有界性

The definition of the absolute value for a fuzzy number is obtained.Furthermore,a lot ofproblems,such as absolute integrability,bounded variation and absolute continuity,arepresented and discussed.The representation theorem of the absolute values of fuzzy num-bers is established.It plays an important role in discussing the problems conceming theabsolute value.The relation between the absolute integrability and integrabili-ty is discussed,and the following result is obtained:aintegrable fuzzy-number-valued function is absolutely integrable iff it is integrable.The relation between theabsolute integrability and the absolute continuity of the primitive for fuzzy-number-valuedfunctions is dealt with.It is also pointed out that a fuzzy number valued function is ab-solutelyintegrable if and only if its integral primitive is fuzzy absolutely continuous.

提出了模糊数绝对值的概念并讨论了与绝对值相关的一系列问题，如绝对可积性、有界变差性、绝对连续性等，给出了模糊数绝对值的定义以及表示定理，该表示定理在涉及绝对值问题的讨论中起非常重要的作用；讨论了绝对可积与可积之间的关系，得到了结论：可积的模糊数值函数绝对可积的充要条件是该模糊数值函数可积；给出了模糊数值函数绝对可积与其积分原函数绝对连续性之间的关系，指出模糊数值函数绝对可积的充要条件是其原函数模糊绝对连续。

In first chapter,we discuss the〓-integrability of thegradients of the very weak solutions to non-linear elliptic systemsdivA=B(2)and〓-regularity of the very weak or the weak solutions to non-linearelliptic systems〓(3)in bounded domain Ω.

第一章讨论有界区域上的非线性椭圆型方程组〓（2）的很弱解的梯度的〓可积性和非线性椭圆型方程组〓（3）的很弱解与弱解的〓正则性。

The uniform bounded stable condition of the residual and its to nonlinear perturbations are proved by using Lyapunov function and uniform bounded lemma.

并利用Lyapunov函数和一致有界引理证明了故障检测残差信号的一致有界稳定条件和对非线性扰动的鲁棒性。

In Chapter Three, we use the method of interpolation spline of differential operater to come up with the reproducing kernel in H01 with respect to bounded linear operator in H10. Then we use the reproducing kernel to develop the expression of the best approximating of bounded linear operator in H10 and prove its convergence.

第三章中，对于H_0~1中的有界线性算子，用微分算子插值样条函数的方法给出了H_0~1空间中的再生核，利用此再生核给出了H_0~1上的有界线性算子的最佳逼近的表达形式，并证明了其收敛性。

On the other hand, we make certain study to the nonwandring property of bounded, unbounded operator semigroups ,and give out concrete application.By the theory of semigroups, we establish if {T_n}_(n≥1) is a bounded linear operator sequence onBanach space X_n converging in the sense of Kato to a bounded operator T on theBanach space X , then their nonwandering property can be inherited by each other under the appropriate conditions.

另一方面，本文对有界和无界算子半群的非游荡性也作了特别的研究，并给出了一些具体的应用；利用半群理论，还证明了算子在Kato意义下逼近时，二者之一的非游荡性可被另一个所保持；并得到了几个相应的结果。

We get the two edge blocking convergencetheorem of sequence of fuzzy numbers and the almost everywhere cut-convergence theorem ofmonotone bounded sequence of fuzzy numbers, and point out that monotone bounded sequenceof fuzzy numbers may not cut-converges and converges.

讨论了模糊数列的收敛、截收敛、几乎处处截收敛性，得到了模糊数列收敛的夹逼定理及单调序有界模糊数列必几乎处处截收敛定理，并指出了单调序有界模糊数列未必截收敛、收敛。

The existence of supremum and infimum of the bounded set in the noncompact fuzzy number space E〓 is proved in a quite different way.

利用完全不同的方法证明了非紧模糊数空间中有界集的确界存在性。

Motivated by Baker\'s result, we introduce a functional index‖E‖_∞to prove that if a mapping f which is from a normed space to a normed algebra satisfying‖ab‖=‖a‖‖b‖satisfies that‖E‖_∞is bounded,then either f is bounded or f is exponential.

受到Baker的结论启发，通过引入一个泛函指标‖E‖∞，证明了从赋范空间到满足范数可乘性的赋范代数的映射f，只要满足‖E‖∞是有界的，则f要么是有界的，要么是指数的。

The existence of pointwise robust convergent algorithm and uniformly robust convergence is next investigated. We propose an optimal l〓 robustness synthesis method for structured perturbations system by taking advantage of the famous Small Gain Theorem.

证明了最优l〓辨识算法的存在性；证明了黑箱辨识存在辨识算法使全局误差收敛于有界区间；提出并证明了逐点鲁棒收敛算法的存在性；证明了一致鲁棒收敛算法的存在性。

The Hausdorff property of a kind of classifying mode is defined. And it is proved that the single-layer perceptron can deal with the classifying problems of any Hausdorff pattern sets. Chapter 5 studies the radial basis function networks and a proof of Cover pattern classifiable theorem is presented.

第四章主要研究多层感知机的万能逼近性和最佳逼近性，包括权值有界和隐单元权有界时的情况，定义了一种分类模式的Hausdorff性，证明了单层感知机能解决任意具有Hausdorff性的模式集的分类问题。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。