The population of planets smaller than approximately 1.7 Earth radii (R⊕) is widely interpreted as consisting rocky worlds, generally referred to super-Earths. This picture largely corroborated by radial velocity mass measurements for close-in super-Earths but lacks constraints at lower insolations. Here we present the results a detailed study Kepler-138 system using 13 Hubble and Spitzer trans...

Abstract Kepler-33 hosts five validated transiting planets ranging in period from 5 to 41 days. The are nearly coplanar orbits and exhibit remarkably similar (appropriately scaled) transit durations indicative of impact parameters. outer three have a radius 3.5 ≲ R p / ⊕ 4.7 closely packed dynamically, thus timing variations can be observed. Photodynamical analysis provide 2 σ upper bounds on t...

Let $${{\mathcal {S}}}\subseteq {{\mathbb {Z}}}^m \oplus T$$ be a finitely generated and reduced monoid. In this paper we develop general strategy to study the set of elements in $${\mathcal {S}}$$ having at least two factorizations same length, namely ideal {L}}_{{\mathcal {S}}}$$ . To end, work with certain (lattice) associated monoid Our can seen as new approach generalizing [9], which only ...

It has been suggested that planetary radii increase with the stellar mass, for planets below 6 R$_{\oplus}$ and host 1 M$_\odot$. In this study, we explore whether inferred relation between size star's mass can be explained by a larger among orbiting more massive stars, inflation of radius due to difference in irradiation, or different compositions structures. Using exoplanetary data measured m...

Abstract Williamson’s theorem states that for any $2n \times 2n$ real positive definite matrix A , there exists a symplectic S such $S^TAS=D \oplus D$ where D is an $n\times n$ diagonal with entries known as the eigenvalues of . Let H be symmetric perturbed $A+H$ also definite. In this paper, we show $\tilde {S}$ diagonalizing in form {S}=S Q+\mathcal {O}(\|H\|)$ Q well orthogonal matrix. Moreo...

a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...

We presented a systematic treatment of Hilbert criterion for stability theory an action real reductive group G on submanifold X Kähler manifold Z. More precisely, we suppose that the compact Lie U with algebra $${\mathfrak {u}}$$ extends holomorphically to complexified $$U^\mathbb {C}$$ and U-action Z is Hamiltonian. If $$G\subset U^\mathbb compatible, there corresponding gradient map $$\mu _{\...

We propose a systematic procedure to construct polynomial algebras from intermediate Casimir invariants arising (semisimple or non-semisimple) Lie $\mathfrak{g}$. In this approach, we deal with explicit polynomials in the enveloping algebra of $\mathfrak{g} \oplus \mathfrak{g} \mathfrak{g}$. present examples show how these can display different behaviours and lead Abelian algebras, quadratic mo...

The geodesic orbit property is useful and interesting in Riemannian geometry. It implies homogeneity has important classes of manifolds as special cases. Those include weakly symmetric naturally reductive manifolds. corresponding results for indefinite metric are much more delicate than signature, but the last few years structural were proved Lorentz Here, we carry out a major step analysis nil...

Given a noncommutative partial resolution $A=\mathrm{End}_R(R\oplus M)$ of Gorenstein singularity $R$, we show that the relative category $\Delta_R(A)$ Kalck-Yang is controlled by certain connective dga $A/^{\mathbb{L}}\kern -2pt AeA$, derived quotient Braun-Chuang-Lazarev. We think AeA$ as kind `derived exceptional locus' $A$, it can be thought universal fitting into suitable recollement. This...