MATHEMATICAL FOUNDATIONS OF NONEXTENSIVE STATISTICAL MECHANICS
PROBABILITY AND STATISTICS Textbook
by Sabir Umarov (University of New Haven, USA) & Constantino Tsallis (Centro Brasileiro de Pesquisas Fisicas, Brazil) The book is devoted to the mathematical foundations of nonextensive statistical mechanics. This is the first book containing the systematic presentation of the mathematical theor y and concepts related to nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs statistical mechanics introduced in 1988 by one of the authors and based on a nonadditive entropic functional extending the usual BoltzmannGibbs-von Neumann-Shannon entropy. Main mathematical tools like the q-exponential function, q-Gaussian distribution, q-Fourier transform, q-central limit theorems, and other related objects are discussed rigorously with detailed mathematical rational. The book also contains recent results obtained in this direction and challenging open problems. Each chapter is accompanied with additional useful notes including the history of development and related bibliographies for further reading.
AN INTRODUCTION TO PROBABILITY With MATHEMATICA®
by Edward P C Kao (University of Houston, USA)
Contents: Combinatorial Analysis; Axiom of Probability; Conditional Probability, Discrete and Continuous Random Variables; Jointly Distributed Random Variables; Dependence; Limit Theorems. R e a d e r s h i p : Undergraduate students specialising in mathematics, engineering, computer science, actuarial science and business.
Contents: Background. q-Generalization of Boltzmann-Gibbs Entropy; q-Algebra and q-Generalizations of Some Elementary Functions; q-Fourier Transform and Its Properties; q-Central Limit Theorems; (q, α)-Stable Distributions; Applications and Observations of q-Gaussian Distributions; Some Open Problems.
350pp 978-981-124-543-5 978-981-124-678-4(pbk)
Readership: Advanced undergraduate and graduate students, researchers, and practitioners. Also interesting for researchers in applied fields like information theory, nonlinear analysis, social and artificial networks, among others. 340pp 978-981-124-515-2
Feb 2022 US$118
Feb 2022 US$128 £115 US$48 £40
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BOOKS
The main objective of this text is to facilitate a student’s smooth learning transition from a course on probability to its applications in various areas. To achieve this goal, students are encouraged to experiment numerically with problems requiring computer solutions.
