Related papers: Hill's Lunar Equations, Series, Convergence, Motio…
Consider a discrete uniformly elliptic divergence form equation on the $d$ dimensional lattice $\Z^d$ with random coefficients. In [3] rate of convergence results in homogenization and estimates on the difference between the averaged…
We determine the rotation curve (RC) of the Milky Way in the range 6 < R < 18 kpc using a sample of 903 carefully selected classical Cepheids with precise proper motions and high-quality radial velocities from \emph{Gaia} DR3. Their…
Using comoving distance $d_c$ and angular diameter distance $d_A$, we recalculate parameters describing kinematical state of the universe, still combining the kinematical model of universe but not relying on dynamical equations for gravity.…
We introduce the flattening equation, which relates the shape of the dark halo to the angular velocity dispersions and the density of a tracer population of stars. It assumes spherical alignment of the velocity dispersion tensor, as seen in…
We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the weak solutions in domains satisfying the so-called…
We investigate aspects of computing the perihelion distances and impact parameters for near stars to the Sun, and, we analyze the solar motion. Keywords: perihelion distance, impact parameter, Oort cloud, solar motion
We study the asymptotic limit of the Cahn-Hilliard equation on an evolving surface with prescribed velocity. The method of formally matched asymptotic expansions is extended to account for the movement of the domain. We consider various…
We study black-hole binaries in the intermediate-mass-ratio regime 0.01 < q < 0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the…
We show that the rate of convergence of solutions of finite-difference approximations for uniformly elliptic Bellman's equations is of order at least $h^{2/3}$, where $h$ is the mesh size. The equations are considered in smooth bounded…
Analysis of PG quasar observations suggests a nonlinear relation between the black hole mass, M_BH, and the bulge mass, M_bulge, although a linear relation, as proposed for nearby galaxies, cannot be ruled out. New M_BH values for nearby…
The very latest observation of $M87$ supermassive black hole (BH) by the Event Horizon Telescope (EHT) provides the accretion onto BHs is an interesting study in the theory of gravity. We study the geodesics structure and accretion near a…
The RR Lyrae distance scale is reviewed. In particular, we discuss theoretical and empirical methods currently adopted in the literature. Moreover, we also outline pros and cons of optical and near-infrared mean magnitudes to overcome some…
A recent study conducted using CALIFA survey data (Lee et al, 2019b) has found that the orbital motions of neighbor galaxies are coherent with the spin direction of a target galaxy on scales of many Megaparsecs. We study this so called…
We study a class of elliptic problems, involving a $k$-Hessian and a very fast-growing nonlinearity, on a unit ball. We prove the existence of a radial singular solution and obtain its exact asymptotic behavior in a neighborhood of the…
Understanding the dynamical evolution of asteroids through the secular Yarkovsky effect requires the determination of many physical properties, including the rotation period. We propose a method aimed at obtaining a robust determination of…
Processing the data of lunar laser ranging (LLR), whose accuracy now reaches a few millimeters, points to the effect of anomalous increase in the lunar semimajor axis (with an excessive rate 1.3 cm/yr), which cannot be attributed to the…
The orbital displacement of the Moon is known to a precision on the order of centimeters from the lunar laser ranging data, while the lunar profile's confidence level is still only about 200 m. The lunar motion is used to measure the solar…
This work reexamines the dynamics of the 5:2 mean motion resonance with Jupiter located in the Outer Belt at $a\sim 2.82$ AU. First, we compute dynamical maps revealing the precise structure of chaos inside the resonance. Being interested…
We demonstrate a new approach to the computation of ratios of elliptic integrals. It turns out that almost closed polygons interscribed between two conics retain some of the properties of such closed polygons. We apply these retained…
We compute the spectrum of linearized gravitational excitations of black holes with substantial angular momentum in the presence of higher-derivative corrections to general relativity. We do so perturbatively to leading order in the…