Symmetries are not only fascinating, but they can also be exploited when designing numerical algorithms and data structures for scientific engineering problems in symmetrical domains. Geometrical symmetries are studied, particularly in the context of so called equivariant operators, which are relevant to a wide range of numerical applications. In these cases, it is possible to exploit the symme...

In this paper, we obtain the distribution functions of the range and the quasi-range of the random variables arising from the extended type I generalized logistic distribution.

‎The aim of this paper is to study distribution of ratios of generalized order statistics from pareto distribution. parameter estimation of Pareto distribution based on generalized order statistics and ratios of them have been obtained. Inferences using method of moments and unbiased estimator have been obtained to develop point estimations. Consistency of unbiased estimator has been illustrate...

let $p(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. in this paper, some algebraic and geometrical properties of the $k$-numerical range of $p(lambda)$ are investigated. in particular, the relationship between the $k$-numerical range of $p(lambda)$ and the $k$-numerical range of its companion linearization is stated. moreover, the $k$-numerical ...

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 $V^k(A)=sigma(A)$.

We investigate the thermodynamic properties of Hamiltonian mean-field(HMF) model as a prototypical long-range system by means of the non-extensive thermostatistics. Especially, the quasi-equilibrium state as extremum state of the generalized Tsallis entropy is studied and its thermodynamic stability is analyzed. Based on these analysis, the connection with quasi-stationary behaviors found in th...