Related papers: Geodesics on weighted projective spaces
In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…
We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…
The direct detection of gravitational waves has provided new opportunities for studying the universe, but also new challenges, such as the detection and characterization of stochastic gravitational-wave backgrounds at different…
Gravitational waves propagate along null geodesics like light rays in the geometrical optics approximation, and they may have a chance to suffer from gravitational lensing by intervening objects, as is the case for electromagnetic waves.…
The expected amplitudes and spectral slopes of relic gravitational waves, plus their specific correlation properties associated with the phenomenon of squeezing, may allow the registration of relic (squeezed) gravitational waves by the…
We prove trace theorems for weighted mixed norm Sobolev spaces in the upper-half space where the weight is a power function of the vertical variable. The results show the differentiability order of the trace functions depends only on the…
We report numerical simulations of surface gravity waves forced at small scale and the subsequent inverse cascade of wave action. We combine the spectral approach to simulating weakly nonlinear waves with the capabilities of modern Graphics…
We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using the mild-slope equation, and analyze the topographic…
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
We perform experiments to study the inverse cascade regime of gravity wave turbulence on the surface of a fluid. Surface waves are forced at an intermediate scale corresponding to the gravity-capillary wavelength. In response to this…
This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…
The inverse acoustic scattering of point objects using multi-frequency sparse measurements are studied. The objects may be a sum of point sources or point like scatterers. We show that the locations and scattering strengths of the point…
We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…
More than ten years ago Ikehata discovered two mathematical methods for the purpose of extracting information about the location and shape of unknown discontinuity embedded in a known background medium from observation data. The methods are…
It is suggested that gravity waves could, in several cases, be detected by means of already (or shortly to be) available technology, independently of current efforts of detection. The present is a follow-up on a recently suggested detection…
Prime geodesic theorems for weighted infinite graphs and weighted building quotients are given. The growth rates are expressed in terms of the spectral data of suitable translation operators inspired by a paper of Bass.
This note begins with an introduction to the inverse isospectral problem popularized by M. Kac's 1966 article in the American Mathematical Monthly, "Can one hear the shape of a drum?" Although the answer has been known for some twenty years…
The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this…
We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in…
The secular equation for surface acoustic waves propagating on an orthotropic incompressible half-space is derived in a direct manner, using the method of first integrals.