We investigate the fermionic condensate and the vacuum expectation values of the energymomentum tensor for a massive spinor field in de Sitter spacetime with spatial topology R × (S). Both cases of periodicity and antiperiodicity conditions along the compactified dimensions are considered. By using the Abel-Plana formula, the topological parts are explicitly extracted from the vacuum expectatio...

In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.

We consider a twisted version of the abelian (2,0) theory placed upon a Lorenzian six-manifold with a product structure,M6 = C×M4. This is done by an investigation of the free tensor multiplet on the level of equations of motion, where the problem of its formulation in Euclidean signature is circumvented by letting the time-like direction lie in the two-manifold C and performing a topological t...

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an `-tensor. The tensor product of s and t is a (k + `)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general...

in this paper, we give a characterization of strongly jordan zero-product preserving maps on normed algebras as a generalization of  jordan zero-product preserving maps. in this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly jordan zero-product preserving maps are completely different. also, we prove that the direct p...

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...

‎In the spirit of the Langlands proposal on  Beyond Endoscopy ‎we discuss the explicit relation between the Langlands functorial transfers and automorphic $L$-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 product $L$-functions in terms of the Langl...

in this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the fourier transform. as a consequence, we extend the fundamental theorems of abelian fourier transform to non-abelian case.

This note deals with preservation of tensor sum and tensor product of Hilbert space operators. Basic operations with tensor sum are presented. The main result addresses to the problem of transferring properties from a pair of operators to their tensor sum and to their tensor product. Sufficient conditions are given to ensure that properties preserved by ordinary sum and ordinary product are pre...

The natural lexicographic semigroupoids associated with Cantor product spaces indexed by countable linear orders are classified. Applications are given to the classification of triangular operator algebras which are direct limits of upper-triangular matrix algebras. 0. Introduction Consider a Cantor space which is presented explicitly as an infinite product of finite topological spaces. The pro...