• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.183-193
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• 1995

Let N be a $II_1$ factor and G be a finite group acting outerly on N. Then the crossed product algebra $M = N \rtimes G$ is also a $II_1$ factor and $N' \cap M = CI$, i.e. N is irreducible in M. Moreover, N is regular in M, in other words, M is generated by the normalizer $N_M (N)$.

• Korean Journal of Soil Science and Fertilizer
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• v.40 no.2
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• pp.131-135
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• 2007

This study was performed as an effort to reduce soil loss by investigating the phase of water flow according to soil texture and rainfall pattern and by determining the canopy cover subfactor in the RUSLE (revised universal soil loss equation). Red pepper was planted at the 15% sloped lysimeter of $2m{\times}5m{\times}0.5m$ ($width{\times}length{\times}depth$) with three different textured soils (loam, clay loam and sandy loam) and the relationship between amount and intensity of rainfall; soil loss and the amount of runoff; and amount of rainfall and runoff at different soil texture were measured at the experiment station of the National Institute of Agricultural Science and Technology (NIAST) during May to October of 2005. The amount of runoff increased with increasing amount of rainfall, showing difference in the relative increase rate of runoff at different soil texture. The increase rate of runoff with unit increase of rainfall for the lysimeter with red pepper was 0.44, 0.41 and 0.13 for loam, clayey loam and sandy loam, respectively. The minimum amount of rainfall for runoff was 23.53 mm for sandy loam, 10.35 mm for loam and 5.46 mm for clayey loam, respectively. The canopy cover subfactors of red pepper were 0.425, 0.459, and 0.478 for sandy loam, loam and clayey loam, respectively.