异质群体定性研究中的广义函数

IF 1.4 3区社会学 Q3 DEMOGRAPHY

Mathematical Population Studies Pub Date : 2019-02-22 DOI:10.1080/08898480.2018.1553395

N. Hritonenko, Y. Yatsenko, A. Boranbayev

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引用次数: 5

摘要

摘要非光滑函数空间的解，包括广义函数和测度，经常出现在最优控制理论中，但在应用中被避免。然而，它们有助于在技术进步的情况下找到新老资本设备投资的最佳分配。相应的经济问题涉及年龄结构人口的线性Lotka-McKendrik模型中的最优控制。最优解不存在于正规函数类中，因此，使用广义函数来构造解。资本和投资的最佳年限分布包括狄拉克函数，并被解释为对特定年限设备的瞬时投资。数值模拟完成了动力学的演示。

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Generalized functions in the qualitative study of heterogeneous populations

ABSTRACT Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.

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来源期刊

Mathematical Population Studies 数学-数学跨学科应用

CiteScore

3.20

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Population Studies publishes carefully selected research papers in the mathematical and statistical study of populations. The journal is strongly interdisciplinary and invites contributions by mathematicians, demographers, (bio)statisticians, sociologists, economists, biologists, epidemiologists, actuaries, geographers, and others who are interested in the mathematical formulation of population-related questions. The scope covers both theoretical and empirical work. Manuscripts should be sent to Manuscript central for review. The editor-in-chief has final say on the suitability for publication.