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.

Flow biocatalysis is a key enabling technology that increasingly being applied to wide array of reactions with the aim achieving process intensification, better control biotransformations, and minimization waste stream. In this mini-review, selected applications flow preparation food ingredients, APIs fat- oil-derived commodity chemicals, covering period 2020-2022, are described.

the need for clean groundwater resources to have sustainable development in a country is undoubted. due to the importance and high quality of karstic waters in supplying water in iran especially in shahrood city, it is attempted in this research work to recognize and explore karstic waters in southwest of tepal area, shahrood. for this purpose, integration of the results obtained from the metho...