Related papers: Spherical Potential Theory: Tools and Applications

The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…

Recently, in an ensemble of small spheres, we proposed a method that converts the force between two large spheres into the pressure on the large sphere's surface element. Using it, the density distribution of the small spheres around the…

We extend the spherical tensorial formalism for polarization to the treatment of electric- and magnetic-multipole transitions of any order. We rely on the spherical-wave expansion to derive the tensor form of the operator describing the…

In this paper we will analyze the quantization of a gauge theory on a four sphere. This will be done by mode expanding all the fields in the theory in terms of harmonic modes. We will also analyse the BRST symmetry of this theory.

We introduce the basic concepts related to subharmonic functions and potentials, mainly for the case of the complex plane and prove the Riesz decomposition theorem. Beyond the elementary facts of the theory we deviate slightly from the…

We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.

We survey aspects of prediction theory in infinitely many dimensions, with a view to the theory and applications of functional time series.

This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…

We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.

The future smart grid is envisioned as a large-scale cyber-physical system encompassing advanced power, communications, control, and computing technologies. In order to accommodate these technologies, it will have to build on solid…

In this paper we introduce a model for hard spheres interacting through attractive Riesz type potentials, and we study its thermodynamic limit. We show that the tail energy enforces optimal packing and round macroscopic shapes.

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…

Applying the DPW version of the theory developed by Burstall and Guest for harmonic maps of finite uniton type, we derive a coarse classification of Willmore two-spheres in $S^{n+2}$ in terms of the normalized potential of their (harmonic)…

We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…

Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We…

We survey various origins and expressions for the quantum potential with some new observations.

Theory was formulated for scattering by a coated chiral sphere of a plane wave of arbitrary polarization state with amplitude modulated by a Gaussian pulse. The spherical core and the concentric shell of the sphere were composed of two…

In this paper, we demonstrate that potential theory provides a powerful framework for analyzing quasistationary fluid flows in bounded geometries, where the bulk dynamics are governed by elliptic equations with constant coefficients. This…

This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…