• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1219-1231
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• 2008

The main object of this paper is to develop a leave-one-out(LOO) bound of all pairwise comparison error correcting output codes (APC-ECOC). To avoid using classifiers whose corresponding target values are 0 in APC-ECOC and requiring pilot estimates we developed a bound based on mean misclassification probability(MMP). It can be used to tune kernel hyperparameters. Our empirical experiment using kernel mean squared estimate(KMSE) as the binary classifier indicates that the bound leads to good estimates of kernel hyperparameters.

• Food Science and Biotechnology
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• v.16 no.2
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• pp.183-186
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• 2007

The type of mixed gel network of $\kappa$-carrageenan/agar was determined by applying rheological principles. Apparent Young's modulus of the mixed gels was mathematically analyzed with (a) simply adding the moduli of two component gels, (b) phase-separated type's upper and lower bound models, (c) interpenetrating type's logarithmic model. The experimental data fitted the estimates from the operation (a). Whereas, as for the models (b), the experimental values in the agar-rich region fitted the estimates of the upper bound model, but in the $\kappa$-carrageenan-rich region slightly deviated from those of the lower bound model. It reflected an evidence of a phase-separated type, although it was not typical, that there must be data good-fit in the agar-rich and $\kappa$-carrageenan-rich regions with the upper and lower bound models, respectively. Experimental values disagreed with estimates of the model (c). Gel time was analyzed to evince the phase-separated type. As agar concentrations increased at a fixed amount of $\kappa$-carrageenan, gel time gradually decreased and then sharply increased and decreased again. The pattern of such change in gel time also represented a typical behavior of phase-separated type's mixed gels.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1315-1325
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• 2021

In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝⁿ. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the (k + 1)^th eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.

• Journal of Korean Society for Quality Management
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• v.22 no.1
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• pp.205-213
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• 1994

We construct a new lower bound of Cramer-Rao type for the median-unbiased estimator in the presence a nuisance parameter. We also identify useful necessary and sufficient conditions for the attainability of the lower bound. Some applications including the analysis of censored reliability data are considered as examples.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.711-716
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• 2008

A circular tube undergoes bucking behavior when it is subjected to axial loading. An upper bound analysis can be an attractive approach to predict the buckling load and energy absorption efficiently. The upper bound analysis obtains the load or energy absorption by means of assumption of the kinematically admissible velocity fields. In order to obtain an accurate solution, kinematically admissible velocity fields should be defined by considering many factors such as geometrical parameters, dynamic effect, etc. In this study, experiments and finite element analyses are carried out for circular tubes with various dimensions and loading conditions. As a result, the kinematically admissible velocity field is newly proposed in order to consider various dimensions and the strain rate effect of material. The upper bound analysis with the suggested velocity field accurately estimates the mean load and energy absorption obtained from results of experiment and finite element analysis.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.205-215
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• 2021

In [1], Beznosova proved that the bound on the norm of the dyadic paraproduct with b ∈ BMO in the weighted Lebesgue space L2(w) depends linearly on the Ad2 characteristic of the weight w and extrapolated the result to the Lp(w) case. In this paper, we provide the weighted norm estimates of the dyadic paraproduct πb with b ∈ VMO and reduce the dependence of the Ad2 characteristic to 1/2 by using the property that for b ∈ VMO its mean oscillations are vanishing in certain cases. Using this result we also reduce the quadratic bound for the commutators of the Calderón-Zygmund operator [b, T] to 3/2.

• Journal of the Korean Institute of Landscape Architecture
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• v.38 no.2
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• pp.25-36
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• 2010

The generally known important functions of forests include air purification and the health benefits that humans can receive when relaxing and enjoying recreation in the forests. In recent years, people have appreciated the value of the natural environment but it is not easy to answer the question how much monetary value a natural environment has. Because environmental property is public property, which is not traded on the market, market prices cannot be established, so it is not easy to assess the currency value. Methods for estimating environmental property value have been studied by economists. The representative method for measuring environmental property value is a contingent valuation method, or CVM. Various methods have been researched and attempted along with the development and fusion of mathematics, statistics, and economics. Representative methods of CVM are single-bound and double-bound logit and probit methods. This study has been carried out to compare four estimates. Estimates are as follows: the lowest estimate is derived from a single-bound logit WTPmedian while the highest estimate is from double-bound probit WTPmean. While there are some preceding studies on price estimation and methods of measurement through CVM, they offer only partial comparisons. This study suggests four analytic methods and prices through 1,123 questionnaires. The results can be used for the subsequent comparison of estimate prices and the methods of measurement

• Journal of the Korean Data and Information Science Society
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• v.19 no.1
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• pp.25-36
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• 2008

Error Correcting Output Codes (ECOC) can improve generalization performance when applied to multicategory classification problem. In this study we propose a new criterion to select hyperparameters included in ECOC scheme. Instead of margins of a data we propose to use the probability of misclassification error since it makes the criterion simple. Using this we obtain an upper bound of leave-one-out error of OVA(one vs all) method. Our experiments from real and synthetic data indicate that the bound leads to good estimates of parameters.

• Computational Structural Engineering : An International Journal
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• v.1 no.2
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• pp.81-87
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• 2001

A framework for reliability analysis of structural components and systems under conditions of statistical and model uncertainty is presented. The Bayesian parameter estimation method is used to derive the posterior distribution of model parameters reflecting epistemic uncertainties. Point, predictive and bound estimates of reliability accounting for parameter uncertainties are derived. The bounds estimates explicitly reflect the effect of epistemic uncertainties on the reliability measure. These developments are enhance-ments of second-moment uncertainty analysis methods developed by A. H-S. Ang and others three decades ago.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.129-136
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• 2001

We consider a solution process of stochastic differential equation(SDE) driven by S'($R^d$)-valued Wiener process and study a large deviation type of estimates for the process. We get an upper bound in exit probability for such a process to leave a ball of radius $\tau$ before a finite time t. We apply the Ito formula to the SDE under the structure of nuclear space.