Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, they constitute a challenging research field of their own. Inequalities also appear directly in mathematical models for applications in science, engineering, and economics.

This edited volume covers divers aspects of this fascinating field. It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts. Within the last five decades, the late Wolfgang Walter has made great contributions to the field of inequalities. His book on differential and integral inequalities was a real breakthrough in the 1970 s and has generated a vast variety of further research in this field. He also organized six of the seven General Inequalities Conferences held at Oberwolfach between 1976 and 1995, and co-edited their proceedings. He participated as an honorary member of the Scientific Committee in the General Inequalities 8 conference in Hungary. As a recognition of his great achievements, this volume is dedicated to Wolfgang Walter s memory. The General Inequalities meetings found their continuation in the Conferences on Inequalities and Applications which, so far, have been held twice in Hungary. This volume contains selected contributions of participants of the second conference which took place in Hajduszoboszlo in September 2010, as well as additional articles written upon invitation. These contributions reflect many theoretical and practical aspects in the field of inequalities, and will be useful for researchers and lecturers, as well as for students who want to familiarize themselves with the area.

Presents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications.

Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.

This textbook introduces advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations. Topics covered include error analysis, computer arithmetic, solution of systems of linear equations, least squares problems, eigenvalue problems, polynomial interpolation and approximation, numerical differentiation and integration, nonlinear equations, optimization, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the MATLAB programming language. This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.

The credit crisis that started in 2007, with the collapse of well-established financial institutions and the bankruptcy of many public corporations, has clearly shown the importance for any company entering the derivative business of modelling, pricing, and hedging its counterparty credit exposure.

Building an accurate representation of firm-wide credit exposure, for both risk and trading activities, is a significant challenge from the technical as well as the practical point of view. This volume can be considered as a roadmap to finding practical solutions to the problem of computing counterparty credit exposure for large books of both vanilla and exotic derivatives usually traded by large Investment Banks. It is divided into four parts, (I) Methodology, (II) Architecture and Implementation, (III) Products, and (IV) Hedging and Managing Counterparty Risk.

Starting from a generic modelling and simulation framework based on American Monte Carlo techniques, it presents a software architecture, which, with its modular design, allows the computation of credit exposure in a portfolio-aggregated and scenario-consistent way. An essential part of the design is the definition of a programming language, which allows trade representation based on dynamic modelling features. Several chapters are then devoted to the analysis of credit exposure of various products across all asset classes, namely foreign exchange, interest rate, credit derivatives, and equity. Finally it considers how to mitigate and hedge counterparty exposure. The crucial question of dynamic hedging is addressed by constructing a hybrid product, the Contingent-Credit Default Swap.This volume addresses these and other problems, as well as recent developments related to counterparty credit exposure, from a quantitative perspective. Its unique characteristic is the combination of a rigorous but simple mathematical approach with a practical view of the financial problem at hand.

This reference provides an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains, and special attention is given to error analysis of edge FEM that are particularly well suited to Maxwell's equations .

The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models.The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker-Planck equation, the Feymann-Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the microscopic model - Langevin type equation. The second main part focuses on providing the high accuracy schemes for these kinds of models, and the corresponding convergence and stability analysis.

This book provides a systematic introduction to the fundamental concepts, major challenges, and effective solutions for Quality of Service in Wireless Sensor Networks (WSNs). Unlike other books on the topic, it focuses on the networking aspects of WSNs, discussing the most important networking issues, including network architecture design, medium access control, routing and data dissemination, node clustering, node localization, query processing, data aggregation, transport and quality of service, time synchronization, and network security. Featuring contributions from researchers, this book strikes a balance between fundamental concepts and new technologies, providing readers with unprecedented insights into WSNs from a networking perspective. It is essential reading for a broad audience, including academics, research engineers, and practitioners, particularly postgraduate/postdoctoral researchers and engineers in industry. It is also suitable as a textbook or supplementary reading for graduate computer engineering and computer science courses.

This book explores four guiding themes - reduced order modelling, high dimensional problems, efficient algorithms, and applications - by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs. Highlighting the most promising approaches for (near-) future improvements in the way uncertainty quantification problems in the partial differential equation setting are solved, and gathering contributions by leading international experts, the book's content will impact the scientific, engineering, financial, economic, environmental, social, and commercial sectors.

Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.

Nowadays there is an increasing emphasis on all aspects of adaptively gener ating a grid that evolves with the solution of a PDE. Another challenge is to develop efficient higher-order one-step integration methods which can handle very stiff equations and which allow us to accommodate a spatial grid in each time step without any specific difficulties. In this monograph a combination of both error-controlled grid refinement and one-step methods of Rosenbrock-type is presented. It is my intention to impart the beauty and complexity found in the theoretical investigation of the adaptive algorithm proposed here, in its realization and in solving non-trivial complex problems. I hope that this method will find many more interesting applications. Berlin-Dahlem, May 2000 Jens Lang Acknowledgements I have looked forward to writing this section since it is a pleasure for me to thank all friends who made this work possible and provided valuable input. I would like to express my gratitude to Peter Deuflhard for giving me the oppor tunity to work in the field of Scientific Computing. I have benefited immensly from his help to get the right perspectives, and from his continuous encourage ment and support over several years. He certainly will forgive me the use of Rosenbrock methods rather than extrapolation methods to integrate in time.

This book provides in-depth and wide-ranging analyses of the emergence, and subsequent ubiquity, of algorithms in diverse realms of social life. The plurality of Algorithmic Cultures emphasizes: 1) algorithms' increasing importance in the formation of new epistemic and organizational paradigms; and 2) the multifaceted analyses of algorithms across an increasing number of research fields. The authors in this volume address the complex interrelations between social groups and algorithms in the construction of meaning and social interaction. The contributors highlight the performative dimensions of algorithms by exposing the dynamic processes through which algorithms - themselves the product of a specific approach to the world - frame reality, while at the same time organizing how people think about society. With contributions from leading experts from Media Studies, Social Studies of Science and Technology, Cultural and Media Sociology from Canada, France, Germany, UK and the USA, this volume presents cutting edge empirical and conceptual research that includes case studies on social media platforms, gaming, financial trading and mobile security infrastructures.

In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly. Important theoretical and practical advances have been made in a number or fronts, although they are not adequately described in any tt'xt currently available. With this in mind, we organized an international workshop, devoted solely to this topic. Tht' workshop took place in Vancouver, B.C., Canada, in July 1()"13, 1984. This volume contains the refereed proceedings of the workshop. Contributions to the workshop were in two formats. There were a small number of invited talks (ten of which are presented in this proceedings); the other contributions were in the rorm or poster sessions, for which there was no parallel activity in the workshop. We had attemptt'd to cover a number of topics and objectives in the talks. As a result, the general review papt'rs of O'Malley and Russell are intended to take a broader perspective, while the other papers are more specific. The contributions in this volume are divided (somewhat arbitrarily) into five groups. The first group concerns fundamental issues like conditioning and decoupling, which have only rect'ntly gained a proper appreciation of their centrality. Understanding of certain aspects or shooting methods ties in with these fundamental concepts. The papers of Russell, dt' Hoog and Mattheij all deal with these issues.

This monograph discusses modeling, adaptive discretisation techniques and the numerical solution of fluid structure interaction. An emphasis in part I lies on innovative discretisation and advanced interface resolution techniques. The second part covers the efficient and robust numerical solution of fluid-structure interaction. In part III, recent advances in the application fields vascular flows, binary-fluid-solid interaction, and coupling to fractures in the solid part are presented. Moreover each chapter provides a comprehensive overview in the respective topics including many references to concurring state-of-the art work. Contents Part I: Modeling and discretization On the implementation and benchmarking of an extended ALE method for FSI problems The locally adapted parametric finite element method for interface problems on triangular meshes An accurate Eulerian approach for fluid-structure interactions Part II: Solvers Numerical methods for unsteady thermal fluid structure interaction Recent development of robust monolithic fluid-structure interaction solvers A monolithic FSI solver applied to the FSI 1,2,3 benchmarks Part III: Applications Fluid-structure interaction for vascular flows: From supercomputers to laptops Binary-fluid-solid interaction based on the Navier-Stokes-Cahn-Hilliard Equations Coupling fluid-structure interaction with phase-field fracture: Algorithmic details

This book, written by the foremost international researchers and practitioners of genetic programming (GP), explores the synergy between theoretical and empirical results on real-world problems, producing a comprehensive view of the state of the art in GP. In this year's edition, the topics covered include many of the most important issues and research questions in the field, such as opportune application domains for GP-based methods, game playing and co-evolutionary search, symbolic regression and efficient learning strategies, encodings and representations for GP, schema theorems, and new selection mechanisms. The book includes several chapters on best practices and lessons learned from hands-on experience. Readers will discover large-scale, real-world applications of GP to a variety of problem domains via in-depth presentations of the latest and most significant results.

This monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials. These models offer several new possibilities for the study of important problems in engineering and mechanics involving multi-porosity materials, including geological materials (e.g., oil, gas, and geothermal reservoirs); manufactured porous materials (e.g., ceramics and pressed powders); and biomaterials (e.g., bone and the human brain). Proceeding from basic to more advanced material, the first part of the book begins with fundamental solutions in elasticity, followed by Galerkin-type solutions and Green's formulae in elasticity and problems of steady vibrations, quasi-static, and pseudo-oscillations for multi-porosity materials. The next part follows a similar format for thermoelasticity, concluding with a chapter on problems of heat conduction for rigid bodies. The final chapter then presents a number of open research problems to which the results presented here can be applied. All results discussed by the author have not been published previously and offer new insights into these models. Potential Method in Mathematical Theories of Multi-Porosity Media will be a valuable resource for applied mathematicians, mechanical, civil, and aerospace engineers, and researchers studying continuum mechanics. Readers should be knowledgeable in classical theories of elasticity and thermoelasticity.

This book highlights latest advancement in Mathematics, Physics and Chemistry. With the theme of "Innovative Science towards Sustainability and Industrial Revolution 4.0", ICFAS 2020 brings together leading experts, scientific communities and industrialists working in the field of applied sciences and mathematics from all over the world to share the most recent developments and cutting-edge discoveries addressing sustainability and industrial revolution 4.0 in the field. The conference topics include green materials, molecular modelling, catalysis, nanodevices and nanosystems, smart materials applications, solar cells technology, computational mathematics, data analysis and visualization, and numerical analysis. The contents of this book are useful for researchers, students, and industrial practitioners in the areas of Mathematics, Physics and Chemistry as most of the topics are in line with IR 4.0.

This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors. It can serve as an introduction to the topics covered, including extrapolation methods, Pade approximation, orthogonal polynomials, continued fractions, Lanczos-type methods etc.; it also provides in depth discussion of the many links between these subjects. A highlight of this book is the presentation of the human side of the fields discussed via personal testimonies from contemporary researchers, their anecdotes, and their exclusive remembrances of some of the "actors." This book shows how research in this domain started and evolved. Biographies of other scholars encountered have also been included. An important branch of mathematics is described in its historical context, opening the way to new developments. After a mathematical introduction, the book contains a precise description of the mathematical landscape of these fields spanning from the 19th century to the first part of the 20th. After an analysis of the works produced after that period (in particular those of Richardson, Aitken, Shanks, Wynn, and others), the most recent developments and applications are reviewed.

This book meets the present and future needs for the interaction between various science and technology/engineering areas on the one hand and different branches of soft computing on the other. Soft computing is the recent development about the computing methods which include fuzzy set theory/logic, evolutionary computation (EC), probabilistic reasoning, artificial neural networks, machine learning, expert systems, etc. Soft computing refers to a partnership of computational techniques in computer science, artificial intelligence, machine learning, and some other engineering disciplines, which attempt to study, model, and analyze complex problems from different interdisciplinary problems. This, as opposed to traditional computing, deals with approximate models and gives solutions to complex real-life problems. Unlike hard computing, soft computing is tolerant of imprecision, uncertainty, partial truth, and approximations. Interdisciplinary sciences include various challenging problems of science and engineering. Recent developments in soft computing are the bridge to handle different interdisciplinary science and engineering problems. In recent years, the correspondingly increased dialog between these disciplines has led to this new book. This is done, firstly, by encouraging the ways that soft computing may be applied in traditional areas, as well as point towards new and innovative areas of applications and secondly, by encouraging other scientific disciplines to engage in a dialog with the above computation algorithms outlining their problems to both access new methods as well as to suggest innovative developments within itself.

The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory. The topics covered are many of those included in an introductory Number Theory course for mathematics majors, but the presentation is carefully tailored to meet the needs of elementary education, liberal arts, and other non-mathematical majors. The text covers logic and proofs, as well as major concepts in Number Theory, and contains an abundance of worked examples and exercises to both clearly illustrate concepts and evaluate the students' mastery of the material.

Here we present numerical analysis to advanced undergraduate and master degree level grad students. This is to be done in one semester. The programming language is Mathematica. The mathematical foundation and technique is included. The emphasis is geared toward the two major developing areas of applied mathematics, mathematical finance and mathematical biology.

Here we present numerical analysis to advanced undergraduate and master degree level grad students. This is to be done in one semester. The programming language is Mathematica. The mathematical foundation and technique is included. The emphasis is geared toward the two major developing areas of applied mathematics, mathematical finance and mathematical biology.

Algorithms and Programming is primarily intended for use in a first-year undergraduate course in programming. It is structured in a problem-solution format that requires the student to think through the programming process, thus developing an understanding of the underlying theory. The book is easily readable by a student taking a basic introductory course in computer science as well as useful for a graduate-level course in the analysis of algorithms and/or compiler construction.

Each self-contained chapter presents classical and well-known problems supplemented by clear and in-depth explanations. The material covered includes such topics as combinatorics, sorting, searching, queues, grammar and parsing, selected well-known algorithms and much more. Students and teachers will find this both an excellent text for learning programming and a source of problems for a variety of courses.

This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It is divided into three parts, with the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire book has been revised to make it more accessible to readers who are actively involved in computations but less so in numerical analysis. Reviews of earlier edition: "The authors have written an excellent book which can be recommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory." (ZAMM, 2002) "In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theory and numerics of plasticity. Scientists as well as lecturers and graduate students will find the book very useful as a reference for research or for preparing courses in this field." (Technische Mechanik) "The book is professionally written and will be a useful reference to researchers and students interested in mathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis." (Math Reviews)

This book disseminates the latest results and envisages new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology. It comprises a collection of the main results presented at the Ninth Edition of the International Workshop "Dynamical Systems Applied to Biology and Natural Sciences - DSABNS", held from 7 to 9 February 2018 at the Department of Mathematics, University of Turin, Italy. While the principal focus is ecology and epidemiology, the coverage extends even to waste recycling and a genetic application. The topics covered in the 12 peer-reviewed contributions involve such diverse mathematical tools as ordinary and partial differential equations, delay equations, stochastic equations, control, and sensitivity analysis. The book is intended to help both in disseminating the latest results and in envisaging new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology.