收敛指数

We improved the merit function in quasi-feasible interior point method and used the exponential function that is the more general function to prove the existence of one order optimality point in feasible problem. We discussed the inner and outer algorithms and made the convergence theorem.

在算法中改进了拟可行内点法中的值函数，使用指数形式的更一般函数，用此值函数证明了可行性问题的一阶最优性点的存在性，并通过对内部算法及外部算法的讨论得到了算法的收敛性定理。

Suppose that the random Doeblin condition is satisfied, we prove that the invariant measure exists and any initial distibution convergence to the measure with an exponential rate.

假设随机"Doeblin"条件成立，我们证明了随机环境的马氏链的不变测度存在，且任何初始分布以指数收敛速度到些不变测度。

The new method has monotone consistency, convex consistency, linear transformation consistency, gradually approaching white exponential law coincidence property and linear convergence rate.

结果表明，这一方法不仅保持了原方法的升凹一致性、线性变换一致性，而且具有渐近白指数律重合性和线性收敛速度。

EFM is not only AP, but second order convergentuniformly with respect to the mean free path in the whole domain.

其中指数拟合法不仅仅是渐近保持的，而且可以证明它在整个计算区间上有对平均自由程一致的二阶收敛性。

When the diffusion matrix is symmetric and locally uniform positive definite, we prove that the solution tends to the thermal equilibrium state exponentially in L〓 norm and relative entropy.

当扩散矩阵对称且局部一致正定时，利用熵方法证明了其解在L〓或相对熵意义下指数衰减到热平衡状态，并且能明确的计算出收敛速率。

By integrated Lyapunov stability analysis, it is guaranteed that all of the closed-loop signals are bounded, and the tracking errors converge exponentially to a residual set, whose size can be adjusted by changing the design parameters.

藉由完备的李雅普诺夫稳定度分析，证明所有闭回路信号是有界的，且追踪误差至少可指数收敛至一残局，其大小可藉由调整参数任意控制。

In fifth chapter,as applications of the existence theorem of〓-optimalcoupling operator for the jump processes,the estimate of the varied expontialconvergence rate for the jump processes and the existence of an order-preservingMarkov coupling for the jump processes are investigated,where,the obtained theexistence theorem of an order-preserving Markov coupling is a general theorem onPolish space endowed with semiorder,it includes the results that existence theoremon countable state apace endowed with total order or finite state space endow withsemiorder have been obtained by the internal and external mathematicians in recentten years.

第五章作为跳过程〓最优耦合算子存在性定理的应用，讨论了跳过程各种指数收敛速度的估计和保序Markov耦合的存在性。其中保序Markov耦合存在定理是具有偏序关系波兰空间上的跳过程最一般的定理，它包括了近10年来国内外对具有全序关系可数状态空间或具有偏序关系有限状态空间上的跳过程关于保序Markov耦合存在定理的研究成果。

The steady-state solution is known to be the positive eigenfuction corresponding to the simple eigenvalue 0 of the system operator.

于是作为半群拟紧性和不可约性的直接结果，得到了系统的时间依赖解指数收敛到其静态解，并且该静态解即为系统算子简单特征值0对应的正的特征向量。

And it was proved that the stabilization controller through the proposed method could guarantee all the states of n-dimensional system exponentially converge to the origin.

并证明了利用该方法设计的控制器可使得高维链式系统各状态指数收敛于原点。

However under a quite general condition (the summability of the φ-mixing coefficients), we establish the exponential convergence of ||f_n~*- f||_1 which gives a first step to prove the LDP for certain φ-mixing processes.

然而，在一个非常一般的条件下，我们得到了||f_n~*-f||1的指数收敛性，这为今后研究特殊的φ-混合过程的大偏差原理打下了基础，接着，我们研究了两种马氏过程的情形，即一致遍历马氏过程和可逆马氏过程。

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