• Kyungpook Mathematical Journal
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• 제57권4호
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• pp.581-600
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• 2017

A classical result of A. Cohn states that, if we express a prime p in base 10 as $$p=a_n10^n+a_{n-1}10^{n-1}+{\cdots}+a_110+a_0$$, then the polynomial $f(x)=a_nx^n+a_{n-1}x^{n-1}+{\cdots}+a_1x+a_0$ is irreducible in ${\mathbb{Z}}[x]$. This problem was subsequently generalized to any base b by Brillhart, Filaseta, and Odlyzko. We establish this result of A. Cohn in $O_K[x]$, K an imaginary quadratic field such that its ring of integers, $O_K$, is a Euclidean domain. For a Gaussian integer ${\beta}$ with ${\mid}{\beta}{\mid}$ > $1+{\sqrt{2}}/2$, we give another representation for any Gaussian integer using a complete residue system modulo ${\beta}$, and then establish an irreducibility criterion in ${\mathbb{Z}}[i][x]$ by applying this result.

• 한국대기환경학회지
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• 제15권6호
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• pp.757-765
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• 1999

Lagrangian particle dispersion model(LPDM) is an effective tool to calculate the dispersion from a point source since it dose not induce numerical diffusion errors in solving the pollutant dispersion equation. Fictitious particles are released to the atmosphere from the emission source and they are then transported by the mean velocity and diffused by the turbulent eddy motion in the LPDM. The concentration distribution from the dispersed particles in the calculation domain are finally estimated by applying a particle count method or a Gaussian kernel method. The two methods for calculating concentration profiles were compared each other and tested against the analytic solution and the tracer experiment to find the strength and weakness of each method and to choose computationally time saving method for the LPDM. The calculated concentrations from the particle count method was heavily dependent on the number of the particles released at the emission source. It requires lots fo particle emission to reach the converged concentration field. And resulting concentrations were also dependent on the size of numerical grid. The concentration field by the Gaussian kernel method, however, converged with a low particle emission rate at the source and was in good agreement with the analytic solution and the tracer experiment. The results showed that Gaussian kernel method was more effective method to calculate the concentrations in the LPDM.

• Geomechanics and Engineering
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• 제28권4호
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• pp.359-374
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• 2022

Geology conditions are crucial in decision-making during the planning and design phase of a tunnel project. Estimation of the geology conditions of road tunnels is subject to significant uncertainties. In this work, the effectiveness of a novel regression method in estimating geological or geotechnical parameters of road tunnel projects was explored. This method, called Gaussian process regression (GPR), formulates the learning of the regressor within a Bayesian framework. The GPR model was trained with data of old tunnel projects. To verify its feasibility, the GPR technique was applied to a road tunnel to predict the state of three geological/geomechanical parameters of Rock Mass Rating (RMR), Rock Structure Rating (RSR) and Q-value. Finally, in order to validate the GPR approach, the forecasted results were compared to the field-observed results. From this comparison, it was concluded that, the GPR is presented very good predictions. The R-squared values between the predicted results of the GPR vs. field-observed results for the RMR, RSR and Q-value were obtained equal to 0.8581, 0.8148 and 0.8788, respectively.

• Journal of the Korean Statistical Society
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• 제36권4호
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• pp.479-488
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• 2007

The elliptic random field is an extension to the Gaussian random field. We proved a theorem which characterizes the elliptic random field. We proposed a heuristic approach to derive an approximation to the distribution of the size of one connected component of its excursion set above a high threshold. We used this approximation to approximate the distribution of the largest cluster size. We used simulation to compare the approximation with the exact distribution.

• Wind and Structures
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• 제26권1호
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• pp.11-24
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• 2018

Full-scale measurements of wind action on the open roof structure of the WuXi grand theater, which is composed of eight large-span free-form leaf-shaped space trusses with the largest span of 76.79 m, were conducted during the passage of Typhoons HaiKui and SuLi. The wind pressure field data were continuously and simultaneously monitored using a wind pressure monitoring system installed on the roof structure during the typhoons. A detailed analysis of the field data was performed to investigate the characteristics of the fluctuating wind pressure on the open roof, such as the wind pressure spectrum, spatial correlation coefficients, peak wind pressures and non-Gaussian wind pressure characteristics, under typhoon conditions. Three classical methods were used to calculate the peak factors of the wind pressure on the open roof, and the suggested design method and peak factors were given. The non-Gaussianity of the wind pressure was discussed in terms of the third and fourth statistical moments of the measured wind pressure, and the corresponding indication of the non-Gaussianity on the open roof was proposed. The result shows that there were large pulses in the time-histories of the measured wind pressure on Roof A2 in the field. The spatial correlation of the wind pressures on roof A2 between the upper surface and lower surface is very weak. When the skewness is larger than 0.3 and the kurtosis is larger than 3.7, the wind pressure time series on roof A2 can be taken as a non-Gaussian distribution, and the other series can be taken as a Gaussian distribution.

• 스마트미디어저널
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• 제4권4호
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• pp.18-23
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• 2015

본 논문에서는 텐서보팅을 이용하여 기존 마르코프 랜덤 필드 메소드 안의 가우시안 혼합 모델 함수의 성능을 향상시킬 수 있는 적합한 클러스터 개수 검출 방법을 제시한다. 제안하는 방법의 핵심 포인트는 텐서보팅의 인풋 데이터 토큰의 연속성인 saliency map을 통한 중심점 개수의 추출이다. 우리는 가장 먼저 주어진 자연 영상에서 전경 및 배경 후보 영역을 분리한다. 다음으로, 분리된 각 후보 영역에 대하여 텐서보팅을 적용하여 적절한 클러스터 개수를 추출한다. 우리는 검출된 클러스터 개수를 이용하여 정확한 가우시안 혼합 모델 모델링을 수행할 수 있다. 그리고 이를 적용한 마르코프 랜덤 필드의 unary term과 pairwise term을 계산하여 자연 영상의 텍스트 이진화 결과를 반환한다. 실험 결과, 제안된 방법이 최적의 클러스터 개수를 반환하고, 향상된 텍스트 이진화 결과를 반환함을 확인하였다.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2006년 창립20주년기념 정기학술대회 및 국제워크샵
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• pp.127-134
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• 2006

Based on a weakly non-Gaussian theory the occurrence probability of freak waves is formulated in terms of the number of waves in a time series and the surface elevation kurtosis. Finite kurtosis gives rise to a significant enhancement of freak wave generation in comparison with the linear narrow banded wave theory. For fixed number of waves, the estimated amplification ratio of freak wave occurrence due to the deviation from the Gaussian theory is 50% - 300%. The results of the theory are compared with laboratory and field data.

• Journal of the Optical Society of Korea
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• 제1권1호
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• pp.23-25
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• 1997

In this paper we will show theoretically that a refractive index grating exhibits a retro-self-focusing effect and an accompanying pinholing effect under the Gaussian intensity distribution of an incident optical field. Those effects result from an effective wave number change of the medium due to the intense optical field.

• 대한수학회지
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• 제50권4호
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• pp.899-916
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• 2013

We develop a version of dipolar conformal field theory in a simply connected domain with the Dirichlet-Neumann boundary condition and central charge one. We prove that all correlation functions of the fields in the OPE family of Gaussian free field with a certain boundary value are martingale-observables for dipolar SLE(4).

• 한국전자통신학회논문지
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• 제4권3호
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• pp.197-203
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• 2009

부호이론이나 암호학의 응용분야에 유한체는 매우 중요한 내용이고, 컴퓨터에서의 구현시에는 종규기저를 사용하는 것이 효과적이다. 본 논문에서는 유한체 타입 I 최적정규기저를 가지는 $GF(2^{mk})$는 $GF(2^m)$의 확대체가 된다는 사실을 이용하여 지금까지 알려진 가장 효율적인 Reyhani-Masoleh and Hasan의 곱셈기보다 25%정도 빠른 곱셈기를 소개하려고 한다.