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This book deals with the algebraic geometric method of studyingmultivariate splines. Topics treated include: the theory ofmultivariate spline spaces, higher-dimensional splines, rationalsplines, piecewise algebraic variety (including piecewise algebraiccurves and surfaces) and applications in the finite element method andcomputer-aided geometric design. Many new results are given.
Audience: This volume will be of interest to researchers andgraduate students whose work involves approximations and expansions,numerical analysis, computational geometry, image processing andCAD/CAM. ... Read more

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Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics.

This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.

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This book explores several aspects of discrete Hamiltoniansystems. It is unique in that it provides interconnections betweensymplectic systems, recessive and dominant solutions, various discreteRiccati equations, and continued fraction representations of solutionsof Riccati equations. It also presents variable step size discretevariational theory, a discrete Legendre transformation from discreteEuler-Lagrange equations to discrete Hamiltonian systems. Noveluse is made of the implicit function theorem to show the importance ofstep size in numerical solutions of Hamiltonian systems. An `a priori'step size criterion shows how one can avoid parasitic numericalsolutions. This book is accessible to students of mathematics,engineering, physics, chemistry and economics at the senior orbeginning graduate level who have completed a course in matrix theory.It provides foundation work for engineering students studying optimalcontrol and estimation as well as the variational problems arising inphysics, chemistry, and economics.
Audience: Mathematics, engineering and physics students who havehad a course in matrix theory. ... Read more

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The optimal continuation parameter provides the best conditions in a linearized system of equations at any moment of the continuation process. This is one of the first books in which the best parametrization is regarded systematically for a wide class of problems. It is of interest to scientists, specialists, and postgraduate students of applied and numerical mathematics and mechanics.

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This book collects survey and research papers on various topics in number theory. Although the topics and descriptive details appear varied, they are unified by two underlying principles: first, readability, and second, a smooth transition from traditional approaches to modern ones. Thus, on one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated.

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Computer vision and image analysis require interdisciplinary collaboration between mathematics and engineering. This book addresses the area of high-accuracy measurements of length, curvature, motion parameters and other geometrical quantities from acquired image data. It is a common problem that these measurements are incomplete or noisy, such that considerable efforts are necessary to regularise the data, to fill in missing information, and to judge the accuracy and reliability of these results. This monograph brings together contributions from researchers in computer vision, engineering and mathematics who are working in this area.

The book can be read both by specialists and graduate students in computer science, electrical engineering or mathematics who take an interest in data evaluations by approximation or interpolation, in particular data obtained in an image analysis context.

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This volume is dedicated to the late Professor Dragoslav S.Mitrinovic(1908-1995), one of the most accomplishedmasters in the domain of inequalities. Inequalities are to be foundeverywhere and play an important and significant role in almost allsubjects of mathematics as well as in other areas of sciences.Professor Mitrinovic used to say: `There are no equalities,even in human life inequalities are always encountered.'
This volume provides an extensive survey of the most current topics inalmost all subjects in the field of inequalities, written by 85outstanding scientists from twenty countries. Some of the papers werepresented at the International Memorial Conference dedicated toProfessor D.S. Mitrinovic, which was held at the University ofNis, June 20-22, 1996.
Audience: This book will be of great interest to researchers inreal, complex and functional analysis, special functions,approximation theory, numerical analysis and computation, and otherfields, as well as to graduate students requiring the most up-to-dateresults. ... Read more

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The notion of convex set, known according to its numerousapplications in linear spaces due to its connectivity which leads toseparation and support properties, does not imply, in fact,necessarily, the connectivity. This aspect of non-connectivity hiddenunder the convexity is discussed in this book. The property ofnon-preserving the connectivity leads to a huge extent of the domainof convexity. The book contains the classification of 100 notions ofconvexity, using a generalised convexity notion, which is theclassifier, ordering the domain of concepts of convex sets. Also, itopens the wide range of applications of convexity in non-connectedenvironment. Applications in pattern recognition, in discreteprogramming, with practical applications in pharmaco-economics arediscussed. Both the synthesis part and the applied part make the bookuseful for more levels of readers.Audience: Researchers dealing with convexity and related topics,young researchers at the beginning of their approach to convexity, PhDand master students. ... Read more

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Despite their novelty, wavelets have a tremendous impact on anumber of modern scientific disciplines, particularly on signal andimage analysis. Because of their powerful underlying mathematicaltheory, they offer exciting opportunities for the design of newmulti-resolution processing algorithms and effective patternrecognition systems.
This book provides a much-needed overview of current trends in thepractical application of wavelet theory. It combines cutting edgeresearch in the rapidly developing wavelet theory with ideas frompractical signal and image analysis fields. Subjects dealt withinclude balanced discussions on wavelet theory and its specificapplication in diverse fields, ranging from data compression toseismic equipment. In addition, the book offers insights into recentadvances in emerging topics such as double density DWT, multiscaleBayesian estimation, symmetry and locality in image representation,and image fusion.
Audience: This volume will be of interest to graduate studentsand researchers whose work involves acoustics, speech, signal andimage processing, approximations and expansions, Fourier analysis, andmedical imaging. ... Read more

Customer Reviews (1)

short review
This book tells us some application on Wavelet in a brand-new way.
But is is not go deep into. ... Read more

Product Description
This book is a systematic description of the variational theoryof splines in Hilbert spaces. All central aspects are discussed in thegeneral form: existence, uniqueness, characterization via reproducingmappings and kernels, convergence, error estimations, vector andtensor hybrids in splines, dimensional reducing (traces of splinesonto manifolds), etc. All considerations are illustrated by practicalexamples. In every case the numerical algorithms for the constructionof splines are demonstrated. ... Read more

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First monograph which considers the theory of more parameter dyadic and classical Hardy spaces. Useful for researchers as well as graduate or postgraduate students whose work involved Fourier analysis, probability theory, stochastic processes and complex variables. ... Read more

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This volume contains the latest developments in the use of iterative methods to block Toeplitz systems. These systems arise in a variety of applications in mathematics, scientific computing, and engineering, such as image processing, numerical differential equations and integral equations, time series analysis, and control theory. Iterative methods such as Krylov subspace methods and multigrid methods are proposed to solve block Toeplitz systems. One of the main advantages of these iterative methods is that the operation cost of solving a large class of mn × mn block Toeplitz systems only requires O (mn log mn) operations.

This book is the first book on Toeplitz iterative solvers and it includes recent research results. The author belongs to one of the most important groups in the field of structured matrix computation. The book is accessible to readers with a working knowledge of numerical linear algebra. It should be of interest to everyone who deals with block Toeplitz systems, numerical linear algebra, partial differential equations, ordinary differential equations, image processing, and approximation theory.

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Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? The present set of lecture notes contains seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions.

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This book is a collection of the various old and new results, centered around the following simple and beautiful observation of J.L. Walsh - If a function is analytic in a finite disc, and not in a larger disc, then the difference between the Lagrange interpolant of the function, at the roots of unity, and the partial sums of the Taylor series, about the origin, tends to zero in a larger disc than the radius of convergence of the Taylor series, while each of these operators converges only in the original disc.

This book will be particularly useful for researchers in approximation and interpolation theory.

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This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.

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A collection of articles on various aspects of q-series and special functions dedicated to Mizan Rahman. It also includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject.

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This volume presents a comprehensive compendium of classicaland new inequalities as well as some recent extensions to well-knownones.
Variations of inequalities ascribed to Abel, Jensen, Cauchy,Chebyshev, Hölder, Minkowski, Stefferson, Gram, Fejér,Jackson, Hardy, Littlewood, Po'lya, Schwarz, Hadamard and a host ofothers can be found in this volume. The more than 1200 citedreferences include many from the last ten years which appear in a bookfor the first time.
The 30 chapters are all devoted to inequalities associated with agiven classical inequality, or give methods for the derivation of newinequalities. Anyone interested in equalities, from student toprofessional, will find their favorite inequality and much more.
... Read more

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This book examines the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.

Customer Reviews (2)

excellent treatment of extremes including regular variation concept
When I was a graduate student at Stanford in the late 1970s Sid Resnick was an assistant professor there. I took a course in stochastic processes from him. His presentation was engaging and humorous as is his writing style. This is more readily appreciated in one of his other books "A Probability Path".
This is one of several good texts on the theory of extremes that came out in the 1980s. The book is rigorous and formal and deals primarily with the iid case (the exception is extremes of moving averages). It differs from the others in that it treats the relationship between extremes and record values.

Resnick also deals with a characterization of tail behavior called regular variation that is a very useful tool in developing some of the theory. Like Leadbetter et al. he uses the point process approach but he does not exploit its application to stationary processes the way they do.

In the 1980s Resnick went on to Colorado State University where he had a very fruitful collaboration with Richard Davis. That is where he was at teh time of this text and the results of their joint research is reflected in the text. It also includes material on multivariate extremes and extremal processes.

Currently Resnick is a professor of statistics and operations research at Cornell University. This was one of Resnick's early works and is now available in a less expensive paperback editon.

extreme values at their extremities
superbly written, lucid , clear text communicating fundamental concepts of basic stochastic processes, probability theory in a fashion, books designed for those subjects fall woefully short relative to resnick's exposition. extreme value theory is clearly presented in a fashion which makes it look easy! ... Read more

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This book is of interest to mathematicians, geologists, engineers and, in general, researchers and post graduate students involved in spline function theory, surface fitting problems or variational methods. From reviews: The book is well organized, and the English is very good. I recommend the book to researchers in approximation theory, and to anyone interested in bivariate data fitting." (L.L. Schumaker, Mathematical Reviews, 2005).

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This is a revision of an earlier Means and Their Inequalities by the present author and Professors Mitrinovic and Vasic. Not only does this book bring the earlier version up to date but enlarges the scope considerably to give a full and in-depth treatment of all aspects of the field. While the mention of means occurs in many books this is the only full treatment of the subject. Outstanding features of the book are the variety of proofs given for many of the basic results, over seventy for the inequality between the arithmetic and geometric means for instance, an exhaustive bibliography and a list of mathematicians who have contributed to this field from the time of Euclid to the present day.

Audience: This book is written in a language that not only the expert on the subject will understand and appreciate, but graduate students worldwide as well. Any person with an interest in means and their inequalities should find this book within their comprehension although to fully appreciate all the topics covered a knowledge of calculus and of elementary real analysis is required.

Customer Reviews (1)

Accessible for the serious professional
This book is just what I was looking for ... and so much more. Here is a complete and in-depth treatment of the subject of means. Chapter 2 ... on arithmetic, geometric, and harmonic means ... is the primary reason I purchased the book ... and I'm NOT disappointed. ... Read more