in this note we characterize polynomial numerical hulls of matrices $a in m_n$ such that$a^2$ is hermitian. also, we consider normal matrices $a in m_n$ whose $k^{th}$ power are semidefinite. for such matriceswe show that $v^k(a)=sigma(a)$.

Potential interactions between connectionist learning syst ems and algorithms modeled aft er evolutionary adapt ation are becoming of increasing interest . In a recent short and elegant paper Hinton and Nowlan extend a version of Holland's genetic algorithm (GA) t o consider ways in which the evolution of species and th e learning of individu als might in teract [17]. Their mod el is valuable b...

In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.

local scouring around bridge piers is a natural phenomenon caused by the erosive process of flowing stream on alluvial beds. the 3d flow field around bridge piers interacting with the bed materials increases complexity of local scour process. the local scour depth develops in accelerated flows and if it is not predicted correctly, the bottom level of local scour hole will exceed the original le...

in this paper, we introduce the notions of c-numerical range and c-spectrum of matrix polynomials. some algebraic and geometrical properties are investigated. we also study the relationship between the c-numerical range of a matrix polynomial and the joint c-numerical range of its coefficients.

in this note, a generalization of higher rank numerical range isintroduced and some of its properties are investigated

to control the nonlinear numerical instability, throughout the time evolution of the eulerian form of the nonlinear rotating shallow water equations, it is necessary to add numerical diffusion to the solution. it is clear that, this extra numerical diffusion degrades the accuracy of the numerical solution and should be kept as small as possible. in a conventional approach a hyper-diffusion is u...