(Abridged) Surveys of protoplanetary disks in nearby star-forming regions (SFRs) have provided important information on their demographics, but due to sample sizes, they cannot be used study how disk properties vary with the environment. We conduct a survey unresolved millimeter continuum emission 873 identified by Spitzer L1641 and L1647 Orion A cloud. This is largest such yet, allowing us ide...

Exoplanet systems with multiple transiting planets are natural laboratories for testing planetary astrophysics. One such system is HD 191939 (TOI-1339), a bright (V=9) and Sun-like (G9V) star, which TESS found to host three (b, c, d). The have periods of 9, 29, 38 days each similar sizes from 3 3.4 $R_{\oplus}$. To further characterize the system, we measured radial velocity (RV) over 415 Keck/...

A nonsingular rational curve $C$ in a complex manifold $X$ whose normal bundle is isomorphic to $\mathcal{O}_{\mathbb{P}^1}(1)^{\oplus p} \oplus \mathcal{O}_{\mathbb{P}^1}^{\oplus q}$ for some nonnegative integers $p$ and $q$ called an unbendable on $X$. Associated with it the variety of minimal tangents (VMRT) at point $x \in C$, which germ submanifolds $\mathcal{C}^C_{x} \subset \mathbb{P} T_...

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...

Let $F_0$ be an absolutely algebraic field of characteristic $p>0$ and $\kappa$ infinite cardinal. It is shown that there exists a $F$ such $F^*\cong F^*_0\oplus(\oplus_\kappa \mathbb{Q})$ with $Br(F)=\{0\}$. $L$ closure $F$. Then for any finite subextension $K$ $L/F$, we have $K^*\cong T(K^*)\oplus(\oplus_\kappa \mathbb{Q})$, where $T(K^*)$ the group torsion elements $K^*$. In addition,...

We describe a compactification by KSBA stable pairs of the five-dimensional moduli space K3 surfaces with purely non-symplectic automorphism order four and $U(2)\oplus D_4^{\oplus 2}$ lattice polarization. These can be realized as minimal resolution double cover $\mathbb {P}^{1}\times \mathbb {P}^{1}$ branched along specific $(4,\,4)$ curve. show that, up to finite group action, this is isomorp...