不共面四边形为边界的双直纹曲面找形与主曲率分析

不共面四边形为边界的双直纹曲面建筑结构具有造型优美、传力路径清晰等优点,已经在建筑结构中被广泛应用.吕梁新城体育场屋面主体结构为钢结构,屋面双向密肋钢梁之间形成了800多个平面投影边长4352mm的正方形单元,每个单元屋面为不共面四边形边界的双直纹曲面预制混凝土壳体.结合吕梁新城体育场屋面单元混凝土壳体的设计、制作和安装,研究了不共面四边形边界双直纹曲面的找形和曲面曲率.以参数-1≤u≤1、-1相似文献   

递推算子和Painlevé性质

利用Painlevé展开有关首项阶数,解分支和共振点的性质,本文给出了一种方法,从给定的具Painlevé性质的一个方程出发去构造具Painlevé性质的一族方程。同时还给出了Burgers族方程所有解分支的共振点。     

Banach空间集值映射的度量正则性与变分方程的Lipschitz稳定性

综述了集值映射的某些概念,例如度量正则性、伪Lipschitz性质(Aubin性质)、度量次正则性和Calm性质和这些概念的相互关系以及某些判据.也给出了他们在变分方程解的鲁棒Lipschitz稳定性、约束优化问题的最优性条件、集合族的线性正则性质和广义方程迭代过程的收敛性.     

一个新的Lie代数和它的应用

通过构造一个新的Lie代数,利用它相应的Loop代数设计等谱Lax对,根据其相容性条件,得到了一族Lax可积方程族,其一种约化形式为著名的AKNS族．根据迹恒等式得到该方程族的Hamilton结构．利用该可积方程族可以进一步研究它的达布变换、对称、代数几何解等相关性质．     

Banach空间上带有非局部条件的二阶发展方程的适度解

讨论了Banach空间中二阶发展方程适度解的存在性.利用Laplace变换及余弦函数族的性质,首先给出了适度解的定义.利用Schauder不动点定理进一步的给出了方程适度解的存在性.改进和推广了已有的一些结果.     

调和函数的Lipschitz型空间和Landau-Bloch型定理

主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性.     

方程族的 Painlev 相容组的求解公式

利用求解Painlevé相容组,本文得到了求解KdV方程族,Kuperschmidt方程族和CDG方程族的Painlevé相容组的递推公式.同时,提供了利用Painlevé相容组寻求孤立子方程族的解的方法.     

超经典Boussinesq系统的守恒律和自相容源

本文研究了超经典Boussinesq系统.利用已有的超经典Boussinesq方程族及其超哈密顿结构,构造了带自相容源的超经典Boussinesq方程族,并通过引入变量F和G,获得了超经典Boussinesq方程族的守恒律.     

具有N-peakon的新可积模型与孤子方程的代数几何解

在孤立子理论中, 寻找新的可积系统是最基础而重要的内容之一. 而如何有效的求得一类孤子方程的精确解, 并研究该精确解的性质, 一直是一个基本而又富有挑战性的课题. 本文便是从这两个方面展开, 一方面构造了两个具有N-peakon 的新可积系统, 为目前并不丰富的具有尖孤子解的可积非线性家族提供了极为重要的可积动力模型; 另一方面, 基于超椭圆代数曲线理论, 本文对Lax 对的有限展开法进行了改进, 并将其拓广到求解相联系的孤子方程可积形变后的代数几何解, 给出了著名的KdV(Korteweg de Vries) 6 方程的解. 进一步, 通过研究与孤子方程族相应的亚纯函数、Baker-Akhiezer 函数和超椭圆曲线的渐近性质和代数几何特征, 本文摆脱了现有代数几何方法中使用Riemann 定理的限制, 构造了mKdV (modified Korteweg de Vries) 型方程和混合AKNS (Ablowitz Kaup Newell Segur)方程等孤子方程的代数几何解. 为构造高阶矩阵谱问题所对应的孤子方程族的代数几何解提供了有力的工具.     

发展方程族Lax表示的广义结构*

本文给出非线性发展方程族的一个生成格式(该格式包含了保谱族与非保谱族作为其两个特殊情况),并提供该格式下发展方程族Lax表示的广义结构.最后,作为应用,我们讨论了Levi族发展方程.     

On the integral invariants of a closed ruled surface

Summary In this paper, it is shown that the dual integral invariant of a closed ruled surface, the dual angle of pitch, corresponds to the dual spherical surface area described by the dual spherical indicatrix of the closed ruled surface. So, new geometric interpretations of the real angle of pitch and the real pitch of a closed ruled surface, and some results are given.     

Intersection theory over quantum ruled surfaces

In this paper, we will extend several results on intersection theory over commutative ruled surfaces to quantum ruled surfaces. Typically, we define the fiber of a closed point, the quasi-section, and the quasi-canonical divisor on a quantum rules surface, and study how these “curves” on a quantum ruled surface intersect with each other.     

Ruled minimal surfaces in the Berger sphere

We show that any ruled minimal surface in the Berger sphere is a helicoid whose axis is a Hopf fiber by solving the ruled minimal surface equation in the parametric form.     

The integral invariants of parallel timelike ruled surfaces

In this paper, we first gave the parallel timelike ruled surface with a timelike ruling and its geometric invariants in terms of the main surface. We then obtained the integral invariants which are the pitch and the dual angle of pitch of the parallel timelike ruled surface with a timelike ruling and also the relations among them and integral invariants of the main surface.     

一类直纹面的研究

本文给出了过任意空间Ｃｋ（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     

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.     

Kähler Surfaces of Positive Scalar Curvature

We construct Kähler metrics of positive scalar curvature on almost all blown-up ruled surfaces of arbitrary genus. The metrics have an explicit form on ruled surfaces blown up at most twice successively from a minimal model. Our surfaces are generic in the sense that they make up a dense set in the deformations of a given ruled surface.     

Approximation by ruled surfaces

Given a surface or scattered data points from a surface in 3-space, we show how to approximate the given data by a ruled surface in tensor product B-spline representation. This leads us to a general framework for approximation in line space by local mappings from the Klein quadric to Euclidean 4-space. The presented algorithm for approximation by ruled surfaces possesses applications in architectural design, reverse engineering, wire electric discharge machining and NC milling.     

复射影直纹面（II）

本文利用几何直纹面及曲线上秩－２局部自由层的一些性质，讨论射影空间中的直纹面一些特性，给出了非正则直纹面次数的下界并讨论了个维射影空间中次数接近下界的非正则直纹面的结构，如奇点集的结构，底曲线的结构及纤维束次数等，完全确定了这类曲面的几何结构。     

Torsen Konstanten Flächenwinkels

In this paper we consider certain developable surfaces, which are circumscribed to a given ruled surface. We give new characterisations of helicoidal ruled surfaces and a result concerning the lines of curvature of ruled surfaces.

---

---

Die vorliegende Arbeit enthält Teile der Dissertation des Verfassers (Technische Universität München 1980).