Frontiers In Entropy Across The Disciplines Panorama Of Entropy Theory Computation And Applications
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Frontiers In Entropy Across The Disciplines Panorama Of Entropy Theory Computation And Applications
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Author : M Zuhair Nashed
language : en
Publisher: World Scientific
Release Date : 2022-08-30
Frontiers In Entropy Across The Disciplines Panorama Of Entropy Theory Computation And Applications written by M Zuhair Nashed and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-30 with Science categories.
Frontiers in Entropy Across the Disciplines presents a panorama of entropy emphasizing mathematical theory, physical and scientific significance, computational methods, and applications in mathematics, physics, statistics, engineering, biomedical signals, and signal processing.In the last century classical concepts of entropy were introduced in the areas of thermodynamics, information theory, probability theory, statistics, dynamical systems, and ergodic theory. During the past 50 years, dozens of new concepts of entropy have been introduced and studied in many disciplines. This volume captures significant developments in this arena. It features expository, review, and research papers by distinguished mathematicians and scientists from many disciplines. The level of mathematics ranges from intermediate level to research level. Each chapter contains a comprehensive list of references. Topics include entropy and society, entropy and time, Souriau entropy on symplectic model of statistical physics, new definitions of entropy, geometric theory of heat and information, maximum entropy in Bayesian networks, maximum entropy methods, entropy analysis of biomedical signals (review and comparison of methods), spectral entropy and its application to video coding and speech coding, a comprehensive review of 50 years of entropy in dynamics, a comprehensive review on entropy, entropy-like quantities and applications, topological entropy of multimodal maps, entropy production in complex systems, entropy production and convergence to equilibrium, reversibility and irreversibility in entropy, nonequilibrium entropy, index of various entropy, entropy and the greatest blunder ever.
Tensor Algebra And Analysis For Engineers With Applications To Differential Geometry Of Curves And Surfaces
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Author : Paolo Vannucci
language : en
Publisher: World Scientific
Release Date : 2023-02-27
Tensor Algebra And Analysis For Engineers With Applications To Differential Geometry Of Curves And Surfaces written by Paolo Vannucci and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-27 with Mathematics categories.
In modern theoretical and applied mechanics, tensors and differential geometry are two almost essential tools. Unfortunately, in university courses for engineering and mechanics students, these topics are often poorly treated or even completely ignored. At the same time, many existing, very complete texts on tensors or differential geometry are so advanced and written in abstract language that discourage young readers looking for an introduction to these topics specifically oriented to engineering applications.This textbook, mainly addressed to graduate students and young researchers in mechanics, is an attempt to fill the gap. Its aim is to introduce the reader to the modern mathematical tools and language of tensors, with special applications to the differential geometry of curves and surfaces in the Euclidean space. The exposition of the matter is sober, directly oriented to problems that are ordinarily found in mechanics and engineering. Also, the language and symbols are tailored to those usually employed in modern texts of continuum mechanics.Though not exhaustive, as any primer textbook, this volume constitutes a coherent, self-contained introduction to the mathematical tools and results necessary in modern continuum mechanics, concerning vectors, 2nd- and 4th-rank tensors, curves, fields, curvilinear coordinates, and surfaces in the Euclidean space. More than 100 exercises are proposed to the reader, many of them complete the theoretical part through additional results and proofs. To accompany the reader in learning, all the exercises are entirely developed and solved at the end of the book.
Generalized Radon Transforms And Imaging By Scattered Particles Broken Rays Cones And Stars In Tomography
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Author : Gaik Ambartsoumian
language : en
Publisher: World Scientific
Release Date : 2023-03-14
Generalized Radon Transforms And Imaging By Scattered Particles Broken Rays Cones And Stars In Tomography written by Gaik Ambartsoumian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-14 with Mathematics categories.
A generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models of various imaging modalities. The GRTs integrating along smooth curves and surfaces (lines, planes, circles, spheres, amongst others) have been studied at great lengths for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. Recently, an interesting new class of GRTs emerged at the forefront of research in integral geometry. The two common features of these transforms are the presence of a 'vertex' in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).This book covers the relevant imaging modalities, their mathematical models, and the related GRTs. The discussion of the latter comprises a thorough exploration of their known mathematical properties, including injectivity, inversion, range description and microlocal analysis. The mathematical background required for reading most of the book is at the level of an advanced undergraduate student, which should make its content attractive for a large audience of specialists interested in imaging. Mathematicians may appreciate certain parts of the theory that are particularly elegant with connections to functional analysis, PDEs and algebraic geometry.
Entropy
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Author : Gerhard Keller
language : en
Publisher: Princeton University Press
Release Date : 2003-10-26
Entropy written by Gerhard Keller and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-26 with Mathematics categories.
The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding.
The Maximum Entropy Method
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Author : Nailong Wu
language : en
Publisher:
Release Date : 1997-05-20
The Maximum Entropy Method written by Nailong Wu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-20 with categories.
Frontiers In Orthogonal Polynomials And Q Series
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Author : Nashed M Zuhair
language : en
Publisher: World Scientific
Release Date : 2018-01-12
Frontiers In Orthogonal Polynomials And Q Series written by Nashed M Zuhair and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-12 with Mathematics categories.
This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10–12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday. The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate. Contents: Mourad Ismail (Richard Askey)Binomial Andrews–Gordon–Bressoud Identities (Dennis Stanton)Symmetric Expansions of Very Well-Poised Basic Hypergeometric Series (George E Andrews)A Sturm–Liouville Theory for Hahn Difference Operator (M H Annaby, A E Hamza and S D Makharesh)Solvability of the Hankel Determinant Problem for Real Sequences (Andrew Bakan and Christian Berg)Convolution and Product Theorems for the Special Affine Fourier Transform (Ayush Bhandari and Ahmed I Zayed)A Further Look at Time-and-Band Limiting for Matrix Orthogonal Polynomials (M Castro, F A Grünbaum, I Pacharoni and I Zurrián)The Orthogonality of Al–Salam–Carlitz Polynomials for Complex Parameters (Howard S Cohl, Roberto S Costas-Santos and Wenqing Xu)Crouching AGM, Hidden Modularity (Shaun Cooper, Jesús Guillera, Armin Straub and Wadim Zudilin)Asymptotics of Orthogonal Polynomials and the Painlevé Transcendents (Dan Dai)From the Gaussian Circle Problem to Multivariate Shannon Sampling (Willi Freeden and M Zuhair Nashed)Weighted Partition Identities and Divisor Sums (F G Garvan)On the Ismail–Letessier–Askey Monotonicity Conjecture for Zeros of Ultraspherical Polynomials (Walter Gautschi)A Discrete Top-Down Markov Problem in Approximation Theory (Walter Gautschi)Supersymmetry of the Quantum Rotor (Vincent X Genest, Luc Vinet, Guo-Fu Yu and Alexei Zhedanov)The Method of Brackets in Experimental Mathematics (Ivan Gonzalez, Karen Kohl, Lin Jiu and Victor H Moll)Balanced Modular Parameterizations (Tim Huber, Danny Lara and Esteban Melendez)Some Smallest Parts Functions from Variations of Bailey's Lemma (Chris Jennings-Shaffer)Dual Addition Formulas Associated with Dual Product Formulas (Tom H Koornwinder)Holonomic Tools for Basic Hypergeometric Functions (Christoph Koutschan and Peter Paule)A Direct Evaluation of an Integral of Ismail and Valent (Alexey Kuznetsov)Algebraic Generating Functions for Gegenbauer Polynomials (Robert S Maier)q-Analogues of Two Product Formulas of Hypergeometric Functions by Bailey (Michael J Schlosser)Summation Formulae for Noncommutative Hypergeometric Series (Michael J Schlosser)Asymptotics of Generalized Hypergeometric Functions (Y Lin and R Wong)Mock Theta-Functions of the Third Order of Ramanujan in Terms of Appell–Lerch Series (Changgui Zhang)On Certain Positive Semidefinite Matrices of Special Functions (Ruiming Zhang) Readership: Graduate students and researchers interested in orthogonal polynomials and
Entropy Methods For The Boltzmann Equation
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2007
Entropy Methods For The Boltzmann Equation written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Dialogues Concerning Two New Sciences
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Author : Galileo Galilei
language : en
Publisher: Courier Corporation
Release Date : 1954-01-01
Dialogues Concerning Two New Sciences written by Galileo Galilei and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954-01-01 with Science categories.
As enjoyable as it is important, this classic encompasses 30 years of highly original experiments and theories. Its lively, readable expositions discuss dynamics, elasticity, sound, strength of materials, more. 126 diagrams.
Predicting Human Decision Making
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Author : Ariel Geib
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Predicting Human Decision Making written by Ariel Geib and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Computers categories.
Human decision-making often transcends our formal models of "rationality." Designing intelligent agents that interact proficiently with people necessitates the modeling of human behavior and the prediction of their decisions. In this book, we explore the task of automatically predicting human decision-making and its use in designing intelligent human-aware automated computer systems of varying natures—from purely conflicting interaction settings (e.g., security and games) to fully cooperative interaction settings (e.g., autonomous driving and personal robotic assistants). We explore the techniques, algorithms, and empirical methodologies for meeting the challenges that arise from the above tasks and illustrate major benefits from the use of these computational solutions in real-world application domains such as security, negotiations, argumentative interactions, voting systems, autonomous driving, and games. The book presents both the traditional and classical methods as well as the most recent and cutting edge advances, providing the reader with a panorama of the challenges and solutions in predicting human decision-making.
On Fuzziness
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Author : Rudolf Seising
language : en
Publisher: Springer
Release Date : 2013-01-12
On Fuzziness written by Rudolf Seising and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-12 with Technology & Engineering categories.
The notion of Fuzziness stands as one of the really new concepts that have recently enriched the world of Science. Science grows not only through technical and formal advances on one side and useful applications on the other side, but also as consequence of the introduction and assimilation of new concepts in its corpus. These, in turn, produce new developments and applications. And this is what Fuzziness, one of the few new concepts arisen in the XX Century, has been doing so far. This book aims at paying homage to Professor Lotfi A. Zadeh, the “father of fuzzy logic” and also at giving credit to his exceptional work and personality. In a way, this is reflected in the variety of contributions collected in the book. In some of them the authors chose to speak of personal meetings with Lotfi; in others, they discussed how certain papers of Zadeh were able to open for them a new research horizon. Some contributions documented results obtained from the author/s after taking inspiration from a particular idea of Zadeh, thus implicitly acknowledging him. Finally, there are contributions of several “third generation fuzzysists or softies” who were firstly led into the world of Fuzziness by a disciple of Lotfi Zadeh, who, following his example, took care of opening for them a new road in science. Rudolf Seising is Adjoint Researcher at the European Centre for Soft Computing in Mieres, Asturias (Spain). Enric Trillas and Claudio Moraga are Emeritus Researchers at the European Centre for Soft Computing, Mieres, Asturias (Spain). Settimo Termini is Professor of Theoretical Computer Science at the University of Palermo, Italy and Affiliated Researcher at the European Centre for Soft Computing, Mieres, Asturias (Spain)