The Classification and Realization of Complete Lie Algebras with Commutative Nilpotent Radicals

in this paper, the classification and realization of complete Lie algebras withcommutative nilpotent radicals are given. From this, some results on the radicals of thesecomplete Lie algebras are obtained.     

sl_2(R)上Harish-Chandra模及其应用

将ｓｌ２（Ｒ）上不可约Ｈａｒｉｓｈ－Ｃｈａｎｄｒａ模及ｓｌ２（Ｒ）上不可分解的Ｈａｒｉｓｈ－Ｃｈａｎｄｒａ模进行了完全分类，得到了与ｓｌ２（Ｃ）上模分类的不同形式．作为应用，又构造了实Ｖｉｒａｓｏｒｏ代数的一类新的不可约表示．     

New classes of 2-weight cyclic codes

We introduce new classes of 2-weight cyclic codes which are direct sums of 1-weight irreducible cyclic codes      

黄芪成分F3新制剂的工艺监测

对黄芪成分F3新制剂中多糖、蛋白质进行了工艺监测，多糖提取达99．2％，蛋白质≤0．2％，符合黄芪成分F3的质量标准要求，达到了选择最佳提取工艺的目的，结果令人满意。     

Permutation representations in molecular symmetry

The reducible representations of the point groups are generally studied because of their relevance to molecular orbital and vibration theory. Triple correlations within the polyhedra are described by group-theoretical invariants that are related to the permutation representations and termed polyhedral isoscalar factors. These invariants are applied in theorems on matrix elements referring to the symmetry-adapted bases at different centres. Further invariants or geometrical weight factors inter-relate different types of reduced matrix elements of irreducible tensors (generalization of the Wigner-Eckart theorem to the polycentric case). As a demonstration a complete tabulation is given for the point group C ₄.     

Electrochemical and structural investigations of oxide films anodically formed on ruthenium-plated titanium electrodes in sulfuric acid

The electrochemical characteristics of ruthenium oxides, formed on Ru-plated Ti electrodes in 0.5 M H₂SO₄ by potential cycling with different CV upper potential limits (E _SU), were systematically compared. The repeated potential cycling between 0.2 and 0.75 V activated the formation/reduction of surface Ru oxides with hysteretic behavior. This application of repeated CVs also modified the ability of Ru deposits for hydrogen adsorption/desorption. An irreducible Ru oxide accumulated on the electrode at potentials more positive than ca. 0.95 V, whose capacitive characteristics are applicable for electrochemical supercapacitors. This irreducible oxide was composed of an aggregate consisting of Ru in various oxidation states, bridged oxygen, OH and water in a 3D-like structure with a relatively ordered and compact nature, from the X-ray photoelectron spectroscopic and voltammetric results. The surface reconstruction of the Ru deposits induced by the repeated potential cycling with E _SU≥0.75 V was clearly observed from the SEM photographs. From the X-ray diffraction patterns, all the anodically formed Ru oxides showed an amorphous nature.     

Component reconstruction in the primary space of spectra and concentrations. Alternating regression and related direct methods

A set of methods that extract the spectral components in a chromatographic run is considered. The methods do not need libraries of previously known spectra or retention times. The methods have been developed for two-dimensional spectra but they can also be used for chromatographic analyses with a single-channel detector. The methods are direct; they do not use principal components as the starting point. Alternating regression (AR) remains in the primary space of spectra and concentrations during the calculations. Random numbers are used as the starting spectra. Regression is used to solve first for the concentrations, then for the spectra. The method uses two kinds of constraints: all spectra and concentrations are forced to be positive; and all concentration profiles are forced to a unimodal shape with a single local maximum. It is assumed that all observations are a linear sum of components. Compact alternating regression (CAR) is a new variant of the basic AR. The idea is to replace multiplication of a large matrix by two multiplications of smaller matrices. This typically speeds up the iterations by a factor of ten. AR and CAR have been successfully used with combined techniques such as gas chromatography—mass spectrometry and liquid chromatography with UV—visible detection. The reliability of the solution is checked by repeatedly injecting noise and performing the analysis several times. This produces estimates of confidence intervals. AR and CAR have recently been extended to handle single-dimensional signals. Examples are single-channel detectors such as the flame ionization detector in gas or liquid chromatography with a fixed-wavelength UV detector. A batch of samples is used as the observation matrix. As a result, one obtains both the concentrations and the elution shapes of individual chromatographic peaks.     

Analogy between real irreducible tensor operator and molecular two-particle operator

. Molecular matrix elements of a physical operator are expanded in terms of polycentric matrix elements in the atomic basis by multiplying each by a geometrical factor. The number of terms in the expansion can be minimized by using molecular symmetry. We have shown that irreducible tensor operators can be used to imitate the actual physical operators. The matrix elements of irreducible tensor operators are easily computed by choosing rational irreducible tensor operators and irreducible bases. A set of geometrical factors generated from the expansion of the matrix elements of irreducible tensor operator can be transferred to the expansion of the matrix elements of the physical operator to compute the molecular matrix elements of the physical operator. Two scalar product operators are employed to simulate molecular two-particle operators. Thus two equivalent approaches to generating the geometrical factors are provided, where real irreducible tensor sets with real bases are used. Received: 3 September 1996 / Accepted: 19 December 1996     

芳香环状低聚物组分分布与单体结构关系的研究

根据Jacoson-Stockmayer(J-S)环化理论,应用基质辅助激光解吸离子化飞行时间质谱(MAIDL-TOFMS),对一系列芳香环状低聚物组分分布进行分析,研究了芳香环状低聚物的组分分布与单体结构的关系,结果表明,在芳香聚酯、聚膦酸酯及芳香聚醚环状低聚物系列中,Incn与Inn呈良好的线性关系,符合J-S理论分布,在环状聚酯及聚膦酸酯系列中,低聚物的组分分布受双酚单体的中心键角影响,单体的中心键角在100°～120°之间,其中心键角愈小,γ值愈大,而在聚醚系列中,在固定一种单体的前提下,环化物的组分分布受另一单体键角的影响与环状聚酯和聚膦酸酯相一致.     

Structure-activity relationship of Ca2+ channel blockers: A study using conformational analysis and chemometric methods

Summary A structure-activity relationship study has been done on 8 compounds with the activity known as Ca²⁺ channel blockers. Conformational analysis was carried out using a molecular mechanics method. The 3D-QSAR approach was used and the most polar functional groups present in all the molecules were considered. Eight interatomic distances are necessary to define the relative spatial disposition of these relevant molecular fragments. The structure-activity relationship between interatomic distances and biological activity was performed using statistic and chemometric methods. In particular, with Principal Component Analysis, it was possible to reduce the number of interatomic distances: only six of the eight distances are sufficient to describe the system in a useful way. A classification method was iteratively used to select the most probable conformations linked to the biological activity and to build a model able to classify conformations according to their biological behaviour. Cluster analysis on the active selected conformations subsequently allowed the identification of two different geometrical patterns for the active compounds. Finally the validity of the model was verified by correctly predicting the activity of other molecules not used in the construction of the model but possessing known activity.