• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1561-1597
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• 2019

In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets. NAIFSs differ from the usual (autonomous) iterated function systems, they are given [32] by a sequence of collections of continuous maps on a compact topological space, where maps are allowed to vary between iterations. Several basic properties of topological pressure and topological entropy of NAIFSs are provided. Especially, we generalize the classical Bowen's result to NAIFSs ensures that the topological entropy is concentrated on the set of nonwandering points. Then, we define the notion of specification property, under which, the NAIFSs have positive topological entropy and all points are entropy points. In particular, each NAIFS with the specification property is topologically chaotic. Additionally, the ${\ast}$-expansive property for NAIFSs is introduced. We will prove that the topological pressure of any continuous potential can be computed as a limit at a definite size scale whenever the NAIFS satisfies the ${\ast}$-expansive property. Finally, we study the NAIFSs induced by expanding maps. We prove that these NAIFSs having the specification and ${\ast}$-expansive properties.

• Proceedings of the KOSOMBE Conference
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• v.1994 no.05
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• pp.43-48
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• 1994

본 논문은 반복 수축 변환의 프랙탈(fractal) 이론에 근거한 심전도 데이터 압축에 관한 연구이다. 심전도 데이터에 반복 함수계(Iterated Function System : IFS) 모델을 적용하여 신호 자체의 자기 유사성(self-similarity)을 반복 수축 변환으로 표현하고, 그 매개변수만을 저장한다. 재구성시는 변환 매개변수를 반복 적용하여 원래의 신호에 근사되어지는 값을 얻게 된다. 심전도 데이타는 부분적으로 자기 유사성을 갖는다고 보고, 부분 자기-유사 프랙탈 모델(piecewise self-affine fractal model)로 표현될 수 있다. 이 모델은 신호를 특정 구간들로 나누어 각 구간들에 대해 최적 프랙탈 보간(fractal interpolation)을 구하고 그 중 오차가 가장 작은 매개변수만을 추출하여 저장한다. 이 방법을 심전도 데이타에 적용한 결과 특정 압축율에 대해 아주 적은 재생오차 (percent root-mean-square difference : PRD)를 얻을 수 있었다.

• Journal of Korea Game Society
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• v.16 no.1
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• pp.119-128
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• 2016

In this paper, we consider an improved deformation method of IFS(iterated function system) fractal using codes of fractal points. In the existing deformation methods, the intermediate results of position dependent partial deformation propagate randomly due to the randomly selected maps of iteration. Therefore, in many cases, the obtained results become somewhat monotonous feeling shapes. To improve these limitations, we propose a method in which the selection of maps are controlled by codes of fractal points. Applying this method, we can obtain interesting fractal deformation conforming with its fractal features. Also, we propose a simple method, incorporating state variables, that can be applied to deformation of some fractal features other than position coordinates.

• Journal of Biomedical Engineering Research
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• v.16 no.1
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• pp.17-24
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• 1995

This paper presents a new compression method (or ECG data using iterated contractive transformations. The method represents any range of ECG signal by piecewise self-afrine fractal Interpolation (PSAFI). The piecewise self-afrine rractal model is used where a discrete data set is viewed as being composed of contractive arfine transformation of pieces of itself. This algorithm was evaluated using MIT/BIH arrhythmia database. PSAFI is found to yield a relatively low reconstruction error for a given compression ratio than conventional direct compression methods. The compression ratio achieved was 883.9 bits per second (bps) - an average percent rms difference (AFRD) of 5.39 percent -with the original 12b ECG samples digitized at 400 Hz.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2000.12a
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• pp.125-128
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• 2000

The conventional fractal decoding was required a vast amount computational complexity. Since every range blocks was implemented to IFS(iterated function system). In order to improve this, it has been suggested to that each range block was classified to iterated and non-iterated regions. If IFS region is contractive, then it can be performed a fast decoding. In this paper, a searched region of the domain in the encoding is limited to the range region that is similar with the domain block, and IFS region is a minimum. So, it can be performed a fast decoding by reducing the computational complexity for IFS in fractal image decoding.

• Journal of the Institute of Convergence Signal Processing
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• v.2 no.2
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• pp.13-19
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• 2001

The conventional fractal decoding was required a vast amount computational complexity, since every range blocks was implemented to IFS(iterated function system). In order to improve this, it has been suggested that each range block was classified to iterated and non-iterated regions. Non-iterated regions is called data dependency region, and if data dependency region extended, IFS regions are contractive. In this paper, a searched region of the domain is limited to the range regions that is similar with the domain blocks, and the domain region is more overlapped. As a result, data dependency region has maximum region, that is IFS regions can be minimum region. The minimizing method of domain region is defined to minimum domain(MD) which is minimum IFS region. Using the minimizing method of domain region, there is not influence PSNR(peak signal-to-noise ratio). And it can be performed a fast decoding by reducing the computational complexity for IFS in fractal image decoding.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.11
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• pp.22-35
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• 1999

The block assembly process takes more than half of the total shipbuilding processes. Therefore, it is very important to have a practically useful block assembly process planning system which can build plans of maximum efficiency with minimum man-hours required. However, the process plans are often not readily executable in the assembly shops due to severe imbalance of workloads. This problem arises because the process planning is done on block by block basis in current practice without paying any attention to the load distribution among the assembly shops. this paper presents the development of an automated hull block assembly process planning system which results in the most effective use of production resources and also produces plans that enable efficient time management. If the load balance of assembly shops is to be considered at the time of process planning, the task becomes complicated because of the increased computational complexity. To solve this problem, a new approach is adopted in this research in which the load balancing function and process planning function are iterated alternately providing to each other contexts for subsequent improvement. The result of case study with the data supplied from the shipyard shows that the system developed in this research is very effective and useful.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.157-163
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• 1997

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover we see that for any odd n, the ratio $r_n$ is still valid for just-touching I.F.S $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.

• Journal of the Korean Society of Radiology
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• v.12 no.4
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• pp.505-510
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• 2018

In this study, we allocate bits by quantizing these fractal coefficients through a quantizer which can extract the probability distribution. In the coding process of IFS, a variable size block method is used to shorten the coding time and improve the compression ratio. In the future, it will be necessary to further improve the coding time and the compression rate while maintaining the best image quality in the fractal coding process.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.5
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• pp.84-93
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• 2000

The conventional fractal decoding was implemented to IFS(iterated function system) for every range regions But a part of the range regions can be decoded without the iteration and there is a data dependence regions In order to decode $R{\times}R$ range blocks, It needs $2R{\times}2R$ domain blocks This decoding can be analyzed to the dependence graph The vertex of the graph represents the range blocks, and the vertex is classified into the vertex of the range and domain The edge indicates that the vertex is referred to the other vertices The in-degree and the out-degree are defined to the number of the edge that is entered and exited, respectively The proposed method is analyzed by a dependence graph to the fractal code, and the decoding order is recomposed by the information of the out-degree That is, If the out-degree of the vertex is zero, then this vertex can be used to the vertex with data dependence Thus, the proposed method can extend the data dependence regions by the recomposition of the decoding order As a result, the Iterated regions are minimized without loss of the image quality or PSNR(peak signal-to-noise ratio), Therefore, it can be a fast decoding by the reducing to the computational complexity for IFS in the fractal Image decoding.