Related papers: Generalised Maxwellian Equations and their Implica…
Based on some previous results, one gives a general formula for introducing electromagnetic multipole expansions in terms of symmetric and traceless cartesian tensors.
We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the conservation of the current. We also start the…
What forms will have an equations of modern physics if the dimensions of our time and space are fractional? The generalized equations enumerated by title are presented by help the generalized fractional derivatives of Riemann-Liouville.
A simple relation between the Maxwell system and the Dirac equation based on their quaternionic reformulation is discussed. We establish a close connection between solutions of both systems as well as a relation between the wave parameters…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…
We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.
On the basis of the ordinary mathematical methods we discuss new classes of solutions of the Maxwell's equations discovered in the papers by D. Ahluwalia, M. Evans and H. M'unera et al.
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
Gauge transformation properties for an associated linear system of model Ishimori's magnet model have been discussed. Explicit formulas for the gauge transformation matrix have been obtained. Darboux Transformation has been suggested and…
In this paper, some tensor commutation matrices are expressed in termes of the generalized Pauli matrices by tensor products of the Pauli matrices.
We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.
In this paper we introduce the notion of generalized Lie algebroid and we develop a new formalism necessary to obtain a new solution for the Weistein's Problem. Many applications emphasize the importance and the utility of this new…
In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional…
The different forms of the Hamiltonian formulations of linearized General Relativity/spin-two theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant…
For research in the field of transformation optics and for the calculation of optically inhomogeneous lenses the method of geometrization of the Maxwell equations seems to be perspective. The basic idea is to transform the coefficients of…
Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined…
The magnetic backgrounds that physically give rise to spacetime noncommutativity are generally treated using noncommutative geometry. In this article we prove that also the theory of generalised complex manifolds contains the necessary…
This note is designed to show some classes of differential-difference equations admitting Lax representation which generalize evolutionary equations known in the literature.
Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue…