We report on a new general class of solutions of the Beltrami equation, with special characteristics. We also provide examples of solutions that also satisfy Maxwell equations. A subset of these solutions can be isolated which corresponds to " gauge " fields. A special projective geometry of vacuum fields is also revealed and discussed. 1. Introduction The notion of a force-free field comes dir...

We consider general torsion components in three-dimensional Einstein-Cartan gravity, providing a geometrical interpretation for matter, and find new solutions of the corresponding equations Riemann curvature torsion. These geometries involve peculiar interplay between vector $(\beta_i)$ singlet $(\tau)$ irreducible which, under conditions, feature formal analogy with equation Beltrami fluid. In...

We consider the Laplace--Beltrami operator on a three-dimensional Riemannian manifold perturbed by potential from Kato class and study whether various forms of Weyl's law remain valid under this perturbation. show that pointwise Weyl holds, modified an additional term, for any with standard sharp remainder term. The term is always lower order than leading but it may or not be In particular, we ...

Persistent homology provides a new approach for the topological simplification of big data via measuring the life time of intrinsic topological features in a filtration process and has found its success in scientific and engineering applications. However, such a success is essentially limited to qualitative data characterization, identification and analysis (CIA). Indeed, persistent homology ha...

The Laplace Beltrami operator, known as an elliptic operator for functions defined on surfaces, appears in some applications in sciences and engineerings. In this paper we consider the Laplace Beltrami operator ∆Γ on surfaces Γ defined as graphs of C2 functions on a flat domain Ω ⊂ Rd−1 (d ≥ 2), ∆Γu = f on Γ, u = 0 on ∂Γ. Based on some properties of differential geometry, we transformed the Lap...

The aim of this paper is to present a new framework for regularization by diffusion. The methods we develop in the sequel can be used to smooth multichannel images, multichannel image sequences (videos), vector fields and orthonormal frame fields in any dimension.1 From a mathematical viewpoint, we deal with vector bundles over Riemannian manifolds and socalled generalized Laplacians. Sections ...

The existence of the Laplace-Beltrami operator has allowed mathematicians to carry out Fourier analysis on Riemannian manifolds [2]. We recall that the Laplace-Beltrami operator ∆ on a compact Riemannian manifold has a discrete set of eigenvalues {λj}j=1, which satisfies λj →∞ as j →∞. This is known as the spectrum of the Laplace-Beltrami operator. Inverse spectral geometry studies how much of ...

Recently Kleides et al [IJMPA 11, 1697 (2008)] found a growing rate for magnetic fields in ideal plasma cosmologies by making use of general relativistic Friedmann model. This growth rate of δB B ∼ (t t H) 1 4 indicates the presence of a slow dynamo in the universe. More recently Hasseein [Phys Plasmas (2009)] have also investigate Beltrami magnetic fields in plasma universe. Here general relat...

We prove that the quasiregular mappings given by the (normalized) principal solution of the linear Beltrami equation (1) and the principal solution of the quasilinear Beltrami equation are inverse to each other. This basic fact is deduced from the Liouville theorem for generalized analytic functions. It essentially simplifies the known proofs of the “measurable Riemann mapping theorem” and its ...