given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  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 the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

a highly selective, rapid and economical differential pulse polarographic method has been developed for the determination of trace amounts of cadmium and lead present together in various standard alloys and biological samples after adsorption of their 1-(2-pyridylazo)-2-naphthol complexes on microcrystalline naphthalene. cadmium and lead complexes are equantitatively adsorbed on microcrystallin...

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

the submodules with the property of the title ( a submodule $n$ of an $r$-module $m$ is called strongly dense in $m$, denoted by $nleq_{sd}m$, if for any index set $i$, $prod _{i}nleq_{d}prod _{i}m$) are introduced and fully investigated. it is shown that for each submodule $n$ of $m$ there exists the smallest subset $d'subseteq m$ such that $n+d'$ is a strongly dense submodule of $m$...

A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...

conclusions these findings showed that 25(oh)d insufficiency was highly prevalent in hd cases and higher amount of 25(oh)d levels prevent shpt. methods a prospective experimental trial of 180 hd patients (f: 81, m: 99, age > 14year) participated in the study. at base line, levels of 25(oh)d, intact parathyroid hormone (ipth), calcium (ca), phosphorous (p), alkaline phosphatase (alk p), and albu...

in this work, a novel method is described for the preconcentration of pb2+, cd2+ and zn2+ ions in environmental samples using uniform silanized mesopor (lus-1) functionalized by ethylenediamine groups as a new extractant. the determination of ions is done by inductively coupled plasma optical emission spectrometry (icp-oes). the extraction time and efficiency, ph and amount of adsorbent, minimu...

We introduce the notion of uniform number of a graph. The  uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$ ...