In this paper, we characterize the function space and L1-space of the [topological] Tensor product of [topological] semigroups. As a consequence, for arbitrary [topological] groups G1 and G2, it will be shown that G1×G2 is an extension of G1ÄsG2  by a proper normal subgroup N i,e G1ÄsG2=G1×G2/N

Let G and H be graphs. The Tensor product GÄH of G and H has vertex set V (G Ä H) = V (G) × V (H) and edge set E(G  Ä H) = {(a, b)(c, d)|ac ∈ E(G) and bd ∈ E(H)}. In this paper, some results on this product are obtained by which it is possible to compute the Wiener and Hyper Wiener indices of Kn Ä G.

Let S be an inverse semigroup with an upward directed set of idempotents E. In this paper we prove that if S is amenable, then l1(S) Ä^ l1(S) is module amenable as an l1(E)-module. Also we show that L1(S) Ä^ l1 (S) is module super-amenable if an appropriate group homomorphic image of S is finite.

In the spirit of the Langlands proposal on Beyond Endoscopy, we discuss the explicit relation between the Langlands functorial transfers and automorphicL -functions. It is well-known that the poles of the L -functions have deep impact to the Langlands functoriality. Our discussion also includes the meaning of the central value of the Tensor productL -functions in terms of the Langlands functoriality. This leads to the theory of the twisted auto morphic descents for cuspidal auto morphic representations of general classical groups.

Tight frames are very similar to orthonormal bases and can be used as a good alternative to them. Scaling frames are introduced as a method to transform a general frame to a tight one. This paper investigates in under what conditions the Tensor product of two frames is a scalable frame. We expand some results concerning frame operations of eigenvalues to Tensor product of Hilbert spaces. Finally, we will show that if one of the frames is scalable, better conditions are obtained for the approximation of Tensor product of frames that is not scalable.

The purpose of this paper is to obtain a necessary and suffcient condition for the Tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph GÅK2 to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the Tensor product of graphs are worked out.