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    This paper studies the properties theφ-distortion function andη-distortion funition Schottky upper boundaries are established.
    文章用无穷乘积表示了Hersch-pflugerφ-函数与Agardη-偏差函数,得出它们的一些性质,由此给出了Schottky上界的估计。
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This paper is divided into four sections. Section 1 and 2 contain the following theorems. Theorem I. Let L_Φ~≠ and L_M~* be Orlicz spaces, Then the foll-owing are equivalent. (i) L_M~* and L_Φ~* have. the property(ii) L_Φ~* and L_M~* have the property(iii) Φ(u) is increasing more rapidly than M(u).Theorem Ⅱ. The following assertions are equivalent. Let L_(?)~* , L_(?)~* be Orlicz spaces with F-norms ||·||_φ,||·||_φgenera-ted by φ-functlons φ(u),(?)(u) respectively. In section 3 a conter-example is given to point...

This paper is divided into four sections. Section 1 and 2 contain the following theorems. Theorem I. Let L_Φ~≠ and L_M~* be Orlicz spaces, Then the foll-owing are equivalent. (i) L_M~* and L_Φ~* have. the property(ii) L_Φ~* and L_M~* have the property(iii) Φ(u) is increasing more rapidly than M(u).Theorem Ⅱ. The following assertions are equivalent. Let L_(?)~* , L_(?)~* be Orlicz spaces with F-norms ||·||_φ,||·||_φgenera-ted by φ-functlons φ(u),(?)(u) respectively. In section 3 a conter-example is given to point out that the second part of Lemma 1 inC.B.Lapin's paper [4] is false. And the following theorem hasbeen proved. Theorem Ⅲ. The following assertions are equivalent.

两个N-函数Ф(u)和M(u)有四种比较概念。本文§1和§2给出其中两种比较概念有关的Orlicz空间的五个补充定理。§3以一个反例指出C.B.Лапив一个引理的错误,详细讨论了两个φ-函数的“快于”比较概念,这补充了作者的文。

In this paper,we determine the structure of the Euler φ-func-tion in the quadratic number fields of which the corresponding class numbers are all one.From the above discussion,it yields that under certain conditions a quadratic integer has primitive roots.

本文确定了类数为1的二次数域上的欧拉φ-“函数”的结构,并由此推导出一个二次代数整数有原根的条件。

How to overcome the sensitivity of the Kalman filters to outliers in samples? Much attention is paid to, for this question, in resistance analysis of state estimator. Based on an innovation process, a quite large filter class, which is called W-filter class, is reasonably constructed in this paper. In order to control breakdown influ-ence of outliers to state filtering, we mianly deal with a bounded-influence subset, and find out the optimal φ-functions, under some constraints about the bound of influences.

如何克服Kalman滤波对采样观测值中包含的异常数据的敏感性?这在状态估计的抗扰性分析中处重要位置。本文基于新息增量过程,引进了一个相当大的滤波族,称为W滤波族。为了控制异常数据对滤波估计的影响,本文主要关心它的一个有界影响子族,并给出在预定的影响界限制下的最优有界影响滤波的φ函数形式。

 
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