Saint-Aubin, Y., University of Montreal, Que., Canada
Vinet, L., University of Montreal, Que., Canada
(Eds.)Algebraic Methods in Physics
A Symposium for the 60th Birthday of Jiri Patera and Pavel Winternitz
2001. Approx. 270 pp. 17 figs. Hardcover
0-387-95125-3
This book pays tribute to two pioneers in the field of Mathematical physics, Jiri Patera and Pavel Winternitz of the CRM. Each has contributed more than forty years to the subject of mathematical physics, particularly to the study of algebraic methods.
Contents: Self-Similarities and Invariant Densities for Model Sets.- Symmetry Operations in the Brain: Music and Reasoning.- Lie Modules of Bounded Multiplicities.- Moving Frames and Coframes.- The Fibonacci-Deformed Harmonic Oscillator.- Continuous and Discrete Linearizable Systems: The Riccati saga.- Superintegrability on Two-Dimensional Complex Euclidean Space.- Hydrodynamic Systems and the Higher-Dimensional Laplace Transformations of Cartan Submanifolds.- Branching Rules and Weight Multiplicities for Simple and Affine Lie Algebras.- Conditions for the Existence of Higher Symmetries and Nonlinear Evolutionary Equations on the Lattice.- Complete Description of the Voronoi Cell of the Lie Algebra Aasub nu Weight Lattice. On the Bounds for the number of d-faces of the n-dimensional Voronoi Cells.- The Relativistic Oscillator and the Mass spectra of Baryons.- Seiberg-Witten Theory Without Tears.- Bargmann Representation for Some Deformed Harmonic Oscillators with non-Fock Representation.-
The Vector-Coherent State Inducing Construction for Clebsch-Gordon Coefficients.- Higest-Weight Representations of Borcheds algebras.- Graded Contractions of Lie Algebras of Physical Interest.
Series: CRM Series in Mathematical Physics.
Shubin, M., Northeastern University, Boston, MA, USA
Pseudodifferential Operators and Spectral Theory
2nd ed. 2001. Approx. 280 pp. Softcover
3-540-41195-X
This is the second edition of Shubin's classical book. It provides an introduction to the theory of
pseudodifferential operators and Fourier integral operators from the very basics. The applications
discussed include complex powers of elliptic operators, Hmander asymptotics of the spectral function and eigenvalues, and methods of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. The book is written for a wide audience of mathematicians, be they interested students or researchers.
Keywords: Pseudodifferential operator, Fourier integral operator, micolocal analysis, spectral asymptotic
Contents: Foundations of PDO Theory.- Complex Powers of Elliptic Operators.- Asymptotic Behaviour of the Spectral Function.- Pseudodifferential Operators in Rn.- Appendix 1. Wave Fronts and Propagation of Singularities.- Appendix 2. Quasiclasical Asymptotic Behaviour of Eigenvalues. - Appendix 3. Hilbert-Schmidt and Trace Class Operators.
Series: Springer Series in Soviet Mathematics.
Pauli, W./ Meyenn, K.von,
Max-Planck-Institut fur Physik, MunchenWissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a. /
Scientific Correspondence with Bohr, Einstein, Heisenberg a.o.
Band/Volume IV Teil/Part III: 1955-1956
2001. XXX, 1000 S. 25 Abb. Geb.
3-540-67591-4
Aus Paulis letztem Lebensjahrzehnt sind uber 2000 Briefe erhalten und in diesem grundlegenden Werk zur Physikgeschichte der Nachkriegszeit zusammengefaﾟt. Nebender Physik wird hier auch der allgemeinere geistesgeschichtliche Hintergrund unserer Naturwissenschaft beleuchtet. Dieser Teilband enthalt wissenschaftliche Korrespondez ・er grundlegende und andere allgemeine Fragen der Physik der Jahre1955-1956. In diese Zeit fallen der Beginn der axiomatischen Feldtheorie, die Anfange von CERN, der Berner Relativitatskongress zur 50-Jahr-Feier von Einsteins Entdeckung sowie N. Bohrs 70. Geburtstag und nat・lich die fr・e Geschichte des Neutrinos. Pauli und seine Briefpartner nehmen aktiv an diesen Ereignissen teil und beleuchten sie in eindrucksvoller Weise in ihrer Korrespondenz. Die reich annotierten und kommentierten Briefe sind chronologischangeordnet und durch Verzeichnisse und Register erschlossen.
From the final decade of Pauli's life, nearly 2000 letters survive. These are collected in this fundamental work on the history of physics in the post-war era. Going beyond physics, these letters also shed light on the cultural and philosophical background of our natural sciences.
This part of the collection contains scientific correspondence about fundamental and other general
questions concerning physics in the years 1955-1956. This period saw the beginnings of axiomatic field theories, the birthof CERN, the Berner Relativity Congress marking the 50th Anniversary of Einstein's discovery, and N. Bohr's 70th birthday. They were also the formative years of neutrino physics. Pauli and his correspondence partners played an active role in these events and illuminate them in an impressive manner in theirletters. The extensively annotated and commented letters are organized chronologically and complemented by indexes and references.
Schlagworte: History of Physics
Contents: Einleitung.- Das Jahr 1955.- Das Jahr 1956.- Anhang. Introduction.- The Year 1955.- The Year 1956.- Appendix.
Series: Sources in the History of Mathematics and Physical Sciences.VOL. 17
Kushner, H.J., Brown University, Providence, RI, USA
Dupuis, P.G., Brown University, Providence, RI, USANumerical Methods for Stochastic Control Problems in Continuous Time
2nd ed. 2001. Approx. 485 pp. 40 figs. Hardcover
0-387-95139-3
This book presents a comprehensive development of effective numerical methods for stochastic control problems in continuous time. The process models are diffusions, jump-diffusions, or reflected diffusions of the type that occur in the majority of current applications. All the usual problem formulations are included, as well as those of more recent interest such as ergodic control, singular control and the types of reflected diffusions used as models of queuing networks. Applications to complex deterministic problems are illustrated via application to a large class of problems from the calculus of variations. The general approach is known as the Markov Chain Approximation Method. The required background to stochastic processes is surveyed, there is an extensive development of methods of approximation, and a chapter is devoted to computational techniques. The book is written on two levels, that of practice (algorithms and applications)
and that of the mathematical development. Thus the methods and use should be broadly accessible. This update to the first edition will include added material on the control of the 'jump term' and the 'diffusion term.' There will be additional material on the deterministic problems, solving the Hamilton-Jacobi equations, for which the authors' methods are still among the most useful for many classes of problems. All of these topics are of great and growing current interest.
Contents: Review of Continuous Time Models.- Controlled Markov Chains.- Dynamic Programming
Equations.- Markov Chain Approximation Method.- The Approximating Markov Chains.- Computational Methods.- The Ergodic Cost Problem.- Heavy Traffic and Singular Control.- Weak Convergence and the Characterization of Processes.- Convergence Proofs.- Convergence Proofs Continued.- Finite Time and Filtering Problems.- Controlled Variance and Jumps.- Problems from the Calculus of Variations: Finite Time Horizon.- Problems from the Calculus of Variations: Infinite Time Horizon.- The Viscosity Solution Approach.
Series: Applications of Mathematics.VOL. 24
Boomsma, A., / Duijn, M.van / Snijders, T
Rijksuniversiteit Groningen, The Netherlands
(Eds.)Essays on Item Response Theory
2001. Approx. 450 pp. 25 figs. Softcover
0-387-95147-4
This collection of papers provides an up to date treatment of item response theory, an important topic in educational testing.
Contents: The Life of Georg Rasch as a Mathematician and as a Statistician Before 1961, Erling B. Anderson and Lina Woehlk Olsen.-e Anne Boomsma.- Marijtje van Duijn.- Measurement of Individual Change Using IRT Models, Gerhard Fischer.- Main and Interaction Effects in Differential Item Functioning, Cees A.W. Glas.- Conditional Independence and Differential Item Functioning in the Two Parameter Logistic Model, Herbert Hoijtink.- Reversibility Revisited and Other Comparisons of Three Types of Polytomous IRT Models, Bas Hemker.- Imputing Missing Scale Data with Item Response Models, Mark Huisman & Ivo W. Molenaar.- Statistical Tests for Differential Test Functioning in Rasch's Model for Speed Tests, Margo G.H. Jansen & Cees A.W. Glas.- On the Interplay Between Nonparametric and Parametric IRT with Some Thoughts About The Future, Brian Junker.- Modeling Learning in Short-Term Learning Tests, Karl Christoph Klauer & Hubert Sydow.- A Logistic IRT Model Allowing Increasing and Decreasing Item Characteristics Curves, Edwin Klinkenberg.- Expected Response Functions in IRT Models, Charles Lewis.- Person-Fit Analysis in Achievement Testing, Rob R. Meijer & Edit M.L.A. van Krimpen-Stoop.- Outline of a Faceted Theory of Item Response Data.
Series: Lecture Notes in Statistics.VOL. 157