A perfect code in a graph $$\Gamma $$ is subset C of $$V(\Gamma )$$ such that no two vertices are adjacent and every vertex ){\setminus } C$$ to exactly one C. Let G be finite group G. Then said if there exists Cayley admiting as code. It proved subgroup H only Sylow 2-subgroup This result provides way simplify the study codes general groups 2-groups. As an application, criterion for determinin...

We report the discovery of the first known symbiotic star in IC10, a starburst galaxy belonging to the Local Group, at a distance of ∼750 kpc. The symbiotic star was identified during a survey of emission-line objects. It shines at V =24.62±0.04, V −RC=2.77±0.05 and RC−IC=2.39±0.02 and suffers from EB−V =0.85±0.05 reddening. The spectrum of the cool component well matches that of solar neighbor...

A long-standing issue regarding the local and long-range structure of V(2)O(5)*nH(2)O xerogel has been successfully addressed. The full three-dimensional structure of the lamellar turbostratic V(2)O(5)*nH(2)O xerogel was determined by the atomic pair distribution function technique. We show that on the atomic scale the slabs of the xerogel can be described well as almost perfect pairs (i.e., bi...

While there is, up to homeomorphism, only one Cantor space, i.e. one zero-dimensional, perfect, compact, nonempty metric space, there are many measures on Cantor space which are not topologically equivalent. The clopen values set for a full, nonatomic measure μ is the countable dense subset {μ(U) : U is clopen} of the unit interval. It is a topological invariant for the measure. For the class o...

The adoption of everyday decisions in public affairs, fashion, movie-going, and consumer behavior is now thoroughly believed to migrate in a population through an influential network. The same diffusion process when being imitated by intention is called viral marketing. This process can be modeled by a (directed) graph G = (V,E) with a threshold t(v) for every vertex v ∈ V , where v becomes act...