• Korean Journal of Mathematics
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• v.27 no.3
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• pp.707-722
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• 2019

For any non-negative real number ${\epsilon}_0$, we shall introduce a concept of the ${\epsilon}_0$-Cauchy sequence in a normed linear space V and also introduce a concept of the ${\epsilon}_0$-completeness in those spaces. Finally we introduce a concept of the generalized Banach spaces with these concepts.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.757-775
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• 2018

For any non-negative real number ${\epsilon}_0$, we shall introduce a concept of the ${\epsilon}_0$-dense subset of $R^m$. Applying this concept, for any sequence {${\epsilon}_n$} of positive real numbers, we also introduce the concept of the {${\epsilon}_n$}-attainable sequence and of the points of {${\epsilon}_n$}-attainable ace in the open subset of $R^m$. We also study the characteristics of those sequences and of the points of {${\epsilon}_n$}-dense ace. And we research the conditions that an {${\epsilon}_n$}-attainable sequence has no {${\epsilon}_n$}-attainable ace. We hope to reconsider the social consideration on the ace in social life by referring to these concepts about the aces.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.8
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• pp.920-926
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• 2008

In this paper, small epsilon negative(ENG) zeroth-order resonance(ZOR) antenna with improved bandwidth is presented. To reduce the size of ENG ZOR antenna without narrowing bandwidth, large shunt inductance is introduced by adding patterns on patch and meandered via. The effective permittivity of meandered via is less dependent of frequency than that of straight via in same size. Thus, ENG ZOR antenna with meandered via has broader bandwidth. As a result, the bandwidth of ENG ZOR antenna with meandered via is 1.38 times as broad as that of spiral ENG ZOR antenna with straight via. On the other hand, the area of ENG ZOR antenna is reduced by 64 % compared with that of conventional mushroom ZOR antenna.

• Journal of the Korea Safety Management & Science
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• v.15 no.1
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• pp.77-85
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• 2013

In the location science, environmental effect becomes a new main consideration for site selection. For the unwanted facility location selection, decision makers should consider the cost of resolving the environmental conflict. We introduced the negative influence cost for the facility which was inversely proportional to distance between the facility and residents. An unwanted facility location problem was suggested to minimize the sum of the negative influence cost and the transportation cost. The objective cost function was analyzed as nonlinear type and was neither convex nor concave. Three GRASP (Greedy Randomized adaptive Search Procedure) methods as like Random_GRASP, Epsilon_GRASP and GRID_GRASP were developed to solve the unwanted facility location problem. The Newton's method for nonlinear optimization problem was used for local search in GRASP. Experimental results showed that quality of solution of the GRID_GRASP was better than those of Random_GRASP and Epsilon_GRASP. The calculation time of Random_GRASP and Epsilon_GRASP were faster than that of Grid_GRASP.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.91-97
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• 2005

If ${\beta}\;>\;1$, then every non-negative number x has a ${\beta}-expansion$, i.e., $$x\;=\;{\epsilon}_0(x)\;+\;{\frac{\epsilon_1(x)}{\beta}}\;+\;{\frac{\epsilon_2(x)}{\beta}}\;+\;{\cdots}$$ where ${\epsilon}_0(x)\;=\;[x],\;{\epsilon}_1(x)\;=\;[\beta(x)],\;{\epsilon}_2(x)\;=\;[\beta(({\beta}x))]$, and so on ([x] denotes the integral part and (x) the fractional part of the real number x). Let T be a transformation on [0,1) defined by $x\;{\rightarrow}\;({\beta}x)$. It is well known that the relative frequency of $k\;{\in}\;\{0,\;1,\;{\cdots},\;[\beta]\}$ in ${\beta}-expansion$ of x is described by the T-invariant absolutely continuous measure ${\mu}_{\beta}$. In this paper, we show the mod M normality of the sequence $\{{\in}_n(x)\}$.

• 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 electromagnetic engineering and science
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• v.13 no.3
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• pp.195-197
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• 2013

A compact ($0.26{\times}0.05$ ${\lambda}_0$ at 2.27 GHz) metamaterial-based zeroth-order resonant antenna system consisting of epsilon-negative (ENG) and mu-negative (MNG) structures is proposed. Although the spacing between the ENG and MNG antennas is only 0.09 ${\lambda}_0$, the isolation is relatively high (27.6 dB at 2.27 GHz). Furthermore, the envelope correlation is only 0.015. The radiation efficiencies of the proposed two radiators are also very high (90% on average).

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.20 no.2
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• pp.59-67
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• 2009

본고를 통해 초고주파 이론과 공학 분야는 물론 물리학, 재료공학의 기초 학문 분야에서도 지대한 관심을 모으고 있는 Metamaterial(MTM) 구조에 대해 조명하고자 한다. 먼저 MTM의 핵심이라고 할 수 있는 Left-Handedness(LH) 왼손 전파 법칙과 LH 발생 재질인 Double Negative(DNG) 재질에서의 전파 특성을 상대 유전율과 상대 투자율 평면에서 확인하고, 일반 매질인 Double Positive(DPS)형인 오른손 전파 법칙 Right-Handedness(=RH) 매질과의 결합(Composite Right-and Left-Hnaded=CRLH)에서 얻어지는 특징들을 살펴본다. 특히 DPS와 DNC의 결합에서 얻을 수 있는 음의 공진과 0차 공진(Zero-Order Resonance)을 언급하고 ZOR을 응용한 RF 부품의 소형화와 특성 개선사례를 소개한다. 또한, 안테나와 전자파 산란 특성에 MTM의 특수한 성질을 이용하여, 크기를 줄이거나 표면파를 억제하거나 혹은 방사 개구를 확대 또는 렌즈 특성을 얻어낸 사례도 언급된다 그리고 LH 특성은 아니지만 MTM 계열인 ENG(Epsilon Negative), MNG(Mu Negative), ENZ(Epsilon Near Zero)를 응용한 예들을 보이고, MTM 관점에서 FSS(Frequency Selective Surface )의 특성을 논의하고, 그간에 발표된 대표적 MTM 연구 결과에 대한 소개를 마치고자 한다.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.505-513
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• 2009

Let {$X_k;k{\in}N^d$} be centered and identically distributed random field which is asymptotically negative dependent in a certain case. In this note we prove that for $p{\alpha}$ > 1 and ${\alpha}$ > ${\frac{1}{2}}$ $E{\mid}X_1{\mid}^p(log^+{\mid}X_1{\mid}^{d-1})$ < ${\infty}$ if and only if ${\sum}_n{\mid}n{\mid}^{p{\alpha}-2}P$($max_{1{\leq}k{\leq}n{\mid}S_k{\mid}}$ > ${\epsilon}{\mid}n{\mid}$) < ${\infty}$ for all ${\epsilon}$ > 0, where log$^+$x = max{1,log x}.

• Journal of electromagnetic engineering and science
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• v.11 no.3
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• pp.201-206
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• 2011

This paper presents a miniaturized epsilon negative (ENG) zeroth-order resonance (ZOR) patch antenna with an improved bandwidth. The miniaturization and the broad bandwidth of the ENG ZOR patch antenna are achieved by using a meandered via and a high permeability substrate instead of a straight via and a dielectric substrate. The use of a meandered via allows miniaturization of the ENG ZOR patch antenna without narrowing the bandwidth. The use of a high permeability substrate allows further miniaturization of the ENG ZOR patch antenna and improvement of the bandwidth. A high permeability substrate consisting of a multi-layered substrate is designed to have a small material loss. The antenna (kr=0.32) has a 10 dB fractional bandwidth of ~1 %, which is 1.74 times as broad as that of an antenna with a dielectric substrate.