• The Korean Journal of Mycology
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• v.16 no.3
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• pp.157-161
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• 1988

The vegetative nuclear divisions in hyphae and chromosome numbers were studied with the aid of Giemsa-HCl techniques from 10 strains of Fusarium oxysporum. The entire nuclear division process occurred within an intact nuclear envelope like other fungus. The results confirmed that 2 strains(F. oxysporum S Hongchun D2, F. oxysporum S Jinyang 4) were n=4; 3 strains(F. oxysporum f. sp. lini KFCC 32585, F. oxysporum f. sp. melongenae KFCC 34743 and F. oxysporum f. sp. raphani) n=5; 2 strains(F. oxysporum f. sp. vasinfectum, and F. oxysporum f. sp. mori KFCC 34742) n=6; 3 strains(F. oxysporum f. sp. cucumerium, F. oxysporum f. sp.niveum, and F. oxysporum f. sp. pisi) n=7.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.7-10
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• 1985

For each a.mem.S and f.mem.m(S), denote by $l_{a}$ f(s)=f(as) for all s.mem.S. If A is a norm closed left translation invariant subalgebra of m(S) (i.e. $l_{a}$ f.mem.A whenever f.mem.A and a.mem.S) containing 1, the constant ont function on S and .phi..mem. $A^{*}$, the dual of A, then .phi. is a mean on A if .phi.(f).geq.0 for f.geq.0 and .phi.(1) = 1, .phi. is multiplicative if .phi. (fg)=.phi.(f).phi.(g) for all f, g.mem.A; .phi. is left invariant if .phi.(1sf)=.phi.(f) for all s.mem.S and f.mem.A. It is well known that the set of multiplicative means on m(S) is precisely .betha.S, the Stone-Cech compactification of S[7]. A subalgebra of m(S) is (extremely) left amenable, denoted by (ELA)LA if it is nom closed, left translation invariant containing contants and has a multiplicative left invariant mean (LIM). A semigroup S is (ELA) LA, if m(S) is (ELA)LA. A subset E.contnd.S is left thick (T. Mitchell, [4]) if for any finite subser F.contnd.S, there exists s.mem.S such that $F_{s}$ .contnd.E or equivalently, the family { $s^{-1}$ E : s.mem.S} has finite intersection property.y.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.961-976
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• 2019

Let R be any commutative ring and S be any multiplicative closed set. We introduce an S-version of $\mathcal{F}$-Mittag-Leffler modules, called $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and define the projective dimension with respect to these modules. We give some characterizations of $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, investigate the relationships between $\mathcal{F}$-Mittag-Leffler modules and $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and use these relations to describe noetherian rings and coherent rings, such as R is noetherian if and only if $R_S$ is noetherian and every $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler module is $\mathcal{F}$-Mittag-Leffler. Besides, we also investigate the $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension of R, and prove that $R_S$ is noetherian if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is zero; $R_S$ is coherent if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is at most one.

• The Korean Journal of Mycology
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• v.17 no.2
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• pp.76-81
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• 1989

The mitotic nuclear divisions in hyphae and chromosome number in 10 strains of Fusarium oxysporum were studies with the aid of Giemsa-HCl techniques. The chromosome number of fungi was ranged from 4 to 8. Of the 10 strains (F. oxysporum f. sp. lycoperici, F. oxysporum Kangnung D2) are n=4; two (F. oxysporum Sachun3, F. oxysporum S Kohung D2) n=5; five (F. oxysporum S Kohung 3, F. oxysporum CS Hongchun D16, F. oxysporum S Bosung 5, F. oxysporum SSunchun4 and F. oxysporum S Haenam 4) n=7 and one (F. oxysporum from the Australia) are n=8. These results along with my previous papers indicate that the basic chromosome number of the F. oxysporum may be n=4 and may have been evolutionary modification within this fugal group through diploidy and aneuploidy. As additional strains are studied, the chromosome number should help to reveal steps possible phylogenetic relationship within the group as well as more clearly defining taxonomic group and variation factors.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.27-36
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• 2014

In this paper, we introduce the notion of f-derivations from a semilattice S to a lattice L, as a generalization of derivation and f-derivation of lattices. Also, we define the simple f-derivation from S to L, and research the properties of them and the conditions for a lattice L to be distributive. Finally, we prove that a distributive lattice L is isomorphic to the class $SD_f(S,L)$ of all simple f-derivations on S to L for every ${\wedge}$-homomorphism $f:S{\rightarrow}L$ such that $f(x_0){\vee}f(y_0)=1$ for some $x_0,y_0{\in}S$, in particular, $$L{\simeq_-}=SD_f(S,L)$$ for every ${\wedge}$-homomorphism $f:S{\rightarrow}L$ such that $f(x_0)=1$ for some $x_0{\in}S$.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.21-25
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• 1979

Abelian군(群)의 presheaf에 관한 직적(直積)과 직화(直和)를 Category 입장에서 정의(定義)하고 presheaf $F_{\lambda}\;({\lambda}{\epsilon}{\Lambda})$들의 두 직적(直積)(또는 直和)은 서로 동형적(同型的) 관계(關係)에 있으며, 특히 ${\phi}:X{\rightarrow}Y$가 homeomorphism이라 하고 ${\phi}_*F$를 X상(上)의 presheaf F의 direct image이라 하면 (1) $({\phi}_*F, \;{\phi}_*(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직적(直積)일 때 오직 그때 한하여 $(F,\;(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직적(直積)이다. (2) $({\phi}_*F,\;{\phi}_*(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직화(直和)일 때 오직 그때 한하여 $(F,\;(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직화(直和)이다. Let $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ be an indexed set of presheaves of abelian group on topological space X. We can define the cartesian product $$\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda}$$ of $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ by $$(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U)=\prod_{{\lambda}{\epsilon}{\Lambda}}(F_{\lambda}(U))$$ for U open in X $${\rho}_v^u:\;(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U){\rightarrow}(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(V)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}(_{\lambda}{\rho}_v^u(s_{\lambda}))_{{\lambda}{\epsilon}{\Lambda}})$$ for $V{\subseteq}U$ open in X where $_{\lambda}{\rho}^U_V$ is a restriction of $F_{\lambda}$, And we have natural presheaf morphisms ${\pi}_{\lambda}$ and ${\iota}_{\lambda}$ such that ${\pi}_{\lambda}(U):\;({\prod}_\;F_{\lambda})(U){\rightarrow}F_{\lambda}(U)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}s_{\lambda})$ ${\iota}_{\lambda}(U):\;F_{\lambda}(U){\rightarrow}({\prod}\;F_{\lambda})(U)(s_{\lambda}{\rightarrow}(o,o,{\cdots}\;{\cdots}o,s_{\lambda},o,{\cdots}\;{\cdots}o)$ for $(s_{\lambda}){\epsilon}{\prod}_{\lambda}\;F_{\lambda}(U)$ and $(s_{\lambda}){\epsilon}F_{\lambda}(U)$.

• Korean Journal of Agricultural and Forest Meteorology
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• v.17 no.3
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• pp.227-235
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• 2015

Using eddy covariance method, net ecosystem exchange (NEE) of $CO_2$ ($F_{CO_2}$), $H_2O$ (LE), and sensible heat (H) can be approximated as the sum of eddy flux ($F_c$) and storage flux term ($F_s$). Depending on strength and distribution of sink/source of scalars and magnitude of vertical turbulence mixing, the rates of changes in scalars are different with height. In order to calculate $F_s$ accurately, the differences should be considered using scalar profile measurement. However, most of flux sites for agricultural lands in Asia do not operate profile system and estimate $F_s$ using single-level scalars from eddy covariance system under the assumption that the rates of changes in scalars are constant regardless of the height. In this study, we measured $F_c$ and $F_s$ of $CO_2$, $H_2O$, and air temperature ($T_a$) using eddy covariance and profile system (i.e., the multi-level measurement system in scalars from eddy covariance measurement height to the land surface) at the Chengmicheon farmland site in Korea (CFK) in order to quantify the differences between $F_s$ calculated by single-level measurements ($F_s_{-single}$ i.e., $F_s$ from scalars measured by profile system only at eddy covariance system measurement height) and $F_s$ calculated by profile measurements and verify the errors of NEE caused by $F_s_{-single}$. The rate of change in $CO_2$, $H_2O$, and Ta were varied with height depending on the magnitudes and distribution of sink and source and the stability in the atmospheric boundary layer. Thus, $F_s_{-single}$ underestimated or overestimated $F_s$ (especially 21% underestimation in $F_s$ of $CO_2$ around sunrise and sunset (0430-0800 h and 1630-2000 h)). For $F_{CO_2}$, the errors in $F_s_{-single}$ generated 3% and 2% underestimation of $F_{CO_2}$ during nighttime (2030-0400 h) and around sunrise and sunset, respectively. In the process of nighttime correction and partitioning of $F_{CO_2}$, these differences would cause an underestimation in carbon balance at the rice paddy. In contrast, there were little differences at the errors in LE and H caused by the error in $F_s_{-single}$, irrespective of time.

• Korean Journal of Soil Science and Fertilizer
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• v.29 no.1
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• pp.53-59
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• 1996

This study was conducted to evaluate the effects of fowl dzopping. saw dust and rice hall on the soil microflora in vitro. The experiment was designed in seven treatments with the various organic materials and they were only soil (control). soil + fowl dropping (S+F), soil+fowl dropping+rice hull (S+F+R) soil+fowl dropping*saw dust (S+F+S). soil+chemical fertilizer (S+C.F), fowl dropping+rice hull (F+R) and fowl dropping+saw dust (F+S). All the samples of treatment were incubated in $28{\pm}2^{\circ}C$ condition and tested the activity of soil microflora for 84 days The activity of fungi, total bacteria, gram-negative bacteria and actinomycetes showed the highest values at, twenty-first day and the spore-forming bacteria was at forty-second day after incubation. The number of fungi and gram-negative bacteria showed the highest values in the treatment of F+S, the spore-forming bacteria and the actinomycetes were in the S+F+S. and the number of total bacteria was in the F+C.F., but in the treatment of F+R. all the microorganism except fungi showed the lowest values in their numbers. The composition ratio of dead bacteria was higher in the treatments of S+F+R and F+R than in those of others as 70% and 40% respectively. Actinomycetes isolated from the treatments of S+F and S+F+S were identified as Streptomyces sp.. Nocardia sp., Micromonospora sp. Actinomadura sp. and Saccharomonospora sp.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.105-115
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• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.83-85
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• 1985

Let K be a real function field over a real closed field F. Then there exists an F-place .phi.:K.rarw.F.cup.{.inf.}. This is Lang's Existence of Rational Place Theorem (6). There is an equivalent version of Lang's Theorem in (4). That is, if K is a function field over a field F, then, for any ordering P$_{0}$ on F which extends to K, there exists an F-place .phi.: K.rarw.F'.cup.{.inf.} where F' is a real closure of (F, P$_{0}$). In [2], Knebusch pointed out the converse of the version of Lang's Theorem is also true. By a valuation theoretic approach to Lang's Theorem, we have found out the following generalization of Lang and Knebusch's Theorem. Let K be an arbitrary extension field of a field F. then an ordering P$_{0}$ on F can be extended to an ordering P on K if there exists an F-place of K into some real closed field R containing F. Of course R$^{2}$.cap.F=P$_{0}$. The restriction K being a function field of F is vanished, though the codomain of the F-place is slightly varied. Therefore our theorem is a generalization of Lang and Knebusch's theorem.