On a result of Ozawa concerning uniqueness of meromorphic functions

In this paper we prove a uniqueness theorem for meromorphic functions sharing three values with some weight which improves some known results.     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

Ergodic properties and thermodynamic behavior of elementary reversible cellular automata. I. Basic properties

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.     

An Algebraic Method for the Exact Solution of the Partition Function of the Canonical Ensemble in Nuclear Multifragmentation

We propose a unified method for deducing recursive relations for the canonical partition function of a system of noninteracting particles with charge conservation if the particles follow the Bose–Einstein, Fermi–Dirac, or Maxwell–Boltzmann statistics or parastatistics. For all these types of statistics, we find recursive relations for the partition function of a new statistical model of nuclear multifragmentation with electric charge and baryon number conservation, accounting for the internal degrees of freedom of the nuclear fragments.     

A note on strong β-I-sets and strongly β-I-continuous functions

Summary In [6], we introduced and investigated the notions of strong β-I-open sets and strong β-I-continuous functions in ideal topological spaces. In this paper, we investigate further their important properties.     

Local Feasible QP-Free Algorithms for the Constrained Minimization of SC1 Functions

We consider the problem of minimizing an SC¹ function subject to inequality constraints. We propose a local algorithm whose distinguishing features are that: (a) a fast convergence rate is achieved under reasonable assumptions that do not include strict complementarity at the solution; (b) the solution of only linear systems is required at each iteration; (c) all the points generated are feasible. After analyzing a basic Newton algorithm, we propose some variants aimed at reducing the computational costs and, in particular, we consider a quasi-Newton version of the algorithm.     

Tribute to Endre Csáki and Pál Révész

Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979. The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.     

On the spectral norm of algebraic numbers

In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $.     

带有回报计划的动态客户关系管理模型及实验应用分析

在客户最大化效用及公司最大化CLV的动态环境下。对所提的带有回报计划的动态客户关系管理模型用于某超市的客户数据库中，发现模型的结果对这类客户是适用的。并给出了不同的客户状态空间对应的有效营销组合策略。结果表明：合适的回报计划可以促进客户的购买、提高公司的利润及缓解价格竞争。回报极限应该比客户的平均购买水平偏高，回报率应该与回报极限的改变方向一致。计划的时间范围应定在一年左右比较合适。对于累积购买水平较高的客户一般不邮寄商品信息。在回报计划的初期与末期不用打折。中期对那些购买次数很少的客户可以实行相应的降价策略。