• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1565-1571
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• 2017

The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the role of bracketing of the indexed class of functions associated with the process. Then we apply the idea of DeHardt (1971) associated with the bracketing method to the process induced by the logistic map. We finally illustrate an application to Monte Carlo integration.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.765-773
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• 2013

We show that for the logistic map, almost every x is a normal number mod 2 with respect to all intervals except for $[a,b]=[\frac{1}{4},1]\;or\;[a,b]=[\frac{1}{2}-\frac{\sqrt{3}}{4},\frac{1}{2}+\frac{\sqrt{3}}{4}]$.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2006.04a
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• pp.339-344
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• 2006

Slope failures are happen to natural disastrous when they occur in mountainous areas adjoining highways in Korea. The accidents associated with slope failures have increased due to rapid urbanization of mountainous areas. Therefore, Regular maintenance is essential for all slope and conducted to maintain road safety as well as road function. In this study, we take priority of making a database of risk factor of the failure of a slope before assesment and analysis. The purpose of this paper is to recommend a standard of Slope Management Information Sheet(SMIS) like as Hazard Map. The next research, we suggest to pre-estimated model of a road slope using Logistic Regression Model.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.12
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• pp.5963-5980
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• 2017

Image scrambling is an important technology in information hiding, where the Arnold transformation is widely used. Several researchers have proposed the application of $H{\acute{e}}non$ map in square image scrambling, and certain improved technologies require scrambling many times to achieve a good effect without resisting chosen-plaintext attack although it can be directly applied to non-square images. This paper presents a non-square image scrambling algorithm, which can resist chosen-plaintext attack based on a chaotic two-dimensional Sine Logistic modulation map and $H{\acute{e}}non$ map (2D-SLHM). Theoretical analysis and experimental results show that the proposed algorithm has advantages in terms of key space, efficiency, scrambling degree, ability of anti-attack and robustness to noise interference.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.37 no.2
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• pp.91-97
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• 2019

In automatic map generalization, the formalization of cartographic principles is important. This study proposes and evaluates the selection method for road network generalization that analyzes existing maps using reverse engineering and formalizes the selection rules for the road network. Existing maps with a 1:5,000 scale and a 1:25,000 scale are compared, and the criteria for selection of the road network data and the relative importance of each network object are determined and analyzed using $T{\ddot{o}}pfer^{\prime}s$ Radical Law as well as the logistic regression model. The selection model derived from the analysis result is applied to the test data, and road network data for the 1:25,000 scale map are generated from the digital topographic map on a 1:5,000 scale. The selected road network is compared with the existing road network data on the 1:25,000 scale for a qualitative and quantitative evaluation. The result indicates that more than 80% of road objects are matched to existing data.

• Journal of the KSME
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• v.31 no.1
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• pp.68-79
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• 1991

이 글에서는 다음의 내용에 대하여 알아보았다. Duffing - holmes 방정식에서의 Chaos Logistic map에서의 Chaos 기타 시스템에서의 Chaos 1) Henon map 2) Bouncty bau map (standard map) 3) 진자에서의 Chaos 4) Taylor-Couette유동 5) Fluid drop Chaos 6) Surface wave Chaos Lyapunov 지수 (Exponent)

• Journal of the Optical Society of Korea
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• v.20 no.1
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• pp.42-54
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• 2016

A hybrid color and grayscale images encryption scheme based on the quaternion Hartley transform (QHT), the two-dimensional (2D) logistic map, the double random phase encoding (DRPE) in gyrator transform (GT) domain and the three-step phase-shifting interferometry (PSI) is presented. First, we propose a new color image processing tool termed as the quaternion Hartley transform, and we develop an efficient method to calculate the QHT of a quaternion matrix. In the presented encryption scheme, the original color and grayscale images are represented by quaternion algebra and processed holistically in a vector manner using QHT. To enhance the security level, a 2D logistic map-based scrambling technique is designed to permute the complex amplitude, which is formed by the components of the QHT-transformed original images. Subsequently, the scrambled data is encoded by the GT-based DRPE system. For the convenience of storage and transmission, the resulting encrypted signal is recorded as the real-valued interferograms using three-step PSI. The parameters of the scrambling method, the GT orders and the two random phase masks form the keys for decryption of the secret images. Simulation results demonstrate that the proposed scheme has high security level and certain robustness against data loss, noise disturbance and some attacks such as chosen plaintext attack.

• Journal of Korean Society for Geospatial Information Science
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• v.14 no.1 s.35
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• pp.85-91
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• 2006

Recently, slope failures are happen to natural disastrous when they occur in mountainous areas adjoining highways in Korea. The accidents associated with slope failures have increased due to rapid urbanization of mountainous areas. Therefore, Regular maintenance is essential for all slope and needs maintenance of road safety as well as road function. In this study, we take priority of making a database of risk factor of the failure of a slope before assesment and analysis. The purpose of this paper is to recommend a standard of Slope Management Information Sheet(SMIS) like as Hazard Map. The next research, we suggest to pre-estimated model of a road slope using Logistic Regression Model.

• Proceedings of the KIPE Conference
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• 2005.07a
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• pp.766-769
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• 2005

본 연구에서는 카오스 랜덤 캐리어 PWM에 의한 3상 유도 전동기의 스위칭 소음 저감에 대하여 다루고 있다. 랜덤 수 발생기로서는 종전부터 사용해 온 선형일치발생기(LCG)대신에 Logistic map의 분기트리를 사용하였다. 카오스 랜덤 수 발생은 80C196 마이크로 콘트롤러가 담당하고 있으며, 80C196으로부터 발생된 카오스 랜덤 수와 MAX038에 의하여 삼각파 랜덤 캐리어가 발생되고 있다. 1.5kw급 3상 유도전동기 구동 시스템에 카오스 랜덤 PWM와 종전의 방법을 적용하여 전동기 전압 및 전류 그리고 스위칭 소음의 스펙트럼을 고찰하였다.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2002.05a
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• pp.469-472
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• 2002

본 논문에서는 카오스에 기반을 둔 ELM(Expanding Logistic Map) 암호화 알고리즘을 개선하기 위해 CELM(Cascade Expanding Logistic Map)을 제안한다. 제안된 암호화 시스템은 3차 방정식에 기반을 둔 ELM의 차수를 증가시켜 키의 범위를 확대하고, 서로 다른 Key 값과 초기 값의 함수를 Cascade연결하여 안정성을 높일 수 있었다.