In the first part, we establish a smooth infinite spot-financial markets model, admit the nonlinear constraints on households portfolio holdings, and define a compact manifold S of states set, so that the original model is extended to smooth infinite economics. Finally, we prove the existence of the financial equilibrium.
在第一部分中，我们建立了光滑无限的现货——金融市场模型，考虑经纪人债券持有的非线性约束，且模型中1期状态集不再是离散的点集，而是紧流形S，从而将原始模型推广到光滑无限经济情形，并证明了此模型金融均衡的存在性。
The lifetimes of the Stark manifold states are measured by using delayed electric field ionization.
采用延迟脉冲场电离方法测量了各斯塔克能态在不同外电场下的寿命。
In the part of the hydrogen supply and flow direction control, it described the designs for the hydrogen manifold, and the monitor scheme of the whole system's states detailedly;
在氢气供应流向控制部分，详细说明了氢气通道的设计及系统状态监测方案；
At a level of fairy generality, it is identified that continuous (or even smooth) controllers can be designed to drive the system states towards a preassigned sliding manifold.
在相当一般的假设条件下，我们指出了可以采用连续（乃至光滑）的控制方案，将系统的状态驱往给定的滑动流形上。
For an inertia wheel pendulum, a control law is designed to ensure that partial states of an inertia wheel pendulum are globally asymptotically stable, whereas other states are globally asymptotically convergent to an invariant manifold.
设计控制律使惯性盘倒立摆的部分变量全局渐近稳定，部分变量全局渐近稳定到不变流形。
By using the invariant manifold and sliding mode variable structure technique, dynamic output feedback stabilization controllers are proposed, based on known state feedback controllers for a class of nonlinear systems with linear unmeasured states.
针对一类具有线性不可测量状态的非线性系统，基于状态反馈稳定控制器，利用不变流形和滑模变结构控制技术设计了动态输出反馈镇定控制器。
Then, we derive the explicit formulae for determining the direction of the Hopf bifurcation and the stability of these periodic solutions bifurcating from the steady states, by using the normal form method and center manifold theorem.
进而应用规范型方法和中心流形理论，我们推导出确定分支周期解的稳定性和分支方向的计算公式。
Establish a smooth infinite spot-financial markets model, admit the nonlinear constraints on households'portfolio holdings, define a compact manifold S of states set, and prove the existence of the financial equilibrium.
建立了光滑无限的现货&金融市场模型，考虑经纪人债券持有的非线性约束，假设1期状态集为紧流形S，并证明了此模型金融均衡的存在性。