In this paper, we characterize invertible matrices over an arbitrary commutative antiring S with 1 and find the structure of GLn(S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every nilpotent n×n matrix over an entire antiring can be written as a sum of log2n square-zero matrices and also find the necessary number of square-zero summands for an arbitrary trace-zero matrix to be expressible as their sum.
In this paper we completely characterize all possible pairs of Jordan canonical forms for mutually annihilating nilpotent pairs, i.e. pairs (A,B) of nilpotent matrices such that AB=BA=0.
The central aim of the carried out research was to determine relations between the origin of the product and the perceived value of a brand and to develop a conceptual structural model of relations between the origin of the product and its impact on the perceived value of a brand and, in doing so, also to consider relations between impacts of the elements on the perceived value of the brand of the selected product. Methods and an extent of latent variable relations in the model were studied.
One of the basic issues of growth theory is the analysis of real convergence. The focus of this book is the opposite to that of the existing solutions. We develop a growth model that enables us to predict the divergence between economies where the assumption on the homogeneity of initial conditions at the aggregate level is fulfilled. For this purpose we develop an original growth model that permits us to predict real divergence of labor productivity between economies, although all the regarded economies experience convergence in technology, human capital and institutional organization.
Transportation costs present significant component in the overall costs of modern logistics companies. Huge effort has been invested in cutting transport costs by computer optimization of vehicle routing. Theoretically, the task is defined as a vehicle routing problem (VRP) and there exist many algorithms for approximate solutions with various tradeoffs. The development of a transport routing application for a distribution centre in Slovenia is presented in this paper.