• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.5
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• pp.713-721
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• 2001

In this paper, parasitic patches gap-coupled microstrip antenna and stacked microstrip patch antenna combined with parallel coupled lines, which are a kind of wideband impedance matching network, are proposed to get the wider bandwidth. The iterative method using a distributed network is proposed to design the parallel coupled lines as a wideband impedance matching network. Measurements show that the proposed antennas provide wider bandwidths ~1.6 times and ~1.5 times those of conventional parasitic gap-coupled microstrip patch antenna and stacked microstrip patch antenna. In addition, measured radiation patterns show no serious variation of radiation patterns though the parallel coupled lines is added. The antenna gain is, however, lowered about 1 dB and 0.5 dB by the coupling loss in the parallel coupled lines.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.111-127
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• 2004

In this note we examined some terms, parallel lines and angles in elementary school mathematics and middle school mathematics respectively. Since some terms are represented early in elementary school mathematics and not repeated after, some students are not easy to apply the terms to their lesson. Also, since the relation between parallel lines and angles are treated intuitively in 7-th grade, applying the relation for a proof in 8-th grade would be meaningless. For the variety of mathematics education, it is desirable that the relation between parallel lines and angles are treated as postulate. Also, for out standing students, it is desirable that we use deductive reasoning to prove the relation between parallel lines and angles as a theorem. In particular, the treatments of vertical angles and the relation between parallel lines and angles in 7-th grade text books must be reconsidered. Proof is very important in mathematics, and the deductive reasoning is necessary for proof. It would be efficient if some properties such as congruence of vertical angles and the relation between parallel lines and angles are dealt in 8-th grade for proof.