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Choose a polynomial in three variables with not more than three or four monomials of moderate degree. Take simple coefficients as 1 and -1. Then draw a picture of the solution variety in real three space using a ray-tracing program like…
The problem of determination of the orbital velocity of an astrometric satellite from its own observational data is studied. It is well known that data processing of microarcsecond-level astrometric observations imposes very stringent…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by PDEs. The goal is to find a placement of sensors, at which experimental data are collected, so as to minimize the uncertainty in…
Questions of `how best to acquire data' are essential to modeling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates…
Here we show how to determine the orbital parameters of a system composed of a star and N companions (that can be planets, brown-dwarfs or other stars), using a simple Fourier analysis of the radial velocity data of the star. This method…
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…
We present a new extensive analysis of the old problem of finding a satisfactory calibration of the relation between the geometric albedo and some measurable polarization properties of the asteroids. To achieve our goals, we use all…
Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the G\"odel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described…
Oriented object detection has been developed rapidly in the past few years, where rotation equivariance is crucial for detectors to predict rotated boxes. It is expected that the prediction can maintain the corresponding rotation when…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
ASTROD I is the first planned space mission in a series of ASTROD missions for testing relativity in space using optical devices. The main aims are: (i) to test General Relativity with an improvement of three orders of magnitude compared to…
The exact solution of the two-dimensional (2D) Ising model at an external magnetic field is derived by a modified Clifford algebraic approach. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic…
We propose new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary conditions. In our approach, the projection boundary conditions near the cycle are…
We discuss the interpretation of the angles in the Geodesic Light-Cone (GLC) coordinates. In particular, we clarify the way in which these angles can be identified with the observed ones. We show that, although this identification is always…
When 3D relative displacement $\mathbf{r}$ and velocity $\mathbf{v}$ between the pair in a gravitationally-bound system are precisely measured, the six measured quantities at one phase can allow elliptical orbit solutions at a given…
We present a novel approach to the detection and 3D pose estimation of objects in color images. Its main contribution is that it does not require any training phases nor data for new objects, while state-of-the-art methods typically require…
We propose an unsupervised vision-based system to estimate the joint configurations of the robot arm from a sequence of RGB or RGB-D images without knowing the model a priori, and then adapt it to the task of category-independent…
Interference detection of arbitrary geometric objects is not a trivial task due to the heavy computational load imposed by implementation issues. The hierarchically structured bounding boxes help us to quickly isolate the contour of…