多工况多约束下离散变量桁架结构的拓扑优化设计

提出了一个多工况下受应力、位移约束的离散变量桁架结构的拓扑优化方法，给出了结构拓扑形式变更时的约束处理方法及杆件删除策略，使基结构设计空间的维数不断降低，达到最优拓扑，避免了奇异解的出现，在算例中指出了截面离散集和位移约束对最优拓扑的影响；算例给出了满意的拓扑优化解。     

关于国家自然科学基金资助摩擦学基础研究的分析与讨论

本文首先对国家自然科学基金在１９８６－１９９１年间资助摩擦学基础研究的情况进行了简洁的分析，接着就其资助办法作了介绍，最后着重对如何利用科学基金促进摩擦学的发展问题作了讨论，指出应当把坚持应用摩擦学学科发展战略的研究成果、鼓励和支持创新性研究、积极支持交叉学科研究和注意扶植新的学科生长点、加强摩擦学研究与实际应用相结合和促进优秀青年摩擦学研究人才的迅速成长等作为国家自然科学基金资助摩擦学基础研究的     

基于功能的结构体系目标可靠度优化决策

根据“投资－效益”准则，提出了基于功能的结构体系目标可靠度优化决策的三种模型：概念模型、参数规划法模型和约束放松法模型；并根据最优性条件Kuhn-Tucher条件证明了当基于功能的结构体系可靠度约束均为作用约束时，参数规划法模型和约束放松法模型的等价性；最后对钢筋混凝土框架结构基于不同抗震功能的目标可靠度指标进行了优化计算。     

A GENERAL FREQUENCY DEPENDENT DIGITAL OPTIMAL PREVIEW SERVO SYSTEM

ＡＧＥＮＥＲＡＬＦＲＥＱＵＥＮＣＹＤＥＰＥＮＤＥＮＴＤＩＧＩＴＡＬＯＰＴＩＭＡＬＰＲＥＶＩＥＷＳＥＲＶＯＳＹＳＴＥＭＡＧＥＮＥＲＡＬＦＲＥＱＵＥＮＣＹＤＥＰＥＮＤＥＮＴＤＩＧＩＴＡＬＯＰＴＩＭＡＬＰＲＥＶＩＥＷＳＥＲＶＯＳＹＳＴＥＭ￥ＬｉａｏＦｕｃｈ...     

Optimal Control of Deployment of a Tethered Subsatellite

One of the most important operations during a tethered satellite system mission is the deployment of a subsatellite from a space ship. We restrict tothe simple but practically important case that the system ismoving on a circular orbit around the Earth. The main problem duringdeployment due to gravity gradient is that the two satellites do not move along the straight radial relative equilibrium position which is stable for a tether of constant length. Instead, deploymentleads to an unstable motion with respect to the radial relativeequilibrium configuration. Therefore we introduce an optimal control strategy using theMaximum Principle to achieve a force controlled deployment of the tethered subsatellite from the radial relative equilibrium position close to the space ship to the radial relative equilibrium position far away from the space ship.     

Optimal Slewing of a Flexible Spacecraft

An optimal slewing program is designed within the class of Euler rotations for a spacecraft with elastic elements. The mathematical model constructed accounts for an arbitrary number of partial modes of elastic vibrations. An optimal reorientation problem is formulated using a nontraditional performance criterion, which minimizes the dynamic overloads of the elastic elements in relative motion. An algorithm for solving the corresponding nonlinear boundary-value problem is developed and implemented in a software package of FORTRAN-programs. A neural network is generated in the space of slew parameters; it may be trained during a preflight period. Known radial basis functions are used to model the process of fast in-flight computation of the optimal reorientation program     

Morris-Lecar系统中通道噪声诱导的自发性动作电位研究

在生物物理学中, 越来越多的现象是由于分段确定性的动力系统与连续时间马氏过程之间的耦合作用而产生的. 因为这种耦合性, 相关的数学模型更适合取为随机混合系统而不是扩散过程(基于It?随机微分方程). 本文从理论上和数值上研究了在弱噪声条件下无鞍点状态的随机混合Morris-Lecar系统中, 由通道噪声诱导的自发性放电现象. 一个动作电位的初始阶段可视为噪声诱导的逃逸事件, 其最优路径和拟势可由辅助Hamilton系统给出. 由于系统不存在鞍点, 因此可选择虚拟分界线(ghost separatrix)为阈值, 研究噪声诱导的自静息态的逃逸事件. 通过计算在阈值处的拟势, 便可发现其值有一个明显的最小值, 其作用类似于鞍点. 通过改进的Monte Carlo模拟方法, 计算了历程概率分布, 其结果对初始阶段和兴奋阶段的理论解均给出了验证. 此外, 基于前人将拟势等高线作为阈值的另一种选择, 我们对两种阈值取法的优劣性进行了比较. 最后, 本文研究了钠离子和钾离子通道噪声的不同组合对最优路径和拟势的影响. 结果表明: 钾离子通道噪声在自发性放电过程中起主导作用, 且两种噪声强度存在一个最优比例能使总的噪声强度达到最小.      

Optimal control and stability analysis of an online game addiction model with two stages

In this paper, we establish a mathematical model of online game addiction with two stages to research the dynamic properties of it. The existence of all equilibria is obtained, and the basic reproduction number is calculated by the method of next-generation matrix. The global asymptotic stability of disease-free equilibrium (DFE) is proved by comparison principle, and the global asymptotic stability of endemic equilibrium (EE) is proved by constructing an appropriate Lyapunov function. Then we use the Pontryagin's maximum principle to find the optimal solution of the model, so that the number of infected people can be minimized. In numerical simulation, firstly, we validate the global stability of DFE and EE. Secondly, we consider three kind of control measures (treatment, isolation, and education) and divide them into four cases. The models with control and without control are solved numerically by using forward and backward sweep Runge-Kutta method. In order to achieve the best control effect, we suggest that three kind of measures should be used simultaneously according to the optimal control strategy.     

Space-time finite element methods stabilized using bubble function spaces

ABSTRACT

In this paper, a stabilized space-time finite element method for solving linear parabolic evolution problems is analyzed. The proposed method is developed on a base of a space-time variational setting, that helps on the simultaneous and unified discretization in space and in time by finite element techniques. Stabilization terms are constructed by means of classical bubble spaces. Stability of the discrete problem with respect to an associated mesh dependent norm is proved, and a priori discretization error estimates are presented. Numerical examples confirm the theoretical estimates.