934 research outputs found
Inversion of centroskewsymmetric Toeplitz-plus-Hankel Bezoutians
No full textIn this paper, the inverse of a nonsingular, centroskewsymmetric Toeplitz-plus-Hankel Bezoutian B of (even) order n are computed, and a representation of B^(−1) as a sum of a Toeplitz and a Hankel matrix is found. Two possibilities are discussed. In the first one, the problem is reduced to the inversion of two skewsymmetric Toeplitz Bezoutians of order n. In the second one, the problem is tackled via the inversion of two Hankel Bezoutians of half the order n/2. The inversion of Toeplitz or Hankel Bezoutians is the subject of a previous paper [T. Ehrhardt and K. Rost. Resultant matrices and inversion of Bezoutians. Linear Algebra Appl., 439:621–639, 2013.]. Both approaches lead to fast O(n^2) inversion algorithms
Factorization in Weighted Wiener Matrix Algebras on Linearly Ordered Abelian Groups
No full textFactorizations of Wiener-Hopf type of elements of weighted Wiener algebras of continuous matrix-valued functions on a compact abelian group are studied. The factorizations are with respect to a fixed linear order in the character group (considered with the discrete topology). Among other results, it is proved that if a matrix function has a canonical factorization in
one such matrix Wiener algebra then it belongs to the connected component of the identity of the group of invertible elements in the algebra, and moreover, the factors of the canonical factorization depend continuously on the matrix function. In the scalar case, complete characterizations of canonical and noncanonical factorability are given in terms of abstract winding numbers. Wiener-Hopf equivalence of matrix functions with elements in weighted Wiener algebras is also discussed
On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II
No full textIn this paper we continue our analysis [3] of the determinant det (I−γKs), γ ∈ (0,1) where K s is the trace class operator acting in L 2(−1, 1) with kernel Ks(λ,μ)=sin s(λ−μ)π(λ−μ) . In [3] various key asymptotic results were stated and utilized, but without proof: Here we provide the proofs (see Theorem 1.2 and Proposition 1.3 below)
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Eigenvalues of Large Dimensional Random Matrices
No full textThis paper demonstrates an introduction to the statistical distribution of eigenval-ues in Random Matrix theory. Using mathematical analysis and probabilistic measuretheory instead of statistical methods, we are able to draw conclusions on large dimen-sional cases and as our dimensions of the random matrices tend to innity. Applicationsof large-dimensional random matrices occur in the study of heavy-nuclei atoms, whereEigenvalues express some physical measurement or observation at a distinct state ofa quantum-mechanical system. This specically motivates our study of Wigner Ma-trices. Classical limit theorems from statistics can fail in the large-dimensional caseof a covariance matrix. By using methods from combinatorics and complex analysis,we are able to draw multiple conclusions on its spectral distributions. The Spectraldistributions that arise allow for boundedness to occur on extreme eigenvalues
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A Stability Problem Involving Approximate Identities, Discrete Convolution Operators, Singular Integral Operators, and Finite Sections
No full textLet tend towards infinity and tend towards 1 with the condition that for some fixed A sequence of bounded linear operators on a Hilbert space is called stable if for all sufficiently large and all sufficiently close to 1 such that is sufficiently close to , each is invertible and these inverses are uniformly bounded. We consider the stability problem for sequences arising from a algebra containing discrete convolution operators, singular integral operators, and their finite sections. Our main result is that a sequence in a certain algebra is stable if and only if a certain collection of operators given by strong limits is invertible. As an application, we relate this result to approximate identities and discuss several concrete examples such as finite sections of Toeplitz operators whose symbols are approximate identities applied to piecewise continuous functions and finite sections of singular integral operators
Entwicklung einer schnellen Pulsformanalyse für asymmetrische AGATA-Germanium-Detektoren
No full textOnTEAM metadata: GDSID: DOC-2007-May-32; Attribute ID: LIBRARY-thesis_diss-2007-005; Title: [GSI Diss 2007-05] Entwicklung einer schnellen Pulsformanalyse für asymmetrische AGATA-Germanium-Detektoren; Author(s): Beck, Torsten; Corporate author(s): ; Publication date: 20070501; Creator: manton; Creation date: 15.05.2007 16:02:12; Change date: 29.10.2008 16:29:34; Access: nur berechtigte Gruppen; Attribute type: Text.Thesis.Diss; Directory path: ['GSI Publications', 'GSI as Publisher']; Attribute path: ['Infrastructure', 'Library and Documentation', 'thesis_diss', 'Added in 2007']; File name(s): ['DOC-2007-May-32-1.pdf']; File title(s): ['']; File access: ['nur berechtigte Gruppen'
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Asymptotics of determinants for finite sections of operators with almost periodic diagonals
No full textLet be a bounded linear operator on whose diagonals are almost periodic sequences. For certain classes of such operators and under certain conditions, we are going to determine the asymptotics of the determinants of the finite sections as their size tends to infinity.Examples of such operators include block Toeplitz operators and the almost Mathieu operator
Manifolds, sheaves, and cohomology
No full textThis book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples. Content Topological Preliminaries - Algebraic Topological Preliminaries - Sheaves - Manifolds - Local Theory of Manifolds - Lie Groups - Torsors and Non-abelian Cech Cohomology - Bundles - Soft Sheaves - Cohomology of Complexes of Sheaves - Cohomology of Sheaves of Locally Constant Functions - Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis Readership Graduate Students in Mathematics / Master of Science in Mathematics About the Author Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany
James Watson, Maclyn McCarty, and Torsten Wiesel
No full textTorsten Wiesel (right) with Professor Emeritus Maclyn McCarty (center), co-author of the paper with Oswald Avery and Colin MacLeod, and James D. Watson, director of Cold Spring Harbor Laboratory, 1994
Photo by Leif Carlsson
To commemorate the fiftieth anniversary of the discovery at The Rockefeller University that genes are made of DNA - considered by many to be the single most important biological discovery of the twentieth century - the university has kicked off a year-long series of events that were running through May 1994. The celebration was formally inaugurated in November 1993 with a lecture by Nobel laureate James D. Watson, best known for discovering the double-helical structure of DNA.
See also Search Winter 1994, vol. 4, no. 1https://digitalcommons.rockefeller.edu/group-portraits/1013/thumbnail.jp
Seltsame Schauspiele. Torsten Fogelqvists Deutschlandreise 1934
No full textIn 1934 Torsten Fogelqvist, a prominent member of the Swedish Academy and a well-known journalist and intellectual, visits Nazi Germany. He writes about his visit to the Third Reich in 17 articles published in the Stockholm daily newspaper Dagens Nyheter. The author, highly critical of the Hitler regime, scrutinizes several aspects of the nazified German society such as the attempts to re-educate the German citizen in accordance with the ideology of the new regime, the hero cult in the Nazi movement, and the relationship between the German state and the churches. In order to further an understanding of political and social developments in Germany Fogelqvist uses a specific strategy. He “translates” them into an imaginary Swedish context. This paper compares his views with those of other Swedish visitors
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