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## G = Dic14⋊6Q8order 448 = 26·7

### 4th semidirect product of Dic14 and Q8 acting via Q8/C4=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C28 — Dic14⋊6Q8
 Chief series C1 — C7 — C14 — C28 — C2×C28 — C2×Dic14 — C4×Dic14 — Dic14⋊6Q8
 Lower central C7 — C14 — C2×C28 — Dic14⋊6Q8
 Upper central C1 — C22 — C42 — C4⋊Q8

Generators and relations for Dic146Q8
G = < a,b,c,d | a28=c4=1, b2=a14, d2=c2, bab-1=a-1, cac-1=a15, ad=da, cbc-1=a21b, bd=db, dcd-1=c-1 >

Subgroups: 364 in 96 conjugacy classes, 45 normal (29 characteristic)
C1, C2, C4, C4, C4, C22, C7, C8, C2×C4, C2×C4, Q8, C14, C42, C42, C4⋊C4, C4⋊C4, C2×C8, C2×Q8, Dic7, C28, C28, C28, C2×C14, Q8⋊C4, C4⋊C8, C4.Q8, C4×Q8, C4⋊Q8, C7⋊C8, Dic14, Dic14, C2×Dic7, C2×C28, C2×C28, C7×Q8, Q8⋊Q8, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4×C28, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, Q8×C14, C28⋊C8, C4.Dic14, C14.Q16, C4×Dic14, C7×C4⋊Q8, Dic146Q8
Quotients: C1, C2, C22, D4, Q8, C23, D7, SD16, C2×D4, C2×Q8, C4○D4, D14, C22⋊Q8, C2×SD16, C8.C22, C7⋊D4, C22×D7, Q8⋊Q8, D4.D7, Q8×D7, Q82D7, C2×C7⋊D4, C2×D4.D7, C28.C23, D143Q8, Dic146Q8

Smallest permutation representation of Dic146Q8
Regular action on 448 points
Generators in S448
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28)(29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84)(85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196)(197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224)(225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252)(253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280)(281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308)(309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336)(337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364)(365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392)(393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420)(421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448)
(1 192 15 178)(2 191 16 177)(3 190 17 176)(4 189 18 175)(5 188 19 174)(6 187 20 173)(7 186 21 172)(8 185 22 171)(9 184 23 170)(10 183 24 169)(11 182 25 196)(12 181 26 195)(13 180 27 194)(14 179 28 193)(29 210 43 224)(30 209 44 223)(31 208 45 222)(32 207 46 221)(33 206 47 220)(34 205 48 219)(35 204 49 218)(36 203 50 217)(37 202 51 216)(38 201 52 215)(39 200 53 214)(40 199 54 213)(41 198 55 212)(42 197 56 211)(57 388 71 374)(58 387 72 373)(59 386 73 372)(60 385 74 371)(61 384 75 370)(62 383 76 369)(63 382 77 368)(64 381 78 367)(65 380 79 366)(66 379 80 365)(67 378 81 392)(68 377 82 391)(69 376 83 390)(70 375 84 389)(85 319 99 333)(86 318 100 332)(87 317 101 331)(88 316 102 330)(89 315 103 329)(90 314 104 328)(91 313 105 327)(92 312 106 326)(93 311 107 325)(94 310 108 324)(95 309 109 323)(96 336 110 322)(97 335 111 321)(98 334 112 320)(113 236 127 250)(114 235 128 249)(115 234 129 248)(116 233 130 247)(117 232 131 246)(118 231 132 245)(119 230 133 244)(120 229 134 243)(121 228 135 242)(122 227 136 241)(123 226 137 240)(124 225 138 239)(125 252 139 238)(126 251 140 237)(141 297 155 283)(142 296 156 282)(143 295 157 281)(144 294 158 308)(145 293 159 307)(146 292 160 306)(147 291 161 305)(148 290 162 304)(149 289 163 303)(150 288 164 302)(151 287 165 301)(152 286 166 300)(153 285 167 299)(154 284 168 298)(253 356 267 342)(254 355 268 341)(255 354 269 340)(256 353 270 339)(257 352 271 338)(258 351 272 337)(259 350 273 364)(260 349 274 363)(261 348 275 362)(262 347 276 361)(263 346 277 360)(264 345 278 359)(265 344 279 358)(266 343 280 357)(393 422 407 436)(394 421 408 435)(395 448 409 434)(396 447 410 433)(397 446 411 432)(398 445 412 431)(399 444 413 430)(400 443 414 429)(401 442 415 428)(402 441 416 427)(403 440 417 426)(404 439 418 425)(405 438 419 424)(406 437 420 423)
(1 95 356 211)(2 110 357 198)(3 97 358 213)(4 112 359 200)(5 99 360 215)(6 86 361 202)(7 101 362 217)(8 88 363 204)(9 103 364 219)(10 90 337 206)(11 105 338 221)(12 92 339 208)(13 107 340 223)(14 94 341 210)(15 109 342 197)(16 96 343 212)(17 111 344 199)(18 98 345 214)(19 85 346 201)(20 100 347 216)(21 87 348 203)(22 102 349 218)(23 89 350 205)(24 104 351 220)(25 91 352 207)(26 106 353 222)(27 93 354 209)(28 108 355 224)(29 172 324 275)(30 187 325 262)(31 174 326 277)(32 189 327 264)(33 176 328 279)(34 191 329 266)(35 178 330 253)(36 193 331 268)(37 180 332 255)(38 195 333 270)(39 182 334 257)(40 169 335 272)(41 184 336 259)(42 171 309 274)(43 186 310 261)(44 173 311 276)(45 188 312 263)(46 175 313 278)(47 190 314 265)(48 177 315 280)(49 192 316 267)(50 179 317 254)(51 194 318 269)(52 181 319 256)(53 196 320 271)(54 183 321 258)(55 170 322 273)(56 185 323 260)(57 430 248 292)(58 445 249 307)(59 432 250 294)(60 447 251 281)(61 434 252 296)(62 421 225 283)(63 436 226 298)(64 423 227 285)(65 438 228 300)(66 425 229 287)(67 440 230 302)(68 427 231 289)(69 442 232 304)(70 429 233 291)(71 444 234 306)(72 431 235 293)(73 446 236 308)(74 433 237 295)(75 448 238 282)(76 435 239 297)(77 422 240 284)(78 437 241 299)(79 424 242 286)(80 439 243 301)(81 426 244 288)(82 441 245 303)(83 428 246 290)(84 443 247 305)(113 165 386 404)(114 152 387 419)(115 167 388 406)(116 154 389 393)(117 141 390 408)(118 156 391 395)(119 143 392 410)(120 158 365 397)(121 145 366 412)(122 160 367 399)(123 147 368 414)(124 162 369 401)(125 149 370 416)(126 164 371 403)(127 151 372 418)(128 166 373 405)(129 153 374 420)(130 168 375 407)(131 155 376 394)(132 142 377 409)(133 157 378 396)(134 144 379 411)(135 159 380 398)(136 146 381 413)(137 161 382 400)(138 148 383 415)(139 163 384 402)(140 150 385 417)
(1 289 356 427)(2 290 357 428)(3 291 358 429)(4 292 359 430)(5 293 360 431)(6 294 361 432)(7 295 362 433)(8 296 363 434)(9 297 364 435)(10 298 337 436)(11 299 338 437)(12 300 339 438)(13 301 340 439)(14 302 341 440)(15 303 342 441)(16 304 343 442)(17 305 344 443)(18 306 345 444)(19 307 346 445)(20 308 347 446)(21 281 348 447)(22 282 349 448)(23 283 350 421)(24 284 351 422)(25 285 352 423)(26 286 353 424)(27 287 354 425)(28 288 355 426)(29 392 324 119)(30 365 325 120)(31 366 326 121)(32 367 327 122)(33 368 328 123)(34 369 329 124)(35 370 330 125)(36 371 331 126)(37 372 332 127)(38 373 333 128)(39 374 334 129)(40 375 335 130)(41 376 336 131)(42 377 309 132)(43 378 310 133)(44 379 311 134)(45 380 312 135)(46 381 313 136)(47 382 314 137)(48 383 315 138)(49 384 316 139)(50 385 317 140)(51 386 318 113)(52 387 319 114)(53 388 320 115)(54 389 321 116)(55 390 322 117)(56 391 323 118)(57 112 248 200)(58 85 249 201)(59 86 250 202)(60 87 251 203)(61 88 252 204)(62 89 225 205)(63 90 226 206)(64 91 227 207)(65 92 228 208)(66 93 229 209)(67 94 230 210)(68 95 231 211)(69 96 232 212)(70 97 233 213)(71 98 234 214)(72 99 235 215)(73 100 236 216)(74 101 237 217)(75 102 238 218)(76 103 239 219)(77 104 240 220)(78 105 241 221)(79 106 242 222)(80 107 243 223)(81 108 244 224)(82 109 245 197)(83 110 246 198)(84 111 247 199)(141 273 408 170)(142 274 409 171)(143 275 410 172)(144 276 411 173)(145 277 412 174)(146 278 413 175)(147 279 414 176)(148 280 415 177)(149 253 416 178)(150 254 417 179)(151 255 418 180)(152 256 419 181)(153 257 420 182)(154 258 393 183)(155 259 394 184)(156 260 395 185)(157 261 396 186)(158 262 397 187)(159 263 398 188)(160 264 399 189)(161 265 400 190)(162 266 401 191)(163 267 402 192)(164 268 403 193)(165 269 404 194)(166 270 405 195)(167 271 406 196)(168 272 407 169)

G:=sub<Sym(448)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252)(253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308)(309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364)(365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392)(393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420)(421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448), (1,192,15,178)(2,191,16,177)(3,190,17,176)(4,189,18,175)(5,188,19,174)(6,187,20,173)(7,186,21,172)(8,185,22,171)(9,184,23,170)(10,183,24,169)(11,182,25,196)(12,181,26,195)(13,180,27,194)(14,179,28,193)(29,210,43,224)(30,209,44,223)(31,208,45,222)(32,207,46,221)(33,206,47,220)(34,205,48,219)(35,204,49,218)(36,203,50,217)(37,202,51,216)(38,201,52,215)(39,200,53,214)(40,199,54,213)(41,198,55,212)(42,197,56,211)(57,388,71,374)(58,387,72,373)(59,386,73,372)(60,385,74,371)(61,384,75,370)(62,383,76,369)(63,382,77,368)(64,381,78,367)(65,380,79,366)(66,379,80,365)(67,378,81,392)(68,377,82,391)(69,376,83,390)(70,375,84,389)(85,319,99,333)(86,318,100,332)(87,317,101,331)(88,316,102,330)(89,315,103,329)(90,314,104,328)(91,313,105,327)(92,312,106,326)(93,311,107,325)(94,310,108,324)(95,309,109,323)(96,336,110,322)(97,335,111,321)(98,334,112,320)(113,236,127,250)(114,235,128,249)(115,234,129,248)(116,233,130,247)(117,232,131,246)(118,231,132,245)(119,230,133,244)(120,229,134,243)(121,228,135,242)(122,227,136,241)(123,226,137,240)(124,225,138,239)(125,252,139,238)(126,251,140,237)(141,297,155,283)(142,296,156,282)(143,295,157,281)(144,294,158,308)(145,293,159,307)(146,292,160,306)(147,291,161,305)(148,290,162,304)(149,289,163,303)(150,288,164,302)(151,287,165,301)(152,286,166,300)(153,285,167,299)(154,284,168,298)(253,356,267,342)(254,355,268,341)(255,354,269,340)(256,353,270,339)(257,352,271,338)(258,351,272,337)(259,350,273,364)(260,349,274,363)(261,348,275,362)(262,347,276,361)(263,346,277,360)(264,345,278,359)(265,344,279,358)(266,343,280,357)(393,422,407,436)(394,421,408,435)(395,448,409,434)(396,447,410,433)(397,446,411,432)(398,445,412,431)(399,444,413,430)(400,443,414,429)(401,442,415,428)(402,441,416,427)(403,440,417,426)(404,439,418,425)(405,438,419,424)(406,437,420,423), (1,95,356,211)(2,110,357,198)(3,97,358,213)(4,112,359,200)(5,99,360,215)(6,86,361,202)(7,101,362,217)(8,88,363,204)(9,103,364,219)(10,90,337,206)(11,105,338,221)(12,92,339,208)(13,107,340,223)(14,94,341,210)(15,109,342,197)(16,96,343,212)(17,111,344,199)(18,98,345,214)(19,85,346,201)(20,100,347,216)(21,87,348,203)(22,102,349,218)(23,89,350,205)(24,104,351,220)(25,91,352,207)(26,106,353,222)(27,93,354,209)(28,108,355,224)(29,172,324,275)(30,187,325,262)(31,174,326,277)(32,189,327,264)(33,176,328,279)(34,191,329,266)(35,178,330,253)(36,193,331,268)(37,180,332,255)(38,195,333,270)(39,182,334,257)(40,169,335,272)(41,184,336,259)(42,171,309,274)(43,186,310,261)(44,173,311,276)(45,188,312,263)(46,175,313,278)(47,190,314,265)(48,177,315,280)(49,192,316,267)(50,179,317,254)(51,194,318,269)(52,181,319,256)(53,196,320,271)(54,183,321,258)(55,170,322,273)(56,185,323,260)(57,430,248,292)(58,445,249,307)(59,432,250,294)(60,447,251,281)(61,434,252,296)(62,421,225,283)(63,436,226,298)(64,423,227,285)(65,438,228,300)(66,425,229,287)(67,440,230,302)(68,427,231,289)(69,442,232,304)(70,429,233,291)(71,444,234,306)(72,431,235,293)(73,446,236,308)(74,433,237,295)(75,448,238,282)(76,435,239,297)(77,422,240,284)(78,437,241,299)(79,424,242,286)(80,439,243,301)(81,426,244,288)(82,441,245,303)(83,428,246,290)(84,443,247,305)(113,165,386,404)(114,152,387,419)(115,167,388,406)(116,154,389,393)(117,141,390,408)(118,156,391,395)(119,143,392,410)(120,158,365,397)(121,145,366,412)(122,160,367,399)(123,147,368,414)(124,162,369,401)(125,149,370,416)(126,164,371,403)(127,151,372,418)(128,166,373,405)(129,153,374,420)(130,168,375,407)(131,155,376,394)(132,142,377,409)(133,157,378,396)(134,144,379,411)(135,159,380,398)(136,146,381,413)(137,161,382,400)(138,148,383,415)(139,163,384,402)(140,150,385,417), (1,289,356,427)(2,290,357,428)(3,291,358,429)(4,292,359,430)(5,293,360,431)(6,294,361,432)(7,295,362,433)(8,296,363,434)(9,297,364,435)(10,298,337,436)(11,299,338,437)(12,300,339,438)(13,301,340,439)(14,302,341,440)(15,303,342,441)(16,304,343,442)(17,305,344,443)(18,306,345,444)(19,307,346,445)(20,308,347,446)(21,281,348,447)(22,282,349,448)(23,283,350,421)(24,284,351,422)(25,285,352,423)(26,286,353,424)(27,287,354,425)(28,288,355,426)(29,392,324,119)(30,365,325,120)(31,366,326,121)(32,367,327,122)(33,368,328,123)(34,369,329,124)(35,370,330,125)(36,371,331,126)(37,372,332,127)(38,373,333,128)(39,374,334,129)(40,375,335,130)(41,376,336,131)(42,377,309,132)(43,378,310,133)(44,379,311,134)(45,380,312,135)(46,381,313,136)(47,382,314,137)(48,383,315,138)(49,384,316,139)(50,385,317,140)(51,386,318,113)(52,387,319,114)(53,388,320,115)(54,389,321,116)(55,390,322,117)(56,391,323,118)(57,112,248,200)(58,85,249,201)(59,86,250,202)(60,87,251,203)(61,88,252,204)(62,89,225,205)(63,90,226,206)(64,91,227,207)(65,92,228,208)(66,93,229,209)(67,94,230,210)(68,95,231,211)(69,96,232,212)(70,97,233,213)(71,98,234,214)(72,99,235,215)(73,100,236,216)(74,101,237,217)(75,102,238,218)(76,103,239,219)(77,104,240,220)(78,105,241,221)(79,106,242,222)(80,107,243,223)(81,108,244,224)(82,109,245,197)(83,110,246,198)(84,111,247,199)(141,273,408,170)(142,274,409,171)(143,275,410,172)(144,276,411,173)(145,277,412,174)(146,278,413,175)(147,279,414,176)(148,280,415,177)(149,253,416,178)(150,254,417,179)(151,255,418,180)(152,256,419,181)(153,257,420,182)(154,258,393,183)(155,259,394,184)(156,260,395,185)(157,261,396,186)(158,262,397,187)(159,263,398,188)(160,264,399,189)(161,265,400,190)(162,266,401,191)(163,267,402,192)(164,268,403,193)(165,269,404,194)(166,270,405,195)(167,271,406,196)(168,272,407,169)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224)(225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252)(253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280)(281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308)(309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364)(365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392)(393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420)(421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448), (1,192,15,178)(2,191,16,177)(3,190,17,176)(4,189,18,175)(5,188,19,174)(6,187,20,173)(7,186,21,172)(8,185,22,171)(9,184,23,170)(10,183,24,169)(11,182,25,196)(12,181,26,195)(13,180,27,194)(14,179,28,193)(29,210,43,224)(30,209,44,223)(31,208,45,222)(32,207,46,221)(33,206,47,220)(34,205,48,219)(35,204,49,218)(36,203,50,217)(37,202,51,216)(38,201,52,215)(39,200,53,214)(40,199,54,213)(41,198,55,212)(42,197,56,211)(57,388,71,374)(58,387,72,373)(59,386,73,372)(60,385,74,371)(61,384,75,370)(62,383,76,369)(63,382,77,368)(64,381,78,367)(65,380,79,366)(66,379,80,365)(67,378,81,392)(68,377,82,391)(69,376,83,390)(70,375,84,389)(85,319,99,333)(86,318,100,332)(87,317,101,331)(88,316,102,330)(89,315,103,329)(90,314,104,328)(91,313,105,327)(92,312,106,326)(93,311,107,325)(94,310,108,324)(95,309,109,323)(96,336,110,322)(97,335,111,321)(98,334,112,320)(113,236,127,250)(114,235,128,249)(115,234,129,248)(116,233,130,247)(117,232,131,246)(118,231,132,245)(119,230,133,244)(120,229,134,243)(121,228,135,242)(122,227,136,241)(123,226,137,240)(124,225,138,239)(125,252,139,238)(126,251,140,237)(141,297,155,283)(142,296,156,282)(143,295,157,281)(144,294,158,308)(145,293,159,307)(146,292,160,306)(147,291,161,305)(148,290,162,304)(149,289,163,303)(150,288,164,302)(151,287,165,301)(152,286,166,300)(153,285,167,299)(154,284,168,298)(253,356,267,342)(254,355,268,341)(255,354,269,340)(256,353,270,339)(257,352,271,338)(258,351,272,337)(259,350,273,364)(260,349,274,363)(261,348,275,362)(262,347,276,361)(263,346,277,360)(264,345,278,359)(265,344,279,358)(266,343,280,357)(393,422,407,436)(394,421,408,435)(395,448,409,434)(396,447,410,433)(397,446,411,432)(398,445,412,431)(399,444,413,430)(400,443,414,429)(401,442,415,428)(402,441,416,427)(403,440,417,426)(404,439,418,425)(405,438,419,424)(406,437,420,423), (1,95,356,211)(2,110,357,198)(3,97,358,213)(4,112,359,200)(5,99,360,215)(6,86,361,202)(7,101,362,217)(8,88,363,204)(9,103,364,219)(10,90,337,206)(11,105,338,221)(12,92,339,208)(13,107,340,223)(14,94,341,210)(15,109,342,197)(16,96,343,212)(17,111,344,199)(18,98,345,214)(19,85,346,201)(20,100,347,216)(21,87,348,203)(22,102,349,218)(23,89,350,205)(24,104,351,220)(25,91,352,207)(26,106,353,222)(27,93,354,209)(28,108,355,224)(29,172,324,275)(30,187,325,262)(31,174,326,277)(32,189,327,264)(33,176,328,279)(34,191,329,266)(35,178,330,253)(36,193,331,268)(37,180,332,255)(38,195,333,270)(39,182,334,257)(40,169,335,272)(41,184,336,259)(42,171,309,274)(43,186,310,261)(44,173,311,276)(45,188,312,263)(46,175,313,278)(47,190,314,265)(48,177,315,280)(49,192,316,267)(50,179,317,254)(51,194,318,269)(52,181,319,256)(53,196,320,271)(54,183,321,258)(55,170,322,273)(56,185,323,260)(57,430,248,292)(58,445,249,307)(59,432,250,294)(60,447,251,281)(61,434,252,296)(62,421,225,283)(63,436,226,298)(64,423,227,285)(65,438,228,300)(66,425,229,287)(67,440,230,302)(68,427,231,289)(69,442,232,304)(70,429,233,291)(71,444,234,306)(72,431,235,293)(73,446,236,308)(74,433,237,295)(75,448,238,282)(76,435,239,297)(77,422,240,284)(78,437,241,299)(79,424,242,286)(80,439,243,301)(81,426,244,288)(82,441,245,303)(83,428,246,290)(84,443,247,305)(113,165,386,404)(114,152,387,419)(115,167,388,406)(116,154,389,393)(117,141,390,408)(118,156,391,395)(119,143,392,410)(120,158,365,397)(121,145,366,412)(122,160,367,399)(123,147,368,414)(124,162,369,401)(125,149,370,416)(126,164,371,403)(127,151,372,418)(128,166,373,405)(129,153,374,420)(130,168,375,407)(131,155,376,394)(132,142,377,409)(133,157,378,396)(134,144,379,411)(135,159,380,398)(136,146,381,413)(137,161,382,400)(138,148,383,415)(139,163,384,402)(140,150,385,417), (1,289,356,427)(2,290,357,428)(3,291,358,429)(4,292,359,430)(5,293,360,431)(6,294,361,432)(7,295,362,433)(8,296,363,434)(9,297,364,435)(10,298,337,436)(11,299,338,437)(12,300,339,438)(13,301,340,439)(14,302,341,440)(15,303,342,441)(16,304,343,442)(17,305,344,443)(18,306,345,444)(19,307,346,445)(20,308,347,446)(21,281,348,447)(22,282,349,448)(23,283,350,421)(24,284,351,422)(25,285,352,423)(26,286,353,424)(27,287,354,425)(28,288,355,426)(29,392,324,119)(30,365,325,120)(31,366,326,121)(32,367,327,122)(33,368,328,123)(34,369,329,124)(35,370,330,125)(36,371,331,126)(37,372,332,127)(38,373,333,128)(39,374,334,129)(40,375,335,130)(41,376,336,131)(42,377,309,132)(43,378,310,133)(44,379,311,134)(45,380,312,135)(46,381,313,136)(47,382,314,137)(48,383,315,138)(49,384,316,139)(50,385,317,140)(51,386,318,113)(52,387,319,114)(53,388,320,115)(54,389,321,116)(55,390,322,117)(56,391,323,118)(57,112,248,200)(58,85,249,201)(59,86,250,202)(60,87,251,203)(61,88,252,204)(62,89,225,205)(63,90,226,206)(64,91,227,207)(65,92,228,208)(66,93,229,209)(67,94,230,210)(68,95,231,211)(69,96,232,212)(70,97,233,213)(71,98,234,214)(72,99,235,215)(73,100,236,216)(74,101,237,217)(75,102,238,218)(76,103,239,219)(77,104,240,220)(78,105,241,221)(79,106,242,222)(80,107,243,223)(81,108,244,224)(82,109,245,197)(83,110,246,198)(84,111,247,199)(141,273,408,170)(142,274,409,171)(143,275,410,172)(144,276,411,173)(145,277,412,174)(146,278,413,175)(147,279,414,176)(148,280,415,177)(149,253,416,178)(150,254,417,179)(151,255,418,180)(152,256,419,181)(153,257,420,182)(154,258,393,183)(155,259,394,184)(156,260,395,185)(157,261,396,186)(158,262,397,187)(159,263,398,188)(160,264,399,189)(161,265,400,190)(162,266,401,191)(163,267,402,192)(164,268,403,193)(165,269,404,194)(166,270,405,195)(167,271,406,196)(168,272,407,169) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28),(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84),(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196),(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224),(225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252),(253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280),(281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308),(309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336),(337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364),(365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392),(393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420),(421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448)], [(1,192,15,178),(2,191,16,177),(3,190,17,176),(4,189,18,175),(5,188,19,174),(6,187,20,173),(7,186,21,172),(8,185,22,171),(9,184,23,170),(10,183,24,169),(11,182,25,196),(12,181,26,195),(13,180,27,194),(14,179,28,193),(29,210,43,224),(30,209,44,223),(31,208,45,222),(32,207,46,221),(33,206,47,220),(34,205,48,219),(35,204,49,218),(36,203,50,217),(37,202,51,216),(38,201,52,215),(39,200,53,214),(40,199,54,213),(41,198,55,212),(42,197,56,211),(57,388,71,374),(58,387,72,373),(59,386,73,372),(60,385,74,371),(61,384,75,370),(62,383,76,369),(63,382,77,368),(64,381,78,367),(65,380,79,366),(66,379,80,365),(67,378,81,392),(68,377,82,391),(69,376,83,390),(70,375,84,389),(85,319,99,333),(86,318,100,332),(87,317,101,331),(88,316,102,330),(89,315,103,329),(90,314,104,328),(91,313,105,327),(92,312,106,326),(93,311,107,325),(94,310,108,324),(95,309,109,323),(96,336,110,322),(97,335,111,321),(98,334,112,320),(113,236,127,250),(114,235,128,249),(115,234,129,248),(116,233,130,247),(117,232,131,246),(118,231,132,245),(119,230,133,244),(120,229,134,243),(121,228,135,242),(122,227,136,241),(123,226,137,240),(124,225,138,239),(125,252,139,238),(126,251,140,237),(141,297,155,283),(142,296,156,282),(143,295,157,281),(144,294,158,308),(145,293,159,307),(146,292,160,306),(147,291,161,305),(148,290,162,304),(149,289,163,303),(150,288,164,302),(151,287,165,301),(152,286,166,300),(153,285,167,299),(154,284,168,298),(253,356,267,342),(254,355,268,341),(255,354,269,340),(256,353,270,339),(257,352,271,338),(258,351,272,337),(259,350,273,364),(260,349,274,363),(261,348,275,362),(262,347,276,361),(263,346,277,360),(264,345,278,359),(265,344,279,358),(266,343,280,357),(393,422,407,436),(394,421,408,435),(395,448,409,434),(396,447,410,433),(397,446,411,432),(398,445,412,431),(399,444,413,430),(400,443,414,429),(401,442,415,428),(402,441,416,427),(403,440,417,426),(404,439,418,425),(405,438,419,424),(406,437,420,423)], [(1,95,356,211),(2,110,357,198),(3,97,358,213),(4,112,359,200),(5,99,360,215),(6,86,361,202),(7,101,362,217),(8,88,363,204),(9,103,364,219),(10,90,337,206),(11,105,338,221),(12,92,339,208),(13,107,340,223),(14,94,341,210),(15,109,342,197),(16,96,343,212),(17,111,344,199),(18,98,345,214),(19,85,346,201),(20,100,347,216),(21,87,348,203),(22,102,349,218),(23,89,350,205),(24,104,351,220),(25,91,352,207),(26,106,353,222),(27,93,354,209),(28,108,355,224),(29,172,324,275),(30,187,325,262),(31,174,326,277),(32,189,327,264),(33,176,328,279),(34,191,329,266),(35,178,330,253),(36,193,331,268),(37,180,332,255),(38,195,333,270),(39,182,334,257),(40,169,335,272),(41,184,336,259),(42,171,309,274),(43,186,310,261),(44,173,311,276),(45,188,312,263),(46,175,313,278),(47,190,314,265),(48,177,315,280),(49,192,316,267),(50,179,317,254),(51,194,318,269),(52,181,319,256),(53,196,320,271),(54,183,321,258),(55,170,322,273),(56,185,323,260),(57,430,248,292),(58,445,249,307),(59,432,250,294),(60,447,251,281),(61,434,252,296),(62,421,225,283),(63,436,226,298),(64,423,227,285),(65,438,228,300),(66,425,229,287),(67,440,230,302),(68,427,231,289),(69,442,232,304),(70,429,233,291),(71,444,234,306),(72,431,235,293),(73,446,236,308),(74,433,237,295),(75,448,238,282),(76,435,239,297),(77,422,240,284),(78,437,241,299),(79,424,242,286),(80,439,243,301),(81,426,244,288),(82,441,245,303),(83,428,246,290),(84,443,247,305),(113,165,386,404),(114,152,387,419),(115,167,388,406),(116,154,389,393),(117,141,390,408),(118,156,391,395),(119,143,392,410),(120,158,365,397),(121,145,366,412),(122,160,367,399),(123,147,368,414),(124,162,369,401),(125,149,370,416),(126,164,371,403),(127,151,372,418),(128,166,373,405),(129,153,374,420),(130,168,375,407),(131,155,376,394),(132,142,377,409),(133,157,378,396),(134,144,379,411),(135,159,380,398),(136,146,381,413),(137,161,382,400),(138,148,383,415),(139,163,384,402),(140,150,385,417)], [(1,289,356,427),(2,290,357,428),(3,291,358,429),(4,292,359,430),(5,293,360,431),(6,294,361,432),(7,295,362,433),(8,296,363,434),(9,297,364,435),(10,298,337,436),(11,299,338,437),(12,300,339,438),(13,301,340,439),(14,302,341,440),(15,303,342,441),(16,304,343,442),(17,305,344,443),(18,306,345,444),(19,307,346,445),(20,308,347,446),(21,281,348,447),(22,282,349,448),(23,283,350,421),(24,284,351,422),(25,285,352,423),(26,286,353,424),(27,287,354,425),(28,288,355,426),(29,392,324,119),(30,365,325,120),(31,366,326,121),(32,367,327,122),(33,368,328,123),(34,369,329,124),(35,370,330,125),(36,371,331,126),(37,372,332,127),(38,373,333,128),(39,374,334,129),(40,375,335,130),(41,376,336,131),(42,377,309,132),(43,378,310,133),(44,379,311,134),(45,380,312,135),(46,381,313,136),(47,382,314,137),(48,383,315,138),(49,384,316,139),(50,385,317,140),(51,386,318,113),(52,387,319,114),(53,388,320,115),(54,389,321,116),(55,390,322,117),(56,391,323,118),(57,112,248,200),(58,85,249,201),(59,86,250,202),(60,87,251,203),(61,88,252,204),(62,89,225,205),(63,90,226,206),(64,91,227,207),(65,92,228,208),(66,93,229,209),(67,94,230,210),(68,95,231,211),(69,96,232,212),(70,97,233,213),(71,98,234,214),(72,99,235,215),(73,100,236,216),(74,101,237,217),(75,102,238,218),(76,103,239,219),(77,104,240,220),(78,105,241,221),(79,106,242,222),(80,107,243,223),(81,108,244,224),(82,109,245,197),(83,110,246,198),(84,111,247,199),(141,273,408,170),(142,274,409,171),(143,275,410,172),(144,276,411,173),(145,277,412,174),(146,278,413,175),(147,279,414,176),(148,280,415,177),(149,253,416,178),(150,254,417,179),(151,255,418,180),(152,256,419,181),(153,257,420,182),(154,258,393,183),(155,259,394,184),(156,260,395,185),(157,261,396,186),(158,262,397,187),(159,263,398,188),(160,264,399,189),(161,265,400,190),(162,266,401,191),(163,267,402,192),(164,268,403,193),(165,269,404,194),(166,270,405,195),(167,271,406,196),(168,272,407,169)]])

61 conjugacy classes

 class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 7A 7B 7C 8A 8B 8C 8D 14A ··· 14I 28A ··· 28R 28S ··· 28AD order 1 2 2 2 4 4 4 4 4 4 4 4 4 4 4 7 7 7 8 8 8 8 14 ··· 14 28 ··· 28 28 ··· 28 size 1 1 1 1 2 2 2 2 4 8 8 28 28 28 28 2 2 2 28 28 28 28 2 ··· 2 4 ··· 4 8 ··· 8

61 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 4 4 type + + + + + + - + + + + - - - + image C1 C2 C2 C2 C2 C2 Q8 D4 D7 SD16 C4○D4 D14 D14 C7⋊D4 C8.C22 D4.D7 Q8×D7 Q8⋊2D7 C28.C23 kernel Dic14⋊6Q8 C28⋊C8 C4.Dic14 C14.Q16 C4×Dic14 C7×C4⋊Q8 Dic14 C2×C28 C4⋊Q8 C28 C28 C42 C4⋊C4 C2×C4 C14 C4 C4 C4 C2 # reps 1 1 2 2 1 1 2 2 3 4 2 3 6 12 1 6 3 3 6

Matrix representation of Dic146Q8 in GL6(𝔽113)

 1 91 0 0 0 0 72 112 0 0 0 0 0 0 25 112 0 0 0 0 2 9 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 83 100 0 0 0 0 78 30 0 0 0 0 0 0 79 34 0 0 0 0 89 34 0 0 0 0 0 0 112 0 0 0 0 0 0 112
,
 66 8 0 0 0 0 63 47 0 0 0 0 0 0 96 101 0 0 0 0 24 17 0 0 0 0 0 0 1 81 0 0 0 0 106 112
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 66 75 0 0 0 0 76 47

G:=sub<GL(6,GF(113))| [1,72,0,0,0,0,91,112,0,0,0,0,0,0,25,2,0,0,0,0,112,9,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[83,78,0,0,0,0,100,30,0,0,0,0,0,0,79,89,0,0,0,0,34,34,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[66,63,0,0,0,0,8,47,0,0,0,0,0,0,96,24,0,0,0,0,101,17,0,0,0,0,0,0,1,106,0,0,0,0,81,112],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,66,76,0,0,0,0,75,47] >;

Dic146Q8 in GAP, Magma, Sage, TeX

{\rm Dic}_{14}\rtimes_6Q_8
% in TeX

G:=Group("Dic14:6Q8");
// GroupNames label

G:=SmallGroup(448,628);
// by ID

G=gap.SmallGroup(448,628);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,120,254,219,100,1123,297,136,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^28=c^4=1,b^2=a^14,d^2=c^2,b*a*b^-1=a^-1,c*a*c^-1=a^15,a*d=d*a,c*b*c^-1=a^21*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽


text:
All Questions

135,537 questions
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I have a set of data of counts of hares in summer and in winter, which is very unbalanced: winter was too cold, and samplings were taken only in some 20 occasions, while during the pleasant summer the ...
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PRISMA Statement: number of records returned by (one/several) databases?

In keeping with the guidelines of the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) Statement, I am trying to fill in their flowchart (Fig. 1) with the details of the ...
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Properties of Nonparametric Test Statistics $B$ [on hold]

Given Consider the upper tail $H_0: \theta \leq 0 \,\,\, \text{vs} \,\,\, H_a: \theta > 0$ sign test with the test statistic $B = \sum_{i=1}^n{\psi_i}$ where $\psi_i = \mathbb{I}(Z_i > \theta)$...
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format: plain


text:
# How to plot a sequence of short lines of specified colours

Further to my impasse with ListVectorPlot questions 155785 and 156025, I am trying to restart from basics. I have tried but couldn't find the right instructions. Sorry to have to ask.

Can anyone please write code to plot a series of short lines from (x,k*sin[x]) to (x+.1*kx,ksin[x]+.1) for {x, -1.57, 1.57, .1} and {k, {.01, .2, .4, .6, 1}} with according colors {Red, Brown, Blue, Pink, Purple} Thank you very much.

Then I could use Show to combine this with a parametric plot of (x,k*sin[x]) with the the same colors for the same k to achieve what I wanted ListVectorPlot to do, but it always mixed up the colours or the scaling of the short lines (representing vectors representing a complex function).

## 1 Answer

color[k_] :=
Switch[k,
Evaluate[Sequence @@ (Flatten@
Transpose[{{0.01, 0.2, 0.4, 0.6, 1}, {Red, Brown, Blue, Pink,
Purple}}])]]

Graphics[Table[
{color[k], Line[{{x, k*Sin[x]}, {x + 0.1*k*x, k*Sin[x] + 0.1}}]},
{x, -1.57, 1.57, 0.1}, {k, {0.01, 0.2, 0.4, 0.6, 1}}]]

Show[
ParametricPlot[
Evaluate@Table[{x, k*Sin[x]}, {k, {0.01, 0.2, 0.4, 0.6, 1}}],
{x, -1.57, 1.57},
PlotStyle -> {Red, Brown, Blue, Pink, Purple}],
Graphics[Table[
{color[k], Line[{{x, k*Sin[x]}, {x + 0.1*k*x, k*Sin[x] + 0.1}}]},
{x, -1.57, 1.57, 0.1}, {k, {0.01, 0.2, 0.4, 0.6, 1}}]]]

• V. grateful for your two suggestions.The first worked beautifully on version 7 here but the second went awry, I couldn't change its strange graph which had dots instead of line segments for x>0 and nothing but the base curve for x<0. But it doesn't matter since the first way works here. – simon Oct 14 '17 at 2:35
• @simon - somehow in the cut and paste a comma got dropped. Try it now with the comma added back. – Bob Hanlon Oct 14 '17 at 2:53
• I found that in the end, I thought it was my computer's cut and paste error.I would have expected an error message from Mathematica. For the base graph I had Plot[Evaluate@Table[k*Sin[x],{k,{.01,.2,.4,.6,1}}],{x,-1.57,1.57},PlotStyle->{Red,Brown,Blue,Pink,Purple}] which is a teeny bit simpler – simon Oct 14 '17 at 3:20
• I never would have figured out that Switch on my own in a miilion years – simon Oct 14 '17 at 3:33


text:
# Algorithms for permutation statistics

@inproceedings{Zeilberger2011AlgorithmsFP,
title={Algorithms for permutation statistics},
author={Doron Zeilberger and Andrew M. Baxter},
year={2011}
}
• Published 2011
• Mathematics
Two sequences u; v of n positive integers are order isomorphic if their terms are in the same relative order. A permutation p said to contain permutation q as a pattern if there is some subsequence of p which is order isomorphic to q. This subsequence is called a copy of q. This notion of pattern containment is generalized to include adjacency restrictions as per dashed patterns. The primary permutation statistics studied in this work are written in terms of the number of copies of a given…
6 Citations

### Refining Enumeration Schemes to Count According to Permutation Statistics

It is proved that when a finite enumeration scheme exists to compute the number of permutations avoiding a given set of vincular patterns, the scheme can also compute the distribution of certain permutation statistics with very little extra computation.

### Some Wilf-equivalences for vincular patterns

• Mathematics
• 2015
We prove several Wilf-equivalences for vincular patterns of length 4, some of which generalize to infinite families of vincular patterns. We also present functional equations for the generating

### Noncommutative Bell polynomials and the dual immaculate basis

• Mathematics
• 2017
We define a new family of noncommutative Bell polynomials in the algebra of free quasi-symmetric functions and relate it to the dual immaculate basis of quasi-symmetric functions. We obtain

### Automatic Generation of Theorems and Proofs on Enumerating Consecutive-Wilf Classes

• Mathematics
• 2013
This article, describes two complementary approaches to enumeration, the positive and the negative, each with its advantages and disadvantages. Both approaches are amenable to automation, and we

## References

SHOWING 1-10 OF 101 REFERENCES

### Decreasing Subsequences in Permutations and Wilf Equivalence for Involutions

• Mathematics
• 2004
In a recent paper, Backelin, West and Xin describe a map φ* that recursively replaces all occurrences of the pattern k... 21 in a permutation σ by occurrences of the pattern (k−1)... 21 k. The

### The Möbius function of the permutation pattern Poset

• Mathematics, Computer Science
• 2009
A large class of pairs of permutations whose intervals in P have Mobius function 0 and a graded poset P is given, which gives a solution to the problem when \sigma occurs precisely once in \tau, and\sigma and\tau satisfy certain further conditions, in which case theMobius function is shown to be either -1, 0 or 1.

### Generalized permutation patterns and a classification of the Mahonian statistics

• Mathematics
• 2000
We introduce generalized permutation patterns, where we allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We show that essentially all Mahonian

### Generalized permutation patterns - a short survey

An occurrence of a classical pattern p in a permutation π is a subsequence of π whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some

### Partially ordered generalized patterns

• S. Kitaev
• Mathematics, Computer Science
Discret. Math.
• 2005

### A Spectral Approach to Consecutive Pattern-Avoiding Permutations

• Mathematics
• 2010
We consider the problem of enumerating permutations in the symmetric group on $n$ elements which avoid a given set of consecutive pattern $S$, and in particular computing asymptotics as $n$ tends to

### Generalized Pattern Avoidance

A complete solution is given for the number of permutations avoiding any single pattern of length three with exactly one adjacent pair of letters, and a new class of set partitions is defined, called monotone partitions, and these partitions are in one-to-one correspondence with non-overlapping partitions.

### Subsequence Containment by Involutions

An exact count of the involutions in S_n which contain a given permutation \tau in S-k as a subsequence is given; this number depends on the patterns of the first j values of \tAU for 1<=j<=k.

### On Growth Rates of Closed Permutation Classes

• Mathematics
Electron. J. Comb.
• 2002
A class of permutations is called closed if 2 implies 2 , where the relation is the natural containment of permutations. Let n be the set of all permutations of 1, 2 ,...,n belonging to . We


text:
# Difficulty with datatool

I want to use the command \DTLstoreinitials from package \usepackage{datatool} in the following way :

\newcommand{\extractInitials}[1]{%
\DTLstoreinitials{#1}{\userInitials}%
\DTLsubstituteall{\userInitials}{.}{}%remove points between the initials
\DTLsubstituteall{\userInitials}{ }{}%remove spaces
\userInitials%
}

If I call the command directly, it works :

\extractInitials{My Name}

gives MN. But if I use an auxiliary command: \newcommand{\nom}{My Name} and try to call

\extractInitials{\nom}

then the compilation fails with error

! Paragraph ended before \@dtl@initials was complete.

How can I fix this?

Here is a minimal example 1 :

\documentclass[12pt]{article}
\usepackage{trackchanges}
\usepackage{datatool}

\newcommand{\extractInitials}[1]{%
%\expandafter\DTLstoreinitials\expandafter{#1}{\userInitials}%
\DTLstoreinitials{#1}{\userInitials}%
\DTLsubstituteall{\userInitials}{.}{}%remove points
\DTLsubstituteall{\userInitials}{ }{}%remove spaces
}
\begin{document}
\extractInitials{AAA BBB}\addeditor{\userInitials}
\extractInitials{CCC DDD}\addeditor{\userInitials}
----------- \\% to see the result of the addeditor commands
\makeatletter
\TC@editorOne\\
\TC@editorTwo\\
\TC@editorThree\\
\makeatother
-----------
\end{document}

The output is CD n/n n/n To compare : example 2

\addeditor{AB}
\addeditor{CD}
----------- \\% to see the result of the addeditor commands
\makeatletter
\TC@editorOne\\
\TC@editorTwo\\
\TC@editorThree\\
\makeatother
-----------

The output is AB CD n/n

-
You don't have to sign with your name since it automatically appears in the lower right corner of your post. I've edited your post accordingly. –  Werner Dec 21 '11 at 23:13
Welcome to TeX.sx! Note that you can edit your posts to add more information. Answer posts are for solutions to the question. –  Martin Scharrer Dec 22 '11 at 22:09
I've added note 3. –  egreg Dec 22 '11 at 22:34
thank you, it solved my problem. –  nicolas roy Dec 22 '11 at 23:42

## 1 Answer

You have two choices.

## First

\newcommand{\extractInitials}[1]{%
\expandafter\DTLstoreinitials\expandafter{#1}{\userInitials}%
\DTLsubstituteall{\userInitials}{.}{}%remove points between the initials
\DTLsubstituteall{\userInitials}{ }{}%remove spaces
\userInitials
}

This can be used if \nom expands immediately to the name and no more processing is needed.

The trick is to access at #1 before processing by \DTLstoreinitials begins. The first \expandafter acts on the second, which in turn expands the first token after the brace: in your case it can be \nom; if you give directly a name nothing happens (but see the second note).

## Second

\makeatletter
\newcommand{\extractInitials}[1]{%
\begingroup\protected@edef\x{%
\endgroup\noexpand\DTLstoreinitials{#1}{\noexpand\userInitials}}\x%
\DTLsubstituteall{\userInitials}{.}{}%remove points between the initials
\DTLsubstituteall{\userInitials}{ }{}%remove spaces
\userInitials
}
\makeatother

This is to be preferred if the contents of \nom is more complicated (say \nom becomes \Prenom\space\Nom. Here we expand until the bottom, but "robusted" macros such as those for accented letters remain untouched.

## Note 1

Using \edef in this context directly is bound to break if the argument of \extractInitials contains accented characters (even when a control sequence is used).

## Note 2

In both cases, results are unpredictable if the first initial is an accented letter. Put it as {É}lie Cartan to get a correct result. However, none of the method works reliably in this case if the input encoding is UTF-8 (for limitations of datatool). Write always a first accented initial in braces.

## Note 3

In case this macro must be fed to another command, the result will depend on what this macro does. For example it will work with \textbf{\extractInitials{My Name}}, since \textbf wants only to print its argument. In other cases a different approach must be taken; for example, in your test document one has to take an indirect path:

\newcommand{\extractInitials}[1]{%
\expandafter\DTLstoreinitials\expandafter{#1}{\userInitials}%
\DTLsubstituteall{\userInitials}{.}{}%remove points between the initials
\DTLsubstituteall{\userInitials}{ }{}%remove spaces
}
\newcommand{\myaddeditor}[1]{%
\extractInitials{#1}\expandafter\addeditor\expandafter{\userInitials}}

and then say \myaddeditor{AAA BBB}

-
Thank you very much. I will use the first one, since \nom expands immediately to the name in my case, and i have accented letter. It works, but i don't quite understand the trick :). Could you explain it to me ? I understand the first \expandafter, it insure that the argumen #1 will be first expanded. But why to "expand" \userItinials ? I thought this is a temporary command where DTLstoreinitials stores the result of the string operation... –  nicolas roy Dec 22 '11 at 9:38
Another problem i'm facing : i'm using the result of \extractInitials in some other command \somecommand{\extractInitials{My Name}} but it fails. This command is one from a package, and i don't know exactly how it is defined. But is there a way to make \extractInitials completely expand, before we give it as an argument to \somecommand, so that the compilation doesnt fails, even if we don't know how \somecommand is build ? –  nicolas roy Dec 22 '11 at 10:22
@nicolasroy Please add to the question a minimal example; you should register on the site (the moderators can then merge other questions you submitted as an unregistered user). –  egreg Dec 22 '11 at 11:45
Well, my question was precisely, how can i make the command \extractInitials sufficiently robust, so that i can use it inside any command in the future... But ok, for the moment, i want to be able to use: \addeditor{\extractInitials{My Name}} where \addeditor is a command from the package trackchanges. –  nicolas roy Dec 22 '11 at 18:11
@nicolasroy If you cut the last \userInitials from the main macro and say \extractInitials{My Name}\addeditor{\userInitials} it might work (maybe with a couple of \expandafters). –  egreg Dec 22 '11 at 18:14


text:
# A look at the pastry distributed hashtable

19 Sep 2020 - tsp
Last update 19 Sep 2020

Please note: Pastry is not my design or invention, it’s well documented in a bunch of papers. There is a quick overview available by the authors of pastry too.

## What is a DHT?

A distributed hash table (DHT) is a distributed database that provides key-value store like semantic. Basically it’s a distributed system that allows one to store values with a given key and retrieve them again using the key. This is called a hash table since the key is usually calculated as a hash value of the stored objects. A hash function is a one way function that should yield a evenly distributed key value that is guaranteed to change whenever an object changes. It’s also often desirable to be collision free - but of course that’s not possible in any case if the keyspace is smaller than the value space; hash tables are usually capable of dealing with such collisions.

The distributed behavior is achieved by assigning nodes IDs from the same keyspace and assigning objects to the numerically nearest node(s). Redundancy can be achieved by using the $n$ closest objects.

Since node IDs are assigned randomly (either by using random number generators, being derived via a hash function from the address of the node or being the hash of a credential like a public key) they’re statistically evenly distributed in keyspace if everything is done right.

Since they operate on some really basic principles DHTs scale well, are self organizing, are robust even in case nodes fail, are fault tolerant and are distributing load evenly on the system. Pastry also offers reduced load on the network by employing a proximity metric while building some of it’s tables. Also pastry is a little bit different than most other DHTs - it includes an overlay routing network that allows one to route messages to nodes that one doesn’t have information about. Routing tables are usually updated whenever a node fails or joins the network.

One can build a huge number of services on top of a DHT:

• Distributed object storage (see for example Ceph - that’s not built using pastry though)
• Filesystems (see for example again Ceph, PAST)
• Publish subscribe systems (for example SCRIBE)
• Distributed caches (see SQUIRREL)
• Content distribution systems (see SplitStream)
• Generic messaging (see POST)
• Peer to peer resource sharing systems (see Scrivener)

There is a nearly unlimited amount of applications - depending on the environment they run in one has to take some security considerations though.

## Network parameterization

First of all pastry uses 128 bit Node IDs (i.e. 16 bytes). There is a number of tunables though:

• The number of bits per digit or subnet inside the keyspace. This is termed $b$ and is usually set to $4$ so each digit in hexadecimal representation would be equal to one routing step.
• The number of nodes is termed $N$.
• The size of the neighborhood set $\mid N \mid$ is usually set to $2*2^b$
• The size of the leaf set $\mid L \mid$ is usually set to $2^b$

## Information kept about other nodes

First lets think about the information required to contact other nodes:

• It’s IP address(es). Depending on the way the system works this might be a single IPv4 or IPv6 address or a collection of potential addresses used during an interactive connectivity establishment process. Usually containing a single IPv4 and a single IPv6 address is sufficient, sometimes a hostname might also be needed (for example when supporting TOR hidden services which requires connections to be made using SOCKS4a and hostnames)
• It’s node ID - usually a 128 bit number.
• Depending on signatures: A public signature key (for example a DSS key)
• Depending on encryption: A public key (for example for RSA or ECC) or a shared secret if all nodes are trusted.

• Proximity information
• Timestamp of last contact
• Error counters
• A network socket handle for an open connection to the given node (depending on the implementation).

## Node state

### Neighborhood set ($N$)

The neighborhood set is not directly used during message routing but is usually used for locality considerations. It contains the $\mid N \mid$ nearest nodes according to the network metric - one could use hop count, latency or other cost based information. Note that it’s not specified by the original paper which metric one should use and the reference implementation allowed external tools like traceroute and ping to be used to determine the proximity value. Usually the application keeps track of the nodes by simply measuring proximity to known nodes and updates this set accordingly - it’s advised to store them in a ordered fashion for faster access.

The size is usually set to $2*2^b$, i.e. for the often used $b=4$ this would lead to 32 entries (in this case linear scan might also be suitable during access).

During join of the network a node initializes it’s neighborhood set to the neighborhood set of it’s initially contacted seed node.

### Routing table ($R$)

The routing table is the main fabric used during message routing .Basically it contains a row for every digit (i.e. group of $b$ bits in the node ID space). For example for 128 bit node IDs and a value of $b=4$ it would contain 32 rows. In the paper describing pastry this number of rows is written as $log_{2^b} N$.

Each row contains $2^b-1$ possible entries - one might implement it due to implementation constraints with $2^b$ entries. Each entry contains the (topologically) closest known node with the corresponding digit that shares the first row-index digits with the current node.

For a node ID of $0123$ the table would start with

 none 1xxx 2xxx 3xxx 4xxx 5xxx 6xxx 7xxx 8xxx 9xxx 00xx none 02xx 03xx 04xx 05xx 06xx 07xx 08xx 09xx 010x 011x none 013x 014x 015x 016x 017x 018x 019x 0120 0121 0122 none 0124 0125 0126 0127 0128 0129

Note that each entry might be empty, occupied by the own node or contain an arbitrary entry that satisfies the given constraint. On average only $log_(2*b) N$ entries are populated though.

The typical network using $b=4$ and 128 bit node IDs would require 32 rows with 15 entries each (or 16 if not optimized to exclude the own node in each row), thus 480 entries which is totally acceptable even for applications on platforms like the ESP8266/ESP32 - depending on the stored information.

### Leaf set ($L$)

The leaf set works somewhat like the neighborhood set and contains the $\frac{L}{2}$ closest nodes that are larger and $\frac{L}{2}$ closest nodes that are smaller than the current node ID - but this time not in proximity space but in key space. Nodes should be stored in order to allow fast binary search. The size of the leaf set is also configurable and is usually set to $2^b$ entries (for a typical $b=4$ i.e. to $16$ entries, which would be small enough even for unordered access).

## Message routing

Note that message routing requires a route to be already joined and join requires message routing to be working on other nodes so this is somewhat an chicken-egg-problem. This routing will be used in a similar way during key-value storage to determine which node is responsible for a given key. First I’ll describe how the message routing works. Basically the node received a message from any other node that has a destination node ID (and usually should also carry the source nodes information).

The node first checks if the destination key is contained inside the range of it’s leaf set. It simply checks if the destination key $D$ is larger or equal to the smallest and smaller or equal to the largest known node ID in the leaf set. If this is the case the message is forwarded to the node with the minimum distance to the destination key.

If the leaf set could not be used it tries to use the routing table. This is done by first determining the length of the prefix that the current node and the destination node are sharing ($l$). Then it tries to look up the routing table in the $l$ row at the position corresponding to the next digit. This can be accomplished by simple binary and if $2^b$ entries are stored per row instead of $2^b-1$. If a node is found in the routing table the message gets forwarded to the given node.

In case this also didn’t work out which is said to be a rare case in the original paper the message is forwarded to any known node (from routing table, leaf set or neighborhood set) that:

• shares a longer or equally long prefix
• has the minimum known distance to the destination node ID

If no such node exists the message has arrived at it’s destination node. Note that during join this is used to determine one of the immediate neighbors of a node. This routing procedure is guaranteed to converge except when $\frac{L}{2}$ of the nearest nodes have failed simultaneously.

## Node join procedure

In case a new node wants to join the DHT ring it first generates - if this has not happened before - it’s own credentials (signature and encryption keys) as well as it’s random node ID. The random node ID is sometimes calculated as the SHA-1 hash of it’s IP address or from the hash of it’s public key. After that it requires at least one seed node that has to be supplied by some external mechanism - like being supplied from a central authority which would introduce a single point of failure, using IP multicast which only works in local networks, being supplied manually, etc.

After the seed node has been located it gets contacted by the new joining node. A join message is transmitted to the seed node with it’s destination set to the new node ID. The message is routed according to the standard routing protocol - all nodes that are encountered during forwarding do transmit all of their tables (neighborhood set, routing table, leaf set) to the newly joining node.

The neighborhood set it initially copied from the seed node since it’s assumed to be in proximity to the newly joining node. From this point on the neighborhood set is tracked as it will be done during the whole lifetime of the node - i.e. in case a node is discovered that is closer by proximity metric than the currently known ones it’s included into the neighborhood set and possibly replaces the most distant one that’s currently included in the set.

The last node that the join message arrives on is used as the seed for leaf set information. The leaf set of this node is copied onto the newly joining nodes leaf set - and from this moment on it’s tracked again to contain the closest $L$ nodes ever seen by this node, replacing more distant nodes if required.

The most problematic table to construct is the routing table. First of all all fields corresponding to the current node (i.e. sharing a prefix of $row * b$ bits with the current node ID) are occupied automatically by the node itself (see example above). The first row can be directly copied from any node that doesn’t share a common prefix with the current node at all and are independent of the current node ID. The other entries have to share a prefix with the current node and can initially be filled by information received from the nodes that the join message has been routed through. Note that the length of the shared prefix gets longer and longer for every node encountered on the join messages path.

Note that this is only the initial build of the routing table. The new node also may request additional information (i.e. state tables) from other nodes encountered during this process. It asks all of the encountered nodes for their state tables and updates it’s own state in case it locates closer nodes. The neighborhood set is pretty useful for this process since it keeps tables of nodes in vicinity consistent.

After it’s own tables have been initialized the node transmits a joined message to all nodes applicable to inform them of their presence so they include the new node in their routing tables.

## Keeping track of the tables during runtime

### Leaf set and neighborhood set

These two sets are the most easy ones to track during runtime. For the leaf set $L$ one can simply track the distance of all active (non currently joining) nodes encountered during any communication process and determine if a more close node is encountered which would lead to the currently known nodes to be replaced by a more local one.

The neighborhood set $N$ which is built according to a proximity metric can be tracked by evaluating the proximity of all encountered nodes on a periodic basis and doing the same thing - just storing nodes that are in proximity of the current node. It’s a good idea to keep track of the worst proximity value for some fast discarding.

### Routing table

The routing table might get updated periodically with newly arriving nodes, nodes that fail can be removed and nodes usually do exchange updates routing information with their neighbors.

When any node provides state information to another node it attaches a timestamp value. The receiving node then updates it’s own routing table according to the state Information and eventually notifies the original node - for example - of it’s arrival. The arriving node attaches the original timestamp so the receiving node can check if it’s own routing information has changed since then - and might signal an restart of routing table update to the now joined node.

## Node leave procedure

Failure and departure is handled the same way. In case a node is discovered to be dead since there is no keep-alive exchanged or a request times out - or in case the node signals the end of it’s connections in connection oriented setups - the node gets removed from the network.

To replace a node inside the leaf set a node contacts the most distant existing entry in the leaf set and asks for it’s leafset to update it’s own information about neighboring nodes.

To repair a failed node entry in the routing table a node contacts another node from the same row (i.e. the same shared prefix length) and asks for it’s entry for the failed prefix and value. In the event that none of the nodes from the same row has a satisfying live node the net gets casted in a wider fashion - i.e. the node contacts nodes sharing even a longer prefix from rows below. This is likely to find an entry in case it exists.

## Network resilience

One of the questions that arises when designing DHTs is the question of resilience against malicious behavior of nodes. Pastry tries to counter malicious nodes by introducing some randomness. Each routing step requires to select a node that lies closer to the target space - but the choice of nodes that fulfill this property can be made arbitrarily with some randomness. It’s entirely possible to collect possible routing hops first and then select one of them. In case of a failed query the query might have to be repeated a number of times but this process of random selection of sub optimal steps allows one to circumvent failed or malicious nodes. Note that of course the probability distribution of the random number generator used during this process should be biased towards the optimal routing decision anyways.

## Network partitions

Underlying network failure (i.e. Internet network failure) may lead to DHT network partitioning. Pastry usually is capable of coping with situations in which a node is only reachable by a subset of nodes as long as the underlying network is not fully partitioned - but in case a network segment gets separated from the Internet (or the local network in which the DHT is used) the routing tables might be updated in a way that isolated islands of the DHT are formed. The DHT itself is not capable of recovering from this situation.

To circumvent such situations one has to circumvent the overlay routing network for node localization. In local networks one might use periodic multicast queries for neighboring nodes that might be introduced into the leaf set so islands will get reintegrated periodically - the same information might be used to update routing tables each step.

One might also use some other kind of centralized coordinator to join separated islands on a random periodic basis.


text:
MATLAB: [title removed]

concatenating 2 matrices with unequal dimensions

I want to concatenate 1st row of a matrix A to all the rows of another matrix B,then the 2 nd row of matrix A to all the rows of matrix B and so on.Both the matrices are of different order.ex A=[1] and B=[2 3; 3 2],ans C=[1 2 3;1 3 2]. Is it possible in matlab to do this ?

• %demo dataA = [1 2 3;4 5 6;7 8 9]B = [2 3; 3 2]%build all combinations of row indices of A and B:[arows, brows] = ndgrid(1:size(A, 1), 1:size(B, 1));%iterate over all combinations to build cell array of rows and convert cell array to matrix:C = cell2mat(arrayfun(@(arow, brow) [A(arow, :), B(brow, :)], arows(:), brows(:), 'UniformOutput', false))


text:
# LifeCycleCost:UseAdjustment[LINK]

Used by advanced users to adjust the energy or water use costs for future years. This should not be used for compensating for inflation but should only be used to increase the costs of energy or water based on assumed changes to the actual use of water or energy, such as due to changes in the future function of the building or the impact of future adjacent buildings on energy use. This object is not commonly used and should be used with caution. The adjustments begin at the start of the service period.

## Inputs[LINK]

#### Field: Name[LINK]

The identifier used for the object.

#### Field: Resource[LINK]

Enter the resource such as:

• Electricity

• ElectricityPurchased

• ElectricityProduced

• ElectricitySurplusSold

• ElectricityNet

• NaturalGas

• Propane

• FuelOilNo1

• FuelOilNo2

• Coal

• Steam

• Gasoline

• Diesel

• OtherFuel1

• OtherFuel2

• Water

#### Field: Year 1 multiplier[LINK]

The multiplier to be applied to the end use cost for the first year in the service period. The total utility costs for the selected end use is multiplied by this value. For no change enter 1.0.

#### Field: Year N multiplier[LINK]

The multiplier to be applied to the end use cost for each following year. The total utility costs for the selected end use is multiplied by this value. For no change enter 1.0. This object often includes 25 to 50 years of values. The maximum number of multipliers used in a simulation is 100.

An example of this object in an IDF:

LifeCycleCost:UseAdjustment,
ElecAdjustment,       !- Name
Electricity,          !- Resource
1.0000,               !- Year 1 Multiplier
1.0022,               !- Year 2 Multiplier
1.0023,               !- Year 3 Multiplier
1.0024,               !- Year 4 Multiplier
1.0025,               !- Year 5 Multiplier
1.0026,               !- Year 6 Multiplier
1.0027;               !- Year 7 Multiplier


text:
# Chapter 7 - Think and Solve: 44

9000 J.

#### Work Step by Step

The total energy of 10,000 J remains the same. $$PE + KE = Total \;E$$ $$1000 J + KE = 10,000 J$$ $$KE = 10,000 J – 1000 J = 9000 J$$ This situation is discussed on page 118.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
# Special directional light type

I am currently trying to implement a specific directional light type.

This light type has been used in the game INSIDE and is called orthogonal spotlight (aka local directional light). I assume that this is a directional light which behaves like a spot light and have a squared or rectangular attenuation but I have some difficulties to integrate it in my deferred pipeline and get the general concept of this light type.

Classical directional light : dot(worldNormal, lightDir)

I hope that you'll be able to give me some clues. Thanks a lot !

• Do you by chance have a screenshot of what you are trying to achieve? (: Oct 3 '16 at 14:05
• Unfortunately not but here is a little diagram. It's easy to do a simple directional light dot(worldNormal, lightDir) but how to limit it.
– MaT
Oct 3 '16 at 14:11
• This isn't a full answer but essentially you want to test if a point is in the oriented box defined by the light. You may want to soften the edges as it gets farther away from the light source but that is more challenging. Oct 3 '16 at 15:27

Alan Wolfe is pretty spot on, but I will sum up any way :)

• render the back-faces of your "unit"-sized-box, [-1;1]
• sample the zbuffer and transform into light-local coordinates (see our slides for a fast way to do that).
• early-out of the pixelshader if outside of the box, i.e. if any coordinate in the local-position is outside of -1;1.
• then do the dot-product between the normal and the lightdir, in whatever space is convenient (you can extract the worldspace-lightdir from the object-to-world matrix).
• projecting a texture is easy, the UV-coordinates are simply the localspace xy (moved to [0;1])
• using a falloff texture is eays, the coordinate is simply the localspace z (moved to [0;1])

In an actual game, you of course want to use some sort of acceleration to discard early; we used old-school stencil culling (and should have used depthbounds), but likely tiled culling, clustered culling or similar is better.

You could use zgreater testing to discard pixels where background is entirely behind the light, but iirc on most modern GPUs this will not actually be an advantage, as there will be no early-discard due to the hierarchical zbuffer being primed in the direction of zless.

• That is coming from the man himself! I'm not sure if it'll be helpful, but here's a raytraced implementation in shadertoy: shadertoy.com/view/4lV3zV Oct 5 '16 at 14:07

I would start by looking into deferred decals (you can start here for example, this blogpost has a lot of useful links)

If you understand how the positions are calculated and compared with the volume then you should be able to apply the same logic in the lighting phase.


text:
Math Help - Complex Numbers (Loci)

1. Complex Numbers (Loci)

Hello!

Q: The complex number w is represented by the point of intersection of the loci |z -8 -6i| = 5 and arg(z -4 -3i) = 2 $\alpha$, where $\alpha$ = $\arctan$ (0.75). Find w, in the form x + iy, giving the exact decimal values of x and y.

Thank you for helping!

2. Originally Posted by Tangera
Hello!

Q: The complex number w is represented by the point of intersection of the loci |z -8 -6i| = 5 and arg(z -4 -3i) = 2 $\alpha$, where $\alpha$ = $\arctan$ (0.75). Find w, in the form x + iy, giving the exact decimal values of x and y.

Thank you for helping!
There is probably some simple geometric way of doing this - it can't be coincidence that the ray $\text{arg} (z - 4 -3i) = \alpha$ passes through the centre of the circle $|z -8 -6i| = 5$ and that the terminus of the ray lies on this circle.

But a blunt apporach is:

Get the Cartesian equation of $|z -8 -6i| = 5$, easy if you recognise it as a circle of radius 5 and centre at (8, 6).

Get the equation of the line that the ray $\text{arg} (z - 4 -3i) = 2 \alpha$ lies on. Note that the gradient of this line is $\tan 2 \alpha = \frac{2 \tan \alpha}{1 - \tan^2 \alpha}$ and it passes through the point (4, 3).

Get the intersection of the circle and the line. The solution you want to keep is the one such that y > 3 (a diagram makes this clear).


text:
Using higher I2C voltage then MCU supply (but still in limits)

I am working on a project where there is 1x MCU and 2x I2C devices

1. device needs 2.8 V using I2C1
2. device needs 3.3 V using I2C2 (I have a need of seperating bus apart)

If I understand correctly, a I2C port is only like a switch? So could I supply my MCU (possible 1.8 - 5.5 V) with 2.8 V and connecting device 1 to I2C1 (2.8 V bus) and device 2 to I2C2 (3.3 bus - which is higher then MCU supply 2.8 but still under 5.5 V)? I would like to exclude the use of level shifter.

Will appreciate any help or thought about this, thank you :)

• An answer to this question depends upon the actual devices involved and their datasheets. – StainlessSteelRat Jun 20 '19 at 14:44
• How are you planning to connect the pullup resistors? – Elliot Alderson Jun 20 '19 at 14:47
• For a slight difference running I2C with the pullups to the lower voltage will work and meet most VIH specs as long as you never misconfigure as a push-pull GPIO, though even that is likely to be within the allowed overvoltage. Also check to see if your 3v3 part cannot run at 2v8, many modern ones (most ARM MCU's etc) can just fine, though older parts (ATmega for example) may hit a clock vs voltage limit. More can't really be said without the identify of the specific parts, information critically missing from your question. – Chris Stratton Jun 20 '19 at 14:51
• There is no problem running 2,8 V on MCU since it is 1,8 - 5,5 and frequency that I need is only16 MHz (which is half of 32 available). I know I can run MCU at 3,3V and have 2,8V bus. But I was wondering if it is possible other way around as well? – Ram - small roar Jun 20 '19 at 17:31
• If I understand correctly, a I2C port is only like a switch? Not really.... It's more like a channel of devices from master to slave. Each I2C slave has an address that you find in the datasheets and you first choose the slave you want and then you read from that slave. I think a lot of your questions can be answered in the datasheet. – KingDuken Jun 20 '19 at 21:34

2 Answers

Your proposal may work as long as you connect the I2C pull-up resistors to 2.8V (the lower voltage) for both I2C1 and I2C2. This way, both I2C busses would be working at 2.8V.

You have to check how much margin you have for I2C2's VOH when the pull-up resistors drive the lines to 2.8V while the I2C peripheral expects 3.3V.

My recommendation is to simply use level shifters with N-FETs. They are extremely simple and work really well.

The following references show how to implement them:

I2C level shifting NXP application note

SparkFun I2C level shifter schematics

If I understand your question correctly, you have the two slaves on separate I2C buses. The pullups on one bus are to 3.3V, the pullups on the other are to 2.8V, and the MCU is powered at 2.8V.

You could check the Absolute Maximum ratings in the MCU's datasheet to see if it is OK to have SDA and SCL at VCC + 0.5V.

However, in general your normal use case shouldn't be in the Abs Max range... It would be much better if you used 2.8V I2C for the 3.3V device. Check the datasheet of the 3.3V device to see if you can do this without violating the VIH spec.


text:
When freshly installing Visual Studio and using windows authentication, you typically run into the “The requested page cannot be accessed because the related configuration data for the page is invalid” error.

Before, you would go to c:\users\[yourusername]\documents\IISExpress\config\applicationhost.config and change the following section

<add name="AnonymousAuthenticationModule" lockItem="true" />

to look like this

<add name="AnonymousAuthenticationModule" lockItem="false" />

Only, with Visual Studio 2015, this does not seem to work anymore. The settings file being used by IISExpress is now localized in C:\path\to\your\solution\.vs\applicationhost.config. Change this file like above, restart your project and IIS Express and you should be back on track again!

<useglobalapplicationhostfile>True</useglobalapplicationhostfile>

to your .csproj file. This way, the applicationhost.config in your documents folder will be used again.

If you want to enable spell checking when you are writing a commit message, you can add

set spell spelllang=en_us

to your .vimrc file. This file is located in your home folder, so e.g. C:\Users\itto\.vimrc.

Errors will be highlighted with a red background. Nice and easy.

When running drush you can run into this error message. In my case, the mysql command line tool provided with Mamp Pro was not available. You can easily test this by typing the command ‘mysql’ in terminal. Your output might be -bash: mysql: command not found.

To solve this, do the following in terminal:
sudo vim ~/.bash_profile
Press i
Move to the last line and append
export PATH=/Applications/MAMP/Library/bin/:\$PATH
Hit escape
Type in :wq (including the colon) to write the file and quit vim.
Reload your profile by running source ~/.bash_profile.

The mysql command AND drush should now work!

private void RestoreDatabase(String databaseName, String backUpFile, String serverName)
{
var connection = new ServerConnection(serverName);
var sqlServer = new Server(connection);
var restore = new Restore();

string pathBackupfile = Path.GetDirectoryName(backUpFile);

if (pathBackupfile != null) {
string logFile = Path.Combine(pathBackupfile, databaseName + "_Log.ldf");
string dataFile = Path.Combine(pathBackupfile, databaseName + ".mdf");

restore.Devices.Clear();
restore.Action = RestoreActionType.Database;
restore.Database = databaseName;
var bkpDevice = new BackupDeviceItem(backUpFile, DeviceType.File);
restore.ReplaceDatabase = true;

//Relocate mdf & ldf files

restore.SqlRestore(sqlServer);
}
}

I was recently writing a webapplication for one of our clients. The application is a training management tool and thus involves sending loads of e-mail. This way people get reminded that they’ll be following a training in the next days or asked to write a review about their training. To make the mail look great, we wanted it to be in HTML and contain the company logo.

A first attempt was made by just writing the html for the mail and use an ordinary image-tag with a reference to the client’s intranet (like this: ). However, the kick-ass intranet-security of our client wouldn’t allow this and each time the mail was opened, the user was prompted for his credentials. Very annoying! So we had to include the image in the mail as an attachment. You see it every day, but apparently the code to do this in c# isn’t that widely spread. So here’s my function to accomplish it:

///
/// Embeds the company logo into the given mail message
///
/// <param name="message">Message in which the logo should be embedded</param>
private static void EmbedCompanyLogo(MailMessage message)
{
AlternateView av1 = AlternateView.CreateAlternateViewFromString(message.Body, null, System.Net.Mime.MediaTypeNames.Text.Html);
string strImageUrl = System.Web.HttpContext.Current.Server.MapPath("~/images/logo_print.gif");
logo.ContentId = "companylogo";
//To refer to this image in the html body, use
}

As mentioned in the code comment, in your mail message you can refer to the image with a source equal to “cid:companylogo”.

If you have any thoughts, remarks or questions, the comments are open…


text:
# How do I calculate the new x,y coordinates and width/height of a re-sized group of objects?

I'd like to resize a group of n-objects -- either circles or rectangles -- all at once and fit them into the newly resized area with newly calculated x,y coordinates and width/height dimensions. The resizing originates in the CENTER of the resized area. It probably helps with some visuals, so please take a quick look at this video:

http://screencast.com/t/AEuJzTS51vja

And here is an image where I'm trying to distill the question as simply as I can. Based on the resizing from the center, I need to know how to calculate the new coordinates and dimensions for "A" "B" and "C" below -- I've given the dimensions of the bounding box, both in its original form, and its resized form.

(I know the x,y width/height of "A" "B" and "C" in the orig box -- they're just not labeled, but you can assume that they're known values)

-
Where is the origin ($(0,0)$) of your coordinate system? –  Isaac Feb 14 '12 at 1:11
the origin is the upper-left of a scrollable canvas -- so the x,y coordinates of the orig box could feasibly be any random x,y coordinates, up to 50000,50000 in this example. not sure if that helps. –  TimDog Feb 14 '12 at 2:22

If the center of resizing (which it sounds like is the center of your outer rectangle—the one point that is not moved by the resizing) is $(x_c,y_c)$ and you're resizing by a factor of $r_x$ in the $x$-direction ($r_x=\frac{83}{185}$ in your example) and $r_y$ in the $y$-direction ($r_y=\frac{330}{185}$ in your example), then $$(x_\text{new},y_\text{new})=(x_c+r_x(x_\text{old}-x_c),y_c+r_y(y_\text{old}-y_c)).$$

-
so awesome, this is working wonderfully...thanks very much. lopsy confirmed the height/width resizing, and this really helped me nail the x,y coordinates -- which was my biggest sticking point, so i'll award the answer here. –  TimDog Feb 14 '12 at 3:24
@Isaac I am assuming that $(c_x,c_y)$ and $(x_c,y_c)$ are the same in the above formula. Or am I missing something? –  asloob May 15 '13 at 6:42
@asloob: yup, fixed now, thanks. –  Isaac May 16 '13 at 1:43

Because you resized the box's y-scale from $185$ to $330$ pixels - a ratio of $\large \frac{330}{185}$ - the y-scale of everything inside must also scale by the same ratio.

For example, if the circle has original y-scale $34$, then the new y-scale will be $34 \times \frac{300}{185}$ which is about $60.6$.

The same ratio logic holds true for the x-scales of the objects, and also for coordinates - assuming the center of your resizing is $(0,0)$, an arbitrary point $(x,y)$ will get sent to $(\frac{83x}{185}, \frac{330y}{185})$ (using the ratios in your example).

-
thanks lopsy....i had something kinda close, but i'm trying to use your advice now...one more question: what if the center of the resizing were 556,785 for example (this would be the middle of the bounding box that's doing the resizing) -- what would the coordinates be with that center in mind? –  TimDog Feb 14 '12 at 2:09


text:
## anonymous 3 years ago Joelle earns her regular pay of $7.50 per hour for up to 40 hours of work in a week. For each hour over 40 hours in a week, she is paid 1 and 1/2 times her regular pay. how much does joelle earn for a week in which she works 42 hours? • This Question is Closed 1. anonymous is the answer$472.50?

2. anonymous

$7.50 an hour = if she works up to 40 hours$7.50 x 1.5 = if she works more than 40 hours.

3. anonymous

no it is not.

4. anonymous

5. anonymous

I multiplied 7.50 by 1.5=11.25 then i multiplied 11.25 by 42 which equals 472.50

6. anonymous

now that is wrong because that only applies for when she works for more than 40 hours.

7. anonymous

she did. she worked 42 hours

8. anonymous

nononono.

9. anonymous

ok. explain

10. anonymous

"More than" 40 hours key word "More than"

11. jim_thompson5910

ashleyb that answer would be correct if she got paid 1 and a half times her regular pay of $7.50 for the entire 42 hours but that overtime bonus only applies for the additional 2 hrs (not the full 42 hrs) 12. anonymous$7.50 an hour = if she works up to 40 hours $7.50 x 1.5 = if she works more than 40 hours. How many hours did she work for more than 40 hours? so 40 + 2 = 42 hours that she worked in total. do you see she has worked 2 hours over 40 hours? 13. stamp $r_{regular}=750\ cents$$r_{overtime}=150\%(r_{regular})$$r_{overtime}=\frac{150}{100}750=15*75=750+5(75)=$$750+375=1125\frac{cents}{hour}=r_{overtime}$ pay = regular + overtime $pay_{cents}=750(40)+1125(2)$ 14. jim_thompson5910 you would have to do it in pieces calculate her total pay for working 40 hrs at$7.50 an hour then add on the additional bonus pay of working 2 hrs at 1.5*7.50 = 11.25 dollars an hour

15. anonymous

yes @jim_thompson5910 says it well, she has worked additionally two hours on top of the 40 base hours.

16. anonymous

jayds: yes

17. anonymous

311.25?

18. anonymous

yes u are right.

19. anonymous

wait.

20. anonymous

i think u may have mistyped it.

21. jim_thompson5910

I'm getting 322.5, so you're 11.25 off somehow

22. anonymous

in the calculator.

23. jim_thompson5910

you must have only calculated 1 additional hour of overtime instead of 2

24. stamp

300 + 22.50 = 322.50 $25. anonymous First 40 hours = base pay of$7.50 per hour additional 2 hours = base pay x 1.5 = 7.50 x 1.5 = 11.25 per hour

26. anonymous

stamp: how did u get 322.50

27. jim_thompson5910

Regular: 40 hours at $7.50 an hour =$300 in total pay Overtime: 2 hours at $11.25 an hour =$22.50 in total pay Overall, she made 300+22.50 = 322.50 dollars working 42 hours

28. anonymous

OHHHHH!!!! i understand!! thankyou!

29. jim_thompson5910

you're welcome