arXiv subjects

Richard J. Drociuk

Publications and source records attributed to Richard J. Drociuk.

2 recordsLinked to original sources

arXiv2004

On the Closed Form Solution for the Geodesics in SdS Space

The closed form solution for the geodesics of classical particles in SdS space are obtained in terms of hyperelliptic modular functions and multiple hypergeometric functions. The closed form solution for the five roots of the fifth degree polynomial are found giving the branch places on the genus two Riemann surface. The `Inversion Problem', for the genus two hyperelliptic integral is solved in a closed form. Thus a couple of mathematical problems that have been around for a couple of centuries are solved. The solution is important in astrophysical applications of measuring the cosmological constant.

gr-qc↗

arXiv2000

On the Complete Solution to the Most General Fifth Degree Polynomial

The motivation behind this note, is due to the non success in finding the complete solution to the General Quintic Equation. The hope was to have a solution with all the parameters precisely calculated in a straight forward manner. This paper gives the closed form solution for the five roots of the General Quintic Equation. They can be generated on Maple V, or on the new version Maple VI. On the new version of maple, Maple VI, it may be possible to insert all the substitutions calculated in this paper, into one another, and construct one large equation for the Tschirnhausian Transformation. The solution also uses the Generalized Hypergeometric Function which Maple V can calculate, robustly.

math.GM↗