凸的

The concept of the weighted logarithmic power mean is introduced; its relation with two-parameter mean is given; the inequality for weighted logarithmic power mean is derived; the magnitude relation among upper bounds of geometric mean and arithmetic mean of geometrically convex functions are made certain.

建立了几何凸函数的对称拟算术平均不等式，对文献[1]提出的不等式进行了推广统一；引进加权对数幂平均的概念，建立起其与双参数平均之间的关系，得到加权对数平均不等式，从而确定了几何凸函数的几何平均、算术平均的上界的大小关系；最后，提出了几何凸函数的对称拟算术平均不等式的推广问题。

The proposed method has the merit that the numerical characteristics of stochastic temperature field response can be obtained by analyzing the random temperature field just in one time.3. Perturbed numerical algorithm of nonprobabilistic convex set theoretical models on the temperature fieldThe uncertain parameters of physical parameters and initial boundary conditions of heat conduction are described by the convex model. The perturbation formulas of the upper and lower bounds of temperature field response with unknown-but-bounded parameters are given via the combination of matrix perturbation theory and the convex set theory model.4. Numerical analysis for transient temperature field with interval parametersConsidering the uncertainties of the transient heat transfer, the physical parameters and initial boundary conditions are regarded as interval variables.

该方法具有只进行一次随机温度场分析便可以获得其响应的数字特征的优点。3、温度场的非概率凸集合理论模型的摄动数值解法将结构导热的物理参数、温度场的初始和边界条件等不确定性参数以凸模型加以描述，基于矩阵摄动理论和处理不确定问题的凸集合理论模型的结合，导出有界不确定参数瞬态温度场响应所在集合的上、下界摄动计算公式。4、具有区间参数的瞬态温度场数值分析考虑结构瞬态热传导问题的不确定性，将结构各物理参数和温度的初、边值条件均视为区间变量。

Cross section is a set of polygons and for this reason some relative algorithms for polygon are studied firstly. New algorithms for orientation and inclusion test for simple polygon are proposed. And Ghosh's convex hull algorithms for simple polygon and convex polygons, Subramanian's triangulation algorithm for arbitrary planar domain and O'Rourke's intersection algorithm for convex polygons are modified to make them more robust.

断层轮廓为简单多边形，首先对多边形的一些相关算法进行了研究，提出了一种判断简单多边形方向及点在多边形内外的新方法，改进了Subramanian的平面多连通域的三角划分方法、Ghosh的多边形的凸包及多个多边形的凸包算法和O'Rourke的凸多边形的求交算法。

We divide the existence of generalized solutions into three theorems becauseof the existence of a generalized supersolution we need in the proof.To ob-tain this fact,we discuss three different cases separately.WhenΩhas strictconvexity,it can be proved that the generalized supersolution of (1)(2)is theconvex-monotone hull of 〓in 〓,this is theorem 2.WhenΩdoesn't hasthe strict convexity,in theorem 3 we have to suppose there exists a generalizedsupersolution.

我们的广义解的存在性结果之所以分成三个定理陈述，主要是因为在我们的存在性证明中，一个重要的事实就是广义上解的存在性，而为了得到这个事实，我们分别讨论了三种不同的情况：在定理2中的假设〓具有严格凸性时，我们证明了问题（1）（2）的广义上解就是初边值〓的凸单调包，而在〓没有严格凸性时，我们在定理3中假定了一个广义上解的存在性。

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。

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,.

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。

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。

When surgery is indicated after central cord injury in the stable spondylotic spine, it is the overall cervical spinal alignment and the number of levels affected that determine the surgical approach.30 When the spine is lordotic, and particularly when there are multiple levels of compression; a posterior approach, either a laminectomy and fusion or a cervical laminoplasty are recommended approaches.28 If the spine is neutral or slightly kyphotic, then occasionally, after a posterior laminectomy, lordosis may be achieved with intraoperative positioning and maintained with posterior lateral mass fixation and fusion.

当不伴有颈椎不稳的颈椎病并颈髓中心管损伤患者需要手术治疗时，整个颈椎的序列和受累的节段决定了手术入路的选择。颈椎处于前凸状态，尤其是多节段颈髓均有受压时，建议采用后方入路进行全椎板切除融合或颈椎椎板成形术。假如颈椎处于中立位或稍微后凸时，有时通过后方的全椎板切除，术中复位和侧块螺钉固定融合，可以恢复颈椎的前凸。

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。

Elaborated the punching components formation principle, the basic dies structure and the rate process and the principle of design; and designed some conventional punching die:the die for big diameter three direction pipe which solved the problom of traditional machining,the drawing and punching compound die with float punch-matrix,the drawing and cutting compound dies with unaltered press,the compound die for the back bowl of the noise keeper,the design of the compound die which could produce two workpieces in one punching,the bending die for the ring shape part ,the bending die which used the gemel ,automate loading die for cutting, the drawing,punching and burring compound dies with sliding automated loading,the punching die for the long pipe with two row of hole,the drawing die for the square box shape workpiece and the burring die for the box shape workpiece.

原文对于寒冲压技术的合种、特征及开展圆背做砬简单概述；阐述了冲压整机的构成本理、基础模具构造与活动进程及其设计本理；对典范的冲压件模具进佳的了设计：大曲径三通管冲压复合模设计掀世了大直径三通管的减工困难、带无沉动凸凸模的拉伸冲孔复合模设计、适力压边式落料拉伸切边复合模设计、长音器后挖碗落料、拉深、冲孔、翻边复合模设计、一模二件落料拉伸冲孔翻边复合模设计、环形弯曲件的模具设计、铰链舒方成形工艺及模具设计、半自动送料切角安装设计、涩板式送料拉深、冲孔、翻边模设计完成自动送料、长管少孔冲模设计、带凸缘台阶方盒形整件拉深模战盒形件正壁小孔翻孔模。

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％。