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.     

Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 1996     

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.     

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．     

Novel pattern formation in the collapse process of floating monolayer at the air-water interface

We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure. The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions. Received: 8 July 1997 / Accepted: 4 November 1997     

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.     

Phase transfer of highly monodisperse iron oxide nanocrystals with Pluronic F127 for biomedical applications

Iron oxide nanoparticles made from the thermal decomposition method are highly uniform in all respects (size, shape, composition and crystallography), making them ideal candidates for many bioapplications. The surfactant coating on the as-synthesized nanoparticles renders the nanoparticles insoluble in aqueous solutions. For biological applications nanoparticles must be water soluble. Here we demonstrate the phase transfer of our nanoparticles with the biocompatible copolymer Pluronic F127. Transmission electron microscopy, Fourier transform infrared spectroscopy and dynamic light scattering indicate that the nanoparticles are coated discretely. Magnetic measurements show that the nanoparticles remain superparamagnetic with saturation magnetization ∼96% of the maximum theoretical value.     

Necessary conditions and non-existence results for autonomous nonconvex variational problems

Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained.     

随机环境中双移民生灭过程的极限性质

引入了随机环境中双移民生灭过程的概念，定义了过程的模态指示函数，在此基础上研究了其转移矩阵的平稳分布，给出了平稳分布众数的位置与模态指示函数之间的关系．研究了平稳分布的众数与边界关系．     

The uv-Decomposition on a Class of D.C. Functions and Optimality Conditions

In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given.