Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

An intermediate spherical model of a ferromagnet

A one-parameter family of partition functions is considered which for zero value of the parameter reduces to the spherical model of a ferromagnet. The model for > 0 is closer to the usual discrete lattice spin model of a ferromagnet than is the spherical model. The first four terms in of the limiting value of the partition function are calculated above and below the critical temperature for arbitrary interactions using the saddle point method to calculate certain correlation functions for the spherical model. These calculations indicate that the critical temperature is independent of for small and certain interactions.Part of this research appeared in the author's doctoral thesis.⁽³⁾     

Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.     

链珠状氢氧化亚镍的准电容特性及其在复合型超电容器中的应用(英)

本文采用溶胶凝聚方法制备了超细氢氧化亚镍电极材料并通过在其中掺加适量碳纳米管的方法大大提高了电极的比容量并有效改善了电极材料的阻抗特性。掺有20%碳纳米管的氢氧化亚镍复合电极材料的单电极比容量可达到320 F·g^-1。本文分别采用氢氧化亚镍/碳纳米管复合电极作为正极，活性炭作为负极，6 mol·L^-1 KOH作为电解液制备了复合型电化学电容器。采用上述方法制备的复合型电容器工作电压达到1.6 V，电容器质量比容量达到60 F·g^-1。复合型电容器能量密度达到20.11 Wh·kg^-1，最大功率密度达到8.6 kW·kg^-1,兼具高能量特性和优良的大电流放电特性。     

多孔二氧化硅中Gd3+ → Eu3+的能量传递

通过水热反应法，获得了单掺和双掺Eu³⁺，Gd³⁺的多孔二氧化硅组装体，研究了掺杂体系的光谱特性，观察到Gd³⁺ → Eu³⁺的能量传递。分析了能量传递过程，探讨了在多孔二氧化硅中Gd³⁺→Eu³⁺的能量传递的机理，其机理主要为电偶极-电偶极相互作用。     

A new sensitive and selective fluorescence method for determination of chlorine dioxide in water using rhodamine S

A new simple, selective and sensitive method for the determination of trace chlorine dioxide in water has been developed, based on the oxidation by chlorine dioxide to reduction the fluorescence of rhodamine dyes in ammonia-ammonium chloride buffer solution. Four rhodamine dyes systems such as rhodamine S, rhodamine G, rhodamine B and butyl-rhodamine B were tested. The rhodamine S system is the best, with a linear range of 0.0060-0.450 μg mL⁻¹ and a detection limit of 0.0030 μg mL⁻¹ ClO₂. It was applied to the determination of chlorine dioxide in synthetic samples and real samples, with satisfactory results. This method has good selectivity, especially, other chlorine species such as chlorine, hypochlorite, chlorite and chlorate do not interfere the determination. The mechanism of fluorescence reduction was also considered.     

球磨-溶剂热诱导法合成WS2纳米棒及其摩擦性能

采用行星式高能球磨机，将WS₂与S粉末混合球磨，得到纳米片状结构的前驱体，然后添加分散剂聚乙二醇(PEG)用溶剂热诱导的方法使纳米片状前驱体发生结构转变，制备了棒状结构的WS₂纳米材料。用XRD、SEM、TEM等方法对WS₂纳米棒进行了形貌和结构表征，并对其作为润滑油添加剂的摩擦性能进行了初步的研究。     

新型镍催化剂催化乙烯聚合的阳离子机理

含氮氧配位原子的镍催化剂是一类新型催化剂.文章以配体为[NH=CH－CH=CH－O]的镍催化剂为模型,用密度泛函方法（DFT）在B3LYP/LANL2MB水平上研究了该类乙烯聚合催化的反应机理.计算结果表明,催化的反应过程中,中心原子镍最先形成带空位的四边形阳离子配合物,乙烯以垂直于催化剂平面的方式占据空位,然后旋转到催化剂平面内以利于插入反应的进行；插入反应发生后,在催化剂中Ni和β-C之间形成一种氢桥键,协助新空位的形成,实现链的增长.     

OUH体系的结构和分析势能函数

采用密度泛涵B3LYP方法优化出了OUH分子的各种结构，确定了最稳定构型和离解能，以及它们的谐性力常数，并导出双原子分子UH,UO的Murrell-Sorbie势能函数及其光谱数据。采用多体项展式方法，导出OUH(X^4A')基态分子的分析势能函数，获得OUH(X^4A')体系的势能面，考察了这个势能函数的基本性质，正确地复现出OUH分子的平衡结构特征，结果表明：U+OH,O+UH,H+UO的反应均为无阈能的放热能反应。为进一步探讨OUH体系的反应动力学过程打下了基础。     

An improved CNDO/2 standard parametrization for bromine containing molecules

Bromine parameters are proposed, matching well the standard values of first and second row atoms, as introduced by Pople et al. This is shown by comparisons of geometries, configurations, conformations, and dipole moments, obtained with different approaches. The new parameter set was found in a very simple and efficient way that may also be useful for other tasks, e.g. in non-empirical calculations.