Related papers: Uniqueness Theorem: With Normal Components Specifi…
A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated. Initial equations depend upon four complex…
In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical spacetime to be singularity-free. The applicability of the theorem is tested on examples provided by the…
We study the properties of spacelike singularities in spherically symmetric spacetimes obeying the Einstein equations, in the presence of matter. We consider in particular matter described by a scalar field, both in the presence of an…
Inversion of potential field data is a central technique of remote sensing in physics, geophysics, neuroscience and medical imaging. In spite of intense research, uniqueness theorems for potential-field inversion are scarce. Applied studies…
We present the Tetrahedral Compactness Theorem which states that sequences of Riemannian manifolds with a uniform upper bound on volume and diameter that satisfy a uniform tetrahedral property have a subsequence which converges in the…
This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric $3D$ Euler equation in the domains $\{(x_1,x_2,x_3) \in \mathbb{R}^3 : x_3^2 \le \mathfrak{c}(x_1^2 +…
We give general sufficient conditions for the existence of trapped surfaces due to concentration of matter in spherically symmetric initial data sets satisfying the dominant energy condition. These results are novel in that they apply and…
The Lorenz--Mie formulation of electromagnetic scattering by a homogeneous, isotropic, dielectric-magnetic sphere was extended to incorporate topologically insulating surface states characterized by a surface admittance $\gamma$.…
A transitional layer matching the asymptotically flat exterior of a charged, massive toroidal body to an interior with spatially cylindrical symmetry is described. The changes in the geometry, which by themselves would require an energy…
The derivation of the Helmholtz theorem of vector decomposition of a 3-vector field requires that the field satisfy certain convergence properties at spatial infinity. This paper investigates if time-dependent electromagnetic radiation wave…
Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the…
We prove that for each positive integer $N$ the set of smooth, zero degree maps $\psi\colon\mathbb{S}^2\to \mathbb{S}^2$ which have the following three properties: (1) there is a unique minimizing harmonic map $u\colon \mathbb{B}^3\to…
A uniqueness theorem is established for autonomous systems of ODEs, $\dot{x}=f(x)$, where $f$ is a Sobolev vector field with additional geometric structure, such as delta-monoticity or reduced quasiconformality. Specifically, through every…
For a Riemannian manifold $M$, possibly with boundary, we consider the Riemannian product $M\times\mathbb{R}^k$ with a smooth positive function that weights the Riemannian measures. In this work we characterize parabolic hypersurfaces with…
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to…
General equations of the unified field theory, obtained using the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of the metric-affine space, and describe the…
Vacuum-energy calculations with ideal reflecting boundaries are plagued by boundary divergences, which presumably correspond to real (but finite) physical effects occurring near the boundary. Our working hypothesis is that the stress tensor…
We extend the usual derivation of the wave equation from Maxwell's equations in vacuum to the case of electromagnetic fields in dispersive homogeneous isotropic linear media. Usually, dispersive properties of materials are studied in…
We present Newtonian and fully general-relativistic solutions for the evolution of a spherical region of uniform interior density \rho_i(t), embedded in a background of uniform exterior density \rho_e(t). In both regions, the fluid is…
At singular points of a wave field, where the amplitude vanishes, the phase may become singular and wavefront dislocation may occur. In this Letter, we investigate for wave fields in one spatial dimension the appearance of these essentially…