Search results for "Polynomial"
showing 10 items of 566 documents
Gradings on the algebra of upper triangular matrices of size three
2013
Abstract Let UT 3 ( F ) be the algebra of 3 × 3 upper triangular matrices over a field F . On UT 3 ( F ) , up to isomorphism, there are at most five non-trivial elementary gradings and we study the graded polynomial identities for such gradings. In case F is of characteristic zero we give a complete description of the space of multilinear graded identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . We finally compute the multiplicities in the graded cocharacter sequence for every elementary G -grading on UT 3 ( F ) .
Standard polynomials and matrices with superinvolutions
2016
Abstract Let M n ( F ) be the algebra of n × n matrices over a field F of characteristic zero. The superinvolutions ⁎ on M n ( F ) were classified by Racine in [12] . They are of two types, the transpose and the orthosymplectic superinvolution. This paper is devoted to the study of ⁎-polynomial identities satisfied by M n ( F ) . The goal is twofold. On one hand, we determine the minimal degree of a standard polynomial vanishing on suitable subsets of symmetric or skew-symmetric matrices for both types of superinvolutions. On the other, in case of M 2 ( F ) , we find generators of the ideal of ⁎-identities and we compute the corresponding sequences of cocharacters and codimensions.
On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques
2020
Abstract We discuss several approaches involving the reconstruction of discontinuous one-dimensional functions using parameter-dependent multiquadric radial basis function (MQ-RBF) local interpolants combined with weighted essentially non-oscillatory (WENO) techniques, both in the computation of the locally optimized shape parameter and in the combination of RBF interpolants. We examine the accuracy of the proposed reconstruction techniques in smooth regions and their ability to avoid Gibbs phenomena close to discontinuities. In this paper, we propose a true MQ-RBF–WENO method that does not revert to the classical polynomial WENO approximation near discontinuities, as opposed to what was pr…
Optical Quality Comparison of Conventional and Hole-Visian Implantable Collamer Lens at Different Degrees of Decentering
2012
To compare the optical quality of implantable Collamer lens (ICL) with and without central hole (Hole ICL and conventional ICL) at different degrees of decentering.Experimental laboratory investigation.Wavefront aberrations of the -3, -6, and -12 diopter (D) V4b and -3, -6, and -12 D V4c ICLs were measured in 3 conditions-centered and decentered 0.3 and 0.6 mm-at 3-mm and 4.5-mm pupils. The root mean square of total higher order aberrations, trefoil, coma, tetrafoil, secondary astigmatism, and spherical aberration were evaluated. In addition, point spread function and simulated retinal images of ICLs were calculated from the wavefront aberrations for each ICL and all conditions of decenteri…
A PSO algorithm for designing 3d highway alignments adopting polynomial solutions
2017
Intelligent optimization algorithms for highway alignments have produced good results so far. However, considering the numerous constraints and factors directly implied in the infrastructure design, the researchers' efforts usually focus only on simplifying the alignment choice, supporting engineers in the design phase. Implementing strategic considerations regarding comfort and safety would be also very important. In this paper, the authors propose a method for designing improved 3D highway alignments using a specific optimization algorithm, based on a Swarm Intelligence technique, adopting an innovative polynomial transition curve as the unique horizontal curvature element, called PPC (Po…
Greedy and K-Greedy algoritmhs for multidimensional data association
2011
[EN] The multidimensional assignment (MDA) problem is a combinatorial optimization problem arising in many applications, for instance multitarget tracking (MTT). The objective of an MDA problem of dimension $d\in\Bbb{N}$ is to match groups of $d$ objects in such a way that each measurement is associated with at most one track and each track is associated with at most one measurement from each list, optimizing a certain objective function. It is well known that the MDA problem is NP-hard for $d\geq3$. In this paper five new polynomial time heuristics to solve the MDA problem arising in MTT are presented. They are all based on the semi-greedy approach introduced in earlier research. Experimen…
Pseudo-Abelian integrals along Darboux cycles
2008
We study polynomial perturbations of integrable, non-Hamiltonian system with first integral of Darboux-type with positive exponents. We assume that the unperturbed system admits a period annulus. The linear part of the Poincare return map is given by pseudo-Abelian integrals. In this paper we investigate analytic properties of these integrals. We prove that iterated variations of these integrals vanish identically. Using this relation we prove that the number of zeros of these integrals is locally uniformly bounded under generic hypothesis. This is a generic analog of the Varchenko-Khovanskii theorem for pseudo-Abelian integrals. Finally, under some arithmetic properties of exponents, the p…
Disposition-Content Congruency in Adolescents’ Alcohol-Related Social Media (Self-) Effects: The Role of the Five-Factor Model
2019
Objective: Accumulating evidence indicates that social networking sites play an increasingly important role in young people’s drinking behavior. The present study adds to this research by assessing the conditionality of the relationships between exposure to and self-sharing of alcohol-related content on social media and adolescents’ drinking behavior. Specifically, the moderating role of the five-factor model of personality is determined. Method: A cross-sectional survey study was conducted among 866 mid-adolescents (Msubsample = 14.85 years, SD = 0.71, 57.5% girls). Polynomial regression analysis with response surface modeling was used to test the interactions. Results: Exposure, but not s…
A New Hybrid Mutation Operator for Multiobjective Optimization with Differential Evolution
2011
Differential evolution has become one of the most widely used evolution- ary algorithms in multiobjective optimization. Its linear mutation operator is a sim- ple and powerful mechanism to generate trial vectors. However, the performance of the mutation operator can be improved by including a nonlinear part. In this pa- per, we propose a new hybrid mutation operator consisting of a polynomial based operator with nonlinear curve tracking capabilities and the differential evolution’s original mutation operator, to be efficiently able to handle various interdependencies between decision variables. The resulting hybrid operator is straightforward to implement and can be used within most evoluti…
Mixed Circular Convolutions and Zak Transforms
2014
In this chapter the notion of mixed circular convolution is introduced. The polynomial and discrete periodic splines defined on uniform grids are special cases of such convolutions. The so-called Zak transforms provide tools to handle mixed circular convolutions