Bilateral generating functions and operational methods

Bilateral generating functions are those involving products of different types of polynomials. We show that operational methods offer a powerful tool to derive these families of generating functions. We study cases relevant to products of Hermite polynomials with Laguerre, Legendre and other polynomials. We also propose further extensions of the method which we develop here.     

Two differential equation systems for equality-constrained optimization

This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving equality-constrained optimization problems. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the two differential systems. First, the Euler discrete schemes with constant stepsizes for the two differential systems are presented and their convergence theorems are demonstrated. Second, we construct algorithms in which directions are computed by these two systems and the stepsizes are generated by Armijo line search to solve the original equality-constrained optimization problem. The constructed algorithms and the Runge–Kutta method are employed to solve the Euler discrete schemes and the differential equation systems, respectively. We prove that the discrete scheme based on the differential equation system with the second order information has the locally quadratic convergence rate under the local Lipschitz condition. The numerical results given here show that Runge–Kutta method has better stability and higher precision and the numerical method based on the differential equation system with the second information is faster than the other one.     

On Basic Constraint Qualifications for Infinite System of Convex Inequalities in Banach Spaces

The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.     

关于李萨如图形讨论的小结

对《大学物理》和其它一些刊物上多年来关于李萨如图形的讨论作了归纳和分析。     

付里叶变换红外光谱仪的操作参数对光谱的影响

本文以二苯基甲酮的ＫＢｒ压片为标样，在Ｂｒｕｋｅｒ ＩＦＳ １２０ＨＲ付里叶变换红外光谱仪上系统考察了该仪器折一些重要操作参数（光源光栏、切趾函数、扫描速度）对光谱质量（信噪比，分辨率）的影响。从而获得了测样时的优化操作条件。     

检测实验室如何开展管理评审工作

详细论述了管理评审的基本概念、如何开展管理评审工作以及中国实验室国家认可委员会的有关政策。     

Selecting parameters and limits for equipment operational qualification

While operational qualification (OQ) is a well-established term within equipment qualification, users of equipment often become unsure when it comes to implementation. The biggest problem is how to select procedures and acceptance criteria. Should these be the vendor's specifications or should the users define their own limits, and, if so, how? Should all instruments of the same type have the same values or should these be optimized for each individual instrument? This article will provide an overall strategy and specific examples for HPLC on how to select procedures and acceptance limits that are based on efficient use of resources, on practicality and on the intended use of the equipment.     

交流示波极谱法中if～E曲线的研究（Ⅱ）：if～E曲线的理论公式

提出利用i_f～E曲线代替常用的dE/dt～E曲线的新的交流示波极谱法,并研究了该法的基本理论,推导出i_f～E曲线的理论公式。     

Semi-micro size-exclusion chromatography: Molecular-weight measurement of poly (ethylene terephthalate) and separation of oligomers and prepolymers

Summary Several polystyrene gels of different pore sizes were packed into a 500 mm×2.1 mm I.D. column. Semi-micro size-exclusion chromatography (SEC) using these columns was carried out with a system consisting of a triple piston pump, a micro loop injector and a flow cell with 1.0-μl cell volume constructed for semi-micro HPLC, because the dead volume of the injector and the cell volume of flow cell for conventional HPLC caused a significant loss in column efficiency. The effects of sample amount, injection volume and mobile phase flow rate on column efficiency and retention volume were examined and the optimized operational variables of the sample amount (below 500 μg), the injection volume (less than 15 μl) and the flow rate range (30–70 μl/min) determiend for semi-micro SEC. Oligostyrene, epoxy resin, phenol-formaldehyde resin and phthalates were analyzed by the optimized semi-micro SEC system under the given conditions. In addition, molecular weight distribution of four different poly(ethylene terephthalate) films was successfully measured by using a mixture of chloroform and hexafluoroisopropanol as the eluent.     

Some results on regularity in vector optimization

In this paper we suggest an approach to regularity in, vector optimization which extends the one given in [9]; some necessary or sufficient regularity conditions are given for a wide class of nondifferentiable vector optimization problems which embraces the convex ones.