In this paper we classify fuzzy subgroups of a rank-3 abelian group $G = mathbb{Z}_{p^n} + mathbb{Z}_p + mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

perishability of blood products as well as uncertainty in demand amounts complicate the management of blood supply for blood centers. this paper addresses a mixed-integer linear programming model for blood platelets production planning while integrating the processes of blood collection as well as production/testing, inventory control and distribution. whole blood-derived production methods for...

objective(s): in regard to the high incidence of asthma and the side-effects of the drugs used, finding novel treatments for this disease is necessary. our previous studies demonstrated the preventive effect of nigella sativa extract on ovalbumin-induced asthma. in addition, water-soluble substances of n. sativa extract and methanol fraction of this plant were responsible for the relaxant effec...

let $g$ be a molecular graph with vertex set $v(g)$, $d_g(u, v)$ the topological distance between vertices $u$ and $v$ in $g$. the hosoya polynomial $h(g, x)$ of $g$ is a polynomial $sumlimits_{{u, v}subseteq v(g)}x^{d_g(u, v)}$ in variable $x$. in this paper, we obtain an explicit analytical expression for the expected value of the hosoya polynomial of a random benzenoid chain with $n$ hexagon...

the tutte polynomial of a graph g, t(g, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. in this paper a simple formula for computing tutte polynomial of a benzenoid chain is presented.