查询词典 uniformly 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。

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。

For example, U-space is uniformly regular and which makes it has fixed point property, U-space is uniformly non-square and thus super-reflexive, uniformly convex space and uniformly smooth space are U-spaces, and an Banach space is an U-space iff its dual space is U-space, etc. In1990s, a lot of work had been done on U-space theory, e.g., Tingfu Wang and Donghai Ji introduced the concepts of pre U-property and nearly U-property. Under the structure of Orlicz space, they made systematic investigation of these properties, and gave the criteria for an Orlicz space to have U-property.

U-空间具有一致正规结构进而具有不动点性质；U-空间是一致非方的，进而也是超自反的；一致凸空间和一致光滑空间是U-空间；Banach 空间为U-空间的充要条件是其对偶空间为U-空间，等等。20世纪90年代，国内外学者对U-空间理论做了很多工作，王廷辅，计东海等人先后引入了准U-性质与似U-性质的概念，并在Orlicz空间框架下对有关性质进行了系统研究，完整给出了Orlicz空间具有各种U-性质的判据。

Among those; studies, Liu and Bek have obtained many important results for the theory and applications of Banach spaces and their geometry on complex number,(see [3],[41])Here, we have investigated the TP modulus of convexity and TP modulus of smoothness, on the one hand, we have defined a class of new spaces called uniformly TP convex ,on the other hand, we have extended martingale inequalities and the martingale spaces.This article is divided into four parts, in the first part, we define the TP modulus of convexity and TP modulus of smoothness of Banach space, and prove that the space which is characterized by uniform convexity is same as the space which is characterized by TP uniform convexity. Then we give TP q-uniformly convex and TP p-uniformly smoothable characterization of the Banach space. At the same time, we prove the famous renormed theorem.

本文分为四部分，第一部分在Banach空间上定义了一个新的TP凸性模和TP光滑模并证明了在Banach空间上它分别和一致凸性和一致光滑性刻划的空间是同构的，即如果Banach空间X是一致TP凸的充分必要条件是存在一个等价范数，使得在此范数下，它是一致凸的；Banach空间X是一致TP光滑的充分必要条件是存在一个等价范数，使得在此范数下，它是一致光滑的，我们还分别得出了判定一致TP凸和一致TP光滑的一些充分必要条件，同时还证明了箸名的重赋范定理。

To generalize convex functions, Zalinescu introduced the concepts of uniformly convex functions in 1983, and discussed some properties for them;under the conditions of upper semicontinuity and lower semicontinuity, some equivalent conditions were given by Yang in 1998, so that criteria for uniformly convex functions are simplified.

作为对凸函数的推广，1983年Zalinescu提出了一致凸函数的概念，并讨论了它们的一些性质特点；1998年Yang在上半连续和下半连续条件下给出了一致凸函数的一些等价条件，简化了一致凸性函数类的判别条件。

Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

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。

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。

Based on the construction of international financial centre, we have pushed forward the explorations in the integration of cultural industries with financial services.

2010年及整个"十二五"期间，上海文化产业面临更有利的发展时机、更坚实的发展基础和更完善的发展环境。

The koala is an animal with a large bag in its body.

树袋熊用它的身体的一个大的袋子是一只动物。