• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.247-260
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• 2015

The special form of Schur complement is extended to have a Schur's formula to obtains the explicit formula of determinant, inverse, and eigenvector formula of the doubly Leslie matrix which is the generalized forms of the Leslie matrix. It is also a generalized form of the doubly companion matrix, and the companion matrix, respectively. The doubly Leslie matrix is a nonderogatory matrix.

• The Mathematical Education
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• v.38 no.2
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• pp.189-197
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• 1999

Discrete mathematics allows students to examine and explore unique, special problem situations which were not used to solve problems by paper-and-pencil procedures or applying common formulas. The use and integration of accessible computer-related technologies such as 'Mathematics' or 'Maple' software programs enables students to explore problem situation dramatically. This study shows that it is possible to introduce computer-based discrete mathematics focused on the Leslie matrix model as modeling age-specific population growth to high school students.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.34 no.5
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• pp.423-429
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• 2001

Prediction of the variation in annual biomass was conducted for the white croaker. Argyrosomus argentatus in Korean waters using leslie Matrix, based upon fishery data for the past 21 years and biological data, We used density-independent and density-dependent Leslie Matrix models. Similar parameters were estimated from two models except that the density-dependent model was influenced by the density effect variable, q(i,t), The eigenvalue of the white croaker population for the $1984\~1995$ period was estimated to be 0.8, indicating a declining pattern of the population. The survival rate of 0-th year class was calculated to be 0.00005. Based on the schedule of the age-specific survival rate and fecundity, the future biomass and catch was predicted for various levels of fishing mortalities (F), If F was set at 0.252/yr ($F_{35x}$) or 0.368/yr ($F_{0.1}$), the biomass and catch increased, and if F was set at 0.922 ($F_{current}$), the biomass and catch decreased, The fishing mortality at equilibrium was estimated to be 0.7/yr. Finally, the management strategy of the white croaker was discussed.

• The Korean Journal of Applied Statistics
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• v.33 no.4
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• pp.421-437
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• 2020

This paper implemented a method to predict the fertility rate, mortality rate, and international migration rate using the R program, which has been widely used in recent years, that calculates population projection by substituting the results into the Leslie matrix. In particular, the generalization log gamma model for the fertility rate by Kaneko (2003), LC-ER model for mortality rate by Li et al. (2013), and functional data model for international migration rates proposed by Ramsay and Silverman (2005) and Hyndman and Booth (2008), Hyndman et al. (2013) can be directly demonstrated with R programs. Demography and bayesPop have been introduced as a representative demographic package implemented in R; however, it can be analyzed only for data uploaded to Human Mortality Database (HMD) and Human Fertility Database (HFD) with data changes and modifications requiring application of other data. In particular, in Korea, there is a limitation in applying this package because it is provided only for short-term data in HMD. This paper introduces an R program that can reflect this situation and the different patterns of low fertility, aging, migration of domestic and foreigners in Korea, and derives a population projection for the year 2117.

• Proceedings of the Korean Society of Fisheries Technology Conference
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• 2001.10a
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• pp.356-357
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• 2001

우리 나라 연근해에서 어획되는 보구치의 어획량은 1975년에서 1984년까지 증가하여 이때 가장 높은 수준을 보이다가 그 이후 감소하기 시작하여 1995년에는 급격히 감소한 것으로 나타났으며, 자원량은 1995년 아주 낮은 수준에 있는 것으로 추정되었다 (Zhang et al., 1999a). 또한 Zhang et al. (1999b)에 의해 추정 된 어획사망계수 (F)로 볼 때, 보구치 자원은 심각한 남획상태에 있는 것으로 나타났다. (중략)

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.25 no.3
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• pp.209-212
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• 2012

In this paper, we have studied on the optimal design of the optical compensation film for the TN-LCDs. To have wide viewing angle panels, several methods such as multi-domain method, optical path method, and phase compensation method have been proposed. Among these methods, this paper focused on the phase compensation method. In the phase compensation method, the phase retardation generated from the optical birefringence for the off-axis incident is compensated by using optical films with refractive anisotropy. To compensate the phase retardation of the TN-LCDs, we have proposed design concept for the biaxial optical films and analyzed the optical performance for the proposed structures. The calculation of the dynamic motion of the liquid crystals was based on the Ericksen-Leslie theory and the optical performance of the TN-LCD was calculated from the Extended Jones Matrix Method. From the results, we have confirmed that the optical characteristics of the TN-LCDs with the biaxial films have been improved considerably compared with the TN-LCDs compensated by the combination of the uniaxial films.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.24 no.4
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• pp.309-313
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• 2011

In this study, we proposed a novel electrode structure for the fringe field switching (FFS) mode LCD and performed a three-dimensional computer simulation to calculate the optical transmittance for the new structure. In the simulation Erickson-leslie equation and Berreman $4{\times}4$ matrix were used for obtaining the director distribution profiles of liquid crystal molecules and the electro-optical characteristics, respectively. Considering the complexity of the motional equation of the liquid crystal molecules, FDM (finite difference method) was used as a numerical method. From the results, We revealed that the light transmission of the newly designed pixel structure is expended to the edge of the pixel electrode. We also confirmed that the light transmittance increased more than 13% compared to that of the conventional electrode structure.