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Combined Measure And Shift Invariance Theory Of Time Scales And Applications
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Book Synopsis Combined Measure and Shift Invariance Theory of Time Scales and Applications by : Chao Wang
Download or read book Combined Measure and Shift Invariance Theory of Time Scales and Applications written by Chao Wang and published by Springer Nature. This book was released on 2022-09-22 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences. Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.
Book Synopsis Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales by : Chao Wang
Download or read book Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales written by Chao Wang and published by Springer Nature. This book was released on 2022-09-20 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems, including their continuous and discrete situations, but are also valid for other fuzzy multidimensional dynamic systems on various hybrid domains. In an effort to achieve more accurate analysis in real world applications, the authors propose a number of uncertain factors in the theory. As such, fuzzy dynamical models, interval-valued functions, differential equations, fuzzy-valued differential equations, and their applications to dynamic equations on time scales are considered.
Book Synopsis Advances in Dynamic Equations on Time Scales by : Martin Bohner
Download or read book Advances in Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory material on the calculus of time scales and dynamic equations.; Numerous examples and exercises illustrate the diverse application of dynamic equations on time scales.; Unified and systematic exposition of the topics allows good transitions from chapter to chapter.; Contributors include Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this field of study.; Useful as a comprehensive resource of time scales and dynamic equations for pure and applied mathematicians.; Comprehensive bibliography and index complete this text.
Book Synopsis Dynamic Equations on Time Scales by : Martin Bohner
Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.
Book Synopsis Theory of Translation Closedness for Time Scales by : Chao Wang
Download or read book Theory of Translation Closedness for Time Scales written by Chao Wang and published by Springer Nature. This book was released on 2020-05-05 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.
Book Synopsis Dynamic Equations on Time Scales and Applications by : Ravi P Agarwal
Download or read book Dynamic Equations on Time Scales and Applications written by Ravi P Agarwal and published by CRC Press. This book was released on 2024-10-18 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. • Presents cutting-edge research trends of dynamic equations and recent advances in contemporary research on the topic of time scales • Connects several new areas of dynamic equations on time scales with applications in different fields • Includes mathematical explanation from the perspective of existing knowledge of dynamic equations on time scales • Offers several new recently developed results, which are useful for the mathematical modeling of various phenomena • Useful for several interdisciplinary fields like economics, biology, and population dynamics from the perspective of new trends The text is for postgraduate students, professionals, and academic researchers working in the fields of Applied Mathematics
Book Synopsis Front-End Vision and Multi-Scale Image Analysis by : Bart M. Haar Romeny
Download or read book Front-End Vision and Multi-Scale Image Analysis written by Bart M. Haar Romeny and published by Springer Science & Business Media. This book was released on 2003-09-30 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Front-End Vision and Multi-Scale Image Analysis is a tutorial in multi-scale methods for computer vision and image processing. It builds on the cross fertilization between human visual perception and multi-scale computer vision (`scale-space') theory and applications. The multi-scale strategies recognized in the first stages of the human visual system are carefully examined, and taken as inspiration for the many geometric methods discussed. All chapters are written in Mathematica, a spectacular high-level language for symbolic and numerical manipulations. The book presents a new and effective approach to quickly mastering the mathematics of computer vision and image analysis. The typically short code is given for every topic discussed, and invites the reader to spend many fascinating hours `playing' with computer vision. Front-End Vision and Multi-Scale Image Analysis is intended for undergraduate and graduate students, and all with an interest in computer vision, medical imaging, and human visual perception.
Book Synopsis Fuzzy Techniques: Theory and Applications by : Ralph Baker Kearfott
Download or read book Fuzzy Techniques: Theory and Applications written by Ralph Baker Kearfott and published by Springer. This book was released on 2019-06-10 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the latest findings related to fuzzy techniques, discussing applications in control, economics, education, humor studies, industrial engineering, linguistics, management, marketing, medicine and public health, military engineering, robotics, ship design, sports, transportation, and many other areas. It also presents recent fuzzy-related algorithms and theoretical results that can be used in other application areas. Featuring selected papers from the Joint World Congress of the International Fuzzy Systems Association (IFSA) and the Annual Conference of the North American Fuzzy Information Processing Society (NAFIPS) IFSA-NAFIPS’2019, held in Lafayette, Louisiana, USA, on June 18–21, 2019, the book is of interest to practitioners wanting to use fuzzy techniques to process imprecise expert knowledge. It is also a valuable resource for researchers wishing to extend the ideas from these papers to new application areas, for graduate students and for anyone else interested in problems involving fuzziness and uncertainty.
Book Synopsis Theory of Translation Closedness for Time Scales by : Chao Wang
Download or read book Theory of Translation Closedness for Time Scales written by Chao Wang and published by Springer. This book was released on 2020-05-06 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.
Book Synopsis Conformable Dynamic Equations on Time Scales by : Douglas R. Anderson
Download or read book Conformable Dynamic Equations on Time Scales written by Douglas R. Anderson and published by CRC Press. This book was released on 2020-08-29 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of derivatives of non-integer order, known as fractional derivatives, first appeared in the letter between L’Hopital and Leibniz in which the question of a half-order derivative was posed. Since then, many formulations of fractional derivatives have appeared. Recently, a new definition of fractional derivative, called the "fractional conformable derivative," has been introduced. This new fractional derivative is compatible with the classical derivative and it has attracted attention in areas as diverse as mechanics, electronics, and anomalous diffusion. Conformable Dynamic Equations on Time Scales is devoted to the qualitative theory of conformable dynamic equations on time scales. This book summarizes the most recent contributions in this area, and vastly expands on them to conceive of a comprehensive theory developed exclusively for this book. Except for a few sections in Chapter 1, the results here are presented for the first time. As a result, the book is intended for researchers who work on dynamic calculus on time scales and its applications. Features Can be used as a textbook at the graduate level as well as a reference book for several disciplines Suitable for an audience of specialists such as mathematicians, physicists, engineers, and biologists Contains a new definition of fractional derivative About the Authors Douglas R. Anderson is professor and chair of the mathematics department at Concordia College, Moorhead. His research areas of interest include dynamic equations on time scales and Ulam-type stability of difference and dynamic equations. He is also active in investigating the existence of solutions for boundary value problems. Svetlin G. Georgiev is currently professor at Sorbonne University, Paris, France and works in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, dynamic calculus on time scales, and integral equations.
Book Synopsis Scale-Space and Morphology in Computer Vision by : Michael Kerckhove
Download or read book Scale-Space and Morphology in Computer Vision written by Michael Kerckhove and published by Springer. This book was released on 2003-05-15 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision, Scale-Space 2001, held in Vancouver, Canada in July 2001. The 18 revised full papers presented together with 23 posters were carefully reviewed and selected from 60 submissions. The book addresses all current aspects of scale-space and morphology in the context of computer vision, in particular, vector distance functions, optic flow, image registration, curve evolution, morphological segmentation, scalar images, vector images, automatic scale selection, geometric diffusion, diffusion filtering, image filtering, inverse problems, active contours, etc.
Book Synopsis Stability Theory for Dynamic Equations on Time Scales by : Anatoly A. Martynyuk
Download or read book Stability Theory for Dynamic Equations on Time Scales written by Anatoly A. Martynyuk and published by Birkhäuser. This book was released on 2018-04-22 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.
Book Synopsis Boundedness and Self-Organized Semantics: Theory and Applications by : Koleva, Maria K.
Download or read book Boundedness and Self-Organized Semantics: Theory and Applications written by Koleva, Maria K. and published by IGI Global. This book was released on 2012-10-31 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book enhances the understanding of the theoretical framework and leading principles of boundedness, aiming to bridge the gap between biology, artificial intelligence, and physics"--Provided by publisher.
Book Synopsis Set Dynamic Equations on Time Scales: A Brief Introduction with Applications by : Shihuang Hong
Download or read book Set Dynamic Equations on Time Scales: A Brief Introduction with Applications written by Shihuang Hong and published by World Scientific Publishing Company. This book was released on 2025-02-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The process of authoring this book is inspired by the recent increased activity of research on dynamic equations on time scales and other closely related areas. This monograph is the first published book that attempts to provide a comprehensive view of the theory and applications of set dynamic equations on time scales. The main focus of the book is the qualitative theory of set dynamic equations and their applications to fuzzy dynamic equations. The key topics include the solvability of set dynamic equations, stability of set dynamic equations, and applications to certain types of fuzzy dynamic equations.There are five chapters in the book, through which the authors examine a wide scope of the concept of set dynamic equations and their applications. Each chapter focuses on theory and proofs to enrich the reader's understanding of the topic.This book will be particularly useful to those experts who work in applied analysis, in general. It will also be a good reference for computer scientists since it covers fuzzy dynamic equations. Researchers and graduate students at various levels interested in learning about set dynamic equations and related fields will find this text a valuable resource of both introductory and advanced material.
Book Synopsis Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, October 4-6, 1992, Victoria, BC, Canada by :
Download or read book Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, October 4-6, 1992, Victoria, BC, Canada written by and published by . This book was released on 1996 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis From Quantum to Cosmos by : Slava G. Turyshev
Download or read book From Quantum to Cosmos written by Slava G. Turyshev and published by World Scientific. This book was released on 2009 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Space-based laboratory research in fundamental physics is an emerging research discipline that offers great discovery potential and at the same time could drive the development of technological advances which are likely to be important to scientists and technologists in many other different research fields. The articles in this review volume have been contributed by participants of the international workshop ?From Quantum to Cosmos: Fundamental Physics Research in Space? held at the Airlie Center in Warrenton, Virginia, USA, on May 21?24, 2006. This unique volume discusses the advances in our understanding of fundamental physics that are anticipated in the near future, and evaluates the discovery potential of a number of recently proposed space-based gravitational experiments. Specific research areas covered include various tests of general relativity and alternative theories, search of physics beyond the Standard Model, investigations of possible violations of the equivalence principle, search for new hypothetical long- and short-range forces, variations of fundamental constants, tests of Lorentz invariance and attempts at unification of the fundamental interactions. The book also encompasses experiments aimed at the discovery of novel phenomena, including dark matter candidates, and studies of dark energy.
Download or read book Scale Invariance written by Annick LESNE and published by Springer Science & Business Media. This book was released on 2011-11-04 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.
