Related papers: Almost Prime Coordinates for Anisotropic and Thin …
In this paper we use the new regularity and stability estimates for Alexandrov solutions to Monge-Ampere equations estabilished by G.De Philippis and A.Figalli to provide a global in time existence of distributional solutions to a…
First, we analyze the discrete Monge--Kantorovich problem, linking it with the minimization problem of linear functionals over adjoint orbits. Second, we consider its generalization to the setting of area preserving diffeomorphisms of the…
We study algebraic points of bounded degree on polarized projective varieties. To do so, we refine further the filtration construction and Subspace Theorem approach, for the study of integral points, which has origins in the work of…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
We start by reviewing our previous work on retrograde orbital configurations and on modeling and identifying retrograde resonances. Then, we present new results regarding the enhanced stability of retrograde configurations with respect to…
In this paper, we establish a sharp Onofri trace inequality on the upper half space $\overline{\mathbb R_+^n} (n\geq 2)$ by considering the limiting case of Sobolev trace inequality and classify its extremal functions on a suitable weighted…
The multistochastic $ (n,k)$-Monge--Kantorovich problem on a product space $\prod_{i=1}^n X_i$ is an extension of the classical Monge--Kantorovich problem. This problem is considered on the space of measures with fixed projections onto…
Quadratic regularization has emerged as a potential alternative to the popular entropic regularization in computational optimal transport, offering the theoretical advantage of producing sparse couplings through its hinge density structure.…
A solution to an equilibrium of irrotational binary polytropic stars in Newtonian gravity is expanded in a power of \epsilon=a_0/R, where R and a_0 are the separation of the binary system and the radius of each star for R=\infty. For the…
For positive integers $p$ and $q$ let $G:=\textrm{PSO}(p,q)$ be the projective indefinite special-orthogonal group of signature $(p,q)$. We study counting problems in the Riemannian symmetric space $X_G$ of $G$ and in the pseudo-Riemannian…
We consider the exceptional set in the binary Goldbach problem for sums of two almost twin primes. Our main result is a power-saving bound for the exceptional set in the problem of representing $m=p_1+p_2$ where $p_1+2$ has at most $2$…
These lectures contain a theoretical introduction to the few-body problem with short-range resonant binary interactions. In the first part we discuss the effective range expansion for the two-body scattering amplitude emphasizing the role…
This paper statistically describes the orbital distribution laws of Jupiter's irregular moons, most of which are members of the Ananke, Carme and Pasiphae groups. By comparing 19 known continuous distributions, it is verified that suitable…
In this work we consider a Fisher-Kolmogorov equation depending on two exponential functions of the spatial variables. We study this equation from the point of view of symmetry reductions in partial differential equations. Through…
We study almost prime solutions of systems of Diophantine equations in the Birch setting. Previous work shows that there exist integer solutions of size B with each component having no prime divisors below $B^{1/u}$, where $u=c_0n^{3/2}$,…
We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our…
A new general Hormander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multi- pliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are…
This paper is devoted to spherical measures and point configurations optimizing three-point energies. Our main goal is to extend the classic optimization problems based on pairs of distances between points to the context of three-point…
We solve some famous conjectures on the distribution of primes. These conjectures are to be listed as Legendre's, Andrica's, Oppermann's, Brocard's, Cram\'{e}r's, Shanks', and five Smarandache's conjectures. We make use of both…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…