• Management Science and Financial Engineering
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• v.16 no.3
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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.

• Journal for History of Mathematics
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• v.24 no.2
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• pp.47-59
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• 2011

Various mathematical models have been widely studied recently in both fields of mathematics and ecology since they help us understand the dynamical process of population changes in biological species living in a certain habitat and give useful predictions. The world population model proposed by Malthus, a British economist, in his work 'An Essay on the Principle of Population' published in the period of 1789~1826 is one of the early mathematical models on population changes. Malthus' models and the carrying capacity models of Verhulst in 1845 were based on exponential type functions. The independent research field of mathematical ecology has been started from Lotka's works in 1920's. Since then various different mathematical models has been proposed and examined. This article mainly deals with single species population change models expressed in terms of ordinary differential equations.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.33 no.3
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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

• Journal of the Korean Society of Safety
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• v.33 no.4
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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.

• Development and Reproduction
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• v.15 no.1
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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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• v.26 no.1
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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.

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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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.

• Journal for History of Mathematics
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• v.33 no.3
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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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• v.17 no.6
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• pp.791-801
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• 2010

This study reviews the concept of disclosure, disclosure risks, and uniqueness. The number of uniqueness in the population is of great importance in evaluating the disclosure risk of micro data files. We approach this problem by considering some basic superpopulation models including the Multinomial-Dirichlet model, the Poisson- Gamma model of Bethlehem et al. (1990) and Takemura (1997), and the Modified Multinomial-Dirichlet model. We decided the critical population size of each superpopulation model for four different superpopulation models.

• Journal for History of Mathematics
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• v.29 no.6
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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.