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Invariants and the Evolution of Nonstationary Quantum Systems
The book contains three papers. The first is a review of various mathematical formulations of the uncertainty relations in quantum mechanics and of equivalent relations in optics and radiophysics. The second deals with invariants and correlated states of nonstationary quantum systems; the third is on the evolution of multidimensional systems.
National Union Catalog
Includes entries for maps and atlases.
Russian Futurism
None
Nonlinear Markov Processes and Kinetic Equations
A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.
A History of the Central Limit Theorem
This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Golden Years of Moscow Mathematics
Encounters with mathematicians by A. P. Yushkevich The Moscow school of the theory of functions in the 1930s by S. S. Demidov About mathematics at Moscow State University in the late 1940s and early 1950s by E. M. Landis Reminiscences of Soviet mathematicians by B. A. Rosenfeld A. N. Kolmogorov by V. M. Tikhomirov On A. N. Kolmogorov by V. I. Arnold Pages of a mathematical autobiography (1942-1953) by M. M. Postnikov Markov and Bishop: An essay in memory of A. A. Markov (1903-1979) and E. Bishop (1928-1983) by B. A. Kushner Etude on life and automorphic forms in the Soviet Union by I. Piatetski-Shapiro On Soviet mathematics of the 1950s and 1960s by D. B. Fuchs In the other direction by A. B. Sossinsky A brief survey of the literature on the development of mathematics in the USSR by S. S. Demidov Russian bibliography by S. S. Demidov Moscow mathematics--Then and now by V. M. Tikhomirov Errata Index of names
Group Theoretical Methods in Physics
These Proceedings cover various topics in modern physics in which group theoretical methods can be applied effectively. The two volumes, containing over 100 papers, cover such areas as representation theory, the theory and applications of dynamical symmetries and coherent states, symmetries in atomic, molecular, nuclear and elementary particle physics, field theory including gauge theories, supersymmetry and supergravity, general relativity and cosmology, the theory of space groups and its applications to solid state physics and phase transitions, the problems of quantum and classical mechanics and paraxial optics, and the theory of nonlinear equations and solitons.
Non-Gaussian Merton-Black-Scholes Theory
This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lvy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory.The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.
Research in Quantum Field Theory
Research In Quantum Field Theory
