{"product_id":"combined-measure-and-shift-invariance-theory-of-time-scales-and-applications-hardcover","title":"Combined Measure and Shift Invariance Theory of Time Scales and Applications - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eChao Wang\u003c\/b\u003e (Author), \u003cb\u003eRavi P. Agarwal\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eThis 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.\u003cbr\u003eFirst 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. \u003cbr\u003eAs 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.\u003cbr\u003eGraduate 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.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003eThis 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.\u003cbr\u003eFirst 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. \u003cbr\u003eAs 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.\u003cbr\u003eGraduate 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.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eChao Wang\u003c\/b\u003e is a Professor and PhD in Mathematics at Yunnan University in China. Dr. Wang has authored the book \"Theory of Translation Closedness for Time Scales\" (978-3-030-38643-6), published by Springer. His research focuses on the fields of nonlinear dynamic systems, control theory, fuzzy dynamic equations, fractional differential equations, bifurcation theory, nonlinear analysis, and numerical modeling.\u003cbr\u003e\u003cb\u003e\u003cbr\u003e\u003c\/b\u003e\u003cb\u003eRavi P. Agarwal \u003c\/b\u003eis a Professor at the Texas A\u0026amp;M University-Kingsville, USA. He completed his PhD at the Indian Institute of Technology, Madras, India, in 1973. Dr. Agarwal has published 1700 research articles in several different fields and authored or co-authored 50 books, including \"Theory of Translation Closedness for Time Scales\" (978-3-030-38643-6), published by Springer. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 434\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e September 24, 2022\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704618447155,"sku":"9783031116186","price":185.18,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/SFRmd2tvN2Vjc3lsUTFZbjE5WHlNdz09.webp?v=1763362687","url":"https:\/\/www.vysn.com\/en-ca\/products\/combined-measure-and-shift-invariance-theory-of-time-scales-and-applications-hardcover","provider":"VYSN","version":"1.0","type":"link"}