基于Leslie模型的中国人口发展预测与分析

以EXCEL为基础,拟合出2001-2005年来中国生育模式和女性死亡率的函数曲线,利用Leslie模型,预测出中国总人口将于2015年、2025年分别达到137772万人和140824万人,2018年2028年这一段是人口的一个小波峰值,2023年左右达到小峰值141024万人.老龄化程度进一步加快,到2025年全国65岁以上老年人口比重达17.2%数量达24201万人,在2041年左右65岁以上老龄人口比重达到一个高峰值26.0%,数量将达34358万人.2006年-2020年,20-29岁生育旺盛期妇女数量形成一个小高峰.     

离散人口系统渐近性与可控性的正矩阵方法

本文将离散人口系统化为一个等价的简单的控制差分模型 .运用正矩阵理论得到人口系统渐近展开与可控性 .极大的简化了已知的结论 .     

城市区域性人口承载力动态综合测度

对马尔萨斯人口增长模型进行研究,设计人口承载力发展路径和基于增长模型的隶属函数,从概率角度构建人口承载力动态综合测度模型,同时,以城市区域为研究对象,以经济作为人口承载力主导影响因素,辅之以自然、环境、资源与科技因素,构建人口承载力综合评价指标体系,多角度、多因素分析区域人口承载力,寻找人口承载短板,为人口承载力研究提供新的研究方法和视角.实证研究结论显示,研究区域人口承载力当前处于承载力强阶段,并开始向适度阶段过渡,其内部指标和子系统发展不平衡,人口系统自身发展稳定,经济和环境人口承载力强,资源和科技承载力较弱,随着区域经济的发展,在相当长一段时间内可进入适度人口阶段.     

人口控制系统的结构模型：可达矩阵在人口控制系统中的应用

本试将可达矩阵理论运用于人口系统结构分析,取得了很好的效果,章通过对影响人口系统各因素的因果关系分析,列出可达矩阵并划分等级,最后构造出人口系统结构模型。     

定常非线性人口发展方程的解及其渐近性质

一、引言 人口发展过程的数学模型是人口发展过程分析预测和定量控制的基础。关于人口发展过程的确定性连续模型,对线性人口发展系统已有不少结果。实践证明:在人类发展的某一历史阶段中,人口发展过程可以用线性方程较准确地刻画。但是线性人口发展方程忽略了社会人口与其生存环境之间的制约关系。从长期的观点来看,研究非线性人口发展模型有着重要意义     

黄冈市人口增长模型的研究

分析了1978年以来黄冈市人口发展的现状,选择黄冈市1978~2004年的总人口统计数据来建立马尔萨斯人口模型和L og istic人口模型,运用2005~2006年的总人口数据来验证模型,并对黄冈市未来8年的总人口数进行了预测.     

基于变动人口的Solow模型

本文在Solow模型框架中引入随时间变动人口增长函数，并假定人口增长率最终趋于零，证明该模型的解是渐近稳定的，收敛于零人口增长率的经典Solow模型的解。通过引入变动人口增长率，讨论人口过渡时期和人口波动对经济增长的影响，并给出数值计算结果。     

上海市人口抽样调查方法的研究和指标的估计

本文对上海市人口变动情况抽样调查作了系统的研究，得出了符合上海市市情的人口抽样调查方法，得到了人口出生率、死亡率和人口总量的估计。     

黑龙江省人口结构与区域经济可持续发展耦合问题研究

在充分查阅相关文献并结合黑龙江省具体情况的基础上,建立了人口结构系统和区域经济系统两大评价指标体系,并运用灰色关联分析方法,构建了二者的耦合度模型.在此基础上,分别在时间角度上分析了黑龙江省人口结构和区域经济可持续发展的演变规律,在空间角度上分析了黑龙江省各个地区人口结构和区域经济可持续发展分布规律.最后,针对以上分析结果,给出了相应的协调发展对策.     

在校大学生数量预测研究

高等教育规模的预测是重要的基础性工作,在校大学生数量是规模的首要因素,而决定大学生数量的要点是适龄人口和毛入学率.基于人口推算模型对未来10年的18-22岁适龄人口数进行计算,利用灰色系统模型对高等教育毛入学率进行预测,在此基础上,将毛入学率的定义式与适龄人口数推算法相结合,推导出用于计算在校大学生数量的毛入学率与适龄人口的乘积模型,计算结果表明,模型对我国2010-2020年的在校大学生数量规模具有良好的预测效果.     

Linear birth and death models and associated Laguerre and Meixner polynomials

We study birth and death processes with linear rates λ_n = n + α + c + 1, μ_{n + 1} = n + c, n 0 and μ₀ is either zero or c. The spectral measures of both processes are found using generating functions and the integral transforms of Laplace and Stieltjes. The corresponding orthogonal polynomials generalize Laguerre polynomials and the choice μ₀ = c generates the associated Laguerre polynomials of Askey and Wimp. We investigate the orthogonal polynomials in both cases and give alternate proofs of some of the results of Askey and Wimp on the associated Laguerre polynomials. We also identify the spectra of the associated Charlier and Meixner polynomials as zeros of certain transcendental equations.     

Distributive and Multiplication Modules and Rings

We study rings in which every ideal is a finitely generated multiplication right ideal.     

Affine-inscribed and affine-circumscribed polygons and polytopes

Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are proved by topological methods. In particular, it is proved that for every interior point O of a convex compact set in ℝ³, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon. It is also proved that every compact convex set in ℝ³ (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram P and contained in a cylinder with directrix P. Bibliography: 29 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 286–298. Translated by B. M. Bekker.     

Partitions and pairwise sums and products

A seven cell partition of N is constructed with the property that no infinite set has all of its pairwise sums and products in any one cell. A related Ramsey Theory question is shown to have different answers for two and three cell partitions.     

Ritz and harmonic Ritz values and the convergence of FOM and GMRES

The Ritz and harmonic Ritz values are approximate eigenvalues, which can be computed cheaply within the FOM and GMRES Krylov subspace iterative methods for solving non‐symmetric linear systems. They are also the zeros of the residual polynomials of FOM and GMRES, respectively. In this paper we show that the Walker–Zhou interpretation of GMRES enables us to formulate the relation between the harmonic Ritz values and GMRES in the same way as the relation between the Ritz values and FOM. We present an upper bound for the norm of the difference between the matrices from which the Ritz and harmonic Ritz values are computed. The differences between the Ritz and harmonic Ritz values enable us to describe the breakdown of FOM and stagnation of GMRES. Copyright © 1999 John Wiley & Sons, Ltd.     

Beliefs and beyond: affect and the teaching and learning of mathematics

The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education.