查询词典 finitely generatable vector space

A section theorem, a minimax inequality and a generalized fixed point theorem where the underlying space is a product space of two topological vector space s, are given.

给出了两个拓扑向量空间的乘积空间上截口定理，极小极大不等式及一个推广的不动点定理。指出这3个形式不同的结果与Tychonov不动点定理是相互蕴含的。并且用截口定理直接证明了多值映射的一个重合定理

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

The method uses techniques such as document space transforming and principal component analysis to map original document vector in very-high-dimension term space to low-dimension principal component space, and then categorizes documents by comparing them to the centroid of each category.

该方法采用了文档空间变换和主成分分析技术，将文档的原始矢量表示从高维词条空间映射到低维主成分空间，并利用文档类别重心进行分类。

For anelliptic curve E over a number field K,the set of K-rational points of it forma group Evia a special kind of"addition".This group is a finitely gener-ated abelian group,and is named Mordell-Weil group of E/K.

数域K上的椭圆曲线E的K-有理点全体，通过特别的"加法"构成一个群E，这是一个有限生成的阿贝尔群，称为莫代尔-威伊（Mordell-Weil）群，其结构是椭圆曲线研究的中心课题。

Analytical expressions for electromagnetic fields of a vertical or horizontal electric dipole over the finitely conducting plane are derived subject to the boundary conditions; Sommerfeld type integral contained in Hertz potential is expressed as the sum of two parts: zeroth order Hankel function and an absolutely convergent series of spherical Hankel function.

在此边界条件下，推导出有限导电平面上垂直和水平电偶极子电磁场的解析表达式；赫芝位函数中的索末菲型积分被表达成零阶汉克尔函数与绝对收敛的球汉克尔函数级数之和的形式。

Every strictly decreasing sequence of elements of the set must terminate after only finitely many steps (assuming the axiom of dependent choice).

注意这个第三点：对于一个良序集，任何严格递减序列都必然是有限的，无论这个集合的基数有多大。

Then we introduce the concept of(n,0)-projective dimension for modules and rings.It measures how far away a finitely generated module is from being n-presented,and how far away a ring is from being Noetherian.

然后，我们介绍环与模的(n，0)-投射维数，它可以衡量一个有限生成模与n-表现模的差距，以及衡量一个环与Noether环的差距。

We give a theorem for the stable range of endomorphism rings of finitely generated projective modules over a formal triangular matrix ring T when T is an exchange ring.

2.6节对有有限exchange性质的形式三角矩阵环T给出了有限生成投射T-模的自同态环有稳定度n的一个具体关系。

For all finitely additive probability measures defined on theσ-algebra ?

上的所有有限可加概率测度的表示理论。

Generalized essential finitely generated -module is defined.

则M一定是有限生成的。7。定义了广义基本有限生成的TS1-模。

A strange and mysterious deep sea creature.

一种奇异、神秘的深海生物。

It's a yellow rectangle .

这是黄色的长方形。