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실수계의 공리를 이용한 지수 a<sup>r</sup>의 학습과 지도
이병수,Lee, Byung-Soo 영남수학회 2012 East Asian mathematical journal Vol.28 No.2
In all Mathematics I Textbooks(Kim, S. H., 2010; Kim, H. K., 2010; Yang, S. K., 2010; Woo, M. H., 2010; Woo, J. H., 2010; You, H. C., 2010; Youn, J. H., 2010; Lee, K. S., 2010; Lee, D. W., 2010; Lee, M. K., 2010; Lee, J. Y., 2010; Jung, S. K., 2010; Choi, Y. J., 2010; Huang, S. K., 2010; Huang, S. W., 2010) in high schools in Korea these days, it is written and taught that for a positive real number $a$, $a^{\frac{m}{n}}$ is defined as $a^{\frac{m}{n}}={^n}\sqrt{a^m}$, where $m{\in}\mathbb{Z}$ and $n{\in}\mathbb{N}$ have common prime factors. For that situation, the author shows his opinion that the definition is not well-defined and $a^{\frac{m}{n}}$ must be defined as $a^{\frac{m}{n}}=({^n}\sqrt{a})^m$, whenever $^n\sqrt{a}$ is defined, based on the field axiom of the real number system including rational number system and natural number system. And he shows that the following laws of exponents for reals: $$\{a^{r+s}=a^r{\cdot}a^s\\(a^r)^s=a^{rs}\\(ab)^r=a^rb^r$$ for $a$, $b$>0 and $s{\in}\mathbb{R}$ hold by the completeness axiom of the real number system and the laws of exponents for natural numbers, integers, rational numbers and real numbers are logically equivalent.
Weakly Relaxed $\alpha$-semi-pseudomonotone Set-valued Variational-like Inequalities
이병수,Bok-Doo Lee 한국수학교육학회 2004 純粹 및 應用數學 Vol.11 No.3
In this paper, we introduce weakly relaxed ��-pseudomonotonicity and weakly relaxed ��-semi-pseudomonotonicity of set-valued maps. Using the KKM technique, we obtain existence of solutions to the variational-like inequalities with weakly relaxed ��-pseudomonotone set-valued maps in re°exive Banach spaces. We also present the solvability of the variational-like inequalities with weakly relaxed ��- semi-pseudomonotone set-valued maps in arbitrary Banach spaces using Kakutani- Fan-Glicksberg ¯xed point theorem.
HIC용 $RuO_2$ 후막저항체에서 유리의 물리적 성질이 TCR에 미치는 영향
이병수,이준,Lee, B.S.,Lee, J. 한국세라믹학회 1993 한국세라믹학회지 Vol.30 No.11
Glass viscosity effects on the electrical properties and microstructure of RuO2 based thick film resistors (TFR) using alumina modified lead borosilicate glasses were studied. AT 85$0^{\circ}C$, the glass viscosities were increased from 4.24Pa.s to 51.5Pa.s when the alumina was added from none to 14 weight percent to the standard glass of 63% PbO, 25% B2O3 and 12% SiO2. The resistivities of resistors were generally decreased and the microstructure development was retarded as the viscosity of the glass increased. This is contrary to the generally accepted thought that the low resistivity is due to fast microstructure development kinetics in TFR. Even though the glass viscosity retards the microstructure development kinetics, the overall network formations are favored for higher viscosity of glass, such that the sheet resistivities were decreased as the glass viscosity increased.
이병수,성길영,반태원,Lee, Byeong Su,Sung, Kil-Young,Ban, Tae-Won 한국정보통신학회 2016 한국정보통신학회논문지 Vol.20 No.12
본 논문은 복수 개의 중계기와 도청자가 존재하는 중계기 통신 네트워크에서 보안 오류 확률을 낮출 수 있는 새로운 중계기 선택 기법을 제안한다. 도청자의 복호 확률을 낮추기 위해서 데이터와 함께 재밍 신호를 전송하는 기존의 중계기 선택 방식에서는 수신자의 데이터 복호 확률도 낮아지는 문제점이 있었다. 본 논문에서 제안하는 새로운 중계기 선택 기법은 수신자의 복호 확률을 높이면서 동시에 도청자의 복호 확률을 낮출 수 있는 중계기를 쌍으로 선택하여 보안 오류 확률을 개선하였다. Monte-Carlo 기반 컴퓨터 시뮬레이션을 통한 성능 분석 결과에 따르면, 제안 중계기 선택 방식은 기존 중계기 선택 방식 대비 보안 오류 확률을 약 10~50배 개선시킬 수 있음을 확인하였다. In this paper, we propose a new relay selection scheme which can decrease the secrecy outage probability in a relay communication network with multiple relays and an eavesdropper. In the conventional relay selection scheme, a relay transmits jamming signal toward an eavesdropper to decrease the successful decoding probability of the eavesdropper. The coventional scheme has a critical problem that the successful decoding probability of a receiver also decreases. The new relay selection scheme proposed in this paper can significantly enhance the secrecy outage probability by selecting a pair of relays which can increase the successful decoding probability of the receiver while decreasing the successful decoding probability of the eavesdropper. We performed extensive computer simulation based on Monte-Carlo. The simulation results reveal that the proposed relay selection scheme can improve the secrecy outage probability by 10 to 50 times compared to the existing relay selection scheme.