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Handbook of Differential Equations: Ordinary Differential Equations
The book contains seven survey papers about ordinary differential equations.The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications.
Symplectic Invariants and Hamiltonian Dynamics
Analysis of an old variational principal in classical mechanics has established global periodic phenomena in Hamiltonian systems. One of the links is a class of sympletic invariants, called sympletic capacities, and these invariants are the main theme of this book. Topics covered include basic sympletic geometry, sympletic capacities and rigidity, sympletic fixed point theory, and a survey on Floer homology and sympletic homology.
Geometric Numerical Integration
This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.
The Riemann Zeta-Function
This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.
Photoelectrochemistry, Photocatalysis and Photoreactors Fundamentals and Developments
This book collects the lectures delivered by the Authors during the NATO ASI "Fundamentals and Developments of Photocatalytic and Photoelectrochemical Processes", held in Erice (Trapani, Italy) from May 20th to June 2nd 1984. The ASI was devoted to the general field of photochemical conversion and storage of solar energy. It had the aim of defining the "state of art" and of outlining perspectives, lines of development and practic al utilization of this form of energy. The world energy crisis has stimulated scientists to investigate new routes for finding and testing methods and processes for obtaining renewable and cheap sources of energy. Within this framework, the possibility of solar ener...
Idiotypes
Idiotypes documents the proceedings of an International Conference on Idiotypes held in Oklahoma City, Oklahoma, at the Oklahoma Medical Research Foundation, October 20-23, 1985. The aims of the conference were to gather active investigators in the study of idiotypes; to assess progress in the field; and to explore directions for future research. The papers presented at the conference cover a wide range of subjects. Several papers deal with defining protein and DNA sequences which determine idiotypes. Evidence points to germ line genes encoding the V region structures which underlie idiotypy. Another subtheme which concerns several contributions is the occurrence of dominant idiotypes in ind...
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