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...

We give a microscopic derivation of the spin-spin components of the optical potential for elastic scattering of a nucleon from a target with nonzero spin. A realistic nucleon-nucleon interaction containing direct and exchange terms is used to generate a folded nucleon-nucleus potential whose spin-spin components are treated in distorted-wave Born approximation. We show how folding leads to spin...

Loop quantum gravity is one of the leading candidate theory to non-perturbatively quantize gravity. In this framework, holonomy corrections to the equation of propagation of gravitons in a FLRW background have been derived. We investigate the consequences of those corrections on the tensor power spectrum in de-Sitter and slow-roll inflations, for n=-1/2. Depending on the value of the Barbero-Im...

It has long been conjectured that hypothesis spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical architectures than with shallow ones. Despite the vast empirical evidence, formal arguments to date are limited and do not capture the kind of networks used in practice. Using tensor factorization, we derive a u...

We studied the relation between cortical oscillatory rhythms and the structural integrity of the corpus callosum in 21 children with spina bifida and hydrocephalus. Participants underwent resting state neuromagnetic recordings and diffusion tensor imaging. Areas of three segments of the corpus callosum (genu, body, splenium) were derived through diffusion tensor imaging-based morphometrics. Chi...

For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental SL-invariant function that relates the coordinate ring of the orbit with the coordinate ring of its closure. For the power sums we can write down this fundam...