• Journal for History of Mathematics
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• v.10 no.1
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• pp.12-18
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• 1997

수학의 각 분야 중에서 선형성을 가지는 부분은 그 이론이 가장 정연하게 처리되나 이것이 선형대수학이라는 학문으로 형성된 것은 최근의 일이며, 더욱이 선형대수는 그 광범위한 응용성으로 인하여 더욱 중요시되게 되었다. 선형대수의 교육적 의의는 함수의 특수한 경우인 선형변환을 다룸으로서 선형성을 지닌 수학의 구조를 쉽게 파악할 수 있다는 것이며 더욱이 해석기하 등에도 쉽게 응용할 수 있게 된다. 본 논문에서는 타인, 쌍곡선, 포물선인 이차곡선을 행렬을 이용하여 표현하고, 좌표축의 회전이동과 평행이동을 통하여 행렬을 대각화하고, 고유치의 부호에 의하여 이차곡선의 변환과 분류를 다루었으며 더불어 곡선의 개형을 알아보았다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.1039-1049
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• 1994

The intermitternt and transient fuel spray have been investigated from the simultaneous measurement of droplet sizes and velocities by using Phase/Doppler Particle Analyzer(PDPA). Measurement have been done on the spray axis and at the edge of the spray near nozzle at various gas-to-liquid density ratios(.rho./sub g//.rho./sub l/) that ranges from those found in free atmospheric jets to conditions typical of diesel engines. Probability density distributions of the droplet size and velocity were obtained from raw data and mathematical probability density functions which can fit the experimental distribations were extracted using the principle of maximum likelihood. In the near nozzle region on the spray axis, droplet sizes ranged from the lower limit of the measurement system to the order of nozzle diameter for all (.rho./sub g/ /.rho./sub l/) and droplet sizes tended to be small on the spray edge. At the edge of spray, average droplet velocity peaked during needle opening and needle closing. The rms intensity is greatly incresed as the radial distance from the nozzle is increased. The probability density function which can best fit the physical breakage process such as breakup of fuel drops is exponecially decreasing log-hypebolic function with 4 parameters.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1994.04a
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• pp.185-190
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• 1994

본 연구에서는 와선 지배방정식의 계산을 위해 쌍곡선 blending 함수를 이용하여 와선운동의 정확한 계산을 할 수 있었고 이 방법을 통하여 임의로 거동하는 와선이 강체구와 간섭하는 경우의 3차원 유동장에 대한 해석과 이에 의한 쌍극 음향장 해석을 수행하였다. 경계치 적분방법을 통해 강체구에 작용하는 힘을 계산할 수 있었고 이 방법은 물체의 형태에 구애 받지 않으므로 임의 형상에 대해서도 유동장과 음향장 계산이 가능하다고 본다.

• Journal of the Korean Geotechnical Society
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• v.26 no.8
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• pp.67-75
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• 2010

In this study, a series of 1 g shaking table tests were carried out for a single pile in soft clay with various input acceleration amplitudes and frequencies. Based on the results, dynamic p-y curves were drawn and, in turn, the dynamic p-y backbone curve was formed by connecting the peak points, corresponding to the maximum soil resistance, of the dynamic p-y curves. In order to represent the p-y backbone curve numerically, Matlock's p-y formulations for clay was used to find the initial stiffness ($k_{ini}$) and the ultimate capacity ($p_u$) of the clay, both of which are required to formulate the p-y backbone curve as a hyperbolic function. The suggested p-y backbone curve was verified through comparisons with currently available p-y curves as well as other researchers' centrifuge test results and numerical analysis results.

• Journal of the Korean Geotechnical Society
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• v.31 no.2
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• pp.47-63
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• 2015

A fundamental study of drilled shafts subjected to lateral cyclic loading in weathered soil was carried out based on field tests and numerical analysis. The emphasis was given on quantifying the cyclic p-y curve function from lateral cyclic loading tests and three-dimensional finite element analysis. Lateral cyclic loading tests and three-dimensional finite element analysis were carried out to investigate the behavior of drilled shafts according to the direction of cyclic loading. Based on the field tests and numerical analysis, a modified lateral load transfer relationship and design chart with degradation factors were proposed by considering the characteristics of cyclic loading. It was found that the prediction by the proposed p-y curve function is in good agreement with the general trends observed by in-situ measurements, and it represents a practical improvement in the prediction of lateral displacement and bending moment distribution of drilled shafts subjected to cyclic loading.

• Journal of the Korean Institute of Gas
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• v.21 no.3
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• pp.61-69
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• 2017

The commercial development of unconventional gas is pursued in North America because it is more feasible owing to the technology required to improve productivity. Shale reservoir have low permeability and gas production can be carried out through cracks generated by hydraulic fracturing. The decline rate during the initial production period is high, but very low latter on, there are significant variations from the initial production behavior. Therefore, in the prediction of the production rate using deterministic decline curve analysis(DCA), it is not possible to consider the uncertainty in the production behavior. In this study, production rate of the Eagle Ford shale is predicted by Arps Hyperbolic and Modified SEPD. To minimize the uncertainty in predicting the Estimated Ultimate Recovery(EUR), Monte Carlo simulation is used to multi-wells analysis. Also, kernel density function is applied to determine probability distribution of decline curve factors without any assumption.

• Geophysics and Geophysical Exploration
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• v.1 no.1
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• pp.8-18
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• 1998

In exploration seismology, the Kirchhoff hyperbola has been successfully used to migrate reflection seismo-grams. The mathematical basis of Kirchhoff hyperbola has not been clearly defined and understood for the application of prestack or poststack migration. The travel time from the scatterer in the subsurface to the receivers (exploding reflector model) on the surface can be a kinematic approximation of Green's function when the source is excited at position of the scatterer. If we add the travel time from the source to the scatterer in the subsurface to the travel time of exploding reflector model, we can view this travel time as a kinematic approximation of the partial derivative wavefield with respect to the velocity or the density in the subsurface. The summation of reflection seismogram along the Kirchhoff hyperbola can be evaluated as an inner product between the partial derivative wavefield and the field reflection seismogram. In addition to this kinematic interpretation of Kirchhoff hyperbola, when we extend this concept to shallow refraction seismic data, the stacking of refraction data along the straight line can be interpreted as a measurement of an inner product between the first arrival waveform of the partial derivative wavefield and the field refraction data. We evaluated the Kirchhoff hyperbola and the straight line for stacking the refraction data in terms of the first arrival waveform of the partial derivative wavefield with respect to the velocity or the density in the subsurface. This evaluation provides a firm and solid basis for the conventional Kirchhoff migration and the straight line stacking of the refraction data.

• Journal of the Korean Geotechnical Society
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• v.25 no.11
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• pp.27-38
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• 2009

In this study, a series of 1 g shaking table model pile tests were carried out in saturated dense and loose sand to evaluate dynamic p-y curves for various conditions of flexural stiffness of a pile shaft, acceleration frequency and acceleration amplitude for input loads. Dynamic p-y backbone curve which can be applied to pseudo static analysis for saturated dense sand was proposed as a hyperbolic function by connecting the peak points of the experimental p-y curves, which corresponded to maximum soil resistances. In order to represent the backbone curve numerically, empirical equations were developed for the initial stiffness ($k_{ini}$) and the ultimate capacity ($p_u$) of soils as a function of a friction angle and a confining stress. The applicability of a p-y backbone curve was evaluated based on the centrifuge test results of other researchers cited in literature, and this suggested backbone curve was also compared with the currently available p-y curves. And also, the scaling factor ($S_F$) to account for the degradation of soil resistance according to the excess pore pressure was developed from the results of saturated loose sand.

• Journal of the Korean Chemical Society
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• v.19 no.5
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• pp.304-316
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• 1975

A formal theory to explain the Stark effect in molecular exciton states is developed using the second-quantization formalism. In this theory not only the Stark effect but also the Davydov effect are explicitly taken into consideration since the observed spectral splitting in the UV spectra for molecular crystals with two or more molecules per unit cell may be the result of combination of the above two effects. Especially for molecular crystals containing two molecules in a unit cell the splitting is shown to be hyperbolically dependent upon the strength of an externally applied, uniform electric field, from which informations regarding the excited state dipole moments of a single molecule may be obtained.

• Geotechnical Engineering
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• v.6 no.4
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• pp.65-74
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• 1990

This paper presents triaxial test (CIVC and CKOUC) results on normally consolidated deep sea clay samples. Based on the test results the pore pressure-strain relations for both isotropicaly and anisotropicaly consgidated samples are expressed with hyperbolic functions of the major princpal strain. The analysis of the difference in pore pressure behavior due to the anisotropy in consolidation stress is carried out with the effective stress pathos of CIVC and CKOUC and finds a factor which correlates the pore pressure of two types of test.