For a suitable irreducible \textit{base} polynomial $f(x)\in \mathbf{Z}[x]$ of degree $k$, family polynomials $F_m(x)$ depending on $f(x)$ is constructed with the properties: (i) there exactly one factor $\Phi_{d,f}(x)$ for each divisor $d$ $m$; (ii) deg $(\Phi_{d,f}(x))=\varphi(d)\cdot\mathrm{deg} (f)$ generalizing factorization $x^m-1$ into cyclotomic polynomials; (iii) when base $f(x) ...

We present the discovery of two small planets transiting HD 93963A (TOI-1797), a G0\,V star (M$_*$=1.109\,$\pm$\,0.043\,M$_\odot$, R$_*$=1.043\,$\pm$\,0.009\,R$_\odot$) in visual binary system. combined TESS and CHEOPS space-borne photometry with data from MuSCAT 2, `Alopeke, PHARO, TRES, FIES, SOPHIE. validated spectroscopically confirmed outer planet 93963 Ac, sub-Neptune an orbital period P$...

ABSTRACT We examine the migration of luminous low-mass cores in laminar protoplanetary discs where accretion occurs mainly because disc winds and planet luminosity is generated by pebble accretion. Using 2D hydrodynamical simulations, we determine eccentricities induced thermal forces as a function gas rates, also evaluate importance torque exerted solid component relative to torque. For rate $...

Mature super-Earths and sub-Neptunes are predicted to be $\simeq$Jovian radius when younger than 10 Myr. Thus, we expect find 5-15$R_\oplus$ planets around young stars even if their older counterparts harbor none. We report the discovery validation of TOI 1227 b, a $0.85\pm0.05R_J$ (9.5$R_\oplus$) planet transiting very low-mass star ($0.170\pm0.015M_\odot$) every 27.4 days. TOI~1227's kinemati...

We report the discovery and validation of four extrasolar planets hosted by nearby, bright, Sun-like (G3V) star HD~108236 using data from Transiting Exoplanet Survey Satellite (TESS). present transit photometry, reconnaissance precise Doppler spectroscopy as well high-resolution imaging, to validate planetary nature objects transiting HD~108236, also known TESS Object Interest (TOI) 1233. The i...

We report the discovery of two exoplanets orbiting around HD 212729 (TOI\,1052, TIC 317060587), a $T_{\rm eff}=6146$K star with V=9.51 observed by TESS in Sectors 1 and 13. One exoplanet, TOI-1052b, is Neptune-mass transits star, an additional planet TOI-1052c radial velocities but not seen to transit. confirm planetary nature TOI-1052b using precise velocity observations from HARPS determined ...

We report the detection of a gas-giant planet in orbit around both stars an eclipsing binary star system that also contains smaller, inner transiting TOI-1338b. The new planet, called TOI-1338/BEBOP-1c, was discovered using radial-velocity data collected with HARPS and ESPRESSO spectrographs. Our analysis reveals it is $65.2~\rm{M_{\oplus}}$ circumbinary period $215.5~$days. This first observat...

In this paper, we study the root distributions of Ehrhart polynomials free sums certain reflexive polytopes. We investigate cases where roots $A_d^\vee$'s or $A_d$'s lie on canonical line $\mathrm{Re}(z)=-\frac{1}{2}$ complex plane $\mathbb{C}$, $A_d$ denotes polytope type A dimension $d$ and $A_d^\vee$ its polar dual. For example, it is proved that $A_m^\vee \oplus A_n^\vee$ with $\min\{m,n\} ...

As an all-sky survey, NASA's $TESS$ mission is able to detect the brightest and rarest types of transiting planetary systems, including young planets that enable study evolutionary processes occur within first billion years. Here, we report discovery a young, multi-planet system orbiting bright K4.5V star, TOI-712 ($V = 10.838$, $M_\star 0.733_{-0.025}^{+0.026} M_\odot$, $R_\star 0.674\pm0.016 ...

Positive MV-algebras are the subreducts of with respect to signature $\{\oplus, \odot, \lor, \land, 0, 1\}$. We provide a finite quasi-equational axiomatization for class such algebras.