Theory of Translation Closedness for Time Scales - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Theory of Translation Closedness for Time Scales write by Chao Wang. This book was released on 2020-05-05. Theory of Translation Closedness for Time Scales available in PDF, EPUB and Kindle. 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.
Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales
Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales write by Chao Wang. This book was released on 2022-09-20. Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales available in PDF, EPUB and Kindle. 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.
Combined Measure and Shift Invariance Theory of Time Scales and Applications
Combined Measure and Shift Invariance Theory of Time Scales and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Combined Measure and Shift Invariance Theory of Time Scales and Applications write by Chao Wang. This book was released on 2022-09-22. Combined Measure and Shift Invariance Theory of Time Scales and Applications available in PDF, EPUB and Kindle. 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.
Studies in Evolution Equations and Related Topics
Studies in Evolution Equations and Related Topics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Studies in Evolution Equations and Related Topics write by Gaston M. N'Guérékata. This book was released on 2021-10-27. Studies in Evolution Equations and Related Topics available in PDF, EPUB and Kindle. This volume features recent development and techniques in evolution equations by renown experts in the field. Each contribution emphasizes the relevance and depth of this important area of mathematics and its expanding reach into the physical, biological, social, and computational sciences as well as into engineering and technology. The reader will find an accessible summary of a wide range of active research topics, along with exciting new results. Topics include: Impulsive implicit Caputo fractional q-difference equations in finite and infinite dimensional Banach spaces; optimal control of averaged state of a population dynamic model; structural stability of nonlinear elliptic p(u)-Laplacian problem with Robin-type boundary condition; exponential dichotomy and partial neutral functional differential equations, stable and center-stable manifolds of admissible class; global attractor in Alpha-norm for some partial functional differential equations of neutral and retarded type; and more. Researchers in mathematical sciences, biosciences, computational sciences and related fields, will benefit from the rich and useful resources provided. Upper undergraduate and graduate students may be inspired to contribute to this active and stimulating field.
Selected Topics in Almost Periodicity
Selected Topics in Almost Periodicity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Selected Topics in Almost Periodicity write by Marko Kostić. This book was released on 2021-11-22. Selected Topics in Almost Periodicity available in PDF, EPUB and Kindle. Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.
