• 대한수학회보
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• 제42권4호
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• pp.671-678
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• 2005

Let R be a noncommutative semi prime ring. Suppose that there exists a derivation d : R $\to$ R such that for all x $\in$ R, either [[d(x),x], d(x)] = 0 or $\langle$$\langle(x),\;x\rangle,\;d(x)\rangle$ = 0. In this case [d(x), x] is nilpotent for all x $\in$ R. We also apply the above results to a Banach algebra theory.

• 대한수학회논문집
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• 제12권2호
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• pp.211-219
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• 1997

In [6] we proved that if a nals X is reflexive, then $X = W_X + V_X$ . In this paper we show that, for a split nals $X = W_X + V_X$, X is reflecxive if and only if $V_X$ and $W_X$ are reflcxive.

• 대한수학회지
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• 제43권2호
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• pp.271-281
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• 2006

The commutative products of the distributions $x^r\;ln^p\;{\mid}x{\mid}\;and\;x^{-r-1}ln^q\;{\mid}x{\mid}$ and of sgn x $x^r\;ln^p\;{\mid}x{\mid}\;and\;sgn\;x\;x^{-r-1}ln^q\;{\mid}x{\mid}$ are evaluated for $r=0,\;\pm1,\;\pm2,...\;and\;p,\;q=0,1,2,....$

• 대한수학회보
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• 제57권4호
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• pp.865-872
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• 2020

Let X ⊂ ℙ^r be an integral and non-degenerate variety. Set n := dim(X). Let 𝜌(X)" be the maximal integer such that every zero-dimensional scheme Z ⊂ X smoothable in X is linearly independent. We prove that X is linearly normal if 𝜌(X)" ≥ 2⌈(r + 2)/2⌉ and that 𝜌(X)" < 2⌈(r + 1)/(n + 1)⌉, unless either n = r or X is a rational normal curve.

• 대한수학회논문집
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• 제14권1호
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• pp.75-80
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• 1999

First, we shall improve the superstability result of the exponential equation f(x+y)=f(x) f(y) which was obtained in [4]. Furthermore, the superstability problems of the functional equation f(x\ulcorner+…+x\ulcorner)=f(x\ulcorner)…f(x\ulcorner) shall be investigated in the special settings (2) and (9).

• 대한수학회보
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• 제33권4호
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• pp.631-638
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• 1996

The parabolic free boundary problem with Puschino dynamics is given by (see in [3]) $$ (1) { \upsilon_t = D\upsilon_{xx} - (c_1 + b)\upsilon + c_1 H(x - s(t)) for (x,t) \in \Omega^- \cup \Omega^+, { \upsilon_x(0,t) = 0 = \upsilon_x(1,t) for t > 0, { \upsilon(x,0) = \upsilon_0(x) for 0 \leq x \leq 1, { \tau\frac{dt}{ds} = C)\upsilon(s(t),t)) for t > 0, { s(0) = s_0, 0 < s_0 < 1, $$ where $\upsilon(x,t)$ and $\upsilon_x(x,t)$ are assumed continuous in $\Omega = (0,1) \times (0, \infty)$.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.657-663
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• 2005

In this paper, we consider groups of permutations S on a set A acting on subsets X of A. In particular, we show that if $X_2{\subseteq}X_1{\subseteq}A$ and Y is an S-normal extension of $X_2 in X_1$, then the Galois group $G_{S}(X_1/Y){\;}of{\;}X_1{\;}over{\;}X_2$ relative to S is an S-closed subgroup of $G_{S}(X_1/X_2)$ in the setting of a Galois theory (correspondence) for this situation.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.91-103
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• 2007

In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by $f(x{\ast}y)+f(x{\ast}y^{-1})-2g(x)-2g(y)={\varphi}(x,y)$, $f(x{\ast}y)+g(x{\ast}y^{-1})-2h(x)-2k(y)={\varphi}(x,y)$, where (G, *) is a group, X is a real or complex Hausdorff topological vector space and f, g, h, k are functions from G into X.

• 한국광학회:학술대회논문집
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• 한국광학회 2001년도 하계학술발표회
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• pp.254-255
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• 2001

No Abstract.See Full-text

• 대한수학회보
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• 제36권2호
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• pp.379-388
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• 1999

In this paper, we introduce a semi-metric on a normed almost linear space X via functional. And we prove that a normed almost linear space X is complete if and only if $V_X$ and $W_X$ are complete when X splits as X=$W_X$ + $V_X$. Also, we prove that the dual space $X^\ast$ of a normed almost linear space X is complete.