• Journal of applied mathematics & informatics
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• v.27 no.1_2
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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.

• Korean Journal of Environmental Biology
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• v.33 no.3
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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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• v.25 no.1_2
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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.

• The Korean Journal of Mycology
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• v.18 no.3
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• pp.132-136
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• 1990

The vegetative nuclear divisions in hyphae and the chromosome of Fusarium were observed by use of HCI-Giemsa technique and light microscope. The chromosome of nuclear in F. moniliforme both 7150 and 7219 were eight. F. subglutinans 1082 was n=8 and n=7 in F. sub­glutinans 1083. F. nygamai 5668 was n=7 and n=5 in F. nygamai 7132. F. beomiforme 9758 and 9760 were n=7. F. coccidicola ATCC 24138 and F. acuminatum ATCC 16560 were n=6. From these results and other reports, the basic chromosomal number of these fungi might be speculated to be four.

• 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.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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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)$$.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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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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• v.5 no.2
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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 $(M_1)_f$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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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 $x_1,{\cdots},x_n{\in}X$.