A necessary and sufficient convergence condition of orthomin(k) methods for least squares problem with weight

A class of Orthomin-type methods for linear systems based on conjugate residuals is extended to a form suitable for solving a least squares problem with weight. In these algorithms a mapping matrix as preconditioner is brought into use. We also give a necessary and sufficient condition for the convergence of the algorithm. Furthermore, we also study the construction of the mapping matrix for which the necessary and sufficient condition holds.     

固支方板对水中爆炸作用的动态响应研究

 分析研究了在装药水中爆炸产生的强冲击载荷作用下固支方板的塑性动力响应过程。通过对水中爆炸理论和板的大变形理论分析，应用能量原理和Lagrangian函数，推导出反映固支方板在冲击载荷作用下变形的最终挠度的解析解。水中爆炸对固边方板破坏的实验在自制的水箱中进行。对不同的装药重量和炸距情况下方板的变形情况进行了理论计算，并对实验结果和误差来源进行了分析。实验结果和理论结果具有较好的一致性。     

阻尼最小二乘－分光光度法用于多组分分析

基于阻尼最小二乘法原理改进ＣＰＡ法。在确定Ｐ系数矩阵时引入阻尼因子从而降低其病态程度即对偶然实验误差的敏感程度。此法用于多组分分析，如测定复合维生素Ｂ结果良好。     

Efficient Estimation of Two Seemingly Unrelated Regression Equations

We derive simpler expressions under a certain structure of design matrices for the two-stage Aitken estimates of the regression coefficients of two seemingly unrelated regression equations. The estimates are shown to have smaller variance than the ordinary least squares estimates for sufficiently large samples.     

A seminorm with square property on a complex associative algebra is submultiplicative

The result stated in the title is proved as a consequence of an appropriate generalization replacing the square property of a seminorm with a similar weaker property which implies an equivalence to the supnorm of all continuous functions on a compact Hausdorff space also.

     

同时序约束下保序正态均值的均方损失

For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be simultaneous order restriction by Shi (Maximum likelihood estimation of means and variances from normal populations under simultaneous order restrictions, J. Multivariate Anal., 50(1994), 282-293.) and an iterative algorithm of computing the order restricted maximum likelihood estimates of μi and σi2 was given in that paper. This paper shows that the restricted maximum likelihood estimate of μi has smaller mean square loss than the usual estimate xi under some conditions.     

A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA

ＡＫＥＲＮＥＬＥＳＴＩＭＡＴＯＲＯＦＡＤＥＮＳＩＴＹＦＵＮＣＴＩＯＮＩＮＭＵＬＴＩＶＡＲＩＡＴＥＣＡＳＥＦＲＯＭＲＡＮＤＯＭＬＹＣＥＮＳＯＲＥＤＤＡＴＡ￥ＺｈｏｕＹｏｎｇ（周勇）（ＰｒｏｂａｂｉｌｉｔｙｌａｂｏｒａｔｏｒｙｉｎＩｎｓｔ．ｏｆＡｐｐｌ．...     

Temperature variation of the Debye-Waller factors of metal and halide ions in CsCl and CsBr powders by X-ray diffraction. I. Debye-Waller factors of Cs+ and Cl− ions in CsCl from room temperature to 90°K

The temperature variation of the Debye-Waller factors of Cs⁺ and Cl⁻ ions in CsCl powder has been studied using X-ray powder diffraction. A continuous flow cryostat has been used to record the diffractograms and the integrated intensities of the Bragg peaks at different temperatures have been obtained. The integrated intensities of the odd and even reflections have been analysed following the structure of the CsCl compound and the Debye-Waller factors of the Cs⁺ and Cl⁻ ions have been estimated. The results have been verified by structure factor least squares refinement. Theoretical shell model lattice dynamical calculations have been done using a 7-parameter model in the harmonic approximation and the values compared with the present X-ray measurements.     

Determination of Roxithromycin Tablets by Capillary Electrophoresis Employing Non—aqueous Media with Square—wave Amperometric Detection

A new method of determination for roxithromycin tablets by non-aqueous capillary electrophoresis (NACE) with square-wave amperometric detection was carried out. Several parameters affecting the NACE-AD determination were studied. The data was modified by spline wavelet least square (SWLS). The method is simple, rapid and highly reliable for routine analysis.