Search results for "LYN"

A note on the rational canonical form of an endomorphism of a vector space of finite dimension

2018

[EN] In this note, we give an easy algorithm to construct the rational canonical form of a square matrix or an endomorphism h of a finite dimensional vector space which does not depend on either the structure theorem for finitely generated modules over principal ideal domains or matrices over the polynomial ring. The algorithm is based on the construction of an element whose minimum polynomial coincides with the minimum polynomial of the endomorphism and on the fact that the h-invariant subspace generated by such an element admits an h-invariant complement. It is also shown that this element can be easily obtained without the factorisation of a polynomial as a product of irreducible polynom…

Group graded algebras and almost polynomial growth

2011

Let F be a field of characteristic 0, G a finite abelian group and A a G-graded algebra. We prove that A generates a variety of G-graded algebras of almost polynomial growth if and only if A has the same graded identities as one of the following algebras: (1) FCp, the group algebra of a cyclic group of order p, where p is a prime number and p||G|; (2) UT2G(F), the algebra of 2×2 upper triangular matrices over F endowed with an elementary G-grading; (3) E, the infinite dimensional Grassmann algebra with trivial G-grading; (4) in case 2||G|, EZ2, the Grassmann algebra with canonical Z2-grading.

Explicit extension maps in intersections of non-quasi-analytic classes

2005

Absolute and monotonic norms

1961

Applications of the Connection between Approximation Theory and Algebra

2009

The aim of this paper is to illustrate a possibility of obtaining various theoretical results using the connection between multivariate interpolation and reduction process with respect to a H-basis of an ideal. Using this connection we can switch between interpolation theory and the theory of ideals. As a application of this connection, we found and proved an interesting identity, which is satisfied for all polynomials in d variables from an interpolation polynomial subspace.

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.

Group Actions and Asymptotic Behavior of Graded Polynomial Identities

2002

Periodic Polynomial Splines

2018

In this chapter, the spaces of periodic polynomial splines and the Spline Harmonic Analysis (SHA) in these spaces are briefly outlined. The stuff of this chapter is used for the design of periodic discrete-time splines and discrete-time-spline-based wavelets and wavelet packets. For a detailed description of the subject we refer to (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [1]. Periodic polynomial splines provide an example of mixed discrete-continuous circular convolution.

Sur les feuilletages alg�briques de Rolle

1997

L'objet de ce travail est l'etude des feuilletages algebriques de Rolle dans \( \Bbb {R}^n \). On montre que leur restriction au complementaire d'un nombre fini de feuilles possede une structure de produit. On precise aussi la topologie de certaines de leurs feuilles.

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…