• 한국수학사학회지
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• 제22권4호
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• pp.129-144
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• 2009

이 연구의 목적은 19세기 대수와 논리 분야에서 드모르간이 구체적으로 어떻게 기여했는지를 살펴보는 것이다. 19세기 대수 분야 발달과정에서 드모르간은, 산술에서 단순히 유추한 형태의 기호대수를 넘어서, 형식으로부터 구성하는 수학의 가능성을 인식하고 이를 명시적으로 나타내어 추상대수학으로 나아갈 수 있는 기초를 닦았다. 드모르간은 19세기 논리학 분야 발달과정에서 아리스토텔레스 논리학의 재구성자인 동시에 수학적 논리학의 창시자로 간주할 수 있다. 그의 연구로 논리학이 철학에서 분리되어 나와 수학과 더욱 긴밀하게 결합하게 되어 수학적 논리학이 하나의 독립적 학문으로 자리 잡게 되었다. 그의 연구 활동을 통하여 우리는 19세기 수학의 발달에서 대수학과 논리학이 현재의 상태로 진화하여 가는 모습을 좀 더 명확하게 알 수 있다.

• 대한수학교육학회지:수학교육학연구
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• 제20권3호
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• pp.275-292
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• 2010

본 연구는 조기대수(Early Algebra)의 연구 동향을 살펴보고, 대수와 관련된 교과의 본질에 대한 탐구를 통하여 조기대수지도에 접근할 수 있는 여러 가지 방법을 논의하였다. 산술과 대수는 형태상 유사하고 대수를 산술의 연장선이라고 보는 관점이 우세하나, 산술과 대수의 근본적인 목적과 기호와 문자의 역할에 있어서 차이가 있다는 인식 또한 제기된다. 또한, 역사적으로 기하가 대수의 출발점이었다는 인식을 할 수 있었다. 본 연구자는 이에 따라 조기대수에 접근할 수 있는 가능성 있는 여러 가지 방향을 도출해 내었다. 조기대수 지도를 위하여 (1) 아동들의 비형식적인 전략을 고려하기 (2) 대수적 관계를 고려한 산술추론하기 (3) 기하적 문제 상황에서 대수추론을 시작하기 (4) 문자와 식의 도구를 제공하기 등을 통하여 조기대수 교육에 접근할 수 있다.

• 대한수학교육학회지:학교수학
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• 제15권4호
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• pp.667-682
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• 2013

이 연구에서는 도형 정의의 재발명에 대해 세 교사가 쓴 lesson play를 통하여, 교사들이 가지고 있었던 정의 개념과 연역적 조직화로서의 정의하기를 가르치고자 할 때 봉착했던 교수학적 문제들을 살펴보았다. 교사들은 lesson play에서 도형의 정의를 주입식으로 전달하지 않았으며 여러 다른 정의의 가능성을 제시하였으나, 연역적 조직화로서의 정의하기를 적극적으로 구현할 수는 없었다. 교사들은 정의를 어떤 용어에 대한 언어적 약속으로 생각하여, 정의를 가르치는 데 있어 연역적 조직화와 같은 과정이 왜 필요한 지를 이해하지 못하였다. 또 수학적 정의의 임의성 및 정의와 정리의 지위가 절대적이지 않다는 사실을 수용하는 데에도 어려움을 겪고 있었다. 이와 같은 결과는 교사들이 도형의 수학적 정의를 자신이 배웠던 방식과 다르게 가르치도록 하기 위해서는, 교사교육에서 단순히 Freudenthal의 이론과 같은 이상적인 교수 방향 및 철학을 소개하는 것만으로는 부족하며, 상식적인 정의 개념과 수학적 정의 개념의 차이를 인식하고 반성해보는 것이 필요함을 보여주고 있다.

• 대한수학교육학회지:수학교육학연구
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• 제14권3호
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• pp.239-266
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• 2004

본 연구는 기존의 수학적 오류에 대한 연구들이 취했던 학생들의 현재 상태를 바탕으로 다양한 오류를 분석하는 방식이 아니라, 학생들의 문제해결과정에서 나타나는 수학적 오류를 인지심리학의 관점에서 분석가능한지를 탐색하는 것을 목적으로 한다. 이에, 본 연구는 Pauscal-Leone의 신피아제 이론을 중심으로 Schoenfeld의 구조 분석 단계(levels of analysis and structure)모형과 개념적, 인과적 관계의 이해를 형식화하는 도구로서 퍼지 인지 맵(Fuzzy Cognitive Map)을 활용하여 학생들의 증명 문제해결 과정에서 나타나는 오류를 분석하고 오도요인을 진단하였다. 연구 결과, 주어진 명제에서 정보를 해석할 때 F조작자가 강하게 활성화되어 나타나는 오도 요인으로 인하여 학생들은 증명에 필요한 개념노드를 충분하게 인출하지 못하거나 인과관계가 없는 개념노드를 나름대로 논리적으로 연결하여 잘못된 증명을 하고 있었다. 오류와 관련된 인지구조는 학생 나름대로의 논리적 알고리듬에 의한 LC 학습의 결과로 형성된 LC 학습구조로 볼 수 있다.

• 한국조경학회지
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• 제28권2호
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• pp.109-109
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• 2000

This study seeks what kind of factors influence to locate dwellings and to establish scenic spots in nature by a case study focused on a meandering stream. The study specially concentrates on the interrelationship between both residences and beautiful sceneries and a meander cut-off-area that reveals a special topographical characteristics, located at Samji village in Youngyang-eup, Youngyang-gun, Koungsangbuk-do. The meander cut-off area, developed at the middle or upper reaches of a river, often makes up specific landscapes such as precipitous cliffs, sheer cliffs and caves. And the area where is specially created by sudden change of flow due to erosion perceived by the cut surface to be the most beautiful scenic spot. These beautiful landscapes were used to be called as Dae, Dam or Gul and managed by Confucian scholars who enjoy refined taste and devote themselves to the study in nature. Moreover, the Ku-Hado-literary means the area of ex-flow-made the scholars' lving with a well prepared basis for agriculture where supplied a cornucopia of organic matters and water. The merit of agriculture made it possible that the scholars became economically independent, and the fact might be the essential point why the meander cut-off area took noticed. Actually, Cho-family has been in Smaji Village for generations, producing a large number of scholars and keeping the actual power of the region. The physical shape of the meander cut-off area, cozily surrounded by mountains, is considered as a good place for the dwelling due to the influence of traditional sight of view for location and P'ungsuchiri which is known as Feng Shui in China and geomancy in the western world. It is a fruit in it own way that we could find the ancestors' discernment and wisdom from this study, who have lived their lives adapting themselves to the given natural environment and also utilizing the nature wisely. But this is a current-argued study on the meander cut-off area. Follow-up studies have to be continued about the landscapes of the meander streams and the meander cut-off areas scattered all over the country except Samji Village and draw the characteristics from the comparative analysis.

• International Journal of Control, Automation, and Systems
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• 제5권5호
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• pp.547-558
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• 2007

This paper proposes a simpler solution to the stabilization problem of a special class of nonlinear underactuated mechanical systems which includes widely studied benchmark systems like Inertia Wheel Pendulum, TORA and Acrobot. Complex internal dynamics and lack of exact feedback linearizibility of these systems makes design of control law a challenging task. Stabilization of these systems has been achieved using Energy Shaping and damping injection and Backstepping technique. Former results in hybrid or switching architectures that make stability analysis complicated whereas use of backstepping some times requires closed form explicit solutions of highly nonlinear equations resulting from partial feedback linearization. It also exhibits the phenomenon of explosions of terms resulting in a highly complicated control law. Exploiting recently introduced Dynamic Surface Control technique and using control Lyapunov function method, a novel nonlinear controller design is presented as a solution to these problems. The stability of the closed loop system is analyzed by exploiting its two-time scale nature and applying concepts from Singular Perturbation Theory. The design procedure is shown to be simpler and more intuitive than existing designs. Design has been applied to important benchmark systems belonging to the class demonstrating controller design simplicity. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and performance is verified using numerical simulations.

• Proceedings of the National Institute of Ecology of the Republic of Korea
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• 제3권1호
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• pp.47-53
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• 2022

The escape behavior of prey fish to predator attack is directly linked to the survival of the fish. In this study, I explored the escape behavior of Medaka fish to bird attacks. To simulate the attack, I designed a model triangular-shaped bird to slide along a fishing line connected between rods at both ends of the tank. The triangular shape was set to 10×15 (S=1), 15×20 (S=2), and 20×25 cm (S=3) with base×height. The slope (θ) of the fishing line, which determines the attack speed of the model bird, was set to values of 15° (θ=1), 30° (θ=2), and 45° (θ=3). The escape behavior was characterized using five variables: escape speed (ν), escape acceleration (α), responsiveness (γ), branch length similarity entropy (ε), and alignment (ϕ). The experimental results showed when (S, θ)=(fixed, varied), the change in values of the five variables were not significant. Thus, the fish respond more sensitively to S than to θ In contrast, when (S, θ)=(varied, fixed), ν, α, and γ showed increasing trends but ε and ϕ did not change much. This indicates the nature of fish escape behavior irrespective of the threat is inherent in ε and ϕ. I found that fish escape behavior can be divided into two types for the five physical quantities. In particular, the analysis showed that the type was mainly determined by the size of the model bird.

• International Journal of Reliability and Applications
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• 제2권3호
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• pp.147-160
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• 2001

The reliability of computer software is of prime importance for all developers of software. The complicated nature of detecting and removing faults from software has led to a plethora of models for reliability growth. One of the most basic of these is the Jelinski Moranda model, where it is assumed that there are N faults in the software, and that in testing, bugs (or faults) are encountered (and removed when defected) according to a stochastic process at a rate which at a given point in time is proportional to the number of bugs remaining in the system. In this research, we consider the possibility that imperfect repair may occur in any attempt to remove a detected bug in the Jelinski Moranda model. We let p represent the probability that a fault which is discovered or detected is actually perfectly repaired. The possibility that the probability p may differ before and after release of the software is also considered. The distribution of both the number of bugs detected and perfectly repaired in a given time period is studied. Cost models for the development and release of software are investigated, and the impact of the parameter p on the optimal release time minimizing expected costs is assessed.

• Advances in Computational Design
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• 제5권2호
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• pp.111-125
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• 2020

The flow behavior of polymer melts within a slit die is an important consideration when designing a die geometry. The quality of the extruded polymer product can be determined through an evaluation of the flow homogeneity, wall shear rate and pressure drop across the central height of the die. However, mathematical formulations cannot fully determine the behavior of the flow due to the complex nature of fluid dynamics and the nonlinear physical properties of the polymer melts. This paper examines two slit die geometries in terms of outlet velocity uniformity, shear rate uniformity at the walls and pressure drop by using the licensed computational fluid dynamics package, Ansys POLYFLOW, based on the finite element method. The Carreau-Yasuda viscosity model was used for the rheological properties of the polypropylene. Comparative analysis of the simulation results will conclude that the modified die design performs better in all three aspects providing uniform exit velocity, uniform wall shear rates, and lower pressure drop.

• Water Engineering Research
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• 제2권3호
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• pp.179-185
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• 2001

The time consuming and expensive nature of experimental research on scouring processes caused by flowing water makes it attractive to develop numerical tools for the predication of the interaction of the fluid flow and the movable bed. In this paper the numerical simulation of scour by a wall jet is presented. The flow is assumed to be two-dimensional, and the alluvium is cohesionless. The solution process, repeated at each time step, involves simulation of a turbulent wall jet flow, solution of the convection-diffusion of sand concentration, and prediction of the bed deformation. For simulation of the jet flow, the governing equations for momentum, mass balance and turbulent parameters are solved by the finite volume method. The SIMPLE scheme with momentum interpolation is used for pressure correction. The convection-diffusion equation is solved for sediment concentration. A boundary condition for concentration at the bed, which takes into account the effect of bed-load, is implemented. The time rate of deposition and scour at the bed is obtained by solving the continuity equation for sediment. The shape and position of the scour hole and deposition of the bed material downstream of the hole appear realistic.