• Proceedings of the KSR Conference
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• 2008.06a
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• pp.1676-1682
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• 2008

The vertical curve of railway is installed in changing point where the gradient is more than a certain degree to ensure safe operation of train and comfort of passengers. As a result of CAD work with 3D coordination by using the existing equation, it was found that the simple equation about vertical curve installation suggested in the surveying engineering or railway regulations did not reflect theoretical curvature of circular curve in a case of steep grade and large vertical radius. In this study, for derive precision equation and transition curve about vertical curve, gradient parameters, equation of circles and transition curve equation were used, and it was verified by CAD that the derived equation is exactly satisfied with parameters of geometrical circular and transition curve. This equation could be used to provide more smoothing operation of train and comfort of passengers on vertical curves, especially in case that railway requires precision vertical alignment of track such as super high-speed railway, LRT or Maglev system.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1265-1280
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• 2023

The aim of this paper is to investigate Betchov-Da Rios equation by using null Cartan, pseudo null and partially null curve in Minkowski spacetime. Time derivative formulas of frame of s parameter null Cartan, pseudo null and partially null curve are examined, respectively. By using the obtained derivative formulas, new results are given about the solution of Betchov-Da Rios equation. The differential geometric properties of these solutions are obtained with respect to Lorentzian causal character of s parameter curve. For a solution of Betchov-Da Rios equation, it is seen that null Cartan s parameter curves are space curves in three-dimensional Minkowski space. Then all points of the soliton surface are flat points of the surface for null Cartan and partially null curve. Thus, it is seen from the results obtained that there is no surface corresponding to the solution of Betchov-Da Rios equation by using the pseudo null s parameter curve.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.572-581
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• 2006

This study is to investigate dynamic response of concrete buried pipelines with various end boundary conditions and develop a curve fitted equation to ensure practicality and convenience for the use at the actual field for the test of resistance of earthquake. Dynamic response under the various end boundary conditions is calculated with analysis on values and computing programs. However, such a method of analysis requires skillfulness in using computing programs for dynamic movement of buried pipelines with dynamic analysis formula and has lower efficiency and practicality because, in the nature of analysis program of values, it needs much time to conduct repeated calculations. Therefore, the study is intended to develop a curve fitted equation to ensure more efficient and practical analysis. This paper tests various degrees of equation with non-linear least square method and developments a curve fitted equation based on the transmission speed with the best results. In the use of curve fitted equation, degree of polynomial and determining coefficient are influenced by the speed of transmission.

• Proceedings of the Korean Geotechical Society Conference
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• 2005.03a
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• pp.362-369
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• 2005

Studying unsaturated soil mechanics, determination of soil water characteristic curve and permeability equation is an essential factor but it is not easy. In this research a new testing apparatus was developed to determine soil water characteristic curve and permeability equation. The testing to get saturated permeability coefficients and soil water characteristic curves for two soils was performed by using the developed testing apparatus. First, a saturated permeability testing was performed and then the testing to get soil water characteristic curve of a drying process was performed. Next, the testing to get soil water characteristic curve of a wetting process was performed. Testing results showed hysteresis phenomena between soil water characteristic curve of a drying process and soil water characteristic curve of a wetting process. The permeability equations were determined by a theoretical method where a saturated permeability coefficient and a soil water characteristic curve were used.

• Journal of Electrochemical Science and Technology
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• v.7 no.4
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• pp.293-297
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• 2016

Here we propose a new equation by which we can estimate the baseline for measuring the peak current of the reverse curve in a cyclic voltammogram. A similar equation already exists, but it is a linear algebraic equation that over-simplifies the voltammetric curve and may cause unpredictable errors when calculating the baseline. In our study, we find a quadratic algebraic equation that acceptably reflects the complexity included in a voltammetric curve. The equation is obtained from a laborious numerical analysis of cyclic voltammetry simulations using the finite element method, and not from the closed form of the mathematical equation. This equation is utilized to provide a virtual baseline current for the reverse peak current. We compare the results obtained using the old linear and new quadratic equations with the theoretical values in terms of errors to ascertain the degree to which accuracy is improved by the new equation. Finally, the equations are applied to practical cyclic voltammograms of ferricyanide in order to confirm the improved accuracy.

• Journal of Soil and Groundwater Environment
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• v.6 no.3
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• pp.61-71
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• 2001

A regional master recession curve model to predict groundwater discharges in a given basin was presented. Considering a stream-aquifer system, both theoretical and experimental baseflow equations were compared and a practical groundwater discharge equation was derived, The groundwater discharge equation was expanded and transformed to the discharge equation at the basin exit. For practical use, the equation was expressed as a function of watershed area, the mean slope of basin and the recession constant. To verify the model, the model was applied to Ssang-chi basin where long-term and temporal hydrological data at the upper basin were collected. Our results show that a master recession curve of unmeasured area can be predicted.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.4
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• pp.709-714
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• 2017

The curved panel is widely used for display of TVs and smart phones. This paper proposes a new auto-focusing method for curved panel inspection system. Since the distance between the camera and the panel varies with the curve position, the camera should change its focus at every inspection time. In order to reduce the focusing time, we propose an effective focusing method that considers the mathematical model of panel curve. The Lagrange polynomial equation is applied to modeling the panel curve. The foci of initial three points are used to get the curve equation, and the other foci are calculated automatically from the curve equation. The experiment result shows that the proposed method can reduce the focusing time.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.369-380
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• 2019

Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).

• Journal of the Korean Geotechnical Society
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• v.21 no.5
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• pp.59-64
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• 2005

In studying unsaturated soil mechanics, determination of soil water characteristic curve and permeability equation though not easy, is an essential factor. In this research a new testing apparatus was developed to determine soil water characteristic curve and permeability equation. A test to get saturated permeability coefficients and soil water characteristic curves for two soils was performed by using the developed testing apparatus. First, a saturated permeability test was performed and then the test to get soil water characteristic curve of a drying process was performed. Next, the test to get soil water characteristic curve of a wetting process was performed. Test results showed hysteresis phenomena between soil water characteristic curve of a drying process and soil water characteristic curve of a wetting process. The permeability equations were determined by a theoretical method where a saturated permeability coefficient and a soil water characteristic curve were used.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1179-1190
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• 2001

Quadratic invariant curve is one of the simplest nonlinear invariant curves and was considered by C. T. Ng and the author in order to study the one-dimensional nonlinear dynamics displayed by a second order delay differential equation with piecewise constant argument. In this paper a functional equation derived from the problem of invariant curves is discussed. Using a different method from what C. T. Ng and the author once used, we define solutions piecewisely and give results in the remaining difficult case left in C. T. Ng and the authors work. A problem of analytic extension given in their work is also answered negatively.