转动系统的相对论性分析力学理论

本文讨论了转动相对论力学理论，主要是建立转动系统的相对论性分析力学理论·构造转动系统的相对论性广义动能函数Ｔｒ＝∑ｎｉ＝１Ｉ０ｉΓｉ２（１－１－θ·２ｉ／Γｉ２）和广义加速度能量函数Ｓｒ＝１２∑ｎｉ＝１Ｉｉ（θ·ｉ·θ¨ｉ）２Γｉ２－θ·２ｉ＋θ¨２ｉ，给出其Ｈａｍｉｌｔｏｎ原理和三种不同形式的Ｄ′Ａｌｅｍｂｅｒｔ原理；对于完整约束系统，建立了转动系统的相对论性Ｌａｇｒａｎｇｅ方程、Ｎｉｅｌｓｅｎ方程、Ａｐｐｅｌ方程和Ｈａｍｉｌｔｏｎ正则方程；对于非完整约束系统，建立了转动系统的相对论性Ｒｏｕｔｈ方程、Чаплыгин方程、Ｎｉｅｌｓｅｎ方程和Ａｐｐｅｌ方程；并给出转动系统的相对论性Ｎｏｅｔｈｅｒ守恒律     

Analysis of nonlinear sliding structures by modified stochastic linearization methods

Probabilistic characteristics of a sliding structure is investigated by using new versions of stochastic linearization technique. The structure is composed of base part and upper part, which are connected to each other in a spring-damping system. Coulomb friction between the base structure and earth ground is considered. Two alternative versions of stochastic linearization approach, suggested by X. Zhang and I. Elishakoff, respectively, are applied to such a sliding structure to evaluate its statistical properties. Compared with the results of Monte Carlo simulation, the two new approaches are performing much better than the conventional one in their applications to the sliding structure. Moreover, numerical results indicate that the criterion proposed by Elishakoff turns out to be superior to all other versions in the problem under study. Numerical results also suggest that the entire structure may be replaced by the rigid body in the sliding problem as long as the difference of velocity responses are considered less important than those of displacement responses.     

第二讲合成孔径声纳成像及其研究进展

文章在介绍了图像声纳的特点、合成孔径声纳（synthetic aperture sonar,SAS）产生背景和发展过程的基础上,对合成孔径声纳的原理、技术难点、成像算法等问题进行了讨论.着重分析了合成孔径声纳成像过程中高分辨率的获取方法、水声信道对成像的影响、多子阵技术及其成像算法、稳定的声纳运动平台和运动监测问题、运动补偿与自聚焦方法等.文章还给出了国内外合成孔径声纳研究的最新进展情况,进而展望了合成孔径声纳的应用前景.     

Dimensional Properties of Fractional Brownian Motion

Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.     

New results for isotropic point scatterers: Foldy revisited

Since 1945, Foldy’s method has been used to predict velocity and attenuation for various types of scatterers. In this paper, it is shown that Foldy’s method also yields predictions of reflection and transmission of scalar waves by a random distribution of point or line scatterers contained in a slab. Results are given in two and three dimensions, and for normal and oblique incidences. Formulae are also obtained for the reflection and transmission of longitudinal waves by point or line scatterers distributed in an elastic (non-viscous) fluid. Energy equations are derived, and expressions are obtained for the energy dissipated in the slab on average over one period. Curves for the reflection and transmission coefficients are presented in the case of solid cylindrical bars immersed in a fluid. The results obtained in this paper are expected to be valid for a low density of scatterers. Potential applications of this work occur in ultrasonic evaluation of materials, seismic exploration and medical ultrasonics, where reflected (or backscattered) data are used to construct maps or images of the materials (metals, composites, earth subsurface, tissue). The formulae of this work are expected to provide useful tools for better and more efficient mapping or imaging.     

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.     

SOLVABILITY OF FORWARD-BACKWARD SDES AND THE NODAL SET OF HAMILTON-JACOBI-BELLMAN EQUATIONS

The solvability of a class of forward-backward stochastic differential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. The authors design a stochastic relaxed control problem, with both drift and difftusion all being controlled, so that the solvability problem is converted to a problem of finding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. This method overcomes the fatal difficulty encountered in the traditional contraction mapping approach to the existence theorem of such SDEs.     

基于专家系统的机器人高层规划

本文介绍一个基于专家系统的机器人高层规划系统,阐述几个潜在应用子系统,并应用专家系统方法进行多机器人协调避碰运动规划。本系统具有良好的规划性能。     

关于双重时序AR-MA模型的相关结构及与ARMA模型的比较

本文在文［４］的基础上讨论了双重时序ＡＲ（１）－ＭＡ（ｑ）模型的相关结构，在不假定白噪声序列为正态的情况下，证明了安鸿志［２］关于模型的相关结构的猜想是正确的，具体地构造了ＡＲ（１）－ＭＡ（３）模型的相关结构，并与ＡＲＭＡ模型进行了初步的比较，给出了一些抛砖引玉的讨论．     

狭义相对论效应──运动时钟变慢的计算机模拟演示实验

利用精炼的C语言进行程序设计，定量模拟狭义相结论的运动时钟变慢，并对处于两种不同时空观的时钟运行进行对比，使得时间膨胀效应变得直观。