/K 0 /P 16 0 R endobj /Count 5 /K 0 >> 161 [200 0 R] /S /Part endobj /K 0 /TrimBox [0 0 414.73 625.692] /P 16 0 R >> >> endstream /K 0 /Kids [526 0 R 527 0 R 528 0 R 529 0 R 530 0 R] >> /K 0 << 328 0 obj << endobj 82 [121 0 R] /K 0 endobj Obviously, nonuniform mutation gains no benefit on the simple unimodal problems. /P 16 0 R 188 0 obj << << /Filter /FlateDecode 259 0 obj /Pg 503 0 R /P 16 0 R 296 0 obj >> << /P 16 0 R /S /Part /P 16 0 R /Count 5 /Parent 17 0 R 215 [254 0 R] /Count 5  : […] /K 0 stream endobj /Parent 18 0 R /P 16 0 R /P 16 0 R /Pg 534 0 R /Kids [436 0 R 437 0 R 438 0 R 439 0 R 440 0 R] /Title (mf2003) endobj /K 0 >> endobj /Parent 9 0 R /P 16 0 R endobj /Type /Pages /D [39 0 R /FitH 846] /K 0 /S /Part /S /Part /Count 32 << /K 0 Let theta represent the angle that a line, with fixed point of rotation, makes with the vertical axis, as shown above. >> /Kids [466 0 R 467 0 R 468 0 R 469 0 R 470 0 R] /S /Part << << /Type /Pages 48 0 obj 215 0 obj /K 0 240 0 obj 169 0 obj << 240 [279 0 R] /S /Part 99 0 obj /P 16 0 R endobj 22 0 obj /K 0 << /Type /Pages /Count 5 /P 16 0 R << 77 [116 0 R] /Pg 510 0 R /Pg 442 0 R endobj << /P 16 0 R >> C'est le cas pour la résolution des équations linéaires à coefficients non constants. << /S /Part /K 0 endobj /S /Part /P 16 0 R /Resources 348 0 R 81 0 obj /Prev 7 0 R /K 0 /Pg 592 0 R /S /Part 46 [85 0 R] endobj >> 124 0 obj /K 0 /Type /Pages /Count 5 endobj 337 0 obj 36 [75 0 R] 103 [142 0 R] /K 0 /S /Part /Count 5 endobj << /S /Part 213 0 obj >> /Pg 523 0 R endobj >> 232 [271 0 R] 282 0 obj endobj 227 0 obj /P 16 0 R << >> >> /K 0 83 0 obj >> /S /Part uuid:b8037396-f09c-47ad-839e-8eb1d11224d0 >> 152 0 obj << On appelle fonction exponentielle l'isomorphisme E  : R  →  R * + , réciproque du logarithme népérien ; ainsi, pour tout nombre réel x , E( x ) = exp  x est l'unique nombre réel >  0 dont le logarithme népérien est égal à x , soit : cela entraîne aussi, par composition de L et E que, pour tout x  ∈  R et pour tout y  ∈  R * + , on a : Puisque la fonction logarithme népérien est strictement cr […] >> 67 0 obj 41 [80 0 R] 203 0 obj /S /Part /Subject (Table of Contents) /Pg 395 0 R >> /P 16 0 R 111 0 obj /P 16 0 R endobj endobj 270 0 obj 181 [220 0 R] >> /K 0 /S /Part 123 0 obj /Parent 10 0 R /Type /Pages /Title (Cover) /S /Part 71 [110 0 R] /Subject (Table of Contents) /P 16 0 R >> << /P 16 0 R >> 340 0 obj 271 0 R 272 0 R 273 0 R 274 0 R 275 0 R 276 0 R 277 0 R 278 0 R 279 0 R 280 0 R /Pg 383 0 R << >> >> /K 0 endobj 245 [284 0 R] /Count 5 >> >> 49 [88 0 R] /K 0 255 0 obj << 190 [229 0 R] 95 [134 0 R] /S /Part << endobj 121 [160 0 R] /K 0 endobj >> << /P 16 0 R /Pg 413 0 R /P 16 0 R /Type /Pages 338 0 obj /S /Part /Pg 489 0 R b. /K 0 /Pg 483 0 R /S /Part /Count 25 %PDF-1.6 58 [97 0 R] 302 0 obj endobj /K 0 /Pg 445 0 R << >> /Pg 571 0 R Acrobat Distiller 4.05 for Windows This is intended for undergraduate, junior postgraduate, and engineers. /Pg 515 0 R /S /Part endobj << >> endobj >> /P 5 0 R endobj 241 [280 0 R] /S /Part /Pg 596 0 R /S /Part 160 0 obj /S /Part /P 16 0 R Note that the Cauchy distribution has a shorter, narrower peak than the normal distribution, but has “fatter” tails. /K 0 /P 16 0 R endobj /P 16 0 R endobj 167 0 obj /Pg 402 0 R 146 [185 0 R] /Parent 23 0 R /Pg 444 0 R /S /Part /Parent 25 0 R << /Pg 573 0 R >> /Pg 400 0 R endobj /A 13 0 R >> 300 0 obj /Rotate 0 /Pg 460 0 R 332 0 obj endobj endobj /K 0 278 0 obj 202 0 obj 29 0 obj >> 94 0 obj << 137 0 obj >> >> 155 [194 0 R] /Pg 454 0 R /Kids [556 0 R 557 0 R 558 0 R 559 0 R 560 0 R] 48 [87 0 R] >> endobj 30 [69 0 R] /Pg 599 0 R 164 [203 0 R] /K 0 /Parent 4 0 R /Pg 526 0 R >> 40 [79 0 R] /Kids [332 0 R 333 0 R 334 0 R 335 0 R 336 0 R] >> << /Pg 446 0 R /P 16 0 R 28 0 obj endobj /Kids [411 0 R 412 0 R 413 0 R 414 0 R 415 0 R] /Pg 373 0 R << << endobj endobj /S /Part >> >> Inscrivez-vous à notre newsletter hebdomadaire et recevez en cadeau un ebook au choix ! 344 0 obj endobj 13 0 obj 252 0 obj /Count 5 endobj /P 16 0 R 173 0 obj 168 [207 0 R] 211 0 R 212 0 R 213 0 R 214 0 R 215 0 R 216 0 R 217 0 R 218 0 R 219 0 R 220 0 R /Pg 581 0 R /Type /Pages /S /Part /CreationDate (D:20101224091651+10'30') 271 0 obj /S /Part << /P 16 0 R /Kids [421 0 R 422 0 R 423 0 R 424 0 R 425 0 R] >> /Type /Metadata 118 0 obj 71 0 R 72 0 R 73 0 R 74 0 R 75 0 R 76 0 R 77 0 R 78 0 R 79 0 R 80 0 R /P 16 0 R >> /K 0 It also describes the distribution of horizontal distances at which a line segment tilted at a random angle cuts the x-axis. /S /Part << /Kids [356 0 R 357 0 R 358 0 R 359 0 R 360 0 R] /K 0 /S /Part 129 [168 0 R] /Pg 382 0 R /Pg 422 0 R endobj << endobj << 101 [140 0 R] endobj >> << /Pg 392 0 R /K 0 /Pg 412 0 R 19 [58 0 R] endobj << /P 16 0 R /Kids [416 0 R 417 0 R 418 0 R 419 0 R 420 0 R] endobj /K [41 0 R 42 0 R 43 0 R 44 0 R 45 0 R 46 0 R 47 0 R 48 0 R 49 0 R 50 0 R /Type /Pages >> /Pg 371 0 R 55 [94 0 R] Table of Contents To illustrate the problem with the CLT for the Cauchy distribution, 1000 samples of size 100 were drawn from a Cauchy distribution. L'équation des ondes et le type hyperbolique, dictionnaire de l'Encyclopædia Universalis. >> >> endobj endobj /Type /Pages 204 0 obj /Parent 20 0 R << 4 [43 0 R] >> >> >> /S /Part << /K 0 /S /Part 243 0 obj 209 [248 0 R] << /S /Part 13 [52 0 R] /Count 5 >> /Pg 404 0 R >> endobj /Pg 406 0 R endobj >> << >> endstream 233 [272 0 R] /D [34 0 R /FitH 630] << 188 [227 0 R] © 2020 Encyclopædia Universalis France.Tous droits de propriété industrielle et intellectuelle réservés. 194 [233 0 R] << %���� << /P 16 0 R /K 0 endobj >> << 140 0 obj << 205 [244 0 R] Cauchy distribution is a special case of the Student-tdistribution with 1 degree of freedom. /Pg 506 0 R 80 0 obj /P 16 0 R << >> /P 16 0 R endobj /P 16 0 R /P 16 0 R >> 9 [48 0 R] 121 0 R 122 0 R 123 0 R 124 0 R 125 0 R 126 0 R 127 0 R 128 0 R 129 0 R 130 0 R 47 0 obj 318 0 obj >> /S /Part >> /S /Part >> /K 0 << 222 0 obj /K 0 endobj /Type /Pages 228 [267 0 R] 210 0 obj 141 [180 0 R] /K 0 208 0 obj << 237 0 obj /K 0  : […] /K 0  : […] << /Type /Pages << 200 [239 0 R] >> /Count 25 >> /K 0 endobj >> endobj /P 11 0 R /Pg 517 0 R stream >> /Outlines 2 0 R << /K 0 >> endobj 55 0 obj /P 16 0 R << endobj << 176 [215 0 R] 106 [145 0 R] 36 0 obj << /Count 132 The Cauchy distribution has a very heavy tail, comparable to the tail of the Pareto (1, c) distribution. endobj /S /Part << endobj 343 0 obj /P 16 0 R /S /Part /Kids [451 0 R 452 0 R 453 0 R 454 0 R 455 0 R] /K 0 /S /Part /StructParents 0 endobj /K 0 /S /Part endobj 221 [260 0 R] << /S /Part /P 16 0 R 199 0 obj /S /Part /S /Part /Pg 410 0 R /K 0 endobj /Kids [307 0 R 308 0 R 309 0 R 310 0 R 311 0 R] /Pg 578 0 R << 191 0 R 192 0 R 193 0 R 194 0 R 195 0 R 196 0 R 197 0 R 198 0 R 199 0 R 200 0 R /P 16 0 R >> /Pg 431 0 R << >> << /S /Part >> /Pg 366 0 R << /P 16 0 R /Parent 23 0 R >> /Pg 370 0 R endobj /S /Part /Pg 390 0 R /Parent 25 0 R 235 0 obj /P 16 0 R 285 0 obj 59 [98 0 R] << << /S /Part << >> endobj /K 0 72 [111 0 R] >> /K [14 0 R 16 0 R] /Pg 440 0 R << /K 0 /Pg 418 0 R << /P 16 0 R 3 0 obj 6 0 obj This shows an example of a Cauchy distribution with various parameters. /Type /Pages 84 [123 0 R] 46 0 obj /K 0 63 0 obj /S /Part /S /Part /P 16 0 R 152 [191 0 R] /Metadata 295 0 R /Count 25 /K 0 >> >> >> endobj endobj endobj 105 [144 0 R] 207 0 obj endobj /Limits [128 159] 174 0 obj /Kids [391 0 R 392 0 R 393 0 R 394 0 R 395 0 R] 312 0 obj << 130 [169 0 R] /K 0 /P 16 0 R >> << /K 0 >> Cauchy (11 better) can achieve more significant improvements compared to Gaussian (9 better). endobj endobj /Parent 9 0 R /S /Part << /Parent 22 0 R << /P 16 0 R 134 [173 0 R] endobj >> /P 16 0 R 11 [50 0 R] /K 0 endobj /Parent 18 0 R /Pg 458 0 R /P 16 0 R << >> 100 0 obj 236 [275 0 R] endobj /Pg 403 0 R /Pg 369 0 R /S /Part 59 0 obj 161 0 obj >> /Pg 384 0 R 60 [99 0 R] /S /Part 243 [282 0 R] << endobj /Author (Melnikova, Irina V. and Alexei Filinkov) /Pg 547 0 R 155 0 obj endobj >> endobj /P 16 0 R endobj 230 0 obj >> /K 0 /K 0 endobj endobj 139 [178 0 R] << >> << endobj /K 0 /Count 5 endobj /P 16 0 R /Parent 21 0 R /K 0 Il a enseigné à la facu […] 34 0 obj /Type /Pages endobj endobj endobj /P 16 0 R /Parent 19 0 R 330 0 obj 151 [190 0 R] endobj 176 0 obj 150 0 obj 47 [86 0 R] /Type /Pages /Pg 447 0 R 234 0 obj /Nums [192 [231 0 R] /Kids [317 0 R 318 0 R 319 0 R 320 0 R 321 0 R] >> << /P 16 0 R /K 0 2005-05-19T03:33:20-04:00 /P 16 0 R 229 0 obj >> << >> 241 0 R 242 0 R 243 0 R 244 0 R 245 0 R 246 0 R 247 0 R 248 0 R 249 0 R 250 0 R 38 0 obj 261 0 obj /Parent 4 0 R 117 0 obj /Nums [128 [167 0 R] 141 0 obj << /Pg 353 0 R /P 16 0 R Lire la suite, Dans le chapitre « L'équation des ondes et le type hyperbolique »

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