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We show the existence of some infinite families of periodic solutions of the planar Newtonian n-body problem --with positive masses-- which are symmetric with respect to suitable actions of finite groups (under a strong--force assumption,…
In this work we deal with a following nonlinear Schrodinger equation in dimension greater or equal to 3, with a subcritical power-type nonlinearity and a positive potential satisfying a local condition. We prove the existence and…
We study the weighted elliptic equation \begin{equation} -div(|x|^{-2a}\nabla u)=|x|^{-bp}|u|^{p-2}u~~~\mbox{in}~\mathbb{R}^N ~~~~~~~~~~~~~~~~~~~~(0.1)\end{equation} with $N\geq 2$, which arises from the Caffarelli-Kohn-Nirenberg…
To establish a self-consistent effective one-body (EOB) theory that describes the dynamical evolution of binary systems based on the post-Minkowskian (PM) approximation, where the Hamiltonian, radiation reaction force, and waveforms are…
We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a…
We compute the moments of the nonlinear binary collision integral in the ultrarelativistic hard-sphere approximation for an arbitrary anisotropic distribution function in the local rest frame. This anisotropic distribution function has an…
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this…
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…
We calculate the real-space trajectory and spin precession of a generic spinning compact binary inspiral at any time instant using the dynamical renormalization group formalism. This method leads to closed-form analytic solutions to the…
Q-conditional symmetries (nonclassical symmetries) for the general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first…
The efficiency of an experimental design is ultimately measured in terms of time and resources needed for the experiment. Optimal sequential (multi-stage) design is studied in the situation where each stage involves a fixed cost. The…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
In a uniformly hyperbolic system, we consider the problem of finding the optimal infinitesimal perturbation to apply to the system, from a certain set $P$ of feasible ones, to maximally increase the expectation of a given observation…
In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how…
We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on…
We consider the problem of optimizing a multivariate quadratic function where each decision variable is constrained to be a complex $m$'th root of unity. Such problems have applications in signal processing, MIMO detection, and the…
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very strong damping and quasi-periodic external forcing. We study…
The recent multiple-solution problem in extracting physics information from a fit to the experimental data in high energy physics is reviewed in a mathematical viewpoint. All these multiple solutions were found via a fit process previously,…
By introducing simple topological constraints and applying a binary decomposition method, we show the existence of a set of prograde double-double orbits for any rotation angle $\theta \in (0, \pi/7]$ in the equal-mass four-body problem. A…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…