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具平行李奇曲率的共形平坦流形
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作者 郭震 《云南师范大学学报(自然科学版)》 1998年第3期14-16,共3页
本文证明了维数大于3的具平行李奇曲率的共形平坦流形局部上必为常曲率流形或两个常曲率流形的黎曼乘积。同时也得到,具平行李奇曲率的3维黎曼流形局部上必为常曲率流形或两个常曲率流形的黎曼积。
关键词 行李奇曲率 共形坦流形 黎曼乘积 黎曼流形
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双车道公路平曲线段径向加速度相关实验研究 被引量:1
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作者 赵敏 杨轸 潘晓东 《交通科学与工程》 2010年第4期7-10,共4页
车辆的径向加速度是车辆在弯道上行驶时驾驶行为的重要表征,通过对加速度的分析,可对驾驶员加速和刹车的行为进行定量描述.通过对双车道公路平曲线处的车辆运行车速现场进行行车实验,获得车辆转弯时的径向加速度,利用Matlab软件建立了... 车辆的径向加速度是车辆在弯道上行驶时驾驶行为的重要表征,通过对加速度的分析,可对驾驶员加速和刹车的行为进行定量描述.通过对双车道公路平曲线处的车辆运行车速现场进行行车实验,获得车辆转弯时的径向加速度,利用Matlab软件建立了车辆加速度与平曲线线形之间的数学模型.实验结果表明,平曲线处车辆行驶时的加、减速行为:车辆从直线进入到曲线时逐渐以较大的减速度减速至该圆曲线半径所对应的运行车速;当汽车离开曲线时,会适当加速至期望车速,然后做匀速行驶. 展开更多
关键词 驾驶行为 径向加速度 曲线曲率 相关性
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Gradient Estimate of Solutions to a Class of Mean Curvature Equations with Prescribed Contact Angle Boundary Problem
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作者 Yuan Shengtong Han Fei 《数学理论与应用》 2024年第3期94-105,共12页
This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum p... This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained. 展开更多
关键词 Moving frame Maximum principle Prescribed contact angle boundary value problem Mean curvature equation
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悬浮隧道不同线形波浪作用受力研究 被引量:2
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作者 邹威 林巍 刘晓东 《中国港湾建设》 2020年第2期45-48,67,共5页
悬浮隧道所受波浪作用与其设计线形相关,而关于两者间联系研究极少。通过工程简化模型、编程和分析,系统地揭露了悬浮隧道管体长度、隧道长度与波浪方向夹角、纵向坡度、平面曲线和其受到波浪力的内在规律。这些规律对悬浮隧道线形设计... 悬浮隧道所受波浪作用与其设计线形相关,而关于两者间联系研究极少。通过工程简化模型、编程和分析,系统地揭露了悬浮隧道管体长度、隧道长度与波浪方向夹角、纵向坡度、平面曲线和其受到波浪力的内在规律。这些规律对悬浮隧道线形设计具有一定指导意义,海上工程设计规范中的拟静力计算方法需进一步发展来适应悬浮隧道设计问题。 展开更多
关键词 悬浮隧道 纵向坡度 平曲率 波浪力 线形设计
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Segmentation of scattered point data through a new curvature analysis algorithm 被引量:3
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作者 贺美芳 周来水 +1 位作者 张丽艳 刘胜兰 《Journal of Southeast University(English Edition)》 EI CAS 2004年第1期90-95,共6页
A systematic scheme is proposed to automatically extract geometric surface features from a point cloud composed of a set of unorganized three-dimensional coordinate points by data segmentation. The key technology is a... A systematic scheme is proposed to automatically extract geometric surface features from a point cloud composed of a set of unorganized three-dimensional coordinate points by data segmentation. The key technology is a algorithm that estimates the local surface curvature properties of scattered point data based on local base surface parameterization. Eight surface types from the signs of the Gaussian and mean curvatures provide an initial segmentation, which will be refined by an iterative region growing method. Experimental results show the scheme's performance on two point clouds. 展开更多
关键词 Feature extraction Image segmentation Three dimensional
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基于CatMull-Rom曲线的道路透视车道线控制点规律分析 被引量:1
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作者 王瑞云 陈雨人 +1 位作者 贺思虹 董永杰 《上海公路》 2014年第3期33-36,58,共5页
驾驶人直观地从道路透视图中获取线形信息,采用CatMull-Rom样条曲线表征驾驶人通过视觉获得的车道线形,确定控制点位,从中提取特征点表征车道控制点分布。通过对两侧车道线特征点位置分析,分别得到不同平曲率和纵坡条件下,车道线特征点... 驾驶人直观地从道路透视图中获取线形信息,采用CatMull-Rom样条曲线表征驾驶人通过视觉获得的车道线形,确定控制点位,从中提取特征点表征车道控制点分布。通过对两侧车道线特征点位置分析,分别得到不同平曲率和纵坡条件下,车道线特征点横、纵向分布规律。研究成果可川于道路平纵线形与透视车道线之间的定量关系分析,进而也可为从驾驶人视觉角度评价线形设计质量提供参考。 展开更多
关键词 CatMull—Rom曲线 透视车道线 控制点 平曲率 纵坡
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李奇曲率平行的黎曼流形到欧氏空间的等距浸入 被引量:6
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作者 郭震 《数学学报(中文版)》 SCIE CSCD 北大核心 1998年第5期1109-1112,共4页
设f:Mn→Rn+p为具平行李奇曲率的黎曼流形到欧氏空间的等距浸入.对p=1。
关键词 行李奇曲率 等距浸入 黎曼流形 欧氏空间
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The Pseudo-umbilical Surfaces in R^4 and Their Gauss Maps 被引量:1
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作者 许志才 徐森林 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第1期46-51,共6页
Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M... Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 . 展开更多
关键词 the pseudo umbilical surface total mean curvature Gauss map TORUS
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The Submanifolds with Parallel Mean Curvature Vector in a Locally Symmetric and Conformally Flat Riemannian Manifold 被引量:8
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作者 孙华飞 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第1期32-36,共5页
In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If the... In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1). 展开更多
关键词 Locally symmetric conformally flat parallel mean curvature vector
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牛顿环实验的研究 被引量:4
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作者 翁存程 冯尚源 《实验室科学》 2017年第2期20-22,共3页
理论和实验研究表明,牛顿环实验中平凸透镜和平板玻璃的弹性形变和磨损,影响平凸透镜曲率半径的准确测量,采用干涉级数差法可以消除平凸透镜的磨损和弹性形变、平板玻璃的磨损对平凸透镜曲率半径测量的影响。另外,平板玻璃的弹性形变会... 理论和实验研究表明,牛顿环实验中平凸透镜和平板玻璃的弹性形变和磨损,影响平凸透镜曲率半径的准确测量,采用干涉级数差法可以消除平凸透镜的磨损和弹性形变、平板玻璃的磨损对平凸透镜曲率半径测量的影响。另外,平板玻璃的弹性形变会引起平凸透镜曲率半径的测量值偏大,可通过测量较高级数的干涉条纹减小这种测量误差。因此,在牛顿环实验中应尽量避免平板玻璃发生弹性形变,也就是干涉圆环的中心暗斑的尺寸应该尽量小,同时测量级数较高的干涉条纹且采用干涉级数差法计算平凸透镜的曲率半径。 展开更多
关键词 牛顿环 干涉级数 凸透镜曲率半径
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On the Compact Spacelike Hypersurfaces in de Sitter Space
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作者 潮小李 《Journal of Southeast University(English Edition)》 EI CAS 1999年第2期105-107,共3页
In this paper, two properties of compact spacelike hypersurfaces in de Sitter space are obtained. When r =1, we recover Montiel's result.
关键词 de Sitter space spacelike hypersurface rth mean curvature
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常曲率流形中具平行李奇曲率的超曲面 被引量:4
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作者 李同柱 郭震 《数学学报(中文版)》 SCIE CSCD 北大核心 2004年第3期587-592,共6页
设f:M^n→M^(n+1)(c)为具平行李奇曲率的黎曼流形到常曲率流形的等距浸入,本文给出了该超曲面的分类。另外,若M^n还是极小超曲面,本文也给出了该超曲面的分类,推广了Lawson的有关结果。
关键词 行李奇曲率 不可约流形 Gauss方程
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Submanifolds with Parallel Mean Curvacture 被引量:2
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作者 贾兴琴 李中林 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第1期101-106,共6页
In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decre... In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decrease. 展开更多
关键词 Riemannian manifold tatall umbilical submanffold paralled mean curravture vector fields
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A level set based segmentation approach for point-sampled surfaces 被引量:4
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作者 MIAO Yong-wei FENG Jie-qing +1 位作者 ZHENG Guo-xian PENG Qun-sheng 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第4期575-585,共11页
Segmenting a complex 3D surface model into some visually meaningful sub-parts is one of the fundamental problems in digital geometry processing. In this paper, a novel segmentation approach of point-sampled surfaces i... Segmenting a complex 3D surface model into some visually meaningful sub-parts is one of the fundamental problems in digital geometry processing. In this paper, a novel segmentation approach of point-sampled surfaces is proposed, which is based on the level set evolution scheme. To segment the model so as to align the patch boundaries with high curvature zones, the driven speed function for the zero level set inside narrow band is defined by the extended curvature field, which approaches zero speed as the propagating front approaches high curvature zone. The effectiveness of the proposed approach is demonstrated by our ex- perimental results. Furthermore, two applications of model segmentation are illustrated, such as piecewise parameterization and local editing for point-sampled geometry. 展开更多
关键词 Point-samoled surfaces SEGMENTATION Level set method Extended curvature field
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Hypersurfaces with constant mean curvature in unit sphere
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作者 王佩君 潮小李 《Journal of Southeast University(English Edition)》 EI CAS 2016年第1期132-134,共3页
The pinching of n-dimensional closed hypersurface Mwith constant mean curvature H in unit sphere S^(n+1)( 1) is considered. Let A = ∑i,j,k h(ijk)~2( λi+ nH)~2,B = ∑i,j,k h(ijk)~2( λi+ nH) ·( ... The pinching of n-dimensional closed hypersurface Mwith constant mean curvature H in unit sphere S^(n+1)( 1) is considered. Let A = ∑i,j,k h(ijk)~2( λi+ nH)~2,B = ∑i,j,k h(ijk)~2( λi+ nH) ·( λj+ nH),S = ∑i( λi+ nH)~2, where h(ij)= λiδ(ij). Utilizing Lagrange's method, a sharper pointwise estimation of 3(A- 2B) in terms of S and |▽h|~2 is obtained, here |▽h|~2= ∑i,j,k h(ijk)~2. Then, with the help of this, it is proved that Mis isometric to the Clifford hypersurface if the square norm of the second fundamental form of Msatisfies certain conditions. Hence, the pinching result of the minimal hypersurface is extended to the hypersurface with constant mean curvature case. 展开更多
关键词 hypersurface with constant mean curvature unit sphere PINCHING
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Three-dimensional Spaces of Quasi-constant Curvature
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作者 蒋声 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第2期32-35,共4页
In this paper some properties of three-dimensional spaces of quasi-constant curvature different from those of cases when dimension n≥4 are proved. In particular, two classes of non-conformally flat solutions of them ... In this paper some properties of three-dimensional spaces of quasi-constant curvature different from those of cases when dimension n≥4 are proved. In particular, two classes of non-conformally flat solutions of them are constructed. In physics,a three-dimensional space of quasi-constant curvature appears as the space-like hypersurface of the rotation-free cosmological model of type D for the fluids with heat flow in General Relativity. 展开更多
关键词 spaces of quasi-constant curvature non-conformally flat METRIC
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A NURBS Fitting Optimization Method for High⁃Speed Five⁃Axis NC Machining Path Based on Curvature Smoothing Preset Point Constraint 被引量:1
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作者 YANG Gaojie XU Xiang +1 位作者 SHI Zhongquan YE Wenhua 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2021年第3期404-414,共11页
Existing curve fitting algorithms of NC machining path mainly focus on the control of fitting error,but ignore the problem that the original discrete cutter position points are not enough in the high curvature area of... Existing curve fitting algorithms of NC machining path mainly focus on the control of fitting error,but ignore the problem that the original discrete cutter position points are not enough in the high curvature area of the tool path.It may cause a sudden change in the drive force of the feed axis,resulting in a large fluctuation in the feed speed.This paper proposes a new non-uniform rational B-spline(NURBS)curve fitting optimization method based on curvature smoothing preset point constraints.First,the short line segments generated by the CAM software are optimally divided into different segment regions,and then the curvature of the short line segments in each region is adjusted to make it smoother.Secondly,a set of characteristic points reflecting the change of the curvature of the fitted curve is constructed as the control apex of the fitted curve,and the curve is fitted using the NURBS curve fitting optimization method based on the curvature smoothing preset point constraint.Finally,the curve fitting error and curve volatility are analyzed with an example,which verifies that the method can significantly improve the curvature smoothness of the high-curvature tool path,reduce the fitting error,and improve the feed speed. 展开更多
关键词 curvature smoothing NC machining path NURBS curve fitting weighted constraint
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Three-dimensional simulation of sintering crunodes of metal powders or fibers by level set method 被引量:1
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作者 谌东东 郑洲顺 +2 位作者 王建忠 汤慧萍 曲选辉 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第7期2446-2455,共10页
The difference of sintering crunodes of metal powders and fibers is discussed. The mathematical model of the surface diffusion described by the difference in mean curvature is defined as a Hamilton-Jacobi-type equatio... The difference of sintering crunodes of metal powders and fibers is discussed. The mathematical model of the surface diffusion described by the difference in mean curvature is defined as a Hamilton-Jacobi-type equation, and the model is numerically solved by the level set method. The three-dimensional numerical simulations of two metal powders and fibers(the fiber angle is 0° or 90°) are implemented by this mathematical model, respectively. The numerical simulation results accord with the experimental ones. The sintering neck growth trends of metal powders and metal fibers are similar. The sintering neck radius of metal fibers is larger than that of metal powders. The difference of the neck radius is caused by the difference of geometric structure which makes an important influence on the curvature affecting the migration rate of atoms. 展开更多
关键词 metal fiber metal powder sintering crunodes mean curvature three-dimensional simulation
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Projectively flat arctangent Finsler metric 被引量:1
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作者 YU Yao-yong 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第12期2097-2103,共7页
In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α, β)-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessa... In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special (α, β)-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian. 展开更多
关键词 Arctangent Finsler metric Projectively flat (α β)-metric Flag curvature
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Hypersurfaces with Constant Mean Curvature in Space Forms
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作者 宋鸿藻 胡泽军 《Chinese Quarterly Journal of Mathematics》 CSCD 1996年第1期42-48,共7页
In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental f... In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental form and the mean curvature. We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval.This improved the relative results of M. Okumura,Shen Yibihg and Sun Ziqi,etc. 展开更多
关键词 totally umbilical second fundamental form mean curvature
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