according to high importance of sodding for fast creating green beds in all seasons, this experiment carried out with aimidentifying suitable substrate and covering plant including two lawn genus and dichondra with blend seed. the trial carried out as factorial experiment with three factors based on complete block design in three replications. experimental factors consisted of planting networks...

let $g=(v‎, ‎e)$ be a graph with $p$ vertices and $q$ edges‎. ‎an emph{acyclic‎ ‎graphoidal cover} of $g$ is a collection $psi$ of paths in $g$‎ ‎which are internally-disjoint and cover each edge of the graph‎ ‎exactly once‎. ‎let $f‎: ‎vrightarrow {1‎, ‎2‎, ‎ldots‎, ‎p}$ be a bijective‎ ‎labeling of the vertices of $g$‎. ‎let $uparrow!g_f$ be the‎ ‎directed graph obtained by orienting the...

recently‎, ‎the authors gave some conditions under which a direct product‎ ‎of finitely many groups is $mathcal{v}-$capable if and only if each of its‎ ‎factors is $mathcal{v}-$capable for some varieties $mathcal{v}$‎. ‎in this paper‎, ‎we extend this fact to any infinite direct product of groups‎. ‎moreover‎, ‎we conclude some results for $mathcal{v}-$capability of direct products of infinitel...

We present the first combinatorial approximation scheme that yields a pure approximation guarantee for linear programs that are either covering problems with upper bounds on variables, or their duals. Existing approximation schemes for mixed covering and packing problems do not simultaneously satisfy packing and covering constraints exactly. We present the first combinatorial approximation sche...

For a xed graph H, the H-cover problem asks whether an input graph G allows a degree preserving mapping f : V (G) ! V (H) such that for every v 2 V (G), f(N G (v)) = N H (f(v)). In this paper we design eecient algorithms for certain graph covering problems according to two basic techniques. The rst is based in part on a reduction to the 2-SAT problem. The second technique exploits necessary and...

Every Seifert Fibre Group is the lift of a Fuchsian group to the universal covering group of PSL (2,R). From this, we work out a form of presentation for such a group. With the calculation of the Euler number, we can establish the presentation of the derived group of a Seifert Fibre Group