• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1515-1528
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• 2019

We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A{\subseteq}F^d_q$ and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions $d{\geq}2t$.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1997.06a
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• pp.3-5
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• 1997

Synthesis of ammonium aluminum hydrogen carbonate(AAHC) via reaction of aluminum bicarbonate and aluminum salt and thermal decomposition is oner of the important processes for preparation of high pure and ultra fine alumina. Kato and coworkers[1] developed this process, at same time Von Erdos and Altorfe[2] found AAHC in the corrosive products of aluminum in the atmosphere of carbon dioxide and ammonia. Murase and Iga[3] synthesized acicular AAHC in a autoclave under 60 to 12$0^{\circ}C$ Hayashi[4] optimized the conditions for preparation of AAHC and alumina. Attemp has been made in this paper to reveal the conditions affect the morphology of the synthesized AAHC and the consequently produced alumina.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.757-768
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• 2003

In 1967, as an answer to the question of P. Erdos on a set of integers having distinct subset sums, J. Conway and R. Guy constructed an interesting sequence of sets of integers. They conjectured that these sets have distinct subset sums and that they are close to the best possible with respect to the largest element. About 30 years later (in 1996), T. Bohman could prove that sets from the Conway-Guy sequence actually have distinct subset sums. In this paper, we generalize the concept of subset-sum-distinctness to k-SSD, the k-fold version. The classical subset-sum-distinct sets would be 1-SSD in our definition. We prove that similarly derived sequences as the Conway-Guy sequence are k-SSD.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.115-126
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• 2016

Let $E{\subset}{\mathbb{F}}^d_q$, the d-dimensional vector space over the finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x, y 2 E by an edge if ${\parallel}x-y{\parallel}:=(x_1-y_1)^2+{\cdots}+(x_d-y_d)^2=1$. We shall prove that the non-overlapping chains of length k, with k in an appropriate range, are uniformly distributed in the sense that the number of these chains equals the statistically correct number, $1{\cdot}{\mid}E{\mid}^{k+1}q^{-k}$ plus a much smaller remainder.

• Journal of The Korean Association For Science Education
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• v.30 no.8
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• pp.1031-1043
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• 2010

The purpose of this study was to develop the brain compatibility index equation for the brain-based analysis method of science teaching-learning program. To develop the index equation, one sample unit in middle school science programs was selected and analyzed by the brain-based analysis frame (CORE Brain Map). Then, the index equation was derived by the CORE Brain Map. In addition, four sample units in elementary science programs were selected to validate the brain compatibleness index equation. From the random network theory of Erdos and Renyi, this study derived the brain compatibility index equation; (BCI=$\frac{L_o}{11(N_o-1)}{\cdot}{\sum}\limits_{i=1}^4l_iw_i$) for quantitative analysis of science teaching-learning program. With this equation, this study could find the quantitative difference among the teaching-learning programs through the unit and curriculum. Brain-based analysis methods for the qualitative and quantitative analysis of science teaching-learning program, which was developed in this study is expected, to be a useful application to analyze and diagnose various science teaching-learning programs.