• Bulletin of the Korean Chemical Society
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• v.35 no.2
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• pp.483-488
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• 2014

The nucleophilic substitution reactions of Y-aryl methyl (8) and Y-aryl propyl (10) chlorothiophosphates with X-pyridines are studied kinetically in acetonitrile at $35.0^{\circ}C$. The Hammett and Bronsted plots with X in the nucleophiles for both substrates exhibit biphasic concave upwards with a break region between X = 3-Me and H. The obtained values of the cross-interaction constants (${\rho}_{XY}$) are negative with 8 while positive with 10 despite the same free energy correlations with X for both substrates. A stepwise mechanism with a rate-limiting bond formation is proposed with 8, whereas a stepwise mechanism with a rate-limiting leaving group departure from the intermediate is proposed with 10 based on the sign of ${\rho}_{XY}$, negative and positive with 8 and 10, respectively. A frontside nucleophilic attack is proposed with strongly basic pyridines based on the considerably great magnitudes of ${\rho}_X$ and ${\beta}_X$ values while a backside attack is proposed with weakly basic pyridines based on the relatively small magnitudes of ${\rho}_X$ and ${\beta}_X$ for both substrates.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.171-180
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• 2011

In this paper, we study the superstability problem bounded by two-variables of Th. M. Rassias type for the generalized sine functional equations $$g(x+y)f(x-y)=f(x)^2-f(y)^2 \\ f(x+y)g(x-y)=f(x)^2-f(y)^2 \\ g(x+y)g(x-y)=f(x)^2-f(y)^2$$, which does not use his iteration method.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.97-104
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• 1997

The purpose of this paper is to prove the following result: Let A be a noncommutative semisimple Banach algebra. Suppose that $D:A{\rightarrow}A$, $G:A{\rightarrow}A$ are linear derivations such that [G(x), x]D(x) = D(x)[G(x), x] = 0, [D(x), G(x)] = 0 hold for all $x{\in}A$. In this case either D = 0 or G = 0.

• Electronics and Telecommunications Trends
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• v.11 no.2 s.40
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• pp.71-79
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• 1996

통신망 환경이 복잡해짐에 따라 분산 정보 저장소 역할을 담당하는 X.500 디렉토리 시스템과, 통신망 관리 서비스를 수행하는 X.700 OSI 시스템 관리의 중요성은 증가한다. 이러한 이유로 인하여 X.500 디렉토리 시스템을 타 응용서비스가 이용하고자 하는 연구는 '80년대 말부터 시작하여 '90년대 중반인 현재까지 꾸준히 진행되었다. 이에 본 고에서는 II장과 III장에서 각각 X.500 디렉토리 시스템과 X.700 OSI 시스템 관리의 기본 사항을 요약한 후, IV장에서는 다양한 분야에서 X.500 디렉토리 시스템을 이용한 사례들을 설명함으로써, 향후 개발될 통신 서비스에서 X.500 디렉토리 시스템 연계시 참고 자료로 사용할 수 있도록 하고자 한다

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.103-108
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• 2016

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(x_1+x_2)+f(x_2+x_3)+{\cdots}+f(x_n+x_1){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that $2{\leq}t$ < n.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.261-265
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• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.695-701
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• 2003

In this paper, we have characterizations of almost P-spaces which are analogous characterizations of P-spaces and we will show that if X is an almost P-space such that it is $C^{*}-embedded$ in every almost P-space in which X is embedded, then $$\mid${\upsilon}X-X$\mid${\leq}1$ and that if $$\mid${\upsilon}X-X$\mid${\leq}1$ and ${\upsilon}X$ is Lindelof, then for any almost P-space Y in which X is dense embedded, then X is $C^{*}-embeded$ in Y.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.269-277
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• 2019

Let X be a nonempty set, ${\rho}$ be an equivalence on X, T(X) be the semigroup of all transformations from X into itself, and $T_{\rho}(X)=\{f{\in}T(X)|(x,y){\in}{\rho}{\text{ implies }}((x)f,\;(y)f){\in}{\rho}\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.603-608
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• 2021

Fix k ≥ 3. If a multiplicative function f satisfies f(x₁ + x₂ + ⋯ + x_k) = f(x₁) + f(x₂) + ⋯ + f(x_k) for arbitrary positive triangular numbers x₁, x₂, …, x_k, then f is the identity function. This extends Chung and Phong's work for k = 2.