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 be a simple connected graph. the generalized polarity wiener index ofg is defined as the number of unordered pairs of vertices of g whosedistance is k. some formulas are obtained for computing the generalizedpolarity wiener index of the cartesian product and the tensor product ofgraphs in this article.

Extending research on organizational learning to multi-product environments is of particular importance given that the vast majority of products are manufactured in such environments. We investigate learning in a multi-product facility drawing on exceptionally rich data for a manufacturing firm that is a leading producer of high technology components. Weekly data for 10 years from the firm's pr...

Due to the development of science and technology, the computer has become a useful tool for supporting engineering activities in product design. Many computer aided tools such as CAD/CAM, product data management (PDM), product life cycle assessment (PLA), etc., have been popularly used in industry for reducing product development lead-time and increasing total product quality. However, the nume...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.