• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.162-172
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• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.541-563
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• 2012

본 원고는 한국 근대 수학교육의 아버지 이상설(李相卨, 1870-1917)이 자연과학-화학-에 기여한 내용을 다루고 있다. 이상설은 "수리(數理)"를 쓴 시기를 전후하여, 같은 시기에 붓으로 총 46쪽에 달하는 "화학계몽초(化學啓蒙抄)"를 필사하였다. 분석해 본 결과 그 원전은 영국인 H. E. Roscoe(羅斯科, 1833-1915)가 1876년 발간한 Science Primers: Chemistry를 영국인 선교사 Joseph Edkins(艾約瑟, 1823-1905)가 번역하여 1886년에 간행한 "화학계몽(化學啓蒙)"으로 "서학계몽(西學啓蒙)" 16종 가운데 하나이다.

• East Asian mathematical journal
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• 제38권5호
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• pp.617-641
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• 2022

In this study, we first present a brief overview of the Korean general insurance market. We then explore the characteristics of the loss ratios of the Korean general insurance industry and apply Markov regime-switching methodology to model the loss ratios of these insurance companies by line of business based on changes in economic regimes. This study applies a number of confirmatory tests such as Zivot-Andrews test (2002), the Chow (1960) test and the Bai and Perron (1998) to confirm the presence of structural breaks in the time series of the loss ratios by line of business. Then, we employ Markov regime-switching methodology to model these loss ratios. We find empirical evidence that the loss ratios reported by insurance companies in Korea is characterized by two distinct regimes; a regime with high volatility and a regime with low volatility, except for vehicle insurance. Our analyses suggest that macro-economic conditions have significant explanatory effect on loss ratios but the direction of effect differs based on the line of business and the regime. Unlike previous studies that have applied linear regressions or divided the samples into different periods and then apply linear regressions to model loss ratios, we argue for the application of Markov regime-switching methodology, which are able to automatically distinguish the different regimes that may be associated with the movements of loss ratios based on differing economic conditions and regulatory upheavals. This study provides a more in depth understanding of loss ratios in the general insurance industry and will be of value to insurance practitioners in modelling the loss ratios associated with their businesses to aid in their decision making. The results may also provide a basis for further studies in other markets apart from Korea as well as for shaping policy decisions related to loss ratios.

• 한국식품과학회지
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• 제24권5호
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• pp.408-413
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• 1992

신속간편법으로서 식품의 성분함량 측정에 이용되는 근적외 반사분광분석에서 문제가 되고 있는 시료의 균질도의 차이가 흡광도에 미치는 영향을 조사하고 흡광도로 나타난 수치를 수학적으로 처리함으로써 예측의 오차는 다음과 같이 감소하였다. 1. 세절도가 일정한 시료의 흡광도를 무변형, 1차 미분 및 2차 미분하여 calibration한 후 세절도가 다양한 시료의 성분을 예측한 결과 예측오차(standard error of prediction)는 수분함량에 있어서 1.478%, 0.658% 및 0.580%, 지방함량의 예측오차 0.949%, 0.637%, 및 0.527%이었으며 단백질 측정시 각각 0.514%, 0.493% 및 0.394%로 2차 미분의 예측오차가 모든 성분측정에서 가장 낮음을 알 수 있었다. 2. 세절도가 다양한 시료의 무변형, 1차 미분 및 2차 미분처리한 calibration을 이용하여 세절도가 다양한 시료의 성분을 예측한 결과 수분함량 예측오차는 각각 1.026%, 0.589% 및 0.568%, 지방함량 예측오차는 각각 0.828%, 0.639% 및 0.602% 이었으며 단백질함량 예측오차는 0.860%, 0.557% 및 0.399%로서 역시 2차 미분, 1차 미분, 무변형의 순으로 정확성이 높았다. 결과를 종합할 때 흡광도를 수학적으로 처리하여 calibration에 이용하므로서 calibration시료의 세절도에 관계없이 측정결과의 정확성은 높아졌다.

• 한국의학물리학회지:의학물리
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• 제23권1호
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• pp.42-47
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• 2012

본 연구는 최근 의공학 분야에서 중요한 영역으로 대두되고 있는 광학과 초음파의 장점을 결합한 영상 방법인 AOT (Acousto-Optical Tomography)의 수학적 모델을 제시하였다. AOT는 광학 필드를 초음파 기둥에서 변화 시켜서 초음파 기둥의 위치 정보를 이용하여 영상을 재구성하는 방법이다. AOT의 수학적 모델은 두 단계로 나뉠 수 있다. 첫 번째 단계에서는 광학 필드의 복원을 하고, 두 번째 단계에서는 획득한 광학 필드를 기반으로 확산 방정식의 역문제를 풀어 흡수함수 ${\mu}$ (absorption coefficient)를 산출한다. 본 연구에서는 두 번째 단계에 해당하는 역문제의 해를 구하기 위하여 수치해석적인 최소화 문제로 변환하고, 수치적 팬텀을 이용하여 시뮬레이션 하였다. 전통적인 기울기 하강 방법을 이용하여 역 문제 시뮬레이션의 결과를 보였다. 전변동 정규화 기반의 최소화 문제를 제안하여 기울기 하강 방법의 결과에서 보인 번짐 효과를 개선하였다.

• 한국축산식품학회지
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• 제29권3호
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• pp.349-355
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• 2009

육류의 품질예측에 가장 적합한 TTI의 조건을 분석하기 위하여, 온도-시간 이력에 따른 TTI의 색 변화와 Pseudomonas spp.의 증식수준을 수학적으로 Simulation 하였다. 일련의 kinetics 및 온도의존성 관련 함수식의 연산에는 수치해석 기법인 Euler's method를 적용하였으며, MS Excel VBA기반 컴퓨터 프로그램을 작성하여 계산하였다. 쇠고기의 저장 유통에 대한 몇 가지 온도-시간 경로에 대하여, 저장 시간에 따른 TTI 색 함수 및 $T_{eff}$(해당 온도-시간 이력에 대한 일종의 대표적 온도 값)의 변화를 simulation 하였다. 온도의존성(활성화에너지)가 서로 다른 TTI에 대하여 Simulation한 결과, 먼저 Pseudomonas 증식의 활성화 에너지와 같은 활성화에너지를 갖는 TTI의 경우 같은 색에 대하여 온도-시간 이력에 상관없이 항상 같은 증식수준을 나타냈다. 반면에 활성화에너지가 서로 다른 경우 TTI가 같은 색에 대하여 온도-시간 이력에 따라 서로 다른 증식수준을 나타냈다. 결론적으로 육류의 특정 품질에 대한 적합한 TTI는 서로 온도의존성이 일치할 때 가장 정확한 예측 값을 얻을 수 있음을 알 수 있었다.

• Journal of the Korean Data and Information Science Society
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• 제17권3호
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• pp.889-904
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• 2006

Our purpose is to ascertain, if possible, whether atomic bomb survivors with cataracts and epilation were more radiosensitive than those survivors with cataracts but without epilation. A major ophthalmologic survey was conducted in Hiroshima and Nagasaki in 1963-64. At that time, 2125 individuals were examined. Among these individuals, estimated eye organ doses, based on the DS86 dosimetry system, and information on the occurrence of epilation within the first 60 days following the bombings are available on 1742. In the analysis of these data we have assumed that each individual represents a sample of one from a binomial distribution, and that the occurrence of cataracts and epilation are independent biological phenomena. We got following results. The threshold for cataract induction and its 95% confidence limits have been estimated from data on the occurrence of cataract and epilation. Among the 1742 study subjects, 40 had both cataracts and severe epilation. The estimated threshold based on these cases is 0.98 sievert(Sv), with 95% lower and upper confidence bounds of 0.72, and 1.32 Sv, respectively, and is highly statistically significant. Among the 27 cases of cataracts where severe epilation was not reported, the estimated threshold is 1.74 Sv with 95% lower and upper confidence bounds of 1.21 Sv, and "not estimable". The difference between these two estimates is not statistically significant although the effect of dose is highly significant in both instances. The potential importance of biases in the DS86 dose estimates is discussed. The difference between the threshold estimated from cataract cases with epilation and that from cases without epilation is not statistically significant at the 5% or 10% level, and thus affords no support for the notion of increased radiosensitivity.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.825-834
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• 2013

In this paper, we study the Yeh convolution of white noise functionals. We first introduce the notion of Yeh convolution of test white noise functionals and prove a dual property of the Yeh convolution. By applying the dual object of the Yeh convolution, we study the Yeh convolution of generalized white noise functionals, which is a non-trivial extension. Finally, we study relations between the Yeh convolution and Fourier-Gauss, Fourier-Mehler transform.

• Journal of Electrochemical Science and Technology
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• 제8권3호
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• pp.244-249
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• 2017

This paper presents the results of an investigation into the isoamperic point of cyclic voltammograms, which is defined as the singular point where the voltammograms of various scan rates converge. The origin of the unique point is first considered from a theoretical perspective by formulating the voltammetric curves as a system of linear equations, the solution of which indicates that a trivial solution is only available at the potential at which the net current is zero during the reverse potential scan. In addition, by way of a mathematical formulation, it was also shown that the isoamperic point is dependent on the switching potential of the potential scanning. To validate these findings, theoretical and practical cyclic voltammmograms were studied using finite-element based digital simulations and 3-electrode cell experiments. The new understanding of the nature of the isoamperic point provides an opportunity to measure the charge transfer effects without the influence of the mass transfer effects when determining the thermodynamic and kinetic characteristics of a faradaic system.

• Journal of Mechanical Science and Technology
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• 제14권7호
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• pp.722-729
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• 2000

The goal of this paper is to describe an advanced method of a crack detection: a new way to localize position and to estimate depth of a crack on rotating shaft. As a first step, the shaft is physically modelled with a finite element method and the dynamic mathematical model is derived using the Hamilton principle; thus, the system is represented by various subsystems. The equations of motion of the shaft with a crack are established by adapting the local stiffness change through breathing and gaping from the crack to an undamaged shaft. This is the reference system for the given system. Based on a model for transient behavior induced from vibration measured at the bearings, a nonlinear state observer is designed to detect cracks on the shaft. This is the elementary NL-observer (Beo). Using the observer, an Estimator (Observer Bank) is established and arranged at the certain position on the shaft. When a crack position is localized, the procedure for estimating of the depth is engaged.