Search results for " Algebra"

Dynamic Finite Element analysis of fractionally damped structural systems in the time domain

2015

Visco-elastic material models with fractional characteristics have been used for several decades. This paper provides a simple methodology for Finite-Element-based dynamic analysis of structural systems with viscosity characterized by fractional derivatives of the strains. In particular, a re-formulation of the well-known Newmark method taking into account fractional derivatives discretized via the Grunwald–Letnikov summation allows the analysis of structural systems using standard Finite Element technology.

On minimal non-PC-groups

2009

On dit qu'un groupe G est un PC-groupe, si pour tout x ∈ G, G/C G (x G ) est une extension d'un groupe polycyclique par un groupe fini. Un non-PC-groupe minimal est un groupe qui n'est pas un PC-groupe mais dont tous les sous-groupes propres sont des PC-groupes. Notre principal resultat est qu'un non-PC-groupe minimal ayant un groupe quotient fini non-trivial est une extension cyclique finie d'un groupe abelien divisible de rang fini.

Almost polynomial growth: Classifying varieties of graded algebras

2015

Let G be a finite group, V a variety of associative G-graded algebras and c (V), n = 1, 2, …, its sequence of graded codimensions. It was recently shown by Valenti that such a sequence is polynomially bounded if and only if V does not contain a finite list of G-graded algebras. The list consists of group algebras of groups of order a prime number, the infinite-dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with suitable gradings. Such algebras generate the only varieties of G-graded algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all sub…

Gradings on the algebra of upper triangular matrices and their graded identities

2004

Abstract Let K be an infinite field and let UT n ( K ) denote the algebra of n × n upper triangular matrices over  K . We describe all elementary gradings on this algebra. Further we describe the generators of the ideals of graded polynomial identities of UT n ( K ) and we produce linear bases of the corresponding relatively free graded algebras. We prove that one can distinguish the elementary gradings by their graded identities. We describe bases of the graded polynomial identities in several “typical” cases. Although in these cases we consider elementary gradings by cyclic groups, the same methods serve for elementary gradings by any finite group.

A simple experimental setup for testing saltwater preference

2011

An experiment to study the structure of the focal volume in apertured focusing systems

2001

We present a simple experiment, specifically designed for students of undergraduate optics courses, where the influence of an aperture stop position on the three-dimensional structure of the focal volume of focusing systems is studied. The experiment, which involves only simple optical elements, permits an undergraduate student to generate different focal structures by simply axially displacing the aperture stop.

Lie algebra on the transverse bundle of a decreasing family of foliations

2010

Abstract J. Lehmann-Lejeune in [J. Lehmann-Lejeune, Cohomologies sur le fibre transverse a un feuilletage, C.R.A.S. Paris 295 (1982), 495–498] defined on the transverse bundle V to a foliation on a manifold M, a zero-deformable structure J such that J 2 = 0 and for every pair of vector fields X , Y on M: [ J X , J Y ] − J [ J X , Y ] − J [ X , J Y ] + J 2 [ X , Y ] = 0 . For every open set Ω of V, J. Lehmann-Lejeune studied the Lie Algebra L J ( Ω ) of vector fields X defined on Ω such that the Lie derivative L ( X ) J is equal to zero i.e., for each vector field Y on Ω : [ X , J Y ] = J [ X , Y ] and showed that for every vector field X on Ω such that X ∈ K e r J , we can write X = ∑ [ Y ,…

An oscillatory population model

2004

Abstract We consider a simple population model which includes time-dependent parameters prompted by the recent work of Lakshmi [Chaos, Solitons & Fractals 16 (2003) 183]. Time-dependent parameters introduce the possibility of chaos into the dynamics of even simple models. We provide some solutions of the model, compare them with the ones obtained by Lakshmi and discuss their behaviour and properties.

Analysis of the Electronic Structure of Non-Spherical Ligand-Protected Metal Nanoclusters: The Case of a Box-Like Ag67

2016

In this work we introduce a new strategy to investigate the electronic shell structure of ligand-protected metal nanoclusters of polyhedral core shape. The central idea is to identify the symmetry of the Kohn–Sham molecular orbitals of an atomistic structure based on their projection onto the electronic states of a jellium system with a similar shape of the background charge density. Herein, we study the connection between a reduced atomistic model of the recently reported box-like [Ag67(SR)32(PR3)8]3+ nanocluster and a jellium box consisting of 32 free electrons. With this approach, we determine the symmetry of electronic states of the metal core and identify those that are involved in the…

Electronic Shell Structure in Icosahedral Metal Clusters

1992

The shell structure of valence electrons in icosahedral and cuboctahedral simple metal clusters is studied using the free electron model and the Huckel model. The shell structure in a 1415 atom icosahedral cluster has still similarities with that of a spherical cluster. The effect of the finite temperature on the shell structure in liquid clusters is discussed.