解析式

The problem of sub-Riemannian geodesics is a Lagrange problem with constraint. How to describe the constraint condition "γ'∈ D, a. e." is a difficult problem.

次黎曼测地线问题是变分学中的一个有约束的Lagrange问题，但在变分的过程中有个难点―如何推出约束条件"γ'∈D，在上几乎处处成立"的解析式。

of martingale was used to analyze the analytical formula of ruin probability and its upper bound estimation.

利用鞅论方法分析模型盈余过程的性质、破产概率的解析式及其上界估计。

A mathematical formula is based on the relationship between solution concentration and refraction angle.

分析了临界光线的折射角与其浓度的关系，给出溶液浓度与折射角之间的简单数学解析式。

This paper gives the analysis formulas and correction algorithms for influence on thesystem error, Observational Gross Error and the noise correlation, which enriches theKalman filter theory, and at the same time raises the capabilities of kinematicpositioning and navigation.

论文对于系统误差，测量粗差，噪声时间的相关性对动态定位结果的影响，给出了其相应的解析式和校正方法，丰富了卡尔曼滤波理论，同时提高了动态定位和导航的能力。

Then, the analytical expressions of average susceptibilities for Pauli paramagnetism of the system in different temperature region are derived by calculating susceptibilities Xp in the limit of thermodynamics at different temperatures.

然后通过计算热力学极限下不同温度范围的磁化率χp，得到不同温度范围内的有限粒子数理想费米系统泡利顺磁性平均磁化率的解析式。

First, sweep line algorithm is used to find fill regions of each tile on the layout. Secondly, the fill regions are classified according to the criticality of the surrounding net segments. Then the fill amount of each fill region is reassigned based on its class.

该算法利用扫描线算法找到填充区域，根据线网关键度将填充区域分类，按照优先级对填充数量进行分配，对每个填充区域采用解析式沙漏模型进行冗余金属插入。

The simulation of RIN based on the rate equations and the comparison with the theoretical result are performed.

推导得到与电场和载流子密度空间分布相对应的解析式。

Now,self-excitation conditions are mathematical formulas under certain postul a te.The model of transient process of self-excitation is linear.

目前，自励磁条件是在一定假设条件下的解析式，而研究自励磁态过程是采用线性模型。

The last part of this paper treated the results with the assistance of spline function and Nth-degree harmonics cam approximate. Thus, the new function of tappet, speed and accelerated speed was gained and the whole designing process was completed.

文章的最后部分分别用样条函数方法和N次谐波凸轮逼近方法对计算结果进行处理，得出新的从动件升程、速度和加速度的解析式，从而完成整个设计过程。

In order to analyze and correct this effect, the method to calculate turn-off time is given. According to theoretical TEM response of multiturn loop source, TEM response affected by linear and half-sine turn-off current was calculated, and Taylor's series expansion was used by calculating TEM response of half-sine turn-off current. The two mode's responses, linear mode's response and half-sine mode's response, were analyzed in turn-off time 2μs-100μs.

为了分析和校正这种影响，文中给出了关断时间的计算方法，根据多匝回线源产生的瞬变场理论解析式，计算了线性和半正弦关断电流影响下瞬变场表达式，计算半正弦关断电流产生的瞬变场时将正弦函数进行泰勒展开；分析了关断时间在2 μs~100 μs之间两种关断模式产生的瞬变响应。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失