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Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.
We believe this to be the first monograph devoted to the physicochemical properties of solutions in organic solvent systems. Although there have 1 been a number of books on the subject of non-aqueous solvents - 4, they have been devoted, almost entirely, to inorganic solvents such as liquid ammonia, liquid sulphur dioxide, etc. A variety of new solvents such as dimethylformamide, dimethylsulphoxide and propylene carbonate have become commercially available over the last twenty years. Solutions in these solvents are of technological interest in connection with novel battery systems and chemical synthesis, while studies of ion solvation and transport properties have fostered academic interest....
A comprehensive overview of nonlinear H∞ control theory for both continuous-time and discrete-time systems, Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H∞-control, nonlinear H∞ -filtering, mixed H2/ H∞-nonlinear control and filtering, nonlinear H∞-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter. Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE)...
VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and well-known (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were ...
This handbook is the second volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, writtenby leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience. . Six chapters covering a variety of problems in ordinary differential equations. . Both, pure mathematical research and real word applications are reflected. Written by leading researchers in the area.
This considerably enriched new edition provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is the shape or the structure of a geometric object.
This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material understandable and useful to chemical engineers and experts in mathematical optimization.
Helps to develop new perspectives and a deeper understanding of organic chemistry Instructors and students alike have praised Perspectives on Structure and Mechanism in Organic Chemistry because it motivates readers to think about organic chemistry in new and exciting ways. Based on the author's first hand classroom experience, the text uses complementary conceptual models to give new perspectives on the structures and reactions of organic compounds. The first five chapters of the text discuss the structure and bonding of stable molecules and reactive intermediates. These are followed by a chapter exploring the methods that organic chemists use to study reaction mechanisms. The remaining cha...
This IMA Volume in Mathematics and its Applications NONSMOOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The purpose of this workshop was to concentrate on powerful mathematical techniques that have been de veloped in deterministic optimal control theory after the basic foundations of the theory (existence theorems, maximum principle, dynamic program ming, sufficiency theorems for sufficiently smooth fields of extremals) were laid out in the 1960s. These advanced techniques make it possible to derive much more detailed information about the structure of so...
This SpringerBrief deals with the control and optimization problem in hybrid electric vehicles. Given that there are two (or more) energy sources (i.e., battery and fuel) in hybrid vehicles, it shows the reader how to implement an energy-management strategy that decides how much of the vehicle’s power is provided by each source instant by instant. Hybrid Electric Vehicles: •introduces methods for modeling energy flow in hybrid electric vehicles; •presents a standard mathematical formulation of the optimal control problem; •discusses different optimization and control strategies for energy management, integrating the most recent research results; and •carries out an overall comparis...