三阶脉冲线性微分方程解的振动性与渐近性

给出引理解决了方程非振动解与其各阶导数的符号关系，并由此得到了若干判别准则，用于判别三阶线性脉冲微分方程解的振动性与渐近性，举例说明了准则的有效性。本文推广了相关文献的结果。     

Lüroth误差和函数的若干性质

本文研究了Lüroth展式的误差和函数.利用误差和函数的Perron-Frobenius算子,得到其积分值.最后,考察并获得其介值性定理,从而得出其图形是一个分形.     

广义多目标minmax问题的最优性条件和极大熵方法

本文讨论了广义多目标minmax问题的最优性条件。利用极大熵逼近函数，研究了广义多目标minmax；问题的逼近问题，在较弱的条件下，证明了由极大熵逼近函数导出的多目标逼近问题的临界点的任一极限点均为原广义多目标minmax问题的临界点。     

Local Lyapunov Exponent for the Bak-Sneppen Model

The chaotic Property of the Bak-Sneppen model is studied from the local Lyapunov exponent in the same way as for dynamical nonlinear systems.Similar behaviour is found for the one- and two-dimensional Bak-Sneppen models.The Lyapunov exponents for the two cases have the same order of magnitude and both decrease at early evolution but show a slow increasing saturation at late evolution.     

静摩擦力教学方法的探讨

当两个互相接触并处于相对静止的物体间存在相对运动趋势时,就有静摩擦力产生.静摩擦力的方向与相对运动趋势方向相反,与接触面相切.为了帮助学生正确处理有关静摩擦力的问题,现介绍以下两种方法.1 根据静摩擦力产生的条件分析     

微分代数多项式系统的可解集

本文对一般微分代数方程给出了几类可解集的概念，并讨论了多项式微分代数方程的可解集，得到子多项式系统具有唯一解。特别是有多于一个的解的条件，并得到了低次多项式在一定意义下的充分必要条件。     

一般组合弹性结构的数学模型

研究由任意多个体、板、梁构成的一般组合弹性结构静态问题. 通过最小势能原理和虚功原理建立问题在向量表示下的数学模型. 在获得了一般组合弹性结构上的广义Korn不等式后, 利用Lax-Milgram引理证明了模型的唯一可解性. 在对解做合理的正则性假设的条件下, 由相应变分形式导出向量表示下的所有平衡方程, 并得到了一个对该问题进行有限元分析时有重要作用的恒等式.     

Spectral Anomalies in the Fraunhofer Diffraction Pattern

We study the spectral characteristics theoretically and experimentally in the Fraunhofer diffraction pattern formed by the diffraction of a spatially coherent, polychromatic light through a slit. It is found that the spectrum in some diffraction directions close to the singular direction is redshifted, compared to the spectrum of the incident polychromatic light, and blueshifted in other directions, and splits into two lines at the singular direction. We show that the experimental results are consistent with the theoretical expectations.     

Temperature-Dependent Dynamic Properties of LixMn2O4 in Monte Carlo Simulations

Monte Carlo (MC) simulations are used to simulate the voltage profile and the ionic conductivity s of Li ions in LixMn2O4 and its dependence on the lithium concentration x. The open circuit potential shows clearly the two plateaus in the charge/discharge curve, which agrees well with the experimental results. The two plateaus become more and more steep when the temperature is increased. The simulated ionic conductivity shows an M-shaped curve in the plot of ionic conductivity cr versus x when the simulation temperature is low. Interestingly,the minimum valley, which lies at the middle single-phase area near x=0.5, disappears gradually when the temperature increases to 453K.     

Banach空间非线性混合型微分-积分方程整体解的存在性和唯一解

研究了Banach空间中非线性混合型微分-积分方程初值问题u′=f(t,u,Tu,Su),u(0)=x0的整体解,完全没有要求f的任何增性,利用Mnch不动点定理和比较结果得到了初值问题整体解的存在性和唯一解,并且给出了一致收敛于唯一解的迭代序列,改进推广和统一了已有的许多结果.