By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing...By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.展开更多
To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simul...To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simulate the two-phase random media, such that the soil(or rock) volume fraction and the inclination of the soil layer can be examined. The finite element method with random media incorporated as the material properties is used to determine the factor of safety of the rock-soil slope. Monte-Carlo simulations are used to estimate the statistical characteristics of the factor of safety. The failure mode of the rock-soil slope is examined by observing the maximum principal plastic strain at incipient slope failure. It is found that the critical surface of a rock-soil slope is fairly irregular, and it significantly differs from that of a pure soil slope. The factor of safety is sensitive to the soil volume faction, but it is predictable. The average factor of safety could be well predicted by the weighted harmonic average between the strength of soil and rock; the prediction model is practical and simple. Parametric studies on the inclination of the soil layer demonstrate that the most instable scenario occurs when the slope angle is consistent with the inclination of the soil layer.展开更多
Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),...Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),A E A}to converge to Brownian motion.By a direct calculation,the author ahows that the result holds for a more general class of set index A,where A is assurned only to have the metric entropy exponentr,0<r<1.and the rate of nonuniform p-mixing is weakened.The result obtained essentially improve those given by Chen[1)and Goldie,Greenwood[6],etc.展开更多
基金National Natural Science Foundation of China! (No. 19701O11) Foundation of "151 talent project" of Zhejiang provience.
文摘By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.
基金supported by the International Science and Technology Cooperation Programme of Hainan Province,China (Grant No.ZDYF2016226)the National Natural Science Foundation of China(Grant No.51879203)
文摘To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simulate the two-phase random media, such that the soil(or rock) volume fraction and the inclination of the soil layer can be examined. The finite element method with random media incorporated as the material properties is used to determine the factor of safety of the rock-soil slope. Monte-Carlo simulations are used to estimate the statistical characteristics of the factor of safety. The failure mode of the rock-soil slope is examined by observing the maximum principal plastic strain at incipient slope failure. It is found that the critical surface of a rock-soil slope is fairly irregular, and it significantly differs from that of a pure soil slope. The factor of safety is sensitive to the soil volume faction, but it is predictable. The average factor of safety could be well predicted by the weighted harmonic average between the strength of soil and rock; the prediction model is practical and simple. Parametric studies on the inclination of the soil layer demonstrate that the most instable scenario occurs when the slope angle is consistent with the inclination of the soil layer.
文摘Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),A E A}to converge to Brownian motion.By a direct calculation,the author ahows that the result holds for a more general class of set index A,where A is assurned only to have the metric entropy exponentr,0<r<1.and the rate of nonuniform p-mixing is weakened.The result obtained essentially improve those given by Chen[1)and Goldie,Greenwood[6],etc.
