• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.971-983
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• 2016

A partially ordered set P is ideal-homogeneous provided that for any ideals I and J, if $$I{\sim_=}_{\sigma}J$$, then there exists an automorphism ${\sigma}^*$ such that ${\sigma}^*{\mid}_I={\sigma}$. Behrendt [1] characterizes the ideal-homogeneous partially ordered sets of height 1. In this paper, we characterize the ideal-homogeneous partially ordered sets of height 2 and nd some families of ideal-homogeneous partially ordered sets.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.279-287
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• 1995

Let $F$ be a set of distributions on R with the topology of weak convergence, and let $A$ be the $\sigma$-field generated by the open sets. We denote by $F_1^\infty$ the space consisting of all infinite sequence $(F_1, F_2, \cdots), F_n \in F and R_1^\infty$ the space consisting of all infinite sequences $(x_1, x_2, \cdots)$ of real numbers. Take the $\sigma$-field $F_1^\infty$ to be the smallest $\sigma$-field of subsets of $F_1^\infty$ containing all finite-dimensional rectangles and take $B_1^\infty$ to be the Borel $\sigma$-field $R_1^\infty$.

• Journal of the Institute of Convergence Signal Processing
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• v.11 no.2
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• pp.151-156
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• 2010

This paper is a study on image noise reduction of modified sigma filter by image decomposition using directivity. Conventional sigma filter has been shown to be a good solution both in terms of filtering accuracy and computational complexity. However, the sigma filter does not preserve well small edges especially for high level of additive noise. In this paper, we propose here a new method using a modified sigma filter. In our proposed method the input image is first decomposed in two components that have features of horizontal, vertical and diagonal direction. Then, two components are applied HPF and LPF. By applying a conventional sigma filter separately on each of them, the output image is reconstructed from the filtered components. Added noise is removed and our proposed method preserves the edges from the image. Comparative results from experiments show that the proposed algorithm achieves higher gains, on average, 2.6 dB PSNR than the sigma filter and 0.5 dB PSNR than the modified sigma filter. When relatively high levels of noise added, the proposed algorithm shows better performance than two conventional filters.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.263-275
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• 2010

Let {$X_n;n\;\geq\;1$} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set $S_n\;=\;{\sum}^n_{k=1}X_k$, $M_n\;=\;max_{k{\leq}n}|S_k|$, $n\;{\geq}\;1$. Suppose $\sigma^2\;=\;EX^2_1+2{\sum}^\infty_{k=2}EX_1X_k$ (0 < $\sigma$ < $\infty$). We prove that for any b > -1/2, if $E|X|^{2+\delta}$(0<$\delta$$\leq$1), then $$lim\limits_{\varepsilon\searrow0}\varepsilon^{2b+1}\sum^{\infty}_{n=1}\frac{(loglogn)^{b-1/2}}{n^{3/2}logn}E\{M_n-\sigma\varepsilon\sqrt{2nloglogn}\}_+=\frac{2^{-1/2-b}{\sigma}E|N|^{2(b+1)}}{(b+1)(2b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2(b+1)}}$$ and for any b > -1/2, $$lim\limits_{\varepsilon\nearrow\infty}\varepsilon^{-2(b+1)}\sum^{\infty}_{n=1}\frac{(loglogn)^b}{n^{3/2}logn}E\{\sigma\varepsilon\sqrt{\frac{\pi^2n}{8loglogn}}-M_n\}_+=\frac{\Gamma(b+1/2)}{\sqrt{2}(b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2b+2'}}$$, where $\Gamma(\cdot)$ is the Gamma function and N stands for the standard normal random variable.

• Environmental and Resource Economics Review
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• v.28 no.1
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• pp.1-37
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• 2019

This study investigates the convergence in per capita $CO_2$ emission by income group for an unbalanced panel of 152 countries from 1980 to 2013 using beta and sigma convergence model. Absolute beta and sigma convergence differed by $CO_2$ emission reduction policies in each countries. Conditional beta convergence shows that per capita income has a negative effect on growth in per capita $CO_2$ emission. In particular, better-quality institutions and technology accelerated the negative effect of per capita income on the speed of convergence of per capita $CO_2$ emission in high-income countries. For middle-income countries, the growth of income affected the convergence of $CO_2$ emission per capita, but institutional quality has an insignificant impact. On the other hand, improvements in the level of technology have a mitigating effect on the negative impact of income in middle-income and low-income countries, contributing to the increase in $CO_2$ emission.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.977-986
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• 2010

Let $X_1$, $X_2$, $\cdots$ be identically distributed negatively associated random variables with $EX_1\;=\;0$ and $E|X_1|^3$ < $\infty$. In this paper we prove $lim_{{\epsilon\downarrow}0}\;\frac{1}{-\log\;\epsilon}\sum\limits_{n=1}^\infty\frac{1}{n^2}ES_n^2I\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;2$ and $lim_{\epsilon\downarrow0}\;\epsilon^{2-p}\sum\limits_{n=1}^\infty\frac{1}{n^p}$ $E|S_n|^pI\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;\frac{2}{2-p}$ for 0 < p < 2, where $S_n\;=\;\sum\limits_{i=1}^{n}X_i$ and 0 < $\sigma^2\;=\;EX_1^2\;+\;\sum\limits_{i=2}^{\infty}Cov(X_1,\;X_i)$ < $\infty$. We consider some results of i.i.d. random variables obtained by Liu and Lin(2006) under negative association assumption.

• Journal of the Korea Convergence Society
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• v.9 no.9
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• pp.41-46
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• 2018

Six sigma methodology is the management tools not only can cause productivity enhancement through the quality control and cost reduction of products and services but also can be applied to various activities of corporates such as research and development. Development of high-density information storage media and devices is indispensible to accomplish the information convergence era. In this paper, we report the case of applying six sigma methodology and tools to the development project of high-density information storage media. The standard DMAIC process was applied to the project and pursuing goals and tools and results in each stage were explained in detail. By adopting the methodology, we could establish fabrication methods of information storage media of recording density higher than $250Gb/in^2$ with high uniformity and reproducibility. The magnetic property and performance of fabricated media were confirmed through measurement of the magnetic hysteresis curve.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.763-772
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• 2001

The rate of convergence for an almost surely convergent series $S_n={\Sigma^n}_{i-1}X_i$ of independent random variables is studied in this paper. More specifically, when S$_{n}$ converges almost surely to a random variable S, the tail series $T_n{\equiv}$ S - S_{n-1} = {\Sigma^\infty}_{i-n} X_i$ is a well-defined sequence of random variables with T$_{n}$ $\rightarrow$ 0 almost surely. Conditions are provided so that for a given positive sequence {$b_n, n {\geq$ 1}, the limit law sup$_{\kappa}\geqn | T_{\kappa}|/b_n \rightarrow$ 0 holds. This result generalizes a result of Nam and Rosalsky [4].

• Journal of the Institute of Convergence Signal Processing
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• v.11 no.3
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• pp.189-196
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• 2010

In this paper, we proposed the adaptive local sigma filter reducing noises generated by an image sensor. The small noises generated by the image sensor are amplified by increased an analog gain and an exposure time of the image sensor together with information. And the goal of this work was the system design that is reduce the these amplified noises. Edge data are extracted by Flatness Index Map algorithm. We made the threshold adaptively changeable by the luminance average in this algorithm that extracts the edge data not in high luminance, but just low luminance. The Local Sigma Filter performed only about the edge pixel that were extracted by Flatness Index Map algorithm. To verify the performance of the designed filter, we made the Window test program. The hardware was designed with HDL language. We verified the hardware performance of Local Sigma Filter system using FPGA Demonstration board and HD image sensor, $1280{\times}720$ image size and 30 frames per second.

• Journal of the Korea Convergence Society
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• v.10 no.11
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• pp.149-159
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• 2019

Six sigma is an innovative management movement which provides improved business process by adapting the paradigm and the trend of market and customers. Suitable selection of six sigma project could highly reduce the costs, improve the quality, and enhance the customer satisfaction. There are existing studies on the selection of Six Sigma projects, but few studies have been conducted to select the correct project under an incomplete information environment. The purpose of this study is to propose the application of integrated MCDM techniques for correct project selection under incomplete information. The project selection process of six sigma involves four steps as follows: 1) determination of project selection criteria 2) calculation of relative importance of team member's competencies 3) assessment with project preference scale 4) finalization of ranking the projects. This study proposes the combination methods by applying group fuzzy Analytical Hierarchy Process (AHP), an easy defuzzified number of Trapezoidal Fuzzy Number (TrFN) and Grey Relational Analysis (GRA). Both of the weight of project selection criteria and the relative importance of team member's competencies can be evaluated by group fuzzy AHP. Project preferences are assessed by easy defuzzified scale of TrFN in case of incomplete information.)