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This result can best be viewed as a quantum black hole version of the third law of thermodynamics. As a result of this area spectrum, the spectrum of M is discrete, bounded below, and can be made positive. Prom the physical point of view, the semiboundedness and positivity of the spectrum are very satisfying results: The semi-boundedness of the spectrum implies that one cannot extract an infinite amount of energy from the system, whereas the positivity of the spectrum is in agreement with the well-known positive-energy theorems of general relativity.

同时根据EMDA黑洞动力学,存在与面积谱对应的大于零且有下界的质量离散谱,从物理上来看,质量谱的半有界性意味着不可能从系统吸取无限的能量,而正定性则与广义相对论中的正能定理一致,也就说稳态轴对称EMDA时空的ADM能量总是大于零。

Because the uncertainty of this class of system is bounded by a linear function of the norm of the delayed states with unknown bounds, an adaptive update law is proposed to estimate the square of these unknown bounds.

论证了鲁棒自适应控制器存在的条件,并给出了能适应未知参数变化且使得最终闭环系统状态一致最终有界的鲁棒控制律的设计方法。

The controller designed counteracts uncertainty and guarantees that all states of the closed-loop system are uniformly bounded.

所设计的控制器可克服模型的不确定性,保证最终的闭环系统所有状态一致有界。

That is to say that, the original signal of the closedloop system asymptotically converges to zero, while all the other signal of the closedloop system are uniformly bounded.

即闭环系统的原始状态是渐近收敛于零的,而其他所有的信号是一致有界稳定的。

We define Condition A,and show that Condition A is thenecessary condition of discrete groups,and uniformly bounded torsion isspecial case of Condition A.

我们引入条件A,并且指出条件A是离散的必要条件,一致有界挠是它的特殊情况,同时在条件A之下,建立了PinchedHadamard流形的等距群的离散准则。

It is also proved that the proposed algorithm could guarantee the closed-loop system to be uniformly ultimately bounded and the output converges to a small neighborhood of zero, so that ship linear path-keeping control can be implemented.

该算法保证了闭环系统的信号是一致最终有界的,使得系统输出收敛到零的一个较小邻域,从而能够实现船舶的直线航迹控制;而且,该算法不需要高频增益符号的任何信息,还解决了可能存在的控制器奇异值问题。

Moreover, classical multigrid methods, such as W-cycle and Variable V-cycle, are shown to be convergent uniformly for this mortar type TRUNC element.

我们还用经典多重网格方法(可变的V-循环、W-循环)求解带mortar条件的TRUNC元解,证明所构造的网格转移算子满足收敛性条件,从而传统多重网格方法作预处理的条件数为一致有界。

It isshown by theories and simulations that uncertain effects such as frictions and external disturbancesor unmodelled dynamices can be eliminatated and global exponential stability or global uniform ultimate boundedness stability can be guaranteed.

理论和仿真均证明,系统的不确定性诸如摩擦力、外部扰动及未建模动力学带来的不确定性影响,均可被设计的控制律补偿,最后可保证全局指数收敛或全局一致最后有界的结果。

Horizontal gene transfer might be one possible reason for such evolutionary intermixing.

虽然这3大类群与生物的三界系统一致,但是每个类群中都混有其他界的微生物视紫红质。

The main work of this thesis is to prove that, in the above two cases, the corresponding BP algorithms with weigh-decay and inner-product penalty are deterministically convergent.

本文主要研究在批处理和在线两种运行模式下,带weigh-decay和inner-product惩罚项的BP算法的收敛性以及引入惩罚项后网络权值的一致有界性。

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