查询词典 convex

In the first part, we will first deal with the strong Bonnesen-style inequality (2.1.3) for closed convex curves in the plane (the numbers of formulae and references are those of them in the context below). Bonnesen had first proved the weaker inequality (2.1.2) in [12] and several years later, he outlined in his monograph [13] various Bonnesen-style inequalities including (2.1.3), he considered, however,(2.1.3) as a direct consequence of Kritikos theorem for convex bodies in higher dimensional Euclidean spaces,. Here, we will give an independent proof of the existence for inequality (2.1.3), and by the way, give an estimate on the width of the bi-enclosing annulus of closed convex curves in the plane.

具体地讲，在第一部分中，首先讨论平面上闭凸曲线的强Bonnesen型不等式(2.1.3)(公式的编号和参考文献的编号引自后面的正文)，Bonnesen在文[12]中先证明了较弱的不等式(2.1.2)，几年以后，在他的著作[13]中，讨论了多种Bonnesen型不等式，其中包括不等式(2.1.3)，不过，他把(2.1.3)作为高维欧氏空间中凸体的Kritikos定理的直接推论，我们这里对不等式(2.1.3)给出独立的存在性证明，并且还对平面闭凸曲线的bi-enclosing环的宽度给出了一个估计。

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。

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。

There are very sophisticated randomized algorithms for convex and non-convex optimization that rely on recently-developed methods for approximately generating uniformly distributed random variables on convex sets.

有一些关于凸型和非凸型最优化的非常复杂的随机算法，它们依赖于最近研究出的一些方法，在凸型集合中近似地产生平均分布的随机变量。

Clarkson introduced the concept of convex modulus while researching uniformly convex spaces, later the relations between numbers of convex modulus and relevant geometric properties had been drawn.

同年，J.Clarkson在研究一致凸时引入了凸性模的定义，而后，人们从多侧面得出了凸性模的取值与相关几何性质之间的关系。

In the second chapter, we introduce the definition of pointwise convex modulus. The relation between numbers of pointwise convex modulus and relevant geometric properties will be discussed. we research the characteristics of numbers of pointwise convex modulus .

在本文第二部分引入了点态凸性模的定义，并讨论了点态凸性模的取值与相关几何性质之间的关系，研究了点态凸性模取值特点。

Secondly, modeling the uncertainties of theb value, the annual occurrence ratev and the upper bound magnitude M uusing convex set models, a convex set-based seismic hazrd analysis approach is developed by integrating the convex theory with the probabilistic based CPSHA (China Probabilistic Seismic Hazard Analysis) theory. By the example of seismic hazard analysis of a city in southern China, this method is demonstrated with a sensitivity analysis.

然后，采用包络界限凸集模型和椭球界限凸集模型描述地震活动性参数b值、年平均发生率v和地震统计区震级上限M u的不确定性，将凸集理论和考虑时空不均匀性的概率地震危险性分析方法相结合，发展了地震危险性分析的凸集分析方法；以南方某市为例，进行地震危险性分析和地震活动性参数的敏感性分析。

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。

A new concept of convex set and its some characteristic properties This paper give a new definition, the support direction of a boundary point of convex set. Then use it to prove a characteric properties of convex set and some other characteric properties.

1凸集的一个新概念与凸集的某些特征性质本文引进支持方向这一新概念并利用它来证明凸集的一个特征性质，最后再用它来证明凸集的另外一些特征性质。

In Chapter 3, we use the sufficient and necessry conditions of minimal point being critical point on closed convex set and construct closed convex sets with some character as more as possible, to discuss the existence of solusion of nonlinear Hammerstein integral equations on different closed convex sets. We get the results of multiple solutions.

在第三章中，我们没有借助于条件，而是利用闭凸集上的极小值点是临界点的充要条件，构造出尽可能多的具有某些特性的闭凸集，在不同的闭凸集上讨论非线性Hammerstein型积分方程的非平凡解的存在性，从而得到多解性的结果。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。