Related papers: Distribution of points with prescribed derivative …

We are interested in comparing probability distributions defined on Riemannian manifold. The traditional approach to study a distribution relies on locating its mean point and finding the dispersion about that point. On a general manifold…

We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…

Let p_N be a random degree N polynomial in one complex variable whose zeros are chosen independently from a fixed probability measure mu on the Riemann sphere S^2. This article proves that if we condition p_N to have a zero at some fixed…

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…

In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of…

We consider diffusion type equations with a distributed order derivative in the time variable. This derivative is defined as the integral in $\alpha$ of the Caputo-Dzhrbashian fractional derivative of order $\alpha \in (0,1)$ with a certain…

Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…

Let $\mathbf{f} = \left(f_1, \dots, f_p\right) $ be a polynomial tuple in $\mathbb{Q}[z_1, \dots, z_n]$ and let $d = \max_{1 \leq i \leq p} \deg f_i$. We consider the problem of computing the set of asymptotic critical values of the…

In this paper, we obtain new results on the critical points of a polynomial. We discuss the Sendov conjecture for polynomials of degree nine.

We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive values for the goods. The prior distributions on those…

Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the…

Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…

We investigate the variation in the total number of points in a random $p\times p$ square in $\mathbb{Z}^2$ where the $p$-adic valuation of a given polynomial in two variables is precisely $1$. We establish that this quantity follows a…

Given any postsingularly finite exponential function $p_\lambda(z) = \lambda \exp(z)$ where $\lambda \in \C^*$, we construct a sequence of postcritically finite unicritical polynomials $p_{d,\lambda_d}(z) = \lambda_d(1+\frac{z}{d})^d$ that…

Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…

Given a number field $K$ and a polynomial $f(z) \in K[z]$, one can naturally construct a finite directed graph $G(f,K)$ whose vertices are the $K$-rational preperiodic points of $f$, with an edge $\alpha \to \beta$ if and only if $f(\alpha)…

In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…

This study is motivated by a series of recent papers that show that, if a given deterministic sequence in the unit interval has a Poisson pair correlation function, then the sequence is uniformly distributed. Analogous results have been…

How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points,…

We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the…