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We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…

Complex Variables · Mathematics 2020-01-29 Mohamed M S Nasser , Matti Vuorinen

We explore the problem of scattering in a medium modulated by a superluminal rectangular pulse, with the pulse modulation realized through transverse excitations. We solve this problem in the moving frame where the modulation appears purely…

Classical Physics · Physics 2018-03-21 Zoé-Lise Deck-Léger , Alireza Akbarzadeh , Christophe Caloz

Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all…

Numerical Analysis · Mathematics 2020-06-18 Daniel H. Baffet , Marcus J. Grote , Jet Hoe Tang

We prove that the range of Strichartz estimates on a model 2D convex domain may be further restricted compared to the known counterexamples due to the first author. Our new family of counterexamples is now built on the parametrix…

Analysis of PDEs · Mathematics 2021-06-14 Oana Ivanovici , Gilles Lebeau , Fabrice Planchon

When are two germs of analytic systems conjugate or orbitally equivalent under an analytic change of coordinates in the neighborhood of a singular point? A way to answer is to use normal forms. But there are large classes of dynamical…

Dynamical Systems · Mathematics 2020-11-26 Christiane Rousseau

This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…

Mathematical Physics · Physics 2012-06-14 Peter C. Gibson

This paper focuses on phase retrieval from phaseless total-field data in biharmonic scattering problems. We prove that a phased biharmonic wave can be uniquely determined by the modulus of the total biharmonic wave within a nonempty domain.…

Analysis of PDEs · Mathematics 2026-02-16 Yuxiang Cheng , Xiaoxu Xu

This paper is part I of a series in which we aim to show that the singular support of the wave trace and the length spectrum of a smooth, strictly convex, and bounded planar billiard table are generally distinct objects. We derive an…

Spectral Theory · Mathematics 2024-04-04 Vadim Kaloshin , Illya Koval , Amir Vig

It is proved the existence of multivalent solutions for the Riemann-Hilbert problem in the general settings of finitely connected domains bounded by mutually disjoint Jordan curves, measurable coefficients and measurable boundary data. The…

Complex Variables · Mathematics 2015-10-19 Vladimir Ryazanov

We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2 -> 2 scattering amplitude for the scalar system.…

High Energy Physics - Phenomenology · Physics 2019-11-06 Gernot Eichmann , Pedro Duarte , M. T. Peña , Alfred Stadler

We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously…

Mathematical Physics · Physics 2011-11-10 Ole Henrik Waagaard , Johannes Skaar

In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…

Analysis of PDEs · Mathematics 2018-12-24 Yu Zhao , Guanghui Hu , Baoqiang Yan

A problem of amplitude reconstruction in terms of the given angular distribution is considered. Solution of this problem is not unique. A class of amplitudes, correspondent to one and the same angular distribution, forms a region in…

High Energy Physics - Phenomenology · Physics 2007-05-23 I. N. Nikitin

We study the inverse scattering from a screen with using only one incoming time--harmonic plane wave but with measurements of the scattered wave done at all directions. Especially we focus on the 2D--case i.e. (inverse) scattering from an…

Analysis of PDEs · Mathematics 2024-09-05 Emilia Blåsten , Petri Ola , Lassi Päivärinta

For finite dimensional CMV matrices the classical inverse spectral problems are considered. We solve the inverse problem of reconstructing a CMV matrix by its Weyl's function, the problem of reconstructing the matrix by two spectra of CMV…

Spectral Theory · Mathematics 2007-05-31 Leonid Golinskii , Mikhail Kudryavtsev

We establish a rigidity theorem for annular sector-like domains in the setting of overdetermined elliptic problems on model Riemannian manifolds. Specifically, if such a domain admits a solution to the inhomogeneous Helmholtz equation…

Analysis of PDEs · Mathematics 2025-06-03 João Marcos do Ó , Jaqueline de Lima , Márcio Santos

This report provides some closed form solutions -- and their inversion -- to a satellite's bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the $J_{2}$ spherical zonal harmonic. The equatorial track of…

Earth and Planetary Astrophysics · Physics 2021-05-26 Alessio Bocci , Giovanni Mingari Scarpello

We construct a stable right inverse for the divergence operator in non-cylindrical domains in space-time. The domains are assumed to be H\"older regular in space and evolve continuously in time. The inverse operator is of Bogovskij type,…

Analysis of PDEs · Mathematics 2024-02-28 Olli Saari , Sebastian Schwarzacher

A standard bilinear $L^2$ Strichartz estimate for the wave equation, which underlies the theory of $X^{s,b}$ spaces of Bourgain and Klainerman-Machedon, asserts (roughly speaking) that if two finite-energy solutions to the wave equation are…

Analysis of PDEs · Mathematics 2009-04-21 Terence Tao

This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…

Optimization and Control · Mathematics 2013-10-01 Zui-Cha Deng , Liu Yang