查询词典 finite dimensional

With the fast development of technology, matrix theory, for its vast utility, has developed into a powerful tool in solving many problems in finite dimensional space.

随着科技的发展，矩阵理论以其极广泛的实用性，已成为现代各科技领域处理大量有限维空间形式与数量关系的强有力的工具。

In particular, for a finite dimensional...

特别地，对于有限维半单Hopf代数，给出了Killing型的根的刻划。

The resulting theory of structure-preserving algorithm for finite dimensional Hamiltonian systems has been well established, it have been applied to many fields.

有限维Hamilton系统保持辛结构即辛几何算法的发展已经相当完善，它已经被应用于许多领域。

In the second part,we have mainly discussed the error es-timates of the numerical methods for solving ill-posed problem,including the error estimate of finite-dimensional regulariza-tion method in Chapter 5,and the error estimate of regulariza-tion-spline method for solving Fredholm integral equation ofthe first kind.

在第二部分，我们主要讨论了不适定问题数值方法的误差估计，包括有限维正则化方法求解不适定问题的误差估计以及用样条正则化方法求解第一类Fredholm积分方程的误差估计，两者均是目前还未有的结果。

Then,the Galerkin method was used to obtain a finite-dimensional dynamical system.

并利用Galerkin方法得到一个有限维的动力系统。

The generating function method is applied to the study of integrability structure of these finite-dimensional systems, by which it is very convenient to prove the involutivity of integrals of motion.

上面所提到的这些连续的和离散的2+1维可积模型被分解成所导出的常微分方程的Hamiltonian系统或常微分方程的Hamiltonian系统以及辛映射所产生的离散流。

Firstly, we define the Killing form over any finite dimensional Hopf algebras using the adjoint action, then we investigate the fundamental properties of the Killing form, and obtain a decomposition of Hopf algebras under the adjoint action.

首先，利用Hopf代数的伴随作用定义了有限维Hopf代数上的Killing型，并讨论了Killing型的基本性质，得到了Hopf代数上的伴随表示分解式。

In chapter 3, the problems of constructing finite-dimensional functional linear invari-ant spaces under a given differential operator as well as an inverse problem concerning thedescription of all operators possessing a given invariant space are investigated.

第三章中讨论了基于算法产生的两个互逆问题，即(1)构造在已知的微分算子下不变的有限维线性函数空间；(2)讨论拥有相同线性不变空间的微分算子的一般表达式。

The problem that under what conditions the - resolvent operator of a maximal TJ - monotone set-valued mapping is a Lipschitz continuous single-valued mapping on whole space, which also answers the open problem mentioned above, is studied on finite dimensional Euclidean spaces.

借助于图收敛理论证明了有限维欧氏空间中的两个极大单调集值映射的和映射在较弱条件下仍是极大单调集值映射，并在此基础上讨论了一般集值变分包含问题解集的凸性、闭性和有界性。

As two important tools, the weight space decomposition of modules of a nilpotent Lie algebra (Section 1) and irreducible finite dimensional representations of solvable Lie superalgebras (Section 2.3) are presented in detail.

讨论过程中，作为两个重要的工具，对幂零李代数其模的权空间分解(第1节)，以及可解李超代数的有限维不可约表示(第2.3节)也作了详细的介绍。

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。