A subset D of vertices of a graph G is a dominating set if for each u ∈ V (G) \ D, u is adjacent to somevertex v ∈ D. The domination number, γ(G) ofG, is the minimum cardinality of a dominating set of G. A setD ⊆ V (G) is a total dominating set if for eachu ∈ V (G), u is adjacent to some vertex v ∈ D. Thetotal domination number, γt (G) of G, is theminimum cardinality of a total dominating set o...

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

mndo semi-empirical scf mo calculations are used to study the pyramidal nitrogen atom inversion and configurational equilibria in the title compounds.

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...

In this study, oil was extracted from the liver and visceral fat of Patin (Pangasianodon hypophthalmus) and refined. The yield of oil after refining was 49.98%. The major yield loss (34.20%) happened during the degumming procedure. Fatty acids found in the crude and refined oil were C12:0, C14:0, C14:1, C16:0, C16:1, C18:0, C18:1, C18:2, C18:3, C18:4, C20:0, C20:1, C20:4, C20:5, and C22:6. The ...

In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

tomato  (l.ycopersicon esculentum  mill.) cv. rio grande  seedlings were nutritionally conditioned with solutions complete fertilizer n(60% no3+40% nh4)-p-k (20-20-20) , n(30%no3+70% nh4)-p-k (15-5-30) , the first two week   n(60% no3+40% nh4)-p-k (20-20-20) and later two week  n(30%no3+70% nh4)-p-k (15-5-30)  and vice versa were  applied in  completely randomized experiment with three replicat...