Normal Families and Shared Values

For f a meromorphic function on the plane domain D and a C,let _f(a) = {z D: f(z) = a}. Let F be a family of meromorphicfunctions on D, all of whose zeros are of multiplicity at leastk. If there exist b 0 and h > 0 such that for every f F,_f(0) = _f^(k)(b) and 0 < |f^(k+1)(z)| h whenever z _f(0), thenF is a normal family on D. The case _f(0) = Ø is a celebratedresult of Gu [5]. 1991 Mathematics Subject Classification 30D45,30D35.  

Connectedness of the efficient set in strictly quasiconcave vector maximization

In this paper, the concepts of quasiconcave set and strictly quasiconcave set are introduced. By using these concepts, we get a new sufficient condition for the efficient outcome set to be connected. This leads to the connectedness of the efficient solution set in strictly quasiconcave vector maximization under the mild condition that the efficient frontier is closed.The authors would like to thank Professor E. U. Choo and the referees for their many valuable comments and helpful suggestions.  

基于变参数模型的中国能源消费经济增长关系研究

本文利用1953—2002年的统计数据和状态空间模型对中国能源消费与经济增长关系进行了研究。我们的结论是:(1)中国能源消费与经济增长之间存在一种随时间不断变化的长期均衡关系即变参数协整关系;(2)基于状态空间模型的变参数估计很好地揭示了中国能源消费弹性的时变规律。  

关于两类污染数据回归分析的参数估计

研究简单回归模型：ｙｊ＝ａ＋βｘｊ＋εｊ，ｊ＝１，２，…，ｎ，其中Ｅεｊ＝０，Ｅε＾２ｊ＝σ＾２ｊ；但ｙ１，ｙ２，…，ｙｎ受到另一独立同分布随机变量序列ｔ，ｔ２，…，ｔｎ两种不同方式的污染，ｔｊ与ｙｊ独立。本文给出了两种污染方式下的ａ、β和污染参数的估计。  

The asymptotic stability of one-parameter methods for neutral differential equations

This paper deals with the asymptotic stability of theoretical solutions and numerical methods for systems of neutral differential equationsx=Ax(t–)+Bx(t)+Cx(t–), whereA, B, andC are constant complexN ×N matrices, and >0. A necessary and sufficient condition such that the differential equations are asymptotically stable is derived. We also focus on the numerical stability properties of adaptations of one-parameter methods. Further, we investigate carefully the characterization of the stability region.  

Normality and shared values

LetF be a family of meromorphic functions on the unit disc Δ and leta andb be distinct values. If for everyf∈F,f andf′ sharea andb on Δ, thenF is normal on Δ. The first author was supported by NNSF of China approved no. 19771038 and by the Research Institute for Mathematical Sciences, Bar-Ilan University.  

Local error estimates for radial basis function interpolation of scattered data

Introducing a suitable variational formulation for the localerror of scattered data interpolation by radial basis functions(r), the error can be bounded by a term depending on the Fouriertransform of the interpolated function f and a certain ‘Krigingfunction’, which allows a formulation as an integral involvingthe Fourier transform of . The explicit construction of locallywell-behaving admissible coefficient vectors makes the Krigingfunction bounded by some power of the local density h of datapoints. This leads to error estimates for interpolation of functionsf whose Fourier transform f is ‘dominated’ by thenonnegative Fourier transform of (x) = (||x||) in the sense . Approximation orders are arbitrarily high for interpolationwith Hardy multiquadrics, inverse multiquadrics and Gaussiankernels. This was also proven in recent papers by Madych andNelson, using a reproducing kernel Hilbert space approach andrequiring the same hypothesis as above on f, which limits thepractical applicability of the results. This work uses a differentand simpler analytic technique and allows to handle the casesof interpolation with (r) = r^s for s R, s > 1, s 2N, and(r) = r^s log r for s 2N, which are shown to have accuracy O(h^s/2)  

区间值模糊集和区间值模糊推理

本文在单位区间的一切子区间集Ⅰ[0,1]上引入t-范、t-余范、交(∩)、并(∪)等概念,在此基础上定义了区间值模糊集中的新的交并运算和区间值模糊关系的新的合成运算,得出若干有趣的性质,并将其应用于区间值模糊推理的合成规则上。  

THE SURVIVAL PROBABILITY IN FINITE TIME PERIOD IN FULLY DISCRETE RISK MODEL

The probabilities of the following events are first discussed in this paper: the insurance company survives to any fixed time k and the surplus at time k equals x≥1. The formulas for calculating such probabilities are deduced through analytical and probabilistic arguments respectively. Finally, other probability laws relating to risk are determined based on the probabilities mentioned above.  

Certificateless signature and proxy signature schemes from bilinear pairings

Due to avoiding the inherent escrow of identity-based cryptography and yet not requiring certificates to guarantee the authenticity of public keys, certificateless public key cryptography has received a significant attention. Due to various applications of bilinear pairings in cryptography, numerous pairing-based encryption schemes, signature schemes, and other cryptographic primitives have been proposed. In this paper, a new certificateless signature scheme based on bilinear pairings is presented. The signing algorithm of the proposed scheme is very simple and does not require any pairing computation. Combining our signature scheme with certificateless public key cryptography yields a complete solution of certificateless public key system. As an application of the proposed signature scheme, a certificateless proxy signature scheme is also presented. We analyze both schemes from security point of view.__________Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 95–103, January–March, 2005.