极限情况

Utilizing the tools of conformal mapping and Cauchy integral formula and so on, the SIFs at the crack tips are obtained, which can be reduced to the known results under the condition of limitation; For the third and the fourth section, the problems of arc crack and parabolic crack are researched in one dimensional hexagonal QCs.

第二节研究了一维六方准晶狭长体中双半无限共线裂纹问题，利用保角变换以及Cauchy积分公式等工具求得了裂尖处的应力强度因子，在极限的情况下可以还原为若干已有的结果。

In this paper,starting with the concept of risk,trying to take the theory of probability,central limit theorem,definition of optimal statistic estimate and economic theory as the basis and according to the concrete situation of the natural gas exploration project,the formula to quantitatively determine the risk is derived.

文章从"风险"的概念入手，尝试以概率论、中心极限定理、最优统计估计量的定义和经济理论为基础，结合天然气勘探项目的具体情况，推导出了定量测定风险的公式。

The generalized central limit theorem shows that these heavy-tailed fluctuations accumulate to a stable probability distribution.

如果尾不是太厚，则方差是有限的，且我们可以找到常见的正态极限分布，即稳定分布一种特殊情况。

The elastic stress diagram design method is behind the times and cant meet the command in practice.In the paper the author collected and analyzed a large amount of data about the SLRCP on several typical domestic model experiments and the projects in practice. By summarizing and analyzing the data, the author set up a typical computing model and analyzed the model by the software ANSYS, by reading the output data of the stress and the crack from the program, combined with the experimental results, the author summarized the destroy procession of the stock. The paper also discussed the influence of other main factors to the crack and the stress besides the internal water pressure, such as the concrete material, the dimension of stock and the way of laid-out steel bars.

本文通过对大量实际工程中的坝后背管资料的收集、归纳和分析，选取了具有代表性的计算模型；用有限元软件ANSYS计算了典型坝后背管结构在实际内水压力作用下的应力分布和裂缝发展情况；以国内几个有代表性的模型试验和有限元计算的成果为依据，分析了在内水压力作用下钢衬钢筋混凝土压力管道管壁裂缝的特点，并尝试总结出此种管道的裂缝出现的原因及其发展规律，同时确定了坝后背管结构极限状态的新的定义方式——以坝后背管的裂缝宽度来定义。

The critical heating rate for different body radius was predicted by comparing the gas pressure when the peak degradation rate occurred with the threshold body strength which was determined by the diametric compression test of the green body during thermal debindering.

摘 要：以聚乙烯醇和NiFe2O4/Ni型金属陶瓷压坯为对象，采用热重分析研究PVA在N2气氛中的热脱脂行为，建立PVA热脱脂速率的数学模型，在此基础上，模拟并计算PVA分解产物气体在多孔粉末压坯内的压力构建情况；结合粉末压坯脱脂强度测试结果，分析粉末压坯在脱脂过程中压坯尺寸、粘结剂含量等因素对升温速率和脱脂时间的影响，获得不同半径尺寸压坯的极限升温速率。

The lowest loss mode fields and the far field divergency angles of output beams of the UPCUR are calculated by use of Prony method. The relations between the mode discriminability, far field divergency angles and the parameters of the resonator are analyzed. And the theoretical results show that the output beams with diffraction limit quality can be obtained by using the UPUR with small magnification (M=1. 3), which is much better than the traditional unstable resonator under the same conditions.

采用Prony方法计算均匀相位输出耦合镜非稳腔的输出模场分布及远场方向性，分析了模式分辨率和光束远场发散角与系统各参数之间的关系，理论计算得到的结果表明，采用均匀相位输出耦合镜非稳腔，可以在小放大倍率(M=1.3)情况下得到质量达到衍射极限的输出光束，远远好于同等条件下的常规非稳腔，因此这种新型的谐振腔适用于在工业用千瓦级氧碘化学激光器。

Torsion deformation is the biggest effect factor on elastic limit equivalent stress.

扭转变形是对钢丝的弹性极限等效应力情况影响最大的因素。

In the paper,according to homogeneous balance principle and F-expantion method,some double-periodic exact solutions of a fifth-order KdV-like equation with variable coefficients are obtained in form of Jacobi elliptic function .

利用齐次平衡原则和F-展开法，求出了一个五阶变系数KdV-like方程的一些用Jacobi 椭圆函数表示的双周期解。并且在极限的情况下，得到了该方程的孤立波解和三角函数表示的周期波解

Under the situation of even distribution of fitting nodes,a mathematic model is established by means of the relation between the number of fitting nodes and the limit error of measurement.

建立了采样点均匀分布情况下，圆度误差测量采样点数量与测量极限误差之间的定量关系数学模型。

The advantages of this method are as follows:①It is available even the ultimate state function is unknown.

该方法的优点是：①可用于极限状态函数未知的情况。

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。