关于一类二次哈密尔顿系统在二次扰动下的极限环个数问题

本文研究了一类具有两个鞍点和一个中心的通用二次哈密尔顿向量场在二次扰动下的三参数开折，证明极限环的最小上界为２。     

Banach空间二阶非线性微分方程的弱Carathéodory解

本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果     

Ⅱ型三角剖分上二次双周期样条

本文用B-网方法确定了△_(nm)~((2))剖分上二次双周期样条函数空间的维数,给出了插值条件的几种提法,证明了解的存在唯一性.     

Hybrid abstractions of affine systems

This paper considers the problem of building a set of hybrid abstractions for affine systems in order to compute over approximations of the reachable space. Each abstraction is based on a decomposition of the continuous state space that is defined by hyperplanes generated by linear combinations of two vectors. The choice of these vectors is based on consideration of the dynamics of the system and uses, for example, the left eigenvectors of the matrix that defines these dynamics. We show that the reachability calculus can then be performed on a combination of such abstractions and how its accuracy depends on the choice of hyperplanes that define the decomposition.     

Spray Freeze-drying – The Process of Choice for Low Water Soluble Drugs?

Most of the novel highly potent drugs, developed on the basis of modern molecular medicine, taking into account cell surface recognition techniques, show poor water solubility. A chemical modification of the drug substance enhancing the solubility often decreases the pharmacological activity. Thus, as an alternative an increase of the solubility can be obtained by the reduction of the size of the drug particles. Unfortunately, it is often difficult to obtain micro or nanosized drug particles by classical or more advanced crystallization using supercritical gases or by milling techniques. In addition, nanosized particles are often not physically stable and need to be stabilized in an appropriate matrix. Thus, it may be of interest to manufacture directly nanosized drug particles stabilized in an inert hydrophilic matrix, i.e. nanostructured and nanocomposite systems. Solid solutions and solid dispersions represent nanostructured and nanocomposite systems. In this context, the use of the vacuum-fluidized-bed technique for the spray-drying of a low water soluble drug cosolubilized with a hydrophilic excipient in a polar organic solvent is discussed. In order to avoid the use of organic solvents, a special spray-freeze-drying technique working at atmospheric pressure is presented. This process is very suitable for temperature and otherwise sensitive drugs such as pharmaproteins.     

A search technique for global optimization in a chaotic environment

We describe a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an unconstrained objective function in search of global minima. The algorithm is unusually adept at avoiding nonoptimal local minima and successfully converging to a global minimum. Trajectories generated by the algorithm for objective functions with many local minima exhibit chaotic behavior, in the sense that they are extremely sensitive to changes in initial conditions and system parameters. In this context, chaos seems to have a beneficial effect: failure to converge to a global minimum from a given initial point can often be rectified by making arbitrarily small changes in the system parameters.     

A dynamical test of phase transition order: New things in old places or old wine in new bottles

We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems.