IMPORTANCE MEASURE OF CORRELATED VARIABLES IN POLYNOMIAL OUTPUT

为了解决一般工程问题中输出量为多项式情况下相关正态输入变量的贡献识别问题，以二次不含交叉项的多项输出量为例，利用多维相关正态分布及其条件分布的性质，解析地推导了相关正态输入变量对输出量总方差的独立贡献及相关贡献，采用算例验证了所推导的解析表达式的正确性．文中所推导的相关正态变量独立贡献和相关贡献的表达式可直接用于输出量为二次不含交叉项多项式或一次多项式情况下的输入变量贡献的识别，并且为其他新的算法提供了对照解，另外此方法亦可以推广至含交叉项的高阶多项式，解决更为复杂输出量情况下输入量的贡献识别问题．     

次线性期望下的一般中心极限定理

受Peng-中心极限定理的启发,本文主要应用G-正态分布的概念,放宽Peng-中心极限定理的条件,在次线性期望下得到形式更为一般的中心极限定理.首先,将均值条件E[X_n]=ε[X_n]=0放宽为|E[X_n]|+|ε[X_n]|=O(1/n);其次,应用随机变量截断的方法,放宽随机变量的2阶矩与2+δ阶矩条件;最后,将该定理的Peng-独立性条件进行放宽,得到卷积独立随机变量的中心极限定理.     

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form     

随机变量变换分布的若干推论及应用

给出了随机变量变换分布的三个推论，这些推论提供了在不同变换下求二维随机变量的函数的概率密度的计算公式，实例应用表明，这些公式应用简便，灵活，实用．     

Effects of experimental variables on PMMA nano-indentation measurements

This work aims to investigate the effects of experimental variables on nano-indentation measurements on PMMA. A wide range of conditions, including different load levels, loading rates, holding times and unloading rates were employed to examine the sensitivity of nano-indentation measurements to the selected experimental variables. The test results indicate that the elastic modulus and hardness of PMMA are approximately load-level invariant. However, they are sensitive to the loading rate, holding time and unloading rate. Both elastic modulus and hardness increase with increasing loading rate, while increasing holding time leads to decreasing elastic modulus and hardness. Moreover, the unloading rate has almost no obvious effect on the hardness of PMMA, while the opposite is true for elastic modulus.     

Multivariate Association of Graph-Theoretic Variables and Physicochemical Properties

Abstract

We used canonical correlation analysis to examine the multivariate association between two distinct data sets commonly measured or calculated for approximately 600 chemicals: (1) measured or calculated values of select physieochemical properties (i.e., K _ow, boiling point, heat of vaporization, molecular weight, water solubility, molecular volume, hydrogen bonding potential, and vapor pressure) and (2) calculated algorithmically-derived variables (i.e., topological and neighborhood indices derived from graph theory). Canonical correlation analysis identified eight highly significant associations between linear combinations of graph-theoretic variables and linear combinations of physicochemical properties. The set of graph theoretic variables was significantly related to all physieochemical properties, explaining 55% to 99% of the variation in these properties.     

Chemical composition variations,allelopathic, and antioxidant activities of Symphyotrichum squamatum (Spreng.) Nesom essential oils growing in heterogeneous habitats

The present study aimed to analyze the chemical composition of Symphyotrichum squamatum EOs growing in two different habitats to explore the ecological implication on the EOs production and evaluate their antioxidant and allelopathic potentialities. The EOs from the aerial parts collected from coastal Mediterranean belt and inland abandoned habitats in the Nile Delta of Egypt, were extracted and analyzed using gas chromatography-mass spectrometry. Sixty compounds were characterized as overall constituents of EOs from both samples. Sesquiterpenes were the main component and represented by 69.77% and 88.68% from coastal and inland sample, respectively. The coastal sample attained a relatively high content of monoterpenes compared to the inland sample. Major compounds from the EOs of the coastal habitat sample, were humulene epoxide, (-)-spathulenol, (-)-caryophyllene oxide, germacrene D, and α-humulene representing 59.72%. However, β-pinene, germacrene D, α-humulene, α-muurolene, humulene epoxide, (-)-caryophyllene oxide, and β-cadinene were the major compounds of EOs of the inland habitat sample, representing 63.70%. The correlation analysis revealed more correlation between the Egyptian inland S. squamatum and the Japanese ecospecies. However, the Egyptian coastal S. squamatum and Turkish ecospecies were more correlated to each other. The present data suggested that chemotypes of S. squamatum maintain their typical pattern despite ecological or climatic differences. The EOs of S. squamatum showed moderate antioxidant activity, wherein coastal and inland EOs have an IC₅₀ value of 382.53 and 559.63 μL L⁻¹, respectively. Also, the EOs from both habitats showed moderate allelopathic activity against the noxious weed Bidens pilosa. However, the activity of the coastal sample was more than inland one and could be attributed to the content of the major compounds, especially the oxygenated terpenes.     

相伴随机变量序列的泛函型几乎处处中心极限定理

对于均值为零的平稳相伴随机变量序列,首先证明了在L(n)=EX_1~2 2 sum from n to j=2 Cov(X_1,X_j)是一个缓变函数的条件下的泛函型几乎处处中心极限定理.另外还给出了正则化部分和函数的对数平均几乎处处收敛性.