• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.57-64
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• 1996

Let $(X, B, \mu)$ be a probability space. Then we say $\tau : X \to X$ is a measure-preserving transformation if $\mu(\tau^{-1} E) = \mu(E)$. and we call it an ergodic transformation if $\mu(\tau^{-1}E\DeltaE) = 0$ for a measurable subset E implies $\mu(E) = 0$. An equivalent definition is that constant functions are the only $\tau$-invariant functions.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.643-654
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• 2000

In this paper, we review some class of t-norms on which fuzzy arithmetic operations preserve the shapes of fuzzy numbers and the Hausdorff-distance between fuzzy numbers as the measure of distance between fuzzy numbers. And we suggest the least Hausdorff-distance square method for fuzzy linear regression model using shape preserving fuzzy arithmetic operations.

• Proceedings of the Korea Information Processing Society Conference
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• 2007.11a
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• pp.1131-1134
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• 2007

본 논문에서는 랜덤대치(random substitution) 기법에 대하여 심도 있는 분석을 실시한다. 랜덤대치 기법의 효율적인 구현을 위하여 데이터 재구축(reconstruction) 과정에서 필요로 하는 역행렬을 구하는 공식을 제시한다. 또한, 랜덤대치에 사용되는 다양한 파라미터들의 의미를 실험적으로 밝혀내며, 정확도와 프라이버시를 합리적으로 측정할 수 있는 새로운 측도(measure)들을 제안한다.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.881-889
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• 1994

Let ($X, \Beta, \mu$) be a measure space with the $\sigma$-algebra $\Beta$ and the probability measure $\mu$. Throughouth this article set equalities and inclusions are understood as being so modulo measure zero sets. A transformation T defined on a probability space X is said to be measure preserving if $\mu(T^{-1}E) = \mu(E)$ for $E \in B$. It is said to be ergodic if $\mu(E) = 0$ or i whenever $T^{-1}E = E$ for $E \in B$. Consider the sequence ${x, Tx, T^2x,...}$ for $x \in X$. One may ask the following questions: What is the relative frequency of the points $T^nx$ which visit the set E\ulcorner Birkhoff Ergodic Theorem states that for an ergodic transformation T the time average $lim_{n \to \infty}(1/N)\sum^{N-1}_{n=0}{f(T^nx)}$ equals for almost every x the space average $(1/\mu(X)) \int_X f(x)d\mu(x)$. In the special case when f is the characteristic function $\chi E$ of a set E and T is ergodic we have the following formula for the frequency of visits of T-iterates to E : $$ lim_{N \to \infty} \frac{$\mid${n : T^n x \in E, 0 \leq n $\mid$}{N} = \mu(E) $$ for almost all $x \in X$ where $$\mid$\cdot$\mid$$ denotes cardinality of a set. For the details, see [8], [10].

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.109-117
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• 2015

We consider the relative entropy for two R-CGMY processes, which are CGMY processes with Y equal to 1, to choose an equivalent martingale measure (EMM) when the underlying asset of a derivative follows a R-CGMY process in the financial market. Since the R-CGMY process leads to an incomplete market, we have to use a proper technique to choose an EMM among a variety of EMMs. In this paper, we derive the closed form expression of the relative entropy for R-CGMY processes.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.4
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• pp.611-617
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• 2004

Pixel classification is one of basic image processing issues. The general characteristics of the pixels belonging to various classes are discussed and the radical principles of pixel classification are given. At the same time. a pixel classification scheme based on image direction measure is proposed. As a typical application instance of pixel classification, an adaptive multi-level median filter is presented. An image can be classified into two types of areas by using the direction information measure, that is. smooth area and edge area. Single direction multi-level median filter is used in smooth area. and multi-direction multi-level median filter is taken in the other type of area. What's more. an adaptive mechanism is proposed to adjust the type of the filters and the size of filter window. As a result. we get a better trade-off between preserving details and noise filtering.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.1
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• pp.85-93
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• 1992

In this paper, we propose a parameter-free smoothing method for speckle images, i.e., an adaptive least squares image smoothing technique implemented in a multistep environment. The pertinent smoothing window size at a given pixel is determined by the discontinuity measure which is defined by the ratio of the local variance and mean squares of intensity values of pixels over the smoothing window centered there. The mode of the discontinuity measure at each step is estimated to replace the noise variance parameter that is required in the adaptive smoothing. Computer simulation shows that the proposed multistep technique can smooth homogeneous regions satisfactorily while preserving fine details near boundaries.

• Journal of the Korean Graphic Arts Communication Society
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• v.30 no.1
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• pp.59-69
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• 2012

This study is Long term preservation measures which is closely related to preserving paper records, record condition evaluation, preservation measure and is conducted as follows. As for Means to Evaluate the Deterioration and Damaged Conditions of Records, research and analysis has been made on the contamination and deterioration examples such as damage, dry, stapler, metal, contamination, acidification which are the characteristics of paper record damage types. The of Paper record is one of the key procedures to evaluate the record material and its physi-chemical status in many criteria and to suggest the best preservation method. Between 1970 and 2000, the main record materials was fine paper and OMR paper along with partly newspaper and coarse paper, whereas the main recording material was ball point pen. Overall damage and deterioration status is, for record materials between 1940 and 1960, high deterioration was found and in urgent need for preservation measure and more damages are caused by tapes, staplers and metals. As for records after 1970, there is light deterioration but needs preservation process. There are approximately 3 million records produces before 2000, and assuming that there are 30 pages per record and that 30% has been damaged or deteriorated, 27 million pages are subject to preservation process. Among damaged or deteriorated records, there are large number of records impossible to go through deacidification process so manual preservation and restoration process is necessary as well. Securing manpower having preservation and restoration skills as well as preservation equipment(deacidification process, preservation and restoration) is in urgent need.

• Journal of KIISE:Databases
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• v.35 no.6
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• pp.481-494
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• 2008

In this paper we propose Fourier magnitudes based privacy preserving clustering on time-series data. The previous privacy-preserving method, called DFT coefficient method, has a critical problem in privacy-preservation itself since the original time-series data may be reconstructed from privacy-preserved data. In contrast, the proposed DFT magnitude method has an excellent characteristic that reconstructing the original data is almost impossible since it uses only DFT magnitudes except DFT phases. In this paper, we first explain why the reconstruction is easy in the DFT coefficient method, and why it is difficult in the DFT magnitude method. We then propose a notion of distance-order preservation which can be used both in estimating clustering accuracy and in selecting DFT magnitudes. Degree of distance-order preservation means how many time-series preserve their relative distance orders before and after privacy-preserving. Using this degree of distance-order preservation we present greedy strategies for selecting magnitudes in the DFT magnitude method. That is, those greedy strategies select DFT magnitudes to maximize the degree of distance-order preservation, and eventually we can achieve the relatively high clustering accuracy in the DFT magnitude method. Finally, we empirically show that the degree of distance-order preservation is an excellent measure that well reflects the clustering accuracy. In addition, experimental results show that our greedy strategies of the DFT magnitude method are comparable with the DFT coefficient method in the clustering accuracy. These results indicate that, compared with the DFT coefficient method, our DFT magnitude method provides the excellent degree of privacy-preservation as well as the comparable clustering accuracy.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.2
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• pp.305-313
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• 2002

The genetic algorithm(GA), an optimization technique based on the theory of natural selection, has proven to be relatively robust means to search for global optimum. It is converged near to the global optimum point without auxiliary information such as differentiation of function. When studying some optimization problems with continuous variables, it was found that premature saturation was reached that is no further improvement in the object function could be found over a set of iterations. Also, the general GA oscillates in the region of the new global optimum point so that the speed of convergence is decreased. This paper is to propose the concept of restarting and elitist preserving strategy as a measure to overcome this difficulty. Some benchmark examples are studied involving 3-bar truss and cantilever beam with plane stress elements. The modifications to GA improve the speed of convergence.