Related papers: No new lower bound for the density of planar Sets …
In the early 1990s, A. Bezdek and W. Kuperberg used a relatively simple argument to show a surprising result: The maximum packing density of circular cylinders of infinite length in $\mathbb{R}^3$ is exactly $\pi/\sqrt{12}$, the planar…
Magnetars and central compact objects (CCOs) are subgroups of neutron stars that show a number of properties distinguished from canonical radio pulsars. We performed radio observations of three magnetars SGR 0418+5729, 1E 2259+586, 4U…
By studying its subgraphs, it is argued that the lower critical percolation threshold of the enhanced binary tree (EBT) is bounded as $p_{c1} < 0.355059$, while the upper threshold is bounded both from above and below by 1/2 according to…
An analysis of the kinematics of 412 stars at 1-4 kpc from the Galactic mid-plane by Moni Bidin et al. (2012) has claimed to derive a local density of dark matter that is an order of magnitude below standard expectations. We show that this…
Discharging arguments demonstrate a connection between local structure and global averages. This makes it an effective tool for proving lower bounds on the density of special sets in infinite grids. However, the minimum density of an…
A blocking set in an affine plane is a set of points $B$ such that every line contains at least one point of $B$. The best known lower bound for blocking sets in arbitrary (non-desarguesian) affine planes was derived in the 1980's by Bruen…
From the analysis of the near-UV spectrum of the QSO 2206-199, obtained with a long series of exposures with STIS on the HST, we deduce a value (D/H) = (1.65 +/- 0.35) x 10(-5) (1 sigma error) for the abundance of deuterium in the z(abs) =…
The union-closed sets conjecture states that in any nonempty union-closed family $\mathcal{F}$ of subsets of a finite set, there exists an element contained in at least a proportion $1/2$ of the sets of $\mathcal{F}$. Using the…
The latest result in the Sloan Digital Sky Survey Quasar Lens Search (SQLS) has set the first cosmological constraints on negative-mass compact objects and Ellis wormholes. There are no multiple images lensed by the above two exotic objects…
We describe an astrometric and spectroscopic campaign to confirm the youth and association of a complete sample of candidate wide companions in Taurus and Upper Sco. Our survey found fifteen new binary systems (3 in Taurus and 12 in Upper…
We study how the Hausdorff measure is distributed in nonsymmetric narrow cones in $\mathbb{R}^n$. As an application, we find an upper bound close to $n-k$ for the Hausdorff dimension of sets with large $k$-porosity. With $k$-porous sets we…
In 2021, Ordentlich, Regev and Weiss made a breakthrough that the lattice covering density of any $n$-dimensional convex body is upper bounded by $cn^{2}$, improving on the best previous bound established by Rogers in 1959. However, for the…
Given finite configurations $P_1, \dots, P_n \subset \mathbb{R}^d$, let us denote by $\mathbf{m}_{\mathbb{R}^d}(P_1, \dots, P_n)$ the maximum density a set $A \subseteq \mathbb{R}^d$ can have without containing congruent copies of any…
A significant tension has become manifest between the current expansion rate of our Universe measured from the cosmic microwave background by the Planck satellite and from local distance probes, which has prompted for interpretations of…
We use current observations on the number statistics of gravitationally lensed optical arcs towards galaxy clusters to derive an upper limit on the cosmological mass density of the Universe. The gravitational lensing statistics due to…
We investigate various sparse sets that satisfy the prime number theorem. The sparsest of these sets, $\{\lfloor x/n^t \rfloor:n \le x\}$, has density approaching $1/x$ as $t$ approaches infinity.
Bounds are derived on the cross section, flux and energy density of new particles that may be responsible for the atmospheric neutrino anomaly. $4.6 \times 10^{-45} cm^2 < \sigma <2.4 \times 10^{-34} cm^2$ Decay of primordial homogeneous…
We prove that among $n$ points in the plane in general position, the shortest distance occurs at most $43n/18$ times, improving upon the upper bound of $17n/7$ obtained by T\'oth in 1997.
We present a new lower bound on the differential entropy rate of stationary processes whose sequences of probability density functions fulfill certain regularity conditions. This bound is obtained by showing that the gap between the…
A long-standing conjecture by Heath, Pemmaraju, and Trenk states that the upward book thickness of outerplanar DAGs is bounded above by a constant. In this paper, we show that the conjecture holds for subfamilies of upward outerplanar…