Combined Measure And Shift Invariance Theory Of Time Scales And Applications
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Combined Measure And Shift Invariance Theory Of Time Scales And Applications
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Author : Chao Wang
language : en
Publisher: Springer Nature
Release Date : 2022-09-22
Combined Measure And Shift Invariance Theory Of Time Scales And Applications written by Chao Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-22 with Mathematics categories.
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.
Dynamic Equations On Time Scales
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Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Dynamic Equations On Time Scales written by Martin Bohner 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 2012-12-06 with Mathematics categories.
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.
Advances In Dynamic Equations On Time Scales
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Author : Martin Bohner
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-12-06
Advances In Dynamic Equations On Time Scales written by Martin Bohner 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 2002-12-06 with Mathematics categories.
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.
Dynamic Equations And Almost Periodic Fuzzy Functions On Time Scales
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Author : Chao Wang
language : en
Publisher: Springer Nature
Release Date : 2022-09-20
Dynamic Equations And Almost Periodic Fuzzy Functions On Time Scales written by Chao Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-20 with Mathematics categories.
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.
Dynamic Equations On Time Scales And Applications
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Author : Ravi P Agarwal
language : en
Publisher: CRC Press
Release Date : 2024-10-18
Dynamic Equations On Time Scales And Applications written by Ravi P Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-18 with Mathematics categories.
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
Theory Of Translation Closedness For Time Scales
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Author : Chao Wang
language : en
Publisher: Springer
Release Date : 2021-05-20
Theory Of Translation Closedness For Time Scales written by Chao Wang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-20 with Mathematics categories.
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.
Theory Of Translation Closedness For Time Scales
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Author : Chao Wang
language : en
Publisher: Springer Nature
Release Date : 2020-05-05
Theory Of Translation Closedness For Time Scales written by Chao Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.
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.
Front End Vision And Multi Scale Image Analysis
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Author : Bart M. Haar Romeny
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-09-30
Front End Vision And Multi Scale Image Analysis written by Bart M. Haar Romeny 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 2003-09-30 with Computers categories.
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.
Fuzzy Techniques Theory And Applications
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Author : Ralph Baker Kearfott
language : en
Publisher: Springer
Release Date : 2019-06-10
Fuzzy Techniques Theory And Applications written by Ralph Baker Kearfott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-10 with Technology & Engineering categories.
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.
Stability Theory For Dynamic Equations On Time Scales
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Author : Anatoly A. Martynyuk
language : en
Publisher: Birkhäuser
Release Date : 2018-04-22
Stability Theory For Dynamic Equations On Time Scales written by Anatoly A. Martynyuk and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-22 with Mathematics categories.
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.
