Stability in Debye series calculation for light scattering by absorbing particles and bubbles

The Debye-series decomposition is of importance for understanding of light scattering features and for the validity of the geometrical optics approximation to light scattering. The numerical stability and accuracy for calculating light scattering with Debye series is studied and an improved algorithm is proposed in this work. The ratios of the Riccati-Bessel functions and the logarithmic derivatives of the Riccati-Bessel functions are employed and calculated with proper recurrences. Exemplifying results are provided to show the improvement of the algorithm.     

Increasing the polynomial reproduction of a quasi-interpolation operator

Quasi-interpolation is an important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain , the d-variate polynomials of degree ≤m. In particular, the reproduction of Π_m leads to an approximation order of m+1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the orthogonal projection onto Π_m for some inner product, finite element methods of precision m, and multivariate spline approximations based on macroelements or the translates of a single spline.For such a quasi-interpolation operator L which reproduces and any r≥0, we give an explicit construction of a quasi-interpolant which reproduces Π_m+r, together with an integral error formula which involves only the (m+r+1)th derivative of the function approximated. The operator is defined on functions with r additional orders of smoothness than those on which L is defined. This very general construction holds in all dimensions d. A number of representative examples are considered.     

Evaluation of dead time calculation in liquid chromatography using a linearization procedure for homologous series

A mathematical method for the calculation of the dead time (t_m) in HPLC was evaluated using a computer simulation approach, in which artificial perturbations were introduced to Simulated homolog retention times. The calculation was based on a modified and extended Grobler and Bálisz (GB) method. Investigated wav how the precision of the calculated t_M is affected by: statistical fluctuations in retention times and which, and how many homolog retention times are used. Based on these simulations a two-step procedure for the t_M calculation is proposed: In the first step the linearity of log t_{R, n} vs carbon number n is checked using as many homolog retention times as possible. The slope value b^o of the first linear regression in the GB method is used for the selection of homolog retention times in the final t_M calculation. In the second step the optimal selection of homologs is made and the final t_M calculation is carried out. Guidelines for homolog selection are given.     

Mathematical Relationships Between Bond-Bending Force Fields

Molecular mechanics softwares adopt various set of force field functions. In some cases, reliable data from one set of force field parameters cannot be used in a software that adopts another set of force field. Using mathematical approach, exact relationships between parameters from three bond-bending force fields, namely the (i) harmonic cosine angle, (ii) polynomial series, and (iii) Fourier series, are herein developed. Parameters from these three potential functions are further related to the approximate form, the harmonic angle function, which is valid for small change in chemical bond angle.     

家具白乳胶中苯系物含量测定

建立了气相色谱内标法测定家具白乳胶中苯系物含量的方法。样品中苯系物经甲醇提取、离心,上清液用60 m EN-20色谱柱分离,气相色谱检测,内标法定量。优化条件下苯系物回收率在96.84%~103.86%,相对标准偏差(RSD)为0.79%~2.28%,定量下限2.4~2.9 mg/L。方法操作简单,准确度和精密度较高,是一种检测白乳胶产品中苯系物含量的有效方法。     

Synthesis and structures of 4,6-disubstituted 2-(5-methyl-1,2,4-oxadiazol-3-yl)-1,3,5-triazines

New 1,2,4-oxadiazolyl-1,3,5-triazines were synthesized from amidoximes derived from sym-triazine mononitriles. The structure of one of the resulting compounds was studied in detail by X-ray diffraction. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1845–1850, August, 2005.     

苯系物扩散管气体标准物质的研制

按照ISO 6145—2003、ISO 6144—1998标准,研制了新型气体标准物质动态配气装置,实现了微机对动态配气装置主要参数数据的实时监控。用该装置研制了氮中微量苯系物扩散管气体标准物质,量值的相对扩展不确定度为2％-3％,并与静态容量法配气进行了比较。