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ISBN: (纸本)7118033731

关键词： 非线性转子-轴承系统   涡动   机械化数学分析   吴文俊消去法   角速度  

摘要： 为研究转子 轴承系统中非线性油膜力引起的半速涡动 ,本文给出了将吴文俊消去法和符号计算相结合的分析方法。基于短轴承假设 ,得到了单盘转子系统涡动时盘心、轴心及涡动角速度相对于无量纲转速的关系式。分析研究了转子涡动角速度变化规律及出现的双稳态现象。

关键词： 建构理论   《数学分析》   助趣式教学   框架式教学   互动式教学  

摘要： 研究了建构理论在数学分析教学中的应用 ,得到了数学分析教学的新模式。

关键词： bonded joint   nonlinear elasticity   asymptotic development  

摘要： Within the framework of nonlinear elasticity, we consider the problem of two adherents joined along their common surface by a thin soft adhesive. Two stored energy functions are considered: the stored energy function of Saint Venant-Kirchhoff and the stored energy function of Ciarlet-Geymonat. Using the asymptotic expansion method, the limit energy associated to each of these stored energy functions is obtained. The aim of this paper is to give a rigorous mathematical analysis of the formally derived limit problem. We show that the limit problem associated to the Saint Venant-Kirchhoff case admits at least one solution and the limit problem associated to the Ciarlet-Geymonat case admits exactly one solution. An analytical comparison in the one-dimensional case and a three-dimensional numerical application are also presented.

关键词： baroreflex delay   computer simulations   heart rate variability   mathematical model   chronic renal failure  

摘要： A model of baroreflex control of blood pressure (BP) is proposed in terms of a delay differential equation and this is used to predict the adaptation of short-term cardiovascular control in chronic renal failure (CRF) patients. Cardiac pump dynamics are explored by means of plots of blood flow vs. mean BP. The parameters of the model were determined from available data and from a sensitivity analysis. The model predicts stable and unstable equilibria close to the steady BP. It is shown that the unstable equilibrium point generates a quasiperiodic solution with two main harmonics for healthy subjects. We also show that the parameters for CRF patients predict solutions whose spectra exhibit a small high frequency component. This is due to the coalescence of the equilibrium points. The heart rate variability (HRV) time series and power spectra from healthy volunteers and CRF patients were compared with the model predictions. As an adequate measure of the sympathovagal balance we use the LF/HF index obtained from the power spectrum. The model allows the interpretation of the variability of the LF/HF index in terms of a specific set of cardiovascular parameters which are known to change from healthy to CRF patients. Comparisons of the changes in the LF/HF index predicted by the model are in agreement with actual observations for both the healthy and the CRF patients. These results show that the cardiac pump has a more restricted response in CRF patients. The model quantifies the cardiovascular adaptations to the CRF condition in terms of increased peripheral resistance and baroreflex delay and decreased arterial compliance, cardiac period, and stroke volume.

ISBN: (纸本)704013988X

关键词： 数学   形象思维   数学分析   函数   逻辑  

摘要： 在高等数学教学中,如何对学生进行数学能力的培养,特别是形象思维能力的培养,是一个非常重要的 问题。在数学分析教学中运用和渗透数学形象思维,对于学生数学能力的培养和发展,具有十分重要的意义。

关键词： 数学分析   教学方法   数学思想方法   解题教学   应用题  

摘要： 本文阐述了在数学分析教学中渗透数学思想方法的必要性,以及介绍了如何实施对数学思想方法的渗透。

关键词： 西方微观经济学   核心原理   数学分析  

摘要： 本文用数学语言、数学分析的方法,着重分析和论证了西方微观经济学的核心原理——效用原理、成 本原理、厂商原理和生产原理的主要内容及内部联系。

关键词： 层面分析法   中药材质量   数学分析  

摘要： 中药材质量的正确评价涉及到多因素共同影响的问题,我们在实际工作中发现,有的药材色泽很好,但闻一下、尝一下,气味却较差,或者看起来性状很好,但测定指标成分的含量并不高,那么,我们在评定其质量等级时,究竟该如何取舍呢.通过深入思考,我们总结出了一套适合于对中药材质量进行评价的方法并结合线性代数的基本理论建立了相关的评价模型.