相关论文: Exponential polynomials with Fatou and non-escapin…

For a finite positive Borel measure $\mu$ on $\mathbb R$ its exponential type, $T_\mu$, is defined as the infimum of $a>0$ such that finite linear combinations of complex exponentials with frequencies between 0 and $a$ are dense in…

A recently-established necessary condition for polynomials that preserve the class of entrywise nonnegative matrices of a fixed order is shown to be necessary and sufficient for the class of nonnegative monomial matrices. Along the way, we…

We study when Fourier transforms of Gibbs measures of sufficiently nonlinear expanding Markov maps decay at infinity at a polynomial rate. Assuming finite Lyapunov exponent, we reduce this to a nonlinearity assumption, which we verify for…

We determine necessary and sufficient conditions for unicritical polynomials to be dynamically irreducible over finite fields. This result extends the results of Boston-Jones and Hamblen-Jones-Madhu regarding the dynamical irreducibility of…

We continue our study of the Widom factors for $L_p(\mu)$ extremal polynomials initiated in [4]. In this work we characterize sets for which the lower bounds obtained in [4] are saturated, establish continuity of the Widom factors with…

We prove theorems of the following form: if $A\subseteq {\mathbb R}^2$ is a big set, then there exists a big set $P\subseteq {\mathbb R}$ and a perfect set $Q\subseteq {\mathbb R}$ such that $P\times Q\subseteq A$. We discuss cases where…

It is known that if a subset of $\mathbb{R}$ has positive Lebesgue measure, then it contains arbitrarily long finite arithmetic progressions. We prove that this result does not extend to infinite arithmetic progressions in the following…

Let $f(T)$ be a monic polynomial of degree $d$ with coefficients in a finite field $\mathbb{F}_q$. Extending earlier results in the literature, but now allowing $(q,2d)>1$, we give a criterion for $f$ to satisfy the following property: for…

Exponential sums with monomials are highly related to many interesting problems in number theory and well studied by many literatures. In this paper, we consider the exponential sums with polynomials and prove a new upper bound. As an…

We say the sets of nonnegative integers A and B are additive complements if their sum contains all sufficiently large integers. In this paper we prove a conjecture of Chen and Fang about additive complement of a finite set.

We address some questions concerning indecomposable polynomials and their behaviour under specialization. For instance we give a bound on a prime $p$ for the reduction modulo $p$ of an indecomposable polynomial $P(x)\in \Zz[x]$ to remain…

In \cite{Ch91a} it was shown that the billiard ball map for the periodic Lorentz gas has infinite topological entropy. In this article we study the set of points with infinite Lyapunov exponents. Using the cell structure developed in…

Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving denseness results in Lebesgue spaces, when inputs and outputs…

We consider the shift transformation on the space of infinite sequences over a finite alphabet endowed with the invariant product measure, and examine the presence of a \emph{hole} on the space. The holes we study are specified by the…

Given a relatively compact set $\Omega \subseteq \mathbb{R}$ of Lebesgue measure $|\Omega|$ and $\varepsilon > 0$, we show the existence of a set $\Lambda \subseteq \mathbb{R}$ of uniform density $D (\Lambda) \leq (1+\varepsilon) |\Omega|$…

For any C1 diffeomorphism with dominated splitting we consider a nonempty set of invariant measures which describes the asymptotic statistics of Lebesgue-almost all orbits. They are the limits of convergent subsequences of averages of the…

We prove estimates at infinity of convolutions $f^{n\star}$ and densities of the corresponding compound Poisson measures for a class of radial decreasing densities on $\mathbb{R}^d$, $d \geq 1$, which are not convolution equivalent.…

Smale's alpha-theory certifies that Newton iterations will converge quadratically to a solution of a square system of analytic functions based on the Newton residual and all higher order derivatives at the given point. Shub and Smale…

We study some properties of the exponents of the terms appearing in the splitting perfect polynomials over $\mathbb{F}_{p^2}$, where $p$ is a prime number. This generalizes the work of Beard et al. over $\mathbb{F}_p$. Corrected paper.…

In the moduli space of degree d polynomials, we prove the equidistribution of postcritically finite polynomials toward the bifurcation measure. More precisely, using complex analytic arguments and pluripotential theory, we prove the…