• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.967-973
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• 2017

We prove that a homogeneous square Einstein Finsler metric is either Riemannian or flat.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.7
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• pp.350-353
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• 2001

In general, the Least Square Error method is used for signal classification to measure distance in the $l^2$ metric or the $L^2$ metric space. A defect of the Least Square Error method is that it does not classify properly some waveforms, which is due to the property of the Least Square Error method: the global analysis. This paper proposes a new linear operator, the Integra-Normalizer, that removes the problem. The Integra-Normalizer possesses excellent property that measures the degree of relative similarity between signals by expanding the functional space with removing the restriction on the functional space inherited by the Least Square Error method. The Integra-Normalizer shows superiority to the Least Square Error method in measuring the relative similarity among one dimensional waveforms.

• Journal of the Korea Computer Graphics Society
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• v.4 no.1
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• pp.41-46
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• 1998

An image processing techniques for image compression and its reconstruction are to be considered seriously for the generated huge size data as in the present multimedia environment based on the graphics. So far some approaches for this matter are proposed such as a Wavelet and JPEG method and got desirable result. In this paper, we have studied for the rms(root mean square) metric which is more effective than the existing sup(supremum)metric, and compared with sup metric by means of mathematical verification.

• Proceedings of the Korea Water Resources Association Conference
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• 2019.05a
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• pp.103-103
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• 2019

본 연구에서는 Terra MODIS 위성영상과 Mapping Evapotranspiration at high Resolution with Internalized Calibration (METRIC) 모형을 이용하여 2012년부터 2017년까지 한반도 전국의 증발산량을 산정하고 플럭스 타워 실측 증발산량과 비교하였다. METRIC은 전 세계에 널리 적용된 바 있는 에너지 수지 기반의 Surface Energy Balance Algorithm for Land (SEBAL) 모형의 개념과 기술을 기반으로 현열(Sensible Heat Flux) 추정 모듈을 개선한 모형이다. 본 연구에서 METRIC 모형은 기존 C#으로 개발되어 있던 SEBAL 코드에서 현열 추정 모듈을 수정하였고 연산 속도 개선을 위해 Python으로 재작성하였다. METRIC 모형의 위성 자료로 Terra MODIS 위성의 MOD13A2(16day, 1km) NDVI, MOD11A1(Daily, 1km) Land Surface Temperature (LST) 및 MCD43A3(Daily, 500m) Albedo를 구축하였으며 500m 공간해상도의 Albedo는 1000m 해상도로 resample하여 활용하였다. 기상자료는 기상청 기상관측소의 풍속, 풍속측정높이, 습도, 10분 간격 이슬점 온도, 일사량 자료를 위성 자료와 같은 공간해상도로 내삽(Interpolation)하여 구축하였다. 모형결과 검증을 위해 국내 플럭스 타워 (설마천, 청미천, 덕유산) 증발산량 관측 자료와의 결정계수(Coefficient of determination, $R^2$), RMSE(Root mean square error) relative RMSE (RMSE%), Nash-Sutcliffe efficiency (NSE) 및 IOA(Index of Agreement)를 산정하고, 기존 SEBAL 모형 결과와의 비교를 통해 본 모형의 개선점을 보이고자 한다.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.249-252
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• 2001

TCM(Trellis Coded Modulation) has soft decision scheme so that BM(Branch Metric) calculates the ED(Euclidean Distance) between the received signal and each code words in signal space. For computing the ED, square and square root computations increase the hardware complexity. Some simplified method is known for convolutional codes with QPSK(Quadrature Phase Shift Keying), PSK(Phase Shift Keying) modulation. But it is not acceptable for QAM (Quadrature Amplitude Modulation)-TCM scheme. In this paper, we suggest that two modified BM computation methods, which is applicable for QAM-TCM. By comparative study, we also assessed two proposed method in the case of hardware complexity and BER (Bit Error Rate) performance.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1293-1307
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• 2017

General (${\alpha},{\beta}$)-metrics form a rich class of Finsler metrics. They include many important Finsler metrics, such as Randers metrics, square metrics and spherically symmetric metrics. In this paper, we find equations which are necessary and sufficient conditions for such Finsler metric to be locally projectively flat. By solving these equations, we obtain all of locally projectively flat general (${\alpha},{\beta}$)-metrics under certain condition. Finally, we manufacture explicitly new locally projectively flat Finsler metrics.

• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.309-322
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• 2024

Identifying algae in water is important for managing algal blooms which have great impact on drinking water supply systems. There have been various microscopic approaches developed for algae classification. Many of them are based on the morphological features of algae. However, there have seldom been mathematical frameworks for comparing the shape of algae, represented as a planar continuous curve obtained from an image. In this work, we describe a recent framework for computing shape distance between two different algae based on the elastic metric and a novel functional representation called the square root velocity function (SRVF). We further introduce statistical procedures for multiple shapes of algae including computing the sample mean, the sample covariance, and performing the principal component analysis (PCA). Based on the shape distance, we classify six algal species in watersheds experiencing algal blooms, including three cyanobacteria (Microcystis, Oscillatoria, and Anabaena), two diatoms (Fragilaria and Synedra), and one green algae (Pediastrum). We provide and compare the classification performance of various distance-based and model-based methods. We additionally compare elastic shape distance to non-elastic distance using the nearest neighbor classifiers.

• Journal of Communications and Networks
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• v.11 no.1
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• pp.42-46
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• 2009

Superimposed training (SIT) design for estimating of time-varying multipath channels is investigated for mobile orthogonal frequency division multiplexing (OFDM) systems. The design of optimum SIT consists of two parts: The optimal SIT sequence is derived by minimizing the channel estimates' mean square error (MSE); the optimal power allocation between training and information data is developed by maximizing the averaged signal to interference plus noise ratio (SINR) under the condition of equal powered paths. The theoretical analysis is verified by simulations. For the metric of the averaged SINR against signal to noise ratio (SNR), the theoretical result matches the simulation result perfectly. In contrast to an interpolated frequency-multiplexing training (FMT) scheme or an SIT scheme with random pilot sequence, the SIT scheme with proposed optimal sequence achieves higher SINR. The analytical solution of the optimal power allocation is demonstrated by the simulation as well.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.10B
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• pp.1732-1743
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• 2000

In this paper a fixed-delay trellis search with decision feedback (FDTrS/DF) for high-density DVD systems (4.7-15GB) is proposed and implemented with FPGA. The proposed FDTrS/DF is derived by transforming the binary tree search structure into trellis search structure implying that FDTrS/DF performs better than the singnal detection techniques based on tree search structure such as FDTS/DF and SSD/DF. Advantages of FDTrS/DF are significant reductions in hardware complexity due to the unique structure of FDTrS composed of only one trellis stage requiring no traceback procedure usually implemented in the Viterbi detector. Also in this paper the PDFS/DF and SSD/DF orginally proposed for high-density magnetic recording systems are modified for the DVD system and compared with the proposed FDTrS/DF. In order to increase speed in the FPGA implementation the pipelining technique and absolute branch metric (instead of square branch metric) are applied. The proposed FDTrS/DF is shown to provide the best performance among various signal detection techniques such as PRML, DFE, FDTS/DF and SSD/DF even with a small hardware complexity.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.30 no.2
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• pp.173-180
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• 2012

The most recent, 80 mega pixels digital camera appeared through the development of digital technology, and nonmetric digital cameras have been using in various field of photogrammetry. In this study, we experimented lens calibration using aerial photographs and ground control points. The aerial photographs were taken a non-metric digital camera which is CMOS(Complementary Metal Oxide Semiconductor) 21.1 mega pixels sensor and 35mm lens at a helicopter. And the ground control points were selected on the 1:1,000 plotting origin data. As a result, we calculated focal length, PPA(Principal Point of Autocollimation) and symmetric radial distortion coefficients from the lens. Also, RMSE(root mean square error) and maximum residual of the ground control points from the aerial triangulation were compared before and after calibration. And we found that the accuracy of the after calibration was improved very significantly.