Related papers: On an explicit lower bound for the star discrepanc…

For a finite set $A\subset \mathbb{R}^d$, let $\Delta(A)$ denote the spread of $A$, which is the ratio of the maximum pairwise distance to the minimum pairwise distance. For a positive integer $n$, let $\gamma_d(n)$ denote the largest…

Based on a fairly precise approximation to the lattice discrepancy of a Lame disc, an asymptotic formula is established for the number of lattice points in a related three-dimensional body, linearly dilated by a large real parameter x.…

We prove that there is a constant $c > 0$ depending only on $M \geq 1$ and $\mu \geq 0$ such that $$\int_y^{y+a}{|g(t)| \, dt} \geq \exp (-c/(a\delta))\,, a \in (0,\pi]\,,$$ for every $g$ of the form $$g(t) = \sum_{j=0}^n{a_j…

A distance-deviation consistency and model-independent method to test the cosmic distance duality relation (CDDR) is provided. The method is worth attention on two aspects: firstly, a distance-deviation consistency method is used to pair…

We consider perfect fluid bodies (stars) in general relativity, characterized by particle number density and entropy per particle. A star is said to be in dynamic equilibrium if it is a stationary, axisymmetric solution to the…

We continue the work of \cite{TLNT}. Let $E$ be a non-Blaschke subset of the unit disc $\mathbb{D}$ of the complex plane $\mathbb{C}$. Fixed $1\leq p\leq \infty$, let $H^p(\mathbb{D})$ be the Hardy space of holomorphic functions in the disk…

The effect of a generalized uncertainty principle on the structure of an ideal white dwarf star is investigated. The equation describing the equilibrium configuration of the star is a generalized form of the Lane-Emden equation. It is…

We present an absolute parallax and relative proper motion for the central star of the planetary nebula NGC 6853 (The Dumbell). We obtain these with astrometric data from FGS 3, a white-light interferometer on {\it HST}. Spectral…

We provide an algorithm to approximate a finitely supported discrete measure $\mu$ by a measure $\nu_{N}$ corresponding to a set of $N$ points so that the total variation between $\mu$ and $\nu_N$ has an upper bound. As a consequence if…

We have determined the location of the line-opacity modified Eddington limit for stars in the LMC using the most recent atmosphere models combined with a precise mapping to the HR Diagram through up-to-date stellar evolution calculations.…

We introduce a class of convex equivolume partitions. Expected star discrepancy results are compared for stratified samples under these partitions, including simple random samples. There are four main parts of our results. First, among…

The gamma density function is usually defined in interval between zero and infinity. This paper introduces an upper and a lower boundary to this distribution. The parameters which characterize the truncated gamma distribution are evaluated.…

In this paper we prove that there exists a constant $C$ such that, if $S,\Sigma$ are subsets of $\R^d$ of finite measure, then for every function $f\in L^2(\R^d)$, $$\int_{\R^d}|f(x)|^2 dx \leq C e^{C \min(|S||\Sigma|, |S|^{1/d}w(\Sigma),…

I make the first estimates of maximum elastic quadrupole deformations sustainable by alternatives to conventional neutron stars. Solid strange quark stars might sustain maximum ellipticities (dimensionless quadrupoles) up to a few times…

We study a model of the neutron star in $\kappa$-deformed space-time in the presence of the cosmological constant ($\Lambda$). The Einstein tensor and the energy-momentum tensor are generalized to $\kappa$-deformed space-time and we…

We update constraints on cosmic opacity by combining recent SN Type Ia data compilation with the latest measurements of the Hubble expansion at redshifts between 0 and 2. The new constraint on the parameter $\epsilon$ parametrising…

In 2013, Koldobsky posed the problem to find a constant $d_n$, depending only on the dimension $n$, such that for any origin-symmetric convex body $K\subset\mathbb{R}^n$ there exists an $(n-1)$-dimensional linear subspace…

Applying functional differentiation to the density field with Newtonian gravity, we obtain the static, nonlinear equation of the three-point correlation function $\zeta$ of galaxies, to the third order density perturbations. We make the…

It is commonly believed that the normalized gaps between consecutive ordinates $t_n$ of the zeros of the Riemann zeta function on the critical line can be arbitrarily large. In particular, drawing on analogies with random matrix theory, it…

Tsirelson's space $T$ is known to be distortable but it is open as to whether or not $T$ is arbitrarily distortable. For $n\in {\Bbb N}$ the norm $\|\cdot\|_n$ of the Tsirelson space $T(S_n,2^{-n})$ is equivalent to the standard norm on…