Stability of Methods for Matrix Inversion

Inversion of a triangular matrix can be accomplished in severalways. The standard methods are characterized by the loop ordering,whether matrix-vector multiplication, solution of a triangularsystem, or a rank-1 update is done inside the outer loop, andwhether the method is blocked or unblocked. The numerical stabilityproperties of these methods are investigated. It is shown thatunblocked methods satisfy pleasing bounds on the left or rightresidual. However, for one of the block methods it is necessaryto convert a matrix multiplication into the solution of a multipleright-hand side triangular system in order to have an acceptableresidual bound. The inversion of a full matrix given a factorizationPA=LU is also considered, including the special cases of symmetricindefinite and symmetric positive definite matrices. Three popularmethods are shown to possess satisfactory residual bounds, subjectto a certain requirement on the implementation, and an attractivenew method is described. This work was motivated by the questionof what inversion methods should be used in LAPACK.     

低通量慢中子对Bi系超导体的辐照效应

本文研究低通量慢中子对Bi系超导体的辐照效应。实验结果表明:(1)Bi系超导体在适量慢中子辐照后,临界电流密度J_c和零电阻温度T_c0都有不同程度提高;(2)低通量慢中子和高通量快中子对Bi系超导体具有相似的辐照效应。 关键词：     

量子混合态的统计角

本文把关于量子纯态之间的统计角概念推广到量子混合态,并提出了单个混合态的发散角这一概念,导出了纯态判据,用到测量上,响应函数不过是量子系统与仪器之间的统计角余弦的平方,而测量过程中的熵增加则显现为混合态发散角的扩大。 关键词：     

Viscosity-splitting scheme for the Navier-Stokes equations

A viscosity-splitting scheme for the initial boundary value problems of the Navier-Stokes equations is considered. In the scheme, the Stokes equation is solved in conjunction with a nonhomogeneous boundary condition which connects the tangent flow with a no-slip flow. Convergence is proved.     

同步辐射与GGG：Nd^3＋晶体的相互作用

用北京同步辐射489A-VUV束线作为连续光源测定了GGG:Nd~(3+)晶体的短波吸收光谱。用束线4B9A-WX作为光源激发GGG:Nd~(3+),测定了它的XEOL(X-ray excited optical luminescence)。     

Irradiation-induced reduction and luminescence properties of Sm doped in BaBPO5

Usually, Sm²⁺ ions could be reduced by heating the materials in reducing atmospheres. Exposure to ionizing radiations is also known to cause Sm³⁺→Sm²⁺ conversion. In this work, BaBPO₅ doped with the samarium ion was prepared by high temperature solid-state reaction. Sm²⁺ ions were obtained by two different reduction methods, i.e., heating in H₂ reduced atmosphere and X-ray irradiation. The measurements of X-ray diffraction (XRD), and scanning electron microscope (SEM) were investigated. It is found that the conversion of Sm³⁺→Sm²⁺ is very efficient in BaBPO₅ hosts after X-ray irradiation. Sm²⁺ ions under these two reduction methods exhibit different characteristics that were studied by measurements of luminescence and decay. The results showed that the luminescence properties of Sm²⁺ ions in BaBPO₅ were highly dependent on the sample preparation conditions.     

重金属Pb2+对玉米苗生长的影响

以水栽培的玉米幼苗为材料，用不同浓度的醋酸铅溶液处理后，分别在第10天、第20天、第30天对玉米苗的根、茎、叶分别进行Pb^2＋含量测定。分析结果：Pb^2＋在玉米体内的分布表现为根〉叶〉茎；玉米中的叶绿素含量均降低；随着Pb^2＋浓度的增大，玉米细胞的膜透性表现根〉叶〉茎依次升高；Pb^2＋对玉米的伤害率的大小表现为根〉叶〉茎。该实验为进一步研究农作物对重金属Pb^2＋的耐性和重金属Pb^2＋在农作物体内的分布提供了可参考的数据。     

Chinese (Mainland) teachers’ views of effective mathematics teaching and learning

This study investigates Chinese teachers’ cultural beliefs concerning effective mathematics teaching through semi-structured interview with nine experienced teachers. For the Chinese teachers, an effective teacher should always be passionate and committed to the teaching profession. She should not only understand the knowledge in the textbook thoroughly but also be able to carefully craft the knowledge from the textbook for teaching by predicting possible students’ difficulties. Although Chinese teachers emphasize student participation and flexible teaching, they tend to see the teacher’s ability to design and lead coherent lessons as the key for facilitating students’ understanding. The result of this study helps researchers and educators understand the teacher-designed and content-oriented teaching model in Chinese classrooms.     

强收敛与弱收敛的微小区别

对于独立同分布随机变量序列{Xn,n≥1},证明了其满足弱大数律的一个必要条件是:对于任何r∈(0,1),E|X|r<∞都成立.另外我们还举例说明了这样的条件不是充分的.     

Synthesis and Crystal Structure of a Ternary Complex: [Ni(phen)2(pmal)]·8H2O

A new ternary complex [Ni(phen)(pmal)]·8H2O (phen = 1,10-phenanthroline,pmal2- = phenethyl malonic acid) has been synthesized by the reaction of nickel acetate, phen and phenethyl malonic acid. Elemental analysis, IR spectra and X-ray single-crystal diffraction were carried out to determine the composition and crystal structure. Crystal data for this complex: triclinic system, space group P1, a = 10.387(5), b = 13.112(6), c = 14.229(6) (A), α = 76.176(7), β =83.778(8), y = 71.770(6)°, C35H42N4O12Ni, Mr= 769.44, Z = 2, F(000) = 808, V = 1786.1 (A)3, Dc =1.431 g/cm3, μ = 0.612 mm-1, the final R = 0.0653 and wR = 0.1033 for 9379 (Rint = 0.0244)independent reflections and 4730 observed reflections (I ＞ 2σ(I)). Structural analysis shows that the coordination geometry of Ni(Ⅱ) is a distorted octahedron. A novel two-dimensional structure is constructed from (H2O)4 and (H2O)12 water clusters, and the complex forms a 3-D network supramolecular structure by hydrogen bonds and π-π stacking of neighboring phens.