定理

In the second step,the parameters estimated in the first step are improved iteratively through a nonlinear optimization,based on the coplanarity condition,taking into account camera distortions.This works well if there are three sets of parallel lines independently in the view scene.

该标定方法分为两步：第一步标定相机内方位元素：由三灭点定理确定体视相机的初步标定参数；第二步标定实际流场：利用同源像线与基线必定确定一平面作为优化约束，对第一步取得的参数进行非线性优化。

Describing the problem of two dimension fuzzy decision existed in the engineering, the concepts of core set and support set are proposed. Using feasible set to constitute corelation between two sets, determinant theorem is presented to judge if the decision can be realized according to the feasible degree.

描述了工程中存在的二维模糊决策问题，提出了决策的核心集和支撑集的概念，用可行集建立了两个集合间的关联，提出以决策的可行度作为决策能否实现的判定定理。

As a result, an open problem following the Corollary of Theorem 10 in [2] is solved in some way.

其结果是，一个开放的问题，的定理10在某种程度上必然得到解决[2]。

Two conservation equations are derived from a Wigner-Fokker-Planck model, they contain a third-order quantum correction term and second-order viscous term...

然后 在弱的亚音速条件下利用截断技术建立解的先验估计，在此基础上根据Leray-Schauder 不动点定理得到四阶方程弱解的存在性。

As to the techniques I learned from him and used: comparative statics of constrained optimization, the correspondence principle and the envelope theorem, factor price equalization in international trade, valuation of real options, the list could go on.

我从他那里所学所用的技能包括了：约束优化的比较静态学、对应原理和包络定理、国际贸易中的要素价格均等化、实物期权估值，这样的例子不胜枚举。

We proposed and proved three theorems through which the theoretical formula of cosine transform spectrum of gravity anomalies of the point mass and the vertical rectangular-cylinder was deduced in order to obtain the general equation of gravity anomalies.

为获得重力异常余弦变换谱的通式，提出并证明了3个定理；利用它们推导了点质量和直立矩形柱体的重力异常余弦变换谱理论公式，同时给出了重力异常余弦变换谱通式。

We proposed and proved three theorems through which the theoretical formula of cosine transform spectrum of gravity anomalies of the point mass and the vertical rectangularcylinder was deduced in order to obtain the general equation of gravity anomalies.

为获得重力异常余弦变换谱的通式，提出并证明了3个定理；利用它们推导了点质量和直立矩形柱体的重力异常余弦变换谱理论公式，同时给出了重力异常余弦变换谱通式。

In this paper,the methods of distance geometry are used to explore the angles of a simplex ,and the second cosine law of a simplex in another form is obtained.

运用距离几何的研究方法，研究了和单形相关的角，给出了单形第二余弦定理的另一种形式，以此为基础得出了BartO¨s体积公式一种简洁的证法；探讨了单形的几个体积公式之间的联系，并推广了单形的一个体积公式。

After trying several different ways to find the map of contour lines, we use color segmentation to construct the map of contour lines, and use the law of cosine to estimate the length of contour line we sample. We also estimate the slope of contour lines and compute how they should extend in the inpainting domain.

所以我们提出一个用来修补卡通的新inpainting演算法，我们使用颜色分群的技术来取得结构性资料或称轮廓线并且使用余弦定理来计算轮廓线取样长度，以我们取样的轮廓线推算出在修补区域内轮廓线的结构性，进而使用类似於现实生活中的贝兹曲线来重建消失的结构性资料。

Via the stochastic averaging method, the four-dimensional system is reduced to a two-dimensional one. Through the logarithmic polar transformation , and then Girsanov theorem and Feynmann-Kac formula, the backword differential operator is then obtained. By expanding the eigenfunctions as a Fourier cosine series, the approximate analytic expansion of the moment Lyapunov exponent is then obtained.

首先在经典二元机翼颤振方程加入随机激励，通过随机平均法，Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题，其次采用Fourier余弦级数对特征函数进行正交展开得到系统矩Lyapunov指数的近似解析式。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新