ON THE GENERALIZATIONS OF DEN JOY-WOLFF THEOREM

We consider generalizations of Denjoy-Wolff theorem on strongly pseudo-convex domains. Beardon [3] gave a general Denjoy-Wolff theorem in hyperbolic domain in the complex plane. Our main results are generalizations of Beardon’s result in a higher dimensional setting.     

N值随机序列的随机选择的强极限定理

将赌博系统的随机选择理论扩展到N值随机序列,利用似然比概念及分析技术,得到一个随机选择下有序数偶相对频率的强极限定理     

Landau定理中上界的一个改进

通过相关文献给出的穿孔平面C\{0,1}的双曲度量的密度函数的新的下界估计,借助广义Schwarz引理我们对Landau定理中关于上界做了进一步改进并得到了一个带参数的上界表达式.并且当参数取到0时,此结论正好为相关文献得到的结果.     

关于任意离散随机序列的一个强偏差定理

引用极限对数似然比的概念作为任意随机序列联合分布与其边缘分布"不相似性"的度量,构造几乎处处收敛的上鞅,讨论了任意离散随机序列的强偏差定理.     

An analog of the Baum-Katz theorem for weakly dependent random variables

In this paper we study the limiting behavior of sums of dependent random variables under a strong mixing condition. We obtain conditions for which an analog of the Baum-Katz theorem holds and cite an example showing their optimality. Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 360–368, March, 2000.     

A Schottky-type theorem for starlike domains in Banach spaces

We show that if is a starlike domain in a Banach space and is a family of holomorphic functions on that omit two distinct values and is bounded at the origin, then is uniformly bounded on each -bounded set.

     

A new proof and generalizations of Gearhart's theorem

Let be a Hilbert space, let be the space of almost periodic functions from to , and let be a closed densely defined linear operator on . For a closed subset , let be the subspace of consisting of functions with spectrum contained in . We prove that the following properties are equivalent: (i) for every function there exists a unique mild solution of equation ; (ii) and . The case yields a new proof of the well-known Gearhart's spectral mapping theorem.

     

A strong limit theorem for generalized Cantor-like random sequences

ＡＳＴＲＯＮＧＬＩＭＩＴＴＨＥＯＲＥＭＦＯＲＧＥＮＥＲＡＬＩＺＥＤＣＡＮＴＯＲ－ＬＩＫＥ　ＲＡＮＤＯＭ　ＳＥＱＵＥＮＣＥＳＬＩＵＷＥＮ（刘文）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＰｈｙｓｉｃｓ,ＨｅｂｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅ...     

On Cartan's theorem for linear operators

In this paper, we describe a second main theorem of holomorphic curves in , of hyper‐order strictly less than 1, that involves a general linear operator . As an application, we derive a truncated second main theorem of degenerate holomorphic curves of hyper‐order strictly less than 1 using Nochka weights.     

Weak Cartan-type second main theorem for holomorphic curves

In this paper, a weak Cartan-type second theorem for holomorphic curve f ： C→P^n（C） intersecting hypersurfaces Dj, 1≤j≤q, in P^n（C） in general position with degree dj is given as follows： For every ε〉0, there exists a positive integer M such that ｜｜（q - （n ＋ 1） ε）Tf（r）≤∑j^q=1 1/dj Nf^M（r,Dj）＋o（Tf（r））, where ＂｜｜＂ means the estimate holds for all large r outside a set of finite Lebesgue measure.     

On the role of Rouché's theorem in queueing analysis

In analytic queueing theory, Rouché's theorem is frequently used, and when it can be applied, leads quickly to tangible results concerning ergodicity and performance analysis. For more complicated models it is sometimes difficult to verify the conditions needed to apply the theorem. The natural question that arises is: Can one dispense with this theorem, in particular when the ergodicity conditions are known? In the present study we consider an M/G/1-type queueing problem which can be modelled byN coupled random walks. It is shown that it can be fully analysed without using Rouché's theorem, once it is known that the relevant functional equation has a unique solution with prescribed regularity properties.     

Extension of the Weierstrass factorization theorem

Dans cette note, nous montrons qu’il est possible d’étendre le théorème de factorisation de Weierstrass pour certains éléments d’une algèbre de BanachA.     

第一类典型域上的Bloch常数

引入第一类典型域R_I(m,n)上的全纯映照子族H_k(R_I(m,n)),当k→+∞时,该映照族就是R_I(m,n)上的局部双全纯映照族.建立了H_k(R_I(m,n))上的Bonk偏差定理.当k=1和k→+∞时,其结果分别都回到了FitzGerad和龚升关于典型域R_I(m,n)上的Bonk偏差定理.当m=n=1时,其结果又回到了Liu和Minda在单位圆盘上的偏差定理.应用偏差定理,给出了映照族H_k(R_I(m,n))上的Bloch常数估计,其结果补全了从k=1和k→+∞之间的R_I(m,n)上Bloch常数估计的所有结果,而且把单位球上的Bloch常数估计推广到R_I(m,n)上.     

On the almost sure (a.s.) central limit theorem for random variables with infinite variance

We give criteria for a sequence (X _n ) of i.i.d.r.v.'s to satisfy the a.s. central limit theorem, i.e.,

Some generalizations of the Hardy-Littlewood-Paley theorem

Translated from Matematicheskie Zametki, Vol. 51, No. 3, pp. 24–34, March, 1992.     

Further generalizations of the Gale-Nikaido-Debreu theorem

A fixed point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subsets of a t.v.s. is applied to generalize Gwinner’s extensions of the Walras excess demand theorem and of the Gale-Nikaido-Debreu theorem.     

On generalizations of Lavrentieff's theorem for Polish group actions

It is shown that for every Polish group that is not locally compact there is a continuous action of on a -complete subset of a Polish space such that cannot be extended to any superset of in . This answers a question posed by Becker and Kechris and shows that an earlier theorem of them is optimal in several aspects.