Convergence Rates in the Law of Large Numbers under Sublinear Expectations

In this note, we study convergence rates in the law of large numbers for independent and identically distributed random variables under sublinear expectations. We obtain a strong L^p-convergence version and a strongly quasi sure convergence version of the law of large numbers.     

非等距三次样条(Ⅰ)型插值函数余项渐近展开

摘要本文利用基样条插值方法,给出非等距I型三次样条插值误差的余项渐近展开式,推广了文献[1]中的结果。     

Uniform nonintegrability of random variables

Recently, T. K. Chandra, T. -C. Hu and A. Rosalsky [Statist. Probab. Lett., 2016, 116: 27–37] introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. We introduce a weaker definition on uniform nonintegrability (W-UNI) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of W-UNI, one of which is a W-UNI analogue of the celebrated de La Vallée Poussin criterion for uniform integrability. In addition, we give some remarks, one of which gives a negative answer to the open problem raised by Chandra et al.     

Convergences of Random Variables Under Sublinear Expectations

In this note, the authors survey the existing convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity property, the authors prove that convergence in capacity is stronger than convergence in distribution, and give some equivalent characterizations of convergence in distribution. In addition, they give a dominated convergence theorem under sublinear expectations, which may have its own interest.     

关于概率空间与次线性期望空间中的随机变量一致可积性的一个注记（英文）

在这篇注记中我们讨论随机变量的一致可积性.在概率空间中,我们引进了随机变量一致可积性的两个新的定义,并证明了他们与经典定义等价.在次线性期望空间中,我们给出了随机变量一致可积性的德拉瓦利普桑准则,并作了一些其它讨论.     

非等距划分下样条函数的渐近展开

本文采用传递插值的方法对非等距划分情况下亏度为(n-1)的(2n-1)次缺插值样条函数余项进行了渐近展开,得到了较普遍的结果。这种方法对非等距情况下的渐近展开具有普遍的意义。     

第31届中国化学奥林匹克(初赛)试题解析(一)

详细分析并解答了第31届中国化学奥林匹克(初赛)试题。对于每一道题目,我们都给出了详尽的讨论,引导读者综合运用所学的化学知识,通过推理、演算、论证等方法顺利解题。对于特定的题目,我们还给出了相关的科学背景介绍与知识拓展,鼓励读者了解题目背后的科学思想,感受化学学习与科研的乐趣。     

Fluorescence quenching and molecular docking study on the binding of four hydroxyanthraquinones to FTO

In this work, the binding of four hydroxyanthraquinones (HAQs) to fat mass and obesity-associated (FTO) protein has been studied using fluorescence, UV-vis absorption and circular dichroism spectroscopy as well as molecular docking analysis. Analysis of fluorescence data showed that the binding of HAQs to FTO occurred via a static quenching mechanism. Thermodynamic analysis and molecular docking results suggested that hydrophobic force played a major role in stabilising the HAQ-FTO complex. Circular dichroism spectra indicated that the secondary structure of FTO was changed by the addition of HAQs. Results also showed that emodin had the strongest quenching and binding ability among four HAQs.     

关于对称拟凸多项式的不相连定理

假定μn为Rn上的标准高斯测度,X为Rn上的随机向量,分布为μn.不相连猜测说的是:如果f与g为Rn上的两个多项式,而且f(X)与g(X)相互独立,则存在Rn上的正交变换Y = LX及整数k使得f o L-1为(y1,y2,…,yk)的函数,goL-1为(yk+1,yk+2,…,yn)的函数.此时,称f与g不相连.在这...     

Laser crystallization of amorphous silicon films investigated by Raman spectroscopy and atomic force microscopy

The intrinsic and phosphorous (P)-doped hydrogenated amorphous silicon thin films were crystallized by laser annealing. The structural properties during crystallization process can be investigated. Observed redshifts of the Si Raman transverse optical phonon peak indicate tensile stress present in the films and become intense with the effect of doping, which can be relieved in P-doped films by introducing buffer layer structures. Based on experimental results, the established correlation between the stress and crystalline fraction (X_C) suggests that the relatively high stress can limit the increase in X_C and the highest crystalline fraction is obtained by a considerable stress release. At high laser energy density of 1250 mJ/cm², the poorer crystalline quality and disordered structure of the film originating from the irradiation damage and defects lead to the low electron mobility.