Related papers: Spherical Potential Theory: Tools and Applications
Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
This paper reviews work, largely due to W. Simon and the author, on multipole theory of static spacetimes. The main purpose is to make this work, which lies at the interface of potential theory, conformal geometry and general relativity,…
Gale transform is a simple but powerful tool in convex geometry. In particular, the use of Gale transform is the main argument in the classification of polytopes with few vertices. Many books and documents cover the definition of Gale…
We consider spinorial fields in polar form to deduce their respective tensorial connection in various physical situations: we show that in some cases the tensorial connection is a useful tool, instead in other cases it arises as a necessary…
This is a survey article on $F$-singularities and their applications.
This is a survey on spectral theory of dynamical systems.
We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The classification is also suitable for a hyperboloid and a…
Geodesy in a Newtonian framework is based on the Newtonian gravitational potential. The general-relativistic gravitational field, however, is not fully determined by a single potential. The vacuum field around a stationary source can be…
Notes for the upcoming Workshop on Symplectic Field Theory IX, Polyfolds for SFT. These notes are essentially the first few chapters of a forthcoming book entitled "Polyfold Constructions: Tools, Techniques, and Functors"
The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in nature - are given and shown to lead to the same objects.…
Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.
We consider integrable spherical analogue of the Darboux potential, which appear in the problem (and its generalizations) of the planar motion of a particle in the field of two and four fixed Newtonian centers. The obtained results can be…
With the advancement of GPS and remote sensing technologies, large amounts of geospatial and spatiotemporal data are being collected from various domains, driving the need for effective and efficient prediction methods. Given spatial data…
A large multitude of scientific computing tools is available today. This article gives an overview of available tools and explains the main application fields. In addition basic principles of number representations in computing and the…
As the possibility to decouple temporal and spatial variations of the electromagnetic field, leading to a wavelength stretching, has been recognized to be of paramount importance for practical applications, we generalize the idea of…
We shall discuss cosmological models in extended theories of gravitation. We shall define a surface, called the model surface, in the space of observable parameters which characterises families of theories. We also show how this surface can…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
This paper assesses the feasibility of exploiting commercial satellite television technologies to broadcast video signals and data from major High Energy Physics facilities to collaborating institutes throughout the world.
An algorithm is presented for numerical computation of choreographies in the plane in a Newtonian potential and on the sphere in a cotangent potential. It is based on stereographic projection, approximation by trigonometric polynomials, and…