• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.69-83
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• 2015

In this paper we introduce and study the separable weak bounded approximation properties which is strictly stronger than the approximation property and but weaker than the bounded approximation property. It provides new sufficient conditions for the metric approximation property for a dual Banach space.

• Proceedings of the KIEE Conference
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• 1999.07c
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• pp.1067-1069
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• 1999

This paper presents a network reduction using weak coupling method. Weak coupling method of identifying coherent generator groups are proposed. The partitioning technique used in this paper is based on a property of sparse matrix factorization. When a matrix has been factorized, a system is divided into study area, boundary buses and external area. A reduction process for external system starts with the load bus elimination and coherent generator aggregation. An identification of coherent generator group, network partitioning and network reduction are presented.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1439-1451
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• 2023

This paper provides a constructive proof of the weak factorizations of the classical Hardy space H¹(ℝⁿ) in terms of multilinear fractional integral operator on the variable Lebesgue spaces, which the result is new even in the linear case. As a direct application, we obtain a new proof of the characterization of BMO(ℝⁿ) via the boundedness of commutators of the multilinear fractional integral operator on the variable Lebesgue spaces.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1345-1356
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• 2017

For a given number field K, we show that the ranks of elliptic curves over K are uniformly finitely bounded if and only if the weak Mordell-Weil property holds in all (some) ultrapowers $^*K$ of K. We introduce the nonstandard weak Mordell-Weil property for $^*K$ considering each Mordell-Weil group as $^*{\mathbb{Z}}$-module, where $^*{\mathbb{Z}}$ is an ultrapower of ${\mathbb{Z}}$, and we show that the nonstandard weak Mordell-Weil property is equivalent to the weak Mordell-Weil property in $^*K$. In a saturated nonstandard number field, there is a nonstandard ring of integers $^*{\mathbb{Z}}$, which is definable. We can consider definable abelian groups as $^*{\mathbb{Z}}$-modules so that the nonstandard weak Mordell-Weil property is well-defined, and we conclude that the nonstandard weak Mordell-Weil property and the weak Mordell-Weil property are equivalent. We have valuations induced from prime numbers in nonstandard rational number fields, and using these valuations, we identify two nonstandard rational numbers.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.25-42
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• 2007

A direct solver for the Legendre tau approximation for the two-dimensional Poisson problem is proposed. Using the factorization of symmetric eigenvalue problem, the algorithm overcomes the weak points of the Schur decomposition and the conventional diagonalization techniques for the Legendre tau approximation. The convergence of the method is proved and numerical results are presented.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.6
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• pp.175-186
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• 2004

We present a hybrid approach of texture-based method and connected component (CC)-based method for text extraction in complex images. Two primary methods, which are mainly utilized in this area, are sequentially merged for compensating for their weak points. An automatically constructed MLP-based texture classifier can increase recall rates for complex images with small amount of user intervention and without explicit feature extraction. CC-based filtering based on the shape information using NMF enhances the precision rate without affecting overall performance. As a result, a combination of texture and CC-based methods leads to not only robust but also efficient text extraction. We also enhance the processing speed by adopting appropriate region marking methods for each input image category.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.721-741
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• 2009

Consider RSA with N = pq, q < p < 2q, public encryption exponent e and private decryption exponent d. We first study cryptanalysis of RSA when certain amount of the Most Significant Bits (MSBs) or Least Significant Bits (LSBs) of d is known. The basic lattice based technique is similar to that of Ernst et al. in Eurocrypt 2005. However, our idea of guessing a few MSBs of the secret prime p substantially reduces the requirement of MSBs or LSBs of d for the key exposure attack. Further, we consider the RSA variant proposed by Sun and Yang in PKC 2005 and show that the partial key exposure attack works significantly on this variant.

• Structural Engineering and Mechanics
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• v.37 no.6
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• pp.671-684
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• 2011

Deciding on an optimal sensor placement (OSP) is a common problem encountered in many engineering applications and is also a critical issue in the construction and implementation of an effective structural health monitoring (SHM) system. The present study focuses with techniques for selecting optimal sensor locations in a sensor network designed to monitor the health condition of Dalian World Trade Building which is the tallest in the northeast of China. Since the number of degree-of-freedom (DOF) of the building structure is too large, multi-modes should be selected to describe the dynamic behavior of a structural system with sufficient accuracy to allow its health state to be determined effectively. However, it's difficult to accurately distinguish the translational and rotational modes for the flexible structures with closely spaced modes by the modal participation mass ratios. In this paper, a new method of the OSP that computing the mode shape matrix in the weak axis of structure by the simplified multi-DOF system was presented based on the equivalent rigidity parameter identification method. The initial sensor assignment was obtained by the QR-factorization of the structural mode shape matrix. Taking the maximum off-diagonal element of the modal assurance criterion (MAC) matrix as a target function, one more sensor was added each time until the maximum off-diagonal element of the MAC reaches the threshold. Considering the economic factors, the final plan of sensor placement was determined. The numerical example demonstrated the feasibility and effectiveness of the proposed scheme.

• The Journal of the Acoustical Society of Korea
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• v.21 no.4
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• pp.361-373
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• 2002

In this paper, we propose a channel normalization method to improve the performance of CMS (cepstral mean subtraction) which is widely adopted to normalize a channel variation for speech and speaker recognition. CMS which estimates the channel effects by averaging long-term cepstrum has a weak point that the estimated channel is biased by the formants of voiced speech which include a useful speech information. The proposed Formant-broadened Cepstral Mean Subtraction (FBCMS) is based on the facts that the formants can be found easily in log spectrum which is transformed from the cepstrum by fourier transform and the formants correspond to the dominant poles of all-pole model which is usually modeled vocal tract. The FBCMS evaluates only poles to be broadened from the log spectrum without polynomial factorization and makes a formant-broadened cepstrum by broadening the bandwidths of formant poles. We can estimate the channel cepstrum effectively by averaging formant-broadened cepstral coefficients. We performed the experiments to compare FBCMS with CMS, PFCMS using 4 simulated telephone channels. In the experiment of channel estimation, we evaluated the distance cepstrum of real channel from the cepstrum of estimated channel and found that we were able to get the mean cepstrum closer to the channel cepstrum due to an softening the bias of mean cepstrum to speech. In the experiment of text-independent speaker identification, we showed the result that the proposed method was superior than the conventional CMS and comparable to the pole-filtered CMS. Consequently, we showed the proposed method was efficiently able to normalize the channel variation based on the conventional CMS.