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The Invariance Principle for p-■Chain

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Acta Mathematica Sinica,English Series 2007年第1期23卷 41-56页

作者： Di he hu Zheng Yan XIAO School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China School of Statistics Renmin University of China Beijing 100872 P. R. China

There are two parts in this paper. In the first part we construct the Markov chain in random environment（MCRE）, the skew product Markov chain and p-θ^→ chain from a random transition matrix and a two-dimensional probability distribution, and in the second part we prove that the invarianee principle for p-θ^→ chain, a more complex non-homogeneous Markov chain, is true under some reasonable conditions. This result is more powerful.

关键词： random transition matrix Markov chain in random environment skew product Markov chain p-θ^→ chain invariance principle

Algorithm for 2D irregular-shaped nesting problem based on the NFP algorithm and lowest-gravity-center principle

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第4期7卷 570-576页

作者： LIU hu-yao he Yuan-jun Department of Computer Science and Technology. Shanghai Jiao Tong University Shanghai 200030 China

The nesting problem involves arranging pieces on a plate to maximize use of material. A new scheme for 2D ir- regular-shaped nesting problem is proposed. The new scheme is based on the NFP (No Fit Polygon) algorithm and a new placement principle for pieces. The novel placement principle is to place a piece to the position with lowest gravity center based on NFP. In addition, genetic algorithm (GA) is adopted to find an efficient nesting sequence. The proposed scheme can deal with pieces with arbitrary rotation and containing region with holes, and achieves competitive results in experiment on benchmark datasets.

关键词： Nesting Cutting stock No Fit Polygon (NFP) Genetic algorithm (GA) Lowest gravity center

Complete Convergence and Complete Moment Convergence for Martingale Diference Sequence

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Acta Mathematica Sinica,English Series 2014年第1期30卷 119-132页

作者： Xue Jun WANG Shu he hu School of Mathematical Science Anhui University

In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference ***,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for marting... 详细信息

关键词： Martingale diference sequence complete convergence complete moment convergence Baum–Katz-type theorem

The Equivalence Forms of Random Kolmogorov Forward(Backward) Equations

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Wuhan University Journal of Natural Sciences 2005年第5期10卷 808-812页

作者： hu Di-he hu Xiao-yu School of Mathematics and Statistics WuhanUniversity Wuhan 430072 HubeiChina Graduate School Chinese Academy of SciencesBeijing 100080 China

The concepts of Markov process in random environment, q-matrix in random environment and q-process in random environment are introduced. Three forms of random Kolmoogrov farward （or backward） equations are introduced and the equivalence of these three forms are also proved. Moreover any conservative q-process in random environment satisfies random Kolmogrov backward equation.

关键词： Markov process in random environment q-matrix in random environment q-process in random enviroment

Harmonic Moments of Branching Processes in Random Environments

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Acta Mathematica Sinica,English Series 2009年第7期25卷 1087-1096页

作者： Wei Gang WANG Ping LV Di he hu School of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 P. R. China Department of Science Hangzhou Normal University Hangzhou 310036 P. R. China School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China

We consider harmonic moments of branching processes in general random environments. For a sequence of square integrable random variables, we give some conditions such that there is a positive constant c that every var... 详细信息

关键词： branching processes in random environments harmonic moments

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

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Applied Mathematics(A Journal of Chinese Universities) 2016年第4期31卷 439-457页

作者： WU Yi WANG Xue-jun hu Shu-he School of Mathematical Sciences Anhui University

In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.

关键词： exponential inequality, complete convergence, negatively superadditive-dependent random vari-ables nonparametric regression model, complete consistency.

The Bahadur Representation for Sample Quantiles Under Dependent Sequence

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 521-531页

作者： Wen-zhi YANG Shu-he hu Xue-jun WANG School of Mathematical Science Anhui University

On the one hand,we investigate the Bahadur representation for sample quantiles underφ-mixing sequence withφ(n)=O(n^-3)and obtain a rate as O(n-3/4 log n),*** the other hand,by relaxing the condition of mixing coeffi... 详细信息

关键词： Bahadur representation sample quantiles mixing sequence

A new dimeric furanocoumarin from Notopterygium incisum

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Chinese Chemical Letters 2008年第8期19卷 940-942页

作者： Shi Biao Wu Yi hua Yu Ying he hu Jin Feng hu Department of Natural Products for Chemical Genetic Research Key Laboratory of Brain Functional Genomics Ministry of Education ＆ Shanghai Key Laboratory of Brain Functional Genomics （MOE ＆ SBFG） East China Normal University Shanghai 200062 China Shanghai Key Laboratory of Functional Magnetic Resonance Imaging East China Normal University Shanghai 200062 China

A new dimeric psoralen-type furanocoumarin, notopterol-（18-O-20＇）-notopol （1）, was isolated from Notopterygium incisum for the first time and its structure was elucidated by spectroscopic methods.

关键词： Notopterygium incisum Umbelliferae Dimeric furanocoumarin Structure elucidation

Thermomechanical Fatigue Behavior of Powder Metallurgical Nickel Based Superalloy FGH96

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Journal of Iron and Steel Research International 2010年第6期17卷 74-79页

作者： GU Yu-li TAO Chun-hu he Yu-huai Beijing Institute of Aeronautical Materials Beijing 100095 China

The fracture behavior of the thermomechanical fatigue （TMF） of the powder metallurgical nickel based superalloy FGH96 was investigated under in-phase （IP） and out-of-phase （OP） loadings in the temperature range from 550 ℃ to 720 ℃ and the mechanical strain amplitude range from 0.3% to 0.8%. The results show that the FGH96 TMF fracture character is intergranular for the IP samples and transgranular cleavage-like for the OP samples, at the same strain amplitude, the fatigue life is shorter for the IP than that for the OP samples that is related to crack propagation along grain boundary on the IP samples, the γ′ size is larger in the IP than that in the OP sample, which is related to the bulk diffusion processes accelerated by the tensile strain during the high temperature portion of the IP cycle. Dislocation pairs and stacking faults are main microstructures induced by IP TMF, and they are hindered by the grain boundary, which likely resulted in the crack propagation along the grain boundary in the IP samples.

关键词： nickel based superalloy powder metallurgy thermomechanical fatigue γ′ size dislocation