耗散函数

The main works are to extend the related conclusions of continuous time systems to discrete time systems and the determination of state reachable set when bounded control input set is used. The properties of system's incremental gain are studied next.

文中第一步先讨论了应用耗散系统基本理论来界定系统诱导范数的方法：给出了确定有效系统耗散函数的方法：主要工作体现在将连续系统的相关结论推广到了离散系统：以及有界控制输入时系统状态能达集的界定。

By means of the theory of internal variable quasi-thermodynamics, the internal relation of Lagrange's dissipative rate function between the 1-D EVP model and a pure plastic model is demonstrated and the reason why the 1-D EVP model has quasi-plastic visco-elastic characteristics is revealed.

利用内变量准热力学理论，揭示了一维EVP模型的Lagrange耗散率函数与纯塑性模型的Lagrange耗散率函数的内在联系，阐明一维EVP模型具有准塑性的黏弹性性质的原因。

Moreover,using Ito differential formul a to the constructed Lyapunov function along solutions of lto stochastic differential systems,Lyapunov method is adopted to set up the fundamental theory of dissipativity in the module corresponding to the theory on the dissipativity of deterministic ordinary dif- fere.

提出了有关Ito型随机微分系统耗散性理论的新概念：按模耗散、按模等度耗散和按模一致耗散，并利用Lyapunov方法，借助于Ito 微分公式沿着Ito型随机微分系统的解对所构造的Lyapunov函数求导数，给出了Ito型随机微分系统有关按模耗散理论的一些代数判据，获得了与确定性常微分系统耗散性理论相对应的结论，最后的算例证明了该方法的有效性和可行性。

It is found that there are similarities in terms of spectral integral among the wind input source terms given by Jeffreys, Sverdrup and Munk, and Plant and among the wave breaking dissipation source terms given by Tsikunov,Hasselmann and Philips,although the original forms and the physical considerations of these source terms are significantly different.

发现Jeffreys，Sverdrup和Munk以及Plant的风能输入源函数在谱积分意义下具有相似性，而Tsikunov，Hasselmann和Phillips的破波耗散源函数在谱积分意义下也具有相似性，尽管这些源函数的原始形式和物理背景显著地不同。

It is proved that the two-dimensional non-hydrostatic Boussinesq equations on the x ? z plane with the kinetic viscous term and the thermal dissipative term are unstable equations in the C 2 function class.2. If we replace the influence of the kinetic viscous term by Rayleigh friction and the thermal dissipative term by Newton cooling, the new generalized equations are stable equations in the C 1 function class. The construction of the solution space and the discriminating method for well-posedness of the problem of determining solution are given.

本文的主要结果如下：1证明了在y方向上均匀的带有运动粘性项以及热耗散项的两维非静力、Boussinesq近似的x-z面上两维旋转流体的控制方程组在C 2函数类中是一个不稳定的方程组。2如果以瑞利摩擦来代替粘性的影响，以牛顿冷却来代替热量的耗散，则所获得的一个新的方程组在C 1函数类中是一个稳定的方程组，给出了其解空间的构造和各种定解问题的适定性的判别方法。

Based on the Lagrangian equation with dissipation function, the motion equation of a microbubble with shell is obtained, and the dynamic characteristics of microbubble with shell in free space are studied. It shows that the inner and outer maximum radii of the microbubble increase when the acoustic pressure and its initial radius increase, as well as when the ultrasonic frequency decreases.

理论上利用有耗散函数的Lagrange方程，建立了有壳微泡的R运动方程，开展了自由空间中有壳微泡动力学特性的研究，表明微泡内外半径增量随声压的增大、超声频率的降低、初始内径的增大及壳厚的减薄而迅速增大。

The robust dissipativity for given supply rate has been studied for uncertain impulsive systems. The dissipativity conditions for such systems are derived by means of storage function method, matrix inequality and dissipativity inequality.

对不确定脉冲动力系统在给定供给率时的鲁棒耗散性进行了研究，利用储存函数法、矩阵不等式以及耗散不等式等方法，得到了不确定脉冲系统的鲁棒耗散性的充分条件。

Some new conceptions are presented about the dissipativity theory of Ito stochastic differential systems as follows:dissipativity in module,equi-dissipativity in module and uniform dissipativity in module.

提出了有关Ito型随机微分系统耗散性理论的新概念：按模耗散、按模等度耗散和按模一致耗散，并利用Lyapunov方法，借助于Ito微分公式沿着Ito型随机微分系统的解对所构造的Lyapunov函数求导数，给出了Ito型随机微分系统有关按模耗散理论的一些代数判据，获得了与确定性常微分系统耗散性理论相对应的结论，最后的算例证明了该方法的有效性和可行性。

Based on the hyperbolic skeleton curve of Hardin-Drnevich, small strain dynamic dissipation function was formulated by adopting the Masing rule.

以Hardin-Drnevich模型的双曲骨架曲线为基础，采用Masing准则构造其滞回圈，形成小应变土体动力耗散函数。

Starting from the skeleton curves of Hardin-Drnevich model and Ramberg-Osgood model and formulating the hysteresis loop by use of Masing\'s rule,the research construct dynamic dissipation function for soils using the assumptions of the beeline and the skeleton curve shift laws by use of thermodynamic approaches.

论文以Hardin-Drnevich模型和Ramberg-Osgood模型的骨架曲线为基础，采用Masing准则构造其滞回圈，对塑性中心移动为直线和骨架曲线两种情况，分别构造了土体动力耗散函数。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失