Related papers: A note on measures whose diffraction is concentrat…
I briefly review: (a) some recent developments in the theory of hard scattering in QCD with polarized beams, and (b) coherent hard diffraction (that is, hard scattering in diffractive events, with the Pomeron behaving in an apparently…
In this work we study the natural focusing of Airy beams symmetric under reflection of the transverse coordinates. Following a recent proposal, their angular spectra depend on the absolute value of the third power of the transverse…
This paper is concerned with the inverse medium problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering…
We derive and discuss general physical bounds on the electromagnetic scattering and absorption of passive structures. Our theory, based on passivity and power conservation, quantifies the minimum and maximum allowed scattering for an object…
In this article we provide lower bounds for the lower Hausdorff dimension of finite measures assuming certain restrictions on their quaternionic spherical harmonics expansion. This estimate is an analog of a result previously obtained by…
We study properties of temperate non-negative purely atomic measures in the Euclidean space such that the distributional Fourier transform of these measures are pure point ones. A connection between these measures and almost periodicity is…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
A general symmetry analysis of the optical conductivity or scattering tensor is used to rewrite the conductivity tensor as a sum of fundamental spectra multiplied by simple functions depending on the local magnetization direction. Using…
In this work we study the concentration properties of log-concave measures that are curved only on a subspace of directions. Proofs uses an adapted version of the stochastic localization process.
We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…
We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a…
Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…
We are interested in dendrites for which all invariant measures of zero-entropy mappings have discrete spectrum, and we prove that this holds when the closure of the endpoint set of the dendrite is countable. This solves an open question…
Uniformly distributed point sets on the unit sphere with and without symmetry constraints have been found useful in many scientific and engineering applications. Here, a novel variant of the Thomson problem is proposed and formulated as an…
We prove that an approximated version of the Brunn--Minkowski inequality with volume distortion coefficient implies a Gaussian concentration-of-measure phenomenon. Our main theorem is applicable to discrete spaces.
We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a $3$-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of…
We prove a convergence theorem on the moduli space of constant $\sigma_{2}$ metrics for conic 4-spheres. We show that when a numerical condition is convergent to the boundary case, the geometry of conic 4-spheres converges to the boundary…
Recently, in an ensemble of small spheres, we proposed a method that converts the force between two large spheres into the pressure on the large sphere's surface element. Using it, the density distribution of the small spheres around the…
We show that if points of supports of two discrete "not very thick" Fourier transformable measures on LCA groups tend to one another at infinity and the same is true for the masses at these points, then these measures coincide. The result…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…