several representations of the generalized drazin inverse of an anti-triangular block matrix in banach algebra are given in terms of the generalized banachiewicz--schur form.

Introduction The first part of the paper presents several properties of saddle point matrices with two vector blocks. In these block matrices, the top-left block is a real square matrix , the topright block is the column vector with all entries , the bottom-left block is transposed, and the bottom-right block has the single entry . If is symmetric, the saddle point matrix can be interpreted as ...

A novel hierarchical approach is proposed to symbolic analysis of large analog circuits. The key idea is to use a graph-based representation—called Determinant Decision Diagram (DDD)— to represent the symbolic determinant and cofactors associated with the MNA matrix for each subcircuit block. By exploiting the inherent sharing and sparsity of symbolic expressions, DDD is capable of representing...

Nonnegative Matrix Factorization (NMF) [1, 2] has been widely used in audio research, e.g. automatic music transcription [3], musical source separation [4], and speech enhancement [5]. The key strategy for applying NMF to audio-related tasks is to find a lower rank representation of the Short Time Fourier Transformed (STFT) input signal and use the basis vectors as dictionaries. For example, in...

and Hajnal [I] introduced the real function f(a) =inf {.P(G) J ~~i~: ~a}. They asked about the behaviour ofj(rx) as rx tends to infinity. The complete bipartite graph Kn,n shows that f(n)~c ·log n for n~2, but originally it was unknown whether f(a) is bouJ1ded or not. Recently Gyarfas, Koml6s and Szemeredi (2] showed that f(a) ~a ·log a, provided that a>b, where a and bare suitable contants. Ob...

matrix metalloproteinases (mmps) play an important role in gastric cancer (gc). accumulated evidence suggests that functional mmp-1 and mmp-7 gene polymorphisms are associated with several tumors. the aim of this study was to investigate two single nucleotide polymorphisms, mmp-1 -1607 1g/2g and mmp-7 -181 a/g, and their potential relationship with gc. we examined 246 gc  patients and 252 age-a...

‎In this paper‎, ‎we find matrix representation of a class of sixth order Sturm-Liouville problem (SLP) with separated‎, ‎self-adjoint boundary conditions and we show that such SLP have finite spectrum‎. ‎Also for a given matrix eigenvalue problem $HX=lambda VX$‎, ‎where $H$ is a block tridiagonal matrix and $V$ is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of Atkin...

‎in this paper‎, ‎we find matrix representation of a class of sixth order sturm-liouville problem (slp) with separated‎, ‎self-adjoint boundary conditions and we show that such slp have finite spectrum‎. ‎also for a given matrix eigenvalue problem $hx=lambda vx$‎, ‎where $h$ is a block tridiagonal matrix and $v$ is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of atkin...

We develop a covariance-matrix-based uncertainty analysis for vector-network-analyzer scattering-parameter measurements. The covariance matrix captures all of the measurement uncertainties and statistical correlations between them. This allows the uncertainties of vector-network-analyzer scattering-parameter measurements to be propagated into the uncertainties of other quantities derived from s...