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

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Предметный указатель

Law of Kepler      22 39 41
Law of Kolmogorov      513ff
Law of mass action      392
Law of thermodynamics, first      366 369ff 379ff
Law of thermodynamics, second      363 365ff 369ff 380ff
Law of thermodynamics, third      385
Law of thermodynamics, zero-th      380
Law of Walras      806
Lax pair      470
Lebesgue spaces      see “Part II”
Left invariant vector field      678
Legendre transformation and conjugate functionals      65ff
Legendre transformation basic ideas of      66
Legendre transformation in elasticity      238 286ff
Legendre transformation in mechanics      74
Legendre transformation in the calculus of variations      284ff
Legendre transformation in thermodynamics      385
Legendre transformation Morse      560 603
Legendre transformation Morse — Tromba      605
Legendre transformation Ricci      642 654 679
Legendre transformation Sperner      797
Legendre transformation Sperner, cubic      815
Legendre — Hadamard condition      218
Lemma of Knaster — Kuratowski — Mazurkiewicz      798
Length contraction in relativity      708
Length preserving maps      644
Lepton number      416
Leray — Schauder principle, constructive      823
Lever principle      14
Lie algebra      676ff
Lie derivative      673ff
Lie derivative motivation for the      674
Lie group      677
Lifetime of black holes      780
Lifetime of elementary particles      130
Lifting of indices      680
Light      107
Light cone      715
Light dualism between wave and particle      107ff
Light quantum hypothesis      102
Light trap      773
Lightlike events      715
Linearization principle for differential equations      842
Linearization principle for flows      842
Linearization principle for maps      550ff
List of important principles      1866 956
List of symbols      933
List of the most important definitions      946
List of theorems      943
Ljapunov bifurcation      867
Ljapunov center theorem      868
Ljapunov stability      20 841
Local coordinates      see “Representatives”
Locally convex space      797
Locally flat      654 684
Longitudinal waves      101
Lorentz group      712
Lorentz transformation general      711
Lorentz transformation proper      711
Lorentz transformation special      706
Lorenz attractor      523
Loss of stability and bifurcation      221ff 227 856ff 860ff
Lower semicontinuous      1456
Lower semicontinuous multivalued mapping      1450
Lowering of indices      680
Magnetic monopoles      750
Manifolds      535
Manifolds affine connected      649
Manifolds basic strategy of the theory of      535
Manifolds center, stable, and unstable      see «Part V”
Manifolds in general relativity      730
Manifolds in special relativity      713
Manifolds metrizable      537
Manifolds one-dimensional      538 585 817ff
Manifolds orientation of      582
Manifolds principles for constructing      555ff 563ff
Manifolds Riemannian      651
Manifolds with boundary      584
Manifolds with countable basis      536
Mapping degree      824ff (see also “Part I”)
Mapping degree and differential topology      824ff
Mapping degree and Sperner simplices      814
Mapping degree for maps on manifolds      670
Maps      see “Operator properties”
Maps area preserving      644
Maps conformai      645
Maps length preserving      644
Maps orientation preserving      582
Mass      26 28 33 37
Mass balance      434
Mass Chandrasekhar      412
Mass in general relativity      731 736
Mass in special relativity      721
Mass of black holes      773 779
Mass of neutron stars      778
Mass of white dwarf stars, maximal      412 778
Mass-energy equivalence      719ff
Mathematical economics      806
Mathematics and physics      Iff
Matrix mechanics in quantum theory      78ff
Maximal monotone operator      see «Part II)
Maximum      see “Minimum”
Maxwell’s velocity distribution      406
Meager set      1802
Mean curvature      637
Mean curvature and minimal surfaces      682
Mean lifetime      104 135 137
Mean value in quantum mechanics      114
Mean value in statistical physics      398
Mean value of velocity in turbulent flows      515
Mechanics      9ff
Mechanics basic ideas of      14
Mechanics Gaussian      45
Mechanics Hamiltonian      72
Mechanics Lagrangian      70
Mechanics Newtonian      25
Mechanics Poissonian      77
Mechanics quantum      112ff
Mesons      131
Metric      620 651
Metric Eddington      774
Metric Friedman      738ff
Metric Kerr — Newman      779
Metric Kruskal      768ff
Metric Newton      735
Metric Schwarzschild      756ff
Metric space      1761
Metric tensor      620 634 651 731
Michelson experiment      703
Minimal surfaces      682
Minimax theorem      803
Minimum bound      III276
Minimum free      III193
Minimum local      III193
Minimum regular      551
Minimum strict      III193
Minimum strictly stable      193
Minimum strongly stable      218
Minkowski space-time manifold      696
Modern mathematical physics      752 952 955
Momentum      28 32
Momentum angular      32
Momentum balance      34 434
Momentum generalized      73
Momentum of a photon      102 722
Monotone operator      see “Part II”
Mooney — Rivlin material      209
Morse index      653
Morse lemma      I110 I343
Morse lemma generalized      560 603

Morse — Tromba lemma      605
Multilinearization of maps      572
Multiplier      846 851
Multiplier asymptotically stable      846
Multiplier critically      846
Multiplier Floquet      850
Multiplier of a fixed point      846
Multiplier of a periodic solution      850
Multiplier of an equilibrium point      846
Multiplier unstable      846
n-body problem      38 42
Nash equilibrium point      802
Natural basis      597 617 632 649
Natural boundary condition      192 299
Natural coordinates      597
Natural projection      542 544 545
Natural system of units      751
Navier — Stokes equations      438 479ff
Navier — Stokes equations basic ideas of the      480ff
Negative retract principle      808 810
Neutron stars      415 778
Newton (unit of force)      884
Newton’s basic equation      25ff 32
Newton’s basic equation in general systems of reference      28ff
Non-Euclidean geometry      655ff
Nondegenerate singular point      561
Nonresonance condition      867 876 880
Normal bundle      591
Normal coordinates      96
Normal forms and catastrophe theory      573ff 578
Normal forms for immersions      554 559
Normal forms for subimmersions      552 558
Normal forms for submersions      553 556
Normal forms of oscillating systems      96
Nowhere dense set      1751
Nuclear forces      132
Ogden’s material      209
Operator properties, important      1889 (see also “The Indices to Parts II and III”)
Orbit      852
Orbitally asymptotically stable      852
Orbitally stable      852 877 881
Orbitally unstable      853
Ordinary differential equations bifurcation theory for      856
Ordinary differential equations center, stable, and unstable manifolds for      see “Part V”
Ordinary differential equations coherent      585
Ordinary differential equations of a manifold      585
Ordinary differential equations of a manifold with boundary      585
Ordinary differential equations on manifolds and flows      548
Ordinary differential equations orientation      582ff
Ordinary differential equations preserving map      582
Ordinary differential equations, stability theory for      841
Oscillating systems, normal form of      96
Parallel axiom      655ff
Parallel transport of tensors      626ff 645ff
Parallel transport of tensors in the sense of Levi-Civita      626ff 645ff 650 682
Parallel transport of tensors in the sense of Lie      675
Parallel transport of tensors, basic ideas of the      627
Parallel transport of tensors, geometric interpretation of the      645
Partial regularity of differential equations      521
Partition function in statistical physics      400
Pascal (unit of pressure)      884
Pauli principle      125ff 413
PCT-invariance in nature      712
Pendulum      92 318 874
Penrose transformation via twisters      789
Perihelion of Mercury, motion of the      758ff
Period of oscillation      99
Periodic system of the elements      127
Permanent waves      448ff
Perpetuum mobile of the second kind      394
Perturbation gas      59 408
Perturbation of orbits      759ff
Perturbation of simple eigenvalues      853ff
Perturbation of the spectrum      874ff
Perturbation phase      100
Perturbation photon      108ff 722
Perturbation space      73
Perturbation theory      853 874
Perturbation theory, singular      519
Perturbation transition      see “Part V”
Perturbation transition in the cosmos      748
Perturbation, equation of motion of a      731
Piola identity      167 775
Piola transformation      175
Piola — Kirchhofftensor first      165 186 189
Piola — Kirchhofftensor second      186
Planck’s quantum of action      78 102 108 126 366 884
Planck’s radiation law      58 366 408ff
Planck’s radiation law and the big bang      58
Plane wave      100
Plastic torsion      see “Part V”
Plasticity basic ideas of      147ff
Plasticity condition of von Mises (yield condition)      156 201
Plasticity dynamical (plastic liquids)      156 (see also “Part V”)
Plasticity historical remarks on      155ff
Plasticity quasi-dynamical      154 348ff
Plasticity quasi-statical      154 251ff
Plasticity statical      154 262ff
Plates      322ff
Plates basic ideas for      322
Plates with obstacles      339
Poincare      (see also “Theorem of Poincare”)
Poincare group      712 781
Poincare model      657
Poincare transformation      711
Poisson brackets      77
Poisson mechanics      77
Poisson number      148
Poisson polarization      101
Polyconvex material of Ball      209 241 273ff
Positive-energy theorem in general relativity      791
Potential      33
potential energy      17 33
Potential of a force      33
Potential of a velocity      454
Potential operator      III229
Power      32 884
Prandtl number      508
Prandtl’s boundary layer equation      520
Pressure      394 435 884
Pressure in the weak sense      487
Pressure pricing system      806
Pressure principal axes of inertia      53
Pressure principal axes of strain      169
Pressure principal axes of stress      178
Principal moments of inertia      53
Principle basic ideas of the      17
Principle bifurcation      821 837 841
Principle door-in/door-out      813 820
Principle for constructing diffeomorphisms      560
Principle for constructing manifolds      555ff 563ff
Principle in elastostatics      188
Principle in hyperelasticity      192
Principle maximal plastic work      345
Principle negative retract      808 810
Principle of Brouwer      797
Principle of causality      716
Principle of constant enthalpy      391
Principle of constant velocity of light      700
Principle of least constraint      45ff
Principle of linearization for dynamical system      842
Principle of linearization for maps      550
Principle of maximal dual energy      245 259ff 262
Principle of maximal entropy      388
Principle of maximal signal velocity      716
Principle of minimal free energy      390
Principle of minimal free enthalpy      391
Principle of minimal potential energy      19 51 244
Principle of multilinearization for maps      560 572ff 604ff
Principle of relativity      695

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