• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.841-849
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• 2009

Let {$X_n$, n ${\ge}$ 1} be a negatively associated sequence of identically distributed random variables with mean zeros and positive finite variances. Set $S_n$ = ${\Sigma}^n_{i=1}\;X_i$. Suppose that 0 < ${\sigma}^2=EX^2_1+2{\Sigma}^{\infty}_{i=2}\;Cov(X_1,\;X_i)$ < ${\infty}$. We prove that, if $EX^2_1(log^+{\mid}X_1{\mid})^{\delta}$ < ${\infty}$ for any 0< ${\delta}{\le}1$, then $\lim_{{\epsilon}\downarrow0}{\epsilon}^{2{\delta}}\sum_{{n=2}}^{\infty}\frac{(logn)^{\delta-1}}{n^2}ES^2_nI({\mid}S_n{\mid}\geq{\epsilon}{\sigma}\sqrt{nlogn}=\frac{E{\mid}N{\mid}^{2\delta+2}}{\delta}$, where N is the standard normal random variable. We also prove that if $S_n$ is replaced by $M_n=max_{1{\le}k{\le}n}{\mid}S_k{\mid}$ then the precise rate still holds. Some results in Fu and Zhang (2007) are improved to the complete moment case.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1273-1283
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• 2019

In matrix analysis, the Wielandt-Mirsky conjecture states that $$dist({\sigma}(A),{\sigma}(B)){\leq}{\parallel}A-B{\parallel}$$ for any normal matrices $A,B{\in}{\mathbb{C}}^{n{\times}n}$ and any operator norm ${\parallel}{\cdot}{\parallel}$ on $C^{n{\times}n}$. Here dist(${\sigma}(A),{\sigma}(B)$) denotes the optimal matching distance between the spectra of the matrices A and B. It was proved by A. J. Holbrook (1992) that this conjecture is false in general. However it is true for the Frobenius distance and the Frobenius norm (the Hoffman-Wielandt inequality). The main aim of this paper is to study the Hoffman-Wielandt inequality and some weaker versions of the Wielandt-Mirsky conjecture for matrix polynomials.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.739-751
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• 1995

Let ${X(t) : 0 \leq t < \infty}$ be an almost surely continuous Gaussian process with X(0) = 0, E{X(t)} = 0 and stationary increments $E{X(t) - X(s)}^2 = \sigma^2($\mid$t - s$\mid$)$, where $\sigma(y)$ is a function of $y \geq 0(e.g., if {X(t);0 \leq t < \infty}$ is a standard Wiener process, then $\sigma(t) = \sqrt{t})$. Assume that $\sigma(t), t > 0$, is a nondecreasing continuous, regularly varying function at infinity with exponent $\gamma$ for some $0 < \gamma < 1$.

• Honam Mathematical Journal
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• v.34 no.4
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• pp.519-531
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• 2012

Let ${\sigma}_s(N)={\sum}_{d{\mid}N}d^s$. Next, the convolution sums ${\sum}_{k<N/3}{\sigma}_1(3^mk){\sigma}_1(2^n(N-3k))$, ${\sum}_{<N/3}{\sigma}_1(2^mk){\sigma}_1(3^n(N-3k))$, etc., are evaluated for all $N{\in}\mathbb{N}$ with $m$, $n{\in}\mathbb{N}{\cup}\{0\}$.

• Proceedings of the Safety Management and Science Conference
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• 2012.04a
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• pp.623-638
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• 2012

Since six sigma program was first introduced in late 1990's, it has been evolved in Korea. The number of six sigma adopting company are getting increased and diversify manufacturing, service, government. In these days, the rapid innovation of internet technology change the media industry's game rule. This paper is concerned with a six sigma applications to internet media portal service company. The main focus of this study is to introduce an empirical study on the implementation of DMAIC procedures for internet media portal service company.

• Journal of the Korea Safety Management & Science
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• v.10 no.4
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• pp.219-227
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• 2008

Since six sigma program was first introduced in late 1990's, it has been evolved in Korea. The number of six sigma adopting company are getting increased and diversify manufacturing, service, government. In these days, the rapid innovation of internet technology change the media industry's game rule. This paper is concerned with a six sigma applications to internet media portal service company. The main focus of this study is to introduce an empirical study on the implementation of DMAIC procedures for internet media portal service company.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.5
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• pp.122-131
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• 1999

저주파의 아날로그 신호를 디지털 신호로 변환하기 위해 sigma-delta 아날로그-디지털 변환기의 이용이 용이하다. 이 변환기는 변조기와 디지털 필터로 구성되는데 본 논문에서는 변조기에 대해서만 언급한다. 모델링을 통해 14비트 분해능을 갖는 2차 sigma-delta 변조기를 설계하기 위한 변조기의 구성요소 즉 연산 증폭기, 적분기, 내부 ADC 및 DAC의 최대 허용 에러 범위를 규정하였으며, 이를 토대로 연산증폭기, 2비트 ADC 및 DAC 등을 설계·검증하고, 이들을 서로 연결하여 2차 sigma-delta 변조기를 구성하였다. 3비트 ADC의 기준전압을 조절하여 변조기 성능 향상을 도모하였으며, 내부 DAC를 축전기 및 간단한 제어회로로 구성하여 비선형성 에러를 최소화하였다. 설계된 각각의 구성요소들은 모델링에서 정의된 에러 범위를 모두 만족하였으며, 전체 변조기는87㏈의 입력범위와 87㏈의 최대 신호 대 잡음 비를 가졌다.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.31 no.1
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• pp.124-131
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• 2008

Goal of "Single PPM Quality Innovation Movement" is to achieve perfect quality through participation of all members in the production line to achieve zero defects. Six Sigma has been used by many leading corporations as a tool for Management Innovation. Recently, the number of small and medium sized companies implementing Six Sigma has increased. Therefore, this research introduces the case of "S" company which utilized Six Sigma and Single PPM together to effectively implement Single PPM Quality Innovation Movement. This paper describes issues identified during the Single PPM Quality Innovation Movement implementation and also suggests improvement plans.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.11a
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• pp.145-148
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• 2000

In contrast to the $\pi$ -conjugated polymers which typically absorb light only in the visible spectral region, the $\sigma$-conjugated polymers can be used as efficient material absorbing light in the UV region. In this work, the electronic and optical properties of I$_2$-doped $\sigma$ -conjugated poly (methyl-phenylsilylene) (PMPSi) polymer were investigated. DC conductivity up to 1.2$\times$10$^{-4}$ S/cm was obtained by I$_2$-doping. In UV/Vis absorbance spectrum, a new peak was observed near 370 nm, which was explained by polaron model. The photoluminescence (PL) intensity decreased with increasing degree of I$_2$-doping, and the Infrared (IR) spectrum analysis revealed that the dopants are not directly coupled to the polymer, but effect motions of the methyl and phenyl groups.

• Proceedings of the Safety Management and Science Conference
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• 2008.11a
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• pp.57-68
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• 2008

Since six sigma program was first introduced in late 1990's, it has been evolved in Korea. The number of six sigma adopting company are getting increased and diversify manufacturing, service, government. In these days, the rapid innovation of internet technology change the media industry's game rule. This paper is concerned with a six sigma applications to internet media portal service company. The main focus of this study is to introduce an empirical case study on the implementation of DMAIC procedures for internet media portal service company.