Related papers: Radon numbers and the fractional Helly theorem
Consider the (almost surely) unique Radon partition of a set of $n$ random Gaussian vectors in $\mathbb R^{n-2}$; choose one of the two parts of this partition uniformly at random, and for $0 \le k \le n$, let $p_k$ denote the probability…
In this note we exhibit the so-called Harbourne constants which capture and measure the Bounded Negativity on various birational models of an algebraic surface. We show an estimation for Harbourne constants for conic configurations on the…
R\'enyi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of R\'enyi…
Weak radiative hyperon decays present us with a long-standing puzzle, namely the question of validity of a hadron-level theorem proved by Hara. We briefly discuss the conflict between expectations based on Hara's theorem and experiment as…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…
Some of the theoretical challenges posed by the general relativistic description of binary systems of compact objects (neutron stars or black holes) are reviewed. We recall the various ways one can use the theory of the motion, and of the…
Given $\alpha\in(0,1]$ and $p\in[1,+\infty]$, we define the space $\mathscr{DM}^{\alpha,p}(\mathbb R^n)$ of $L^p$ vector fields whose $\alpha$-divergence is a finite Radon measure, extending the theory of divergence-measure vector fields to…
The Hamiltonian Theory of the fractional quantum Hall (FQH) regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this paper we include disorder in our treatment, and show…
Sum rules for the variation of finite-density spectral density of vector channel with baryon density are derived based on dispersion relations and the operator product expansion. These sum rules may serve as constraints on the…
Fourier-transformable Radon measures are called doubly sparse when both the measure and its transform are pure point measures with sparse support. Their structure is reasonably well understood in Euclidean space, based on the use of…
This paper establishes connections between the group-Fourier transform and the geometry of measures in the Heisenberg group. Firstly, it is shown that if the Fourier transform of a compactly supported, finite, Radon measure is square…
A contribution is presented to the study of hadron spectroscopy through the use of fractals and discrete scale invariance implying log-periodic corrections to continuous scaling. The masses of mesons and baryons, reported by the Particle…
The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation…
We resolve a conjecture of Kalai relating approximation theory of convex bodies by simplicial polytopes to the face numbers and primitive Betti numbers of these polytopes and their toric varieties. The proof uses higher notions of…
We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons. The same relation is followed by 2693 points in 153 galaxies with very different morphologies,…
In this paper, we present a second partial solution for the problem of cardinality calculation of the set of fractals for its subcategory of the random virtual ones. Consistent with the deterministic case, we show that for the given…
A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…
It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…
In this article, we prove a quantitative version of Carleson's $\varepsilon^2$ conjecture in higher dimension: we characterise those Ahlfors-David regular domains in $\mathbb{R}^{n+1}$ for which the Carleson's coefficients satisfy the…
We study relative differential closure in the context of Hardy fields. Using our earlier work on algebraic differential equations over Hardy fields, this leads to a proof of a conjecture of Boshernitzan (1981): the intersection of all…