Download or read book Higher Initial Ideals of Homogeneous Ideals written by Gunnar Fløystad and published by American Mathematical Soc.. This book was released on 1998 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a homogeneous ideal I and a monomial order, the initials ideal in (I) can be formed. The initial idea gives information about I, but quite a lot of information is also lost. The author remedies this by defining a series of higher initial ideals of a homogenous ideal, and considers the case when I is the homogenous ideal of a curve in P3 and the monomial order is reverse lexicographic. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Integral Closure of Ideals Rings and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Download or read book Basic Almost Poised Hypergeometric Series written by Wenchang Chu and published by American Mathematical Soc.. This book was released on 1998 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a systematic treatment for the evaluation of basic almost poised series. Some 200 identities are covered, among which most are believed to be new. Their connections with the q-Clausen formulae as well as Rogers-Ramanujan identities are sketched. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension written by Guy David and published by American Mathematical Soc.. This book was released on 2000 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in calculus of variations and optimal control; optimization.
Download or read book Algebraic and Strong Splittings of Extensions of Banach Algebras written by William G. Bade and published by American Mathematical Soc.. This book was released on 1999 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors address the following: Let $A$ be a Banach algebra, and let $\sum\:\ 0\rightarrow I\rightarrow\frak A\overset\pi\to\longrightarrow A\rightarrow 0$ be an extension of $A$, where $\frak A$ is a Banach algebra and $I$ is a closed ideal in $\frak A$. The extension splits algebraically (respectively, splits strongly) if there is a homomorphism (respectively, continuous homomorphism) $\theta\: A\rightarrow\frak A$ such that $\pi\circ\theta$ is the identity on $A$. Consider first for which Banach algebras $A$ it is true that every extension of $A$ in a particular class of extensions splits, either algebraically or strongly, and second for which Banach algebras it is true that every extension of $A$ in a particular class which splits algebraically also splits strongly. These questions are closely related to the question when the algebra $\frak A$ has a (strong) Wedderburn decomposition. The main technique for resolving these questions involves the Banach cohomology group $\cal H2(A,E)$ for a Banach $A$-bimodule $E$, and related cohomology groups. Later chapters are particularly concerned with the case where the ideal $I$ is finite-dimensional. Results are obtained for many of the standard Banach algebras $A$.
Download or read book Invariants under Tori of Rings of Differential Operators and Related Topics written by Ian Malcolm Musson and published by American Mathematical Soc.. This book was released on 1998 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X) $ has properties very similar to those of enveloping algebras of semisimple Lie algebras. In this book, the authors show that this is indeed the case when $G$ is a torus and $X=k \times (k ) $. They give a precise description of the primitive ideals in $D(X) $ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X) $. The latter are of the form $B =D(X) /({\germ g}-\chi({\germ g}))$ where ${\germ g}= {\rm Lie}(G)$, $\chi\in {\germ g} ast$ and ${\germ g}-\chi({\germ g})$ is the set of all $v-\chi(v)$ with $v\in {\germ g}$. They occur as rings of twisted differential operators on toric varieties. It is also proven that if $G$ is a torus acting rationally on a smooth affine variety, then $D(X/\!/G)$ is a simple ring.
Download or read book Rational Homotopical Models and Uniqueness written by Martin Majewski and published by American Mathematical Soc.. This book was released on 2000 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie Tlgebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition we show the same for the cellular Lie algebra model which we build from the simplicial analog of the classical Adams-Hilton model. It turns out that this cellular Lie algebra model is one link in a chain of models connecting the models of Quillen and Sullivan.The key result which makes all this possible is Anick's correspondence between differential graded Lie algebras and Hopf algebras up to homotopy. In addition we show that the Quillen model is a rational homotopical equivalence, and we conclude the same for the other models using our main result. Theconstruction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.
Download or read book Hopf Algebras Polynomial Formal Groups and Raynaud Orders written by Lindsay Childs and published by American Mathematical Soc.. This book was released on 1998 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.
Download or read book Categories of Operator Modules Morita Equivalence and Projective Modules written by David P. Blecher and published by American Mathematical Soc.. This book was released on 2000 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: We employ recent advances in the theory of operator spaces, also known as quantized functional analysis, to provide a context in which one can compare categories of modules over operator algebras that are not necessarily self-adjoint. We focus our attention on the category of Hilbert modules over an operator algebra and on the category of operator modules over an operator algebra. The module operations are assumed to be completely bounded - usually, completely contractive. Wedevelop the notion of a Morita context between two operator algebras A and B. This is a system (A,B,{} {A}X {B},{} {B} Y {A},(\cdot,\cdot),[\cdot,\cdot]) consisting of the algebras, two bimodules {A}X {B and {B}Y {A} and pairings (\cdot,\cdot) and [\cdot,\cdot] that induce (complete) isomorphisms betweenthe (balanced) Haagerup tensor products, X \otimes {hB} {} Y and Y \otimes {hA} {} X, and the algebras, A and B, respectively. Thus, formally, a Morita context is the same as that which appears in pure ring theory. The subtleties of the theory lie in the interplay between the pure algebra and the operator space geometry. Our analysis leads to viable notions of projective operator modules and dual operator modules. We show that two C*-algebras are Morita equivalent in our sense if and only ifthey are C*-algebraically strong Morita equivalent, and moreover the equivalence bimodules are the same. The distinctive features of the non-self-adjoint theory are illuminated through a number of examples drawn from complex analysis and the theory of incidence algebras over topological partial orders.Finally, an appendix provides links to the literature that developed since this Memoir was accepted for publication.
Download or read book Differential Equations Methods for the Monge Kantorovich Mass Transfer Problem written by Lawrence C. Evans and published by American Mathematical Soc.. This book was released on 1999 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors demonstrate under some assumptions on $f $, $f $ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\mu{ }=f dx$ onto $\mu =f dy$ can be constructed by studying the $p$-Laplacian equation $- \roman{div}(\vert DU_p\vert p-2}Du_p)=f -f $ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1, -\roman{div}(aDu)=f -f $ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f $ and $f $
Download or read book Cutting Brownian Paths written by Richard F. Bass and published by American Mathematical Soc.. This book was released on 1999 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long open problem in probability theory has been the following: Can the graph of planar Brownian motion be split by a straight line? In this volume, the authors provide a solution, discuss related works, and present a number of open problems.
Download or read book Annihilating Fields of Standard Modules of mathfrak sl 2 mathbb C sim and Combinatorial Identities written by Arne Meurman and published by American Mathematical Soc.. This book was released on 1999 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde{\frak g}$, they construct the corresponding level $k$ vertex operator algebra and show that level $k$ highest weight $\tilde{\frak g}$-modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level $k$ standard modules and study the corresponding loop $\tilde{\frak g}$-module--the set of relations that defines standard modules. In the case when $\tilde{\frak g}$ is of type $A{(1)} 1$, they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of Rogers-Ramanujan type combinatorial identities.
Download or read book The Riemann Problem for the Transportation Equations in Gas Dynamics written by Wancheng Sheng and published by American Mathematical Soc.. This book was released on 1999 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which has been merely discussed so far. The generalized Rankine-Hugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically
Download or read book Non Additive Exact Functors and Tensor Induction for Mackey Functors written by Serge Bouc and published by American Mathematical Soc.. This book was released on 2000 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: First the author introduces a generalization of the notion of (right)-exact functor between abelian categories to the case of non-additive functors. The main result of this section is an extension theorem: any functor defined on a suitable subcategory can be extended uniquely to a right exact functor defined on the whole category. Next those results are used to define various functors of generalized tensor induction, associated to finite bisets, between categories attached to finite groups. This includes a definition of tensor induction for Mackey functors, for cohomological Mackey functors, for p-permutation modules and algebras. This also gives a single formalism of bisets for restriction, inflation, and ordinary tensor induction for modules.
Download or read book Caustics for Dissipative Semilinear Oscillations written by Jean-Luc Joly and published by American Mathematical Soc.. This book was released on 2000 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in partial differential equations.
Download or read book Inverses of Disjointness Preserving Operators written by Yuri A. Abramovich and published by American Mathematical Soc.. This book was released on 2000 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices
Download or read book Splitting Theorems for Certain Equivariant Spectra written by L. Gaunce Lewis and published by American Mathematical Soc.. This book was released on 2000 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in algebraic topology.
