01790nam 2200373 n 450 99639117670331620200824121750.0(CKB)4940000000105484(EEBO)2240925733(UnM)99855227e(UnM)99855227(EXLCZ)99494000000010548419920821d1603 uy |engurbn||||a|bb|An antilogie or counterplea to An apologicall (he should haue said) apologeticall epistle published by a fauorite of the Romane separation, and (as is supposed) one of the Ignatian faction[electronic resource] wherein two hundred vntruths and slaunders are discouered, and many politicke obiections of the Romaines answered. Dedicated to the Kings most excellent Maiestie by Andrevv Willet, Professor of DiuinitieLondon Printed [by Richard Field and Felix Kingston] for Thomas Man1603[32], 269 [i.e. 279], [1] pA reply to: Broughton, Richard. An apologicall epistle.Kingston printed B-2I; Field printed the rest (STC).The first leaf is blank.P. 279 misnumbered 269.Reproduction of the original in Yale University. Library.[par.]4 creased. Beginning-p.3 from Harvard University. Library copy filmed at end.eebo-0198Willet Andrew1562-1621.1001089Cu-RivESCu-RivESCStRLINWaOLNBOOK996391176703316An antilogie or counterplea to An apologicall (he should haue said) apologeticall epistle published by a fauorite of the Romane separation, and (as is supposed) one of the Ignatian faction2303767UNISA04978nam 22006495 450 991030014520332120200706054504.03-319-05140-710.1007/978-3-319-05140-6(CKB)2560000000149018(EBL)1731643(SSID)ssj0001204975(PQKBManifestationID)11962954(PQKBTitleCode)TC0001204975(PQKBWorkID)11181050(PQKB)10589610(MiAaPQ)EBC1731643(DE-He213)978-3-319-05140-6(PPN)178321117(EXLCZ)99256000000014901820140419d2014 u| 0engur|n|---|||||txtccrMethods of Small Parameter in Mathematical Biology /by Jacek Banasiak, Mirosław Lachowicz1st ed. 2014.Cham :Springer International Publishing :Imprint: Birkhäuser,2014.1 online resource (295 p.)Modeling and Simulation in Science, Engineering and Technology,2164-3679Description based upon print version of record.3-319-05139-3 Includes bibliographical references and index.1 Small parameter methods – basic ideas -- 2 Introduction to the Chapman–Enskog method – linear models with migrations -- 3 Tikhonov–Vasilyeva theory -- 4 The Tikhonov theorem in some models of mathematical biosciences -- 5 Asymptotic expansion method in a singularly perturbed McKendrick problem -- 6 Diffusion limit of the telegraph equation -- 7 Kinetic model of alignment -- 8 From microscopic to macroscopic descriptions. - 9 Conclusion.This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant and preserves the salient features of the dynamics. The aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools described allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value.   The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques.   Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and  graduate students in appled and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.Modeling and Simulation in Science, Engineering and Technology,2164-3679Differential equationsBiomathematicsOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Mathematical and Computational Biologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M31000Genetics and Population Dynamicshttps://scigraph.springernature.com/ontologies/product-market-codes/M31010Differential equations.Biomathematics.Ordinary Differential Equations.Mathematical and Computational Biology.Genetics and Population Dynamics.515.35Banasiak Jacekauthttp://id.loc.gov/vocabulary/relators/aut314207Lachowicz Mirosławauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300145203321Methods of Small Parameter in Mathematical Biology2512354UNINA