查询词典 global lipschitz condition

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

Furthermore, replacing the local Lipschitz condition by the global Lipschitz condition, the same conclusion is obtained, that is to say, the Euler method is strong convergent under the global Lipschitz condition.

进一步，将局部Lipschitz条件换成全局Lipschitz条件，结论也成立，即欧拉方法在全局Lipschitz条件下也是强收敛的。

The observer is adaptive one because an adaptation law which can adjust the Lipschitz constant of Lipschitz term is introduced. For this reason, the Lipschitz constant can be unknown in our design.

通过引进一项对Lipschitz非线性项的Lipschitz常数自适应调节的微分调节项，使得观测器具有自适应性，从而设计具有不必知道Lipschitz常数之大小的优点。

Inspired by these results, in this paper, we first give the definition of a new mapping ? uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space, then construct three-step iterative sequences of uniformly Lipschitz asymptotically nonexpansive mapping in this subset . We proved the convergence of this three-step iterative sequences for uniformly Lipschitz asymptoticallynonexpansive mapping, Further more, we proved this three-step iterative sequences with an error member converge to fixed points.

从中得到启发，在本文我们首先定义了一致凸Banach空间某非空紧子集上的一种新的映射——一致李普希兹渐进非扩张映射，在该紧子集上构造关于一致李普希兹渐进非扩张映射的三步迭代序列以及具误差的三步迭代序列，先来讨论三步迭代序列的收敛性，进而讨论具误差的三步迭代序列的收敛性。

The main tool is the notion of the Lipschitz condition with positive non-decreasing integrable function L-average along the piecewise geodesic which includes theclassical Lipschitz condition as well as theγ-condition as special cases.

同时，我们在研究中引入了沿着分段测地线的关于取正值非减可积函数L-平均的Lipschitz条件的概念，从而把流形上的Kantorovich定理及Smale理论统一起来研究。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

This paper presents the design methods of nonlinear observer in accordance with nonlinear term satisfying Lipschitz condition and dissatisfying Lipschitz condition based on single variable transmission.

本文以单变量传输为前提，基于观测器理论，针对混沌系统的非线性项满足Lipschitz条件和不满足Lipschitz条件两种情况，分别给出了非线性观测器的设计方法。

We present the design methods of nonlinear observer in accordance with nonlinear term satisfying Lipschitz condition and dissatisfying Lipschitz condition based on single variable transmission.

以单变量传输为前提，基于观测器理论，针对混沌系统的非线性项满足Lipschitz条件和不满足Lipschitz条件两种情况，分别给出不同的非线性观测器设计方法。

Under the conditions that the system without impulse effect satisfies the one-side Lipschitz condition, and the impulsive terms satisfy the corresponding Lipschitz conditions, a sufficient condition which can be easily checked the stability of the analytic solution is obtained.

在不受脉冲影响的原方程满足单边Lipschitz条件，及脉冲项满足相应的Lipschitz条件的情况下，给出了一个容易判别的解析解渐近稳定的充分条件。

The nonlinear items only satisfy the local Lipschitz condition, but not the uniformly Lipschitz condition. The step function is applied to the approximate controllability problem of the corresponding linear system.

这类非线性系统中的非线性项只满足局部Lipschitz条件，于是采用了阶梯函数的方法，对于热传导方程的逼近能控性进行了讨论，得到了线性系统的逼近能控性，并给出了控制的显式表达，而在文献[103]中控制的具体求法是未知的。

The antiquarian refers the vase to the second century.

古董收藏家认为这花瓶是公元2世纪的文物。

Meanwhile,it also products more and better products foe the customers bothe at home and abroad.

同时也为国内外客户的不同需求提供更多更好的产品。