SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION

The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).

Integrating Factors and Conservation Theorems of Nonholonomic Dynamical System of Relative Motion

The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.

Stabilization and trajectory tracking of autonomous airship's planar motion

The stabilization and trajectory tracking problems of autonomous airship＇s planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying Lyapunov stability method, the state feedback control laws are designed and the close-loop error systems are proved to be uniformly asymptotically stable by Matrosov theorem. In particular, the controller does not need knowledge on system parameters in the case of set-point stabilization, which makes the controller robust with respect to parameter uncertainty. Numerical simulations illustrate the effectiveness of the controller designed.

EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

Complete Real Solution of the Five-orientation Motion Generation Problem for a Spherical Four-bar Linkage

For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been studied.In order to obtain six real RR dyads,based on Strum＇s theorem,the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method.Moreover,the Grashof condition and the circuit defect condition are taken into account.Given the relationships between the design parameters and the aforementioned two conditions,two objective functions are constructed and optimized by the adaptive genetic algorithm（AGA）.Two examples with six real spherical RR dyads are obtained by optimization,and the results verify the feasibility of the proposed method.The paper provides a method to synthesize the complete real solution of the five-orientation motion generation,which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.

HOLDITCH THEOREM FOR THE CLOSED SPACE CURVES IN LORENTZIAN 3-SPACE

In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.

GENERALIZATION OF STEINER FORMULAFOR THE HOMOTHETIC MOTIONS ONTHE PLANAR KINEMATICS

The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.

Some limit results on supremum of Shepp statistics for fractional Brownian motion

Define the incremental fractional Brownian field ZH（τ, s） = BH（s＋τ） -BH（s）,where BH（s） is a standard fractional Brownian motion with Hurst parameter H ∈ （0, 1）. Inthis paper, we first derive an exact asymptotic of distribution of the maximum MH（Tu） =supτ∈[0,1],s∈[0,xτu] ZH（τ, s）, which holds uniformly for x ∈ [A, B] with A, B two positive con-stants. We apply the findings to analyse the tail asymptotic and limit theorem of MH （τ） witha random index τ. In the end, we also prove an almost sure limit theorem for the maximum M1/2（τ） with non-random index T.

A LIMIT LAW FOR FUNCTIONALS OF MULTIPLE INDEPENDENT FRACTIONAL BROWNIAN MOTIONS

Let B={B^H(t)}t≥0 be a d-dimensional fractional Brownian motion with Hurst parameter H∈(0,1).Consider the functionals of k independent d-dimensional fractional Brownian motions 1/√n∫0^ent1⋯∫0^entk f(B^H,1(s1)+⋯+B^H,k(sk))ds1⋯dsk,where the Hurst index H=k/d.Using the method of moments,we prove the limit law and extending a result by Xu\cite{xu}of the case k=1.It can also be regarded as a fractional generalization of Biane\cite{biane}in the case of Brownian motion.

Wave Motion in an Ice Covered Ocean Due to Small Oscillations of a Submerged Thin Vertical Plate

In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at large distance from the plate, in both cases, are obtained by a suitable application of Green＇s integral theorem. These are then studied graphically for various values of the ice cover parameter.

空间运动刚体加速度瞬轴位置的分析

针对空间运动刚体的加速度分析,本文提出了在各种情况下确定空间运动刚体加速度瞬轴(或动轴)位置的方法。研究结果表明,对于空间运动的刚体,当角速度矢与角加速度矢平行时,存在加速度瞬轴(或动轴),此时,刚体可视为绕加速度瞬轴(或动轴)作转动,即用加速度瞬轴(或动轴)法求解刚体上任一点的加速度。用这种方法分析空间运动刚体上各点加速度的时候更加方便快捷。

关于魔力弹簧的收缩时间和上端运动问题

针对有关魔力弹簧研究中的几个问题进行探讨和澄清.建立了预收缩力弹簧的模型,推出其形变规律.根据质心运动定理,导出这种弹簧自由下落时,收缩到原长所用的时间、其上端的运动方程和速度公式.研究表明,对于通常演示所用的魔力弹簧,在自由下落时的收缩阶段,其上端不是作匀速直线运动.

旋转周期为曲柄二整周的平面双曲柄四杆机构

Grashof Neutral机构存在切换点(Change point)位置。通常认为机构在其切换点位置具有运动不确定性,其输入输出角速度比为0/0型不定式。根据运动连续性原理和洛毕达极限法则,首次导出了确定此类机构切换点(Change point)角速度比的解析公式。并通过机构运动分析、仿真,以及机构原型的制作和实验,证明:GrashofNeutral机构旋转通过切换点(Change point)时的运动是完全确定的,具其运动周期为驱动曲柄旋转二整周。特别是,当机构相对杆长差取很小值时,将输出有反向自锁特征和近似长停歇期的间歇运动,具有工业实用价值。

行为控制月球车路径规划技术

提出了一种新的路径规划方法即自主行为路径规划方法.该方法能够自动构造大范围自然环境下与路径规划任务相关的一类拓扑结构,从而大大地提高自然环境下月球车路径规划速度.该方法在Tangent-Bug切线法基础上引入一组自适应行为来构造切线拓扑图,它是人工路径规划行为的模仿,克服了计算几何路径规划方法非线性计算时间的不足.文中给出了相关定义、定理、算法及真实环境下的仿真结果.

模糊神经网络在自适应双轴运动控制系统中的应用

为了更好地提高工艺加工平台的精确度,结合自适应控制与区间二型模糊神经网络理论设计了一个双轴运动控制系统。该系统通过控制两个场向永磁同步电机来定位X-Y双轴运动转子的位置,从而跟踪预设的蝶形曲线。针对由区间二型模糊神经网络的有限规则产生的不可避免的逼近误差和优化的参数向量等集中不确定性因素,设计了自适应集中不确定性估计律,并通过在线鲁棒补偿器处理集中不确定性的值。最后,通过TMS320C32数字信号处理器运行了本文提出的控制算法。实验结果验证了基于区间二型模糊神经网络设计的双轴运动控制系统的轨迹跟踪精确度较高。与一型模糊神经网络控制系统相比,区间二型模糊神经网络控制系统具有更好的控制性能,鲁棒性更强。

基于总体冲突概率和三维布朗运动的冲突探测算法

随着空中交通流量的增加,冲突探测在空中交通管理系统中的作用越来越重要。该文提出了一种概率型冲突探测算法,计算向前看时间内的总体冲突概率。基于飞机3维布朗运动模型,飞机的预测航迹可以表示为确定航迹外加布朗运动扰动。对于两飞机速度为常值的运动情况,冲突概率可以表示为做布朗运动的飞机进入运动的飞机保护区的概率,使用坐标变换和Bachelier-Levy定理进行估计;对于两飞机运动为非匀速运动情况,预测航迹则可以使用足够多速度为分段常值的片段来近似,计算出每一片段内的冲突概率,并给出了向前看时间内总体冲突概率的上下界。与蒙特卡罗仿真结果比较,算法满足冲突探测精度要求,对及时发现冲突和冲突解决具有重要意义。

用复矢量法研究平面机构的运动

用复数－极坐标矢量法［１］（简称复矢量法），证明了牵连运动为平面运动时，点的加速度合成定理，给出了求解平面机构运动的新方法．

计算碰撞力的方法

在子结构离散的柔性多体系统的动力学基础上，由质点系统的质心运动定理建立了与接触碰撞有关约束的Ｌａｇｒａｎｇｅ乘子和撞击力的关系．计算了平面三连杆机构在撞击过程中撞击力的变化规律和一些特殊节点相对浮动坐标系的平移位移，以及太阳电池阵展开过程中各构件之间的撞击力．通过计算发现，撞击力经过一定时间达到峰值后逐渐下降．在撞击发生时参加碰撞的物体的动力学响应较大，但其他物体的动力学响应很小，由此可见，冲击波在柔性体中传播需要一定的时间．

近场波动数值模拟稳定性问题分析

本文利用分析一维双曲型偏微分方程初边值问题数值稳定性的GKS定理的物理解释和推广 ,以出平面波动为例 ,分析了集中质量显式有限元方法及中心有限差分方法分别与多次透射公式简单结合构成的封闭数值求解系统的稳定性 ,并用数值试验进行了验证。旨在从概念上说明讨论人工边界稳定性时 ,必须与计算区域内的具体算法结合分析才有意义 ,单纯地说人工边界在数值计算中稳定或不稳定是不正确的。

基于洛毕达极限法则的机构奇异位置运动分析

提出了运用洛毕达极限法则分析机构通过死点或切换点时的角速度或速比的新方法 ,并具体应用于具有切换点的GRASHOFneutral机构和GALLOWAY机构的运动分析 .计算分析和实验结果证明 :这两种特殊的平面双曲柄机构的运动周期是原动曲柄旋转二整周 ,而并非通常的一整周 .发现当GALLOWAY机构的相对杆长差取很小值时 ,机构能输出具有超长近似停歇期和反向自锁特性的间歇运动 。