For nonlinear systems affine in the input with state x ∈ R, input u ∈ R and output y ∈ R, it is a well-known fact that, if the function mapping (x, u, . . . , u(n−1)) into (u, . . . , u(n−1), y, . . . , y(n−1)) is an injective immersion, then the system can be locally transformed into an observability normal form with a triangular structure appropriate for a high-gain observer. In this technica...

We present a method to perform histogram matching between two color images based on the concept of harmonic mapping between Riemannian manifolds. The key idea is to associate the histogram of a color image to a Riemannian manifold. In this context, the energy of the matching between the two images is measured by the Dirichlet energy of the mapping between the Riemannian manifolds. Then, we assi...

This work is concerned with developing moving mesh strategies for solving problems defined on a sphere. To construct mappings between the physical domain and the logical domain, it has been demonstrated that harmonic mapping approaches are useful for a general class of solution domains. However, it is known that the curvature of the sphere is positive, which makes the harmonic mapping on a sphe...

the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

Ruscheweyh and Sheil-Small proved that convexity is preserved under the convolution of univalent analytic mappings in K. However, when we consider the convolution of univalent harmonic convex mappings in K H , this property does not hold. In fact, such convolutions may not be univalent. We establish some results concerning the convolution of univalent harmonic convex mappings provided that it i...

The frequency-to-channel mapping for Cochlear implant (CI) signal processors was originally designed to optimize speech perception and generally does not preserve the harmonic structure of music sounds. An algorithm aimed at restoring the harmonic relationship of frequency components based on semitone mapping is presented in this article. Two semitone (Smt) based mappings in different frequency...