积分公式

In order to solve the problem, We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddlepoint method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量（地面点到地下相点的水平距离）的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

According to the space domain iteration method of the Fredholm integral equation of the first kind, the wave number domain iteration formula is deduced for calculating the wave spectrum of the potential field on a lower horizontal plane.

根据第一类Fredholm积分方程的空间域迭代解法，推导出计算向下延拓水平面上位场波谱的波数域迭代公式。

A systematic study on computing the integral curvature line on NURBS surface is presented. Discrete normal is used to simplify calculation of the second fundamental form of the surface, resulting in accelerating the Euler iteration process in solving the differential equation of curvature line. Discrete points on the curvature line are then obtained and approximated by an explicitly presented B-spline curve on the NURBS surface using singular mixed interpolation and capable of controlling the error within a given tolerance.

对NURBS曲面的曲率线的积分进行了系统的公式推导，并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算，加速了Euler法迭代求解曲率线微分方程的过程；在求得曲率线上的离散点集以后，应用奇异混合插值技术，在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线。

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。

In this paper we contribute the general integral formula of second order linear differential equation with constant coefficients by means of decreasing order So we can integrate directly to solve this kind differential equation .

本文通过降阶法给出了求二阶常系数线性微分方程通解的方法，并根据特征根的不同情形给出了具体的通解公式，即可通过积分直接求微分方程的通解。

With the latest NASA model of sea surface topography in 1996, we get the sea geoid.

另外，本文还介绍了利用逆 Stokes 公式和 Hotine 积分求解重力异常和重力扰动的快速算法。

3We obtain the analytical price formulas for vanilla, forward-start and in-progress fixed-strike and floating-strike continuous geometric average Asian options and a put-call parity under generalized Black-Scholes with time-dependent parameters by risk neutral valuation and properties of stochastic integration.

在依赖时间参数的推广的Black-Scholes模型下，利用风险中性定价及随机积分的性质，得到平凡、远期开始和进展中的固定和浮动执行价格的连续几何平均欧式亚洲期权价格的解析公式和一个平价关系。

Employing the GREEN theorem, the boundary integral equations for solving the ground surface potential are derived for the first time, both for one object underground and for complicated geological structure.

利用格林公式首次推导出了单一目标体和复杂地质结构两种情况下直流电阻率正演模拟中求解表面电位的边界积分方程。

We present a strict derivation by applying Green′s theorem for a linear integral expression of the gravity anomaly produced by a 2D homogeneous source. The result thus acquired coincides with a documented formula, but our method is simpler and mathematically compact.

本文基于格林公式，给出了均匀二度体重力异常线积分表达式的严格数学推导过程，其结果与前人推导出的结果完全相同，但我们的方法在数学上更简单，也更严谨。

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。