Let π1 : K H , π2 : H G and π2π1 : K G be three finite regular coverings of graphs, and let σ be a representation of the covering transformation group of π1. We show that the L-function of G associated to the representation of the covering transformation group of π2π1 induced from σ is equal to that of H associated to σ by means of ordinary voltage assignments. © 2003 Elsevier Science Ltd. All ...

If M is compact Kählerian and ρ is semi-simple, that is that the Zariski closure of the image of ρ in GL(n,C) is semi-simple 1, by means of a result of Donaldson (in the case of Riemann surfaces, [5]) and Corlette (in the higher dimensional case, [4]), there exists a unique harmonic metric u on V, equivalently, a ρ-equivariant harmonic map from the universal covering M̃ of M into Pn := GL(n,C)/U...

In this paper, we define the fundamental group of a topological space and explore its structure, and we proceed to prove Van-Kampen’s Theorem, a powerful result useful for calculating the fundamental groups of spaces which decompose into spaces whose fundamental groups are already known. With these tools, we show that the circle, 2-sphere, torus, and figure-8 space are topologically distinct. W...

We use reformulation techniques to model and solve a complex sphere covering problem occurring in the configuration of a gamma ray machine radiotherapy equipment unit.

In this paper, a model is presented to locate ambulances, considering backup facility (to increase reliability) and the restriction of ambulance capacity. This model is designed for emergencies. In this model the covered demand for each demand point depends on the number of coverage times and the amount of demand. The demand amount and ambulance coverage radius are considered...