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.

We select a close “major-merger candidate” galaxy pair sample in order to calculate the Ks luminosity function (LF) and pair fraction representative of the merger/interaction component of galaxy evolution in the local universe. The pair sample (projected separation 5 h kpc ≤ r ≤ 20 h kpc, Ks-band magnitude difference ∆Ks ≤ 1 mag) is selected by combining the Two Micron All Sky Survey (2MASS) wi...