Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.     

一类具有红灯环境下随机游动的极限性态

就某类红灯随机环境下随机游动{Xn}n∈Z ,建立相应的Markov-双链{ηn}n∈Z ={(Xn,Tn)}n∈Z ;并给出在该红灯环境下,{Xn}n∈Z 的发展受红灯环境影响的关系式;以及由此关系式得出:由于红灯环境的影响减缓了{Xn}n∈Z 的发展速度.     

随机单调的离散时间马氏链强遍历速度的估计I

研究了离散时间马氏链的强遍历性,对随机单调的离散时间马氏链,给出了最大强遍历收敛速度的下界估计。     

单位球上βP空间到Za型空间的加权Cesàro算子

利用泛函分析多复变的方法,研究了单位球上βP空间到Za空间的加权Cesàro算子的有界性和紧性问题.获得了单位球上βP空间到Za空间的加权Cesàro算子为有界算子和紧算子的充要条件.     

多圆柱上μBloch空间之间的加权Cesàro算子

分别给出了多圆柱上μ-Bloch空间βμ之间、βμ,0空间之间的加权Cesàro算子Tg为有界算子和紧算子的充要条件.     

单位球上μ-Bloch空间到Zygmund型空间的加权Cesàro算子

设α>0,g是单位球B上的全纯函数,μ(r)是［0,1）上的正规权函数,利用泛函分析多复变的方法,讨论了单位球上μ-Bloch空间到Zygmund型空间的加权Cesàro算子T_g的有界性和紧性问题.并给出了单位球上μ-Bloch空间到Zygmund型空间的加权Cesàro算子T_g为有界算子和紧算子的充要条件.     

利用四元数方法研究各态遍历偏振态发生器

各态遍历偏振态发生器(PSG)是偏振测量不可或缺的基本设备,偏振态和偏振器件的描述对于编写偏振态发生器的控制算法是至关重要的。采用四元数来描述和分析各态遍历偏振态发生器中偏振态与偏振控制器,导出了三级偏振控制器的四元数公式,得到了描述其旋转轴与旋转角度的公式。实验测量了单级偏振控制器的四元数,得到了普通单模光纤受挤压时对应的应力四元数公式以及改变电压时的四元数公式,利用该公式编制的算法,实现了各态遍历的偏振态发生器。     

Some ergodic theorems for a parabolic Anderson model

In this paper,we study some ergodic theorems of a class of linear systems of interacting diffusions,which is a parabolic Anderson model.First,under the assumption that the transition kernel a=(a(i,j)) i,j∈s is doubly stochastic,we obtain the long-time convergence to an invariant probability measure νh starting from a bounded a-harmonic function h based on self-duality property,and then we show the convergence to the invariant probability measure νh holds for a broad class of initial distributions.Second,if(a(i,j)) i,j∈S is transient and symmetric,and the diffusion parameter c remains below a threshold,we are able to determine the set of extremal invariant probability measures with finite second moment.Finally,in the case that the transition kernel(a(i,j)) i,j∈S is doubly stochastic and satisfies Case I(see Case I in [Shiga,T.:An interacting system in population genetics.J.Math.Kyoto Univ.,20,213-242(1980)]),we show that this parabolic Anderson model locally dies out independent of the diffusion parameter c.     

Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods

We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue problem.By using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the lower bound of the eigenvalue.Additionally,we use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue,which only needs to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented.Thus,we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once.Some numerical results are also presented to demonstrate our theoretical analysis.     

广义{1,3,5}-{1,4,5}自相似集的Lipschitz 等价

讨论广义{1,3,5}-{1,4,5}自相似集D=(r₁D)∪(r₂D+ (1+r₁-r₂-r₃)/2)∪(r₃ D+1-r₃)以及E=(r₁E)∪(r₂E+1-r₂-r₃)∪(r₃E+1-r₃)的Lipschitz等价性, 并证明了D与E为Lipschitz等价当且仅当存在正整数m和n, 使得 r₁^m=r₃ⁿ.