Parallel Extension of a Dynamic Performance Forecasting Tool
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Parallel Extension of a Dynamic Performance Forecasting Tool Eddy Caron, Fr´ed´eric Suter. No 4470 June 2002. ISSN 0249-6399. ISRN INRIA/RR--4470--FR+ENG. ` THEME 1. apport de recherche.
(3)
(4)
(5) !"#$% &'("#) *+ #),-/.0! 1 2(23457698;:&<>=?6A@B2(@C69DFEHGIJLKC6 M&NPOQRSUTWV XAYZRA[]\_^`RabYZc_YdaeOQRAY f>gehjidRakV RAlm[]f Vb[jnonph]gZakq_RrgZR9stNoRgtstNoRvuw]x]x_y'z{TWlm[Lc+|]z]zB|rTSL}n7[j~]R9Y. ` A'o ]] M&NoY,[jgZaZsR>nogeRAYZRuBaeY[jurR^aZRAuPYZhCuhjaZNoR)7ogt[jgec aehkNP[ju7q_RnP[jgt[jRAjgeh]\_aeuoR9Y pY&[q_cuP[]Qsn7RAghCgZQ![]uPsRbh]geRAs[CYdaeuP~aZhhCpu[QRat[]sh]Qno\_aeuo~RugZhCuoQRuBaA(kRAgZRUR nPgZhCn7hBYRraeh+shCQouoRR9YdaeQ![jaZh]uPYb~]]RucHp0[jph]\_arYR9 C\PRuBaZ[jsh]Qno\oae['aehCugZhC\_aZuoR9Yb[ju7q uPRad)h]ge¡[L'[j[joadc+aZh`n7[jgt[jRAgeh]\_aeuoRQhqoRYsh]QuP~¢geh]Q [juP[]c_YZYAM&NPYU[]YeYh_s[jaZh]u pRq_R£PuoRAq[]uPq+qoRae[]RAqhCu`ad)hR^o[jQnoRAY&[ju7q+'[]qo['aeRAq+R^_npRgeQRuBat[jcC ¤¥B¦;§e¨© 'ª] f(RgZh]geQ[]uPsRh]geRAsA[]YaZuo~[juPqQh_q_RuP~P«_nP[]ge[]R¬geh]\_aeuPRAYA. ®¬¯Z°²±A³&¯ ´µ°²¶F·¸ ÚÛÆÛtÜPݹ,ÞƺLÞZßÆ»½¼>ßÆßP¾F¿ÁàÔÀáe¾&â9㻽äZ¼åeÂtæýçZ¼FâPÄàèÆÂdÅÆéÂtÞe»½êLÃÇëZÂtìLÈLíý¿Ât¼)ÂÉÊ¿d¼F¿ÂtÉÌËFº`ÉÊ¿dÍjÄÆÉʾ ÄtÎ,¾ÌºL¿bÏ_ÂtÈjÄÆÉFÂe¾ÌÄÆ»½ÉÌ¿UÐL¿kÃÑ ÒÔÓ9ÎÄÆÉÊÕkÂe¾Ì»½ÖA×L¿kÐL×ØPÂtÉÌÂtýýÙdý»½¼FÕ ¿. Unit´e de recherche INRIA Rhˆone-Alpes 655, avenue de l’Europe, 38330 MONTBONNOT ST MARTIN (France) T´el´ephone : 04 76 61 52 00 - International : +33 4 76 61 52 00 T´el´ecopie : 04 76 61 52 52 - International : +33 4 76 61 52 52.
(6) %( +`
(7) +#+!+" + { &('?"# Ra[jgZaZsRnogZX9YRAuBaZR\ouoRR^aeRuPYZhCu qoR[oohjaeNoOA B\oR`p
(8) nph]\PgU[~]R9YdaehCu q_R geh]\oaZuoRAYnP[jgt[jOAR9YHpRAYa\ou h]\_ae&q_R¢nogeXAqosaZh]u q_cuP[]Q B\oR`qoR`npRgZh]geQ[]uPsR9Yqo[]uPY\Pu RAuBgeh]uouoQRAuCaUq_RQRat[]shCQno\_aZuo~7 khC\PYknPgZhCn7hBYhCuPY s(q_Rsh]QPuoRAgbRAYbRAYaZQ[jaZh]uPYbh]\PgZuoRAY n7[jg7;shCuPsRAgZu7[juBabRAYUgZhC\_aZuoR9YYZXA B\oRAuCaeRARAYUq_Rs[js\PRaURAYUq_Ynph]uPo aeXAYrq_\HgeXAYZRA[]\m[L]R9s qoRAYQh_q_OAR9YYeY\PY)q_RU [ju7[jcYZR] RaZaZRr[]YeYh_s[jaZh]u!YRAge[q_X£7uoRC«_q_Xat[jXRUY\og&q_RA\_^¢R^_RQnoRAYRa '[]q_XRrR^npXgeQRAuBae[jRQRAuCa9 ! © 9 § # " fgZX9q_saZh]uq_RrnpRgZh]geQ[]uPsR9Y)RakQh_q_XYe['aehCu,«_geh]\_aeuoR9Y&nP[jgt[jORAYA.
(9)
(10) 0p . ( +# M&N7[juo¡_YaZh QRae[Csh]Qno\oaZuo~"!Sj«>|_«#%$kaYuoh' nphCYeYoR`aeh{npRgZh]geQ shCQnP\_ae[jaZh]uPYh]u hCgZq q_R`YZnogeRA[Cq{Q![CstNouPRAYAmM&NoYYaZNoR+nogeh]QYZR!hjk[N\o~CR`shCQno\_ae[jaZh]uP[]>nph'RAg7R9s[]\PYR`QhBYda uBaZRAge[CsÆaZ]R!Q![CstNouPRAY[]gZR!\ou7q_Rg &F\7YR9q¬lmh]geRh']RAgA«sh]Qno\oae['aehCuPYsh]\oq07R`n7RAghCgZQRAq0hCu0aZNoR QhBYda[]nonogeh]noge['aZRsh]Qno\_aeRg9( ')\_arY\PstNmYZh]\_aehCuPYb[]gZRqo* )¢s\P aUaZh`[CstNoR]R NoR¡CRRAnouP~¢~]hh_q R)¢sRuPsc], +uoRrhjaZNPRgZR9[]YZh]uPY)Y&aZNP[ja aZNoR9YRrQ![]stNPuoR9Y s[]uRA aeNoRg pR)h]ge¡Yae[jaZh]uPYA«_s\PYaZRgtY&h]g RA]RAu{YZNP[jgeRAqHQRAQh]gecnP[jgt[jRAsh]Qno\_aeRgtYM&NoYrNoRaeRgeh]~]RAuoRadcu{aZRAgZQ!Yrh])shCQno\_aZuo~n7h')Rg []uPquoRad)h]ge¡shCuouoRAsaZ adcQnoR9YaZNP[ja?aZNoR R^R9s\_aehCuaeQR h]p[UgZhC\_aZuoR&Q![Lc'[jgec[juPqYaZgeh]uo~Cc qoRnpRuPqoYh]umaZNoRR^_RAs\_aZh]unP[jah]geQ. -vaZgeRuPqmhj>QRat[]shCQno\_aZuo~7«;sA[jR90q /,1123456879 :;45 <:=>@?j«;[jh'kY&Q\oaZq_Yesnou7[jgec+[jnPnos[jaZh]uPY aZh¢[]sAsR9YZY sh]Qno\_at['aZh]u7[jYZRge]RAgeY)[![]~]RAuCatY M&NPRAYZR[j~CRuBaeY[jgeR>ustNP[]gZ~CR>hjPaZNoR&stNoh]sRhjoaeNoR)QhBYda([jnonPgZhCnogZ['aeRYZRge]Rg[juPqhj_at[]YZ¡YZstNoR9q_\ouP~ []uPq{no[CsRAQRAuBaAB AÁu YZ\PstN{[sh]uBaZR^Bara7R9sh]QR9YCRgecQnph]gZae[]uCaraehN7[L]Raehh]Y[joRaehsh]RAsÆa ¡uoh' RAqo~]R[]7hC\_aYZRge]RgtYb[jagZ\ouBaeQRaZh+h]geRAsA[]YaaeNoR!R^_R9s\_aehCuHaeQRAYrh]aeNoRae[]YZ¡_YUaZhYestNoRA@q & \PRCD Co\ogZaZNPRgeQhCgZRC«,u0[QRat[]sh]Qno\_aeuo~msh]uBaZR^aA«)RQ~CNCaqoRA[j aeN NPRAge[]gestNos[](uoRad)h]ge¡_Y h]NoRaZRAgZhC~]RuPRh]\7Ysh]Qno\_aeRgtY aeNNPRAge[]gestNos[]QRAQhCgZRAYAF E>]RAu Yh]Ôad)[]gZRnP[]st¡'[]~]RAYR^_Yda aeh [Cs B\ogZR`u_hCgZQ![jaZh]u
(11) uoRARAq_R9q []7hC\_aphjaeN sh]Qno\_aeRg![juPq uoRad)h]ge¡ \PYuo~ Qh]uoaZhCgZuo~aeRAstGN & uP B\oR9(Y !Sx $F«aeNoRc¢h]ÔaZRAu`\PYZRI[ H7[ja&[]uPq+Noh]Qh]~CRuoRAh]\PYRAhj[QRat[]sh]Qno\_aeuo~YZcYaZRAQ(Mh7R shBYRAgaehgeRA[]adcRNP[L]RbaZhQhqoR,shCQno\_ae[jaZh]u¢geh]\oaZuoRAY) aZNgZRA~C[jgtqaZhaZNPRUsh]Qno\_aeRg& NostN ,R^_RAs\_aZRUaeNoRQ AÁu aZNPR!uoR^aYZRAsÆaehCu0R~]]R![]u{h'CRgeBR hjpK JC7[]YBa -k~]RAuBa BY Lc_YdaeRQ M&QRg MN!½y_«>S] S $F« aeNoRmq_cuP[]Qsn7RAghCgZQ![]uPsR+h]geRAsA[]YaZuo~Haehh] )RN7[L]RR^aZRAuPq_R9q¬F AÁuYZRAsaZh]Fu Rnogeh]nphCYZR[ sh]Qou7['aZh]upRad)RRAuqocBu7[jQsqo['at[![]s B\oYZ aehCu[]uPqsh_q_R[]uP[jc_YY& NostN pRaeNoRshCgZRh] aeNoRR^aZRAuPYZhCu
(12) hj¢p aZh0NP[ju7q_RnP[]ge[]R)gZhC\_aZuoR9Y M&NPRu )Rq_Rat[j&aZNoRR^aeRuPYZhCu hCu
(13) ad)h R^o[jQnoRAYUhj)nP[jgt[jRA(gZhC\_aZuoRAYUu YZRAsaZh]u xPO CuP[]cmu YZRAsaZh]u }`)R~]]RYhCQRR^npRgeQRAuBae[j geRAYZ\oaeY&'[jqo['aeuo~hC\ogk[jnonPgZhB[]stN, . & R <T VUXWZY[ p\J6CP[CYdaB-b~]RuBa YILc_YaZRAQ$M&QRAg5MO!ÇyB«>SCS$Y[q_cuP[jQsn7RAghCgZQ![ju7sRh]geRAsA[]YaZuo~`aehh]?u0[ QRae[]sh]Qno\_aeuP~{RAuBgZhCuoQRuBa!q_RAYZ~CuoRAq
(14) aZh0NP[]uPq_R+aeNoRAYZRQnph]gZae[juBa!YZYZ\oRAYAZ AÁuoh]geQ[jaZh]u[]s & B\ogeRAq
(15) c7%sh]uPsRgeuPYYR9 B\oRuBaZ[j sh]Qno\_at['aZh]u gZhC\_aZuoR9Y![juPq
(16) aZNoRAg!R^R9s\_aehCu nP[jah]geQ!Y CPh]g R^_[]QnoRrabs[]u+pR\PYZR\o¬aeh![!YZstNoR9q_\oRg)aZh!hCn_aZQ ]ARUae[]YZ¡¢Q![jnPnouP~P -Y+YZNoh' uK u C~]\PgZR SC«b7 Y`shCQn7hBYR9qhjradh Q[]u Qh_q_\oRAY`h ^;RgeuP~ [0\PYZRXg -b_f A` aeNoaR 64X>b0b45c dGef Qh_q_\PR![ju7qHaeNogR >h9iO4j>kl4mcdGe6 Qh_q_\oR]!M&NoRhCgZQRg Qh_q_RAY(aeNoR aeQRb[]uPqYnP[CsR uoRARAqoY>hj,[YR9 B\oRuBaZ[josh]Qno\_at['aehCu!gZhC\_aZuoR h]u![r~CCRuQ[CstNouoR&h]g [+~]]RAu{YZRahj)nP[jgt[jQRaZRgtYA«p NPRaeNoR!['aaeRgUh]geRAsA[]YaeYbaZNoRpRNP[Lh]grhj)q_cuP[jQs[jcmstNP[juo~CuP~ geRAYZh]\PgesRAYAn« =op?qo rhCgZ¡hC[]q,«)7[juPq_ qaeN,«kQRQh]gec\PYRC«Aep gZRARAY`h]u%h't sBRCRbYZhjÔad&[jgeR n7[]st¡'[j~CRAYAu CgtYda9w« vyx-bz f !S9%z $ Y\PYZRAq
(17) aZh YaZh]geR+Yae[jaZsqo['at[o M&NoRAu
(18) aeh0[Cs B\ogZRq_cuP[jQs+qP['ae[ p+YRAYeYRAuCae[]c7[]YZRAqh]uaeNoR {\LgJ kRadhCgZB¡ {{R9['aZNPRtg L_RgeBs%R Mt!SAx $²«B[nPgZh]idRAsÆa>uoaZ['aeRAq!['a |buo]RgtYZ adch] []h]geuon [ L_[j}u xRA~]hP~ A²aY>[q_YdaegZo\_aeRAq!YZc_YdaeRQvaeNP['a>npRgehqosA[jcQhCuoaZh]gtY?[ju7q qocBu7[jQsA[jchCgZR9s[]YaeYnpRgZh]geQ[]uPsRhj'[]gZh]\PYbuoRad)h]ge¡[juPq{shCQnP\_ae[jaZh]uP[]geRAYZh]\ogtsR9Y {\L P. QSR. Ó 5.
(19) x.
(20) o mr,o72dG . As [juQhCuo aeh]g(YRA]RAge[]]geRAYZh]\ogtsR9Y,uPs\Pq_uo~sh]QQ\PuosA['aehCuPYuo¡_Y« fw|«jq_Y¡YZnP[]sR[ju7qQRQh]gec] lmh]geRh']RAgA« {\LY&uoh]akh]uoc+[]oRUaeh!h]_at[juQR9[]YZ\ogZRAQRuBaeYA« asA[ju[jYhhCgZR9s[]Ya&aZNoRRA]hC\_aehCu h]aeNoRQh]uoaZhCgZR9q+YZc_YdaeRQ p R^aZRAuPqoY {\L[]Y aU[]h'kY)aZh+q_RaeRgeQuoRaeNoRhCgZRaZs[],uoRR9qoY h]?sh]Qno\_at['aehCugZhC\_aZuoRAY uaZRAgZQ!Ybhj?R^_RAs\_aZh]uaeQR[]uPqQRQh]gec]&M&NoRs\ogegZRAuCakCRgtYh]uh]7 h]uPc+NP[juPqoR9YkgeR~]\P[]g YZRA B\oRAuBaZ[j,geh]\_aeuPRAYk¡]RaeNohCYZRhj?aeNoRq_RAuPYZRuoR9[jgb[]~CRogt[ogt[jgeXc '<v-(L! $²kkh')R]RAg '<vy-.L ¡CRgeuoRYrgeRnogeRAYZRuBaraZNoR`NoRA[]gahj&Q![juc{[]nonosA['aehCuPY«RAYZn7R9s[jc{u0u\oQRges[jYQ\o['aehCu,`M&NoR []nonogehC[CstNstNohBYRAuBc¢p+aZhhCgZR9s[]Ya>R^_R9s\_aehCuaZQR9Yh],Y\PstN!geh]\oaZuoRAY?Y)[ju!R^aeRuPYZCR 7RAuPstGN & Q![]gZ¡ h]h'R9q0Bc
(21) [Hn7hCcuohCQ[]geR~CgZR9YZYZhCu, AÁuPq_RR9q aeNoY¡uPq
(22) h]kgZhC\_aZuoRAYYh]ÔaZRAu YaZgeh]uo~Cc hCn_aZQ ]ARAq aZN geR~B[jgtq
(23) aeh aZNoR{no['ahCgZQ«&RaZNPRg`c]RAuPq_h]gtYh]g`Bc[j\oaZh]Q![jaZssh_q_Rm~CRuoRAge[ & aehCu !=S %$²a - sh_q_R`[]uP[jc_YYUaZh£7uPq [ju
(24) [Css\Pge[jaZRQhqoR>aeN\PYpRAsh]QRAYaZRAqohC\PYa Co\PgaeNoRgeQh]geR aeNohCYZRhCn_aZQ ]9['aehCuPY[]gZRhjÔaeRuH7[]YZRAqmhCuH[+7RaaZRAgr\PYRhjQRAQh]gecsA[]stNoR9YrM&NoRAu{[ju{R^aZRAuPYZCR pRu7stNoQ![jge¡hj)[sh]Qno\_aeRgr >[]st¡h])[]sAs\ogt[]sc7R9s[j\7YRaZNPRu\oQ7RAghj, HPhC[jaZuo~+hCn7RAge[jaZh]uPY aeNP['aUs[jupR[]stNoRCRAqh]u[!sh]Qno\_aeRgkY uoh]ashCuPYdat[juBak[]Y aq_RAn7RAuPqoYbh]uNoh' [gZhC\_aZuoR\PYZRAY h] sA[]stNoRC AÁuaeNoYknP[]n7RAgkRhs\PYkhCuaZNoRuBaZRA~]gt['aehCuh]?nP[jgt[jRA,geh]\_aeuoRN7[juPq_uo~¢uCaeh+p M&NoR9YR geh]\oaZuoRAY)[jgeRkNP[]geq_RAg>aehaeQRr[juPqaeN\PYaZhpRu7stNoQ![jge¡P\_a)R9[]YZRAg>aeh[ju7[jqc ]AR]~ AÁuPq_RARAq!aeNoRc!h]ÔaZRAu sA[ju0pR!gZR9q_\PsR9q{aZhm[YZ\PssRAYeYh]u hjkshCQno\_ae[jaZh]u [ju7q sh]QQ\PuosA['aehCu{noN7[]YZRAYA h]Qno\_at['aehCu nPNP[]YZRAY¢[]gZR{sh]QnphCYZRAqhjsA[jY¢aZh
(25) hCuoRmhCg`YRA]RAge[]bYR9 B\oRuBaZ[jgZhC\_aZuoR9Y! NoR sh]QQ\ouos['aehCu nPNP[]YZRAY)[jgeRbQ![]qoRh]n7hCuBa sCaZh sBnph]uBah]g&~ChCP[jpR^ostNP[]uo~]R9YM&Quo~pRAsh]QRAY)RA]Ru+Qh]geRkaZR9q_h]\PY _R>[CqoqaZNoRNP[juPqouo~ hj_qo[jae[&geRAq_YdaegZo\_aehCu[juPqaZNPR>stNoh]sR?h]CaeNoR>gZaZ\7[jjnogeh_sR9YZYZh]g;~]geq NPRgeR sh]Qno\_at['aehCuPY [jgeRrn7RAghCgZQRAq,w Lh abYZRRAQYkn7hBYZYZPR[ju7q+uBaZRAgZR9Ydaeuo~aehsh]QouPRsh_q_R[juP[]c_YZY []uPq+u_hCgZQ![jaZh]u~]]RucpH[]7hC\_abYR9 B\oRuBaZ[j¬R^_RAs\oaZh]u+aZQR9Yk[ju7q`uoRadhCgZ¡¢[L'[][jo adcC VUXWZY[ + $% ¢+ Mh h]oae[ju[kYe['aeYcuo~kYestNoR9q_\oR?h]g[knP[jgt[jRA][jnPnos[jaZh]uraYQ![juPqo[jaZhCgZcbaZhkuoaZ[jcrq_RaeRgeQuoR aeNoRsh]Qno\_at['aehCuraZQR)hj_R9[]stNhjoaeYae[CY¡_Y[juPqsh]QQ\ouPsA['aZh]ushCYaeYuBaZgeh_q_\PsRAqcUnP[jgt[jRAYZQ M&NPRQhCYa>shCQQhCuQRaeNoh_qaehrqoRaZRAgZQuoRaZNoR9YR)aZQRAY(YaZhrq_RAYesge7RaZNoR []nonosA['aZh]u[juPqQh_q_R aeNoRnP[]ge[]R¬shCQno\_aZRAg&aZNP[jakR^_RAs\_aZR9Y)aZNoRgeh]\oaZuoR] M&NoRQh_q_RAuo~!hj?[nP[jgt[jR,shCQno\_aZRAgk[juPqQh]geRrnogeRAsYZRc!hj?sh]QQ\ouos['aehCushCYaeY sA[ju7R sh]uPYZq_RgeRAqgeh]Q q_ ^pRAgZRAuBanph]uCatYbh]>RA. CgeYa)R~]uohCgZRsh]QQ\PuosA['aehCumshCYaeY[¢nP[]ge[]R geh]\oaZuoRs[jupRQh_q_RRAq\PYZuP~ -bQ!qo[jNo Yk[L>M&NoYk¡BuPqh]Qh_q_RY uPhjakgeRA[jYdaesUu+aeNoRsA[]YZR h])q_YaZgeo\oaZRAq QRQhCgZcH[]gestNP aeRAsÆae\ogeRAYAO AÁu7q_RR9q{hCu YZ\PstN0no['aZh]geQYsh]QQ\PuosA['aehCuPYUgZRAnogZR9YRAuBa []u0Qnph]gZae[juBanP[]gah]&aZNoR!aehjat[j>R^R9s\_aehCu aZQR`hjk[ju [jnPnos[jaZh]u,a Co\PgaeNoRgeQh]geRaeNoYQh_q_R qohBR9Y)uohja [jh'%aZhNP[juPqoRUaZNPRQnP[]sa&h]nogeh_sR9YZYZh]g~]geq+YNP[]n7RUh]u+gZhC\_aZuoRUn7RAghCgZQ![]uPsRC_ +baeNoRg Qh_q_RAY¡]8R >b h !S9%| $ []uP q ?% ! x $&ae[]¡]R+sh]QQ\PuosA['aehCuPYuBaZh{[Cssh]\ouBaA0M&NoR+h]geQRg[CY[ sh]uPYae[]uBarq_RA[L c
(26) m NoRaZNoR['aZaZRgsh]uPYZq_RgtYh]\ograeNoRhCgZRaZs[j(nP[]ge[]QRaZRAge;Y `kaege[]uPYZQYeYh]uaeQR geh]Q [+nogeh_sRAYeYZh]gaZh[juHh]aZNoRA}g J,M«shCQno\_ae[jaZh]u{h']RgeNoR9[]qh][+sh]QQ\PuosA['aehC"u JM«,uoRadhCgZ¡ 7[juPq_ qae0N JM)[juPq`u\oQpRg&hjnogZh_sRAYeYhCge(Y JIMÆ>bh'RA]RAg>aZNPRAYZRQh_q_RY)uBaegZh_q_\PsRRAYeYh]g&Qh]geR n7[jgt[jQRaeRgtYaeNP[ju NP[jakY&uoR9sR9YZYe[jgecaZhh]oae[juRAYaZQ!['aZh]uYZG\ )¢sRuBaZc`shCYZRUaZh!geRA[]adc] . Ò~,Ò.
(27)
(28) 0p. } Client Application. Knows about Computer CPU speed Available memory Batch System Network Bandwidth Latency Topology Protocol Computations Feasibility Needed space Needed time. 1. 4. FAST. Parallel Extension Fast API Static Data Acquisition 2 LDAP. Dynamic Data Acquisition. Knows about Computer Status (up/down) CPU load Memory load Batch status Network Bandwidth Latency. 3 NWS. Low Level Software. C~]\ogeRSb`w+]RAgZRhjaZNoRpm[jgtstNoaZRAsaZ\ogeRb aZN+aZNPRUR^aZRu7Yh]u`aZhNP[ju7q_RUnP[]ge[]R;geh]\_aeuoR9Y. M&NoRU£PgtYa)CRgtYh]u!h]aZNPRR^BaeRuPYZh]u`hCuoc!NP[juPqoR9Y)YZh]QRUgZhC\_aZuoR9Yh]aZNPRnP[]ge[]R¬q_RAuPYZRuPRA[jg ][ ~CRogt[ogt[jgecjLos[bv-kf - 9Coh]gUY\7stNmgZhC\_aZuoR9Y aZNPRq_R9YZsgZn_aZh]umYaZRAnmh]uPcshCuPYYaeYku{qoRaZRAg & Quouo~ NostN YZRA B\oRAuCae[]>shC\ouBaZRgenP[]gatYU[]gZR!sA[jR9q¬«¬aZNPRgs[]uP~n7[jgt[jQRaeRgtYOJ o ;o r&qo['at[Y ]R9Y« Q\oaZnocuo~rÊ[]saZhCgeYA«'aZgt[ju7YnphCYZ aehCu,«_AmM«jaZNPRbshCQQ\ouos[jaZh]uYZstNoRAQRAY?[ju7qaeNoRk[jQhC\ouBa>hjpqP['ae[ R^ostNP[juo~CRAq¬ +uPsRraZNoY[]uP[jc_YY&YbshCQnoRaZR9qaZNoRsh]Qno\oae['aehCunP[jgZas[]uRA[]YZc7Rh]geRAs[CYdaeRAq¬ AÁu7q_RR9q`YZuPsRrpY&[joRbaehR9YdaeQ![jaZRURA[]stN+YR9 C\PRuBaZ[j;shC\ouBaZRgenP[]ga9«pms[]Y)[jgeRRAuoh]\o~CN!aZh qoRaZRAgZQuoRUaZNoRAgbR^_RAs\_aZh]u+aZQRAYA CP\ogaeNoRgeQh]geR nogeh_sR9YZYZh]gtYmR^R9s\_aeuP~ [ L_s[ vy-k f - sh_q_R N7[L]R
(29) aeh pRNoh]QhC~]RuPRh]\7YaZh [CstNoR]R~]hh_qmnpRgZh]geQ![juPsR]} LQ[jgecaeNoRuoRad)h]ge¡pRad)RRu{aZNPRAYZR!nogZh_sRAYeYhCgeYU[jYhNP[CYbaeh7R NPh]Qh]~CRuoRAh]\PYAw A²ar[jh'kY \7Y ad)h!Q[jidh]gbYZQnP£7s[jaZh]uPYA CgtYdanogZh_sRAYeYhCgeY&pRuo~¢NohCQh]~]RAuoRhC\PYA« aeNoR`pRu7stNoQ![jge¡Buo~noN7[]YZR¢hjps[]u 7R+R^_RAs\_aZR9q h]u hCuoc h]uPR¢nogehsRAYeYhCgAM&NoRAu
(30) shCuPsRAgZGu & uo~Hsh]QQ\PuosA['aehCuPY)R¢h]uoc NP[L]RaehmQh]uoaZhCg[R geRnPgZR9YRAuCat['aeCRuo¡_YaZhHh]_at[ju
(31) [~]hh_q h'CRgeRA hjaZNoR~ChCP[j;pRNP[Lh]g9 CPh]g>aeNoRbR9YdaeQ![jaZh]u!hj,nph]uBa>aZhn7hCuBa)sh]QQ\PuosA['aehCuPY?)RstNohBYR&aeNo R !Qh_q_Rp NoRgeR YaZNoR&['aeRuPschjoaeNoRuPRad)h]ge¡p« maZNoR YZ ]ARh]oaZNPR)QR9YZYe[j~CR[ju7 q aeNoR)aZQRaehaege[]uPYRg([juRARAQRuBaA« o =o raZNoRu]RAgeYZRhj(aeNoRuoRadhCgZ¡+P[ju7q_ q_aZN, %sA[jupRq_RaZRAgZQuoRAqq_\PgZuo~!aeNoR[]uP[jc_YY NoR H[juP. q s[]u7RR9YdaeQ![jaZRAq aZNHp{sA[jYA_ AÁum[ogehC[Cqos[CYda h]npRgt['aehCu`aeNo R H[juP q shCuPYdat[juBaeY []gZR`gZRAno[CsR9q0Bc{\ouPsaZh]uPYq_RAn7RAuPq_uo~{hCu0aZNoRnogeh_sRAYeYZh]g~]geq aZh]nph]h]~C"c ! $²l A²k)R+sh]uPYZq_Rg[ ~CgZq aZ N
(32) geh'kYb[ju7q !shC\oQuPY aZNoR7RaZNoR['aZRAuPschCgU[+sh]\oQumh]
(33) Hnogeh_sR9YZYZh]gtY&aZh PgZhB[]qosA[]Ya aZNoRAgUqo['atl[ JÊ[CYZYZ\oQuo~`[!\ouP hCgZQ q_YdaegZo\_aehCu M&aeh¢nogeh_sRAYeYZh]gtY)aZNP[jaU[jgeRhCuaZNoRYZ[]QR geh'[]uPq ,pRraZNPRP[juPqo qaeN, AÁu+aZNoRYe[jQRr)[L c []uPq q_RAuohjaeRaeNoRraZQRrh]gk[uoR Ó 5.
(34)
(35) o mr,o72dG . h] !nogeh_sR9YZYZh]gtY aeh+ogehC[Cqos[CYdaaZNoRAgqo[jae[`aZhnogehsRAYeYhCgeYkaZNP[ja[jgeRh]uHaZNoR!Ye[jQRsh]\oQu,M&NoR9YR \PuPsÆaehCuPY?q_RnpRu7qqogeRAsaZch]uaZNPR QnoRQRuBat['aZh]uhj7aZNoR PgZhB[]qosA[]YaAyCPh]g?R^o[]QnPRC«jh]u[rs\PYdaeRg h]P)h]ge¡Yae[jaZh]uPYshCuouoRAsaZR9qaZNPgZhC\o~]N[UYZ atstN,«LaZNoRaZgeRR)ogehC[Cqos[CYdaY([]saZ\P[]crR^_RAs\_aZR9qhCh' uP~ [!aZgeRR]< AÁuaeNoYUs[CYR pRR9 C\7[j¬aeh H[]uPq R9 C\7[j,aeh
(36)
(37) NPRgeR mYNohC\oq`pRuBaeRgenogZRaZR9q+[CY)aZNoR['aeRuPsc!h]g hCuoRruoh_q_R[juPq [CY)aZNoR[LCRgt[j~CRkP[ju7q_ q_aZN, +\og&)h]ge¡!s[ju`aZNoRAu+pRshCuPYq_RAgZR9q!RaZNoRAgk[]Y&sRuBa&[]nonosA['aehCu`hjkph]g&[]Y&[ju+R^aZRAuPYZhCu aeh!NP[ju7q_Rn7[jgt[jRA¬gZhC\_aZuoRAYAM&NoRYZNP[Cq_RAq+nP[jgZakau C~]\ogeR!SYZNoh'kY& NoRgeRrh]\ogbhCgZ¡at[j¡]R9Y&no[]sR uaZNPRp[jgtstNoaZR9sÆaZ\PgZRCy AÁuPq_RARAqR9YdaeQ!['aehCuPY?h]7[jgeR ujidRAsÆaeRAquBaZh[Qh_q_R7sh]Quo~rgeh]Q sh_q_RU[]uP[jc_YYA +uPsRUaZNoY&sh]QouP['aehCu`npRgZh]geQR9q!aeNoRrR^_RAs\_aZh]u+aZQRUh],aZNPRUQh_q_RAR9q`nP[]ge[]R geh]\oaZuoRUsA[ju+7RrRAYaZQ!['aeRAq¢c+pm[]uPq`YaZN\PY&[L'[j[]oRbaeNogZhC\o~]N¢aZNoRpmYdat[juPqP[jgtq -k_f AÆ AÁu aeNoRuoR^aUYZRAsÆaehCuR~]]R[!R hj(aZNPRshCuBaZRuBabh](aZNoRR^aZRu7Yh]ucq_Rat[juo~¢phjaeNmR^o[jQnoRAY h]q_RAuPYZRQ[jaZge q^ sQ[jaZge ^¢Q\oaZnos[jaZh]u[juPq+aegZ[juo~C\o[jg&YhCCR] ¢" %(
(38) + "!$#&%'( "!)#*+-,).!$/0,!213.!4657'498;:, M&NPRUgeh]\oaZuoR=<.>@?.ACBD+B hjaeNoRBL_sA[bvy-bf - ogt[jgec¢npRgZh]geQ!YaeNoRnogeh_q_\PsÆa EGFIH
(39) KJ-
(40) KLM ON E NoRAgZR
(41) ( J-< JÊgZR9Yn
(42) KLM M(s[jupRJ hCgPJ;wQ JÊgZR9Yn,RL h]gPLSQ M~AÁuaZNPY(nP[]n7RAg?R)NP[LCRh_s\7YR9q hCu`aeNoR EGF J-L s[]YZRCLT UJ Y)aeNoRu[juWVX ZY Q!['aZge^;«.L [[Y\ ^$ ] Q![jaZge ^¬«_[juPq+aeNoRrgZR9Y\oa E [ V_ `] Q[jaZge ^¬-bYaeNoRAYZRQ![jaZgesRAY)[jgeRq_YdaegZo\_aeRAq`h]u+[
(43) a nPgZh_sR9YZYZh]g~]geq¢u[oh_st¡!sc_ss &[Lc! aZN[oh_st¡`YZ ]RhjRb «PshCQnP\_ae[jaZh]u+aZQRsA[ju7RR^_nogZR9YZYZRAq+[]Y c Y
(44) g h^heikj)lmhngpo JdS=M bed`f NoRAgZR
(45) Dgh^hqij)lmhng Y&~CCRuc!aZNoRrhCh' uo~`p{s[] r3s t jui9v Ch
(46) wij)lmhng@i;xug t jy Kz t juo
(47) ghZhei
(48) @g t v{o
(49) g h^hei&j)lmhngC « NoRAgZR|z t j Y hCuoR hj{aZNoR nogeh_sRAYeYZh]gtY
(50) uBCh]]R9q u aeNoR sh]Qno\oae['aehCu h]}<.>p?.ACBpB [ju7q
(51) g h^hei
(52) pg t v Y>[YaZge\PsÆae\ogeRksh]uBat[juouP~Uu_hCgZQ!['aehCu!Y\PstN![CY(aZNoRY ]R h]7aeNoRkQ!['aegZsR9Y(u]hCCRAq¬« aeNoRg&aZgt[ju7YnphCYZ aehCu,«;AZlm[jaZgesRAYnP[]YeYR9q¢u[]gZ~C\oQRuBaeYaehaeNP['apms[]¬[]gZRUhj(Y ]R~{ 0 ab hCg&aZNoRr£7geYa h]npRgt[juPq[juPq^b| ~C h]g&aeNoRYR9shCuPq`hCuoR] Mh+[Css\Pge[jaZRcRAYaZQ[jaZRaZNoRsh]QQ\ouos['aehCuaZQRaYbQn7hCgat[juBabaeh+sh]uPYZqoRgkaeNoRS<.>p?.ACBpB sh]QQ\PuosA['aehCuYestNoRAQRC -)a+R9[]stN YaZRnh]uoRmnPChja`oh_st¡sh]\oQu[ju7qh]uoRmnPChja`oh_st¡ geh' []gZRogehC[]qPs[]YaZR9qaZh[](nogeh_sRAYeYZh]gtY«¬[ju7qmuPq_RnpRu7q_RuBanogeh_q_\PsÆatYae[j¡CRnP[CsR]O-kQh]\PuCatYrhjqP['ae[ sh]QQ\PuosA['aeRAq[jgeRaeNoRyu `&V ^Y$h]gkaZNoRogehC[Cqos[CYda&hj(geh'kY [juPqnY\ n] hCg&aZNoRogZhB[]qosA[]Ya)h] aeNoR`sh]\oQuPYX E[]stN h]aeNoRAYZR¢ogehC[Cqos[CYdatYUYn7RAghCgZQRAq oh_st¡HcHPh_st¡;+M&NoR+sh]QQ\ouos['aehCu shCYa hjaeNoR=<.>p? ACBDB+gZhC\_aZuoRY)aZN\PY ¹,ºL¿?Ät¾ÌºL¿dÉËÂt¼Ì¿¼ÂtÉÊ¿¼Ì»½Õ »½ÃÇÂtÉ í Ò~,Ò.
(53)
(54) 0p. y. KVX ^Ye Y\ n]
(55) . . . cY. . JÌ|bM. bed. -YZYZ\oQuP~+aeNP['aPgZhB[]qosA[]Yah]npRgt['aehCuPYr[jgeRnpRgZh]geQRAqHh]h' uo~[+aZgeRR]« « « []uPq As [ju{7RgeRno[]sRAqcaZNPRgL[]\PRAYrq_RnpRu7q_uP~+hCu0[juPq ,M&NoRAYZRad)h`'[]gZ[jo RAYr[] gZRRA YaZQ[jaZR9q c!aeNoRrh]h' uo~`pHsA[jY r3s t jui;x s
(56) l
(57) @jzS t
(58) {v gpo
(59) pg t juo J Æ«_[ju7q r3s t jui s j$g v t Cv g@o
(60) @g t juo &J-VGL J-« NPRgeRaZNoRuo¡pRad)RRAu t {v g![ju7q
(61) @g t j Yh]uPRhj(aeNohCYZRQh]uP aeh]geRAqcHp. A²aRA[CqoYk\PYbaZh aeNoRrh]h' uo~RAYaZQ!['aehCu`hCg< >p?.ACBDBsh]QQ\ouos['aehCu+shCYa " !$#. . +*. . #&%. J. . ' $! #&%(#. . . ). .
(62) .9 c Y bd & J-VGL(aJ. . JM. "!P5.-6+-,$R0/46,"16:G'498;:, M&NPRUgeh]\oaZuoR0< > 2435 `B h]aeNoRBL_s[vy-bf9- ogt[jgec¢s[]u+pR\PYZRAq`aZh!YhCCRbaeNoRrh]h' uo~YZcYaZRAQ!Y` F*H L []uPq
(63) J0 F H L NoRAgZR
(64) J0YR9 B\P[jaZh
(65) J h]g JQÆ J Y[ ] ]
(66) ( J0 \Pnon7RAgkf7h]g 6 h')Rg&aZge[juo~C\o6 []g&f Q[jaZge ^+ NostNsA[ju7R\Puo at[jgec`hCg uohja9 [juPqnL pRuo~adh V n] ,. Q![jaZgesRAYA. 6. Upper / Lower. Left / Right. Transposition. U. L. N. U. R. T. U. L. T. U. R. N. L. L. N. L. R. T. L. L. T. L. R. N. Operation. B. =. B. = α. B. =. B. = α. A. B. A B. Case. \ αB A. /. 1. 2. \ αB. 3. /. 4. A. h]gegZR9Ynph]uPqoRuPsRm7RadRARu%'[]\oR9Y`h]s[]uP~
(67) nP[jgt[jQRaZRgtY`[]uPq%[CsÆaZ\7[jcnpRgZh]geQR9q sh]Qno\_at['aehCuPY)h]g&aeNoR=<.>82435 B+gZhC\_aZuoR] C~]\ogeR{|`. C~]\ogeR|+nogeRAYZRuBatYb~Cge[]noNos[jRA B\o'[jRuBaeYrh]-<.> 2435 B{s[]Yrq_RnpRu7q_uP~hCuHaeNoR'[j\oRAYUhjaZNoR aeNogeRRrnP[jgt[jQRaZRgtY9&:4;&<P«&=
(68) >$?4@¢[]uPqBAC4D4E&=8DqoR£Puouo~geRAYZn7R9sÆaZ]RAc` NoRaeNoRgJ Y&\ononpRgbh]g h'RAg Ó 5.
(69)
(70) o mr,o72dG . aegZ[juP~]\o[jg9« 6 YhCuHaeNoR¢RÔahCggZ~]NBaYZq_Rh]J []uPq{ ;J NP[CYraZhpRaZgt[juPYZnphCYZRAq{h]guoh]aA`M&NoR RA~CNBarnphCYeYZoRs[jYs[ju{7R!~CgZhC\onpRAqmuBaZhh]\Pgs[]YZRAYr[CYUYZNoh' u u8C~C\ogeR|oM&NPRAYZRsA[]YZRAYrs[]u []YZh 7R~]geh]\Pn7R9q
(71) uCaeh adh Ê[jQc NostN[]stNPRA]R+qo*^;RgeRuBa¢¡u7qoYhjUn7RAghCgZQ![ju7sRq_RnpRuPqouo~ hCu
(72) aeNoRYNP[]n7RhjaZNoRnogeh_sRAYeYZh]g~]geq¬ M&NoR`hCgZQRAguPs\PqoRAYs[CYR9Y [ju7q [juPq R^_RAs\_aZR Ê[CYdaeRg>hCu!gZh't s_q_h]QuP[juBa?~]geqoY«] NoR aeNoRb['aZaZRgsh]uBat[juPY>s[CYR9Y []uPq [juPq 7[]stNPRA]R pRaaeRg npRgZh]geQ![juPsRhCush]\oQ@u sqoh]Qu7[juBa ~]geqoYA Mhm[juP[]@c ]AR Nc{YZh]QR!YZNP[jnpRAY[]gZR!sRA[]gZcmpRaZaZRgaZNP[]u0YZh]QRhjaeNoRg9«)Rh_s\PYhCu aZNoR¢sA[]YZR J6 F L NoRAgZR J Y [uPh]Gu &²\ouoae[]gZc¢\Pnon7RAg aZge[juo~C\o[]gQ![jaZge ^¬ M&NoYgeh]\oaZuoR¢Y[]saZ\P[]c0sh]QnphCYZRAq hjbsA[jYaZhaeNoR+YZ\oogeh]\_aeuPR`< > 2435 B NostN
(73) sh]Qno\_aeRAY aeNoRYe[jQRh]npRgt['aehCu[]Y<.> 243
(74) 5 BP\_akaZNPRu\oQpRghj?gZh'kY&h]UL YkR9YZYbh]gkR9 C\7[j¬aeh!aZNoRY ]Rh]([ qoYaZgeP\_aZh]u+oh_st¡;_ Lhu[sA[j7aeh <.> 2435 B«CRUNP[L]RnV brs[]YaZhM< .> 2435 B«C NoRgeR-b Y)aZNoR qoYaZgeP\_aZh]uohst¡+Y ]RC x F x s
(75) x F x x s s 2. . . . . x F x x
(76) s x s s x F x x
(77) s ! x " s " # s $ C~]\ogeRn`. hCQnP\_ae[jaZh]uPY&npRgZh]geQRAq+u[. < >2435 B`sA[jÌ«o NPRgeR=J Yk[ju ohst¡`Q[jaZge ^¬ Mh YZh]]RaZNPR{YZcYaZRAQ h]RA B\P['aehCuPY¢nPgZR9YRAuCaeRAqu\C~C\ogZR0 J NoRAgZR
(78) J Y+[ju Ph_st¡ Q![jaZge ^ MÆ«oaZNoRnPgZuPsnoRYkaZNoRh]h' uo~PM&NoRnogeh_sRAYeYZh]g)aZNP[jabh' uPY)aeNoRs\PgZgeRuBabq_[j~Ch]uP[]pPh_st¡ J&%"%n7RAghCgZQ!Y [!YZRA B\oRAuCae[];aZge[]uo~]\P[]gkYhCCRaeh¢shCQnP\_aZR x Z% M&NoRgeRAYZ\oaZuo~!ohst¡+YkogZhB[]qosA[]Ya aehHnogeh_sR9YZYZh]gtYrh]u aeNoRYZ[]QR`gZh' M&NoR`geRAsR]RgtYsA[ju
(79) \on;qo[jaZR¢aeNoR\ouPYZh]]RAq0Ph_st¡_YaeNoRc h' u,« o =o rshCQno\_aZR[x x % s % «phCg-l('*),+ UM&NPYUYR9 B\oRuPsRYaZN\PYgZRAn7R9['aZR9qh]gURA[CstNHq_[j~Ch]uP[]. Ph_st¡; h]uPsRgeuouo~aZNoR\on;qo['aeRnoNP[CYRC«Pad)h¢Ydaege[jaZRA~]RAYk[]gZR[]nonoR9qq_RnpRu7q_uP~`h]uaeNoRYZNP[]n7Rh] aeNoRbnPgZh_sR9YZYZh]g?~CgZq¬~AÁuPq_RARAq¬«BaZNPRs[CYR NPRgeR aZNoR~]geqY[gZh'«C NostN!YaZNoRb7R9Yda&s[]YZR]«q_hRAYuohja RAQnoh'c+non7RAuouo~` NoRaZNoRhjaZNPRgtYbq_h7&M&NPYbnonpRuoRsh]uPYZYaeYkumYZno aZaZuo~¢aeNoR\on;qo['aeRnoN7[]YZR uad)h`YaZRn7YbM&NPR£PgtYdaU\on;qo['aeRAYbaZNoR^ &£PgeYaPh_st¡_BY JÊ NoRgeR YkaeNoRu\oQ7RAgh]>gZh'kY h] aeNoR¢~CgZq M NoR!aeNoR`YZRAsh]uPq0q_R9[jYr aeN0aZNoR¢geRQ![]uouo~oh_st¡YAa +u7sRaZNPR!£PgtYdanP[]gaN7[]YpRRAu \Pnpqo[jaZR9q¬«oa&Y YZRuBa&aZhaZNoRnPgZh_sR9YZYZh]g) NostN+Y&h]u+aZNPRrYe[jQRshC\PQu[ju7q`hCu`aeNoRruoR^a gZh'?M&NoR geRAsRuo~nogeh_sRAYeYZh]g)aZNoRAun7RAghCgZQ!Y&[ju[]sAs\oQ\o['aZh]u`aZh¢sh]QnoRaZRUaeNoR\on;qo['aeRhj( atY&oh_st¡_YA { RN7[L]RaehqoYaZuo~]\PYZNaZNPRAYZRad)h+YaZgt['aeR~]RAYuHh]\PgQh_q_RYA«pP\_arYZh]QRs[]Ykaehp pRaZNoR!Ye[jQRu{7h]aZN ]RgtYZhCuPYI CPh]gruPYdat[juPsR["j t hei9j)lmh^gB«;aZNPRaeQRaZhshCQno\_aZR![YR9 B\oRuBaZ[j aegZ[juP~]\o[jg YZh]]R]« 7RR9YdaeQ!['aeRAq+c r3sDt jui9v Ch
(80) wij)lmh^gpi;xug t jy Kz t juo "j t hei
(81) @g t v{o"j t hei9j)l hng{Æ« Ò~,Ò.
(82)
(83) 0p #. NoRAgZRkz t j¬Y,h]uPR>hjaZNPRnogeh_sRAYeYZh]gtY;u]hCCRAqUuraZNoR)sh]Qno\oae['aehCuhj <.> 2435 B[juPq="j t hqi
(84) pg t v YU[`YaZge\PsÆae\ogZRshCuCat[juouo~¢u_h]geQ!['aZh]uhCumQ!['aegZsR9Y[]uPqms[]uo~¢nP[]ge[]QRaZRAgeYAblm[jaZgesRAYnP[]YeYR9q u`[]gZ~C\oQRuBaeY(aehaeNP['a 7sA[j7[jgeRkh]Y ]Rb b ')gZhB[]qosA[]YaeY?h]YhCCRAqoh_st¡Y[jgeRknpRgZh]geQR9q sh]uPYZq_RgeuP~[ nPgZh_sR9YZYZh]g)geh' []Y [geuo~P_ ')\_a aeNoRsgeaZs[j¬n7['aZNh]9< > 2435 B¢hCh'kY)aZNPYbgZuo~P L_h)RNP[L]Rh]uocaehsh]uPYZq_RgUaZNPRsh]QQ\PuosA['aehCuHpRad)RRu{aZNPR!nogZh_sRAYeYhCgkaZN7['ashCQno\_aZR9YUaZNoR YZRA B\oRAuBaZ[jYZh]]R[]uPqaeYgZ~]NBabuPR~]N7hCgA A²aUNP[]YkaZh+7RuohjaesRAqaeNP['aUq_RaeQR9YbQ![Lc[jnonpRA[]gbu aeNoYknon7RAuoR[CY R^_no[juoR9q+u ! $[]7hC\_akaZNPR vÊ[]saZhCgZ ]A[jaZh]u,M&NPRAYZRq_RaeQRAYb pRat[j¡]RAu uBaZh[Cssh]\ouBau¢ aeNoRbuoR^a]RAgeYZh]uhj,hC\ogR^BaeRuPYZh]u, -bYaZNPR[jQhC\ouBahjqo[jae[sh]QQ\ouos['aeRAqnpRg PgZhB[]qosA[]Ya)Y9b «P[ogehC[Cqos[CYda&h]npRgt['aehCu+s[]u+pRRAYaZQ!['aeRAqc J 6J0VG(L J o
(85) F b Jqx M Q NoRAgZR 6J0VG(L J [juPq -J []gZR¢R9YdaeQ![jaZRAq
(86) Bc aeNoRps[]YnPgZR9YRAuCaeRAq0u
(87) aeNoR+Q![jaZge ^ Q\oaZnos[jaZh]uQhqoRF M&NoRrq_ ^pRAgZRAuPsR7RadRARu!aeNoRbgeh' s[CYRb[]uPqaeNoRh]aZNoRAg>at[j¡]R9YnP[CsRku¢aeNoRbu\oQ7RAgh]sh]\oQuPY h]aeNoRYZRAsh]uPqh]npRgt[ju7q`h]>@?.ACBDBshCQno\_ae[jaZh]u,)M&NoRr£PgtYdakhCn7RAge[]uPqYb[j)[Lc_Y [`b ^b Q[jaZge ^¬ M&NPY ' []% \oRqoRnpRuPqoYbh]uNoh' Q![juc`oh_st¡_Y NP[L]R[]geRA[Cq_c¢pRRumYZh]]R9q+[]uPqs[]u7RR^nPgZR9YZYZRAq[]Y b ~C NoRgeRkl¬aZNoR u\oQ7RAg?hj;YhCCRAqPh_st¡_Y AÁuaZNoR ~CRuoRAge[]BsA[]YZRaeNoY(L[]\PR&sA[juuohja?R^_sRR9q b []Yh]uocaZNPR£PgtYa[ bgeh'kYb[jgeR\Pnpqo[jaZR9q¬M&NoYUR9[]qoYU\PYaZh+aZNPRhCh' uP~p sA[jY r3sDt jui9v Ch
(88) wij)lmh^gpi;xug t jy Kz t juo
(89) g h^hei
(90) pg t v{i o
(91) Dgh^hqi9j)lmhng@i -« []uPq r3s t jui9v Ch
(92) wij)lmhng@i;xug t jy Kz t juo
(93) ghZhei
(94) @g t v{o
(95) g h^hei&j)lmhngC Mh`h]npRgt['aZh]u7Yk[jgeRYdaeaZh¢R9YdaeQ!['aeRaZhshCQnPRaZRaeNoR~CRuoRAge[],s[]YZRQh_q_Rf `&M&NoR 2>[ju7q aeNoNR 4m4dGiOdG f+h]npRgt['aZh]u7Y~ Coh]g7h]aZN!hjpaZNPRQ«C)R NP[LCR&aZNoRbYe[jQR geRAYaZgesaZh]uh]uaZNPRku\oQpRg h]sh]\oQuPYk[]YhCg&aZNoRS>p?.ACBpBhCn7RAge[jaZh]u,?M&NoY&RA[]qPY&\PY&aZhaeNoRrh]h' uo~R^_nogeRAYeYZhCuPY F b| ^hZl bMo b c ] b l)b d J 6J-VGL JSo JÌb} M []uPq r3s t jui9v Ch
(96) wij)lmhng@i;xug t jy Kz t juo s
(97)
(98) i
(99) @g t v{o s
(100)
(101) "ij)lmhngC E B\P[jaZh]uPY []uPqy&~CCRAY;aeNoRsh]Qno\_at['aZh]ushCYaQh_q_RY,hCg,aeNoRU< .> 235 Brgeh]\_aeuPR>gZR9YnpRAsaZ]RAc hCu[geh' []uPq`uaZNoR~CRuoRAge[]¬s[]YZR] ! j" t hei9j)lmh^g J M
(102) Q
(103) g h^heikj)lmhngpi - % ! j" t hei9j)l hng JFyM
(104) Q
(105) Dgh^hqikj)lmh^g s
(106)
(107) i9j)lmh^g{ % Mhh]_at[ju`aeNoRsh]Qno\oae['aehCushCYa)h]aeNoR=<.8> 2435 B¢geh]\oaZuoRrhj Losb[ v-k f - «aZNPRAYZRrshCYaeY)NP[LCR aeh7RQ\o aenPRAqc "! [CY&RA[]stNs[];aeh[< > 2435 B`YZh]]R9Y)[Ph_st¡¢h]geh'kYh] 6 Ó 5.
(108) S9z.
(109) o mr,o72dG . { &(" +r Mh'[jqo[jaZRh]\ogN7[juPq_uo~hjn7[jgt[jRAgeh]\oaZuoRAYUuCaehm7«)Rge[]u{YZRCRgt[jaZR9YdatYrP[]YZRAq{h]u{aZNoR Losb[ v-k f - Q![jaZge q^ sBQ![jaZge ^Q\P aenos['aehCu0gZhC\_aZuoR]!M&NoR9YRaeRAYaeYr)RgeRR^R9s\_aeRAq h]u 43d@ NPstN¢Y&[s\PYaZRAgh]kf R s]RAsaZgt[uoh_q_R9.Y JÊf(RuBaZ\oS Q A AA)y lm ] aZN|]} gl 'hj,QRAQhCgZcnpRg uPhqo=R Mksh]uouPRAsÆaeRAqaeNogeh]\o~CNHD[ C7[]Y(a E?aeNoRgeuoRaruoRadhCgZ¡+B[`bff>geh_s\oge]RxCz]zCz!Y aestNPRAYA Lh`aZNoR aegZRARrogZhB[]qosA[]Ya)Y []saZ\P[]c¢R^R9s\_aeRAq+h]h' uo~[aZgeRRC 9 /k.+8 4 946.:w13 @
(110) 1y1y+.P1 C~]\ogeRx+nogeRAYZRuBaeYU[`sh]QnP[jgeYhCu7RadRARuaeNoRR9YdaeQ![jaZRAqmaZQR~CCRumch]\ogUQh_q_R JÔaeh]n M[ju7q aeNoR[]sÆae\P[jR^_R9s\_aehCumaZQjR JÊ7h]aaeh]Q M hCgUaZNoRM<.>@?.ACBDBgeh]\_aeuPRhCuH[j(n7hBYZYZPR~]geqoYbgeh]Q S\Pn aeh C|HnogZh_sRAYeYhCgeYhjO 4 3d@k Æ%lH['aZgesRAY[]gZRhjrY ]Rm|jz]x [juPq aZNPRPh_st¡ YZ ]ARY£o^_R9q aeh xP M&NPRq^ &Á['^_YrgZRAnogeRAYZRuBaeYaZNPR!uB\PQpRgh])geh'kYrhj)aZNoR!nPgZh_sR9YZYZh]gr~CgZq¬«,aeNoR!qc &²[j^_YUaeNoR!u\oQpRgh] sh]\oQuPY)[juPqaeNoR ]&²[j^_Y>aZNoRUR^_RAs\_aZh]u¢aZQRuYR9shCuPqoYA { RsA[ju`YZRRbaZNP[jaaZNPRR9YdaeQ!['aehCu¢~]]RAu c h]\og!R^BaeRuPYZh]uY¢]Rgec shBYRaeh0aZNoRmR^_n7RAgZQRuBae[]kR^_RAs\_aZh]uaeQRAYA M&NPRQ[j^_Q![jbRgegZhCg Yh]uoc ! NoR+aeNoR[L]RAge[]~]R¢RAgZgeh]gY CP\ogaeNoRgeQh]geR¢aeNoRAYZR£P~]\ogeRAY[]YZh sh]u_£7gZQ " aeNoRQnP[CsÆar hj? aZhCn7hChC~]ch]uHn7RAghCgZQ![ju7sR]. AÁuPq_RARAq{ sh]QnP[CsÆaU~]geqoYU[]stNPRA]RpRaZaZRgrnpRgZh]geQ![juPsR aeNP[juHRh]uo~B['aZR9qh]uoR9YkpRAsA[j\PYZRhj?aeNoRYcQQRaZgesshCQQ\ouos[jaZh]unP[jaaZRAgZuHhj?aZNPRgeh]\_aeuoRCM&NoR qo* ^;RgeRuBakYdat[j~CRAYh]g geh'%[juPqshC\oQu+aZhCn7hChC~]RAY)s[jupRUR^_no[]uPRAq¢c!aeNoR aZRgeQ uBaZgehqo\PsR9q c!aeNoRogehC[Cqos[CYda)aZgeRRC AÁuaeNoRYZRAsh]uPqR^npRgeQRAuBabRaZgeR9qaZh¢'[]qo['aeRaZNPR[]sAs\ogt[]sc¢hj(aeNoRR^BaeRuPYZh]uh]gU[!~]]RAu nPgZh_sR9YZYZh]g!~CgZq¬ C~C\ogZR }0YNoh'kY!aZNoR{RgegZhCg!ge[jaZRhjraeNoRmhCgZR9s[]Ya! aeN%geR~C[]geq aZh
(111) aZNoR []sÆae\P[j R^_RAs\oaZh]uaZQRhCgkQ!['aZge^Q\o aenPs[jaZh]uPYbR^_RAs\_aZR9qh]um[ `nogZh_sRAYeYhCg ~]geq¬klH['aZgesRAYb[jgeR h]YZ ]ARAY \Pn`ae h ! $o~ -k~B[ju`h]\Pg)R^aZRu7Yh]u+nogZh'q_RAY]RAgZc![Css\Pge[jaZRh]geRAs[CYdatY>aeNoR[L]RAge[]~]R RAgZgeh]g)gt['aZRrY h]uPc .o 9+ * " !2,!$ !25 /$1 #;:w8-+,2!.5 -&%q465& :y# M&NPRh]_idR9sÆaZ]Rrh]hC\og R^aZRAuPYZhCuh]b7HY&aeh!nogeh'Bq_R[]sAs\ogt['aeRru_hCgZQ![jaZh]u[jh' uo~[!sRAuCa []nonosA['aehCu,2« =op?o r,[YestNoR9q_\oRg9«jaZhq_RaeRgeQuoR NostN!Y?aeNoRbpRAYa)YZh]\_aehCu[]Qh]uo~YZRCRgt[joYesRAuP[jgeÌ -YZYZ\oQR aeNP['a)RkNP[LCR)adhQ![jaZgesRAYUJ%[]uPq`L )Rb[jQ aZhQ\o aenPcC(M&NPRAYZR Q[jaZgesRAY[jgeR hj,YZ[]QR YZ ]RUo\_akq_YdaegZo\_aeRAq+u[oh_st¡¢sc_ssb&[Lch]u¢ad)hq_YÊidh]uBaZR9q¢nogeh_sRAYeYZh]g~CgZqoY JgeRAYZnpRAsÆaeCR(c ' []uP)q ' MB AÁu0Y\PstN0[s[]YZR aYQ![]uPqo['aeh]gecaZh[j~CuHQ!['aegZsR9YU7Rh]geRnpRgZh]geQuo~+aZNPRnPgZh_q_\PsaA L_R]RAge[]stNPh]sRAYU[jgeRaZNoRAu{nphCYeYobR `UV RAq_YaZgeo\oaZR`L hC* u ' «gZR9q_YaZgeo\_aZR[J h]*u ' h]gq_R£7uoR[ gae\P[j~]geq aeN []?[L'[j[joRnogeh_sRAYeYZh]gtY C~C\ogZR JaZh]2n Mb YZ\oQQ![jge ]ARAYbaZNoRgt[jQR)h]ge¡+h]>aZNPY R^_n7RAgZQRuBaA?M&NoR9YRr~]geqoY&[jgeRU[CsÆaZ\7[jc`YZRatY)hj(uoh_q_RAYgeh]Q [YZuo~CRUnP[]ge[]R¬shCQno\_aZRAIg JhCg&s\7Y & aeRg MÆ(f>geh_sRAYeYZh]gtY[jgeRkaeNoRuNohCQhC~]RAuoRhC\PY Co\PgaeNoRgeQh]geRbuCaeRg s[]uPq¢uBaZgt%[ sB~CgZqoYsh]QQ\ouos['aehCu shCYaeY sA[ju7Rsh]uPYZqoRgeRAq`[CY YQ[jg9 |bu_h]gZaZ\ou7['aZRAc`aZNoRs\ogegZRAuBak]RgtYZhCu`hjp{Y uPhjab[jPRraeh!RAYaZQ[jaZRraeNoRshBYdakh]([geRAqoYaZge* & P\_aZh]u¢pRad)RRAu!ad)hnogehsRAYeYhCgYZRaeYA(M&NoYnogeh]oRQ YuPq_RARAq!CRgecNP[]gequ!aeNoR~CRuoRAge[]Ps[CYBR ! } $F L_h+hCgraZNoYR^npRgeQRAuBar)R!NP[LCRq_RaZRAgZQuoRAq0[jQhC\ouBaeYUhj qo['at[+aZgt[juPYRgeRAqH7RadRARu0RA[CstN{nP[]g h]?nogZh_sRAYeYhCgeY []uPqaZNoRshCQQ\ouos[jaZh]umYestNoRQR~]RAuoRgt['aeRAqc+aZNoNR Losb[ v-k f - geRAq_YdaegZo\_aehCu Ò~,Ò.
(112)
(113) 0p. SCS. 35,00. Exectuion times (in sec.). 30,00. 25,00. 20,00. 15,00. 10,00. 5,00. 0,00 1 6 1. 11. 6. 16. Number of rows (p). 11 16. 21 21. 26 31. 26 31. Number of columns (q). 35,00. Execution times (in sec.). 30,00. 25,00. 20,00. 15,00. 10,00. 5,00. 0,00 1 6 1. 11. 6. 16. Number of rows (p). 11 16. 21 21. 26 31. 26 31. Number of columns (q). C~]\ogeR x ` h]QnP[]gZYhCupRad)RRAu!RAYaZQ!['aZR9qaZQRNJÔaZhCn M?[]uPq![]saZ\P[]oR^_RAs\_aZh]uaeQRBJÊ7h]aaZhCQ M h]g aeNoR=<.>p? ACBDB+gZhC\_aZuoRrh]u[j,nphCYeYoRr~]geqoYgeh]Q S\Pn+aeh}C|nogehsRAYeYhCgeYhjt4 *d@5k Æ Ó 5.
(114) SL|.
(115) o mr,o72dG . 10 9 8 7 Error rate (in %). 6 5 4 3 2 1 0 1024. 2048. 3072. 4096. 5120. 6144. 7168. 8192. 9216. 10240. Matrix sizes. C~]\ogeRHG} `0E>gegZhCg!ge[jaZRpRad)RRuhCgZR9s[CYdaeRAq[juPq[CsÆaZ\7[jkR^R9s\_aehCuaZQRh]g`[
(116) Q[jaZge ^qsQ[jaZge ^ Q\oaZnos[jaZh]uh]u[ [ nogeh_sR9YZYZh]g)~]geq,. geh]\oaZuoR] M&NPRuR\PYZRpaeh{hCgZR9s[CYdaaZNoRshBYdatYhjR9[]stN n7hCuBaaZh0n7hCuBa¢shCQQ\ouos[jaZh]u, C~]\ogeR JÊ7h]aaeh]Q M(~]]R9Y?[shCQn7[jgeYZh]u7RadRARuh]geRAsA[]YaZR9q[]uPqQRA[]YZ\ogeRAqaZQRAY(hCg>RA[CstNhj;aZNoR ~CgZqoY)nogeRAYZRuBaZR9q`u C~C\ogZR JÔaZhCn MÆ { NP[jab)RrsA[juYZRRUaZNP[ja aZNoRnP[jgt[jRA;R^aZRAuPYh]uh]kp [jh'kYaZh¢[Css\oge[jaZRAchCgZR9s[]Ya NP['a YbaZNoRpRAYarYZh]\_aZh]u«pu7[jQRc[ Z ¢nogeh_sRAYeYZh]gb~CgZq¬ A²>aeNoYrYZh]\_aZh]uHYaZNPRQhCYaruBaZRAgZR9YdaeuP~ geh]Q aeNoRUsh]Qno\_at['aehCu¢n7hCuBa&hjR«a)Y&[jYhaeNoRUR9YZY) R )¢sRAuCagZhCQ aZNoRUgeRAq_YdaegZo\_aehCu¢nph]uCa h]R%M&NoR\PYZRhj`ps[]uaZNoRAu[]h' aeh n7RAghCgZQ [{£PgtYa!YZRRAsaZh]uq_RnpRu7q_uP~ h]uaZNoR nPgZh_sR9YZYZh]gkYZnpRRAq uoRadhCgZ¡+P[juPqo qaeNmgt['aZhP CP\ogZaZNoRAgZQh]geRaYbuBaZRAgZR9Ydaeuo~aeh+YZRRaeNP['aURCRu aeNoRstNohCsRraZh`sh]Qno\_aeRh]u ' Yb[!aaZRQhCgZRR^npRu7Y]RauPq_\PsRAYbR9YZYksh]QQ\PuosA['aehCuPYk[ju7q qoYestNP[jge~]R9Ykx+nogZh_sRAYeYhCgeYkh]grhjaeNoRgUn7h]aZRAuCae[](n7RAuPq_uo~`at[]YZ¡_YI CuP[jcm[`aZhhC¡]RaeNoRR^aZRAuPq_R9q CRgtYh]u+hjp{sA[juq_RaeRAsab NoRu[!sh]Qno\_at['aZh]u uoRR9qQhCgZRrQRQhCgZc!aeNP[juaeNoR[L'[j[]oR []Qh]\ouBa&hj[sRAgat[jush]u_£7~]\ogt['aehCu`[juPq¢aZN\PY&uPq_\PsRY&[jnMcnosA[jcaeNoR M nogZh_sRAYeYhCg~CgZq 7uohhCuo~]RAgpRUsh]uPYZq_RgeRAq![CYYZhh]u¢[]Y)RbgeRA[]stN¢[nogZhCoRQ Y ]RR^osRARAq_uo~aZNoRbaZhjat[j;s[]nP[]s adc h]u]h]]R9q¢nogeh_sR9YZYZh]gtY CohCg []gZ~CRg)nogeh]oRQ YZ ]RAY)aeNoR ` Q![Lc`[]YZh7RqoYes[]geq_R9q¬ M&NoYR^_n7RAgZQRuBaYZNoh'kYaeNP['aaZNoR+R^aZRAuPYZhCu hjp aZhHN7[juPq_R¢nP[]ge[]RgZhC\_aZuoR9Y )7R CRgec!\PYZR\oaZh![!YZstNPRAq_\oRgk[CY& aknPgZh'q_RAY&RAuoh]\o~CN+u_hCgZQ!['aehCu`aeh!7R[]oRaeh¢stNohhCYZR[]ssh]gtq_uo~ aeh YZR]RAge[]bsgeaZRge[ `0luPQ\oQ sh]QnoRaehCuaZQR]«bsh]QQ\ouPsA['aZh]u QuoQ ]A[jaZh]u,«buB\PQpRg`h] nPgZh_sR9YZYZh]gtYu]hCCRAq¬«;A . Ò~,Ò.
(117)
(118) 0p. S=. A. Matrices. Distributions. Some possible virtual grids. B. Ga. Gb. Gv2. Gv1. 50 Product. 45. Redistribution. 40 35 30 25 20 15 10 5 0 Ga. Gb. Gv1. Gv2. measured estimated measured estimated measured estimated measured estimated. C~]\ogeR `>[]qo['aehCumhj(aeNoRR^BaeRuPYZh]uuaZNoRs[CYRh][!Q!['aegZ^[]~]uPQRAuBakh]h')RAqc[!Q\P* & aenPs[jaZh]uhCgx+BgZaZ\P[]nogeh_sR9YZYZh]gk~CgZqoYNJÔaZhCn MÆnCPh]geRAs[CYdaeRAqaeQRAYU[jgeRsh]QnP[]gZR9qaZh`QR9[]YZ\ogZR9q hCuoRAnY JÊ7h]aaeh]Q M&q_Ydaeuo~C\oYNouo~geRAq_YdaegZo\_aehCu[]uPqshCQnP\_ae[jaZh]u,. Ó 5.
(119) SAx.
(120) o mr,o72dG . # *¢`( . AÁuaZNPY(nP[]n7RAg?R)nogeh]nphCYZRAq[juR^aZRAuPYh]uaZhUaZNPR&qocBu7[jQs)npRgZh]geQ![juPsRhCgZR9s[]YaZuo~baZhh]PpaZh. N7[juPq_RknP[]ge[]RPgZhC\_aZuoRAYA(M&NoYR^aeRuPYZhCu!\PYZRAY?aeNoRbu_hCgZQ!['aehCunogZh'q_RAqcaZNoRU[]saZ\P[]P]RAgeYZh]u h]7+[jph]\_aYZRA B\oRAuCae[]_gZhC\_aZuoR9Y?[juPquoRad)h]ge¡[L'[j[joadc]M&NoY(u_hCgZQ![jaZh]uY?u'idR9sÆaZR9quBaZh [Qh_q_Rsh]Quo~gZhCQ$shqoR[]uP[jc_YYAM&NPR!gZR9Y\oas[]u{pR¢shCuPYZq_RAgZR9q{[CY[uoR \ouPsaZh]u0aY nphCYeYZoRaZhRAYaZQ[jaZRcms[jaZh+aZNoR¢p -k_f AÆ Coh]gUuPYdat[juPsRa (7RnphCYeYoRaeh[CY¡mp aehh]geRAsA[]Ya?aZNoRbR^_RAs\_aZh]uaeQRkh];n7[jgt[jRAoQ!['aZge^ sQ!['aZge^Q\P aenos['aehCu!h]g>n7[jgt[jRA_aZge[]uo~]\P[]g YZh]]RC LhCQR+R^npRgeQRAuBaeYL[]qo[jaZRAq
(121) aZNoR[]sAs\ogt[]sc{h]kaZNPR+nP[]ge[]R)R^aeRuPYZhCu
(122) RaZNPRgh]gq_ ^pRAgZRAuCa ~CgZq YNP[]n7R9Y aZN
(123) [+£o^_RAq0Q!['aegZ^{YZ ]AR!h]grhCgq_ ^pRAgZRAuCaYZ ]RAYhj&Q[jaZgesRAYrhCu0[£P^R9q nogZh_sRAYeYhCg ~CgZq¬~ AÁu¢phjaZN¢sA[]YZRAYA«jaeNoR[LCRgt[j~]R&RAgZgeh]g?gt['aeRk7RadRARu!R9YdaeQ!['aeRAq¢[]uPqQRA[CY\ogeRAqR^_RAs\oaZh]uaZQRAY Y&\ouPqoR(g { R[]YZhYZNoh'R9qNoh' [YZstNPRAq_\oRgsh]\Pq!pRuPR£oa)hj¬h]\ogR^aZRAuPYZhCuaZhp AÁuPq_RR9q a&[jh'kY [YestNoR9q_\oRg(aZhQ[]¡]R&Q![jnonPuo~stNPh]sRAY>P[]YZRAqh]u![rgeRA[]Ydaes)RhjpaZNoRbR^_RAs\_aZh]uno['aZh]geQ [ju7q [Css\oge[jaZRURAYaZQ!['aZh]u7Y)h]g R^_R9s\_aehCu`aeQRAYkhjae[]YZ¡_Y&[juPqqo[jae[Qh']RQRAuCa shBYdatY +\og>£PgeYa?hCgZ¡ opR&aZhnogeh]npRgecNP[juPqoR nonpRuouo~[]uPqq_R&aZQRAY?uaZNPR< > 2435 Bgeh]\oaZuoR] M&NPRu`)RUno[]u`aehR^aZRu7q!aZNPRU)h]ge¡nogeRAYZRuBaZR9q¢u`aeNoY)nP[]n7RAg)aZhaZNoRrRuBaegeR Losb[ v-k f - Pge[]gZc uh]gtq_Rg)aehnPgZh'q_Rrn7RAghCgZQ![ju7sRh]geRAs[CYdaeuP~aehBhC;h]gk[shCQnoRaZRq_RAuPYZRUuoRA[]gk[j~]RPge[¡]RAgZuoRAÌ -buohjaeNoRgn7hCuBaaZh{q_RCRh]n YraeNoR`shCYaRAYaZQ[jaZh]u0hj&geRAq_YdaegZo\_aehCu,D A²&aeNoR¢~]RAuoRgt[j>sA[]YZRY[ qo* )¢s\P a nogeh]oRQ«)RbaeNouP¡¢Rrs[]u`P[CYRUh]\Pg)R9YdaeQ![jaZh]uPY)\onph]u[YZRa hjgZR9q_YaZgeo\_aZh]us[]YeYR9Y M&NPRAYZRs[CYZYZRAY[]gZRo\Paq_RAn7RAuPq_uo~h]u0Qh_q_ £ps['aehCuPYrQ![]q_RaehaZNoR¢YZh]\PgesR~CgZqHaZhh]oae[ju aZNoR qoRAYaZuP['aehCu+~CgZq¬_ CohCg u7Ydat[juPsRraZNoRgeRAq_YaZgeo\oaZh]u+gZhCQ ' [juPq ' &aeh 'uQ[Cq_Ru L_RAsÆaehCu} Q~]NBa 7RRARAQRuBaeY h]aeNoRYZ[]QRrs[CYZYA«_ NoRAgZRrgeRAq_YdaegZo\_aehC uPY&h]uPc¢\7YR[nogeh]nph]gZaZh]uP[]7uPsgZR9[]YZR h]aeNoRu\oQpRgkh]uPRAY h]aZNPRnogZh_sRAYeYhCg~CgZq¬. # !T - k" . M&NPY))h]ge¡&[]Y)YZ\ononph]gZaZRAq`u+nP[jgZa&BcaeNoRUnogZh]idRAsaeYt- A rV Axs
(124) rV Ax -.Lf[]uPq`V bM v -(Lf \PuPq_RAqc!aeNoRICogeRuPstNQuoYaZgec¢h]geRAYZRA[jgtstN, RAuB{ aZRRg9«)aZNPh]\oY q)h]ge¡]¡!RNPaZh![LaeNPuo[j~uop¡`RaZRANouNR q_Ah]xvuoR[jhCpu`h]gtae['NoaenR h]geAxc!h]kgkf ~Cges[]\PuBYaZaZuoRAgI~¢J[] sA24s2pRA<YeY)aZh` atY 5 2.\PA Ydae3Rg uB h]?Q"no! \_3aeMÆuo ~ . . ' &( +#) !S$Vb['id¡\oQ![jg ')\occC[o«¬R9q_aZh]g9$#n*?&%g i}945 3d@ i19dG6@?j«]h]\oQRSb`(-bgestNP aeRAs& ae\ogeRAYk[]uPjq L_cYaZRAQ!Y?f>geRuBaesRr[jÌ«S;#b##oA LG' z&tS;&ÁzoS=By jx&y ! | $Vb['id¡\oQ![jg ')\occC[o«pRAqo aeh]g9' #n*?&% i}94m 3d@ i 12dGfq?]«¬]hC\PQR|G` f>geh]~Cge[]QO& Quo~¢[ju7Xq -bnonosA['aZh]u7Y?f>geRuBaesRr[jÌ«;S #b##o~ A LG' z&tS;&²zPS;By jxb&dy_ Ò~,Ò.
(125)
(126) 0p. SL}. [jgeh]u,G« xh]QuP B\oRIv[]\PgZRC«o[juPq U| ae[]geq,?fRAghCgZQ![]uPsRUf>geRAq_sÆaehCu[]uPqa-kuP[]c_YZY h])f?[]ge[]R,+\_a&Fh]& hCgZRlm[jaZge ^0C7[]saZh]ge ]A['aehCu,}AÁuZt=45 m 5>q? } % % 262 ; 945 O #I*? %X i 245 i 12dGfq? #n «PnP[]~]RAYrS S spSLy]|_«qxbR9s|jz]zCzo ! xb$nxU[Lq \oRg9«kV stNP[jgtq [jgen,« x[Lq f?['aZaZRgtYZh]u,« -kPNo idg a L_[jNP[LcC« []\PY E>gels L_stNP[]\PYRAgA« E\ouosg R L_[juBaehCYA«(Vb[jQRAYZN L\Poge[]Qh]uo[ju,«?[]uPq M&NohCgeYaZRAu ]hCuu E>st¡]Ru8 vh]~Cf `~- f>gt[]saZs[j lmhqoRPh]pf?[]ge[]R hCQnP\_ae[jaZh]u, iNiOdG 456. % /
(127) q« b# JS]%S M`Çy %sG#C}o« bh'`;S ## ! } $nCPgZX9q_Xges xbR9YnogeR ]C« B[]st. ¡ xbhCuo~C[]gZgt[o;« -kuBaZhCuoRfRaZaZRaA« cgZ]Vk[]uPq_ge[]Q[]gZh7«[ju7q >]RAYV h]pRgZaA LostNoRAq_\PuoI ~ ')h_stq¡ & csts -kgege[LcV R9q_YdaegZo\_aehCu, AÁu Ek b x kh][juPq_RAgA« V ]hC\opRgZaAb« C) P f(RaZRgtYA«[juP0q |,MgZh]aaeRu7RAgZ~7«¬RAq_aZhCgeYA« i 12dGfq? dG2>i} p5r,/,1b19345f 2>B I 546Æ«onP[]~]R9Yk|]|C=y s_b| jxP khCgaeNbh][]uPq¬«¬;S ## P ! $nCPgZX9q_XgeX s xRAYZnogeR ]]« C[Cst8¡ xh]uP~C[jgegt[o«?[juP"q ')RgeuP[jgtq
(128) Mh]\ogt[juPstNPRA[j\{f(RgZh]geQ![juPsjR LBae\Pq_c
(129) h] v| C([]saZhCgZ ]A[jaZh]u ae\ N v,h' h]QQ\ouos['aehCK u +]RAgZNoR9[]qh]u%lm\o aenPgZh_sR9YZYZh]gtYA <;45 55@? y 6k 5t«P} JÌ| M`S9}C=y spS #o«P;S #b#B}_ !½%y $nCPgZX9q_XgeX s xRAYZnogeR ]]«>lH[jgZaZu \ouPYZh]u,«>[]uPZq CPgZX9q_Xgejs L\_aeRg9u xbcuP[]Qs+fRAghCgZQ![]uPsjR Coh]ge R & sA[]YaZuo~!hCg kRadhCgZD¡ E>uP[jPR9lq LRge]RAgeYkum[¢bRaeRgeh]~]RAuoRhC\P<Y E>ugeh]uPQRAuBaA AÁ0u t=45 5 m>q? % k 9f2 = 245 Nj 2>Ief dGk 5>It=45 5q?"! 54 %@ c d n2> /t1b19345f# $.%!q/ &« C\ouoR|]z]zoSC ! $B[]stn ¡ xh]uo~B[jgege[P« CRgeRQ.c x\ gZh ]]« L]RAub[]QQ[]gZuo~P«'[ju7qV stNP[jgtq[juPYZh]u,@ -kNu E?^aZRAuPq_RAq L_Rakhj Ch]gZaZgt[jj u ')[CYs v,uoRA[]g -k~]RPge}[ L\oPgZhC\_aZuoRAYAw / '
(130) !o
(131) % i}f45y795ko« SAx J=S M`S s;SLy_«7=S # P ! #$ Ad[]Z u CohBYdaeRg[]uPq []gZ R9YZYZRQ![ju,«RAqo aeh]gtY( ! % *)<>+#,3d 19 _ j-B i 12dGfq? ;56d 46dGm ?lhCgZ~B[jGu & [j\_Q![]uou,«p;S #b# o !SAz $rM&Q/kh')RAYA«blm[]ge0 s LQ aeN,«U[]uPq UhCgeq_hCu Uhh_q¬/ .~2> 5k2>q? 2>F>b k12 hq? 0 /( > 54 kh :=4m Ælm[CsQ[]uMRAstNouPsA[j¬f>\oPYNPuo~7«,;S ##b#P A LG' B`, S &d}Cy By'z &²zy'z &eSC !S]S $rlH[jgZaZ u \ou7YhCu, xbcuP[]Qsf(RgZh]geQ![juPsnR Coh]geRAsA[]YaZuo~h]g kRad)h]geq¡ &fEuP[joRAq LRAgZCRgtY&um[ lmRae[CshCQnP\_aZuo~ E>ugeh]uPQRAuBaAD AÁ"u <;45 5 5>@?X }% k 9f921 43%m1\u 5 i 245
(132) ;> *q?r_
(133) t:*d fr9>6196iO87=fu( _2>Ief dGk 5> 7 h%k iN
(134)
(135) 6956:I7 <;= « -bnog|]z]zC|o !S9| $ saZhCg)Vk[Lc&[jgt@q &LQ aeN, |EK M L_stNoRAqo\ouo~ aeXN |kuP a AÁuBaZRAgZnogeh_sR9YZYZh]g hCQQ\ouos[jaZh]Du x R & [Lc_Y$ Be4 k ./t1b12* m>
(136) % i 64 Æ«S `½}]=} sPySC«P;S # By_ !;S $rV uBaZh]X u { NP[jRc+[juP#q C[Cst¡ xh]uP~C[jgegt[oy -b\_aZhCQ[jaZs[]c¢M\PuoRAXq v,uoRA[]<g -b~CRogtN[ L_hjÔad&[jgeR J6-?M vy-.LMÆ_ AÁl u tm;45 5 5>q?Bm
(137) _
(138) _
(139) 7 > ? «;S ## P !Sbx $rVkstO N {{hCYZ¡Ì« kR Lnogeuo~P«][]uP2q CQ b[LcCRAYAM&NPR bRad)h]ge¡ { RA['aeNoRwg L_RgeBsR `y-FxbYaZgeo\oaZRAq VkRAYZh]\ogtsR?f(RgZh]geQ![juPs_R CohCgZR9s[]YaZuo~ LRAgZsR?hCglRat[]sh]Qno\_aeuo~7 dG6dG ) 9 mf i5 19dG6@?}72h% iB5r
(140) 4mi19dG6@?55d «¬S9} JÌ%} s M `½y]}C=y soy oq« +UsaA¬=S #b#b#P ! $ Eqoq_c. Ó 5.
(141) Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST MARTIN Unit´e de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unit´e de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex. ´ Editeur INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France)
(142). ISSN 0249-6399.
(143)
Documents relatifs
Dans chaque ville et pour toutes les lignes de tramway considérées, il faudrait disposer des trafics avant et après ouverture d’une ligne et de plusieurs projections d’évolution
Le fait d’écrire à partir d’une oeuvre d’art visuelle ressemble à une forme de contrainte; nous croyons par ailleurs que cette pratique a eu un effet durable sur l’écriture
variables d'ordre psychologique: soit f.amiliale ou personnelle, soit so- ciale, soit professionnelle, soit une combinaison de ces facteurs. Ce patient a récupéré
For the two coolest objects in Figure 3.6, HD 4539 and PG 1716+426, both at Ta < 27, 000 K, there is a good match between the predicted synthetic spectra and the FUSE data: the
lui inculquer le registre li'lquistioue, les l1abitudes alimen- taires et vestimentaires ainsi que le comportement des bour- geois de Québec. Pierrette Paul doit
La conciliation emploi-famille : des mesures à développer dans les milieux de travail Tableau 4 : Les dispositions favorisant la conciliation travailfamille dans les
Figure 2.4 Predicted (continuous lines) and observed values (filled circles: stands aged from trees with root collar; open circles: stands aged from trees without root collar)
Cette posture permet de dégager deux idées centrales : le poids des milieux professionnels locaux dans l’intermédiation et le transit des idées, modèles et pratiques