Let T be a linear operator defined on a complex vector space X and let n be a positive integer. Kaplansky [4] proved that T is algebraic of degree at most n if and only if for every x ∈ X the vectors x, Tx, . . . , Tnx are linearly dependent. One consequence of Kaplansky’s result is that if X is a Banach space and T : X → X a bounded linear operator, then T is algebraic if and only if for every...

in this paper, we generalize a theorem of shao [12] by assuming that is a sequence of linear negatively dependent random variables. also, we extend some theorems of chao [6] and thrum [14]. it is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of real numbe...

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cramér-Lundberg processes we obtain the Laplace transform in space of the probability that ...

We perform molecular dynamics simulations to investigate the Poisson's ratio of graphene oxide. We find that the Poisson's ratio can be effectively tuned by increasing the degree of oxidation of graphene oxide. More specifically, the Poisson's ratio decreases linearly from positive to negative with increasing oxidation, turning negative at room temperature for a degree of oxidation of 0.27, and...

A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a finite locally linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the ...

Abstract In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant {(t, x)| t ≥ 0, x ≥ 0} is investigated. Under the assumption that the right hand side satisfies matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence a...

PURPOSE To characterize total retinal blood flow in a group of healthy subjects. METHODS Included in this study were 64 healthy volunteers. Retinal venous diameters were measured using a dynamic vessel analyzer. Retinal blood velocities were measured using bidirectional laser Doppler velocimetry. All vessels with a diameter of >60 μm entering the optic nerve head were measured. Total retinal ...