Related papers: Rearrangement and polarization
The primary objective of this paper is to establish several sharp results concerning the Bohr inequality, the refined Bohr inequality, and the improved Bohr inequality for the classes of analytic functions and harmonic mappings defined on…
Some prominent discretisation methods such as finite elements provide a way to approximate a function of $d$ variables from $n$ values it takes on the nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in $L^2$-norm, where…
We present a novel analysis method for measurements of polarization transferred in $A(\vec{e},e'\vec{N})$ experiments, which can be applied to other kinds of polarization measurements as well. In this method the polarization transfer…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…
A general theory of partial balayage on Riemannian manifolds is developed, with emphasis on compact manifolds. Partial balayage is an operation of sweeping measures, or charge distributions, to a prescribed density, and it is closely…
We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller…
Using polarization measurements in remote sensing and optical studies allows retrieving more information. We consider relationship between the reflection coefficients of plane and rough surfaces for linearly polarized waves. Certain…
With the forthcoming release of high precision polarization measurements, such as from the Planck satellite, the metrology of polarization needs to improve. In particular, it is crucial to take into account full knowledge of the noise…
Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…
High precision polarization measurements open new opportunities for the study of the magnetic field structure as traced by polarimetric measurements of the interstellar dust emission. Polarization parameters suffer from bias in the presence…
We characterize Poincar\'{e} inequalities in metric spaces using rearrangement inequalities
Radiocommunication systems have evolved significantly in recent years in order to meet present and future demands. Historically, time, frequency and more recently, spatial dimensions have been used to improve capacity and robustness.…
We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…
Modern dual-polarization receivers allow a radio telescope to characterize the full polarization state of incoming insterstellar radio waves. Many astronomers incorrectly consider a polarimeter to be the "backend" of the telescope. We go to…
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…
We use the reconfiguration framework to analyze problems that involve the rearrangement of items among groups. In various applications, a group of items could correspond to the files or jobs assigned to a particular machine, and the goal of…
In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…
The polarization of x-rays plays an outstanding role in experimental techniques such as non-resonant magnetic x-ray scattering and resonant x-ray scattering of magnetic and multipolar order. Different instrumental methods applied to…
We apply concepts of majorization theory to derive new insights in the field of extremal dependence structures. In particular, we consider the Rearrangement Algorithm by Puccetti and Rueschendorf, where majorization arguments yield a…