Alexandroff duplicate and βκ

[EN] We discuss spaces and the Alexandroff duplicates of those spaces that admit a C-S embedding into the Cech-Stone compactification of a discrete space.Szymanski, AA. (2022). Alexandroff duplicate and βκ. Applied General Topology. 23(1):225-234. https://doi.org/10.4995/agt.2022.15586OJS22523423

5SRNAdb: an information resource for 5S ribosomal RNAs

Ribosomal 5S RNA (5S rRNA) is the ubiquitous RNA component found in the large subunit of ribosomes in all known organisms. Due to its small size, abundance and evolutionary conservation 5S rRNA for many years now is used as a model molecule in studies on RNA structure, RNA–protein interactions and molecular phylogeny. 5SRNAdb (http://combio.pl/5srnadb/) is the first database that provides a high quality reference set of ribosomal 5S RNAs (5S rRNA) across three domains of life. Here, we give an overview of new developments in the database and associated web tools since 2002, including updates to database content, curation processes and user web interfaces

OGLE-2018-BLG-0532Lb: Cold Neptune With Possible Jovian Sibling

We report the discovery of the planet OGLE-2018-BLG-0532Lb, with very obvious signatures in the light curve that lead to an estimate of the planet-host mass ratio $q=M_{\rm planet}/M_{\rm host}\simeq 1\times10^{-4}$. Although there are no obvious systematic residuals to this double-lens/single-source (2L1S) fit, we find that $\chi^2$ can be significantly improved by adding either a third lens (3L1S, $\Delta\chi^2=81$) or second source (2L2S, $\Delta\chi^2=65$) to the lens-source geometry. After thorough investigation, we conclude that we cannot decisively distinguish between these two scenarios and therefore focus on the robustly-detected planet. However, given the possible presence of a second planet, we investigate to what degree and with what probability such additional planets may affect seemingly single-planet light curves. Our best estimates for the properties of the lens star and the secure planet are: a host mass $M\sim 0.25\,M_\odot$, system distance $D_L\sim 1\,$kpc and planet mass $m_{p,1}= 8\,M_\oplus$ with projected separation $a_{1,\perp}=1.4\,$au. However, there is a relatively bright $I=18.6$ (and also relatively blue) star projected within $<50\,$mas of the lens, and if future high-resolution images show that this is coincident with the lens, then it is possible that it is the lens, in which case, the lens would be both more massive and more distant than the best-estimated values above.Comment: 48 pages, 9 figures, 7 table

A Gas Giant Planet in the OGLE-2006-BLG-284L Stellar Binary System

We present the analysis of microlensing event OGLE-2006-BLG-284, which has a lens system that consists of two stars and a gas giant planet with a mass ratio of $q_p = (1.26\pm 0.19) \times 10^{-3}$ to the primary. The mass ratio of the two stars is $q_s = 0.289\pm 0.011$, and their projected separation is $s_s = 2.1\pm 0.7\,$AU, while the projected separation of the planet from the primary is $s_p = 2.2\pm 0.8\,$AU. For this lens system to have stable orbits, the three-dimensional separation of either the primary and secondary stars or the planet and primary star must be much larger than that these projected separations. Since we do not know which is the case, the system could include either a circumbinary or a circumstellar planet. Because there is no measurement of the microlensing parallax effect or lens system brightness, we can only make a rough Bayesian estimate of the lens system masses and brightness. We find host star and planet masses of $M_{L1} = 0.35^{+0.30}_{-0.20}\,M_\odot$, $M_{L2} = 0.10^{+0.09}_{-0.06}\,M_\odot$, and $m_p = 144^{+126}_{-82}\,M_\oplus$, and the $K$-band magnitude of the combined brightness of the host stars is $K_L = 19.7^{+0.7}_{-1.0}$. The separation between the lens and source system will be $\sim 90\,$mas in mid-2020, so it should be possible to detect the host system with follow-up adaptive optics or Hubble Space Telescope observations

OGLE-2019-BLG-0960 Lb: The Smallest Microlensing Planet

We report the analysis of OGLE-2019-BLG-0960, which contains the smallest mass-ratio microlensing planet found to date (q = 1.2-1.6 × 10-5 at 1s). Although there is substantial uncertainty in the satellite parallax measured by Spitzer, the measurement of the annual parallax effect combined with the finite source effect allows us to determine the mass of the host star (M L = 0.3-0.6 M o?), the mass of its planet (m p = 1.4-3.1 M ?), the projected separation between the host and planet (a ? = 1.2-2.3 au), and the distance to the lens system (D L = 0.6-1.2 kpc). The lens is plausibly the blend, which could be checked with adaptive optics observations. As the smallest planet clearly below the break in the mass-ratio function, it demonstrates that current experiments are powerful enough to robustly measure the slope of the mass-ratio function below that break. We find that the cross-section for detecting small planets is maximized for planets with separations just outside of the boundary for resonant caustics and that sensitivity to such planets can be maximized by intensively monitoring events whenever they are magnified by a factor A \u3e 5. Finally, an empirical investigation demonstrates that most planets showing a degeneracy between (s \u3e 1) and (s \u3c 1) solutions are not in the regime (log s| » 0) for which the close / wide degeneracy was derived. This investigation suggests that there is a link between the close / wide and inner/outer degeneracies and also that the symmetry in the lens equation goes much deeper than symmetries uncovered for the limiting cases