• Journal of Korean Association for Spatial Structures
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• v.19 no.4
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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.

• Journal for History of Mathematics
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• v.33 no.6
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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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• v.66 no.1
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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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• v.6 no.1
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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)

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.1
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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.

• Korean Journal Plant Pathology
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• v.3 no.3
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• pp.198-202
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• 1987

Toxic metabolites ('Toxins'), produced by Helminthosporium sativum causing leaf blotch in barley and root rot in barley and wheat were partially purified through C-18 column. The partially purified toxins appeared heat unstable and lipophilic. The responses of toxins to wheat and barley root corresponded with those to lettuce growth with the different concentrations. The determination of the concentration of toxins produced was developed using the dilution end-points. The equation [Y = a log X + b) was obtained from the semi-log­graphy with the linear analysis. The values 'a' and 'b' were discussed with the responses of several plants on the toxin produced by H. sativum.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.2 s.119
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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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• v.37 no.2
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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.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.1-16
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• 2005

Chosun dynasty mathematician Park Yul (1621 - ?) wrote San Hak Won Bon(算學原本) which was posthumously published in 1700 by his son Park Du Se (朴斗世). It is the first mathematics book whose publishing date is known, although we have Muk Sa Jib San Bub (默思集算法) by Gyung Sun Jing (慶善徵, 1616-?). San Hak Won Bon is the first Chosun book which deals with tian yuan shu (天元術) and was quoted by many Chosun authors. We do find it in the library in Korea University. In this paper, we investigate its contents together with its historical significance and influences to the development of Chosun dynasty Mathematics and conclude that Park Yul is one of the most prominent Chosun dynasty mathematicians.

• Journal of Korean Society of Forest Science
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• v.90 no.3
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• pp.338-345
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• 2001

This study was conducted to elucidate the relationship between the root structure and the crown structure of Norway spruce(Picea abies [L.] Karst), and thereafter to obtain the regression equation for the estimation of relative root and needle biomass using the tree height and diameter at breast height(DBH) without measurement of root and needle biomass. The study site was Barbis stands of Harz region located in central part of Germany. Five dominant and three co-dominant trees of 30 to 40 year-old Norway spruce were selected and tree height, diameter at breast height, clear bole length, weight of total needle and branch, cross section and sapwood area at breast height for biomass of above ground part and also the length of root, the number of root, the weight of root, the cross section area of root etc. by dividing the horizontal and vertical roots for below ground part of tree were measured. The significantly correlation was shown between the biomass of most of variables of above ground parts and those of below ground parts. For the diameter of breast height to the weight of total root, regression equation was Y = 3.56X - 45.94 and decision coefficient was 0.96 showing highly correlation. The weight of total branches and needles, and the tree height etc. of above ground parts showed highly positive relationship with below ground biomass. The results obtained from this study can be used to the estimating of biomass of below ground using variables of above ground such as DBH in the 30 to 40 year-old Norway spruce stands.