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Staicu V. (ed.) Ч Differential Equations, Chaos and Variational Problems
Staicu V. (ed.) Ч Differential Equations, Chaos and Variational Problems

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Ќазвание: Differential Equations, Chaos and Variational Problems

јвтор: Staicu V. (ed.)


Differential equations are a fast evolving branch of mathematics and one of the mathematical tools most used by scientists and engineers. This book gathers a collection of original articles and stateЦofЦtheЦart contributions, written by highly distinguished researchers working in differential equations, delayЦdifferential equations, differential inclusions, variational problems, Young measures, control theory, dynamical systems, chaotic systems and their relations with physical systems. The forefront of research in these areas is represented in this volume.

The book and all contributions are dedicated to Arrigo Cellina and James A. Yorke on their 65th anniversary. Their remarkable scientific career covered all the above areas and was one of the main driving forces behind the work of many of the authors and the editor of this volume.

For researchers and graduate students in mathematics, physics and engineering, the material in this book will be a valuable resource, and a tool for everyone working in differential equations, chaos and variational problems. It brings the reader to the frontiers of research in the areas mentioned above and will stimulate further research.

язык: en

–убрика: ћатематика/

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

ed2k: ed2k stats

√од издани€: 2008

 оличество страниц: 435

ƒобавлена в каталог: 10.12.2009

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ѕредметный указатель
"Bare" theory      116Ч125
"Bare" theory, "effective" knowledge in      119Ч120
"Bare" theory, emergence of "probabilities" in      120Ч123
"Bare" theory, self-measurement in      180Ч186
"Color" (as a property of electrons)      1
"Hardness" as a property of electrons      1
"Ignorance" interpretation of probabilities in Bohm's theory      135 139Ч140
"Ignorance" interpretation of superpositions      15
"Modal" interpretations of quantum mechanics      191Ч197
Action at a distance (in Bohm's theory)      159Ч160 see
Aharonov Ч Bohm effect      11Ч12
Aharonov, Yakir      12n 195n
Aicardi, F.      106
Albert, D.      101 129n 131n 133n 185n 189n 191n
Barrett, J.      115 123n
Basis of a state space      31 33 40Ч41
Basis of a vector space      21Ч25 40Ч41
Bell's theorem      66Ч70 131 158
Bell, J.      61 68 70 134 160n
Bohm's theory      134Ч179
Bohm's theory, contextuality      153Ч155
Bohm's theory, effective collapse      161Ч164
Bohm's theory, epistemology      164Ч169
Bohm's theory, metaphysics      134Ч135
Bohm's theory, nonlocality      155Ч161
Bohm's theory, probability      135 140
Bohm's theory, relation to "modal" (Kochen Ч Healy Ч Dieks) interpretations of quantum mechanics      191 194
Bohm's theory, relation to many-minds theories      176Ч179 188n
Bohm's theory, self-measurement      187Ч188
Bohm, D.      12n 134
Bohr, Neils      17
Borsellino, A.      106
Brain states, discoverability of, by introspection      116Ч120
Brain states, relation to mental states      77 104Ч110 126Ч132 170Ч176 180Ч189
Brain states, time evolution of      77Ч79 104Ч110 119Ч125 180Ч189
Brain surgery, science-fictional      107Ч108 170Ч173
Brains, observables of      180Ч186
Causality      64Ч65n
Classical mechanics      43Ч44 134Ч135
Collapse of the wave function      36 37 51Ч53
Collapse of the wave function, effective (in Bohm's theory)      161Ч164
Collapse of the wave function, effective (in the "bare" theory)      119Ч120
Collapse of the wave function, effective (in the single-mind theory)      127Ч129
Collapse of the wave function, empirical consequences of      75Ч76 78 84Ч92 176n
Collapse of the wave function, for systems consisting of more than a single particle, or with more than one degree of freedom      51Ч53
Collapse of the wave function, lack of experimental evidence for      110Ч111
Collapse of the wave function, theories of      80Ч84 92Ч111
Commutators/commutation relations and compatibility      42Ч43 182Ч184n
Commutators/commutation relations and compatibility, the case of position and momentum      44
Compatible/incompatible observables      7 14Ч15 32Ч33 42Ч43
Compatible/incompatible observables, simultaneous knowability/unknowability of      7 165Ч170 183Ч188
Complex numbers/vector spaces      39Ч41
Contextuality, of deterministic replacements for quantum mechanics      153Ч155
Coordinate space      18Ч19
Coordinate space, quantum-mechanical formalism for      43Ч47 140Ч141 142Ч143
Copenhagen interpretation of quantum mechanics      17 38
Correspondence, principle of      43Ч44
Cosmology      133
D'Espagnat, B.      127n
Daneri, A.      91n 124n
deBroglie, L.      134
Decoherence      see "Environmental decoherence effects"
Degrees of freedom      53
Determinism of Bohm's theory      135 137 187Ч188
Determinism of the quantum-mechanical equations of motion      34 36 37
Deutsch, David      115n
DeWitt, B.      113
Dieks, D.      191
Dualism, mind-body      81Ч82 126 130Ч132
Eigenstates      31
Eigenvalues/eigenvectors      29
Einstein Ч Podolsky Ч Rosen (EPR) argument      61Ч66 69
Einstein, A.      61 69
Elementary particles      93Ч94
Empirical equivalence/inequivalence/incommensurability of theories      176Ч179
Energy non-conservation (in the GRW theory)      97Ч98
Environmental decoherence effects      88Ч92 161Ч164
Epistemology of Bohm's theory      165Ч170 183Ч186 187Ч188
Epistemology of the many-minds theory      132Ч133 183Ч187
Equation of motion (Schroedinger equation)      34
Everett, H., III      112Ч113
Fields, force      135
Fields, relativistic quantum      59Ч60 160n
Gell-Mann, M.      91n 124n
Ghirardi, G.C.      96 106
Ghirardi, Rimini, and Weber (GRW) theory of the collapse of the wave function      92Ч111 153n 176n
Ghirardi, Rimini, and Weber (GRW) theory of the collapse of the wave function, nonconservation of energy      97Ч99
Ghirardi, Rimini, and Weber (GRW) theory of the collapse of the wave function, significance of position      93 101Ч104 153n see
Gleason, A.M.      155n
Gottfried, K.      91n 124n
Grassi, R.      106
Hartle, J.      91n 124n
Healy, R.      191
Hermitian operators      40Ч41
Inner product, of two vectors      20
introspection      see "Brain states"
Kochen and Specker theorem      154n
Kochen, S.      155n 191
Light, speed of      65n
Linearity, as a property of dynamical laws      34
Linearity, as a property of operators      26
Locality      64Ч65
Locality, of the many-minds theory      131Ч132 see
Lockwood, Michael      124n
Loewer, B.      129n 131n 191n
Loinger, A.      91n 124n
Macroscopic systems/superpositions      83Ч84 see principle "Environmental
Many-minds theory      130Ч132
Many-minds theory and locality      131Ч132
Many-minds theory and self-measurement      186Ч187
Many-minds theory and the vacuum      133
Many-minds theory, relation to Bohm's theory      176Ч179 188n
Many-stories interpretation of quantum mechanics      115Ч116
Many-worlds interpretation of quantum mechanics      113Ч115 187
Matrices      27Ч28
Measurement      34Ч38 39 50Ч53 see
Measurement, approximate      194Ч197
Measurement, forms of outcomes of      92Ч93 99 100Ч111 170Ч179 191Ч197
Measurement, interactions      73Ч79
Momentum, observable of      44 see
Newman, J.      124n
Norm, of a vector      21
Normalized vectors, use of, in quantum mechanics      30
Observables      30Ч31 see "Operators"
Observables, complete      40Ч41
Operators      25Ч30 31Ч32 36
Operators, Hermitian      40Ч41
Orthogonal vectors      21
Orthonormal bases      21
Orthonormal bases, theorems about      40Ч41
Peres, A.      91n 124n
photons      101 102Ч104
Podolsky, B.      61 69
POSITION      170Ч176
Position, observable of      44Ч47
Position, special role of, in Bohm's theory      134Ч135
Position, special role of, in the Ghirardi Ч Rimini Ч Weber theory      93 100Ч111
Privacy, the quantum mechanics of      184Ч186 187Ч188
Probability in Bohm's theory      135 139Ч140
Probability in Kochen Ч Healy Ч Dieks-type theories      193
Probability in many-worlds and many-stories theories      114Ч116
Probability in single-mind and many-minds theories      126Ч129 130
Probability in the Ghirardi Ч Rimini Ч Weber theory      93Ч95 97Ч98
Probability in the standard formulation of quantum mechanics      34Ч36 46
Projection postulate      see "Collapse of the wave function"
Prosperi, G.M.      91n 124n
Putnam, Hilary      187
Quantum mechanics, coordinate-space formalism      43Ч47
Quantum mechanics, general formalism      30Ч43
Quantum mechanics, multiple degree-of-freedom formalism      53
Quantum mechanics, multiple-particle formalism      47Ч52 142Ч143
Quantum mechanics, relativistic formalism      60Ч61
quantum states      30
Relativity and Bohm's theory      160Ч161 169 see
Relativity and locality      65n
Retinas      105
Rimini, A.      96
Rosen, N.      61 69
Schroedinger's cat      73Ч80
Schroedinger's equation      see "Equation of motion"
Senses, human      103 105Ч106
Senses, nonhuman      107
Senses, superhuman      107Ч111 170Ч176
Separability/nonseparability      49 see "Nonlocality"
Simultaneity      see "Relativity" see
Single-mind theory      126Ч130
Space      see "Coordinate space" see "State "Vector
Space-time structure, and the foundations of quantum mechanics      177
Specker, E.P.      155n
Spin angular momentum      1 33
State space      30Ч33 40Ч41
State vector      30
State vector reduction      see "Collapse of the wave function"
State, quantum-mechanical      30
Statistical mechanics      135
Superposition      11
Superposition, phenomenology of      116Ч125 see
Supervenience of the mental on the physical      see "Brain states"
Time evolution      see "Equation of motion"
Two-slit experiment      12Ч14
Uncertainty principle      7 see "Compatible/incompatible
Underdetermination of theory by experiment      see "Empirical equivalence/inequivalence/incommensurability of theories"
Vacuum, quantum-mechanical      133
Vaidman, L.      101
van Fraassen, B.      196
Vector/vector space      17Ч25
von Neumann, J.      80
Wave functions      see "Quantum mechanics coordinate-space
Weber, T.      96
Wigner's friend      76Ч79
Wigner, E.P.      81Ч82
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