We present an intensive effort to refine the mass and orbit of enveloped terrestrial planet GJ 1214 b using 165 radial velocity (RV) measurements taken with HARPS spectrograph over a period ten years. conduct joint analysis RVs archival Spitzer/IRAC transits measure planetary radius $8.17\pm 0.43 M_{\oplus}$ $2.742^{+0.050}_{-0.053} R_{\oplus}$. Assuming is Earth-like core surrounded by H/He en...

We show that the moduli space of $$U\oplus \langle -2k \rangle $$ -polarized K3 surfaces is unirational for $$k \le 50$$ and \notin \{11,35,42,48\}$$ , other several values k up to $$k=97$$ . Our proof based on a systematic study projective models elliptic in $${\mathbb {P}}^n$$ $$3\le n 5$$ containing either union two smooth rational curves or curve an intersecting at one point.

For $n\geq 1$, let $C_n$ denote a cyclic group of order $n$. Let $G=C_n\oplus C_{mn}$ with 2$ and $m\geq $k\in [0,n-1]$. It is known that any sequence $mn+n-1+k$ terms from $G$ must contain nontrivial zero-sum length at most $mn+n-1-k$. The associated inverse question to characterize those sequences maximal $mn+n-2+k$ fail subsequence $k\leq this the for Davenport Constant. $k=n-1$, $\eta(G)$ i...

We detect Lyman $\alpha$ absorption from the escaping atmosphere of HD 63433c, a $R=2.67 R_\oplus$, $P=20.5$ d mini Neptune orbiting young (440 Myr) solar analogue in Ursa Major Moving Group. Using HST/STIS, we measure transit depth $11.1 \pm 1.5$% blue wing and $8 3$% red. This signal is unlikely to be due stellar variability, but should confirmed by an upcoming second visit with HST. do not i...

We present a reanalysis of the K2-106 transiting planetary system, with focus on composition K2-106b, an ultra-short period, super-Mercury candidate. globally model existing photometric and radial velocity data derive mass radius for K2-106b $M_{p} = 8.53\pm1.02~M_{\oplus}$ $R_{p} 1.71^{+0.069}_{-0.057}~R_{\oplus}$, which leads to density $\rho_{p} 9.4^{+1.6}_{-1.5}$ $\rm g~cm^{-3}$, significan...

We present the results of a uniform search for additional planets around all stars with confirmed hot Jupiters observed by Transiting Exoplanet Survey Satellite (TESS) in its Cycle 1 survey southern ecliptic hemisphere. Our comprises 184 total planetary systems $R_{p}$ > 8$R_\oplus$ and orbital period < 10 days. The Transit Least Squares (TLS) algorithm was utilized to periodic signals that may...

After giving an overview of the existing theory regarding periods sequences defined by linear recurrences over finite fields, we give explicit descriptions sets that arise if one considers all $\mathbb{F}_q$ generated for a fixed choice degree $k$ in range $1 \leq k 4$. We also investigate rings form $\mathbb{F}_{q_1} \oplus \ldots \mathbb{F}_{q_r}$.

The James Webb Space Telescope (JWST) will be able to probe the atmospheres and surface properties of hot, terrestrial planets via emission spectroscopy. We identify 18 potentially planet candidates detected by Transiting Exoplanet Survey Satellite (TESS) that would make ideal targets for these observations. These cover a broad range radii ($R_{\rm p} \sim 0.6 - 2.0 R_\oplus$) orbit stars vario...

The light curve of the microlensing event KMT-2021-BLG-0912 exhibits a very short anomaly relative to single-lens single-source form. We investigate for purpose identifying origin anomaly. model under various interpretations. From this, we find four solutions, in which three solutions are found assumption that lens is composed two masses (2L1S models), and other solution source comprised binary...