Variable bandwidth and one-step local M-estimator

A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the one-step local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.     

一类非线性变系数差分方程正解的振动性

研究了一类具有时滞的非线笥变系数差分方程Ｘｎ＋１＝Ｘｎｅｘｐ（ｒｎ１－ｘｎ－ｋ／１－ｃｘｎ－ｋ解的振动性,获得了其正解关于正平衡点ｘ＝１振动的好的充分条件。     

Topological Invariants and Solutions with a High Complexity for Scalar Semilinear PDE

In this paper topological invariants of dynamics of scalar parabolic equations are defined. Conservation of these invariants causes persistence of complex spatially chaotic patterns in the dynamics. It implies, in particular, the existence of extremely many stable essentially different spatially complex solutions of scalar semilinear parabolic, elliptic and hyperbolic equations in the situation when coefficients of equations depend on the spatial variable strongly enough and the domain is large or unbounded, the number of different solutions exponentially depends on the volume of domain. Another implication of the conserved quantities is persistence of complexity of solutions in the dynamics.     

可伸长变截面杆的弹性过屈曲模型及其数值解

在Ｋｉｒｃｈｈｏｆｆ基本假设下,基于轴线可伸长弹性杆的几何非线性理论,建立了一端简支另一端固定夹紧变截面直什的过屈曲控制方程,并应用打靶法直接数值求解相应的强非线性过值问题,获得了数值意义上的精确解。     

IMPLICIT ITERATIVE METHODS WITH VARIABLE CONTROL PARAMETERS FOR ILL-POSED OPERATOR EQUATIONS

This paper discusses a kind of implicit iterative methods with some variable parameters,which are called control parameters,for solving ill-posed operator equations.The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features,especially the methods can be implemented parallelly.     

关于信源的Tunstall编码方法

在信源编码理论中,Ｔｕｎｓｔａｌｌ码是渐近最优的Ｖ－Ｂ码（Ｖ代表变长消息,Ｂ代表定长码字）。本文进一步研究了Ｔｕｎｓｔａｌｌ码的性质,给出了Ｔｕｎｓｔａｌｌ码的码率的新的上界,刻划了Ｔｕｎｓｔａｌｌ树和扩展次数之间的一些较深刻的内在联系,并且给出了一个寻找ε－最优的Ｔｕｎｓｔａｌｌ码的扩展次数的算法。     

变系数二元线性差分方程解的显式表示

文章讨论了变系数二元线差分方程求解公式,并给出两个应用实例。     

球面上变阶分数次积分的Lipschitz有界性

本文引入一种平均意义下的变阶Ｌｉｐｓｃｈｉｔｚ空间,并讨论了球面上变阶分数次积分的Ｌｉｐｓｃｈｉｔｚ有界性。     

Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent

In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Littlewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley g*λ-functions, is established on the Lebesgue spaces with variable exponent. Furthermore,the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.     

变量控制在实验探究专题教学中的应用与评价*——以“镁+水”反应体系为例

在以“Mg+H₂O”反应体系为核心的实验探究专题教学活动中,通过变量控制的方法设计实验方案,采用常规实验、数字化实验等方式,多层次探究加速“Mg+H₂O”反应速率的原因和控制条件。在有层次的教学活动中递进式发展学生通过变量控制的方法设计实验方案的能力、拓宽对影响化学反应速率因素的认识角度,通过对活动环节的评价,诊断并发展学生的实验探究能力。