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Vol.23 No.4
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.
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).
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.
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).
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>.
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
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