复射影直纹面(Ⅰ)

本文讨论了ＣＰｎ中低次直纹面的有理纤维化的纤维次数，给出了文［４，５］中结果的简单证明，并通过ＣＰｎ中的曲面的极小非奇异化收缩到极小曲面所用收缩的个数这个参数，改进了文［４，５］中的主要结果     

关于二次直纹面判定的一种方法

关于二次直纹面判定的一种方法王卫东（湖北民族学院计算机与数学系）众所周知：二次柱面、二次锥面、单叶双曲面、双曲抛物面都是二次直纹面．现在的问题是，如果已知一个一般二次曲面的方程，怎样判定它是否是直纹面呢？本文试给出一种方法来判定一个给定的二次曲面是否...     

二次曲面直纹性的工程应用

高等数学教材中关于二次曲面形状的讨论都采用截痕法.教学中引入直纹面概念,可为建筑施工专业的学生密切联系工程实际提供理论依据,收到较好的教学效果.     

一类直纹面的研究

本给出了过任意空间C^k(k≥3)类光滑曲线的直纹面是可展曲面的充要条件．同时得到了该空间曲线为相应直纹面的曲率线,测地线和渐近曲线的充要条件。     

关于集合_uf（X）的结构与计算

集会_ｕｆ（Ｘ）在非光滑规划的最优性判定条件中起着重要作用。本文探讨了ｕｆ（ｘ）的结构，给出了计算方案及与函数正则性的关系，最后给出了主要定理的几个应用实例．     

复射影曲线上特殊线丛的射影正规性

本文给出复射影曲线上特殊线丛正规生成的一系列充分条件.     

复射影空间中全实子流形的刚性（英文）

本文研究了复射影空间中的全实子流形.通过使用活动标架的方法和DDVV不等式,得到了两个刚性定理和一个积分不等式,改进了相关的结果.     

基于xL（a）n－1（x）之零点的（0，1，…，m－2，m）插值

本文给出了基于xL^（a）_n－1（x）之零点的（０，１，…，ｍ－２，ｍ）插值的正则性的充要条件，其中xL^（a）_n－1（x）为（ｎ－１）次Ｌａｇｕｅｒｒｅ多项式。同时基函数（若存在的话）的明显表达式也在文中给出。再者，还证明了，若该插值问题有无穷多个解，则其解的一般形式为ｆ₀（ｘ）＋Ｃｆ₁（ｘ）这里Ｃ为任意常数。     

单边EXCHANGE环

本文引进研究了单边Exchange环和Msta-sjded Exchange环．给出了单边Exchange环的一类等价条件，得到了约化条件下这几类环的等价性．证明了单边EXCHANGE环上模的直和消去也等价于部分单位正则性．     

具非正则奇异性的偏微分方程的形式解（Ⅱ）

本文研究了具非正则奇异性的一阶全特征型偏微分方程的形式幂级数解.利用待定系数法证明了形式幂级数解的存在唯一性,并给出了其Gevrey类指标的计算公式.     

On Finite Morphisms of Ruled Surfaces

We prove that a surjective morphism :XX between ruled surfaces is finite and it descends to a finite morphism :CC between base curves of X and X. When is restricted to the fibres of X, it has a constant degree, say a, and then deg=a deg. In addition, we have several properties on the inverse image of a minimal section and a fibre of X as well as on the direct images. We also investigate precisely the case when both C and C are elliptic and X is the fibre product C ×_C X especially.     

The Brauer and Witt Groups of Real Ruled Surfaces

The Brauer group and the Witt group of a real irrational ruled surface are determined by using equivariant cohomology.     

Kinematic Generation of Ruled Surfaces

This paper presents a method for kinematic generation of free-form ruled surfaces. The method is based on the kinematic displacement of lines. The ruled surfaces are represented as curves on a dual unit sphere. The curves are created by using the Lie Group structure of the dual space to generate dual displacement matrices for the lines. Free-form surfaces are created by repeated geodesic interpolation using the displacement matrices. An application for these surfaces is presented in five-axis cylindrical milling.     

On Rational Surfaces Ruled by Conics

Abstract

We study projective rational surfaces ruled by conics, describing their singularities and special fibres. In particular, if Sis smooth, we give a “canonical” procedure to determine a minimal model among the geometrically ruled surfaces birational to S.     

Bonnet Ruled Surfaces

We consider the Bonnet ruled surfaces which admit only one non-trivial isometry that preserves the principal curvatures. We determine the Bonnet ruled surfaces whose generators and orthogonal trajectories form a special net called an A-net.     

On the Singularities of Surfaces Ruled by Conics

We classify the singularities of a surface ruled by conics: they are rational double points of type A _n or D _n . This is proved by showing that they arise from a precise series of blow-ups of a suitable surface geometrically ruled by conics. We determine also the family of such surfaces which are birational models of a given surface ruled by conics and obtained in a “minimal way” from it.     

A Generalisation of Nagata's Theorem on Ruled Surfaces

We prove a generalisation of a theorem of Nagata on ruled surface to the case of the fiber bundle E/P X, associated to a principal G-bundle E. Using this we prove boundedness for the isomorphism classes of semi-stable G-bundles in all characteristics.     

On Quasi-Polarized Surfaces of General Type Whose Sectional Genus is Equal to the Irregularity

Let (X,L) be a quasi-polarized surface over the complex number field. In this paper, we classified quasi-polarized surfaces (X,L) with g(L)=q(X), (X)=2, and h0(L)>0.     

On Ruled Real Hypersurfaces in Complex Space Forms

Ruled real hypersurfaces of complex space forms are investigated by using the fact that such hypersurfaces can be constructed by moving a 1-codimensional complex totally geodesic submanifold of the ambient space along a curve. Among other results, a classification of minimal ruled real hypersurfaces and an example of a homogeneous ruled real hypersurface are given.