Описание: A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. They are scattered in research papers or outlined in surveys, and they often use topological notions not commonly known among combinatorialists or computer scientists.This book is the first textbook treatment of a significant part of such results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level (for example, homology theory and homotopy groups are completely avoided). No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained. This text started with a one-semester graduate course the author taught in fall 1993 in Prague. The transcripts of the lectures by the participants served as a basis of the first version. Some years later, a course partially based on that text was taught by GГјnter M. Ziegler in Berlin. The book is based on a thoroughly rewritten version prepared during a pre-doctoral course the author taught at the ETH Zurich in fall 2001.Most of the material was covered in the course: Chapter 1 was assigned as an introductory reading text, and the other chapters were presented in approximately 30 hours of teaching (by 45 minutes), with some omissions throughout and with only a sketchy presentation of the last chapter.
Описание: Treats the dynamics of both iteration of functions and solutions of ordinary differential equations. This book introduces various concepts for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. It concentrates on properties of the whole system or subsets of the system.
Автор: M.M. Hapaev Название: Averaging in Stability Theory ISBN: 9401051682 ISBN-13(EAN): 9789401051682 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Yu.G. Reshetnyak Название: Stability Theorems in Geometry and Analysis ISBN: 0792331184 ISBN-13(EAN): 9780792331186 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Covers the metric theory of spatial mappings and incorporates results in the theory of quasi-conformal, quasi-isometric and other mappings. The main subject of this text is the study of the stability problem in Liouville`s theorem on conformal mappings in space.
Автор: Giovanni Gallavotti Название: The Fermi-Pasta-Ulam Problem ISBN: 3642092098 ISBN-13(EAN): 9783642092091 Издательство: Springer Рейтинг: Цена: 15672.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume reviews the current understanding of the Fermi-Pasta-Ulam (FPU) Problem without trying to force coherence on differing perspectives on the same problem by various groups or approaches.
Описание: The authors consider the energy super critical semilinear heat equation $\partial _{t}u=\Delta u u^{p}, x\in \mathbb{R}^3, p>5.$. The authors draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.
Автор: Ravi P. Agarwal; Donal O`Regan; Samir H. Saker Название: Oscillation and Stability of Delay Models in Biology ISBN: 3319381393 ISBN-13(EAN): 9783319381398 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Researchers in the fields of mathematical modeling, mathematical biology, and population dynamics will be particularly interested in this material.
Описание: This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices.The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control.Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.
Описание: This book offers a detailed description of Lyapunov functional construction. It features profuse analytical and numerical examples and demonstrates a method that can be usefully applied in economic, mechanical, biological and ecological systems.
Описание: How to study the stability of dynamical systems influenced by time delays is a fundamental question. Mastering Frequency Domain Techniques for the Stability Analysis of LTI Time Delay Systems addresses this question for linear time-invariant (LTI) systems with an eigenvalue-based approach built upon frequency domain techniques.
Studies on current challenges in stability issues for numerical differential equations.- Long-Term Stability of Symmetric Partitioned Linear Multistep Methods.- Markov Chain Monte Carlo and Numerical Differential Equations.- Stability and Computation of Dynamic Patterns in PDEs.- Continuous Decompositions and Coalescing Eigen values for Matrices Depending on Parameters.- Stability of linear problems: joint spectral radius of sets of matrices.
Автор: Vladimir Stojanovi?; Predrag Kozi? Название: Vibrations and Stability of Complex Beam Systems ISBN: 3319367315 ISBN-13(EAN): 9783319367316 Издательство: Springer Рейтинг: Цена: 13059.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book reports on solved problems concerning vibrations and stability of complex beam systems.
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