Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m in T(M)$. In this paper we study the domination number of $T(Gamma(M))$ a...

The number theoretic analogue of a net in metric geometry suggests new problems and results in combinatorial and additive number theory. For example, for a fixed integer g ≥ 2, the study of h-nets in the additive group of integers with respect to the generating set Ag = {0}∪{±g : i = 0, 1, 2, . . .} requires a knowledge of the word lengths of integers with respect to Ag. A g-adic representation...

let $r$ be a commutative ring and $m$ be an $r$-module with $t(m)$ as subset,   the set of torsion elements. the total graph of the module denoted   by $t(gamma(m))$, is the (undirected) graph with all elements of   $m$ as vertices, and for distinct elements  $n,m in m$, the   vertices $n$ and $m$ are adjacent if and only if $n+m in t(m)$. in this paper we   study the domination number of $t(ga...

The $$\mathrm {SU}(r)$$ Vafa–Witten partition function, which virtually counts Higgs pairs on a projective surface S, was mathematically defined by Tanaka–Thomas. On the Langlands dual side, first-named author recently introduced virtual of $$\mu _r$$ -gerbes. In this paper, we instead use Yoshioka’s moduli spaces twisted sheaves. Using Chern character rational B-field, give new mathematical de...

evaluation of urmia medical university faculty member views about research obstacles r salem safy ,ma bn ashraf rezaei ,?bsc r sadatian , msc z moshirie , msc n sheikhy , a baniadam , msc received: 7april, 2009 accepted: 27 july, 2009 abstract background & aims: identifying research obstacles, assessment of faculty members’ ability in research skills and faculty members’ satisfaction of researc...

Let f (z) be an arbitrary entire function and M(f ,r) = max |z|=r | f (z)|. For a polynomial P(z) of degree n, having no zeros in |z| < k, k ≥ 1, Bidkham and Dewan (1992) proved max |z|=r |P (z)| ≤ (n(r + k) n−1 /(1 + k) n)max |z|=1 |P(z)| for 1 ≤ r ≤ k. In this paper, we generalize as well as improve upon the above inequality.