In this paper, the equations of motion for geodesics in the neutral rotating Black Ring metric are derived and the separability of these equations is considered. The bulk of the paper is concerned with sets of solutions where the geodesic equations can be examined analytically specifically geodesics confined to the axis of rotation, geodesics restricted to the equatorial plane, and geodesics th...

The closedness condition for real geodesics on n–dimensional ellipsoids is in general transcendental in the parameters (semiaxes of the ellipsoid and constants of motion). We show that it is algebraic in the parameters if and only if both the real and the imaginary geodesics are closed and we characterize such double–periodicity condition via real hyperelliptic tangential coverings. We prove th...

Ordinary differential equation (ODE) systems are commonly used many different fields. The de-facto method to implement an ODE system in Python programming using SciPy requires the entire system to be implemented as a single function, which only allow for inline documentation. Although each equation can be broken up into sub-equations, there is no compart-mentalization of sub-equations to its OD...

Let S = Sg,n be a connected, orientable surface of genus g ≥ 0 with n ≥ 0 punctures. Let Teich(S) denote the corresponding Teichmüller space, and let Mod(S) denote the mapping class group of S. Understanding the analogy of Teich(S) with symmetric spaces is a wellknown theme. Recall that a complete Riemannian manifold X is symmetric if it is symmetric at each point x ∈ X: the map γ(t) 7→ γ(−t) w...

BACKGROUND/AIMS 9-[2-(phosphonomethoxy)ethyl]guanine (PMEG) is one of the most active antiproliferative compounds in a series of acyclic nucleoside phosphonates and is active in intraperitoneal P388 tumors in mice. METHODS We synthesized octadecyloxyethyl (ODE) and hexadecyloxypropyl esters of PMEG and compared their antiproliferative activity with unmodified PMEG in primary human fibroblasts...

We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.

In this note based on paper [3] we deal with domains D (i.e. connected open subsets) of a Finsler manifold (M, F ). At first we carry out a comparison between different notions of convexity for their boundaries. Then a careful application of variational methods to the geodesic problem yields that the convexity of ∂D is equivalent to the existence of a minimal geodesic for each pair of points of...

In this paper, we prove that on every Finsler n-sphere (S, F ) for n ≥ 6 with reversibility λ and flag curvature K satisfying ( λ λ+1 )2 < K ≤ 1, either there exist infinitely many prime closed geodesics or there exist [ 2 ] − 2 closed geodesics possessing irrational average indices. If in addition the metric is bumpy, then there exist n − 3 closed geodesics possessing irrational average indice...