• 대한수학회논문집
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• 제34권3호
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• pp.951-965
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• 2019

Let $f:X{\rightarrow}X$ be a continuous map on a compact metric space (X, d) and for an arbitrary $x{\in}X$, $${\mathcal{SC}}_d(x,f):=\{y{\mid}x{\text{ can be strong }}d-{\text{chain to }}y\}$$. We give an example to show that ${\mathcal{SC}}_d(x,f)$ is dependent on the metric d on X but it is a closed and f-invariant set. We prove that if ${\mathcal{SC}}_d(x,f){\supseteq}{\Omega}(f)$ or f has the asymptotic-average shadowing property, then ${\mathcal{SC}}_d(x,f)=X$. Also, we show that if f has the shadowing property, then ${\lim}\;{\sup}_{n{\in}{\mathbb{N}}}\{f^n\}={\mathcal{SC}}_d(f)$ where ${\mathcal{SC}}_d(f)=\{(x,y){\mid}y{\in}{\mathcal{SC}}_d(x,f)\}$. For each $n{\in}{\mathbb{N}}$, we give an example in which ${\mathcal{SCR}}_d(f^n){\neq}{\mathcal{SCR}}_d(f)$. In spite of it, we prove that if $f^{-1}:(X,d){\rightarrow}(X,d)$ is an equicontinuous map, then ${\mathcal{SCR}}_d(f^n)={\mathcal{SCR}}_d(f)$ for all $n{\in}{\mathbb{N}}$.

• Journal of Microbiology and Biotechnology
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• 제28권2호
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• pp.218-226
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• 2018

Nanometric Lactobacillus plantarum nF1 (nLp-nF1) is a biogenics consisting of dead L. plantarum cells pretreated with heat and a nanodispersion process. In this study, we investigated the immune-enhancing effects of nLp-nF1 in vivo and in vitro. To evaluate the immunostimulatory effects of nLp-nF1, mice immunosuppressed by cyclophosphamide (CPP) treatment were administered with nLp-nF1. As expected, CPP restricted the immune response of mice, whereas oral administration of nLp-nF1 significantly increased the total IgG in the serum, and cytokine production (interleukin-12 (IL-12) and tumor necrosis factor alpha (TNF-${\alpha}$)) in bone marrow cells. Furthermore, nLp-nF1 enhanced the production of splenic cytokines such as IL-12, TNF-${\alpha}$, and interferon gamma (IFN-${\gamma}$). In vitro, nLp-nF1 stimulated the immune response by enhancing the production of cytokines such as IL-12, TNF-${\alpha}$, and IFN-${\gamma}$. Moreover, nLp-nF1 given a food additive enhanced the immune responses when combined with various food materials in vitro. These results suggest that nLp-nF1 could be used to strengthen the immune system and recover normal immunity in people with a weak immune system, such as children, the elderly, and patients.

• 대한수학회보
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• 제58권4호
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• pp.915-937
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• 2021

In this paper we deal with the open problem posed by Lü, Li and Yang [10]. In fact, we prove the following result: Let f(z) be a transcendental meromorphic function of finite order having finitely many poles, c₁, c₂, …, c_n ∈ ℂ\{0} and k, n ∈ ℕ. Suppose fⁿ(z), f(z+c₁)f(z+c₂) ⋯ f(z+c_n) share 0 CM and fⁿ(z)-Q₁(z), (f(z+c₁)f(z+c₂) ⋯ f(z+c_n))^(k) - Q₂(z) share (0, 1), where Q₁(z) and Q₂(z) are non-zero polynomials. If n ≥ k+1, then $(f(z+c_1)f(z+c_2)\;{\cdots}\;f(z+c_n))^{(k)}\;{\equiv}\;{\frac{Q_2(z)}{Q_1(z)}}f^n(z)$. Furthermore, if Q₁(z) ≡ Q₂(z), then $f(z)=c\;e^{\frac{\lambda}{n}z}$, where c, λ ∈ ℂ \ {0} such that e^{λ(c₁+c₂+⋯+c_n)} = 1 and λ^k = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권1호
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• pp.31-34
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• 1995

Let R$^n$be n-th Euclidean space. Let be the n-th spere embeded as a subspace in R$\^$n+1/ centered at the origin. In this paper, we are going to consider the function space F = {f│f : S$^n$\longrightarrow S$^n$} metrized by as follow D(f,g)=d(f($\chi$), g($\chi$)) where f, g $\in$ F and d is the metric in S$^n$. Finally we want to find certain relation these spaces.(omitted)

• 미생물학회지
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• 제27권4호
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• pp.342-347
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• 1989

Fusarium 속의 20균주를 PDA 배지에서 배양하고. HCI-Giemsa 염색법을 이용하여 균사 내에서의 영양핵의 핵분열을 관찰하였고, 염색체 수를 세었다. 관찰한 모든 Fusarium 속의 균주들익 염색체 수는 4-8개 사이에 있었다. 그 중에서 3균주인 F. solari S Hongchun D4. F. moniiforme(from banana), F. raphani (from radish)는 n=8개이고, F, solani 7468(from Sydney), F, solani 7475 (from Sydney), F, oxyporum (from tomato), F, oxyporum(from tomato). F F. roseum(from rice), F, sporotrichioides C. Jungsun 1, F. avenaceum C Kosung 6. F, avenaceum46039 등의 7균주에서는 n=7개였다 F. monilzfonne (from rice), F. graminellrum, F. probiferatum 6787(from Sydney), F. anguioides ATCC20351의 5균주는 n=6개 F. moniliforme NRRL2284. F. poae NRRL3287. F. tricintum NRRL 3299의 3균주는 n=5개였고 가장 적은 수의 n=4개인 균주로는 F. sporotrichioides NRRL3510과 F. equiscli KFCC 11843 IFO 030198의 3균주였다. 이상의 균주들의 염색체 수를 비교 고찰할 때 Fusarium 속의 기본 염색체 수는 반수체가 4개이며 종 분화과정에서 이수체와 배수체가 되었을 것으로 추론된다.

• 자연과학논문집
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• 제11권1호
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• pp.15-17
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• 1999

{f(n)}은 양의 수열로 f(n)$\rightarrow$$\infty$ 이며, {X$_n$,n$\geq1$} 은 쌍별독립인 확률변수 열일 때 정규화된 부분 합 $sum_{i=1}^n$(X$_i$-EX$_i$)/f(n) 이 0에 수렴활 확률이 1이되는 {X$_n$,n$\geq1$} 의 조건을 찾고자 한다.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.537-543
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• 2010

Let X be a regular $T_1$-space such that each single point set is a $G_{\delta}$ set. Denot 'hereditarily closure-preserving' by 'HCP'. To consider a question of closed maps of S. Lin in [6], we improve some results of Foged in [1], and prove the following propositions. Proposition 1. $D\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}:x{\in}F\}\mid{\geq}{\aleph}_0\}$ is discrete and closed if $\cal{F}$ is a collection of HCP. Proposition 2. $\cal{H}\;=\;\{{\cup}\cal{F}'\;:\;F'$ is an fininte subcolletion of $\cal{F}_n\}$ is HCP if $\cal{F}$ is a collection of HCP. Proposition 3. Let (X,$\tau$) have a $\sigma$-HCP k-network. Then (X,$\tau$) has a $\sigma$-HCP k-network F = ${\cup}_n\cal{F}_n$ such that such tat: (i) $\cal{F}_n\;\subset\;\cal{F}_{n+1}$, (ii) $D_n\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}_n\;:\;x{\in}F\}\mid\;{\geq}\;{\aleph}_0\}$ is a discrete closed set and (iii) each $\cal{F}_n$ is closed to finite intersections.

• 한국균학회지
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• 제17권2호
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• pp.76-81
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• 1989

Fusarium oxysporum은 하나의 종내에 많은 formae speciales(분화종)과 races 등이 분화되어 있다. 그 중에서 10균주에 대하여 균사 내에서의 영양핵의 분열상을 찾아 Giemsa staining 용액으로 염색하여 그들의 염색체 수를 비교 관찰하였다. 균주에 따라 염색체 수에 차이가 있었으며 2균주(F. oxysporum f. sp. lycoperici, F. oxysporum Kangnung D2)는 n=4, 2균주(F. oxysporum S Sachun 3, F. oxysporum S Kohung 2)는 n=5, 5균주(F. oxysporum S Kohung 3, F. oxysporum CS Hongchun D16, F. oxysporum S Bosung 5, F. oxysporum S Sunchun 4, F. oxysporum S Haenam 4)는 n= 7개를 관찰할 수 있었고 Australia의 Sydney 대학에서 분양받은 F. oxysporum 14-39는 n=8개로 전체로 보아 4-8개의 염색체를 관찰할 수 있었다. 본인의 앞서 본문의 결과와 종합하여 고찰할 때 F. oxysporum의 기본염색체 수는 반수체가 4개로 추론되며 여기에서부터 여러가지 요인으로 인하여 diploidy, aneuploidy가 되어 다양한 염색체 수를 가진 것으로 사료된다.

• 대한수학회보
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• 제46권6호
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• pp.1079-1089
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• 2009

In this paper, we shall show that for any entire function f, the function of the form $f^m(f^n$ - 1)f' has no non-zero finite Picard value for all positive integers m, n ${\in}\;{\mathbb{N}}$ possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if $f^m(f^n$-1)f' and $g^m(g^n$-1)g' share the value 1 weakly, then f $\equiv$ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.115-122
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• 2004

We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. Let $S_{n}(F)$ be the space of all $n\;\times\;n$ symmetry matrices over a field F with 2, $3\;\in\;F^{*}$, then T is an additive injective operator preserving rank-additivity on $S_{n}(F)$ if and only if there exists an invertible matrix $U\;\in\;M_n(F)$ and an injective field homomorphism $\phi$ of F to itself such that $T(X)\;=\;cUX{\phi}U^{T},\;\forallX\;=\;(x_{ij)\;\in\;S_n(F)$ where $c\;\in;F^{*},\;X^{\phi}\;=\;(\phi(x_{ij}))$. As applications, we determine the additive operators preserving minus-order on $S_{n}(F)$ over the field F.