Related papers: Improving a Constant in High-Dimensional Discrepan…
Connecting galaxies with their descendants (or progenitors) at different redshifts can yield strong constraints on galaxy evolution. Observational studies have historically selected samples of galaxies using a physical quantity, such as…
We present a determination of the Hubble constant from the joint, free-form analysis of 8 strongly, quadruply lensing systems. In the concordance cosmology, we find $H_0 = 71.8^{+3.9}_{-3.3}\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$…
W.M.Schmit[11] conjectured that for any$\;\theta$ with deg$\;\theta\geq 3,$ there is no constant$\;C=C(\theta)$ so that$\;|p-q\theta|>Cq^{-1}$ for every rationa$\;p/q.$ [12,p26] states that the computations of the first several thousand…
In this work, we analyzed all available determinations of the Galactic rotation parameters $R_0$ and $\Omega_0$ made during last 10 years to derive the most probable value of the Galactic aberration constant $A = R_0 \Omega_0^2/c$. We used…
We establish new inequalities involving classical exponents of Diophantine approximation. This allows for improving on the work of Davenport, Schmidt and Laurent concerning the maximum value of the exponent $\hat{\lambda}_{n}(\zeta)$ among…
Let $ex_r(N,g)$ be the maximum number of edges in an $r$-uni\-form hypergraph on $N$ vertices with girth at least $g$. We are interested in the asymptotic behavior of this value when $N$ is increasing but parameters $g\in\{6,8\}$ and…
The classical Crossing Lemma by Ajtai et al.~and Leighton from 1982 gave an important lower bound of $c \frac{m^3}{n^2}$ for the number of crossings in any drawing of a given graph of $n$ vertices and $m$ edges. The original value was $c=…
For nonnegative integers $n$ and $d$, let $A(n,d)$ be the maximum cardinality of a binary code of length $n$ and minimum distance at least $d$. We consider a slight sharpening of the semidefinite programming bound of Gijswijt, Mittelmann…
Given an isotropic random vector $X$ with log-concave density in Euclidean space $\Real^n$, we study the concentration properties of $|X|$ on all scales, both above and below its expectation. We show in particular that: \[ \P(\abs{|X|…
Asteroseismology of solar-like oscillators often relies on the comparisons between stellar models and stellar observations in order to determine the properties of stars. The values of the global seismic parameters, $\nu_\mathrm{max}$ (the…
We verify an upper bound of Pach and T\'oth [Combinatorica 17(1997), 427-439, Discrete and Computational Geometry 36(2006), 527-552] on the midrange crossing constant. Details of their $\frac{8}{9\pi^2}$ upper bound have not been available.…
Using 25 years of data from uninterrupted monitoring of stellar orbits in the Galactic Center, we present an update of the main results from this unique data set: A measurement of mass of and distance to SgrA*. Our progress is not only due…
We find the exact lower bound of the discrepancy of shifted Niedereiter's sequences.
The GLIMPSE (Galactic Legacy Mid-Plane Survey Extraordinaire) Point Source Catalog of ~ 30 million mid-infrared sources towards the inner Galaxy, 10 < |l| < 65 degrees and |b| < 1 degree, was used to determine the distribution of stars in…
We report a robust constrain on the possible variation of fine-structure constant, alpha = e^2/(hbar*c), obtained using O III 4959,5007, nebular emission lines from QSOs. We find Delta-alpha/alpha=-(2.1 +/- 1.6) x 10^(-5) based on a well…
The k-means problem consists of finding k centers in the d-dimensional Euclidean space that minimize the sum of the squared distances of all points in an input set P to their closest respective center. Awasthi et. al. recently showed that…
Spectral enhancement -- which aims to undo spectral broadening -- leads to integral equations which are ill-posed and require special regularisation techniques for their solution. Even when an optimal regularisation technique is used,…
According to astrophysical observations value of recession velocity in a certain point is proportional to a distance to this point. The proportionality coefficient is the Hubble constant measured with 5% accuracy. It is used in many…
Given a non-principal Dirichlet character chi mod q, an important problem in number theory is to obtain good estimates for the size of L(1,chi). In this paper we focus on sharpening the upper bounds known for |L(1,chi)|; in particular, we…
In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepancy measures in a more general context, we focus on the…