查询词典 finite dimensional

Under the constraints between potentials and eigenfunctions, the Lax systems are nonlinearized to be finite dimensional completely integrable systems in Liouville sense.

在位势与特征函数之间的约束条件下，Lax系统被非线性化成为有限维Liouville完全可积系统。

In Chapter 3, by using the technique of finite dimensional approximation of Seiberg-Wittentheory, the equivariant K-theory and some other methods, we study the problem of topologicalrestriction when there are smooth groups acting on Spin 4-manifolds such as the alternatinggroup A_5, cyclic group Z_6 and symmetric group S_3 with actions of odd type, consequently weimprove Furutas 10/8 theorem under the condition of group actions.

第三章运用Seiberg-Witten理论的有限维逼近技巧和等变K-理论等工具，研究了Spin 4-流形X上分别存在光滑交错群A_5、循环群Z_6和奇型三阶对称群S_3作用时，X的拓扑限制问题，在群作用下改进了Furuta的10／8定理。

To combine dichromatic reflection model with the finite dimensional linear model to derive the normalized deviation body reflectance, has been demonstrated to be an important method to realize color constancy.

利用双色反射模型和有限维线性模型，提取归一化偏差本体反射特征，被实验证明是实现颜色恒常性的一个重要途径。

The Maschke's Theorem of group algebras is well known, and [Mo2] gives us a version of Maschke's and Dual Maschke's Theorem of finite-dimensional Hopf algebras.

半格分次弱Hopf代数是弱Hopf代数的一类特殊情况，而且又是Hopf代数的一种推广，在第1.3节中，我们将会给出半格分次弱Hopf代数的Maschke和对偶Maschke定理的结论及其应用。

Wanka studied two kinds of dualproblem in finite dimensional space, namely, an extended Fenchel type and Fenchel-Lagrange dual based on the conjugate theorem in convex optimization problem.

Wanka利用有限维空间中凸优化问题的共轭理论，研究了两类对偶问题，即广义Fenchel对偶问题和Fenchel-Lagrange对偶问题，后者是经典Fenchel和Lagrange对偶问题的组合，二者都是在扰动理论基础上产生的，还提出了一个约束条件保证其凸优化问题中强对偶成立。

W anka studied two kinds of dualproblem in finite dimensional space,namely,an extended Fenchel type and FenchelˉLagrange dual based on the conjugate theorem in convex optimization problem.The latter is a"combination"of the classical Fenchel dual and Lagrange dual,which are based on perturbation theory.Then they introduced a constraint qualification whose fulfillment is sufficient in order to guarantee strong duality.

W anka利用有限维空间中凸优化问题的共轭理论，研究了两类对偶问题，即广义Fenchel对偶问题和FenchelˉLagrange对偶问题，后者是经典Fenchel和Lagrange对偶问题的组合，二者都是在扰动理论基础上产生的，还提出了一个约束条件保证其凸优化问题中强对偶成立。

Basic concepts of stochastic processes: family of finite dimensional distribution functions, numerical characteristics of stochastic processes.

随机过程的基本概念：有限维分布函数族，随机过程的数字特征。

The main aim of this paper is to classify finite dimensional Hopf algebras, especially basic Hopf algebras.

本论文的主要目的是分类有限维的Hopf代数，特别地去分类有限维的基本Hopf代数。

Assume the underlying vector space is finite dimensional (therefore issues such as continuity of a projection need not be considered).

假定底层的向量空间是有限维的(因此问题如投影的连续性不需要考虑)。

A dynamical system is just a finite dimensional representation of the system quiver Q with dimension vector .

一个动力系统就是系统箭图Q的一个维数向量为的有限维表示。

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。