Maximal multilinear Calderón-Zygmund operators with non-doubling measures

Under the assumption that μ is a non-doubling measure on ℝ ^d which only satisfies some growth condition, the authors prove that the maximal multilinear Calderón-Zygmund operator is bounded from (μ) × … × (μ) into L ^p (μ) for any p ₁, … p _m ∈ (1, ∞) and p with 1/p = 1/p ₁ + … + 1/p _m , and bounded from (μ) × … × (μ) into weak- ^{L p} (μ) if there exists any p _i = 1. Furthermore, the authors establish a weighted weak-type estimate for the maximal multilinear Calderón-Zygmund operator. The second (corresponding) author is supported by Tianyuan Fund of China (No. 10626055) and National Natural Science Foundation of China (No. 10701078).     

Expanding convex immersed closed plane curves

We study the evolution driven by curvature of a given convex immersed closed plane curve. We show that it will converge to a self-similar solution eventually. This self-similar solution may or may not contain singularities. In case it does, we also have estimate on the curvature blow-up rate.     

The Asymptotic Expansion of Solutions for the Navier-Stokes Equations with Large Parameters

In this paper, we decomposite the coefficient matrix of the Navier-Stokes equations with large parameter in λ power. By factor analysis and energy estimation, the long time existence and asymptotic expansion of the solution tor the system are obtained. Key words Navier-Stokes equations; expansion; approximation.     

Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations

The main object of this paper is to investigate several general families of hyper-geometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.     

Existence and convergence of solutions of singular boundary value problems for second order ordinary differential equations and applications

In this paper,we consider the singular boundary value problems for second order quasilinear ordinary differential equations and prove existence and convergence on second order perturbation terms.The result is applied to solve the Riemann problem for 2×2 hyperbolic conservation laws,which is a partial differential equation arising in applied mathematical area.     

一类新的广义零差分平衡函数及其应用

2008-2009年,丁存生在构造最佳常组合码与优化及完善差分系统中首次引入了零差分平衡(简称ZDB)函数的概念,据此学者们构造出了最佳组成权重码和最优跳频序列.作者将零差分平衡函数的定义推广到一般的广义零差分平衡函数,并利用2分圆陪集构造了一类广义零差分平衡函数,由此构造出一类新的常组合码和差分系统.     

Levitin–Polyak well-posedness by perturbations for the split inverse variational inequality problem

In this paper, we extend the notion of Levitin–Polyak wellposedness by perturbations to the split inverse variational inequality problem. We derive metric characterizations of Levitin–Polyak wellposedness by perturbations. Under mild conditions, we prove that the Levitin–Polyak well-posedness by perturbations of the split inverse variational inequality problem is equivalent to the existence and uniqueness of its solution.     

A new two‐phase structure‐preserving doubling algorithm for critically singular M‐matrix algebraic Riccati equations

Among numerous iterative methods for solving the minimal nonnegative solution of an M‐matrix algebraic Riccati equation, the structure‐preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1/2. In this paper, we first undertake a delineatory convergence analysis that reveals that the approximations by SDA can be decomposed into two components: the stable component that converges quadratically and the rank‐one component that converges linearly with the linear rate 1/2. Our analysis also shows that as soon as the stable component is fully converged, the rank‐one component can be accurately recovered. We then propose an efficient hybrid method, called the two‐phase SDA, for which the SDA iteration is stopped as soon as it is determined that the stable component is fully converged. Therefore, this two‐phase SDA saves those SDA iterative steps that previously have to have for the rank‐one component to be computed accurately, and thus essentially, it can be regarded as a quadratically convergent method. Numerical results confirm our analysis and demonstrate the efficiency of the new two‐phase SDA. Copyright © 2015 John Wiley & Sons, Ltd.     

Banach空间中一类n阶积分-微分方程初值问题的解

利用一个新的比较定理和乘积空间的锥理论,得出了Banach空间中的一般高阶积分—微分初值问题的解存在性.     

一类正则锥在非线性奇异边值中的应用

本文构造了一个新的正则锥,运用非紧减算子的不动点定理,得到了一类非线性奇异边值问题正解的唯一性,改进了有关结果.