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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 chapter 2, using the favorable characters of the function Q = ch{x - 1, we construct the hyperbolic cosine penalty function and algorithms and proved its convergence .

在第二章中，我们利用函数Q=ch-1良好的性质，提出一种用双曲余弦函数作罚项的双曲余弦罚函数及算法，证明了该罚函数和算法的合理性及迭代点列的收敛性。

In chapter 3, combining the traditional augmented Lagrange function and the hyperbolic cosine function, we construct a new hyperbolic penalty function multiplier method for the equality constrained optimization and deduced the iterative formulas, and proved the convergence under some conditions.

在第三章中，我们把传统的增广Lagrange函数和双曲余弦函数结合，构造了一类新的在等式约束下的双曲罚函数乘子法，推导出了双曲乘子迭代公式。

EVER SINCE the law of Copernicus was discovered and proved, the mere recognition that not the sun, but the earth moves, has destroyed the whole cosmography of the ancients.

自从哥白尼体系被发现和证实以后，仅仅承认太阳不会运转，而是地球运转这一事实，就足以破除古人的全部宇宙观了。

CHAPTER XII Chinese EVER SINCE the law of Copernicus was discovered and proved, the mere recognition that not the sun, but the earth moves, has destroyed the whole cosmography of the ancients.

第十二章英文自从哥白尼体系被发现和证实以后，仅仅承认太阳不会运转，而是地球运转这一事实，就足以破除古人的全部宇宙观了。

The news brought by the Cossack, confirmed by scouts, proved conclusively that the time was ripe.

派出的侦察骑兵证实了那个哥萨克的报告，这足以证明，时机已经成熟。

But the business that AOL does now proved his is not the Gu Ge that ready awaits, latter still is the cosset of capital market, and AOL late evening is long already, it ever dialed with offerring online service is main income, but must face the anguish that dials the user sheds estrangement transition however now.

但AOL现在所做的事情证明了其不是甘于等待的谷歌，后者仍是资本市场的宠儿，而AOL迟暮已久，它曾以提供拨号上网服务为主要收入，但现在却不得不面对拨号用户流失和转型的痛苦。

The maximum principle of the optimal control for the stochastic systems described by Zakaj stochastic partial sifferential equationis proved by approximately minimum point theorem of E. Ekeland. The convexity and compactness of the set of control values is not assumed, and it is not necessary for the maximum principle about differentiability in control variables included in drift term of the stoch astic system and the integrand in index functional, and costate process satisfies the stochastic partial ...

在不假便定控制变量取值的集合是凸的和紧的，不要求随机系统的漂移项和指标泛函的被积函数关于控制变量具有可微性的情况下，用E，Ekeland的近似极小点定理证明了Zakai随机偏微分方程描述的随机系统的最优控制的最大值原理，和用很简洁的方法证明了协态过程满足一个随机偏微分方程。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

By means of the curcuit mapping transformation developed in electrical network analysis, it is proved that the total reaction forces and moments are not independent but ran be linearly represented by two sets of independent ones, namely, cotree forces and cotree moments, respectively.

本文根据研究内容不同分成两篇，第一篇提出了一种基于网络分析方法的平面连杆机构运动学和静力学理论研究体系，侧重探讨和揭示了机构运动和力分析数学模型的内在联系，研究了机构组成的计算机辅助识别原理、策略、方法及软件设计技术。

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