Search results for "Polynomial"

On-eye optical quality of daily disposable contact lenses for different wearing times

2012

Purpose To quantify the optical quality of various daily disposable contact lenses in vivo and to ascertain its variation in terms of wearing time by means of objective non-invasive determination of wavefront patterns. Methods The crx1 adaptive-optics system was used to measure the wavefront aberrations in 15 myopic eyes before and at 2-h intervals after contact lens fitting, over a 12-h wearing period. Seven types of contact lenses having different material, water content and lens design were evaluated in this study: Dailies Total1, Dailies AquaComfort Plus, Proclear 1 Day, 1-Day Acuvue TruEye, 1-Day Acuvue moist, SofLens daily disposable and Clariti 1-Day. The aberration data were analyse…

Age-related dermal collagen changes during development, maturation and ageing - a morphometric and comparative study.

2014

The tissue organisation of dermal collagen is gaining importance as a contributing factor both in development and ageing, as well as in skin maturation processes. In this work we aim to study different representative parameters of this structural organisation in 45 human skin samples of assorted ages, by means of image analysis. The variation of these parameters on the basis of age was assessed using several regression models (linear, quadratic and cubic). The area occupied by collagen was significantly reduced as a function of age in the papillary dermis (R(2) = 0.437, P < 0.0001), as well as the thickness of the collagen bundles (R(2) = 0.461, P < 0.0001), following statistical models of …

Uncertainty quantification in simulations of epidemics using polynomial chaos.

2012

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equa…

Computing the ℤ2-Cocharacter of 3 × 3 Matrices of Odd Degree

2013

Let F be a field of characteristic 0 and A = M 2, 1(F) the algebra of 3 × 3 matrices over F endowed with the only non trivial ℤ2-grading. Aver'yanov in [1] determined a set of generators for the T 2-ideal of graded identities of A. Here we study the identities in variables of homogeneous degree 1 via the representation theory of the symmetric group, and we determine the decomposition of the corresponding character into irreducibles.

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.