• 한국공간구조학회논문집
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• 제19권4호
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• pp.69-76
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• 2019

A stadium roof that uses the pin-jointed spatial truss system has to be designed by taking into account the unstable phenomenon due to the geometrical non-linearity of the long span. This phenomenon is mainly studied in the single-free-node model (SFN) or double-free-node model (DFN). Unlike the simple SFN model, the more complex DFN model has a higher order of characteristic equations, making analysis of the system's stability complicated. However, various symmetric conditions can allow limited analysis of these problems. Thus, this research looks at the stability of the DFN model which is assumed to be symmetric in shape, and its load and equilibrium state. Its governing system is expressed by nonlinear differential equations to show the double Duffing effect. To investigate the dynamic behavior and characteristics, we normalize the system of the model in terms of space and time. The equilibrium points of the system unloaded or symmetrically loaded are calculated exactly. Furthermore, the stability of these points via the roots of the characteristic equation of a Jacobian matrix are classified.

• 한국수학사학회지
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• 제33권6호
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• pp.303-314
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• 2020

Extending the method of extractions of square and cube roots in Jiuzhang Suanshu, Jia Xian introduced zengcheng kaifangfa in the 11th century. The process of zengcheng kaifangfa is exactly the same with that in Ruffini-Horner method introduced in the 19th century. The latter is based on the synthetic divisions, but zengcheng kaifangfa uses the binomial expansions. Since zengcheng kaifangfa is based on binomial expansions, traditional mathematicians in East Asia could not relate the fact that solutions of polynomial equation p(x) = 0 are determined by the linear factorization of p(x). The purpose of this paper is to reveal the difference between the mathematical structures of zengcheng kaifangfa and Ruffini-Honer method. For this object, we first discuss the reasons for zengcheng kaifangfa having difficulties to connect solutions with linear factors. Furthermore, investigating multiple solutions of equations constructed by tianyuanshu, we show differences between two methods and the structure of word problems in the East Asian mathematics.

• Structural Engineering and Mechanics
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• 제66권1호
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• pp.125-138
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• 2018

This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.

• Journal of Oral Medicine and Pain
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• 제6권1호
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• pp.15-18
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• 1981

The author had selected the roots and root-canal as measurable parts and sought the area ratio by measuring the respective areas of the root. Further, heplotted out a root caual index and studied the correlation with age. The teeth used as reserch material were permanent maxillary central incisors of Korean female. Some 296 teeth of known age were selected on condition that there is no caries or filling material and that they were not malformed in showing normal signs in roentgenograms. The $3" {\times} 4"$ printing paper so as to measure easily. On the ocassion of measureing the area of measured parts with a planimeter (Koizumi, type kp-27, Japan), the cervical lines were joined up into a straight line on a photograph (Figure 1) Root canal index = Area of the root / Area of the root canal The results of the root canal index in Korean female age groups were as follows : 1. The root canal index of maxilary central incisor in women was 4.74 im 20 years of age, 5.44 in 30, 5.90 in 40, 6.32 in 50, 6.63 in 60 in the order. 2. Root canal index and age were in positive correlation ; there was a tendency that the root canal index increase as age advances. 3. The regression equation was as follows : Y = 5.36x + 7.71 (r = 0.54, n= 296 ) (Y = estimated age, x = root canal index)

• 한국소음진동공학회논문집
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• 제26권1호
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• pp.75-81
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• 2016

In this study, a transfer matrix method in which can produce an infinite number of accurate natural frequencies using a single element for the bending vibration of rotating Bernoulli-Euler beam with linearly reduced width, is developed. The roots of the differential equation in the proposed method are calculated using the Frobenius method in the power series solution. To demonstrate the accuracy of the method, the calculated natural frequencies are compared with the results given by using the commercial finite element analysis program(ANSYS), and the comparison results between these two methods show the excellent agreement. Based on the comparison results, a parametric study is performed to investigate the effect of the centrifugal forces on the non-dimensional natural frequencies for rotating beam with the variable width.

• 한국식물병리학회지
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• 제3권3호
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• pp.198-202
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• 1987

밀 보리에서 crown root rot 및 leaf blotch를 이르키는 Helminthosporium sativum의 독소물질을 분리하였다. 이는 독소물질에 대한 어떤 손상도 없이 C-18 column으로 분리되었으며, 실험적으로 가능한 inhibitor를 제거하였다. Lettuce 성장과 독소물질의 농도의 반응에는 semi-log 표에서 비례하였다. 또한 pathogen host인 밀 보리의 뿌리 성장에 사용한 결과 Lettuce의 반응과 동일한 결과를 얻었다. 또한, pathogen host인 밀 보리의 뿌리 성장에 사용한 결과 Lettuce의 반응과 동일한 결과를 얻었다. 독소물질과 식물의 반응을 측정하여 dilution end-points.의 결과로, 직접적으로 독소물질의 농도를 측정하는 방법을 개발하였다. (Y=a log x+b)의 공식과 통계처리로 사용하여 얻은 a와 b의 의미를 토론하였다.

• 한국소음진동공학회논문집
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• 제17권2호
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• pp.121-129
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• 2007

There has been much effort to find suitable methods for structural analysis in the mid-frequency region where traditional low frequency methods have increasing uncertainties whilst statistical energy analysis is not strictly applicable. Systems consisting of relatively stiff beams coupled to flexible plates have a particularly broad mid-frequency region where the beams support only a few modes whilst the plate has a high modal density and modal overlap. A system of two parallel beams coupled to a plate is investigated based on the wave method, which is an approximate method. Muller's method is utilised for obtaining complex roots of a dispersion wave equation, which does not converge in the conventional wave method based on a simple iteration. The wave model is extended from a single-beam-plate system, to a plate with two identical beams which is modelled using a symmetric-antisymmetric technique. The important hypothesis that the coupled beam wavenumber is sufficiently smaller than the plate free wavenumber is experimentally verified. Finally, experimental results such as powers and energy ratios show the validity of the analytical wave models.

• Journal of Ginseng Research
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• 제37권2호
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• pp.254-260
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• 2013

Greenhouse and field experiments with American ginseng (Panax quinquefolius L.) stratified seed sown at depths of 10 to 100 mm were carried out to determine effects of seeding depth on seedling emergence, growth and development and to calculate optimum seeding depth. The time to 50% seedling emergence ($E_{50}$) in the field increased linearly from 17 d at 20 mm seeding depth to 42.5 d at 80 mm. Seedling emergence and root weight (economic yield) at the end of the first year each increased quadratically with the increase of seeding depth. Maximum emergence and root yields were produced at sowing depths of 26.9 and 30.6 mm respectively. In a greenhouse pot experiment, increasing seeding depth from 10 to 100 mm increased partitioning of dry matter to leaves from 23.6% to 26.1%, to stems from 6.9% to 14.2%, and decreased dry matter to roots from 69.5% to 59.7%. Optimum seeding depth was 31.1 mm for a corresponding maximum root weight of 119.9 mg. A predictor equation [X (seeding depth, mm)=Y (seed weight, mg)/9.1+20.96] for seeding depth for ginseng, based on data for ten vegetable crops, their seed weights and suggested seeding depths, predicted a seeding depth of 28.3 mm for ginseng similar to that reported above for most pot and field experiments.

• 한국수학사학회지
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• 제18권4호
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• pp.1-16
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• 2005

17세기 이전에 조선 산학자가 저술한 산서로 그 출판 연대가 확인된 것은 숙종26년(1700)에 출판된 박율(1621-?)의 산학원본이 유일하다. 이보다 먼저 출판된 것으로 추정되는 산서는 경선징(1615-?)의 묵사집산법이 있다. 조선의 산서로 산학원본은 천원술을 최초로 사용하고 있는 산서이고, 이는 그 후 여러 산서에서 인용되었다. 산학원본을 고려대학교 도서관에서 찾아내었다. 이 논문은 산학원본의 역사적 가치와 함께 조선 산학의 발전에 끼친 영향을 조사하고, 이를 통하여 박율이 지대를 앞서간 뛰어난 수학자임을 확인한다

• 한국산림과학회지
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• 제90권3호
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• pp.338-345
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• 2001

본 연구는 독일가문비나무의 지하부인 뿌리구조와 지상부인 수관과의 상호관계를 밝혀, 어렵게 뿌리를 굴취하거나 침엽 생체량을 측정하지 않고도 수고와 흉고직경에 의한 상대적인 뿌리와 침엽 생체량 추정을 위한 회귀식을 구하기 위하여 실시하였다. 독일 중부 Harz 지방의 Barbis 임분에서 30~40년생의 우세목 5본과 준우세목 3본을 선발한 후 조사목의 지상부에 대하여 수고, 흉고직경, 지하고, 침엽량, 가지량, 횡단면, 변재면 등을 조사하였다. 그리고 5본에 대해서는 지하부의 뿌리길이, 뿌리수, 뿌리무게, 뿌리횡단면 등을 수평과 수직뿌리로 구분하여 조사하였다. 조사된 염분에서 독일가문비나무의 지상부(수고, 흉고직경, 침엽량, 가지량 등)와 지하부(뿌리길이, 무게, 수, 횡단면 등) 생체량 사이에는 서로 밀접한 상관을 나타내었다. 측정이 용이한 흉고직경에 대한 지하부 뿌리생체량은 Y = 3.56X - 45.94의 관계식으로 결정계수가 0.96으로 매우 높은 상관관계를 나타내었다. 가지량, 침엽량과 수고에 있어서도 지하부 생체량과 높은 상관관계를 나타내었다. 본 연구에서 얻어진 회귀식은 30~40년생 독일 가문비나무 임분에서 흉고직경을 이용하여 지하부의 상대적인 뿌리 생체량을 추정하는데 유용하게 이용될 수 있을 것이다.