• 대한수학회보
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• 제47권1호
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• pp.187-193
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• 2010

In this paper, the moments of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs(RNT) distribution over a general interval [a, b] $\subset$ [0, 1], are found through the moments of the RNT distribution over the unit interval, [0, 1]. This is done using some special features of the distribution and the fact that [0, 1] is a self-similar set in a dynamical system generated by the RNT distribution. The results are important for the study of the orthogonal polynomials with respect to the RNT distribution over a general interval.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권4호
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• pp.263-279
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• 2022

This paper presents an automatic inspection of defects in semiconductor images. We devise a statistical method to find defects on homogeneous background from the observation that it has a log-normal distribution. If computer aided design (CAD) data is available, we use it to construct a signed distance function (SDF) and change the pixel values so that the average of pixel values along the level curve of the SDF is zero, so that the image has a homogeneous background. In the absence of CAD data, we devise a hybrid method consisting of a model-based algorithm and two neural networks. The model-based algorithm uses the first right singular vector to determine whether the image has a linear or complex structure. For an image with a linear structure, we remove the structure using the rank 1 approximation so that it has a homogeneous background. An image with a complex structure is inspected by two neural networks. We provide results of numerical experiments for the proposed methods.

• 해양환경안전학회지
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• 제1권2호
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• pp.61-67
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• 1995

This study examines experimentally and theoretically, the wave deformation by two large cylindrical structure in relation to the case of one structure. The wave height around the structures varies, according to the changes of the incident wave angles, the number of the structure, and the distances between the two structures. The wave deformation around the large cylindrical structures is shown to be well predicted theoretically by the diffraction theory based on the singular point distribution method using a vertical line wave source Green's function.

• 충청수학회지
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• 제24권2호
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• pp.247-252
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• 2011

We study some properties of the Riemann-Stieltjes integrals with respect to the Riesz-$N\acute{a}gy$-$Tak\acute{a}cs$ distribution $H_{a,p}$ and its inverse $H_{p,a}$ on the unit interval satisfying the equation 1 - a = $a^2$ and p = 1 - a. Using the properties of the dual distributions $H_{a,p}$ and $H_{p,a}$, we compare the Riemann-Stieltjes integrals of $H_{a,p}$ over some essential intervals with that of its inverse $H_{p,a}$ over the related intervals.

• 천문학회지
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• 제29권2호
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• pp.119-136
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• 1996

To examine the effect of neighboring galaxies on the gravitational lensing statistics, we performed numerical simulations of lensing by many galaxies. The models consist of a galaxy in the rich cluster like Coma, or a galaxy surrounded by field galaxies in $\Omega_0 = 1$ universe with $\Omega_{gal} = 0.1,\;\Omega_{gal} = 0.3\;or\;\Omega_{gal}=1.0\;,\;where\;\Omega_{gal}$ is the total mass in galaxies. Field galaxies either have the same mass or follow Schechter luminosity function and luminosity-velocity relation. Each lensing galaxy is assumed to be singular isothermal sphere (SIS) with finite cutoff radius. In most simulations, the lensing is mainly due to the single galaxy. But in $\Omega_{gal} = 3$ universe, one out of five simulations have 'collective lensing' event in which more than two galaxies collectively produce multiple images. These cases cannot be incorporated into the simple 'standard' lensing statistics calculations. In cases where 'collective lensing' does not occur, distribution of image separation changes from delta function to bimodal distribution due to shear induced by the surrounding galaxies. The amount of spread in the distribution is from a few $\%\;up\;to\;50\%$ of the mean image separation in case when the galaxy is in the Coma-like cluster or when the galaxy is in the field with $\Omega_{gal} = 0.1\;or\;\Omega_{gal}=0.3.$ The mean of the image separation changes less than $5\%$ compared with a single lens case. Cross section for multiple image lensing turns out to be relatively insensitive to the presence of the neighboring galaxies, changing less than $5\%$ for Coma-like cluster and $\Omega_{gal}=0.1,\;0.3$ universe cases. So we conclude that Coma-like cluster or field galaxies whose total mass density $\Omega_{gal}<0.3$ do not significantly affect the probability of multiple image lensing if we exclude the 'collective lensing' cases. However, the distribution of the image separations can be significantly affected especially if the 'collective lensing' cases are included. Therefore, the effects of surrounding galaxies may not be negligible when statistics of lensing is used to deduce the cosmological informations.

• 대한기계학회논문집A
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• 제20권4호
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• pp.1177-1185
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• 1996

The crack growth under creep condition is one of the major damage mechanisms which determines remaining life of the component operating at high temperatures. In this paper, the creep crack growth by grain boundary cavitation is studied, which is frequently observed failure mechanism for creep brittle materials. As a result of diffusive growth of creep cavities, it is shown that the crack-tip stress field is modified from the original stress distribution by the amount of singularity attenuation parameter which is function of crack growth rate and material properties. Also, the stress relaxation at crack-tip results in the extension of cavitating area by the load dump effect to meet the macroscopic force equilibrium conditdion.

• Smart Structures and Systems
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• 제4권5호
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• pp.629-640
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• 2008

A new algorithm is proposed to determine optimal accelerometer locations (OAL) when a structure is identified by frequency domain system identification (SI) method. As a result, a guideline is presented for selecting OAL which can reflect modal response of a structure properly. The guideline is to provide a minimum number of necessary accelerometers with the variation in the number of measurable target modes. To determine OAL for SI applications effectively, the modal sensitivity effective independence distribution vector (MS-EIDV) is developed with the likelihood function of measurements. By maximizing the likelihood of the occurrence of the measurements relative to the predictions, Fisher Information Matrix (FIM) is derived as a function of mode shape sensitivity. This paper also proposes a statistical approach in determining the structural parameters with a presumed parameter error which reflects the epistemic paradox between the determination of OAL and the application of a SI scheme. Numerical simulations have been carried out to examine the proposed OAL algorithm. A two-span multi-girder bridge and a two-span truss bridge were used for the simulation studies. To overcome a rank deficiency frequently occurred in inverting a FIM, the singular value decomposition scheme has been applied.

• 한국통신학회논문지
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• 제42권3호
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• pp.604-611
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• 2017

무선 센서 네트워크에서 센서 노드는 제한된 전력을 사용하기 때문에 에너지 사용을 효율적으로 하는 것이 중요하다. 본 논문에서는 에너지사용효율을 높이기 위해 일정지역에서 측정되는 센서 값으로 이루어진 행렬이 low rank일 때 Matrix Completion을 이용하여 패킷 생성량을 줄이고, 센서가 측정값에 대응시킨 time slot으로 센서 ID 전송을 시도할 때 확률밀도함수로 예측한 전송 성공 확률에 따라 전송을 결정하여 overhead와 충돌을 줄이는 방법을 제안한다. 전산 모의실험을 통해 CSMA/CA와 비교하여 제안된 방법이 전송 실패 수가 17% 감소하고 패킷 생성량은 73%로 감소함을 보였다. 또한 CSMA/CA에 비해 시간 지연이 22%로 감소하고 fusion center에서 Singular Value Thresholding(SVT)로 센서 값을 복원한 경우 MSE error가 CSMA/CA에 비해 86%로 낮음을 보였다.

• 대기
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• 제20권4호
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• pp.495-503
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• 2010

Satellite data have an intrinsic problem due to a number of various physical parameters, which can have a similar effect on measured radiance. Most evaluations of satellite performance have relied on comparisons with limited spatial and temporal resolution of ground-based measurements such as soundings and in-situ measurements. In order to overcome this problem, a new way of satellite data evaluation is suggested with statistical tools such as empirical orthogonal function(EOF), and singular value decomposition(SVD). The EOF analyses with OMI and OMI HCHO over northeast Asia show that the spatial pattern show high correlation with population density. This suggests that human activity is a major source of as well as HCHO over this region. However, this analysis is contradictory to the previous finding with GOME HCHO that biogenic activity is the main driving mechanism(Fu et al., 2007). To verify the source of HCHO over this region, we performed the EOF analyses with vegetation and HCHO distribution. The results showed no coherence in the spatial and temporal pattern between two factors. Rather, the additional SVD analysis between $NO_2$ and HCHO shows consistency in spatial and temporal coherence. This outcome suggests that the anthropogenic emission is the main source of HCHO over the region. We speculate that the previous study appears to be due to low temporal and spatial resolution of GOME measurements or uncertainty in model input data.

• 천문학회지
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• 제27권2호
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• pp.103-117
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• 1994

To extend the work of Gott, Park, and Lee (1989), statistical properties of gravitational lensing in a wide variety of cosmological models involving non-zero cosmological constant is investigated, using the redshifts of both lens and source and observed angular separation of images for gravitational lens systems. We assume singular isothermal sphere as lensing galaxy in homogenous and isotropic Friedmann­Lemaitre-Robertson- Walker universe, Schechter luminosity function, standard angular diameter distance formula and other galaxy parameters used in Fukugita and Turner (1991). To find the most adequate flat cosmological model and put a limit on the value of dimensionless cosmological constant $\lambda_0$, the mean value of the angular separation of images, probability distribution of angular separation and cumulative probability are calculated for given source and lens redshifts and compared with the observed values through several statistical methods. When there is no angular selection effect, models with highest value of $\lambda_0$ is preferred generally. When the angular selection effects are considered, the preferred model depends on the shape of the selection functions and statistical methods; yet, models with large $\lambda_0$ are preferred in general. However, the present data can not rule out any of the flat universe models with enough confidence. This approach can potentially select out best model. But at the moment, we need more data.