工程力学矢量的规范表示与弹性力学的不变性

通过引入规范变换，消除了工程力学矢量数学表示上的物理缺陷，使规范化力学矢量与力学张量具有物理上的等价表示，从而奠定了不变性弹性力学的基础，为它在不同坐标下的具体应用提供了理论保障。     

振荡燃烧的动态测试及信息处理

作者用随机信息处理方法研究了某型火箭发动机的燃烧状况,不仅发现该型发动机存在有振荡燃烧,而且获得了振荡燃烧信息的功率谱及功率谱阵。针对振荡燃烧信息在时间域和频率域上的随机性特点,作者精心地设计了测试系统,并对系统的性能参数进行了全面标定。经多次实测证明该系统工作可靠,信噪比较高。测试与分析结果表明:该型发动机振荡燃烧的主振测率为800Hz,最大振幅为43dB;并存在有1600Hz和2500Hz两个次级振荡频率;而且该发动机的振荡燃烧是以纵向振荡为主。为研究该型火箭发动机振荡燃烧的产生原因和消除方法提供了科学依据。     

Monodromy and nonintegrability in complex Hamiltonian systems

This paper investigates the monodromy representation of the normal variational equation along a phase curve of a two-dimensional complex analytic Hamiltonian system. Geometrical conditions are presented which guarantee reducibility, together with additional hypotheses to ensure complete reducibility. Symmetries in the equations are treated in detail. Applications to establishing the nonintegrability of specific systems are presented.     

求解复杂湍流的非线性涡黏性系数模型和代数应力模型

非线性涡黏性系数模型和代数应力模型联系了线性涡黏性系数湍流模型和完整的微分 雷诺应力模型.随着它们受到日益关注,其形式也越来越多样化.本篇综述的目的是对这些模 型加以总结并比较它们之间的共同点及不同之处,指出它们与完整微分雷诺应力模型之间的 关系,以及相对于线性涡黏性系数模型而言它们在预报流场上所具有的优势.     

On the boundary value problem of elastostatics in terms of stresses

The boundary value problem of elastostatics in terms of six components of the stress consists of nine equations and three boundary conditions. In this paper, we distinguished between the possible cases and impossible cases, i.e., the problem is or is not equivalent to a boundary value problem of six equations and six boundary conditions.     

数字式有源磁悬浮技术

介绍了数字式有源磁悬浮的应用背景和数字式有源磁悬浮的工作原理、元件结构设计、力的计算方法。实验证明，采用数字式有源磁悬浮技术提高了陀螺仪的精度，对陀螺仪性能的提升起到了关键的作用。     

用人工产生的拟湍流信号检验相干结构的检测方法

本文利用计算机产生拟湍流脉动信号，将数据进行频谱分析和能谱分析，发现湍流中相干结构不仅包合低频成分还包含一定数量高频成分，因而简单地认为湍流中低频部分是相干结构而高频部分是小尺度脉动，来确定相干结构能量在湍流中所占成分是不科学的；本文还将得到的数据用几种条件采样方法检测相干结构数量和位置，以此判断检测方法的优劣，发现就这类信号而言ＭＵ—ＬＥＶＥＬ法要比ＶＩＴＡ法准确性要高一些。     

Intertwining wavelets or multiresolution analysis on graphs through random forests

We propose a new method for performing multiscale analysis of functions defined on the vertices of a finite connected weighted graph. Our approach relies on a random spanning forest to downsample the set of vertices, and on approximate solutions of Markov intertwining relation to provide a subgraph structure and a filter bank leading to a wavelet basis of the set of functions. Our construction involves two parameters q and $q^{\prime }$. The first one controls the mean number of kept vertices in the downsampling, while the second one is a tuning parameter between space localization and frequency localization. We provide an explicit reconstruction formula, bounds on the reconstruction operator norm and on the error in the intertwining relation, and a Jackson-like inequality. These bounds lead to recommend a way to choose the parameters q and $q^{\prime }$. We illustrate the method by numerical experiments.