查询词典 concave convex game

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。

Two He-Ne lasers have been designed in experiment,one with simplest 2D axisymmetric folded-combined cavity that are composed of a concave-plano-concave folded cavity and a plano-concave cavity , and other with simplest 3D axisymmetric folded-combined cavity that are composed of two concave-plano-concave folded cavities and a plano-concave cavity.

本文实验设计了由一个凹-平-凹折迭腔与一个平凹腔组合的二维轴对称折迭-组合腔型He-Ne激光器及由两个凹-平-凹折迭腔与一个平凹腔组合的最简单立体轴对称折迭-组合腔型He-Ne激光器。

Inequality proof of various ways, they were: use derivative testify inequality nature, Includes using functional monotonicity and extreme value, the function and the concave and convex inequality, proving is concave and convex function in the original definition of equivalent definitions and a lemma is proposed on the basis of relevant concave and convex function of several theorems about inequality, and briefly discusses how to use the definitions and theorems in proof of inequality.

不等式的证明方法多种多样，它们分别是：用导数性质证明不等式；包括利用函数单调性，极值与最值，函数凹凸性证明不等式，其中在给出凹凸函数原始定义等价的解析定义和一个引理的基础上提出有关凹凸函数关于不等式的几个定理，并简要阐述了利用定义和定理在证明不等式中的运用。

Have known concave-convex soil of landed estate and the new model compound adsorption driers taking the person as raw material such as Anhui Ming Guang , Jiangsu Xuyi, local concave-convex structure and water absorption function, think that concave-convex soil has but is H2 , N completely compared with zeolite molecular sieve, 2, O 2, air waits for the inactive gas adsorption drier.

了解了安徽明光、江苏盱眙等地产凹凸土及以其为原料的新型复合吸附干燥剂，凹凸土的结构和吸水性能，认为与沸石分子筛相比，凹凸土完全有可作为H2、N 2、O 2、空气等惰性气体的吸附干燥剂。

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。

Closed has carried on the reasonable determination highly to the mold, but also designs the mold the major parts to fall the material concave mold, the convex-concave mold, the counter- drawing raised mold, the counter- drawing concave mold, the concave mold dead plate and so on.

对模具的闭合高度进行了合理的确定，还设计出模具的主要零件落料凹模、凸凹模、反拉深凸模、反拉深凹模、凹模固定板等。

The thickness of the ice cover on the wall surface heat transfer is greater than the thickness of it on the air heat transfer form. The thickness of the ice cover on the wall surface heat transfer along the way changes slowly, but it on the air heat transfer along the way changes significantly. Reducing the entrance velocity, lowering the wall surface or air temperature, the formation of the thickness of the ice cover will increase; in the 3D circumstances, The thickness of the ice cover was relatively uniform in the import of the U-turn model, the ice cover was gradual accumulation in the convex bank when the stream traversed the import of the U-turn model, the thickness of the ice cover in the convex bank was significantly bigger than the thickness in the concave bank. The temperature field under the ice cover tends to be complex because of the existence of the secondary flows. The temperature in the convex bank is greater than it in the concave bank. Compared with the data from experiments, the laws in the numerical simulation are similar with them in the experiments

模拟结果显示：二维情况下，运用壁面传热形成的冰盖厚度大于运用空气传热形成的冰盖厚度，壁面传热形成的冰盖厚度沿程变化缓慢，而空气传热形成的冰盖厚度沿程变化明显，减小入口流速，降低壁面或空气温度等，形成冰盖的厚度都会增大；三维情况下，弯道入口处凸、凹岸形成的冰盖厚度基本相同，进入弯道后，凸岸形成的冰盖厚度逐渐增大，而凹岸的冰盖厚度逐渐减小，受横向环流的影响，冰盖下水流的温度场趋向复杂，并且凸岸的温度小于凹岸的温度；与实验室实验所得数据相比较，数值模拟研究得到的规律基本符合实验规律。

Quasi-convex relaxation algorithm, which aims to solve ordinary constraint global optimization problems, is produced by a combination of branch-and-bound method with quasi-convex lower bound and quasi-concave upper bound functions developed from quasi convex-concave extension. This algorithm extends the interval algorithm with box constraint to general constraint global optimization problem.

利用拟凸-凹扩张中构造出的函数的拟凸下界函数和拟凹上界函数，与分枝定界方法相结合，建立了求一般约束全局优化问题的拟凸松弛算法，这一算法是将盒子约束的区间算法推广到一般约束优化问题中。

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。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48