Geometric Approach to Response Theory in Non-Hamiltonian Systems

The theory of differential forms and time-dependent vector fields on manifolds is applied to formulate response theory for non-Hamiltonian systems. This approach is manifestly coordinate-free, and provides a transparent derivation of the response of a thermostatted system to a time-dependent perturbation.     

学习钱学森技术科学思想的体会

以个人体会从几个方面介绍钱学森先生的技术科学思想：什么是科学技术：技术科学的重要性;技术科学如何为应用服务;技术科学工作应具有的基础知识;钱学森技术科学思维在建立力学研究所中的实践,最后谈一谈关于力学要继续走技术科学道路的一些想法。     

SISO多维控制系统的反馈镇定性及算法的数学机械化实现

从代数学的理想论以及代数簇理论,探讨了SISO多维控制系统的可反馈镇定条件,并给出反馈控制的表示.文中的主要结果建立在判定一个多变元多项式的零点集是否与由多项式刻画的凸集相交的前提之上,并用数学机械化方法实现了这一判定的过程.     

一簇Lorenz映射的混沌行为与统计稳定性

该文研究一簇Ｌｏｒｅｎｚ映射犛犪：［０,１］→［０,１］（０＜犪＜１）犛犪（狓）＝狓＋犪　狓∈ ［０,１－犪）｛（狓＋犪－１）／犪　狓∈ ［１－犪,１］．从拓扑的角度考虑了犛犪的混沌行为,证明了：犛犪有稠密轨道;犛犪的周期的集合犘犘（犛犪）＝｛１,犿＋１,犿＋２,…｝,其中犿为使犪犿＜１－犪成立的最小正整数;犛犪的拓扑熵犺（犛犪）＞０;几乎所有（关于Ｌｅｂｅｓｇｕｅ测度）的点狓的Ｌｙａｐｕｎｏｖ指数λ（犛犪,狓）＝λ犪＞０．从统计的角度讨论了犛犪的稳定性．我们用下界函数方法证明了犛犪是统计稳定的,并且狌犵犪（犃）＝∫犃犵犪（狓）ｄ狓（犃∈犅）为犛犪的唯一绝对连续（关于Ｌｅｂｅｓｇｕｅ测度）不变概率测度．同时,不变密度犵犪在参数扰动和随机作用的随机扰动下是稳定的．     

高校数学基础课教师教学质量评价方法的研究

分析了高校教师教学质量评价体系存在的突出问题.针对所存在的突出问题,结合数学基础课程的教学特点,构建了高校数学基础课教师教学质量评价方法,并取得了良好的应用效果.     

一个新的秋千参激振动的数学模型

提出了一个新的秋千参激振动的数学模型,并根据此模型对秋千的参激振动现象作出了理论解释．     

Segregation effect in symmetric cellular automata model for two-lane mixed traffic

Segregation effects commonly exist in granular mixtures with difference in size, shape or density. In mixed traffic flow, slow vehicle and fast vehicle, as two types of particles, have different desired speed. We investigate the segregation along the road in mixed traffic flow by using a symmetric two-lane cellular automata model. A parameter D, which quantifies the degree of segregation, is defined. We study the density dependency of the parameter at different randomization probability. Simulation results show that segregation is more obviously in free flow region. We argue that the overtaking maneuvers have similar effect as percolation in granular flow.     

Kinetic market models with single commodity having price fluctuations

We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of trading or exchange of money and commodity proceeds, with local (in time) fluctuations in the price of the commodity. These distributions are studied in markets with agents having uniform and random saving factors. The self-organizing features in money distribution are similar to the cases without any commodity (or with consumable commodities), while the commodity distribution shows an exponential decay. The wealth distribution shows interesting behavior: gamma like distribution for uniform saving propensity and has the same power-law tail, as that of the money distribution, for a market with agents having random saving propensity.     

将数学建模思想融入工科“概率统计”教学中

提出‘概率统计”课程的一种教学改革思路,注重理论联系实际,强调应用案例中融入数学建模思想的新的教学法.改革课堂教学方法,探索新的教学模式.加强学生的实践性教学环节,培养学生的应用能力和创新能力.     

医用硬性内窥镜畸变的评定基础和方法

建立医用硬性内窥镜畸变的评定基础和方法,用视轴对称的球面Z视场为模型来模拟体腔凹面特征,以建立内窥镜物像共轭的分析基础;运用光学原理并结合ISO9039:1994“光学和光学仪器光学系统质量评价———畸变的测定”的定义原则,并根据理论畸变的临床要求确定畸变定义;采用主光线追迹原理推导不同球面Z形状的畸变换算通式。创立了医用硬性内窥镜以单位相对畸变表述的定义和表达式,并导出变换视场面的畸变换算通用公式和测试方法。本文建立的畸变评定基础和方法适用于医用硬性内窥镜的标准应用。