Zeidler E. — Nonlinear Functional Analysis and its Applications IV: Applications to Mathematical Physic :: Электронная библиотека попечительского совета мехмата МГУ

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Zeidler E. — Nonlinear Functional Analysis and its Applications IV: Applications to Mathematical Physic

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Название: Nonlinear Functional Analysis and its Applications IV: Applications to Mathematical Physic

Автор: Zeidler E.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 1007

Добавлена в каталог: 23.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Absolute derivative      625
Absolute differential      625
Absolute space      29 31 702 704ff
Absolute temperature      see “Temperature”
Absolute time      31 702
Acceleration      11
Accessory quadratic variational problem      218
action      81 884
Action propagation of      81
Addition theorem for velocities in relativity      708ff
Adiabatic process      380 394
Admissible chart      535
Admissible coordinate system      632
Affine connected manifolds      649
Airy’s stress function      328 337 345
Algebraically simple eigenvalue      1374 853ff
Alternating differential forms      664ff (see also «“Part V”)
Alternating differential forms, basic ideas of the calculus for      665
Alternating differential forms, differentiation of      665 668
Alternating differential forms, integration of      665 669
Amplitude      101
Analytic map      1362
Angular frequency      28 99
Angular momentum in quantum mechanics      115
Angular momentum tensor      725ff
Angular velocity      12
Antisymmetric (skew-symmetric)      622
Approximation methods in elasticity      224ff 252
Approximation methods in general relativity      735
Approximation methods in hydrodynamics      483
Approximation methods in quantum mechanics      129
Approximation models in elasticity      163 240ff
Area preserving maps      644
Asymptotically stable      842
Atlas      534
Atlas abstract      602
Atlas equivalent      536
Atlas maximal      535
Atlas oriented      583
Autonomous differential equations      548 841
B-space (Banach space)      1769ff
Baire category      1802
Baire space      1801
Balance of angular momentum      34
Balance of energy      34
Balance of momentum      34
Banach manifold      see “Manifold”
Banach space      see “B-space”
Baryon number      416
Basic equations in mathematical physics, list of      953
Basis space of a bundle      544
Beam equation      315ff
Benard problem      505ff 518
Bending of beams and rods      311ff
Bernoulli constant      453
Bernoulli equation      433 438 453
Betti number      688
Bifurcation and loss of stability      221ff 227 841 856ff 860ff
Bifurcation for beams and rods      311ff 320
Bifurcation for dynamical systems      856ff (see also «“Part V”)
Bifurcation for plates      323 333
Bifurcation for variational inequalities      303ff
Bifurcation in elasticity      221 227 303ff 311ff 332 346
Bifurcation in hydrodynamics      448 495 505
Bifurcation point of a variational inequality      304
Bifurcation point of an operator equation      1358
Bifurcation principle      821 837 841
big bang      57ff 742ff
Bilinear form      1141
Bilinear form compact      see “Part II”
Bilinear form nondegenerate      561
Bilinear form strictly positive      see “Part II”
Bilinear form strongly positive      see “Part II”
Bilinear form weakly nondegenerate      561
Black hole      768 771ff 778ff
Black-body radiation      410ff
Black-white dipole hole      768 775ff
Blowing-up lemma      606
Bohr’s atomic model      137
Boltzmann constant      59 366 400 884
Boltzmann statistics      420
Bose statistics      402 408
Bose statistics, basic ideas of      401
Boson      126 751
Boundary layers      518ff
Boundary of stability      222
Boussinesq approximation      506 512
Brouwer’s fixed-point theorem      151
Brouwer’s fixed-point theorem elementary proof of      799
Brouwer’s fixed-point theorem equivalent statements to the      795 810
Brouwer’s principle      797
Buckling force      304 314
Bundle      544
Bundle abstract      544
Bundle cotangent      545
Bundle fiber      see “Part V”
Bundle isomorphism      544
Bundle morphism      544
Bundle normal      591
Bundle space      544
Bundle tangent      542
Bundle vector      590
Canonical equation      21 72 83ff
Canonical transformation      83
Carnot’s cycle      394
Catastrophe theory      572ff
Catastrophe theory basic ideas of      572
Causal structure of manifolds      787
Causality      714ff
Cavities      471
Center of mass      33
Center theorem of Ljapunov      868
Center theorem, general      see “Part V”
Center, stable, and unstable manifolds      see “Part V”
Centrifugal force      30
Chain rule for tangent maps      543
Chandrasekhar mass, critical      412 778
Characteristic classes      690
Chart      533
Chart abstract      536
Chart admissible      535
Chart admissible oriented      584
Chart compatible      534
Chart image      534
Chart map      535
Chart space      534
Chebyshev inequality      115 398
chemical potential      374 398
Chemical potential as a Lagrange multiplier      398
Chemical potential of a photon gas      409
Chemical potential of an ideal gas      377 406
Chemical potential of elementary particles      416
Chemical reactions      373 389ff
Christoffel symbols      623
Christoffel symbols effective calculation of the      734
Christoffel symbols intuitive meaning of the      682
Circulation      438
Closed map      551
Cnoidal waves      466ff
Cobasis      576
Coboundary      671
Cocycle      671
Codimension      1765
Codimension of a map      576
Codimension of a submanifold      557
Coherently oriented      585
Cohomology      671
Cohomology class      671
Cohomology group      671
Compact operator      153

Compact set      1756 1769
Compact spacelike support      724
Compensated compactness      264ff
Complex flow potential      454
Complex velocity      453
Complexification      1770
Component of a set      1757
Cone      1276
Configuration space      22 48
Conformai maps      645
Conjugate functional      65ff
Connected set      1757
Connection in a principal fiber bundle      690 (see also «“Part V”)
Conservation laws      34 422ff 724
Conservation laws in relativity      724 (see also «Part V)
Conservation laws, basic ideas of      422
Conservation laws, differential forms and      782
Conservation of angular momentum      35
Conservation of energy      34
Conservation of mass      423
Conservation of momentum      35
Conservative force      33
Conserved quantities in mechanics      32
Constitutive laws basic ideas of      147ff
Constitutive laws convex material      237 244ff
Constitutive laws dual      237 246
Constitutive laws elastic energy of the cuboid and      198 230
Constitutive laws elasto-viscoplastic material      151ff 348ft 354
Constitutive laws for homogeneous bodies      205ff
Constitutive laws for homogeneous isotropic bodies      206
Constitutive laws for the friction tensor      436ff
Constitutive laws Fourier’s law      424
Constitutive laws hardening and      148 151ff 348ff 353
Constitutive laws Hencky material      202 256
Constitutive laws Hooke’slaw      8 201 233ff 255
Constitutive laws ideal plastic material      149
Constitutive laws ideal plastic von Mises liquid      157 (see also «“Part V”)
Constitutive laws in heat conduction      424
Constitutive laws in hydrodynamics      434ff
Constitutive laws in hyperelasticity      190
Constitutive laws in linear elasticity      201 208 255
Constitutive laws in nonlinear elasticity      176 185
Constitutive laws in plasticity      148ff 154ff 200ff 257ff 348ff
Constitutive laws inverse (dual)      237 246
Constitutive laws linear material      201 208 255 259
Constitutive laws Mooney — Rivlin material      209
Constitutive laws Navier — Stokes liquid      438
Constitutive laws non-Newtonian liquid      157 (see also «“PartV”)
Constitutive laws Ogden’s material      209
Constitutive laws polyconvex material      209 241 273
Constitutive laws rubberlike material      208 277
Constitutive laws Saint Venant — Kirchhoffmaterial      208
Constitutive laws theory of invariants and      202ff
Constitutive laws viscoplastic Bingham liquid      157 (see also «“Part V”)
Constitutive laws viscoplastic material      149ff 348ff
Constitutive laws viscous material      150
Constitutive laws viscous Williamson liquid      157 (see also «“Part V”)
Constraining force      46ff
Constraining force of a pendulum      93
Continuation method in heat conduction      422ff
Continuation method in nonlinear elasticity      224ff
Continuation method in numerical mathematics      818ff
Continuity equation      434
Continuous operator      1755 1770
Contra variant tensor      619
Contraction of tensors      622
Convex functional      III245 III380
Convex set      III245
Coriolis force      30
Cosmos early      63 747ff
Cosmos future of the      745ff
Cotangent bundle      545
Cotangent vector      545 595
Couette flow      497
Coulomb (unit of charge)      884
Coulomb’s law      38
Countable basis      1754 536
Covariance      720
Covariant differentiation      623
Covariant differentiation motivation of the      626
Covariant differentiation on surfaces      646
Covariant tensor      618
Covector field on a manifold      546
Critical mass density of the universe      60 744
Critical temperature for elementary particles      62
Cross section for elementary particle processes      106 137 139
Current density vector      422ff 725
Curvature scalar      731
Curvature tensor      642ff 650 653 655 683 731 734 784
Curvature tensor analytic meaning of the      650
Curvature tensor definition of the      642
Curvature tensor geometric meaning of the      654 683
Curvature tensor important properties of the      643 784
Curvature tensor in general relativity      730ff 734
Curvature tensor Riemann’s theorem on local flatness and the      654
Curvature tensor theorema egregium of Gauss and th      642
Curve following algorithm      812ff 822 837
de Broglie matter wave      112
De Rham cohomology      671
Dead water problem      471
Decay of particles      105
Decay probability      106
Deflection of light in general relativity      765
Deformation      177
Deformation of a cuboid      198
Degree of a tensor      619
Derivation      600
Dielectricity constant      38 884
Diffeomorphism      537
Diffeomorphism construction of a      560
Diffeomorphism local      538
Differentiable structure      536
Differential      595
Differential absolute      625
Differential and numerical mathematics      817ff
Differential and the fixed-point index      825
Differential and the mapping degree      825
Differential calculus on manifolds      648 663ff
Differential forms      599
Differential forms and conservation laws      782
Differential forms in mechanics      see “Part V”
Differential forms in thermodynamics      383ff
Differential topology      688ff
Differentiation absolute      625 650
Differentiation alternating      664
Differentiation covariant      623 650
Differentiation Lie      673
Differentiation of differential forms      665ff
Differentiation on manifolds      540ff 663ff
Dimension analysis and boundary layers      521
Dimension analysis and turbulence      440 515
Dimension analysis basic ideas of      89
Dimension of a manifold      535
Direct sum      1766
Directional derivative      595 600 673
Dispersion in quantum mechanics      114
Dispersion in statistical physics      398 407
Dispersion in turbulence      515
dispersion relation      100 102 449
Divergence of a tensor      166
Door-in/door-out principle      813 820
Doppler effect      91
Doppler effect and the red shift of galaxies      57
Double splitting maps      531
Dual elastic energy      245
Dualism between waves and particles      107ff
Duality in elasticity      235 237 245ff 289
Duality in plasticity      259 262
Duality in the calculus of variations      284
Duality of Friedrichs      284ff

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