查询词典 laplace beltrami operator

It is to ask whether every bounded linear operator on a separable Hilbert space has a nontrivial invariant subspace and it can be reduced to the case of diagonal operator.

不变子空间问题是一个引人瞩目的公开问题，它是说在一个可分的Hilbert空间上是否每一个有界线性算子都存在非平凡的不变子空间？

Assignment of infinite many poles for the first order generalized distributed parameter control system, coupled with the first order generalized lumped parameter control system, is discussed in Hilbert space with functional analysis and operator theory. The solutions with the constructive expression are given by the generalized inverse one of bounded linear operator.

应用泛函分析算子理论的方法，讨论了Hilbert空间中一阶广义分布参数控制系统与一阶广义集中参数控制系统所构成的一阶耦合广义控制系统的无限多极点配置问题，利用有界线性算子的广义逆给出了问题的解及解的构造性表达式。

In this paper we have discussed the best approximating operator and the best approximating of bounded linear operator in H01 and H1a,+∞.

本文主要讨论了索伯列夫空间H~1a，+∞与H_0~1

In Chapter Three, we use the method of interpolation spline of differential operater to come up with the reproducing kernel in H01 with respect to bounded linear operator in H10. Then we use the reproducing kernel to develop the expression of the best approximating of bounded linear operator in H10 and prove its convergence.

第三章中，对于H_0~1中的有界线性算子，用微分算子插值样条函数的方法给出了H_0~1空间中的再生核，利用此再生核给出了H_0~1上的有界线性算子的最佳逼近的表达形式，并证明了其收敛性。

In[6],Prof Gong and Wang Libin discussed the property of Ho and K when A is an bounded linear operator, he also study the spectral theory of compact operator with these twe subspaces.

龚为邦教授和王利彬博士在[6]中讨论了算子A为一般有界线性算子时子空间H_0和K的性质，并利用H_0和K研究了紧算子的谱理论。

Simultaneously, we identify that the perturbation of these operators by a small norm operator is still nonwandering; further, we can obtain the theory that every bounded linear operator can be decompositioned into nonwandering operators.

同时，证明了这些算子经一小扰动后，可保持它们的非游荡性不变；进而可获得有界线性算子关于非游荡算子的分解理论。

Based on general orthogonal polynomials and general hybrid orthogonal functions, a new linear, continuous and bounded operator has been proposed in the dissertation. The definitions and properties of PGOPO are given, a various operational rules of the operator have been set up in a systematic way, the convergence of approximate solutions has been discussed. After introducing PGOPO and discussing its main properties and operational rules, a systematic methodology for solving various control problems via PGOPO has been developed.

本文在广义正交多项式及广义混合正交函数的基础上，提出了一种新的线性、连续、有界算子—分段广义正交多项式算子，探讨了这种算子的基本性质，并系统地建立了与该算子有关的各种运算规则及收敛性结论，给出了它在控制理论中的各种应用。

Let X be a real Banach space with strictly convex dual space X(superscript *) and G a bounded, open subset of X. T: DX→2 is a m-accretive operator, C: D→X is bounded operator.

设X是一个实Banach空间，X为其对偶空间，G是X的开、有界子集。T：DX→2是m-增生算子，C：D→X是有界算子。

A new particle swarm optimization, PSO with bounded mutation operator, was developed. In contrast to the original PSO, in this algorithm, PSO with bounded mutation operator would make the particles redistributed cquably close to boundary when place of particle exceeds feasible region during iteration.

提出了一种新的粒子群优化算法——带边界变异的PSO，其原理是：在迭代的过程中，当粒子的位置超出可行域时，带边界变异的PSO让粒子的位置重新均匀分布在边界附近；当粒子的速度超出可行域时，则使其均匀分布到整个可行区间，而不是像原始PS0那样在这2种情况下都只是简单地取边界值。

In addition, the mutual combination between teleoperation and autonomous control is the development direction of space robot for the long time, it not only can make use of the intellignece of human being but also can make operator release from the trivial busywork to resolve the problem of excess fatigue and easy mistake of operator.

另外，遥控操作与自主控制相互结合的共享控制是今后很长时间空间机器人的发展方向，它不但能最大限度发挥人的智能，而且使操作员从琐碎的作业中解放出来，解决操作员的过度疲劳与失误问题。

I was up all night because I was in pain, she said.

我整夜，因为我在疼痛，她说。

A crow caws /craoks.

乌鸦叫。 51-论文网