• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.7
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• pp.42-51
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• 1992

This paper suggests a measure constraint locus which is the loci of points satisfying the necessary constraint for optimality of a measure in the configuration space. The characterization of four measures for singularity avoidance is worked out by using the measure constraint locus. It gives a global look at the performance of an inverse kinematic algorithm whien each of measures in a kinematically redundant robot is used. The invertible workspace without singularities and the topological properties both on the configuration and operational spaces are analyzed. We discuss also some limitations, based on the topological arguments of measure constraint locus, of the inverse kinematic algorithms, and compare global properties of each of measure. Therfore, a new concept called measure constraint locus gives a methodology for obtaining a conservative joint trajectory without singularities for almost entire workspace.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.525-531
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• 2007

We newly introduce the concept of summable in measure and investigate on some its properties. In addition to this, we consider a size of given series by means of we are giving Lebesgue measure to an associated series.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.385-389
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• 2015

In this paper we introduce the notions of expansiveness and measure expansiveness for homeomorphisms on a compact metric space, and we study the measure expansiveness of circle homeomorphisms.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.613-619
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• 2005

In this paper, we consider various types of convergence theorems of Choquet integral. We also show that the autocontinuity of finite fuzzy measure is equivalent to a convergence theorem with respect to convergence in measure.

• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.337-350
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• 2000

This paper suggests a new diagnostic measure and a stopping rule for detecting influential observations in multiple discriminant analysis (MDA). It is developed from a Bayesian point of view using a default Bayes factor obtained from the fractional Bayes factor methodology. The Bayes factor is taken as a discriminatory information in MDA. It is shown that the effect of an observation over the discriminatory information is fully explained by the diagnostic measure. Based on the measure, we suggest a stopping rule for detecting influential observations in a given training sample. As a tool for interpreting the measure a graphical method is sued. Performance of the method is used. Performance of the method is examined through two illustrative examples.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.495-507
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• 2002

In this paper, the characterization results related to Chernoff-type inequalities are applied for exponential-type (continuous and discrete) families. Upper variance bound is obtained here with a slightly different technique used in Alharbi and Shanbhag [1] and Mohtashami Borzadaran and Shanbhag [8]. Some results are shown with assuming measures such as non-atomic measure, atomic measure, Lebesgue measure and counting measure as special cases of Lebesgue-Stieltjes measure. Characterization results on power series distributions via Chernoff-type inequalities are corollaries to our results.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.577-588
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• 2007

Bearman's rotation theorem is not only very important in pure mathematics but also plays the key role for various research areas, related to Wiener measure. In 2002, the author and professor Im introduced the concept of analogue of Wiener measure, a kind of generalization of Wiener measure and they presented the several papers associated with it. In this article, we prove a formula on analogue of Wiener measure, similar to the formula in Bearman's rotation theorem.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.723-732
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• 2008

In this note, we establish the uniqueness theorem of conditional expectation on analogue of Wiener measure space for given distributions and prove the simple formula of conditional expectation on analogue of Wiener measure which is essentially similar to Park and Skoug's formula on the concrete Wiener measure.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.293-310
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• 2007

Recently a risk measure pricing and hedging is replacing a utility-based maximization problem in the literature. In this paper, we treat the optimal problem of risk measure pricing and hedging in the friction market, i.e. in the presence of transaction costs. The risk measure pricing is also verified with the contexts in the literature.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.91-103
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• 2022

In this paper, we introduce Toeplitz operators and Hankel operators with complex Borel measures on the closed unit disk. When a positive measure 𝜇 on (-1, 1) is a Carleson measure, it is known that the corresponding Hankel matrix is bounded and vice versa. We show that for a positive measure 𝜇 on 𝔻, 𝜇 is a Carleson measure if and only if the Toeplitz operator with symbol 𝜇 is a densely defined bounded linear operator. We also study Hankel operators of Hilbert-Schmidt class.