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 in the Rössler System—A Computer Assisted Proof

Using rigorous numerical methods, we validate a part of the bifurcation diagram for a Poincaré map of the Rössler system (Rössler in Phys. Lett. A 57(5):397–398, 1976)—the existence of two period-doubling bifurcations and the existence of a branch of period two points connecting them. Our approach is based on the Lyapunov–Schmidt reduction and uses the C ^r -Lohner algorithm (Wilczak and Zgliczyński, available at http://www.ii.uj.edu.pl/~wilczak) to obtain rigorous bounds for the Rössler system.     

具有i个强分支的有向图的幂敛指数集

本文给出了ｎ阶具有ｉ个强分支的有向图的幂敛指数集Ｒ（ｎ，ｉ）的一个明显表达式。     

The fundamental group of period domains over finite fields

We determine the fundamental group of period domains over finite fields. This answers a question of M. Rapoport raised in [M. Rapoport, Period domains over finite and local fields, in: Proc. Sympos. Pure Math., vol. 62, part 1, 1997, pp. 361-381].     

应用LPFG/EFPI集成式光纤传感器实现温度及应变的同时测量

叙述了基于LPFG/EFPI的集成式光纤传感器的结构、温度和应变同时测量的原理及实验,首次制作了该传感器并测试了其性能.实验结果表明温度精度为±0.5℃,应变精度为±20με,可满足实际应用的要求.     

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。     

一种改进的可阻止SPH数值断裂的方法

首先通过人为设定数值断裂,从数值上分析数值断裂对计算精度的影响。然后引进一种可适用于大变形的并保证系统质量守恒、动量守恒和能量基本守恒的简单加点技术,用以阻止数值断裂。并用改进的smoothed particle hydrodynamics(SPH)方法对钢弹撞击飞机蒙皮进行数值模拟以验证其阻止数值断裂的有效性。在130~250 m/s的碰撞速度下,用改进的SPH方法得到的变形区直径、剩余速度以及弹坑深度与试验结果吻合较好。     

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.     

层叠Blumlein线脉冲叠加特性

利用传输线等效放电模型对层叠Blumlein线的脉冲叠加特性进行了分析。结果表明:外部短路阻抗是降低层叠Blumlein线脉冲叠加效率的主要因素,其中,短路电感产生输出波形平顶的衰减,相对衰减量取决于叠加级数以及短路等效电感与传输线电感之比,短路电容产生输出波形前沿的慢化,前沿慢化的相对值取决于叠加级数以及短路等效电容与传输线等效电容之比;由于各级开关导通时间分散性的存在,输出波形的前沿及后沿皆呈阶段状,相当于产生了时间量等于开关导通分散性时间的前沿及后沿慢化现象。增加传输线外部的短路阻抗、减小多开关的导通分散性是提高层叠Blumlein线的脉冲叠加效率、改善输出波形的有效途径。     

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.