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Chapter 2 deals with some refinements of the central limit theorem for a class of non-uniformly hyperbolic dynamical systems called Young\'s system, such as local central limit theorem and so-called Berry-Esseen theorem giving the rate of convergence in the central limit theorem.

在第二、三章中，我们考虑一类重要的非一致双曲动力系统的统计性质-中心极限定理，及其进一步的精细结果如局部中心极限定理，带有收敛速度的中心极限定理。

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。

In addition, we also give the characteristic of uniformly integrable martingale in the rearrangement invariant martingale space and the relationship between one martingale and the accompanying martingale associated with it which is particular in the rearrangement invariant martingale space under the action of some most important martingale operators such as maximal operator, square operator, the greater operator and the smaller operator.

此外我们还考虑了重排不变鞅空间中的鞅是否一致可积的特征以及极大算子、均方算子和上、下算子在重排不变鞅空间及其相伴鞅空间上作用的特殊性质。

Pisier\'s results,under tree martingale valued space X is isomorphic toan a-uniformly convex space (2≤a＜∞),some quasi-normal or normal inequalitiesof a-variation maximal operator and a-conditional variation maximal operator of X-valued predictable tree martingales are identified.

同时，用G.Pisier's结果在树鞅取值空间X同构于a一致凸Banach空间条件下，证明了几个X-值树鞅α-方极大算子和a-条件方极大算子的拟范数不等式与范数不等式。

An extremely high temperature of anode humidification is also unreasonable; as a result, when the current density is high, the liquid water should be injected directly into anode gas channel to guarantee both high inlet H〓 concentration and well-humidified membrane. 4. The utilization of Pt in the cathode catalyst layer will decrease with the increasing current density; as a result, based on the principle of maximal Pt utilization, the catalyst layer can be designed much thinner or not uniformly in the catalyst distribution.

而在此截面上，交指型流场燃料电池阳极侧的液态水饱和度的极值位置并不确定；在电池阴极处，液态水饱和度的极值总是出现在z=0.002m处的气体扩散层和膜的界面上，并且该处的液态水饱和度沿x方向存在一个最大值，与此相应的氧气的质量浓度分数在该处达到极小值，因此极限电流密度将首相出现该处，但总体来说液态水饱和度沿x方向的分布较为均匀。4。

To get the uniformly valid representation of vibration mode, Ruo-jing Zhang published three generalized related functions.

为了得到振动模态的全域一致有效表达式，张若京给出了三类广义相关函数。

We conclude that normalized cubic Gauss sums which modular is primes in arithmetic progressions are uniformly distributed around the circle and we get that there is no rule like quadratic Gauss sums.

并由此得出，模为算术级数中素数的正规化三次高斯和在单位圆周上是一致分布的。因此，在三次情况下不存在类似二次高斯和的判别准则。

The uniformly most powerful test can exactly judge leakage signals of above both situations and obtain the detection probability of 95 percent.

对以上两种情况无须预先假设可能发生的有关泄漏量统计知识，利用该方法即能做出准确判断，检测概率均达到95%以上。

Compared with Ni-A coating, Ni-B coating has only needle-shaped Cr rich phase distributing in the spray coating uniformly.

Ni-B样品喷焊层内只有针状富Cr第二相，在整个喷焊层内均匀分布。

There is no reason but herd mentality why handles have remained uniformly octagonal for so long.

没有什么特别理由，只是惯性思维，拍柄统一都是八面形保持了如此长的时间。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。