Spectrum-Generating Symmetries for the Superpotentials Acot θ and Btanh y

The hierarchy of supersymmetric partner Schrödinger equations for the superpotentials Acot?θ and Btanh?y with A and B as half-integer and negative integer numbers are solved. The number of bound states for given trigonometric and hyperbolic potentials are infinite and finite, respectively. In addition to the spectrum-generating corresponding to the standard supersymmetry which is based on shifting potential parameter, there exist three other different methods for generating the spectrum. The first method is based on supersymmetrizing two given models via infinite and finite number of their bound states. This is realized by the ladder operators which shift only quantum numbers. The second and third methods are based on supersymmetrizing any of the models via all bound states corresponding to hierarchy of their partner potentials. They are respectively realized via simultaneous increasing or decreasing of quantum number and the potential parameter, and also, increasing one of them while decreasing the other. Any of the second and third methods leads to introducing two different classes of the algebraic solutions for both models.     

On spectral radii of matrices governing some numerical estimating algorithms with incomplete data

Summary Many estimating procedures are carried out with incomplete data by means of different types of EM algorithms. They allow us to obtain maximum likelihood parameter estimates in classical inference and also estimates based on the posterior mode in Bayesian inference. This paper analyzes in detail the spectral radii of the Jacobian matrices algorithm as a possible way to evaluate convergence rates. The eigenvalues of such matrices are explicitly obtained in some cases and, in all of them, a geometric convergence rate is, at least, guaranteed near the optimum. Finally, a comparison between the leading eigenvalues of EM and direct and approximate EM-Bayes algorithms may suggest the efficiency of each case.     

Application of the sequential gradient-restoration algorithm to thermal convective instability problems

The problem of the thermal stability of a horizontal incompressible fluid layer with linear and nonlinear temperature distributions is solved by using the sequential gradient-restoration algorithm developed for optimal control problems. The hydrodynamic boundary conditions for the layer include a rigid or free upper surface and a rigid lower surface. The resulting disturbing equations are solved as a Bolza problem in the calculus of variations. The results of the study are compared with the existing works in the literature.The authors acknowledge valuable discussions with Dr. A. Miele.     

A REGULAR VALUE OF COMPACT DEFORMATION

Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one value in a specific open ball. The proof of the result is constructive and based upon continuation methods.     

菌类多糖链构象及其表征方法研究进展 （专题报道）

 概述了菌类多糖在溶液中链构象及其表征方法的研究进展.主要报道从各种真菌（香菇、茯苓、灵芝、木耳、黄单胞菌、裂褶菌等）中提取的多糖在溶液中的分子量、分子形态和尺寸,即链构象.同时介绍多糖链构象对生物活性的影响,并且指出多糖刚性链带电基团及适量分子量有利于促进它与免疫细胞上受体结合,从而抑制肿瘤细胞增殖.由此表明,多糖链构象的研究对弄清其生物功能和推动生命科学发展十分重要.多糖在溶液中主要以无规线团、双螺旋、三螺旋、蠕虫状、棒状链以及聚集体构象存在,它取决于单糖组成、糖苷键、支链结构以及分子内和分子间作用力.测定链构象的方法主要包括光散射、黏度、显微技术（透射电镜,扫描电镜以及原子力显微镜）、微量热法和小角X-射线散射等.此外,介绍了多糖溶液理论以及计算链构象参数的表达式.     

镍系非晶态合金催化剂的研究进展

镍系非晶态合金催化剂作为一类以镍为主要活性组分的环境友好型催化剂,具有高活性、高选择性和价格低廉等特性,被广泛应用于不饱和化合物的催化加氢、化合物脱硫、硼氢化物水解和燃料电池中的电催化氧化等方面。本文概述了镍系非晶态合金催化剂的结构特点,综述了镍系非晶态合金催化剂近年来国内外的研究状况,重点总结金属助剂、载体、制备方法对镍系非晶态合金催化剂的性能的影响,并对镍系非晶态催化剂的未来研究方向进行了分析展望。     

地质环境样品中挥发酚分析现状与进展

挥发酚被列为环境优先控制的有机污染物,已成为评价环境污染的重要指标之一。该文简述了挥发酚的化学性质及地质环境来源,概括了国内外挥发酚测定的相关标准方法,从样品预处理技术和检测技术两方面综述了近年来地质环境样品中挥发酚分析的研究现状。重点对溶剂萃取、蒸馏、固相萃取、固相微萃取和吹扫捕集等样品预处理技术,以及4-氨基安替比林分光光度法、紫外和荧光分光光度法、溴化容量法、气相色谱法、液相色谱法和酚生物传感器法等技术在地质环境样品中挥发酚分析上的应用进行了较为全面的总结,并对其未来的发展趋势进行了展望,为进一步研究挥发酚的分析技术及其环境应用提供参考。     

基于SIMPLER算法的多重网格方法研究

以二维方腔顶盖驱动流为模型,将多重网格方法和SIMPLER算法进行耦合,对不同雷诺数下多重网格加速SIMPLER算法和SIMPLER算法的计算效率进行了对比,数值计算表明:多重网格加速SIMPLER算法不仅能够解决SIMPLER算法不能准确模拟较高雷诺数流场的问题,而且其计算效率远远高于SIMPLER算法.本文也对松弛因子的选取、多重网格实现形式以及网格层数对多重网格加速SIMPLER算法的影响进行了研究,从而为多重网格加速SIMPLER算法的实施提供了计算技术.     

测定微小晶体结构的电子晶体学图像处理技术

介绍了2005年国家自然科学奖二等奖获奖项目“微小晶体结构测定的电子晶体学研究”.研究目的是建立一种借助高分辨电子显微像测定晶体结构的新方法.为此提出了高分辨电子显微学与衍射晶体学相结合的思想,在实现此思想的过程中,研究了像衬的规律,得出实用的像衬公式和理论,阐明了不同种类原子像衬与晶体厚度的关系,而且用理论指导实验,观察到晶体中锂原子的像衬.以此理论为依据,把衍射晶体学中的多种分析方法特包是直接法引入到高分辨电子显微学中,建立了一套全新的电子晶体学图像处理技术,开发了相应的可视化专用软件包,并应用于测定多个未知晶体结构.文中逐一介绍了研究工作全过程的关键问题和研究结果.