• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.37.3-38
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• 2017

우리나라의 천문 관측의 기록의 역사는 삼국시대 이전 선사시대까지 거슬러 올라간다. 선사시대에는 천문 현상을 바위나 건축 유물에 기록을 남기고 역사를 기록하기 시작한 이후에는 일반 역사 기록 속에 항상 함께 기록하고 있다. 특히 동양은 역사기록 자체가 인간이 남긴 자취뿐만 아니라 하늘과 땅에 일어나는 다양한 자연 현상도 함께 동시에 남겼다. 고대로부터 인간은 하늘과 땅과 항상 유기적인 관계를 갖는다고 믿었기 때문이다. 우리나라는 정사로서 가장 오래된 역사 기록인 삼국사기와 삼국유사에 일식, 혜성 출현, 별똥과 유성우, 달과 행성 운행, 초신성 관측 등 250회 이상의 천문 기록이 나타나며 대부분 실제로 일어났던 사실을 그대로 기록하고 있다. 그 후 고려사와 조선왕조실록에는 이루 헤아릴 수 없을 정도로 많은 천문 기록을 남기고 있다. 이러한 천문 기록뿐만 아니라 일찍부터 중국으로부터 역법을 도입하여 천체 운행을 이용하여 우리 생활에 필요한 시각법을 사용하고 달력을 제작하였다. 특히 달과 태양의 운행 원리를 파악하여 일식과 월식을 직접 추산하였다. 역법의 운용은 천체 운행의 원리를 이해하고 수학을 발전시키는데 큰 역할을 하였다. 이러한 천문 관측과 정확한 시각 체계를 유지하고 정밀한 역법을 사용하기 위해서는 끊임없이 천체를 정밀하게 관측할 필요성이 있다. 이를 위해 다양한 천문 관측기기를 개발하고 제작하였다. 천문 의기는 천체의 위치를 측정하고 천체의 운행을 이용하여 시각 체계를 유지 관리를 위해 필수불가결한 기기이다. 우리나라 천문학 발달의 네 가지 축인 천문(天文), 역법(曆法), 의상(儀象), 구루(晷漏)등은 조선 초기 세종시대 완성을 보게 되었다. 이는 단일 왕조가 이룬 업적으로 다른 문화권에서 볼 수 없을 정도의 우수한 과학 기술의 유산이다. 특히 칠정산내편과 외편의 완성은 중국의 역법에서 벗어나 독자적인 역법을 완성하려는 시도였다. 이 모든 것은 당시 이를 주도하던 세종대왕의 지도력과 천문학과 수학에 뛰어난 천문학자가 이룩한 업적이다. 그 후 조선 중기로 접어들면서 쇠퇴하다가 임진왜란과 병자호란을 겪으면서 거의 모든 과학기술의 유산이 파괴되거나 유실되었다. 조선 현종 이후에 세종시대의 유산을 복원하려는 노력 중에 중국을 통하여 서양의 천문학을 도입하게 되었다. 중국에 들어와 있던 서양 선교사들이 주도하여 중국의 역법 체계를 바꾸었다. 즉, 일식과 월식의 예측력이 뛰어난 시헌력을 만들어 사용하기 시작했다. 시헌력에는 서양의 대수학과 기하학을 이용한 다양한 수학적 기법이 사용되었다. 조선 후기에 이 시헌력을 익히기 위한 노력을 하는 과정에서 서양의 수학과 기하학을 접하게 되고 새로운 우주 체계를 도입하게 되었다. 특히 서양의 천문도와 지도 제작에 기하학의 투사법이 사용되어 복잡한 대수학적 계산을 단순화시켜 활용하였다. 조선 후기에 전문 수학자뿐만 아니라 많은 유학자들도 서양의 수학과 기하학에 깊은 관심을 갖고 연구하였다. 고천문학 전체를 조망해 볼 때 핵심은 현대의 천체물리학이 아니라 위치천문학이다. 따라서 고천문학을 연구하는데 필수적인 요소가 지구의 자전과 공전 운동에 의해서 일어나는 현상과 세차운동에 의한 효과를 정확하게 이해하고 있어야 한다. 그중에서도 구면천문학과 천체역학에 대한 원리를 알고 있는 상태에서 접근해야 한다. 고천문학의 중심인 천문(天文), 역법(曆法), 의상(儀象), 구루(晷漏) 등의 내용은 이러한 위치천문학이 그 기본 골격을 이루고 있다. 예를 들어 고려사의 천문 현상을 모아 놓은 천문지(天文志)와 일식과 월식 계산 원리가 들어있는 역지(曆志)를 연구하기 위해서는 위치천문학의 기본 개념 없이는 연구하는데 한계가 있다. 인문학을 전공하는 학자가 고천문을 연구하는데 가장 큰 걸림돌이 되는 점이 위치 천문학의 기본 개념 없이 접근하는 것이다. 심지어 조선시대 유학자들조차 저술한 많은 천문 관련 기록을 보면 상당부분 천체 운행 원리를 모르고 혼란스럽게 기록된 내용이 적지 않다. 우리나라 수학사를 연구할 경우 방정식 해법, 보간법, 삼각법, 일반 기하 원리에 대한 것을 연구하는데 큰 문제가 없다. 그러나 천문 현상이나 천문 의기 제작에 사용되는 수학은 천문 현상에 대한 원리를 모르면 접근하기 어렵게 된다. 수학사를 하더라고 기본적인 위치 천문학의 기본개념을 이해하고 있어야 폭 넓은 수학사 연구에 성과를 거둘 수 있다. 의외로 천문 현상 추산을 위해 사용되는 수학이나 기하학 원리가 수학사 연구에 중요한 요소가 된다. 더구나 한문으로 기록된 천문 내용을 한문 해독이 능숙한 학자라 하더라도 내용을 모르고 번역하면 도무지 무슨 내용인지 알아볼 수 없는 경우가 많다. 그래서 한문으로 된 천문 현상 기록이나 역법 관련 기록의 번역 내용 중에 많은 오역을 발견하게 된다. 문제는 한번 오역을 해 놓으면 몇 십 년이고 그대로 그 내용을 무비판적으로 인용하게 되고 사실로서 인정하는 오류를 범하게 된다. 이 때문에 우리 선조들이 남긴 고천문 관련 기록에 관한 이해는 우리 현대 천문학자의 역할이 대단히 크다.

• Journal of Korean Ophthalmic Optics Society
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• v.7 no.2
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• pp.1-11
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• 2002

A mathematical model is proposed to analyze the force; acting on the hard contact lens fitted on the cornea. The model incorporates the nonlinear equations and their numerical solution program, based on the formulations of surface tension force arising from the capillary action in the tear-film layer between the lens and cornea. The model simulates how the adhesion between lens and cornea varies according to the base curves and diameters of the lenses. When the spherical lens is fitted on the spherical cornea it is to rotate downward due to the weight of lens itself until it reaches an equilibrium position along the cornea where the counter(upward) moment caused by net force between the upper and lower portion of the periphery of lens. It is found that both the adhesion and displacement of lens along the cornea, where the gravity of lens balances the capillary-induced upward force, increases rapidly as the base curve of lens increases, i.e., as the lens gets flatter, while the increase in the diameter of lenses has resulted in the less increase in the rotation and adhesion. With the base curve and diameters of lenses being remained constant the increase in surface tension of tear film yields the increase in the adhesion between the cornea and lens while the initial rotation of lens is inversely proportional to the surface tension of the tear film.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.197-206
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• 2003

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid and hollow hemispherical shells of revolution of arbitrary wall thickness having arbitrary constraints on their boundaries. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components μ/sub Φ/, μ/sub z/, and μ/sub θ/ in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the Φ and z directions. Potential (strain) and kinetic energies of the hemispherical shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Novel numerical results are presented for solid and hollow hemispheres with linear thickness variation. The effect on frequencies of a small axial conical hole is also discussed. Comparisons are made for the frequencies of completely free, thick hemispherical shells with uniform thickness from the present 3-D Ritz solutions and other 3-D finite element ones.

• Journal of Korea Water Resources Association
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• v.42 no.8
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• pp.619-629
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• 2009

The objective of this study is to estimate bed-resistance in gravel-bed rivers using the equivalent roughness height($k_s$). We calculated the friction factor(f) with the measured data from 8 domestic gravel-bed rivers and investigated the size distributions of the bed materials. The averaged $k_s$ in each cross-section, which is determined under the hypothesis that the vertical velocity distribution follows the logarithmic law, is compared with the reach $k_s$ which is calculated with the cumulative grain diameter distribution curve of bed materials. Moreover, the applicability of existing formulae, such as Strickler type equations, is examined by comparing with Manning's n value converted from the $k_s$. According to the results, the reach $k_s$ proves to be a good indicator of representative characteristic of bed materials in a reach, and the Manning's n based on the reach $k_s$ is appropriate for practical estimation of the bed-resistance, for RMS errors between calculated and measured Manning's n is less than 0.003. The correlation between the $k_s$ and specified bed-material size($D_i$) is very low, so it is difficult to select a proper one among the existing empirical equations.

• Membrane Journal
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• v.20 no.1
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• pp.29-39
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• 2010

This study focuses on the modeling of DMFC to predict the characteristics and to improve its performance. This modeling requires deep understanding of the design and operating parameters that influence on the cell potential. Furthermore, the knowledge with reference to electrochemistry, transport phenomena and fluid dynamics should be employed for the duration of mathematical description of the given process. Considering the fact that MEA is the nucleus of DMFC, special attention was made to the development of mathematical model of MEA. Multiscale modeling is comprised of process modeling as well as a computational fluid dynamics (CFD) modeling. The CFD packages and process simulation tools are used in simulating the steady-state process. The process simulation tool calculates theelectrochemical kinetics as well as the change of fractions, and at the same time, CFD calculates various balance equations. The integrated simulation with multiscal modeling explains experimental observations of transparent DMFC.

• Korean Journal of Soil Science and Fertilizer
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• v.34 no.4
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• pp.245-254
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• 2001

Effects of soil moisture and temperature on the degradation rate of imazamethabenz were studied in two soils, a Declo sandy loam soil with 1.5% organic matter and pH of 8.0, and a Pancheri silt loam soil with 2.1% organic matter and pH of 7.7. Soils were incubated for 12 weeks under controlled conditions. Treatments were a factorial arrangements with combinations of three soil moistures (45, 75, 100% of field capacity) and two soil temperatures (20, 30C). Imazamethabenz degradation followed first-order kinetics for all soil moisture-soil temperature combinations. Imazamethabenz degradation rate was proportional to increase of soil moisture and temperature. Soil moisture effect on imazamethabenz degradation was greater when soil moisture was increased from 45 to 75% of field capacity (half-life decreased 2.6 fold) than when moisture increased from 75 to 100% of field capacity (half-life decreased 1.2 fold). Imazamethabenz degradation occurred more rapidly in the Pancheri silt loam than the Declo sandy loam soil. Formation of imazamethabenz acid from imazamethabenz followed a quadratic trend for most soil-moisture-soil temperature combinations. Imazamethabenz acid formation initially increased at earlier stages, but later gradually decreased. In most cases, increasing soil moisture and temperature appeared to accelerate it's acid breakdown to other metabolites.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.7
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• pp.607-615
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• 2020

The purpose of this study was to analyze the research status and trends related to the industrial mathematics based on text mining techniques with a sample of 4910 papers collected in the SIAM Journal on Applied Mathematics from 1970 to 2019. The R program was used to collect titles, abstracts, and key words from the papers and to analyze topic modeling techniques based on LDA algorithm. As a result of the coherence score on the collected papers, 20 topics were determined optimally using the Gibbs sampling methods. The main results were as follows. First, studies on industrial mathematics were conducted in a variety of mathematics fields, including computational mathematics, geometry, mathematical modeling, topology, discrete mathematics, probability and statistics, with a focus on analysis and algebra. Second, 5 hot topics (mathematical biology, nonlinear partial differential equation, discrete mathematics, statistics, topology) and 1 cold topic (probability theory) were found based on time series regression analysis. Third, among the fields that were not reflected in the 2015 revised mathematics curriculum, numeral system, matrix, vector in space, and complex numbers were extracted as the contents to be covered in the high school mathematical curriculum. Finally, this study suggested strategies to activate industrial mathematics in Korea, described the study limitations, and proposed directions for future research.

• Journal of Korean Ophthalmic Optics Society
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• v.9 no.1
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• pp.145-159
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• 2004

A mathematical model and its computer solution program were proposed to analyze the motion of contact lenses which are being subject to lid-blinking. The equation was derived by incorporating an acceleration induced lid's force exerting on the contact lens, the viscous damping resistance in the tear layer beneath the lens and the sliding frictional force between the lid and the contact lens surface into the formulation of differential equation describing the vibration. The model predicts the time-dependent displacement from the equilibrium postion during/after the blinking. During the blinking, as the time for the completion of one cycle of blinking decreases the off-the-equilibrium displacement of contact lens increases while the decrease of diameter in the contact cause the opposite effect. It is found that lid pressure exerting on the lens cause an insignificant lens displacement from the equilibrium position. After blinking the frequency of damped oscillation of contact lens decreases as the diameter of lens increases, due to the incresed surface while the reduced blinking time does not cause a significant frequency change. This is because that driving force for the contact lens movement posterior to blinking is the capillary-induced force not the lid force.

• Journal of Korean Ophthalmic Optics Society
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• v.16 no.1
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• pp.97-106
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• 2011

Purpose: This review article was written to theoretically compare the depressing force (pressure, adhesion) to the cornea between when the spherical lenses were being tightly and flat fitted. Methods: Mathematical equations and their numerical solution programs (model) were formulated to calculate the depressing (adhesion) force to the cornea by both the tightly and flat fitted contact lenses. Based on this proposed model the effects of parameters characterizing a contact lens such as BCs, diameters, edge shape and corneal shape (ratio of long and short corneal axis, p) on the depressing force to the cornea were predicted/analyzed in both tightly and flat fitting regimes. Results: Corneal adhesion increased as the corneal p-value increased. Adhesion increase caused by the increased p-value was much larger in flat fitted case than in tight fitted one. Corneal adhesion reduced abruptly as the BC increased in flat fitting regimes while the adhesion rise was insignificant in tight fitting ones. Reduction in corneal adhesion due to lens-size increase was predicted to be insignificant in both tight and flat fitting regimes. Both the lens edge shape (edge angle) and thickness were relevant only in tight fitting regime. Corneal adhesion increased as the increased with tight-fitted lenses. As the thickness of tight fitted lenses increased, corneal adhesion inversely decreased. Conclusions: The two most significantly affecting the depressing force to cornea were found to be the degree of corneal bending toward the periphery and the BCs of lenses.

• Journal of Korean Ophthalmic Optics Society
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• v.16 no.1
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• pp.107-116
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• 2011

Purpose: The review article was written to establish an excel program that could calculate minimal Dk of contact lens without $O^2$ deficiency and actual $O^2$ concentration on cornea when contact lens were being fitted by changing lens-related factors. Methods: An excel program was formulated to calculate the thickness of post-lens lacrimal layer, Dk of contact lens and $O^2$ concentration on cornea. Results: With the excel program established, minimal $O^2$ concentration needed on cornea could be calculated when the thickness of post-lens lacrimal layer was changed by varying lens-related factors. A different route in the excel program was needed to choose based on the shape of lacrimal layer. The thickness of lacrimal layer was determined by the shape of meniscus made of tear between lens edge and cornea with flat fit. Thus, the $O^2$ concentration showing negative number in calculation decreased on peripheral cornea with flatter fitting and actual $O^2$ concentration would be zero on cornea. With tight fitting, the thickness of post-lens lacrimal layer is much thicker than lens itself thus negative number in calculation by the excel program is shown indicating zero oxygen on cornea. It can cause $O^2$ deficiency regardless of Dk of contact lens. Conclusions: The calculation of thickness of post-lens lacrimal layer and $O^2$ concentration on cornea by the established excel program is suggested to avoid $O^2$ deficiency when fitting state is varied by changing lens-related factors.