Let $G$ be a non-abelian group and let $Z(G)$ be the center of $G$. Associate with $G$ there is agraph $Gamma_G$ as follows: Take $Gsetminus Z(G)$ as vertices of$Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $Gamma_G$ is called the non-commuting graph of $G$. In recent years many interesting works have been done in non-commutative graph of groups. Computing the clique...

the difficulty of assessing the writing skill is well known. different testing facets seem to affect the result of assessing the writing skill. in addition to the writer’s ability, the topic of the writing task, and methods of rating may contribute to the writer’s score. in this study, 50 efl learners wrote four different types of writing tasks (convincing, describing, instructing, and explaini...

intimately connected with duality theory (the notation is that of [1]). In both cases the middle algebra is the closure of L(G) in the dual of the first algebra and also the predual of the third algebra (at least when G is amenable in the second case). Furthermore, the third algebra is closely connected with the multiplier algebra of the first algebra. For abelian groups, compact or discrete, V...

recently, the algebraic theory of mv -algebras is intensively studied. in this paper, we extend the concept of derivation of $mv$-algebras and we give someillustrative examples. moreover, as a generalization of derivations of $mv$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $mv$-algebras.also, we investigate some properties of them.

‎Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge‎ ‎set E(G)‎. ‎The (first) edge-hyper Wiener index of the graph G is defined as‎: ‎$$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=frac{1}{2}sum_{fin E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$‎ ‎where de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(f,g|G). ‎In thi...

We show that the problem of computing the vacuum expectation values of gauge invariant operators in the strong coupling limit of topologically massive gauge theory is equivalent to the problem of computing similar operators in the G k /G model where k is the integer coefficient of the Chern-Simons term. The G k /G model is a topological field theory and many correlators can be computed analytic...

We study the action of the mapping class group of an oriented genus g surface Sg,n with n punctures on a Poisson algebra which arises in the combinatorial description of Chern-Simons gauge theory on R × Sg,n when the gauge group is a semidirect product G ⋉ g . We prove that the mapping class group acts on this algebra via Poisson isomorphisms and express the action of Dehn twists in terms of an...

the optical spectrum band positions and epr parameters (g factors g//, g^ and hyperfine structure constants a// and a^) for vo2+ ions in zn(antipyrine)2(no3)2 are theoretically studied from the complete diagonalization (of energy matrix) method (cdm) and the perturbation theory method (ptm). in the two methods, the contributions from the spin–orbit (so) coupling of central 3dn ion and ligand ar...

We give a derivation of the Verlinde formula for the Gk WZW model from Chern-Simons theory, without taking recourse to CFT, by calculating explicitly the partition function ZΣ×S1 of Σ × S 1 with an arbitrary number of labelled punctures. By a suitable gauge choice, ZΣ×S1 is reduced to the partition function of an Abelian topological field theory on Σ (a deformation of non-Abelian BF and Yang-Mi...

We quantise a Poisson structure on Hn+2g, where H is a semidirect product group of the form G ⋉ g. This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group G ⋉ g on R × Sg,n, where Sg,n is a surface of genus g with n punctures. The quantisation of this Poisson structure is a key step in the quantisation of Chern-Simons theory with...