| 1. | Russell ( [ 17 ] ) has showed that , a compact perturbation , generated from unitary operator groups in infinite - dimensional linear hilbert spaces , is unable to make the perturbed semigroup exponentially stable
Russell ( [ 17 ] )曾指出，无限维hilbert空间中的酉算子群对生成的紧扰动不能使被扰动半群具有指数稳定性。 |
| 2. | Then linear control technique is applied to the linear subsystem of the transformed equivalent systems to design the controller , thus a nonlinear controller of the original chaotic systems is obtained , which is proved to be exponentially stable
然后利用线性控制方法对变换后的等价系统中的线性子系统进行了控制器设计，由此设计出原混沌系统的非线性控制器，并证明其具有指数稳定性。 |
| 3. | These conditions can be used both to design globally exponentially stable and periodical oscillatory neural networks with time - varying delays , and to enlarge the area of designing neural networks . our work has important significance in related theory and it ' s application
这些条件可用于设计全局指数稳定的和周期振荡的具可变时滞的神经网络，大大扩展了神经网络设计的范围，这在理论上和应用中都有着重要意义。 |
| 4. | Chapter 3 investigates the estimation of the domains of attraction of equilibrium points for hopfield neural networks with delays , where hopfield neural networks with discrete and distributed delays are considered . we derive a sufficient condition for an equilibrium point to be locally exponentially stable
分别针对带离散时间延迟和带分布式时间延迟的hopfield神经网络,得出了平衡点局部指数稳定的充分条件,同时提出了一种指数稳定平衡点的吸引域的估计方法。 |
| 5. | For viscous shock waves c , by the spectral analysis we prove that in l2 ( r ) space the essential spectra and the eigenvalues ( except the simple zero eigenvalue ) of the linearized operator have negative real parts , thus we show that the viscous shock waves c is locally asymptotically exponentially stable in l2 ( r ) space
对粘性冲击波c利用类似方法，我们证得在l ~ 2 ( r )空间线性化算子的本质谱和除简单特征值零以外的特征值均具有负实部。于是，我们得到粘性冲击波c在l ~ 2 ( r )空间的局部渐近指数稳定。 |
| 6. | In this paper , we have proved that an anti - bounded c _ ( 0 ) - group in infinite - dimensional reflexive banach spaces is not exponentially stable under generating compact perturbation , and that a c _ ( 0 ) - isometric semigroup in infinite - dimensional hilbert spaces has the same property . so , we have extended and improved russell theorem
在本文中，我们分别证明了无限维自反banach空间中的反有界c _ 0 -群和无限维hilbert空间中的c _ 0 -等距半群在生成的紧扰动下一定不具指数稳定性，从而推广和改进了russell定理。 |
