A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.

The book collects contributions from experts worldwide addressing recent scholarship in social network analysis such as influence spread, link prediction, dynamic network biclustering, and delurking. It covers both new topics and new solutions to known problems. The contributions rely on established methods and techniques in graph theory, machine learning, stochastic modelling, user behavior analysis and natural language processing, just to name a few. This text provides an understanding of using such methods and techniques in order to manage practical problems and situations. Trends in Social Network Analysis: Information Propagation, User Behavior Modelling, Forecasting, and Vulnerability Assessment appeals to students, researchers, and professionals working in the field.

Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literature-notably in the area of convex analysis-essential in developing many of the important results in this book, and not usually found in conventional texts. Unlike other books on convex optimization, which usually discuss algorithms along with some basic theory, the sole focus of this book is on fundamental and advanced convex optimization theory. Although many results presented in the book can also be proved in infinite dimensions, the authors focus on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. They address semi-infinite optimization problems; approximate solution concepts of convex optimization problems; and some classes of non-convex problems which can be studied using the tools of convex analysis. They include examples wherever needed, provide details of major results, and discuss proofs of the main results.

The book gives a comprehensive overview of the state-of-the-art research and engineering in theory and application of Lattice Automata in design and control of autonomous Robots. Automata and robots share the same notional meaning. Automata (originated from the latinization of the Greek word " ") as self-operating autonomous machines invented from ancient years can be easily considered the first steps of robotic-like efforts. Automata are mathematical models of Robots and also they are integral parts of robotic control systems. A Lattice Automaton is a regular array or a collective of finite state machines, or automata. The Automata update their states by the same rules depending on states of their immediate neighbours. In the context of this book, Lattice Automata are used in developing modular reconfigurable robotic systems, path planning and map exploration for robots, as robot controllers, synchronisation of robot collectives, robot vision, parallel robotic actuators. All chapters are written in an accessible manner and lavishly illustrated. The book will help computer and robotic scientists and engineers to understand mechanisms of decentralised functioning of robotic collectives and to design future and emergent reconfigurable, parallel and distributed robotic systems.

This two-volume work introduces the theory and applications of Schur-convex functions. The first volume introduces concepts and properties of Schur-convex functions, including Schur-geometrically convex functions, Schur-harmonically convex functions, Schur-power convex functions, etc. and also discusses applications of Schur-convex functions in symmetric function inequalities.

This dissertation focuses on the calculation of transport coefficients in the matter created in a relativistic heavy-ion collision after chemical freeze-out. This matter can be well approximated using a pion gas out of equilibrium. We describe the theoretical framework needed to obtain the shear and bulk viscosities, the thermal and electrical conductivities and the flavor diffusion coefficients of a meson gas at low temperatures. To describe the interactions of the degrees of freedom, we use effective field theories with chiral and heavy quark symmetries. We subsequently introduce the unitarization methods in order to obtain a scattering amplitude that satisfies the unitarity condition exactly, then go on to calculate the transport properties of the low-temperature phase of quantum chromodynamics - the hadronic medium - which can be used in hydrodynamic simulations of a relativistic heavy-ion collision and its subsequent evolution. We show that the shear viscosity over entropy density exhibits a minimum in a phase transition by studying this coefficient in atomic Argon (around the liquid-gas phase transition) and in the linear sigma model in the limit of a large number of scalar fields (which presents a chiral phase transition). Finally, we provide an experimental method for estimating the bulk viscosity in relativistic heavy-ion collisions by performing correlations of the fluctuating components of the stress-energy tensor.

This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection."

"Now, however, weface an Age of Discontinuity in world economy and tech- nology. We might succeed in making it an age of great economic growth as weil. But the one thing that is certain so far is that it will be a period of change-in technology and in economic policy, in industry structures and in economic theo- ry, in the knowledge needed to govern and manage, and in economic issues. While we have been busy finishing the great nineteenth-century economic ed- ijice, the foundations have shifted beneath our feet." Peter F. Drucker, 1968 The A~e Qf DiscQntinuity, p. 10 This project has had a lQng gestatiQn period, probably ultimately dating to a YQuthful QbsessiQn with watershed divides and bQundaries. My awareness Qf the problem Qf discQntinuity in eCQnQmics dates tQ my first enCQunter with the capi- tal theQry paradQxes in the late 1960s, the fruits Qf which can be seen in Chapter 8 Qf this book. This awareness led tQ a frostratiQn Qver the apparent lack Qf a mathematics Qf discQntinuity, a lack that was in the process of rapidly being QverCQme at that time.

Exploring roles critical to environmental toxicology, Modeling and Simulation in Ecotoxicology with Applications in MATLAB (R) and Simulink (R) covers the steps in modeling and simulation from problem conception to validation and simulation analysis. Using the MATLAB and Simulink programming languages, the book presents examples of mathematical functions and simulations, with special emphasis on how to develop mathematical models and run computer simulations of ecotoxicological processes. Designed for students and professionals with little or no experience in modeling, the book includes: General principles of modeling and simulation and an introduction to MATLAB and Simulink Stochastic modeling where variability and uncertainty are acknowledged by making parameters random variables Toxicological processes from the level of the individual organism, with worked examples of process models in either MATLAB or Simulink Toxicological processes at the level of populations, communities, and ecosystems Parameter estimation using least squares regression methods The design of simulation experiments similar to the experimental design applied to laboratory or field experiments Methods of postsimulation analysis, including stability analysis and sensitivity analysis Different levels of model validation and how they are related to the modeling purpose The book also provides three individual case studies. The first involves a model developed to assess the relative risk of mortality following exposure to insecticides in different avian species. The second explores the role of diving behavior on the inhalation and distribution of oil spill naphthalene in bottlenose dolphins. The final case study looks at the dynamics of mercury in Daphnia that are exposed to simulated thermal plumes from a hypothetical power plant cooling system. Presented in a rigorous yet accessible style, the methodology is versatile enough to be readily applicable not only to environmental toxicology but a range of other biological fields.

This thesis describes a high-quality, high-precision method for the data analysis of an interesting elementary particle reaction. The data was collected at the Japanese B-meson factory KEKB with the Belle detector, one of the most successful large-scale experiments worldwide. CP violation is a subtle quantum effect that makes the world look different when simultaneously left and right and matter and antimatter are exchanged. This being a prerequisite for our own world to have developed from the big bang, there are only a few experimental indications of such effects, and their detection requires very intricate techniques. The discovery of CP violation in B meson decays garnered Kobayashi and Maskawa, who had predicted these findings as early as 1973, the 2008 Nobel prize in physics. This thesis describes in great detail what are by far the best measurements of branching ratios and CP violation parameters in two special reactions with two charm mesons in the final state. It presents an in-depth but accessible overview of the theory, phenomenology, experimental setup, data collection, Monte Carlo simulations, (blind) statistical data analysis, and systematic uncertainty studies.

This book serves a dual purpose: firstly to combine the treatment of circuits and digital electronics, and secondly, to establish a strong connection with the contemporary world of digital systems. The need for this approach arises from the observation that introducing digital electronics through a course in traditional circuit analysis is fast becoming obsolete. Our world has gone digital. Automata theory helps with the design of digital circuits such as parts of computers, telephone systems and control systems. A complete perspective is emphasized, because even the most elegant computer architecture will not function without adequate supporting circuits. The focus is on explaining the real-world implementation of complete digital systems. In doing so, the reader is prepared to immediately begin design and implementation work. This work serves as a bridge to take readers from the theoretical world to the everyday design world where solutions must be complete to be successful.

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.

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.

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.

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 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.

The aim of this book is to bring students of economics and finance who have only an introductory background in mathematics up to a quite advanced level in the subject, thus preparing them for the core mathematical demands of econometrics, economic theory, quantitative finance and mathematical economics, which they are likely to encounter in their final-year courses and beyond. The level of the book will also be useful for those embarking on the first year of their graduate studies in Business, Economics or Finance. The book also serves as an introduction to quantitative economics and finance for mathematics students at undergraduate level and above. In recent years, mathematics graduates have been increasingly expected to have skills in practical subjects such as economics and finance, just as economics graduates have been expected to have an increasingly strong grounding in mathematics. The authors avoid the pitfalls of many texts that become too theoretical. The use of mathematical methods in the real world is never lost sight of and quantitative analysis is brought to bear on a variety of topics including foreign exchange rates and other macro level issues.

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.

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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.

"...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