• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1163-1184
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• 2007

In this presentation dedicated to the tricentennial birth anniversary of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707-1783), we begin by remarking about the so-called Basler problem of evaluating the Zeta function ${\zeta}(s)$ [in the much later notation of Georg Friedrich Bernhard Riemann (1826-1866)] when s=2, which was then of vital importance to Euler and to many other contemporary mathematicians including especially the Bernoulli brothers [Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)], and for which a fascinatingly large number of seemingly independent solutions have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. We then investigate various recent developments on the evaluations and representations of ${\zeta}(s)$ when $s{\in}{\mathbb{N}}{\backslash}\;[1],\;{\mathbb{N}}$ being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ${\zeta}(2n+1)(n{\in}{\mathbb{N}})$ which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ${\zeta}(3)$ can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger $Ap\'{e}ry$ (1916-1994) in his proof of the irrationality of ${\zeta}(3)$. Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.

• Journal of the Korea Society of Computer and Information
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• v.25 no.10
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• pp.15-22
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• 2020

In this study, we propose an improvement method that can create U-Net model which detect fine concrete cracks by applying a weighted loss function. Because cracks in concrete are a factor that threatens safety, it is important to periodically check the condition and take prompt initial measures. However, currently, the visual inspection is mainly used in which the inspector directly inspects and evaluates with naked eyes. This has limitations not only in terms of accuracy, but also in terms of cost, time and safety. Accordingly, technologies using deep learning is being researched so that minute cracks generated in concrete structures can be detected quickly and accurately. As a result of attempting crack detection using U-Net in this study, it was confirmed that it could not detect minute cracks. Accordingly, as a result of verifying the performance of the model trained by applying the suggested weighted loss function, a highly reliable value (Accuracy) of 99% or higher and a harmonic average (F1_Score) of 89% to 92% was derived. The performance of the learning improvement plan was verified through the results of accurately and clearly detecting cracks.

• Journal of the Korean Institute of Telematics and Electronics
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• v.8 no.3
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• pp.1-14
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• 1971

A relay servo, one of the nonlinear sytsems, is inherently compact compared to a linear system for an equivalent control problem. The power element or actuator is not adjusted proportionally in accordance with an error signals but rather is switched abruptly between several discrete conditions. Usually switched conditions are off, full, forward or full reverse. The relay system is a particularly simple and compact one, but probably more effort has been expended on its analysis and design than on all other systems together. Early studies in the art were made by Goldfarb, austin, Oppelt and Kochenburger on the describing function method, which can be used as an approximate check on the stability of the system. The describing function method is based on the assumption that any periodic wave could be approximated as a fundamental one in wide ranges of practical applications. A relay servo system usually operates on a limit cycle condition as the loop gain increases. The stability analysis compensation or any improvement effort based on the describing function method sometimes may present considerable discrepancies on physically realized practical systems. An approach to exact periodic solutions of a relay servo system is much important for the analysis, design and system improvement. This paper dells with periodic solutions of a relay servo system on the basis of describing function and generalized chopper wave form which is composed of infinite number of harmonic series. Various ways of graphical representation were attempted to get periodic solutions, some of which have shown its validity in rapid approach to exact solutions and also in judgement of system behavior.

• Proceedings of the Korean Vacuum Society Conference
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• 2011.02a
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• pp.185-185
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• 2011

ZnTe semiconductor is very attractive materials for optoelectronic devices in the visible green spectral region because of it has direct bandgap of 2.26 eV. The prototypes of ZnTe light emitting diodes (LEDs) have been reported [1], showing that their green emission peak closely matches the most sensitive region of the human eye. Another application to photovoltaics proved that ZnTe is useful for the production of high-efficiency multi-junction solar cells [2,3]. By using the pulse laser deposition system, ZnTe thin films were deposited on ZnO thin layer, which is grown on (0001) Al2O3substrates. To produce the plasma plume from an ablated ZnO and ZnTe target, a pulsed (10 Hz) YGA:Nd laser with energy density of 95 mJ/$cm^2$ and wavelength of 266 nm by a nonlinear fourth harmonic generator was used. The laser spot focused on the surface of the ZnO and ZnTe target by using an optical lens was approximately 1 mm2. The base pressure of the chamber was kept at a pressure around $10^{-6}$ Torr by using a turbo molecular pump. The oxygen gas flow was controlled around 3 sccm by using a mass flow controller system. During the ZnTe deposition, the substrate temperature was $400^{\circ}C$ and the ambient gas pressure was $10^{-2}$ Torr. The structural properties of the samples were analyzed by XRD measurement. The optical properties were investigated by using the photoluminescence spectra obtained with a 325 nm wavelength He-Cd laser. The film surface and carrier concentration were analyzed by an atomic force microscope and Hall measurement system.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.21 no.3
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• pp.292-300
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• 2010

In this paper, we propose a RF front-end architecture based on hybrid conversion which is available to receive both broadband and multiband DVB-H receiver, and a multi-function circuit for implementing the RF front-end is fabricated. A multi-function circuit is operated as a sub-harmonic mixer mode in the case of receiving a broadband VHF/UHF band, which show a conversion loss of -10.0 dB, noise figure of 7.0 dB and IIP3 of 2.0 dBm. On the other hand, it is performed as a attenuation mode with a insertion loss of -10.0 dB in receiving a multiband, L-band.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.569-577
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• 2012

In this study, a theoretical investigation of optimized sleeper spacing which can suppress resonances of a railway track is attempted. To achieve this, we introduced a minimization problem in which the objective function is given by the wave transmittance and the design variable is defined by sleeper distribution. In the analysis the rail is modeled by a Timoshenko beam and the sleeper is represented by a mass. The infinite track analysis is realized by attaching the transmitting boundaries at both ends of the finite optimization region. Through numerical analyses the sleeper spacing effective in reduction of the transmittance is discussed. Furthermore, the feasibility of the proposed method is validated in the aspect of vibration reduction through response analyses for a harmonic load.

• Journal of the Society of Naval Architects of Korea
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• v.54 no.3
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• pp.227-241
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• 2017

In this study, a Volterra system for the variations of metacentric height (GM) in waves is employed to simulate the parametric roll phenomena of ships in head sea condition. Using the present Volterra system, the transfer function of each harmonic component in the GM variation is computed for different ship models, including mathematical models and a real containership, and the results are validated through the comparison with the values obtained using the direct calculations based on a weakly nonlinear time-domain method. Then, a semi-analytic approach employing a 1-degree of freedom equation for roll motion is developed to simulate the parametric roll motions in irregular waves. In the derived approach, the nonlinear and time-varying restoring forces in the waves are approximated using the Volterra system. Through simulations of the parametric roll for different sea states, the effects of the 1st and 2nd-order harmonic components of the variations in the occurrence and amplitude of the parametric roll motions are investigated. Because of the strong nonlinearities in the phenomena, a stochastic analysis is conducted to examine the statistical properties of the roll motions in consideration of the sensitivities and uncertainties in the computations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.1
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• pp.83-91
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• 2004

Nonlinear system responses of an impact system under randomly perturbed harmonic excitations are predicted in the probability domain by adopting the semi-analytical procedure previously developed. The semi-analytical procedure is obtained by solving the Fokker-Planck equation corresponding to the stochastic differential equation of the given impact system by utilizing the path-integral solution. The evolutionary joint probability density functions are generated by using the method, and the characteristics of nonlinear dynamic response behaviors of the system are examined. Noise effects on the responses are also examined. It Is found that the semi-analytical method can provides the accurate information of the responses via the joint probability functions for the impact system. It is found that the noises weaken and eventually terminate the chaos in the responses, but it is also found that the chaotic signatures reside in the presence of the external noise with relatively high intensity. The joint probability density function shows that the ensemble of the system responses are weakly stationary.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.50 no.8
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• pp.387-393
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• 2001

This paper describes an advanced measuring method and precise evaluation of the ground resistance for the grounding system of energized substations and power equipments. A grounding system of substations consists of all interconnected grounding connections of grounded conductors, neutral ground wires, underground conductors of distribution lines, cable shields, grounding terminals of equipments, and etc. It is very difficult to measure the accurate ground resistance of the grounding terminals of equipments, and etc. It is very difficult to measure the accurate ground resistance of the grounding system of high voltage energized substations because of harmonic components caused by switched power supplies or overloads. The conventional fall-of-potential method may be subject to big error if stray ground currents and potentials are present. In this work, to improve the precision in measurements of the ground resistance by eliminating the effects of harmonic components and stray currents and potentials, the investigations of the ground resistance measurement by using a low pass filter in a model energized grounding system were conducted. The accuracy of ground resistance mesurements was evaluated as a function of the ratio of the test signal to noise (S/N). The errors due to the proposed ground resistance measurement method were decreased with increasing S/N and were less than 5[%] as S/N is 10. The proposed ground resistance measurement method appears to be considerably more accurate than the conventional fall-of -potential method. It is allows cancellation of the parasitic resistance of energized grounding systems, to employ the measurement method that allows cancellation of the parasitic effects due to other circulating ground currents and ground potential rises in practical situations.

• Proceedings of the KSRS Conference
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• v.2
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• pp.831-835
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• 2006

NOAA/AVHRR data were used to analyze sea surface temperatures (SSTs) and thermal fronts (TFs) in the Korean seas. Temporal and spatial analyses were based on data from 1993 to 2000. Harmonic analysis revealed mean SST distributions of $10{\sim}25^{\circ}C$. Annual amplitudes and phases were $4{\sim}11^{\circ}C$ and $210{\sim}240^{\circ}$, respectively. Inverse distributions of annual amplitudes and phases were found for the study seas, with the exception of the East China Sea, which is affected by the Kuroshio Current. Areas with high amplitudes (large variations in SSTs) showed 'low phases' (early maximum SST); areas with low amplitudes (small variations in SSTs) had 'high phases' (late maximum SST). Empirical orthogonal function (EOF) analyses of SSTs revealed a first-mode variance of 97.6%. Annually, greater SST variations occurred closer to the continent. Temporal components of the second mode showed higher values in 1993, 1994, and 1995. These phenomena seemed to the effect of El $Ni{\tilde{n}}o$. The Sobel edge detection method (SEDM) delineated four fronts: the Subpolar Front (SPF) separating the northern and southern parts of the East Sea; the Kuroshio Front (KF) in the East China Sea, the South Sea Coastal Front (SSCF) in the South Sea, and a tidal front (TDF) in the West Sea. Thermal fronts generally occurred over steep bathymetric slopes. Annual amplitudes and phases were bounded within these frontal areas. EOF analysis of SST gradient values revealed the temporal and spatial variations in the TFs. The SPF and SSCF were most intense in March and October; the KF was most significant in March and May.