The present study is an attempt to find a solution for Volterra's Population Model by utilizing Spectral methods based on Rational Christov functions. Volterra's model is a nonlinear integro-differential equation. First, the Volterra's Population Model is converted to a nonlinear ordinary differential equation (ODE), then researchers solve this equation (ODE). The accuracy of method is tested i...

This work investigates the performance of Differential Evolution (DE) and its opposition-based version (ODE) on large scale optimization problems. Opposition-based differential evolution (ODE) has been proposed based on DE; it employs opposition-based population initialization and generation jumping to accelerate convergence speed. ODE shows promising results in terms of convergence rate, robus...

This article is concerned with geodesics in spaces of Hermitian metrics of positive curvature on an ample line bundle L → X over a Kähler manifold. Stimulated by a recent article of Phong-Sturm [PS], we study the convergence as N → ∞ of geodesics on the finite dimensional symmetric spaces HN of Bergman metrics of ‘height N ’ to Monge-Ampére geodesics on the full infinite dimensional symmetric s...

In pseudo-Riemannian geometry the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generaliza...

We investigate the set of tangent vectors at a Weierstrass point tangent to complete simple geodesics, which we think of as an innnitesimal version of the Birman Series set, showing that they are a Cantor set of Haus-dorr dimension 1. The gaps in the Cantor set are classiied in terms of the topological behavior of those geodesics tangent to the vector bounding them and deduce 3 new identities f...

We suggest an approach for description of integrable cases of the Abel equations using the procedure of increasing the order and equivalence transformations for the induced secondorder equations. A diversity of methods were developed to date for finding solutions of nonlinear ordinary differential equations (ODE). Everybody who encounters integration of a particular ODE uses, as a rule, the acc...

Nicotinic acetylcholine receptors (nAChRs) of parasitic nematodes are required for body movement and are targets of important "classical" anthelmintics like levamisole and pyrantel, as well as "novel" anthelmintics like tribendimidine and derquantel. Four biophysical subtypes of nAChR have been observed electrophysiologically in body muscle of the nematode parasite Oesophagostomum dentatum, but...

In pseudo-Riemannian geometry the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generaliza...

As the name suggests, Curve Shortening is a gradientflow for the length functional on the space of immersed curves in the surfaceM. One can therefore try to use Curve Shortening to prove existence of geodesics by variational methods. In my talk at S’Agarro I observed that geodesics always are curves without self-tangencies, and recalled that the space of such curves has many different connected...