• Title, Summary, Keyword: iterated function system

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ON SOME GRONWALL TYPE INEQUALITIES FOR A SYSTEM INTEGRAL EQUATION

  • KIM, BYUNG-IL
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.789-805
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    • 2005
  • In this paper we consider analogous of Gronwall-type inequalities involving iterated integrals in the inequality (1.2) for functions when the function u in the right-hand side of the in­equality (1.2) is replaced by the function $u^P$ for some p. These inequalities are effective tools in the study of a system of an integral equation. We also provide some integral inequalities involving iterated integrals.

Efficient Image Transmission System Using IFS (IFS를 이용한 고효율 영상전송 시스템)

  • Kim, Sang Hyun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.15 no.11
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    • pp.6810-6814
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    • 2014
  • The concept of IFS (Iterated Function System) was applied to compress and transmit image data efficiently. To compress the image data with IFS, self-similarity was used to search a similar block. To improve the coding performance for the iterated function system with natural images, the image will be formed of properly transformed parts of itself to minimize the coding error. The simulation results using the proposed IFS represent high PSNR performance and improved compression efficiency with the coefficient of a recursive function.

엑셀과 Fantastic Fractals을 이용한 Iterated Function System

  • An, Dae-Yeong
    • Communications of Mathematical Education
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    • v.9
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    • pp.283-297
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    • 1999
  • 수학에서는 컴퓨터를 활용해야 하고, 사회생활에서는 수학을 활용해야 한다. 이런 의미에서 엑셀을 수업 시간에 활용하는 것이 필요하다. 수학II의 일차변환을 엑셀을 어떻게 활용할 수 있는 가를 제시한다. 일차변환의 응용으로서, 이동을 포함시킨 아핀변환을 이용하여 프랙탈을 생성하는 방법을 찾아본다. 프랙탈을 생성하기 위해서는 IFS(Iterated Function System)에 의해 수 만번의 합성변환을 필요하므로 소프트웨어가 필수적이다. 여기서는 Fanstic Fractals 프로그램을 이용하여 직관적으로 얻은 그림에서 변환 행렬의 값을 구하여, 엑셀에서 두 가지 방법으로 분석하였다.

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ON TOPOLOGICAL ENTROPY AND TOPOLOGICAL PRESSURE OF NON-AUTONOMOUS ITERATED FUNCTION SYSTEMS

  • Ghane, Fatemeh H.;Sarkooh, Javad Nazarian
    • 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.

ECG Data Compression Using Iterated Function System (반복 함수계(Iterated Function Systems)를 이용한 심전도 데이타 압축)

  • Jun, Young-Il;Lee, Soon-Hyouk;Lee, Gee-Yeon;Yoon, Young-Ro;Yoon, Hyung-Ro
    • 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.

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A Propagation Control Method Using Codes In The Fractal Deformation (코드를 활용한 프랙탈 변형의 전파 제어 방법)

  • Han, Yeong-Deok
    • 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.

A Fast Fractal Image Decoding Using the Encoding Algorithm by the Limitation of Domain Searching Regions (정의역 탐색영역 제한 부호화 알고리듬을 이용한 고속 프랙탈 영상복원)

  • 정태일;강경원;권기룡;문광석;김문수
    • Proceedings of the Korea Institute of Convergence Signal Processing
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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.

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