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Dependent sets of a family of relations of full measure on a probability space

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Science China Mathematics 2007年第4期50卷 475-484页

作者： jin-cheng xiong Feng TAN Jie Lü School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

For a probability space (X, B, μ) a subfamily F of the σ-algebra B is said to be a regular base if every B ∈ B can be arbitrarily approached by some member of F which contains B in the sense of the measure theory. Assume that {R γ } γ∈Γ is a countable family of relations of the full measure on a probability space (X, B, μ), i.e. for every γ ∈ Γ there is a positive integer s γ such that R γ ? $X^{s_\gamma } $ with $\mu ^{s_\gamma } $ (R γ ) = 1. In the present paper we show that if (X, B, μ) has a regular base, the cardinality of which is not greater than the cardinality of the continuum, then there exists a set K ? X with μ*(K) = 1 such that (x 1, …, $x_{^{s_\gamma } } $ ) ∈ R γ for any γ ∈ Γ and for any s γ distinct elements x 1, …, $x_{^{s_\gamma } } $ of K, where μ* is the outer measure induced by the measure μ. Moreover, an application of the result mentioned above is given to the dynamical systems determined by the iterates of measure-preserving transformations.

关键词： probability space measure-preserving transformation dependent set chaos dynamical system 28A12 28A35 37A05

Furstenberg family and chaos

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Science China Mathematics 2007年第9期50卷 1325-1333页

作者： jin-cheng xiong Jie LU Feng TAN School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

A Furstenberg family F is a family,consisting of some subsets of the set of positive integers,which is hereditary upwards,i.e.A?B and A∈F imply B∈*** a given system(i.e.,a pair of a complete metric space and a continuous self-map of the space)and for a Furstenberg family F,the definition of F-scrambled pairs of points in the space has been given,which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be F-scrambled pairs corresponding respectively to suitable Furstenberg family *** the present paper we explore the basic properties of the set of F-scrambled pairs of a *** generically F-chaotic system and the generically strongly F-chaotic system are defined.A criterion for a generically strongly F-chaotic system is showed.

关键词： Furstenberg family scrambled pair scrambled set generically F-chaotic map generically strongly chaotic map

Three-dimensional fracture of UO2 ceramic pellets by phase field modeling

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Science China(Physics,Mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 169-180页

作者： Wei xiong Xuan Ye Hongzhang cheng Xiaoming Liu Institute of Nuclear and New Energy Technology Collaborative Innovation Center of Advanced Nuclear Energy Technology Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences School of Engineering Science University of Chinese Academy of Sciences

Fracture is the primary failure type for the UO2ceramic pellets,which are operated under irradiation and thermal processes,and physically confined by the *** this work,by combining closely coupled physical processes of heat conduction,heat transfer,and mechanical deformation with the cohesive phase field framework,we proposed a high-precision modeling of quasistatic cracking of three-dimensional （3D） UO2ceramic fuel pellets under high temperature and *** simulation results agree well with the experimental results,indicating that the proposed method has the potential to capture 3D crack modes in the interested time ***,we studied the relation of the 3D fracture patterns of fuel pellets with the peak power *** was found that the power level plays a critical role in determining the competition between radial and circumferential cracks,as well as transverse penetrating cracks.

关键词： phase field method nuclear fuel pellet coupled thermo-mechanical model thermal fracture

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基于Copula的车轮Gamma退化过程

东北大学学报（自然科学版） 2021年第4期42卷 544-549,566页

作者：吕昊金雄程林录样东北大学机械工程与自动化学院辽宁沈阳110819

通过Gamma随机过程描述机车轮缘与滚动圆直径的磨耗过程,研究了运用Copula函数和四阶矩方法计算轮缘退化与滚动圆直径退化的相关可靠性方法,通过动力学软件仿真得到列车不同阶段的动力学指标.研究了镟修周期为20万km的车轮退化过程的可... 详细信息

通过Gamma随机过程描述机车轮缘与滚动圆直径的磨耗过程,研究了运用Copula函数和四阶矩方法计算轮缘退化与滚动圆直径退化的相关可靠性方法,通过动力学软件仿真得到列车不同阶段的动力学指标.研究了镟修周期为20万km的车轮退化过程的可靠性及车轮直径退化过程的灵敏度,利用Monte Carlo仿真(MCS)验证了该方法的正确性.结果表明:镟修周期为20万km时车轮达到预期寿命的可靠性高,基于Copula函数相关失效退化模型计算的可靠性高于独立失效模型计算的可靠性,轮径退化可靠性模型的灵敏度研究说明镟修过程中应该要选取对轮径削减较少的方案.

关键词： Gamma过程退化过程四阶矩镟修周期可靠性维修

赣中地区周潭群斜长角闪岩年龄、成因及对华南新元古代构造演化的地质意义

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地球化学 2021年第6期50卷 537-549页

作者：程进雄李武显中国科学院广州地球化学研究所同位素地球化学国家重点实验室广东广州510640 中国科学院大学北京100049

赣中周潭地区发育的周潭群为一套高角闪岩相变质且强烈变形的火山-沉积岩组合,其形成年龄一直存在争议。本次研究对周潭群中斜长角闪岩和黑云母片岩开展了锆石U-Pb年代学和岩石地球化学研究。斜长角闪岩有两种类型的锆石,第一种变质锆... 详细信息

赣中周潭地区发育的周潭群为一套高角闪岩相变质且强烈变形的火山-沉积岩组合,其形成年龄一直存在争议。本次研究对周潭群中斜长角闪岩和黑云母片岩开展了锆石U-Pb年代学和岩石地球化学研究。斜长角闪岩有两种类型的锆石,第一种变质锆石的定年结果为(417±47) Ma,第二种捕获锆石;Pb/;U表观年龄在873~716 Ma之间。黑云母片岩中全部为碎屑锆石,锆石;Pb/;U表观年龄在861~658 Ma之间。斜长角闪岩具有平坦型的稀土分布模式和正的ε;(t)值(1.72~2.69),其Nb/La(0.73~0.94)、Nb/Y(0.10~0.12)以及Zr/Y(1.61~2.54)比值类似于洋中脊玄武岩(N-MORB);在Nb/Yb与TiO;/Yb、La与La/Nb构造判别图解中,斜长角闪岩全部落在N-MORB区域,表明斜长角闪岩来自亏损地幔。对比扬子东南缘850~760 Ma的N-MORB型基性岩的ε;(t)值、Zr/Y和Sm/Nd比值,斜长角闪岩类似于皖南铺岭组约760 Ma的基性岩,暗示它们形成于相同岩浆岩事件。结合斜长角闪岩和黑云母片岩中小于820 Ma的捕获锆石年龄,表明周潭群的顶界年龄小于760 Ma,因此周潭群不仅包含了类似于四堡群和冷家溪群等相应地层,还应该包含类似于板溪群或丹洲群等相应地层。综合本次报道的周潭群N-MORB型斜长角闪岩和前人报道的850~760 Ma双峰式火山岩、基性-超基性岩墙以及低δ;O锆石,表明华南地块从约900 Ma闭合完毕之后一直处于陆内伸展环境中。

关键词：地球化学特征斜长角闪岩周潭群年龄 N-MORB 华南

Expression of MCMV M83 mRNA in Infected Testes and Its Relationship with Testicular Lesions

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Journal of Reproduction and Contraception 2005年第3期16卷 147-156页

作者： jin-wen xiong cheng-liang xiong Yuan ZHU Yong-hongTIAN Center of Reproductive of Medicine Research Institute of Family Planning Tongji Medical College Huazhong University of Science and Technologe Wuhan 430030 China

Objective To investigate the expression of routine cytomegalovirus （MCMV） M83 mRNA in mouse testes at the different periods of MCMV infection and its relationship with the severity of testicular lesions Methods Used digoxin-labeled MCMV mRNA oligonucleotide probe, the mouse testicular tissues at the different periods following MCMV inoculation were detected by in situ hybridization（ISH）. The average absorbency （A） of ISH positive signals represented the resticular MCMV load. The expression of MCMV M83 mRNA in the infected testes and its relation with the severity of testicular lesions were analyzed. Results At different periods after MCMV inoculation, the expression of MCMV M83 mRNA was detectable in the testicular tissues. The ISH positive signals were mainly located in cytoplasm of the testicular interstitial cells. The average A values at d 9 after MCMV infection were the highest （comparison between the experimental groups, P〈O. O01）. There were pathological inJTammatory changes to varying degrees in seminiferous epithelia and interstitial cells at the diJferent periods of infection, especially during d 6 to d 9. Conclusion In testicular MCMV infection, the levels of MCMV M83 mRNA were related with the severity of testicular lesions, suggesting the dynamic detection of MCMV M83 mRNA could evaluate the prognosis of MCMV infection.

关键词： muring cytomegalovirus M83 gene in situ hybridization(ISH) testis

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周期吸附系统的分布混沌

数学学报（中文版） 2008年第6期51卷 1109-1114页

作者：吕杰熊金城谭枫华南师范大学数学科学学院广州510631

由一个紧致度量空间X以及连续映射f:X→X所组成的偶对(X,f)称之为一个动力系统.若存在f的不动点p以及另一周期点q,使得对于任一非空开集U(?)X,都有∪_(n=0)~∞f^n(U)含有p和q,则称(X,f)是一个周期吸附系统,其中f^i表示f的i次迭代.本文指... 详细信息

由一个紧致度量空间X以及连续映射f:X→X所组成的偶对(X,f)称之为一个动力系统.若存在f的不动点p以及另一周期点q,使得对于任一非空开集U(?)X,都有∪_(n=0)~∞f^n(U)含有p和q,则称(X,f)是一个周期吸附系统,其中f^i表示f的i次迭代.本文指出:若(X,f)是一个周期吸附系统并且X是自密的,则存在一个f的分布混沌集D,使得D与每一非空开集之交都包含着一个Cantor集.

关键词：分布混沌周期吸附系统动力系统

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(F_1,F_2)-攀援集的一些注记

数学学报（中文版） 2010年第4期53卷 727-732页

作者：李占红汪火云熊金城广州大学数学与信息科学学院广州510006 华南师范大学数学科学学院广州510631

研究(F_1,F_2)-攀援集的迭代不变性.定义了与正整数k相关的Furstenberg族的性质P(k)和Q(k).指出:对任意介于0,1之间的实数s而言,Furstenberg族M(s)具有性质P(k)和Q(k),其中■(s)表示非负整数集的所有上密度不小于s的无限子集构成的集族... 详细信息

研究(F_1,F_2)-攀援集的迭代不变性.定义了与正整数k相关的Furstenberg族的性质P(k)和Q(k).指出:对任意介于0,1之间的实数s而言,Furstenberg族M(s)具有性质P(k)和Q(k),其中■(s)表示非负整数集的所有上密度不小于s的无限子集构成的集族.据此证明了:对任意正整数k,S为系统(X,f)的(■(s),■(t))-攀援集当且仅当S为系统(X,f^k)的(■(s),■(t))-攀援集,其中s,t是介于0,1之间的任意给定的实数.

关键词： Furstenberg族攀援集混沌

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数据仓库中的数据清洗

医学信息 2008年第11期21卷 1939-1943页

作者：刘玉陈金雄福州大学物理与信息工程学院南京军区福州总医院

本文以病种分析为例,介绍了在数据仓库中数据清洗的方法――二次清洗法,二次清洗完成的工作是不同的,第一次的清洗主要负责清洗源数据中的"脏数据",第二次清洗则负责维度的提取。

关键词：数据清洗二次清洗数据仓库