Series: Monographs in Theoretical Computer Science. An EATCS Series
2010, XV, 231 p. 81 illus., Hardcover
ISBN: 978-3-642-02994-3
About this book
Coalgebraic logic is an important research topic in the areas of concurrency theory, semantics, transition systems and modal logics. It provides a general approach to modeling systems, allowing us to apply important results from coalgebras, universal algebra and category theory in novel ways. Stochastic systems provide important tools for systems modeling, and recent work shows that categorical reasoning may lead to new insights, previously not available in a purely probabilistic setting.
This book combines coalgebraic reasoning, stochastic systems and logics. It provides an insight into the principles of coalgebraic logic from a categorical point of view, and applies these systems to interpretations of stochastic coalgebraic logics, which include well-known modal logics and continuous time branching logics. The author introduces stochastic systems together with their probabilistic and categorical foundations and gives a comprehensive discussion of the Giry monad as the underlying categorical construction, presenting many new, hitherto unpublished results. He discusses modal logics, introduces their probabilistic interpretations, and then proceeds to an analysis of Kripke models for coalgebraic logics.
The book will be of interest to researchers in theoretical computer science, logic and category theory.
Series: Springer Series in Computational Mathematics , Vol. 14
1st ed. 1996. 2nd printing, 2010, XVI, 614 p., Softcover
ISBN: 978-3-642-05220-0
Due: February 7, 2010
The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). There is a chapter on one-step and extrapolation methods for stiff problems, another on multistep methods and general linear methods for stiff problems, a third on the treatment of singular perturbation problems, and a last one on differential-algebraic problems with applications to constrained mechanical systems. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g. in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.
"This is a superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text." Mathematics Today
Series: Springer Series in Computational Mathematics , Vol. 27
Originally published by Prentice Hall, 1962
2nd. ed. 2000. 2nd printing, 2009, X, 358 p., Softcover
ISBN: 978-3-642-05154-8
This is the softcover reprint of a very popular hardcover edition, a revised version of the first edition, originally published by Prentice Hall in 1962 and regarded as a classic in its field. In some places, newer research results, e.g. results on weak regular splittings, have been incorporated in the revision, and in other places, new material has been added in the chapters, as well as at the end of chapters, in the form of additional up-to-date references and some recent theorems to give the reader some newer directions to pursue. The material in the new chapters is basically self-contained and more exercises have been provided for the readers. While the original version was more linear algebra oriented, the revision attempts to emphasize tools from other areas, such as approximation theory and conformal mapping theory, to access newer results of interest. The book should be of great interest to researchers and graduate students in the field of numerical analysis.
Series: Springer Monographs in Mathematics
2010, Approx. 280 p., Hardcover
ISBN: 978-1-4419-5541-8
Due: February 2010
This book is concerned with basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type.
This is a monograph about the most significant results obtained in this area in last decades but is also written as a graduate textbook on modern methods in partial differential equations with main emphasis on applications to fundamental mathematical models of mathematical physics, fluid dynamics and mechanics.
This book is selfcontained while the prerequisites in functional analysis are necessary to understand as it is being presented in a preliminary chapter. An up-to-date list of references and extended comments are included.
Fundamental Functional Analysis.- Maximal Monotone Operators in Banach Spaces.- Accretive Nonlinear Operators in Banach Spaces.- The Cauchy Problem in Banach Spaces.- Existence Theory of Nonlinear Dissipative Dynamics.
Series: Understanding Complex Systems
2010, XVI, 320 p. 16 illus. in color., Hardcover
ISBN: 978-3-642-04628-5
Due: February 21, 2010
This book is a collection of contributions on various aspects of active frontier research in the field of dynamical systems and chaos.
Each chapter examines a specific research topic and, in addition to reviewing recent results, also discusses future perspectives.
The result is an invaluable snapshot of the state of the field by some of its most important researchers.
The first contribution in this book, "How did you get into Chaos?", is actually a collection of personal accounts by a number of distinguished scientists on how they entered the field of chaos and dynamical systems, featuring comments and recollections by James Yorke, Harry Swinney, Floris Takens, Peter Grassberger, Edward Ott, Lou Pecora, Itamar Procaccia, Michael Berry, Giulio Casati, Valentin Afraimovich, Robert MacKay, and last but not least, Celso Grebogi, to whom this volume is dedicated.
"How Did you Get Into Chaos?".- Singular Perturbations of Complex Analytic Dynamical Systems.- Heteroclinic Switching in Coupled Oscillator Networks: Dynamics on Odd Graphs.- Dynamics of Finite-Size Particles in Chaotic Fluid Flows.- Langevin Equation for Slow Degrees of Freedom of Hamiltonian Systems.- Stable Chaos.- Superpersistent Chaotic Transients.- Synchronization and Climate Dynamics.- Stochastic Synchronization.- Experimental Huygens Synchronization of Oscillators.- Controlling Chaos: The OGY Method, its Use in Mechanics, and an Alternative Unified Framework for Control of Non-Regular Dynamics.- Detection of Patterns Within Randomness