Commutators of weighted lipschitz functions and multilinear singular integrals with non-smooth kernels

This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.     

Multilinear commutators of BMO functions and multilinear singular integrals with non-smooth kernels

This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.     

Boundedness for parabolic singular integral with rough kernels and its commutators on Triebel-Lizorkin spaces

In this paper, the authors give the boundedness on Triebel-Lizorkin spaces for the parabolic singular integral with rough kernel and its commutator.     

Generalized commutators for Marcinkiewicz type integrals with variable kernels

Let A be a function with derivatives of order m and D γ A ∈■β (0 < β < 1, |γ| = m). The authors in the paper prove that if Ω(x, z) ∈ L ∞ (R n ) × L s (S n 1 ) (s ≥ n/(n β)) is homogenous of degree zero and satisfies the mean value zero condition about the variable z, then both the generalized commutator for Marcinkiewicz type integral μ A Ω and its variation μ A Ω are bounded from L p (R n ) to L q (R n ), where 1 < p < n/β and 1/q = 1/p β/n. The authors also consider the boundedness of μ A Ω and its variation μ A Ω on Hardy spaces.     

A new kernel function yielding the best known iteration bounds for primal-dual interior-point algorithms

Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields an algorithm with the best known complexity bound for both large- and small-update methods.     

具周期性的含卷积核与余割核混合的积分方程

运用所给出的引理及离散的Fourier变换, 在$L_2[-\pi, \pi]$上讨论了一类具周期性的含卷积核与余割核$\csc(\tau-\theta)$混合的奇异积分方程,把此类方程转化为离散跃度问题, 得到了方程的可解条件和一般解的显式.     

含余割核奇异积分修改的反演问题

针对含余害核奇异积分反演问题在指κ＜0时一般无解的情况，本文提出并求解两种修改的反演问题，而后一种修改反演问题的提法与此前类似问题颇不相同，由于运用了推广的留数定理和Bertrand型换序公式使本问题及类似问题解法得以简化。     

农残水平测试中数据多态性分析及指定值估计研究

对全国农残水平测试中毒死蜱、氯氰菊酯数据进行统计分析,在数据统计分布特征研究基础上,使用内核密度估计进行数据多态性分析,使用bootstrap模拟取样法对数据样本值重复取样,以获得稳健的水平测试样品待测物含量代表值估计、标准误差及置信区间描述,证明以bootstrap模拟取样法获取的均值与标准偏差作为有限单次样本代表值是合理、有效的,解决了四分位稳健统计方法对非正态多态分布代表值估计不稳定问题及取样理论中取样样本数限制的瓶颈,为能力验证计划指定值的获取提供了一种新方法。     

矿产品水分含量代表值Bootstrap模拟取样估计

在对矿产品水分含量基础统计学特征描述的基础上,采用内核密度估计对水分含量数据多态性进行了分析,根据双态分布的特点,使用Bootstrap模拟取样方法对试验样本值模拟重复取样,以多次Bootstrap模拟取样的均值与标准偏差作为矿产品水分含量有限样本代表值及标准偏差的稳健估计,实践证明Bootstrap模拟取样估计对矿产品水分含量代表值的估计是有效的,该项研究为矿产品水分含量代表值的准确评估提供了一种新方法.