定理

Under the cases of the linear interconnected systems with all its subsystems are one dimension, a theorem to judge the properties of single loop interactions has been given; the study also indicated that the properties of interactions cann't independent of the properties of subsystems in the multi-loop interaction conditions, and a all field root locus method has been proposed to decide the properties of interactions; a interaction stabilizable theorem has been given, and the efficacy of interactions with respect to the interconnected systems has been configured, Some primary results are reported which are induced by using a method of computer aided test to study block interactions, the stationary feedback efficacy of closed loop interactions have been discussed and a stability guess has been proposed.

本文提出互连系统的合作稳定性概念及其原理，给出了互连系统的本原稳定度、稳定中心、回路关连的级数以及关连的性质等基本定义；并在此基础上对线性互连系统进行关连分析，给出了一系列涉及到关连与互连系统稳定性关系的命题、引理、定理及其证明；其中，在子系统都是一维的线性定常互连系统情况，得出了单回路关连性质判断的定理；并指出在多回路关连条件下，关连的性质不能独立于子系统的性质，以及用全域根轨迹法判断关连性质的方法；给出了关连可稳定理，并对关连对互连系统的影响作用进行了分析。本文还用机辅试验的方法研究块阵关连并给出一些初步结果，本中还探讨了回路关连的静态反馈作用并提出一个判稳猜想。

The intermediate value theorem for discontinuous function is studied,the problem of discontinuous points when the left and right limit exists is considered by ZHU Le-min.

研究了非连续函数的介值定理，受朱乐敏等考虑的具有左、右极限存在的跳跃间断点的非连续函数的介值性定理的启发，利用上、下极限把介值定理推广到具有一般间断点的非连续函数的情况。

In fourth chapter of this paper,we mainly investigate the properties of a subclass S_p~* of starlike functions of orderα,including its coefficient estimate,distortion theorem,closure theorem and extreme points theorem.

在第四章中，我们主要研究了α次星形函数一类子族S_p~*的性质，包括系数估计，偏差定理，闭包定理，极值点定理。

By using the limits of functions and the exchange limit theorem,we considered the relationship between the double limit of function with two variables and its repeated limit s.

应用函数列的极限与函数的极限交换次序定理，研究了二元函数的二重极限与它的两个累次极限的关系定理，研究了二元函数的两个二阶混合偏导数可交换次序定理。

In the study of finiteness conjecture, there are two important conclusions, that is Revised Dulac"s Theorem and Il"yashenkos Theorem. But the discusses and demonstrations of these two theorems are very brief and simple in existing documents.

在有限性猜测的研究中有两个十分重要的结果，即修正的Dulac定理和Il'yashenko定理，现有的文献对这两个定理的讨论和证明非常简要。

We analyse the Lewy theorem and the provement idea of the theorem, and find the equation (7)and (8)are not equivalent under the reversible transformation, this lead to the absurdity in the provement does not come into existence .

分析Lewy定理及定理的证明思想，发现在证明中所述的可逆变换下，方程（7）与（8）并不等价，导致Lewy定理证明中归谬不成立。

Ruck, Hirano and Reich extended Baillon抯 theorem to a uniformly convex Banach space with a Frechet differentiable norm. Hirano-Kido-Takahashi, Oka, Park and Jenong proved the ergodic theorem for commutative semigroups of nonexpansive mappings and asymptotically nonexpansive mappings in the uniformly convex I3anach space with the Frechet differentiable nonn.

aillon的定理被Bruck，Hirano及Reich推广到具Frechet可微范数的一致凸Banach空间中，而当G是一般交换拓扑半群时，Hirano-Kido-Takahashi，Oka，Park及Jeong分别给出了具Frechet可微范数的一致凸Banach空间中非扩张半群及渐近非扩张半群的遍历压缩定理和遍历收敛定理。

Some equivalent conditions for unique ergodicity are included in theorem 6 and theorem 7 and the methods of the proof of theorem 7 is from functional analysis.

定理6及定理7给出唯一遍历的等价条件，定理7的证明采用的是泛函分析的方法。

Chapter 7 gives the H-stability of the eqilibrium point set first (theorem7.1), and the other two theorems (theorem7.2-7.3) provide an estimation result for the attractive region of different eqilibrium points.

首先给出了非凸梯度神经网络平衡点集合的H—稳(来源：AB29e6C论文网www.abclunwen.com)定性结果(定理7.1)，另外的两个定理(定理7.2—7.3)给出了不同平稳点的吸引域估计。

In recent years, along with the intensive study and extension of residue theorem, the residue theorem has been more intensively used, which illustrates the importance of residue theorem and its use value to a certain extent

近年来随着留数定理的深入研究与推广，留数定理得到了愈加广泛的运用，这在一定的程度上也说明了留数定理的重要性及其运用价值

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新