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Ellipsoidal Calculus for Estimation and Control (Systems & Control: Foundations & Applications)

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Ellipsoidal Calculus for Estimation and Control (Systems & Control: Foundations & Applications) Overviews

Gives an account of an ellipsoidal calculus and ellipsoidal techniques, developed by the authors, that allows presentation of the set-valued solutions to these problems in terms of approximating ellipsoidal-valued functions. DLC: Control theory - Data processing.

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Integrability: The Seiberg-Witten and Witham Equations

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This volume presents selected papers on Integrability: the Seiberg-Witten and Whitham Equations and reviews the general algebro-geometric and geometric structures underlying integrability and aims to clarify the appearance of integrable structures in Seiberg-Witten theory.

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Bernoulli Free-Boundary Problems (Memoirs of the American Mathematical Society)

Bernoulli Free-Boundary Problems (Memoirs of the American Mathematical Society) Review










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When a domain in the plane is specified by the requirement that there exists a harmonic function which is zero on its boundary and additionally satisfies a prescribed Neumann condition there, the boundary is called a Bernoulli free boundary. (The boundary is 'free' because the domain is not known a priori and the name Bernoulli was originally associated with such problems in hydrodynamics.) Questions of existence, multiplicity or uniqueness, and regularity of free boundaries for prescribed data need to be addressed and their solutions lead to nonlinear problems.In this paper an equivalence is established between Bernoulli free-boundary problems and a class of equations for real-valued functions of one real variable. The authors impose no restriction on the amplitudes or shapes of free boundaries, nor on their smoothness. Therefore the equivalence is global, and valid even for very weak solutions. An essential observation here is that the equivalent equations can be written as nonlinear Riemann-Hilbert problems and the theory of complex Hardy spaces in the unit disc has a central role. An additional useful fact is that they have gradient structure, their solutions being critical points of a natural Lagrangian. This means that a canonical Morse index can be assigned to free boundaries and the Calculus of Variations becomes available as a tool for the study. Some rather natural conjectures about the regularity of free boundaries remain unresolved.

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Self-Similarity and Multiwavelets in Higher Dimensions (Memoirs of the American Mathematical Society)

Self-Similarity and Multiwavelets in Higher Dimensions (Memoirs of the American Mathematical Society) Review










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Let $A$ be a dilation matrix, an$n \times n$ expansive matrix that maps a full-rank lattice $\Gamma \subset \R^n$ into itself. Let $\Lambda$ be a finite subset of$\Gamma$, and for $k \in \Lambda$ let $c_k$ be $r \times r$ complex matrices. The refinement equation corresponding to $A$,$\Gamma$, $\Lambda$, and $c = \set{c_k}_{k \in \Lambda}$ is $f(x) = \sum_{k \in \Lambda} c_k \, f(Ax-k)$. A solution $f \colon \R^n \to \C^r$, if one exists, is called a refinable vector function or a vector scaling function of multiplicity $r$. In this manuscript we characterize the existence of compactly supported $L^p$ or continuous solutions of the refinement equation, in terms of the $p$-norm joint spectral radius of a finite set of finite matrices determined by the coefficients $c_k$.We obtain sufficient conditions for the $L^p$ convergence ( \le p \le \infty$) of the Cascade Algorithm $f^{(i+1)}(x) = \sum_{k \in \Lambda} c_k \, f^{(i)}(Ax-k)$, and necessary conditions for the uniform convergence of the Cascade Algorithm to a continuous solution. We also characterize those compactly supported vector scaling functions which give rise to a multiresolution analysis for $L^2(\R^n)$ of multiplicity $r$, and provide conditions under which there exist corresponding multiwavelets whose dilations and translations form an orthonormal basis for $L^2(\R^n)$.

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Banach Spaces for Analysts (Cambridge Studies in Advanced Mathematics)

Banach Spaces for Analysts (Cambridge Studies in Advanced Mathematics) Review




This book is a very readable introduction to the main techniques in functional analysis. It is worth reading, not only for a researcher in Banach space theory, but also for anyone working in mathematical analysis or anyother field of mathematics. Its content overlaps with some other recent and classical books, such as "Topics in Banach space theory" by Albiac and Kalton and "A short course in classical Banach spaces" by Carothers.



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This is an introduction to modern Banach space theory, in which applications to other areas such as harmonic analysis, function theory, orthogonal series, and approximation theory are also given prominence. The author begins with a discussion of weak topologies, weak compactness, and isomorphisms of Banach spaces before proceeding to the more detailed study of particular spaces. The book is intended to be used with graduate courses in Banach space theory, so the prerequisites are a background in functional, complex, and real analysis. As the only introduction to the modern theory of Banach spaces, it will be an essential companion for professional mathematicians working in the subject, or to those interested in applying it to other areas of analysis.

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An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics)

An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics) Review










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The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.

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Difference Methods for Singular Perturbation Problems (Monographs and Surveys in Pure and Applied Math)

Difference Methods for Singular Perturbation Problems (Monographs and Surveys in Pure and Applied Math) Review










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  Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods.

The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. The authors develop a technique for constructing and justifying ε uniformly convergent difference schemes for boundary value problems with fewer restrictions on the problem data.

Containing information published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter. This part also studies both the solution and its derivatives with errors that are independent of the perturbation parameters.

Co-authored by the creator of the Shishkin mesh, this book presents a systematic, detailed development of approaches to construct ε uniformly convergent finite difference schemes for broad classes of singularly perturbed boundary value problems.

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Cracking the AP Calculus AB & BC Exams, 2010 Edition (College Test Preparation)

Cracking the AP Calculus AB & BC Exams, 2010 Edition (College Test Preparation) Review




Princeton Review's powerful AP Exam guides are many and are top picks for any reference library. They've updated some 17 guides to Advanced Placement tests and offer high school students fine study courses that include two full-length practice tests and reviews of the subject matter on the test. From BIOLOGY and CALCULUS AB AND BC to PSYCHOLOGY and STATISTICS and more, these are comprehensive guides not to be missed.



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If you are preparing for the AP Calculus AB or BC exam, you’ll find all the techniques and information you need in this guide. Cracking the AP Calculus AB & BC Exams, 2010 Edition comes from the test-prep experts at The Princeton Review, and it includes:

•5 full-length AP Calculus practice tests — 3 for Calculus AB and 2 for Calculus BC
•Comprehensive subject review covering the essential test topics: derivatives, logarithmic functions, integrals, and more
•Numerous problem sets for practice and review
•Detailed explanations for answers to all AP Calculus practice and test questions
•List of critical Calculus formulas and prerequisite math

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fast shipping and book is in good condition - X. Hu - Seattle, WA USA
Shipping is fast!! and the book is in very good condition, just like it described. Very good service!


Perfect - Riley Jones - Boulder, CO USA
This guide is easy to read and perfectly tailored for the AP exams. I hated my actual textbook because it was so verbose.
This has simple straightforward explanations, no messing around. All material is covered plus practice exams.
It helped me get a 5 on the AB test. Need I say more?





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