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Neumann Systems For The Algebraic Akns Problem
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Book Synopsis Neumann Systems for the Algebraic AKNS Problem by : Randolph James Schilling
Download or read book Neumann Systems for the Algebraic AKNS Problem written by Randolph James Schilling and published by American Mathematical Soc.. This book was released on 1992 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is concerned with an algebraically completely integrable Hamiltonian system whose solutions may be used to describe the finite gap solutions of the AKNS spectral problem, a first order two-by-two matrix linear system. Trace formulas, constraints, Lax paris, and constants of motion are obtained using Krichever's algebraic inverse spectral transform. Computations are carried out explicityly over the class of spectral problems with square matrix coefficients.
Book Synopsis Filtrations on the Homology of Algebraic Varieties by : Eric M. Friedlander
Download or read book Filtrations on the Homology of Algebraic Varieties written by Eric M. Friedlander and published by American Mathematical Soc.. This book was released on 1994 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work provides a detailed exposition of a classical topic from a very recent viewpoint. Friedlander and Mazur describe some foundational aspects of ``Lawson homology'' for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles. Attention is paid to methods of group completing abelian topological monoids. The authors study properties of Chow varieties, especially in connection with algebraic correspondences relating algebraic varieties. Operations on Lawson homology are introduced and analysed. These operations lead to a filtration on the singular homology of algebraic varieties, which is identified in terms of correspondences and related to classical filtrations of Hodge and Grothendieck.
Book Synopsis Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields by : Oscar Zariski
Download or read book Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields written by Oscar Zariski and published by American Mathematical Soc.. This book was released on 1951 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Duality for Actions and Coactions of Measured Groupoids on von Neumann Algebras by : Takehiko Yamanouchi
Download or read book Duality for Actions and Coactions of Measured Groupoids on von Neumann Algebras written by Takehiko Yamanouchi and published by American Mathematical Soc.. This book was released on 1993 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through classification of compact abelian group actions on semifinite injective factors, Jones and Takesaki introduced a notion of an action of a measured groupoid on a von Neumann algebra, which was proven to be an important tool for such an analysis. In this paper, elaborating their definition, the author introduces a new concept of a measured groupoid action that may fit more perfectly in the groupoid setting. The author also considers a notion of a coaction of a measured groupoid by showing the existence of a canonical "coproduct" on every groupoid von Neumann algebra.
Book Synopsis Associated Graded Algebra of a Gorenstein Artin Algebra by : Anthony Ayers Iarrobino
Download or read book Associated Graded Algebra of a Gorenstein Artin Algebra written by Anthony Ayers Iarrobino and published by American Mathematical Soc.. This book was released on 1994 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Random Perturbations of Hamiltonian Systems by : Mark Iosifovich Freĭdlin
Download or read book Random Perturbations of Hamiltonian Systems written by Mark Iosifovich Freĭdlin and published by American Mathematical Soc.. This book was released on 1994 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.
Book Synopsis Enright-Shelton Theory and Vogan's Problem for Generalized Principal Series by : Brian D. Boe
Download or read book Enright-Shelton Theory and Vogan's Problem for Generalized Principal Series written by Brian D. Boe and published by American Mathematical Soc.. This book was released on 1993 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the composition series of generalized principal series representations induced from a maximal cuspidal parabolic subgroup of a real reductive Lie group. Boe and Collingwood study when such representations are multiplicity-free (Vogan's Problem #3) and the problem of describing their composition factors in closed form. The results obtained are strikingly similar to those of Enright and Shelton for highest weight modules. Connections with two different flag variety decompositions are discussed.
Book Synopsis Loop Groups, Discrete Versions of Some Classical Integrable Systems, and Rank 2 Extensions by : Percy Deift
Download or read book Loop Groups, Discrete Versions of Some Classical Integrable Systems, and Rank 2 Extensions written by Percy Deift and published by American Mathematical Soc.. This book was released on 1992 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors show how to interpret recent results of Moser and Veselov on discrete versions of a class of classical integrable systems, in terms of a loop group framework. In this framework the discrete systems appear as time-one maps of integrable Hamiltonian flows. Earlier results of Moser on isospectral deformations of rank 2 extensions of a fixed matrix, can also be incorporated into their scheme.
Book Synopsis Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations by : Jaume Llibre
Download or read book Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations written by Jaume Llibre and published by American Mathematical Soc.. This book was released on 1994 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the criticalleaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonain perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of "almost all" the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.
Book Synopsis Weakly Nonlinear Dirichlet Problems on Long or Thin Domains by : Edward Norman Dancer
Download or read book Weakly Nonlinear Dirichlet Problems on Long or Thin Domains written by Edward Norman Dancer and published by American Mathematical Soc.. This book was released on 1993 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we discuss the existence, uniqueness and asymptotic behavior of positive solutions of the equation −[capital Greek]Delta[italic]u = [lowercase Greek]Lambda[function]ƒ([italic]u) in [capital Greek]Omega[surmounted by macron] [times symbol] [−[italic]n, [italic]n], [and] [italic]u = 0 on [partial derivative/boundary/degree of a polynomial symbol]([capital Greek]Omega[surmounted by macron] [times symbol] [−[italic]n, [italic]n]) for [italic]n large. Here [capital Greek]Omega[surmounted by macron] is a bounded domain in [italic capital]R[superscript italic]k with smooth boundary. Note that by rescaling the equation (including [lowercase Greek]Lambda), our theory covers problems on domains ([set membership symbol][capital Greek]Omega[surmounted by macron]) [times symbol] [−1,1] where [set membership symbol] is small.
Book Synopsis The Problem of Integrable Discretization by : Yuri B. Suris
Download or read book The Problem of Integrable Discretization written by Yuri B. Suris and published by Birkhäuser. This book was released on 2012-12-06 with total page 1078 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.
Book Synopsis The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations by : Ian Anderson
Download or read book The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations written by Ian Anderson and published by American Mathematical Soc.. This book was released on 1992 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centres on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coicides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. a number of new examples illustrate the effectiveness of this approach.
Book Synopsis Continuous Images of Arcs and Inverse Limit Methods by : Jacek Nikiel
Download or read book Continuous Images of Arcs and Inverse Limit Methods written by Jacek Nikiel and published by American Mathematical Soc.. This book was released on 1993 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous images of ordered continua are investigated. The paper gives various properties of their monotone images and inverse limits of their inverse systems (or sequences) with monotone bonding surjections. Some factorization theorems are provided. Special attention is given to one-dimensional spaces which are continuous images of arcs and, among them, various classes of rim-finite continua. The methods of proofs include cyclic element theory, T-set approximations and null-family decompositions. The paper brings also new properties of cyclic elements and T-sets in locally connected continua, in general.
Book Synopsis Extension of Positive-Definite Distributions and Maximum Entropy by : Jean-Pierre Gabardo
Download or read book Extension of Positive-Definite Distributions and Maximum Entropy written by Jean-Pierre Gabardo and published by American Mathematical Soc.. This book was released on 1993 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.
Book Synopsis Degenerate Principal Series for Symplectic Groups by : Chris Jantzen
Download or read book Degenerate Principal Series for Symplectic Groups written by Chris Jantzen and published by American Mathematical Soc.. This book was released on 1993 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with induced representations for $p$-adic groups. In particular, Jantzen examines the question of reducibility in the case where the inducing subgroup is a maximal parabolic subgroup of $Sp_{2n (F)$ and the inducing representation is one-dimensional. Two different approaches to this problem are used. The first, based on the work of Casselman and of Gustafson, reduces the problem to the corresponding question about an associated finite-dimensional representation of a certain Hecke algebra. The second approach is based on a technique of Tadi\'c and involves an analysis of Jacquet modules. This is used to obtain a more general result on induced representations, which may be used to deal with the problem when the inducing representation satisfies a regularity condition. The same basic argument is also applied in a case-by-case fashion to nonregular cases.
Book Synopsis Markov Cell Structures near a Hyperbolic Set by : F. Thomas Farrell
Download or read book Markov Cell Structures near a Hyperbolic Set written by F. Thomas Farrell and published by American Mathematical Soc.. This book was released on 1993 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors' argument is a spiritual descendent of earlier work of Adler and Weiss, Sinaĭ, and Bowen, and involves a close study of triangulations. The discussion is long and technical, but the outline of the proof is sketched clearly in Section 1 for the special case of [italic]F an expanding immersion. A concluding section lists problems on hyperbolic sets, Markov partitions, and related matters; remarks on topological invariants, including the conjectured vanishing of Pontryagin classes for manifolds supporting Anosov diffeomorphisms, may be of particular interest.
Book Synopsis On Axiomatic Approaches to Vertex Operator Algebras and Modules by : Igor Frenkel
Download or read book On Axiomatic Approaches to Vertex Operator Algebras and Modules written by Igor Frenkel and published by American Mathematical Soc.. This book was released on 1993 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromy-free axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators.
