| 1. | Abstract complete algebraic variety
完备抽象代数簇 |
| 2. | Conjugate algebraic variety
共轭代数簇 |
| 3. | Abstract algebraic variety
抽象代数簇 |
| 4. | Complex algebraic variety
复代数簇 |
| 5. | 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。 |
| 6. | This course covers the fundamental notions and results about algebraic varieties over an algebraically closed field . it also analyzes the relations between complex algebraic varieties and complex analytic varieties
本课程包括了代数闭域上代数簇的基本概念和结果，同时也讨论了复代数簇和复解析簇之间的关系。 |
| 7. | 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。 |
| 8. | 4 . applying the techniques of real radical ideal , p - radical ideal ( p is a cone ) , decomposition of semi - algebraic set in ( [ 72 ] ) , affine hilbert polynomial and b - net form of polynomials on simplex , this paper obtains two theorems of real c ? piecewise algebraic variety dimensions and the real nullstellensatz in c
L 、 ）数的一个下界计算公上巳4 ：应用多项式在单纯形上的b网形式以及文献门21 ）中的实根理想，锥根理想，半代数簇分解定理，本文得出了实c ”分片代数簇的二个维数定理和c 。 |
| 9. | 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。 |
| 10. | 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。 |
