单圈图的测地谱

单圈图是顶点数等于边数的连通图,本文研究了单圈图的测地谱并指出除了圈以外的单圈图的谱都是连续的。     

基于二维有监督测地线判别投影的戴眼镜人脸识别

针对戴眼镜人脸识别问题,提出了二维有监督测地线判别投影(2D Supervised Geodesic Discriminant Projection,2DSGDP)方法.该方法在扩充虚拟样本库的基础上,分析戴眼镜人脸图像和不戴眼镜人脸图像,及戴不同眼镜人脸图像的差异,提取判别特征用于识别.该特征同时考虑类内类间差异,寻...     

WDC-D大地测量学数据分类与编码的初步研究

首先,运用线分类法将大地测量数据分为四个层次,从第一到第四层次的数据量分别为7、35、121和385．然后,采用层次码编码方法对数据进行编码．码长共有9位．第1位用J表示大地测量数据分类在WDC-D中的顺序;第2位用“1～9”表示第一层次数据;第3、4位,第5、6位．第7、8位均用“00～99”分别表示第二、三、四层次数据,第9位用“1～3”表示数据的共享级别．     

球面上极小子流形和全脐子流形的新特征

定义两个Ｓｃｈｒｏｄｉｎｇｅｒ算子Ｌ１，Ｌ２先详细研究球面Ｓ＾ｎ＋ｐ中的极小子流形和全脐子流形，然后由算子Ｌ１和Ｌ２的第一特征值的估计给出Ｃｌｉｆｆｏｒｄ环，Ｖｅｒｏｎｅｓｅ曲面和一类全脐子流形的新特征。     

完备黎曼流形上的Jacobi场

证明了在具非负曲率完备黎曼流形上，沿无共轭点测地线的正常平行向量场必为Ｊａ－ｃｏｂｉ场．     

Friedman׳s thesis

This essay examines Friedman׳s recent approach to the analysis of physical theories. Friedman argues against Quine that the identification of certain principles as ‘constitutive’ is essential to a satisfactory methodological analysis of physics. I explicate Friedman׳s characterization of a constitutive principle, and I evaluate his account of the constitutive principles that Newtonian and Einsteinian gravitation presuppose for their formulation. I argue that something close to Friedman׳s thesis is defensible.     

On the status of the geodesic principle in Newtonian and relativistic physics

A theorem due to Geroch and Jang (1975) provides a sense in which the geodesic principle has the status of a theorem in General Relativity. I have recently shown that a similar theorem holds in the context of geometrized Newtonian gravitation (Newton–Cartan theory) (Weatherall, J.O., 2011). Here I compare the interpretations of these two theorems. I argue that despite some apparent differences between the theorems, the status of the geodesic principle in geometrized Newtonian gravitation is, mutatis mutandis, strikingly similar to the relativistic case.     

Pogorelov定理的推广

Ａ．Ｖ．Ｐｏｇｏｒｅｌｏｖ曾证明，若正则凸闭曲面Ｆ的Ｇａｕｓｓ曲率都不大于某一常数Ｋ，则Ｆ上的封闭测地线的长不小于，本文将这定理推广成为下列定理。定理设凸闭曲面Ｆ的比值曲率≤Ｋ，则Ｆ上连接Ａ，Ｂ两定点的测地线的长或等于ρ（Ａ，Ｂ），或不小于。关键词：     

A new method for designing a developable surface utilizing the surface pencil through a given curve

This paper proposes a new method for designing a developable surface by constructing a surface pencil passing through a given curve, which is quite in accord with the practice in industry design and manufacture. By utilizing the Frenet trihedron frame, we derive the necessary and sufficient conditions to construct a developable surface through a given curve. Considering the requirements in shoemaking and garment-manufacture industries, we also study the special case of specifying the given curve as a geodesic. The given geodesic can be classified into three types corresponding to each type of developable surface. We also present the polynomial representation of the developable surface. The algorithm is convenient and efficient for applications in engineering.