We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logari...We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.展开更多
目的阐述含水率对非饱和砂土热传导系数的影响,为模型的参数选择提供科学依据.方法选用分选良好的粗砂、中砂和细砂以及毛乌素沙地的风积沙作为实验介质,利用JW-Ⅲ型热流计测定不同含水率条件下砂土的热传导系数,绘制热传导系数和含水...目的阐述含水率对非饱和砂土热传导系数的影响,为模型的参数选择提供科学依据.方法选用分选良好的粗砂、中砂和细砂以及毛乌素沙地的风积沙作为实验介质,利用JW-Ⅲ型热流计测定不同含水率条件下砂土的热传导系数,绘制热传导系数和含水率的关系曲线,运用非线性最小二乘法对实测数据与常用的热传导系数模型Campbell及Chung and Horton模型进行拟合.结果含水率在0～5%内热导率急剧增长,当含水率>10%时热导率的增长缓慢并趋于稳定.两模型基本能反映各试验介质的热传导系数和含水率的变化规律,对于扰动样该模型在含水率较小时不能很好地表征其变化规律.结论随着含水率的增加热导率值增加速率不同.在利用预测模型和经验公式时,应利用实测数据对其进行校正,减小误差.展开更多
Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 ＋... ＋ Xn, n≥1. The author proves that, if EX^2I{｜X｜≥t} = 0（（log log t）^-1） as t→∞, then for ...Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 ＋... ＋ Xn, n≥1. The author proves that, if EX^2I{｜X｜≥t} = 0（（log log t）^-1） as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1＋a（1/√1＋a-ε）b＋1 ∑n=1^∞（logn）^a（loglogn）^b/nP{max κ≤n｜Sκ｜≤√σ^2π^2n/8loglogn（ε＋an）}=4/π（1/2（1＋a）^3/2）^b＋1 Г（b＋1）,whenever an = o（1/log log n）. The author obtains the sufficient and necessary conditions for this kind of results to hold.展开更多
Let XH = {xH（t）,t ∈ R＋} be a subfractional Brownian motion in Rd. We provide asufficient condition for a self-similar Gaussian process to be strongly locally nondeterministic and show that XH has the property of s...Let XH = {xH（t）,t ∈ R＋} be a subfractional Brownian motion in Rd. We provide asufficient condition for a self-similar Gaussian process to be strongly locally nondeterministic and show that XH has the property of strong local nondeterminism. Applying this property and a stochastic integral representation of XH, we establish Chung＇s law of the iterated logarithm for XH.展开更多
1 Introduction Imagery of the Western United States typically evokes vast wheat fields,cowboys,and rolling mountain valleys.Few would associate the American West with Chinese medicine.This article describes a remote t...1 Introduction Imagery of the Western United States typically evokes vast wheat fields,cowboys,and rolling mountain valleys.Few would associate the American West with Chinese medicine.This article describes a remote town called John Day,which is located in a mountainous terrain in Oregon,and presents the remarkable story of the Kam Wah Chung Museum(Fig.1).展开更多
Let {β（s）,s ≥ O} be the standard Brownian motion in R^d with d ≥ 4 and let ｜Wr（t）｜ be the volume of the Wiener sausage associated with {β（s）, s ≥ O} observed until time t. Prom the central limit theorem o...Let {β（s）,s ≥ O} be the standard Brownian motion in R^d with d ≥ 4 and let ｜Wr（t）｜ be the volume of the Wiener sausage associated with {β（s）, s ≥ O} observed until time t. Prom the central limit theorem of Wiener sausage, we know that when d ≥ 4 the limit distribution is normal. In this paper, we study the laws of the iterated logarithm for ｜Wr（t）｜ - e｜Wr（t）｜ in this case.展开更多
In about 1949,there was a large-scale migration of architects from the mainland to Hong Kong,China.Among them were those important figures in the modern Chinese architectural history such as Robert Fan,Su Gin-Djih,and...In about 1949,there was a large-scale migration of architects from the mainland to Hong Kong,China.Among them were those important figures in the modern Chinese architectural history such as Robert Fan,Su Gin-Djih,and Chu Pin.Their arrival at this colony had changed its architectural practice substantially from professional organization to actually built environment.Their unique contributions to Hong Kong’s modern architecture have been a new research interest in recent years.This paper tells a story about Robert Fan and his design of the Chung Chi College campus in the 1950s with an intention to reveal the multiaspects of the so called“migrant architects”through a single architectural event.The author tries to capture the intertwining relationship between the migrant architects and educators through the reconstruction of the recruitment process for a campus architect by Chung Chi College and to identify Mr.Robert Fan’s concept of campus planning with reference to his early design experience in the mainland of China.展开更多
In this paper,we investigate functional limit problem for path of a Brownian sheet,Chung’s functional law of the iterated logarithm for a Brownian sheet is obtained.The main tool in the proof is large deviation and s...In this paper,we investigate functional limit problem for path of a Brownian sheet,Chung’s functional law of the iterated logarithm for a Brownian sheet is obtained.The main tool in the proof is large deviation and small deviation for a Brownian sheet.展开更多
基金This research supported by Grants from the National Natural Science Foundation of China(No.11225104)and the Fundamental Research Funds for the Central Universities.
文摘We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.
文摘目的阐述含水率对非饱和砂土热传导系数的影响,为模型的参数选择提供科学依据.方法选用分选良好的粗砂、中砂和细砂以及毛乌素沙地的风积沙作为实验介质,利用JW-Ⅲ型热流计测定不同含水率条件下砂土的热传导系数,绘制热传导系数和含水率的关系曲线,运用非线性最小二乘法对实测数据与常用的热传导系数模型Campbell及Chung and Horton模型进行拟合.结果含水率在0～5%内热导率急剧增长,当含水率>10%时热导率的增长缓慢并趋于稳定.两模型基本能反映各试验介质的热传导系数和含水率的变化规律,对于扰动样该模型在含水率较小时不能很好地表征其变化规律.结论随着含水率的增加热导率值增加速率不同.在利用预测模型和经验公式时,应利用实测数据对其进行校正,减小误差.
基金National Natural Science Foundation of China (No.10471126)
文摘Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 ＋... ＋ Xn, n≥1. The author proves that, if EX^2I{｜X｜≥t} = 0（（log log t）^-1） as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1＋a（1/√1＋a-ε）b＋1 ∑n=1^∞（logn）^a（loglogn）^b/nP{max κ≤n｜Sκ｜≤√σ^2π^2n/8loglogn（ε＋an）}=4/π（1/2（1＋a）^3/2）^b＋1 Г（b＋1）,whenever an = o（1/log log n）. The author obtains the sufficient and necessary conditions for this kind of results to hold.
基金Supported by NSFC(Grant Nos.11201068,11671041)“the Fundamental Research Funds for the Central Universities”in UIBE(Grant No.14YQ07)
文摘Let XH = {xH（t）,t ∈ R＋} be a subfractional Brownian motion in Rd. We provide asufficient condition for a self-similar Gaussian process to be strongly locally nondeterministic and show that XH has the property of strong local nondeterminism. Applying this property and a stochastic integral representation of XH, we establish Chung＇s law of the iterated logarithm for XH.
文摘1 Introduction Imagery of the Western United States typically evokes vast wheat fields,cowboys,and rolling mountain valleys.Few would associate the American West with Chinese medicine.This article describes a remote town called John Day,which is located in a mountainous terrain in Oregon,and presents the remarkable story of the Kam Wah Chung Museum(Fig.1).
基金Supported by National Natural Science Foundation of China （Grant No. 10871153）
文摘Let {β（s）,s ≥ O} be the standard Brownian motion in R^d with d ≥ 4 and let ｜Wr（t）｜ be the volume of the Wiener sausage associated with {β（s）, s ≥ O} observed until time t. Prom the central limit theorem of Wiener sausage, we know that when d ≥ 4 the limit distribution is normal. In this paper, we study the laws of the iterated logarithm for ｜Wr（t）｜ - e｜Wr（t）｜ in this case.
基金cosponsored by Chung Chi College of The Chinese University of Hong Kong and a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project no.CUHK4668/06H/2007/Architecture).
文摘In about 1949,there was a large-scale migration of architects from the mainland to Hong Kong,China.Among them were those important figures in the modern Chinese architectural history such as Robert Fan,Su Gin-Djih,and Chu Pin.Their arrival at this colony had changed its architectural practice substantially from professional organization to actually built environment.Their unique contributions to Hong Kong’s modern architecture have been a new research interest in recent years.This paper tells a story about Robert Fan and his design of the Chung Chi College campus in the 1950s with an intention to reveal the multiaspects of the so called“migrant architects”through a single architectural event.The author tries to capture the intertwining relationship between the migrant architects and educators through the reconstruction of the recruitment process for a campus architect by Chung Chi College and to identify Mr.Robert Fan’s concept of campus planning with reference to his early design experience in the mainland of China.
基金supported by the Natural Science Foundation of Guangxi(Grant No.2020GXNSFAA159118)Guangxi Science and Technology Project(Grant No.Guike AD20297006)the Innovation Project of School of Mathematics and Computing Science of GUET Graduate Education(Nos.2021YJSCX05,2022YJSCX04)。
文摘In this paper,we investigate functional limit problem for path of a Brownian sheet,Chung’s functional law of the iterated logarithm for a Brownian sheet is obtained.The main tool in the proof is large deviation and small deviation for a Brownian sheet.
