Darboux Transformation for Drinfel'd-Sokolov-Wilson Equation

A coupled system known as the Drinfel'd-Sokolov-Wilson equation is reexamined. With the help of a Lax operator of fourth order, its proper Darboux transformation is constructed. Also, a nonlinear superposition formula is worked out for the associated Bäcklund transformation and some solutions are calculated.     

基于红外吸收光谱的瓦斯气体浓度检测技术

针对现有矿井瓦斯传感器的缺点,基于红外光谱吸收原理,采用差分吸收技术设计了红外瓦斯气体浓度探测系统。该系统采用单光路吸收气室和单光路双波长探测技术,利用差动放大电路为核心的微弱信号处理电路实现瓦斯浓度输出信号的检测,并采用线性关系式拟合瓦斯浓度和输出电压的关系曲线,实现了对瓦斯浓度的全量程精确探测。实验表明,该系统的测量误差小于2%,具有很高的测量精度,具备了煤矿应用的基础。     

A review ofL=λW and extensions

A fundamental principle of queueing theory isL=W (Little's law), which states that the time-average or expected time-stationary number of customers in a system is equal to the product of the arrival rate and the customer-average or expected customer-stationary time each customer spends in the system. This principle is now well known and frequently applied. However, in recent years there have been extensions, such as H=G and the continuous, distributional, ordinal and central-limit-theorem versions, which show that theL=W relation, when viewed properly, has much more power than was previously realized. Moreover, connections have been established between H=G and other fundamental relations, such as the rate conservation law and PASTA (Poisson arrivals see time averages), which show that there is a much greater unity in the overall theory than was previously realized. This paper provides a review.This paper is dedicated to the memory of our colleague Professor Peter Franken (1937–1989), who contributed greatly to the subject of this paper and to queueing theory more generally.     

关于γ—可重排列方面的一个计数公式

本文给也了规格为２＾ｍ的２ｍ个元的γ－可重排列的个数的一个计算公式。     

Speeding up the FMMR perfect sampling algorithm: A case study revisited

In a previous paper by the second author, two Markov chain Monte Carlo perfect sampling algorithms—one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling—are compared using as a case study the move‐to‐front (MTF) self‐organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user‐chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial state used in the previous study gives the stochastically largest running time. By changing from worst choice to best choice of initial state we achieve remarkable speedup of FMMR for MTF; for example, we reduce the running time (as measured in Markov chain steps) from exponential in the length n of the list nearly down to n when the items in the list are requested according to a geometric distribution. For this same example, the running time for CFTP grows exponentially in n. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003     

炮管在新应力函数作用下的解析计算

为解决长期以来利用均布压力近似代替电磁发射炮管厚壁所受变力所造成的误差的难题,在三维空间提供了电磁发射炮管受双曲余弦函数载荷压力的数学模型,构造一个既满足边界条件,又满足双调和方程的特殊应力函数,推导出电磁发射炮管在柱面上受双曲余弦分布压力、端面上受常力时的解析解并导出电磁发射炮管所受压力沿轴向不变时的极限即为Lamè公式,又求出其解析解并解出电磁发射炮管所受压力沿轴向不变时的极限,通过记录电磁炮发射时炮管的应变值,比较其理论与实验结果,可以得出这两者有较高的吻合度。这为今后求解各类电磁发射炮管受任意分布压力作用的变形计算问题以及将其实践化以便延长炮管使用寿命。促进电磁炮的实用化进程提供理论依据,同时也为液压缸等轴对称圆筒件的应力分析奠定了理论基础。     

Non-parametric Estimation for the M/G/∞ Queue

Given an M/G/ queue with input rate and service-time distribution G, we consider the problem of estimating and G from data on the queue-length process Q = (Q_t). Our motivation is to study departures of G from exponentiality, following recent work of Bingham and Dunham (1997, Ann. Inst. Statist. Math., 49, 667–679).     

内埋武器高速风洞弹射投放模型试验关键技术研究

针对新一代战斗机超声速内埋武器弹射投放分离安全性问题,采用高速风洞投放实验技术研究内埋武器从开式武器舱弹射投放分离动态运动过程,风洞投放模型试验过程中采用除垂直加速度不足外,其余全部运动严格相似的轻模型相似设计方法,并针对轻模型法垂直加速度不足所导致的投放垂直位移偏离实物位移问题,采用一种简单易行的公式修正法进行补偿,试验给出了不同初始弹射投放分离条件下,内埋武器从载机投放分离后运动轨迹与姿态角随分离时间的变化规律,试验马赫数$Ma = 1.5$.研究结果表明:初始投放分离角速度对内埋武器投放分离后的运动轨迹及姿态角有较大的影响,当初始投放分离角速度$\omega _{z0}^s = 0^\circ/{\rm s}$时,内埋导弹出舱后先向下运动远离载机的流场干扰区,之后逐渐向载机方向抬升靠近并最终碰撞载机,高速风洞投放试验结果是不安全的,但经过公式修正后投放试验结果比较乐观,垂直方向运动仍然一直下降远离载机,这说明采用高速风洞投放试验得出的导弹不安全投放分离对真实载机来说不一定会出现,高速风洞投放试验结果比较保守. 当初始投放分离角速度$\omega _{z0}^s= 15^\circ/{\rm s}$和$\omega _{z0}^s = 30^\circ/{\rm s}$时,内埋导弹投放分离后运动趋势几乎一致, 均没出现向载机靠近的现象,内埋导弹具有一定的初始投放分离角速度有利于内埋武器的安全分离.      

A kinematic formula for integral invariant of degree 4 in real space form

In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.     

Lefschetz Formulae for p-Adic Groups

In this paper,Lefschetz formulae for torus actions on p-adic groups are proven. These are similar to comparable formulae for real Lie groups.Applications lie in the realm of dynamical zeta functions.