TOI-561 is a galactic thick disk star hosting an ultra-short period (0.45 day orbit) planet with radius of 1.37 R$_{\oplus}$, making it one the most metal-poor ([Fe/H] = -0.41) and oldest ($\sim$10 Gyr) sites where Earth-sized has been found. We present new simultaneous radial velocity measurements (RVs) from Gemini-N/MAROON-X Keck/HIRES, which we combined literature RVs to derive mass M$_{b}$=...

AU Mic is a young, active star whose transiting planet was recently detected. We report our analysis of its TESS data, where we modeled the BY Draconis type quasi-periodic rotational modulation by starspots simultaneously to flaring activity and planetary transits. measured flare occurrence rate 6.35 flares per day for with amplitudes in range $0.06\% < f_{\rm max} 1.5\%$ flux. employed Bayesia...

We present updated radial-velocity (RV) analyses of the AU Mic system. is a young (22 Myr) early M dwarf known to host two transiting planets - $P_{b}\sim8.46$ days, $R_{b}=4.38_{-0.18}^{+0.18}\ R_{\oplus}$, $P_{c}\sim18.86$ $R_{c}=3.51_{-0.16}^{+0.16}\ R_{\oplus}$. With visible RVs from CARMENES-VIS, CHIRON, HARPS, HIRES, {\sc {\textsc{Minerva}}}-Australis, and TRES, as well near-infrared (NIR...

Given two coprime numbers $$q_1$$ and $$q_2$$ , let $$\Gamma =q_1\mathbb {Z}\oplus q_2 \mathbb {Z} $$ . Let $$\Delta +X$$ be the discrete periodic Schrödinger operator on $$\mathbb {Z}^2$$ where is Laplacian $$X:\mathbb {Z}^2\rightarrow {C}$$ -periodic. In this paper, we develop tools from complex analysis to study isospectrality of operators. We prove that if -periodic potentials X Y are Fermi...

Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. Then ${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$ becomes a module extension Banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on ${mathcal{S...

In this paper, ‎The powers of fuzzy neutrosophic soft square matrices (FNSSMs) under the operations $oplus(=max)$ and $otimes(=min)$ are studied‎. ‎We show that the powers of a given FNSM stabilize if and only if its orbits stabilize for each starting fuzzy neutrosophic soft vector (FNSV) and prove a necessary and sufficient condition for this property using the associated graphs of the FNSM‎. ...

We study complex algebraic K3 surfaces with finite automorphism groups and polarized by rank-fourteen, 2-elementary lattices. Three such lattices exist, namely $H \oplus E_8(-1) A_1(-1)^{\oplus 4}$, D_4(-1)$, D_8(-1) D_4(-1)$. As part of our study, we provide birational models for these as quartic projective hypersurfaces describe the associated coarse moduli spaces in terms suitable modular in...

Let $G$ be a finite abelian group. The Davenport constant $\mathsf{D}(G)$ is the maximal length of minimal zero-sum sequences over $G$. For groups form $C_2^{r-1} \oplus C_{2k}$ known for $r\leq 5$. In this paper, we get precise value $\mathsf{D}(C_2^{5} C_{2k})$ $k\geq 149$. It also worth pointing out that our result can imply $\mathsf{D}(C_2^{4} C_{2k})$.

Eight-dimensional non-geometric heterotic strings with gauge algebra $\mathfrak{e}_8\mathfrak{e}_7$ were constructed by Malmendier and Morrison as duals of F-theory on K3 surfaces $\Lambda^{1,1}\oplus E_8\oplus E_7$ lattice polarization. Clingher, Shaska extended these constructions to eight-dimensional $\mathfrak{e}_7\mathfrak{e}_7$ E_7\oplus polarized surfaces. In this study, we analyze the p...

We report on the discovery of an Earth-sized transiting planet ($R_p=1.015\pm0.051\,R_\oplus$) in a $P=4.02$ day orbit around K2-415 (EPIC 211414619), M5V star at 22 pc. The candidate was first identified by analyzing light curve data K2 mission, and is here shown to exist most recent from TESS. Combining curves with secured our follow-up observations including high-resolution imaging near infr...