Search results for "Matrix"
showing 10 items of 3205 documents
GRADED IDENTITIES FOR THE ALGEBRA OF n×n UPPER TRIANGULAR MATRICES OVER AN INFINITE FIELD
2003
We consider the algebra Un(K) of n×n upper triangular matrices over an infinite field K equipped with its usual ℤn-grading. We describe a basis of the ideal of the graded polynomial identities for this algebra.
Benchmarking parameter-free AMaLGaM on functions with and without noise.
2013
We describe a parameter-free estimation-of-distribution algorithm (EDA) called the adapted maximum-likelihood Gaussian model iterated density-estimation evolutionary algorithm (AMaLGaM-ID[Formula: see text]A, or AMaLGaM for short) for numerical optimization. AMaLGaM is benchmarked within the 2009 black box optimization benchmarking (BBOB) framework and compared to a variant with incremental model building (iAMaLGaM). We study the implications of factorizing the covariance matrix in the Gaussian distribution, to use only a few or no covariances. Further, AMaLGaM and iAMaLGaM are also evaluated on the noisy BBOB problems and we assess how well multiple evaluations per solution can average ou…
Optimal Impulse Control Problems and Linear Programming
2009
Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the optimal impulse control problem via a binary linear programming proble…
Superinvolutions on upper-triangular matrix algebras
2018
Let UTn(F) be the algebra of n×n upper-triangular matrices over an algebraically closed field F of characteristic zero. In [18], the authors described all abelian G-gradings on UTn(F) by showing that any G-grading on this algebra is an elementary grading. In this paper, we shall consider the algebra UTn(F) endowed with an elementary Z2-grading. In this way, it has a structure of superalgebra and our goal is to completely describe the superinvolutions which can be defined on it. To this end, we shall prove that the superinvolutions and the graded involutions (i.e., involutions preserving the grading) on UTn(F) are strictly related through the so-called superautomorphisms of this algebra. We …
Trace identities and almost polynomial growth
2021
In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.
Varieties of special Jordan algebras of almost polynomial growth
2019
Abstract Let J be a special Jordan algebra and let c n ( J ) be its corresponding codimension sequence. The aim of this paper is to prove that in case J is finite dimensional, such a sequence is polynomially bounded if and only if the variety generated by J does not contain U J 2 , the special Jordan algebra of 2 × 2 upper triangular matrices. As an immediate consequence, we prove that U J 2 is the only finite dimensional special Jordan algebra that generates a variety of almost polynomial growth.
Jacobian-free approximate solvers for hyperbolic systems: Application to relativistic magnetohydrodynamics
2017
Abstract We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers hav…
Jacobian-Free Incomplete Riemann Solvers
2018
The purpose of this work is to present some recent developments about incomplete Riemann solvers for general hyperbolic systems. Polynomial Viscosity Matrix (PVM) methods based on internal approximations to the absolute value function are introduced, and they are compared with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Moreover, they can be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions. Some numerical experiments involving the relativistic magnetohydrodyn…
Model of the mechanical response of short flax fiber reinforced polymer matrix composites
2011
Abstract Natural-fiber-reinforced short-fiber composites are finding more applications lately, therefore there is a need for estimation of the mechanical properties of such composites based on the properties of the constituents. The fibers themselves also possess complicated internal structure, resulting in anisotropy of their properties. Taking into account the internal structure of bast fiber, we evaluate the elastic properties of a composite unit cell, consisting of a fiber of average length and matrix according to the fiber volume fraction in the composite. The unit cell properties are used to estimate the stiffness of a misaligned short-fiber composite by means of orientation averaging…
Study of thermal properties of polyethylene and polypropylene nanocomposites with long alkyl chain-substituted POSS fillers
2016
The effect of incorporation of octakis({alkyl}dimethylsiloxy)octasilsesquioxanes molecules with n-octyl, n-octadecyl and 4-methyl-hexyl substituents on thermal properties of polypropylene (PP), low-density polyethylene (LDPE) and high-density polyethylene (HDPE) was investigated. Thermal properties of those composite materials were evaluated by means of the differential scanning calorimetry (DSC) and thermogravimetric analysis (TG) methods. The type and mass% content of POSS nanofillers influenced the crystallization and melting properties as well as thermal stability of the obtained polyolefin nanocomposites. The incorporated POSS particles—acting as nucleating agents—improved the crystall…