• East Asian mathematical journal
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• v.35 no.2
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• pp.141-161
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• 2019

The purpose of this paper is to reinterpret and visualize the trisection line construction of general angle in the Medieval Islam using conic sections. The geometry field in the current 2015 revised Mathematics curriculum deals mainly with the more contents of analytic geometry than logic geometry. This study investigated four trisecting problems shown by al-Haytham, Abu'l Jud, Al-Sijzī and Abū Sahl al-Kūhī in Medieval Islam as one of methods to achieve the harmony of analytic and logic geometry. In particular, we studied the above results by 3 steps(analysis, construction and proof) in order to reinterpret and visualize.

• Journal of the Korean Electrochemical Society
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• v.4 no.1
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• pp.26-33
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• 2001

This article involves the application of the fractal geometry to interfacial electrochemistry. Especially, we gave our attention to impedance behaviour of the fractal electrode. First, this article briefly explained the constant phase element (CPE) in electrochemical impedance and the do Levie's transmission line model. Second, we introduced the Nyikos and Pajkossy's theoretical works to approach the CPE phenomena using the fractal geometry. Finally this article presented other various fractal models for analysing the ac response of the rough electrodes.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.421-437
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• 2019

We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.

• 유체기계공업학회:학술대회논문집
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• 2001.11a
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• pp.54-60
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• 2001

In this research, we developed a computer code that designs a compressor impeller, which serves as an essential component of a vacuum cleaner, and predicted its performance. The TEIS model originally developed by Japikse(1985), and the mean line analysis m combined to design the centrifugal impeller optimally. In this program the inlet geometry is designed by using the mean line analysis, and with assumption of resonable exit blade angle, the optimal geometry is searched by means of TEIS model and iterative scheme. The performance of designed impeller was compared with experimental data, and the far-field noise by the rotating impeller is also predicted.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1743-1755
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• 2017

Let B be a simply-connected projective variety such that the first cohomology groups of all line bundles on B are zero. Let E be a vector bundle over B and $X={\mathbb{P}}(E)$. It is easily seen that a power of any endomorphism of X takes fibers to fibers. We prove that if X admits an endomorphism which is of degree greater than one on the fibers, then E splits into a direct sum of line bundles.

• The Mathematical Education
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• v.50 no.4
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• pp.429-440
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• 2011

This paper analysed gifted middle students' conception of the definitions of point and line and the uses of definitions in proving. The findings of this paper suggest that the concept of mathematical definitions is very unnatural to students, therefore teachers and textbooks need to explain explicitly the characteristics of mathematical definitions which are different from dictionary definitions using common sense. Also introducing undefined terms in middle school geometry would give students a critical chance to deal with the transition from dictionary definitions to mathematical definitions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.912-915
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• 2002

It has been known that general velocity and force of a rigid body in space can be described in forms of a twist and a wrench by use of screws. However, the geometrical meaning of acceleration has not been clearly disclosed. It has been a normal practice to analyze or synthesize the acceleration effect of manipulator using some complex mathematical equations, which do not represent any geometrical meanings. In other words, such a technique doesn't clearly provide information about the overall acceleration state of manipulator at that instant. In this study, the geometrical meaning of acceleration of a rigid body has been investigated and thereby a geometrical procedure which can be applied to inverse acceleration analysis of a general non-redundant manipulator is presented as an application.

• Journal for History of Mathematics
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• v.29 no.3
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• pp.157-172
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• 2016

Sophus Lie's research is regarded as one of the most important mathematical advancements in the $19^{th}$ century. His pioneering research in the field of differential equations resulted in an invaluable consolidation of calculus and group theory. Lie's group theory has been investigated and constantly modified by various mathematicians which resulted in a beautifully abstract yet concrete theory. However Lie's early intentions and ideas are lost in the mists of modern transfiguration. In this paper we explore Lie's early academic years and his object of studies which clarify the ground breaking ideas behind his theory.

• Proceedings of the KSR Conference
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• 2008.06a
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• pp.299-304
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• 2008

Catenary and Pantograph are a power supply devices for electric trains and shall be steadily contacted. Rail catenary must be installed precisely and managed for stable train operations. But external factors such as weathers, nature, etc., or aging affect catenary geometry. Changed catenary height causes high voltage spark or instant electric disconnection. Big spark and disconnection damage pantograph shoe and catenary coating and might interrupt rail operations. To prevent a big scale spark or electric disconnection catenary maintenance shall be required with catenary geometry measurement systems. In this paper, we describe the development of catenary height and stagger measurement system. The catenary height and stagger measurement system uses Acuity company's AR4000 Range Finder for distance measurement and AccuRange Line Scanner for degree measurement. This system reports suspicious overhead line sections with excessive height and stagger variance.

• Journal of The Korean Astronomical Society
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• v.54 no.6
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• pp.183-190
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• 2021

We have revisited Monte Carlo radiative transfer calculations for clumpy molecular clouds. Instead of introducing a three-dimensional geometry to implement clumpy structure, we have made use of its stochastic properties in a one-dimensional geometry. Taking into account the reduction of spontaneous emission and optical depth due to clumpiness, we have derived the excitation conditions of clumpy clouds and compared them with those of three-dimensional calculations. We found that the proposed approach reproduces the excitation conditions in a way compatible to those from three-dimensional models, and reveals the dependencies of the excitation conditions on the size of clumps. When bulk motions are involved, the applicability of the approach is rather vague, but the one-dimensional approach can be an excellent proxy for more rigorous three-dimensional calculations.