Homogeneous Integral Table Algebras Of Degree Three A Trilogy
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Homogeneous Integral Table Algebras Of Degree Three A Trilogy
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Author : Harvey I. Blau
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Homogeneous Integral Table Algebras Of Degree Three A Trilogy written by Harvey I. Blau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three. On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism oforder three. Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.
The Spectrum Of A Module Category
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Author : Henning Krause
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
The Spectrum Of A Module Category written by Henning Krause and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
These notes present an introduction into the spectrum of the category of modules over a ring. We discuss the general theory of pure-injective modules and concentrate on the isomorphism classes of indecomposable pure-injective modules which form the underlying set of this spectrum. The interplay between the spectrum and the category of finitely presented modules provides new insight into the geometrical and homological properties of the category of finitely presented modules. Various applications from representation theory of finite dimensional algebras are included.
Joint Hyponormality Of Toeplitz Pairs
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Author : Raúl E. Curto
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Joint Hyponormality Of Toeplitz Pairs written by Raúl E. Curto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This work explores joint hyponormality of Toeplitz pairs. Topics include: hyponormality of Toeplitz pairs with one co-ordinate a Toeplitz operator with analytic polynomial symbol; hyponormality of trigonometric Toeplitz pairs; and the gap between $2$-hyponormality and subnormality.
Layer Potentials The Hodge Laplacian And Global Boundary Problems In Nonsmooth Riemannian Manifolds
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Author : Dorina Mitrea
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Layer Potentials The Hodge Laplacian And Global Boundary Problems In Nonsmooth Riemannian Manifolds written by Dorina Mitrea and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds. In the first part (ss1-4), we develop a theory for Cauchy type operators on Lipschitz submanifolds of co dimension one (focused on boundedness properties and jump relations) and solve the $Lp$-Dirichlet problem, with $p$ close to $2$, for general second-order strongly elliptic systems. The solution is represented in the form of layer potentials and optimal non tangential maximal function estimates are established.This analysis is carried out under smoothness assumptions (for the coefficients of the operator, metric tensor and the underlying domain) which are in the nature of best possible. In the second part of the monograph, ss5-13, we further specialize this discussion to the case of Hodge Laplacian $\Delta: =-d\delta-\delta d$. This time, the goal is to identify all (pairs of) natural boundary conditions of Neumann type. Owing to the structural richness of the higher degree case we are considering, the theory developed here encompasses in a unitary fashion many basic PDE's of mathematical physics. Its scope extends to also cover Maxwell's equations, dealt with separately in s14. The main tools are those of PDE's and harmonic analysis, occasionally supplemented with some basic facts from algebraic topology and differential geometry.
Complexes Associated To Two Vectors And A Rectangular Matrix
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Author : Andrew R. Kustin
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Complexes Associated To Two Vectors And A Rectangular Matrix written by Andrew R. Kustin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for graduate student and research mathematicians interested in commutative rings and algebras.
Estimating The Error Of Numerical Solutions Of Systems Of Reaction Diffusion Equations
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Author : Donald J. Estep
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Estimating The Error Of Numerical Solutions Of Systems Of Reaction Diffusion Equations written by Donald J. Estep and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.
An Ergodic Ip Polynomial Szemeredi Theorem
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Author : Vitaly Bergelson
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
An Ergodic Ip Polynomial Szemeredi Theorem written by Vitaly Bergelson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The authors prove a polynomial multiple recurrence theorem for finitely many commuting measure preserving transformations of a probability space, extending a polynomial Szemerédi theorem appearing in [BL1]. The linear case is a consequence of an ergodic IP-Szemerédi theorem of Furstenberg and Katznelson ([FK2]). Several applications to the fine structure of recurrence in ergodic theory are given, some of which involve weakly mixing systems, for which we also prove a multiparameter weakly mixing polynomial ergodic theorem. The techniques and apparatus employed include a polynomialization of an IP structure theory developed in [FK2], an extension of Hindman's theorem due to Milliken and Taylor ([M], [T]), a polynomial version of the Hales-Jewett coloring theorem ([BL2]), and a theorem concerning limits of polynomially generated IP-systems of unitary operators ([BFM]).
Well Posedness Of The Cauchy Problem For N Times N Systems Of Conservation Laws
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Author : Alberto Bressan
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Well Posedness Of The Cauchy Problem For N Times N Systems Of Conservation Laws written by Alberto Bressan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for graduate students and researchers interested in the mathematical physics and PDE.
Control And Relaxation Over The Circle
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Author : Bruce Hughes
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Control And Relaxation Over The Circle written by Bruce Hughes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This work formulates and proves a geometric version of the fundamental theorem of algebraic K-theory which relates the K-theory of the Laurent polynomial extension of a ring to the K-theory of the ring. The geometric version relates the higher simple homotopy theory of the product of a finite complex and a circle with that of the complex. By using methods of controlled topology, we also obtain a geometric version of the fundamental theorem of lower algebraic K-theory. The main new innovation is a geometrically defined nil space.
Existence Of The Sectional Capacity
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Author : Robert Rumely
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Existence Of The Sectional Capacity written by Robert Rumely and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
In the case where the norms are induced by metrics on the fibres of ${\mathcal L}$, we establish the functoriality of the sectional capacity under base change, pullbacks by finite surjective morphisms, and products. We study the continuity of $S Gamma(\overline{\mathcal L})$ under variation of the metric and line bundle, and we apply this to show that the notion of $v$-adic sets in $X(\mathbb C v)$ of capacity $0$ is well-defined. Finally, we show that sectional capacities for arbitrary norms can be well-approximated using objects of finite type.