Real-time recursive estimation of statistical parameters

Recursive algorithms for the computation of standard deviation and average deviation are derived and their applications in data acquisition are discussed. The relative speeds and accuracies of the two algorithms are compared for synthetic data. The performance of recursive estimation under shot and proportional noise limitations is also described. As an example of the utility of these algorithms, absorbance data with constant confidence intervals are collected regardless of incident and transmitted intensities. The desired precision is specified prior to data acquisition and used to control signal-averaging of the data in real time.     

An Algebraic Method for the Exact Solution of the Partition Function of the Canonical Ensemble in Nuclear Multifragmentation

We propose a unified method for deducing recursive relations for the canonical partition function of a system of noninteracting particles with charge conservation if the particles follow the Bose–Einstein, Fermi–Dirac, or Maxwell–Boltzmann statistics or parastatistics. For all these types of statistics, we find recursive relations for the partition function of a new statistical model of nuclear multifragmentation with electric charge and baryon number conservation, accounting for the internal degrees of freedom of the nuclear fragments.     

Bivariate Recursive Equations on Excess-of-loss Reinsurance

This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.     

On the covariance of the level sizes in random recursive trees

In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519–539, 2002     

LIMITING BEHAVIOR OF UNIFORM RECURSIVE TREES

The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity.The limiting distribution ofζ_(n,m),the number of branches with size m in a uniform recursive tree of order n,converges weakly to a Poisson distribution with parameter 1/m with convergence of all moments.The size of any large branch tends to infinity almost surely.     

Recursive solution of linear-quadratic Nash games for weakly interconnected systems

A recursive method is developed for the solution of coupled algebraic Riccati equations and corresponding linear Nash strategies of weakly interconnected systems. It is shown that the given algorithm converges to the exact solution with the rate of convergence ofO(²), where is a small coupling parameter. In addition, only low-order systems are involved in algebrdic computations; the amount of computations required does not grow per iteration and no analyticity assumption is imposed on the system coefficients.This work was supported by Rutgers University Research Council under Grant No. 2-02188.     

Accuracy and CPU time of JE-TLM,PLRC-TLM and CRC-TLM methods for plasma medium

The current density (JE), the piecewise linear recursive convolution (PLRC) and the constant convolution recursive (CRC) techniques are developed and integrated into the transmission line matrix (TLM) algorithm. A comparison of these three schemes according to the criteria of accuracy and CPU time is presented. Numerical experiments show that JE provides the most accurate solution and requires the least CPU time; PLRC is nearly as accurate but consumes more CPU time than CRC.     

Recursive dynamics simulator (ReDySim): A multibody dynamics solver

Recursive formulations have significantly helped in achieving real-time computations and model-based control laws. The recursive dynamics simulator (ReDySim) is a MATLAB-based recursive solver for dynamic analysis of multibody systems. ReDySim delves upon the decoupled natural orthogonal complement approach originally developed for serial-chain manipulators. In comparison to the commercially available software, dynamic analyses in ReDySim can be performed without creating solid model. The input parameters are specified in MATLAB environment. ReDySim has the capability to incorporate any control algorithm with utmost ease. In this work, the capabilities of ReDySim for solving open-loop and closed-loop systems are shown by examples of robotic gripper, KUKA KR5 industrial manipulator and four-bar mechanism. ReDySim can be downloaded for free from http://www.redysim.co.nr and can be used almost instantly.     

关于不定方程x3-1=749y2

利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x³-1=749y²仅有整数解(x,y)=(1,0).     

一种基于Gauss von Mises分布模型的非线性量测更新方法

基于状态空间模型的许多传统滤波算法都基于Rn空间中的高斯分布模型,但当状态向量中包含角变量或方向变量时,难以达到理想的效果。针对J.T.Horwood等提出的nS?R流形上的Gauss Von Mises(GVM)多变量概率密度分布,扩展了狄拉克混合逼近方法,给出了联合分布的GVM逼近方法,推导了后验分布的GVM参数计算公式,设计了量测更新状态估计算法。将J.T.Horwood等的时间更新算法与所提出的量测更新算法相结合,可实现基于GVM分布的递推贝叶斯滤波器(GVMF)。仿真结果表明,当状态向量符合GVM概率分布模型时,GVMF对角变量的估计明显优于传统的扩展卡尔曼滤波器。