Spectral properties of special matrices matrices have been widely applied. We focus on monomial matrices over a finite field Fp, p 6= 2. We describe a way to find the minimal annihilating polynomial, a set of linearly independent eigenvectors.

Pairs (A,B) of mutually annihilating operators AB = BA = 0 on a finite dimensional vector space over an algebraically closed field were classified by Gelfand and Ponomarev [Russian Math. Surveys 23 (1968) 1–58] by method of linear relations. The classification of (A,B) over any field was derived by Nazarova, Roiter, Sergeichuk, and Bondarenko [J. Soviet Math. 3 (1975) 636–654] from the classifi...

In this paper we study the following system of reaction-diffusion equations: ∂ /∂t = ∆ − V + λδ0, (0, x) ≡ 0, ∂V/∂t = − V, V (0, x) ≡ 1. Here (t, x) and V (t, x) are functions of time t ∈ [0,∞) and space x ∈ R. This system describes a continuum version of a model in which particles are injected at the origin at rate λ, perform independent simple symmetric random walks on Z, and are annihilated ...

The ππ and qq̄ annihilation mechanisms of dilepton production during relativistic nuclear collisions are studied. We focus on the modifications caused by the specific features of in-medium pion and quark states rather than by medium modification of the ρ-meson spectral density. The main ingredient emerging in our approach is a form-factor of the multi-pion (multi-quark) system. Replacing the usu...

Spiking neural P systems with anti-spikes (shortly named ASN P systems) are a class of distributed and parallel neural-like computing systems. Besides spikes, neurons in ASN P systems can also contain a number of anti-spikes. Whenever spikes and anti-spikes meet in a neuron, they annihilate each other immediately in a maximal manner, that is, the annihilation has priority over neuron’s spiking....

In this paper, we propose a sparse and low-rank decomposition of annihilating filter-based Hankel matrix for removing MR artifacts such as motion, RF noises, or herringbone artifacts. Based on the observation that some MR artifacts are originated from k-space outliers, we employ a recently proposed image modeling method using annihilating filter-based low-rank Hankel matrix approach (ALOHA) to ...