Related papers: On an explicit lower bound for the star discrepanc…
The metric dimension reduction modulus $k^\alpha_n(\ell_\infty)$ is the smallest $k$ such that every $n$--point metric space can be embedded into some $k$-dimensional normed space, with bi--Lipschitz distortion at most $\alpha$. Determining…
It is stated in many text books that the any metric appearing in general relativity should be locally Lorentzian i.e. of the type $\eta_\mn = {\rm diag} (1,-1,-1,-1)$ this is usually presented as an independent axiom of the theory, which…
We present strong constraints on the spacetime variation of the fine-structure constant $\alpha$ using the Dark Energy Spectroscopic Instrument (DESI). In this pilot work, we utilize $\sim110,000$ galaxies with strong and narrow O III…
Two types of stability boundaries exist for any planetary system consisting of one star and two planets. Lagrange stability requires that the planets remain bound to the star, conserves the ordering of the distance from the star, and limits…
Our goal is to study the existing star formation rate calibrations based on emission-line luminosities and to provide new ones. We use the SDSS data release DR4, which gives star formation rates and emission-line luminosities of more than…
We use 612 single stars with previously published trigonometric parallaxes placing them within 25 pc to evaluate parallaxes released in Gaia's first data release (DR1). We find that the Gaia parallaxes are, on average, $0.24 \pm 0.02$ mas…
According to the Erd\H{o}s discrepancy conjecture, for any infinite $\pm 1$ sequence, there exists a homogeneous arithmetic progression of unbounded discrepancy. In other words, for any $\pm 1$ sequence $(x_1,x_2,...)$ and a discrepancy…
Let $\mathbf{X} = (X_i)_{1\leq i \leq n}$ be an i.i.d. sample of square-integrable variables in $\mathbb{R}^d$, \GB{with common expectation $\mu$ and covariance matrix $\Sigma$, both unknown.} We consider the problem of testing if $\mu$ is…
The presence of an isotropic tricritical Lifshitz point for the O(N) scalar theory is investigated in the 1/N expansion by means of the Functional Renormalization Group equations. At leading order, the non-trivial Lifshitz point is observed…
We investigate astrophysical contributions to the statistical uncertainty of precision radial velocity measurements of stellar spectra. We analytically determine the uncertainty in centroiding isolated spectral lines broadened by Gaussian,…
We proved that for every sufficiently large $n$, the complete graph $K_{2n}$ with an arbitrary edge signing $\sigma: E(K_{2n}) \to \{-1, +1\}$ admits a high discrepancy $1$-factor decomposition. That is, there exists a universal constant $c…
We propose a new parameterization to measure the neutrino mass hierarchy, namely $\Delta=(m_3-m_1)/(m_1+m_3)$ which is dimensionless and varies in the range $[-1,1]$. Taking into account the results of neutrino oscillation experiments,…
Given an equidistributed set in the whole Euclidean space, we have established in [1] that there exists a constant positive $C$ such that the observability inequality of diffusion equations holds for all $T\in]0,1[$, with an observability…
We aim to constrain the average star formation associated with neutral hydrogen gas reservoirs at cosmic noon. Using a unprecedented sample of 1716 high column density Damped Ly-$\alpha$ absorbers (DLAs) from the Sloan Digital Sky Survey…
Let $S(t) = \frac{1}{\pi}\Im \log\zeta\left(\frac{1}{2}+it\right)$. We prove an unconditional lower bound on the measure of the sets $\{t\in [T,2T] \colon S(t) \geq V\}$ for $\sqrt{\log\log T} \leq V \ll \left(\frac{\log T}{\log \log…
We determine the Hubble constant $H_0$ precisely ($2.3\%$ uncertainty) in a manner independent of cosmological model through Gaussian process regression, using strong lensing and supernova data. Strong gravitational lensing of a variable…
We study the properties of compact objects in a particular 4D Horndeski theory originating from higher dimensional Einstein-Gauss-Bonnet gravity. Remarkably, an exact vacuum solution is known. This compact object differs from general…
Let $\Delta(x)$ denote the error term in the Dirichlet divisor problem, and $E(T)$ the error term in the asymptotic formula for the mean square of $|\zeta(1/2+it)|$. If $E^*(t) = E(t) - 2\pi\Delta^*(t/(2\pi))$ with $\Delta^*(x) = -\Delta(x)…
We consider the problem of digitalizing Euclidean segments. Specifically, we look for a constructive method to connect any two points in $\mathbb{Z}^d$. The construction must be {\em consistent} (that is, satisfy the natural extension of…
We present half-light sizes measured from H${\alpha}$ emission tracing star-formation in 281 star-forming galaxies from the KMOS3D survey at 0.7 < z < 2.7. Sizes are derived by fitting 2D exponential disk models, with bootstrap errors…