Ali, S.T., Concordia University, Montreal, Que., Canada
Antoine, J.-P., Institut de Physique Theorique, Louvain-la-Neuve, Belgium
Gazeau, J.-P., University of Paris, France
Coherent States, Wavelets, and Their Generalizations
2000. XIII, 418 pp. 14 figs.
0-387-98908-0
A survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing
mathematical structures. Starting from the standard theory of coherent states over Lie groups, the
authors generalize the formalism by associating coherent states to group representations that are
square integrable over a homogeneous space; a further step allows the group context to be
dispensed with altogether. The unified background makes transparent otherwise obscure properties
of wavelets and of coherent states. Many concrete examples, such as semisimple Lie groups, the
relativity group, and several kinds of wavelets, are discussed in detail. The book concludes with
physical applications, centering on the quantum measurement problem and the quantum-classical
transition. Intended as an introduction to current research for graduate students and others entering
the field, the mathematical discussion is self- contained. With its extensive references to the
research literature, the book will also be a useful compendium of recent results for physicists and
mathematicians already active in the field.
Contents: Preface.- Introduction.- Canonical Coherent States.- Positive Operator-Valued Measures
and Frames.- Some Group Theory.- Hilbert Spaces.- Square Integrable and Holomorphic Kernels.-
Covariant Coherent States.- Coherent States from Square Integrable Representations.- Some
Examples and Generalizations.- CS of General Semidirect Product Groups.- CS of Product
Groups.- Wavelets.- Discrete Wavelet Transforms.- Multidimensional Wavelets.- Wavelets Related
to Other G Groups.- The Discretiaztion Problem: Frames Sampling, and all that.- Conclusion.
Series: Graduate Texts in Contemporary Physics.
Fields: Quantum Physics; Topological Groups, Lie Groups, Lie Algebra
Written for: Mathematical physicists, applied mathematicians
Book category: Monograph
Publication language: English
Tymoczko, T. / Henle, J., Smith College, Northhampton, MA, USA
Sweet Reason
A Field Guide to Modern Logic
2000. XXII, 644 pp.
0-387-98930-7
A revolutionary, introductory text for courses on modern logic. While the basic rudiments of formal and informal logical are all clearly described here, it also focuses students on the real world, where the discipline of logic adds substance and meaning to all kinds of human discourse. Everything from puzzles, paradoxes, and mathematical proofs, to campaign debate excerpts, government regulations, and cartoons are used to show how logic is put to work by philosophers, mathematicians, advertisers, computer scientists, politicians, and others. As the book alternately discusses, instructs, questions, teases, and challenges, readers will find themselves absorbing the fundamentals of the discipline, becoming fluent in the language of logic, understanding how logic works in the real world, and enjoying logic's ability to entertain, surprise, subvert, and enlighten.
Contents: Preface for the General Reader.- Preface for Logic Teachers: How to Use this Book in Logic
Courses.- Introduction.- A Taste of Logic.- Everything All at Once and a Warning.- Statement Logic, Formal
Languages, and Informal Arguments.- Valid Arguments, Convincing Arguments, and Punk Logic.- Predicates,
Programs, and Antique Logic.- Deduction, Infinity, and a Haircut.- Symbolic Sophistication, Induction, and
Business Logic.- Completeness, Disbelief, Debates, and Dinner.- Paradox, Impossibility, and the Law.- Notes.-
References.- Hints.- Some Answers.- Index.
Series: Textbooks in Mathematical
Fields: Mathematical Logic and Set Theory; Computer Science, general
Written for: Professors
Book category: Undergraduate Textbook
Publication language: English
Weber, D.C., Miami University, Oxford, OH, USA
Skillings, J.H., Miami University, Oxford, OH, USA
A First Course in the Design of Experiments
A Linear Models Approach
2000. 693 pp.
0-8493-9671-9
This text stands apart from other books on experiment design. It presents theory and methods, emphasizes both the design selection for an experiment and the analysis of data, and integrates the analysis for the various designs with the general theory for linear models. It begins with a general introduction to the subject, then leads readers through the theoretical results, the various design models, and the analytical concepts that provide the techniques that enable analysis of virtually any design. Rife with examples and exercises, the text also encourages using computers to analyze data. It features the SAS software package, but also demonstrates how any regression program can be used for analysis. With its clear, highly readable style, A First Course in the Design of Experiments proves ideal as both a reference and a text.
Keywords: Experiment design
Contents:
Introduction to the Design of Experiments.- Definition of a Linear Model.- Least Squares Estimation
and Normal Equations.- Linear Model Distribution Theory.- Distribution Theory for Statistical Inference.-
Inference for Multiple Regression Models.- The Completely Randomized Design.- Planned Comparisons.-
Multiple Comparisons.- Randomized Complete Block Design.- Incomplete Block Designs.- Latin Square Designs.- Factorial Experiments with Two Factors.- Analysis of Covariance.- Random and Mixed Models.- Nested Designs and Associated Topics.- Other Designs and Topics.- Appendix A: Matrix Algebra.- Appendix B: Tables.- References.- Index.
Fields: Statistics for Engineering, Physical Sciences, Computer Science; Math. Appl. in Engineering
Written for: Statisticians, professionals from various fields involved in experimental design, students in experimental design or linear models courses
Book category: Manual
Publication language: English
Nathanson, M.B., Lehmann College, Bronx, NY, USA
Elementary Methods in Number Theory
2000. XVIII, 513 pp.
0-387-98912-9
Elementary Methods in Number Theory begins with "a first course in number theory" for students with no
previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is
also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods. Part II is about multiplicative number theory, and includes two of the most famous results in mathematics: the Erd?s-Selberg elementary proof of the prime number theorem, and Dirichlet theorem on primes in arithmetic progressions. Part III is an introduction to three classical topics in additive number theory: Waring problems for polynomials, Liouville method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions. Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of the two other graduate texts: Additive Number Theory: The Classical Bases and Additive Number Theory: Inverse Problems and the Geometry of Sumsets.
Contents: I A first course in number theory: Divisibility and primes. Congruences. Primitive roots and
quadratic reciprocity. The abc conjecture.- II Divisors and primes in multiplicative number theory:
Arithmetic functions. Divisor functions. Prime Numbers. The prime number theorem.- Primes in arithmetic
progressions.- III Three problems in additive number theory: Waring's problem. Sums of sequences of
polynomials. Liouville's identity. Sums of an even number of squares. Partition asymptotics. An inverse theorem for partitions.
Series: Graduate Texts in Mathematics.VOL. 195
Fields: Number Theory
Written for: Undergraduate math students, graduate math students, mathematicians
Book category: Undergraduate Textbook
Publication language: English
Hoppensteadt, F.C., Arizona State University, Tempe, AZ, USA
Analysis and Simulation of Chaotic Systems
2nd ed. 2000. Approx. 340 pp. 73 figs.
0-387-98943-9
Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable models for further mathematical analysis or computer simulations. For the most part, derivations are based on perturbation methods, and the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro-differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.
Contents:
Linear Systems.- Dynamical Systems.- Stability Methods for Nonlinear Systems.- Bifurcation and
Topological Methods.- Regular Perturbation Methods.- Iterations and Perturbations.- Methods of Averaging.-
Quasistatic-State Approximations.- References.- Index.
Series: Applied Mathematical Sciences.VOL. 94
Fields: Analysis; Math. Appl. in Life Sciences
Written for: Graduate students, researchers
Book category: Graduate Textbook
Publication language: English
Wolf-Gladrow, D.A., Alfred Wegener Inst. for Polar and Marine Research Bremerhaven, Germany
Lattice-Gas Cellular Automata and Lattice Boltzmann Models
An Introduction
2000. IX, 308 pp.
3-540-66973-6
Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising
methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
Keywords: Stokes and Naier-Stokes equations point-mapping properties cellular automata numerical analysis gas flows Boltzmann equations
Contents: .
Introduction 1.1 Preface 1.2 Overview 1.3 The basic idea of lattice-gas cellular automata and lattice
Boltzmann models 2. Cellular Automata 2.1 What are cellular automata? 2.2 A short history of cellular automata 2.3 One-dimensional cellular automata 2.4 Two-dimensional cellular automata 3.Lattice-gas cellular automata 3.1 The HPP lattice-gas cellular automata 3.2 The FHP lattice-gas cellular automata 3.3 Lattice tensors and isotropy in the macroscopic limit 3.4 Desperately seeking a lattice for simulations in three dimensions 3.5 FCHC 3.6 The pair interaction (PI) lattice-gas cellular automata 3.7 Multi-speed and thermal lattice-gas cellular automata 3.8 Zanetti ("staggered") invariants 3.9 Lattice-gas cellular automata: What else? 4. Some statistical mechanics 4.1 The Boltzmann equation 4.2 Chapman-Enskog: From Boltzmann to Navier-Stokes 4.3 The maximum entropy principle 5. Lattice Boltzmann Models 5.1 From lattice-gas cellular automata to lattice Boltzmann models 5.2 BGK lattice Boltzmann model in 2D 5.3 Hydrodynamic lattice Boltzmann models in 3D 5.4 Equilibrium distributions: the ansatz method 5.5 Hydrodynamic LBM with energy equation 5.6 Stability of lattice Boltzmann models 5.7 Simulating ocean circulation with LBM 5.8 A lattice Boltzmann equation for diffusion 5.9 Lattice Boltzmann model: What else? 5.10 Summary and outlook 6. Appendix 6.1 Boolean algebra 6.2 FHP: After some algebra one finds ... 6.3 Coding of the collision operator of FHP-II and FHP-III in C 6.4 Thermal LBM: derivation of the coefficients 6.5 Schl?fli symbols 6.6 Notation, symbols and abbreviations
Series: Lecture Notes in Mathematics.VOL. 1725
Fields: Differential,Difference and Integral Equations; Global Analysis and Analysis of Manifolds; Numerical Analysis and Computation
Written for: Researchers and graduate students in Stokes and Navier-Stokes equations, Point-mapping properties, cellular automata, numerical analysis, gas flows, Boltzmann Equation
Book category: Monograph
Publication language: English