解析曲线

The trajectory of antisubmarine homing torpedo is a complex space curve, so there is big limitation in accounting its trajectory length by plane geometry.

由于反潜自导鱼雷的弹道是一条复杂的空间曲线，因而平面几何解析法求解其弹道长度有较大的局限性。

Due to the introduction of IP curves, the method detects the symmetry and axis of objects by using the expressions of function instead of using the optimization method. Consequently, the computational cost of the method is low.

由于是基于隐含多项式曲线进行对称性检测，因而并不需要复杂的优化算法，仅用明确的解析式即可验证对称性并检测出相应的对称轴。

In this research a new mathematical model - cubic polynom with two given derivatives at end points - was proposed which can good match the S-shpae curve.This model has a number of analytical features:describing the geographic phinomena prosesses in three hierarchies (textural fractal,structural fractal and state fractal); the boundary values of the structural fractal can be considered as the boundary values of interval of scaleless.

在研究中提出了扩展分维表达函数：带导数三次多项式，它能很好地表达反S形分布曲线，具有一系列解析特征：可从三个层次（纹理分形、结构分形和态势分形）上描述地理现象或过程；其中结构分形的边界可近似地看作是非扩展分维无标度区的上下界。

Further study of this paper has shown that reason for"camel peak"phenomenon in the adhesion-creep test curves is difference between sliding-and static coefficient of friction and discussed the analytic formulae for line contact as well as one direction slip and special correction Lemk's method for point contact when their change is considered as stage jump function.

通过进一步的理论研究指出造成轮/轨粘着率与弹性滑移率实验曲线呈"驼峰"状的原因是滑动区和粘着区的动、静摩擦系数变化，给出了当它们为阶跃变化时线接触条件下的解析解和对点接触情况的独特的"修正"Lemke算法。

Through the process of learning different kinds of theorems, solving various geometry problems involving using those theorems, as well as combining the usage of plane geometry methods with analytic geometry, especially with conic section, we gained our own unique understanding and strong interest of plane geometry.

通过对平面几何各种定理的了解、证明，结合高中数学联赛具体题目中各种定理、推论的应用，以及平面几何与解析结合在圆锥曲线问题中的实际结合，我们对平面几何有了自己独特的见解和浓厚的兴趣。

A universal analytic potential energy function is derived using the cosine function with a phase factor,which is suitable to be applied to the interactions between two atoms in a molecule or molecule and ion.5 kinds of common potential curves are obtained by adjusting phase factors.

利用一种带相位因子的余弦函数，导出了适用于双原子分子或分子离子间相互作用的普适性解析势能函数，通过调节相位因子可获得5种常见形态的势能曲线。

As a result, it shows thatthe static or dynamic subsystem optimum alone is not equal to the system optimum. Three initial value problems met in the optimal design of flying vehicle are studied andconclusions are derived that: orthogonal test method can be adopted to decide the initial valueof static optimization problem, some mathematical techniques can be used to deal with thecostate variables of Maximum Principle and decide the initial value of the costate variable,the indirect method can be used to get the analytical solution under ideal case to guide thechoice of the initial control curve in the direct method. With some numerical examples oftrajectory optimization, it shows that all these methods are useful not only in accelerating theconvergence but also in converging to the global optimum.

针对飞行器优化设计中的三种初始值问题进行了研究，以远程弹道导弹弹道的工程优化为例说明，对于静态优化问题，采用正交试验法选取初始值，不仅可以大大加快收敛的速度，而且更有可能收敛到全局最优解；以气动力辅助变轨问题为例说明，用共态变量的一阶泰勒级数展开可以解决极大值原理中共态变量初值难于确定的问题；以二级弹道导弹的主动段弹道优化为例说明，利用间接法在理想情况下得到的解析解来指导直接法初始控制曲线的选择，将大大有利于提高直接法的收敛速度。

The dawsonite in oil-bearing reservoir was identified accurately with X-ray diffraction method for the first time in China,and its diffraction characteristics was given in detail.

运用X衍射手段准确鉴定了石油储层中的碳钠铝石矿物，详细解析了其衍射曲线特征，这在我国尚属首次。

The author identified the dawsonite in oil-bearing reserver well and truly with X-ray diffraction method for the first time in China,and detailedly analyzed its diffraction characteristic.

作者首次在中国运用 X 衍射手段准确鉴定了石油储层中的碳钠铝石矿物，详细解析了其衍射曲线特征。

The analytic expression of a probability current is derived by using the power series expansion method and used to generate the curve characteristics of the current varying with other parameters.

采用幂级数展开的方法得到了几率流的解析式，给出几率流随外参数变化的特性曲线。

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