相关论文: A lower bound of the distance between two elliptic…

We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in (Gronchi et al 2015), which uses a…

We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and…

In this paper we prove that an isometry between orbit spaces of two proper isometric actions is smooth if it preserves the codimension of the orbits or if the orbit spaces have no boundary. In other words, we generalize Myers-Steenrod's…

It is often stated in the physics literature that maximally-spinning Kerr black-hole spacetimes are characterized by near-horizon co-rotating circular geodesics of radius $r_{\text{circular}}$ with the property $r_{\text{circular}}\to…

We prove several new results concerning action minimizing periodic orbits of Tonelli Lagrangian systems on an oriented closed surface $M$. More specifically, we show that for every energy larger than the maximal energy of a constant orbit…

We study the secular effects in the motion of an asteroid with negligible mass in a spatial restricted elliptic three body problem with arbitrary inclination. Averaging over mean anomalies of the asteroid and the planet are applied to…

We establish boundary regularity estimates for elliptic systems in divergence form with VMO coefficients. Additionally, we obtain nondegeneracy estimates of the Hopf-Oleinik type lemma for elliptic equations. In both cases, the moduli of…

We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence type elliptic operators. The construction is applied in two settings. First, we show…

Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…

We have developed an exact, general method to compute Casimir interactions between a finite number of compact objects of arbitrary shape and separation. Here, we present details of the method for a scalar field to illustrate our approach in…

Many Kepler multiplanet systems have planet pairs near low-order, mean-motion resonances. In addition, many Kepler multiplanet systems have planets with orbital periods less than a few days. With the exception of Kepler-42, however, there…

The equations of motion of two point masses have recently been derived at the 3PN approximation of general relativity. From that work we determine the location of the innermost circular orbit or ICO, defined by the minimum of the binary's…

Co-orbital planets have not yet been discovered, although they constitute a frequent by-product of planetary formation and evolution models. This lack may be due to observational biases, since the main detection methods are unable to spot…

We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the case of half-spaces we obtain the sharp constant while for a…

When an asteroid has a few observations over a short time span the information contained in the observational arc could be so little that a full orbit determination may be not possible. One of the methods developed in recent years to…

A few studies have reported a significant dearth of exoplanets with Neptune mass and radius with orbital periods below $2$--$4$ d. This cannot be explained by observational biases because many Neptunian planets with longer orbital periods…

We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard's corner point. We prove that smooth…

We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide uniform resolvent estimates for the realizations of these…

We present \texttt{ethraid}, an open source Python package designed to measure the mass ($m_c$) and separation ($a$) of a bound companion from measurements covering a fraction of the orbital period. \texttt{ethraid} constrains $m_c$ and $a$…

A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann--Tzeng (HT) bound is formulated…