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On the Foundations of Nonlinear Generalized Functions I and II
In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.
Some Generalized Kac-Moody Algebras with Known Root Multiplicities
Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.
Differential Forms Orthogonal to Holomorphic Functions or Forms, and Their Properties
The authors consider the problem of characterizing the exterior differential forms which are orthogonal to holomorphic functions (or forms) in a domain $D\subset {\mathbf C}^n$ with respect to integration over the boundary, and some related questions. They give a detailed account of the derivation of the Bochner-Martinelli-Koppelman integral representation of exterior differential forms, which was obtained in 1967 and has already found many important applications. They study the properties of $\overline \partial$-closed forms of type $(p, n - 1), 0\leq p\leq n - 1$, which turn out to be the duals (with respect to the orthogonality mentioned above) to holomorphic functions (or forms) in several complex variables, and resemble holomorphic functions of one complex variable in their properties.
Differential Topology, Foliations, and Group Actions
This volume contains the proceedings of the Workshop on Topology held at the Pontificia Universidade Catolica in Rio de Janeiro in January 1992. Bringing together about one hundred mathematicians from Brazil and around the world, the workshop covered a variety of topics in differential and algebraic topology, including group actions, foliations, low-dimensional topology, and connections to differential geometry. The main concentration was on foliation theory, but there was a lively exchange on other current topics in topology. The volume contains an excellent list of open problems in foliation research, prepared with the participation of some of the top world experts in this area. Also presented here are two surveys on group actions---finite group actions and rigidity theory for Anosov actions---as well as an elementary survey of Thurston's geometric topology in dimensions 2 and 3 that would be accessible to advanced undergraduates and graduate students.
Second International Conference on Algebra
This book contains papers presented at the Second International Conference on Algebra, held in Barnaul in August 1991 in honour of the memory of A. I. Shirshov (1921--1981). Many of the results presented here have not been published elsewhere in the literature. The collection provides a panorama of current research in PI-, associative, Lie, and Jordan algebras and discusses the interrelations of these areas with geometry and physics. Other topics in group theory and homological algebra are also covered.
Chaotic Numerics
Much of what is known about specific dynamical systems is obtained from numerical experiments. Although the discretization process usually has no significant effect on the results for simple, well-behaved dynamics, acute sensitivity to changes in initial conditions is a hallmark of chaotic behavior. How confident can one be that the numerical dynamics reflects that of the original system? Do numerically calculated trajectories always shadow a true one? What role does numerical analysis play in the study of dynamical systems? And conversely, can advances in dynamical systems provide new insights into numerical algorithms? These and related issues were the focus of the workshop on Chaotic Numerics, held at Deakin University in Geelong, Australia, in July 1993. The contributions to this book are based on lectures presented during the workshop and provide a broad overview of this area of research.
The Reconstruction of Trees from Their Automorphism Groups
0 An extended introduction (starting p. 1) -- 1 Some preliminaries concerning interpretations, groups and [actual symbol not reproducible]-categoricity (starting p. 29) -- 2 A new reconstruction theorem for Boolean algebras (starting p. 43) -- 3 The completion and the Boolean algebra of a U-tree (starting p. 57) -- 4 The statement of the canonization and reconstruction theorems (starting p. 63) -- 5 The canonization of trees (starting p. 73) -- 6 The reconstruction of the Boolean algebra of a U-tree (starting p. 87) -- 7 The reconstruction of PT(Exp(M)) (starting p. 135) -- 8 Final reconstruction results (starting p. 153) -- 9 Observations, examples and discussion (starting p. 155) -- 10 Augmented trees (starting p. 169) -- 11 The reconstruction of [actual symbol not reproducible]-categorical trees (starting p. 205) -- 12 Nonisomorphic 1-homogeneous chains which have isomorphic automorphism groups (starting p. 243) -- Bibliography (starting p. 251) -- A list of notations and definitions (starting p. 253)
The Mathematical Legacy of Wilhelm Magnus: Groups, Geometry and Special Functions
Wilhelm Magnus was an extraordinarily creative mathematician who made fundamental contributions to diverse areas, including group theory, geometry and special functions. This book contains the proceedings of a conference held in May 1992 at Polytechnic University, Brooklyn to honour the memory of Magnus. The focus of the book is on active areas of research where Magnus' influence can be seen. The papers range from expository articles to major new research, bringing together seemingly diverse topics and providing entry points to a variety of areas of mathematics.
The Cech Centennial: A Conference on Homotopy Theory
The June 1993 conference was organized to commemorate the 100th anniversary of the birth of Czech mathematician Edward Cech. The main topics of the conference were the most recent results in the stable and unstable homotopy theory. Among the topics in 22 refereed papers: on finiteness of subgroups of self-homotopy equivalences; the Chen groups of the pure braid group; Morava's change of rings theorem; the Boardman homomorphism; and a comparison criterion for certain loop spaces. No index. Annotation copyright by Book News, Inc., Portland, OR
