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.     

The optimization of silica gel synthesis from chemical bottle waste using response surface methodology

To reduce the amount of hazardous chemical bottle waste in the environment, we report the optimization research of silica extraction in chemical bottle waste into silica gel. Alkali fusion and sol–gel process were utilised to prepare silica gel effectively. The alkali fusion process was carried out by adding sodium hydroxide to produce sodium silicate. Afterwards, silica gel was prepared by the sol–gel method using hydrochloric acid. Box-Behnken Design (BBD) was applied to Optimisation factors the poptimiseactors affecting the silica recovery. The factors that optimised mass ratio, particle size, and temperature. The optimum recovery of silica gel was obtained by SiO₂: NaOH mass ratio of 1:3, the particle size of 63–74 µm, and a temperature of 800 °C. The purity of silica gel optimum is 63.74% characterised using X-ray fluorescence. The structure of silica gel is the appearance of amorphous peaks at 2θ 20-30° characterised using an x-ray diffractogram. The silica gel surface was characterises using scanning electron microscopy-energy dispersive x-ray. It showed an irregular surface and characteristic showed that silica gel had a radius of 15.74 nm and a specific surface area of 297.08 m².     

Evaluation of the Coulomb energy in relativistic self-consistent-field theory

 Computational schemes are presented with which to evaluate the electrostatic Coulomb energy in relativistic molecular electronic structure calculations using a basis of four-component Dirac spinor amplitudes. We demonstrate that algorithms may be constructed and implemented which differ only in minor details from those in common use in nonrelativistic quantum chemistry, and that the four-component formalism is neither as complicated nor as expensive as has been suggested recently in the literature. Spherically symmetrical atomic basis sets are presented which indicate that accurate representations of the Coulomb energy may be obtained using modest expansions of the electronic density in a scalar auxiliary basis set of spherical harmonic Gaussian-type functions. Received: 15 April 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

Electrophoresis simulations using Chebyshev pseudo-spectral method on a moving mesh

We present the implementation and demonstration of the Chebyshev pseudo-spectral method coupled with an adaptive mesh method for performing fast and highly accurate electrophoresis simulations. The Chebyshev pseudo-spectral method offers higher numerical accuracy than all other finite difference methods and is applicable for simulating all electrophoresis techniques in channels with open or closed boundaries. To improve the computational efficiency, we use a novel moving mesh scheme that clusters the grid points in the regions with poor numerical resolution. We demonstrate the application of the Chebyshev pseudo-spectral method on a moving mesh for simulating nonlinear electrophoretic processes through examples of isotachophoresis (ITP), isoelectric focusing (IEF), and electromigration-dispersion in capillary zone electrophoresis (CZE) at current densities as high as 1000 A/m. We also show the efficacy of our moving mesh method over existing methods that cluster the grid points in the regions with large concentration gradients. We have integrated the adaptive Chebyshev pseudo-spectral method in the open-source SPYCE simulator and verified its implementation with other electrophoresis simulators.     

On the automatic restricted-step rational-function-optimization method

The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states. Received: 18 June 1998 / Accepted: 17 September 1998 / Published online: 23 November 1998     

Overlapping spectra resolution using non-negative matrix factorization

Non-negative matrix factorization (NMF), with the constraints of non-negativity, has been recently proposed for multi-variate data analysis. Because it allows only additive, not subtractive, combinations of the original data, NMF is capable of producing region or parts-based representation of objects. It has been used for image analysis and text processing. Unlike PCA, the resolutions of NMF are non-negative and can be easily interpreted and understood directly. Due to multiple solutions, the original algorithm of NMF [D.D. Lee, H.S. Seung, Nature 401 (1999) 788] is not suitable for resolving chemical mixed signals. In reality, NMF has never been applied to resolving chemical mixed signals. It must be modified according to the characteristics of the chemical signals, such as smoothness of spectra, unimodality of chromatograms, sparseness of mass spectra, etc. We have used the modified NMF algorithm to narrow the feasible solution region for resolving chemical signals, and found that it could produce reasonable and acceptable results for certain experimental errors, especially for overlapping chromatograms and sparse mass spectra. Simulated two-dimensional (2-D) data and real GUJINGGONG alcohol liquor GC-MS data have been resolved soundly by NMF technique. Butyl caproate and its isomeric compound (butyric acid, hexyl ester) have been identified from the overlapping spectra. The result of NMF is preferable to that of Heuristic evolving latent projections (HELP). It shows that NMF is a promising chemometric resolution method for complex samples.