曲线

Based on the Guldin's first theorem, it was deduced that the general formula to calculate the rotating surface area which is shaped by rotating the curve Г in a plane around the L-axis in the space by using curve integral.

依据古鲁金第一定理推证，得到利用曲线积分计算空间某一平面上的曲线Г绕直线L旋转而成的旋转曲面面积的通用公式；利用曲线积分计算xoy面上的曲线c绕直线L旋转而成的旋转曲面面积的通用公式。

Secondly, it is not the same fractal diagram by the same codes of IFS to produce fractal diagram. The two graphs are extraordinary similar, but they are different in detail. The problem is researched and the algorithm which calculates the intersection points of two graphs created by the same coefficient of the IFS is proposed. The curve described changing of the intersection points number is drawn. The conclusion is that the curve fluctuates in the tiny range and is smooth when it is seen as a whole. In fact, the curve is a fractal curve.

其次，针对同一IFS迭代码两次迭代绘制得到的分形图并非完全相同这一问题展开研究，提出了IFS分形覆盖相交交点变化曲线的概念，给出了覆盖相交交点变化曲线的绘制算法，在此基础上进一步研究了分形覆盖相交交点变化曲线的变化率情况，得到了分形覆盖相交交点变化曲线宏观上比较光滑，但实际上小范围内异常波动的实验结果。

Aimed at the characteristic of multiple types of faults possibly happened in nuclear power plant, large scale of training sample, and requirement of quick and accurate diagnosing, after the analysis of large sample number generated by large fault type exceeds limitation of 64K paragraph in DOS and large number of local minmum in error surface, measurements of same format of data file, Win95/NT operating system platform, resetting weight learning rate, dynamic training set in quick learning algorithm and improvement on quick learning algorithm using homotopy method which can avoid local minmum points in error surface have been adopted to ensure quickly and effective process of the course of neural network's training and testing.

针对核动力装置可能发生的故障种类多，训练样本规模大，故障诊断需要快速准确的特点等，分析了样本多和故障种类多产生的训练样本量超出DOS段大小和网络误差曲面上局部极小值多的情况，采取了使用相同格式数据文件、Win95/NT操作系统平台，对快速学习算法采用重置神经网络权值学习率和动态训练集、并采用能够有效克服网络误差曲面上局部极小点的同伦方法对学习算法进行改进等措施保证神经网络训练测试过程的快速、有效地进行；针对装置发生的故障须快速、准确诊断的需要，分析了故障的产生对装置参数变化的影响及操纵员对故障诊断的基础，在核动力装置发生故障时参数曲线的变化量与正常运行时参数曲线的变化量存在明显差异的基础上，提出采用参数曲线的变化量作为神经网络的输入，并围绕参数变化量的方法采用二次曲线拟合滤波求变化量和阈值技术来保证神经网络得到精确的装置参数变化量，从而得到准确的诊断结果。

Deformation greatly promoted carbonitride isothermal precipitation and made C-curve shift leftwards. The position and shape of C-curve depended on the content of Nb and N to a great extent, C-curve shifted leftwards a little when N content increased and its nose temperature was raised with Nb content increased. 3 when cooling rate increased, start temperature and finish temperature of continuous cooling precipitation decreased, full precipitation became difficult to take place, the volume fraction of carbonitride precipitation decreased, molar fraction of Nb and C dissolved in austenite increased, and the precipitation grain was further refined. Deformation shorten precipitation start time during continuous cooling, raised precipitation start temperature, accelerated precipitation kinetics of carbonitrides.

计算表明：1在Fe—Nb—C系统中，随着温度的降低，析出相的平衡体积分数增加，溶解在奥氏体中的Nb、C的摩尔分数降低，析出相中C和Nb的原子分数的比值v增加；2变形大大促进了碳氮化物的等温析出，使C曲线左移，Nb和N的含量与C曲线的位置和形状有一定的关系，N含量的增加，使C曲线略有左移，而Nb的含量的增加使得C曲线的鼻子区上移；3随着冷却速率的增大，连续冷却析出的开始温度和结束温度均有所降低，并且析出变得越来越不充分，析出相体积分数明显减小，溶解在奥氏体中Nb和C的摩尔分数增大，析出相粒子被明显细化，变形大大缩短了CCP过程碳氮化物析出的开始时间，提高了析出的开始温度，促进了析出动力学。

After introducing the primary approximation approaches for curve and surface offset, we give an optimal approximation approach for offsetting curve based on shifting control points, which relies on approximating the normal by Legendre polynomial approximation.

在全面介绍了等距曲线曲面逼近的主要方法以后，作者首先利用Legendre多项式得到基曲线法矢曲线的最佳平方逼近，由此给出了基于控制顶点偏移的等距曲线最优逼近的算法，它在算法效果和效率上都远优于其他同类算法。

The sonic log curve is reconstructed by using BP neural network technology combining SP,Rt,Gr curves data as to enhance the information quality of curve reconstruction and ensure the accuracy of curve reconstruction.

运用BP神经网络技术综合了自然电位、电阻率、自然伽马等多条曲线的信息对声波曲线进行重构，以此增加曲线重构的信息量，为曲线重构的准确性提供了保障。

The macroscopic rheological parameters and microstructure parameters were closely related, it is helpful to explain the essence of multiple rheological properties through the analysis of which the wax evolution process and microstructure of the crude oil which is waxy and high viscosity; the yield time of gelled waxy crude oil monotone increases along with the decreasing of rate of shear (the time of stress effect prolonged), there was power function relationship between them, it can be expressed with ; when adding diesel oil to Sudan crude oil, dilute proportion bigger the eccentricity degree of paraffin particles were bigger too, that was to say the symmetry of wax crystal was better, the wax crystal form fabric more hardly when the intermolecular interaction was smaller; in the light of macroscopica, the fall extent of the abnormity temperature, solidifying point and viscosity could be larger along with the accretion of dilute proportion, as a result, it's rheological properties could be improved.

SD原油析蜡点为94℃，析蜡高峰为50～30℃，异常点为40℃；其蜡晶颗粒细小、对称性差，所以具有较大的比表面能，容易形成联生、联锁结构；损耗角曲线与储能模量曲线或损耗模量曲线的交点所对应的温度与原油凝点或倾点温度非常接近，大约在39℃左右；也就是说，含蜡原油粘弹特性曲线的交点可以表征其流动性；原油宏观流变参数与微观结构参数密切相关，原油析蜡过程及蜡晶微观结构分析有助于诠释易凝高粘原油多重流变特性的本质；胶凝含蜡原油的屈服时间随剪切速率的降低而单调增加，二者显然存在幂函数关系，可用关系式描述；当SD原油加柴油稀释处理时，稀释比越高，蜡晶颗粒的偏心度也越大，亦即蜡晶对称性越好，分子间作用力越小，蜡晶颗粒越不易形成结构，宏观表现为异常点、凝点及表观粘度等流变参数下降的幅度越大，流动性越好。

Firstly, we normalized the basic voxel by constructing its minimum oriented bounding box. Secondly, we constructed its D2 shape distribution curve, and computed the values of EMD(earth mover's distance) compared with the corresponding curves of the normal cone and cylinder respectively, and the corresponding top diameters. Finally, we compared the top diameters and obtained the parameters by the bounding box.

首先建立基本体素的MOBB，对体素进行标准化；然后生成其D2形状分布曲线，计算此曲线分别与标准圆锥体形状分布曲线、标准圆柱体形状分布曲线的EMD(earth mover's distance)值以及相应的上底直径；最后通过比较两个上底直径的大小来判断此体素是否为圆台体，并由包围盒的边长给出圆台体的参数。

In the meantime, a new relation between the coefficient of variation for a normal variate and its sample size is achieved, where the probability to make mistake Ⅱ is considered 5 The probability distribution of fatigue strength at given life under large sample size determined by a new method is found to follow the log-normal distribution and normal distribution, and a new method are developed to estimate the characteristic parameters of probability distribution of fatigue strength from the probability distribution of traditional tensile properties.

根据P-S-N曲线的要求，采用概率统计方法，导出了考虑犯Ⅱ类错误的概率时获取给定精度P-S-N曲线所需的最少子样容量，引入了不同方法获取的P-S-N曲线结果是否趋同的判别标准，得到了P-S-N曲线的寿命求解法和系数求解法获得趋同结果的条件。 5）研究了大子样条件下指定寿命时疲劳强度的概率分布，并提出了根据拉伸性能的分布估算材料疲劳强度概率分布参数的一种方法。

Then, based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the principal normal surfaces of curves, the curves with constant Gaussian curvature and the two curves of which the ratio of their functions is constant can all be obtained, as well as the properties of geodesic curve and lumbar curve.

再根据平均曲率、高斯曲率及主曲率函数，能得到曲线的主法线曲面的极小轨迹、常高斯曲率曲线及两个主曲率函数之比为常数的曲线。还给出曲面上测地线和腰曲线的性质。

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。