Chapter 15 DEA/AR analysis of the 1988–1989 performance of the Nanjing textiles corporation

This article employs new data envelopment analysis/assurance region (DEA/AR) methods to evaluate the efficiency of the 35 textile factories of the Nanjing Textiles Corporation (NTC), Nanjing, China. The returns to scale (RTS) of these factories were studied without assuming that the optimal DEA solutions were unique. All DMUs are identified with pointsE (Extreme Efficient),E (Efficient but not an extreme point) andF (Frontier but not efficient). We then further identify the nonfrontier DMUs with pointsNE, NE andNF according to whether they are projected onto a point inE, E, orF en route to evaluating their performances. All of the inefficient factories were in classNF and had unique optimal primal-dual solution pairs. Consequently, the solution pairs satisfy the strong complementary slackness condition (SCSC). Application of cone-ratio (CR) ARs reduced significantly the number of factories in classE, and showed that some AR-efficient factories were more flexible in adopting the mixture of central planning and market economies that China currently is trying to use. Also, linked-cone (LC) ARs were applied to measure maximum and minimum profit ratios. The SCSC multiplier space approach was utilized to analyze the sensitivity of the efficiency results to potential errors in the data with and without ARs. The results in this article suggest that collective units had a better performance than state-owned units in the two consecutive years analyzed.This paper was written while the author was at the School of Economics and Management, Southeast University, Nanjing 210018, P.R. China.     

一类分层三角剖分下三次样条空间的维数

本文定义了平面单连通多边形域的一类较任意的三角剖分－分层三角剖分，并通过分析二元样条的积分协调条件，确定了分层三角剖分卜三次Ｃ^１作条函数空间的维数．     

多非线性控制项的Luré系统绝对稳定的充要条件

本文对具有多非线性控制项的控制系统，得到了绝对稳定的一般性充要条件，并对其特殊情况给出了构造性充要条件．     

非平稳ρ混合序列的完全收敛性

本文进一步研究了ρ－混合序列的完全收敛性，讨论了无界非平稳情形完全收敛性成立的充分和必要条件，获得了理想的结果．     

The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

物性依赖温度的热传导方程的近似解(Ⅰ)

1引言在热传导方程中式中P、C分别是介质的密度和比热,k是热传导系数。用0表示相对温度,即0—t一f＿,这里t＿表示环境温度。在很多情形下,热传导系数以幂次依赖于温度,例如等离子体中的电子热传导,即假设P,C为常数,则方程（1）变为其中a—00／pcm。本课题考虑对称物体的边界（两端）始终为环境温度,即对称区域（－－,l）上具有零边界条件0（士人,）一0（4）的近似解。关于这一问题,尽管许多中外学者对其解析解（分析解）有着很大的兴趣,然而在很多情形下,解析解是不可能得到的。同时,我们也注意到,对于半无限大和无限大固…     

Condition number as a measure of noise performance of diffusion tensor data acquisition schemes with MRI

Diffusion tensor mapping with MRI can noninvasively track neural connectivity and has great potential for neural scientific research and clinical applications. For each diffusion tensor imaging (DTI) data acquisition scheme, the diffusion tensor is related to the measured apparent diffusion coefficients (ADC) by a transformation matrix. With theoretical analysis we demonstrate that the noise performance of a DTI scheme is dependent on the condition number of the transformation matrix. To test the theoretical framework, we compared the noise performances of different DTI schemes using Monte-Carlo computer simulations and experimental DTI measurements. Both the simulation and the experimental results confirmed that the noise performances of different DTI schemes are significantly correlated with the condition number of the associated transformation matrices. We therefore applied numerical algorithms to optimize a DTI scheme by minimizing the condition number, hence improving the robustness to experimental noise. In the determination of anisotropic diffusion tensors with different orientations, MRI data acquisitions using a single optimum b value based on the mean diffusivity can produce ADC maps with regional differences in noise level. This will give rise to rotational variances of eigenvalues and anisotropy when diffusion tensor mapping is performed using a DTI scheme with a limited number of diffusion-weighting gradient directions. To reduce this type of artifact, a DTI scheme with not only a small condition number but also a large number of evenly distributed diffusion-weighting gradients in 3D is preferable.     

LINEAR AND NONLINEAR SEMICLASSICAL THEORY OF WHISPERING-GALLERY-MODE MICROSPHERE LASER

A complete whispering-gallery-mode microsphere laser theory is developed, which combines usual laser semiclassical theory with Lorenz-Mie theory. The linear and nonlinear problems of the microsphere lasing are dealt with in the universal mode picture. The threshold condition, average amplitude of the steady state and frequency effect are obtained. A comparison between the theory and experiments is also made.     

由因式化L算子所构成的经典可积动力学体系

用因式化的L算子构造了一类在非周期边界条件下的可积模型.对体系的transfer矩阵取三角和标度极限情况下,得到了n维体系(n为奇数)的经典哈密顿量的具体形式.结果表明,这类可积体系与Calogero等人所发现的一系列可积体系是相类似的.     

基于红外光谱环类锻件内壁状态监测方法研究

考虑到环类锻件内壁状态对于保证工业的生产安全具有重要作用, 而基于红外光谱的测温方法可以大大提高测温精度, 因此研究基于红外光谱的环类锻件内壁状态监测方法具有重要的意义。为了实时掌握环类锻件的内壁状态, 提出一种红外光谱环类锻件内壁状态监测方法。首先利用红外光谱构建了三级FP型LCTF的测温系统, 通过获取锻件表面辐射的两个单一光谱运用红外双色测温原理实现锻件表面温度的测量。相比传统的测温方法大大提高了锻件表面的测温精度。其次在拉普拉斯导热微分方程的基础上, 运用分离变量法建立了环类锻件内壁状态监测模型;结合红外光谱测温系统测量的温度数据和锻件自身参数信息, 实现了环类锻件的内壁状态监测;最后通过仿真实验验证了所提出方法的可行性, 实现了环类锻件的内壁状态监测, 为保证环类锻件的正常运行提供了理论依据。