Approximation of Matrices and a Family of Gander Methods for Polar Decomposition

Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank approximants. Properties of Gander methods are investigated in details. AMS subject classification (2000) 65F30, 15A18     

S—R分解定理的唯一性,存在性和客观性

对于连续体的一切物理可能的变形场，其变形梯度张量F可被分解为一个对称张量S和一个正交张量R的直和，这便是S-R分解定理．本文通过矩阵方法和张量方法证明了S-R分解定理的唯一性、存在性和客观性．     

用区域分解算法结合蒙特卡罗法求坦克温度场和红外辐射出射度

本文将区域分解算法和蒙特卡罗法相结合，求坦克温度场和红外辐射出射度．采用蒙特卡罗法计算辐射传递系数，可以考虑界面的复杂辐射特性，如：镜反射、各向异性发射、各向异性反射等；可直接考虑界面的复杂几何特性，如:相互遮挡、太阳入射方向上的投影面积等．引入辐射传递系数，分离了计算的难点，使得在时间域（计算步骤）上能把整个问题分解为若干个子问题并行处理、在空间域（计算区域）上将坦克分解为若干个子区域，缩小计算规模，并可使用多个处理器并行计算；同时减轻了蒙特卡罗法编程的难度，缩短了计算时间．     

重建吸收介质参数(ρ(3),α(3))(英)

本文考虑重建吸收介质的密度ρ（3）和吸收系数α（3）的双参数反演问题。通过波动方程特征积分的方法并引人辅助函数，我们得到了原反问题的一个等价的封闭的积分方程组。利用本文的反演方法，ρ（3）tα（3）可以由反射数据f（t）和透射数据g（t）在深度变量子下同时恢复出来。     

模糊集单调型分解定理

模糊集的分解集定理有两种形式，第一种形式与模糊集的λ—截集有关：Ａ＝其中Ａ＿λ是的λ—截集￣［１］．第二种形式与集合套有关：其中Ｈ（λ）为集合套￣［２］或者Ａ＝其中Ｈ（λ）为集合套，Ｑ为（０，１）的可列稠密子集＿［３］，．其实，这两种形式在本文提出的基本模糊集的概念下，可以统一起来成为任何模糊集可以分解为一些（可数或不可数）基本模糊集的和。不仅如此，本文还提出简单模糊集的概念，并证明了任何模糊集都可以表示成为可数个单调上升的简单模糊集的和，或等价地，可以表示成可数个单调上升的简单模糊集的极限，所用的证明方法是构造性的，所以对模糊集的结构也得出了一个清晰的认识．     

Amorphous Fe–Mg alloy thin films: magnetic properties and atomic vibrational dynamics

Amorphous (a-) Fe _x Mg_1?x alloys are interesting materials for the investigation of non-Debye-like low-energy vibrational excitations. We have prepared a-Fe _x Mg_1?x alloy thin films (0.3 ≤ × ≤0.7) by vapour quenching. The amorphous state was confirmed by conversion electron Mössbauer spectroscopy between 4.2–300 K, and the x- and temperature-dependence of the isomer shift and hyperfine magnetic field was measured. For x= 0.6 and 0.7, magnetic ordering occurs below ~150 K. The atomic vibrational density of states, g(E), was determined by nuclear resonant inelastic scattering, providing clear evidence for the non-Debye-like low-energy vibrational excitations.     

Metallic radii of nonmetals

Experimental data are used to determine the atomic volumes and radii of the elements of subgroups IV–VIIA in the structures of metallic phases at high pressures. Metallic radii of nonmetals are compared with values based on Pauling and Goldschmidt calculations.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 220–222, February, 1994.     

The dehydration of copper(II) acetate monohydrate

The thermal dehydration of copper(II) acetate hydrate has been studied between 353 and 406 K, over a range of humidities. The dehydration is controlled by nucleation-and-growth kinetics at low temperatures, with an activation energy of 154 kJ·mol⁻¹, which changes to contracting-disc kinetics at higher temperatures with a lower activation energy of 76 kJ·mol⁻¹. Frequency factors have also been derived; the value for the high temperature process is low (10⁷s⁻¹) and that for the low temperature step is high (10¹⁷s⁻¹). Optical microscopy has been used to clarify the bulk kinetics; there is evidence for a reactive layer at the surface of the decomposing solid. In celebration of the 60^th birthday of Dr Andrew K. Galwey     

A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.     

Electron excitation cross section of atomic transitions in the two‐state approximation

The cross section of the 3s → 3p transition of sodium produced by electron impact has been calculated by performing a numerical integration of the coupled differential equations. The potential functions have been calculated exactly using the hydrogen‐like wave functions for the valence electron of the sodium with an effective charge adjusted to fit the experimental 3s → 3p line strength. The results compare very well with experimental data and with those obtained using more elaborate and sophisticated models.