Let $SM_n(\mathbb{R})^g$ denote $g$-tuples of $n \times n$ real symmetric matrices and set $SM(\mathbb{R})^g = \cup_n SM_n(\mathbb{R})^g$. A free quadrilateral is the collection tuples $X \in SM(\mathbb{R})^2$ which have positive semidefinite evaluation on linear equations defining a classical quadrilateral. Such closed under rich class convex combinations called matrix combination. That is, gi...

Abstract We study radiative charm decays $$D \rightarrow P_1 P_2 \gamma $$ D → P 1 2 γ , $$P_{1,2}=\pi ,K$$ , = π K</mml...

Aims. The main purpose of this work is to provide a method derive tabulated observational constraints on the halo mass function (HMF) by studying magnification bias effect high-redshift submillimeter galaxies. Under assumption universality, we parametrize HMF according two traditional models, namely Sheth and Tormen (ST) Tinker fits assess their performance in explaining measured data within {\...

In the Directed Disjoint Paths problem, we are given a digraph $D$ and set of requests $\{(s_1, t_1), \ldots, (s_k, t_k)\}$, task is to find collection pairwise vertex-disjoint paths $\{P_1, P_k\}$ such that each $P_i$ path from $s_i$ $t_i$ in $D$. This problem NP-complete for fixed $k=2$ W[1]-hard with parameter $k$ DAGs. A few positive results known under restrictions on input digraph, as bei...

We study the interstellar medium (ISM) properties as a function of molecular gas size for 77 infrared-selected galaxies at $z \sim 1.3$. Molecular sizes are measured on ALMA images that combine CO(2-1), CO(5-4) and underlying continuum observations, include CO(4-3), CO(7-6)+[CI]($^3 P_2-^3P_1$), [CI]($^3 P_1-^3P_0$) observations subset sample. The $\gtrsim 46 \%$ our have compact reservoir, lie...

Observations from space missions have allowed significant progress in many scientific domains due to the absence of atmospheric noise contributions and having uninterrupted data sets. In context asteroseismology, this has been extremely beneficial because oscillation frequencies with small amplitudes, not observable ground, can be detected. One example success is large number hybrid delta Sct-g...

The orbit of the outer satellite Alexhelios (216) Kleopatra is already constrained by adaptive-optics astrometry, obtained with VLT/SPHERE instrument. However, there also a preceding occultation event in 1980 attributed to this satellite. Hereinafter, we try link all observations, spanning 1980--2018. We find nominal exhibits an unexplained shift $+60^\circ$ true longitude. Using both periodogr...

A bstract The genus zero contribution to the four-point correlator $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle O p 1 2 3 4 </mm...

To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution multiple moons, orbiting extremely irregular body and including their mutual interactions. Such orbits are generally non-Keplerian orbital elements not constants. Consequently, use a modified $N$-body integrator, which was significantly extended include the multipole expansion gravitational field up o...