查询词典 finite dimensional

In this paper, some decision theorems are suggested about the matrix orthogonal problem on the subspace of the finite dimensional Euclidan subspace. In addition, some concise results are obtained by matrix representation of the orthogonal complement and injection of vectors on the subspace.

利用向量组的Gram矩阵和向量的坐标矩阵对有限维欧氏空间中子空间的正交性给出了矩阵判定条件，对子空间的正交补及向量在子空间上的内射影给出了矩阵表示，获得了一些简捷有用的结果。

Finite dimensional euclidean spaces Scalar products, norms, orthonormal basis and orthonormalization.

有限维欧几里德空间标量的产品，规范，标准正交基和正交化。

The Kolmogorov extension proceeds along the following lines: assuming that a probability measure on the space of all functions exists, then it can be used to specify the joint probability distribution of finite-dimensional random variables .

收益的Kolmogorov延长其内容大致如下：假设概率测度空间上存在的所有功能，那么它可以用来指定联合概率分布的有限维随机变量。

In recent years,representation theory of finite-dimensional algebras has intersected and permeated through Lie algebras,which is one of the important features.

与李代数的交叉与渗透是近年来有限维代数表示理论发展的重要特点之一。

The research is carried on from four aspects. One is, based on answering the above open problem on a finite dimensional Euclidean space by means of partially ordered theory, to research the existence of solutions, global error bounds of proximal solutions and sensitivity of parametric unique solutions and present a class of variable-parameter three-step iterative algorithms for generalized set-valued variational inclusion problems by using - resolvent operator of set-valued mapping.Two is to consider the convexity, closedness and boundedness of the solution set of general set-valued variational inclusion problems and the sensitivity of the parametric solution set by means of graphical convergence theory. Three is to discuss directly the existence of solutions by using analytical methods for set-valued mixed quasi-variational-like inequalities and suggest a class of direct variable-parameter three-stepiterative algorithms for solving generalized set-valued variational inclusions.

研究分有三个方面：一是借助于偏序理论在有限维欧氏空间中解决了上述公开问题，在此基础上利用集值映射的η-预解算子，研究了广义集值变分包含问题解的存在性、逼近解的全局误差界、参数唯一解的灵敏性，并提出了一类变参数三步迭代算法；二是借助于图收敛理论研究了一般集值变分包含问题解集的凸性、闭性和有界性以及参数解集的灵敏性；三是用分析的方法直接讨论了集值混合拟类变分不等式问题解的存在性并提出了一类求解广义集值变分包含问题的直接变参数三步迭代算法。

For a new kind of linear chaotic operator, one class of nonwande-ring operators (invertible and bounded linear nonwandering operators) are studied, and their invariance under small perturbation in finite dimensional separable Banach Space is proved.

对于一种新型的线性混沌算子―非游荡算子，研究Banach空间上的一类特殊非游荡算子―可逆线性有界非游荡算子，证明它的小扰动下的不变性。

Thesame rank Lipschitz continuous development of single-valued mappings is proven by means of partially ordered theory on finite dimensional Euclidean spaces.

借助于冲一预解算子研究了有限维欧氏空间中的集值混合类变分不等式问题和广义集值变分包含问题的全局误差界。

We also can give the structure theorem for finite dimensional basic Hopf algebra of tame type in the radical graded case.

对于Tame型的Basic Hopf代数，我们可以给出的是根分次情形的结构定理。

Based on the surjection of maximal monotone operators, we prove that some semilinear heat equations with weak Lipschitz nonlinear terms are exactly controllable by L〓 0, T: H〓(Ω control; Based on the critical point theorem of coercive convex functionals, we prove that some parabolic equations with Lipschitz nonlinear terms are globally approximately controllable and finite-dimensional exactly controllable by controls acting on mobile supports, and finally, we extend the results to parabolic equations in R〓.

首先利用极大单调算子的满射原理证明了半线性热方程在较弱Lipschitz条件下可通过L〓0.T；H〓(Ω控制实现精确能控。然后通过构造强制凸泛函并利用其临界点理论证明了带Lipschitz非线性项的抛物型方程可通过作用在在移动支集上的控制来实现整体近似能控与有限维精确能控，最后将整体近似能控与有限维精确能控结论推广到无界区域R〓上。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

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。