Moments, Positive Polynomials and Their Applications

Author: Jean-Bernard Lasserre

Publisher: World Scientific

ISBN: 1848164467

Category: Mathematics

Page: 384

View: 304

Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP) . This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials. In the second part, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal control, mathematical finance, multivariate integration, etc., and examples are provided for each particular application. Errata(s). Errata. Sample Chapter(s). Chapter 1: The Generalized Moment Problem (227 KB). Contents: Moments and Positive Polynomials: The Generalized Moment Problem; Positive Polynomials; Moments; Algorithms for Moment Problems; Applications: Global Optimization over Polynomials; Systems of Polynomial Equations; Applications in Probability; Markov Chains Applications; Application in Mathematical Finance; Application in Control; Convex Envelope and Representation of Convex Sets; Multivariate Integration; Min-Max Problems and Nash Equilibria; Bounds on Linear PDE. Readership: Postgraduates, academics and researchers in mathematical programming, control and optimization.

Introduction to Magnetohydrodynamics

Author: P. A. Davidson

Publisher: Cambridge University Press

ISBN: 1107160162

Category: Science

Page: 498

View: 1841

Comprehensive textbook prioritising physical ideas over mathematical detail. New material includes fusion plasma magnetohydrodynamics.

Numerical Linear Algebra

Author: Holger Wendland

Publisher: Cambridge University Press

ISBN: 1107147131

Category: Computers

Page: 418

View: 1510

This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.

Singularities: Formation, Structure and Propagation

Author: J. Eggers,M. A. Fontelos

Publisher: Cambridge University Press

ISBN: 1107098416

Category: Mathematics

Page: 460

View: 9789

Explores a wide range of singular phenomena. Provides mathematical tools for understanding them and highlights their common features.

Introduction to Risk Analysis

A Systematic Approach to Science-based Decision Making

Author: Daniel M. Byrd,C. Richard Cothern

Publisher: Rowman & Littlefield

ISBN: 0865876967

Category: Business & Economics

Page: 433

View: 2187

Written for safety and loss-control, environmental, and quality managers, this is the first comprehensive, integrated guide to developing a complete environmental risk analysis for regulated substances and processes. Unlike other books, Introduction to Risk Analysis looks at risk from a regulatory perspective, allowing both professionals in regulatory agencies concerned with risk including OSHA, EPA, USDA, DOT, FDA, and state environmental agencies and professionals in any agency-regulated industry to understand and implement the methods required for proper risk assessment. The authors examine risk and the structure of analysis. Emphasizing the predictive nature of risk, they discuss the quantitative nature of risk and explore quantitative-analysis topics, including data graphing, logarithmic thinking, risk estimating, and curve fitting. Chapters include discussions on functions, models, and uncertainties; the regulatory process; risk assessment; exposure; dosimetry; epidemiology; toxicology; risk characterization; comparative risk assessment; ecological risk assessment; risk management; and risk communication. Six in-depth case studies, an annotated bibliography, and more than 50 figures are also included."

Semidefinite Optimization and Convex Algebraic Geometry

Author: Grigoriy Blekherman,Pablo A. Parrilo,Rekha R. Thomas

Publisher: SIAM

ISBN: 1611972280

Category: Mathematics

Page: 476

View: 1852

An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.

Introduction to Interval Analysis

Author: Ramon E. Moore,R. Baker Kearfott,Michael J. Cloud

Publisher: SIAM

ISBN: 089871771X

Category: Interval analysis (Mathematics)

Page: 223

View: 3440

An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.

Introduction to Information Retrieval

Author: Christopher D. Manning,Prabhakar Raghavan,Hinrich Schütze

Publisher: Cambridge University Press

ISBN: 1139472100

Category: Computers

Page: N.A

View: 4312

Class-tested and coherent, this textbook teaches classical and web information retrieval, including web search and the related areas of text classification and text clustering from basic concepts. It gives an up-to-date treatment of all aspects of the design and implementation of systems for gathering, indexing, and searching documents; methods for evaluating systems; and an introduction to the use of machine learning methods on text collections. All the important ideas are explained using examples and figures, making it perfect for introductory courses in information retrieval for advanced undergraduates and graduate students in computer science. Based on feedback from extensive classroom experience, the book has been carefully structured in order to make teaching more natural and effective. Slides and additional exercises (with solutions for lecturers) are also available through the book's supporting website to help course instructors prepare their lectures.

Representations and Invariants of the Classical Groups

Author: Roe Goodman,Nolan R. Wallach

Publisher: Cambridge University Press

ISBN: 9780521663489

Category: Mathematics

Page: 703

View: 8930

Presents an updated version of Weyl's invariant theory of the classical groups, together with many of the important recent developments.

Positive Polynomials and Sums of Squares

Author: Murray Marshall

Publisher: American Mathematical Soc.

ISBN: 0821844024

Category: Mathematics

Page: 187

View: 2271

"This book provides an elementary introduction to positive polynomials and sums of squares, the relationship to the moment problem, and the application to polynomial optimization. The focus is on the exciting new developments that have taken place in the last 15 years, arising out of Schmudgen's solution to the moment problem in the compact case in 1991. The book is accessible to a well-motivated student at the beginning graduate level. The objects being dealt with are concrete and down-to-earth, namely polynomials in n variables with real coefficients, and many examples are included. Proofs are presented as clearly and as simply as possible. Various new, simpler proofs appear in the book for the first time. Abstraction is employed only when it serves a useful purpose, but, at the same time, enough abstraction is included to allow the reader easy access to the literature. The book should be essential reading for any beginning student in the area."--BOOK JACKET.

Introduction to Applied Linear Algebra

Vectors, Matrices, and Least Squares

Author: Stephen Boyd,Lieven Vandenberghe

Publisher: Cambridge University Press

ISBN: 1316518965

Category: Business & Economics

Page: 500

View: 8990

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

How to Count

An Introduction to Combinatorics, Second Edition

Author: R.B.J.T. Allenby,Alan Slomson

Publisher: CRC Press

ISBN: 1420082612

Category: Mathematics

Page: 444

View: 1761

Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.

High-Dimensional Probability

An Introduction with Applications in Data Science

Author: Roman Vershynin

Publisher: Cambridge University Press

ISBN: 1108415199

Category: Business & Economics

Page: 296

View: 7910

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Ideals and Reality

Projective Modules and Number of Generators of Ideals

Author: Friedrich Ischebeck,Ravi A. Rao

Publisher: Springer Science & Business Media

ISBN: 3540263705

Category: Mathematics

Page: 336

View: 4973

Besides giving an introduction to Commutative Algebra - the theory of c- mutative rings - this book is devoted to the study of projective modules and the minimal number of generators of modules and ideals. The notion of a module over a ring R is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules possessing a basis are called free. So a finitely generated free R-module is of the form Rn for some n E IN, equipped with the usual operations. A module is called p- jective, iff it is a direct summand of a free one. Especially a finitely generated R-module P is projective iff there is an R-module Q with P @ Q S Rn for some n. Remarkably enough there do exist nonfree projective modules. Even there are nonfree P such that P @ Rm S Rn for some m and n. Modules P having the latter property are called stably free. On the other hand there are many rings, all of whose projective modules are free, e. g. local rings and principal ideal domains. (A commutative ring is called local iff it has exactly one maximal ideal. ) For two decades it was a challenging problem whether every projective module over the polynomial ring k[X1,. . .

Introduction to Probability

Author: Charles Miller Grinstead,James Laurie Snell

Publisher: American Mathematical Soc.

ISBN: 0821894145

Category: Probabilities

Page: 510

View: 861

This text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject. The text is also recommended for use in discrete probability courses. The material is organized so that the discrete and continuous probability discussions are presented in a separate, but parallel, manner. This organization does not emphasize an overly rigorous or formal view of probability and therefore offers some strong pedagogical value. Hence, the discrete discussions can sometimes serve to motivate the more abstract continuous probability discussions. Features: Key ideas are developed in a somewhat leisurely style, providing a variety of interesting applications to probability and showing some nonintuitive ideas. Over 600 exercises provide the opportunity for practicing skills and developing a sound understanding of ideas. Numerous historical comments deal with the development of discrete probability. The text includes many computer programs that illustrate the algorithms or the methods of computation for important problems. The book is a beautiful introduction to probability theory at the beginning level. The book contains a lot of examples and an easy development of theory without any sacrifice of rigor, keeping the abstraction to a minimal level. It is indeed a valuable addition to the study of probability theory. --Zentralblatt MATH

Convex Optimization

Author: Stephen P. Boyd,Lieven Vandenberghe

Publisher: Cambridge University Press

ISBN: 9780521833783

Category: Business & Economics

Page: 716

View: 3373

A comprehensive introduction to the tools, techniques and applications of convex optimization.

Mathematical Biology

Author: James D. Murray

Publisher: Springer Science & Business Media

ISBN: 3662085429

Category: Mathematics

Page: 770

View: 6683

Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.

The Student's Introduction to MATHEMATICA ®

A Handbook for Precalculus, Calculus, and Linear Algebra

Author: Bruce F. Torrence,Eve A. Torrence

Publisher: Cambridge University Press

ISBN: 1139473735

Category: Computers

Page: N.A

View: 2420

The unique feature of this compact student's introduction is that it presents concepts in an order that closely follows a standard mathematics curriculum, rather than structure the book along features of the software. As a result, the book provides a brief introduction to those aspects of the Mathematica software program most useful to students. The second edition of this well loved book is completely rewritten for Mathematica 6 including coverage of the new dynamic interface elements, several hundred exercises and a new chapter on programming. This book can be used in a variety of courses, from precalculus to linear algebra. Used as a supplementary text it will aid in bridging the gap between the mathematics in the course and Mathematica. In addition to its course use, this book will serve as an excellent tutorial for those wishing to learn Mathematica and brush up on their mathematics at the same time.


A Practical Introduction to Programming and Problem Solving

Author: Stormy Attaway

Publisher: Butterworth-Heinemann

ISBN: 0124058930

Category: Computers

Page: 560

View: 344

MatLab, Third Edition is the only book that gives a full introduction to programming in MATLAB combined with an explanation of the software’s powerful functions, enabling engineers to fully exploit its extensive capabilities in solving engineering problems. The book provides a systematic, step-by-step approach, building on concepts throughout the text, facilitating easier learning. Sections on common pitfalls and programming guidelines direct students towards best practice. The book is organized into 14 chapters, starting with programming concepts such as variables, assignments, input/output, and selection statements; moves onto loops; and then solves problems using both the ‘programming concept’ and the ‘power of MATLAB’ side-by-side. In-depth coverage is given to input/output, a topic that is fundamental to many engineering applications. Vectorized Code has been made into its own chapter, in order to emphasize the importance of using MATLAB efficiently. There are also expanded examples on low-level file input functions, Graphical User Interfaces, and use of MATLAB Version R2012b; modified and new end-of-chapter exercises; improved labeling of plots; and improved standards for variable names and documentation. This book will be a valuable resource for engineers learning to program and model in MATLAB, as well as for undergraduates in engineering and science taking a course that uses (or recommends) MATLAB. Presents programming concepts and MATLAB built-in functions side-by-side Systematic, step-by-step approach, building on concepts throughout the book, facilitating easier learning Sections on common pitfalls and programming guidelines direct students towards best practice