we study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesx_{i}. we introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by x boxtimesy. we investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

Within the field of numerical multilinear algebra, block tensors are increasingly important. Accordingly, it is appropriate to develop an infrastructure that supports reasoning about block tensor computation. In this paper we establish concise notation that is suitable for the analysis and development of block tensor algorithms, prove several useful block tensor identities, and make precise the...

The purpose of this paper is to obtain a necessary and sufficient 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 $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...

Most existing flow visualization techniques focus on the analysis and visualization of the vector field that describes the flow. In this paper, we employ a rather different approach by performing tensor field analysis and visualization on the gradient of the vector field, which can provide additional and complementary information to the direct analysis of the vector field. Our techniques focus ...

Multidimensional data have various representations. Thanks to their simplicity in modeling multidimensional data and the availability of various mathematical tools (such as tensor decompositions) that support multi-aspect analysis of such data, tensors are increasingly being used in many application domains including scientific data management, sensor data management, and social network data an...

We present a novel analysis of the dynamics of tensor power iterations in the overcomplete regime where the tensor CP rank is larger than the input dimension. Finding the CP decomposition of an overcomplete tensor is NP-hard in general. We consider the case where the tensor components are randomly drawn, and show that the simple power iteration recovers the components with bounded error under m...