• 대한수학회보
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• 제46권3호
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• pp.435-437
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• 2009

In this paper we prove that every Jordan $\theta$-derivation on a Lie triple system is a $\theta$-derivation. Specially, we conclude that every Jordan derivation on a Lie triple system is a derivation.

• 대한수학회논문집
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• 제26권4호
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• pp.585-589
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• 2011

Using algebraic methods, we prove that every Jordan (${\varphi},{\psi}$derivation is a (${\varphi},{\psi}$derivation under certain conditions. In particular, we conclude that every Jordan ${\theta}$-derivation is a ${\theta}$-derivatio.

• 대한수학회논문집
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• 제31권2호
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• pp.229-235
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• 2016

In this paper we study the regularity of inside (or outside) (${\theta},{\phi}$)-derivations in BCI-algebras X and prove that let $d_{({\theta},{\phi})}:X{\rightarrow}X$ be an inside (${\theta},{\phi}$)-derivation of X. If there exists a ${\alpha}{\in}X$ such that $d_{({\theta},{\phi})}(x){\ast}{\theta}(a)=0$, then $d_{({\theta},{\phi})}$ is regular for all $x{\in}X$. It is also shown that if X is a BCK-algebra, then every inside (or outside) (${\theta},{\phi}$)-derivation of X is regular. Furthermore the concepts of ${\theta}$-ideal, ${\phi}$-ideal and invariant inside (or outside) (${\theta},{\phi}$)-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If $d_{({\theta},{\phi})}:X{\rightarrow}X$ is an outside (${\theta},{\phi}$)-derivation of X, then $d_{({\theta},{\phi})}$ is regular if and only if every ${\theta}$-ideal of X is $d_{({\theta},{\phi})}$-invariant.

• Journal of the Korean Statistical Society
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• 제19권2호
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• pp.182-185
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• 1990

Let a p-component vector y have a p-variate normal distribution $N(b\theta, \Sigma), \Sigma$ unknown, b specified, then for testing $\theta = 0$ against general $\theta$, Khatri and Rao (1987) derive a certain t test and obtain its power function. This paper presents a direct derivation of this power function in terms of the original variates unlike Khatri and Rao (1987) who resort to the canonical transformations of the original variates and the conditional distributions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권4호
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• pp.207-215
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• 2003

Let R be a prime ring with characteristic different from two and let $\theta,\varphi,\sigma,\tau$ be the automorphisms of R. Let d : $R{\rightarrow}R$ be a nonzero ($\theta,\varphi$)-derivation. We prove the following results: (i) if $a{\in}R$ and [d(R), a]$_{{\theta}o{\sigma},{\varphi}o{\tau}}$=0, then $\sigma(a)\;+\;\tau(a)\;\in\;Z$, the center of R, (ii) if $d([R,a]_{\sigma,\;\tau)\;=\;0,\;then\;\sigma(a)\;+\;\tau(a)\;\in\;Z$, (iii) if $[ad(x),\;x]_{\sigma,\;\tau}\;=\;0;for\;all\;x\;\in\;RE$, then a = 0 or R is commutative.

• 충청수학회지
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• 제19권1호
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• pp.27-36
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• 2006

In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. We introduce the concept of linear ${\theta}$-derivations on $JB^*$-triples, and prove the Cauchy-Rassias stability of linear ${\theta}$-derivations on $JB^*$-triples.

• 충청수학회지
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• 제18권2호
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• pp.175-193
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• 2005

In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. In this paper, we introduce the concept of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalizd (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras, and prove the Cauchy-Rassias stability of generalized (${\theta}$, ${\phi}$)-derivations on Poisson Banach algebras and of generalized (${\theta}$, ${\phi}$)-derivations on Jordan Banach algebras.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.139-150
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• 2014

We introduce the concept of generalized (${\theta}$, ${\phi}$)-derivations on Banach algebras, and prove the Cauchy-Rassias stability of generalized (${\theta}$, ${\phi}$)-derivations on Banach algebras.

• 응용통계연구
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• 제7권2호
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• pp.263-268
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• 1994

베이스(Thomas Bayes)는 역사적인 1764년 논문에서 공 W의 위치 $\theta$에 대한 추론 문제를 생각한 바 있다. 이 때 그는 $\theta$에 대한 사전(prior) 분포로서 균일(uniform) 분포를 가정하였는데, 본 소고에서는 이 사전분포가 단순한 주관적 확률이 아닌 논리적 확률로 간주될 수 있음을 보일 것이다.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.313-321
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• 2003

In this Paper we show the following: Let R be a prime ring (with characteristic different two) and a $\in$ R. Let Θ, $\phi$ : R longrightarrow R be automorphisms and let d : R longrightarrow R be a nonzero Θ-derivation. (i) if［d($\chi$), a］Θo$\phi$ = 0 (or d(［$\chi$, a］$\phi$ = 0) for all $\chi$ $\in$ R, then a+$\phi$(a) $\in$ Z, the conte. of R, (ii) if〈d($\chi$), a〉 = 0 for all $\chi$$\in$R, then d(a) =0. (iii) if [ad($\chi$), $\chi$］$\phi$= 0 for all $\chi$$\in$R, then either a = 0 or R is commutative.