let $r$ be a commutative ring. we write $mbox{hom}(mu_a, nu_b)$ for the set of all fuzzy $r$-morphisms from $mu_a$ to $nu_b$, where $mu_a$ and $nu_b$ are two fuzzy $r$-modules. we make$mbox{hom}(mu_a, nu_b)$ into fuzzy $r$-module by redefining a function $alpha:mbox{hom}(mu_a, nu_b)longrightarrow [0,1]$. we study the properties of the functor $mbox{hom}(mu_a,-):frmbox{-mod}rightarrow frmbox{-mo...

Let G be a simple connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is k. Some formulas are obtained for computing the generalized polarity Wiener index of the Cartesian product and the tensor product of graphs in this article.

Tensor networks are a central tool in condensed matter physics. In this paper, we initiate the study of tensor network non-zero testing (TNZ): Given a tensor network T , does T represent a non-zero vector? We show that TNZ is not in the Polynomial-Time Hierarchy unless the hierarchy collapses. We next show (among other results) that the special cases of TNZ on nonnegative and injective tensor n...

A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.

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.

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...

We examine the question of when the ∗–homomorphism λ : A ∗D B → Ã ∗ D̃ B̃ of full amalgamated free product C∗–algebras, arising from compatible inclusions of C∗–algebras A ⊆ Ã, B ⊆ B̃ and D ⊆ D̃, is an embedding. Results giving sufficient conditions for λ to be injective, as well of classes of examples where λ fails to be injective, are obtained. As an application, we give necessary and sufficient ...