一类非线性微分方程的脉冲镇定

针对一般形式的常微分系统提出了脉冲指数镇定的概念，具体研究了一类分离变量型非线性常微分方程的脉冲镇定问题，得到了该方程可脉冲指数镇定的充分判据，全文的概念及结论突出了脉冲在方程稳定性方面的控制效果。     

Oscillation theorems for differential equations with a nonlinear damping term

In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity, and, as a consequence, our results apply to wider classes of nonlinear differential equations. Two illustrative examples are considered.     

On Oscillation Criteria of Fourth Order Linear Differential Equations

The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives.     

非线性Schrdinger方程的高精度守恒差分格式

本文首先分析线性Schrodinger方程一种高阶差分格式的构造方法,得到方程的耗散项.在此基础上对三次非线性Schrodinger方程,提出了一种精度为O(r2 h2)的差分格式,证明了该格式保持了连续方程的两个守恒量,且是收敛的与稳定的.并通过数值例子与已有隐格式进行了比较,结果表明,本文格式在计算量类似的情况下,提高了数值精度.     

对流扩散方程的一种新型差分格式

对流扩散方程可以描述众多的物理化学现象，因而对其寻求稳定的，实用的数值解法有着重要的现实意义。本文针对形式较一般的一维非定常对流扩散方程，构造了对角元严格占优的Crank-Nicholson差分格式，然后对其分别用分离变量的方法以及能量估计的方法作了稳定性的分析，最后给出了数值试验的结果，数值结果表明本文构造的格式能够较好的处理经典的Crank-Nicholson格式所不能处理的对流项系数较大的对流扩散方程，并具有较好的精度。     

Comment on: “Confined states in two-dimensional flat elliptic quantum dots and elliptic quantum wires” [Physica E 11 (2001) 345]

We argue that the two-dimensional elliptic quantum dot problem with finite barrier cannot be exactly solved, contrary to a recent assertion (van den Broek and Peeters, Physica E 11 (2001) 345. We also prove it explicitly by numerically calculating the correct energy spectrum.     

OSCILLATION RESULTS FOR A SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.     

UV‐ignited frontal polymerization of an epoxy resin

By combining frontal polymerization and radical‐induced cationic polymerization, it was possible to cure thick samples of an epoxy monomer bleached by UV light. The effect of the relative amounts of cationic photoinitiator and radical initiator was thoroughly investigated and was related to the front's velocity and its maximum temperature. The materials obtained were characterized by quantitative conversion also in the deeper layers, not reached by UV light. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2066–2072, 2004     

Photoinitiators with functional groups. VII. Covalently bonded camphorquinone—amines

Camphorquinone (CQ), a widely used photoinitiator (PI) in dental applications, was covalently bonded to aromatic amines to enhance the rate of electron and proton transfer effect due to the close vicinity of the diketone and the amine group. 10‐bromocamphorquinone and 10‐bromomethylcamphorquinone were selected as suitable precursors for esterification with the carboxyl group containing aromatic amines based on 4‐dimethylaminobenzoic acid. Properties of the new photoinitiating systems were investigated by UV spectroscopy and differential scanning photocalorimetry in lauryl acrylate. Compared to physical mixtures, in all cases similar or even better performance was obtained. Surprisingly, 10‐acetyl derivatives 7 – 9 and 18 especially, were found to be highly reactive. Compared to CQ/ethyl 4‐dimethylaminobenzoate, the rate of photopolymerization was increased by a factor of up to 2. Intramolecular reaction was confirmed by photo‐differential scanning calorimetry experiments with varying PI concentrations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4948–4963, 2004     

Synthesis and characterization of new segmented polyurethanes with side‐chain,liquid‐crystalline chain extenders

Liquid‐crystalline, segmented polyurethanes with methoxy–biphenyl mesogens pendant on the chain extender were synthesized by the conventional prepolymer technique and esterification reaction. Two, side‐chain, liquid‐crystalline (SCLC) polyurethanes with mesogens having spacers of six and eight methylene units were prepared. The structures of the mesogenic units and SCLC polyurethanes were confirmed by Fourier transform infrared spectroscopy and ¹H NMR. Polymer properties were also examined by solubility tests, water uptakes, and inherent viscosity measurements. Differential scanning calorimetry studies indicated that the transition temperature of the isotropic to the liquid‐crystalline phase decreased with increasing spacer length. Wide‐angle X‐ray diffraction (WAXD) studies revealed the existence of liquid‐crystalline phases for both SCLC polyurethanes. Polarized optical microscopic investigations further confirmed the thermotropic liquid‐crystalline behaviors and nematic mesophases of both samples. Thermogravimetric analysis displayed better thermal stabilities for both SCLC polymers and indicated that the presence of mesogenic side chains may increase the thermal stability of segmented polyurethanes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 290–302, 2004