涉及分担函数与分担值的正规定则

研究了涉及分担函数的正规定则,证明了:设F为定义在区域D内的一族亚纯函数,n,k是两个正整数,满足n≥k+3.如果对于F中任意一个函数f,(fn)(k)-z至多有一个不同的零点,则F在D内正规.此结论说明在(fn)(k)具有不动点的情形下,1990年杨乐在Notre Dame大学举行的学术会议上提出的断言仍然成立.     

The structure of stratified systems and the structure of mobility: A first approximation to a structural theory of vertical mobility

This essay summarizes an inquiry that explores relations between the structure of stratified systems and the processes of vertical mobility. The inquiry considers economic stratification (the distribution of wealth) and is directed to determining whether the structural properties of stratification systems are sufficient to generate basic patterns in vertical mobility observed in empirical research, especially, the rank‐distance effect. In particular, the question is whether these patterns can be generated even if movement is constrained by nothing more than the size of the population over which wealth is distributed and the total amount of wealth to be distributed. Our results show that the rank‐distance effect emerges even under these minimal assumptions and, further, that rates and distances of vertical mobility are closely related to changes in these boundary parameters of a stratified system. The basic theory developed to relate structure and mobility provides results that are highly consistent with many empirical observations. It also challenges existing claims concerning the nature of the mechanisms determining the relative status immobility of most people in large scale systems. The theory implies that the way in which system structure constrains opportunity for movement is, by itself, sufficient to produce this result and others commonly observed.     

Shared Secret Reconstruction

In this paper we consider the secret reconstruction problem in a secret sharing scheme. We emphasize that a shared secret should be reconstructed in a fair way, i.e., all involved participants should have the same chance to be able to reconstruct the shared secret. We propose and analyze several methods to achieve such a fair reconstruction of shared secrets.     

Shared values and normality

This paper investigates the relationship between the normality and the shared values for a meromorphic function on the unit disc Δ. Based on Marty’s normality criterion and through a detailed analysis of the meromorphic functions, it is shown that if for every f ∈ , f and f ^(k) share a and b on Δ and the zeros of f(z) − a are of multiplicity k ⩾ 3, then is normal on Δ, where is a family of meromorphic functions on the unit disc Δ, and a and b are distinct values. Selected from Journal of East China Normal University (Natural Science), 2003, 4: 12–18. This work was supported by the National Natural Science Foundation of China under grant number 10271122 and by Shanghai City Foundation for selected academic research     

分担值和正规族

设F是单位圆盘△上的亚纯函数族,a是一个非零的有穷复数,如果f∈F,满足1)f的零点是重级的; 2)f和f'IM分担a, 则F在△上正规.相应于正规函数的结果也得到了证明.     

涉及分担函数的正规定则

设k为正整数,M为正数;F为区域D内的亚纯函数族,且其零点重级至少为k;h为D内的亚纯函数(h(z)≠0,∞),且h(z)的极点重级至多为k.若对任意给定的函数f∈F,f与f~((k))分担0,且f~((k))(z)-h(z)=0?|f(z)|≥M,则F在D内正规.     

分担集合与正规族

This paper deals with the problem of normal families concerning share sets. Moreover, the examples show that the conditions of theorem are necessary.     

Sharp bounds on mobility of the Lyapunov exponents of linear Hamiltonian systems under small average perturbations

Sharp bounds on mobility of the Lyapunov exponents of linear Hamiltonian systems are found for arbitrarily small average linear perturbations of the coefficients, with the help of the Millionshchikov turning method. The stabilizability and destabilizability of any solution by the indicated perturbations in the class of linear Hamiltonian systems are proved.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 14, pp. 125–139, 1989.     

分担值与正规族

本文主要证明了如下的结论:设■为定义在区域D内的一族亚纯函数,a_1, a_2和a_3分别为三个互异的有限复数,如果对于任意的f∈■,有f和f′分担集合S={a_1,a_2,a_3},那么■在D内正．     

正规族与分担函数

设a(≠0)和b(■0)是区域D上的两个全纯函数,并且在函数b的零点处a'不取0.■={f}是区域D内的一族亚纯函数,若每个f的零点都是重级的,且满足f=af'=b,则■在区域D内正规.举例说明结论成立的条件是必不可少的.     

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.     

Normal Functions Concerning Shared Values

In this paper we discuss normal functions concerning shared values. We obtain the follow result. Let F be a family of meromorphic functions in the unit disc A, and a be a nonzero finite complex number. If for any f ∈F, the zeros of f are of multiplicity, f and f′ share a, then there exists a positive number M such that for any f∈F1（1-｜z｜^2） ｜f′（z）｜/1＋｜f（z）｜^2≤M.     

Monotone mobility matrices

The transition matrix of a discrete Markov chain is called monotone if each row stochastically dominates the row above it. Monotonicity is an ideal assumption to impose on a Markov chain model of mobility. Monotonicity is behaviorally weak yet mathematically strong. It is behaviorally weak in the sense that it is theoretically plausible and is empirically supported. It is mathematically strong in the sense that monotone Markov chains have a number of convenient mathematical properties. This paper reviews the convenient properties and applies the monotonicity concept to immobility measurement.     

涉及分担值的正规定则

设F是区域D上的一个亚纯函数族,k(≥2)是一个正整数,b是一个非零复数,M是一个正数.若对任意给定的f∈F,f的零点重数至少为k,且f(z)=0=|f~((k))(z)|≤M.如果对任意给定的函数f,g∈F,L(f)与L(g)的零点都为重零点,且L(f)与L(g)在区域D内分担b,则F在区域D内正规.     

与分担值相关的正规族

设F是区域D上的一族亚纯函数,a,b,c是有穷复数,a≠b,c≠0.本文证明:如果对任意的f∈F,f的零点重级至少是k,并且这里我们记(?)Ef（a）={z∈D:f（z）=a},则F在D上正规.同时我们将举例说明对f的零点重级条件的限制是必要的.     

Indirect measurement of mobility trends: The case of male intragenerational mobility

Much of what has been written about trend in mobility is based on the use of indirect standardization to infer changes in unobserved rates of upward mobility. This method, which consists of interpreting the differences between actual and hypothetical destination percentages (d values), has not been critically examined. Here we investigate two procedures for applying indirect standardization. The first procedure is modeled after previous use in the literature. Applied to data on one‐year male intragenerational mobility, this procedure erroneously concludes that there was an increase in the overall probability of upward mobility. The second procedure, which is based on the decomposition of d values into weighted sums of changes in aggregate mobility rates, produces results that are generally valid though diffuse. For two reasons, previous use of indirect standardization has been biased toward overstating increases in upward mobility: d values are not sensitive to upward shift in origin distribution, and d values do not distinguish between increase in upward mobility and reductions in downward mobility.     

Markov models of occupational mobility: Theoretical development and empirical support. Part 2: Continuously operative job systems

This paper, consisting of two parts, presents an analysis of the current state of Markov model building for intragenerational occupational mobility. Part 1 examined models of careers; Part 2 analyzes models of continuously operative job systems. In Part 2 we find considerable predictive power for the simple MC model of personnel flows and the job vacancy chain model. Major analytical work has extended in two primary directions: the theoretical conceptualization of job vacancies to further explicate the underlying causal structure of mobility and the use of control theory to shift the focus to manpower decision making and policy formulation. Moreover, the diversity of job systems in which the models have been tested points to their general applicability.     

Shared value in a finite-dimensional Banach manifold

Sufficient conditions are given to assert that two C¹-mappings share only one value in a connected compact Banach manifold modelled over ?ⁿ. The proof of the result, which is based upon continuation methods, is constructive.     

分担集合的亚纯函数的正规性*

本文研究了亚纯函数及其 k 阶导数分担两个不同集合的亚纯函数族的正规性问题.证明了如下结论: 设 F 是平面区域 D上的亚纯函数族, 其中函数的零点重数至少为 k+1. 设S₁, S₂是两个集合,且|S₁|=m, |S₂|=n, S₂ ≠ 0, 这里m, n是正整数. 如果任意f(z) ∈ F,满足f(z) ∈ S₁?f^(k)(z) ∈ S₂, z ∈ D, 则 F 在区域 D 上正规.本文的研究结果是对刘晓俊和庞学诚[刘晓俊, 庞学诚. 分担值与正规族 [J].数学学报(中文版),2007, 50(2):409--412] 2007年研究结果的改进.