• 대한수학회논문집
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• 제38권1호
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• pp.243-256
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• 2023

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C¹ generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.

• 충청수학회지
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• 제20권3호
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• pp.343-348
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• 2007

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the limit sets of wandering points whose stable sets have nonempty interior consist of single periodic orbit.

• 충청수학회지
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• 제23권4호
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• pp.871-878
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• 2010

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the points whose stable sets have nonempty interior are periodic points.

• 한국정보처리학회논문지
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• 제4권2호
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• pp.596-605
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• 1997

복소 평면상의 임의의 점을 c값으로 고려한 2차 복소함수,$f(Z)=z^2+c$의 동력한 시스템은 초기 값0을 대입함으로써 획득된 순열의 발산성에 따라 C값을 분류한 만델브로트 집합을 제공한다[2]. 각 화소의 발산성을 나타내는 전형적인 만델브로트 집합 영상의 생성 에 소요되는 단축하기 위해 영역분할법(divide-and-conquer)과 삼각형을 이용한 경계 선 추적법( riangular boundary tracing)들이 제안되었다[4,6]그러나, 영역분할법은 만델브로트 집합의 생성에 영향을 주지 못하는 화소에 대한 순열의 발산여부를 조사하고 , 삼각형을 이용한 경계선 추적법은 8-연결성으로 연열된 일부 영상을 표현하지 못 하는 단점이 있다. 본 논문에서는 삼각형 추적 기법의 문제점을 해결한 화소의 8-연결성을 이용한 경계선 추적 알고리즘을 제안한다. 제안된 경계선 추적 기법은 8-연결성에 기초한 경계선 추적으로 만델브로트 영상을 생성할 때 영향을 주지 못하는 화소에 대한 발산 검사를 하지 않을 뿐만 아니라, hairly 구조와 같이 8-연결성을 갖는 만델 브로트 집합의 정확한 표현을 얻을 수 있다.

• 한국컴퓨터그래픽스학회논문지
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• 제26권1호
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• pp.7-15
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• 2020

점집합을 매끄러운 다양체 표면으로 가시화하는 과정에서 전역 조명 기법을 사용하면 다양한 조명 효과로 사실적인 장면을 렌더링 할 수 있다. 광선 추적법에 대한 지속적인 요구와 그래픽스 하드웨어의 발전을 바탕으로 광선 추적법을 위한 전용 GPU와 프로그래머블 파이프 라인이 근래에 소개되었다. 본 논문에서는 광선 추적법의 가속을 지원하는 GPU와 렌더링 파이프라인을 사용하여 점집합 모델에 대한 실시간 전역 조명 렌더링을 수행하는 방법을 제시한다. 즉, 이동 최소 자승법을 적용하여 점집합을 부드러운 음함수 표면으로 근사한 후, GPU기반 광선 추적법을 이용하여 표면과의 광선 교차 검사를 수행하고 교차점에서 쉐이딩 효과를 적용하여 전역 조명 렌더링을 수행한다. 그 결과 오십만개 이상의 점으로 구성된 복잡한 점집합 모델이 포함된 장면을 실시간에 생성할 수 있다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2008년도 추계학술대회 논문집 전기설비전문위원
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• pp.140-143
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• 2008

In this study, it was studied about the improved road light design for drivers and pedestrians using ray- or reverse ray-tracing method. Many of conventional road lights are not suitable for drivers and pedestrians because it has some serious problems such as glare effect or randomicity of illuminated areas. It was oriented from customary design method which was pointed at simple target such as luminance or electrical power. But it was not truth any more that the high luminance or electrical power consumption mean more bright and good mad light. We studied ray-tracing method for road light reflector design to get the several goals. It means that good road light has easy for drivers and Pedestrians eyes and illuminating objects on the road clearly. So, we set the design targets such as uniformity on the road area per one road light, shading angles and continuous luminance uniformity on the long distance road. We designed ideal road light conditions using ray-tracing method. We set the height of drivers and pedestrians eyes and calculated design guideline to make above design targets. Then we designed road light reflector using reverse ray-tracing method. And we achieved same luminance on the road almost half power consumption because we reduced loss of light. We achieved ideal design guide as 75 degrees of shading angles and 0.5 of luminance uniformity on the road area. Finally, we suggested reflector design for 250 watts power consumption CDM light source.

• 전기학회논문지P
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• 제58권3호
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• pp.347-350
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• 2009

In this study, it was studied about the improved road light design for drivers and pedestrians using forward or reverse ray-tracing method. Many of conventional road lights are not suitable for drivers and pedestrians because it has some serious problems such as glare effect or randomicity of illuminated areas. It was oriented from customary design method which was pointed at simple target such as luminance or electrical power. But it was not truth any more that the high luminance or electrical power consumption mean more bright and good road light. We studied ray-tracing method for road light reflector design to get the several goals. It means that good road light has easy for drivers and pedestrians eyes and illuminating objects on the road clearly. So, we set the design targets such as uniformity on the road area per one road light, shading angles and continuous luminance uniformity on the long distance road. We designed ideal road light conditions using ray-tracing method. We set the height of drivers and pedestrians eyes and calculated design guideline to make above design targets. Then we designed road light reflector using reverse ray-tracing method. And we achieved same luminance on the road almost half power consumption because we reduced loss of light. We achieved ideal design guide as 75 degrees of shading angles and 0.5 of luminance uniformity on the road area. It is superior than conventional road light ability such as 0.35 of luminance uniformity of 400 watts power consumption lamp. Finally, we suggested reflector design for 250 watts power consumption CDM Iight source.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2008년도 추계학술대회 논문집 Vol.21
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• pp.327-328
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• 2008

In this study, it was studied about the improved road light design for drivers and pedestrians using ray- or reverse ray-tracing method. Many of conventional road lights are not suitable for drivers and pedestrians because it has some serious problems such as glare effect or randomicity of illuminated areas. It was oriented from customary design method which was pointed at simple target such as luminance or electrical power. But it was not truth any more that the high luminance or electrical power consumption mean more bright and good road light. We studied ray-tracing method for road light reflector design to get the several goals. It means that good road light has easy for drivers and pedestrians eyes and illuminating objects on the road clearly. So, we set the design targets such as uniformity on the road area per one road light, shading angles and continuous luminance uniformity on the long distance road. We designed ideal road light conditions using ray-tracing method. We set the height of drivers and pedestrians eyes and calculated design guideline to make above design targets. Then we designed road light reflector using reverse ray-tracing method. And we achieved same luminance on the road almost half power consumption because we reduced loss of light. We achieved ideal design guide as 75 degrees of shading angles and 0.5 of luminance uniformity on the road area. Finally, we suggested reflector design for 250 watts power consumption CDM light source.

• Transactions on Electrical and Electronic Materials
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• 제11권4호
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• pp.194-196
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• 2010

A study is presented of improved road light design for drivers and pedestrians with the use of a ray- or reverse ray-tracing method. Many existing road lights are unsuitable for drivers and pedestrians because of serious problems such as glare effect or randomicity of illuminated areas. This situation has arisen because in customary design methods the emphasis has been on simple factors such as luminance or electrical power. However a high luminance or electrical power consumption, alone, do not guarantee bright and good road lighting. So we have applied a ray-tracing method to the design of a road light reflector with the goals of ensuring that illuminated objects on the road can be seen more clearly and that the illuminating light is more comfortable for the eyes of drivers and pedestrians. We have set design targets for factors such as the uniformity of lighting on the road area per road light, the shading angles and the continuous luminance uniformity on long lengths of road. For set heights of the eyes of drivers and pedestrians eyes we have calculated a design guideline for the achievement of the above design targets. Then we designed a road light reflector using the reverse ray-tracing approach. Also we have achieved the same luminance on the road with almost half the power consumption, through the reduction of lighty loss. In an ideal design optimum parameters are suggested to be a shading angle of 75 degrees and a luminance uniformity of 0.5 on the road area. This reflector performance is achievable with a 250 watt power consumption ceramic discharge metal light source.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.1029-1038
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• 2000

In this paper, we show that if x is a positively Lyapunov stable point of an expansive homeomorphism with the pseudo-orbit-tracing-property, then x is a periodic point or its positive limit set consists of only one periodic orbit, and their periods are predictable. We give a necessary and sufficient condition that a basic set is to be a sink or source. Also, we consider some dynamical properties of basic sets.