相关论文: A few results on permittivity variations in electr…

The main difficulty in solving the Helmholtz equation within polygons is due to non-analytic vertices. By using a method nearly identical to that used by Fox, Henrici, and Moler in their 1967 paper; it is demonstrated that such eigenvalue…

We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a…

In this paper we derive boundary integral identities for the bi-Laplacian eigenvalue problems under Dirichlet, Navier and simply-supported boundary conditions. By using these identities, we first obtain the uniqueness criteria for the…

We consider an Einstein-Maxwell action modified by the addition of three terms coupling the electromagnetic strength to the curvature tensor. The corresponding generalized Maxwell equations imply a variation of the speed of light in a…

This paper produces explicit strongly Hermitian Einstein-Maxwell solutions on the smooth compact $4$-manifolds that are $S^2$-bundles over compact Riemann surfaces of any genus. This generalizes the existence results by C. LeBrun in…

We consider a singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent interchange of type of boundary condition on a lateral surface. These boundary conditions are prescribed by partition of lateral surface in…

A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…

We show that phase space bounds on the eigenvalues of Schr\"{o}dinger operators can be derived from universal bounds recently obtained by E. M. Harrell and the author via a monotonicity property with respect to coupling constants. In…

In this paper, we discuss a class of spectral partition problems with a measure constraint, for partitions of a given bounded connected open set. We establish the existence of an optimal open partition, showing that the corresponding…

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading…

The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…

Maxwell's equations for the time-dependent electromagnetic field in a homogeneous chiral medium are reduced to a single quaternionic equation. Its fundamental solution satisfying the causality principle is obtained which allows us to solve…

The paper is devoted to optimization of resonances in a 1-D open optical cavity. The cavity's structure is represented by its dielectric permittivity function e(s). It is assumed that e(s) takes values in the range 1 <= e_1 <= e(s) <= e_2.…

Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges (electric and magnetic) are obtained in unique, simple…

A local permittivity model is proposed to accurately characterize spatial dispersion in non-local wire-medium (WM) structures with arbitrary terminations. A closed-form expression for the local thickness-dependent permittivity is derived…

We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…

The Einstein-Maxwell equations on a smooth compact 4-manifold are reformulated as a purely Riemannian variational problem analogous to Calabi's variational problem for extremal Kahler metrics. Next, Seiberg-Witten theory is used to show…

For systems of linear differential equations on a compact interval, we investigate the~dependence on a parameter $\varepsilon$ of the solutions to boundary-value problems in the Sobolev spaces $W^{n}_{\infty}$. We obtain a constructive…

We develop a minisuperspace formulation of the classical double copy for anisotropic Lifshitz spacetimes in arbitrary dimension. By imposing static symmetries at the level of the action, the gravitational system reduces to an effective…

We develop a compact theory that can be applied to a variety of time-varying dispersive materials. The continuous wave reflection and transmission coefficients are replaced with equivalent operator expressions. In addition to comparing this…