• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.261-266
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• 2017

H. R. Ebrahimi Vishki et al. conjectured in [1], that if every Jordan higher derivation on a trivial generalized matrix algebra $\mathcal{G}=(A,M,N,B)$ is a higher derivation, then either M = 0 or N = 0. In this note, we will give a class of counter examples.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.497-502
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• 2006

An asymmetric Fuglede-Putnam theorem for $p$-hyponormal operators and class ($\mathcal{Y}$) is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.27-36
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• 2014

In this paper, we introduce the notion of f-derivations from a semilattice S to a lattice L, as a generalization of derivation and f-derivation of lattices. Also, we define the simple f-derivation from S to L, and research the properties of them and the conditions for a lattice L to be distributive. Finally, we prove that a distributive lattice L is isomorphic to the class $SD_f(S,L)$ of all simple f-derivations on S to L for every ${\wedge}$-homomorphism $f:S{\rightarrow}L$ such that $f(x_0){\vee}f(y_0)=1$ for some $x_0,y_0{\in}S$, in particular, $$L{\simeq_-}=SD_f(S,L)$$ for every ${\wedge}$-homomorphism $f:S{\rightarrow}L$ such that $f(x_0)=1$ for some $x_0{\in}S$.

• Journal of Practical Engineering Education
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• v.14 no.3
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• pp.513-522
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• 2022

Course evaluation serves as helpful information to improve the quality of college education and improve lectures. This study derived the factors through preceding research and FGI to explore the factors that constitute course evaluation and identified the relative importance and priority of the factors through the Analytic Hierarchy Process (AHP). For this, it derived five factors and 15 evaluation items as follows. To secure expertise and fairness in the factor development of course evaluation, the researcher conducted a questionnaire surveying students and teachers and collected a total of 20 valid data. The weight of each evaluation item was calculated based on the data that had been verified for consistency. The analysis concluded that students rated class content, class method, class operation, class evaluation, and class plan as the critical factors in the order of importance, while teachers evaluated class content, class operation, class method, class evaluation, and class plan as important, in that order. Based on the results of this study, I hope that various analyses and studies will be conducted to improve the efficiency and reliability of course evaluation for the quality management of college education.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.63-71
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• 2015

Let H be a separable infinite dimensional complex Hilbert space, and let $\mathcal{L}(H)$ denote the algebra of all bounded linear operators on H into itself. Let $A,B{\in}\mathcal{L}(H)$ we define the generalized derivation ${\delta}_{A,B}:\mathcal{L}(H){\mapsto}\mathcal{L}(H)$ by ${\delta}_{A,B}(X)=AX-XB$, we note ${\delta}_{A,A}={\delta}_A$. If the inequality ${\parallel}T-(AX-XA){\parallel}{\geq}{\parallel}T{\parallel}$ holds for all $X{\in}\mathcal{L}(H)$ and for all $T{\in}ker{\delta}_A$, then we say that the range of ${\delta}_A$ is orthogonal to the kernel of ${\delta}_A$ in the sense of Birkhoff. The operator $A{\in}\mathcal{L}(H)$ is said to be finite [22] if ${\parallel}I-(AX-XA){\parallel}{\geq}1(*)$ for all $X{\in}\mathcal{L}(H)$, where I is the identity operator. The well-known inequality (*), due to J. P. Williams [22] is the starting point of the topic of commutator approximation (a topic which has its roots in quantum theory [23]). In [16], the author showed that a paranormal operator is finite. In this paper we present some new classes of finite operators containing the class of paranormal operators and we prove that the range of a generalized derivation is orthogonal to its kernel for a large class of operators containing the class of normal operators.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.227-237
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• 2018

There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra. We find all the derivations of a growing algebra in the paper. The dimension of derivations of the growing algebra is one and every derivation of the growing algebra is outer. We show that there is a class of purely outer algebras in this work.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.1-6
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• 2009

Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h ${\in}$ B(X) : h is hermitian}, and J(X) = {x ${\in}$ B(X) : x = $x_1$ + $ix_2$, $x_1$ and $x_2$ ${\in}$ H(X)}. Let ${\delta}_a$ ${\in}$ B(B(X)) denote the derivation ${\delta}_a$ = ax - xa. If J(X) is an algebra and ${\delta}_a^{-1}(0){\subseteq}{\delta}_{a^*}^{-1}(0)$ for some $a{\in}J(X)$, then ${\parallel}a{\parallel}{\leq}{\parallel}a-(x^*x-xx^*){\parallel}$ for all $x{\in}J(X){\cap}{\delta}_a^{-1}(0)$. The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = $C_p$, the von Neumann-Schatten p-class, are considered.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.16 no.4 s.95
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• pp.418-426
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• 2005

Based upon three level approximation and the steepest descent path(SDP) method, we consider an optimum choice of approximation path for derivation of new class of closed-flrm Green's functions which can lead to the analytic evaluation of MoM(Method of Moment) matrix elements. It is observed that the present method can give more accurate evaluation of the spatial Green's functions than the previous method, even without the advance investigation of the spectral functions, over a wide frequency range. In order to check the validity of the present method, some numerical results are presented.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.575-588
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• 1999

Lower dimensional cases of Einstein's connection were al-ready investigated by many authors for n =2,4. This paper is to ob-tain a surveyable tensorial representation of n-dimensional Einstein's connection in terms of the unified field tensor with main emphasis on the derivation of powerful and useful recurrence relations which hold in n-dimensional Einstein's unified field theory(i.e., n-*g-UFT): All con-siderations in this paper are restricted to the third class only.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.509-532
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• 2004

Lower dimensional cases of Einstein's connection were already investigated by many authors for n = 2, 3, 4, 5, 6, 7. This paper is the first part of the following series of two papers, in which we obtain a surveyable tensorial representation of 8-dimensional Einstein's connection in terms of the unified field tensor, with main emphasis on the derivation of powerful and useful recurrence relations which hold in 8-dimensional Einstein's unified field theory(i.e., 8-g-UFT): I. The recurrence relations in 8-g-UFT II. The Einstein's connection in 8-g-UFT All considerations in these papers are restricted to the second class only, since the case of the first class are done in [1], [2] and the case of the third class, the simplest case, was already studied by many authors.