Igor Jex's Books

Models of Random Processes

A Handbook for Mathematicians and Engineers

By: Igor N. Kovalenko,Nickolaj Yu. Kuznetsov,Valentin M. Shurenkov

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Models of Random Processes

A Handbook for Mathematicians and Engineers

By: Igor N. Kovalenko,Nickolaj Yu. Kuznetsov,Valentin M. Shurenkov

Devising and investigating random processes that describe mathematical models of phenomena is a major aspect of probability theory applications. Stochastic methods have penetrated into an unimaginably wide scope of problems encountered by researchers who need stochastic methods to solve problems and further their studies. This handbook supplies the knowledge you need on the modern theory of random processes. Packed with methods, Models of Random Processes: A Handbook for Mathematicians and Engineers presents definitions and properties on such widespread processes as Poisson, Markov, semi-Markov, Gaussian, and branching processes, and on special processes such as cluster, self-exiting, double stochastic Poisson, Gauss-Poisson, and extremal processes occurring in a variety of different practical problems. The handbook is based on an axiomatic definition of probability space, with strict definitions and constructions of random processes. Emphasis is placed on the constructive definition of each class of random processes, so that a process is explicitly defined by a sequence of independent random variables and can easily be implemented into the modelling. Models of Random Processes: A Handbook for Mathematicians and Engineers will be useful to researchers, engineers, postgraduate students and teachers in the fields of mathematics, physics, engineering, operations research, system analysis, econometrics, and many others.

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Page Count

456

Publisher

CRC Press

Published Date

ISBN 10

0849328705

ISBN 13

9780849328701

The Art of Abduction

By: Igor Douven

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The Art of Abduction

By: Igor Douven

A novel defense of abduction, one of the main forms of nondeductive reasoning. With this book, Igor Douven offers the first comprehensive defense of abduction, a form of nondeductive reasoning. Abductive reasoning, which is guided by explanatory considerations, has been under normative pressure since the advent of Bayesian approaches to rationality. Douven argues that, although it deviates from Bayesian tenets, abduction is nonetheless rational. Drawing on scientific results, in particular those from reasoning research, and using computer simulations, Douven addresses the main critiques of abduction. He shows that versions of abduction can perform better than the currently popular Bayesian approaches—and can even do the sort of heavy lifting that philosophers have hoped it would do. Douven examines abduction in detail, comparing it to other modes of inference, explaining its historical roots, discussing various definitions of abduction given in the philosophical literature, and addressing the problem of underdetermination. He looks at reasoning research that investigates how judgments of explanation quality affect people’s beliefs and especially their changes of belief. He considers the two main objections to abduction, the dynamic Dutch book argument, and the inaccuracy-minimization argument, and then gives abduction a positive grounding, using agent-based models to show the superiority of abduction in some contexts. Finally, he puts abduction to work in a well-known underdetermination argument, the argument for skepticism regarding the external world.

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Page Count

371

Publisher

MIT Press

Published Date

ISBN 10

0262046709

ISBN 13

9780262046701

Phase Transitions of the Second Order

Collective Variables Method

By: Igor? Rafailovich I?U?khnovski?,Igor? Rafailovich I?Ukhnovski?

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Phase Transitions of the Second Order

Collective Variables Method

By: Igor? Rafailovich I?U?khnovski?,Igor? Rafailovich I?Ukhnovski?

This book gives an original and up-to-date theory of the second order phase transitions based on the effective functional integral method. Unlike previous works, this theory is constructed ab initio, leading to a consistent description starting from the basic principles of statistical physics. The author introduces a new basic density measure, different from the Gaussian one, to describe the fluctuation in the system in the vicinity of the phase transition point. A new efficient method for partition function integration over the phase space layers is shown, as well as complete solutions of the recursion relations. For the first time, equations are found for the critical temperature and analytical calculations are accompanied by accurate numerical computations. The extensions of the theory for the cases of binary alloys and n-component Stanley model are considered and the collective variables representation for the cluster ferroelectric model are obtained. This modern theory of the phenomena at the second order phase transitions is a breakthrough in this area and would make an exceptionally valuable book for scientists, as well as an important textbook for postgraduates and undergraduates.

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Page Count

344

Publisher

World Scientific

Published Date

ISBN 10

9971500876

ISBN 13

9789971500870

Methods of Quantum Field Theory in Statistical Physics

By: Alekse? Alekseevich Abrikosov,Lev Petrovich Gor?kov,I. E. Dzyaloshinski,Igor? Ekhiel?evich Dzi?aloshinski?

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Methods of Quantum Field Theory in Statistical Physics

By: Alekse? Alekseevich Abrikosov,Lev Petrovich Gor?kov,I. E. Dzyaloshinski,Igor? Ekhiel?evich Dzi?aloshinski?

This comprehensive introduction to the many-body theory was written by three renowned physicists and acclaimed by American Scientist as "a classic text on field theoretic methods in statistical physics.

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383

Publisher

Courier Corporation

Published Date

ISBN 10

0486632288

ISBN 13

9780486632285

Wavelet Theory

By: Igor Iakovlevič Novikov (mathématicien).),Vladimir I︠U︡rʹevich Protasov,Marii︠a︡ Aleksandrovna Skopina

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Wavelet Theory

By: Igor Iakovlevič Novikov (mathématicien).),Vladimir I︠U︡rʹevich Protasov,Marii︠a︡ Aleksandrovna Skopina

Wavelet theory lies on the crossroad of pure and computational mathematics, with connections to audio and video signal processing, data compression, and information transmission. The present book is devoted to a systematic exposition of modern wavelet theory. It details the construction of orthogonal and biorthogonal systems of wavelets and studies their structural and approximation properties, starting with basic theory and ending with special topics and problems. The book also presents some applications of wavelets. Historical commentary is supplied for each chapter in the book, and most chapters contain exercises. The book is intended for professional mathematicians and graduate students working in functional analysis and approximation theory. It is also useful for engineers applying wavelet theory in their work. Prerequisites for reading the book consist of graduate courses in real and functional analysis.

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Page Count

522

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821849840

ISBN 13

9780821849842

Computational Methods for Nanoscale Applications

Particles, Plasmons and Waves

By: Igor Tsukerman

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Computational Methods for Nanoscale Applications

Particles, Plasmons and Waves

By: Igor Tsukerman

Positioning itself at the common boundaries of several disciplines, this work provides new perspectives on modern nanoscale problems where fundamental science meets technology and computer modeling. In addition to well-known computational techniques such as finite-difference schemes and Ewald summation, the book presents a new finite-difference calculus of Flexible Local Approximation Methods (FLAME) that qualitatively improves the numerical accuracy in a variety of problems.

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Page Count

543

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387747788

ISBN 13

9780387747781

Book's by Igor Jex

Models of Random Processes

Models of Random Processes

The Art of Abduction

The Art of Abduction

Phase Transitions of the Second Order

Phase Transitions of the Second Order

Methods of Quantum Field Theory in Statistical Physics

Methods of Quantum Field Theory in Statistical Physics

Wavelet Theory

Wavelet Theory

Computational Methods for Nanoscale Applications

Computational Methods for Nanoscale Applications

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