代数空间

By using these convergence theorems,it presents the Silverman-To-eplitz regular theorem and Samaratunga-Sember theorem on the Abelian topologicalgroups,the Vitali-Hahn-Saks theorem on algebras and the weak sequentially completenesstheorem of 〓-dual spaces of sequence spaces,etc.

这是抽象分析中的两个基本定理。作为应用，给出了Abelian拓扑群上的Silverman-Toeplitz正则性定理、Samaratunga-Sember定理、代数上的Vitali-Hahn-Saks定理，以及序列空间的〓对偶空间之弱序列完备性定理等。

We researched the problem of Lagrange interpolation of polynomial space on the algebraic manifold.

研究高维空间中代数流形上多项式空间的Lagrange插值问题。

Discusses algebraically and geometrically the properties of the ruled surfaces in the Euclidean three-space, especially, the principal normal surfaces on which there are some special curves, such as Mannheim curves, Bertrand curves and general helices.

在三维欧氏空间中，作为特殊曲线，Mannheim曲线、Bertrand曲线以及一般螺线具有良好的几何和代数性质。讨论了三维欧氏空间中特殊曲线的主法线曲面。

We discuss the completely tr-rank nonincreasing linear maps on finite vN algebras and prove that a unital self-adjoint and surjective linear map on finite vN algebras is completely tr-rank preserving if and only if it is a spatial 〓-automorphism that leaves the central elements fixed.

我们刻画了有限vN代数上完全迹秩不增的线性映射；也证明了有限vN代数上保单位元的自伴线性满射完全保迹秩当且仅当它是空间〓-自同构且限制到中心上是恒等映射。

Over a field of arbitrary characteristic, we construct a class of associative superalgebras of Weyl type and a class of Lie superalgebras of Weyl type from ∧(2, 2) and the polynomial algebra of the special deravation subalgebra of it. In addition, we prove that the sufficient and necessary conditions of the simplicity of the associative and the Lie superalgebras.

在任意特征域上，从∧(2，2)和它的特殊导子的子空间的多项式代数出发，构造了一类Weyl型结合超代数和一类Weyl型李超代数，进而给出并证明了它们为单的充要条件。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

Tensor of the dual space and in the "Linear Algebra"(version 2) At the same time to explain, which is "Linear Algebra"(version 2) is a major feature.

对偶空间和张量在《线性代数》(第2版)同时讲解，这也是《线性代数》(第2版)的一大特色。

By learning this course, students should proficiently use algebraic methods to solve geometric problems and practical problems, and proficiently grasp the basic ideas and methods of vector algebra and geometric properties of spatial line, plane and quadratic surface.

通过本课程的学习使学生熟练掌握运用代数方法解决几何问题并应用于实际问题之中，并熟练掌握向量代数的基本思想和方法，同时使学生熟练掌握空间的直线、平面和二次曲面及其各种几何性质。

Then,it notices that all infi-nite matrix operators between the sequence spaces with the WGHP may form a topologicalalgebra.It also studies the weak sequentially completeness of this class of topological al-gebras and some other basic properties.

其次发现了具有WGHP序列空间上无穷矩阵算子所成之拓扑代数，并研究了这类无穷矩阵拓扑代数的弱序列完备性等一些基本性质。

As a matter of fact we develop our study in the more general and more natural context of a theory ~ internally defined with respect to a topos of sheaves on a frame (i.e. a complete Heyting algebra; for example the algebra of open subsets of a topological space).

作为一个事实上我们在发展中的一个理论更普遍，更自然的环境研究国内关于对一帧的捆一topos中定义的（即完全Heyting代数，例如以开放的子集代数拓扑空间）。

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