基础拓扑

In order to solve the problem of assigning minimum protection capacity, some ideal topologies are given and the algorithm of spanning tree construction is analyzed, and then an algorithm based on these is proposed to solve the problem of one link failure.

为了解决如何分配更少的保护容量的问题，该文提出了一些理想的拓扑结构，研究了支撑树算法。在这两者的基础上针对一条链路出现故障的问题给出了利用理想拓扑的保护容量分配算法。

For regular topology surface, intermediate surface local texture mapping are used; for irregular topology surface, subdivision surface local texture mapping are used. So different topology surface using different texture mapping methods can solve the contradiction between texture effect and processing speed when they are dealt with by single method. The three judge conditions of texture distortion in the process of mapping onto the sphere surface are discussed and the exiting algorithms of mapping are analyzed, the new algorithms of mapping onto the sphere surface are presented. In order to enhance the realistic of graphics, a new function of wood texture is presented. OpenGL is also introduced in this papers and some realization examples of texture mapping based on OpenGL under the environment of VC++ and POV-RAY are presented in some chapters.

对于简单拓扑表面，利用改进的两步纹理映射，对于复杂拓扑表面利用新的面片分割算法，初步解决了颜色纹理中速度与走样之间的矛盾；通过对球面纹理时纹理不变形的三个判断条件的研究，分析了现在各种球面纹理映射算法，并在此基础上提出了一种基于等面积的半球面纹理映射算法，明显减少了球面纹理的纹理变形；针对现有的木纹纹理中，两种表示木纹的颜色差距表现出的颜色突变问题进行研究，提出对这两种颜色进行线性插值或二次插值，使生成的木纹纹理颜色更加连续，更加逼真；在VC++环境下，通过调用Open GL的图形库及在Pov-Ray软件环境下，实现了参数化纹理、球面纹理、凹凸纹理及木纹纹理等各种算法。

In the paper the separate theorem of convex set with weak topology σ(L ∞,L 1) is proved, and the topological characterization about No Free Lunch with Vanishing Risk Condition is given, from it, the equivalency between exist of equivalent martingale measures and NFLVR is proved, this is the first fundamental theorem of asset pricing.

资产定价的第一基本定理是数量金融学中核心的定理之一，本文证明了在 L∞的弱*拓扑σ(L∞，L1)中的凸集分离定理，并在此定理的基础上给出了没有无风险免费午餐的拓扑描述，证明了市场公平性与没有无风险免费午餐条件的等价性，从而重新证明了资产定价的第一基本定理。

Based on the topological dimension reduction method presented by B. Zhang et al for the problem of motion planning in the environment consisting of precisely known polygonal or polyhedral obstacles, we further discuss the problem of motion planning for a multi—joint robotic arm.

对由完全精确已知的多边形或多面体组成的障碍环境中的运动规划问题，在张钹等提出的拓扑降维法的基础上，本论文进一步探讨了应用拓扑法的多关节机械手的运动规划问题，其中重点解决了状态空间中连通块的划分问题和连通块之间连通性的判别问题。

However, few reports discuss the smooth Lorenz-like system with multi-wing attractors,and the attractors with both hyperchaotic dynamics and multi-wing topological structure are seldom reported. Based on the existing smooth hyperchaotic system,the common characteristics of these systems are analyzed.

构造超混沌系统在目前并非难事，在Chua系统基础上构造具有多涡卷拓扑结构的吸引子也有很多系统方法，但较少有文献讨论基于Lorenz系统族的拥有多翼结构吸引子的光滑混沌系统，而同时具备超混沌特性和多翼拓扑结构吸引子的光滑混沌系统则更少报道。

Based on the molecular topological theory,we introduce a new topological index Y and use it to study for salt effect constant k s of aliphatic acids in the salt solution.

以分子拓扑理论为基础，提出了新的拓扑指数Y ，并用Y研究了 4种脂肪酸在盐水溶液中的盐效应常数ks。

A new element bonding parameter topological index H_ is based on H_E.

在元素键参数拓扑指数 HE的基础上定义了一个新的拓扑指数HER并与镧系元素的11种物理化学性质显示高度的线性相关性。

Based on concepts of relative algebraic interior and relative topological interior of sets,some conditions assuring Ari+Bri in a linear space and conditions assuring riA+Bri in a linear topological space are given respectively,according to Tanaka and Kuroiwa' s conclusions.

根据Tanaka和Kuroiwa的结论，在集合相对代数内部和相对拓扑内部概念的基础上，分别讨论了线性空间中Ari+Bri和线性拓扑空间中riA+Bri成立的条件，从而将Tanaka和Kuroiwa关于内部的结论推广到了相对内部的情形

Firstly, based on the generalized function,φ-mapping topological current are rigorously proved to be of delta-function form δ and can be labelled by the nodal indices of the vector field, namely by Hopf indices and Brouwer degrees of this vector field, which reveals the inner relationships between our theory and the topology of vector bundle.

论文首先以广函数为基础严格证明了，φ-映射拓扑流具有δ函数形式，并且可以向量场的零点指标表征，即以其Hopf数和Brouwer度拓扑量子化，从而揭示了它与向量丛的拓扑学之间的内在联系。

Firstly,based on the generalized function,φ-mapping topological currentare rigorously proved to be of delta-function formδand can be labelledby the nodal indices of the vector field,namely by Hopf indices and Brouwerdegrees of this vector field,which reveals the inner relationships between ourtheory and the topology of vector bundle.A singular divergence theorem isalso presented.

论文首先以广函数为基础严格证明了，φ-映射拓扑流具有δ函数形式，并且可以向量场的零点指标表征，即以其Hopf数和Brouwer度拓扑量子化，从而揭示了它与向量丛的拓扑学之间的内在联系。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。