• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.935-945
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• 2010

The mixed width-integrals of convex bodies are defined by E. Lutwak. In this paper, the mixed brightness-integrals of convex bodies are defined. An inequality is established for the mixed brightness-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes. An isoperimetric inequality (involving the mixed brightness-integrals) is presented which generalizes an inequality recently obtained by Chakerian and Heil. Strengthened version of this general inequality is obtained by introducing indexed mixed brightness-integrals.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.45-49
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• 1996

In this paper, we will define Choquet integrals of set-valued functions. Then, we show some properties of Choquet integrals of set-valued functions.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.95-107
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• 2004

In this paper, we consider fuzzy number-valued functions and fuzzy number-valued Choquet integrals. And we also discuss positively homogeneous and monotonicity of Choquet integrals of fuzzy number-valued functions(simply, fuzzy number-valued Choquet integrals). Furthermore, we prove convergence theorems for fuzzy number-valued Choquet integrals.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.903-924
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• 2016

In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.355-364
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• 2004

In this paper, we consider fuzzy integrals defined by max-measures and discuss some properties of these fuzzy integrals of measurable functions.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.139-147
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• 2003

In this paper, we consider Choquet integrals of interval number-valued functions(simply, interval number-valued Choquet integrals). Then, we prove a convergence theorem for interval number-valued Choquet integrals with respect to an autocontinuous fuzzy measure.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.487-499
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• 2021

We prove a decay estimate for oscillatory integrals with Hölder amplitudes and polynomial phases. The estimate allows us to answer certain questions concerning the uniform boundedness of oscillatory singular integrals on various spaces.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.549-556
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• 2006

In this paper, we consider interval-valued Choquet integrals and fuzzy measures. Using these properties, we discuss some applications of them in multicriteria decision aid. In particular, we show how these interval-valued Choquet integrals can model behavioral analysis of aggregation in ulticriteria decision aid.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.1-3
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• 2001

In this paper, we define the convergence in measure and convergence in distribution for set-valued Choquet integrals. Using there definitions, we discuss convergence theorems for set-valued Choquet integrals.

• Journal of the Korean Chemical Society
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• v.23 no.3
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• pp.125-131
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• 1979

A method for calculation of two center overlap integrals for a pair of Slater type orbitals was developed by Mulliken et al. In this method the spherical polar coordinates for a pair of Slater type orbitals located at two different points are required to be transformed into a spheroidal coordinate set for calculation of two center overlap integrals. A new method, the expansion method for spherical harmonics, in which Slater type orbitals, located at two different points, are expressed in a common coordinate system has been applied for computation of two center overlap integrals. The new method for computation of two center overlap integrals is required to translate Slater type orbitals centered at two different points into the reference point for computation of two center overlap integrals. This work has been expanded the expansion method for spherical harmonics for computation of two center overlap integrals to $|3s{\g}$, $|5s{\g}$ and $|5s{\g}$. Master formulas for two center overlap integrals are derived for these orbitals, using the general expansion formulas. The numerical values of the two center overlap integrals evaluated for a hypothetical NO molecule are in agreement with those of the previous works.