Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

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...

This paper develops a model of endogenous product selection by firms. The theory is motivated by new evidence we present on the importance of product switching by U.S. manufacturers. Two-thirds of continuing firms change their product mix every five years, and product switches involve more than 40% of firm output and almost half of existing products. The theoretical model incorporates heterogen...

A Software Product Line (SPL) is a set of related programs. A SPL of a SPL (SPL), or a product line of a product line, is a fundamental scaling of product line concepts. A member of a SPL is not a program, but a SPL. The idea recurses: a SPL is a SPL of a SPL, and so on. The depth of recursion is the rank of the product line. We present an algebra to understand and build feature-based product l...

The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices, when kronecker product is used between them is given. It is shown that the non-commutative matrices after kronecker product are similar or they are similar ...

Abstract Requirements engineering and requirements management are essential sub-processes of product development an integrated part virtually all models industrial process descriptions. Proprietary context specific processes for working with used in design practice. However, these not appropriately reflected existing development. Existing standards describe the content generation documents but ...

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.