• Management Science and Financial Engineering
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• 제16권3호
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• pp.49-70
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• 2010

Customer population management models can be classified into three categories: the first category includes the models that analyze the customer population at cohort level; the second one deals with the customer population at aggregate level; the third one has interest in the interactions among the customer populations in the competitive market. Our study proposes a model that can analyze the dynamics of customer population in consumer-durables market at aggregate level. The dynamics of customer population includes the retention curves from the purchase or at a specific duration time, the duration time expectancy at a specific duration time, and customer population growth or decline including net replacement rate, intrinsic rate of increase, and the generation time of customer population. For this study, we adopt mathematical ecology models, redefine them, and restructure interdisciplinary models to analyze the dynamics of customer population at aggregate level. We use the data of previous research on dynamic customer population management at cohort level to compare its results with those of ours and to demonstrate the useful analytical effects which the precious research cannot provide for marketers.

• 한국수학사학회지
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• 제24권2호
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• pp.47-59
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• 2011

일정 영역에 서식하는 생물 종의 개체 수가 변화하는 역학적 과정을 이해하고 실질적인 예측을 하는데 도움을 주는 여러가지 수학적 모델이 현재 수학과 생태학 분야에서 활발하게 연구되고 있다. 영국의 경제학자 Malthus가 1798년부터 시작하여 1826년까지 출간한 An Essay on the Principle of Population에서 제안했던 세계인구 변화 모델과 1845년 Verhulst의 한계수용모델은 개체 수 변화에 대한 초기 수학적 모델로서 지수적 형태에 기초한 것이었다. 수리생물학으로 불리는 학문분야는 1920년경 Lotka의 연구에서 본격적으로 시작되었다고 할 수 있다. 이때부터 여러 가지 다양한 수학적 모델들이 제안되어지고 검증되어져 왔다. 이 논문에서는 주로 상미분방정식(ordinary differential equations)으로 표현되는 단일 생물종에 대한 개체 수 변화모델들을 살펴본다.

• 한국측량학회지
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• 제33권3호
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• pp.145-153
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• 2015

This study aims to accurately estimate population distribution more specifically than administrative unites using a RK (Regression-Kriging) model. The RK model is the areal interpolation technique that involves linear regression and the Kriging model. In order to estimate a population’s distribution using a sample region, four different models were used, namely; a regression model, RK model, OK (Ordinary Kriging) model and CK (Co-Kriging) model. The results were then compared with each other. Evaluation of the accuracy and validity of evaluation analysis results were the basis RMSE (Root Mean Square Error), MAE (Mean Absolute Error), G statistic and correlation coefficient (ρ). In the sample regions, every statistic value of the RK model showed better results than other models. The results of this comparative study will be useful to estimate a population distribution of the metropolitan areas with high population density

• 한국안전학회지
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• 제33권4호
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• pp.98-104
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• 2018

Macroscopic accident analyses have been conducted to incorporate transportation safety into long-term transportation planning. In macro-level accident prediction model, exposure variable(e.g. a settled population) have been used as fundamental explanatory variable under the concept that each trip will be subjected to a probable risk of accident. However, a settled population may be embedded error by exclusion of active population concept. The objective of this research study is to develop macro-level accident prediction model using floating population variable(concept of including a settled population and active population) collected from mobile phone data. The concept of accident prediction models is introduced utilizing exposure variable as explanatory variable in a generalized linear regression with assumption of a negative binomial error structure. The goodness of fit of model using floating population variable is compared with that of the each models using population and the number of household variables. Also, log transformation models are additionally developed to improve the goodness of fit. The results show that the log transformation model using floating population variable is useful for capturing the relationships between accident and exposure variable and generally perform better than the models using other existing exposure variables. The developed model using floating population variable can be used to guide transportation safety policy decision makers to allocate resources more efficiently for the regions(or zones) with higher risk and improve urban transportation safety in transportation planning step.

• 한국발생생물학회지:발생과생식
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• 제15권1호
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• pp.9-15
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• 2011

The population growth and reproduction of Tetrahymena pyriformis were studied under shaken (aerobic) and unshaken (anaerobic) conditions by applying the growth models, exponential and logistic growth models and the population growth of Tetrahymena was showed the logistic growth model under both, shaken and unshaken conditions and also, the more oxygenated samples had greater population size (N) and three times faster growth rate (r) than less oxygenated samples during incubation periods.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.83-92
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• 2021

This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.

• 천문학회지
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• 제29권spc1호
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• pp.49-51
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• 1996

New population synthesis models, with the effects of metallicity spread and the horizontal-branch (HB) morphology, provide a way to break the well-known age-metallicity degeneracy in the analysis of the integrated light of elliptical galaxies. Our models suggest that the far- UV radiation of these systems is dominated by a minority population of metal-poor, hot HB stars and their post-HB progeny, while the optical radiation is dominated by a metal-rich population. The systematic variation of UV upturn depends on the contribution from metal-poor, hot HB stars and their post-HB progeny, which in turn depends on the ages of old stellar populations in galaxies. Our result implies a prolonged epoch of galaxy formation, in the sense that more massive galaxies (in denser environments) formed first. Our models also suggest that the strenghth of H$\beta$ index is strongly affected by HB stars, and hence previous age estimation without detailed modeling of the HB would underestimate the ages of ellipticals by $\~$7 Gyr.

• 한국수학사학회지
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• 제33권3호
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• pp.167-177
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• 2020

Cooperative behavior may seem contrary to the notion of natural selection and adaptation, but is widely observed in nature, from the genetic level to the organism. The origin and persistence of cooperative behavior has long been a mystery to scientists studying evolution and ecology. One of the important research topics in the field of evolutionary ecology and behavioral ecology is to find out why cooperation is maintained over time. In this paper we take a historical overview of mathematical models representing cooperative relationships from the perspective of mathematical biology, which studies population dynamics between interacting biological groups, and analyze the mathematical characteristics and meanings of these cooperative models.

• Communications for Statistical Applications and Methods
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• 제17권6호
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• pp.791-801
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• 2010

마이크로데이터 제공시 발생될 수 있는 노출(disclosure)과 노출위험을 나타내는데 사용되는 측도인 유일성(uniqueness) 그리고 모집단 유일성의 개수를 추정하기 위한 초모집단 모형으로 Multinomial-Dirichlet 모형, Takemura의 Poisson-Gamma 모형, Modified Multinomial-Dirichlet 모형, Bethlehem의 Poisson-Gamma 모형을 다룬다. 이 4개의 모형에 대해 마이크로데이터 제공에 따른 임계모집단 크기(critical population size)를 결정한다.

• 한국수학사학회지
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• 제29권6호
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• pp.353-363
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• 2016

In mathematical population ecology which is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats, PDE models have been studied in many aspects and found to have different properties from the classical ODE models. And different approaches to PDE type models in mathematical biology are still being tried currently. This article investigate various forms to express diffusion effects and review the history of PDE models involving diffusion terms in mathematical ecology. Semi-linear systems representing the spatial movements of each individual as random simple diffusion and quasi-linear systems describing more complex diffusions reflecting interspecific interactions are studied. Also it introduce a few of important problems to be solved in this field.