A multivariate Gaussian input density achieves capacity for multiple-input multiple-output flat fading channels with additive white Gaussian noise and perfect receiver channel state information. Capacity computation for these channels reduces to the problem of finding the best input covariance matrix, and is in general a convex semi-definite program. This paper presents Kuhn-Tucker optimality c...

In this paper, we study the dynamic phase transition for one dimensional Brusselator model. By linear stability analysis, define two critical numbers \begin{document}$ {\lambda}_0 $\end{document} and id="M2">\begin{document}$ {\lambda}_1 control parameter id="M3">\begin{document}$ {\lambda} in equation. M...

let $g$ be a simple graph with vertex set $v(g) = {v_1, v_2,ldots, v_n}$ and edge set $e(g) = {e_1, e_2,ldots , e_m}$. similar tothe randi'c matrix, here we introduce the randi'c incidence matrixof a graph $g$, denoted by $i_r(g)$, which is defined as the$ntimes m$ matrix whose $(i, j)$-entry is $(d_i)^{-frac{1}{2}}$ if$v_i$ is incident to $e_j$ and $0$ otherwise. naturally, therandi'c incidenc...

The eigenvalues of a nonhermitian Toeplitz matrix A are usually highly sensitive to perturbations, having condition numbers that increase exponentially with the dimension N. An equivalent statement is that the resolvent ( ZZ A)’ of a Toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest-exponentially large as a function of N, even when z is far from the spectrum. B...

This paper presents a version of the Bartels-Stewart algorithm for solving Sylvester and Lyapunov equations that utilizes Jordan-Schur form equation matrices. The is type Schur which contains additional information about Jordan structure corresponding matrix. can be used to solve more efficiently in some cases. A two-level implemented allows us find directly non-scalar blocks solution These hav...

the stability analysis of islanded inverter-based microgrids (ibmgs) is increasingly an important and challenging topic due to the nonlinearity of ibmgs. in this paper, a new linear model for such microgrids as well as an iterative method to correct the linear model is proposed. using the linear model makes it easy to analyze the eigenvalues and stability of ibmgs due to the fact that it derive...

The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...