有限维的

It is shown that, any reprersentation finite special biserial algebra has a Groebner basis theory, and a finite-dimensional basic algebra over an algebraically closed field is representation finite if and only if every module over it has a right Groebner basis theory.

证明了表示有限特殊双列代数有Groebner基，从而扩大了Groebner基理论的应用范围；证明了一个代数封闭域上的有限维代数是表示有限特殊双列代数当且仅当其上每个右模都有右Groebner基理论，从而扩大了右Groebner基理论的应用范围。

From the famous Gabriel's theorem ,a basic connected finite dimensional associative algebra A over an algebraically closed field can be looked as a quotient of a path algebra decided by a connected finite quiver Q.

由Gabriel 定理，代数闭域上基的，连通的有限维结合代数A 同构于一个由连通有限箭图Q 确定的路代数的商代数。

Ngai and Wang [9] introduced the notion of finite type and described a scheme for computation of the Hausdorff, Box dimension when the finite type occurs, which, however, forces the ratios to be exponentially commensurable.

Ngai和Wang[9]提出了有限型的定义并给出了当迭代函数系统是有限型时计算系统吸引子Hausdorff，Box维数的方法，但有限型的定义要求相似变换的压缩比必须满足对数值可公度。

Construct the three-dimensional manifold element covering hexahedron, provide cover displacement function, strain matrix, stiffness matrix and stress matrix of the three-dimensional manifold element by the previous research work.

6在前人研究的基础上，构造了六面体有限覆盖的三维流形单元，推导了三维流形单元覆盖位移函数、应变矩阵、刚度矩阵、荷载矩阵等表达式。

In practice, such systems are simplified as finite dimensional systems, and then treated via existing finite dimensional control theory.

在工程应用中大多采用有限维近似模型，并应用现有的有穷维控制理论进行处理。

In a proper condition,U* is a generalized solution of the differential equation system.

不同于[1-2]用有限维空间去逼近无穷维空间，本文空间是不变的。2。

By extending the concepts of supremum and infimum in real space to the casein any finite-dimensional Euclidean space a weak supremum set and infimumset theory with respect to cones for the set in finite-dimensional Euclideanspace is developed,and several similar properties to the set in real space are ob-tained,with the concepts of this weak supremumset,w-D-conjugate maps and w-D-subdifferentials theory for the point-to-setmap are developed,and its several properties and its relationships with weakefficient solutions of the multiobjective programming are studied.

推广实空间中上、下确界的概念至任意有限维欧氏空间，建立了有限维欧氏空间中集合的锥弱上、下确界集理论，得到了与实空间中十分相似的性质。借助于这一理论，应用上、下确界的概念，给出了点集映象的w-D-共轭映象及w-D-次微分理论，并研究了它们的若干特性及其与弱有效解之间的关系，此外还讨论了弱鞍点问题。

For the original infinite dimensional problem, if the inexact quasi-newton method with Broyden updating can not converge quickly , for example, it can not attain super linear convergence rate , then when the discretization is becoming finer and finer , we can not get fast convergence rate for the corresponding finite dimensional problem.

对于原来的无限维问题，如果使用不精确Broyden方法不能得到较快的收敛速度，比如超线性收敛性，那么当离散化逐渐加细的时候，对于所得的有限维问题使用不精确Broyden方法也不可能得到较快的收敛速度，所以有必要在无穷维空间上对收敛性问题加以分析，从而为不精确拟牛顿法结合投影法求解算子方程做好准备。

For the multidimensional representation of finite fields, we define a new Mannheim distance, under which codes over finite fields are discussed.

对有限域的任意多维表示，定义了一种Mannheim距离，并在这种距离之下讨论了有限域上的线性分组码。

It is shown that such a model can be used to design a nonlinear controller by techniques of norm H(subscript ∞) with the goal of maintaining relative equibalance water level along the open-channel reach.

以节制闸紧急启闭造成的水位波动和渠道物理建模的不确定性为抑制目标，采用泰勒级数和基于泛函估计有限差分法对Saint-Venant方程进行逼近形成了有限维状态方程，在H范数意义下对模型进行求解。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。