The p-Blocks of the Mackey Algebra

Let p be a prime number. This paper describes the primitive idempotents and prime spectrum of the crossed Burnside algebra of a finite group over a p-local ring. The main application is a formula for the block idempotents of the p-local Mackey algebra of the group, in terms of the corresponding bloks of the group algebra.     

Invariant properties of representations under cleft extensions

The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable.     

利用单模光纤中的交叉相位调制产生单周期化脉冲的研究

描述了利用光纤中的交叉相位调制（XPM）效应产生单周期化脉冲的基本原理.详细分析了不同初始脉冲条件对脉冲频谱展宽的影响，然后针对具体事例用分步傅里叶方法对分析结果进行了验证.最终得到了200—1000THz的超宽带频谱，并给出了理想压缩脉冲的时域脉宽和形状. 关键词： 单周期化脉冲 交叉相位调制 超宽带频谱     

Mathematical Modelling of Cable Stayed Bridges: Existence, Uniqueness, Continuous Dependence on Data, Homogenization of Cable Systems

A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected with the homogenizing procedure is proposed and the existence and uniqueness of a solution are proved.     

考虑随机弱化二阶效应的电缆流变断裂学分析

将电缆视作为ｎ股子束构成的线束，而每股子束由ｍ个平行的受拉元件组成，受拉元件就是渍于树脂基体的聚合物肌绳。未破坏的元件在任一时刻都按照某种规律承载，表现出电缆断裂对持载时间和载荷特征的相依性，从而，电缆的断裂是一个非平衡态不可逆热力学相容的一个非线性动力学演化假设下，我们考虑单个元件受载断裂与线束受载的关系。认识到元件的数目一一大时，线事的破坏时间是近正态分析的。     

FORCED WAVE PROPAGATION IN VISCOELASTIC CABLE WITH SMALL SAG

Based on the linear viscoelastic differential constitutive law and cable structural model, the coupled longitudinal-transverse waves that propagate along a viscoelastic cable with small curvature is investigated. A mathematical model is presented that describes the three-dimensional nonlinear response of a viscoelastic cable. An asymptotic form of this model is obtained for the linear response of cables having small equilibrium curvature. The spectral relation governing the propagating waves is derived using transform methods. The spectral relation is employed in deriving a Green's function that is then used to construct solutions for in-plane response under distributed harmonic excitation. Analysis of forced response reveals the existence of two types of periodic waves that propagate through the cable, one characterizing extension-comprehensive deformation and the other characteristic transverse deformation. Project supported by the National Natural Science Foundation of China (No. 59635140).     

基于漏磁检测的桥梁拉索断丝识别

为实现桥梁拉索漏磁(MFL)检测中低信噪比(SNR)时的断丝识别,提出了基于有效短时互相关(STCC)的损伤识别方法.对拉索进行重复测试并提取对应的信号片段进行互相关分析,通过重新归一化,在短时互相关序列中融入短时能量特征,再结合双阈值法进行断丝识别.制作了含有多种断丝损伤的足尺拉索模型进行漏磁检测试验,基于试验结果验证所提出的方法.结果表明:该方法的损伤判别精度比既有方法提高了15.7%～16.9%,在低信噪比下仍取得了较高的损伤识别精度.     

拉索钢丝电化学腐蚀进程的元胞自动机模拟方法

为了模拟拉索在实际环境中的腐蚀演化进程并探究氯离子在索体腐蚀过程中的催化作用,基于金属电化学腐蚀的基本原理建立了模拟拉索钢丝电化学腐蚀进程的元胞自动机模型,将腐蚀系统中的关键元素抽象成4种元胞类型,并将整个拉索腐蚀系统离散成500×500的元胞网格,通过定义的局部规则模拟钢丝在介观尺度上的腐蚀演化过程,分析了腐蚀性溶液浓度和腐蚀概率对钢丝腐蚀进程的影响,研究发现：当元胞自动机特征参数选取合理,并适当加大中心元胞与切线方向上的邻居元胞的接触概率,蚀坑形貌也就越接近真实形貌。元胞自动机模拟产生的蚀坑形貌与实际蚀坑形貌十分接近;钢丝腐蚀面积随时间不断变大的同时腐蚀速率也将逐步增快,表明一旦钢丝腐蚀出现蚀坑,钢丝腐蚀面积越来越大的同时其腐蚀速率也将越来越快;在拉索腐蚀的过程中具有氯离子的腐蚀性元胞具有主导地位,无氯离子的腐蚀元胞的腐蚀概率对钢丝腐蚀速率的影响不大,控制并减少周边环境中氯离子的浓度是减缓拉索腐蚀的有效途径。     

From Lie algebra crossed modules to tensor hierarchies

The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity rely on a pairing – the embedding tensor – between a Leibniz algebra and a Lie algebra. Two such algebras, together with their embedding tensor, form a triple called a Lie-Leibniz triple, of which Lie algebra crossed modules are particular cases. This paper is devoted to showing that any Lie-Leibniz triple induces a differential graded Lie algebra – its associated tensor hierarchy – whose restriction to the category of Lie algebra crossed modules is the canonical assignment associating to any Lie algebra crossed module its corresponding unique 2-term differential graded Lie algebra. This shows that Lie-Leibniz triples form natural generalizations of Lie algebra crossed modules and that their associated tensor hierarchies can be considered as some kind of ‘lie-ization’ of the former. We deem the present construction of such tensor hierarchies clearer and more straightforward than previous derivations. We stress that such a construction suggests the existence of further well-defined Leibniz gauge theories.     

单层平面索网幕墙结构的风振响应分析及实用抗风设计方法

单层平面索网玻璃幕墙结构是广泛应用于大型公共建筑中的一种新型结构形式,由于其具有柔性大、质量轻、阻尼小、自振频率低的特点,属风敏感结构。由于单索幕墙具有较高的几何非线性,本文采用基于随机振动理论的模态叠加频域方法进行了单索幕墙结构的风振响应分析。将模态叠加频域方法的计算结果和非线性时程分析方法的精确计算结果进行了比较,证明了该方法的准确性。并且本文通过分析各阶模态对单索幕墙结构风振响应的贡献,得到脉动风荷载下结构的振动以第一阶模态为主的结论。根据该结论本文采用频域方法推导了单索幕墙结构的位移均方差和索内力均方差的实用计算公式,同时考虑单索幕墙的结构特点提出了基于结构响应的单索幕墙结构实用抗风设计方法。