函数的积分

"According to the fundamental theorem of calculus, a definite integral can be calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated)."

根据微积分基本原理，利用函数的反导数可以算出定积分。

By using of complex variable and integral equation methods, the antiplane multiple elliptical holes and multiple cracks problem of infinite region was considered.

摘 要：运用复变函数及积分方程方法，求解了无限域中的多椭圆孔多裂纹反平面问题。

We first consider the stochastic Dirichlet problem and from which we derive a system of integro-differential equations and the boundary conditions satisfied by the function.

首先，通过研究随机Dirichlet问题得到了Gerber-Shiu函数满足的积分-微分方程及边值条件。

According to the problem of transient response, the method of sensitivity analysis of equivalent integration form of constraint is presented.

对瞬态振动响应问题，给出约束函数等效积分的灵敏度计算方法。

The solution to the dual integral equations with exponential function can be discussed,too.

最后给出了含余弦函数对偶积分方程的数值算例。

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。

The integral calculus of Bernhard Riema of the function .

2齐次 函数的二重积分。

Two numerical methods using the integral function to do!

采用了两种数值方法做的积分函数！

The transient free-surface Green function was used to formulate the integral equation on the body surface.

采用时域自由面 Green 函数将定解问题转化为物面上的积分方程，进而求解水动力系数和船舶运动方程。

Themapping function sequences including circular cutouts and elliptical cutouts aregiven in this chapter.

然后为方便地满足圆柱壳大开孔的边界条件，通过复变函数方法中的用来求解多边形映射问题的Schwarz-Christoffel积分表达式，将圆柱壳展开面上的非圆非椭的开孔边界曲线保角映射成为单位圆，给出了在不同开孔率情况下的关于圆孔和椭圆孔的保角映射函数的具体形式。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。