部分相干环状偏心光束通过海洋湍流的传输特性

推导出了部分相干环状偏心光束在海洋湍流中传输的平均光强和光束质心位置的解析表达式, 并给出了最大光强位置满足的传输方程. 研究发现: 经足够长距离传输后, 在自由空间中最大光强位置比光束质心更靠近传输z轴, 并且其位置随着光束相干参数的增大而靠近传输z 轴, 随着光束偏心参数和遮拦比的增大而远离传输z轴. 但是, 在海洋湍流中最大光强位置趋于质心位置, 并且海洋湍流的增强会加速最大光强位置趋于质心位置的进程. 在海洋湍流中光束的相干性对光束传输特性的影响明显减小. 另一方面, 光束质心位置与光束的相干性、光束传输距离以及海洋湍流均无关系, 并且光束质心位置随着光束偏心参数和遮拦比的增大而远离传输z 轴. 所得结果对工作于水下湍流环境中的部分相干环状偏心光束的应用具有重要意义.     

STUDY ON DAMAGE BIFURCATION AND INSTABILITY OF ROCK-LIKE MATERIALS

The critical bifurcation orientation and its corresponding hardening modulus for rock-like geomaterials are derived by considering the effect of stiffness degradation and volumetric dilatancy under the assumption of isotropic damage. The dependency of the localized orientation on the degree of damage and initial Poisson's ratio of rock is examined and the bifurcation behavior of the uniaxial compression sample under the plane-stress condition is compared with that under plane-strain condition. It is shown that the localization orientation angle intimately depends on both the initial Poisson's ratio and degree of damage for the rock sample under the uniaxial compression condition. As the initial Poisson's ratio or degree of damage increases, the orientation angle of the plane on which localization tends to be initiated gets to decrease. At the same time, the localization orientation angle of a rock sample under the plane-stress condition is larger than that under the plane-strain condition.     

Joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples

In this paper, we obtain the joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also obtained.     

最大度与最小度相差不超过2的图的平衡judicious划分

图G的顶点集V(G)的一个二部划分V_1和V_2叫做平衡二部划分,如果||V_1|-|V_2||≤1成立.Bollobas和Scott猜想:每一个有m条边且最小度不小于2的图,都存在一个平衡二部划分V_1,V_2,使得max{e(V_1),e(V_2)}≤m/3,此处e(V_i)表示两顶点都在V_i(i=1,2)中的边的条数.他们证明了这个猜想对正则图(即△(G)=δ(G))成立.颜娟和许宝刚证明了每个(k,k-1)-双正则图(即△(G)-δ(G)≤1)存在一个平衡二部划分V_1,V_2,使得每一顶点集的导出子图包含大约m/4条边.这里把该结论推广到最大度和最小度相差不超过2的图G.     

一类状态受限的随机延迟最优控制问题的最大值原理

本文考虑一类状态受限的随机延迟最优控制问题,其中控制域为凸集且扩散项系数中含有控制变量.控制域可以是无界集合.用最大值原理方法建立了最优控制满足的必要条件.也给出了充分最优性条件,从而有助于找到最优控制.     

Understanding chicken walks on n × n grid: Hamiltonian paths,discrete dynamics,and rectifiable paths

Understanding animal movements and modeling the routes they travel can be essential in studies of pathogen transmission dynamics. Pathogen biology is also of crucial importance, defining the manner in which infectious agents are transmitted. In this article, we investigate animal movement with relevance to pathogen transmission by physical rather than airborne contact, using the domestic chicken and its protozoan parasite Eimeria as an example. We have obtained a configuration for the maximum possible distance that a chicken can walk through straight and nonoverlapping paths (defined in this paper) on square grid graphs. We have obtained preliminary results for such walks which can be practically adopted and tested as a foundation to improve understanding of nonairborne pathogen transmission. Linking individual nonoverlapping walks within a grid‐delineated area can be used to support modeling of the frequently repetitive, overlapping walks characteristic of the domestic chicken, providing a framework to model fecal deposition and subsequent parasite dissemination by fecal/host contact. We also pose an open problem on multiple walks on finite grid graphs. These results grew from biological insights and have potential applications. © 2014 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.     

Maximum principle for optimal distributed control of viscous weakly dispersive Degasperis–Procesi equation

This paper is concerned with the optimal distributed control of the viscous weakly dispersive Degasperis–Procesi equation in nonlinear shallow water dynamics. It is well known that the Pontryagin maximum principle, which unifies calculus of variations and control theory of ordinary differential equations, sets up the theoretical basis of the modern optimal control theory along with the Bellman dynamic programming principle. In this paper, we commit ourselves to infinite dimensional generalizations of the maximum principle and aim at the optimal control theory of partial differential equations. In contrast to the finite dimensional setting, the maximum principle for the infinite dimensional system does not generally hold as a necessary condition for optimal control. By the Dubovitskii and Milyutin functional analytical approach, we prove the Pontryagin maximum principle of the controlled viscous weakly dispersive Degasperis–Procesi equation. The necessary optimality condition is established for the problem in fixed final horizon case. Finally, a remark on how to utilize the obtained results is also made. Copyright © 2015 John Wiley & Sons, Ltd.     

一个新的具有单调降失效率的寿命分布

本文由Pareto分布和Logarithmic分布"混合"生成两参数具有单调降失效率的新型寿命分布,研究了该分布的矩、熵、失效率函数、平均剩余寿命和参数的极大似然估计,应用EM算法求参数的极大似然估计,进行了数值模拟.     

光滑平稳高斯过程极值几乎处处极限定理的一个推广

本文研究了连续均方可微的平稳高斯过程的极限性态. 通过选择一个不同于Tan (2013) 的权重函数, 在较弱的条件下得到了连续均方可微平稳高斯过程极值的一个几乎必然仅限定理, 推广了Tan(2013) 的结论.     

Multivariate measurement error models for replicated data under heavy‐tailed distributions

In this paper, we deal with multivariate measurement error models for replicated data under heavy‐tailed distributions, providing appealing robust and adaptable alternatives to the usual Gaussian assumptions. The models contain both error‐prone covariates and predictors measured without errors. The surrogates of the response and the multiple error‐prone covariates are replicated and are allowed unpaired and/or unequal cases. Under the scale mixtures of normal distribution class, we provide an explicit iterative formula of the maximum likelihood estimation via an expectation‐maximization‐type algorithm. Closed forms of asymptotic variances of the estimators are also given. The effect and robustness performances are confirmed by the simulation studies. Two real data sets are analyzed by the proposed models. Copyright © 2015 John Wiley & Sons, Ltd.