导函数

As we all know, if the two partial derivations of binary function are continuous ,the function is differentiable.

摘要众所周知，当二元函数的两个偏导数都连续时，函数可微。

Two mathematical derivations of them have been introduced by using the properties of differentiable function and the derivation algorithm of multiple function in present paper, and several mistakes in some derivative methods have also been pointed out.

介绍了应用可微函数的性质及多元复合函数的求导性质推导热力学中著名的麦克斯韦关系式的方法，指出了有关文献中推导过程的不

Theorem 2 If has continuous partial derivatives at , then is differentiable at .

定理2如果函数在点的偏导数连续，则函数在该点可微分。

Then after the author researches the interaction problem of the partial derivative operators with respect to the two points P and Q, analytical expressions as well as series expansions of the kernel function within disturbing gravity field elements are determined, and their explicit expressions which can be applied practically are given for the first time.

深入研究了关于 P 和 Q 两点局部导数算子的相互作用问题，得到了扰动场元之间核函数和协方差函数的解析与级数展开式，首次给出了较为实用的明晰表达式。

Mathieu functions are frequently encountered in many radiation,scattering and guided wave problems, which are formulated in the elliptic cylindrical coordinate system.

本文给出了计算马丢函数和变型马丢函数及其导数值的程序流图和相应的有用数学公式，并讨论了算法。

This can be done adding a penalty term into target function used in the standard BP algorithm, and the penalty term is related to the first derivative of the target function.

具体的做法是在标准BP算法中的目标函数项内增加一惩罚项来完成的，而此惩罚项与目标函数的一阶导数相关。

Course Content:The main part of this course is about infinitesimal calculus and ordinary differential equations,including :functions and limits,derivative and differential integral and their application,differential methods of function of several variables and its application,heavy integral,curve integral,camber integral,infinite progression and differential equations.

课程内容：学科教学法与CAI研究与实践是师范计算机专业教学系统的重要组成部分，学科教学法与CAI研究与实践课程是计算机科学教育的主要内容。通过本课程的学习使学生掌握现代学科教学法与CAI研究与实践的基本概念，基本原理和基本方法；能设计并使用所学的教学理论进行中学信息技术课程的教学设计，试讲，试教。课程内容：以微积分学和常微分方程为主干，介绍函数与极限，导数与微分，中值定理。不定积分，定积分及其应用，多元函数微分法及其应用，重积分，曲线积分与曲面积分，无穷级数及微分方程等。

The variational problems of the complete functional in calculus of variations are studied deperding on the arbitrary arguments,arbitrary multivariable functions and arbitrary-order partial derivatives of multivariable functions.

研究变分法中依赖于任意个自变量、任意个多元函数和任意阶多元函数偏导数的完全泛函的变分问题；提出并证明了完全泛函的变分问题的定理，采用偏微分算子，给出了完全欧拉方程组。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

It consists of fitting seismic ray traveltimes and positions to data calculated by ray tracing. In order to improve inversion stability and efficiency, seismic ray is described by Hamilton function and ray tracing is done in phase space. Validation tests on synthetic and practical data are analyzed. The tests show that this tomographic method is effective for estimating velocity field in complex media.

为提高反演的稳定性和计算效率，引入了Hamilton函数描述射线，在相空间计算反演所需的射线路径和目标函数对模型参数的导数，对理论模型和实际地震资料进行了试算，试算表明该方法对复杂介质具有较强的适应能力。

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。