• East Asian mathematical journal
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• v.35 no.3
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• pp.319-329
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• 2019

In this paper, we provide sufficient conditions of a pair of weights (u, v) and a function b so that the dyadic paraproduct is bounded from $L^2_u(X)$ into $L^2_v(X)$, where X is a space of homegeneous type. In order to prove the main result we use the honest dyadic system introduced in [10].

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.717-737
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• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.10A
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• pp.943-951
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• 2006

Multi-input-multi-output (MIMO) systems are considered to improve the capacity and reliability of next generation mobile communication. However, the multiple RF chains associated with multiple antennas are costly in terms of size, power and hardware. Antenna selection is a low-cost low-complexity alternative to capture many of the advantages of MIMO systems. We proposed new joint Tx/Rx antenna selection algorithm with low complexity. The proposed algorithm is a method selects $L_R{\times}L_T$ channel matrix out of $L_R{\times}L_T$ entire channel gain matrix where $L_R{\times}L_T$ matrix selects alternate Tx antenna with Rx antenna which have the largest channel gain to maximize Frobenius norm. The feature of this algorithm is very low complexity compare with Exhaustive search which have optimum capacity. In case of $4{\times}4$ antennas selection out of $8{\times}8$ antennas, the capacity decreases $0.5{\sim}2dB$ but the complexity also decreases about 1/10,000 than optimum exhaustive search.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.317-333
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• 2007

In 2002, the author and professor Ryu introduced the concept of analogue of Wiener measure. In this paper, we prove the existence theorem of Fourier-Feynman transform on analogue of Wiener measure in $L_2-norm$ sense.

• Journal of the Chungcheong Mathematical Society
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• v.2 no.1
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• pp.65-73
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• 1989

To smooth a given data in two-way tables with the order restriction, we propose the dual problem and construct an algorithm utilizing the network flows which ends up with the minimum L1-norm after a finite number of iterations.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1341-1353
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• 2019

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.841-852
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• 2019

We establish the generalized Myers theorem for Finsler manifolds under integral Ricci curvature bound. More precisely, we show that the forward complete Finsler n-manifold whose part of Ricci curvature less than a positive constant is small in $L^p$-norm (for p > n/2) have bounded diameter and finite fundamental group.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.485-505
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• 2020

We present a complete description of all the extreme points of the unit ball of 𝓛_s(²𝑙³_∞) which leads to a complete formula for ║f║ for every f ∈ 𝓛_s(²𝑙³_∞)^∗. We also show that $extB_{{\mathcal{L}}_s(^2l^3_{\infty})}{\subset}extB_{{\mathcal{L}}_s(^2l^n_{\infty})}$ for every n ≥ 4. Using the formula for ║f║ for every f ∈ 𝓛_s(²𝑙³_∞)^∗, we show that every extreme point of the unit ball of 𝓛_s(²𝑙³_∞) is exposed. We also characterize all the smooth points of the unit ball of 𝓛_s(²𝑙³_∞).

• Journal of Computing Science and Engineering
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• v.11 no.4
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• pp.121-129
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• 2017

Feature selection has been widely established as an efficient technique for microarray data analysis. Feature selection aims to search for the most important feature/gene subset of a given dataset according to its relevance to the current target. Unsupervised feature selection is considered to be challenging due to the lack of label information. In this paper, we propose a novel method for unsupervised feature selection, which incorporates embedded learning and $l_{2,1}-norm$ sparse regression into a framework to select genes in microarray data analysis. Local tangent space alignment is applied during embedded learning to preserve the local data structure. The $l_{2,1}-norm$ sparse regression acts as a constraint to aid in learning the gene weights correlatively, by which the proposed method optimizes for selecting the informative genes which better capture the interesting natural classes of samples. We provide an effective algorithm to solve the optimization problem in our method. Finally, to validate the efficacy of the proposed method, we evaluate the proposed method on real microarray gene expression datasets. The experimental results demonstrate that the proposed method obtains quite promising performance.

• Journal of the Institute of Convergence Signal Processing
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• v.20 no.3
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• pp.145-150
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• 2019

We develop the system realization of whale sound reconstruction by inverse MFCC algorithm with the weighted L2-norm minimization techniques. The output products from this research will contribute to the whale tourism and multimedia content industry by combining whale sound contents with the prototype of 3D printing. First of all, we develop the softwares for generating whale sounds and install them into Raspberry Pi hardware and fasten them inside a 3D printed whale. The languages used in the development of this system are the C++ for whale-sounding classification, MATLAB and Python for whale-sounding playback algorithm, and Rhino 6 for 3D printing.