Search results for "algebra"

THE GROUP OF AUTOMORPHISMS OF THE SEMIGROUP OF ENDOMORPHISMS OF FREE COMMUTATIVE AND FREE ASSOCIATIVE ALGEBRAS

2007

Let W(X) be a free commutative or a free associative algebra. The group of automorphisms of the semigroup End (W(X)) is studied.

On the projectives of a group algebra

1980

MULTIPLICITIES IN THE MIXED TRACE COCHARACTER SEQUENCE OF TWO 3 × 3 MATRICES

2006

We find explicitly the multiplicities in the (mixed) trace cocharacter sequence of two 3 × 3 matrices over a field of characteristic 0 and show that asymptotically they behave as polynomials of seventh degree. As a consequence we obtain also the multiplicities of certain irreducible characters in the cocharacter sequence of the polynomial identities of 3 × 3 matrices.

Visual Discrimination of the 17 Plane Symmetry Groups

2011

Within most of the 17 plane symmetry groups, individual symmetry operations act in multiple, nonequivalent ways. This, and the fact that many groups can be realized on the basis of different unit cells and generating regions, poses difficulties for visual discrimination and identification. Because of inherent confounds, only few of the groups can be studied by traditional experimental methodology. The use of an oddity paradigm and specific tiling patterns that camouflage groups in complex textures are recommended as partial remedy to this impasse. In order to prepare readers for an appreciation of the aforementioned issues and to provide a rationale for their investigation, the reporting of…

Linear representations of Artin groups

2016

Let Г be a Coxeter graph. Let W be the Coxeter group, A be the Artin group, and A+ be the Artin monoid associated with Г. Let G be a group of symmetries of Г. Then G acts on W, A and A+. The fixed subgroup WG is known to be a Coxeter group, the fixed submonoid A+G is known to be an Artin monoid, and, when Г is of spherical type, the fixed subgroup AG is known to be an Artin group. This thesis studies the behavior of WG, A+G and AG with respect to some faithful linear representations of W, A and A+, respectively.Firstly, we consider the rooted representations of the Coxeter groups introduced by Krammer in his Ph. D. Thesis. These are a generalization of the canonical representations. We take…

MetaEdit— A flexible graphical environment for methodology modelling

1991

Existing CASE tools are often rigid and do not support the users' native methodologies. To alleviate this, more flexible and customisable tools called CASE shells are emerging. However, the customisation of those tools is still cumbersome and error-prone, and demands several configuration files that follow a rigid syntax of some metamodelling language(s). In order to make the customisation easier, we propose a graphical metamodelling editor, MetaEdit, with which the conceptual structures of the user methodology can be modelled easily using an easy-to-grasp graphical notation. With MetaEdit, methodology models can be constructed with less effort and the configuration files for the CASE shell…

Getting even with CLE

2018

In the landscape of approaches toward the simulation of Lattice Models with complex action the Complex Langevin (CL) appears as a straightforward method with a simple, well defined setup. Its applicability, however, is controlled by certain specific conditions which are not always satisfied. We here discuss the procedures to meet these conditions and the estimation of systematic errors and present some actual achievements.

Error Estimates of Theoretical Models: a Guide

2014

This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover inter-dependencies by correlation analysis. The basic concepts are illustrated through simple examples. By providing theoretical error bars on predicted quantities and using statistical methods to study correlations between observables, theory can significantly enhance the feedback between experiment and nuclear modeling.

On the classification of visual patterns: systems analysis using detection experiments.

1977

Behavioral experiments are indispensable for the analysis of biological systems for cognition and recognition. When these are carried out as detection experiments three types of description can be used for the problem of visual pattern recognition which allow conclusions to be drawn on the operating function of the system. Provided that the signals to be recognized have additive noise superimposed on them, system description is possible: 1. on the basis on the probabilities of recognition and of mix-up,--2. through the analysis of the transformation of distribution densities of the noise,--3. by means of the measurable distances of the patterns from each other in feature space.-The analysis…

epiModel: A system to build automatically systems of differential equations of compartmental type-epidemiological models

2011

In this paper we describe epiModel, a code developed in Mathematica that facilitates the building of systems of differential equations corresponding to type-epidemiological linear or quadratic models whose characteristics are defined in text files following an easy syntax. It includes the possibility of obtaining the equations of models involving age and/or sex groups. © 2011.