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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。

Based on the analysis of models proposed, the cumulative distribution functions and probability density functions of strength of systems were derived respectively.

在研究系统可靠性模型的基础上，建立了系统强度的累积分布函数和概率密度函数。

Although cursor movement is a general operation shared by all these functions, the specific nature of that movement is unique to each of these functions.

虽则这几个函数共享的一般性动作都是光标移动，但特殊的移动性质却互不相同。

Based on them, the simulation system of UAV decimeter wave instrument landing system was designed with the support of LabView's abundant graphic functions and powerful mathematics functions.

以此为基础，充分利用虚拟仪器软件lab View的图形功能和数学计算功能，设计了无人机分米波仪表着陆系统的虚拟仿真系统软件。

The result shows that: The variation rhythm of the sensitivity index changed unanimously for Jensen,Blank and Stewart water production functions of spring wheat in Liangzhou city,the volume is small in the former stage,then become large at the middle stage,and less at the last stage. Jensen and Stewart water production functions are better of spring wheat in Gulang County in 1987-1989. The Variation rhythm of water deficiency sensitive index is unanimous: the volume are small at first,then large at middle,and diminish at last. The Variation rhythm of water deficiency sensitive index is unanimous in Jensen,Blank and Minhas of flax in Liangzhou county in 1987-1989. The water deficiency sensitive index in Gulang district in 1987-1989 models bad,are too many minus.

结果表明：1985-1986 年凉州春小麦Jensen 模型、Blank 模型和Stewart 模型的敏感指数变化规律接近一致，在前期较小，中期增大，最后再减小。1987-1989 年古浪春小麦水分生产函数以Jensen 模型和Stewart 模型拟合较好，其敏感指数变化规律比较一致，敏感指标值前期较小，中期增大，后期又减小。1983-1985 年凉州亚麻水分生产函数以Jensen 模型、Blank 模型和Minhas 模型敏感指标值变化规律比较一致：先减小，后增大，最后再减小。1987-1989 古浪亚麻敏感指数出现负值较多，模型拟合较差。

The result shows that: The variation rhythm of the sensitivity index changed unanimously for Jensen,Blank and Stewart water production functions of spring wheat in Liangzhou city,the volume is small in the former stage,then become large at the middle stage,and less at the last stage. Jensen and Stewart water production functions are better of spring wheat in Gulang County in 1987-1989. The Variation rhythm of water deficiency sensitive index is unanimous: the volume are small at first,then large at middle,and diminish at last. The Variation rhythm of water deficiency sensitive index is unanimous in Jensen,Blank and Minhas of flax in Liangzhou county in 1987-1989. The water deficiency sensitive index in Gulang district in 1987-1989 models bad,are too many minus. 3 Establishing the non-linear model to definitive the irrigation quota and dimension of single crop,according the three prototype Precipitation,allocating the limited water optimally according to full water supply,95 percent,75 percent and 50 percent. Economy benefit is the biggest aim function,so getting three groups for irrigation quota,irrigation dimension and benefit,the biggest benefit is the most optimal result.

结果表明：1985-1986 年凉州春小麦Jensen 模型、Bl(来源：10a1ABC论文网www.abclunwen.com)ank 模型和Stewart 模型的敏感指数变化规律接近一致，在前期较小，中期增大，最后再减小。1987-1989 年古浪春小麦水分生产函数以Jensen 模型和Stewart 模型拟合较好，其敏感指数变化规律比较一致，敏感指标值前期较小，中期增大，后期又减小。1983-1985 年凉州亚麻水分生产函数以Jensen 模型、Blank 模型和Minhas 模型敏感指标值变化规律比较一致：先减小，后增大，最后再减小。1987-1989 古浪亚麻敏感指数出现负值较多，模型拟合较差。3 建立单作物种植条件下灌溉定额与灌溉面积的确定的非线性规划模型，将有限的水量按照充分供水，95%、75%和50%供水来分配水资源，以经济效益最大为目标函数，得出三组灌区灌溉面积和效益结果，其中以效益最大为最优解。

A new approximation function based on the coupling of radial basis functions and polynomial basis functions is obtained, which has the property of Delta function.

径向基函数和多项式基函数耦合可以构造具有插值特性的近似函数。

It is shown that in complex system like L-tyrosine, using a locally dense basis set with a large number of atomic basis functions for the carbon atom of interest and smaller sets of atomic functions for the other atoms can not only save the disk capacity and computing time but also produce satisfactory results.

由从头计算获得的结果与实验值符合较好，说明对于具有复杂结构的多原子体系，对杂原子使用较小的基函数，而对所关心的碳原子使用较大的基函数以提高计算精度，这样可以达到既节省计算机空间与计算时间而不影响计算精度的目的。

In order to achieve the simultaneous optimization of the two major electrophoretic performance goals for efficient and fast separations, the Derringer desirability functions were chosen as the optimization criteriaon. The selected parameters were encoded into binary bit strings, and then genetic algorithm calculations were performed to generate a new set of experimental conditions by the values of total desirability functions.

并用Derringer功效函数作为多指标同时优化的评价指标，以取得较高的分离度和较快分离速；通过对实验参数给予编码，转化为二进制字符串，根据得到的总功效函数値大小进行遗传算法操作，产生新的一组实验条件。

In fact, in Europe, the concept of removing the traditional diet of kitchen functions, most also commercial entertainment, leisure, family emotional communication, social gatherings and many other functions.

事实上，在欧洲，厨房的概念除去传统的饮食功能，大部分还兼有娱乐、休闲、家庭情感沟通、朋友聚会等诸多功能。

We stopped by the old fashion ice cream parlor Manhattan Beach Creamery for some refreshment. The "No Shoes, No Shirt, No Problem" sign on the wall epitomizes the beach lifestyle.

我们去商店区的一家老式冰淇淋店坐坐，墙上挂著「没鞋，没上衣，没问题」的牌子完全捕捉了海滩生活的随性及风格。

"If therefore", argues Bellarmine we can offer our prayers and our satisfactions in behalf of those detained in purgatory, because we are members of the great body of Christ, why may not the Vicar of Christ apply to the same souls the superabundant satisfaction of Christ and his saints--of which he is the dispenser?

" "因此，如果"，认为贝拉明（德indulgentiis ，十四）"我们可以提供我们的祈祷和我们满意的代表那些被拘留在炼狱，因为我们是成员的伟大基督的奥体，为什麼可能不是牧师基督适用於同样的灵魂满意的过剩是耶稣和他的圣人-他是在配药？