函数的积分

In the single and double integral terms of Green function, the kernel function of wave-making resistance expression, Special function expansion method and Chebyshev polynomial approach method have been adopted respectively, which greatly increase the calculation speed.

对作为兴波阻力计算核函数的Green函数的单、双积分项分别采用特殊函数展开、切比雪夫多项式逼近的方法进行计算，提高了计算速度。

Using the continued fraction method other than the traditional recurrence methods to generate the Bessel function, we built an accurate code for calculating the Mie scattering.

2利用Mie散射模式计算气溶胶散射相函数的展开式系数，直接提供逐次散射计算中所需要的立体角积分网格上的相函数，避免为获得相函数而进行内插。

When the second surface integral is calculated and the integral surface has some coordinate plane symmetry, computation can be simplified according to the integral odevity.

在计算第二型曲面积分时，当积分曲面关于某个坐标面对称时，则可根据被积函数的奇偶性进行化简。

Then the integral-differential equations were reduced to the form with degenerate core by expanding Green＇ s function as series of characteristic function.

再使用展开法求出格林函数，即将格林函数展开为特征函数的级数形式，积分微分方程就成为具有退化核的形式，从而容易得到关于时间的非线性常微分方程组。

The paper introduces the method of calculating double integral with symmetry,and then puts forward a calculating method by rebuilding integrand and domain of integration reasonably.

本文还介绍了如何利用对称性来计算二重积分，并提出了通过适当改造被积函数和积分区域以利用对称性来简化计算的方法。

In this paper, the performance of SVM based on Fourier kernel is studied which aims at the regression in signal processing questions, and the influence of parameter q on performance of SVM is analyzed. A conclusion is drew that the integral of Fourier kernel in one period is a constant and the concept of equivalent kernel function width is proposed.

本文针对信号处理中的回归问题，研究了基于傅立叶核函数支持向量机的性能，并分析了参数q对其性能的影响；根据推导得出傅立叶核函数在单个周期内积分为常数的结论，并提出了等效核宽度的概念；最后的仿真结果证实了，在信号处理领域，采用傅立叶核函数的支持向量机比采用径向基核函数的有着更好的性能。

However, due to the oscillation and singularity of the integrand of Green's function and that integral interval is infinite, it is difficult to compute the function and to control the accuracy.

而格林函数中被积函数的振荡性，奇异性和积分区间为无穷使得该函数的计算较为困难，精度不易控制。

As an application of continuous wavelet transform,we discuss the relationsbetween some differemtial equaltions and the integral equations by using thecontinuous wavelet transform in 〓,vector function space andabstract function space respectively;prove that they are equivalent not only in theweak topology but also in the strong topology.

作为连续小波变换的应用，分别利用〓上的，多元函数空间上的，向量函数空间上的和抽象函数空间上的连续小波变换分别得到了某些线性微分方程，某些线性偏微分方程，某些向量线性微分方程和某些抽象函数的微分方程分别等价于其相应的积分方程，证明了它们不仅在弱收敛意义下而且在范数收敛意义下是等价的。

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

我们把立体匹配过程看作泛函的极小化过程，因此选用变分问题近似解法的Ritz法构造数值算法，以多项式函数为基构作匹配函数的近似解，进而又利用多项式过样值点的拟合将离散的灰度图象变换为多项式函数，因此计算中所需的求导，积分，及梯度运算的结果仍然是多项式函数，最终将待定系数方程组化为线性代数方程组。

In chapter 4, we discuss further some properties of generalized fuzzy inte-grable functions, and prove that not only generalized fuzzy integrable functions have the weak integral absolute continuity, but also sequences of generalized fuzzy integrable functions have uniform weak and absolute continuity.

进一步讨论了广义模糊可积函数的某些性质，证明了在广义三角模S满足(S-1)的条件下，不仅广义模糊可积函数具有弱积分绝对连续性，而且广义模糊可积函数列具有一致弱绝对连续性。

No clear conclusions can be made about the predictie alidity of specific measures, they found, except for criteria for the underuse of drugs for cardioascular disease.

除了心血管病不合理用药标准外，对于特定评价方法的预测效度没有明确的结论。

The third and last is that almost all of them, being infinite in number, have been impostures, and by idle and crafty brains merely contrived and feigned after the event past.

第三、即最后一点是：几乎所有这些不胜枚举的预言都是欺人之谈，都是在事件过后由无聊而狡猾的脑筋推测与凭空捏造的。