• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.143-159
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• 2020

We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L² and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.

• Smart Structures and Systems
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• v.25 no.6
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• pp.679-691
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• 2020

To identify the bridge information from the response of test vehicles passing on it (also known as the indirect approach) has aroused the interest of many researchers thanks to its economy, easy implementation and less disruption to traffic. The surface roughness of bridge remains an obstacle for such method as it contaminates the vehicle response severely and thereby renders many vehicle-response-based bridge identification methods ineffective. This study aims to eliminate such effect with the responses of two different test vehicles. The proposed method can estimate the surface profile of a bridge based on the acceleration data of the vehicles running on the bridge successively, and obtain the normalized contact point response, which proves to be relatively immune to surface roughness. The frequencies and mode shapes of bridge can be further extracted from the normalized contact point acceleration with spectral analysis and Hilbert transform. The effectiveness of the proposed method is verified numerically with a three-span continuous bridge. The influence of measurement noise is also examined.

• Journal for History of Mathematics
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• v.32 no.1
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• pp.1-15
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• 2019

We divide the timeline of the history of Finsler geometry, which dates back to Riemann's inaugural lecture in 1854, into three periods (hibernation, hiatus, rebirth) and we study formation of Romanian Finsler school around Iasi, Romania during the hiatus period. We look for the history centered around Radu Miron who is a third generation geometer of Iasi University and the mathematical heritage there through five generations. We also investigate mathematical impact of T. Levi-Civita, D. Hilbert, ${\acute{E}}$ Cartan who are considered as top mathematicians at their time.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.203-221
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• 2022

In this paper, we introduce new hybrid inertial contraction projection algorithms for solving variational inequality problems over the intersection of the fixed point sets of demicontractive mappings in a real Hilbert space. The proposed algorithms are based on the hybrid steepest-descent method for variational inequality problems and the inertial techniques for finding fixed points of nonexpansive mappings. Strong convergence of the iterative algorithms is proved. Several fundamental experiments are provided to illustrate computational efficiency of the given algorithm and comparison with other known algorithms

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.2
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• pp.265-274
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• 2011

In this paper, it is studied on wide radiating slot antenna's miniaturization for ultra wide-band(UWB) technologies and notch structure to prevent interference between UWB systems and existing wireless systems for using Wi-Fi service of IEEE standards 802.11 a/n. Proposed antenna that wide slot is decreased from $\lambda/2$ to $\lambda/4$ length of resonant frequency has decreased by 72 % compared with conventional antenna. And optimized T-shaped CPW-fed stub has satisfied UWB bandwidth for 3.0~11.8 GHz. Then, creating 2-order Hilbert curve slot line in the stub's patch area, 4.9~5.6 GHz that centered frequency is 5 GHz is eliminated. Finally, the designed antenna constructed on FR4-epoxy has $20{\times}15\;mm^2$ dimension. The measured results that are obtained return loss under -10 dB through 3.2~11.8 GHz without Wi-Fi bandwidth, a linear phase characteristic, a stable group delay, and omnidirectional radiation patterns are presented.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.65-72
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• 2012

Let T > 0 be given. Let $(C[0,T],m_{\varphi})$ be the analogue of Wiener measure space, associated with the Borel proba-bility measure ${\varphi}$ on ${\mathbb{R}}$, let $(L_{2}[0,T],\tilde{\omega})$ be the centered Gaussian measure space with the correlation operator $(-\frac{d^{2}}{dx^{2}})^{-1}$ and ${\el}_2,\;\tilde{m}$ be the abstract Wiener measure space. Let U be the space of all sequence $<c_{n}>$ in ${\el}_{2}$ such that the limit $lim_{{m}{\rightarrow}\infty}\;\frac{1}{m+1}\;\sum{^{m}}{_{n=0}}\;\sum_{k=0}^{n}\;c_{k}\;cos\;\frac{k{\pi}t}{T}$ converges uniformly on [0,T] and give a set function m such that for any Borel subset G of $\el_2$, $m(\mathcal{U}\cap\;P_{0}^{-1}\;o\;P_{0}(G))\;=\tilde{m}(P_{0}^{-1}\;o\;P_{0}(G))$. The goal of this note is to study the relationship among the measures $m_{\varphi},\;\tilde{\omega},\;\tilde{m}$ and $m$.

• Journal of Broadcast Engineering
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• v.16 no.1
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• pp.96-107
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• 2011

Recently, studies of 3D HDTV broadcasting technology have been processed actively. Korea is making efforts to modify Advanced Television Systems Committee (ATSC) 8-Vestigial Side Band (8-VSB) systems for terrestrial 3D HDTV broadcasting services. We intend to adopt a new frame structure to use PN (Pseudo-Noise) sequence as frame header, and VSB modulation. PN sequence is used to recover carrier freqeuncy offset, carrier phase error. In this paper, we will describe this system as the modified ATSC systems. The receiver of the modified ATSC system should be able to estimate and recover carrier frequency offset exactly. A existing ATSC systems inserts pilot to recover carrier frequency offset, on the other hand the modified ATSC systems use PN sequence to recovery carrier frequency offset without the use of pilot. In this paper, we introduce carrier frequency recovery (CFR) scheme for the modified ATSC systems. The proposed CFR scheme is composed of coarse CFR scheme using Fitz algorithm and fine CFR scheme using a simple PN sequence correlation algorithm. And, the symbol information of QAM modulated signal is contained in both In-phase (I)channel and Quadrature-phase (Q)channel. However the symbol information of VSB modulated signal is contained in I channel, and Q channel is just Hilbert transform of I channel. For the reason, VSB modulated symbols can not have fixed phase like QAM modulated symbols, and VSB modulated symbols is more sensitive to carrier frequency offset. Therefore we perform phase correction of received PN sequence to improve performance.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.321-338
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• 2014

In this paper, we introduce the history and the present status of the Mathematics Genealogy Project (MGP). The cases of David Hilbert and the first author were used to show how it works. As an example, we explain how to gain useful information such as the granting year of mathematics Ph. D degree holders, the title of dissertation, advisors and descendants from the MGP website. Through a survey of three different groups in MGP on 20~30 significant Korean mathematicians, we found that Korean records in the academic genealogy project are missing or poorly presented in the database of the MGP website. In conclusion, we found a way to improve the situation and provide instructions to submit our information to MGP. We expect our effort can help Korean mathematics and mathematicians to become better exposed to the world. It will help others to understand both the modern history and the future prospect of Korean mathematics.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.2
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• pp.1020-1042
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• 2019

Reversible data hiding in encrypted images (RDHEI) provides some real-time cloud applications; i.e. the cloud, acting as a data-hider, automatically embeds timestamp in the encrypted image uploaded by a content owner. Many existing methods of RDHEI only satisfy user privacy in which the data-hider does not know the original image, but leaks owner privacy in which the receiver can obtains the original image by decryption and extraction. In the literature, the method of Zhang et al. is the one providing weak content-owner privacy in which the content-owner and data-hider have to share a data-hiding key. In this paper, we take care of the stronger notion, called strong content-owner privacy, and achieve it by presenting a new reversible data hiding in encrypted images. In the proposed method, image decryption and message extraction are separately controlled by different types of keys, and thus such functionalities are decoupled to solve the privacy problem. At the technique level, the original image is segmented along a Hilbert filling curve. To keep image privacy, segments are transformed into an encrypted image by using random permutation. The encrypted image does not reveal significant information about the original one. Data embedment can be realized by using pixel histogram-style hiding, since this property, can be preserved before or after encryption. The proposed method is a modular method to compile some specific reversible data hiding to those in encrypted image with content owner privacy. Finally, our experimental results show that the image quality is 50.85dB when the averaged payload is 0.12bpp.