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De Witt L. Sumners — New Scientific Applications of Geometry and Topology (Proceedings of Symposia in Applied Mathematics, V. 45)
De Witt L. Sumners — New Scientific Applications of Geometry and Topology (Proceedings of Symposia in Applied Mathematics, V. 45)



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Название: New Scientific Applications of Geometry and Topology (Proceedings of Symposia in Applied Mathematics, V. 45)

Автор: De Witt L. Sumners

Аннотация:

Geometry and topology are subjects generally considered to be "pure" mathematics. Recently, however, some of the methods and results in these two areas have found new utility in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction of mathematical models to exporting theoretical methods of attack on long-standing problems of mathematical interest. Based on an AMS Short Course held in January 1992, this book contains six introductory articles on these intriguing new connections. There are articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science. All are expository and require no specific knowledge of the science and mathematics involved. Because this book communicates the excitement and utility of mathematics research at an elementary level, it is an excellent textbook in an advanced undergraduate mathematics course.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель без номеров страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 260

Добавлена в каталог: 24.04.2020

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$n$th Vassiliev invariant      219
$q$-spin network      172
$q$-spin recoupling theory      176
$q$-state Potts model      168
$q$-symmetrizer      172 173 180
$q-6j$ symbol      178 180 184
$S$-matrix      196
$\textbf{v_{ac}}$      22
$\Theta$-symbol      178 184
3-manifold      186
4-plat      47
4-valent plane graph      154
Achiral      45
Alexander polynomial      131 132 134 211 225
Alexander — Conway polynomial      225
Algebraic topology      131
almost unknotted embedding      82 83
almost unknotted graphs      75
Alternating diagram      46
Ambient isotopy      42 156
Amplitude      140 141 143 144
Angular momentum      195
angular momentum recoupling      177
annihilation of particles      143
annihilations      141
Antisymmetrizer      204
Artin braid group      131 139 161
atoms      131
Base pairs      54
BFACF algorithm      88
binor calculus      201
bracket evaluation      163
bracket identity      173
Bracket polynomial      153 157 169 198
Braids      161
braket      142
Bras      142
Burau representation      215
CAP      187
Categories      145
Catenane      2 59 99 104
Chebyshev polynomial      176
Chern — Simons Lagrangian      140 222
Chiral      45 100
Chirality      99
Chromatic polynomial      153 170
classifying vector      47
Collapse of the wave function      144
combinatorial knot theory      186
combinatorial state model      219
Combinatorics      133 153
Completeness      143
complex numbers      140
Composite      45
Composition of morphisms      188
conceit      137
Conformal field theory      133 139 140 186 224
Conformal quantum field theory      172
Connective constant      77 78
Conway      132
creations      141
cross-channeling      134
Crossing      135 143 187 191
Crossing number      45 81
Cup      187
Curvature      223
curvature tensor $F$      222
Determinant      211
Dirac formalism      143
Dirac string trick      146
Direct repeats      58
distributive recombination      59
DNA on protein complexes      25
DNA repair      6
DNA replication      4
DNA topology      1
DNase      54
Dubrovnik polynomial      198
Elementary braid      161
Elliot — Biedenham identity      180 181
Energy      168
entanglement complexity      75 81 89 91
entanglement number      90
Enzyme mechanism      61
EPSILON      194
Ether      131
evolution of the topological structure of DNA      1
Feynman integrals      133
Feynman path integral      137 141
Four color theorem      170 172
Fox derivation      214
Framed link      220
Framing      226 227
Free differential calculus      211 213 215
Free fermion model      211
Functional integral      139 186 224
functors      145
Fundamental group      134 205 211 216
Gauge equivalence      140
Gauge field theory      222
Gauge potentials      137 140 222
Gel electrophoresis      56 88
generalized Feynman path integral      225
Generalized polynomial      213
genetic sequence      54
Grassmann variable      211
H      30
Handlebody      140
Hecke algebra      210
helical repeat      26 30
heuristic integral      222
Higher dimensions      146
Hilbert space      140 142
Holonomy      137 138
holonomy of $A$      222
Homfly polynomial      198 219 225 226
Hopf algebra      132 199 200 201
In vitro      56
In vivo      56
infinite cyclic cover      211
integral      201
integral formalism      220
integral heuristics      219
integral tangle      50
Integrase      57
interactions      141 143
Inverted repeats      59
Ising model      132
Jacobian matrix      211
Jones polynomial      131 137 139 145 153 211 216 225 226
Jones projector      176
Jordan Euler trail      218
Kauffman polynomial      225 227
ket-bras      142
Kets      142
Knot      41
knot epistemology      228
Knot polynomial      81
knot probability      76 85
Knot theory      131 132 143 153
knot type      42
knot-set      230
Knotted      133
Knotted arc      79 90
knotted ball pair      79 80
Knottedness      134
knotting      2
Kronecker delta      192 194
Lie algebras      132 137
Ligase      54
Light scattering      87
Link      41
link crystal      136
Link diagram      43 132 143 154 167 172
Link invariant      200
Linker DNA      33
linker regions      32
Linking      18
Linking number      2 18 19 20 44
linking number difference      24
links with singularities      146
Lk($\textbf{C}$, $\textbf{A}$)      18
local knots      75
Loop value      173
Lorentz transformation      195
Mass spectrometry      116
Mathematical physics      132
Matrix elements      191
Matrix multiplication      145
Matveev moves      185
Matveev representation      182
Maxima      143 191
medial construction      156
medial link diagram      156 169
Metropolis sampling      85
minichromosome      32
Minima      143 191
Minimal diagram      46
Mirror images      131
Mobius ladder graphs      101
Mobius ladders      122
molecular Mobius band      106
molecular trefoil knot      97
Monte Carlo      85 87
Morphism      137 145 187 188
multiplicative relations      164
multivariable Alexander polynomial      211
negative supercoiling      10
NMR      117
Nonstandard set theory      231
Normal vector field      220
Nucleic acid      1
Nucleosome      25
one—dimensional genetic code      5
Operand      136
Operator      136
Operator algebras      132
Orientation preserving      42
Oriented      42
original Jones polynomial      161
orthogonality identity      181
outside bound tangle $O_b$      61
outside free tangle $O_f$      61
outside tangle $O$      62
parental tangle $P$      61
Parity      51
particle interaction      135
Partition function      133 134 168 169 186 205
pattern theorem      78 90
Penrose Binor Calculus      194
Penrose spin network      198 201
Permutation      174 186 204
physical level of rigor      224
physical state      134
Physics      131
Pivot algorithm      76 85
Plane graph      156
plane graph G      170
plat closure      166 167
plat trace      170
Platonic      132
plectonemic supercoiling      46
Potts model      132 168
Potts partition function      153 168 170
Prime      45
Process      140
processive recombination      59
PRODUCT      57
product equation      62
projected writhing number      20
Quantum field theory      133 137 153 186
Quantum gravity      205
Quantum group      145 153 186 198 200
quantum knots      143
quantum mechanics      140 144
Quantum state      142
Radius of gyration      87
Rapidity      195 196
Rapidity parameter      195
Rational tangles      50
recombinant tangle R      61
recombination equations      62
recombination site      57
recursive definitions      132
Recursive form      231
Regular isotopy      219
Reidemeister move      88 135 145 155 219
Reidemeister torsion      186 187 212 224
Relaxed DNA      54
Reshetikhin — Turaev invariant      185 186
ribbon knot      212 213
Riemann surface      139 140
ring polymers      74
RNA      2
Scattering amplitude      195
Scattering matrix      135
Seifert pairing      211
Self reference      232
Self-avoiding polygon      74 78
Self-avoiding walk      74 76 78 89
Set theory      229
SI($n$) quantum group      210
site—specific recombination      11
Skein      227
skein calculation      211 227
skein identity      219
skein polynomial      132 225
Skein relation      221
skein theoretic      137
SL(2)      194
SL(2) quantum group      187
SL(2)$q$ quantum group      153
SL(2)$q$ re-coupling theory      172
Slice knot      212 213
slide move      189
SLk      26
Space-time      195
Spin      195
Spin network      172 180 205
Spinor      201
State      158 191
state summation model      153
State transitions      134
states of a braid      162
Statistical mechanics      132 153 211
Stereoisomers      114
strand closure      163
SU(2)      139
Substrate      57
substrate equation      62
supercoil      54
supercoiled      17
Supercoiling      24 39
superhelical stress      9
Surface linking number      25 26
surface of a protein      25
SV40      25 34
SV40 molecule      24
Symmetric group      173
symmetry presentation      103
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