Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

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     

更新时间概率模型及其无偏估计定理的论证

本文提出应用小参数法 ,探讨 Markov链中相邻两次更新时刻内稀疏事件的概率估计问题 .建立了三种最重要的具有更新时间的概率模型 .通过小参数的引入和对概率式的幂展开 ,进而推证出幂渐近展开系数的模型估算法 .论证了无偏估计的重要定理 ,给出了概率估计式和无偏估计精度 .亦将许多算法扩展到Markov链的任意状态空间     

DIELS-ALDER REACTIONS OF FURAN WITH DIENOPHILES CATALYZED BY YbCl3

The yield and stereoselectivity of the Diels-Alder reactions between furan(or 2-methylfuran)and different dienophiles are markedly enhanced by the catalysis of anhydrous YbCl₃.     

Essay on gravitation: Present-time variation of Newton's gravitational constant in superstring theories

Superstring theories provide an appropriate framework for studying the time variation of fundamental coupling constants. The present time variation of coupling constants in Superstring theories with currently favorable internal backgrounds critically depends on the shape of the potential for the size of internal space. If the potential is almost flat, as in perturbation theory to all orders, the present value of ¦/G¦ for Newton's gravitational constant is calculable and estimated to be 1×10^–11±1yr^–1, which is just at the edge of the present observational bound for/G. If the potential has a minimum with finite curvature due to unknown nonperturbative effects,/G will become unobservably small. The improvement of the measurement of/G of 1 or 2 orders of magnitude would discriminate between the two situations. Problems with the time variation of other coupling constants are also discussed.This essay received the fourth award from the Gravity Research Foundation for the year 1987-Ed.     

醌亚胺类碱性染料在极谱分析中的应用——用天青Ⅰ测定痕量亚硝酸根

本文提出一个基于在酸性介质中,是青Ⅰ与NO_2~-发生亚硝化反应单扫描示波极谱法测定痕量NO_2~-的新方法。在0.06mol/L盐酸介质中。天青Ⅰ的亚硝化产物于-0.65V(vs.SCE)产生一灵敏的二次导数峰。峰高与NO_2~-浓度在0.002～0.24μg/mL范围内成直线关系。方法应用于水样、土壤中NO_2~-的测定,结果满意。     

液/液两相催化新进展--温控非水液/液两相催化

温控非水液/液两相催化,是指一类由两种或多种液态有机物组成的催化反应体系,其特点是体系的相态变化可通过温度来调控,即体系在高温时相互混溶呈均相,低温不溶分成两相,催化剂和产物分别处于两相,从而为解决均相催化剂分离难的问题开拓了一个新方向,是液/液两相催化研究领域最引人注目的进展之一.首次以"温控"为主线将氟两相催化作为温控液/液两相催化的一个特定类型纳入"温控非水液/液两相催化"范畴,并与其它通过温度来调控的有机液/液两相和作者提出的温控相分离催化串在一起作一较为详细的评述.     

Recent Advances in Rare‐Earth Polypnictides

The polypnictide complexes of rare earth cations have drawn the attention of the scientific community for their uncommon bonding modes and potential applications. Herein, we present a systematic and comprehensive summary on recent advances in the field of rare earth polypnictides, focusing on their synthesis, structures, and reactivities. The structural stabilizing effects imposed by the electropositive rare earth cations as well as the reducing capability of rare earth precursors in the synthesis of these polypnictide complexes are described in this review. We also disscuss in detail the bonding interactions and coordination modes between rare earth cations and polypnictide clusters as well as the similarities and the peculiarity of some structures.     

Synthesis and structure of a new rhodium(I) complex [Rh{P(OPh)3}3CN]

Summary The [Rh(acac){P(OPh)₃)}₂] complex (Hacac = 2,4-pentadione) reacts in solution with gaseous HCN in the presence of P(OPh)₃ to give [Rh{P(OPh)₃}₃CN]. Structural investigations of this complex including its³¹P n.m.r. spectra are reported.