-PDF Download- Decision Problems For Equational Theories Of Relation Algebras EBOOK

Decision Problems for Equational Theories of Relation Algebras

Author: H. Andréka

Publisher: American Mathematical Soc.

Published: 1997-01-01

Total Pages: 148

ISBN-13: 9780821863275

This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. The provide researchers in algebra and logc with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.

Decision Problems for Equational Theories of Relation Algebras

Author: H. Andréka

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 146

ISBN-13: 0821805959

DOWNLOAD EBOOK →

"We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural numbers has a decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract.

Decision Problems for Equational Theories of Semigroups and General Algebras

Author: Peter Graham Perkins

Publisher:

Published: 1966

Total Pages: 126

ISBN-13:

DOWNLOAD EBOOK →

Hodge Theory in the Sobolev Topology for the de Rham Complex

Author: Luigi Fontana

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 114

ISBN-13: 0821808303

DOWNLOAD EBOOK →

In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L2$ topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. It features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems; theorems completely explained and proved; and new geometric tools for differential analysis on domains and manifolds.

Model Theory and Linear Extreme Points in the Numerical Radius Unit Ball

Author: Michael A. Dritschel

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 77

ISBN-13: 0821806513

DOWNLOAD EBOOK →

This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented: a complete description of the linear extreme points of the non-matrix (numerical radius) unit ball; several equivalent characterizations of matricial extremals in the unit ball, that is, those members which do not allow a nontrivial extension remaining in the unit ball; and applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks.

Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras

Author: Michael David Weiner

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 121

ISBN-13: 0821808664

DOWNLOAD EBOOK →

Begins with the bosonic construction of four level -1/2 irreducible representations of the symplectic affine Kac-Moody Lie algebra Cl. The direct sum of two of these is given the structure of a vertex operator algebra (VOA), and the direct sum of the other two is given the structure of a twisted VOA-module. The dissertation includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type Dl. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Generalized Symplectic Geometries and the Index of Families of Elliptic Problems

Author: Liviu I. Nicolaescu

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 98

ISBN-13: 0821806211

DOWNLOAD EBOOK →

In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eigh symmetries in the real case and two in the complex case). This text will also be of interest to those working in geometry and topology.

Cutting Brownian Paths

Author: Richard F. Bass

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 113

ISBN-13: 0821809687

DOWNLOAD EBOOK →

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.

Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems

Author: Hasna Riahi

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 127

ISBN-13: 0821808737

DOWNLOAD EBOOK →

In this work, the author examines the following: When the Hamiltonian system $m i \ddot{q} i + (\partial V/\partial q i) (t,q) =0$ with periodicity condition $q(t+T) = q(t),\; \forall t \in \germ R$ (where $q {i} \in \germ R{\ell}$, $\ell \ge 3$, $1 \le i \le n$, $q = (q {1},...,q {n})$ and $V = \sum V {ij}(t,q {i}-q {j})$ with $V {ij}(t,\xi)$ $T$-periodic in $t$ and singular in $\xi$ at $\xi = 0$) is posed as a variational problem, the corresponding functional does not satisfy the Palais-Smale condition and this leads to the notion of critical points at infinity. This volume is a study of these critical points at infinity and of the topology of their stable and unstable manifolds. The potential considered here satisfies the strong force hypothesis which eliminates collision orbits. The details are given for 4-body type problems then generalized to n-body type problems.

Short-Time Geometry of Random Heat Kernels

Author: Richard Bucher Sowers

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 145

ISBN-13: 0821806491

DOWNLOAD EBOOK →

This volume studies the behaviour of a random heat kernel associated with a stochastic partial differential equation, and gives short-time expansion of this heat kernel. The author finds that the dominant exponential term is classical and depends only on the Riemannian distance function. The second exponential term is a work term and also has classical meaning. There is also a third non-negligible exponential term which blows up. The author finds an expression for this third exponential term which involves a random translation of the index form and the equations of Jacobi fields. In the process, he develops a method to approximate the heat kernel to any arbitrary degree of precision.