查询词典 invariance theorem

Supposing the nonlinear term bounded, by using homotopy invariance theorem, we proved the existence of solutions of boundary value problems for a class of nonlinear ordinary differential equations.

在假设一类常微分方程边值问题中的非线性项有界的条件下，运用同伦映射不变性定理，得出了解的存在性结论。

We establish an asymptotic Lipschitz homotopy invariance theorem for these K-homology groups and K-theory groups. We show that the asymptotic index maps are isomorphisms for the asymptotically scaleable spaces, which include Euclidean cones, simply connected complete Riemannian manifolds with nonpositive curvature.

我们证明了这些K-同调群和K-理论群具有渐近Lipschitz同伦不变性；对于渐近可标度的几何空间（包括欧氏锥、单连通非正曲率完备黎曼流形等），证明了渐近指标映射为同构。

By using the continuation theorem of coincidence degree theory, homotopy invariance property and Lyapunov's approach, some sufficient conditions ensuring the existence and stability of positive periodic solutions of the system are obtained.

利用Mawhin重合度理论，并结合同伦不变性质，以及Lyapunov方法，获得该系统正周期解的存在性和全局稳定性的充分条件，推广和改进最近一些文献的结果。

The condition for the existence of positive elliptic periodic solution was found using Floquet theory; and the theorem of the existence of positive elliptic periodic solution was proved by the method of upper and lower solutions and homotopy invariance theory of topology degree; then an example was given.

利用Floquet理论得到了该方程的正椭圆周期解存在的条件；然后利用上下解方法和拓扑度的同伦不变性理论，证明了该模型正椭圆周期解的存在性定理，并进行了实例验证。

Based on the cross-ratio invariance theorem, a new method for acquiring characteristic points in the calibration of line structure-light sensor was proposed.

提出了一种基于双重交比不变性的线结构光传感器标定点获取的方法，利用该方法和设计的标定靶标，可方便的获取大量的高精度的标定点，解决了线结构光传感器标定点不易产生且数量少的问题，从而可以在一定程度上提高标定的精度。

The Lyapunov theorem and Lasalle invariance principle are applied to optimization sub-problem in augmented Lagrange multiplier method.

3.3同时本文还给出了一种基于基因算法和传统优化算法相结合的途径解决连续的MINIMAX优化问题。

The total energy of the system is employed to show the passivity property of TORA, and then a proper Lyapunov function including energy item is designed. Based on Lyapunov theory, a state feedback control algorithm is achieved. The stability of the control system is based on LaSalle invariance theorem.

基于拉格朗日方程，建立了TORA的动力学模型，从能量的角度出发，说明了系统的无源特性，在此基础上设计了一个合适李亚普诺夫函数，从而得到了系统的控制算法；采用拉萨尔不变性原理分析了控制系统的稳定性。

The stability of the system is proven by Lyapunov techniques and Lasalle's invariance theorem. Simulation results show that the designed adaptive controller achieves a superior performance for the overhead crane system.

对系统稳定性，文中通过李雅普诺夫理论及拉塞尔不变性原理进行了证明，仿真结果也证实了这种自适应控制器能够对吊车系统进行良好的控制。

The stability of the closed-loop system is proven by Lyapunov techniques and LaSalle's Invariance Theorem. Simulation results demonstrate that the designed adaptive controller achieves a superior performance for the overhead crane system.

对于闭环系统的稳定性，文中通过李雅普诺夫理论及拉塞尔不变性原理进行了证明，仿真结果也证实了这种自适应控制器能够对吊车系统进行良好的控制。

In this method, an interim variable is defined by combining one variable of each subsystem. The interim variable is used to construct the sliding-mode function and the total control law can be derived to guarantee the equilibrium point is reachable in finite time. Using LaSalle invariance theorem, it can be proved further that the equilibrium field only includes one equilibrium point and the equilibrium point is asymptotically stable.

该方法将各个子系统的一个变量进行组合定义成一个中间变量，然后从这个中间变量出发构造滑模函数，通过求取总的控制量保证中间变量在有限时间内收敛到平衡点；进一步利用LaSalle不变性原理证明该收敛域内只有一个平衡点且是渐近稳定的。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐