Least squares solutions to AX = B for bisymmetric matrices under a central principal submatrix constraint and the optimal approximation

A matrix A∈R^n×n is called a bisymmetric matrix if its elements a_i,j satisfy the properties a_i,j=a_j,i and a_i,j=a_n-j+1,n-i+1 for 1?i,j?n. This paper considers least squares solutions to the matrix equation AX=B for A under a central principal submatrix constraint and the optimal approximation. A central principal submatrix is a submatrix obtained by deleting the same number of rows and columns in edges of a given matrix. We first discuss the specified structure of bisymmetric matrices and their central principal submatrices. Then we give some necessary and sufficient conditions for the solvability of the least squares problem, and derive the general representation of the solutions. Moreover, we also obtain the expression of the solution to the corresponding optimal approximation problem.     

微柱高效液相色谱与火焰光度检测器联用的初步研究

本文研究了常规高效液相色谱(HPLC)及微柱高效液相色谱(Micro-Column HPLC)与气相色谱火焰光度检测器(FPD)的联用技术及其应用.丁基锡等化合物经HPLC分离后,流出液通过FPD进行特效检测.接口采用将毛细管直接引入燃烧头的方式.文中对各有关参数进行了选择、优化和讨论, 对FPD作为HPLC的在线检测器的可能性作了初步探讨.     

高维Cotes优化积分数值算法及其余项估计

利用一维Cotes公式及高维积分Cartesian积空间上的求积法则,将Cotes公式推广到了n维空间上,并给出了简单的误差估计.该公式具有比文[4],[5],[6]相关结果更小的误差和更高的收敛阶等优点.     

关于Hayman问题与分担值

设 f 为非常数亚纯函数, n(≥ 4)为正整数, a 为非零有穷复数. 若a 为f ⁿ与 (f ⁿ)′ 的CM分担值, 则nf ’=f.     

Analysis of Phosphorescence Decay in Heterogeneous Systems: Consequences of Finite Excitation Flash Duration

Analysis of phosphorescence lifetimes using the Stern-Volmer equation is a reliable means of determining quencher concentration for a uniform sample. Methods of analysis for heterogeneous systems are based on the assumption that the excitation is produced by a momentary flash. This condition is an idealization because a real flash has a finite duration and a complex time profile. In the case of a heterogeneous quencher concentration, an excitation flash produces different initial intensities and different times of peak intensity from compartments having different concentrations of quencher. We formulated a model to explore the effects of flash duration on the shape of the emission curve obtained from systems in which the heterogeneity is continuous. We developed mathematical models that can be used to recover fitting parameters of continuous distributions of reciprocal lifetimes approximated as rectangular or Gaussian distributions, or an arbitrary histogram. We also formulated a procedure to convert the distribution of reciprocal lifetimes into a volume distribution of quencher concentration. We found that (1) the Stern-Volmer ratio of phosphorescence intensities cannot be employed for interpretation of pulse phosphorometric data in terms of a volume distribution of quencher; (2) shortening the flash duration decreases the difference of initial intensities between compartments having high and low quencher concentration; (3) the parameters of the volume distribution of quencher concentration can be recovered correctly only after taking account of the difference in initial intensities; and (4) calibration of the initial intensities for a given fitting delay and flash function is necessary.     

N-辛基-N′-(氨基对苯磺酸钠)硫脲的合成及与钯(Ⅱ)显色反应的研究和应用

介绍了N-辛基-N′-(氨基对苯磺酸钠)硫脲(OPT) 的合成方法。通过红外、紫外和元素分析等方法测试，确定了其组成和结构。并研究了该试剂与钯(Ⅱ)的显色反应，从而建立了光度法测定微量钯的新方法。在 pH4.0～5.5 的 HAc-NaAc 缓冲体系中，Pd     

Supramolecular motif and macroscopic pattern in alpha-methylferrocenemethanol films cast from organic solution

The macroscopic patterns were formed in alpha-methylferrocenemethanol films cast from organic solutions. The macroscopic pattern was composed of concentric rings in the solid film. The concentric rings consist of convex ridges and concave valleys; the ordered phase constitutes the convex ridges, while the concave valleys barely contain anything. It has been found that, as for the solvent which can form hydrogen bonding with the solute and has suitable evaporation rate, macroscopic pattern could be observed in the solid film; while as for the solvent that cannot form hydrogen bonding with the solute, no macroscopic pattern would appear. It was suggested that, intermolecular hydrogen bonding and aromatic π stacking interactions of the solute is responsible for the formation of the microscopic crystalline structure; while the hydrogen bonding between the solute and the solvent, and the solvent-evaporation-induced crystallization process, as well as the solvent-evaporation-induced convections are responsible for the formation of the macroscopic pattern. The results could offer a facile way to the electronic material films with well-defined spatial alignment.