颈腰曲弓形面积测量法——240例正常颈腰曲弓形面积报告

目的:测量正常颈曲、腰曲的弓形面积,为临床观察颈、腰曲变化提供数据。方法:按Borden法和Seze法的标准,测出正常颈曲和腰曲,然后按数学几何学扇形面积计算公式,即S_(弓形)=(πr^2α/360°)-(2/1)Lh,计算出正常的颈曲、腰曲的弓形面积,并统计正常颈曲126例,正常腰曲114例,经统计学处理得出均值和标准差。结果:正常颈曲弓形面积为均值(x)14.10cm2(标准差2.86cm2),正常腰曲弓形面积为均值(x)32.36cm2(标准差5.26cm2)。结论:对椎曲弓形面枳进行计算,统计出其正常值范围,将为临床观察椎曲的改变提供数据化的观测方法,为整脊疗法的标准化提供依据。

颈腰曲弓形面积测量法——240例正常颈腰曲弓形面积报告

目的测量正常颈曲、腰曲的弓形面积，为临床观察颈、腰曲变化提供数据。方法按Borden法和seze法的标准，测出正常颈曲和腰曲，然后按数学几何学扇形面积计算公式，即S弓形=πr^2α/360°-1/2 Lh计算出正常的颈曲、腰曲的弓形面积，并统计正常颈曲126例，正常腰曲114例，经统计学处理得出均值和标准差。结果正常颈曲弓形面积为均值X14．10cm^2标准差S2．86cm^2）正常腰曲弓形面积为均值X32．36cm^2（标准差S5．26cm^2）。

谈谈对坐标的曲面积分概念的引入法

曲面积分无论在高等数学、工程数学以及物理、力学、电学等课程里都是举足轻重的重要概念和运算工具之一，然而学生在学习这部份内容时(特别是对坐标的曲面积分)却往往感到比较困难，究其原因，除因这部份内容所占学时过少、进度过快外，笔者认为主要原因还在于学生对概念重视不够，特别是对引入概念起着奠基作用的实例(通常都以流量为例)中的物理背景理解不透所致。为此笔者在教学过程申采取了以下措施，实践结果效果较好，

表面曲截面积密度概念及测算方法研究

本文系统定义了曲截面、曲截线、曲截线密度、曲截面符号密度、表面曲截面积密度和曲截面交点密度，导出表面曲截面积密度测算公式：ＡＳ＝ＩＣＩ／ＩＣ＝ＬＣＩ／Ｂ，即：表面曲截面积密度等于曲截线密度等于曲截面交点密度。式中ＩＣＩ为测试线与曲截面的交点数，ＩＣ为测试线与整个曲面结构的交点数，Ｂ为该曲面在二维平面上所形成的曲线长度，ＩＣＩ为曲截线长度。对表面曲截面积密度参数的应用问题和组织收缩的校正问题等进行了讨论并举例说明了计算方法。

颈椎病腰曲改变437例X线片分析报告

目的研究颈椎病颈曲改变与腰曲的关系,探讨颈椎病在结构力学和运动力学的病因、病理基础。方法用随机抽样法对诊断明确的颈椎病,同时摄有腰椎正侧位X线照片者共437例,分别测量颈、腰椎曲弓形面积并进行分级,按性别、不同年龄组,各病种分类统计分析。结果颈曲减小的颈椎病,腰曲也同样减小者占98.63%。颈曲改变与腰曲改变无统计学差异(P>0.05)。颈曲改变并腰曲改变与年龄呈正相关,差异具统计学意义(P<0.01)。结论腰曲改变是导致颈曲改变并发颈椎病的重要病因。

颈椎病腰曲改变437例X线片分析报告

目的：研究颈椎病颈曲改变与腰曲的关系，探讨颈椎病在结构力学和运动力学的病因、病理基础。方法：用随机抽样法对诊断明确的颈椎病，同时摄有腰椎正侧位x线照片者共437例，分别测量颈、腰椎曲弓形面积并进行分级，按性别、不同年龄组，各病种分类统计分析。结果：椎曲减小的颈椎病，腰曲也同样减小者占98．63％。颈曲改变与腰曲改变无统计学差异（P〉0．05）。颈曲改变并腰曲改变与年龄呈正相关，差异具统计学意义（P〈0．01）。结论：腰曲改变是导致颈曲改变并发颈椎病的重要病因。

腰曲对颈曲影响的动态下X线片研究

目的:研究腰曲对颈曲的影响,探讨颈椎病和颈腰综合征在脊柱解剖生理学与运动力学的病因病理。方法:选青春期健康青年男女27例,分别以站立位及坐位1h后摄腰椎、颈椎标准侧位片,并应用数学几何学弓形面积计算法测量其颈、腰曲站、坐前后X线片的弓形面积,进行对照。结果:端坐1h后,颈、腰椎侧位X线片,腰曲弓形面积平均较站立位缩小53.14%,颈曲弓形面积也缩小48.33%,经统计学处理P<0.05,差别显著。结论:(1)腰曲变化影响到颈曲,病理改变与久坐有关。(2)腰曲改变是颈椎病、颈腰综合征重要病因和病理改变。

腰曲对颈曲影响的动态下X线片研究

目的：研究腰曲对颈曲的影响，探讨颈椎病和颈腰综合征在脊柱解剖生理学、运动力学的病因病理。方法：选青春期健康青年男女27例，分别以站立位及坐位1h后摄腰椎、颈椎标准侧位片，并应用数学几何学弓形面积计算法测量其颈、腰曲站、坐前后椎曲X线片的弓形面积，进行对照。结果：端坐1h后，27例颈、腰椎侧位X线片，腰曲弓形面积平均较站立位缩小53．14％，颈曲弓形面积也缩小48．33％，经统计学处理P〈0．05，差别显著。结论：腰曲变化影响到颈曲，病理改变与久坐有关。腰曲改变是颈椎病、颈腰综合征重要病因和病理改变。

基于变工况运行的泵能耗指标计算方法

为了对变工况运行水泵的能耗进行合理的评价,根据水泵性能曲线和流量随时间变化规律,在三维空间建立了水泵运行状态体系。通过功率对时间进行积分求得水泵在某时段的电能,通过二重积分计算水泵在该时段的提水量与扬程之积,进而提出了一种变工况条件下水泵能耗指标的计算模型,解决了现有水泵能耗指标计算方法的局限性。以某泵站水泵运行数据为实例,运用新的能耗指标计算方法进行了计算,证明该计算方法能够对变工况下运行的水泵能耗进行合理的计算。

“探究式小班教学”在新生微积分课程中的实践与设想

探究式小班教学是我国高等教育教学改革的重要突破口,具有重要价值。本文以第一类曲面积分为例,较为细致地讲解了探究式小班教学在新生微积分课程中的实践,表明探究式小班教学可以很好地培养学生的思考能力和创新能力。

IMPROVEMENTS IN HIDDEN LINE REMOVAL ALGORITHM FOR BI-PARAMETRIC SURFACES

A hidden line removal algorithm for bi parametric surfaces is presented and illustrated by some experimental results. The enclosure test is done using area coordinates. A technique of moving box of encirclement is presented. It is found that the algorithm is of general purpose, requires minimal computer storage, has high accuracy and simplicity, and is very easy to be implemented on a computer.

On a Fixed Value Theorem for Directed Areas in Conic Circumscribed Polygons and Applications

Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.

Designing Bézier surfaces minimizing the L^2-norm of the Gaussian curvature

In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.

Optimization of press bend forming path of aircraft integral panel

In order to design the press bend forming path of aircraft integral panels,a novel optimization method was proposed, which integrates FEM equivalent model based on previous study,the artificial neural network response surface,and the genetic algorithm.First,a multi-step press bend forming FEM equivalent model was established,with which the FEM experiments designed with Taguchi method were performed.Then,the BP neural network response surface was developed with the sample data from the FEM experiments.Furthermore,genetic algorithm was applied with the neural network response surface as the objective function. Finally,verification was carried out on a simple curvature grid-type stiffened panel.The forming error of the panel formed with the optimal path is only 0.098 39 and the calculating efficiency has been improved by 77%.Therefore,this novel optimization method is quite efficient and indispensable for the press bend forming path designing.

Adaptive Surface Reconstruction Based on Tensor Product Algebraic Splines

Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput. Math., 17 （2002）, pp. 135-152） based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler＇s method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.

Tensile Characteristics Evaluation of Corroded Reinforcing Bars Extracted from Actual Structures

The analysis used simple finite elements is performed to simulate the tensile behavior of corroded reinforcing bars extracted from three actual concrete structures. The cross-sectional area of the elements is set to have the actual distribution measured by 3D laser scanner system. The variable factor in the analysis is the length of the elements. The analysis results show that the length of the elements has a major influence on the deformation capacity after yielding. The calculated stress-strain curves, obtained using the elements with a length that is 2 times the bar diameter, are in good agreement with the tensile test results. The calculated stress-strain curves are modeled using a bi-linear model to facilitate the FEA （finite element analysis） of an overall concrete structure. From the analysis results, both the tensile and yield strengths decrease in proportion to the reduction of the minimum cross-sectional area of corroded bars. The ultimate strain has a remarkable decrement as the reduction of the minimum cross-sectional area. Formulas for determining these values are proposed as a function of the decrement ratio of the minimum cross-sectional area of a corroded bar.

Process Optimization and Characterization of Sorghum Based Extruded Product

Expanded snacks made up of corn, wheat and rice is very popular because of their texture. Sorghum is one of the important cereals, which is not so far studied well for extrusion processing. Due to presence of high amount of starch （56%-73%）： sorghum could be the good candidate for manufacturing of expanded snacks. The extruded products obtained using extrusion conditions such as feed moisture content （12%-16%）, die temperature （150-190℃）, screw speed （150-210 rpm） and feed rate （50-70 g min1） are further characterized by analyzing bulk density, expansion ratio, water absorption index （WAI）, water solubility index （WSI）, textural properties, color and sensory evaluation. Increase in feed moisture content resulted in extrudates with gradual increase in density, WAI and hardness and decrease in expansion, WSI, crispness and whiteness. Higher barrel temperature reduced the extrudate expansion, bulk density and hardness and increased the WSI and crispness of the extrudates. The most acceptable product is obtained using response surface methodology （RSM）.

关于托利切利喇叭的注记

本文构造一个有限体积无限曲面积的光滑有界几何体。它是微积分教材中经典的托利切利喇叭的一个变形。

Reverse Bonnesen style inequalities in a surface X_∈~2 of constant curvature

We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style inequalities that extend the known Bottema＇s result in the Euclidean plane E2.

Area-preserving mean curvature flow of rotationally symmetric hypersurfaces with free boundaries

We consider the area-preserving mean curvature flow with free Neumann boundaries. We show that a rotationally symmetric n-dimensional hypersurface in R^(n+1)between two parallel hyperplanes will converge to a cylinder with the same area under this flow. We use the geometric properties and the maximal principle to obtain gradient and curvature estimates, leading to long-time existence of the flow and convergence to a constant mean curvature surface.