Related papers: Mean value estimates for Weyl sums in two dimensio…
In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
We apply a symbolic approach of the general quadratic decomposition of polynomial sequences - presented in a previous article referenced herein - to polynomial sequences fulfilling specific orthogonal conditions towards two given…
We use ideas from our previous work to obtain some theorems that will allow us to obtain the integer solution of a quadratic polynomial in two variables that represents a natural number
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
An asymptotic formula for the number of prime solutions of a general diagonal system of Diophantine equations is established, contingent on the existence of an appropriate mean value bound and on local solvability. In conjunction with the…
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
In this note, an upper bound for the sum of fractional parts of certain smooth functions is established. Such sums arise naturally in numerous problems of analytic number theory. The main feature is here an improvement of the main term due…
We obtain pointwise estimates for solutions of semilinear parabolic equations with a potential on connected domains both of $\mathbb R^n$ and of general Riemannian manifolds.
We present a numerical scheme for immiscible two-phase flows with one compressible and one incompressible phase. Special emphasis lies in the discussion of the coupling strategy for compressible and incompressible Euler equations to…
We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
We study radially symmetric solutions to the 2D Vlasov-Maxwell system and construct solutions that initially possess arbitrarily small $C^k$ norms ($k \geq 1$) for the charge densities and the electric fields, but attain arbitrarily large…
We obtain new estimates - both upper and lower bounds - on the mean values of the Weyl sums over a small box inside of the unit torus. In particular, we refine recent conjectures of C. Demeter and B. Langowski (2022), and improve some of…
We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present methods to compute the…
We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in 22 or more variables. Our methods involve the estimation of a certain entangled two-dimensional 21st moment of quartic smooth Weyl sums via a novel…
We present a variationally separable splitting technique for the generalized-$\alpha$ method for solving parabolic partial differential equations. We develop a technique for a tensor-product mesh which results in a solver with a linear cost…
We investigate the problem of numerical differentiation of bivariate functions from weighted Wiener classes using Chebyshev polynomial expansions. We develop and analyze a new version of the truncation method based on Chebyshev polynomials…
We present the applications of variational--wavelet approach for computing multiresolution/multiscale representation for solution of some approximations of Vlasov-Maxwell equations.
In this paper, we focus on the strong subconvexity bounds for triple product L-functions in the cubic level aspect. Our proof on the Weyl-type bound synthesizes techniques from classical analytic number theory with methods in automorphic…