积分公式

Earlier, in 1952, the idea of distinguishing reliabilities of formulas in the propo-sitional logic was proposed by Rosser and Turquette.

在王国俊教授提出的积分语义学理论的基础上，一些学者在赋值域是连续值的情形下展开了对公式真确度的讨论。

In chapter 3 we introduce a volume elementon 〓 and give some formulas of integration on 〓 under this volumeelement.The singular matrix Liouville distribution is introduced through theuse of this volume element.

第三章较详细地介绍了〓上的体积元素，给出了在这个体积元素之下的若干积分的计算公式，在此基础上提出了退化矩阵Liouville分布，讨论了这个分布的一些性质。

Using the perturbation method and Stroh's formula, a nonideal crack, which is mathematically sharp and the opposing crack faces still have a gap in which a stiffless dielectric fills, the two-field problem is reduced to a standard Riemann-Hilbert problem. The internal electric field distribution is obtained by solving a singular integral equation, and then the full field both inside and outside the crack is obtained and the electro-mechanical intensity factors to the first order of accuracy are given.

采用摄动方法对裂尖理想尖锐而裂纹面又具有一定张开的非理想裂纹进行分析，裂隙内含有无刚度的各向同性电介质，利用Stroh公式，将二域问题化为标准的Riemann-Hilbert问题，裂隙内电场分布通过解一个奇异积分方程获得，从而得到裂纹内外的力电全场分布，进而给出一阶精度下的力电强度因子的表达式。

For experimental setup to calibrate spectral radiance by applying a diffuse plane, the measured spectral radiance can be obtained through integral of spectral radiation flux entering the spectrometer.

在利用漫反射板标定光谱辐亮度的实验装置中，标准灯完全可以近似为点光源。通过对进入光谱仪的辐射通量的数值积分，可以对应求出仪器的实测光谱辐亮度的计算公式。

Dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesn't calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.

通过结构地震反应在小波基下的动力可靠性分析说明：无论是单自由度还是多自由度从理论上推导在这四种小波下的结构动力可靠性是可行的，而且考虑的结构地震反应都是非平稳的高斯过程，方法实现也比较容易；在Littlewood—Paley小波基下求得的结构的动力可靠度比较大，由改造的meyer小波和谐波小波求得的动力可靠度略有差异；单边指数小波下的结构动力可靠性分析非常简单，不用求功率谱函数来积分，只需求得结构地震反应的位移方差，速度方差，利用最大值分布公式就可得到结构的动力可靠时程；另外也考虑了超越界限对结构动力可靠度的影响，超越界限越小，结构的动力可靠度越小，即破坏概率越大。

Dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesnt calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.

通过结构地震反应在小波基下的动力可靠性分析说明：无论是单自由度还是多自由度从理论上推导在这四种小波下的结构动力可靠性是可行的，而且考虑的结构地震反应都是非平稳的高斯过程，方法实现也比较容易；在Littlewood—Paley小波基下求得的结构的动力可靠度比较大，由改造的meyer小波和谐波小波求得的动力可靠度略有差异；单边指数小波下的结构动力可靠性分析非常简单，不用求功率谱函数来积分，只需求得结构地震反应的位移方差，速度方差，利用最大值分布公式就可得到结构的动力可靠时程；另外也考虑了超越界限对结构动力可靠度的影响，超越界限越小，结构的动力可靠度越小，即破坏概率越大。

The representation of functionals of Brownian motion in terms of stochastic integral with respect to Brownian motion is known as Clark formula.

布朗泛函以布朗运动随机积分来表示是可被称之为克拉克公式。

Jacobian Davis iterative method of solving equations AX = B, least squares polynomial fitting, portfolio Simpson formula for integration, with a triangular decomposition method of solving equations AX = B.

拉格朗日插值多项式拟合，牛顿插值多项式，欧拉方程解偏微分方程，使用极限微分求解导数，微分方程组的N=4龙格库塔解法，雅可比爹迭代法解方程AX=B，最小二乘多项式拟合，组合辛普生公式求解积分，用三角分解法解方程

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用&去行去列法&和&置大数法&进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

It is well known that the Cartan form is nonunique for higher-order Lagrangian density, we find it was caused by higher-order mixed multiple integral in using Stokes formula in actually calculus variation.

众所周知，高阶Lagrangian对应的Cartan形式是不唯一的，在实际的变分计算中，我们发现Cartan形式的不唯一性是由利用Stokes公式求高阶混合多重积分的不唯一性引起的。

The good news is that after formatting from the command line to FAT32 (format /fs:fat32 /a:4096 drive:) all but one of the problematic games that I tested work perfectly.

好消息是，从指挥线后格式化了FAT32(格式/曾荫权：了FAT32/答：4096年径：)所有问题，但其中的游戏测试工作，我很好。

In Amsterdam. He is a Dutch painter, draftsman, and etcher of the 17th century, the greatest artist of the Dutch school, a master of light and shadow whose paintings, drawings, and etchings made him a giant in the history of art.

伦勃朗是一位17世纪画家、绘图家、版画家，荷兰学派的最伟大艺术家，他的明暗法的大师，他的绘画、素描和版画使他成为一位艺术史上的巨匠，其画作体裁广泛，擅长肖像画、风景画、风俗画、宗教画、历史画等。