| 1. | The theory of linear series of the piecewise algebraic curve is a kind generalization of that of linear series of the algebraic curve ( [ 71 ] )
分片代数曲线的完全列是由所有属于同一等价类的有效正常循环以及所有与它特等价的有效奇异循环构成。 |
| 2. | Essentially , a key problem on the interpolation by multivariate splines is to study the piecewise algebraic curve and the piecewise algebraic variety for n - dimensional space rn ( n > 2 )
本质上，解决多元样条函数空间的插值结点的适定性问题关键在于研究分片代数曲线，在高维空间里就是研究分片代数簇。 |
| 3. | In this paper the g2 - continuous blending conditions of two algebraic curves implicitly defined based on the construction of algebraic curves that interpolate the geometric constraints are presented
本文在对插值一类几何约束的隐式代数曲线的构造基础上，给出了这样的隐式三次代数曲线二阶几何连续光滑拼接的条件，并给出了实验结果。 |
| 4. | Piecewise n ( ? ) ther type theorems on the partitions of ? l and a star region . 2 . in this paper , the theory of the so - called " linear series " of sets of places on the piecewise algebraic curve is estabilished and the singular cycle is put into the linear series
2 ：本文将奇异循环纳入分片代数曲线的线性列中，建立了由分片代数曲线的支组所构成的“线性列”理论，这一理论是相应代数曲线“线性列”理论( [ 71 ] )的推广。 |
| 5. | The paper applies algebraic geometry , computational geometry , approximation theory to study the following problems : the nother type theory and the riemann - roch type theory of the piecewise algebraic curve ; the number of real intersection points of piecewise algebraic curves ; the real piecewise algebraic variety and the b - net resultant of polynomials
本文应用代数几何，计算几何，函数逼近论等学科的基本理论，分别就分片代数曲线的n ( ? ) ther型与riemann - roch型定理；分片代数曲线的实交点数；实分片代数簇以及多项式的b -网结式进行研究。 |
| 6. | Second , combining with the construction principle of geometry - goppa codes , we present a kind of new algebraic - geometry code by using the properties of algebraic curves on finite fields . we determine the value of the code - length n and d imension k , and the lower bound of the minimal distances of the new algebraic - geometry code . the new algebraic - geometry code have the following characteristics : ( l ) the new code is the generalization of geometry - goppa codes and the algebraic - geometry code constructed by chaoping xing and san ling in 2000 ( 2 ) compared with brouwer ' table of the best known codes , we find more new codes , there are at least 60 new codes under two - dimension cases
其次，结合几何goppa码的构造原理，利用有限域上代数曲线的特点来构造代数几何码，确定了新的代数几何码的码长n和维数k的取值，给出了最小距离d的下限，这类码的特点是： ( 1 )新的代数几何码是几何goppa码和新加坡国立大学chaopingxing和sanling在2000年所构造的代数几何码的推广； ( 2 )这类码中有许多种码的参数优于brouwer码表，仅二维情形时，就有60多种码优于brouwer码表。 |
| 7. | 3 . by using the techniques of an explicit criterion to determine the number of real roots of a univariate polynomial in ( [ 13 ] , [ 73 ] ) ; b - net form of bivariate splines function ; discriminant sequence of polynomial ( cf . [ 13 ] , [ 73 ] ) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence , this paper determines the number of real intersection points two piecewise algebraic curves whose common points are finite . a lower bound of the number of real intersection points is obtained in terms of method of rotation degree of vector field
大连理工大学博士论义：分片代数价线i片代数簇的若十m穴3 ：利用杨路，张景中，侯晓荣在文献v13 ， 73 ）中关于一元多项式实根的显式判准，以及二元样条函数的b网形式，多项式的判别序列和sturm序列的最高次数项系数序列的变号数，本文给出了两个分片代数曲线的丈交点数（假设公共点是有限的）的计算公式。 |
| 8. | The piecewise algebraic curve and the piecewise algebraic variety , as the set of zeros of a bivariate spline function and the set of all common zeros of multivariate splines respectively , are new and important concepts in algebraic geometry and computational geometry . it is obvious that the piecewise algebraic curve ( variety ) is a kind of generalization of the classical algebraic curve ( variety respectively )
分片代数曲线作为二元样条函数的零点集合，分片代数簇作为一些多元样条函数的公共零点集合，它们是代数几何与计算几何中一种新的重要概念，显然也是经典代数曲线与代数簇的推广。 |
