一致正规结构与Reich的公开问题的解答

在具有一致正规结构且其范数是一致Gateaux可微的Banach空间中,研究了Reich提出的公开问题.在给渐近非扩张映象作更适当的假设下,对Reich的公开问题给出了一个肯定的答复.所得结果在下列方面推广与改进了张石生教授的最新结果:(ⅰ)去掉了张教授的较强条件“迭代参数列收敛到零”;(ⅱ)去掉了张教授的较强假设“渐近非扩张映象有不动点”;(ⅲ)也去掉了张教授的较强条件“Banach压缩映象原理生成的序列强收敛”.而且,这些结果也推广与改进了先前由Reich,Shioji,Takahashi,Ueda及Wittmann等多位作者得到的相应结果.     

Second-Order Optimality Conditions in Generalized Semi-Infinite Programming

This paper deals with generalized semi-infinite optimization problems where the (infinite) index set of inequality constraints depends on the state variables and all involved functions are twice continuously differentiable. Necessary and sufficient second-order optimality conditions for such problems are derived under assumptions which imply that the corresponding optimal value function is second-order (parabolically) directionally differentiable and second-order epiregular at the considered point. These sufficient conditions are, in particular, equivalent to the second-order growth condition.     

Generalized synchronization of continuous dynamical system

Generalized synchronization between two continuous dynamical systems is discussed.By exploring the Liapunov stability theory and constructing appropriately unidirectional coupling term,a sufficient condition for determining the generalized syn- chronization between continuous systems is proved.Two examples are used to show the effectiveness of this result.     

Convolution functions that are nowhere differentiable

In 1951 V. Jarník constructed two continuous functions whose Volterra convolution is nowhere differentiable. We generalize Jarník?s results by proving that the set of such functions is maximal lineable. This would shed some light on a question posed in 1973 on the structure of the set of continuous functions whose Volterra convolution is nowhere differentiable.     

人造地震动合成中的位移误差分析

三角函数级数法是合成人工地震动常用算法之一,但是通过对加速度积分求取位移时,却存在与零线漂移相类似的位移漂移现象。     

本刊英文版Vol.30(2014),No.12论文摘要(英文)北大核心CSCD

Regularity of the Inverse of a Homeomorphism with Finite Inner Distortion Chang Yu GUO Abstract Let f:Ω→f（Ω）Rⁿ be a W^1,1-homeomorphism with L¹-integrable inner distortion.We show that finiteness of min{lip_f（x）,k_f（x）},for every x∈Ω\E,implies that f^-1∈W^1,nand has finite distortion,provided that the exceptional set E hasσ-finite H¹-measure.Moreover,f has finite distortion,differentiable a.e.and the Jacobian J_f>0 a.e.     

Weak convergence theorems for strict pseudo-contractions in Banach spaces

In this paper, it is shown that there is a gap in the paper [Chidume, C. E., Shahzad, N.: Weak convergence theorems for a finite family of strict pseudo-contractions. Nonlinear Anal., 72, 1257–1265(2010)], consequently, the main results of the paper do not hold in uniformly smooth Banach spaces. Meanwhile, it is also shown that the main results(Lemma 3.4, Theorems 3.5–3.6, 3.8–3.9) in the paper [Cholamjiak, P., Suantai, S.: Weak convergence theorems for a countable family of strict pseudo-contractions in Banach spaces. Fixed Point Theory Appl., 2010, Article ID 632137, 16 pages(2010)] do not hold in Lpfor p 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lpfor p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above.     

一个无限可微函数类的最优Lagrange 插值

本文研究\,$[-1,1]$上的一个无限可微函数类$F_\infty$在空间$L_\infty[-1,1]$及加权空间$L_{p,\omega}[-1,1]$, $1\le p< \infty$ ($\omega$是$(-1,1)$上的非负连续可积函数)的最优Lagrange插值.我们证明了基于首项系数为1且于$L_{p,\omega}[-1,1]$上有最小范数的多项式零点的Lagrange插值对$1\le p< \infty$是最优的. 同时我们给出了当结点组包含端点时的最优结点组.     

Tubular surfaces of center curves on spacelike surfaces in Lorentz‐Minkowski 3‐space

In this paper, we introduce three kinds of tubular surfaces associated to original center curves γ lying in spacelike surfaces in Lorentz‐Minkowski 3‐space. It is demonstrated that these tubular surfaces can occur some singularities and the types of these singularities can be characterised by several invariants, respectively. Some interesting relations between the contacts of original curve γ with osculating model surfaces, the contacts of γ with slices, and the singularities of three kinds of surfaces are further revealed. Several examples are presented to explain the theoretical results.