Related papers: RF Basics I and II
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We give a formula for matrix exponentials and partial fraction decompositions.
1. Introduction 2. Basics and outline of the method 2.1 Regions around an isolated source 2.2 The quadrupole formalism 2.3 Outline of the method 3. Properties of radiative gravitational fields 3.1 The field in the exterior domain (D_e) 3.2…
We present boundary-integral equations for Maxwell-type problems in a differential-form setting. Maxwell-type problems are governed by the differential equation $(\delta\mathrm{d}-k^2)\omega = 0$, where $k\in\mathbb{C}$ holds, subject to…
In this paper, we study the regularity of the solutions of Maxwell's equations in a bounded domain. We consider several different types of low regularity assumptions to the coefficients which are all less than Lipschitz. We first develop a…
The paper shows the relationship between the major wave equations in quantum mechanics and electromagnetism, such as Schroedinger's equation, Dirac's equation and the Maxwell equations. It is shown that they can be derived in a striking…
We show that the Gersten derivation of Maxwell equations can be generalized. It actually leads to additional solutions of `S=1 equations'. They follow directly from previous considerations by Majorana, Oppenheimer, Weinberg and Ogievetskii…
Maxwell extension of affine algebra with additional tensorial generators is given. Using the methods of nonlinear realizations, we found the transformation rules for group parameters and corresponding generators. Gauging the Maxwell-affine…
We consider the time dependent Maxwell system in the sense of distributions in the context of temporal interfaces. Just as with spatial interfaces, electromagnetic waves at temporal interfaces scatter and create a transmitted and reflected…
We propose a unified approach to addition of some physical quantities (among which resistors and capacitors are the most well-known) that are usually encountered in introductory physics such that the formulae required to solve problems are…
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which…
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the…
This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object,…
We study homogenization of multiscale Maxwell wave equation that depends on $n$ separable microscopic scales in a domain $D\subset{\mathbb R}^d$ on a finite time interval $(0,T)$. Due to the non-compactness of the embedding of…
This contribution is divided in two parts. The first part provides a text-book level introduction to gravitational radiation. The key concepts required for a discussion of gravitational-wave physics are introduced. In particular, the…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
A few formulas and theorems for statistical structures are proved. They deal with various curvatures as well as with metric properties of the cubic form or its covariant derivative. Some of them generalize formulas and theorems known in the…