Related papers: Improving Pinwheel Density Bounds for Small Minimu…

We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following…

We consider hard-disc mixtures with disc sizes within ratio $\sqrt{2}-1$, that is, the small disc exactly fits in the hole between four large discs. For each prescribed stoichiometry of large and small discs, the densest packings are…

Motivated by modern applications like image processing and wireless sensor networks, we consider a variation of the famous Kepler Conjecture. Given any infinite set of unit balls covering the whole space, we want to know the optimal (lim…

We perform a fit to precise electroweak data to determine the Higgs and top masses. Penalty functions taking into account their production limits are included. We find ${\displaystyle m_H=65^{+245}_{-4}\ GeV}$ and ${\displaystyle…

We show that the counts of galaxy clusters in future deep cluster surveys can place strong constraints on the matter density, Omega_m, the vacuum energy density, Omega_L, and the normalization of the matter power spectrum, sigma_8.…

Let $P$ be a finite set of points in the plane in general position, that is, no three points of $P$ are on a common line. We say that a set $H$ of five points from $P$ is a $5$-hole in $P$ if $H$ is the vertex set of a convex $5$-gon…

Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density $\lambda_c^{(d)}$ for $d$-dimensional Poisson random geometric…

In 1976, Coffman and Sethi conjectured that a natural extension of LPT list scheduling to the bicriteria scheduling problem of minimizing makespan over flowtime optimal schedules, called LD algorithm, has a simple worst-case performance…

In this paper, we study the minimality of the boundary of a Coxeter system. We show that for a Coxeter system $(W,S)$ if there exist a maximal spherical subset $T$ of $S$ and an element $s_0\in S$ such that $m(s_0,t)\ge 3$ for each $t\in T$…

We analyze non-universal 5D standard model extension, where some or all of the gauge and Higgs fields propagate in a flat extra dimension, while all other degrees of freedom are localized on a S^1/Z_2 orbifold brane. From LEP data,…

The ambient gas pressure is determined for the onset of splashing of low-viscosity liquid drops on smooth dry surfaces as we change the control parameters: drop impact velocity, drop radius, viscosity, surface tension, density, and gas…

For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the $100(1-\alpha)%$ Bayesian HPD credible set associated with priors which are truncations of…

Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…

We find new bounds on the conformal dimension of small cancellation groups. These are used to show that a random few relator group has conformal dimension 2+o(1) asymptotically almost surely (a.a.s.). In fact, if the number of relators…

We consider ensembles of Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. We show the convergence of the Stieltjes transform towards the Stieltjes transform of the…

Variational turbulence is among the few approaches providing rigorous results in turbulence. In addition, it addresses a question of direct practical interest, namely the rate of energy dissipation. Unfortunately, only an upper bound is…

Determining the minimum density of a covering of $\mathbb{R}^{n}$ by Euclidean unit balls as $n\to\infty$ is a major open problem, with the best known results being the lower bound of $\left(\mathrm{e}^{-3/2}+o(1)\right)n$ by Coxeter, Few…

We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…

Let $S$ be a set of $n$ points in $\mathbb{R}^d$, where $d \geq 2$ is a constant, and let $H_1,H_2,\ldots,H_{m+1}$ be a sequence of vertical hyperplanes that are sorted by their first coordinates, such that exactly $n/m$ points of $S$ are…

Inertial particles in 2D driven by a Gaussian white noise forcing are considered. For two examples of the forcing (compressible and incompressible) upper and lower bounds are found for the mean number of caustics as a function of Stokes…