A cover of a hypergraph is a collection of edges whose union contains all vertices. Let H = (V, E) be a k-uniform, D-regular hypergraph on n vertices, in which no two vertices are contained in more than o(D/e log D) edges as D tends to infinity. Our results include that if k = o(log D), then there is a cover of (1 + o(1))n/k edges, extending the known result that this holds for fixed k. On the ...

About at the break of sixties and seventies of this century the first functional and publicly used information system developed from originally experimental and non commercial applications of computer technology in storing and retrieval of document records. At the beginning these were mostly parallel editions of bibliographies in both printed and magnetic format. Thus developed on one hand data...

In the economical caching problem, an online algorithm is given a sequence of prices for a certain commodity. The algorithm has to manage a buffer of fixed capacity over time. We assume that time proceeds in discrete steps. In step i, the commodity is available at price ci ∈ [α, β], where β > α ≥ 0 and ci ∈ N. One unit of the commodity is consumed per step. The algorithm can buy this unit at th...

This manuscript is dedicated to history of economical relations and reconstruction of commercial routes on territory of Nuratau from 20 century B.C. till beginning of 20 century. This time interval was conditionally divided onto three periods: before, in time and past of existing the Great Silk Road (GSR). An attempt to reconstruct commercial routes in the region based on analysis of more than ...

The economical and secure operation of power systems has significant importance. Due to technical limitations, the best economical operation point is not always the desired operating point for system stability or power losses. In this study, first, the most economical operating point is obtained by solving the nonlinear, network-constrained economic dispatch problem using a genetic algorithm. T...