The development of technology has brought some alternative means in education. enabling role been widely recognized second language teaching and learning. Second Life (SL) is an online virtual world popular with digital natives. Some educators apply this application to foreign-language university courses because its benefits students’ immersion focus, imagination, creativity Language learners c...

For integers l ≥ 1, d ≥ 0 we study (undirected) graphs with vertices 1, . . . , n such that the vertices can be partitioned into l parts such that every vertex has at most d neighbours in its own part. The set of all such graphs is denoted Pn(l, d). We prove a labelled rst-order limit law, i.e., for every rst-order sentence φ, the proportion of graphs in Pn(l, d) that satisfy φ converges as n→∞...

If $E/F$ is a quadratic extension $p$-adic fields, we first prove that the $\mathrm{SL}_n(F)$-distinguished representations inside distinguished unitary L-packet of $\mathrm{SL}_n(E)$ are precisely those admitting degenerate Whittaker model with respect to character $N(E)/N(F)$. Then establish global analogue this result. For this, let be number fields and $\pi$ an $\mathrm{SL}_n(\mathbb{A}_F)$...

Let $S(G)$ be the Seidel matrix of a graph $G$ of order $n$ and let $D_S(G)=diag(n-1-2d_1, n-1-2d_2,ldots, n-1-2d_n)$ be the diagonal matrix with $d_i$ denoting the degree of a vertex $v_i$ in $G$. The Seidel Laplacian matrix of $G$ is defined as $SL(G)=D_S(G)-S(G)$ and the Seidel signless Laplacian matrix as $SL^+(G)=D_S(G)+S(G)$. The Seidel signless Laplacian energy $E_{SL^+...

The study of representations of the fundamental groups of finite volume hyperbolic surfaces and finite volume hyperbolic 3-manifolds into Lie groups has been long studied. Classical cases such as the case of the Lie groups SL(2,R), SL(2,C) and SU(2) have provided powerful tools to bring to bear in the study of these groups, and the geometry and topology of the manifolds. More recently, this has...