凸的

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。

In this project, the theory of convex models is generalized from convex domain to non-convex domain, from small-range algorithm based on Taylor's series to large-range one so that the range of its application is extended and the computational precision is improved.

本项目将凸区域的凸模型理论推广到非凸区域上，将小范围泰勒展式算法拓广到大范围问题的求解中，扩大了凸模型理论的适用范围，提高了运算精度。

And a counter example about a result of E-convex programming is given.

给出了一类广义的凸集和凸函数——E-凸集和E-凸函数的一个性质；并给出了关于E-凸规划命题的一个反例。

Ervertebralis of scoliosis goat apical vertebral,there is no significant difference in distribution of any two sections' sympathetic fiber in normal peoples annulus fibrosus disci intervertebralis,and there is significant difference between the sympathetic fiber distribution of convex side and concave side in annulus fibrosus disci intervertebralis of AIS apical vertebral-the sympathetic nerve supply of convex side to gain advantage concave side.

结果成功构建山羊脊柱侧凸模型，研究发现正常山羊椎间盘纤维环四个区的交感神经分布无显著差异；侧凸山羊顶椎区椎间盘凸凹侧纤维环交感神经分布无显著差异；正常人椎间盘纤维环四个区的交感神经分布无显著差异；青少年特发性脊柱侧凸患者顶椎区椎间盘凸凹侧纤维环交感神经分布有显著差异，凸侧明显多于凹侧。

It was demonstrated that cuticles of some animals such as dung beetle and ground beetle, display the varied non-smooth or textured morphologies, For examples, the convex domes, dimpled or scaly form morphologies.

设计并制备了七种分布的凸包型非光滑表面，在JFY50型热压机上通过热压成型的方法制备了轻质碳酸钙填充酚醛树脂基复合材料凸包结构，并通过粘接方法将凸包固定在45钢底板上，制备了凸包型仿生非光滑表面试样。

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。

Convex analysis part will study convex set, convex function and its subdifferential, Lipschitz function and its G-subdifferential in infinitive dimension.

第一，凸分析部分，包括无限维空间的凸集、凸函数和凸映射，凸函数的次微分，Lipschitz函数的G-次微分。

Crown and flatness semi-decoupling design was put forward according to the coupling models' characteristic. A crown and flatness decoupling control system and its application strategy for tandem cold mills were designed to accomplish a dynamic shape control system.

然后针对耦合模型特点进行凸度平坦度半解耦设计，以补偿凸度控制和平坦度控制之间的耦合影响关系，进而设计凸度平坦度解耦控制系统，并给出冷连轧机组凸度平坦度解耦控制应用策略，组成完整的动态板形控制系统。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。