دانلود کتاب Mathematical Structures and Applications: In Honor of Mahouton Norbert Hounkonnou

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Dedication......Page 6
Preface......Page 8
Acknowledgments......Page 12
Contents......Page 13
Contributors......Page 15
1 Introduction......Page 18
2 Metric Operators......Page 19
3 Similar and Quasi-Similar Operators......Page 21
4 The Lattice Generated by a Single Metric Operator......Page 25
5 Quasi-Hermitian Operators......Page 27
6 The LHS Generated by Metric Operators......Page 29
7.1 General pip-Space Operators......Page 31
7.2 The Case of Symmetric pip-Space Operators......Page 32
8 Semi-Similarity of pip-Space Operators......Page 33
9 Pseudo-Hermitian Hamiltonians......Page 34
References......Page 36
Beyond Frames: Semi-frames and Reproducing Pairs......Page 38
1 Introduction......Page 39
2.1 Frames......Page 40
2.2 Semi-frames......Page 41
3 Reproducing Pairs......Page 44
3.1 The Hilbert Spaces Generated by a Reproducing Pair......Page 45
3.2 Duality Properties of the Spaces Vϕ(X, μ)......Page 47
4 Existence and Nonuniqueness of Reproducing Partners......Page 51
5.1.1 Orthonormal Basis......Page 52
5.2.2 1D Continuous Wavelets......Page 53
5.2.3 A Continuous Upper Semi-frame: Affine Coherent States......Page 54
5.2.4 Continuous Wavelets on the Sphere......Page 55
6 Interlude: Reproducing Pairs and pip-Spaces......Page 57
7.1 A Hilbertian Approach......Page 58
7.2 The General Case......Page 59
8 Reproducing Pairs and Genuine pip-Spaces......Page 62
9.1 The General Construction......Page 66
9.2 Examples......Page 67
10 The Case of Lp Spaces......Page 69
11 Concluding Remarks......Page 72
Appendix: Lattices of Banach or Hilbert Spaces......Page 73
References......Page 75
1 Introduction......Page 77
2.1 Basics on von Neumann Algebras......Page 79
2.2 Hilbert Space of Hilbert-Schmidt Operators......Page 95
2.3.1 Modular Theory......Page 97
2.3.2 Vector State and von Neumann Algebras......Page 100
2.3.3 von Neumann Algebras Generated by Unitary Operators......Page 104
2.4 Modular Theory-Thermal State......Page 112
2.5.1 Electron in a Magnetic Field......Page 114
2.5.2 Coherent States built from the Thermal State......Page 115
3 Noncommutative Quantum Harmonic Oscillator Hilbert Space......Page 121
4 Application......Page 122
4.1 Coherent States Construction......Page 125
4.2 Density Matrix and Diagonal Elements......Page 128
4.3 Lowest Landau Levels and Reproducing Kernel......Page 130
4.4 Statistical Properties......Page 132
References......Page 133
1 Introduction......Page 135
2.1 Preliminaries......Page 136
3.1 Coadjoint Cocycle......Page 137
3.2 The Orbits of an Affine Action......Page 143
4 Towards a Generalization......Page 148
References......Page 151
1 Introduction......Page 152
2.1 Difference Derivative and Integral......Page 154
2.2 Linear Difference Equations of First Order......Page 155
3 Difference Integral Inequalities......Page 157
3.1 Hölder and Cauchy-Schwartz Inequalities......Page 158
3.2 Minkowski Inequality......Page 159
3.3 Grönwall Inequality......Page 160
3.4 Bernoulli Inequality......Page 164
3.5 Lyapunov Inequality......Page 165
References......Page 167
1 Introduction......Page 168
2 Two Classical Parametric Estimators......Page 169
2.1 Maximum Likelihood Estimation......Page 170
2.2 Whittle Estimation......Page 171
3.1 R/S and Modified R/S Statistics......Page 172
3.2 Second-Order Quadratic Variations......Page 174
3.3 Detrended Fluctuation Analysis (DFA)......Page 176
3.4 Increment Ratio Statistic......Page 178
3.5 Wavelet Based Estimator......Page 181
4.2 Results of Simulations......Page 185
References......Page 187
1 Introduction......Page 189
2.1 Viability Concept: Definition and Characterization......Page 190
2.2.1 Definitions and Examples......Page 192
2.2.2 Characterization......Page 196
2.3 Minimal Lethal Disturbance (MLD)......Page 198
3.1 Viability Kernel and Viability Radius......Page 201
3.2.1 Problem Statement......Page 202
3.2.2 Problem Approach......Page 204
3.2.3 Example......Page 207
4 Connection with Minimal Lethal Dose in Toxicity......Page 210
References......Page 211
Walker Osserman Metric of Signature (3,3)......Page 213
2.1 Affine Manifolds......Page 214
2.2 Affine Osserman Manifolds......Page 216
2.3 The Riemann Extension Construction......Page 217
3 Example of Affine Osserman Connections......Page 218
4 Example of Walker Osserman Metric......Page 220
Appendix 1: Components of the Curvature Tensor......Page 222
References......Page 223
Conformal Symmetry Transformations and Nonlinear Maxwell Equations......Page 225
2.1 Conformal Transformations in Minkowski Space......Page 226
2.2 Conformal Compactification......Page 227
3.1 Motivation and Definition......Page 228
3.3 Some Comments......Page 229
4.1 Motivation and Framework for Nonlinear Maxwell Fields......Page 230
4.2 Transformations Under Conformal Inversion......Page 231
4.3 Steps Toward General Nonlinear Conformal-Invariant Electrodynamics......Page 232
5.1 The Space Y(6 )......Page 233
5.3 The Hexaspherical Space Q(6)......Page 234
6.1 Nonlinear Maxwell Equations in Y(6)......Page 235
6.2 Invariants for the General Nonlinear Maxwell Theory with Conformal Symmetry......Page 236
References......Page 237
The Yukawa Model in One Space - One Time Dimensions......Page 239
References......Page 246
Towards the Quantum Geometry of Saturated Quantum Uncertainty Relations: The Case of the (Q,P) Heisenberg Observables......Page 248
1 Introduction......Page 249
2 The Uncertainty Relation for the Heisenberg Algebra......Page 252
3 A Reference Fock Algebra......Page 254
4.1 Reversible Parametrisation Packages......Page 260
4.2 Correlated Squeezed Fock Algebras and Their Vacua......Page 265
4.3 Squeezed Fock Vacua and SR-UR Saturating Quantum States......Page 267
5 Overcompleteness and Kernel Representation......Page 269
6.1 Squeezed State Configuration Space Wave Functions......Page 271
6.2 The Fundamental Overlap \"426830A Ωz2(u2)|Ωz1(u1)\"526930B of Squeezed States......Page 274
7 Conclusions......Page 276
Appendix 1: Cauchy–Schwarz Inequality and Quantum Uncertainty Relations......Page 278
Appendix 2: Baker–Campbell–Hausdorff Formulae......Page 281
References......Page 286
The Role of the Jacobi Last Multiplier in Nonholonomic Systems and Locally Conformal Symplectic Structure......Page 287
1 Introduction......Page 288
2 Preliminaries......Page 289
2.1 Inverse Problem and the Jacobi Last Multiplier......Page 290
3 Nonholonomic Free Particle, Conformal Structure, and Jacobi Last Multiplier......Page 293
3.1 Reduction, Constrained Hamiltonian and Nonholonomic Systems......Page 294
3.2 Hamiltonization and Reduction Using Jacobi Multiplier......Page 296
3.3 Conformally Hamiltonian Formulation of Nonholonomic Systems......Page 297
4 Integrability of Nonholonomic Dynamics and Locally Conformally Symplectic Structure......Page 298
4.1 Role of Jacobi\'s Multiplier and Integrability of Nonholonomic Dynamical Systems......Page 299
4.2 JLM and Commuting of Vector Fields......Page 300
5 Final Comments and Outlook......Page 301
References......Page 302
1 Introduction......Page 304
2 U(1)d Tensorial Group Field Theory......Page 305
3 Functional Renormalization Group with Closure Constraint......Page 310
3.1 Flow Equations in the UV Regime......Page 312
4.1 Vicinity of the Gaussian Fixed Point......Page 315
4.2 Non-Gaussian Fixed Points......Page 316
5 Concluding Remarks......Page 319
References......Page 320
Ternary Z2 and Z3 Graded Algebras and Generalized Color Dynamics......Page 322
1.1 Z2 and Z3 Symmetries and Gradings......Page 323
2 Examples of Z3-Graded Ternary Algebras......Page 325
3 Ternary and Cubic Algebras......Page 327
4.2 The Z3 Graded Differential Forms......Page 331
4.3 Ternary Clifford Algebra......Page 333
5 Generalized Z2 Z3-Graded Ternary Algebra......Page 334
6 Two Distinct Gradings: Z3 Z2 Versus Z6......Page 337
7 Low-Dimensional Algebras......Page 339
8 Ternary Dirac Equation......Page 345
9 Solutions......Page 351
10 Relativistic Invariance......Page 356
11 Propagators......Page 360
12 Conclusion......Page 365
References......Page 367
1 Introduction......Page 369
2.1 Development of the Algebraic Approach......Page 372
2.2 Proposed Algorithm......Page 374
3.1 Rates of Traders Thinking of the Trade in Terms of Its Dangerous Character......Page 378
3.2 Rates of Traders Susceptible to Give Up Trading......Page 380
4 Discussion......Page 381
5 Conclusion......Page 382
References......Page 383
1 Introduction......Page 385
2 The Seiberg–Witten Equations......Page 386
3 Curvature Estimates......Page 391
4 Einstein Metrics......Page 397
References......Page 400
1 Introduction......Page 402
2 Mathematical Formulation of SUSYQM: Integrability Condition and Coherent State Construction......Page 403
3 Construction of Photon-Added Coherent States for Shape Invariant Systems......Page 412
3.1 Definition of the PA-SIPCS......Page 413
3.3 Overcompleteness......Page 414
3.4 Thermal Statistics......Page 415
4 Pöschl–Teller Potential......Page 417
4.1 First Choice of the Functional Zj......Page 419
4.2 Second Choice of the Functional Zj......Page 424
5 Concluding Remarks......Page 428
References......Page 429
1 Introduction......Page 431
2 Preliminaries......Page 432
3 A Pre-Hilbert Module Structure on L2(G, B(H))......Page 433
4 The Fourier Transform of Functions in L2(G, B2(H))......Page 435
5 The ρ-Fourier Transform for L2(G, B(H)) Functions......Page 436
References......Page 438
1 Introduction......Page 440
2 Theoretical Analysis......Page 441
3 Conclusion......Page 443
References......Page 445
1 Star Product on Polynomials......Page 446
1.1 Moyal Product......Page 447
1.2 Star Product......Page 448
1.3 Equivalence and Geometric Picture of Weyl Algebra......Page 449
2.1 Star Product on Certain Holomorphic Function Space......Page 451
3.1 Definition......Page 452
3.2 Examples......Page 453
4.1 Star Hermite Function......Page 454
4.2 Star Theta Function......Page 455
4.3 *-Delta Functions......Page 456
References......Page 457
Index......Page 459