This thesis presents a groundbraking methodology for the radar international community. The detection approach introduced, namely perturbation analysis, is completey novel showing a remarkable capability of thinking outside the box. Perturbation analysis is able to push forward the performance limits of current algorithms, allowing the detection of targets smaller than the resolution cell and highly embedded in clutter. The methodology itself is extraordinary flexibe and has already been used in two other large projects, funded by the ESA (European Space Agency): M-POL for maritime surveillance, and DRAGON-2 for land classification with particular attention to forests. This book is a perfectly organised piece of work where every detail and perspective is taken into account in order to provide a comprehensive vision of the problems and solutions.

The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

Mechanical design includes an optimization process in which designers always consider objectives such as strength, deflection, weight, wear, corrosion, etc. depending on the requirements. However, design optimization for a complete mechanical assembly leads to a complicated objective function with a large number of design variables. It is a good practice to apply optimization techniques for individual components or intermediate assemblies than a complete assembly. Analytical or numerical methods for calculating the extreme values of a function may perform well in many practical cases, but may fail in more complex design situations. In real design problems, the number of design parameters can be very large and their influence on the value to be optimized (the goal function) can be very complicated, having nonlinear character. In these complex cases, advanced optimization algorithms offer solutions to the problems, because they find a solution near to the global optimum within reasonable time and computational costs.

"Mechanical Design Optimization Using Advanced Optimization Techniques" presents a comprehensive review on latest research and development trends for design optimization of mechanical elements and devices. Using examples of various mechanical elements and devices, the possibilities for design optimization with advanced optimization techniques are demonstrated. Basic and advanced concepts of traditional and advanced optimization techniques are presented, along with real case studies, results of applications of the proposed techniques, and the best optimization strategies to achieve best performance are highlighted. Furthermore, a novel advanced optimization method named teaching-learning-based optimization (TLBO) is presented in this book and this method shows better performance with less computational effort for the large scale problems.

"Mechanical Design Optimization Using Advanced Optimization Techniques" is intended for designers, practitioners, managers, institutes involved in design related projects, applied research workers, academics, and graduate students in mechanical and industrial engineering and will be useful to the industrial product designers for realizing a product as it presents new models and optimization techniques to make tasks easier, logical, efficient and effective.

This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available in from the author's Web site. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder-Mead search algorithm.

Discrete Event Systems: Diagnosis and Diagnosability addresses the problem of fault diagnosis of Discrete Event Systems (DESs). This book provides the basic techniques and approaches necessary for the design of an efficient fault diagnosis system for a wide range of modern engineering applications. This book classifies the different techniques and approaches according to several criteria such as: modeling tools (Automata, Petri nets, Templates) that is used to construct the model; the information (qualitative based on events occurrences and/or states outputs, quantitative based on signal processing, data analysis) that is needed to analyze and achieve the diagnosis; the decision structure (centralized, decentralized) that is required to achieve the diagnosis; as well as the complexity (polynomial, exponential) of the algorithm that is used to determine the set of faults that the proposed approach is able to diagnose as well as the delay time required for this diagnosis. The goal of this classification is to select the efficient method to achieve the fault diagnosis according to the application constraints. This book will include illustrated examples of the presented methods and techniques as well as a discussion on the application of these methods on several real-world problems.

This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quadratic finite elements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normal derivatives of the numerical solution at the grid points. This work is the first publication to contain a rigorous analysis of the discontinuous Galerkin methods for wave control problems. It will be of interest to a range of researchers specializing in wave approximations.

The objective of this book is to advance the current knowledge of sensor research particularly highlighting recent advances, current work, and future needs. The goal is to share current technologies and steer future efforts in directions that will benefit the majority of researchers and practitioners working in this broad field of study.

"Introduction to Computational Science" was developed over a period of two years at the University of Utah Department of Computer Science in conjunction with the U.S. Department of Energy-funded Undergraduate Computation in Engineering Science (UCES) program. Each chapter begins by introducing a problem and then guiding the student through its solution. The computational techniques needed to solve the problem are developed as necassary, making the motivation for learning the computing alwasy apparent. Each chapter will introduce a single problem that will be used to motivate a single computing concept. The notes currently consist of 15 chapters. The first seven chapters deal with Maple and the last eight with C. The textbook will contain 20 to 30 chapters covering a similar mix of concepts at a finer level of detail.

This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations.

The book is divided into fourteen chapters, each containing several sections.

Most of it (the first nine Chapters) addresses two-dimensional domains, where

only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associatedgeneralized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice forpredicting failure initiation in brittlematerial on a daily basis. Several failure lawsfor two-dimensional domains with V-notches arepresented and their validity is examined by comparison to experimental observations.A sufficient simple and reliable condition for predicting failureinitiation (crack formation) in micron level electronic devices, involving singularpoints, is still a topic of active research and interest, and is addressed herein.

Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions.

This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.

"

This book is based on the belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities that will establish an experiential base for any future verbal explanations and to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies, as well as on the substantial experience of the authors in teaching Abstract Algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the math-like programming language ISETL; the main tool for reflection is work in teams of two to four students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. The text section is written in an informal, discursive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are presented in a lecture.

Since most of the problems arising in science and engineering are nonlinear, they are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems and often fail when used for problems with strong nonlinearity. Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer presents the current theoretical developments of the analytical method of homotopy analysis. This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis method. The particular focus lies on fluid flow problems governed by nonlinear differential equations. This book is intended for researchers in applied mathematics, physics, mechanics and engineering.

Both Kuppalapalle Vajravelu and Robert A. Van Gorder work at the University of Central Florida, USA."

Mathematica is a computer program (software) for doing symbolic, numeric and graphical analysis of mathematical problems. In the hands of economists, financial analysts and other professionals in econometrics and the quantitative sector of economic and financial modeling, it can be an invaluable tool for modeling and simulation on a large number of issues and problems, besides easily grinding out numbers, doing statistical estimations and rendering graphical plots and visuals. Mathematica enables these individuals to do all of this in a unified environment. This book's main use is that of an applications handbook. Modeling in Economics and Finance with Mathematica is a compilation of contributed papers prepared by experienced, "hands on" users of the Mathematica program. They come from

Whether different types of costs are to be reduced, benefits to be maximized or scarce resources to be managed, scheduling theory provides intelligent methods for practitioners and scientists. The just-in-time (JIT) production philosophy has enriched the classical scheduling theory with models that consider characteristics such as inventory costs, set-up times, lot sizing, or maintenance. This edited volume considers the specifics of just-in-time systems. It provides knowledge and insights on recent advances in scheduling theory where just-in-time aspects are considered. Contributions on models, theory, algorithms, and applications, that bring the theory up-to-date on the state-of-the-art of JIT systems are presented. Professionals, researchers and graduate students will find this book useful.

The projectors are considered as simple but important type of matrices and operators. Their basic theory can be found in many books, among which Hal mas [177], [178] are of particular significance. The projectors or projections became an active research area in the last two decades due to ideas generated from linear algebra, statistics and various areas of algorithmic mathematics. There has also grown up a great and increasing number of projection meth ods for different purposes. The aim of this book is to give a unified survey on projectors and projection methods including the most recent results. The words projector, projection and idempotent are used as synonyms, although the word projection is more common. We assume that the reader is familiar with linear algebra and mathemati cal analysis at a bachelor level. The first chapter includes supplements from linear algebra and matrix analysis that are not incorporated in the standard courses. The second and the last chapter include the theory of projectors. Four chapters are devoted to projection methods for solving linear and non linear systems of algebraic equations and convex optimization problems.

One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated. The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education.

Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, computational complexity, graph theory, geometry, real algebraic geometry and quantum computing. This book is an introduction to selected aspects of semidefinite programming and its use in approximation algorithms. It covers the basics but also a significant amount of recent and more advanced material.

There are many computational problems, such as MAXCUT, for which one cannot reasonably expect to obtain an exact solution efficiently, and in such case, one has to settle for approximate solutions. For MAXCUT and its relatives, exciting recent results suggest that semidefinite programming is probably the ultimate tool. Indeed, assuming the Unique Games Conjecture, a plausible but as yet unproven hypothesis, it was shown that for these problems, known algorithms based on semidefinite programming deliver the best possible approximation ratios among all polynomial-time algorithms.

This book follows the "semidefinite side" of these developments, presenting some of the main ideas behind approximation algorithms based on semidefinite programming. It develops the basic theory of semidefinite programming, presents one of the known efficient algorithms in detail, and describes the principles of some others. It also includes applications, focusing on approximation algorithms."

The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations.

This volume highlights the latest developments and trends in advanced materials and their properties, the modeling and simulation of non-classical materials and structures, and new technologies for joining materials. It presents the developments of advanced materials and respective tools to characterize and predict the material properties and behavior.

Among the group of physics honors students huddled in 1957 on a Colorado mountain watching Sputnik bisect the heavens, one young scientist was destined, three short years later, to become a key player in America s own top-secret spy satellite program. One of our era s most prolific mathematicians, Karl Gustafson was given just two weeks to write the first US spy satellite s software. The project would fundamentally alter America s Cold War strategy, and this autobiographical account of a remarkable academic life spent in the top flight tells this fascinating inside story for the first time.

Gustafson takes you from his early pioneering work in computing, through fascinating encounters with Nobel laureates and Fields medalists, to his current observations on mathematics, science and life. He tells of brushes with death, being struck by lightning, and the beautiful women who have been a part of his journey."

Fracture mechanics is a vast and growing field. This book develops the basic elements needed for both fracture research and engineering practice. The emphasis is on continuum mechanics models for energy flows and crack-tip stress- and deformation fields in elastic and elastic-plastic materials. In addition to a brief discussion of computational fracture methods, the text includes practical sections on fracture criteria, fracture toughness testing, and methods for measuring stress intensity factors and energy release rates. Class-tested at Cornell, this book is designed for students, researchers and practitioners interested in understanding and contributing to a diverse and vital field of knowledge.

This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.

The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.

Accurately predicting the behaviour of multiphase flows is a problem of immense industrial and scientific interest. Modern computers can now study the dynamics in great detail and these simulations yield unprecedented insight. This book provides a comprehensive introduction to direct numerical simulations of multiphase flows for researchers and graduate students. After a brief overview of the context and history the authors review the governing equations. A particular emphasis is placed on the 'one-fluid' formulation where a single set of equations is used to describe the entire flow field and interface terms are included as singularity distributions. Several applications are discussed, showing how direct numerical simulations have helped researchers advance both our understanding and our ability to make predictions. The final chapter gives an overview of recent studies of flows with relatively complex physics, such as mass transfer and chemical reactions, solidification and boiling, and includes extensive references to current work.

This book will have strong appeal to interdisciplinary audiences, particularly in regard to its treatments of fluid mechanics, heat equations, and continuum mechanics. There is also a heavy focus on vector analysis. Maple examples, exercises, and an appendix is also included.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific dis ciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathe matics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A successful concurrent numerical simulation requires physics and math ematics to develop and analyze the model, numerical analysis to develop solution methods, and computer science to develop a concurrent implemen tation. No single course can or should cover all these disciplines. Instead, this course on concurrent scientific computing focuses on a topic that is not covered or is insufficiently covered by other disciplines: the algorith mic structure of numerical methods.