Related papers: Resonances as Viscosity Limits for Exponentially D…

We discuss the virtual Compton scattering amplitude $\gamma^\ast+\pi\to \gamma+\pi$ which enters the reaction $\pi^-+e^-\to\pi^-+e^-+\gamma$. The low-energy scattering amplitude is divided into a model-independent part, involving only the…

In the paper we prove the convergence of viscosity solutions $u_{\lambda}$ as $\lambda\rightarrow0_+$ for the parametrized degenerate viscous Hamilton-Jacobi equation \[ H(x,d_x u, \lambda u)=\alpha(x)\Delta u,\quad \alpha(x)\geq 0,\quad…

This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a…

We provide a general theoretical framework to describe the electromagnetic properties of viscous charged fluids, consisting for example of electrons in certain solids or plasmas. We confirm that finite viscosity leads to multiple modes of…

In this paper the method of compensated compactness is applied to the problem of isometric immersion of a two dimensional Riemannian manifold with negative Gauss curvature into three dimensional Euclidean space. Previous applications of the…

In this letter, a methodology is proposed to improve the scattering powers obtained from model-based decomposition using Polarimetric Synthetic Aperture Radar (PolSAR) data. The novelty of this approach lies in utilizing the intrinsic…

This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lam\'{e} parameters and density. Our contributions are fourfold. First, we construct an…

An algorithm$^{\ref{Fig1}}$ has been developed with the purpose of obtaining inverse potentials, where the Riccati-type non-linear differential equation, also called phase equation, has been kept in tandem with the Variational Monte Carlo…

A full calculation of lepton-pair angular characteristics is carried out for $e^+e^-$ pairs created in $pp$, $pn$ and $pd$ collisions at intermediate energies. It is demonstrated that the proposed new observable, the dilepton decay…

Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method…

We prove weighted-$L^\infty$ and pointwise space-time decay estimates for weak solutions of a class of wave equations with time-independent potentials and subject to initial data, both of low regularity, satisfying given decay bounds at…

In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for…

We study solutions of $-\Delta u + V u = \lambda u$ on $\mathbb{R}^n$. Such solutions localize in the `allowed' region $\left\{x \in \mathbb{R}^n: V(x) \leq \lambda\right\}$ and decay exponentially in the `forbidden' region $\left\{x \in…

Under a perturbation by a decaying electric potential, the Landau Hamiltonian acquires some discrete eigenvalues between the Landau levels. We study the perturbation by an "expanding" electric potential $V(t^{-1}x)$, $t>0$, and derive a…

Electromagnetic decays of the scalar mesons are shown to be constrained by chiral symmetry as a consequence of the fact that, in the chiral limit, the two and three-point functions $<SS-PP>$ and $<VVS>$ satisfy super-convergent dispersion…

We report on new H$(e,e^\prime p)\gamma$ measurements in the $\Delta(1232)$ resonance at $Q^2=0.06$ (GeV/c) carried out simultaneously with H$(e,e^\prime p)\pi^0$. It is the lowest $Q^2$ for which the virtual Compton scattering (VCS)…

Complex potentials are constructed as Darboux-deformations of short range, radial nonsingular potentials. They behave as optical devices which both refracts and absorbs light waves. The deformation preserves the initial spectrum of energies…

We study the scattering poles of $\sqrt{-\Delta} + V$, where $V$ is a compactly supported, bounded and complex valued potential. We show that the resolvent operator $ \chi R_V \chi$ has a meromorphic continuation to the whole Riemannian…

We examine a class of exact solutions for the eigenvalues and eigenfunctions of a doubly anharmonic oscillator defined by the potential $V(x)=\omega^2/2 x^2+\lambda x^4/4+\eta x^6/6$, $\eta>0$. These solutions hold provided certain…

We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of poles generated by both the bounded component of the resonator…