This paper presents an overview of new approaches in rapid product development in production networks from design points of view. The manufacturing industries are changing their focus to global sourcing as a means to improve performance and enhance competitiveness. Some partnerships created with this strategy improve product development through collaborative design. With the advent of e-Commerc...

Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of...

for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...

Let G and H be graphs. The strong product GH of graphs G and H is the graph with vertex set V(G)V(H) and u=(u1, v1) is adjacent with v= (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we first collect the earlier results about strong product and then we present applications of ...

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.

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...

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.

In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...