Methods of Nonlinear Analysis

This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem

For graduate students looking for an introduction to this area of nonlinear analysis, Liu (mathematics, Stanford U.) offers a self-contained study of shock waves explaining the new wave interactions f

This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomia

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.

This book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The appr

This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretic

This book is on the analysis and design of nonlinear analog integrated circuits that form the basis of present-day communication systems. The material is intended to be a textbook for class use but s

Noise-Driven Phenomena in Hysteretic Systems provides a general approach to nonlinear systems with hysteresis driven by noisy inputs, which leads to a unitary framework for the analysis of various sto

Soft condensed matter physics relies on a fundamental understanding at the interface between physics, chemistry, biology, and engineering for a host of materials and circumstances that are related to, but outside, the traditional definition of condensed matter physics. Featuring contributions from leading researchers in the field, this book uniquely discusses both the contemporary experimental and computational manifestations of soft condensed matter systems. From particle tracking and image analysis, novel materials and computational methods, to confocal microscopy and bacterial assays, this book will equip the reader for collaborative and interdisciplinary research efforts relating to a range of modern problems in nonlinear and non-equilibrium systems. It will enable both graduate students and experienced researchers to supplement a more traditional understanding of thermodynamics and statistical systems with knowledge of the techniques used in contemporary investigations. Color vers

Proven statistical reliability analysis methods-available for the first time to engineers in the West While probabilistic methods of system reliability analysis have reached an unparalleled degree of

Written in a clear, logical and concise manner, this comprehensive resource provides discussion on essential mathematical tools, required for upgraded system performance. Understanding of basic principles and governing laws is essential to reduce complexity of the system, and this guide offers detailed discussion on analytical and numerical techniques to solve mathematical model equations. Important concepts including nonlinear algebraic equations, initial value ordinary differential equations (ODEs) and boundary value ODEs are discussed in detail. The concepts of optimization methods and sensitivity analysis, which are important from subject point of view, are explained with suitable examples. Numerous problems and MATLAB®/Scilab exercises are interspersed throughout the text. Several case studies involving full details of simulation are offered for better understanding. The accompanying website will host additional MATLAB®/Scilab problems, model question papers, simulation exercises,

Based on the author's forty years of teaching experience, this unique textbook covers both basic and advanced concepts of optimization theory and methods for process systems engineers. Topics covered include continuous, discrete and logic optimization (linear, nonlinear, mixed-integer and generalized disjunctive programming), optimization under uncertainty (stochastic programming and flexibility analysis), and decomposition techniques (Lagrangean and Benders decomposition). Assuming only a basic background in calculus and linear algebra, it enables easy understanding of mathematical reasoning, and numerous examples throughout illustrate key concepts and algorithms. End-of-chapter exercises involving theoretical derivations and small numerical problems, as well as in modeling systems like GAMS, enhance understanding and help put knowledge into practice. Accompanied by two appendices containing web links to modeling systems and models related to applications in PSE, this is an essential

This is an advanced 1997 text for first-year graduate students in physics and engineering taking a standard classical mechanics course. It was the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organising principle of the text is integrability vs. nonintegrability. Flows in phase space and transformations are introduced early and systematically and are applied throughout the text. The standard integrable problems of elementary physics are analysed from the standpoint of flows, transformations, and integrability. This approach then allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will be of value to physicists and engineers taking graduate courses in classical mechanics. It will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.

This is an advanced 1997 text for first-year graduate students in physics and engineering taking a standard classical mechanics course. It was the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organising principle of the text is integrability vs. nonintegrability. Flows in phase space and transformations are introduced early and systematically and are applied throughout the text. The standard integrable problems of elementary physics are analysed from the standpoint of flows, transformations, and integrability. This approach then allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will be of value to physicists and engineers taking graduate courses in classical mechanics. It will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.

A practical guide to methods of survival analysis for medical researchers with limited statistical experience. Methods and techniques described range from descriptive and exploratory analysis to multi

A practical guide to methods of survival analysis for medical researchers with limited statistical experience. Methods and techniques described range from descriptive and exploratory analysis to multi

Analysis of methods of stormwater management, and suggestions for how these methods might be effectively applied.

This new manual is an indispensable working lab guide and reference for water/wastewater quality analysis. Based on procedures from "Standard Methods" and "Methods for Chemical Analysis of Water and W

This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research.

This is the second of three volumes of Methods in Molecular Biology that deal with Physical Methods of Analysis. The first of these, Spectroscopic Methods and Analyses dealt with NMR spec- troscopy, m

《非線性雙曲型方程的一些問題與應用(國內英文版)》內容簡介：This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear

This book provides a comprehensive treatment of the Gross–Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the periodic potential. It takes the mean-field model of the Bose–Einstein condensation as the starting point of analysis and addresses the existence and stability of localized modes. The mean-field model is simplified further to the coupled nonlinear Schrödinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrödinger equations. One of the important features of such systems is the existence of band gaps in the wave transmission spectra, which support stationary localized modes known as the gap solitons. These localized modes realise a balance between periodicity, dispersion and nonlinearity of the physical system. Written for researchers in applied mathematics, this book mainly focuses on the mathematical properties of the Gross–Pitaevskii equation. It also serves as a reference for theoretical physicists inter

IAU Symposium 271 enhances our understanding of some of the important dynamical processes that are ubiquitous in many objects in the Universe, from stars like our Sun to galaxies. A wide range of temporal and spatial scales are generally present, so instabilities, highly nonlinear states and turbulence play a central role. Understanding the behaviour and evolution of such systems requires high-accuracy, multi-scale observations and thoughtful analysis of the data gathered, coupled with detailed theoretical study. High-performance numerical simulations have become an essential and revealing tool for assessing the often subtle highly nonlinear regime of such models. In IAU S271 world experts share their knowledge and perspectives on the latest advances in studying the common underlying processes from the field of nonlinear astrophysical dynamics. The symposium also celebrates the long and illustrious career of Professor Juri Toomre and his achievements in many realms of astrophysical dyn

This book teaches basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Cov

Machine learning is a novel discipline concerned with the analysis of large and multiple variables data. It involves computationally intensive methods, like factor analysis, cluster analysis, and disc

This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows. Vortex methods have matured, offering an interesting alternative to finite difference and spectral methods for high-resolution numerical solutions of the Navier–Stokes equations. Research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character that was the motivation for their introduction. Scientists working in the areas of numerical analysis and fluid mechanics will benefit from this book, which may serve both communities as both a reference monograph and a textbook for computational fluid dynamics courses.

This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows. Vortex methods have matured, offering an interesting alternative to finite difference and spectral methods for high-resolution numerical solutions of the Navier–Stokes equations. Research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character that was the motivation for their introduction. Scientists working in the areas of numerical analysis and fluid mechanics will benefit from this book, which may serve both communities as both a reference monograph and a textbook for computational fluid dynamics courses.

Providing an easy explanation of the fundamentals, methods, and applications of chemometrics‧ Acts as a practical guide to multivariate data analysis techniques‧ Explains the methods used in Chemometr

The book introduces most of the basic tools of chemometrics including experimental design, signal analysis, statistical methods for analytical chemistry and multivariate methods. It then discusses a n

The volume offers an exploration of methods for analysis of emotion in negotiation, such as cognitive modeling, discourse analysis, all testing, subsequent multidimensional scaling, impression rating,

This four volume major reference work covers the main issues, methods of analysis, and alternatives, of causality, including the classic texts applying these alternative concepts and methods to empir

This Toolkit provides a framework, guidelines, and practical tools for conducting an analysis and diagnostics of trade competitiveness of the services sector. The methods of analysis are fully customi

A self-contained, contemporary treatment of the analysis of long-range dependent data Long-Memory Time Series: Theory and Methods provides an overview of the theory and methods developed to deal with

This book focuses on the history of Hungarian parliamentarism. Beside classic methods of historiography, the author utilizes statistical and GIS methods in his analysis. He combines the micro and macr

This new volume of Methods in Cell Biology looks at methods for lysosomes and lysosomal diseases. Chapters focus upon practical experimental protocols to guide researchers through the analysis of mult

There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. In Bayesian statistics the rules of

The use of Bayesian methods for the analysis of data has grown substantially in areas as diverse as applied statistics, psychology, economics and medical science. Bayesian Methods for Categorical Data

Leading forensic experts from around the world describe in detail their time-proven methods for identity testing through DNA analysis. Their state-of-the-art collection of easily reproducible methods

In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis

This book presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. The relationship between domain decomposition and multigrid methods is carefully explained at an elementary level, and discussions of the implementation of domain decomposition methods on massively parallel super computers are also included. All algorithms are fully described and explained, and a mathematical framework for the analysis and complete understanding of the methods is also carefully developed. In addition, numerous numerical examples are included to demonstrate the behaviour of this important class of numerical methods. This book is ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods.