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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流形上数学规划问题的Fritz John型最优性条件。

At many occasions they arise quite natu-rally.For example,they appear in the Iwasawa decomposition of the isometry group ofa non-compact Riemannian symmetric space.Also,every connected homogeneous Rie-mannian manifold of non-positive sectional curvature can be represented as a connectedsolvable Lie group with a left-invariant Riemannian metric.

它们出现在非紧致黎对称空间的等距群的Iwasawa分解中;任一非正截面曲率的连通齐性和黎流形可以表为带有左不变黎度量的连通可解李群等,带有左不变黎度量的幂零及可解李群的微分几何,调和分析和谱几何是重要的研究课题。

In chapter 4, the influence of the wave-front curvature of Raman pulses on the measurement precision of gravitational acceleration in atom interferometers is analyzed with the method of a transmission matrix. It is shown that the measurement precision of gravitational acceleration is highly dependent on the spot size of the Raman pulse, the temporal interval between Raman pulses and the optical path difference of the two counter-propagating Raman pulses.

第四章运用高斯光束传输矩阵的方法计算了原子干涉仪实验中拉光束波前弯曲对重力加速度测量精度的影响,得出了精度与拉光束光斑大小,拉脉冲作用的间隔时间,以及拉光束光程差之间的关系。

There are numerous kinds of leishmaniasis but the two most common kinds of Leishmaniasis are cutaneous leishmaniasis, which produces skin sores, and visceral leishmaniasis , which impact on some of the internal parts of the body such as spleen, liver and bone marrow.

有许多种利什病,但两个最常用的利什病是皮肤利什病,产生皮肤溃疡和内脏利什病,影响到一些内部的身体部位,如脾,肝和骨marrow。

"The big question is going to be how he relates to the new leadership," said Watson, who recommended Cashman to the Yankees' ownership."Hank is different than his brother, Hal, and they're both different than Steve Swindal and Joe Molloy. All those people we were working for, each one of them had a different style. It remains to be seen how he adjusts to them and how they adjust to him."

鲍伯瓦森(Bob Watson-凯许前的洋基总经理说,当年是他向老板建议凯许的)说:"现在最大的问题将会是他如何处理反应和与新老板间的互动,汉克和霍尔两兄弟是很不同的,他们和Steve Swindal及Joe Molloy这两个他们以前工作过的老板也很不同,每个人都有不同的行事风格,现在就要看凯许如何调整和适应与他们两兄弟共事,也要看他们兄弟两个人如何调整与适应和凯许共事。"

Observing that in seeking more, Ahriman had spread his power thinly, parcelling elements of himself inside those he corrupted, gathering his forces of light Ormazd exploited this weakness to strike. Destroying the Corrupted one by one, Ormazd weakened Ahriman's grip on the universe. When, at last only six of Ahriman's puppets remained Ormazd captured them and pulled them into the Tree of Life. With the six remaining Corrupted sealed inside the tree, Ahriman found himself tethered to the trap unable to break his connection with his six dark servants.

他注意到阿瑞的战线拉的过长,局部的黑暗力量比较薄弱,于是他采取分而治之的战术,逐个逐个的净化被腐蚀的世界和灵魂,从而有效地削弱了阿瑞对宇宙的控制力,最后,残存下来的六位阿瑞的黑暗侍从被奥玛兹一网打尽,锁入了生命树,倒霉的阿瑞发现他与那六位侍从之间的联系过于紧密,以至于他的能力也受到了封锁。

Result] The extracted liquid from D. stramonium could decrease the germination rates of 4 vegetables and the seed germination of tomato and pepper. After treatment by 0.2, 0.4 g/ml extracted liquid , the seed germination of tomato and pepper were decreased by 10.2%, 9.4% and 46.7%, 34.7% than that of CK resp. The extracted liquid at 0.2 g/ml could inhibit the growth of vegetable root, but had some promotion on growth of vegetable stem. The extracted liquid at 0.4 g/ml had the strong inhibition on the growth of vegetable root, but its inhibition on growth of vegetable stem was greatly variable in different species.

结果]陀罗浸提液可降低4种蔬菜种子的发芽速率,降低番茄和辣椒种子的发芽率;0.2、0.4 g/ml陀罗浸提液处理后,番茄和辣椒种子的发芽率分别比对照降低了10.2%、9.4%和46.7%、34.7%。0.2 g/ml陀罗浸提液抑制蔬菜根的生长,而对茎的生长却表现出促进作用;0.4 g/ml陀罗浸提液对蔬菜根的生长有很强的抑制作用,对茎段生长的抑制作用因物种不同而有很大差异。

Shen prove a short time existence theorem for manifolds with umbilical boundary. He also derived the Simons' identity for the boundary under the Ricci flow. And as a corollary, Shen show that any three-manifolds with totally geodesic boundary which admits positive Ricci curvature can be deformed to a space form with totally geodesic

而带边流形上的Ricci流的研究始于Shen,在1996年,Shen在中考虑带边三维流形上的黎度量的Ricci形变,证明了如果初始三维流形的黎度量具有正Ricci曲率和全测地边界,则此三维黎流形上存在着常正曲率的黎度量。

Gurr (1981); A Bibliography of Katherine Mansfield by BJ Kirkpatrick (1990); Katherine Mansfield by Jane Phillimore (1990); Katherine Mansfield: A Study of Her Shorter Fiction by JF Kobler (1990); Critical Essays on Katherine Mansfield, ed.

古尔(1981年);由北京帕特里克书目凯瑟琳斯菲尔德(1990年);凯瑟琳由Jane菲利莫尔(1990)斯菲尔德,凯瑟琳斯菲尔德:她的短由JF凯柏勒(1990年)小说研究;在斯菲尔德批评文章,编。

My demonstration is focused on her two major conundrums of identity: gender and nationality. Firstly, she had been not confirmed her gender as conventionally and socially acknowledged female. She was a put-on woman, both bisexual and masculine. Her psychological trauma resulted from this everlasting confusion in gender. Secondly, her national identity remained uncertain. Though born in New Zealand, she was more Londonish than native spiritually.

对于斯菲尔德来说,她的两大身份标志并不明确:一是她的女性身份,她有明显的同性恋倾向以及男性气质,与约定俗成的女性身份界定不符;另一个是她的国家身份,斯菲尔德并非英国殖民地——新西兰的土著,她的祖父来自伦敦,斯菲尔德自己作家身份的确立也是在伦敦完成的,但是后来成为她大部分小说题材的是她在新西兰度过的童年,这种身份的不确定性必然影响了斯菲尔德的个性稳定以及心灵健康。

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推荐网络例句

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm~150rpm时取得最大值,此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世,形体几无变化。

When I was in school, the rabbi explained everythingin the Bible two different ways.

当我上学的时候,老师解释《圣经》用两种不同的方法。