الصفحة 5
الصفحة 5
Integrable Hamiltonian Hierarchies : Spectral and Geometric Methods
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform. The book brings together the spectral and the geometric approaches and as such will be useful to a wide readership: from researchers in the field of nonlinear completely integrable evolution equations to graduate and post-graduate students.
Instability in Models Connected with Fluid Flows II
Instability in Models Connected with Fluid Flows II presents chapters from world renowned specialists. The stability of mathematical models simulating physical processes is discussed in topics on control theory, first order linear and nonlinear equations, water waves, free boundary problems, large time asymptotics of solutions, stochastic equations, Euler equations, Navier-Stokes equations, and other PDEs of fluid mechanics. Fields covered include: the free surface Euler (or water-wave) equations, the Cauchy problem for transport equations, irreducible Chapman--Enskog projections and Navier-Stokes approximations, randomly forced PDEs, stability of equilibrium figures of uniformly rotating viscous incompressible liquid, Navier-Stokes equations in cylindrical domains, Navier-Stokes-Poisson flows in a vacuum.
Instability in Models Connected with Fluid Flows I
Instability in Models Connected with Fluid Flows I presents chapters from world renowned specialists. The stability of mathematical models simulating physical processes is discussed in topics on control theory, first order linear and nonlinear equations, water waves, free boundary problems, large time asymptotics of solutions, stochastic equations, Euler equations, Navier-Stokes equations, and other PDEs of fluid mechanics. Fields covered include: controllability and accessibility properties of the Navier- Stokes and Euler systems, nonlinear dynamics of particle-like wavepackets, attractors of nonautonomous Navier-Stokes systems, large amplitude monophase nonlinear geometric optics, existence results for 3D Navier-Stokes equations and smoothness results for 2D Boussinesq equations, instability of incompressible Euler equations, increased stability in the Cauchy problem for elliptic equations.
Information criteria and statistical modeling
One of the main objectives of this book is to provide comprehensive explanations of the concepts and derivations of the AIC and related criteria, including Schwarz’s Bayesian information criterion (BIC), together with a wide range of practical examples of model selection and evaluation criteria. A secondary objective is to provide a theoretical basis for the analysis and extension of information criteria via a statistical functional approach. A generalized information criterion (GIC) and a bootstrap information criterion are presented, which provide unified tools for modeling and model evaluation for a diverse range of models, including various types of nonlinear models and model estimation procedures such as robust estimation, the maximum penalized likelihood method and a Bayesian approach.
Identification of nonlinear systems using neural networks and polynomial models : A block-oriented approach
The book gives a comparative study of their gradient approximation accuracy, computational complexity, and convergence rates and furthermore presents some new and original methods concerning the model parameter adjusting with gradient-based techniques. "Identification of Nonlinear Systems Using Neural Networks and Polynomal Models".
Hyperbolic Systems of Balance Laws : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003
The present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan’s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.
Hyperbolic Problems and Regularity Questions
This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics.The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.
Hydropower Economics
HYDROPOWER ECONOMICS examines sustainable alternate energy sources beginning with modeling hydropower and extending the model to include thermal power and wind power. The book will use various econometric measures, equilibrium metrics, OR methods, and DEA/productivity analyses to analyze and model the optimal use of these alternate energy sources. Because these problems are dynamic in nature, dynamic methods are used to model the problems. The book derives results on the allocation of the amounts of alternate sources of energy (water, thermal, and wind) required to produce electricity at acceptable levels over time. Graphic illustrations of the analytical and mathematical modeling used to reach research conclusions are used throughout the book.
Hydrodynamics of Explosion : Experiments and Models
Hydronamics of Explosion presents the research results for the problems of underwater explosions and contains a detailed analysis of the structure and the parameters of the wave fields generated by explosions of cord and spiral charges, a description of the formation mechanisms for a wide range of cumulative flows at underwater explosions near the free surface, and the relevant mathematical models. Shock-wave transformation in bubbly liquids, shock-wave amplification due to collision and focusing, and the formation of bubble detonation waves in reactive bubbly liquids are studied in detail. Particular emphasis is placed on the investigation of wave processes in cavitating liquids, which incorporates the concepts of the strength of real liquids containing natural microinhomogeneities, the relaxation of tensile stress, and the cavitation fracture of a liquid as the inversion of its two-phase state under impulsive (explosive) loading. The problems are classed among essentially nonlinear processes that occur under shock loading of liquids and may be of interest to researchers in physical acoustics, mechanics of multiphase media, shock-wave processes in condensed media, explosive hydroacoustics, and cumulation.
Human-Like Biomechanics : A Unified Mathematical Approach to Human Biomechanics and Humanoid Robotics
The book contains six Chapters and an Appendix. The first Chapter is an Introduction, giving a brief review of mathematical techniques to be used in the text. The second Chapter develops geometrical basis of human-like biomechanics, while the third Chapter develops its mechanical basis, mainly from generalized Lagrangian and Hamiltonian perspective. The fourth Chapter develops topology of human-like biomechanics, while the fifth Chapter reviews related nonlinear control techniques. The sixth Chapter develops covariant biophysics of electro-muscular stimulation. The Appendix consists of two parts: classical muscular mechanics and modern path integral methods, which are both used frequently in the main text.
Homotopy-Based Methods in Water Engineering
Exploring the concept of homotopy from topology, different kinds of homotopy-based methods have been proposed for analytically solving nonlinear differential equations, given by approximate series solutions. Homotopy-Based Methods in Water Engineering attempts to present the wide applicability of these methods to water engineering problems. It solves all kinds of nonlinear equations, namely algebraic/transcendental equations, ordinary differential equations (ODEs), systems of ODEs, partial differential equations (PDEs), system of PDEs, and integro-differential equations using the homotopy-based methods
H-infinity control for nonlinear descriptor systems
The authors present a study of the H-infinity control problem and related topics for descriptor systems, described by a set of nonlinear differential-algebraic equations. They derive necessary and sufficient conditions for the existence of a controller solving the standard nonlinear H-infinity control problem considering both state and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of Hamilton–Jacobi inequalities and a weak coupling condition; a parameterization of output feedback controllers solving the problem is also provided. All of these results are then specialized to the linear case. The derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. Among other important topics covered are balanced realization, reduced-order controller design and mixed H2/H-infinity control.
High-dimensional chaotic and attractor systems : A comprehensive introduction
If we try to describe real world in mathematical terms, we will see that real life is very often a high–dimensional chaos. Sometimes, by ‘pushing hard’, we manage to make order out of it; yet sometimes, we need simply to accept our life as it is. To be able to still live successfully, we need tounderstand, predict, and ultimately control this high–dimensional chaotic dynamics of life. This is the main theme of the present book.
Hard Disk Drive Servo Systems
The second edition of this monograph provides a systematic treatment of the design of modern hard disk drive servo systems updated with the latest research results to reflect recent improvements in spindle speed and bit density and other changes in this fast-moving field. In particular, it focuses on the applications of some newly developed results in control theory, i.e., robust and perfect tracking control and composite non-linear feedback control which are suitable for track following and seeking respectively. Emphasis is placed on hard disk drive servo systems with single- or dual-stage actuation using a voice-coil-motor actuator enhanced in the latter case by the addition of a micro-actuator providing faster responses and therefore higher bandwidth in track following. Other issues such as modeling and compensation of nonlinearities and friction in microdrives, disturbance rejection and resonance compensation are also addressed.
Handbook on Modelling for Discrete Optimization
This handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It will be done in an academic handbook treatment outlining the state-of-the-art for researchers across the domains of the Computer Science, Math Programming, Applied Mathematics, Engineering, and Operations Research. Included in the handbook's treatment are results from Graph Theory, Logic, Computer Science, and Combinatorics.
Handbook of Optimization in Telecommunications
The Handbook of Optimization in Telecommunications includes planning and design of telecommunication networks, routing, network protection, grooming, restoration, wireless communications, network location and assignment problems, Internet protocol, World Wide Web, and stochastic issues in telecommunications. The editors’ objective is to provide a reference tool for the increasing number of scientists and engineers in telecommunications who depend upon optimization in some way. Each chapter in the handbook is of an expository nature, but of scholarly treatment, and includes a brief overview of the state-of-the-art thinking relative to the topic, as well as pointers to the key references in the field. Specialists as well as nonspecialists should find this handbook stimulating and helpful.
Handbook of Multilevel Analysis
Multilevel analysis is the statistical analysis of hierarchically and non-hierarchically nested data. The simplest example is clustered data, such as a sample of students clustered within schools. Multilevel data are especially prevalent in the social and behavioral sciences and in the bio-medical sciences. The models used for this type of data are linear and nonlinear regression models that account for observed and unobserved heterogeneity at the various levels in the data. This book presents the state of the art in multilevel analysis, with an emphasis on more advanced topics. These topics are discussed conceptually, analyzed mathematically, and illustrated by empirical examples. The authors of the chapters are the leading experts in the field.
Handbook of brain connectivity
The Handbook provides an account of the current knowledge on the measurement, analysis and theory of the anatomical and functional connectivity of the brain. All contributors are leading experts in various fields concerning structural and functional brain connectivity.
Hamiltonian Methods in the Theory of Solitons
The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation, rather than the (more usual) KdV equation, is considered as a main example.
Guidelines for the use of advanced numerical analysis
It is an authoritative guide that explains in detail the potential restrictions and pitfalls and so help engineers undertake advanced numerical analysis. It discusses the major approximations involved in nonlinear numerical analysis and describes some of the more popular constituitive models currently available and explores their strengths and weaknesses.
