Related papers: Efficient equidistribution of periodic nilsequence…
We state a kind of Euclidian division theorem: given a polynomial P(x) and a divisor d of the degree of P, there exist polynomials h(x),Q(x),R(x) such that P(x) = h(Q(x)) +R(x), with deg h=d. Under some conditions h,Q,R are unique, and Q is…
Neville's algorithm is known to provide an efficient and numerically stable solution for polynomial interpolations. In this paper, an extension of this algorithm is presented which includes the derivatives of the interpolating polynomial.
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton…
It is shown that the solutions of certain systems of nonlinear \"Orst-order recursions with polynomial right-hand sides may be rather easily ascertained, and display interesting evolutions in their ticking time variable (taking integer…
The exact computation of the nearest-neighbor spacing distribution P(s) is performed for a rectangular billiard with point-like scatterer inside for periodic and Dirichlet boundary conditions and it is demonstrated that for large s this…
We apply to the $n\times n$ chessboard the counting theory from Part I for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen. Part I showed that the number of ways to place $q$ identical…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
We provide a monotone non increasing sequence of upper bounds $f^H_k$ ($k\ge 1$) converging to the global minimum of a polynomial $f$ on simple sets like the unit hypercube. The novelty with respect to the converging sequence of upper…
Let G be a semisimple Lie group without compact factor and $\Gamma$ < G a torsion-free, cocompact, irreducible lattice. According to Selberg, periodic orbits of regular Weyl chamber flows live on tori. We prove that these periodic tori…
Sorting algorithms have attracted a great deal of attention and study, as they have numerous applications to Mathematics, Computer Science and related fields. In this thesis, we first deal with the mathematical analysis of the Quicksort…
We prove a nonlinear regularity principle in sequence spaces which produces universal estimates for special series defined therein. Some consequences are obtained and, in particular, we establish new inclusion theorems for multiple summing…
In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…
We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
Fox, Gromov, Lafforgue, Naor, and Pach proved a regularity lemma for semi-algebraic $k$-uniform hypergraphs of bounded complexity, showing that for each $\epsilon>0$ the vertex set can be equitably partitioned into a bounded number of parts…
In this paper we propose some continuation theorems for the periodic problem \begin{equation*} \begin{cases} \, x_{i}' = g_{i}(t,x_{i+1}), &i=1,\ldots,n-1, \\ \, x_{n}' = h(t,x_{1},\ldots,x_{n}), \\ \, x_{i}(0)=x_{i}(T), &i=1,\ldots,n,…
In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…
A polygon is called rational if the angle between each pair of sides is a rational multiple of $\pi.$ The main theorem we will prove is Theorem 1: For rational polygons, periodic points of the billiard flow are dense in the phase space of…
We introduce an algorithm based on semidefinite programming that yields increasing (resp. decreasing) sequences of lower (resp. upper) bounds on polynomial stationary averages of diffusions with polynomial drift vector and diffusion…