相关论文: Exceptional sets for the derivatives of Blaschke p…

Numerical methods for stochastic differential equations with non-globally Lipschitz coefficients are currently studied intensively. This article gives an overview of our work for the case that the drift coefficient is potentially…

Let $\chi$ be a non-principal Dirichlet character and $L(s, \chi)$ be the associated Dirichlet $L$-function. Let us use $\mathcal{L}(s,\chi)$ to denote its logarithmic derivative $L'(s, \chi)/L(s, \chi)$. We first prove some arithmetic…

We extend the matrix-resolvent method for computing logarithmic derivatives of tau-functions to the Ablowitz--Ladik hierarchy. In particular, we derive a formula for the generating series of the logarithmic derivatives of an arbitrary…

The gradient bounds of generalized barycentric coordinates play an essential role in the $H^1$ norm approximation error estimate of generalized barycentric interpolations. Similarly, the $H^k$ norm, $k>1$, estimate needs upper bounds of…

Observing that the logarithm of a product of two elliptic operators differs from the sum of the logarithms by a finite sum of operator brackets, we infer that regularised traces of this difference are local as finite sums of noncommutative…

Motivated by a dictionary between polynomials and finite Blaschke products, we study both Smale's mean value conjecture and its dual conjecture for finite Blaschke products in this paper. Our result on the dual conjecture for finite…

We prove that the size of the product set of any finite arithmetic progression $\mathcal{A}\subset \mathbb{Z}$ satisfies \[|\mathcal A \cdot \mathcal A| \ge \frac{|\mathcal A|^2}{(\log |\mathcal A|)^{2\theta +o(1)} } ,\] where…

The goal of this paper is to investigate the family of Blasche products $B_a(z)=z^3\frac{z-a}{1-\bar{a}z}$, which is a rational family of perturbations of the doubling map. We focus on the tongue-like sets which appear in its parameter…

Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at…

In this paper we give a simple proof of the endpoint Besov-Lorentz estimate $$ \|I_\alpha F\|_{\dot{B}^{0,1}_{d/(d-\alpha),1}(\mathbb{R}^d;\mathbb{R}^k)} \leq C \|F \|_{L^1(\mathbb{R}^d;\mathbb{R}^k)} $$ for all $F \in…

We study the growth of the quantity $\int_{\mathbb{T}}|R'(z)|\,dm(z)$ for rational functions $R$ of degree $n$, which are bounded and univalent in the unit disk, and prove that this quantity may grow as $n^\gamma$, $\gamma>0$, when…

Using a new Borel type growth lemma, we extend the difference analogue of the lemma on the logarithmic derivative due to Halburd and Korhonen to the case of meromorphic functions $f(z)$ such that $\log T(r,f)\leq r/(\log r)^{2+\nu}$,…

Recently, it has been shown in [Jentzen, A., M\"uller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14, 2016] that there exists a system of autonomous stochastic differential equations (SDE) on the time interval $[0,T]$ with…

This paper is concerned with the existence and uniqueness of weak solutions to the Cauchy-Dirichlet problem of backward stochastic partial differential equations (BSPDEs) with nonhomogeneous terms of quadratic growth in both the gradient of…

The main aim of the paper is to give a formula for computing the separation \L ojasiewicz exponents for two real analytic set germs via the Newton--Puiseux expansions of their defining functions. Moreover, we present an effective exponent…

For Borel subsets A and B of the Euclidean n-space the intersection of A with generic rotations and translations of B has often Hausdorff dimension at least dim A + dim B - n. Estimates for the exceptional set of rotations are derived.

Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \Vert f(z) \Vert=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty…

We prove that a functional with Lipschitzian derivative, when restricted to suitable spheres centered at a noncritical point, has a unique maximum.

In this paper, we study one-dimensional backward stochastic differential equation (BSDE, for short), whose coefficient $f$ is Lipschitz in $y$ but only continuous in $z$. In addition, if the terminal condition $\xi$ has bounded Malliavin…

We consider normalizing sequences that can give rise to nondegenerate limittheorems for Birkhoff sums under the iteration of a conservative map. Mostclassical limit theorems involve normalizing sequences that are polynomial,possibly with an…