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关键词： 问题解决教学策略   数学思想   数学方法   数学思维  

摘要： 本文结合教学实际探讨了问题解决教学策略在数学分析课程教学的几个环节中的应用。

关键词： 单调性   函数   数学分析   一致收敛   一致连续   不动点定理  

摘要： 文章利用函数的单调性,对数学分析中的某些定理作进一步的研究,给出了其定理的新形式。

关键词： 参数   函数   凹性   数学分析  

摘要： 本文给出含参数的函数f(x,t)的凹性定义,并应用它的性质证明一些不等式.

关键词： 体质档案   数据结构   模糊聚类分析   计算机辅助诊断专家系统  

摘要： 本文介绍体质档案的数据结构并作评价分析 ;引入模糊数学方法处理体质数据 :计算机软件编程实现的框架结构 。

关键词： 光学电流互感器   相位误差   矩阵光学理论   数学分析   IEC60044-8  

摘要： 基于矩阵光学理论的数学分析 ,推导出光学电流互感器 (OCT)光电转换后输出电压信号的数学表达式 ;分析了OCT的相位误差来源及误差 ,论证出若两路电压信号的相差在 1 80°± 2 5 6°内 ,能达到IEC6 0 0 4 4 - 8标准对 0 .2级OCT的相位准确度的要求 ,否则 ,应采取相位补偿措施 ,将数字移相技术用于OCT中 。

关键词： 不定积分   定积分   数学分析   微分学   高等教育自学考试   自学指导  

摘要： 积分学与微分学是数学分析的姊妹篇。两者一起构成数学分析的主体。数学分析中研究多种积分，如不定积分、定积分、重积分、曲线积分、曲面积分、非正常积分、含参变量积分等。其中，不定积分是求导运算的逆运算：定积分是其他各种积分的基础；而定积分的计算大多可归结为求不定积分。因此，不定积分与定积分是整个积分学的基础。本文着重介绍不定积分与定积分的几种求法，以期对广大考生有所帮助。

关键词： 柯西极限定义   等价定义   教学   邻域   有限项   无限项   数学分析  

摘要： 本文证明了一个柯西极限定义的等价定义 ,同时论述了这个定义在教学中的作用 .

关键词： synchronization   homoclinic chaos   periodic control theory   pattern recognition   bifurcation analysis   continuation techniques  

摘要： This is the second of two papers introducing a new dynamical phenomenon, strongly related to the problems of synchronization and control of chaotic dynamical systems, and presenting the corresponding mathematical analysis, conducted both experimentally and theoretically. In particular, it is shown that different dynamical models (ordinary differential equations) admitting chaotic behavior organized by a homoclinic bifurcation to a saddle-focus (Shil'nikov-like chaos) tend to have a particular selective property when externally perturbed. Namely, these systems settle on a very narrow chaotic behavior, which is strongly correlated to the forcing signal, when they are slightly perturbed with an external signal which is similar to their corresponding generating cycle. Here, the "generating cycle" is understood to be the saddle cycle colliding with the equilibrium at the homoclinic bifurcation. Oil the other hand, when they are slightly perturbed with a generic signal, which has no particular correlation with their generating cycle, their chaotic behavior is reinforced. This peculiar behavior has been called qualitative resonance underlining the fact that such chaotic systems tend to resonate with signals that are qualitatively similar to an observable of their corresponding generating cycle. Here, a detailed mathematical analysis of the qualitative resonance phenomenon is presented, confirming the intuitions given by the geometrical model discussed in Part I.

摘要： Calcium sparks are local regenerative releases of Ca2+ from a cluster of ryanodine receptors on the sarcoplasmic reticulum. During excitation-contraction coupling in cardiac cells, Ca2+ sparks are triggered by Ca2+ entering the cell via the T-tubules (Ca2+-induced Ca2+ release). However under conditions of calcium overload, Ca2+ sparks can be triggered spontaneously. The exact process by which Ca2+ sparks terminate is still an open question, although both deterministic and stochastic processes are likely to be important. In this article, asymptotic methods are used to analyze a single Ca2+ spark model, which includes both deterministic and stochastic biophysical mechanisms. The analysis calculates both spark frequencies and spark duration distributions, and shows under what circumstances stochastic transitions are important. Additionally, a model of the coupling of the release channels via the FK-binding protein is analyzed.

关键词： 可持续发展理论   数学分析   Logistic曲线   发展过程   泛函   最值问题  

摘要： 　运用Logistic曲线分析了系统的一般发展过程,根据其发展速度将发展过程分为起步、成长、成熟和饱和4个时期,并结合可持续发展的内涵与实质,提出了可持续发展理论的数学依据和数学实质。