We consider two covering variants of the network design problem. are given a set origin/destination pairs, called O/D and each such pair is covered if there exists path in from origin to destination whose length not larger than threshold. In first problem, Maximal Covering Network Design one must determine that maximizes total fulfilled demand pairs subject budget constraint on costs network. s...

In this article we offer group-theoretic, field-theoretic, and topological interpretations of the Gaussian binomial coefficients their sum. For a finite p-group G rank n, show that coefficient (nk)p is number subgroups are minimally expressible as an intersection n – k maximal G, sum precisely either or G. We provide field-theoretic interpretation these quantities through lens Galois theory inv...

Abstract One of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. Practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. Change in problem parameters during the pl...

We examine the maximal ν e → ν s and ν e → ν µ,τ oscillation solutions to the solar neutrino problem. These solutions lead to roughly a 50% solar flux reduction for the large parameter range 3 × 10 −10 < ∼ δm 2 /eV 2 < ∼ 10 −3. It is known that the earth regeneration effect may cause a potentially large night-day effect even for maximal neutrino oscillations. We investigate the night-day asymme...