Higher Multiplicities And Almost Free Divisors And Complete Intersections
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| Author | : James Damon |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 130 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821804812 |
Almost free divisors and complete intersections form a general class of nonisolated hypersurface and completer intersection singularities. They also include discriminants of mappings, bifurcation sets, and certain types of arrangements of hyperplanes such as Coxeter arrangements and generic arrangements. Associated to the singularities of this class is a "singular Milnor fibration" which has the same homotopy properties as the Milnor fibration for isolated singularities. This memoir deduces topological properties of singularities in a number of situations including: complements of hyperplane arrangements, various nonisolated complete intersections, nonlinear arrangements of hypersurfaces, functions on discriminants, singularities defined by compositions of functions, and bifurcation sets.
| Author | : Paul Kirk |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 73 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 082180538X |
The analytic perturbation theory for eigenvalues of Dirac operators on odd dimensional manifolds with boundary is described in terms of [italic]extended L2 eigenvectors [end italics] on manifolds with cylindrical ends. These are generalizations of the Atiyah-Patodi-Singer extended [italic capital]L2 kernel of a Dirac operator. We prove that they form a discrete set near zero and deform analytically, in contrast to [italic capital]L2 eigenvectors, which can be absorbed into the continuous spectrum under deformations when the tangential operator is not invertible. We show that the analytic deformation theory for extended [italic capital]L2 eigenvectors and Atiyah-Patodi-Singer eigenvectors coincides.
| Author | : George Xian-Zhi Yuan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 157 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821807471 |
This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.
| Author | : Gregory L. Cherlin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 188 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9780821808368 |
In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use.
| Author | : Valentina Barucci |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 95 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821805444 |
In Chapter I, various (numerical) semigroup-theoretic concepts and constructions are introduced and characterized. Applications in Chapter II are made to the study of Noetherian local one-dimensional analytically irreducible integral domains, especially for the Gorenstein, maximal embedding dimension, and Arf cases, as well as to the so-called Kunz case, a pervasive kind of domain of Cohen-Macaulay type 2.
| Author | : Ambar Sengupta |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821804847 |
In this paper we develop a concrete description of connections on principal bundles, possibly non-trivial, over compact surfaces and use this description to construct the Yang-Mills measure which underlies the Euclidean quantum theory of gauge fields, involving compact gauge groups, on compact connected two-dimensional Riemannian manifolds (possibly with boundary). Using this measure we compute expectation values of important random variables, the Wilson loops variables, corresponding to a broad class of configurations of loops on the surface.
| Author | : Jack E. Graver |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 89 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821805568 |
The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their end. The 1-ended graphs in this class were identified by Grünbaum and Shephard; Watkins characterized the 2-ended members. Any remaining graphs in this class must have uncountably may ends. In this work, infinite-ended members of this class are shown to exist. A more detailed classification scheme in terms of the types of Petrie walks in the graphs in this class and the local structure of their automorphism groups is presented.
| Author | : Eldar Straume |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 90 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821804839 |
The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. We are concerned with the classification of differentiable compact connected Lie transformation groups on (homology) spheres, with [italic]c [less than or equal to symbol] 2, and the main results are summarized in five theorems, A, B, C, D, and E in part I. This paper is part II of the project, and addresses theorems D and E. D examines the orthogonal model from theorem A and orbit structures, while theorem E addresses the existence of "exotic" [italic capital]G-spheres.
| Author | : Christopher Keil McCord |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 106 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821806920 |
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.
| Author | : Richard Bucher Sowers |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 145 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821806491 |
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.
