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Yaglom A.M., Yaglom I.M. Ч Probability and Information
Yaglom A.M., Yaglom I.M. Ч Probability and Information

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Ќазвание: Probability and Information

јвторы: Yaglom A.M., Yaglom I.M.

јннотаци€:

This book has a long history. It began over two decades ago as the first half of a book then in progress on information and ergodic theory.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1983

 оличество страниц: 439

ƒобавлена в каталог: 04.02.2014

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
"Comma", as separating symbol      140
"Saturation" of a block of elements      243Ч244
"Saturation" of a block of elements, calculation of values of by Frolushkin      243
Abramson, N.      175 179 193 233 397
Absolute value (or norm) of elements      41Ч42 388
Absolute value (or norm) of numbers      41Ч42
Aczel, Y.      96 399
Adenine      253 255
Afonin, V.A.      248 405
Ahlswede, R.      323(fn) 406
Air, G.M.      257 400
Aitham      198
Aksakov, S.T.      201 210
Alekseev, P.M.      400
Algebra of events      36ff. 37 40
Algebra of numbers      37
Algebra of sets      37
Algebra, boolean      41Ч43
Algebra, Boolean, link with probability theory      42
Algebra, Boolean, normed      41Ч43
Algebraic coding theory      328Ч329
Algebraic concepts      xvi 364Ч391
Algebraic operations      364
Algebraic, system      37 41 365
Algorithm, Euclidean      376
Algorithmic approach to the concept of amount of information      xvii
Alphabet      139 252 see
Alphabet, contraction of      153Ч157 172
Alphabet, contraction of one-fold      154
Alphabet, contraction of two-fold      154
Alphabet, inclusive of space      203Ч206
Alphabet, spaceless      203Ч206
Amino-acid      253 255
Amino-acid, proline      257
Amusing problems      see "Recreative problems"
Aphasic persons' speech, entropy of      210 221
Apostel, L.      209 400
Arabic alphabet      194
Arithmetic mean      31Ч35 290 297 349Ч350
Arithmetic mean, theorem      355
Arithmetic with two symbols (2-arithmetic)      355 370Ч371
Arithmetic, q-      365Ч366 368
Arithmetic, Qx-      378
Ash, R.B.      21 281 290 306 333 338 346 397
Ashby, W.R.      xii 397
Atal, B.S.      197Ч198 214 405
Attneave, C.      223 226
Attneave, F.      85 191 223 226 399
bacteria      253
Baghdady, E.J.      406
Balasubrahmanyam, P.      197 214 405
Balmont, K.D.      178(fn)
Bar-Hillel, Y.      xvii 397
Bareli, B.C.      257 400
Barnard, G.A.      193 299 400 405 406
Bartee, T.C.      306 333 338 346 406
Basharin, G.P.      179 197 400
Baudot code      138 140
Beauchamp, J.      224 402
Bektaev, K.B.      191 195Ч196 211Ч212 216 404
Belar, H.      224 228 404
Belevitch, V.      400
Bellman, R.      120 399
Berg, A.I.      406
Berlekamp, E.R.      305 314(fn) 333 336 338 346 389 406
Bernstein, S.N.      42
Berry, J.      217 401
Binary channel      see "Communication channel"
Binary code      see "Code"
Binary field      317
Binary number system      143 145 307
Binary system of logarithms      xiii xv(fn)
Binary unit (bit)      45 144
Birkhoff, G.      306 333 338 346 406
Black, J. W.      219 401
Block codes      see "Code"
Block, N-letter      162 289
Bluhme, H.      197 401
Blyth, C.R.      179 401
Boltyanskii, V.G.      vii(fn)
Boole, G.      41
Boolean algebra      41Ч43
Boolean algebra, link with probability theory      42
Boolean algebra, normed      41Ч43
Bose, R.C.      316 334 341(fn) 406
Bourbaki, N.      210
Brawly, J.W.      224
Brightness levels      230Ч233
Brillouin, L.      xii 47 82 177 397
Brooks, F.P.      223Ч224 226 401
Burton, N.G.      189 191 401
Carnap, R.      xvii 397
Carson, D.H.      205 401
Carterette, E.C.      211 401
Centre of gravity      353
Centroid      353
Channel capacity      see "Communication channel"
Chebyshev's inequality      26f. 33Ч36
Chebyshev, A.P.      33Ч36 299 306
Chentsov, N.N.      111 116 400
Cherry, Collin      177 209 219 397 404 406
Cherry, E.C.      220 401
Chiplunkar, V.N.      197Ч198 214 405
Chromatic scale      222Ч223
Chromosome structure      253
Chromosome structure, double helix      253
Code(s)      138 141 338
Code(s), (7, 4)-single error correcting      310Ч311 314
Code(s), (N, M)      313Ч314 344
Code(s), advantageous (efficient)      137f. 190
Code(s), Baudot      138 140
Code(s), binary      138 141Ч142 148Ч149
Code(s), binary, Golay perfect      341
Code(s), binary, most efficient, construction of      142
Code(s), binary, non-uniform      140
Code(s), binary, uniform, most efficient      144
Code(s), block      145 313(fn)
Code(s), Bose Ч Chaudhuri Ч Hocquenghem      xx 316 334Ч337 345(fn) 346
Code(s), Bose Ч Chaudhuri Ч Hocquenghem, (N, M)      344
Code(s), Bose Ч Chaudhuri Ч Hocquenghem, check matrix of      335
Code(s), Bose Ч Chaudhuri Ч Hocquenghem, non-primitive      324(fn) 341(fn) 342
Code(s), Bose Ч Chaudhuri Ч Hocquenghem, primitive      324(fn)
Code(s), check matrix of      321 323Ч324 327Ч328 345
Code(s), composition      256
Code(s), correction by check signal      310
Code(s), cyclic      331 334 344
Code(s), cyclic, polynomial of      333
Code(s), decimal      174
Code(s), degenerate      257
Code(s), depsely-packed      339Ч340
Code(s), distance      338
Code(s), double-error correcting      314 326Ч327 334Ч335 344
Code(s), error-detecting and error-correcting      304Ч346
Code(s), error-detecting and error-correcting, definition      308
Code(s), Fano      150
Code(s), Fano, efficiency (economy) of      137Ч147
Code(s), generated by a polynomial      329Ч331
Code(s), genetic      255Ч258
Code(s), genetic without comma      257
Code(s), genetic, Gamow's postulation      255
Code(s), genetic, structure of      257
Code(s), Golay      341
Code(s), group      319Ч321 339
Code(s), Hamming      314Ч315 325Ч326 333 341Ч342 345
Code(s), Hamming, extended      326
Code(s), Huffman      xvi 147f. 153Ч157 171Ч172 259 313(fn)
Code(s), Huffman, optimality of      156 172 177
Code(s), Huffman, ternary, construction of      172
Code(s), instantaneously decipherable      141 157 175Ч177
Code(s), linear      319Ч321 339
Code(s), m-ary      147 172Ч173 175
Code(s), Morse      138 140
Code(s), non-uniform      140Ч141 143
Code(s), optimal      156Ч158 336
Code(s), overlapping      255Ч256
Code(s), parity-check      310 312Ч313 315Ч316 318 321 323 333
Code(s), parity-check, (N, M)      317Ч318
Code(s), parity-check, decoding of      322
Code(s), parity-check, matrix of      319
Code(s), parity-check, non-random      324
Code(s), parity-check, random      323
Code(s), parity-check, systematic      319
Code(s), perfect      339Ч342
Code(s), polynomial      329 332
Code(s), polynomial, ideal in      332
Code(s), quasi-perfect      342
Code(s), redundancy      308Ч309
Code(s), Shannon Ч Fano      xvi 147 150Ч153 171 259 313(fn)
Code(s), single-error-correcting      309Ч314 327 335 344 345(fn)
Code(s), systematic      319
Code(s), ternary      138
Code(s), triple repetition      308Ч309 313(fn)
Code(s), triple-error-correcting      335 346
Code(s), triplet      257
Code(s), uniform      138 140Ч141 143 148 166
Code(s), uniquely decipherable      140 150 175Ч177
Code(s), with/without separating symbol, comma      140 256
Code-word      140 144 155 159Ч160 166 175
Code-word, choice of simple method for      306Ч307
Code-word, length      144
Code-word, length, average      151 156Ч157
Coding      122 138 249 251Ч253 255
Coding and statistical laws      148
Coding, advantageous (efficient)      139
Coding, algebraic theory of      317(fn) 318
Coding, block      146 152Ч153 157 289
Coding, fundamental theorem of      xvi 147f. 157Ч163 172Ч173 246 274
Coding, fundamental theorem of noisy (due to Shannon)      xvi 274Ч275 289Ч306
Coding, fundamental theorem of noisy (due to Shannon), converse of      xvi 273 283Ч290
Coding, fundamental theorem of noisy (due to Shannon), strongly converse of      290
Coding, Huffman method of      155Ч157
Coding, method      293 307
Coding, random      292Ч297 301(fn) 306 323
Coding, Shannon Ч Fano method of      152Ч153 155Ч156 158
Coding, theory      xvi 305Ч307
Coding, theory, notion of entropy in      161
Codon      255Ч256 258
Cohen, J.E.      224 401
Communication channel      xii xiii
Communication channel and statistical regularities      55
Communication channel, associated with hereditary phenomenon      252
Communication channel, binary, asymmetric      273
Communication channel, binary, symmetric      263 265 275 277 280 299 301(fn) 302 307Ч308 311 323 342
Communication channel, binary, symmetric, erasure      267 269Ч270 323
Communication channel, capacity      xiii 246Ч251
Communication channel, capacity in absence of noise      173 262
Communication channel, capacity in presence of noise      262Ч263 272 297
Communication channel, capacity, zero-error      283
Communication channel, human organism as      249Ч251
Communication channel, m-ary symmetric      266
Communication channel, new forms of      249
Communication channel, noisy      252 260Ч262
Communication channel, noisy, code selection for every      274
Communication channel, noisy, mathematical model of      260Ч261
Communication channel, non-binary      317(fn) 346
Communication channel, transmission of speech over      219
Communication, specific content of      55
Complement of a set      39
Constant, mean value of a      28
Constant, number p      1
Convex k-gon      354
Coset      368
Counterfeit coin problems      viii 108Ч121 136 147
Cover, T.M.      xx 191 199 201Ч203 210 401
Crick, F.H.C.      256Ч257 401
Culbertson, J.T.      398
Cullman, G.      305 333 338 346 397 406
Current pulse      137 139 246 251
Cytoplasm      252Ч253
Cytosine      253 255
Czech language, entropy of      214
Daroczy, Z.      96 399
Decimal number system      143
Decimal system of logarithms      xiii xv
Decimal unit (dit)      xv 46
Decoding      140Ч141 249 251Ч253 255
Decoding error probability      293 296
Decoding error probability, mean      339Ч340 342
Decoding error probability, mean, Hamming lower bound on      340
Decoding method      293 299 306Ч307
Decoding rule      322
Decoding, instantaneous      141
Decoding, sequential      251 323Ч324
Decoding, unique      140
Delbriick, M.      256 402
Denes, P.      219 401
Denis-Papin, M.      177 397
Deoxyribonucleic acid (DNA)      253Ч254
Deoxyribonucleic acid (DNA), molecules, four-letter alphabet      253
Deutsqh, S.      238Ч239 401
Devide, V.      120 399
Dewey, G.      186 401
Diamond, S.      4 398
Die, imperfect      42
Die, throw      1Ч2
Disjoint equal spheres, closest packing of      389
Dispersion (or spread)      27Ч34 36 see "Variance
Distance      387
Distance, code      338
Distance, Euclidean      389
Distance, geometrtc      338
Distance, Hamming      338 340 342 389(fn)
Distance, Hamming, utility in coding theory      389
Distance, Lee      389
Distance, Minkowski      388
Distributive law      38
DIT      xv 46
Divisor of numbers, greatest common      40 365 375
Dmitriev V.I.      248 405
Dobrushin, R.L.      xiv xvii 89 177 181 281 306 323(fn) 324 333 338 399 401 405 406
Dolezel, L.      195 213Ч214 403
Dravidian languages, entropy of      197 214
Drygas, H.      323(fn) 406
Ear, resolving power of      247
Eidelnant, M.I.      xiv
Eldridge, R.C.      401
Element(s), difference of      365
Element(s), identity      364
Element(s), inverse of an      365
Element(s), symmetric      364Ч365
Element(s), unit      365 371
Elias, P.      281 306 323(fn) 338 346 406
Eminescu, M.      214
Endres, W.      xvii 195 219Ч220 401
English alphabets      139 192 203
English language, average information in stressed words of      217
English language, average word-length in      181 188
English language, coding text-letters in, Shannon Ч Fano method      180
English language, digram frequency in      182Ч183 186
English language, entropy of letters/words in      179Ч181 187 194
English language, estimation by Cover and King      202Ч203
English language, first-order approximation to      181 186
English language, letter-guessing experiments for      191 196
English language, letter/word frequency in      178Ч179 182 186
English language, redundancy for      185 188 191 195Ч196
English language, second-order approximation to      183 186Ч187
English language, statistical characteristics of letters/words      186Ч188
English language, third-order approximation to      183
English language, trigram frequency in      183 186
English language, zero-order approximation to      178
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