In the present paper we study the Lie sphere geometry of Legendre surfaces by the method of moving frame and we prove an existence theorem for real-analytic Lie-minimal Legendre surfaces.

By convention, the translation and scale invariant functions of Legendre moments are achieved by using a combination of the corresponding invariants of geometric moments. They can also be accomplished by normalizing the translated and/or scaled images using complex or geometric moments. However, the derivation of these functions is not based on Legendre polynomials. This is mainly due to the fa...

On the basis of our Fokker-Planck code “FPI”, a new kernel for nonlocal electron transport in plasmas has been developed. Large scale simulations of plasma macroscopic characteristics have been made by using both this Fokker-Planck and a new Hydrodynamic code using the new kernel [1]. However, these simulations were made with the approximation of spherical Rosenbluth potentials. We have now add...

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials ar...