查询词典 finitely generatable vector space

A criterion theorem of having no finite coverings for a finitely generated module M over a semisimple ring R is given.

对半单环上有限生成左模给出一个无有限覆盖的判定定理。

In [3], Professor Wang Xian-dong discussed the evaluation modules of Loop algebras of Lie algebras with a triangular decomposition; particularly, irreducibility of the tensor product of finitely many such modules was partially determined.

在[3]中，王宪栋教授讨论了可三角分解李代数其Loop代数的赋值模；特别值得一提的是，在一定程度上确定了有限多个赋值模其张量积的不可约性。

We show that for any subshift of finite type determined by an irreducible and aperodic matrix, there is a finitely chaotic set with full Hausdorff dimension.

指出：对于由本原方阵所决定的符号空间有限型子转移而言，存在满Hausdorff维数的有限型混沌集。

Its main goal is to explore information relating to the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other important problems such as the Novikov conjecture, the Baum-Connes conjucture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature and so on.

其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）大尺度几何结构的信息，建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Baum-Connes猜测， Gromov-Lawson-Rosenberg正标量曲率猜测等。

Its main goal is to explore information in the K-theory groups of the index C*-algebras, the Roe algebras C*, by using the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other relating problems, say, the Novikov conjecture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature, the idempotent problem in the theory of C*-algebras.

粗几何上的指标理论是"非交换几何"领域九十年代以来发展起来的重要研究方向，它孕育于非紧流形上的指标理论，其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）的大尺度几何结构探索指标代数，即 Roe代数，的K-理论群的信息，从而建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Gromov-Lawson-Rosenberg正标量曲率猜测、群C*-代数幂等元问题等。

Consequently, when applied to minimize a strictly convex quadratic function, the proposed methods terminate at the solution of the problem finitely.

因此，当目标函数是严格凸的二次函数，且采用精确线性搜索时，这些修正的共轭梯度法具有共轭性和二次终止性。

Based on nonsmooth analysis theory, the viability criterion is verified under the condition that the set-valued mapping in the right hand side is a polytope and the boundary function of the region is subdifferentiable and its subdifferential is a convex hull of finitely many points.

当右端集值映射为多面体，边界为次可微函数，且次微分为有限点集凸包时，基于非光滑分析理论，给出了在一点处检验生存性条件是否成立的方法。

There are finitely many solutions to this problem.

有有限多个解决这个问题的方法。

There are only finitely many boxes, so eventually our choice procedure comes to an end.

只有有限多个盒子，所以我们的选择过程最终会结束。

Finitely,I would think this is one of the most important aspects when dealing with the public in any way.

肯定重要。我认为不论以什么方式与公众打交道都应提供友好的服务。

We have something to do in the new stage.

在这段崭新的时期中，我们有一些要做的。

The difference between tourism decision-making under uncertainty and risky tourism decision-making is indistinctive.

其中不确定性旅游决策和风险旅游决策的界线比较模糊，两者的区分是相对的。