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Vol.23 No.4

Jeon, Young Ju ; Kim, Chang Il pp.329-337 https://doi.org/10.7468/jksmeb.2016.23.4.329
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Abstract

In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QFK of K is also a Wallman compactification of the inverse image <TEX>${\Phi}_K^{-1}(X)$</TEX> of the space X under the covering map <TEX>${\Phi}_K:QFK{\rightarrow}K$</TEX>. Using these, we show that for any space X, <TEX>${\beta}QFX=QF{\beta}{\upsilon}X$</TEX> and that a realcompact space X is a projective object in the category <TEX>$Rcomp_{\sharp}$</TEX> of all realcompact spaces and their <TEX>$z^{\sharp}$</TEX>-irreducible maps if and only if X is a quasi-F space.

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Abstract

The set of priors in the representation of Choquet expectation is expressed as the one of equivalent martingale measures under some conditions. We show that the set of priors, <TEX>$\mathcal{Q}_c$</TEX> in (1.1) is the same set of <TEX>$\mathcal{Q}^{\theta}$</TEX> in (1.3).

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Abstract

Let R be a 3!-torsion free noncommutative semiprime ring, U a Lie ideal of R, and let <TEX>$D:R{\rightarrow}R$</TEX> be a Jordan derivation. If [D(x), x]D(x) = 0 for all <TEX>$x{\in}U$</TEX>, then D(x)[D(x), x]y - yD(x)[D(x), x] = 0 for all <TEX>$x,y{\in}U$</TEX>. And also, if D(x)[D(x), x] = 0 for all <TEX>$x{\in}U$</TEX>, then [D(x), x]D(x)y - y[D(x), x]D(x) = 0 for all <TEX>$x,y{\in}U$</TEX>. And we shall give their applications in Banach algebras.

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Abstract

The set of priors in the representation of coherent risk measure is expressed in terms of quantile function and increasing concave function. We show that the set of prior, <TEX>$\mathcal{Q}_c$</TEX> in (1.2) is equal to the set of <TEX>$\mathcal{Q}_m$</TEX> in (1.6), as maximal representing set <TEX>$\mathcal{Q}_{max}$</TEX> defined in (1.7).

Lee, Sung Jin ; Lee, Jung Rye pp.385-387 https://doi.org/10.7468/jksmeb.2016.23.4.385
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Abstract

<TEX>$Fo{\check{s}}ner$</TEX> [4] defined a generalized module left (m, n)-derivation and proved the Hyers-Ulam stability of generalized module left (m, n)-derivations. In this note, we prove that every generalized module left (m, n)-derivation is trival if the algebra is unital and <TEX>$m{\neq}n$</TEX>.

Paek, Dae Hyun ; Yi, Jinhee pp.389-389 https://doi.org/10.7468/jksmeb.2016.23.4.389
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Abstract

After publication of the original article [1], the authors noticed that the title was incorrect as follows: `On evaluations of the cubic continued fraction by a modular equation of degree 9.' The correct version of the title is below: On evaluations of the cubic continued fraction by modular equations of degree 9

Jeonga, Seungpil ; Kim, Kyong Hoon ; Kim, Gwangil pp.391-391 https://doi.org/10.7468/jksmeb.2016.23.4.391
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Abstract

After publication of the original article [1], the authors noticed that the addresses of the second and third authors were incorrect as follows: `Department of Mathe- matics, Gyeongsang National University, Jinju, 52828, Republic of Korea.' The correct version of the address of the second author is below: Department of Informatics, Gyeongsang National University, Jinju, 52828, Re- public of Korea The correct version of the address of the third author is below: Department of Mathematics, Gyeongsang National University, Jinju, 52828, Re- public of Korea; Research Institute of Natural Science, Gyeongsang National Uni- versity, Jinju, 52828, Republic of Korea

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics