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Evolution equations. --- Differential equations, Partial. --- Semigroups. --- Functional analysis. --- Evolution equations --- Differential equations, Partial --- Semigroups --- Functional analysis --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- 517.1 Mathematical analysis --- Mathematical analysis

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This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.

Mathematical analysis. --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- 517.1 Mathematical analysis --- Mathematical analysis --- Logic, symbolic and mathematical

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The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations that attempt to model phenomena that change with time. The infi­ nite dimensional aspects occur when forces that describe the motion depend on spatial variables, or on the history of the motion. In the case of spatially depen­ dent problems, the model equations are generally partial differential equations, and problems that depend on the past give rise to differential-delay equations. Because the nonlinearities occurring in thse equations need not be small, one needs good dynamical theories to understand the longtime behavior of solutions. Our basic objective in writing this book is to prepare an entree for scholars who are beginning their journey into the world of dynamical systems, especially in infinite dimensional spaces. In order to accomplish this, we start with the key concepts of a semiflow and a flow. As is well known, the basic elements of dynamical systems, such as the theory of attractors and other invariant sets, have their origins here.

Differentiable dynamical systems. --- Evolution equations. --- Differentiable dynamical systems --- Evolution equations --- Mathematical analysis. --- Analysis (Mathematics). --- Topology. --- Statistical physics. --- Dynamical systems. --- Analysis. --- Complex Systems. --- Statistical Physics and Dynamical Systems. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- 517.1 Mathematical analysis --- Mathematical analysis --- Statistical methods

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The complexity of new financial products as well as the ever-increasing importance of derivative securities for financial risk and portfolio management have made mathematical pricing models and comprehensive risk management tools increasingly important. This book adresses the needs of both researchers and practitioners. It combines a rigorous overview of the mathematics of financial markets with an insight into the practical application of these models to the risk and portfolio management of interest rate derivatives. It may also serve as a valuable textbook for graduate and PhD students in mathematics who want to get some knowledge about financial markets. The first part of the book is an exposition of advanced stochastic calculus. It defines the theoretical framework for the pricing and hedging of contingent claims with a special focus on interest rate markets. The second part is a mathematically biased market-oriented description of the most famous interest rate models and a variety of interest rate derivatives. It covers a selection of short and long-term oriented risk measures as well as their application to the risk management of interest rate portfolios. Interesting and comprehensive case studies based on real market data are provided to illustrate the theoretical concepts and to illuminate their practical usefulness.

Money. Monetary policy --- Interest rates --- Taux d'intérêt --- Mathematical models. --- Modèles mathématiques --- -332.82015195 --- Money market rates --- Rate of interest --- Rates, Interest --- Interest --- Mathematical models --- Taux d'intérêt --- Modèles mathématiques --- Finance. --- Probabilities. --- Mathematical analysis. --- Analysis (Mathematics). --- Economics, Mathematical . --- Finance, general. --- Probability Theory and Stochastic Processes. --- Analysis. --- Quantitative Finance. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- 517.1 Mathematical analysis --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Funding --- Funds --- Currency question --- Methodology

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The subject of this book is numerical methods that preserve geometric properties of the flow of a differential equation: symplectic integrators for Hamiltonian systems, symmetric integrators for reversible systems, methods preserving first integrals and numerical methods on manifolds, including Lie group methods and integrators for constrained mechanical systems, and methods for problems with highly oscillatory solutions. A complete theory of symplectic and symmetric 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 and related perturbation theories. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.

519.62 --- 681.3*G17 --- Numerical methods for solution of ordinary differential equations --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Differential equations --- Hamiltonian systems. --- Numerical integration. --- Numerical solutions. --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 519.62 Numerical methods for solution of ordinary differential equations --- Hamiltonian systems --- Numerical integration --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Numerical analysis --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- 517.91 Differential equations --- Numerical solutions --- 517.91 --- Dynamique différentiable. --- Systèmes hamiltoniens. --- Differentiable dynamical systems. --- Numerical analysis. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical physics. --- Physics. --- Biomathematics. --- Numerical Analysis. --- Analysis. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Methods in Physics. --- Numerical and Computational Physics, Simulation. --- Mathematical and Computational Biology. --- Biology --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Physical mathematics --- Physics --- 517.1 Mathematical analysis --- Mathematical analysis --- Numerical solutions&delete& --- Systèmes hamiltoniens --- Integration numerique --- Analyse numerique --- Equations differentielles