Let $G=(V,E)$ be a graph, $D\subseteq V(G)$ and $u$ be any
vertex in $D$. The out degree of $u$ with respect to $D$ denoted
by $ od_{_{D}}(u)$, is defined as $od_{_{D}}(u)=|N(u)\D)|$.
Let $G=(V,E)$ be a graph, $D\subseteq V(G)$ and $u$ be any
vertex in $D$. The out degree of $u$ with respect to $D$ denoted
by $ od_{_{D}}(u)$, is defined as $od_{_{D}}(u)=|N(u)\cap (V-D)|$. $D$ is called a near equitable dominating set of $G$ if for every $v\in V-D$, there exists a vertex $u\in D$ such that $u$ is
adjacent to $v$ and $|od_{_D}(u)-od_{_{V-D}}(v)|\leq 1$. The
minimum cardinality of such a dominating set is denoted by
$\gamma_{ne}$ and is called the near equitable domination number
of $G$. In this paper, we introduce the concept of near equitable
domination. The minimal near equitable dominating sets are
established. The relation between $\gamma_{ne}(G)$,
$\gamma_{e}(G)$ and $\gamma(G)$ are obtained, bounds for
$\gamma_{ne}(G)$ are found. Near equitable domatic partition in a
graph $G$ is also studied.
In the modified theory of relativity proposed by Barber [1], we have investigated in this paper the spherical symmetric cosmological models in presence of sting with bulk viscosity. Determinate solutions are obtained under two cases and sub cases also considered. The various physical and geometrical features of the models are also discussed.