积分公式

By adapting the existed numerical methods for ordinary and delay differential equations, and matching certain suitable numerical quadrature formulas, Rosenbrock methods are constructed for delay integro-differential equations, the stability criteria of the methods are derived.

通过改造现有常及离散型延迟微分方程的数值方法，并匹配以适当数值求积公式，构造了求解时滞积分微分方程的Rosenbrock方法，导出了其稳定性准则。

This paper, starting from a simple formula of rational proper fraction and partial fraction, discusses about a way to improve rational functional integral, a way simpler and more convenient than comparative coefficient.

本文从有理真分式分解为部分分式的一个简洁公式出发，讨论了有理函数积分的一种改进方法，相对于比较系数法而言，该方法更为简单、方

According to the plane cross section assumption, configuration of a rod is expressed as a history of the cross section with arc coordinate. A special solution which stands for equilibrium in straight line state is obtained from differential equilibrium equation. Linear perturbation equation is derived and its general solution is obtained in which the integral constants are determined by constrained conditions at two ends of the rod. The condition of existence of non zero solution of the integral constants gives to the Greenhill formula of exact elastic rod model, which shows that the boundary of stable area is a closed curve and of symmetry, and inference of shearable and extensible to stability of the rod is depend on three factors: difference between flexibility of shear and extension of a section of the rod, bending stiffness and the length of the rod.

基于平面截面假定，弹性杆的位形表达为截面的弧坐标历程，根据平衡微分方程得到了两端受力螺旋作用时的直线平衡特解，导出了线性化扰动方程及其通解，积分常数根据两端铰支时的边界条件确定，并根据其存在非零解的条件得到弹性直杆精确模型的Greenhill公式，表明稳定域为一对称的封闭区域，拉/压和剪切对稳定性的影响取决于：拉/压柔度与剪切柔度之差，抗弯刚度和杆长这三个因素

Therefore,a series studies of ice-pier vibration are performed from different aspects in this paper.The main work of this his thesis is summarized as follows:(1) Ice response spectra is proposed based on the idea of a seismic response spectra analysis of str .. uctures.Firstly,ice response spectra on the basis of power spectra density function is established;Secondly,based on the assumption of quadratic parabolic interpolation method,the nonlinear interpolation analysis method of ice response spectra is studied from both theoretical and practical points of view,and the successive computation formulas including ice displacement,velocity and acceleration response spectrum are deduced by Duhamel integral.Furthermore,to analyze the effectivity and applicability of the method, the real temporal curves of ice pressure are used to be studied.The results show that the presented method is more convenient and accurate to study the structural response induced by ice force,also it can be effectively applied in the design of ice resistance.

鉴于此，本文针对冰激桥墩结构振动问题从不同方面展开了一系列与之相关的研究，主要研究内容如下：(1)根据结构抗震反应分析思想提出了冰振反应谱，首先建立了基于功率谱密度函数的冰振反应谱；其次借鉴地震反应谱内插法的思想从理论和实际观点出发，假定在等距离微小时间间隔内冰荷载按二次抛物线规律变化，由Duhamel积分推导出冰振位移、速度以及加速度反应谱的一系列连锁公式，建立了基于非线性内插法的冰振反应谱，并利用实际冰压力时程曲线进行了冰振反应谱数值分析，为以后冰激结构振动的研究提供一种方便、简捷、精确的分析方法，也能够将其有效地应用到结构的抗冰计算中。

The modifier formula is put forward which is based on the study on many practical observation data in order to further increase the precision of the probability integral method.

为了进一步提高概率积分法的预计精度，在研究许多实测资料的基础上，提出了修正公式。

As compared with the results predicted by probability integral, it has been verified that the prediction accuracy of SPDP system is obviously higher than one's under the complicated geological and mining conditions.

最后，通过与现行概率积分法的预计结果进行对比分析，证实了在复杂地质采矿条件下SPDP系统的地表移动预计精度更高，而在平面分布煤层情况下两者的地表移动预计公式形式相同，这也说明了SPDP系统的广泛适用性及预计结果的可靠性。

In order to accurately calculate the mining induced subsidence in thick alluvium areas so as to decrease the mining damage and environment disruption,the calculation of surface subsidence caused by water loss of clay was discussed based on probability integral method and used in a real case.

为了更加精确地计算厚冲积层矿区的煤矿开采沉陷问题，减小采动损害与环境破坏，基于煤矿开采沉陷计算的概率积分法，探讨了由于黏土体失水引起的地表沉陷计算问题，推导了黏土体失水引起的地表下沉计算公式，并应用于煤矿实际地表沉陷，加以分析论证。

In order to accurately calculate the mining induced subsidence in thick alluvium areas so as to decrease the mining damage and environment disruption, the calculation of surface subsidence caused by water loss of clay was discussed based on probability integral method and used in a real case.

摘要为了更加精确地计算厚冲积层矿区的煤矿开采沉陷问题，减小采动损害与环境破坏，基于煤矿开采沉陷计算的概率积分法，探讨了由于黏土体失水引起的地表沉陷计算问题，推导了黏土体失水引起的地表下沉计算公式，并应用于煤矿实际地表沉陷，加以分析论证。

Then for complicated sine integral and prolix formulae, the study on symmetrical dipole can be easily solved by MATLAB.

对于复杂的正弦积分和冗长的公式，都可以通过简单的编程实现仿真。

The calculation model was constructed by equating CWG with rectangular waveguide. The scattering formula was deduced by Integral Equation Method, which was validated by Finite Element Method.

通过将同轴波导等效为窄边是磁壁的矩形波导，建立了金属支撑杆的散射场计算模型，用积分方程法得到了散射场的计算公式，其计算结果与有限元方法仿真结果吻合良好。

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。