In the modern world of gigantic datasets, which scientists and practioners of all fields of learning are confronted with, the availability of robust, scalable and easy-to-use methods for pattern recognition and data mining are of paramount importance, so as to be able to cope with the avalanche of data in a meaningful way. This concise and pedagogical research monograph introduces the reader to two specific aspects - clustering techniques and dimensionality reduction - in the context of complex network analysis. The first chapter provides a short introduction into relevant graph theoretical notation; chapter 2 then reviews and compares a number of cluster definitions from different fields of science. In the subsequent chapters, a first-principles approach to graph clustering in complex networks is developed using methods from statistical physics and the reader will learn, that even today, this field significantly contributes to the understanding and resolution of the related statistical inference issues. Finally, an application chapter examines real-world networks from the economic realm to show how the network clustering process can be used to deal with large, sparse datasets where conventional analyses fail.

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations.

In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential equations and spatial- and time-dependent differential equations.

The practical part of the text applies the methods to benchmark and real-life problems, such as waste disposal, elastics wave propagation, and complex flow phenomena. The book also examines the benefits of equation decomposition. It concludes with a discussion on several useful software packages, including r3t and FIDOS.

Covering a wide range of theoretical and practical issues in multiphysics and multiscale problems, this book explores the benefits of using iterative splitting schemes to solve physical problems. It illustrates how iterative operator splitting methods are excellent decomposition methods for obtaining higher-order accuracy.

Continuing the theme of the first, this second volume continues the study of the uses and techniques of numerical experimentation in the solution of PDEs. It includes topics such as initial-boundary-value problems, a complete survey of theory and numerical methods for conservation laws, and numerical schemes for elliptic PDEs. The author stresses the use of technology and graphics throughout for both illustration and analysis.

This book introduces the basic concepts and methods that are useful in the statistical analysis and modeling of the DNA-based marker and phenotypic data that arise in agriculture, forestry, experimental biology, and other fields. It concentrates on the linkage analysis of markers, map construction and quantitative trait locus (QTL) mapping, and assumes a background in regression analysis and maximum likelihood approaches. The strength of this book lies in the construction of general models and algorithms for linkage analysis, as well as in QTL mapping in any kind of crossed pedigrees initiated with inbred lines of crops.

The study of wall-bounded turbulent ows is of considerable interest from both scienti c and practical view points. As such it has attracted a great deal of research over the last 100 years. Much research has concentratedon ows over smooth walls since these are simpler from experimental, numerical and theoretical standpoints. The ow over rough walls has still received considerable attention but progress has necessarilybeenslower.Perhapsthemostessentialproblem(certainlyfromaprac- cal point of view) is to be able to predict the skin-frictiondrag acting on a plate (or a body) given a certain known roughness characteristic of the surface. Unfortunately this has proved to be very dif cult since even the simplest rough surfaces can be characterised by a number of different parameters and we still cannot directly c- nectthese tothe uiddynamicdragin a givensituation.Varioustheoriesandmodels have been proposed in order to make progress but there is still some disagreement in the community as to the correct understanding of these important ows.

Pulsed-Power Systems describes the physical and technical foundations for the production and application of high-voltage pulses of very high-power and high-energy character. In the initial chapters, it addresses materials, components and the most common diagnostics. In the second part, three categories of applications with scientific and industrial relevance are detailed: production of strong pulsed electric and magnetic fields, intense radiation sources and pulsed electric (plasma) discharges.

This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory's role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.

This thesis focuses on the theoretical foundation of the Standard Model valid up to the Planck scale, based on the current experimental facts from the Large Hadron Collider. The thesis consists of two themes: (1) to open up a new window of the Higgs inflation scenario, and (2) to explore a new solution to the naturalness problem in particle physics. In the first area, on the Higgs inflation scenario, the author successfully improves a large value problem on a coupling constant relevant to the Higgs mass in the Standard Model, in which the coupling value of the order of 105 predicted in a conventional scenario is reduced to the order of 10. This result makes the Higgs inflation more attractive because the small value of coupling is natural in the context of ultraviolet completion such as string theory. In the second area, the author provides a new answer to the naturalness problem, of why the cosmological constant and the Higgs mass are extremely small compared with the Planck scale. Based on the baby universe theory originally proposed by Coleman, the smallness of those quantities is successfully explained without introducing any additional new particles relevant at the TeV energy scale.

This textbook, designed for a single semester course, begins with basic set theory, and moves briskly through fundamental, exponential, and logarithmic functions. Limits and derivatives finish the preparation for economic applications, which are introduced in chapters on univariate functions, matrix algebra, and the constrained and unconstrained optimization of univariate and multivariate functions. The text finishes with chapters on integrals, the mathematics of finance, complex numbers, and differential and difference equations.

Rich in targeted examples and explanations, Mathematical Economics offers the utility of a handbook and the thorough treatment of a text. While the typical economics text is written for two semester applications, this text is focused on the essentials. Instructors and students are given the concepts in conjunction with specific examples and their solutions.

This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.

This book describes the solution of electrodynamic boundary problems, which arose in the practical life of a designer. Only a few problems can be solved analytically and some of these solutions are given in the book, for example, the computation of a strip line in a rectangular or circular cylinder capacitance. Practical lines' configurations require computational work. As the authors' practice shows, the use of Green functions, leading to singular integral equations, is a powerful and pretty universal method to solve different boundary problems, including electrodynamic ones. The book presents the results of computations of microstrip lines on magnetized (longitudinally and transversally) ferrite and semiconductor substrates taking into account all the geometric sizes. The properties of gyrotropic media are described in the book for the reader's convenience. The geometrical shape may be practically any. The integral equations are exact and give the proper field near the edges. Actually, the use of singular integral equations reduces the experimental verification to minimum. The book will be useful for students, engineers, designers and researchers. It contains a lot of computed results, which are verified experimentally and can be used immediately.

STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD

Linear Statics

Volume 1: The Basis and Solids

Eugenio Onate

The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years.

Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elastic foundations, stress smoothing, error estimation and adaptive mesh refinement techniques, among others. The text concludes with a chapter on the mesh generation and visualization of FEM results.

The book will be useful for students approaching the finite element analysis of structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis.

STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD

Linear Statics

Volume 2: Beams, Plates and Shells

Eugenio Onate

The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM).The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years.

Volume 2 presents a detailed description of the finite element formulation for analysis of slender and thick beams, thin and thick plates, folded plate structures, axisymmetric shells, general curved shells, prismatic structures and three dimensional beams. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems Emphasis is put on the treatment of structures with layered composite materials.

The book will be useful for students approaching the finite element analysis of beam, plate and shell structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis.

"

Today, a major component of any project management effort is the combined use of qualitative and quantitative tools. While publications on qualitative approaches to project management are widely available, few project management books have focused on the quantitative approaches. This book represents the first major project management book with a practical focus on the quantitative approaches to project management. The book organizes quantitative techniques into an integrated framework for project planning, scheduling, and control. Numerous illustrative examples are presented. Topics covered in the book include PERT/CPM/PDM and extensions, mathematical project scheduling, heuristic project scheduling, project economics, statistical data analysis for project planning, computer simulation, assignment and transportation problems, and learning curve analysis. Chapter one gives a brief overview of project management, presenting a general-purpose project management model. Chapter two covers CPM, PERT, and PDM network techniques. Chapter three covers project scheduling subject to resource constraints. Chapter four covers project optimization. Chapter five discusses economic analysis for project planning and control. Chapter six discusses learning curve analysis. Chapter seven covers statistical data analysis for project planning and control. Chapter eight presents techniques for project analysis and selection. Tables and figures are used throughout the book to enhance the effectiveness of the discussions. This book is excellent as a textbook for upper-level undergraduate and graduate courses in Industrial Engineering, Engineering Management, and Business, and as a detailed, comprehensive guidefor corporate management.

Written to be more rigorous than other books on the same topics No other book on the topics explores programming and software in this manner Requires only undergraduate prerequisites

"...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic

Unlike other books that focus only on selected specific subjects this book provides both a broad and rich cross-section of contemporary approaches to stochastic modeling in finance and economics; it is decision making oriented. The material ranges from common tools to solutions of sophisticated system problems and applications.
In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities.
Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects.
Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study. Selected examples of successful applications in finance, production planning and management of technological processes and electricity generation are presented. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories.
In Part IV, the sections devoted tostochastic calculus cover also more advanced topics such as DDS Theorem or extremal martingale measures, which make it possible to treat more delicate models in Mathematical Finance (complete markets, optimal control, etc.)
Audience: Students and researchers in probability and statistics, econometrics, operations research and various fields of finance, economics, engineering, and insurance.

This book presents, in a methodical way, updated and comprehensive descriptions and analyses of some of the most relevant problems in the context of fluid-structure interaction (FSI). Generally speaking, FSI is among the most popular and intriguing problems in applied sciences and includes industrial as well as biological applications. Various fundamental aspects of FSI are addressed from different perspectives, with a focus on biomedical applications. More specifically, the book presents a mathematical analysis of basic questions like the well-posedness of the relevant initial and boundary value problems, as well as the modeling and the numerical simulation of a number of fundamental phenomena related to human biology. These latter research topics include blood flow in arteries and veins, blood coagulation and speech modeling. We believe that the variety of the topics discussed, along with the different approaches used to address and solve the corresponding problems, will help readers to develop a more holistic view of the latest findings on the subject, and of the relevant open questions. For the same reason we expect the book to become a trusted companion for researchers from diverse disciplines, such as mathematics, physics, mathematical biology, bioengineering and medicine."

This monograph is devoted to the creation of a comprehensive formalism for quantitative description of polarized modes' linear interaction in modern single-mode optic fibers. The theory of random connections between polarized modes, developed in the monograph, allows calculations of the zero shift deviations for a fiber ring interferometer. The monograph addresses also the Sagnac effect and the Thomas precession. Devices such as gyroscopes, used in navigation and flight control, work based on this technology. Given the ever increasing market for navigation and air traffic, researchers and practitioners in research and industry need a fundamental and sound understanding of the principles. This work presents the underlying physical foundations.

The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.

This book presents details of a text-to-speech synthesis procedure using epoch synchronous overlap add (ESOLA), and provides a solution for development of a text-to-speech system using minimum data resources compared to existing solutions. It also examines most natural speech signals including random perturbation in synthesis. The book is intended for students, researchers and industrial practitioners in the field of text-to-speech synthesis.

This volume contains survey and original articles presenting the state of the art on the application of GrAbner bases in control theory and signal processing. The contributions are based on talks delivered at the Special Semester on GrAbner Bases and Related Methods at the Johann Radon Institute of Computational and Applied Mathematics (RICAM), Linz, Austria, in May 2006.

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars' GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory. Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource.

There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by the General Secretariat of Research and Tech nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming."

This thesis examines the Z box contribution to the weak charge of the proton. Here, by combining recent parity-violating electron-deuteron scattering data with our current understanding of parton distribution functions, the author shows that one can limit this model dependence. The resulting construction is a robust model of the and Z structure functions that can also be used to study a variety of low-energy phenomena. Two such cases are discussed in this work, namely, the nucleon's electromagnetic polarizabilities and quark-hadron duality. By using phenomenological information to constrain the input structure functions, this important but previously poorly understood radiative correction is determined at the kinematics of the parity-violating experiment, QWEAK, to a degree of precision more than twice that of the previous best estimate. A detailed investigation into available parametrizations of the electromagnetic and interference cross-sections indicates that earlier analyses suffered from the inability to correctly quantify their model dependence.