This volume contains contributions from the Gulf International Conference in Applied Mathematics, held at the Gulf University for Science & Technology. The proceedings reflects the three major themes of the conference. The first of these was mathematical biology, including a keynote address by Professor Philip Maini. The second theme was computational science/numerical analysis, including a keynote address by Professor Grigorii Shishkin. The conference also addressed more general applications topics, with papers in business applications, fluid mechanics, optimization, scheduling problems and engineering applications, as well as a keynote by Professor Ali Nayfeh.

In this thesis, novel Monte Carlo methods for precisely calculating the critical phenomena of the effectively frustrated quantum spin system are developed and applied to the critical phenomena of the spin-Peierls systems. Three significant methods are introduced for the first time: a new optimization algorithm of the Markov chain transition kernel based on the geometric weight-allocation approach, the extension of the worm (directed-loop) algorithm to nonconserved particles, and the combination with the level spectroscopy. Utilizing these methods, the phase diagram of the one-dimensional XXZ spin-Peierls system is elucidated. Furthermore, the multi-chain and two-dimensional spin-Peierls systems with interchain lattice interaction are investigated. The unbiased simulation shows that the interesting quantum phase transition between the 1D-like liquid phase and the macroscopically-degenerated dimer phase occurs on the fully-frustrated parameter line that separates the doubly-degenerated dimer phases in the two-dimensional phase diagram. The spin-phonon interaction in the spin-Peierls system introduces the spin frustration, which usually hinders the quantum Monte Carlo analysis, owing to the notorious negative sign problem. In this thesis, the author has succeeded in precisely calculating the critical phenomena of the effectively frustrated quantum spin system by means of the quantum Monte Carlo method without the negative sign.

This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.

The focus of this book is on establishing theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets. It proposes a series of innovative theories, models and methods such as the representation theorem and extension principle of intuitionistic fuzzy sets, ranking methods of intuitionistic fuzzy numbers, non-linear and linear programming methods for intuitionistic fuzzy multi-attribute decision making and (interval-valued) intuitionistic fuzzy matrix games. These theories and methods form the theory system of intuitionistic fuzzy decision making and games, which is not only remarkably different from those of the traditional, Bayes and/or fuzzy decision theory but can also provide an effective and efficient tool for solving complex management problems. Since there is a certain degree of inherent hesitancy in real-life management, which cannot always be described by the traditional mathematical methods and/or fuzzy set theory, this book offers an effective approach to using the intuitionistic fuzzy set expressed with membership and non-membership functions. This book is addressed to all those involved in theoretical research and practical applications from a variety of fields/disciplines: decision science, game theory, management science, fuzzy sets, operational research, applied mathematics, systems engineering, industrial engineering, economics, etc.

Leonardo wrote, “Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics�; replace “Mechanics� by “Fluid mechanics� and here we are. - From the Preface to the Second Edition Although the exponential growth of computer power has advanced the importance of simulations and visualization tools for elaborating new models, designs and technologies, the discipline of fluid mechanics is still large, and turbulence in flows remains a challenging problem in classical physics. Like its predecessor, the revised and expanded Second Edition of this book addresses the basic principles of fluid mechanics and solves fluid flow problems where viscous effects are the dominant physical phenomena. Much progress has occurred in the half a century that has passed since the edition of 1964. As predicted, aspects of hydrodynamics once considered offbeat have risen to importance. For example, the authors have worked on problems where variations in viscosity and surface tension cannot be ignored. The advent of nanotechnology has broadened interest in the hydrodynamics of thin films, and hydromagnetic effects and radiative heat transfer are routinely encountered in materials processing. This monograph develops the basic equations, in the three most important coordinate systems, in a way that makes it easy to incorporate these phenomena into the theory. The book originally described by Prof. Langlois as "a monograph on theoretical hydrodynamics, written in the language of applied mathematics" offers much new coverage including the second principle of thermodynamics, the Boussinesq approximation, time dependent flows, Marangoni convection, Kovasznay flow, plane periodic solutions, Hele-Shaw cells, Stokeslets, rotlets, finite element methods, Wannier flow, corner eddies, and analysis of the Stokes operator.

The book describes the science gateway building technology developed in the SCI-BUS European project and its adoption and customization method, by which user communities, such as biologists, chemists, and astrophysicists, can build customized, domain-specific science gateways. Many aspects of the core technology are explained in detail, including its workflow capability, job submission mechanism to various grids and clouds, and its data transfer mechanisms among several distributed infrastructures. The book will be useful for scientific researchers and IT professionals engaged in the development of science gateways.

This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.

This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.

This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.

A comprehensive introduction to the most commonly used statistical methods relevant in atmospheric, oceanic and climate sciences. Each method is described step-by-step using plain language, and illustrated with concrete examples, with relevant statistical and scientific concepts explained as needed. Particular attention is paid to nuances and pitfalls, with sufficient detail to enable the reader to write relevant code. Topics covered include hypothesis testing, time series analysis, linear regression, data assimilation, extreme value analysis, Principal Component Analysis, Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. The specific statistical challenges that arise in climate applications are also discussed, including model selection problems associated with Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. Requiring no previous background in statistics, this is a highly accessible textbook and reference for students and early-career researchers in the climate sciences.

Julia is an open-source and fast-growing programming language for scientific computing that offers clarity and ease of use for beginners but also speed and power for advanced applications. Fundamentals of Numerical Computation: Julia Edition provides a complete solution for teaching Julia in the context of numerical methods. It introduces the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. A clear progression from simple to more advanced methods allows for use in either a one-semester course or a two-semester sequence. The book includes more than 40 functions and 160 examples fully coded in Julia and available for download, online supplemental content including tested source materials for student projects and in-class labs related to every chapter, and over 600 exercises, evenly split between mathematical and computational work, and solutions to most exercises for instructors.

Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks.

Using an inquiry-based learning approach, "Numerical Analysis" is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases.

The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject.Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin

Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.

In scientific computing (also known as computational science), advanced computing capabilities are used to solve complex problems. This self-contained book describes and analyzes reported software failures related to the major topics within scientific computing: mathematical modeling of phenomena; numerical analysis (number representation, rounding, conditioning); mathematical aspects and complexity of algorithms, systems, or software; concurrent computing (parallelization, scheduling, synchronization); and numerical data (such as input of data and design of control logic). Readers will find lists of related, interesting bugs, MATLAB examples, and ""excursions"" that provide necessary background, as well as an in-depth analysis of various aspects of the selected bugs. Illustrative examples of numerical principles such as machine numbers, rounding errors, condition numbers, and complexity are also included. This book is intended for students, teachers, and researchers in scientific computing, computer science, and applied mathematics. It is also an entertaining and motivating introduction for those with a minimum background in mathematics or computer science. Bits and Bugs can be used for courses in numerical analysis, numerical methods in linear algebra/ODEs/PDEs, introductory software engineering, introductory scientific computing, and parallel programming.

This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008. Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture. Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples. Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume. This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.

Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.