ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures.     

改性壳聚精膜用于醇水混合液分离的研究──Ⅲ．超细粉末填充壳聚精膜

首次制备了用Ｓｉ３Ｎ４，ＳｉＯ２，ＴｉＨ４超细粉末填充的改性壳聚精膜，并将其用于乙醇／水混合液的分离中。实验表明壳聚糖膜经超细粉末填充后强度增大，溶胀度减小。用于乙醇／水混合液渗透蒸发分离时，分离因子和渗透通量都有提高，并在填充量为１６．７％附近出现极大值。随着料液中乙醇含量的增大，渗透通量减小，分离因子增大；随着料液温度的升高渗透通量显著增大，分离因子则稍有下降。并简单讨论了超细粉末在乙醇／水混合液分离中的作用。     

正负系数中立型差分方程的正解的存在性

In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature     

Quantum Cosmology in CGBD Theory

We apply the theory developed in quantum cosmology to a model of charged generalized Brans–Dicke gravity. This is a quantum model of gravitation interacting with a charged Brans–Dicke type scalar field which is considered in the Pauli frame. The Wheeler–DeWitt equation describing the evolution of the quantum Universe is solved in the semiclassical approximation by applying the WKB approximation. The wave function of the Universe is also obtained by applying both the Vilenkin-like and the Hartle–Hawking-like boundary conditions. We then make predictions from the wave functions and infer that the Vilenkin's boundary condition is more reasonable in the Brans–Dicke gravity models leading a large vacuum energy density at the beginning of the inflation.     

On superlinear convergence of quasi-Newton methods for nonsmooth equations

We show that strong differentiability at solutions is not necessary for superlinear convergence of quasi-Newton methods for solving nonsmooth equations. We improve the superlinear convergence result of Ip and Kyparisis for general quasi-Newton methods as well as the Broyden method. For a special example, the Newton method is divergent but the Broyden method is superlinearly convergent.     

Influence of preparation method on SrMoO4 impurity content and magnetotransport properties of double perovskite Sr2FeMoO6 polycrystals

The magnetic and electric properties of the Sr₂FeMoO₆ compound produced under different preparation conditions were studied. Depending on the preparation condition, a strong variation in the nonmagnetic SrMoO₄ impurity content was found, which in turn determined the metallic or semiconducting behavior of the resistivity of the Sr₂FeMoO₆ compound. There was also evidence that SrMoO₄ played a crucial role in modifying the low magnetic field intergrain tunneling magnetoresistance in Sr₂FeMoO₆. In addition, we have established a simple method to prepare the single phase Sr₂FeMoO₆ polycrystals.     

取代对苯二酚醚化物的合成研究

本文从取代的对苯三酚３出发、利用Ｗｉｌｌｉａｍｓｏｎ醚化反应合成了一系列它的醚化产物４ａ－４Ｈ，给出了它们的核磁共振数据（氢谱和碳谱）。讨论了影响醚化反应的一些因素，比较了不同烷化剂发生醚化反应的活泼性。     

Continuous approximation schemes for stochastic programs

One of the main methods for solving stochastic programs is approximation by discretizing the probability distribution. However, discretization may lose differentiability of expectational functionals. The complexity of discrete approximation schemes also increases exponentially as the dimension of the random vector increases. On the other hand, stochastic methods can solve stochastic programs with larger dimensions but their convergence is in the sense of probability one. In this paper, we study the differentiability property of stochastic two-stage programs and discuss continuous approximation methods for stochastic programs. We present several ways to calculate and estimate this derivative. We then design several continuous approximation schemes and study their convergence behavior and implementation. The methods include several types of truncation approximation, lower dimensional approximation and limited basis approximation.His work is supported by Office of Naval Research Grant N0014-86-K-0628 and the National Science Foundation under Grant ECS-8815101 and DDM-9215921.His work is supported by the Australian Research Council.