LEADER 04851nam 22006855 450 001 996418267303316 005 20200801182217.0 010 $a3-030-38644-9 024 7 $a10.1007/978-3-030-38644-3 035 $a(CKB)4100000011243677 035 $a(DE-He213)978-3-030-38644-3 035 $a(MiAaPQ)EBC6191810 035 $a(PPN)248394789 035 $a(EXLCZ)994100000011243677 100 $a20200505d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTheory of Translation Closedness for Time Scales $b[electronic resource] $eWith Applications in Translation Functions and Dynamic Equations /$fby Chao Wang, Ravi P. Agarwal, Donal O' Regan, Rathinasamy Sakthivel 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XVI, 577 p. 17 illus., 8 illus. in color.) 225 1 $aDevelopments in Mathematics,$x1389-2177 ;$v62 300 $aIncludes index. 311 $a3-030-38643-0 327 $aPreface -- Preliminaries and Basic Knowledge on Time Scales -- A Classification of Closedness of Time Scales under Translations -- Almost Periodic Functions and Generalizations on Complete-Closed Time Scales -- Piecewise Almost Periodic Functions and Generalizations on Translation Time Scales -- Almost Automorphic Functions and Generalizations on Translation Time Scales -- Nonlinear Dynamic Equations on Translation Time Scales -- Impulsive Dynamic Equations on Translation Time Scales -- Almost Automorphic Dynamic Equations on Translation Time Scales -- Analysis of Dynamical System Models on Translation Time Scales -- Index. 330 $aThis monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences. 410 0$aDevelopments in Mathematics,$x1389-2177 ;$v62 606 $aDifference equations 606 $aFunctional equations 606 $aHarmonic analysis 606 $aMathematical models 606 $aFunctions of real variables 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 606 $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aHarmonic analysis. 615 0$aMathematical models. 615 0$aFunctions of real variables. 615 14$aDifference and Functional Equations. 615 24$aAbstract Harmonic Analysis. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aReal Functions. 676 $a511 700 $aWang$b Chao$4aut$4http://id.loc.gov/vocabulary/relators/aut$0675172 702 $aAgarwal$b Ravi P$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aO' Regan$b Donal$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSakthivel$b Rathinasamy$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418267303316 996 $aTheory of Translation Closedness for Time Scales$92230323 997 $aUNISA