• Journal for History of Mathematics
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• v.19 no.1
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• pp.65-78
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• 2006

The law of refraction, which is called Snell's law in physics, has a significant meaning in mathematics history. After Snell empirically discovered the refraction law $\frac{v_1}{sin{\theta}_1}=\frac{v_2}{sin{\theta}_2$ through countless observations, many mathematicians endeavored to deduce it from the least time principle, and the need to surmount these difficulties was one of the driving forces behind the early development of calculus by Leibniz. Fermat solved it far advance of others by inventing a method that eventually led to the differential calculus. Historically, mathematics has developed in close connection with physics. Physics needs mathematics as an auxiliary discipline, but physics can also belong to the lived-through reality from which mathematics is provided with subject matters and suggestions. The refraction law is a suggestive example of interrelations between mathematical and physical theories. Freudenthal said that a purpose of mathematics education is to learn how to apply mathematics as well as to learn ready-made mathematics. I think that the refraction law could be a relevant content for this purpose. It is pedagogically sound to start in high school with a quasi-empirical approach to refraction. In college, mathematics and physics majors can study diverse mathematical proof including Fermat's original method in the context of discussing the phenomenon of refraction of light. This would be a ideal environment for such pursuit.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.11
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• pp.2022-2028
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• 2017

Recently, the energy shortage of sensors and the leakage of private information are considered as serious problems as the number of sensors is increasing due to the technological advance in Internet-of-Things. RF energy harvesting, in which sensors collect energy from external RF signals, and physical layer security become increasingly important to solve these problems. In this paper, we propose a time switching-based network analog coding for improving information security in wireless networks where the relay can harvest energy from source signals. We formulate 2-hop relay networks where an eavesdropper tries to overhear source signals, and find an optimal time switching ratio for maximizing the minimum required secrecy capacity using mathematical analysis. Through simulations under various environments, it is shown that the proposed scheme improves the minimum required secrecy capacity significantly, compared to the conventional scheme.

• The Journal of the Acoustical Society of Korea
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• v.21 no.8
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• pp.695-702
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• 2002

The question how man can perceive the direction of a sound is one of the traditional psychoacoustical problems. Rayleigh already began to investigate this subject in 1870s and kept on interesting himself intermittently throughout his research career. Rayleigh was only concerned with this subject among those of perception of sound and focused more interest on it than any other acoustical problems. At first he insisted on the perception of the direction of a sound by the difference of intensity of a sound in two ears. but was phased in accepting that by the difference of phase of a sound there. Thus he arrived at the modern view that the perception of the sound direction is caused by the difference of intensity in high frequencies and the difference of phase in low frequencies. Rayleigh presented his ability as an excellent experimenter by employing very cautious and ingenious experimental settings and acquired persuasive results by linking the consequences of his mathematical theorization with his experiments.