• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.97-103
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• 2009

Suppose F is a field of characteristic not 2 and $F\;{\neq}\;Z_3$. Let $M_n(F)$ be the linear space of all $n{\times}n$ matrices over F, and let ${\Gamma}_n(F)$ be the subset of $M_n(F)$ consisting of all $n{\times}n$ involutory matrices. We denote by ${\Phi}_n(F)$ the set of all maps from $M_n(F)$ to itself satisfying A - ${\lambda}B{\in}{\Gamma}_n(F)$ if and only if ${\phi}(A)$ - ${\lambda}{\phi}(B){\in}{\Gamma}_n(F)$ for every A, $B{\in}M_n(F)$ and ${\lambda}{\in}F$. It was showed that ${\phi}{\in}{\Phi}_n(F)$ if and only if there exist an invertible matrix $P{\in}M_n(F)$ and an involutory element ${\varepsilon}$ such that either ${\phi}(A)={\varepsilon}PAP^{-1}$ for every $A{\in}M_n(F)$ or ${\phi}(A)={\varepsilon}PA^{T}P^{-1}$ for every $A{\in}M_n(F)$. As an application, the maps preserving inverses of matrces also are characterized.

• 환경생물
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• 제33권3호
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• pp.290-305
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• 2015

Ten new species of the genus Falcileptoneta are described; Falcileptoneta bifurca n. sp., F. boeunensis n. sp., F. chiakensis n. sp., F. cornuta n. sp., F. digitalis n. sp., F. hansanensis n. sp., F. juwangensis n. sp., F. moakensis n. sp., F. naejangenesis n. sp., and F. unmunensis n. sp. And six species previously known as Leptoneta spiders are transferred to Falcileptoneta as fo11ows; Falcileptoneta coreana (Paik and Namkung, 1969), F. hwanseonensis (Namkung, 1987), F. secula (Namkung, 1987), F. simboggulensis (Paik, 1971), F. yebongsanensis (Kim, Lee and Namkung, 2004), and F. yongdamgulensis (Paik and Namkung, 1969), all n. comb.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.17-33
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• 2007

Suppose F is an arbitrary field. Let ${\mid}F{\mid}$ be the number of the elements of F. Let $T_{n}(F)$ be the space of all $n{\times}n$ upper-triangular matrices over F. A map ${\Psi}\;:\;T_{n}(F)\;{\rightarrow}\;T_{n}(F)$ is said to preserve idempotence if $A-{\lambda}B$ is idempotent if and only if ${\Psi}(A)-{\lambda}{\Psi}(B)$ is idempotent for any $A,\;B\;{\in}\;T_{n}(F)$ and ${\lambda}\;{\in}\;F$. It is shown that: when the characteristic of F is not 2, ${\mid}F{\mid}\;>\;3$ and $n\;{\geq}\;3,\;{\Psi}\;:\;T_{n}(F)\;{\rightarrow}\;T_{n}(F)$ is a map preserving idempotence if and only if there exists an invertible matrix $P\;{\in}\;T_{n}(F)$ such that either ${\Phi}(A)\;=\;PAP^{-1}$ for every $A\;{\in}\;T_{n}(F)\;or\;{\Psi}(A)=PJA^{t}JP^{-1}$ for every $P\;{\in}\;T_{n}(F)$, where $J\;=\;{\sum}^{n}_{i-1}\;E_{i,n+1-i}\;and\;E_{ij}$ is the matrix with 1 in the (i,j)th entry and 0 elsewhere.

• 한국균학회지
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• 제18권3호
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• pp.132-136
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• 1990

Fusarium속의 10균주를 PDA 배지에서 배양하고 HCI-Giemsa 염색법을 이용하여 균사내에서의 영양핵의 핵분열을 관찰하였다. 관찰한 결과는 F. moniliforme 1750과 7219는 n=8개였다. F. subglutinans 1082는 n=8개, F subglutinans 1083은 n=7개로 균주에 따라 염색체수에 차이가 있었다. F. nygamai 5668과 F. nygamai 7132는 각각 n=7, n=5개로 달랐다. F. beomiforme 9758과 9760은 두 균주 모두 n=7개였고, F. coccidicola ATCC 24138과 F. acuminatum ATCC 16560은 n=6개였다. 본 실험의 재료에서는 n=5-8개의 염색체수를 나타내고 있으나 다른 여러 종들에 대한 보고 등을 고려할 때 본 속의 기본 염색체수는 n=4개로 추정하였다.

• 한국균학회지
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• 제16권3호
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• pp.157-161
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• 1988

Fusarium oxysporum은 하나의 종내에서 다양한 변이를 하여 100 이상의 formae specials과 races가 있는 것으로 알려진 종이다. 그중에서 10 strains에 대하여 균사내의 영양핵의 분열상을 찾아 Giemsa staining sol.으로 염색하여 관찰하였고, 그들의 염색체수를 확인하였다. 결과는 10 strains중에서 F. oxysporuml S Hongchun D2와 F. oxysporum S Jinyang 4의 2strains은 n=4개 를, F. oxysporum f. sp. lini KFCC 32585, F. oxysporum f. sp. melongenae KFCC 34743, F. oxysporum f. sp. raphani의 3 strains은 n= 5, F. oxysporum f. sp. vasinfectum과 F. oxysporum f. sp. mori KFCC 34742의 2 strain은 n=6개를, 그리고 F. oxysporum f. sp. cucumerium, F. oxysporum f. sp. niveum과 F. oxysporum f. sp. pisi등의 3 strains은 n=7개로 관찰되 었다.

• 대한수학회논문집
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• 제20권4호
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• pp.641-644
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• 2005

Let L/F be a Galois quadratic extension such that F contains a primitive n-th root of 1. Let N = L(${\alpha}^{{\frac{1}{n}}$) where ${\alpha}{\in}L{\ast}$. We show that if $N_{L/F}({\alpha})\;{\in}L^n{\cap}F$, and [N : L] = m, then $G(N/ F) {\simeq}D_m$ or generalized quaternion group whether $N_{L/F}({\alpha})\;{\in}\;F^n\;or\;{\notin}F^n$, respectively.

• 대한수학회보
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• 제53권2호
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• pp.365-371
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• 2016

Let f be a transcendental meromorphic function in the complex plane $\mathbb{C}$, and a be a nonzero constant. We give a quantitative estimate of the characteristic function T(r, f) in terms of $N(r,1/(f^2(f^{\prime})^n-a))$, which states as following inequality, for positive integers $n{\geq}2$, $$T(r,f){\leq}\(3+{\frac{6}{n-1}}\)N\(r,{\frac{1}{af^2(f^{\prime})^n-1}}\)+S(r,f)$$.

• 대한수학회논문집
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• 제12권3호
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• pp.709-715
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• 1997

For a fibration (E,B,p) with fiber F and a fiber map f, we show that if the inclusion $i : F \to E$ has a left homotopy inverse, then $G^f_n(E,F)$ is isomorphic to $G^f_n(F,E) \oplus \pi_n(B)$. In particular, by taking f as the identity map on E we have $G_n(E,F)$ is isomorphic to $G_n(F) \oplus \pi_n(B)$.

• Korean Journal of Mathematics
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• 제5권2호
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• pp.119-125
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• 1997

We show that there exists an isomorphism between the basic construction $(M_f)_1$ for $N_f{\subset}M_f$ and the reduction $(M_1)_f$ of the basic construction $M_1$ for $N{\subset}M$, where $f$ is a nontrivial projection in N. For a nontrivial projection $f{\in}N^{\prime}{\cap}M$ we give the basic construction $(M_f)_1$ for $N_f{\subset}M_f$ and compare it with $(M_1)_f$.

• 충청수학회지
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• 제20권1호
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• pp.37-45
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• 2007

Let X, Y be vector spaces. In this paper, we investigate the generalized Hyers-Ulam-Rassias stability problem for a cubic function $f:X{\rightarrow}Y$ satisfies $$r^3f(\frac{\Sigma_{j=1}^{n-1}x_j+2x_n}{r})+r^3f(\frac{\Sigma_{j=1}^{n-1}x_j-2x_n}{r})+8\sum_{j=1}^{n-1}f(x_j)=2f{\sum_{j=1}^{n-1}}x_j)+4{\sum_{j=1}^{n-1}}(f(x_j+x_n)+f(x_j-x_n))$$ for all $x_1,{\cdots},x_n{\in}X$.