• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.510-514
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• 2004

In this paper, we introduce Fuzzy Beppo Levi's Theorem in which we use the supremum instead of addition in the expression of Beppo Levi's Theorem. That holds under the conditions which are continuity of t-seminorm ┬and the fuzzy additivity of a fuzzy measure g.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.2952-2962
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• 2000

The design of experiment(DOE) is getting more attention in the engineering community since it is easy to understand and apply. Recently, engineering designers are adopting DOE with orthogonal arrays when they want to design products in a discrete design space. In this research, a design flow with orthogonal arrays is defined for structural design according to the general DOE. The design problem is defined as a general structural optimization problem. Sensitivity information is evaluated by the analysis of variance(ANOVA), and an optimum design is determined from analysis of means(ANOM). Interactions between design variables are investigated to achieve additivity which should be valid in DOE. When strong interactions exit, a method is proposed. Some methods to consider the problem are suggested.

• Journal of the Korean Chemical Society
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• v.26 no.4
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• pp.211-217
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• 1982

Assuming krypton molecules adsorbed on the graphite surface as a two-dimensional (2D) gas, 4th virial coefficient of the virial equation is calculated by the use of cluster integrals. The Henry's law constant, and 2nd and 3rd virial coefficients are also calculated. Adsorption isotherms calculated from this virial equation agree very satisfactorily with experimental results. The interaction energy of Kr-graphite surface is calculated assuming the pairwise additivity of Lennard-Jones(12,6) potential, and parametars therein are taken as; ${\varepsilon}_{gs}$/k = 71.1 K, ${\varepsilon}_{gg}$/k = 170 K, ${\sigma}_{gs}$ = 354 pm, and ${\sigma}_{gg}$ = 368 pm.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.08a
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• pp.297-306
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• 2004

This study investigated Austenite Grain Size (AGS) distribution in Low-Speed Round-Oval Rolling. Rolling experiments were done along with the AGS numerical modeling to characterize the final AGS distribution and its kinetics behavior. For bar rolling experiment, we utilized the pilot rolling mill, operating at 34 fixed rpm, at POSCO Technical Research Laboratories. To investigate the microstructural observation, the rigid-viscoplastic finite element analysis was combined with Hodgson's AGS evolution model. To consider the transient thermal history in the integrative AGS modeling, additivity rule was introduced. The integrated analysis revealed that static or meta-dynamic recrystallization is responsible for the AGS difference in the inner or outer region of rolled bar. Comparative study showed that the current AGS modeling approach can be used to model the overall AGS distribution in bar rolling processes. For more accurate AGS prediction, the AGS modeling method should be verified under the various rolling conditions such as different rolling speeds and different deformations.

• Asian-Australasian Journal of Animal Sciences
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• v.20 no.7
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• pp.1092-1099
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• 2007

Two experiments were conducted to determine the additivity of apparent or true digestibility of phosphorus (P) in soybean meal (SBM), peas, faba beans, corn, oats, broken rice meal, rough rice meal, buckwheat, and sorghum for growing pigs. Chromic oxide (0.3%) was used as a digestion marker in both experiments. Each experiment lasted for 12 d, which consisted of a 7-d dietary adaptation period followed by a 5-d fecal collection period. Experiment 1 involved 6 diets: the SBM-based control diet; 4 diets with corn, oats, rough rice meal and broken rice meal substituted for SBM; and an additional diet with a representative mixture of the 5 ingredients. In Experiment 2, 6 diets were prepared similarly, except that the tested ingredients besides SBM were faba beans, peas, buckwheat, and sorghum. In each experiment, six barrows with an initial average individual BW of 20.5 kg were fed one of the six diets according to a $6{\times}6$ Latin square design. The apparent and true P digestibility values for the nine tested ingredients were determined by the substitution method. There were no differences (p>0.05) between the determined and the predicted true P digestibility values for the mixture of ingredients in Experiments 1 and 2. However, the determined and the predicted apparent P digestibility values for the mixture of ingredients differed (p = 0.059) in Experiment 1, but not in Experiment 2. These results indicate that true P digestibility values are additive in ingredients containing low levels of phytate phosphorus and anti-nutritional factors, whereas the apparent P digestibility values are not always additive in single feed ingredients for growing pigs.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2027-2034
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• 2013

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from $M_n(\mathcal{A})$ ($\mathcal{A}$ is not necessarily a prime algebra) onto an arbitrary ring $\mathcal{R}^{\prime}$ is additive.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.211-218
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• 2007

Nonlinear ARMA model $X_n\;=\;h(X_{n-1},{\cdots},X_{n-p},e_{n-1},{\cdots},e_{n-p})+e_n$ is considered and easy-to-check sufficient condition for strict stationarity of {$X_n$} without some irreducibility or continuity assumption is given. Threshold ARMA(p, q) and momentum threshold ARMA(p, q) models are examined as special cases.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.555-564
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• 1997

Uncertainty, which arises when little information is revealed, can be represented by a non-additive probability, while risk is described by an additive one. This paper demonstrates that in the presence of uncertainty a steady state probability exists, which implies that we can estimate an average over a long period even under uncertainty. It is also shown that the steady state probability may not be unique in the presence of uncertainty. This implies that the estimated average under uncertainty is less accurate than under risk.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.121-131
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• 2009

In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.

• Journal of the Korean Ceramic Society
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• v.25 no.1
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• pp.1-6
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• 1988

The IR edge absorption of the important pure components of ZrF4-based glasses, including two previously uncharacterized components(ZrF4 and AlF3), has been measured. Values of the glass IR edge absorption coefficients have been calculated from these results, assuming additivity, and are compared with experimental glass absorption coefficients. The calculated ${\alpha}$ values are about a factor of two lower than the experimental values for ZrF4-based glasses, and the ZrF4 makes the largest contribution to the calculated ${\alpha}$ value.