Related papers: Uniqueness for an inverse problem in electromagnet…
Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than…
We consider the time-harmonic Maxwell equations set on a domain made up of two subdomains that represent a magnetic conductor and a non-magnetic material, and we assume that the relative magnetic permeability $\mu_{r}$ between the two…
It is a commonplace to note that in a world governed by special or general relativity, an observer has access only to data within her past lightcone (if that). The significance of this for prediction, and thus for confirmation, does not…
New Lagrangians, depending on the field strengths and the electric and magnetic sources are found, which lead to the Maxwell equations. One new feature is that the equations of motion are obtained by varying the Lagrangian with respect to…
The Maxwell equations with accounting for tensors properties of time have been considered. The effects that follow from such consideration are described. These are the appearance of vacuum polarization, anisotropy of electromagnetic wave…
Considering the ambiguousness of the discrete-time phase retrieval problem to recover a signal from its Fourier intensities, one can ask the question: what additional information about the unknown signal do we need to select the correct…
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse…
A conformal gauge theory is used to describe and unify myriad electromechanical and magnetomechanical coupling effects observed in solid continua. Using a space-time pseudo-Riemannian metric in a finite-deformation setup and exploiting the…
Uniqueness problem of static axially symmetric black hole in magnetic Universe filled with {\it dark matter} component has been considered. The {\it dark matter} model comprises the additional $U(1)$-gauge field ({\it dark photon})…
An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite number of pieces whose graphs are solutions of a linear…
We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material…
In the present work, we investigate a uniqueness of solution of the inverse source problem with non-local conditions for mixed parabolic-hyperbolic type equation with Caputo fractional derivative. Solution of the problem we represent as…
Considering two static, electrically charged, elementary particles, we demonstrate a possible way of proving that all known fundamental forces in the nature are the manifestations of the single, unique interaction. We re-define the gauging…
The inverse problem of finding the velocity profile from the surface measurements of acoustic field is considered. The dimensionalities of the data and of the unknown velocity profile are equal, both are equal 3. Analytical explicit…
In this note we explore monodromy defects for non-invertible symmetries in Maxwell theory, exploiting the conformal mapping to $AdS_{3} \times S^{1}$. With this approach we recover the spectrum of the defect conformal primaries. We also…
We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the…
Today's textbooks of electromagnetism give the particular solution to Maxwell's equations involving the integral over the charge and current sources at retarded times. However, the texts fail to emphasize the role played by the choice of…
We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional (3D) axisymmetric, ideal, incompressible magnetohydrodynamic (IMHD) equations, in a wall-bounded cylindrical…