A long-time tail for random walk in random scenery

Consider a simple random walk on ^d whose sites are colored black or white independently with probabilityq, resp. 1–q. Walk and coloring are independent. Letn _k be the number of steps by the walk between itskth and (k+1) th visits to a black site (i.e., the length of itskth white run), and let _k =E(n _k )–q ^–1. Our main result is a proof that (*) lim _k k ^d/2 _k = (1 –q)q ^{d/2 – 2}(d/2) ^d/2. Since it is known thatq ^{– 1} _k =E(n ₁ n _{k + 1} B) –E(n ₁ B)E(n _{k + 1} B), withB the event that the origin is black, (*) exhibits a long-time tail in the run length autocorrelation function. Numerical calculations of _k (1k100) ind=1, 2, and 3 show that there is an oscillatory behavior of _k for smallk. This damps exponentially fast, following which the power law sets in fairly rapidly. We prove that if the coloring is not independent, but is convex in the sense of FKG, then the decay of _k cannot be faster than (*).     

基于时域约束的卷帘曝光星敏感器星点校正方法

针对卷帘曝光模式星敏感器动态星点成像形状畸变和成像位置误差导致的导航星点定位精度降低、测姿误差增大的问题,提出了一种基于时域约束的导航星点校正方法.基于卷帘曝光的时间异步性特点,结合基于卡尔曼滤波的导航星点位置和帧间速度最优估计,将时域中不同时刻的导航星点校正到相同时刻,从而有效地解决星点畸变与位置偏移问题.展开了不同...     

Observations of Bell Inequality Violations with Causal Isolation between Source and Detectors

We report the experimental observations of Bell inequality violations (BIV) in entangled photons causally separated by a rotating mirror. A Foucault mirror gating geometry is used to causally isolate the entangled photon source and detectors. We report an observed BIV of CHSH-S=2.30±0.07>2.00. This result rules out theories that explain correlations with traveling communication between source and detectors, including super-luminal and instantaneous communication.     

Dynamic Programming BN Structure Learning Algorithm Integrating Double Constraints under Small Sample Condition

The Bayesian Network (BN) structure learning algorithm based on dynamic programming can obtain global optimal solutions. However, when the sample cannot fully contain the information of the real structure, especially when the sample size is small, the obtained structure is inaccurate. Therefore, this paper studies the planning mode and connotation of dynamic programming, restricts its process with edge and path constraints, and proposes a dynamic programming BN structure learning algorithm with double constraints under small sample conditions. The algorithm uses double constraints to limit the planning process of dynamic programming and reduces the planning space. Then, it uses double constraints to limit the selection of the optimal parent node to ensure that the optimal structure conforms to prior knowledge. Finally, the integrating prior-knowledge method and the non-integrating prior-knowledge method are simulated and compared. The simulation results verify the effectiveness of the method proposed and prove that the integrating prior knowledge can significantly improve the efficiency and accuracy of BN structure learning.     

On Fourier-Based Inequality Indices

Inequality indices are quantitative scores that take values in the unit interval, with a zero score denoting complete equality. They were originally created to measure the heterogeneity of wealth metrics. In this study, we focus on a new inequality index based on the Fourier transform that demonstrates a number of intriguing characteristics and shows great potential for applications. By extension, it is demonstrated that other inequality measures, such as the Gini and Pietra indices, can be usefully stated in terms of the Fourier transform, allowing us to illuminate characteristics in a novel and straightforward manner.     

低约束试件断裂韧性测试方法研究进展 1)

低约束试件断裂韧性测试对油气管道安全运营具有重要意义。本文回顾了低约束试件断裂韧性测试方法及发展过程,介绍了裂纹尖端张开位 移(crack tip opening displacement, CTOD)和J积分等常用断裂韧性表征参数,并对断裂韧性测试中应力强度因子、J积分塑性因子、J积分与CTOD转换因子、裂纹尺寸测量方法、数 字图像相关方法等关键问题进行对比分析,总结需要深入研究的问题,为低约束试件断裂韧性测试发展提供一定依据。     

An FEM approximation for a fourth-order variational inequality of second kind

A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.     

蒸发器支撑板板孔精密测量系统

建立了蒸发器支撑板板孔精密测量系统,并提出了基于边缘约束条件的轮廓参量测量方法.首先采用图像处理技术将待测目标转化为二维离散坐标点,计算其最小外接矩形并对轮廓进行预定位;然后将轮廓分割成相互重合的扩展邻域轮廓,建立以曲率角为原则的边缘约束算法对各轮廓段精确定界,实现对轮廓参量的精密测量.实验和误差分析表明,该系统测量准确度优于0.02mm,对具有复杂轮廓的零件参量测量有参考价值.     

A Hardy–Trudinger–Moser Inequality Involving LpNorm in the Hyperbolic Space

Let B be the unit disc in R~2, H be the completion of C_0∞(B) under the norm■ .By the method of blow-up analysis and an argument of rearrangement with respect to the standard hyperbolic metric ■, we prove that, for any fixed■ ,the supremum■ .This is an analog of early results of Lu–Yang(Discrete Contin. Dyn. Syst., 2009) and Yang(Trans.Amer. Math. Soc., 2007), and extends those of Wang–Ye(Adv. Math., 2012) and Yang–Zhu(Ann.Global Anal. Geom., 2016).     

Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems

This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems. Firstly, the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action. Secondly, the determining equations and structure equation of Lie symmetry of the system are obtained. Thirdly, the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems. Finally, an example is discussed to illustrate the application of the results.