• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.69-86
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• 2019

In this paper, we introduce a concept of the ${\epsilon}_0$-limits of vector and multiple valued sequences in $R^m$. Using this concept, we study about the concept of the ${\epsilon}_0$-dense subset and of the points of ${\epsilon}_0$-dense ace in the open subset of $R^m$. We also investigate the properties and the characteristics of the ${\epsilon}_0$-dense subsets and of the points of ${\epsilon}_0$-dense ace.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.33-41
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• 2020

We introduced the concept of the 𝜖₀-density and the 𝜖₀-dense ace in [1]. This concept is related to the structure of employment. In addition to the double capacity theorem which was introduced in [1], we need the minimal dense subset. In this paper, we investigate a concept of the minimal 𝜖₀-dense subset in the Euclidean m dimensional space.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.19 no.1
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• pp.29-34
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• 2006

The effects of $B_2O_3$ addition on the low-temperature sintering behavior and microwave dielectric properties of $(Zn_{0.8}Mg_{0.2})TiO_3$ ceramic system were investigated. Highly dense samples were obtained at the sintering temperatures below $900^{\circ}C$. The $Q{\times}f_o$ values were determined by the microstructures and sintering shrinkages which are affected by the amount of $B_2O_3$ and sintering temperature. Temperature coefficient of resonance frequency($T_f$) changes to a positive value with increasing the amount of $B_2O_3$ due to the increased amount of rutile phase which is one of the reaction products between $(Zn_{0.8}Mg_{0.2})TiO_3$ and $B_2O_3$. For $6.19 moi.{\%}B_2O_3$-added $(Zn_{0.8}Mg_{0.2})TiO_3$ system, it exhibits ${\epsilon}_r$ = 23.5, $Q{\times}f_o$ = 53,000 GHz, and $T_f$ = 0 ppm/$^{\circ}C$ when sintered at $900^{\circ}C$ for 5 h.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2004.11a
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• pp.435-438
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• 2004

The effects sintering additives such as $xwt%(0.242Bi_2O_3-0.782V_2O_5)$ on the microwave dielectric and sintering properties of $MgCo_2(VO_4)_2$ ceramics were investigated. Highly dense samples were obtained for $MgCo_2(VO_4)_2$ at the sintering temperature of $950^{\circ}C$ with $0.242Bi_2O_3-0.758V_2O_5$ additions of $0.5{\sim}5wt%$. The microwave dielectric properties of $MgCo_2(VO_4)_2$ with $0.5wt%(0.242Bi_2O_3-0.758V_2O_5)$ sintered at $950^{\circ}C$ were as follows : $Q{\times}f_0\;=\;45,375GHz,\;\epsilon_r\;=\;9.7\;and\;\tau_f\;=\;-23.2ppm/^{\circ}C$.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2003.07b
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• pp.677-680
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• 2003

The effect of $B_2O_3$ addition on the sintering behavior and microwave dielectric properties of $(Zn_{0.8}Mg_{0.2})TiO_3$ ceramic system were investigated. Highly dense samples were obtained at the sintering temperatures below $900^{\circ}C$. Temperature coefficient of resonance frequency(${\tau}_f$) changes to a positive value with increasing the amount of $B_2O_3$ because of the increased amount of rutile phase. The $Q{\times}f_o$ values were determined by the microstructures and sintering shrinkages which are affected by the rutile or second phase. When 6.19 mol.% of $B_2O_3$ added and sintered at $900^{\circ}C$ for 5h, it exhibits ${\epsilon}_r$ =23.5, $Q{\times}f_o$= 67,500 GHz, and ${\tau}f=-1.42ppm/^{\circ}C$.