‎A rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operations‎. ‎Moreover‎, ‎by using this equality and Theorems 8 and 10 in [Chen M‎. ‎and et al‎. ‎On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications‎, ‎The Scientific World Journal 2014 (2014)‎, ‎Article ID 702413‎, ‎7 page...

Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...

In the present paper, we introduce the sequence space [{l_p}(E,Delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {E_n}} x_j - sum_{j in E_{n + 1}} x_jright| ^p < infty right},] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of fin...

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...

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.

in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

we present a detailed analysis of the static tuning characteristics of three section tunable distributed bragg reflector (dbr) laser. the analysis is based on the transfer matrix method (tmm), transmission line and scattering theory. the key feature of the analysis is the use of modified oscillation condition. with the exact oscillation condition, the static tuning characteristics such as thres...

we denote by $ls[n](t,k,v)$ a large set of $t$-$(v,k,lambda)$ designs of size $n$, which is a partition of all  $k$-subsets ofa $v$-set into $n$ disjoint  $t$-$(v,k,lambda)$ designs and$n={v-t choose k-t}/lambda$.   we use the notation$n(t,v,k,lambda)$ as the maximum possible number of mutuallydisjoint cyclic $t$-$(v,k,lambda)$designs. in this paper we givesome new bounds for $n(2,29,4,3)$ and ...

the paper presents lower and upper bounds on the number of parity check digits required for a linear code that detects solid bursts of length $b$ or less and simultaneously any $e$ or less random errors. an example of such a code is also provided. further, codes capable of detecting and simultaneously correcting such errors have also been dealt with.