP„m=tp^tmutwŠ£›`_=`LpPm£›tp rtwvPq `{¦Re{p k¡£› ~JŠsumut›` 2l² „ `Qk ` ŸHmo`p kutyPp k~Sy{sumu`pDmckuq^s}£›`„ yP_¡~Sy{sumu`L_=`pDm}‚l`Lk _ŠmursotwŠqlŸ„y{p kšmutmuqJŠpDmok £›`LkckšyP£tw‚l`Lk `Lp „ yPpDmo{„ mL¦S§6`Lke~^sotpJ„ t›~ ŠqlŸ0„y{_=~JyPsšmo`_=`pDmkcŠŽSy{s‚lrL`Lkckuy{pDmc£w¢Htwku„yHr£w{kšmutw„ tmur'» 6 2l¦Œµ½² £A« r£w{kšmuyŠ¤ ~ £›Pknmot›„t­mor~ ŠsuªÇŠtmu`» 6 2l¦ P½` mƒ£›¢Dtwko„ y{~ £›Pknmot›„t­mor'» 6 2H¦ ) ½¦± `Lkc` ŸHmu`Lp kšt›y{pJk²S¥‚l`Lkƒ„ yP_=~JyPsšmo`_=`pDmok ‚^t›kokšt›~ ŠmutªÇk~J`Lsu_=` mumu`LpPmc{£yPsok‚l`Qk r¢œ{£q Šmut›y{p k{p Š£›jDmutwvPq `Lk ‚lqȄ yH`¬„t`LpDm ‚^`#su`Qknmot­moqlmut›y{p6¦ xy{q s-mo`so_¡t›p^`Ls p^yPq k `Lkoku{t`LsuyPp k-‚l`ƒ„ yPp „ £›q^so`» 6 ¼P½-kšq s £›`Lk ~SyPkokšt›Ž^t›£tmurQk vDq^tWp^yPq k kuy{pDm yŠžW`sumu`Lk ~Sy{q s`Lkšmut›_¡`LsŠp {£jDmutwvDq^`_=`LpPm£›`Ȅ yH` ¬„ t›`pDm‚l`,so`LkšmutmuqlmotyPp {tp kut}vDq^`,£`Qk=` žWy{sumok{q „y{pDmoP„mL¦ acy{q k‚lyPp^p^`LsuyPp kOp^y{muso`ƒµ¢Htwk kuq^s„ `8vDq6« t›£W`Lkšm ~SyPkokutŽ^£›`ƒ`p „y{so`e‚« `Lku~JrLsu`Ls „y{_=_=`ƒ‚^r¢{`L£yP~^~S`_=`pDmok {p Š£›jDmutwvDq^`Lk ª®soq „moq^`qlŸ3` m}£w¥¡y 3£Y« `_=~^£›y{t¨‚6« yPqlmut›£›k}pDq _¡rLsutwvDq^`Lk ~ {so{t­m}‚lrQkšyPsu_{t›k t›p ‚ltwkš~S`p koŠŽ £`P¦ . . . # #5, ) # #"  . ± `8mosoµ¢œŠt›£¡r mur#_=y{mut›¢{r8` m}sorL{£twkšrƒ`pȄy{£›£›{ŽJyPsoŠmut›y{pµ¢P`L„e£›=kuyl„ t›r murhl„\ p^`tw‚l`s ¾-£`Q„musotw„Š² vDq^t = kuy{qlmo`pHq¯ p ŠpJ„ t›]so`_=`pDm}„ `#~^soyŠzn`mL¦^§¨`Lk Šq^mu`q sok mot`Lp^p^`pDmQ²^`p,~ {sšmot›„q^£t›`sQ²^¥¡su`L_=`s„ t›`s dÈtw„\^`£ cŽ {‚^t`P²^¾RŸl~J`Lsšmehl¾ hHt_q^£wœmut›y{pȂl`d0rL„{p^twkš_=`LkL²^etso`L„ mut›y{p0hl„ t›`pDmot­¯JvDq^`#`mc[¨`Q„\^p^twvDq^`{²^~Sy{q s}£` ¢Htªt›pDmurLsu¿m vDq6« t›£¨¡~JyPsšmor8¥=„`8musµ¢µ{t£W`m}~JyPq^s}kšyPp`LpDmu\^yPq kštw{ku_=`#„ y{_=_q^p^tw„œmot­ªn¦. ÍÍ ÒT'UWV

(40) XY.

(41) ¼. W!   ! .   

(42) 3 *,:})7 .    3,,. . ..0# $% ,  )+ 

(43) %#*'# ) 4  )  '  / #   ' # ,  ' #  / 0; *0* 0 N6  -

(44) / ,* 0* . Là “ Dà ÈÆ ©–—“HÅ • H” ǖ ^ŊÃQ” }¯ p‚l`-„y{_=~^so`p ‚lso`£Y« qlmot£›t­mor-‚l`O£wp^y{mut›y{p#‚« t_=~ P„m6`pDmosu`Okuy{£›t›‚^`LkL² p^y{qJk„ y{pJkštw‚lrsoy{pJkW£Y« ` Ÿl`_=~^£›` P„P‚lr_=twvPq `‚« q^p^`ku~^\^]so`=‚l`=_=Pkuku` M vDq^tR`pDmuso`¡`pÀ„ y{pDm{„m#µ¢{`Q„q^p"~^£wŠp6¦± `mƒ`Ÿl`_=~^£›`¡`Qknm t›£›£q kšmusor#¥¡£›¡¯ ‘Pq^so`ŒP¦ K(g). M x v0 x M v0 0 K(g) g. g K(g). 0. g. . . Œ/"! $ %'! $#  R %&%(' E $ !  ) % !. hHt£A« yPpÈp^r‘P£t›‘{`£›`Lkc` žW` mkc‚l`£›~S`LkoŠpDmo`q^sQ² £›`LkcrLvDq œmotyPp k}vDq^tsurL‘{twkuku`pDm}£›`_=y{q^¢P`_=`pDme‚^`£› ku~^\^]Lsu`#kuy{pDm £`Qk kšq t¢œŠpDmo`Lk5   ¨=R M x »nŒQ½ R = K(g, ˙ g)   x(t ˙ = 0) = v y  R `Lkšmƒ£wsorLP„motyPp0‚l`¡„y{pDmoP„m8kšq^~ ~JyDkšrL`9¿ mosu`q^p^`ª®y{p „ mut›y{p ‚^` g ` m#‚l` g˙ ²Jso`Lku~S`L„mot¢P`_=`pDmƒ£› ‚^t›kšmo{p „ `e` m £›9¢Ht­mo`Lkokš`ƒsu`L£›Šmut›¢{`}`LpDmuso`e£wku~^\^]Lsu`e` m£`ƒ~^£wŠp6¦ ± `mšmu`ƒso`£wœmut›y{pvPq tS£›t›`e£w‚^t›kšmo{p „ ` ¥ £wsorLP„mut›y{pȂl`¡„ yPpPm{„ me‚lr~S`pJ‚0‚l`£w‚lrª®y{so_=Šmut›y{p0{q0„ y{q soke‚lq0„ yPpPm{„ me‚l`Lke„ yPsu~ kL² `mƒ‚lyPp „g‚l` £›`q s‘PryP_¡rmusot` ` mO‚l`£›`q^sR„LŠs{„morsot›kšmutwvDq^`-_Šmursot›`£›£`P¦Š´ep¡‚ly{p p^` kšq^s£we¯ ‘{q^so` }£A« {££›q^so` „£›PkukutwvPq ` vDq^`8~S`qlme~^su`Lp ‚lso`e£w=sorL{„ mut›y{p~J`Lp ‚^ŠpDm}£›`ƒmu`_=~ kc‚l`„ yPpPm{„ mL¦ ± yPp kštw‚lrLsuyPp k-vDq^`ƒ„ `Lk „ yPsu~Jk-kuy{pDm sot‘Pt›‚^`LkL²{y kštS£Y« y{p'~^surª®]so`evDq^`e£›‚lr ª®yPsu_œmotyPp‚l`e„`Lk „ yPsu~ k `Qknmp^r‘P£t›‘{`QŠŽ^£›`{¦µ§¨cso{t›‚^`q^srLvDq^t›¢µ{£`LpDmu` su`L£twŠpDm¨£wcsorLP„motyPp¥}£we‚ltwkšmoŠpJ„ `-so`£wœmot¢P`O¢œe‚^y{p „Omu`pJ‚lsu` 0. Ë®ÌÍ6ËÏÎ.

(45)  

(46)  

(47)          !"# $&%'! 

(48) ( G. R. ∆t. t. W  !=

(49)   =   ' ! !    W    $ %. ¢P`sk-£A« tpl¯Jp^tY¦^§¨`e_ŠŸHt›_9q _ ‚^`ƒsorLP„motyPp'‚l`8„ y{pDm{„m mu`Lp ‚{£yPsok-¢{`Lsok £Y« t›pl¯ p^t`Lp'_=¿_=`ƒmu`L_¡~Jk vDq^` £›`ƒmu`L_¡~Jkmu`Lp ‚,‚l`„ yPpPm{„ m mo`p ‚3¢P`sk 0 ¦ [soP‚ltmut›y{p^p^`L££›`_=`LpPmQ²{yPp'„ yPp kštw‚l]Lsu`}{£yPsokRp y{p~^£›q k £›surQ{„motyPp‚l`e„y{pDmoP„m-_Štwk-kuy{pt›pDmurL‘{sŠ£›` kuq^s#£›`¡mu`_=~ kL²¨„{« `Qknm9¥,‚lt›su`=£w,~J`Lso„q kokšt›y{p6¦W¾Op—kuq^~^~SyPkoŠpDmvDq^`„ `mšmu`t›pDmurL‘{sŠ£›`so`Lkšmu`‚lr¯ p^t›`{²6yPp rQ„ sot­m}{£yPsok £A« rQvPqJœmut›y{p,‚lq,_=y{q^¢P`_=`pDm}kuy{q k£wª®y{so_¡`#kuq^t›¢µ{pDmu`  # "Z Z »A{½ R dt ⇒ M (v(t ) − v(t )) = I Mx ¨ dt = lim ‚ Šp k£w{vDq^`L££›`8£›¡~S`s„ q kokšt›y{p3`Lkšm}‚lr ¯Jp^t`#~JŠs Z Z ») ½ K(g, g) ˙ dt R dt = lim I = lim ± `mšmu`e_=yH‚^r£›t›koœmotyPp‚lq'„ yPpDmo{„ m-`pDmosu`ckuy{£›tw‚l`Lk-sut›‘{tw‚l`Lk-p^y{qJk-Š_=]Lp^`c‚lyPp „}¥#moso{t­mo`s-‚^`Lk ~^\ {ku`Lk ‚^`-¢{yP£›k¨£t›Ž^so`Lk„ yP_¡_=` q^p^` ‚^jDpJŠ_=t›vDq^` „ yPpPmotpHq^` ` m¥c„ yPp kut›‚lrLsu`Ls‚l`Qk‚^t›ko„ yPpPmotpHq^tmurQk{qlŸ8_¡yP_=`pDmok ‚^`Lk6t›_=~ {„ moksu`L£twŠpDm¨£w ¢œŠsotwœmut›y{p‚^`-vDq ŠpDmutmur ‚l`-_=yPq^¢{`L_¡`LpDm¥ £w ~J`Lso„q kokšt›y{p6¦œ± ` mumu` ‚^r_Šs„\^`-‚l` _=yl‚lrL£twkuŠmut›y{psu`Qknmo`e¢œŠ£›tw‚l`ƒmoŠpDm}vDq^`ƒ£`Qk kšyP£tw‚l`Lk ~S`q^¢P`pDm ¿ mosu`8„ yPp kštw‚lrLsurQk „y{_=_=`esot›‘{tw‚l`LkL¦H¾O££›`#kš` ‘Prp^rLso{£twku`}ªÇ{„t£›`_=`LpPm}{qlŸ'kšjlkšmu]L_¡`Qk _9q^£mut¤Z„y{so~ k `p3surLrL„sut›¢œŠpDm £›`Lk rQvPqJœmut›y{pJk ‚^`8ac` moy{pl¤Z¾Oq^£›`s `Lpmu`Lsu_=`Qk ‚l`e~J`Lso„q kokšt›y{p k-` m‚l`c¢œŠsotwœmut›y{pJkOt›p knmŠpDmo{p^r`Qk-‚l`e¢Ht­mo`Lkokš`¡»  ¸  œ²WŒ GPˆ )

(50)   ¸ R² {‹{‹P‹P½¦ ± `mšmu`8_=yl‚lr£›twkuŠmut›y{p~^sorLku`pDmo`cq^p3tpDmorso¿ m~ Šsumutw„ q^£›t›`s‚lq'~Sy{t›pDm‚l`8£wsorLkuy{£›qlmut›y{p‚lq~ suyPŽ^£]L_=` vDq6« `£›£›`'kšyPt­m9{p Š£›jDmutwvDq^`y{q³pHq^_=rsotwvPq `{¦6¾O£›£›`~J`Lsu_=`m‚« `pH¢Ht›koŠ‘P`s#q^p—kujlknmo]_=`'‚ljHp {_¡twvDq^`p^yPp sor‘Pq^£›t`Ls9Šq³£›t`Lq—‚« q^p^`kujlknmo]_=`sor‘{q £t›`s#mosu]QksŠtw‚l`` m=‚ly{pJ„‚lt¬„t£›`'¥Èt›pDmurL‘{so`sQ¦¨c`~^£›q k²`£›£` ~S`so_=` m ‚^`}p^r‘P£t›‘{`LsR£`Qk-‚lrª®y{so_œmut›y{pJkO‚l`ckuy{£›t›‚^`LkOvDq^t{zny{q^`LpPm `p‘{rLp^rsŠ£A²œq^ps {£›`}kš`Q„ yPp ‚^Št›so`‚ Šp k £›`Lk9kšjlkšmu]_=`Qk‚l`'kuy{£›t›‚^`Lk#_{kokut­ªÇkL¦± `mšmu`'\DjH~SyŠmo\^]Lku`‚l`'kuy{£›t›‚^`Lk#sot‘Pt›‚^`Lkkuy{q^_=twkŠq^Ÿ©t›_¡~J{„mkp^` ku`s~ {kso`_=twkš`8`pȄLŠq ku`ƒ‚^`„ `#sŠ~^~Sy{sumL¦ t0 +∆t. t0 +∆t. ∆t→0. +. t0. t0. t0 +∆t. t0 +∆t. ∆t→0. ÍÍ ÒT'UWV

(51) XY. t0. ∆t→0. t0. −.

(52) ŒQ‹. W!   ! . 9Â*—Å=0 * / à 0**H”LÃA0®ÃQ•¨Ã0Ç / *DÃ$* <- QÃQ” ^• O0ǖJ6^Å{ÃL” §¨`LkrLvDq Šmut›y{p k‚lq9_=yPq^¢{`L_¡`LpDmvDq^tHsor‘{twkokš`LpPm£›ƒ‚ljHp Š_=twvDq^` ‚l`Qk„ y{so~ kkšyPq^_=t›k{qlŸ#t_=~ P„mokp^` kuql¬ku`pDm ~ {k¥surQkšyPq ‚lso`e£›`8~^suyPŽ^£›]_=`{¦ °£WªÇŠq^m {~^~Sy{sumu`sq^p `ƒt›plª®yPsu_œmotyPpkuq^~^~^£›r_=`LpPmŠt›su`#kuq^s£` „y{_=~Sy{sumu`_=`LpPmO‚l`Qk-„y{so~ k~J`Lp ‚^{pPmO£A« t_=~ P„mL¦D§¨ š£yPt ‚« t_=~ P„m  `Lkšm-q^p ` £yPt „ yPp knmot­moqlmut›¢{`}vDq^t ~J`Lsš¤ _=`m ‚l`ƒ~^sorL„ twku`s-£›`e„y{_=~Sy{sumu`_=`LpPm ‚l`Lk kšyP£tw‚l`Qk kuy{q^_=twk-{qlŸt_=~ P„mokL¦Hb}p^`8‚lr ¯Jp^t­motyPp‘{rLp^rsŠ£›`c‚l` „` vPq ` ~S`q^mO¿ muso`q^p^`£›y{t^‚« t_=~ P„mR`LkšmO‚ly{p p^r` ‚^{p k »     ¸ R²ŠŠ‹P‹{‹P½ ¦œa}y{qJkp^y{q kR„y{pDmu`LpDmu`soy{pJk ‚ Šp ke„ `9sŠ~ ~JyPsšme‚6« q^p `‚lr¯ p^tmut›y{p ~ £q keso`Lkšmusot›„ mut›¢{`vDq^tªÇŠtmƒŠ~ ~J`L£¥'£›'p^yŠmotyPp0‚l`„yD`¬„ t›`pDmƒ‚l` so`Lkšmutmuq^mut›y{p6¦J± `#„ yH`¬„t`LpDm ‚^`#su`Qknmot­moqlmut›y{p3~J`Lsu_=`m ‚^`8mu`p ts}„y{_=~lmu`#‚l`Qk~^\^rLp^y{_=]p `Lk ‚ltwkukut›~ œmot­ªÇk vDq^t6ku`#~^soyl‚lq^twkš`LpPm}{qlŸ't›_¡~J{„mk²l‘Ps P„ `8¥¡£›‚lr¯ p^tmut›y{pȂ« q^p,~ ŠsŠ_=]muso`eq^p t›vDq^`P¦ – 7 / *D” 0 0ǔQA” 06là 0 Z” ^:• O 0YN– 6 ^ŊÃQ” }¯ p—‚l`„\^yPt›kut›sƒq p^`‚lr ¯Jp^t­motyPp³‚lq³„ yH` ¬„ t›`pDm9‚l` 4 @“ / ÂSJ so`Lkšmutmuq^mut›y{p vDq^tcp^yPq k'ku`_Ž^£›`0{‚^{~lmurL`0ŠqlŸ ~^soy{Ž^£›]_=`Lk=so`pJ„ y{pDmosurQk²Rp^yPq k'{££›y{pJk=muyPqlm‚« ŠŽSy{s‚ sŠ~ ~J`L£`Ls £`Qk ~^sotp „t~JŠqlŸ'~ \^rp^yP_=]p^`Qk ~^\HjlkštwvDq^`Lk ‚ltwkokšt›~ œmot­ªÇkcvPq tkuy{pDm su`Lp „ yPpPmosurQk Šq,„ yPq^sok ‚6« q^p „\ yH„{¦ hl{p kªÇ{tso`q^p^` £›t›kšmu` `ŸH\JŠq kšmut›¢{` ‚l`Qk~^\^rp y{_=]p^`QkR~^\HjlkštwvDq^`LkRvDq^tJkš` ‚lrLsuyPq^£`LpDm£›y{skR‚« q^p„\^yl„Š² yPp~S`q^m}so{~^~J`L£`LsL²Hmoy{qlmc‚^`#_¡¿L_=`{²l£›`Lk ~^sot›p „ t›~ Š£›`Lkkuy{q^s„ `Qk‚l`‚ltwkukut~Jœmut›y{p3rp `so‘{r mot›vDq^`  „ yP_=~JyPsšmo`_=`pDmokt›p^rL£›Pknmot›vDq^`Qk ‚l`Lk_œmorsot›{qlŸ l~^£›Pknmot›„t­mor{²^¢Htwku„yPkut­mor{²l`Lp ‚ly{_=_Š‘P`_=`pDm` m}soq^~l¤ • muq^so` „ yP_=~JyPsšmo`_=`pDmok t›p^r£w{kšmutwvDq^`Lk ‚^`Lk t›pDmu`suªÇ{„`Lk Pª®soyŠmumu`L_¡`LpDmc¥£A« tpDmu`LsšªÇP„ `P²lq kšq su` • r• p `so‘{t›`ƒ„LŠ~lmor`#~ {s £›`Lk}y{p ‚l`Qkr£w{kšmutwvDq^`Lk ` m}rL_=t›kokšt›y{p,{„y{q kšmutwvDq^`{¦ ± `Qk ~^\^rLp^y{_=]p `Lk~^\HjlkštwvDq^`Lk ~S`q^¢P`pDm}¿ mosu`8sŠp^‘PrLk‚^{p k ‚l`q^Ÿ3„ŠmurL‘{y{sot›`Lk ‚lt›kšmut›p „ mu`Lk   %  R $ ' R

(53)  W!"

(54) +$ %D   $  '    !   

(55) '

(56) &$ !    R :    )

(57) ! ! ¦D§¨`LkR‚l`LqlŸ~^so` ¤ _=t]Lsu`Qk „£›Pkuku`Lk ‚l`8~^\^rLp^y{_=]Lp^`Lkku`ƒ‚ltwkšmut›p^‘{q^`LpDm‚l`8£w‚^`sop^t]Lsu`e~ Šs£›`cªÇ{t­m}vDq6« `£›£`Qk ~J`Lq^¢{`LpPm kšq ~^~JyDkš`Ls £›yl„{£`Qk-Šq„ y{pDm{„mQ¦{¾O£›£›`LkkšyPpDm ‚ly{pJ„}`p'~^sut›y{sotmur}ª®yPp „motyPp'‚l`e£›9‘{ryP_=r musot›`}£yl„LŠ£›` Šq „ yPpDmo{„ mL²R‚l`Qk„ yPp ‚ltmut›y{p k{qlŸ £›t_=tmu`Lk'vPq tckšyPpDm{~^~^£›t›vDq^rL`LkL²OŠt›p kut}vPq `,‚^q „y{_=~Sy{sumu` ¤ _=`pDm}‚l`Lk_œmorsot›{qlŸ¦ ´ep3kuq^~^~SyPku`s^²D`p3` žW` mQ² vDq^`e£›`Lk~ \^rp^yP_=]p^`Qktp^rL£›Pknmot›vDq^`Qk‚^Šp k £›`Lk _œmurLsutwŠq^Ÿ'su`Qknmo`pDm}„ yPpl¯ p^rQk ‚^Šp k£w¡ÊyPp^`#‚l`„ yPpPm{„ m`LpDmuso`ƒ£›`Lk „y{so~ kL¦  %  R $ ' R

(58)  W!"

(59) %F %'! !   J$#  R= ¦S¾Op0„ `vDq^t„ y{pJ„ `sop^`8£w‚lt›kokut~ Šmut›y{pȂlq^`{qlŸ y{p ‚^`Lkr£w{kšmutwvDq^`LksorLkut›‚lq `£›£`QkvDq^tl~S`q ¢{`pDmOku` ~^soyl‚lq^t›su`‚^{p k£`QkR„ y{so~ kL²Lt›£^kL« {‘{tm‚« q^p¡~^\^rLp^yŠ¤ _=]p^` ~^£›q k¨‘P£yPŽ Š£DvDq^tD‚^r~S`p ‚‚^` £w}kšmusoq „moq^su` ‚l`Lkkuy{£›t›‚l`Qk¦µhHtH‚l`Lk„ yH` ¬„t`LpPmk‚^`-so`LkšmutmuqlmotyPp ~J`Lq^¢{`LpDmƒ¿muso`‚lr¯ p^twkc~Sy{q^sƒmo`p^t›sƒ„y{_=~lmo`‚l`=„ `Qkc~^\ rp^yP_¡]Lp^`LkL²St£wke‚^`¢Ht`Lp^p^`LpPm8p^rQ„ `LkokoŠt›su`¤ _=`pDmc‚lr~S`pJ‚^ŠpDmc‚l`#£w¡‘{ryP_=r musot›`e`LpPmot]Lsu`#‚l`Qk}„ yPsu~Jk `LpȄ y{pDm{„mQ¦ ƒŠp k-£›9kšq^tmu`P²{p^yPq kO„y{p „`pDmuso`soy{p kp yPkO`žSyPsšmkOkuq^sO£›`LkO~ \^rp^yP_=]p^`QkO£›yH„LŠqlŸ=Šq„y{pDmoP„mOp6« t_¡¤ ~ £twvDq ŠpDm9~ Pk9£wÈsoq^t›p^`'‚l`3„ y{so~ k9`p „y{pDmoP„mL¦§6`Qk9{ku~S`L„mk9‚« `pJ‚ly{_=_Š‘P`_=`pDmL²‚l`ª®s{„ muq^so`yPq ‚6« q kuq^so`cp^`ƒkš`LsuyPpDm ~ Pk-`LpD¢Htwku{‘{rQk¦{e`ƒ_¡¿L_=`{²H£`Qk-~ \^rp^yP_=]p^`Qk ‚ltwkokšt›~ œmot­ªÇk ‘{£›y{ŽJŠqlŸp^`ƒkš`LsuyPpPm ~ {k ~ sutwkƒ`p©„y{_=~lmo`{¦e{p kƒ£`„L{kƒ‚l`„ y{so~ ke_{kokštªÇk²„` mšmo`\HjH~SyŠmu\ ]Lku``Qknm8£`=~^£›q k8kuy{q^¢P`pDm-znq kšmut¯ rL`{¦ xyPq^s¡‚^`Lk=„ yPsu~ k¡_=t›p „ `Qk²y{q™~JyPq^s‚l`Lk¡t›_=~ {„ mokmusŠp ku¢{`Lsoku`Lk9kšq^s‚l`Qk=„ y{so~ k~JyDkukurL‚ ŠpDm¡q p^`3‚^t­¤ _=`Lp kšt›y{p3„{soP„murLsutwkšmutwvPq `}‘{sŠp ‚^`ƒ‚l`L¢œŠpDm moy{qlmo`e£›`Lk {qlmuso`Lk ‚lt›_=`p kutyPp kL²D£A« ` žW` mc‚l`ƒ£›~^soy{~ {‘PŠmut›y{p ‚6« yPp ‚l`Lk-‚ly{tmO¿ mosu` ~^sotwk`p„ yP_=~lmu`P¦{c`Qkmusµ¢œŠqlŸy{pDmO~JyPsšmor}kšq sR£Y« tpDmor‘{sœmotyPp¡‚^` ~^\^rp y{_=]p^`QkRp^yPp £›yl„{qlŸ'‚^ŠpJk£Y« `Lkšmut›_œmut›y{p,‚lqȄ yH`¬„t`LpDm ‚^`ƒso`Lkšmutmuq^mut›y{p6¦J´ep3~J`Lqlmc„ tmu`Ls}¥=„ `8~^soy{~SyPk £`Qk musµ¢œŠqlŸ ‚^`8‚6« ¶ 6¸ º   »šAŒ GGP¼P½-` mc‚l` =·^¸  ^·   =»nŒ GG=GP½¦ 3, 3. . . . . Ë®ÌÍ6ËÏÎ.

(60) ŒPŒ.  

(61)  

(62)          !"# $&%'! 

(63) (. @ 0O 0 K• / ÅP * —Å0 * / à 0* *H”LÃA0®ÃQ•¨Ã0Ç /  ¯ pÀ‚l`¡ª®y{q sup^t›s8‚l`Lk8`Qknmot_œmotyPp kƒŠp {£jDmutwvDq^`Lk8‚l` „yH` ¬„ t›`pDm ‚^`ƒso`Lkšmutmuq^mut›y{p6²Dp^y{qJk¨znqJknmot­¯ yPp k Ž^sot]L¢{`_=`LpPm‚^ŠpJk „`c~ {so{‘{sŠ~^\ `}£`8„\^yPt­ŸvDq^tW`Lkšm ªÇ{t­m ‚^`ƒso` mo`p^t›s q^p^`‚^r ¯ p^tmut›y{p,rLp^`so‘{rmutwvPq `8‚^q,„yH` ¬„ t›`pDm}‚l`#so`LkšmutmuqlmotyPp6¦ ± `mšmu`‚^r ¯ p^tmut›y{p0¡rmur8ª®y{so_Š£›t›kur`ƒ~ {s  ¹¸$·©»AŠ‹P‹{‹P½ ¦lc`#£w=_=¿_=`#_Šp^t›]so`#vPq `#~JyPq^s £` „yH` ¬„ t›`pDm ‚l`cxyPt›kokuy{p6²ŠyPpkšq ~^~JyDkš`}vDq^`c£`ƒ„\^yl„ kš`c‚^rL„ yP_=~JyDkš` `Lp'‚l`q^Ÿ¡~Srsotyl‚l`QkO‚ltwknmotpJ„mu`Qk Dq^p^` ~Srsot›yH‚^`e‚l`ƒ„ y{_=~^so`LkokutyPp `m q^p `c~Srsotyl‚l`ƒ‚l`cso`LkšmutmuqlmotyPp ¦l§6`ƒ„Šsosor}‚lq„yD`¬„ t›`pDm ‚l` so`Lkšmutmuq^mut›y{p'`Qknm}{£yPsok ‚lr ¯ p [0,t6„ ty{]_=_=`ƒ£`8sŠ~^~Sy{sum ‚lqmusµ¢œŠt›£S‚^`ƒ£A[t« ` žW,y{tsum ] p^yPsu_{£Y² F Šq,„ yPq^sok ‚l`ƒ£› so`Lkšmutmuq^mut›y{p,kšq^s}„`£›q^t¨‚l`#£w=„ yP_¡~ su`QkukutyPp6²lkšyPt­m . c. c. f. n. e2∗ =. y. Wnr Wnc. tf. Z. Fn vn dt. = Ztctc. Fn vn dt. »®‰D½. `Lkšm}£w¢Htmu`Qkuku`8su`L£›Šmut›¢{`ƒp^y{so_Š£›`8‚^q3~Sy{t›pDm}‚lqȄ y{pDm{„mQ¦ ± `mšmu`‚^r ¯ p^tmut›y{pȄy{_=~JyPsšmo`8~^£qJkšt›`q^sk µ¢œŠpDmo{‘{`Qk²HvDq^t¨kuy{pDm £`Qk kšq^t›¢œŠpDmok , b}p^`0‚lr¯ p^tmut›y{p rp `so‘{r mot›vDq^`,ku`_9Ž £`3muyPqlm'‚« ŠŽSy{s‚ pJœmuq su`L££›`Èkšt £A« yPp kšyPq^\ Štmu`ÈvDq {£t¯ `s=£›`Lk ~J`Lsšmo`Lk rLp^`so‘{rmutwvDq^`Lk £›y{sk ‚« q p,„\ yH„{¦ 3 ¾Op9„Pk¨‚l` „\^yl„k‚ltso`L„ mokL²L‚l` „\^yl„kku{p kª®soyŠmumu`_=`LpPmy{q`Lp „ yPsu`O‚^{p k6£›` „L{k¨y #£›`-‘{£›twkuku`_=`pDm¨`Qknm q^p^tw‚lt›su`Q„mut›y{p p^`£A²S„` mumu`9‚lr¯ p^tmut›y{p0rLp^`so‘{rmutwvDq^`9„ y YpJ„ tw‚l`µ¢{`Q„8£`Qkc‚lr¯ p^tmut›y{p ke~^£›q k}q kuq^`L££›`Lk ‚l`Lkc„ yH` ¬„ t›`pDmk ‚l`#a}` moy{p,` mc‚^`#xyPt›kokuy{p6¦ 9  ± ` mšmo`‚lr¯ p^tmut›y{pÈ`Qknme„y{\^rLsu`LpDmu`‚« q^p0~Sy{t›pDme‚l`¢Hq^`rLp^`so‘{rmutwvDq^`kšt¨mo{p^‘{`LpPmot`L££›`_=`LpPmQ² £w‚ltwkn¤ kšt›~ Šmut›y{pÀ`Lkšm9kš`Lq^£›`_=`pDm9‚lq^`{q ª®soyŠmumu`L_¡`LpDmL¦´epÀ`pDmo`p ‚"~ {s#£›ÈvDq^`£wÈ„ yP_¡~SyPkoŠpDmo`9mŠpl¤ ‘{`LpPmot`L££›`‚^`9£w¢Ht­mo`Lkokš`9su`L£›Šmut›¢{`p6« `p ‘{`pJ‚lsu`9~ {kƒ‚l`‚^t›kokšt›~ Šmut›y{pÈt›p^r£w{kšmutwvDq^`»Ç~^£›Pknmot›„t­mor9yPq ¢Ht›ko„ yDkštmurµ½O‚^{p k-£›`ƒ_=ŠmurLsutwŠq6¦l± ` mumu`ƒ\DjH~SyŠmo\^]Lku`c`Qknm¢{rLsut¯ r`ekštW£w9kuy{q^~^£›`Lkoku` mo{p^‘{`LpPmot`L££›`c`Qknm p^r‘P£t›‘{rL`8y{q,kšt6£›`Lk ‚^r ª®y{so_œmotyPp k moŠp ‘{`pDmot`L££›`Lk ‚l`Qk}kuy{£›t›‚l`Qk su`Qknmo`pDm r£w{kšmutwvPq `LkL¦ hHy{qJk „` mšmo`e\HjH~SyŠmu\ ]Lku`{²{£›`8„ yH` ¬„ t›`pDm‚l`cso`LkšmutmuqlmotyPpso`~^sorLku`pDmu`eŠ£›y{skR£Y« `pJkš`L_9Ž^£›`e‚l`e£›‚ltwkn¤ kšt›~ Šmut›y{p™‚^q^`3{qlŸ—~^\^rLp^y{_=]Lp^`Lktp r£w{kšmutwvPq `Lk=‚^ŠpJk9£›`Lk¡_œmorsot›{qlŸ¦¾O£›£›`3~S`so_=` m‚ly{pJ„‚l` ‚ly{p p^`s}‚l`Qk`Lkšmut›_œmut›y{pJk ‚lqȄ yH` ¬„ t›`pDm}‚l`8so`LkšmutmuqlmotyPp3vDq^t¨kuy{pDmq^p^twvDq^`_=`pDmc‚lrL~J`Lp ‚^{pPmo`Lk ‚l`Lk'„Šs{„ murLsutwknmot›vDq^`Qk=‚l`Lk=_œmorsot›{qlŸ `m'‚l`È£›À‘PryP_¡rmusot`,‚l`È£wÀÊyPp^`Ȃl`0„ yPpPm{„ mL¦ ± `mšmu` ‚lr ¯Jp^t­motyPp,`Lkšmc‚ly{p „8t›p ‚lrL~J`Lp ‚^{pPmo`‚lq3ª®suy{mšmo`_=`pDm}` mc‚^`#£›=„ yPpl¯ ‘Pq^soŠmut›y{p3„ t›p^r_œmot›vDq^`‚^q kšjlkšmu]L_¡`P¦ ± `mšmu`e‚lr ¯ p t­motyPp6²PPkukuyl„ t›r` ¥8£Y« \HjH~Jy{mu\^]Qkš`}‚l` p y{p‚ltwkukut~Jœmut›¢Ht­mormo{p^‘{`LpPmo` `p‚l`L\^y{skO‚lq¡ª®soyŠmšmo` ¤ _=`LpPmQ²P~S`so_=` m‚l`ƒ‚^y{p^p^`Ls ‚l`Qk-`Qknmot_Šmut›y{p k ‚l`e„yD`¬„ t›`pDm ‚l`esu`Qknmot­moqlmut›y{pvPq tSkuy{pDm t›p ‚lrL~J`Lp ‚^{pPmo`Lk ‚^qª®soyŠmšmo`_=`pDm` mR‚l` £›e„ t›p^r_œmot›vDq^`‚lq¡„\^yl„Š¦Š± y{_=_=` p^yPq k£` ¢{`Lsusoy{p k‚^ŠpJk¨£wekuq^tmu`P²Q`L££›` ~J`Lsu_=` m ‚^y{p „‚« `Lkšmut›_=`s£›`'„yD`¬„ t›`pDm9‚l`so`LkšmutmuqlmotyPpÀ` m9£›`Lk#`žSyPsšmk{kokuyH„trQk#Šq—„\^yl„kuq^sq^p³~ suyPŽ^£]L_=` ‚6« t›p ‚l`LpPmœmotyPp©‚lt›su`Q„mo`=‚^`=‚^`qlŸ „y{so~ k¦ƒŠp k8£›`Lkƒ~ {sšmot`Qk8kšq^t›¢œŠpDmu`Qk²Wp^yPq k8Š£›£yPp k8‚ly{pJ„~ suyP~JyDkš`Ls ‚^`Lk_¡yl‚l]L£`Qk9q p^t›‚^tso`L„ mut›y{p^p^`L£›k,»Ykšq^t›¢œŠpDm£w ‚^tso`L„ mut›y{p—p^yPsu_{£`µ½‚l`,„ yPpPm{„ mL²vDq^t~Sy{q^sosoy{pDm9¿ mosu` `Ÿl~^£yPt­mo`s}‚^{p k ‚l`Qk „ t›p^r_œmot›vDq^`Qk~^£›q k ¢œŠsotrL`Lkkut6£Y« \HjH~Jy{mu\^]Qkš`ƒª®y{pJ‚^Š_=`pDmŠ£›`ƒ`Qknm ¢Prsot­¯ rL`{¦ 0. vn. ÍÍ ÒT'UWV

(64) XY.

(65) Œµ  . W!   !  ,     

Références

Documents relatifs

1) La recherche des victimations dans les établissements scolaires, à commencer par la Martinique et la Guadeloupe (territoires français d’Amérique), puis sur les

Repérer les signes, les traces et les discours de la commande au sein des espaces de l’édition professionnelle, comme nous l’avons fait pour le cas particulier des éditions du

Dans ce contexte, afin de venir en aide aux différentes parties prenantes présentes sur le terrain de la collabora- tion et afin d’appuyer les décideurs dans leur

can observe that it is composed of three layers: (i) service instance layer, which represents the services, denoted by a service instance; (ii) network slice instance layer,

Les deux indicateurs précédents (encadrés 1 et 2) donnent la synthèse des asymétries existant entre les structures d’exportation, par branche et par destination, d’un PECO et

dant, il décrit les utilisateurs de covoiturage comme des personnes « militantes » ou « associatives » et leur pratique du covoiturage s’apparente plus à la mise en commun

Para um diagnóstico preliminar do nível de resíduos presentes nos frutos de mamão comercializados no atacado de São Paulo se montou uma parceria entre os projetos “Otimização

34 Although the radical cyclization route was a useful approach for the synthesis of helicenes due to the facile preparation of the stilbene-type starting material and