代数空间

Using the substitution-elimination method affine algebraic variety can be resolved to pure d-dimensional subvariety and expressed by an algebraic hypersurface on d+1-dimensional space with a sequence of elimination-polynomial systems. All 0-dimensional solution can be found, too.

利用变换消元法可以把代数簇分解成纯d维的子簇，并把代数簇表示为d+1维子空间上的超曲面形式和一系列的消元多项式组，且能求出全部孤立解，同时给出了算法及其在多项式因式分解中的应用。

In this paper, we use some algebraic geometry methods to study the construction of χ-invariant algebras of some linear corresponding moduli space of these systems. Moreover, we completely determine the stable and semistable locus of these systems.

本文，我们以代数几何中的一些方法来研究某些线性动力系统的χ-不变代数的构造，并给出这类系统的相应的参量空间的刻划，进一步，完全决定了这类系统的稳定点、半稳定点的轨迹。

On the other hand, equivariant algebraic topology concerns the study of algebraic invariants of space with group actions. It is really a study of symmetries on spaces, and has always occupied a central role in mathematics.

在另一方面，等变代数拓扑关注于带有群作用的拓扑空间代数不变量的研究，其更深刻的本质在于对空间对称性的揭示，因此从来都在数学研究中占有重要的地位。

Content: This course discusses the line, plane and quadratic surface in space through algebraic methods, and aims at developing the students' ability to solve geometric problems through analytic methods and to relate geometric intuitive image with algebraic quantitative relation.

主要内容：本课程运用代数方法研究空间解析几何中的直线、平面与二次曲面，培养学生运用解析方法解决几何问题的能力，以及将几何直观形象与代数数量关系相联系的能力。

Applying the techniques of real radical ideal, P-radical ideal , 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〓 spline ring.

4：应用多项式在单纯形上的B-网形式以及文献（[72]）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〓样条空间的实零点定理。

Based on the methods and techniques of covering theory, the structure of module category of tame concealed algebra, one-point extension, vector space category, finite enlargement, degeneration theory, stable equivalence and combinatorial method, we will classify all of the three-point algebras with Gabriel quiver the system quiver Q according to representation type. We get the classification theorem: Let A=kQ/I be a three-point algebra given by the system quiver Q.

本文综合利用覆盖理论，tame concealed代数模范畴的结构，单点扩张，向量空间范畴，有限enlargement，退化理论，稳定等价以及组合的方法等多种方法和技巧，将所有由系统箭图Q给出的三点代数按表示型进行分类，得到如下分类定理：Q是系统箭图，I是kQ的一个admissible理想。

By studying measure theory, the students are asked to understand σ-algebras, measure, measurable functions, integral, the measure theory of product spaces, Fubini theorem, and the representation theory of Boolean algebras.

通过本课程学习，使学生掌握σ-代数、测度、可测函数、积分，初步掌握乘积测度空间的构造及Fubini定理，以及布尔代数的表示理论。

Lastly,Using the extension theory of〓-algebras founded and developed by Brown-Douglas-Fillmore in 70s,inparticular,using the homotopy invariance of the extensions and the indexformule of Toeplitz operator matrices,the paper characterized the automorphismgroup of the continuous function symbol Toeplitz 〓-algebra in terms of thetopological degrees of the continuous mappings on the n-dimensional sphere.

最后，本文利用Brown-Douglas-Fillmore在七十年代建立并发展起来的C*-代数扩张理论，尤其是扩张的同伦不变性，以及Toeplitz算子矩阵的指标公式，通过球面上连续映射的拓扑度，刻划了高维球面Hardy空间上连续符号Toeplitz 〓代数的自同构群。

In the final section, we give the form of surjective isometric Jordan isomorphisms on triangular Banach algebras, and prove that such isomorphisms .

第四节给出了三角Banach代数上满等距Jordan同构的一般形式，并证明了一些特殊的三角Banach代数上满等距Jordan同构的酉空间实现性。

As two important tools, the weight space decomposition of modules of a nilpotent Lie algebra (Section 1) and irreducible finite dimensional representations of solvable Lie superalgebras (Section 2.3) are presented in detail.

讨论过程中，作为两个重要的工具，对幂零李代数其模的权空间分解(第1节)，以及可解李超代数的有限维不可约表示(第2.3节)也作了详细的介绍。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了