• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.259-296
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• 2008

Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A $\rightarrow$ A such that $D(x)^2$[D(x),x] $\in$ rad(A) or [D(x),x]$D(x)^2$ $\in$ rad(A) for all x $\in$ A. In this case, we have D(A) $\subseteq$ rad(A).

• Journal of the Korean Statistical Society
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• v.19 no.2
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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.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.325-331
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• 2023

Let 𝔄 be a prime ring of char(𝔄 ≠ 2, ℒ a non-central Lie ideal of 𝔄, ℱ a generalized skew derivation of 𝔄 and p ∈ 𝔄, a nonzero fixed element. If pℱ(η)η ∈ C for any η ∈ ℒ, then 𝔄 satisfies S₄.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.678-681
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• 2023

Let G be a cyclic group of prime power order p^k, and let I be the augmentation ideal of the integral group ring ℤ[G]. We define a derivation on ℤ/p^kℤ[G], and show that for 2 ≤ n ≤ p, an element α ∈ I is in Iⁿ if and only if the i-th derivative of the image of α in ℤ/p^kℤ[G] vanishes for 1 ≤ i ≤ (n - 1).

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.129-129
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• 1985

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.71-71
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• 1985

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.10
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• pp.960-965
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• 2011

This paper presents the mathematical derivation of a maximum likelihood(ML)-based monopulse ratio(MR) curve. The derived form is, with the linear array assumed, shown to be the function of the number of array elements and the elements' spacing. Through some simulations, the acquired form is equivalent to the expected MR curve. Furthermore, we show the form, which consists of several terms, can be simplified by one tangent function.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.359-366
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• 1996

A linear map T from a Banach algebra A into a Banach algebra B is almost multiplicative if $\left\$\mid$ T(fg) - T(f)T(g) \right\$\mid$ \leq \in\left\$\mid$ f \right\$\mid$\left\$\mid$ g \right\$\mid$(f,g \in A)$ for some small positive $\in$. B.E.Johnson [4,5] studied whether this implies that T is near a multiplicative map in the norm of operators from A into B. K. Jarosz [2,3] raised the conjecture : If T is an almost multiplicative functional on uniform algebra A, there is a linear and multiplicative functional F on A such that $\left\$\mid$ T - F \right\$\mid$ \leq \in', where \in' \to 0$ as $\in \to 0$. B. E. Johnson [4] gave an example of non-uniform commutative Banach algebra which does not have the property described in the above conjecture. He proved also that C(K) algebras and the disc algebra A(D) have this property [5]. We extend this property to a derivation on a Banach algebra.

• Journal of Korean Society of Rural Planning
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• v.12 no.1 s.30
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• pp.1-10
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• 2006

This study aimed at derivation of planning factors and applicable planning factors of residential environment for the elderly in Korean rural village in the more detailed level. Literature review, questionnaire and depth interview with the elderly of case rural villages keeping face with investigation of residential environment was carried out for the derivation of planning factors. Study of related legal factors and interviewing with experts for advice was conducted also for the verification and complement of planning factors. The goal of this study was improvement of residential environment for the elderly or existing rural village not the new one and planning factors was intended to include all the considerable elements. Planing factors was classified two groups which were factors of village outdoor and the inside and outside of a house. The former was also divided into spacial factors and facilities factors and the latter was divided into inside factors and outside factors. The results may contribute to improving residential environment for rural elderly with relation of health and medical service.

• Journal of the Korean earth science society
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• v.33 no.1
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• pp.11-31
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• 2012

Kaula's theory of satellite orbit and Kepler's law are re-visited. All the mathematical steps of derivation are thoroughly shown including the ones, which had been omitted in Kaula's original publication. Particularly in evaluations of the 15 independent Lagrange brackets, simplicity and clarity are attained by using orthogonal property of transformation matrix. Explanations of important physical concepts are included as well in the midway of derivation. One conceptual blunder of Kaula's is corrected.