• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.413-424
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• 2023

The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ ℂ², for 1 < p < ∞, the Bergman projection 𝓟 is bounded from L^p(Ω, dV ) to the Bergman space A^p(Ω); from L^∞(Ω) to the holomorphic Bloch space BlHol(Ω); and from L¹(Ω, P(z, z)dV) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.241-252
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• 2011

Let $\{\Omega_{\tau}\}_{\tau{\in}I}$ be a family of strictly convex domains in $\mathbb{C}^n$. We obtain explicit estimates for the solution of the $\bar{\partial}$-equation on $\Omega{\times}I$ in H$\ddot{o}$lder space. We also obtain explicit point-wise derivative estimates for the $\bar{\partial}$-equation both in space and parameter variables.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.180-185
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate natural frequencies of concave plates with arbitrary shape. Originally, the MNDIF method cannot yield accurate natural frequencies for concave plates. To overcome this weak point, a new approach of dividing a concave plate into two convex domains is proposed and the validity and accuracy is shown in a verification example.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.10a
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• pp.658-663
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate eigenvalues of concave acoustic cavities with arbitrary shapes. It is said that the MNDIF method cannot yield accurate eigenvalues for concave cavities. To overcome this weak point, a new approach of dividing a concave cavity into two convex domains is proposed. The validity of the proposed method is shown through a case study.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.145-156
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• 2004

Let $D_1,\;D_2$ be convex domains in complex normed spaces $E_1,\;E_2$ respectively. When a mapping $f\;:\;D_1{\rightarrow}D_2$ is holomorphic with f(0) = 0, we obtain some results like the Schwarz lemma. Furthermore, we discuss a condition whereby f is linear or injective or isometry.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.8
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• pp.742-747
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• 2012

A modified NDIF method using a sub-domain approach is introduced to extract highly accurate eigenvalues of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that it can be applicable for only convex cavities. It was revealed that the solution of the NDIF method is very inaccurate or is not suitable for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave domain into several convex domains. Finally, the validity of the proposed method is verified in two case studies, which indicate that eigenvalues obtained by the proposed method are more accurate compared to the exact method, the NDIF method, or FEM(ANSYS).

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.9
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• pp.830-836
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• 2012

The NDIF method based on a sub-domain technique is introduced to extract highly accurate natural frequencies of arbitrarily shaped plates with the simply-supported boundary condition. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped plates with various boundary conditions, has the feature that it yields highly accurate natural frequencies thanks to its effective theoretical formulation, compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that it can be applicable for only convex plates. It was revealed that the NDIF method offers very inaccurate natural frequencies or no solution for concave cavities. To overcome the weak point, the paper proposes the sub-domain method of dividing a concave plate into several convex domains. Finally, the validity of the proposed method is verified in various case studies, which indicate that natural frequencies obtained by the proposed method are very accurate compared to the exact method and FEM(ANSYS).

• International Journal of Computer Science & Network Security
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• v.23 no.10
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• pp.115-128
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• 2023

Deep learning has been incorporating various optimization techniques motivated by new pragmatic optimizing algorithm advancements and their usage has a central role in Machine learning. In recent past, new avatars of various optimizers are being put into practice and their suitability and applicability has been reported on various domains. The resurgence of novelty starts from Stochastic Gradient Descent to convex and non-convex and derivative-free approaches. In the contemporary of these horizons of optimizers, choosing a best-fit or appropriate optimizer is an important consideration in deep learning theme as these working-horse engines determines the final performance predicted by the model. Moreover with increasing number of deep layers tantamount higher complexity with hyper-parameter tuning and consequently need to delve for a befitting optimizer. We empirically examine most popular and widely used optimizers on various data sets and networks-like MNIST and GAN plus others. The pragmatic comparison focuses on their similarities, differences and possibilities of their suitability for a given application. Additionally, the recent optimizer variants are highlighted with their subtlety. The article emphasizes on their critical role and pinpoints buttress options while choosing among them.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.16 no.2
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• pp.81-86
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• 2016

Term weighting is a popular technique that effectively weighs the term features to improve accuracy in document classification. While several successful term weighting algorithms have been suggested, none of them appears to perform well consistently across different data domains. In this paper we propose several reasonable methods to combine different term weight vectors to yield a robust document classifier that performs consistently well on diverse datasets. Specifically we suggest two approaches: i) learning a single weight vector that lies in a convex hull of the base vectors while minimizing the class prediction loss, and ii) a mini-max classifier that aims for robustness of the individual weight vectors by minimizing the loss of the worst-performing strategy among the base vectors. We provide efficient solution methods for these optimization problems. The effectiveness and robustness of the proposed approaches are demonstrated on several benchmark document datasets, significantly outperforming the existing term weighting methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.37-41
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• 2007

The semi-convexity for planar shapes has been recently introduced in [2]. As a generalization of the convextiy, semi-convexity is closed under the Minkowski sum. But the definition of semi-convexity requires that the shape boundary should satifisfy a differentiability condition $C^{1:1}$, which means that it should be possible to take the normal vector field along the domain's extended boundary. In view of the fact that the semi-convextiy is a most natural generalization of the convexity in many respects, this is a severe restriction for the semi-convexity, since the convexity requires no such a priori differentiability condition. In this paper, we generalize the semi-convexity to the closure of the class of semi-convex $\mathcal{M}$-domains for any Minkowski class $\mathcal{M}$, and show that this generalized semi-convexity is also closed under Minkowski sum.