optimal control of differential equations

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Monte Carlo Methods, Basics

ISBN: , SKU: , AUTHOR: Kalos, Malvin H. / Whitlock, Paula A., PUBLISHER: Wiley-VCH Verlag GmbH, This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It focuses on two basic themes. The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on that example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks. The detailed discussion of variance reduction includes Monte Carlo evaluation of finite-dimensional integrals. Special attention is given to importance sampling, partly because of its intrinsic interest in quadrature, partly because of its general usefulness in the solution of integral equations. One significant feature is that Monte Carlo Methods treats the "Metropolis algorithm" in the context of sampling methods, clearly distinguishing it from importance sampling. Physicists, chemists, statisticians, mathematicians, and computer scientists will find Monte Carlo Methods a complete and stimulating introduction.

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Quantum-Classical Correspondence: Dynamical Quantization and

ISBN: , SKU: , AUTHOR: Bolitschek, Josef, PUBLISHER: Springer, At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entree to an intriguing and thorny issue at the core of modern physics.

Quantum Mechanics and Gravity

ISBN: , SKU: , AUTHOR: Sachs, Mendel, PUBLISHER: Springer, This book describes a paradigm change in modern physics from the philosophy and mathematical expression of the quantum theory to those of general relativity. The approach applies to all domains - from elementary particles to cosmology. The change is from the positivistic views in which atomism, nondeterminism and measurement are fundamental, to a holistic view in realism, wherein matter - electrons, galaxies, - are correlated modes of a single continuum, the universe. A field that unifies electromagnetism, gravity and inertia is demonstrated explicitly, with new predictions, in terms of quaternion and spinor field equations in a curved spacetime. Quantum mechanics emerges as a linear, flatspace approximation for the equations of inertia in general relativity.

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Multidimensional Integral Equations and Inequalities

ISBN: , SKU: , AUTHOR: Pachpatte, B. G., PUBLISHER: Atlantis Press, Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.

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A European Central Bank?: Perspectives on Monetary

ISBN: , SKU: , AUTHOR: De Cecco, Marcello, PUBLISHER: Cambridge University Press, Based on a conference held by the Italian Macroeconomic Policy Group and the Centre for Economic Policy Research, this study examines the issues raised by European monetary unification. An introduction describes recent developments and identifies the motivations for creating a European central bank. Theoretical papers analyze the interactions of capital controls, financial intermediation, and seigniorage in open economies, the optimal design of centralized banks of issue by sovereign countries, and some new aspects of the "optimal currency area" question. The volume concludes with a panel discussion on the feasibility of European monetary unification, featuring leading academics and central bankers.

Elements of the Differential and Integral Calculus With

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Approximation and Optimization of Discrete and Differential

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The Pullback Equation for Differential Forms

ISBN: , SKU: , AUTHOR: Csat, Gyula / Dacorogna, Bernard / Kneuss, Olivier, PUBLISHER: Birkhauser Boston, An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map so that it satisfies the pullback equation: *(g) = f. In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 k n 1. The present monograph provides the first comprehensive study of the equation. The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge Morrey decomposition and to give several versions of the Poincar lemma. The core of the book discusses the case k = n, and then the case 1 k n 1 with special attention on the case k = 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses H lder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on H lder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation. The Pullback Equation for Differential Forms is a self-contained and concise monograph intended for both geometers and analysts. The book may serve as a valuable reference for researchers or a supplemental text for graduate courses or seminars.

Geometric Curve Evolution and Image Processing

ISBN: , SKU: , AUTHOR: Emmerich, Heike J. / Cao, Frederic / Cao, Frdric, PUBLISHER: Springer, In image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous and self-contained exposition of the techniques of "motion by curvature." The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved.

Capital Controls, Exchange Rates, and Monetary Policy in the

ISBN: , SKU: , AUTHOR: Edwards, Sebastian, PUBLISHER: Cambridge University Press, This volume's essays, written by well-known academics and policy analysts, discuss the impact of increased capital mobility on macroeconomic performance. The authors highlight the most adequate ways to manage the transition from a semi-closed economy to a semi-open one. Additionally, issues related to the measurement of openness, monetary control, optimal exchange rates regimes, sequencing of reforms, and real exchange rate dynamics under different degrees of capital mobility are carefully analyzed; areas covered include Europe, the Asian Pacific region, and Latin America.

Optimal Design of Planar Metamaterials Simulation,

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The Handbook of Electrical Engineering

ISBN: , SKU: , AUTHOR: Research & Education Association / Rea / Staff of Research Education Association, PUBLISHER: Research & Education Association, This handbook is a review of the important facts and concepts in electrical engineering. Comprehensive and concise, it is a handy reference source at all times for the professional and the student. It condenses the vast amount of detail characteristic of the subject mater and summarizes the essentials of the field. The book provides quick access to the important facts, principles, theorems, and equations in electrical engineering.

Guns in the United States

ISBN: , SKU: , AUTHOR: Dolan, Edward F. / Scariano, Margaret M., PUBLISHER: Franklin Watts, Examines the controversial issue of gun control. The authors give a brief history of firearms in the United States, tackle the pros and cons of gun control legislation, and describe the ways that the various proposals to control guns would work.

The Wellness Tree: The Six-Step Program for Optimal Wellness

ISBN: , SKU: , AUTHOR: O'Brien, Justin / Justin O'Brien PH D / Jaidev, PUBLISHER: Yes International Publishers, From the self-care expert who teaches wellness to doctors, comes the handbook of optimal wellness. Dr. Justin O'Brien, who has taught wellness for twenty-five years, wrote the first edition of this breakthrough primer in . This is the new third edition which continues to help readers change their lives. Rich in ancient tradition and current mind research, The Wellness Tree challenges you to transform ordinary health and ensuing decline into powerful possibilities for rejuvenation and awakened consciousness.

Estimation Problems in Hybrid Systems

ISBN: , SKU: , AUTHOR: Sworder, David D. / Boyd, John E., PUBLISHER: Cambridge University Press, Recent developments in sensor and processor sophistication have created a need for effective estimation and control algorithms for hybrid, nonlinear systems. This volume presents a highly effective, flexible family of estimation algorithms that can be used in estimating or controlling a wide variety of nonlinear plants. Several applications are studied, including tracking a maneuvering aircraft, automatic target recognition, and the decoding of signals transmitted across a wireless communications link. The authors begin by setting out the necessary theoretical background. They then develop a practical, finite-dimensional approximation to an optimal estimator. Throughout the chapters they illustrate theoretical results by simulation of control and estimation in real-world hybrid systems, drawn from a variety of engineering fields. The book will be of great interest to graduate students and researchers in electrical and computer engineering. It will also be a useful reference for practicing engineers involved in the design of estimation, tracking or wireless communications systems.

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Pediatric Imaging

ISBN: , SKU: , AUTHOR: Ward, Robert J. / Blickman, Hans, PUBLISHER: C.V. Mosby, Part of the popular Case Review series, this new resource challenges readers' mastery of today's essential knowledge in pediatric diagnostic imaging. 200 case studies, accompanied by 400 images and hundreds of review questions, cover a full range of pediatric imaging topics from a multi-modality perspective-with an emphasis on differential diagnoses, pertinent radiologic findings, and relevant clinical points.

Game Theory and National Security

ISBN: , SKU: , AUTHOR: Brams, Steven / Kilgour, D. Marc, PUBLISHER: Wiley-Blackwell, In this path-breaking theoretical work, political scientist Steven Brams and mathematician Mark Kilgour show how game theory can be applied to the rigorous development and thoughtful analysis of several critical problems that afflict the security of nations, from the deterrence of foes who might launch attacks, to the stabilization of crises that could explode into wars. In addition, they analyze a variety of related questions, including the interlocking preferences that fuel arms races, the strategic impact that Star Wars may have on nuclear deterrence, and optimal strategies for verifying arms control treaties. Of interest to students on international relations and foreign policy as well as those concerned with the formal analysis of conflict, Game Theory and National Security provides new foundations for understanding the rational basis of international conflict.

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