Symplectic Cobordism and the Computation of Stable Stems
Symplectic Cobordism and the Computation of Stable Stems

Author: Stanley O. Kochman

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 105

ISBN-13: 0821825585

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This memoir consists of two independent papers. In the first, "The symplectic cobordism ring III" the classical Adams spectral sequence is used to study the symplectic cobordism ring [capital Greek]Omega[superscript]* [over] [subscript italic capital]S[subscript italic]p. In the second, "The symplectic Adams Novikov spectral sequence for spheres" we analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres.

A Proof of the $q$-Macdonald-Morris Conjecture for $BC_n$
A Proof of the $q$-Macdonald-Morris Conjecture for $BC_n$

Author: Kevin W. J. Kadell

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 93

ISBN-13: 0821825526

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Macdonald and Morris gave a series of constant term [italic]q-conjectures associated with root systems. Selberg evaluated a multivariable beta-type integral which plays an important role in the theory of constant term identities associated with root systems. K. Aomoto recently gave a simple and elegant proof of a generalization of Selberg's integral. Kadell extended this proof to treat Askey's conjectured [italic]q-Selberg integral, which was proved independently by Habsieger. We use a constant term formulation of Aomoto's argument to treat the [italic]q-Macdonald-Morris conjecture for the root system [italic capitals]BC[subscript italic]n. We show how to obtain the required functional equations using only the q-transportation theory for [italic capitals]BC[subscript italic]n.

Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting
Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting

Author: I. V. Evstigneev

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 113

ISBN-13: 0821825976

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Various notions of the Markov property relative to a partial ordering have been proposed by both physicists and mathematicians. This work develops techniques for stying Markov fields on partially ordered sets. We introduce random transformations of the index set which preserves the Markov property of the field. These transformations yield new classes of Markov fields starting from relatively simple ones. Examples include a model for crack formation and a model for the distribution of fibres in a composite material.

Associated Graded Algebra of a Gorenstein Artin Algebra
Associated Graded Algebra of a Gorenstein Artin Algebra

Author: Anthony Ayers Iarrobino

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 128

ISBN-13: 0821825763

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In 1904, Macaulay described the Hilbert function of the intersection of two plane curve branches: It is the sum of a sequence of functions of simple form. This monograph describes the structure of the tangent cone of the intersection underlying this symmetry. Iarrobino generalizes Macaulay's result beyond complete intersections in two variables to Gorenstein Artin algebras in an arbitrary number of variables. He shows that the tangent cone of a Gorenstein singularity contains a sequence of ideals whose successive quotients are reflexive modules. Applications are given to determining the multiplicity and orders of generators of Gorenstein ideals and to problems of deforming singular mapping germs. Also included are a survey of results concerning the Hilbert function of Gorenstein Artin algebras and an extensive bibliography.

Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds
Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds

Author: Takashi Shioya

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 90

ISBN-13: 082182578X

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This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.

Textile Systems for Endomorphisms and Automorphisms of the Shift
Textile Systems for Endomorphisms and Automorphisms of the Shift

Author: Masakazu Nasu

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 230

ISBN-13: 0821826069

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We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.

Chapter 16 of Ramanujan's Second Notebook: Theta-Functions and $q$-Series
Chapter 16 of Ramanujan's Second Notebook: Theta-Functions and $q$-Series

Author: Chandrashekar Adiga

Publisher: American Mathematical Soc.

Published: 1985

Total Pages: 99

ISBN-13: 0821823167

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The first part of Chapter 16 in Ramanujan's second notebook is devoted to q-series. Several of the results obtained by Ramanujan are classical, but many are new. In particular, certain elegant q-continued fraction expansions have not appeared heretofore in print. In the remainder of this chapter, Ramanujan develops the theory of the classical theta-functions in a manner different from his nineteenth century predecessors such as Jacobi. Although many of Ramanujan's discoveries about theta-functions are well-known, several new results are also to be found.