微分

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 and Minkowski 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、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，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。

In this paper, we consider the properties of so_called N_analytic functions , integral formula of Cauchy type and the problem of Riemann boundary value.

研究了N 解析函数的性质、Cauchy型积分公式及相应的Riemann边值问题，然后将其结果应用到一类奇异微分—积分复方程的可解性理论中，建立了其特征方程解的积分表示式。

In this dissertation,we investigate systematically somefundamental problems concerning the Cauchy problem for linear operatordifferential equations.

在本文中，我们就抽象空间中线性算子微分方程Cauchy问题的一些基本问题进行比较系统的研究，主要的工作是

The invention discloses an optical differentiator based on a silicon-based annular cavity resonator, which belongs to the field of optical fiber communication technology.

一种基于硅基环形谐振腔的光微分器，属于光纤通信技术领域。

The principle of the optical differentiator is that when the silicon-based annular cavity resonator meets or is close to a critical coupling state, the spectra characteristic of the silicon-based annular cavity resonator is quite similar to the differentiator within certain range with the resonant wavelength as the center.

本发明的原理是当硅基环形谐振腔满足或接近临界耦合状态时，其在谐振波长为中心的一定范围内的频谱特性是微分器的很好的近似。

Birkhoff, Siegel, Kolmogorov, Arnold, Moser, Herman, and many others investigated the ideas of stability and found complicated behavior for systems arising in celestial mechanics and other such physical systems, which could be described by what are called Hamiltonian differential equations .

Birkhoff ， Siegel ， Kolmogorov ， Arnold ， Moser ， Herman 和其他很多研究者研究稳定性的思想，发现了具有复杂行为的系统出现在天体力学和其它相似的物理系统中，这些都可以用称为 Hamilton 微分方程来描述。

The distributed parameter model is changed into variable coefficient nonlinear stiff ordinary differential equations by central difference method.

运用中心差分法将分布参数形式的系统模型转换为一变系数非线性的刚性常微分方程组。

On the basis of the properties of central projection and orthographic projection, the differences of different rectification approaches based on orthographic projection are explained, and it is suggested that oblique-plane-rectified photograph can produce orthographic representation of flat terrain cover; differential rectification of RS imagery based on DEM can produce orthographic representation of waved terrain cover; and true orthographic rectification based on digital ground-object model can produce orthographic representation of single objects on ground.

根据中心投影和正射投影的特点，从理论上说明了不同正射投影纠正方法之间存在的差异，认为：基于透视变换的像片倾斜纠正可生成水平地表覆被的正射投影表达；基于DEM的正射影像微分纠正可生成起伏地表覆被的正射投影表达；基于数字地物模型的真正射纠正可生成独立地物的正射投影表达。

Secondly, an adaptive real-time interpolation algorithm for B-spline curves is proposed combined with the chord error control and the largest centripetal acceleration control based on the differential geometry and the properties of B-spline curves.

其次，根据B样条曲线的特性以及微分几何原理，实现了一种带弦高误差控制和法向最大加速度控制的进给步长自适应B样条曲线实时插补算法。

The dynamic equation of motion chain is a group of high non-linear differential equations, the solution is difficulty.

锚泊线的运动方程是一组高非线性的偏微分方程组，求解困难。

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。