Since the appearance of the paper by Bilal et al. in '91, [1], it has been widely assumed that W –algebras originating from the Hamiltonian reduction of an SL(n, C)-bundle over a Riemann surface give rise to a flat connection, in which the Beltrami differential may be identified. In this letter, it is shown that the use of the Beltrami parametrisation of complex structures on a compact Riemann ...

The Laplace-Beltrami operator is an extension of the Laplacian from flat domains to curved manifolds. It was proven to be useful for color image processing as it models a meaningful coupling between the color channels. This coupling is naturally expressed in the Beltrami framework in which a color image is regarded as a two dimensional manifold embedded in a hybrid, five dimensional, spatial-ch...

In this paper, we solve two problems for some nonlinear SPDE driven by FiskStratonovich stoachastic integral. The main assumption is the commuting property of the drift and diffusion vector fields with respect of the Lie bracket. In the first problem (P1) we construct a classical solution for some nonlinear SPDE of parabolic type by assuming the compatibilty condition concerning the mentioned v...

The improvements of Digital Subscriber Line (DSL) technology enable telephone companies to optimize the utilization of their twisted-pair access networks in a flexible way, closely relating bandwidth demand and system costs. However, for the definition of VDSL systems as the next generation of DSL spectral compatibility with other DSL systems and with amateur radio systems has to be considered....

In this article I give a rigorous construction of the classical and quantum photon field on non-compact manifolds with boundary in possibly inhomogeneous media. Such is complicated by presence zero-modes that may appear non-trivial topology manifold or boundary. An important special case $\mathbb{R}^3$ obstacles. zero modes have direct interpretation terms obstacle. formula for renormalised str...

Techniques of constrained approximation are used to recover solutions to elliptic partial differential equations from incomplete and corrupted boundary data. The approach involves the use of generalized Hardy spaces of functions whose real and imaginary parts are related by formulae similar to the Cauchy–Riemann equations. A prime motivation for this is the modelling of plasma confinement in a ...