相关论文: $C^{1,\alpha}$ estimates for the parallel refracto…

In this paper, we verify Carl de Boor's conjecture on ideal projectors for real ideal projectors of type partial derivative by proving that there exists a positive $\eta\in \mathbb{R}$ such that a real ideal projector of type partial…

The planewave response of a linear passive material generally cannot be characterized by a single scalar refractive index, as directionality of energy flow and multiple wavevectors may need to be considered. This is especially significant…

We investigate the observational viability of a class of $\alpha$-attractors inflationary models in light of the most recent Cosmic Microwave Background (CMB) and Large-Scale Structure (LSS) data. By considering a double-well potential we…

In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

This paper presents a study of causality in a reversible, concurrent setting. There exist various notions of causality in pi-calculus, which differ in the treatment of parallel extrusions of the same name. In this paper we present a uniform…

We consider planar Coulomb systems consisting of a large number $n$ of repelling point charges in the low temperature regime, where the inverse temperature $\beta$ grows at least logarithmically in $n$ as $n \longrightarrow \infty$, i.e.,…

A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying $\mathcal{PT}$-symmetry. It is illustrated that unlike in…

We establish a new $W^{1,2\frac{n-1}{n-2}}$ estimate for the extremal solution of $-\Delta u=\lambda f(u)$ in a smooth bounded domain $\Omega$ of $\mathbb{R}^n$, which is convex, for arbitrary positive and increasing nonlinearities $f\in…

Aspects of of plane wave electromagnetic scattering by a radially inhomogeneous sphere is discussed. The vector problem is reduced to two scalar radial `Schr\"odinger-like' equations, and a connection with time-independent potential…

We prove duality estimates for time-fractional and more general subdiffusion problems. An important example is given by subdiffusive porous medium type equations. Our estimates can be used to prove uniqueness of weak solutions to such…

In the standard inflationary scenario with inflaton potential $V(\Phi)=M^4-{1\over4}\lambda\Phi^4$, the resulting density perturbations $\delta\rho/\rho$ are proportional to $\lambda^{1/2}$. Upper bounds on $\delta\rho/\rho$ require…

We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is a similar to the inverse back-scattering…

Undesired wave reflections, which occur at domain boundaries in flow simulations with free-surface waves, can be minimized by applying source terms in the vicinity of the boundary to damp the waves. Examples of such approaches are absorbing…

We consider the Boltzmann equation with external fields in strictly convex domains with the specular reflection boundary condition. We construct classical $C^1$ solutions away from the grazing set under the assumption that the external…

Mathematical structure of the reflection coefficients for the one-dimensional Fokker-Planck equation is studied. A new formalism using differential operators is introduced and applied to the analysis in high- and low-energy regions.…

We consider sufficient conditions which guarantee that a planar embedding has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding.

A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…

We extended a previous study of the Eaton lens at specific refraction angles to the Eaton lens at any refraction angle. The refractive index of the Eaton lens is complicated and has not analytical form except at a few specific angles. We…

In this study, we elaborate on the concept of scalable anomalous reflector (AR) to analyze the angular response, frequency response, and spatial scalability of a designed AR across a broad range of angles and frequencies. We utilize…

This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a coarse propagator. We provide a theoretical analysis of the…