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Kaczynski T., Mischaikow K.M. — Computational Homology
Kaczynski T., Mischaikow K.M. — Computational Homology

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Название: Computational Homology

Авторы: Kaczynski T., Mischaikow K.M.

Аннотация:

Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2004

Количество страниц: 480

Добавлена в каталог: 10.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      420
Abelian group, free      441
Abelian group, free, generated by      445
abs      453
acyclityTest      240
Algorithm      451
Algorithm, CCR      165 170
Algorithm, cubical homology      138
Algorithm, homology of a map      243
Algorithm, index pair      350
Algorithm, linear equation solver      124
Algorithm, preboundary, algebraic      140
Algorithm, preboundary, cubical      252
Algorithm, quotient group finder      128
Algorithm, reduction of a pair      170
Algorithm, Smith normal form      122
AND      454
Array      455
Automorphism      435
Average      451
Ball      399
Ball, closed      403
Barycentric coordinates      379
Barycentric subdivision      385
Basis      431
Basis of a group      441
Basis, canonical      431 445 449
Betti number      93
Bijection      409
Bolzano — Weierstrass theorem      416
bool      454
Borsuk theorem      324
Boundary of a chain      23 60
Boundary operator      21 85
Boundary operator, cubical      54
Boundary operator, simplicial      384
Boundary, f-boundary      346
Boundary, group of boundaries      85
Boundary, map      54
Boundary, map, simplicial      381
Boundary, relative      281
Boundary, topological      405
Boundary, weak      305 328
boundaryMap      134 169 241
boundaryOperator      137
boundaryOperatorMatrix      137
Branching      459
break      460
Brouwer fixed-point theorem      324
Cahn — Hilliard equation      10 259
canonicalCoordinates      134
Category      389
Category of cubical sets      389
Category of representations of cubical polyhedra      390
Category, small      390
CEILING      44
Cell, elementary      44
Chain      27
Chain complex, abstract      85
Chain complex, augmented      89
Chain complex, cubical      59
Chain complex, finitely generated free      86
Chain complex, free      85
Chain complex, relative      281
Chain equivalence      153
Chain group      48 53
Chain, elementary      47
Chain, homotopy      151
Chain, isomorphism      144
Chain, map      144
Chain, relative      280
Chain, selector      185 212
Chain, selector theorem      210
Chain, subcomplex      87
chainComplex      169
chainFromCanonicalCoordinates      135
chainMap      241
chainSelector      241
Chaotic dynamics      15
checkForDivisibility      120
chest      252
Collapse, elementary      71
Collar      344
columnAdd      104
columnAddOperation      106
columnEchelon      117
columnExchange      104
columnExchangeOperation      106
columnMultiply      104
columnMultiplyOperation      106
combinatorialEnclosure      345
Commutative diagram      145
Component, nondegenerate      41
Conjugacy, semiconjugacy      358
Conjugacy, topological      358
Conley index      357
Connected component      66
Connected simple system      391
Contractible      232
Convex set      378
Convex, hull      378
Coordinate isomorphism      94
Coordinate vector      431
coordinates      242
Coset      424
Coset of a subgroup      424
Covering      418
cube      134
Cube, elementary      40 154
Cube, elementary, dual      48
Cube, unitary      45
Cubical acyclic set      79
Cubical carrier      216
Cubical pair      280
Cubical product      51
Cubical set      43
Cubical wrap      344
cubicalChainComplex      137
cubicalChainGroups      136
cubicalSet      134 345
cubicalWrap      345
cuPreBoundary      252
cutFirst      454
CYCLE      22 60
Cycle, group of cycles      85
Cycle, reduced      89
Cycle, relative      281
Darboux theorem      412
Data structure      452
Data type      452
Decomposition disjoint      364
Decomposition, normal      131
defined      459
Deformation, retract      76
Deformation, retraction      76 232
degenerateDimensions      237 240
Degree of a map      333
Degree of a map, topological      337
DIM      140
Dimension of a cube      41
Dimension of a vector space      431
Direct sum      426
divides      454
Dynamical system      308
Dynamical system, invertible, noninvertible      308
Echelon form, column      108
Echelon form, row      107
EDGE      17 43
Edge path      67
Edge, connected      67
Elementary cell      179
elementaryCubes      238
Embedding number      41
Enclosure, combinatorial      344 345
Endomorphism      435
Endpoint      134 453
Epimorphism      290 434
Equivalence class      425
Equivalence relation      425
Euler number      331
Evaluate      236 241
evaluatelnverse      350
Excision isomorphism theorem      287
Existence and uniqueness theorem      318
Face, free      71
Face, maximal      71
Field      428 429
firstlndex      455
Fitzhugh — Nagumo equations      267
FLOOR      44
Flow      318
Full solution      308 347
Full, cubical set      344
Function between pairs      286
Function size      271 273 277 282
Function, continuous      407
Function, lower semicontinuous      408
Function, measuring      271
Function, overloading      461
Function, rational      174
Function, uniformly continuous      417
Function, upper semicontinuous      408
functor      390
Functor, homology      390 392
Fundamental decomposition theorem      94 130
Gaussian elimination      107
Generator      169
generatorsOfHomology      138
Graph      17
Graph of a cubical map      209
Graph, combinatorial      18
Graph, combinatorial, equivalent      46
Graph, connected      18
Graph, cubical transition      365
Grey-scale      6
Group of weak boundaries      305 328
Group, cyclic      423
Hash      458
Hash element      458
Hash key      458
Hash value      458
Henon map      362
Homeomorphism      409
Homology      138
Homology of a chain complex      86
Homology, complex      86
Homology, cubical      60
Homology, cubical, group      60
Homology, functor      390 392
Homology, map      214
Homology, reduced      89
Homology, relative      281
Homology, simplicial      384
Homology, with $Z_2$ coefficients      29 382
homologyGroupOfChainComplex      133
homologyOfMap      243
Homomorphism      433
Homomorphism, connecting      293
Homotopy class      234
Homotopy invariance theorem      233
Homotopy of maps      231
Homotopy of spaces      231
Homotopy on pairs      338
Homotopy type      231
Hopf trace theorem      328
Hull, closed      202
Hull, open      202
IdentityMatrix      457
Image      434
Image, binary      8
Image, grey-scale      8
IN      457
Index map      355
Index pair      346
Injection      409
int      453
INTERFACE      262
Intermediate Value Theorem      412
Intersection      457
interval      134
Interval arithmetic      174 176
Interval, elementary      40
Interval, elementary, degenerate      40
Interval, elementary, nondegenerate      40
Invariant, isolated set      346
Invariant, maximal set      315 319 348
Invariant, subset      309 319
invariantPart      349 350
Isolating neighborhood      346 350
Isomorphism coordinate      94
Isomorphism of groups      434
Join      457
Kernel      434
kernellmage      116
Keys      458
Keyword      452
Klein bottle      384
lastlndex      455
Lefschetz fixed-point theorem      327
Lefschetz fixed-point theorem, relative      363
Lefschetz number      326
Left      453
Length      454
Level set      273
Limit of a sequence      415
Limit set, omega, alpha      311 319
LIST      454
Literal      452
Map, antipodal      335
Map, bilinear      50
Map, boundary, cubical      54
Map, chain      144
Map, cubical      179 206
Map, cubical, acyclic-valued      210
Map, cubical, combinatorial      178 206 343
Map, Henon      362
Map, inclusion      145
Map, index      355
Map, induced in homology      214
Map, linear      437
Map, logistic      15 358
Map, multivalued      178 206
Map, multivalued, lower semicontinuous      207
Map, multivalued, upper semicontinuous      207
Map, projection      147
Map, shift      309
Matrix      438
Matrix, canonical      449
Matrix, change of coordinates      95
Matrix, elementary      100
Matrix, integer      447
Matrix, nonsingular      439
Matrix, of f in bases      448
Matrix, submatrix      103
Matrix, transition      315 360 373
Matrix, transpose      100 439
Matrix, Z-invertible      448
Mayer — Vietoris sequence      299
Metallurgy      9
Metric      398
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