On sums of independent random variables without power moments

In 1952 Darling proved the limit theorem for the sums of independent identically distributed random variables without power moments under the functional normalization. This paper contains an alternative proof of Darling’s theorem, using the Laplace transform. Moreover, the asymptotic behavior of probabilities of large deviations is studied in the pattern under consideration.     

向量空间中若干问题的入微分析和研究

对向量空间中若干有代表性的问题进行了深入细致的分析和研究.     

Analytic description of statistics of spectra of quantum graphs

We discuss how to obtain exact and approximate distributions for various statistical characteristics of the spectra of quantum graphs using previously found exact solutions of the spectral problem. We indicate the relation between the appearing spectral decompositions and the theory of weakly dependent random variables and indicate the relation between the known limit theorems for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 38–66, July, 2008.     

Banach空间的Chung-Teicher型大数律

设{Xn，n≥1}是实可分Banach空间独立随机变量，讨论了在弱大数律的假设下使得Chung-Teicher型强大数律也成立，即bn^-1｜｜∑k=1^n（Xk-EXkI（｜｜Xk｜｜≤bk））｜｜→^p0当且仅当bn^-1｜｜∑中k=1^n（Xk-EXkI（｜｜Xk｜｜≤bk））｜｜→^a.s.0.     

保费收取过程是随机过程的双险种风险模型

研究保费收取过程是一个随机过程的双险种风险模型,得出了Lundberg上界、最终破产概率、不破产所满足的微积分方程、索赔服从指数分布的不破产概率、有限时间不破产所满足的微积分方程.     

哈密尔顿性和部分平方图的独立集

设G是一个图,G的部分平方图G*满足V(G*)=V(G),E(G*)=E(G)∪{uv:uv■E(G),且J(u,v)≠■},这里J(u,v)={w∈N(u)∩N(v):N(w)■N[u]∪N[v]}.利用插点方法,证明了如下结果:设G是k-连通图(k2),b是整数,0min {k,(2b-1+k)/2}(n(Y)-1),则G是哈密尔顿图.同时给出图是1-哈密尔顿的和哈密尔顿连通的相关结果.     

Weak edge-degree domination in hypergraphs

In this paper we extend the notion of weak degree domination in graphs to hypergraphs and find relationships among the domination number, the weak edge-degree domination number, the independent domination number and the independence number of a given hypergraph.     

高效选取线性独立的原子特征构建精确机器学习势函数

机器学习势由于具有与第一性原理计算相当的准确性,且低得多的计算成本,在原子模拟中极具前景. 然而原子机器学习势的可靠性、速度和可迁移性在很大程度上取决于原子构型的表示. 适当地选取用作机器学习程序输入的描述符是一个成功的机器学习表示的关键. 本文发展了一种简单有效的方法,可以基于训练数据固有的相关性,从大量待选的描述符中自动选取一组最佳的线性独立原子特征. 通过对几个具有较少冗余线性独立嵌入密度描述符的基准分子构建嵌入原子神经网络势的应用,证明了这种新方法的有效性和准确性. 该算法可以大大简化原子特征的初始选取,并极大地提高原子机器学习势的性能.     

Correlation‐assisted nearest shrunken centroid classifier with applications for high dimensional spectral data

High throughput data are frequently observed in contemporary chemical studies. Classification through spectral information is an important issue in chemometrics. Linear discriminant analysis (LDA) fails in the large‐p‐small‐n situation for two main reasons: (1) the sample covariance matrix is singular when p > n and (2) there is an accumulation of noise in the estimation of the class centroid in high dimensional feature space. The Independence Rule is a class of methods used to overcome these drawbacks by ignoring the correlation information between spectral variables. However, a strong correlation is an essential characteristic of spectral data. We proposed a new correlation‐assisted nearest shrunken centroid classifier (CA‐NSC) to incorporate correlation information into the classification. CA‐NSC combines two sources of information [class centroid (mean) and correlation structure (variance)] to generate the classification. We used two real data analyses and a simulation study to verify our CA‐NSC method. In addition to NSC, we also performed a comparison with the soft independent modeling of class analogy (SIMCA) approach, which uses only correlation structure information for classification. The results show that CA‐NSC consistently improves on NSC and SIMCA. The misclassification rate of CA‐NSC is reduced by almost half compared with NSC in one of the real data analyses. Generally, correlation among variables will worsen the performance of NSC, even though the discriminatory information contained in the class centroid remains unchanged. If only correlation structure information is used (as in the case of SIMCA), the result will be satisfactory only when the correlation structure alone can provide sufficient information for classification. Copyright © 2015 John Wiley & Sons, Ltd.     

Director configurations in nematic droplets with tilted surface anchoring

The polymer dispersed nematic liquid crystal (LC) with the tilted surface anchoring has been studied. The droplet orientational structures with two point surface defects – boojums and the surface ring defect – are formed within the films. The director tilt angle α = 40° ± 4° at the droplet interface and LC surface anchoring strength W_s ~ 10^–6 (J m^?2) have been estimated. The bipolar axes within the studied droplets of oblate ellipsoidal form can be randomly oriented are oriented randomly relatively to the ellipsoid axes as opposed to the droplets with homeotropic and tangential anchoring.