Search results for "Applied Mathematics"

Brauer's height zero conjecture for the 2-blocks of maximal defect

2012

Codimension growth of special simple Jordan algebras

2009

Let $R$ be a special simple Jordan algebra over a field of characteristic zero. We exhibit a noncommutative Jordan polynomial $f$ multialternating on disjoint sets of variables which is not a polynomial identity of $R$. We then study the growth of the polynomial identities of the Jordan algebra $R$ through an analysis of its sequence of Jordan codimensions. By exploiting the basic properties of the polynomials $f$, we are able to compute the exponential rate of growth of the sequence of Jordan codimensions of $R$ and prove that it equals the dimension of the Jordan algebra over its center. We also show that for any finite dimensional special Jordan algebra, such exponential rate of growth c…

A Lattice-Geometric Proof of Wedderburn’s Theorem

1993

This note presents a proof of Wedderburn’s theorem concerning the classification of semisimple rings within the conceptual frame of projective lattice geometry.

Blocks with 𝑝-power character degrees

2005

Let B B be a p p -block of a finite group G G . If χ ( 1 ) \chi (1) is a p p -power for all χ ∈ Irr ⁡ ( B ) \chi \in \operatorname {Irr}(B) , then B B is nilpotent.

Volume growth and parabolicity

2001

Multiplication of Distributions in One Dimension: Possible Approaches and Applications to δ-Function and Its Derivatives

1995

We introduce a new class of multiplications of distributions in one dimension merging two different regularizations of distributions. Some of the features of these multiplications are discussed in detail. We use our theory to study a number of examples, involving products between Dirac delta functions and its successive derivatives. © 1995 Academic Press. All rights reserved.

Asymptotically good codes from generalized algebraic-geometry codes

2005

We consider generalized algebraic-geometry codes, based on places of the same degree of a fixed algebraic function field over a finite field. In this note, using a method similar to the Justesen's one, we construct a family of such codes which is asymptotically good.

Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics

2010

Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz pro…

An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation

2007

A preconditioner defined by an algebraic multigrid cycle for a damped Helmholtz operator is proposed for the Helmholtz equation. This approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRES method are studied with linear, quadratic, and cubic finite element discretizations. Numerical experiments are performed with two-dimensional problems describing acoustic scattering in a cross-section of a car cabin and in a layered medium. Asymptotically the number of iterations grows linearly with respect to the frequency while for lower freq…

A damping preconditioner for time-harmonic wave equations in fluid and elastic material

2009

A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains. peerReviewed