• The Mathematical Education
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• v.52 no.1
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• pp.83-95
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• 2013

The purpose of this paper is to explain and reinterprets Apollonius' Symptoms on conic sections based on the current secondary curriculum of mathematics, present the historical background of Apollonius' Symptoms to teachers and students and introduce visualization proof of Apollonius' symptoms on a parabola, a hyperbola and an ellipse by a new method using dynamic geometry software(GSP) respectively.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2013.05a
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• pp.457-458
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• 2013

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.3
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• pp.15-24
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• 2015

Jacket matrices which are defined to be $m{\times}m$ matrices $J^{\dagger}=[J_{ik}^{-1}]^T$ over a Galois field F with the property $JJ^{\dagger}=mI_m$, $J^{\dagger}$ is the transpose matrix of element-wise inverse of J, i.e., $J^{\dagger}=[J_{ik}^{-1}]^T$, were introduced by Lee in 1984 and are used for Digital Signal Processing and Coding theory. This paper presents some square matrices $A_2$ which can be eigenvalue decomposed by Jacket matrices. Specially, $A_2$ and its extension $A_3$ can be used for modifying the properties of hyperbola and hyperboloid, respectively. Specially, when the hyperbola has n times transformation, the final matrices $A_2^n$ can be easily calculated by employing the EVD[7] of matrices $A_2$. The ideas that we will develop here have applications in computer graphics and used in many important numerical algorithms.

• Journal of Bio-Environment Control
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• v.27 no.2
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• pp.132-139
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• 2018

The photosynthetic rate is an indicator of the growth state and growth rate of crops and is an important factor in constructing efficient production systems. The objective of this study was to develop a canopy photosynthetic rate model of romaine lettuce using the three variables of $CO_2$ concentration, light intensity, and growth stage. The canopy photosynthetic rates of the lettuce were measured at five different $CO_2$ concentrations ($600-2,200{\mu}mol{\cdot}mol^{-1}$), five light intensities ($60-340{\mu}mol{\cdot}m^{-2}{\cdot}s^{-1}$), and four growth stages (5-20 days after transplanting) in three closed acrylic chambers ($1.0{\times}0.8{\times}0.5m$). A simple multiplication model expressed by multiplying three single-variable models and the modified rectangular hyperbola model including photochemical efficiency, carboxylation conductance, and dark respiration, which vary with growth stage, were also considered. In validation, the $R^2$ value was 0.923 in the simple multiplication model, while it was 0.941 in the modified rectangular hyperbola model. The modified rectangular hyperbola model appeared to be more appropriate than the simple multiplication model in expressing canopy photosynthetic rates. The model developed in this study will contribute to the determination of an optimal $CO_2$ concentration and light intensity with the growth stage of lettuce in plant factories.

• Journal of computational fluids engineering
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• v.16 no.2
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• pp.1-10
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• 2011

A new computational program, which is based on the CIP/CCUP(Constraint Interpolation Profile/CIP Combined Unified Procedure) method, has been developed to numerically analyse sloshing phenomena dealt as multiphase-flow problems. For the convection terms of Navier-Stokes equations, the RCIP(Rational function CIP) method was adopted and the THINC-WLIC(Tangent of Hyperbola for Interface Capturing-Weighted Line Interface Calculation) method was used to capture the air/water interface. To validate the present numerical method, two-dimensional dam-breaking and sloshing problems in a rectangular tank were solved by the developed method in a stationary Cartesian grid system. In the case of sloshing problems, simulations by using a improved MPS(Moving Particle Simulation) method, which is named as PNU-MPS(Pusan National University-MPS), were also carried out. The computational results are compared with those of experiments and most of the comparisons are reasonably good.

• KSTLE International Journal
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• v.1 no.2
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• pp.101-106
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• 2000

Variable displacement axial piston pumps are widely used for raising the energy level of the fluid in hydraulic systems. And the regulator is the device which regulates the discharge flow of the piston pump by controlling the swivel angle. The regulator receives the hydraulic pilot pressure and controls the pump output flow depending on the machine load and engine speed. This work deals with constant power control (horsepower control) in the design of a regulator by using a bent-axis type piston pump. In order to effectively use engine power, we must keep the horsepower from the engine to the pump constant. Therefore the regulator operates the constant power control. As a result, optimum power usage is obtained by accurately following the power hyperbola. This study focused on developing a simulation model of a regulator. First, the governing equations of the regulator are derived, and analysis is performed by computer simulation, which can identify significant parameters of regulator. As a result, the variation of the swivel angle, flow rate, hyperbolic curve, inner leakage and responsibility are simulated, and significant parameters of a regulator are identified.

• ETRI Journal
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• v.39 no.2
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• pp.264-274
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• 2017

Recently, mobile positioning enhancement has attracted much attention in the 3rd generation partnership project long-term evolution system. In particular, for urban canyon environments, the need for three-dimensional (3D) positioning has increased to enable the altitude of users to be measured. For several decades, several time difference of arrival (TDOA-) based 3D positioning methods have been studied; however, they are only available when at least four evolved Node Bs (eNBs) exist nearby or when all eNBs have the same height. Therefore, in this paper, we propose a new 3D positioning method that estimates the 3D coordinates of a user using three types of two-dimensional (2D) TDOAs. However, the give inaccurate results owing to the undefined axis of the 2D coordinate plane. Therefore, we propose a novel derivation of the hyperbola equation, which includes the undefined axis coordinate in the 2D hyperbola equation. Then, we propose an interaction algorithm that mutually supplies the undefined axis coordinate of users among 2D TDOAs. By performing extensive simulations, we verify that the proposed method is the only solution applicable by using three eNBs with different heights.

• Journal of Ocean Engineering and Technology
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• v.27 no.2
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• pp.39-46
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• 2013

In this study, the impact loads on tank walls by sloshing phenomena and on a tall structure in a three-dimensional rectangular tank were predicted using multiphase flow simulations. The solver was based on the CIP/CCUP (Constraint interpolation CIP/CIP combined unified procedure) method, and the THINC-WLIC (Tangent hyperbola for interface capturing-weighted line interface calculation) scheme was used to capture the air-water interface. For the convection terms of the Navier-Stokes equations, the USCIP (Unsplit semi-lagrangian CIP) method was adopted. The results of simulations were compared with those of experiments. Overall, the comparisons were reasonably good.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.483-495
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• 2023

In his book "Exercitationum Mathematicalarum," a 17th-century mathematician van Schooten proposed linkages for drawing parabola, ellipse, and hyperbola. The linkages proposed by van Schooten can be used in action-based mathematics education and as a material for using mathematical history in school mathematics. In particular, students are not provided with the opportunity to learn by manipulating the quadratic curves in the high school curriculum, so van Schooten's linkages can be used for school mathematics. To this end, a method of implementing van Schooten's linkage in a dynamic geometry environment was presented, and proved that the traces of the figure drawn using van Schooten's linkage were parabola, ellipse, and hyperbola.

• Journal of The Korean Society of Agricultural Engineers
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• v.66 no.1
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• pp.15-24
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• 2024

Unlike artificially created homogeneous materials, the process of calculating the elastic modulus of natural soil involves the possibility of errors. Because the stress-strain behavior of soil is nonlinear, the secant modulus of elasticity is often used based on 1/2 of the stress at failure. Since soil has the property of changing its elastic modulus depending on the confining pressure, numerical analysis models that analyze its behavior inevitably include complex elements. The hyperbolic model, which relatively accurately simulates the behavior immediately after loading in soft ground, assumes that the stress-strain curve of the consolidated undrained triaxial test is hyperbolic and requires the slope of the tangent line at the starting point. However, the slope of the initial tangent in the stress-strain curve obtained from an actual triaxial test is difficult to have regularity according to changes in confining pressure. Additionally, due to the characteristics of a hyperbola, even small changes in related factors cause large changes in the hyperbola. Therefore, there is a lot of randomness in the process of calculating model parameters from the triaxial test results, which causes large differences in the results. Therefore, the method of calculating the initial elastic modulus by the consolidation test presented in this study is also used to verify the method by the triaxial test. It can be applied. However, since this study was applied to only one sample showing typical consolidation characteristics, it is necessary to check samples with various physical properties in the future.