• 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.

• 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.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10b
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• pp.217-219
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• 2001

복잡한 제어가 필요한 설비의 운전 정보나 네트워크 연결 상태 또는 웹 문서간의 정보 등을 제한된 컴퓨터 화면에 효과적으로 배치하는 시각화 기법에 관한 논의가 활발히 진행되고 있다. 이 경우 한눈에 전체 정보의 계층 구조를 파악하도록 하는 환경을 제공하며, 사용자가 관심 있는 정보에 대해서는 전체 정보 계층 구조를 유지하면서 보다 상세히 그 내용을 보여주는 그래픽 기반의 사용자 인터페이스 판결의 개발이 필요하다. 이에 쌍곡선 기하학(Hyperbolic Geometry)을 기반으로 한 시각화기법으로 새로운 제어 환경을 구현하여 사용자의 편의를 도모하도록 한다.

• Journal of Korean Association for Spatial Structures
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• v.13 no.1
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• pp.51-57
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• 2013

There can be diverse causes in the destruction of a large space structure by strong wind such as characteristics of construction materials and changes in internal and external wind pressure of the structure. To evaluate the wind pressure of roof against the large space structure, wind pressure experiment is performed. However, in this wind pressure experiment, peak internal pressure coefficient is set according to the opening of the roof in Korea wind code. In this article, it was tried to identify the change of internal pressure coefficient and the characteristics of wind pressure coefficient acting on the roof by two kinds of opening on the side of the structure with Hyperbolic Paraboloid Spatial Structures roof. When analyzing internal pressure coefficient according to roof shape, it was found that minimum (52%) and maximum (30%~80%) overestimation was made comparing to partial opening type proposed in the current wind load. It is judged that evaluation according to the opening rate of the structure should be made to evaluate the internal pressure coefficient according to load.

• International Journal of Highway Engineering
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• v.7 no.4 s.26
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• pp.31-39
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• 2005

Tests are conducted to analyze the compaction characteristics of domestic river sand used frequently for backfill in construction of electrical pipeline. As a result of test, the range of specific gravity of sand is found to be in between 2.63 and 2.67, and of maximum dry weight of sand is in between $1.70g/cm^3\;and\;1.86g/cm^3$. Also, the optimum moisture content is found to be in between 11.3% and 13.8%. The variability of compaction degree with respect to compaction energy is well captured by hyperbolic function.

• Geotechnical Engineering
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• v.2 no.1
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• pp.15-26
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• 1986

Consolidated undrained standard triaxial tests for two remoulded clays and one undisturbed clay were carried out in order to find out the relationship between excess pore water pressure and axial strain in mortally consolidatated saturated clays during undrained shear. Tests were performed with isotropically-normally consolidated specimens by strain controlled and stress controlled loading. As the result of this stud!'a hyperbolic function expressing the relationship between pore water pressure and strain was found out, and it showed the same form as the Kondner's hyperbolic function for stress·strain behaviour. Two parameters used for the function can be obtained by CU-triaxial test.

• Journal of the Korean Geotechnical Society
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• v.16 no.3
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• pp.163-172
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• 2000

최종침하 예측기법들은 분석상 간단명료하고 경제적인 기법이라 현장에서 널리 이용되고 있지만, 현장계측상의 문제들이 다분히 있는 실측치에 크게 의존함으로써 설계단계에서 침하량예측에 분석가의 주관적 판단이 큰 변수로 작용할 수 있으므로 객관성이 결여되는 결점을 안고 있다. 그 중 쌍곡선법(Hypervolic Method)이 가장 널리 쓰이고 있지만, 현장 계측치에 따라 가정 기본식의 선형성이 다소 뚜렷하지 않아 분석가에 따라 해석결과가 다르게 나타날 수 있으므로, 기술 적용상의 어려움과 경제적 비용을 더욱 가중시키는 결과를 초래할 수 있다. 따라서, 본 연구에서는 현장 계측자료 분석에 있어서 대표적으로 널리 적용되고 있는 쌍곡선법의 기본 가정식의 선형성 문제에 주안점을 두어 기본 가정식의 선형성을 확보하고, 그 선형구간을 확장한 새로운 침하예측기법을 제안하였다. 성토완료 직후의 현장 자료를 배수재가 설치된 지역과 배수재가 설치되지 않은 지역으로 구분하여 최종 1차 압밀침하량, 수직압밀계수 등을 기존예측기법 및 현장계측자료와 비교 검토하여 제안된 침하예측기법의 적용성을 검증하였다.

• Geotechnical Engineering
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• v.12 no.6
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• pp.79-86
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• 1996

This study develops a new method for interpreting the yield load from load tests on drilled shaft foundations ended on general soils, which is defined as a point where the maximum curvature on the hyperbolic-approximated load-settlement curve occurs. How ever, the point of maximum curvature is a variable depending on the units and scales of the load and settlement. Therefore, to obtain a unique maximum curvature point, both the load and settlement must be normalized by proper parameters, respectively, and be expressed on the same scaled arses(1:1). Normalization has been processed so that the yield load by the new interpretation is to be close to the average of yield loads interpreted by other methods investigated in this study. The quantitative comparison between the new criterion and other conventitonal methods is presented.

• Journal of the Korean GEO-environmental Society
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• v.3 no.3
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• pp.53-63
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• 2002

Until recently the other attempts except linear elastic analysis using assumed elastic modulus had not been made in order to evaluate the settlement of the rock fill materials in Korea. Especially, it was almost impossible to predict the precise settlement of the breakwater structure made with dumped rubble stone. In this study, 3 sets of large scaled triaxial compression tests for porous basaltic quarry rocks were carried out and numerical simulation of those triaxial compression tests were performed applying non linear elastic model. Two stress-strain behaviors were compared to study the adaptability of hyperbolic constitutive model for the rubble stone. The results showed quite good agreements between the two stress-strain behaviors. Thus, the hyperbolic constitutive model is thought to be alternative approach evaluate the settlements of the loose rock-fill material.

• School Mathematics
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• v.15 no.4
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• pp.995-1013
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• 2013

The purpose of this paper was to investigate mathematics teachers' mathematical content knowledge about quadratic curves. Three components of mathematical knowledge are needed for teaching: (i) knowing school mathematics, (ii) knowing process of school mathematics, (iii) making connections between school mathematics and advanced mathematics. 24 mathematics teachers were asked to perform 10 questions based on mathematics curriculum. The results showed that mathematics teachers had some difficulties in conic section definitions and eccentricity definitions of ellipse and hyperbola. And they also got difficulty in Dandellin sphere proof of the equivalence of conic section definitions and quadratic curve definitions. Especially, no one answered correctly to the question about the definition of eccentricity. The ratio of correct answer for the question about constructing tangent lines of quadratic curves is less than that for the question about the applications of the properties of tangent lines. These findings suggests that it is needed that to provide plenty of opportunities to learn mathematical content knowledge in teacher education programs.