الصفحة 2
الصفحة 2
Number Theory ; Vol. I : Tools and Diophantine Equations
The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.
Notions of Convexity
The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed, leading up to Trépreau’s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category.
Nonstandard Analysis
The book is an introduction with emphasis on those more advanced applications in analysis which are hardly accessible by other methods. Examples of such topics are a deeper analysis of certain functionals like Hahn-Banach limits or of finitely additive measures: From the viewpoint of classical analysis these are strange objects whose mere existence is even hard to prove. From the viewpoint of nonstandard analysis, these are rather 'explicit' objects.
Nonsmooth Vector Functions and Continuous Optimization
A recent significant innovation in mathematical sciences has been the progressive use of nonsmooth calculus, an extension of the differential calculus, as a key tool of modern analysis in many areas of mathematics, operations research, and engineering. Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems and variational inequalities in finite dimensions.
Nonsmooth Variational Problems and their Inequalities : Comparison Principles and Applications
The main purpose of this book is to provide a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method. This method is an effective and flexible technique to obtain existence and comparison results of solutions. Also, it can be employed for the investigation of various qualitative properties, such as location, multiplicity and extremality of solutions. In the treatment of the problems under consideration a wide range of methods and techniques from nonlinear and nonsmooth analysis is applied, a brief outline of which has been provided in a preliminary chapter in order to make the book self-contained.
Nonlinear Waves : Classical and Quantum Aspects
Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.
Nonlinear Problems of Elasticity
This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus of variations to problems for these bodies. The book continues with chapters on tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.
Nonlinear Partial Differential Equations with Applications
This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. It balances the abstract functional-analysis approach based on nonlinear monotone, pseudomonotone, weakly continuous, or accretive mappings with concrete partial differential equations in their weak (or more general) formulation. Methods of Galerkin or of Rothe are exposed in a large generality. Other methods include various direct methods, regularization, or fixed points. The exposition leads general theory as fast as possible towards the analysis of concrete equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are rather an introduction into the subject while some others form an advanced textbook. The intended audience is graduate and PhD students and researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems.
Nonlinear Partial Differential Equations for Scientists and Engineers
This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership.
Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors
This book presents recent results concerning the global existence in time, the large-time behaviour, decays of solutions and the existence of global attractors for some nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations arising from physics, mechanics and material science, such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. To keep the book as self-contained as possible, the first chapter introduces to the needed results and tools from functional analysis, Sobolev spaces, differential and integral inequa.
Nonlinear Oscillations of Hamiltonian PDEs
After introducing the reader to classical finite-dimensional dynamical system theory, including the Weinstein–Moser and Fadell–Rabinowitz resonant center theorems,the author develops the analogous theory for completely resonant nonlinear wave equations. Within this theory, both problems of small divisors and infinite bifurcation phenomena occur, requiring the use of Nash–Moser theory as well as minimax variational methods. These techniques are presented in a self-contained manner together with other basic notions of Hamiltonian PDEs and number theory.
Nonlinear Ill-posed Problems of Monotone Type
This monograph offers a systematic and thorough exposition of the theory and applications of non-linear equations and variational inequalities with monotone and accretive operators. … The authors have collected, classified, and properly arranged a great deal of results . The present book will certainly help the reader to obtain an introduction to basic ideas and results of the contemporary theory of solution methods for nonlinear monotone problems.
Nonlinear H2/H-Infinity Constrained Feedback Control : A Practical Design Approach Using Neural Networks
In this book the authors present algorithms for H2 and H-infinity design for nonlinear systems which, unlike earlier theories, provide solution techniques for the core Hamilton–Jacobi equations that yield control systems which can be implemented in real systems; neural networks are used to solve the nonlinear control design equations.
Nonlinear Fokker-Planck Equations : Fundamentals and Applications
Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, population dynamics, and computational physics.
Nonlinear Finite Element Methods
Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics.
Nonlinear Elliptic and Parabolic Problems : A Special Tribute to the Work of Herbert Amann
The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.
Nonlinear dynamics in complex systems via fractals and fractional calculus
Current advances in the knowledge of nonlinear dynamical networks, systems and processes, as well as their unified repercussions, allow us to include some typical complex natural phenomena, from the nanoscale to an extra-galactic scale, in an unitarian comprehensive manner. In other words, the physical, biological and financial data, as well as technological ones (mechanical or electronic devices), of complex systems available today can be managed by the same unique conceptual approach, both analytically and through a computer simulation, using effective nonlinear dynamics procedures. This volume collected some important advances in the fields of fractal curves, fractal analysis and fractional calculus, as well as new solutions of fractal differential equations.
Nonlinear and Optimal Control Theory : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 19–29, 2004
The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle.
Nonlinear Analyses and Algorithms for Speech Processing ; International Conference on Non-Linear Speech Processing, NOLISP 2005, Barcelona, Spain, April 19-22, 2005, Revised Selected Papers
We present in this volume the collection of ?nally accepted papers of NOLISP 2005 conference. It has been the third event in a series of events related to N- linear speech processing, in the framework of the European COST action 277 “Nonlinear speech processing”. Many speci?cs of the speech signal are not well addressed by conv- tional models currently used in the ?eld of speech processing. The purpose of NOLISP is to present and discuss novel ideas, work and results related to alternative techniques for speech processing, which depart from mainstream approaches. With this intention in mind, we provide an open forum for discussion. Alt- nate approaches are appreciated, although the results achieved at present may not clearly surpass results based on state-of-the-art methods. The call for papers was launched at the beginning of 2005, addressing the following domains: 1. Non-Linear Approximation and Estimation 2. Non-Linear Oscillators and Predictors 3. Higher-Order Statistics 4. Independent Component Analysis 5. Nearest Neighbors 6. Neural Networks 7. Decision Trees 8. Non-Parametric Models 9. Dynamics of Non-Linear Systems 10. Fractal Methods 11. Chaos Modeling 12. Non-Linear Di?erential Equations 13. Others All the main ?elds of speech processing are targeted by the workshop, namely: 1. Speech Coding:Thebit rateavailablefor speechsignalsmustbe strictly l- ited in order to accommodate the constraints of the channel resource.
Noise-Induced Transitions : Theory and Applications in Physics, Chemistry, and Biology
This classic text, an often-requested reprint, develops and explains the foundations of noise-induced processes. At its core is a self-contained, textbook-style presentation of the elements of probability theory, of the theory of Markovian diffusion processes and of the theory of stochastic differential equations, on which the modeling of fluctuating natural and artificial environments is based. Following an introduction to the mathematical tools, the occurrence and the properties of noise-induced transitions are then analyzed for rapidly fluctuating environments describable by the white-noise idealization. Subsequently, more realistic and general types of colored noises are considered. Appropriate practical methods for dealing with these situations are developed. The latter part of the book contains applications and experimental studies illustrating the many facets of noise-induced transitions. The following applications are considered in Noise-Induced Transitions: population dynamics, electrical circuits, chemical and photochemical reactions, non-linear optics, and hydrodynamical systems.
