Search results for "computing"
showing 10 items of 25279 documents
Local functions on finite groups
2020
We study local properties of finite groups using chains of p p -subgroups.
Properties of Generalized Polynomial Spaces in Three Variables
2009
Multivariate interpolation is a topic which often appears in practical modeling problems. Different type of spaces of functions are used for solving interpolation problems. When the interpolation conditions are of different kind, by example, spacial and temporal, one possibility for modeling the problem is to use a generalize degree, in which the monomials exponents are weighted with a weight vector with integer components. In order to use such a generalize polynomial space as interpolation space, it is necessary to know the dimension and a basis of it. The aim of this article is to study and prove many properties of the generalize polynomial spaces in three variables.
One-loop integrals with XLOOPS-GiNaC
2001
We present a new algorithm for the reduction of one-loop tensor Feynman integrals within the framework of the XLOOPS project, covering both mathematical and programming aspects. The new algorithm supplies a clean way to reduce the one-loop one-, two- and three-point Feynman integrals with arbitrary tensor rank and powers of the propagators to a basis of simple integrals. We also present a new method of coding XLOOPS in C++ using the GiNaC library.
Partial {$*$}-algebras of closable operators. II. States and representations of partial {$*$}-algebras
1991
This second paper on partial Op*-algebras is devoted to the theory of representations. A new definition of invariant positive sesquilinear forms on partial *-algebras is proposed, which enables to perform the familiar GNS construction. In order to get a better control of the corresponding representations, we introduce and study a restricted class of partial Op*-algebras, called partial GW*-algebras, which turn up naturally in a number of problems. As an example, we extend Powers' results about the standardness of GNS representations of abelian partial *-algebras.
Some Problems on Homomorphisms and Real Function Algebras
2001
In this paper we solve a problem about the representation of all homomorphisms on a real function algebra as point evaluations and another two about function algebras in which homomorphisms are point evaluations on sequences in the algebra.
Vectors, Tensors, Manifolds and Special Relativity
2015
Assuming that the reader is familiar with the notion of vectors, within a few pages, with a few examples, the reader will get to be familiar with the generic picture of tensors. With the specific notions given in this chapter, the reader will be able to understand more advanced tensor courses with no further effort. The transition between tensor algebra and tensor calculus is done naturally with a very familiar example. The notion of manifold and a few basic key aspects on Special Relativity are also presented.
Ensuring High Performance of Consensus-Based Estimation by Lifetime Maximization in WSNs
2015
The estimation of a parameter corrupted by noise is a common tasks in wireless sensor networks, where the deployed nodes cooperate in order to improve their own inaccurate observations. This cooperation usually involves successive data exchanges and local information updates until a global consensus value is reached. The quality of the final estimator depends on the amount of collected observations, hence the number of active nodes. Moreover, the inherent iterative nature of the consensus process involves a certain energy consumption. Since the devices composing the network are usually battery powered, nodes becoming inactive due to battery depletion emerges as a serious problem. In this wo…
Solving word problems algebraically in a spreadsheet environment in a primary school
2013
This paper presents some results from an investigation into the teaching of the algebraic solving of word problems in a spreadsheet environment in the sixth grade of primary school in Spain (11-12 year old pupils). The main aim of the study was to investigate whether the spreadsheet could be a mediator to the teaching of algebraic problem solving. Through the analysis of excerpts from a case study, the core of the paper is focused on two different types of the difficulties that students showed when solving problems algebraically in a spreadsheet environment.
The Bernstein Basis and its applications in solving geometric constraint systems
2012
International audience; This article reviews the properties of Tensorial Bernstein Basis (TBB) and its usage, with interval analysis, for solving systems of nonlinear, univariate or multivariate equations resulting from geometric constraints. TBB are routinely used in computerized geometry for geometric modelling in CAD-CAM, or in computer graphics. They provide sharp enclosures of polynomials and their derivatives. They are used to reduce domains while preserving roots of polynomial systems, to prove that domains do not contain roots, and to make existence and uniqueness tests. They are compatible with standard preconditioning methods and fit linear program- ming techniques. However, curre…
A Teaching proposal for the study of eigenvectors and eigenvalues
2017
[EN] In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students¿ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.