随机条件概率的一个极限性质与条件矩母函数方法

设Ｘｎ,ｎ〉０是在ｓ＝１,２,…,Ｎ中取值的一列随机变量,ｐｋ（ｘｋ↓ｘ０,…ｘｋ－１）＝ｐ（Ｘｋ＝ｘｋ↓Ｘ０＝ｘｋ－１＝ｘｋ－１）。本文得到随机概率｛ｐｋ（Ｘｋ↓Ｘ０,…Ｘｋ－１）,１〈ｋ〈ｎ↓）的调和平均ａ．ｅ．收敛的一个定理．证明中提出了将关开网的微分法和条件矩母函数的工具应用于强极限定理的研究的一种途径。     

Longtime Behaviour of Stochastic Hamiltonian Systems: The Multidimensional Case

Hamiltonian systems perturbed by a white noise force are discussed in several dimensions. By using an appropriate scaling of the stochastic force a convergence theorem for the invariants of the deterministic motion is proved. This corresponds to convergence of the system to a stationary distribution. Especially motion in a central force field is considered; the energy and angular momentum processes are investigated.     

关于随机选择的一个强极限定理

本文利用似然比和区间剖分法研究相依Ｎ值随机变量序列选择的极限性质,得到关于赌博方法的一个强极限定理的若干推广。     

相依二值随机变量序列游程的一类强极限定理

本文利用文献[1]与[2]中提出的方法和思想,研究相依二值随机变量序列游程的极限性质,得到游程平均数的一类强极限定理.     

Gaussian spectral rules for second order finite-difference schemes

Earlier the authors suggested an algorithm of grid optimization for a second order finite-difference approximation of a two-point problem. The algorithm yields exponential superconvergence of the Neumann-to-Dirichlet map (or the boundary impedance). Here we extend that approach to PDEs with piecewise-constant coefficients and rectangular homogeneous subdomains. Examples of the numerical solution of the 2-dimensional oscillatory Helmholtz equation exhibit exponential convergence at prescribed points, where the cost per grid node is close to that of the standard five-point finite-difference scheme. Our scheme demonstrates high accuracy with slightly more than two grid points per wavelength and reduces the grid size by more than three orders as compared with the standard scheme.     

一类五次多项式系统的奇点量与极限环分支

该文研究一类五次多项式微分系统在高次奇点与无穷远点的极限环分支问题. 该系统的原点是高次奇点, 赤道环上没有实奇点. 首先推导出计算高次奇点与无穷远点奇点量的代数递推公式,并用之计算系统原点、无穷远点的奇点量，然后分别讨论了系统原点、无穷远点中心判据. 给出了多项式系统在高次奇点分支出5个极限环同时在无穷远点分支出2个极限环的实例. 这是首次在同步扰动的条件下讨论高次奇点与无穷远点分支出极限环的问题.     

Charge coupled devices （CCD） photometry and long-term optical variability of gamma-ray-loud BL Lacertae object Mkn 421

Evidence for the long-term optical curve variability and colour behaviour of the BL Lac object Mkn 421 is presented. Our results show that the amplitude of the optical variations of Mkn 421 is only about {\Delta} B=4.7 magnitude in the B-band for its photometric history from 1899 to 2002. The results of optical photometric monitoring of the Mkn 421 from April 2000 to Jan 2002 are provided. During our observation, Mkn 421 shows significant rapid variations and exhibits short time variability of 2.42 hours in the B band. A strong correlation between the B-V colour index and the magnitude in the B band is found. Our charge coupled device (CCD) photometry of Mkn 421 shows that the measured results are in good agreement with the predicted optical variability period of about 23 years.     

Quantum logic gates with two-level trapped ions beyond Lamb--Dicke limit

In the system with two two-level ions confined in a linear trap, this paper presents a simple scheme to realize the quantum phase gate (QPG) and the swap gate beyond the Lamb--Dicke (LD) limit. These two-qubit quantum logic gates only involve the internal states of two trapped ions. The scheme does not use the vibrational mode as the data bus and only requires a single resonant interaction of the ions with the lasers. Neither the LD approximation nor the auxiliary atomic level is needed in the proposed scheme. Thus the scheme is simple and the interaction time is very short, which is important in view of decoherence. The experimental feasibility for achieving this scheme is also discussed.     

Modified Wave Particle Duality and Black Hole Physics

de Broglie relation is revisited, in consideration of a generalization of canonical commuting relation. The possible effects on particle's localization and black hole physics are also discussed, in a heuristic manner.     

Stratified model for estimating fatigue crack growth rate of metallic materials

Introduction Thefatiguedestructionisoneofthemaintypesofthemetaldamage.Therelationcurve betweenthefatiguecrackgrowthrateda/dNandthestressstrengthfactoramplitudeΔKisthe importantdatiumoffatiguecapabilityindesigningthemetaldamagetolerantlimitsandpredicting thelifeofmetalcomponentparts.Duetovariabilityofthefatiguecrackgrowthrate,alarge amountoftestsamplesareusuallyrequiredtoderiveahighlyreliableda/dN_ΔKcurve. However,inmostactualengineeringpractice,itishardtofindmultiplespecimenswithvery simil…