• Wind and Structures
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• v.23 no.4
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• pp.367-383
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• 2016

The influence mechanism of mean value components, noted as $P_0$, on POD applications for complete random fields $P_C(t)$ and fluctuating random fields $P_F(t)$ are illustrated mathematically. The critical philosophy of the illustration is introduction of a new matrix, defined as the correlation function matrix of $P_0$, which connect the correlation function matrix of $P_C(t)$ and $P_F(t)$, and their POD results. Then, POD analyses for several different wind pressure fields were presented comparatively as validation. It's inevitable mathematically that the first eigenmode of $P_C(t)$ resembles the distribution of $P_0$ and the first eigenvalue of $P_C(t)$ is close to the energy of $P_0$, due to similarity of the correlation function matrixs of $P_C(t)$ and $P_0$. However, the viewpoint is not rigorous mathematically that the first mode represents the mean pressure and the following modes represent the fluctuating pressure when $P_C(t)$ are employed in POD application. When $P_C(t)$ are employed, POD results of all modes would be distorted by the mean value components, and it's impossible to identify $P_0$ and $P_F(t)$ separately. Consequently, characteristics of the fluctuating component, which is always the primary concern in wind pressure field analysis, can only be precisely identified with $P_0$ excluded in POD.

• Bulletin of the Korean Chemical Society
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• v.31 no.11
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• pp.3139-3144
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• 2010

A model system has been established for the evaluation of the uncertainty of the value from measurements of multiple subsamples by isotope dilution mass spectrometry (IDMS). In this report, we apply this model system for the evaluation of measurement uncertainty in determination of folic acid in infant formula. Five subsamples were analyzed by IDMS. The mean of the measurement results of the five subsamples was assigned as the final measurement value. The standard deviation (s) of the results from five subsamples was attributable to repeatability of the measurement. The uncertainty components in the IDMS measurement methods were categorized into two groups. Group I includes uncertainty components which give common systematic effects to all subsamples and do not contribute to the variation among multiple measurements (repeatability). Group II includes uncertainty components that give random effects on the measurement results, and are related with the measurement repeatability. These random effects are attributed to s. Therefore, the uncertainty of the final value was calculated by combining the standard deviation of the mean of multiple measurements, $s/{\surd}n$ (where n = 5), and the measurement uncertainty associated with the uncertainty components that give systematic effects.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.1
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• pp.109-116
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• 1991

In recent years, hydrologists have been interested in the radial spectrum and its estimation in two dimensional storm field to construct simulation model of the rainfall. This paper deals with the problem of transformation from the spectrum or isotropic covariance function to two dimensional random field. The extended turning band method for the generation of random field is applied to the problem using the line generation method of one dimensional stochastic process by G.Matheron. Examples of this generation is chosen in the random components of the multidimensional rainfall model suggested by Bras and are given with a comparison between theoretical and sample statistics. In this numerical experiments it is observed that first and second order statistics can be conserved. Also the example of moving storm simulation through Bras model is presented with the appropriate parameters and sample size.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.224-227
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• 2007

This paper introduces the results of acoustic loads test conducted on the upper stage assembly of KSLV-I, which is the first Korea space launch vehicle. A launch vehicle and its payloads are subjected to severe acoustic pressure loading when they lift off and ascent during the transonic periods. Acoustic loadings are spreaded out broad frequncy-spectrum up to 10,000Hz. Acoustic loads are a primary source of structural random vibration of the upper stage and payloads. Therefore, in order to verify the structural integrity of the upper stage assembly of KSLV-I and the survivability of its components under severe random vibration environment, acoustic loads test is conducted in the high intensity acoustic chamber with 142dB (overall SPL). The results show the structural design and component random vibration specifications well meet with the environmental requirements.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.434-437
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• 2003

Evaluation or the patterning accuracy of e-beam lithography machines requires a high precision inspection system that is capable of measuring the true xy-locations of fiducial marks generated by the e-beam machine under test. Fiducial marks are fabricated on a single photo mask over the entire working area in the form of equally spaced two-dimensional grids. In performing the evaluation, the principles of self-calibration enable to determine the deviations of fiducial marks from their nominal xy-locations precisely, not being affected by the motion errors of the inspection system itself. It is. however, the fact that only repeatable motion errors can be eliminated, while random motion errors encountered in probing the locations of fiducial marks are not removed. Even worse, a random error occurring from the measurement of a single mark propagates and affects in determining locations of other marks, which phenomenon in fact limits the ultimate calibration accuracy of e-beam machines. In this paper, we describe an uncertainty analysis that has been made to investigate how random errors affect the final result of self-calibration of e-beam machines when one uses an optical inspection system equipped with high-resolution microscope objectives and a precision xy-stages. The guide of uncertainty analysis recommended by the International Organization for Standardization is faithfully followed along with necessary sensitivity analysis. The uncertainty analysis reveals that among the dominant components of the patterning accuracy of e-beam lithography, the rotationally symmetrical component is most significantly affected by random errors, whose propagation becomes more severe in a cascading manner as the number of fiducial marks increases

• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.305-315
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• 2010

In this paper, a frequentistic approach to impute the values of R, G, B-components in random missing pixels of color image is provided. Under assumption that the given image is a realization of Gaussian Markov random field, its model is designed such that each neighbor pixel values for a given pixel follows (independently) the normal distribution with covariance matrix scaled by an evaluates of the similarity between two pixel values, so that the imputation is not to be affected by the neighbors with different color. An approximate EM-based algorithm maximizing the underlying likelihood is implemented to estimate the parameters and to impute the missing pixel values. Some experiments are presented to show its effectiveness through performance comparison with a popular interpolation method.

• Journal of the Korean Statistical Society
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• v.10
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• pp.91-96
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• 1981

The development of Minimum Norm Quadratic Unbiased Estimation (MINQUE) has introduced a unified approach for the estimation of variance components in general linear models. The computational problem has been studied by Liu and Senturia (1977) and Goodnight (1978, setting a-priori values to 0). This paper further simplifies the computation and gives efficient and compact computational algorithm for the MINQUE and dispersion matrix in general linear random model.

• Journal of the Korean Data and Information Science Society
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• v.4
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• pp.121-130
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• 1993

For the One-way random effects model with unbalanced data, the AOV and MINQUE estimates of variance components are frequently found to be negative. The primary objective of present study is placed on the computation of the probability of the main effect variance component, being negative. The probability of negative estimators from AOV and MINQUE can be obtained by theoretical computation under the normality assumption. It is, however, difficult to compute the probability of negative estimates for these estimators under arbitrary distributions, and hence their probabilities of being negative were computed by simulation experiment in this study. It was shown that there was no significant difference between the theoretical probability under normality and calculated probability by simulation experiment, and that probability of negative estimates decreases as sample size, number of levels and the value of increase.

• Water for future
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• v.22 no.2
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• pp.201-211
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• 1989

Using the storm data which was augmented by the stochastic correlation with it's neighbors, the multiquadric equation of random surface of total storm depth is constructed. And to separate the local components from it's regionals and find the regional characteristics, a double Fourier analysis was applied to the total depths of storm data. The local components, storm residuals of each storm was assumed to be homogeneous random field and investigated with it's autocorrelation function. For the practical application, isotropic was assumed and that was identified with emprical data. Coefficients of normalized autocorrelation for all storms showed similar apperance. Using this emprical result, an example of the radial spectral distribution function which represints the spatial characteristics of rainfall over Han River Basin during 1975-1983 is presented.