三阶拟线性全双曲方程及其上下解序列

本文运用微分不等式定理,定义了三阶拟线性全双曲方程特征问题的上下解,构造了收敛于特征问题解的一对上、下解单调序列,提供了寻求近似解的一种可行方法。     

Numerical calculation of singular integrals appearing in three-dimensional potential flow problems

Two approximate methods for calculating singular integrals appearing in the numerical solution of three-dimensional potential flow problems are presented. The first method is a self-adaptive, fully numerical method based on special copy formulas of Gaussian quadrature rules. The singularity is treated by refining the partitions of the copy formula in the vicinity of the singular point. The second method is a semianalytic method based on asymptotic considerations. Under the small curvature hypothesis, asymptotic expansions are derived for the integrals that are involved in the calculation of the scalar potential, the velocity as well as the deformation field induced from curved quadrilateral surface elements. Compared to other methods, the proposed integration schemes, when applied to practical flow field calculations, require less computational effort.     

Equations of attainable set dynamics,part 1: Integral funnel equations

In control theory, there is growing interest in the evolution of sets, especially attainable sets at timet. This is caused due to their applications to control under uncertainty, optimal control, and differential games. Recently, a new mathematical theory for attainable set evolution was developed. It is based on the concept of approximate localization, instead of differentiation. Here, we give a generalization of this theory.     

Dynamic mechanical behavior of acrylonitrile butadiene rubber/poly(ethylene‐co‐vinyl acetate) blends

The dynamic mechanical behavior of uncrosslinked (thermoplastic) and crosslinked (thermosetting) acrylonitrile butadiene rubber/poly(ethylene‐co‐vinyl acetate) (NBR/EVA) blends was studied with reference to the effect of blend ratio, crosslinking systems, frequency, and temperature. Different crosslinked systems were prepared using peroxide (DCP), sulfur, and mixed crosslink systems. The glass‐transition behavior of the blends was affected by the blend ratio, the nature of crosslinking, and frequency. sThe damping properties of the blends increased with NBR content. The variations in tan δ_max were in accordance with morphology changes in the blends. From tan δ values of peroxide‐cured NBR, EVA, and blends the crosslinking effect of DCP was more predominant in NBR. The morphology of the uncrosslinked blends was examined using scanning electron and optical microscopes. Cocontinuous morphology was observed between 40 and 60 wt % of NBR. The particle size distribution curve of the blends was also drawn. The Arrhenius relationship was used to calculate the activation energy for the glass transition of the blends, and it decreased with an increase in the NBR content. Various theoretical models were used to predict the modulus of the blends. From wide‐angle X‐ray scattering studies, the degree of crystallinity of the blends decreased with an increasing NBR content. The thermal behavior of the uncrosslinked and crosslinked systems of NBR/EVA blends was analyzed using a differential scanning calorimeter. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1556–1570, 2002     

Effect of the segmental mobility restriction on the thermoset chemical kinetics

The cure kinetics of an epoxy–amine commercial thermoset system have been investigated with the isothermal differential scanning calorimetry technique. In particular, a kinetic study has been performed in the glass–transition zone, in which diffusion phenomena compete with the chemical transformations and the overall reaction rate is partially slowed by the reduced segmental chain mobility. A generalized form of the Vogel equation has been formulated to account for the effect of the increasing glass–transition temperature on the chain mobility and, therefore, on the overall reaction rate. The kinetic model has been expressed with two factors representing the chemical reaction rate and the segmental mobility reduction. As the main result, the activation energy relative to the diffusion phenomena has been found to be very low, having a value of 42.5 K ≈ 0.356 kJ/mol, which is compatible only with the small‐angle rotation of the reactive unit. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3757–3770, 2002     

Cure kinetics of the ring‐opening metathesis polymerization of dicyclopentadiene

The cure kinetics of polydicyclopentadiene prepared by ring‐opening metathesis polymerization with three different concentrations of Grubbs' catalyst were examined with differential scanning calorimetry. The experimental data were used to test several different phenomenological kinetic models. The data were best modeled with a model‐free isoconversional method. This analysis revealed that the activation energy increased significantly for degrees of cure greater than 60%. The catalyst concentration had a large effect on the cure kinetics. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2373–2383, 2002     

具转向点常微分方程混合边值问题的一致收敛差分格式

本文得到了具转向点的二阶常微分方程混合边值问题解的导数估计,提出了Il′in型差分格式,证明了此差分格式按L~1模关于小参数ε的一阶一致收敛性。最后,给出了一个数值例子,计算结果与理论分析一致。     

Morse inequalities, a function space integral approach

In this paper we prove the Morse inequalities in the non-degenerate and degenerate cases. Like the approach of J.-M. Bismut, ours is based on the idea suggested by Witten. In fact, if anything, our approach is closer to Witten's original idea than Bismut's.     

Lie-algebraic approach for pricing moving barrier options with time-dependent parameters

In this paper we apply the Lie-algebraic technique for the valuation of moving barrier options with time-dependent parameters. The value of the underlying asset is assumed to follow the constant elasticity of variance (CEV) process. By exploiting the dynamical symmetry of the pricing partial differential equations, the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly, and thus provides an efficient way for computing the prices of the moving barrier options. The method is also able to provide tight upper and lower bounds for the exact prices of CEV barrier options with fixed barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.     

Smooth and Nonsmooth Lipschitz Controls for a Class of Vector Differential Equations

This paper is devoted to the study of a class of control problems associated to a nonlinear second-order vector differential equation with pointwise state constraints. The control is realized via a function of the state. We extend the results of Akkouchi, Bounabat, and Goebel to vector differential equations and furthermore consider the more general case. Under proper conditions, we prove the existence of optimal controls in the class of Lipschitz functions and obtain an optimality condition which looks somehow like the Pontryagin maximum principle for a smooth optimal control function. For a nonsmooth optimal control function, we derive a suboptimality condition by means of the Ekeland variational principle.Communicated by M. J. BalasThis work was supported by 985 Project of Jilin University. The author thanks Professor Yong Li for valuable suggestions. He also thanks Professor M. J. Balas and the anonymous referees for their comments.