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For program (2), we can classify finite dimensional basic Hopf algebras of finite representation type completely now.

对于(2)，目前，我们已经给出了有限型的完整分类。

In particular, we compute Hochschild homology and cohomology groups of infinitedimensional path algebras and some of their quotient algebras, and we prove that for a general monomial algebra (not necessary finite-dimensional), all Hochschild cohomology groups of positive degrees vanish if and only if its Gabriel quiver is a finite tree.

特别地，我们计算了无限维路代数以及某些商代数的Hochschild同调群和上同调群，而且给出了一般单项代数的各正次Hochschild上同调群为零的充分必要条件，即它的Gabriel箭图是有限树。

The Galerkin's method was used to truncate the infinite-dimensional partial differential equations into a set of finite-dimensional ordinary differential equations with time dependent coefficients,which can be solved with numerical methods.

对于电梯工业来说，目前世界上绝大部分电梯仍然是依靠钢丝绳提升的曳引式电梯。

The infinite dimensional inverse problem was approximated by a problem in the finite dimensional space by using approximation theory.

将该算法应用于复杂函数的自动演化建模，也取得了理想的效果，因此该算法具有良好的通用性。

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。

On the foundation of the conception of orthonormal basis in finite dimensional Euclidean space,this paper provides the theory of completely orthonormal system in infinite dimensional Euclidean space.

从有限维欧氏空间的标准正交基概念出发，构建了无限维欧氏空间的完全规范正交系理论。

At present time thesemaps have become important objectors and tools in studying operator algebras. Nestalgebras is a class of most importaut non-semisimple, non-prime and non-self adjointoperator algebras. Their finite dimensional models are upper triangular matrix algebras,but the infinite dimensional models are more complex.

本文在已有成果的基础上，研究了一些类型的算子代数上的Jordan可乘映射，Jordan-triple可乘映射，Lie-skew可乘映射，初等映射，Jordan-triple初等映射，Lie导子，Jordan导子，局部导子和局部同构及其刻画问题。

The sufficient and neccessary con-dition is given for finite-dimensional or infinite-dimensional dissipativity of the methods,respectively.

在上述两章，我们还给出了某些一般性的结果。

In 1997,Their infinite-dimensional dissipativity wasfurther studied by Hill,who also studied the finite-dimensional and infinite-dimensionaldissipativity of one-leg methods.However,up to now,no papers have been concernedwith the dissipativity of delay dynamical systems and their numerical solutions.Thethird part of the thesis is devoted to discussing it.

当用数值方法求解这些系统时，自然希望数值方法能保持系统的该重要特性。1994年，Humphries和Stuart首次研究了Runge-Kutta方法对有限维系统的散逸性。1997年Hill进一步研究了Runge-Kutta方法的无穷维散逸性和单支方法的有限维和无穷维散逸性。

Since symplectic algorithms were brought forward by Kang Feng, two overflying developments took on: one is the generalization from finite dimensional Hamiltonian system to the infinite dimensional, the other is the generalization to multisymplectic algorithms.

自从冯康院士提出辛算法以后，这一算法有了两次大的飞跃和发展，一次是从有限维向无限维的推广，一次是向多辛算法的深入发展。

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。