We present the discovery of a new Jovian-sized planet, TOI-3757 b, lowest density planet orbiting an M dwarf (M0V). It orbits solar-metallicity discovered using TESS photometry and confirmed with precise radial velocities (RV) from HPF NEID. With planetary radius $12.0^{+0.4}_{-0.5}$ $R_{\oplus}$ mass $85.3^{+8.8}_{-8.7}$ $M_{\oplus}$, not only does this object add to small sample gas giants ($...

We show that compactifications of the heterotic string on a circle exhibit at boundary moduli space ($R\to 0$, or equivalently decompactification limit $R \to \infty$) tower winding momentum modes enhance $E_8 \times E_8$ $SO(32)$ gauge symmetry to affine algebras $(E_9 \oplus E_9)/\sim$ (the identification means two copies $E_9$ share same central extension) and $\hat{D}_{16}$, respectively. a...

Abstract For X a smooth projective variety and $D=D_1+\dotsb +D_n$ simple normal crossing divisor, we establish precise cycle-level correspondence between the genus $0$ local Gromov–Witten theory of bundle $\oplus _{i=1}^n \mathcal {O}_X(-D_i)$ maximal contact multiroot stack $X_{D,\vec r}$ . The proof is an implementation rank-reduction strategy. We use this point view to clarify relationship ...

Given a vector bundle $A\to M$ we study the geometry of graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these objects to classical such as higher Courant algebroids on $A\oplus\bigwedge^{k-1}A^*$ Dirac structures therein, semi-direct products Lie algebroid $A$ with coadjoint representations up homot...

One of the generalizations supplemented modules is Goldie*-supplemented module, defined by Birkenmeier et al. using $\beta^{\ast}$ relation. In this work, we deal with concept cofinitely as a version module. A left $R$-module $M$ called module if there supplement submodule $S$ $C\beta^{\ast}S$, for each cofinite $C$ $M$. Evidently, are Goldie*-supplemented. Further, Goldie*-supplemented, then $...

We study the structure of a $3-$Leibniz algebra $T$ graded by an arbitrary abelian group $G,$ which is considered dimension and over base field $\bbbf.$ show that form $T=\uu\oplus\sum_jI_j,$ with $\uu$ linear subspace $T_1,$ homogeneous component associated to unit element $1$ in any $I_j$ well described ideal $T,$ satisfying $$ [I_j, T, I_k] = I_k, T] [T, I_j, 0, if $j\neq k.$ In case being m...

Abstract For a closed, connected direct product Riemannian manifold $$(M, g)=(M_1, g_1) \times \cdots (M_l, g_l)$$ ( M , g ) = 1 × ⋯ <mml:mi...

For which values of $n$ is it possible to color the positive integers using precisely colors in such a way that for any $a$, numbers $a,2a,\dots,na$ all receive different colors? The third-named author posed question around 2008-2009. Particular cases appeared Hungarian high school journal KöMaL April 2010, and general version May 2010 on MathOverflow, posted by D. Pálvölgyi. remains open. We d...

Symmetry fractionalization (SF) on topological excitations is one of the most remarkable quantum phenomena in orders with symmetry, i.e., symmetry-enriched phases. While much progress has been theoretically and experimentally made 2D, understanding SF 3D far from complete. A long-standing challenge to understand looplike which are spatially extended objects. In this work, we construct a powerfu...

We present \textit{ALMA} 1.3 mm and 0.86 observations of the nearby (17.34 pc) F9V star q1 Eri (HD 10647, HR 506). This system, with age ${\sim}1.4$ Gyr, hosts a ${\sim}2$ au radial velocity planet debris disc highest fractional luminosity closest 300 FGK type stars. The images, resolution ${\sim}0.5''$, reveal broad (34{-}134 au) belt millimeter emission inclined by $76.7{\pm}1.0$ degrees maxi...