部分双曲集附近的拟跟踪性

引入部分双曲集的概念,证明了紧黎曼流形上的微分同胚在其部分双曲集的小邻域内具有如下形式的拟跟踪性:设f为紧黎曼流形M上的一个微分同胚,Λ为f的部分双曲集.则存在Λ的邻域O(Λ),使得对于任意ε0,存在δ0,使得f在O(Λ)中的任意δ-伪轨{x_k}k∈Z,存在点列{y_k}k∈Z,和中心向量列{u_k∈E_(xk)~c}k∈Z满足d(x_k,y_k)ε,其中y_k=exp_(x_k)(exp_(x_k)~(-1)(f(y_(k-1)))+u_k).作为一个应用,给出任意微分同胚在C~0扰动下,如果在双曲集邻域内存在不变集,则其是拓扑拟稳定的.     

基于柔性羧酸配体和含氮辅助配体的金属有机配位聚合物的合成、结构及表征

本文通过水热合成的方法制备得到了一个新型的二维金属有机配位聚合物[Co2(L1)(4,4’-bipy)(3H2O).2H2O]n (1), (H4L1 = 3,3'-(1,4-苯二氧基)二邻苯二甲酸; 4,4’-bipy = 4,4’-联吡啶),并对其结构进行了系统的表征。研究表明3,3'-(1,4-苯二氧基)二邻苯二甲酸配体中的羧酸采用μ1-η1-η0和μ1-η1-η1两种桥联的方式跟两个钴离子配位形成十四圆环,形成的十四圆环被3,3'-(1,4-苯二氧基)二邻苯二甲酸配体连接进一步形成之字形的一维链状结构。最终,辅助配体4,4’-联吡啶将这些一维链状结构连接起来形成二维的(44)-sql网状拓扑结构。在本文中,我们还一步研究了这个配位聚合物的红外光谱以及热稳定性。     

具反馈控制的LOGISTIC增长模型

讨论具反馈控制的Logistic增长模型{dn(t)/dt=rn(t)(1-n(t-τ）/k-cμ（t）），dμ（t）/dt=aμ（t） bn(t-τ),其中μ表示反馈控制变量，k,r,τ,a,b,c为正常数，获得了（*）的正平衡点的全局渐近稳定性，改进了已有结果，证明[1]中的猜想在更弱的条件下为真。     

Effect of Gas Pressure on Nanocrystalline Diamond Films Prepared by Electron-Assisted Chemical Vapour Deposition

With use of electron-assisted chemical vapour deposition （EACVD） technology, nanocrystalline diamond films are successfully deposited on an α-SiC single phase ceramics substrate by means of reduction of the reactive gas pressure. The structure and surface morphology of the deposited films are characterized by Raman spectroscopy, x-ray diffraction （XRD）, field emission scanning electron microscopy （FE-SEM） and atomic force microscopy （AFM）. The results examined by FE-SEM and AFM show that when the gas pressure was reduced to 0.5- 1 kPa, the surface grain size and surface roughness of the diamond film are decreased greatly to 18-32nm and 34-58nm respectively. The grain sizes estimated from full with at half maximum of （111） XRD peak by the Scherrer formula are 6-28 nm. However, too high secondary nucleation rate may result in pores and defects in the deposited films. Only at suitable gas pressure （1 kPa） to deposit films can we obtain densification and better quality nanocrystalline films.     

三轴SHPB冲击作用下岩石破坏机理的研究

本文应用三轴SHPB高速冲击试验机对岩石试体进行三向应力状态（对试件施加围压2=3和冲击应力1）下的冲击试验,分析研究岩石的破坏机理。由试验结果对三轴状态下岩石的破坏类型进行分类,分析其内部受力状况;得出岩石动态破坏强度,画出动态三轴、动态单轴和静态单轴的破坏强度比较曲线。通过对破坏类型的分析,以最大剪应力条件建立岩石的破坏判据,建立三轴动态破坏强度、单轴动态破坏强度与围压的关系式。     

Secondary Buckling Analysis of Thin Rectangular Plates Based on the Wavelet Galerkin Method北大核心CSCD

Application of the wavelet Galerkin method (WGM) to numerical solution of nonlinear buckling problems was studied with classical elastic thin rectangular plates. First, the discretized scheme of the von Kármán equation were introduced, then a simple calculation approach to the Jacobian and Hessian matrices based on the WGM was proposed, and the wavelet discretized scheme-based eigenvalue equation method, the extended equation method and the pseudo arc-length method for nonlinear buckling analysis were discussed. Second, the secondary post-buckling equilibrium paths of elastic thin rectangular plates and the effects of aspect ratios, boundary conditions and bi-directional compression on the mode jumping behaviors, were discussed in detail. Numerical results show that, the WGM possesses good convergence for solving buckling loads on rectangular plates, and the obtained equilibrium paths are in good agreement with those from the stability experiments, the 2-step perturbation method and the nonlinear finite element method. Given the feasibility of combination with different bifurcation computation methods, the WGM makes an efficient spatial discretization method for complex nonlinear stability problems of typical plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

数字图像相关测试技术在材料力学实验教学中的应用

为丰富实验教学手段和提高教学质量,我们引入了基于数字图像相关的平面应变测试技术并应用于材料力学实验教学。籍由此技术,学生获得了低碳钢和铝镁合金材料在单轴拉伸下的力学性能参数和全场应变等丰富的可视化信息,加深了学生对应变等理论知识的理解,显著调动了学习积极性,培养了他们的科学思维能力。     

收缩段对燃气轮机排气蜗壳性能影响的数值研究

燃气轮机排气蜗壳与试验风洞匹配需增设收缩段部件,本文采用数值方法研究了收缩段对排气蜗壳内部流场和性能的影响。通过仿真软件CFX计算了有无收缩段及整流锥的两种排气蜗壳流场,分析了各截面上总压损失系数及流线分布规律。结果表明在蜗壳进口前增设收缩段与整流锥对排气蜗壳气动性能无显著影响,可通过试验获得排气蜗壳相应气动性能参数。     

引入改进的K-means算法的电缆监测数据优化技术的研究

分布式光纤是一种新型在线监测技术,能极大程度提高电缆健康状态的监测效率。由于光纤处于复杂环境影响中,以及分布式节点实时产生庞大的数据群,这对监测数据的处理技术提出了更高的要求。基于传统的数字式平均法,引入一种改进的k-means聚类算法,实时对各节点产生的数据集处理,能准确的识别因噪声影响而产生的奇异数据,提高了数据反馈的效率和准确性,从而减少了监测系统的漏报和误报现象。现有的实验仿真表明改进的算法较传统算法在数据处理的准确性和快速性上都有明显的提升。     

N-乙基-N-(6-碘代己基)十二烷酰胺的合成

以己二醇和月桂酸为起始原料,经多步反应合成了N-乙基-N-(6-碘代己基)十二烷酰胺,总产率21.05%,其结构经1H NMR和MS表征.