• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.647-673
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• 2002

There are many models to study topological $R^2$-planes. Unlike topological $R^2$-planes, it is difficult to find models to study topological R$^3$)-spaces. If an 4-dimensional affine plane intersects with R$^3$, we are able to get a geometrical structure on R$^3$ which is similar to R$^3$-space, and called $R^2$-divisible R$^3$-space. Such spatial geometric models is useful to study topological R$^3$-spaces. Hence, we introduce some classes of topological $R^2$-divisible R$^3$-spaces which are induced from 4-dimensional anne planes.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.109-120
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• 2008

Today linear algebra is one of compulsory courses for university mathematics by virtue of its theoretical fundamentals and fruitful applications. However, a mechanical computation-oriented instruction or a formal concept-oriented instruction is difficult and dull for most students. In this context, how to teach mathematical concepts successfully is a very serious problem. As a solution for this problem, we suggest establishing original concepts in linear algebra from the students' point of view. Any original concept means not only a practical beginning for the historical order and theoretical system but also plays a role of seed which can build most of all the important concepts. Indeed, linear algebra has exactly two original concepts : geometry of planes, spaces and linear equations. The former was investigated in [2], the latter in the present paper.

• The Journal of Engineering Geology
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• v.21 no.4
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• pp.323-336
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• 2011

The hydro-mechanical behavior of the Earth's crust is strongly dependent on the fractional volume and geometrical structure of effective pore spaces. This study aims to understand the characteristics of pores using electrical impedance. We measured the electric impedance of core samples (diameter, 38-50 mm; length, 70-100 mm) of three types of granite (Hwangdeung, Pocheon, and Yangsan) and two types of sandstone (Boryung and Berea) with different porosities and pore structures, after saturation with saline water of varying salinities. The results show that resistance decreases but capacitance increases with increasing salinity of the pore fluid. For a given salinity, the resistivity and formation factor are reduced with increasing porosity of the rocks, and the capacitance increases. Berea sandstone shows anisotropy in resistance, tortuosity, and cementation factor, with these factors being highest normal to bedding planes. This result indicates that the connectivity of pores is weakest normal to bedding. In conclusion, the electrical characteristics of the tested samples are related not only to their porosity but also to the pore geometry.