微分

Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory.

为eigenvalues和30个开放式问题也提供古典isoperimetric 不平等的拘谨的赠送，这本书将是对纯并且被使用数学家有用的，特别是对偏微分方程，变分法，不同几何学或者光谱的理论感兴趣的那些。

A PID control method based on BP neural network was proposed,concerning the multi-layered temperature control of calenderer rollers and the limitations of the conventional PID control which resulted from the control of the nonlinear and time-varying system.The system design and software development were also presented.

针对压延机辊筒多段温度控制以及常规PID控制在非线性的、时变系统中控制效果的局限性，提出了一种基于BP神经网络整定的PID控制方法，给出了计算机控制系统设计，建立了比例、积分和微分三种参数自学习的PID控制器。

To construct canonical equation for the constrained Hamiltonian systems dynamics

在最后，介绍了一般的微分/代数方程组的一些重要概念，如指标等

Stochastic differential equations can be used to resolving the price of interest rate derivatives. It has a canonical equation of interest rate changing with time and its derivative accords with the traded behavior in finance market, but the resolving process is very fussy and difficult and can not receive closed solution in many cases.

随机微分方程被用于利率衍生产品的定价，它给出利率随时间变动的一个规范的方程，而且其推导过程与金融市场中的交易行为一致，但其求解过程很繁琐且困难，在很多情况下甚至无法得到封闭解。

Movement stabilization criterion of nonlinear relative rotation system was obtained by transferring the fundamental matrix of the solution of the ordinary differential equation to Jordan canonical .

利用一类周期性变系数线性常微分方程解的基本矩阵的Jordan形，分析一类非线性相对转动系统扭转的运动稳定性，从而得到非线性相对转动周期系统的运动稳定准则。

A differential equation is introduced to construct canonical dual function. The corresponding perfect duality theory is established to show the relationship between the KKT points of the primal problem and the canonical dual problem.

通过引入常微分方程和构造Canonical对偶函数的局部形式，引入了相应的对偶定理，勾勒出了原问题的KKT点和对偶问题的KKT点两者之间的关系。

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

AIM: To name the basic waves of reconstructed impedance differential cardiogram, and to investigate the amplitude and time interval of the waves.

目的：对重建心阻抗微分图的基本波命名，探讨有关波幅和时间间期。

Intruduce impedance cardiography and describe its theoretical background, measuring methods, generation of impedance signals and its clinical meaning,and application of the impedance cardiography.

介绍心阻抗法的工作原理、测量方法、阻抗微分波的产生和临床意义，以及心阻抗法的临床用途。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。