Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Estimation of kinetics parameters for the adsorption of human serum albumin onto hydroxyapatite-modified silver electrodes by piezoelectric quartz crystal impedance analysis.

The adsorption of human serum albumin onto hydroxyapatite-modified silver electrodes has been in situ investigated by utilizing the piezoelectric quartz crystal impedance technique. The changes of equivalent circuit parameters were used to interpret the adsorption process. A kinetic model of two consecutive steps was derived to describe the process and compared with a first-order kinetic model by using residual analysis. The experimental data of frequency shift fitted to the model and kinetics parameters, k1, k2, psi1, psi2 and qr, were obtained. All fitted results were in reasonable agreement with the corresponding experimental results. Two adsorption constants (7.19 kJ mol(-1) and 22.89 kJ mol(-1)) were calculated according to the Arrhenius formula.     

Codiameters of 3‐connected 3‐domination critical graphs

A graph G is 3‐domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Let G be a 3‐connected 3‐domination critical graph of order n. In this paper, we show that there is a path of length at least n?2 between any two distinct vertices in G and the lower bound is sharp. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 76–85, 2002     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

Synthesis of some chiral liquid crystals and study of the effect of intramolecular hydrogen bonding on the phase behaviour

The synthesis of three new series of chiral Schiff's bases containing benzilideneaniline and 2-hydroxybenzilideneaniline moieties as mesogenic cores is presented. Differential scanning calorimetry, optical polarizing microscopy and X-ray diffraction measurements were used to study the phase transition temperatures and behaviour. The results reveal that most of these materials show chiral smectic mesomorphism.     

荧光光纤温度传感器激励光源的选择

本文分析计算了荧光光纤温度传感器的温敏元件——GsAlAs/GaAs双异质结半导体材料的荧光辐射效率与激励光波长的关系。讨论了温度测量范围及温敏元件GaAlAs层铝含量对激励光源的限制,在0～200℃测温范围内,若采用LED作激励光源,其峰值波长应在0.70～0.76μm之间选择。     

经济增长与宏观经济运行模型

对国民经济进行宏观调控，如同经济增长问题一样是一个永恒问题，对宏观调控的基本内容，手段，方法，国内外学者已进行了较多的规范性讨论，尤其是在数理分析方面，也已有许多具有普遍意义的成果，但是，要把那些成果转化为“生产力”从而变成清晰的，简明的，可操作的手段和方法，尚需人们不断的探索，本文通过对国民经济运行过程中若干宏观经济变量之间的数量关系分析，并以此建立了的国民经济宏观数量模型，就是尝试性的探索。     

锰（Ⅱ）—邻菲口罗啉配合物极谱吸附波及其应用

在ｐＨ９．５ＮＨ３ＮＨ４Ｃｌ缓冲溶液中，Ｍｎ（Ⅱ）与邻菲口罗啉形成的配合物在－１．３６Ｖ（ｖｓ．ＳＣＥ）处产生一灵敏的吸附波，一阶导数峰电流与Ｍｎ（Ⅱ）浓度在５×１０－８５×１０－６ｍｏｌ／Ｌ范围内呈线性关系，检出限为２×１０－８ｍｏｌ／Ｌ对极谱性质及反应机理进行了研究，用该法测定了大豆和茶叶中的微量锰，结果满意     

A light-driven rotaxane molecular shuttle with dual fluorescence addresses

[reaction: see text] A molecular shuttle containing an alpha-CD macrocycle, an azobenzene unit, and two different fluorescent naphthalimide units was synthesized. The cis-trans photoisomerization of the azobenzene unit resulted in the motion of the CD macrocycle on the track. Because of the easy regulation and full reversibility of the fluorescence change of the two stopper units, the molecular shuttle could be used as a molecular storage medium or switch with all-optical inputs and outputs.     

Structures, stabilities, and electronic and optical properties of c(58) fullerene isomers, ions, and metallofullerenes.

The 1205 classical isomers of fullerene C58, as well as one quasi-fullerene C58 isomer with a heptagonal ring (labeled as Cs:hept) have been investigated by the quantum chemical methods PM3, HCTH/3-21G, and B3LYP/6-31G(d). Isomer C3v:0001, which has the lowest number of adjacent pentagons, is predicted to be the most stable isomer, but the quasi-fullerene isomer Cs:hept is only 2.50 kcal mol-1 higher in energy. Systematic investigations of the electronic properties of C3v:0001 and Cs:hept find that the C3v:0001 isomer has high vertical electron affinity (3.19 eV). The nucleus-independent chemical shifts (NICS) value at the center of Cs:hept (-5.1 ppm) is more negative than that of C60 (-2.8 ppm). The NICS value at the center of the heptagonal ring in Cs:hept (-2.5 ppm) indicates weakly aromatic character. In contrast, the C58(6-) and C58(8-) ions of the C3v:0001 and Cs:hept geometries possess large aromatic character, with NICS values between -14.0 and -26.2 ppm. To clarify the thermodynamic stabilities of C58 isomers at different temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP/6-31G(d) level. The C3v:0001 isomer prevails in a wide range of temperatures, and the Cs:hept isomer is also an important component around 2800 K. The IR spectra of C58 isomers are simulated to facilitate experimental identification of different isomers. In addition, the electronic spectra and the second-order hyperpolarizabilities are predicted by ZINDO and the sum-over-states model. The static second-order hyperpolarizability of the C3v:0001 isomer is 96.5 % larger than that of C60, and its second-order hyperpolarizabilities at external field frequencies are at least nine times larger than those of C60.