Monoesterification of styrene–maleic anhydride copolymers with alcohols in ethyl benzene: Catalysis and kinetics

A kinetic investigation on the monoesterification reaction of the maleic anhydride residue (MA) in styrene-maleic anhydride copolymers with aliphatic alcohols was carried out in ethyl benzene solution. By comparison to classic catalysts such as tributylamine (TBA) and pyridine, 4-dimethylaminopyridine (4DMAP) is by far the most effective catalyst for this reaction. While both general base and nucleophilic mechanisms contribute to the reaction catalyzed by TBA or pyridine, a nucleophilic mechanism prevails with 4DMAP. This reaction is reversible, and its chemical equilibrium constant decreases significantly with increasing temperature. Both kinetic and thermodynamic results showed that in the presence of 4DMAP, the forward and reverse reactions are second and first order, respectively. The existence of side reactions, reactivity of two styrene-maleic anhydride copolymers of different MA contents as well as two aliphatic alcohols of different lengths are also addressed. © 1993 John Wiley & Sons, Inc.     

A Method for Establishing Optimality Conditions for a Nonsmooth Vector-Valued Minimax Problem

Using a method of uniform approximations, necessary and sufficient conditions for a nonsmooth constrained vector-valued minimax problem are established in terms of Mordukhovich subdifferentials.     

映象方程多解问题的某些研究

本文用ｆｐ－同伦方法，在一定的技巧和变换的配合下，在紧性条件支持下，研究了赋范线性空间中一类集值映象方程的多解问题。还给出所得理论结果的一个应用。     

周期单元中相对论Boltzmann方程初值问题整体解的存在性

本文证明了周期单元中带有某些硬相互作用的相对论Ｂｏｌｔｚｍａｎｎ方程初值问题在初值满足质量、能量和熵有限的条件下具有一个整体温和解．     

On weak spreadability of distributed-parameter systems and its achievement via linear--quadratic control techniques

In this paper, the concept of weak spreadability is introduced.It constitutes an extension of the idea developed by El Jai& Kassara. In the case of linear distributed systems weconsider quadratic control techniques with a conveniently penalizedcriterion which makes the system weakly spreadable. The approachis outlined for a convection—diffusion system, and theresults of a numerical study are also included to illustratethe main features of the considered problem.     

Formulation,Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems

In this paper, we present a unified treatment and analysis of a dynamic traffic network model with elastic demands formulated and studied as a projected dynamical system. We propose a travel route choice adjustment process that satisfies the projected dynamical system. Under certain conditions, stability and asymptotical stability of the equilibrium patterns are then derived. Finally, two discrete-time algorithms, the Euler method and the Heun method, are proposed for the computation of the solutions, and convergence results established. The convergence results depend crucially on stability analysis. The performance of the algorithms is then illustrated on several transportation networks.     

The Nonexistence of Procedures with Bounded Performance Characteristics in Certain Parametric Inference Problems

This paper gives a condition which implies the nonexistence of parametric statistical procedures with bounded risk or error performance characteristics. Many examples for which such a condition is satisfied are considered.     

多重积分Nash平衡点的Lipschitz估计

设F（p，q）和G（p，q）在无穷远点的邻域内是分别关于p和q的近似凸函数，且具有二次增长．考虑由F和G构成的一对定义在Soblev空间中的泛函．本文利用blowup技巧，证明了这样一对泛函的Nash平衡点实际上是Lipschitz连续的．     

Comparison of Thermodynamic Characteristics of a Potential Well under Quantum and Classical Approaches

The conjecture according to which the mean energy of an equilibrium system in quantum theory exceeds the mean energy of the corresponding classical system is considered. It is rigorously proved that the conjecture holds for the potential well. The estimates for the mean energy of the potential well at high and low temperatures are of special interest.