• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1105-1117
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• 2022

In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of Pⁿ(C) where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.779-787
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• 2007

This paper presents a highly efficient moving least squares finite difference method (MLS FDM) for a heat transfer problem of bi-material with interfacial boundary. The MLS FDM directly discretizes governing differential equations based on a node set without a grid structure. In the method, difference equations are constructed by the Taylor polynomial expanded by moving least squares method. The wedge function is designed on the concept of hyperplane function and is embedded in the derivative approximation formula on the moving least squares sense. Thus interfacial singular behavior like normal derivative jump is naturally modeled and the merit of MLS FDM in fast derivative computation is assured. Numerical experiments for heat transfer problem of bi-material with different heat conductivities show that the developed method achieves high efficiency as well as good accuracy in interface problems.

• Information Systems Review
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• v.24 no.4
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• pp.23-40
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• 2022

Although Support Vector Machine(SVM) has been used in various fields such as bankruptcy prediction model, the hyperplane learned by SVM in class imbalance problem can be severely skewed toward minority class and has a negative impact on performance because the area of majority class is expanded while the area of minority class is invaded. This study proposed optimized uneven margin SVM(OPT-UMSVM) combining threshold moving or post scaling method with UMSVM to cope with the limitation of the traditional even margin SVM(EMSVM) in class imbalance problem. OPT-UMSVM readjusted the skewed hyperplane to the majority class and had better generation ability than EMSVM improving the sensitivity of minority class and calculating the optimized performance. To validate OPT-UMSVM, 10-fold cross validations were performed on five sub-datasets with different imbalance ratio values. Empirical results showed two main findings. First, UMSVM had a weak effect on improving the performance of EMSVM in balanced datasets, but it greatly outperformed EMSVM in severely imbalanced datasets. Second, compared to EMSVM and conventional UMSVM, OPT-UMSVM had better performance in both balanced and imbalanced datasets and showed a significant difference performance especially in severely imbalanced datasets.