• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.789-795
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• 1995

For nonintegrable weight $-\rho$, some weight multiplicities of the irreducible module $L(-\rho)$ over $A^{(1)}_{(1)}$ affine Lie algebras are expressed in terms of the colored partition functions. Also we find the multiplicity of $L(-\rho)$ in ther Verma module $M(-\rho)$ for any affine Lie algebras.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.823-828
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• 1999

We extend the notion of category $O^g$ for Kac-Moody algebras to generalized Kac-Moody algebras and prove some analogues of results for Kac-Moody algebras.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.519-524
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• 1997

We extent the notion of equivalent relation $\approx$ for Kac-Moody algebras to generalized Kac-Moody algebras and prove some analogues of results for Kac-Moody algebras.

• Journal of Electrical Engineering and Technology
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• v.9 no.5
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• pp.1739-1745
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• 2014

Prediction of fault-prone modules continues to attract researcher's interest due to its significant impact on software development cost. The most important goal of such techniques is to correctly identify the modules where faults are most likely to present in early phases of software development lifecycle. Various software metrics related to modules level fault data have been successfully used for prediction of fault-prone modules. Goal of this research is to predict the faulty modules at design phase using design metrics of modules and faults related to modules. We have analyzed the effect of pre-processing and different machine learning schemes on eleven projects from NASA Metrics Data Program which offers design metrics and its related faults. Using seven machine learning and four preprocessing techniques we confirmed that models built from design metrics are surprisingly good at fault proneness prediction. The result shows that we should choose Naïve Bayes or Voting feature intervals with discretization for different data sets as they outperformed out of 28 schemes. Naive Bayes and Voting feature intervals has performed AUC > 0.7 on average of eleven projects. Our proposed framework is effective and can predict an acceptable level of fault at design phases.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.559-581
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• 2013

This paper is motivated by a 2001 paper of Choie and Kim and a 2006 paper of Bump and Choie. The paper of Choie and Kim extends an earlier result of Bol for elliptic modular forms to the setting of Siegel and Jacobi forms. The paper of Bump and Choie provides a representation theoretic interpretation of the phenomenon, and shows how a natural generalization of Choie and Kim's result on Siegel modular forms follows from a natural conjecture regarding ($g$, K)-modules. In this paper, it is shown that the conjecture of Bump and Choie follows from work of Boe. A second proof which is along the lines of the proof given by Bump and Choie in the genus 2 case is also included, as is a similar treatment of the result of Choie and Kim on Jacobi forms.