Download or read book The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras written by Hans Plesner Jakobsen and published by American Mathematical Soc.. This book was released on 1994 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work contains a complete description of the set of all unitarizable highest weight modules of classical Lie superalgebras. Unitarity is defined in the superalgebraic sense, and all the algebras are over the complex numbers. Part of the classification determines which real forms, defined by anti-linear anti-involutions, may occur. Although there have been many investigations for some special superalgebras, this appears to be the first systematic study of the problem.
Download or read book Inverse Nodal Problems Finding the Potential from Nodal Lines written by Ole H. Hald and published by American Mathematical Soc.. This book was released on 1996 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We show that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is shown which, when the additive constant is given, yields an approximation to the potential at a dense set of points. We present an estimate for the error made by the formula. A substantial part of this work is the derivation of the asymptotic forms for a rich set of eigenvalues and eigenfunctions for a large set of rectangles.
Download or read book Hilbert s Projective Metric and Iterated Nonlinear Maps written by Roger D. Nussbaum and published by American Mathematical Soc.. This book was released on 1988 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Classification of C algebras of Real Rank Zero Inductive Limits of Matrix Algebras over Non Hausdorff Graphs written by Hongbing Su and published by American Mathematical Soc.. This book was released on 1995 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper a [italic capital]K-theoretic classification is given of the real rank zero [italic capital]C*-algebras that can be expressed as inductive limits of sequences of finite direct sums of matrix algebras over finite connected graphs (possibly with multiple vertices). The special case that the graphs are circles is due to Elliott.
Download or read book Tilting in Abelian Categories and Quasitilted Algebras written by Dieter Happel and published by American Mathematical Soc.. This book was released on 1996 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: We generalize tilting with respect to a tilting module of projective dimension at most one for an Artin algebra to tilting with respect to a torsion pair in an Abelian category. Our construction is motivated by the connection between tilting and derived categories. We develop a general theory for such tilting, and are led to a generalization of tilting algebras which we call quasitilted algebras. This class also contains the canonical algebras, and we show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. We also give other characterizations of quasitilted algebras, and give methods for constructing such algebras.
Download or read book Intersection Pairings on Conley Indices written by Henry L. Kurland and published by American Mathematical Soc.. This book was released on 1996 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is a careful and detailed study of the intersection pairing in the Conley index. The Conley index associates to an isolated invariant set of a semiflow (with some mild compactness conditions) a homotopy type of a space, constructed to be invariant under perturbations of the flow. The homology of this space is the homology Conley index. For a (two-sided) flow, each isolated invariant set has two indices defined: one for the forward flow, and one for the reverse. In general, there is no relationship between these two indices, but when the flow is on an orientable manifold, the two indices can be related by an intersection pairing. It is this pairing that receives a careful and detailed study in this memoir. Results are then applied to the motivating example of the work: the existence of transition layer behavior for two-point boundary value problems of singularly perturbed systems.
Download or read book On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions written by Peter D. T. A. Elliott and published by American Mathematical Soc.. This book was released on 1994 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The correlation of multiplicative arithmetic functions on distinct arithmetic progressions and with values in the complex unit disc, cannot be continually near to its possible maximum unless each function is either very close to or very far from a generalized character. Moreover, under accessible condition the second possibility can be ruled out. As a consequence analogs of the standard limit theorems in probabilistic number theory are obtained with the classical single additive function on the integers replaced by a sum of two additive functions on distinct arithmetic progressions.
Download or read book Subgroup Lattices and Symmetric Functions written by Lynne M. Butler and published by American Mathematical Soc.. This book was released on 1994 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents foundational research on two approaches to studying subgroup lattices of finite abelian p-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.
Download or read book Discretization of Homoclinic Orbits Rapid Forcing and Invisible Chaos written by Bernold Fiedler and published by American Mathematical Soc.. This book was released on 1996 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerically speaking, continuous time dynamical systems do not exist. Rather, a discretized version is studied and interpreted in analogy to the continuous time dynamical system. Over fixed finite time intervals, this analogy is quite close and well understood in terms of discretization errors and sophisticated discretization schemes. Over large or infinite time intervals, this analogy is not so clear, because discretization errors tend to accumulate exponentially with time. In this paper, we specifically investigate the correspondence between continuous and discrete time dynamical systems for homoclinic orbits. By definition, these are orbits which tend to the same stationary point for both large positive and large negative times.
Download or read book Second Order Sturm Liouville Difference Equations and Orthogonal Polynomials written by Alouf Jirari and published by American Mathematical Soc.. This book was released on 1995 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir presents machinery for analyzing many discrete physical situations, and should be of interest to physicists, engineers, and mathematicians. We develop a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. We discuss the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate [italic capital]L2 setting, and give necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions.
Download or read book The 2 Dimensional Attractor of x t mu x t f x t 1 written by Hans-Otto Walther and published by American Mathematical Soc.. This book was released on 1995 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: See attachment.
Download or read book Generalized Tate Cohomology written by John Patrick Campbell Greenlees and published by American Mathematical Soc.. This book was released on 1995 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let [italic capital]G be a compact Lie group, [italic capitals]EG a contractible free [italic capital]G-space and let [italic capitals]E~G be the unreduced suspension of [italic capitals]EG with one of the cone points as basepoint. Let [italic]k*[over][subscript italic capital]G be a [italic capital]G-spectrum. Let [italic capital]X+ denote the disjoint union of [italic capital]X and a [italic capital]G-fixed basepoint. Define the [italic capital]G-spectra [italic]f([italic]k*[over][subscript italic capital]G) = [italic]k*[over][subscript italic capital]G [up arrowhead symbol] [italic capitals]EG+, [italic]c([italic]k*[over][subscript italic capital]G) = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G), and [italic]t([italic]k[subscript italic capital]G)* = [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) [up arrowhead symbol] [italic capitals]E~G. The last of these is the [italic capital]G-spectrum representing the generalized Tate homology and cohomology theories associated to [italic]k[subscript italic capital]G. Here [italic capital]F([italic capitals]EG+,[italic]k*[over][subscript italic capital]G) is the function space spectrum. The authors develop the properties of these theories, illustrating the manner in which they generalize the classical Tate-Swan theories.
Download or read book An Arithmetic Riemann Roch Theorem for Singular Arithmetic Surfaces written by Wayne Aitken and published by American Mathematical Soc.. This book was released on 1996 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following gives a development of Arakelov theory general enough to handle not only regular arithmetic surfaces but also a large class of arithmetic surfaces whose generic fiber has singularities. This development culminates in an arithmetic Riemann-Roch theorem for such arithmetic surfaces. The first part of the memoir gives a treatment of Deligne's functorial intersection theory, and the second develops a class of intersection functions for singular curves which behaves analogously to the canonical Green's functions introduced by Arakelov for smooth curves.
Download or read book The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux written by Christian Krattenthaler and published by American Mathematical Soc.. This book was released on 1995 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory of counting nonintersecting lattice paths by the major index and its generalizations is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given final points, where the starting points lie on a line parallel to [italic]x + [italic]y = 0. In some cases these determinants can be evaluated to result in simple products. As applications we compute the generating function for tableaux with [italic]p odd rows, with at most [italic]c columns, and with parts between 1 and [italic]n. Moreover, we compute the generating function for the same kind of tableaux which in addition have only odd parts. We thus also obtain a closed form for the generating function for symmetric plane partitions with at most [italic]n rows, with parts between 1 and [italic]c, and with [italic]p odd entries on the main diagonal. In each case the result is a simple product. By summing with respect to [italic]p we provide new proofs of the Bender-Knuth and MacMahon (ex-)conjectures, which were first proved by Andrews, Gordon, and Macdonald. The link between nonintersecting lattice paths and tableaux is given by variations of the Knuth correspondence.
Download or read book Algebraic and Analytic Geometry of Fans written by Carlos Andradas and published by American Mathematical Soc.. This book was released on 1995 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a description is possible locally around every point, by means of analytic inequalities varying with the point, the set is called semianalytic. If one single system of strict inequalities is enough, either globally or locally at every point, the set is called basic. The topic of this work is the relationship between these two notions. Namely, Andradas and Ruiz describe and characterize, both algebraically and geometrically, the obstructions for a basic semianalytic set to be basic semialgebraic. Then they describe a special family of obstructions that suffices to recognize whether or not a basic semianalytic set is basic semialgebraic. Finally, they use the preceding results to discuss the effect on basicness of birational transformations.
Download or read book The Operator Hilbert Space OH Complex Interpolation and Tensor Norms written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1996 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recently developed duality theory of operator spaces, bounded operators are replaced by 'completely bounded' ones, isomorphism by 'complete isomorphisms' and Banach spaces by 'operator spaces'. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into [italic capital]B([italic capital]H) (with H being Hilbert). One of the main results is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (which we denote by [italic capitals]OH) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces.
Download or read book Geometry of Loop Spaces and the Cobar Construction written by Hans J. Baues and published by American Mathematical Soc.. This book was released on 1980 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The homology of iterated loop spaces [capital Greek]Omega [superscript]n [italic]X has always been a problem of major interest because it gives some insight into the homotopy of [italic]X, among other things. Therefore, if [italic]X is a CW-complex, one has been interested in small CW models for [capital Greek]Omega [superscript]n [italic]X in order to compute the cellular chain complex. The author proves a very general model theorem from which he can derive models, in addition to very technical proofs of the model theorem for several other models.
