• Journal of KIISE:Software and Applications
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• v.27 no.1
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• pp.50-61
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• 2000

Recently the stereo vision based on conics has received much attention by many authors. Conics have many features such as their matrix expression, efficient correspondence checking, abundance of conical shapes in real world. Extensions to higher algebraic curves met with limited success. Although irreducible algebraic curves are rather rare in the real world, lines and conics are abundant whose products provide good examples of higher algebraic curves. We consider plane algebraic curves of an arbitrary degree $n{\geq}2$ with a fully calibrated stereo system. We present closed form solutions to both correspondence and reconstruction problems. Let $f_1,\;f_2,\;{\pi}$ be image curves and plane and $VC_P(g)$ the cone with generator (plane) curve g and vertex P. Then the relation $VC_{O1}(f_1)\;=\;VC_{O1}(VC_{O2}(f_2)\;∩\;{\pi})$ gives polynomial equations in the coefficient $d_1,\;d_2,\;d_3$ of the plane ${\pi}$. After some manipulations, we get an extremely simple polynomial equation in a single variable whose unique real positive root plays the key role. It is then followed by evaluating $O(n^2)$ polynomials of a single variable at the root. It is in contrast to the past works which usually involve a simultaneous system of multivariate polynomial equations. We checked our algorithm using synthetic as well as real world images.

• Communications of Mathematical Education
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• v.10
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• pp.125-141
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• 2000

현행 교육과정에서는 서로 만나는 두 직선의 둘레로 회전하여 얻는 곡면 즉 직원뿔을 꼭지점을 지나지 않는 평면으로 잘라 만들어지는 원추곡선 중에서 원을 제외한 포물선, 타원, 쌍곡선에 대한 시각적 직관적 개념 형성 지도가 미흡한 실정이다. 이에 시각적, 직관적 개념 형성에 적합한 상황과 대상을 제공할 수 있는 컴퓨터 응용소프트웨어를 이용하여 이차곡선을 도입하고 Computer Algebra System을 적용한 MathView를 이용하여 포물선, 타원, 쌍곡선 방정식의 개념 지도 방안을 구안하였다.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.103-121
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• 2017

Taxicab geometry was a typical non-Euclid geometry for mathematically gifted. Most educational material related quadratic curves on taxicab geometry for mathematically gifted served them to inquire the graph of the curves defined by focis and constant. In this study, we provide a shape of quadratic curves on taxicab geometry by applying three definitions(geometric algebraic definition, eccentricity definition, conic section definition).

• 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.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.39-54
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• 2008

This paper investigate Descartes' , which is significant in the history of mathematics, from standpoint of problem-solving. Descartes has clarified the general principle of problem-solving. What is more important, he has found his own new method to solve confronting problem. It is said that those great achievements have exercised profound influence over following generation. Accordingly this article analyze Descartes' work focusing his method.

• Journal of the Korean Geotechnical Society
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• v.23 no.10
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• pp.73-84
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• 2007

For standard piezocones with shoulder filter elements immediately behind the cone tip, general dissipation curves show monotonically decreasing pore pressure from the initial value. However, dilatory dissipation behavior, showing a temporary increase in pore pressure followed by a decrease in the hydrostatic pressure, has been observed in lightly overconsolidated cohesive soils $(1. This unusual dissipation behavior was reported mostly in heavily overconsolidated ground and previous researches were limited to such cases. In this study, the mechanism of dilatory dissipation in lightly overconsolidated cohesive soils was investigated. The relativities of the ground properties evaluated from the CPTu data to the dilatory dissipation were analyzed. And, finite difference analyses on dissipation after cone penetration were performed. It was found that dilatory dissipation occurs in lightly overconsolidated soils since the higher excess pore pressure at the cone face propagates upward to the shoulder filter. Also, it was shown that the ratio of initial excess pore pressure at the cone face to that of the shoulder filter $({\Delta}u_{1i}/{\Delta}u_{2i})$, which is related to overconsolidation ratio (OCR) and hydrostatic pressure $(u_0)$, affects the dilatory dissipation.

• Journal of the Korean Academy of Esthetic Dentistry
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• v.24 no.2
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• pp.86-100
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• 2015

To harmonize with the remaining natural teeth a dentist and technician make an effort to do. Dental ceramic perfectly reproduce the functionality and esthetic is so moved that will deliver to the patient. However It is not easy to overcome the problem. Actually, it can't have the same spectrum curve between different object. The spectrum curve and reflectance is a unique feature of an object like fingerprints. So it is not that the identification of spectral curves that we usually focuses color. We need to understand the process of matamerism makes something like a combination of color perception. In other word that will tell in our field with ceramic teeth of the patient wish to match the color matching process to simulate the cone in our retinas with the same combination.

• Transactions of the Korean Society of Automotive Engineers
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• v.14 no.1
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• pp.54-59
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• 2006

An analytical solution for deflection-load characteristics of a conical disk spring used especially in the automotive manual transmission clutch applications is proposed in order to take into account the effects of friction and large deformation. The conical disk spring, or the diaphragm spring, has a hinge support, an application point of release load at the tip of the fingers and an application point of clamp load near but inside the outer perimeter of the conical disk spring. The friction coefficient is assumed to be a constant regardless of the speed of deflection and the magnitude of loads. Comparison with experimental shows a good agreement with the analytical prediction. Also, the sensitivity of the clamp load due to variations in the geometrical parameters of the conical disk spring is calculated and discussed.

• Journal of Korean Society of Forest Science
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• v.83 no.1
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• pp.63-74
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• 1994

One of the essential factors to estimate the stem and stand growth is to correctly portray a stem form (profile). It is also required to numerically approximate a stem form in order to dynamically grasp and represent a stand growth. A whole stem form seems to be a conical form but a stem outline at various positions tapers off differently. Accordingly it is difficult to model a whole stand form with single taper equation. A stem taper equation with different coefficients on each subinterval can be useful tools to accurately portray a stem form. This article presents the derivation method of individual stem taper curve using spline function. It is also in this paper aimed to study how a stand taper curve car, be derived from the population of single stem taper curve in a stand. These taper equations numerically formulated enable to dynamically represent and prognosticate the development process of a stand and prepare the foundation of variety on growth model study and rational forest planning model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.4
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• pp.452-462
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• 1985

The axisymmetric forward extrusion is analyzed by using the rigid-plastic finite element formulation. The distribution of stresses and strains as well as the deformation pattern in solid extrusion is very important for the improvement of product quality. The initial velocity field is determined by assuming the material as a Newtonian fluid through an arbitrarily shaped axisymmetric die. The workhardening effect and the friction of the die-material interface are considered in the formulation. Some reduction of area and die shapes(conical and biquadratic-curved) are chosen for computation. Experiments are carried out for steel alloy(SCM4) specimens using conical and curved dies. It is found that experimental observation is in good agreement with FEM results. The strain distribution is curved(biquadratic) dies is shown to be more uniform than in conical dies at the same reduction of area.