• Communications of the Korean Mathematical Society
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• v.38 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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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.

• The Transactions of the Korea Information Processing Society
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• v.4 no.2
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• pp.596-605
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• 1997

The synamic systrm emplohing the self-squared function, , $f(Z)=z^2+c$, provides the Mandelbrot set which classifies constants c using the divergence of the sequence starting from the origin.To speed-up the generation of Mandelbrot set images, two approaches , called as the divide-and-conquer technique and the triangular boundary tracing technique, have been developed.However , the divede-and-conquer technique genrates sequences of some pixels that so not affect graphical representations of the Mandelbrot set.The triangular boundary tracing tech-mique does noot represent some 8-connected components of the Mandelbrost set.In this paper, we prorose a new ;method which solves the 8-connectivity problem of triangular boundary tracing technique.This algorithm considers the divergence for only pixels which are essential to the graphical repressentation of the Mandelbrot set.It also foves good representations for 8-connected components like hairly structures.

• Journal of the Korea Computer Graphics Society
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• v.26 no.1
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• pp.7-15
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• 2020

In the process of visualizing a point set representing a smooth manifold surface, global illumination techniques can be used to render a realistic scene with various effects of lighting. Thanks to the continuous demand for ray tracing and the development of graphics hardware, dedicated GPUs and programmable pipeline for ray tracing have been introduced in recent years. In this paper, real-time global illumination rendering is studied for a point-set model using ray-tracing GPUs. We apply the moving least-squares (MLS) method to approximate the point set to a smooth implicit surface and render it using global illumination by performing massive ray-intersection tests with the surface and generating shading effects at the intersection point. As a result, a complicated point-set scene consisting of more than 0.5M points can be generated in real-time.

• Proceedings of the KIEE Conference
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• 2008.09a
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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.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.58 no.3
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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.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2008.11a
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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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• v.11 no.4
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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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• v.7 no.3
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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.