被积函数

Under the constraints between potentials and eigenfunctions, the Lax systems are nonlinearized to be finite dimensional completely integrable systems in Liouville sense.

在位势与特征函数之间的约束条件下，Lax系统被非线性化成为有限维Liouville完全可积系统。

This network's multidimensional wavelet basis function is built by substituting norm of the vector for that vector, not scalar product function of the vector, thus the cost of calculation of high dimensionalities is decreased nearly to the situation of one dimensionality.

此网直接用矢量的范数代替矢量来构造多维小波基函数，而不是采用通常的矢量的标量积函数的方法构造多维基函数，这样多维情况的运算量被降低到几乎和一维的情况基本相当的程度。

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

The coordinate transform method is used to calculate the weak singular integral.

为了获得O(1／r)弱奇异积分高精度的解，采用坐标变换的方法，消除被积函数中的奇异性。

The strongly singular integral can not be calculated by using the constitutive and equilibrium equations.

对于被积函数中含有强奇异积分的情形，即：，在单元内采用本构方程和平衡方程建立线性方程组，求解的方法间接获得要求得结果。

On the analogy between plane elasticity and plate bending theory, moment functions of plate bending in polar coordinates are introduced as original variables to establish a symplectic space in circumferential direction for the bending of annular sector plate with an appropriate definition of symplectic inner product.

根据平面弹性与薄板弯曲问题的相似性原理，极坐标系板弯曲的弯矩函数被引入作为原变量，并通过恰当的辛内积定义建立了环扇形薄板弯曲问题的一个辛几何空间。

In our systems,integrands in cost functionals need notto be concave in the state variables.

需要指出的是，在这里不必假定指标泛函中被积函数关于状态变量的凹性。

First, based on the measurements of absorption cross-section, the absorption characters of the main polluted gases in flue gas were deeply studied, and found that SO_2、 NO、 NO_2、 NH_3 had a character of approximate periods absorption at some wave band, which is a good chance of a new measurement introduced. Secondly, the factors about absorption cross-section of the gases measured, which affect on the measurement precision of DOAS, is studied deeply. The influence of pressure and temperature on absorption cross-section was given special research, and the compensated measures were given to the gases based on the character of the gases. Thirdly, in practical measurement, it must have been satisfied that the monochromator was consisted with the reference spectrum, which was based on absorption cross-section. In order to satisfy the consistency, the technique of reversion in the image was introduced, the reversions of spectrums were realized with wiener filter and noise elimination based on wavelet transform.

首先从吸收截面的测量入手，对烟气中主要的污染气体SO_2、NO、NO_2、NH_3的吸收特性进行详细研究，发现这些气体在局部区域具有准周期吸收特征，这为引入新的测量方法提供了契机；其次，对决定DOAS测量精度的被测气体吸收截面的诸多问题进行了深入研究，重点研究了压力、温度对被测气体吸收截面的影响，并针对被测气体的特征提出了相应的修正措施；再次，在实际测量中，要求所使用的光谱仪必须与以吸收截面为基础的参考光谱相匹配，为了满足匹配这一条件，文中将图像复原技术引入到光谱复原，使用维纳滤波和小波消噪实现了光谱的复原，将复原后的光谱与所使用光谱仪的仪器函数卷积，即可实现；最后，在对DOAS测量原理详细分析的基础上，对传统的最小二乘—差分吸收光谱法进行了详细的阐述，通过实验证实两点：1。

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。