Download or read book The Structure of K CS Transitive Cycle Free Partial Orders written by Richard Warren and published by American Mathematical Society(RI). This book was released on 2014-09-11 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text defines the class of cycle-free partial orders (CFPOs) and gives detailed analysis of the CFPOs fulfilling a natural transitivity assumption, called k-connected set transitivity (k-CS-transitivity). Classification in many cases is given. This work generalizes Droste's classification of the countable k-transitive trees (k>1). In a CFPO, the structure can branch downwards as well as upwards and can do so repeatedly (though it never returns to the starting point by a cycle). Mostly it is assumed that k>2 and that all maximal chains are finite. The main classification splits into the sporadic and skeletal cases. The former is complete in all cardinalities. The latter is performed only in the countable case. The classification is considerably more complicated than for trees and skeletal CFPOs exhibit elaborate and rather surprising behaviour.
Download or read book The Structure of k CS Transitive Cycle Free Partial Orders written by Richard Warren and published by American Mathematical Soc.. This book was released on 1997 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of cycle-free partial orders (CFPOs) is defined, and the CFPOs fulfilling a natural transitivity assumption, called k-connected set transitivity (k-CS-transitivity), are analysed in some detail. Classification in many of the interesting cases is given. This work generlizes Droste's classification of the countable k-transitive trees (k>1). In a CFPO, the structure can be branch downwards as well as upwards, and can do so repeatedely (though it neverr returns to the starting point by a cycle). Mostly it is assumed that k>2 and that all maximal chains are finite. The main classification splits into the sporadic and skeletal cases. The former is complete in all cardinalities. The latter is performed only in the countable case. The classification is considerably more complicated than for trees, and skeletal CFPOs exhibit rich, elaborate and rather surprising behaviour.
Download or read book Relations Related to Betweenness Their Structure and Automorphisms written by Samson Adepoju Adeleke and published by American Mathematical Soc.. This book was released on 1998 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is about tree-like structures, namely semilinear ordering, general betweenness relations, C-relations and D-relations. It contains a systematic study of betweenness and introduces C- and D- relations to describe the behaviour of points at infinity (leaves or ends or directions of trees). The focus is on structure theorems and on automorphism groups, with applications to the theory of infinite permutation groups.
Download or read book Groups Modules and Model Theory Surveys and Recent Developments written by Manfred Droste and published by Springer. This book was released on 2017-06-02 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.
Download or read book Combinatorial Theory of the Free Product with Amalgamation and Operator Valued Free Probability Theory written by Roland Speicher and published by American Mathematical Soc.. This book was released on 1998 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free probability theory, introduced by Voiculescu, has developed very actively in the last few years and has had an increasing impact on quite different fields in mathematics and physics. Whereas the subject arose out of the field of von Neumann algebras, presented here is a quite different view of Voiculescu's amalgamated free product. This combinatorial description not only allows re-proving of most of Voiculescu's results in a concise and elegant way, but also opens the way for many new results. Unlike other approaches, this book emphasizes the combinatorial structure of the concept of ``freeness''. This gives an elegant and easily accessible description of freeness and leads to new results in unexpected directions. Specifically, a mathematical framework for otherwise quite ad hoc approximations in physics emerges.
Download or read book Morava K Theories and Localisation written by Mark Hovey and published by American Mathematical Soc.. This book was released on 1999 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working in group theory and generalizations.
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 Algebraic Structure of Pseudocompact Groups written by Dikran N. Dikranjan and published by American Mathematical Soc.. This book was released on 1998 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental property of compact spaces - that continuous functions defined on compact spaces are bounded - served as a motivation for E. Hewitt to introduce the notion of a pseudocompact space. The class of pseudocompact spaces proved to be of fundamental importance in set-theoretic topology and its applications. This clear and self-contained exposition offers a comprehensive treatment of the question, When does a group admit an introduction of a pseudocompact Hausdorff topology that makes group operations continuous? Equivalently, what is the algebraic structure of a pseudocompact Hausdorff group? The authors have adopted a unifying approach that covers all known results and leads to new ones, Results in the book are free of any additional set-theoretic assumptions.
Download or read book Treelike Structures Arising from Continua and Convergence Groups written by Brian Hayward Bowditch and published by American Mathematical Soc.. This book was released on 1999 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working in group theory and generalizations
Download or read book The Integral Manifolds of the Three Body Problem written by Christopher Keil McCord and published by American Mathematical Soc.. This book was released on 1998 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The phase space of the spatial three-body problem is an open subset in R18. Holding the ten classical integrals of energu, center of mass, linear and angular momentum fixed defines an eight dimensional manifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the well-known bifurcations due to central configurations, and three are due to "critical points at infinity". This disproves Birkhoffs conjecture that the bifurcations occur only at central configurations.
Download or read book Short Time Geometry of Random Heat Kernels written by Richard Bucher Sowers and published by American Mathematical Soc.. This book was released on 1998 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 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 Matching of Orbital Integrals on GL 4 and GSp 2 written by Yuval Zvi Flicker and published by American Mathematical Soc.. This book was released on 1999 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: The trace formula is the most powerful tool currently available to establish liftings of automorphic forms, as predicted by Langlands principle of functionality. The geometric part of the trace formula consists of orbital integrals, and the lifting is based on the fundamental lemma. The latter is an identity of the relevant orbital integrals for the unit elements of the Hecke algebras. This volume concerns a proof of the fundamental lemma in the classically most interesting case of Siegel modular forms, namely the symplectic group Sp(2). These orbital integrals are compared with those on GL(4), twisted by the transpose inverse involution. The technique of proof is elementary. Compact elements are decomposed into their absolutely semi-simple and topologically unipotent parts also in the twisted case; a double coset decomposition of the form H\ G/K--where H is a subgroup containing the centralizer--plays a key role.
Download or read book Iterated Function Systems and Permutation Representations of the Cuntz Algebra written by Ola Bratteli and published by American Mathematical Soc.. This book was released on 1999 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working in functional analysis.
Download or read book Conjugacy of mathrm Alt 5 and mathrm SL 2 5 Subgroups of E 8 mathbb C written by Darrin D. Frey and published by American Mathematical Soc.. This book was released on 1998 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exceptional complex Lie groups have become increasingly important in various fields of mathematics and physics. As a result, there has been interest in expanding the representation theory of finite groups to include embeddings into the exceptional Lie groups. Cohen, Griess, Lisser, Ryba, Serre and Wales have pioneered this area, classifying the finite simple and quasisimple subgroups that embed in the exceptional complex Lie groups. This work contains the first major results concerning conjugacy classes of embeddings of finite subgroups of an exceptional complex Lie group in which there are large numbers of classes. The approach developed in this work is character theoretic, taking advantage of the classical subgroups of Eg(C). The machinery used is relatively elementary and has been used by the author and others to solve other conjugacy problems. The results presented here are very explicity. Each known conjugacy class if listed by its fusion pattern with an explicit character afforded by an embedding in that class.
Download or read book Structurally Stable Quadratic Vector Fields written by Joan C. Artés and published by American Mathematical Soc.. This book was released on 1998 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book solves a problem that has been open for over 20 years--the complete classification of structurally stable quadratic vector fields modulo limit cycles. The authors give all possible phase portraits for such structurally stable quadratic vector fields. No index. Annotation copyrighted by Book News, Inc., Portland, OR