Alexander V. Evako

Solution of a Parabolic Partial Differential Equation on Digital Spaces: A Klein Bottle, a Projective Plane, a 4D Sphere and a Moebius Band

This paper studies a parabolic partial differential equation on digital spaces and digital n-dimensional manifolds, which are digital models of continuous n-manifolds. Conditions for the existence of solutions of equations are determined and investigated. Numerical solutions of the equation on a Klein bottle, a projective plane, a 4D sphere and a Moebius strip are presented.

Periodicity of Generalized Fibonacci-like Sequences

Generalized Fibonacci-like sequences appear in finite difference approximations of the Partial Differential Equations based upon replacing partial differential equations by finite difference equations. This paper studies properties of the generalized Fibonacci-like sequence . It is shown that this sequence is periodic with the period ( ) if | | .