On the monotonicity of the period function of reversible centers On the monotonicity of the period function of reversible centers

In this paper we study the period function of centers for a class of reversible systems and give a criteria to determine the monotonicity of the period functions.     

PDMS梯度光栅结构制备技术研究

由于传统方法制作的梯度光栅,工艺条件苛刻,制作过程复杂,难以控制,制作成本高,周期较长,提出了一种成本低、工艺简单、可大量制备梯度光栅的工艺方法,采用基于刚性薄膜/柔性衬底的自组装工艺和氧等离子体(Plasma)的方法制备了微米尺度的梯度光栅,利用Plasma时间的可控性和聚二甲基硅氧烷(PDMS)优异的弹性制得所需要尺寸的光栅。首先在聚乙烯对苯二酸脂(PET)薄膜上旋涂一层PDMS薄膜,待PDMS薄膜固化后将双层薄膜弯曲并用Plasma处理,在其表面生成一层刚性氧化层,借助柔性的PET对刚性层施加均匀应力,当应力超过临界值时,在PDMS基底上自组装形成光栅褶皱结构。由于弯曲时预应力的变化,所以在PDMS薄膜上会形成周期和高度呈阶梯状的的光栅褶皱,也就是梯度光栅。采用可见光作为梯度光栅的性能测试光源,选用一级衍射光作为检测对象,从图谱中可以看出以PDMS为基底制备的光栅具有很好的衍射效应,并可实现很好的分光效果。实验表明：梯度光栅具有明显的衍射现象,并且衍射角变化显著,可广泛用于应力测量。这种方法制备的柔性梯度光栅也可以作为微型应变装置来检测应力的变化,未来有望用于微型光谱仪、扫描仪、光通讯等领域中。     

Non-linear dynamics of a cracked cantilever beam under harmonic excitation

The presence of cracks in a structure is usually detected by adopting a linear approach through the monitoring of changes in its dynamic response features, such as natural frequencies and mode shapes. But these linear vibration procedures do not always come up to practical results because of their inherently low sensitivity to defects. Since a crack introduces non-linearities in the system, their use in damage detection merits to be investigated. With this aim the present paper is devoted to analysing the peculiar features of the non-linear response of a cracked beam.The problem of a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite elements; the behaviour of the breathing crack is simulated as a frictionless contact problem. The modification of the response with respect to the linear one is outlined: in particular, excitation of sub- and super-harmonics, period doubling, and quasi-impulsive behaviour at crack interfaces are the main achievements. These response characteristics, strictly due to the presence of a crack, can be used in non-linear techniques of crack identification.     

Mesures d'indépendance linéaire de carrés de périodes et quasi-périodes de courbes elliptiques

A linear independence measure over Q is obtained for values of some generalized hypergeometric functions at rational points and for the squares of real periods and quasi-periods of elliptic curves in Legendre form y²=x(x−1)(x−1/q) for almost every q∈Z.     

Period Doubling and Chaos of Spontaneous Oscillatory Phenomena on Iron

Summary.  A new self-oscillating system introducing spontaneous oscillatory phenomena on iron in a sulfuric acid solution of hydrogen peroxide is discussed. This phenomenon can be explained by a continuous oscillation between the active and passive state of iron. Unlike other published systems that only show one-peak oscillations, the potential of iron shows highly complex dynamics: depending on the concentration of hydrogen peroxide and sulfuric acid, a period doubling and non-periodic oscillations in a self-oscillating system were observed for the first time. The reactions were analyzed by methods based on chaos theory and could finally be identified as an example of deterministic chaos. Received April 24, 2001. Accepted May 7, 2001     

有向图幂敛指数的Brualdi-Ross型上界

本文证明了n阶恰含i个极小强连通分支的有向图的幂敛指数的一个Brualdi-Ross型上界,并给出了幂敛指数达到此上界的有向图的完全刻划。     

Eichler integrals and harmonic weak Maass forms

Recently, K. Bringmann, P. Guerzhoy, Z. Kent and K. Ono studied the connection between Eichler integrals and the holomorphic parts of harmonic weak Maass forms on the full modular group. In this article, we extend their result to more general groups, namely, H-groups by employing the theory of supplementary functions introduced and developed by M.I. Knopp and S.Y. Husseini. In particular, we show that the set of Eichler integrals, which have polynomial period functions, is the same as the set of holomorphic parts of harmonic weak Maass forms of which the non-holomorphic parts are certain period integrals of cusp forms. From this we deduce relations among period functions for harmonic weak Maass forms.