PYRIDINATION OF POLY（VINYL CHLORIDE） via A HOMOLYTIC PATHWAY

PVC was subjected to a chemical modification aiming at replacing the chlorine atoms by pyridine groups via a homolytic route. Pyridine groups were peculiarly affixed to the PVC matrix via a carbon-carbon bond rather than a carbon-nitrogen one. PVC was first iodinated using the Conant-Finkelstein reaction, followed by the application of the homolytic conditions of Minisci to generate pyridinated PVC with a varying degree of substitution. The extent of substitution was not high; the reaction on 30% iodinated PVC afforded a degree of modification no greater than 3%.     

不确定条件下具有容差项的Markowitz证券组合投资模型的最优化解法

在分析证券市场中证券组合投资不确定性质的基础上,通过对Markowitz模型中证券期望收益与方差引入容差项来度量证券市场的不确定性,建立了不确定条件下具有容差项的Markowitz证券组合投资模型;分类讨论了容差的上界与下界所对应的两类有效组合前沿,得到了不确定条件下的证券组合投资模型的最优化解法及相关定理;最后给出了一个具体的数值实例．     

STEFAN PROBLEMS WITH KINETIC CONDITIONS AT THE FREE BOUNDARY

In this paper,we prove the existence theorems of locbal or global classical solutions to Stefan problems with various kinetic conditions at the free boundary.     

Strict (ε, δ)-Subdifferentials and Extremality Conditions

A new abstract definition of extremality is introduced extending traditional extremality notions in optimization problems. The set of points satisfying the new definition includes points not necessarily optimal in the usual sense but nevertheless having some extremal properties. Necessary and sufficient extremality conditions are derived. Contrary to usual notions of extremality the new one is stable relative to small deformations of the data.     

Multifunction Optimization Problems Involving Parameters: Necessary Optimality Conditions

We prove the Fritz John and Kuhn-Tucker necessary optimality conditions for vector optimization problems involving multifunctions and parameters under relaxed assumptions.     

Problems for Ordinary Differential Equations with Transmission Conditions

We investigate a boundary-functional problem with transmission conditions for ordinary differential-operator equation in Sobolev spaces with a weight. We prove an isomorphism, coerciveness with respect to the spectral parameter, completeness and Abel basis of a system of root functions of the problem. Obtained results in the article are new even in case of Sobolev spaces without the weight.     

On the continuity of a Lagrangian multiplier function in input optimization

We show that a Lagrangian multiplier function in input optimization is generally discontinuous on regions of stability and then we find conditions for its continuity.Research partly supported by the Natural Sciences and Engineering Research Council of Canada.Presented at TIMS/ORSA Meeting in Boston, Massachusetts, April 29-May 1, 1985.The contribution of this author is part of his M.Sc. thesis in Applied Mathematics at McGill University.     

HALOMETHYLATION OF POLYSTYRENE AND SUBSEQUENT PYRIDINATION VIA A HOMOLYTIC PATHWAY

Chloromethylation of polystyrene （PS） with two different chloromethylating systems methylal/thionyl chloride and paraformaldehyde/trimethylchlorosilane was studied. Soluble chloromethylated polystyrene with a degree of substitution of 89% was obtained. The Conant-Finkelstein reaction on the chloromethylated PS afforded soluble iodomethylated polystyrene with a degree of substitution as high as 96%. The reaction conditions of Minisci were employed to radically pyridinate PS via its iodomethylated derivative. Polyelectrolytes were formed which could be converted to normal polymers by treatment with a 20% aqueous solution of NaOH.     

The gradient volume principle for fast evaluation of optimum conditions for isocratic analysis

Summary The paper describes by simple experiments in a pragmatical way by easy rules of thumbs gradient optimization. Besides selection of the stationary phase and initial and final conditions the two other important variables are program time and eluent flow rate. It is demonstrated, that when the product of both, the gradient volume, is kept constant, the solutes are always eluted with the same eluent composition at column outlet. At constant gradient volume, peak broadening depends on flow rate and on the eluent properties (viscosity) at which the solutes elute, and on the time the solutes spend in the column. Because peak broadening increases with increasing gradient volume, the peak capacity in gradient elution shows an optimum at gradient volumes around 15 empty column volumes (program times 45 to 60 min at flow rates of 1 ml/min with standard columns).Gradient elution can also be used for fast evaluation of optimum eluent composition for isocratic analysis. This procedure requires a calibration of the equipment for determination of eluent composition at column outlet. The sample is chromatographed in a standard gradient run of 10 to 15 empty column volumes. The eluent composition at which the solute of interest elutes during the gradient is used for isocratic analysis, where the k' value of this solute will then be around 2.Part of Ph. D. Thesis H. Elgass, Saarbrücken, 1978, present address Hewlett-Packard, Waldbronn, FRG. In part presented at Eastern Analytical Symposium, New York, 1982.     

具有Friction边界条件的Navier-Stokes方程的两重牛顿校正算法

基于压力投影稳定有限元方法,给出一个求解具有Friction边界条件的Navier-Stokes方程的两重牛顿校正算法．从获得的误差估计可以看出,如果细网格尺度满足h=O（H^4）,那么该两重牛顿校正算法与一重稳定有限元方法具有相同的收敛阶．与有关文献相比,该算法的计算效率更高．