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Faber Systems And Their Use In Sampling Discrepancy Numerical Integration
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Book Synopsis Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration by : Hans Triebel
Download or read book Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration written by Hans Triebel and published by European Mathematical Society. This book was released on 2012 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the author's book, ``Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration'' (EMS, 2010), from unweighted spaces (preferably in cubes) to weighted spaces. The obtained assertions are used to study sampling and numerical integration in weighted spaces on the real line and weighted spaces with dominating mixed smoothness in the plane. A short chapter deals with the discrepancy for spaces on intervals.
Book Synopsis Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration by : Hans Triebel
Download or read book Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration written by Hans Triebel and published by European Mathematical Society. This book was released on 2010 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first chapters of this book deal with Haar bases, Faber bases and some spline bases for function spaces in Euclidean $n$-space and $n$-cubes. These are used in the subsequent chapters to study sampling and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity. This book is addressed to graduate students and mathematicians who have a working knowledge of basic elements of function spaces and approximation theory and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy).
Book Synopsis Hyperbolic Cross Approximation by : Dinh Dũng
Download or read book Hyperbolic Cross Approximation written by Dinh Dũng and published by Springer. This book was released on 2018-11-02 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic survey of classical and recent results on hyperbolic cross approximation. Motivated by numerous applications, the last two decades have seen great success in studying multivariate approximation. Multivariate problems have proven to be considerably more difficult than their univariate counterparts, and recent findings have established that multivariate mixed smoothness classes play a fundamental role in high-dimensional approximation. The book presents essential findings on and discussions of linear and nonlinear approximations of the mixed smoothness classes. Many of the important open problems explored here will provide both students and professionals with inspirations for further research.
Book Synopsis Theory of Besov Spaces by : Yoshihiro Sawano
Download or read book Theory of Besov Spaces written by Yoshihiro Sawano and published by Springer. This book was released on 2018-11-04 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.
Book Synopsis A Course on Elation Quadrangles by : Koen Thas
Download or read book A Course on Elation Quadrangles written by Koen Thas and published by European Mathematical Society. This book was released on 2012 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of elation generalized quadrangle is a natural generalization to the theory of generalized quadrangles of the important notion of translation planes in the theory of projective planes. Almost any known class of finite generalized quadrangles can be constructed from a suitable class of elation quadrangles. In this book the author considers several aspects of the theory of elation generalized quadrangles. Special attention is given to local Moufang conditions on the foundational level, exploring, for instance, Knarr's question from the 1990s concerning the very notion of elation quadrangles. All the known results on Kantor's prime power conjecture for finite elation quadrangles are gathered, some of them published here for the first time. The structural theory of elation quadrangles and their groups is heavily emphasized. Other related topics, such as $p$-modular cohomology, Heisenberg groups, and existence problems for certain translation nets, are briefly touched. This book starts from scratch and is essentially self-contained. Many alternative proofs are given for known theorems. This course contains dozens of exercises at various levels, from very easy to rather difficult, and will stimulate undergraduate and graduate students to enter the fascinating and rich world of elation quadrangles. More accomplished mathematicians will find the final chapters especially challenging.
Book Synopsis Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration by : Hans Triebel
Download or read book Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration written by Hans Triebel and published by . This book was released on with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the author's book Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration (EMS, 2010) from unweighted spaces (preferably in cubes) to weighted spaces. The obtained assertions are used to study sampling and numerical integration in weighted spaces on the real line and weighted spaces with dominating mixed smoothness in the plane. A short chapter deals with the discrepancy for spaces on intervals. The book is addressed to graduate students and mathematicians having a working knowledge of basic elements of function spaces and approximation theory.
Book Synopsis Theory of Function Spaces IV by : Hans Triebel
Download or read book Theory of Function Spaces IV written by Hans Triebel and published by Springer Nature. This book was released on 2020-01-23 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the continuation of the "Theory of Function Spaces" trilogy, published by the same author in this series and now part of classic literature in the area of function spaces. It can be regarded as a supplement to these volumes and as an accompanying book to the textbook by D.D. Haroske and the author "Distributions, Sobolev spaces, elliptic equations".
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Street-Fighting Mathematics by : Sanjoy Mahajan
Download or read book Street-Fighting Mathematics written by Sanjoy Mahajan and published by MIT Press. This book was released on 2010-03-05 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
Book Synopsis Function Spaces with Dominating Mixed Smoothness by : Hans Triebel
Download or read book Function Spaces with Dominating Mixed Smoothness written by Hans Triebel and published by . This book was released on 2019 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book is devoted to function spaces in Euclidean $n$-space with dominating mixed smoothness. Some new properties are derived and applied in the second part where weighted spaces with dominating mixed smoothness in arbitrary bounded domains in Euclidean $n$-space are introduced and studied. This includes wavelet frames, numerical integration and discrepancy, measuring the deviation of sets of points from uniformity. These notes are addressed to graduate students and mathematicians having a working knowledge of basic elements of the theory of function spaces, especially of Besov-Sobolev type. In particular, it will be of interest for researchers dealing with approximation theory, numerical integration and discrepancy.
Book Synopsis Cohen-Macaulay Representations by : Graham J. Leuschke
Download or read book Cohen-Macaulay Representations written by Graham J. Leuschke and published by American Mathematical Soc.. This book was released on 2012-05-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Auslander-Buchweitz's MCM approximation theory, and a careful treatment of nonzero characteristic. The remaining seven chapters present results on bounded and countable CM type and on the representation theory of totally reflexive modules.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Thermal and Mechanical Behavior of Metal Matrix and Ceramic Matrix Composites by : John M. Kennedy
Download or read book Thermal and Mechanical Behavior of Metal Matrix and Ceramic Matrix Composites written by John M. Kennedy and published by ASTM International. This book was released on 1990 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of interest to researchers and practitioners in materials science, especially in the aerospace industry, 16 papers from a symposium in Atlanta, Georgia, November 1988 discuss the analysis, modeling, and behavior of both continuous and discontinuous ceramic and metal matrix composites, and methods of
Download or read book Physics Briefs written by and published by . This book was released on 1991 with total page 1328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics, Supplement III by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics, Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Download or read book The Engineer written by and published by . This book was released on 1877 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Principles of Numerical Analysis by : Alston S. Householder
Download or read book Principles of Numerical Analysis written by Alston S. Householder and published by Courier Corporation. This book was released on 2006-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer science rests upon the building blocks of numerical analysis. This concise treatment by an expert covers the essentials of the solution of finite systems of linear and nonlinear equations as well as the approximate representation of functions. A final section provides 54 problems, subdivided according to chapter. 1953 edition.
