关于矩阵方程X—A^＊X^-pA=Q（P〉1）

本文讨论了非线性矩阵方程X-A*X-pA=Q在p>1时正定解存在的必要条件和充分条件以及正定解的一些性质,推导出此方程存在唯一正定解的充分条件,同时构造了数值求解的迭代方法,并且把某些已知的结论推广到任意实数p>1.     

一类混合型Lyapunov矩阵方程的对称正定解

本文研究了一类混合型Lyapunov矩阵方程的对称正定解问题。首先将此方程转化为等价的含参矩阵方程,然后运用矩阵分解和紧凸集上不动点定理,给出了方程具有对称正定解的一些必要和充分条件:其次建立两种求方程对称正定解的参数迭代算法,分析了迭代的收敛性及参数的选取方法,并指出这两种算法的适应性和特点;数值算例表明上述算法的可行性和有效性,并对比出两种迭代的敛速。     

C~*-代数中方程x+a~*x~(-1)a=1的正定解

应用压缩映射原理证明了 C* -代数中方程 x +a* x-1 a=1的正定解的存在唯一性并给出了正定解的递归叙列及误差估计     

子空间上矩阵方程AX=B的亚正定与亚半正定解

研究了矩阵方程AX=B在子空间Ω={x∈Rn｜Gx=0,G∈Rk×n}上的亚正定及亚半正定解,给出了解存在的充分必要条件及其通解表达式。     

全导数为半负定时Lyapunov函数的存在性

在文[1]中Lehnigk证明了对于实方阵A存在严格半正定阵C使系统x=Ax之零解渐近稳定的充分必要条件是Lyapunov矩阵方程A'B+BA=-C有正定矩阵解B.但由于C的构造复杂且对于给定的A只能得到一个C,这个结果事实上是难于应用的. 本文得到:若A没有这样的特征向量,其第l_1,…,l_m位分量为零,对于任意第l_1,…,1_m位的部分正定阵C,系统x=Ax之零解渐近稳定的充要条件是上述矩阵方程有正定矩阵解B.由于不须求解矩阵A的特征问题,且部分正定阵C的类型广泛,易于构造,从而圆满地解决了这一问题。     

矩阵方程X-m∑i-1A*iXδAi=Q的正定解

基于正规锥上单调算子的不动点定理,本文研究非线性矩阵方程X-m∑i-1A*iXδAi=Q的正定解.给出了正定解的存在性定理,并且构造了求解的m步定常迭代方法,最后证明了该迭代法的收敛性.     

子空间上矩阵方程AX=B的正定与半正定解

研究了矩阵方程ＡＸ＝Ｂ在子空间上的正定及半正定解并出了解的存在的充要条件及解的表达式。     

求解广义Lyapunov方程的非单调谱投影梯度法

本文研究双线性控制系统中的一类广义Lyapunov方程的半正定解．基于凸函数的局部极小解就是全局极小解这一良好性质,首先将广义Lyapunov方程的半正定解问题等价转化为凸优化问题．利用非单调线搜索技术确定步长,构造了非单调谱投影梯度方法求解这一等价问题．最后用数值例子验证了新方法的可行性和有效性．     

矩阵方程X＋A^＊X^qA=I（0〈q〈1）Hermite正定解的扰动分析

本文利用不动点理论研究了非线性矩阵方程Hermite正定解存在及唯一性条件,并给出了解的存在区间.讨论了方程唯一解的扰动边界,并说明方程是适定的.用数值例子对以上结果作了说明.     

一类递推矩阵方程有对称正定解序列的充要条件

证明了一类递推矩阵方程ＡＸｋ＋１＝Ｘｋ，有对称正定解序列的充要条件。     

Estimation of Parameters of Universal Distribution of Moments of Failure of Products

A method is proposed for estimating the parameters of a mixture of exponential and Weibull distributions for which the accuracy of preliminary estimates obtained by graphical analysis is refined in accordance with the criterion of maximum likelihood. The efficiency of the proposed method is supported by the results of statistical modeling.     

Evaluation of optical properties of highly scattering media by moments of distributions of times of flight of photons

A novel method for the determination of the optical properties of tissue from time-domain measurements is presented. The data analysis is based on the evaluation of the first moment and the second centralized moment, i.e., the mean time of flight and the variance of the measured distribution of times of flight (DTOF) of photons injected by short (picosecond) laser pulses. Analytical expressions are derived for calculation of absorption and of reduced scattering coefficients from these moments by application of diffusion theory for infinite and semi-infinite homogeneous media. The proposed method was tested on experimental data obtained with phantoms, and results for absorption and reduced scattering coefficients obtained by the proposed method are compared with those obtained by fitting of the same data with analytical solutions of the diffusion equation. Furthermore, the accuracy of the moment analysis was investigated for a range of integration limits of the DTOF. The moment analysis may serve as a comparatively fast method for evaluating optical properties with sufficient accuracy and can be used, e.g., for on-line monitoring of optical properties of biological tissue.     

Estimation of potentialities of methods of summation of direct measurement errors

Conventional methods for summation of direct measurement errors are considered. Conditions under which these methods provide consistent results are stated. It is proposed to utilize for characteristic of the total error, its interval estimator or the half-sum of the value obtained by adding up its arithmetic and geometric random errors.Translated from Izmeritel'naya Tekhnika, No. 4, pp. 10–12, April, 1995.     

卧式金属罐容量的测量结果不确定度

本文根据多年的实践检定经验 ,参照JJF1 0 59- 1 999《测量不确定度评定与表示》以及《测量不确定度表达 1 0讲》 ,对卧式金属罐容量的测量结果不确定度进行了评定。     

盐酸浓度不确定度的评估

通过对盐酸浓度标定的过程分析，找出影响结果的各个分量，进行不确定度的评定，按照计量技术规范给出标准的表示法。     

Analysis of the rate of propagation of the wave of change of boiling modes

An approximate analytical expression is derived for the velocity of the front of the wave of change of boiling modes on a rod and on a plate. The impact of the Thomson effect and of the heater orientation in the gravity field is included. Adequate agreement is demonstrated between the derived relations and experimental data.     

空压机轴承箱蜗壳温度探头油封改造

由于空压机进气侧轴承箱蜗壳温度探头密封效果不好,使空压机及其后续管道受到油污染。后将温度探头的O形圈密封改为骨架油封,杜绝了轴承箱漏油问题。文章简介空压机的结构和技术参数,详细介绍了骨架油封的制作和优点。