查询词典 convex

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

Two new rules represented in equality for Demyanov difference: the Demyanov difference of summations of two pairs of convex compact complementary sets;the Demyanov difference of a set, which is the convex hull of finite number of convex compact sets, and a convex compact set complementary to these sets,are given.

为此给出了两个关于Demyanov差的新的用等式表述的运算法则：两个彼此互补的凸紧集对的和的Demyanov差，有限个凸紧集的凸包和与这些凸紧集正交互补的凸紧集的Demyanov差。

The convex function develeped so many years that convex functionals are now a class of very universal functionals.The kinetic energy in the classical is the most natural convex function.Others like entropy and so on are convex functions.The economic core is closely connected with the convex function.The western economic core question is the optimized question.The optimized theory has something to do with the convex function and the concave function.

凸函数的发展经年已相当完善其应用非常广泛，在古典力学中的动能，就是最自然直接的凸函数，其他如熵……等均是，连经济学的核心都与之有极密切相关，西方经济学的核心问题是最优化问题，最优化理论又与凸函数与凹函数密切相关。

Chapter 4 establishes the theory of convex fuzzy mappings: The concepts, such as Jensen's inequality, positively homogeneous, infimal convolution, right scalar multiplication and convex hull are introduced. The corresponding theorems are demonstrated by using the parametric representations of fuzzy numbers. In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved. The notions of subgradient, subdifferential, differential with respect to convex fuzzy mappings are investigated, which provides the basis of the theory of fuzzy extremum problems.

在第4章中，建立了有关凸模糊映射的理论：建立了关于凸模糊映射的Jensen不等式、模糊正齐次映射、凸模糊映射的下卷积、右数乘和凸包等概念，利用模糊数的参数化表示，给出了相应的定理；在反模糊数空间，对凸模糊映射的共轭也作了探讨，证明了凸模糊映射的共轭集合和共轭映射都是凸的；最后对凸模糊映射的次梯度、次微分和微分等概念进行了研究，为模糊极值理论打下了基础。

Based on the previous work of other researchers, we presented the definition of global convex: a surface is globally convex if it happens to be the surface of a convex body or part of the surface of a convex body.

曲面微分几何，总结了自由曲面形状分析技术手段，对著名CAD软件中曲面分析工具特点进行了简要分析，指出了它们对曲面全局形状分析能力的不足。

As pointed out by Deville et al., a class of connected row-convex constraints is shown to be tractable.

相接行凸(connected row-convex，简称CRC)约束网络是Deville等人提出的一类易处理问题。

To solve the optimization problems, apply the DCA （difference of convex functions algori-thms） which is a general framework for nonconvex continuous optimization. This leads to a successive linear programming algorithm with finite convergence.

为解决优化问题，应用了突函数差异算法（difference of convex functions algorithms，DCA）这一进行非突连续优化的通用框架，致使连续线性规划算法有限收敛。

In this paper, a varieties of concepts of compactness of sets and sunsets are introduced in a complex locally convex space, which are respectively the generalizations of the known sunsets and convex sets. By establishing the relationship between restricted p-centers of a set in a complex locally convex space and restricted Chebyshev centers of the corresponding set in the quotient space with respect to ker, characterizations and uniqueness of restricted p-centers of sets in a complex locally convex space are obtained. These results are better than any other known ones when we restrict them in real normed linear spaces and real locally convex space.

本文首先在复局部凸空间中引入了几种紧性及几种太阳集的概念，它们分别是已有紧性和凸集概念的推广；然后通过建立局部凸空间中集的限制p-中心和关于ker的商空间中对应集的限制Chebyshev中心的关系，来研究局部凸空间中集的限制p-中心问题，本文即使是在实赋范空间和在实局部凸空间中所得的结果都分别是有关已知结果的深化和推广。

Technical characteristics: concavo-convex Nano-imprint lithography processing is a common business card printing and membership card making products that decoration, he uses the Teletext match concavo-convex stempelsysteme, by mechanical action make printing surface correspond to the Office of the permanent press deformation occurred in oilysludge, in the printing surface stereo pictures and texts, in recent years with the electronic sculpture and laser engraving technique, concavo-convex stempelsysteme mismachining standard qualitative leap, given the drlling of concavo-convex stempelsysteme makes it possible for the processing of via concavo-convex Nano-imprint lithography printed matter is more true to life on the surface of the graphics and text.

工艺特点：凹凸压印加工是一种常见的制卡和会员卡制作品表明装饰工艺，他使用图文信息相互匹配的凹凸印模，通过机械作用使印品表面对应处基材发生永久性挤压变形后，在印品表面形成立体图文，近年来随着电子雕刻和激光雕刻技术的不断提高，凹凸印模的加工水平有了质的飞跃，精雕细凿的凹凸印模使得经凹凸压印加工的印品表面之图文更加惟妙惟肖。

This is not an ordinary box, which is used as a background picture of the dialog box, very pretty.

详细说明：这可不是一个一般的对话框，它是用图片作为背景的对话框，非常好看。

Conceal me what I am,and be my aid for such disguise as haply shall become the form of my intent.

遮掩我的身份，帮助我，我的面具将成为我的目的。