Search results for "Linear map"

Cocharacters of Bilinear Mappings and Graded Matrices

2012

Let Mk(F) be the algebra of k ×k matrices over a field F of characteristic 0. If G is any group, we endow Mk(F) with the elementary grading induced by the k-tuple (1,...,1,g) where g ∈ G, g2 ≠ 1. Then the graded identities of Mk(F) depending only on variables of homogeneous degree g and g − 1 are obtained by a natural translation of the identities of bilinear mappings (see Bahturin and Drensky, Linear Algebra Appl 369:95–112, 2003). Here we study such identities by means of the representation theory of the symmetric group. We act with two copies of the symmetric group on a space of multilinear graded polynomials of homogeneous degree g and g − 1 and we find an explicit decomposition of the …

Cyclic response of masonry infilled RC frames: Experimental results and simplified modeling

2014

The recent large interest in nonlinear seismic analysis methods, static and dynamic, has required proper strategies of modeling based on reliable, and at the same time easy to use, constitutive laws for the structural elements. Regarding the behavior of framed structures, special attention has to be devoted to infills because of the key role they play in modifying overall stiffness, strength and ductility under seismic excitation. Pointing out the attention on this topic the paper discusses a criteria for modeling the structural behavior of infills based on a macromodeling approach, that is to say on the substitution of infills with diagonal pin jointed struts. Is here shown how multilinear…

Centralizers and Multilinear Polynomials in Non-Commutative Rings

1979

Closed injective ideals of multilinear operators, related measures and interpolation

2020

[EN] We introduce and discuss several ways of extending the inner measure arisen from the closed injective hull of an ideal of linear operators to the multilinear case. In particular, we consider new measures that allow to characterize the operators that belong to a closed injective ideal of multilinear operators as those having measure equal to zero. Some interpolation formulas for these measures, and consequently interpolation results involving ideals of multilinear operators, are established. Examples and applications related to summing multilinear operators are also shown.

Application of molecular topology for the prediction of the reaction times and yields under solvent-free conditions

2010

Ball milling and conventional magnetic stirring can be used to support different laboratory techniques with a highly efficient mixing of reagents under solvent-free conditions. By using multilinear regression and linear discriminant analysis, topological-mathematical models have been built to predict the yield and the reaction time for organocatalytic reactions, Suzuki reactions and reactions of synthesis of heterocyclic compounds. The results from the in silico predictions confirm the usefulness of the approach followed.

QuBiLS-MIDAS: A parallel free-software for molecular descriptors computation based on multilinear algebraic maps

2014

The present report introduces the QuBiLS-MIDAS software belonging to the ToMoCoMD-CARDD suite for the calculation of three-dimensional molecular descriptors (MDs) based on the two-linear (bilinear), three-linear, and four-linear (multilinear or N-linear) algebraic forms. Thus, it is unique software that computes these tensor-based indices. These descriptors, establish relations for two, three, and four atoms by using several (dis-)similarity metrics or multimetrics, matrix transformations, cutoffs, local calculations and aggregation operators. The theoretical background of these N-linear indices is also presented. The QuBiLS-MIDAS software was developed in the Java programming language and …

On Spatio-Temporal Saliency Detection in Videos using Multilinear PCA

2016

International audience; Visual saliency is an attention mechanism which helps to focus on regions of interest instead of processing the whole image or video data. Detecting salient objects in still images has been widely addressed in literature with several formulations and methods. However, visual saliency detection in videos has attracted little attention, although motion information is an important aspect of visual perception. A common approach for obtaining a spatio-temporal saliency map is to combine a static saliency map and a dynamic saliency map. In this paper, we extend a recent saliency detection approach based on principal component analysis (PCA) which have shwon good results wh…

Multilinear sparse decomposition for best spectral bands selection

2014

Optimal spectral bands selection is a primordial step in multispectral images based systems for face recognition. In this context, we select the best spectral bands using a multilinear sparse decomposition based approach. Multispectral images of 35 subjects presenting 25 different lengths from 480nm to 720nm and three lighting conditions: fluorescent, Halogen and Sun light are groupped in a 3-mode face tensor T of size 35x25x2 . T is then decomposed using 3-mode SVD where three mode matrices for subjects, spectral bands and illuminations are sparsely determined. The 25x25 spectral bands mode matrix defines a sparse vector for each spectral band. Spectral bands having the sparse vectors with…

Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation

2017

In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization t…

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 ) .