Stability and bifurcation analysis in the delay-coupled van der Pol oscillators

In this paper, the dynamics of a system of two van der Pol equations with a finite delay are investigated. We show that there exist the stability switches and a sequence of Hopf bifurcations occur at the zero equilibrium when the delay varies. Using the theory of normal form and the center manifold theorem, the explicit expression for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.     

A novel approach to determine the molecular overlap of polyelectrolyte using an ultrafiltration membrane

The overlapping of charged polymers (e.g., polyelectrolyte) in the liquid phase is one of the key parameters affecting the processing of the macromolecular solutions. This work focused on the development of a novel method for determining the overlap concentration of polyelectrolytes with stirred cell ultrafiltration (UF) techniques. A new, simplified equation that incorporated the resistance-in-series UF model into the osmosis phenomenon caused by polymers was developed, and then applied to estimate the threshold concentration for macromolecular overlap. The overlap concentrations of model polymers, such as poly(dimethylamine-co-epichlorohydrin-co-ethylenediamine) and poly(diallyldimethylammonium chloride), were evaluated with different, initial polymer concentrations and membrane pore sizes. In the correlation between ln R_t/C_r and ln C_r, the concentration where ln R_t/C_r had the minimal value was referred to as the overlap concentration. The gyration radius of polyelectrolytes was calculated using the overlap concentration, which can provide insight into the understanding of the size of polymers and their rejections by membranes. Determining the overlap concentration of polymers with a UF membrane appeared to be viable and practical.     

Second-Order Smoothing Objective Penalty Function for Constrained Optimization Problems

In this article, a novel objective penalty function as well as its second-order smoothing is introduced for constrained optimization problems (COP). It is shown that an optimal solution to the second-order smoothing objective penalty optimization problem is an optimal solution to the original optimization problem under some mild conditions. Based on the second-order smoothing objective penalty function, an algorithm that has better convergence is introduced. Numerical examples illustrate that this algorithm is efficient in solving COP.     

图的Smarandachely邻点无圈边色数的一个上界

提出了图的Smarandachely邻点无圈边染色的概念,讨论了图的Smarandachely 邻点无圈边染色与邻点可区别无圈边染色之间的关系,并运用概率方法得到了图G的Smarandachely邻点无圈边色数的一个上界,其中G为无孤立边的图.     

支持向量机回归法在近红外光谱测定植物纤维原料中甲氧基含量中的应用

以26个植物纤维原料为实验材料,由20个样品作校正样品,采用径向基核函数方法对纤维原料中甲氧基含量与纤维原料样品近红外光谱进行支持向量机(SVM)回归建模.以所建SVM回归模型对6个纤维原料样品中甲氧基含量进行预测,回归模型的预测结果与采用改良的维伯克法确定的甲氧基含量的相关系数为0.977,预测样本集的标准偏差为0.43.将SVM回归模型的预测效果与PLS回归模型的预测结果进行比较,所建近红外光谱测定植物纤维原料中甲氧基含量的SVM回归模型可用于实际植物纤维原料样品的定量分析,且具有较好的分析效果.     

上证指数收益率分布的拟合

本文旨在讨论上证指数收益率序列的分布特征 ,通过对上证指数 1 997年 5月 2 3日至 2 0 0 1年 7月1 3日 ,总计 1 0 0 0多个交易日的统计分析 ,发现上证指数收益率的分布具有“尖峰、厚尾”的特性 .我们试图用文献 [1 ]给出 Lévy flight来拟合其分布 ,但结果并不理想 .为此我们提出了一种类似 Weibull分布的函数来拟合上证指数收益率分布 ,模拟结果较好 .同时 ,我们按通常的方法对尾部作了截尾处理 ,以更接近实际数据在尾部表现出来的“厚尾”现象     

Parametric estimation of discretely sampled Gamma-OU processes

The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.     

非光滑多目标规划的不动点算法(英)

本文讨论不动点算法在非光滑多目标规划中的应用，得到了一些新的最优性条件以及不动点与非光滑多目标的解之间的关系，并且给出了解非光滑多目标规划的不动点算法的收敛性．     

Hamilton体系与与弹性力学Saint－Venant问题

本文一改传统的在Ｌａｇｒａｎｇｅ体系欧几里德空间中用半道法讨论Ｓａｉｎｔ－Ｖｅｎａｎｔ问题的方法，而在具有守恒性的Ｈａｍｉｌｔｏｎ体系中辛空间里研究该问题．通过讨论Ｈａｍｉｌｔｏｎ算子矩阵的零本征值及其Ｊｏｒｄａｎ型，直接求解出全部Ｓａｉｎｔ－Ｖｅｎａｎｔ问题的解．     

弹塑性梁在轴向应力波下的动态屈曲

本文考虑轴向应力波效应，利用分叉理论研究各种支承半无限长弹塑性梁的动态屈曲问题。在轴向阶梯载荷和脉冲载荷冲击下得到了梁的临界屈曲载荷及初始屈曲模态。其结果与实验现象相一致。同时也为研究结构动态屈曲问题提供了有效途径。