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EXPONENTIAL CONVERGENCE OF SAMPLE AVERAGE APPROXIMATION METHODS FOR A CLASS OF STOCHASTIC MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

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Journal of Computational Mathematics 2006年第6期24卷 733-748页

作者： Fan-wen Meng Hui-fu Xu The Logistics Institute - Asia Pacific National University of Singapore 1 Law Link Singapore School of Mathematics University of Southampton Highfield Southampton S017 1B J UK School of Mathematics University of Southampton Highfield Southampton S017 1B J UK

In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.

关键词： Stochastic mathematical programs with complementarity constraints Sampleaverage approximation Weak stationary points Exponential convergence.

[Solid-phase extraction coupled with high performance liquid chromatography-triple quadrupole mass spectrometry for simultaneous determination of seven coumarins in water samples from drinking water treatment plants]

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Se pu = Chinese journal of chromatography 2025年第1期43卷 78-86页

作者： wen-Mei Jiao Jing-Ming Yang Ce Xu fu-Kang Gao Lu-Yao Shen Yu-Bo Yuan Zhi-Fen Guo Guang Huang School of Life Sciences and Chemical Engineering Jiangsu Second Normal University Nanjing 211200 China. School of Stomatology Nanjing Medical University Nanjing 210029 China. School of Public Health Nanjing Medical University Nanjing 211166 China. Key Laboratory of Modern Toxicology Ministry of Education School of Public Health Nanjing Medical University Nanjing 211166 China.

Chlorinated coumarins, which are as cytotoxic as highly toxic halobenzoquinones toward CHO-K1 cells, have recently been identified as disinfection byproducts in drinking water disinfection processes. Therefore, detecting coumarins in water samples collected at various stages from drinking water treatment plants helps assess the formation of chlorinated coumarins in drinking water. Hence, a simple, rapid, accurate, and sensitive method for quantifying coumarins in water samples is required. In this study, a method was developed based on solid-phase extraction coupled with high performance liquid chromatography-triple-quadrupole mass spectrometry for analyzing seven coumarins in water samples from drinking water treatment plants, including 6,7-dihydroxycoumarin, 7-hydroxycoumarin, 6-hydroxy-4-methylcoumarin, 8-chloro-7-hydroxycoumarin, coumarin, 7-chloro-6-hydroxy-4-methylcoumarin, and 3,8-dichloro-7-hydroxycoumarin. Sample pretreatment involved solid-phase extraction using HLB columns, followed by elution with water and methanol, each containing 0.25% formic acid. The extracted solution was separated via gradient elution using a Phenomenex Luna C18 column (100 mm×2.0 mm, 3 mm) with 0.1% formic acid aqueous solution and methanol as the mobile phases, with analytes detected by triple-quadrupole mass spectrometry equipped with electrospray ionization source in multiple reaction monitoring mode. The matrix effect, precision, and accuracy of the developed method were investigated using raw and treated water as matrices. Matrix effects of 0.84-1.12 were recorded for the detection of 6,7-dihydroxycoumarin, 7-hydroxycoumarin, 6-hydroxy-4-methylcoumarin, and coumarin in raw water, while values of 0.67-0.70 were recorded for 8-chloro-7-hydroxycoumarin, 7-chloro-6-hydroxy-4-methylcoumarin, and 3,8-dichloro-7-hydroxycoumarin in finished water. The three chlorinated coumarins exhibited matrix effects above 0.80 after the finished water matrix had been diluted four times. These re

关键词： coumarins disinfection byproducts drinking water high performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS) solid-phase extraction (SPE)

Evolution of inclusions in a pipeline steel during continuous casting and hot rolling process

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Journal of Iron and Steel Research International 2022年第1期29卷 175-185页

作者： Yi Wang Wei-fu Li wen Yang School of Metallurgical and Ecological Engineering University of Science and Technology BeijingBeijing 100083China

Industrial trials were performed to study the evolution of inclusions in a pipeline steel during the continuous casting and hot rolling *** main composition of inclusions changed from Al_(2)O_(3)-CaO in the liquid steel to Al_(2)O_(3)-CaO-CaS in the slab,and then to Al_(2)O_(3)-CaS in the rolled *** area fractions of inclusions increased from 47.0×10^(-6) to 76.7×10^(-6),and to 144.3×10^(-6).It was explained by thermodynamic calculations that the thermodynamic equilibrium between inclusions and the steel varied with the *** contents of Al,Ca,Mg,S,and O in the steel decreased during the solidification and cooling *** to the difference in the cooling rate,the transformation ratio of CaS increased from 61% at the slab surface to 95% in the slab *** was also affected by the size of inclusions as smaller inclusions provided better kinetic *** diameters of inclusions for the composition transformation were *** the hot rolling process,the average aspect ratio of inclusions increased from 1.4 in the slab to 2.8 in the rolled *** the hot rolling process,a part of inclusions was crushed into small particles of CaS phase and Al_(2)O_(3)-CaO-MgO cores,leading to a decrease in CaS content of inclusions.

关键词： Inclusion Pipeline steel Continuous casting Hot rolling Deformation

A Weibo local network growth model constructed from the perspective of following-followed

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CHINESE PHYSICS B 2024年第12期33卷 128702-128702页

作者： Nian, fu-Zhong Yao, Ran-qing Lanzhou Univ Technol Sch Comp & Commun Lanzhou 730050 Peoples R China

In order to explore the evolution process of the Weibo local network, this study first defines four factors influencing the evolution of the Weibo network. On this basis, the BA scale-free network model was enhanced by incorporating these four factors and accounting for directionality, resulting in a Weibo local network evolution model based on user attributes and behavioral similarity. The model's validity was validated by comparing simulation results with real data. The findings indicate that the Weibo local network exhibits both small-world characteristics and distinctive features. The results show that the Weibo local network exhibits both small-world characteristics and distinctive properties. The in-degree distribution follows a mixed pattern of exponential and power-law distributions, the degree-degree shows isomatching, and both the in-degree centrality and eigenvector centrality values are relatively low. This research contributes to our understanding of user behaviour in the Weibo network, and provides a structural basis for exploring the impact of Weibo network structure on information dissemination.

关键词： Weibo network user similarity attribute characteristics network evolution topology analysis 87.23.Ge 87.23.Kg 05.90.+m 89.75.-k

Availability analysis of private cloud safety computer platform based on the Markov process

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Transportation Safety and Environment 2024年第1期6卷 103-108页

作者： Limin fu Jiakun wen Southwest Jiaotong University The School of Information Science&TechnologyChengduSichuan 610097China CRSC Research&Design Institute Group Co. LtdBeijing 100070China

To ensure the correctness of train control system design and development,the ways of simulation,test and formalization were *** to the safe critical attribute of train control system,the characters related to system safety were propounded such as real time,hybrid,distribution(concurrence)and reactivity,and the specific formal methods associated with every character were introduced in *** analysis and classification of the methods were done based on their mathematical basis and applications,and their advantages and disadvantages were *** result indicates that every method has determinate limitations,which is determined by the essences of model checking and theory *** is pointed out that the presentation of new method,the expansion of existing methods and the integration of many methods will be the development trend of formalization in train control system.

关键词： safety computer Markov process cloud computing availability analysis

Convergence of the Cesaro Mean for Rational Orthonormal Bases

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Acta Mathematica Sinica,English Series 2009年第4期25卷 581-592页

作者： Ying Xiong fu Luo qing LI Key Laboratory of Applied Mathematics Hubei ProvinceFaculty of Mathematics and Computer Science Hubei UniversityWuhan 430062 P. R. China

This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided.

关键词： Cesaro mean trigonometric series rational orthonormal basis

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辽朝详稳渊源新论

古代文明（中英文） 2025年第1期19卷 117-127,M0006,M0007页

作者：田富吉林大学历史文化学院吉林长春130012

以往学界多认为辽朝详稳源于突厥语“sangun”,为将军之意。本文通过考证详稳与相温、相公、将军等概念的异同,认为辽朝详稳一词源自汉语“相”,“稳”是指契丹语语法中修饰“详”字的附加成分。辽朝详稳官职来源于突厥、回鹘、吐蕃等... 详细信息

以往学界多认为辽朝详稳源于突厥语“sangun”,为将军之意。本文通过考证详稳与相温、相公、将军等概念的异同,认为辽朝详稳一词源自汉语“相”,“稳”是指契丹语语法中修饰“详”字的附加成分。辽朝详稳官职来源于突厥、回鹘、吐蕃等边疆民族之“相”制,又在“会同改制”过程中脱离其原义,遂成为一种特殊的部族官职。

关键词：辽朝详稳相相温国相

The Support of the Solution for Stochastic Differential Equations Driven by G-Brownian Motion

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Acta Mathematica Sinica,English Series 2012年第12期28卷 2417-2430页

作者： fu qing GAO Ming Zhou XU Department of Mathematics and Statistics Wuhan University

By a linear interpolation approximation method, we obtain a characterization of the support of the solution for stochastic differential equations driven by G-Brownian motion.

关键词： G-Brownian motion G-stochastic differential equation support theorem

Local functional Limit Theorems of Increments for Brownian Motion

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Acta Mathematica Sinica,English Series 2018年第7期34卷 1074-1086页

作者： fu qing GAO Yong Hong LIU School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin 541004 P. R. China

In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy＇s modulus of contin... 详细信息

关键词： Keywords Brownian motion increment local functional limit rate of convergence large deviation small deviation