• Korean Journal of Mathematics
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• v.29 no.1
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• pp.105-120
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• 2021

In this paper, we extend some results related to the growth rates of entire functions by introducing the relative logarithmic order ����g(f) of a nonconstant entire function f with respect to another nonconstant entire function g. Next we investigate some theorems related the behavior of ����g(f). We also define the relative logarithmic proximate order of f with respect to g and give some theorems on it.

• Journal of Microbiology and Biotechnology
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• v.19 no.10
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• pp.1142-1149
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• 2009

Several bioactive metabolites, including pyrrolnitrin, N-acylhomoserine lactones, and polyhydroxyalkanoates were isolated from Burkholderia sp. O33. Effects of various nutrients, including sugars, gluconolactone, glycerol, tryptophan, chloride, and zinc were investigated in relation to the production of these metabolites. Logarithmic increase of pyrrolnitrin was observed between 2-5 days and reached a maximum at 7-10 days. Tryptophan concentration reached the maximum at 3 days, whereas 7-chlorotryptophan was gradually increased throughout the studies. Among various carbon sources, gluconolactone, trehalose, and glycerol enhanced pyrrolnitrin production, whereas strong inhibitory effects were found with glucose. Relative concentrations of pyrrolnitrin and its precursors were in the order of pyrrolnitrin$\gg$dechloroaminopyrrolnitrin or aminopyrrolnitrin throughout the experiments. Among three N-acylhomoserine lactones, the N-octanoyl analog was the most abundant quorum sensing signal, of which the concentrations reached the maximum in 2-3 days, followed by a rapid dissipation to trace level. No significant changes in pyrrolnitrin biosynthesis were observed by external addition of N-acylhomoserine lactones. Polyhydroxyalkanoates accumulated up to 3-4 days and decreased slowly thereafter. According to the kinetic analyses, no strong correlations were found between the levels of pyrrolnitrin, N-acylhomoserine lactones, and polyhydroxyalkanoates.

• Journal of The Geomorphological Association of Korea
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• v.17 no.2
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• pp.1-13
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• 2010

The technique of mountain ordering developed by Yamada(1999) has been tested to two small islands (Namhaedo: 301km², Geojedo: 378km²). The results and experiences above were extended and applied to the whole area of the southern part of Korean Peninsula. Three areas such as Seorak-Taebaek Mountains, Jiri-Deogyu Mountains, and Youngnam Alps are identified as the highest, 5th order mountains. 10 areas are classified as the 4th order and 87 areas as the 3rd order. It is suggested that the 5th order mountains are related to the axis of uplift and the 4th and 3rd order mountains have the same direction (NE-SW) as that of the secondary mountain systems in the Korean Peninsula. The logarithmic values of number, area, and relative altitude of the ordered mountains have the linear relationship with the order, as the laws of stream order. The several mountains which are not included in the existing mountain systems could be identified among the ordered mountains, and those mountains could be used as the basis to understand the geological structure of the Korean Peninsula. Most of the National Parks and the Provincial Parks are distributed on the 3rd, 4th, 5th order mountains. It is especially confirmed that the Songnisan National Park take a role to link the Seorak-Taebaek Mountains and Jiri-Deogyu Mountains as a important ecological axis. Therefore, it would be validated that the technique of mountain ordering has the practical values as well as the geomorphological significances.