Series: Applied and Numerical Harmonic Analysis
1st Edition., 2010, Approx. 265 p. 30 illus., Hardcover
ISBN: 978-0-8176-4979-1
Due: May 28, 2010
Collected topics represent a wide foundation of applied mathematical tools not often found together in one book
Interdisciplinary approach provides students the mathematical tools required for studying computational topics in engineering and physics
Contains over 150 exercises
Presents a smooth introduction to the idea of the mathematical proof
For a wide audience, including graduate students, researchers, and practitioners in mathematics, physics, and engineering
This graduate-level textbook presents a detailed exposition of key mathematical tools in analysis, which will appeal to students and professionals across science and engineering. Every topic covered has been specifically chosen because it plays a role outside the field of pure mathematics, so although the treatment of each is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are quite useful when exploring the computational areas of physics and engineering. A central theme of the textbook is the structure of various vector spaces (most importantly, Hilbert spaces) and expansions of elements in these spaces in terms of bases. Particular attention is given to the space of square-integrable functions, L2(R).
As a textbook that provides a deep understanding of central issues in mathematical analysis, Functions, Spaces, and Expansions is intended for graduate students, researchers, and practitioners in applied mathematics, physics, and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. They should also be familiar with the basic concepts of calculus and real analysis, including Riemann integrals and the infinite series of real or complex numbers.
Preface.- Prologue.- Mathematical Background.- Normed Vector Spaces.- Banach Spaces.- Hilbert Spaces.- The L^p-spaces.- The Hilbert Space L^2.- The Fourier Transform.- An Introduction to Wavelet Analysis.- A Closer Look on Multiresolution Analysis.- B-splines.- Special Functions.- Appendix.- List of Symbols.- References.- Index.
Collection: Mathematiques et Applications, Vol. 67
1st Edition., 2010, XX, 530 p., Broche
ISBN: 978-3-642-11471-7
Due: March 2010
Il est souvent necessaire de realiser des experiences afin de modeliser le comportement d’un phenomene complexe. La methode des plans d’experience a pour objectif d’obtenir un maximum d’information sur le phenomene etudie en un minimum d’experiences. Ceci est primordial si l’objectif est un gain de temps ou de qualite. Cet ouvrage detaille les fondements theoriques de la methode mathematique des plans d’experience. Ceci est aborde tout au long des quatre parties suivantes. Presentation generale de la methode et des outils mathematiques. Plans d’experience pour facteurs quantitatifs : modele d’ordre un, modele a effets d’interactions, surface de reponse, modele a effets de blocs et modele pour melanges. Plans d’experience pour facteurs qualitatifs : modele additif, modele a effets d’interactions et modele a effets de blocs. Efficacite et optimalite : optimalite uniforme, A, D et E-efficacite, generalisation a la notion de Fq-efficacite, optimalite universelle. De nombreux exemples sont utilises afin d’illustrer les diverses techniques presentees. Les demonstrations mathematiques de la plupart des resultats enonces figurent en annexe.
When a complex phenomenon is studied it is common to run experiments in order to fit a model. In such situations experimental designs can be used to find a maximum of information in a minimum of trials. This is of prime importance when the goal is to save time or improve quality. This book is structured in four parts: a general presentation of the method and mathematical background, experimental designs for
quantitative factors, experimental designs for qualitative factors, and optimality of experimental designs. Numerous examples are introduced in order to illustrate the applications and mathematical proofs for most of the results are given in appendices.
2010, Approx. 200 p., Softcover
ISBN: 978-3-0346-0476-5
Due: April 2010
Estimates of weak solutions to the transmission problem for linear elliptic equations with minimal smooth coefficients in n-dimensional conic domains
Investigation of weak solutions for general divergence quasi-linear elliptic second-order equations in n-dimensional conic domains or in domains with edges
The goal of this book is to investigate the behaviour of weak solutions to the elliptic transmisssion problem in a neighborhood of boundary singularities: angular and conic points or edges. We consider this problem both for linear and quasi-linear (till now very little studied) equations.
Chapter 1 is of auxiliary character. Chapter 2 deals with the eigenvalue problem for the m-Laplace-Beltrami operator. By the variational principle we prove a new integro-differential Friedrichs-Wirtinger type inequality. This inequality is a basis for the obtaining of precise exponents of the decreasing rate of the solution near boundary singularities. Chapter 3 deals with the investigation of the transmission problem for linear elliptic second order equations in the domains with boundary conic point. Chapter 4 is devoted to the transmission problem in conic domains with N different media for an equation with the Laplace operator in the principal part. Chapters 5, 6 and 7 deal with the investigation of the transmission problem for quasi-linear elliptic second order equations in the domains with boundary conic point or with an edge at the boundary of a domain.
Preface.- Introduction.- 1 Preliminaries.- 2 Eigenvalue problem and integro-differential inequalities.- 3 Best possible estimates of solutions to the transmission problem for linear elliptic divergence second order equations in a conical domain.- 4 Transmission problem for the Laplace operator with N different media.- 5 Transmission problem for weak quasi-linear elliptic equations in a conical domain.- 6 Transmission problem for strong quasi-linear elliptic equations in a conical domain.- 7 Best possible estimates of solutions to the transmission problem for a quasi-linear elliptic divergence second order equation in a domain with a boundary edge.- Bibliography.- Index.- Notation Index.
Series: Statistics and Computing
1st Edition., 2010, XXII, 542 p., Hardcover
ISBN: 978-1-4419-1317-3
Due: March 29, 2010
Read data from various types of text files and Stata data sets
Manage your data through transformations, recodes, and combining data sets from both the add-cases and add-variables approaches and restructuring data from wide to long formats and vice versa
Create publication quality graphs including bar, histogram, pie, line, scatter, regression, box, error bar, and interaction plots
Perform the basic types of analyses to measure strength of association and group differences and be able to know where to turn to cover much more complex methods
Stata is the most flexible and extensible data analysis package available from a commercial vendor. R is a similarly flexible free and open source package for data analysis, with over 3,000 add-on packages available. This book shows you how to extend the power of Stata through the use of R. It introduces R using Stata terminology with which you are already familiar. It steps through more than 30 programs written in both languages, comparing and contrasting the two packages' different approaches. When finished, you will be able to use R in conjunction with Stata, or separately, to import data, manage and transform it, create publication quality graphics, and perform basic statistical analyses.
A glossary defines over 50 R terms using Stata jargon and again using more formal R terminology. The table of contents and index allow you to find equivalent R functions by looking up Stata commands and vice versa. The example programs and practice datasets for both R and Stata are available for download.
Introduction.- Installing and Updating R.- Running R.- Help and Documentation.- Programming Language Basics.- Data Acquisition.- Selecting Variables.- Selecting Observations.- Selecting Variables and Observations.- Data Management.- Enhancing Your Output.- Generating Data.- Managing Your Files and Workspace.- Graphics Overview.- Traditional Graphics.- Graphics with ggplot2.- Statistics.- Conclusion.
Series: Lecture Notes in Mathematics, Vol. 1992
1st Edition., 2010, XII, 260 p., Softcover
ISBN: 978-3-642-11921-7
Due: April 2010
Unites the pseudodifferential calculus, the global and the semiclassical ones
Utilizes powerful, flexible techniques
Gathers results formerly scattered throughout the literature
This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
Series: Probability and its Applications
1st Edition., 2010, 216 p., Hardcover
ISBN: 978-3-642-11193-8
Due: May 2, 2010
First book to our knowledge that solely treats the Poisson-Dirichlet distribution.
Focuses also on recent progresses in evolutionary dynamics and asymptotic behaviors.
The Poisson-Dirichlet distribution is an infinite dimensional probability
distribution. It was introduced by Kingman over thirty years ago, and has
found applications in a broad range of areas including Bayesian statistics,
combinatorics, differential geometry, economics, number theory, physics,
and population genetics. This monograph provides a comprehensive study
of this distribution and some related topics, with particular emphasis
on recent progresses in evolutionary dynamics and asymptotic behaviors.
One central scheme is the unification of the Poisson-Dirichlet distribution,
the urn structure, the coalescent, the evolutionary dynamics through the
grand particle system of Donnelly and Kurtz. It is largely self-contained.
The methods and techniques used in it appeal to researchers in a wide variety
of subjects.