This volume presents applications of the Pi-Theorem to fluid mechanics and heat and mass transfer. The Pi-theorem yields a physical motivation behind many flow processes and therefore it constitutes a valuable tool for the intelligent planning of experiments in fluids. After a short introduction to the underlying differential equations and their treatments, the author presents many novel approaches how to use the Pi-theorem to understand fluid mechanical issues. The book is a great value to the fluid mechanics community, as it cuts across many subdisciplines of experimental fluid mechanics.

A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.

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.

This second volume of the series Lecture Notes in Applied and Computational Mechanics is the second part of the compendium of reviewed articles presented at the 11th EUROMECH-MECAMAT conference entitled "Mechanics of microstructured solids: cellular materials, fibre reinforced solids and soft tissues," which took place in Torino (Italy) in March 10-14, 2008, at the Museo Regional delle Scienze. This EUROMECH-MECAMAT conference was jointly organized by the Dipartimento di Matematica dell'Universita di Torino, Italy and the INPL Institute (LEMTA, Nancy-Universite, France). Prof. Franco Pastrone and Prof. Jean-Francois Ganghoffer were the co-chairmen.

* Metivier is an expert in the field of pdes/math physics, with a particular emphasis on shock waves.

* New monograph focuses on mathematical methods, models, and applications of boundary layers, present in many problems of physics, engineering, fluid mechanics.

* Metivier has good Birkhauser track record: one of the main authors of "Advances in the Theory of Shock Waves" (Freistuehler/Szepessy, eds, 4187-4).

* Manuscript endorsed by N. Bellomo, MSSET series editor...should be a good sell to members of MSSET community, who by-in-large are based in Europe.

* Included are self-contained introductions to different topics such as hyperbolic boundary value problems, parabolic systems, WKB methods, construction of profiles, introduction to the theory of Evans' functions, and energy methods with Kreiss' symmetrizers.

This volume will contain selected papers from the lectures held at the BAIL 2010 Conference, which took place from July 5th to 9th, 2010 in Zaragoza (Spain). The papers present significant advances in the modeling, analysis and construction of efficient numerical methods to solve boundary and interior layers appearing in singular perturbation problems. Special emphasis is put on the mathematical foundations of such methods and their application to physical models. Topics in scientific fields such as fluid dynamics, quantum mechanics, semiconductor modeling, control theory, elasticity, chemical reactor theory, and porous media are examined in detail.

Arguably, many industrial optimization problems are of the multiobjective type. The present work, after providing a survey of the state of the art in multiobjective optimization, gives new insight into this important mathematical field by consequently taking up the viewpoint of differential geometry. This approach, unprecedented in the literature, very naturally results in a generalized homotopy method for multiobjective optimization which is theoretically well-founded and numerically efficient. The power of the new method is demonstrated by solving two real-life problems of industrial optimization.
The book presents recent results obtained by the author and is aimed at mathematicians, scientists, students and practitioners interested in optimization and numerical homotopy methods.

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.

Column Generation is an insightful overview of the state-of-the-art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by FranAois Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).

The book is the first systematic treatment of column generation methodologies. It will provide students, researchers, and experienced column generation users with a much-needed state-of-the-art survey of the field.

This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.

This book gathers selected contributions by top Portuguese and international researchers in the field of Operations Research, presented at the 19th Congress of APDIO (Portuguese Association of Operational Research). The papers address a broad range of complex real-world problems, which are approached using recent theoretical techniques. Of particular interest are the applications of e.g. linear, nonlinear and mixed-integer programming, multiobjective optimization, metaheuristics and hybrid heuristics, multicriteria decision analysis, data envelopment analysis, clustering techniques and decision support systems, in such varied contexts as: supply chain management, scheduling problems, production management, logistics, energy, finance and healthcare. This conference, organized by APDIO and held in Aveiro, Portugal in September 2018, offered an ideal opportunity to discuss the latest developments in this field and to build new bridges between academic researchers and practitioners. Summarizing the outcomes, this book offers a valuable tool for all researchers, students and practitioners who wish to learn about the latest trends in this field.

Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems.

This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation.

Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics.

A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.

The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.

This book evolved out of a graduate course given at the University of New Orleans in 1997. The class consisted of students from applied mathematics andengineering. Theyhadthebackgroundofatleastafirstcourseincomplex analysiswithemphasisonconformalmappingandSchwarz-Christoffeltrans- formation, a firstcourse in numerical analysis, and good to excellent working knowledgeofMathematica* withadditionalknowledgeofsomeprogramming languages. Sincetheclasshad nobackground inIntegralEquations, thechap- tersinvolvingintegralequationformulations werenotcoveredindetail,except for Symm's integral equation which appealed to a subsetofstudents who had some training in boundary element methods. Mathematica was mostly used for computations. In fact, it simplified numerical integration and other oper- ations very significantly, which would have otherwise involved programming inFortran, C, orotherlanguageofchoice, ifclassical numericalmethods were attempted. Overview Exact solutions of boundary value problems for simple regions, such as cir- cles, squares or annuli, can be determined with relative ease even where the boundaryconditionsarerathercomplicated. Green'sfunctionsforsuchsimple regions are known. However, for regions with complex structure the solution ofa boundary value problem often becomes more difficult, even for a simple problemsuchastheDirichletproblem. Oneapproachtosolvingthesedifficult problems is to conformally transform a given multiply connected region onto *Mathematica is a registered trade mark of Wolfram Research, Inc. ix x PREFACE simpler canonical regions. This will, however, result in change not only in the region and the associated boundary conditions but also in the governing differential equation. As compared to the simply connected regions, confor- mal mapping ofmultiply connected regions suffers from severe limitations, one of which is the fact that equal connectivity ofregions is not a sufficient condition to effect a reciprocally connected map ofone region onto another.

The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations. An essential step in such investigations is the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration.

The book, consisting of twenty seven selected chapters presented by well-known specialists in the field, is an outgrowth of the Eighth International Conference on Integral Methods in Science and Engineering, held August 2a "4, 2004, in Orlando, FL. Contributors cover a wide variety of topics, from the theoretical development of boundary integral methods to the application of integration-based analytic and numerical techniques that include integral equations, finite and boundary elements, conservation laws, hybrid approaches, and other procedures.

The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.

This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. Its contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 14th International Symposium of Dynamic Games and Applications held in Banff.

"Advances in Dynamic Games" covers a variety of topics, ranging from evolutionary games, theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as mathematical biology, environmental management, finance and economics, engineering, guidance and control, and social interaction. Featured throughout are valuable tools and resources for researchers, practitioners, and graduate students interested in dynamic games and their applications to mathematics, engineering, economics, and management science. "

The book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos. All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4-6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and engineers with a platform that encouraged them to exchange their innovative ideas in mathematical analysis and its applications as well as to form interdisciplinary collaborations. The content of the book is divided into three parts: Part I contains contributions from participants whose topics are related to nonlinear dynamics and its applications in biological sciences. Part II has contributions which concern topics on nonlinear analysis and its applications to a variety of problems in science, engineering and industry. Part III consists of contributions dealing with some problems in applied analysis.

Analysis, Control and Optimization of Complex Dynamic Systems gathers in a single volume a spectrum of complex dynamic systems related papers written by experts in their fields, and strongly representative of current research trends. Complex systems present important challenges, in great part due to their sheer size which makes it difficult to grasp their dynamic behavior, optimize their operations, or study their reliability. Yet, we live in a world where, due to increasing inter-dependencies and networking of systems, complexity has become the norm. With this in mind, the volume comprises two parts. The first part is dedicated to a spectrum of complex problems of decision and control encountered in the area of production and inventory systems. The second part is dedicated to large scale or multi-agent system problems occurring in other areas of engineering such as telecommunication and electric power networks, as well as more generic context.

Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates; and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area. "

This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Topics and features: provides theoretical and programming exercises at the end of each chapter; presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms; discusses algorithms for calculating exact or approximate ESPs in the plane; examines the shortest paths on 3D surfaces, in simple polyhedrons and in cube-curves; describes the application of rubberband algorithms for solving art gallery problems, including the safari, zookeeper, watchman, and touring polygons route problems; includes lists of symbols and abbreviations, in addition to other appendices.

Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization. Originally, it started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications.
The current volume is the quintessence of an international workshop in September 1997 in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques.

Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a fair value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.

Mobile Intention Recognition addresses problems of practical relevance for mobile system engineers: how can we make mobile assistance systems more intelligent? How can we model and recognize patterns of human behavior which span more than a limited spatial context? This text provides an overview on plan and intention recognition, ranging from the late 1970s to very recent approaches. This overview is unique as it discusses approaches with respect to the specificities of mobile intention recognition. This book covers problems from research on mobile assistance systems using methods from artificial intelligence and natural language processing. It thus addresses an extraordinary interdisciplinary audience.

The theory of complex Ginzburg-Landau type phase transition and its applica tions to superconductivity and superfluidity has been a topic of great interest to theoretical physicists and has been continuously and persistently studied since the 1950s. Today, there is an abundance of mathematical results spread over numer ous scientific journals. However, before 1992, most of the studies concentrated on formal asymptotics or linear analysis. Only isolated results by Berger, Jaffe and Taubes and some of their colleagues touched the nonlinear aspects in great detail. In 1991, a physics seminar given by Ed Copeland at Sussex University inspired Q. Tang, the co-author of this monograph, to study the subject. Independently in Munich, K.-H. Hoffmann and his collaborators Z. Chen and J. Liang started to work on the topic at the same time. Soon it became clear that at that time, groups of mathematicians at Oxford and Virginia Tech had already studied the subject for a couple of years. They inspired experts in interface phase transition problems and their combined effort established a rigorous mathematical framework for the Ginzburg-Landau system. At the beginning Q. Tang collaborated with C.M. Elliott and H. Matano."

Computational Electromagnetics is a young and growing discipline, expanding as a result of the steadily increasing demand for software for the design and analysis of electrical devices. This book introduces three of the most popular numerical methods for simulating electromagnetic fields: the finite difference method, the finite element method and the method of moments. In particular it focuses on how these methods are used to obtain valid approximations to the solutions of Maxwell's equations, using, for example, "staggered grids" and "edge elements." The main goal of the book is to make the reader aware of different sources of errors in numerical computations, and also to provide the tools for assessing the accuracy of numerical methods and their solutions. To reach this goal, convergence analysis, extrapolation, von Neumann stability analysis, and dispersion analysis are introduced and used frequently throughout the book. Another major goal of the book is to provide students with enough practical understanding of the methods so they are able to write simple programs on their own. To achieve this, the book contains several MATLAB programs and detailed description of practical issues such as assembly of finite element matrices and handling of unstructured meshes. Finally, the book aims at making the students well-aware of the strengths and weaknesses of the different methods, so they can decide which method is best for each problem.

In thissecond edition, extensive computer projects are added as well as new material throughout.

Reviews of previous edition:

"The well-written monograph is devoted to students at the undergraduate level, but is also useful for practising engineers." (Zentralblatt MATH, 2007)"