Gleason's Theorem and Its Applications

Author: Anatolij Dvurecenskij
Publisher: Springer Science & Business Media
ISBN: 940158222X
Category: Mathematics
Page: 325
View: 3452

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For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found interesting theories which then (sometimes after many years) have been reflected in physics, confirming the thesis that nothing is more practical than a good theory. The same is true for the younger physical discipline -of quantum mechanics. In the 1930s two events, not at all random, became: The mathematical back grounds of both quantum mechanics and probability theory. In 1936, G. Birkhoff and J. von Neumann published their historical paper "The logic of quantum mechanics", in which a quantum logic was suggested. The mathematical foundations of quantum mechanics remains an outstanding problem of mathematics, physics, logic and philosophy even today. The theory of quantum logics is a major stream in this axiomatical knowledge river, where L(H), the system of all closed subspaces of a Hilbert space H, due to J. von Neumann, plays an important role. When A.M. Gleason published his solution to G. Mackey's problem showing that any state (= probability measure) corresponds to a density operator, he probably did not anticipate that his solution would become a cornerstone of ax iomati cal theory of quantum mechanics nor that it would provide many interesting applications to mathematics.

Quantum Statistical Mechanics

Author: William C. Schieve,Lawrence P. Horwitz
Publisher: Cambridge University Press
ISBN: 0521841461
Category: Science
Page: 414
View: 4335

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Introduces many-body theory of modern quantum statistical mechanics to graduate students in physics, chemistry, engineering and biology.

Semantic Techniques in Quantum Computation

Author: Simon Gay,Ian Mackie
Publisher: Cambridge University Press
ISBN: 052151374X
Category: Computers
Page: 478
View: 9819

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Explores quantum computation from the perspective of the branch of theoretical computer science known as semantics.

Graph Theory and Its Applications, Second Edition

Author: Jonathan L. Gross,Jay Yellen
Publisher: CRC Press
ISBN: 1420057146
Category: Mathematics
Page: 800
View: 1403

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Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come. The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. What else is new? New chapters on measurement and analytic graph theory Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

Foundations of Probability and Physics - 5

Author: Luigi Accardi,Guillaume Adenier,Andrei Y. Khrennikov
Publisher: Amer Inst of Physics
Category: Computers
Page: 390
View: 3700

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Deals with the fundamental questions raised by quantum mechanics, especially in quantum information theory.

Quantum probability and applications III

proceedings of a conference held in Oberwolfach, FRG, January 25-31, 1987
Author: Luigi Accardi,Wilhelm Waldenfels
Publisher: Springer
Category: Mathematics
Page: 373
View: 3178

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These proceedings of the first Quantum Probability meeting held in Oberwolfach is the fourth in a series begun with the 1982 meeting of Mondragone and continued in Heidelberg ('84) and in Leuven ('85). The main topics discussed were: quantum stochastic calculus, mathematical models of quantum noise and their applications to quantum optics, the quantum Feynman-Kac formula, quantum probability and models of quantum statistical mechanics, the notion of conditioning in quantum probability and related problems (dilations, quantum Markov processes), quantum central limit theorems. With the exception of Kümmerer's review article on Quantum Markov Processes, all contributions are original research papers.

Real Functions '94

Summer School on Real Functions Theory, Liptovský Ján, September 12-16, 1994
Author: Ján Borsík,L̓ubica Holá,Tibor Šalát
Publisher: N.A
Category: Functions of real variables
Page: 247
View: 2526

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Mathematics in Signal Processing

Based on the Proceedings of a Conference Organized by the Institute of Mathematics and Its Applications on Mathematics in Signal Processing, Held at University of Bath, in September 1985
Author: Tariq S. Durrani
Publisher: Oxford University Press, USA
ISBN: 9780198536130
Category: Science
Page: 677
View: 3097

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This book is based on the proceedings of the first I.M.A. International Conference on Mathematics in Signal Processing, the purpose of which was to bring together mathematicians and signal processing experts to explore the many areas of mutual interest and identify fruitful avenues for further research. The rich variety of papers presented here is clear evidence that this goal was achieved. The contributors' findings are divided into six categories: Signal Analysis and Modelling; Spectral Analysis; Inverse Problems; Image Reconstruction; Numerical Algorithms and Architectures; and Adaptive Techniques. A wealth of new ideas and interesting reading is presented for mathematicians, scientists, and engineers working in signal processing.

BTL Talks and Papers

Author: Bell Telephone Laboratories, inc. Technical Information Libraries
Publisher: N.A
Category: Physics
Page: N.A
View: 1053

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Quantum Measures and Spaces

Author: Gudrun Kalmbach
Publisher: Kluwer Academic Pub
ISBN: 9780792352884
Category: Mathematics
Page: 343
View: 6397

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This book has evolved from lectures and seminars given by the author at different academic institutions during the years 1983-1998. It can be divided into four parts. Noncommutative measure theory is the theme of the first part of the book. The relevant quantum structures are algebraically introduced. This is then used in the axiomatic, geometric model discussed in the second part of the book, where old and partly new groups and finite-dimensional R, C, H-spaces or spheres are studied for particle-series, a bag and the four basic interactions of physics. The third part investigates infinite dimensional spaces, particularly Archimedean and non-Archimedean orthomodular spaces, which generalize classical Hilbert spaces. The last part of the book contains short reviews on related topics which are useful to have at hand. Audience: This volume will be of interest to graduate students and researchers whose work involves mathematics of physics relativity and gravitation, order, lattices, and algebraic structures.