A Yu Khrennikov's Books

Proceedings of the Conference Foundations of Probability and Physics

Växjö, Sweden, 25 November-1 December, 2000

By: A. Khrennikov

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Proceedings of the Conference Foundations of Probability and Physics

Växjö, Sweden, 25 November-1 December, 2000

By: A. Khrennikov

In this volume, leading experts in experimental as well as theoretical physics (both classical and quantum) and probability theory give their views on many intriguing (and still mysterious) problems regarding the probabilistic foundations of physics. The problems discussed during the conference include EinsteinOCoPodolskyOCoRosen paradox, Bell's inequality, realism, nonlocality, role of Kolmogorov model of probability theory in quantum physics, von Mises frequency theory, quantum information, computation, OC quantum effectsOCO in classical physics. Contents: Locality and Bell's Inequality (L Accardi & M Regoli); Refutation of Bell's Theorem (G Adenier); Forcing Discretization and Determination in Quantum History Theories (B Coecke); Some Remarks on Hardy Functions Associated with Dirichlet Series (W Ehm); Ensemble Probabilistic Equilibrium and Non-Equilibrium Thermodynamics without the Thermodynamic Limit (D H E Gross); An Approach to Quantum Probability (S Gudder); Innovation Approach to Stochastic Processes and Quantum Dynamics (T Hida); Origin of Quantum Probabilities (A Khrennikov); OC ComplementarityOCO or Schizophrenia: Is Probability in Quantum Mechanics Information or Onta? (A F Kracklauer); A Probabilistic Inequality for the KochenOCoSpecker Paradox (J-A Larsson); Quantum Stochastics. The New Approach to the Description of Quantum Measurements (E Loubenets); Is Random Event a Core Question? Some Remarks and a Proposal (P Rocchi); Quantum Cryptography in Space and Bell's Theorem (I Volovich); and other papers. Readership: Graduate students and researchers in quantum physics, mathematical physics, theoretical physics, stochastic processes, and probability & statistics.

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Page Count

406

Publisher

World Scientific

Published Date

ISBN 10

9812810803

ISBN 13

9789812810809

Gibbs Measures on Cayley Trees

By: Utkir A. Rozikov

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Gibbs Measures on Cayley Trees

By: Utkir A. Rozikov

The Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Moreover, the Gibbs measure is the unique measure that maximizes the entropy for a given expected energy. The method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees, and nonlinear analysis. This book discusses all the mentioned methods, which were developed recently.

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404

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World Scientific

Published Date

ISBN 10

9814513385

ISBN 13

9789814513388

The Pauli-Jung Conjecture and Its Impact Today

By: Harald Atmanspacher,Christopher A. Fuchs

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The Pauli-Jung Conjecture and Its Impact Today

By: Harald Atmanspacher,Christopher A. Fuchs

Related to the key areas of Pauli's and Jung's joint interests, the book covers overlapping issues from the perspectives of physics, philosophy, and psychology. Of primary significance are epistemological questions connected to issues such as realism, measurement, observation, consciousness, and the unconscious. The contributions assess the extensive material that we have about Pauli's and Jung's ideas today, with particular respect to concrete research questions and projects based on and related to current knowledge.

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Page Count

333

Publisher

Andrews UK Limited

Published Date

ISBN 10

1845407598

ISBN 13

9781845407599

Elliptic Regularity Theory by Approximation Methods

By: Edgard A. Pimentel

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Elliptic Regularity Theory by Approximation Methods

By: Edgard A. Pimentel

A modern account of elliptic regularity theory, with a rigorous presentation of recent developments for fundamental models.

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203

Publisher

Cambridge University Press

Published Date

ISBN 10

1009096664

ISBN 13

9781009096669

Equivalents of the Riemann Hypothesis

By: Kevin Broughan

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Equivalents of the Riemann Hypothesis

By: Kevin Broughan

This third volume presents further equivalents to the Riemann hypothesis and explores its decidability.

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705

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Cambridge University Press

Published Date

ISBN 10

1009384805

ISBN 13

9781009384803

Integration on Infinite-Dimensional Surfaces and Its Applications

By: A. Uglanov

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Integration on Infinite-Dimensional Surfaces and Its Applications

By: A. Uglanov

It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.

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280

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401596220

ISBN 13

9789401596220

Gibbs Measures In Biology And Physics: The Potts Model

By: Utkir A Rozikov

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Gibbs Measures In Biology And Physics: The Potts Model

By: Utkir A Rozikov

This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.

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Page Count

367

Publisher

World Scientific

Published Date

ISBN 10

9811251258

ISBN 13

9789811251252

Invariance of Modules under Automorphisms of their Envelopes and Covers

By: Ashish K. Srivastava,Askar Tuganbaev,Pedro A. Guil Asensio

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Invariance of Modules under Automorphisms of their Envelopes and Covers

By: Ashish K. Srivastava,Askar Tuganbaev,Pedro A. Guil Asensio

Provides a unified treatment of the study of modules invariant under automorphisms of their envelopes and covers.

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235

Publisher

Cambridge University Press

Published Date

ISBN 10

1108949533

ISBN 13

9781108949538

Wonders of Numbers

Adventures in Mathematics, Mind, and Meaning

By: Clifford A. Pickover

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Wonders of Numbers

Adventures in Mathematics, Mind, and Meaning

By: Clifford A. Pickover

Who were the five strangest mathematicians in history? What are the ten most interesting numbers? Jam-packed with thought-provoking mathematical mysteries, puzzles, and games, Wonders of Numbers will enchant even the most left-brained of readers. Hosted by the quirky Dr. Googol--who resides on a remote island and occasionally collaborates with Clifford Pickover--Wonders of Numbers focuses on creativity and the delight of discovery. Here is a potpourri of common and unusual number theory problems of varying difficulty--each presented in brief chapters that convey to readers the essence of the problem rather than its extraneous history. Peppered throughout with illustrations that clarify the problems, Wonders of Numbers also includes fascinating "math gossip." How would we use numbers to communicate with aliens? Check out Chapter 30. Did you know that there is a Numerical Obsessive-Compulsive Disorder? You'll find it in Chapter 45. From the beautiful formula of India's most famous mathematician to the Leviathan number so big it makes a trillion look small, Dr. Googol's witty and straightforward approach to numbers will entice students, educators, and scientists alike to pick up a pencil and work a problem.

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420

Publisher

Oxford University Press

Published Date

ISBN 10

0195348001

ISBN 13

9780195348002

Neutron Interferometry

Lessons in Experimental Quantum Mechanics, Wave-Particle Duality, and Entanglement

By: Helmut Rauch,Samuel A. Werner

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Neutron Interferometry

Lessons in Experimental Quantum Mechanics, Wave-Particle Duality, and Entanglement

By: Helmut Rauch,Samuel A. Werner

The quantum interference of de Broglie matter waves is probably one of the most startling and fundamental aspects of quantum mechanics. It continues to tax our imaginations and leads us to new experimental windows on nature. Quantum interference phenomena are vividly displayed in the wide assembly of neutron interferometry experiments, which have been carried out since the first demonstration of a perfect silicon crystal interferometer in 1974. Since the neutron experiences all four fundamental forces of nature (strong, weak, electromagnetic, and gravitational), interferometry with neutrons provides a fertile testing ground for theory and precision measurements. Many Gedanken experiments of quantum mechanics have become real due to neutron interferometry. Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the second edition of this book. It discusses more than 40 neutron interferometry experiments along with their theoretical motivations and explanations. The basic ideas and results of interference experiments related to coherence and decoherence of matter waves and certain post-selection variations, gravitationally induced quantum phase shifts, Berry`s geometrical phases, spinor symmetry and spin superposition, and Bell's inequalities are all discussed and explained in this book. Both the scalar and vector Aharonov-Bohm topological interference effects and the neutron version of the Sagnac effect are presented in a self-contained and pedagogical way. Interferometry with perfect crystals, artificial lattices, and spin-echo systems are also topics of this book. It includes the theoretical underpinning as well as connections to other areas of experimental physics, such as quantum optics, nuclear physics, gravitation, and atom interferometry. The observed phase shifts due to the Earth's gravity and rotation indicate a close connection to relativity theory. Neutron interferometry can be considered as a central technique of quantum optics with massive particles. It has stimulated the development of interferometry with atoms, molecules and clusters. The book is written in a style that will be suitable at the senior undergraduate and beginning of graduate level. It will interest and excite many students and researchers in neutron, nuclear, quantum, gravitational, optical, and atomic physics. Lecturers teaching courses in modern physics and quantum mechanics will find a number of interesting and historic experiments they may want to include in their lectures.

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461

Publisher

OUP Oxford

Published Date

ISBN 10

0191021253

ISBN 13

9780191021251

Writing History in Twentieth-Century Russia

A View from Within

By: A. Litvin

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Writing History in Twentieth-Century Russia

A View from Within

By: A. Litvin

In this fascinating book Alter Litvin tells us what life was really like for professional Soviet historians from Lenin to Gorbachev, and assesses the efforts made since 1991 to create a more truthful picture of the turbulent Russian past. Passionate yet fair-minded, this is the first account of the subject to appear in English. Designed primarily for the general reader, it contains much fresh material of specialist interest and an ample up-to-date bibliography.

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203

Publisher

Springer

Published Date

ISBN 10

1403913897

ISBN 13

9781403913890

Theory of P-Adic Distributions

Linear and Nonlinear Models

By: Sergio Albeverio,A Yu Khrennikov,V M Shelkovich

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Theory of P-Adic Distributions

Linear and Nonlinear Models

By: Sergio Albeverio,A Yu Khrennikov,V M Shelkovich

A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.

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368

Published Date

ISBN 10

1139127772

ISBN 13

9781139127776

Book's by A Yu Khrennikov

Proceedings of the Conference Foundations of Probability and Physics

Proceedings of the Conference Foundations of Probability and Physics

Gibbs Measures on Cayley Trees

Gibbs Measures on Cayley Trees

The Pauli-Jung Conjecture and Its Impact Today

The Pauli-Jung Conjecture and Its Impact Today

Elliptic Regularity Theory by Approximation Methods

Elliptic Regularity Theory by Approximation Methods

Equivalents of the Riemann Hypothesis

Equivalents of the Riemann Hypothesis

Integration on Infinite-Dimensional Surfaces and Its Applications

Integration on Infinite-Dimensional Surfaces and Its Applications

Gibbs Measures In Biology And Physics: The Potts Model

Gibbs Measures In Biology And Physics: The Potts Model

Invariance of Modules under Automorphisms of their Envelopes and Covers

Invariance of Modules under Automorphisms of their Envelopes and Covers

Wonders of Numbers

Wonders of Numbers

Neutron Interferometry

Neutron Interferometry

Writing History in Twentieth-Century Russia

Writing History in Twentieth-Century Russia

Theory of P-Adic Distributions

Theory of P-Adic Distributions

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