• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.467-479
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• 2009

This paper ultimately aims to develop noninvasive techniques to identify the inside of a given electrical network. Based on the theory of the partial differentiation equations and mathematical modeling, this paper devises the algorithms to find the locations of possible abnormalities. To ensure the certainty of the algorithms, this study restricted the forms of the network and the number of abnormalities, rendering it easy to prove the uniqueness of the position of the abnormalities.

• ETRI Journal
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• v.33 no.5
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• pp.814-817
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• 2011

In this letter, the distributions of direct current (DC) coefficients for P-frames in H.264/AVC are analyzed, and the distortion model of the Gaussian source under the quantization of the dead-zone plus-uniform threshold quantization with uniform reconstruction quantizer is derived. Experimental results show that the DC coefficients of P-frames are best approximated by the Laplacian distribution and the Gaussian distribution at small quantization step sizes and at large quantization step sizes, respectively.

• The Journal of the Acoustical Society of Korea
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• v.30 no.6
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• pp.308-314
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• 2011

This paper presents techniques for estimating directions of multiple sound sources ranging from $0^{\circ}$ to $360^{\circ}$ using circular probability distributions having a periodic property. Phase differences containing direction information of sources can be modeled as mixtures of multiple probability distributions and source directions can be estimated by maximizing log-likelihood functions. Although the von Mises distribution is widely used for analyzing this kind of periodic data, we define a new class of circular probability distributions from Gaussian and Laplacian distributions by adopting a modulo operation to have $2{\pi}$-periodicity. Direction estimation with these circular probability distributions is done by implementing corresponding EM (Expectation-Maximization) algorithms. Simulation results in various reverberant environments confirm that Laplacian distribution provides better performance than von Mises and Gaussian distributions.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.1
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• pp.263-267
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• 2011

This paper analyzed randomness characteristics of output data in generator based on hardware noise source. Also it is enhanced security randomness in the output stream of generator, which is applied on Laplacian filter. First it reviews criteria of randomness verification of output stream of hardware noise generator, and presents the enhanced results of output stream of generator, which is applied on Laplacian filter.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.541-551
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• 1995

The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2188-2191
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• 2003

이 논문에서는 라플라스 밀도함수에 대한 최적 홑양자기 지지역은 양자점의 개수와 로그선형 관계가 있음을 증명한다. 그리고, 극상한값을 유도하여 최적 지지역의 로그선형 증가가 어떤 상수값을 초과하지 않음을 증명한다. 이 결과들로부터, 학계에 경험적으로 알려져 왔던 최적 지지역의 로그선형 증가를 증명한다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.5C
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• pp.413-421
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• 2008

The paper derives asymptotic formulas for the MSE distortion and the signal-to-noise ratio of a mismatched fixed-rate minimum MSE Laplacian quantizer. These closed-form formulas are expressed in terms of the number N of quantization points, the mean displacement $\mu$, and the ratio $\rho$ of the standard deviation of the source to that for which the quantizer is optimally designed. Numerical results show that the principal formula is accurate in that, for rate R=$log_2N{\geq}6$, it predicts signal-to-noise ratios within 1% of the true values for a wide range of $\mu$, and $\rho$. The new findings herein include the fact that, for heavy variance mismatch of ${\rho}>3/2$, the signal-to-noise ratio increases at the rate of $9/\rho$ dB/bit, which is slower than the usual 6 dB/bit, and the fact that an optimal uniform quantizer, though optimally designed, is slightly more than critically mismatched to the source. It is also found that signal-to-noise ratio loss due to $\mu$ is moderate. The derived formulas can be useful in quantization of speech or music signals, which are modeled well as Laplacian sources and have changing short-term variances.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.10A
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• pp.1566-1575
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• 2000

This paper studies mismatched scalar quantization of a generalized gamma source by a quantizer that is optimally (in the mean square error sense) designed for another generalized gamma source. Specifically, it considers variance-mismatched quantization which occurs when the variance of the source to be quantized differs from tat of the designed-for source. The main result is the two distortion formulas derived from Bennett's integral. The first formula is an approximation expression that uses the outermost threshold of an optimum scalar quantizer, and the second formula, in turn, uses an approximation formula for this outermost threshold. Numerical results are obtained for Laplacian sources, which are example of a generalized gamma source, and comparisons are made between actual mismatched distortions and the two formulas. These numerical results show that the two formulas become more accurate, as the number of quantization points gets larger and the ratio of the source variance to that of the designed-for source gets bigger. For example, the formulas are within 2~4% of the actual distortion for approximately 64 quantization points or more. In conclusion, the proposed approximation formulas are considered to have contribution as closed formulas and for their accuracy.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2008.11a
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• pp.81-84
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• 2008

최근 센서네트워크와 같은 에너지 제한 환경을 위한 경량화 부호화 기술의 필요성이 대두됨에 따라 분산 소스 부호화 기술(Distributed Source Coding)의 응용기술로 비디오 부호화 복잡도의 대부분을 차지하는 움직임 예측/보상과정을 부호화기가 아닌 복호화기에서 수행하는 분산 비디오 부호화 기술(Distributed Video Coding)에 대한 연구가 활발히 이루어져 왔다. 이에 가장 대표적인 기술인 Wyner-Ziv 코딩 기술은 채널 코드를 이용하여 원본 프레임과 이에 대한 복호화기의 예측영상인 보조정보 사이의 잡음을 제거하여 영상을 복원한다. 일반적으로 보조정보는 원본영상에 유사한 키 프레임간의 프레임 보간을 통하여 생성되며 채널 코드는 Shannon limit에 근접한 성능을 보이는 Turbo 코드나 LDPC 코드가 사용된다. 이와 같은 채널 코드의 복호화는 채널 잡음 모델에 기반하여 수행되어지며 Wyner-Ziv 코딩 기술에서는 이 채널 잡음 모델을 '상관 잡음 모델' (Correlation Noise Modeling)이라 하고 일반적으로 Laplacian이나 Gaussian으로 모델화 한다. 하지만 복호화기에는 원본 영상에 대한 정보가 없기 때문에 정확한 상관 잡음 모델을 알 수 없으며 잡음 모델에 대한 예측의 부정확성은 잡음 제거를 위한 패리티 비트의 증가를 야기해 부호화 기술의 압축 성능 저하를 가져온다. 이에 본 논문은 원본 프레임과 보조정보 사이의 잡음을 정확하게 예측하여 잡음을 정정할 수 있는 향상된 상관 잡음 모델을 제안한다. 제안 방법은 잘못된 잡음 예측에 의해 Laplacian 계수가 너무 커지는 것을 방지하면서 영상내의 잡음의 유무에 별다른 영향을 받지 않는 새로운 문턱값을 사용한다. 다양한 영상에 대한 제안 방법의 실험 결과는 평균적으로 약 0.35dB에 해당하는 율-왜곡 성능 향상을 보여주었다.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1159-1173
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• 2009

This paper deals with the critical blow-up and extinction exponents for the non-Newton polytropic filtration equation. We reveals a fact that the equation admits two critical exponents $q_1,\;q_2\;{\in}\;(0,+{\infty})$) with $q_1\;{<}\;q_2$. In other words, when q belongs to different intervals (0, $q_1),\;(q_1,\;q_2),\;(q_2,+{\infty}$), the solution possesses complete different properties. More precisely speaking, as far as the blow-up exponent is concerned, the global existence case consists of the interval (0, $q_2$]. However, when q ${\in}\;(q_2,+{\infty}$), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval ($q_1,+{\infty}$), while for q ${\in}\;(0,\;q_1$), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q = $q_1$ is concerned, the other parameter ${\lambda}$ will play an important role. In other words, when $\lambda$ belongs to different interval (0, ${\lambda}_1$) or (${\lambda}_1$,+${\infty}$), where ${\lambda}_1$ is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely different properties.