The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a Hölder continuous function. More precisely, let η ∈ C0,α(ω), 0 < α < 1 and let Ωη be a domain which is locally subgraph of a function η. We prove that mapping γη : u 7→ u(x, η(x)) can be extended by continuity to a linear, continuous mapping from H(Ωη) to Hs(ω), s < α/2. This study is...

Let Z and X be Banach spaces, U ⊂ Z an open convex set and f : U → X a mapping. We say that f is a delta-convex mapping (d. c. mapping) if there exists a continuous convex function h on U such that y ◦ f + h is a continuous convex function for each y ∈ Y , ‖y∗‖ = 1. We say that f : U → X is locally d. c. if for each x ∈ U there exists an open convex U ′ such that x ∈ U ′ ⊂ U and f |U ′ is d. c....

Land cover mapping for large regions often employs satellite images of medium to coarse spatial resolution, which complicates mapping of discrete classes. Class memberships, which estimate the proportion of each class for every pixel, have been suggested as an alternative. This paper compares different strategies of training data allocation for discrete and continuous land cover mapping using c...

A natural mapping from the set of complex analytic isolated hypersurface singularities to the set of finite dimensional Lie algebras is first defined. It is proven that the image under this natural mapping is contained in the set of solvable Lie algebras. This approach gives rise to a continuous inequivalent family of finite dimensional representations of a solvable Lie algebra.

This paper presents a method to construct a smooth seamless conformal surface for the genus-0 manifold. The method is developed for the conformal self-organizing map [10]. The constructed surface is both piecewise smooth and continuous. The mapping between the model surface and the sphere surface is one-to-one and onto. We show experiments in surface reconstruction and texture mapping.