具有细链双曲无穷远鞍点的二次系统

本文得到：具有细链双曲无穷远鞍点和一个细焦点的二次系统至多存在一个极限环,若有细无穷远分界线环S,则其内部不存在极限环,其稳定性与它包围的奇点的稳定性相反．     

A POLYNOMIAL ALGORITHM FOR FINDING THE MINIMUM FEEDBACK VERTEX SET OF A 3-REGULAR SIMPLE GRAPH

1IntroductionLetG=(VE)beaconnectedsimplegraph.AsubsetFofvertexsetViscalIedafeedbackvertexsetofGifthegraPhGFisaf0rest.ThecardinaIity0faminimumfeedbackvertexset0fGisdenotedbyf(G).AvertexsubsetJofvertexsetViscaJledallonseparatingindependentsetofG,ifJisanilldependentsetofVandGJisconnected.Thema-xiammcardinalityofnollseparatingindependelltsetofGisden0tedbyz(G)andiscalledthenonseparatingindepelldentnumberofG,AgraphGiscalledacactusifGisc0nnectedandanytwocyclesofGaredisjoint.Avertexvofacon…     

利用加速度反馈的大型光电设备主轴控制技术

随着光电跟踪设备的大型化,在系统的惯量增大的同时,机械谐振频率一般会降低,此时控制系统的带宽设计将受到限制,而且大型的光电设备更容易受到风阻、地基振动等各种干扰的影响,从而降低系统的控制精度。由于惯性测量元件——加速度计直接感受被测对象的受力情况,通过引入加速度反馈控制回路,在不增大系统带宽的前提下,中低频段的扰动抑制传递函数幅值下降约25 dB。理论、仿真和实验三方面均验证了该控制方式的有效性。     

Postbuckling Behavior of Thin-Walled Open Cross-Section Compression Members

ABSTRACT

The postbuckling behavior of simply supported columns with thin-walled open cross section is investigated by means of the general nonlinear theory of elastic stability. Fourth-order terms in the series expansion of the total potential energy are disregarded.

It is shown that interaction between linearly independent simultaneous buckling modes is responsible for neutral equilibrium at bifurcation if the column cross section has two axes of symmetry, and unstable if it has only one. If the buckling modes are not simultaneous, the equilibrium is neutral in both cases. Finally, the equilibrium at bifurcation is usually unstable if the cross section has no axis of symmetry.     

Suppression of chaos in a MEMS resonator by delayed position feedback

A delayed position feedback control is applied on DC voltage source for suppressing chaos of a typical MEMS resonator actuated by electrostatic forces. A theoretical necessary condition for chaotic oscillation of the controlled system is presented. Numerical results and the analytical prediction reveal the evolution of dynamical behavior of the system with AC voltage amplitude and the control effect of delayed feedback on reducing chaos of the system. It shows that the delayed feedback control is effective on suppressing chaos of the micro mechanical resonator.     

非线性函数参数的线性化率定方法

非线性函数参数率定基本上都是以误差平方和目标函数为信息依据的,其过程通常包括误差平方和目标函数构建和一阶函数求导为零得其参数优值解这两步操作.本文通过研究发现以上两步操作给非线性函数参数增加了不相关的局部极优值,提出了非线性函数参数的线性化率定方法.该方法对非线性函数以参数为自变量求导,再通过导函数差分线性化,并对线性化的参数用误差平方和目标函数进行率定,然后逐步迫近非线性函数参数的最优值.本文在理论上证明了该方法的收敛性,检验了此方法的合理性、优点和效果,解决了非线性函数参数以误差平方和为目标函数增加不相关的局部极优值的理论性问题,而且该方法的实用性和效果都比较好.     

Displacement fields and self-energies of circular and polygonal dislocation loops in homogeneous and layered anisotropic solids

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order −1, we have shown that the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.     

Long-time dynamics for a nonlinear Timoshenko system with delay

This paper is concerned with a nonlinear Timoshenko system with a time delay term in the internal feedback together with initial data and Dirichet boundary conditions. Under some suitable assumptions on the weights of feedback, we obtain the existence of a global attractor with finite fractal dimension for the case of equal speed wave propagation. Furthermore, the existence of exponential attractors is also derived.     

Beyond statistical methods: teaching critical thinking to first-year university students

We discuss a major change in the way we teach our first-year statistics course. We have redesigned this course with emphasis on teaching critical thinking. We recognized that most of the students take the course for general knowledge and support of other majors, and very few are planning to major in statistics. We identified the essential aspects of a first-year statistics course, given this student mix, focusing on a simple question, ‘Given this is the last chance you have to teach statistics, what are the essential skills students need?’ We have moved from thinking about statistics skills needed for a statistician to skills needed to participate in today's society. We have changed the way we deliver the course with less emphasis on lectures and more on alternative resources including on-line tutorials, Excel, computer-based skills testing, web-based learning materials and smaller group activities such as study groups and example classes. Feedback from students shows that they are very receptive and enthusiastic.     

A three‐dimensional finite element model for the control of certain non‐linear bioreactors

This paper deals with the dynamics of non‐linear distributed parameter fixed‐bed bioreactors. The model consists of a pair of non‐linear partial differential (evolution) equations. The true spatially three‐dimensional situation is considered instead of the usual one‐dimensional approximation. This enables one to take into account the effects of flow profiles and the true location of the measurement transducer. The (output) evolution of the corresponding open‐loop control system is simulated. Furthermore, the associated closed‐loop system with respect to the relevant output function is considered. Especially, the asymptotic output tracking is found to be successful by applying the usual process based on the state feedback linearization. Copyright © 2000 John Wiley & Sons, Ltd.