Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

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.     

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.     

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.     

分子力场进展

分子力学（简称ＭＭ）是近年来化学家常用的一种计算方法。与量子力学从头计算和半经验方法相比，用分子力学处理大分子可以大大节省计算时间，而且，在大多数情况下，用分子力学方法计算得到的分子几何构型参数与实验值之间的差值可在实验误差范围之内。所以，分子力学是研究生物化学体系的有效和可行的手段。分子力学的核心是分子力场。本文介绍了分子力场的量子力学背景、分子力场和光谱力场之间的关系。分子力场的一般形式、分力     

Structure and Phase Transitions of SnP2O7

SnP₂O₇ is a member of the ZrP₂O₇ family of materials, several of which show unusual thermal expansion behavior over certain temperature ranges and which show a number of displacive phase transitions on cooling from high temperature. Here we describe the structural properties of SnP₂O₇ from 100 to 1243 K as determined by X-ray and neutron powder diffraction. These studies reveal that SnP₂O₇ shows two phase transitions in this temperature range. At room temperature the material has a pseudo-cubic 3×3×3× superstructure. Electron diffraction studies show that the symmetry of this structure is P2₁3 or lower. On warming to ∼560 K it undergoes a phase transition to a structure in which the subcell reflections show a triclinic distortion; above 830 K the subcell reflections show a rhombohedral distortion. Significant hysteresis in cell parameters is observed between heating and cooling. The structure of SnP₂O₇ is discussed with references to other members of the AM₂O₇ family of materials.