• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.405-413
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• 1999

By assuming a type-II censoring, we propose the approximate maximum likelihood estimators (AMLEs) of the location and the scale parameters of the two-parameter Rayleigh distribution and calculate the asymptotic variances and covariance of the AMLEs.

• Journal of the Korean Data and Information Science Society
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• v.15 no.1
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• pp.239-250
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• 2004

We shall propose maximum likelihood, Bayesian and generalized maximum likelihood estimation for the reliability of the two-unit hot standby system with Rayleigh lifetime distribution that switch is perfect. Each estimation will be compared numerically in terms of various mission times, parameter values and asymptotic relative efficiency through Monte Carlo simulation.

• Water for future
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• v.10 no.1
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• pp.101-117
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• 1977

The statatistical characteristics and spectra of sea waves at Mookho were analysed by several statistical methods. As the results, the following conclusions are obtained: 1. Values of surface elevation of sea wave are better fitted to Gram Charlier distribution than Gaussian distribution. This proves that sea waves have not only characters of irregularity but also non-linearity. 2. Distribution of maxima of surface elevation practically follows the distribution of Cartwright and Longuet-Higgins, also spectral width parameter is found to be increased with the increase of root mean square of surface elevation. 3. Sea wave may have spectrum of broad frequency band, however distributions of wave heights and periods follow the Rayleigh distribution which is derived from the assumption of narrow frequency band. 4. Ratios among mean wave heights from observed data show good agreements with theoretical values from Rayleigh distribution. 5. Spectral density and spectral width parameter increase with increase of wind velocity. And wave period at optimum band gas higher value than significant wave period by about 10 percent.

• Steel and Composite Structures
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• v.33 no.1
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• pp.133-142
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• 2019

In the present study, microstructure-dependent static stability analysis of inhomogeneous tapered micro-columns is performed. It is considered that the micro column is made of functionally graded materials and has a variable cross-section. The material and geometrical properties of micro column vary continuously throughout the axial direction. Euler-Bernoulli beam and modified couple stress theories are used to model the nonhomogeneous micro column with variable cross section. Rayleigh-Ritz solution method is implemented to obtain the critical buckling loads for various parameters. A detailed parametric study is performed to examine the influences of taper ratio, material gradation, length scale parameter, and boundary conditions. The validity of the present results is demonstrated by comparing them with some related results available in the literature. It can be emphasized that the size-dependency on the critical buckling loads is more prominent for bigger length scale parameter-to-thickness ratio and changes in the material gradation and taper ratio affect significantly the values of critical buckling loads.

• YAKHAK HOEJI
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• v.28 no.5
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• pp.275-282
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• 1984

The interaction between azo dyes and cationic surfactant was studied by absorption spectroscopy and fluorescent Rayleigh scattering. In order to presume the structure of formed micelle, methyl orange and ethyl orange as azo dyes and cetyltrimethylammonium bromide (CTAB) as cationic surfactant were used. Infomations about interaction parameter including absorption maxima, optimal conditions, and intensity of fluorescent Rayleigh scattering were obtained. When azo dyes and CTAB are formed 1 : 1 complex, it showed the strongest intensity of fluorescent Rayleigh scattering. On going from mixed micelle to homomicell, It suggests successively several intermediate steps of complex structure which can be distinguished clearly from one another.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.5
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• pp.606-613
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• 2011

In this paper, patterns of laser scattering and detection of micro defects have been investigated based on Rayleigh criterion for silicon wafer in solar cell. Also, a new laser scattering mechanism is designed using characteristics of light scattering against silicon wafer surfaces. Its parameters are to be optimally selected to obtain effective and featured patterns of laser scattering. The optimal parametric ranges of laser scattering are determined using the mean intensity of laser scattering. Scattering patterns of micro defects are investigated at the extracted parameter region. Among a lot of pattern features, both maximum connected area and number of connected component in patterns of laser scattering are regarded as the important information for detecting micro defects. Their usefulness is verified in the experiment.

• Communications for Statistical Applications and Methods
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• v.25 no.4
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• pp.411-430
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• 2018

The Bayesian approach is a suitable alternative in constructing appropriate models for observed record values because the number of these values is small. This paper provides an objective Bayesian analysis method for upper record values arising from the Rayleigh distribution. For the objective Bayesian analysis, the Fisher information matrix for unknown parameters is derived in terms of the second derivative of the log-likelihood function by using Leibniz's rule; subsequently, objective priors are provided, resulting in proper posterior distributions. We examine if these priors are the PMPs. In a simulation study, inference results under the provided priors are compared through Monte Carlo simulations. Through real data analysis, we reveal a limitation of the appropriate confidence interval based on the maximum likelihood estimator for the scale parameter and evaluate the models under the provided priors.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.5
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• pp.750-756
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• 2002

The effect of equivalence ratio and velocity on the stability of flame in dump combustor was studied in an atmospheric pressure, laboratory scathe dump combustor operating natural gas. Traditionally, peak-to-peak pressure, fluctuation of the heat release rate and Rayleigh index were used to find and control the combustion instability. Cross correlation coefficients, Ci,j which is defined as the normalized value of the integration of the product of two of the mixer pressure, dump plane pressure and heat release rate, are introduced to see whether the flame is stable or not. Ci,j shows more sensitive to combustion status than Rayleigh index in steadily burning flame. Also, the result indicates that the amplitude of Ci,j between heat release and mixer pressure goes up before the flame at the rich de-stabilizing equivalence ratio near $\psi$=0.85. t means Ci:j at this case has a potential to detect the de-stablizing moment in prior to becoming unstable in dump combustor.

• Advances in nano research
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• v.9 no.3
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• pp.157-172
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• 2020

The aim of this present research is the effect of the higher-order terms of the governing equation on the forced longitudinal vibration of a nanorod model and making comparisons of the results with classical nonlocal elasticity theory. For this purpose, the free axial vibration along with forced one under the two various linear and harmonic axial concentrated forces in zigzag Single-Walled Carbon Nanotube (SWCNT) are analyzed dynamically. Three various theories containing the classical theory, which is called Eringen's nonlocal elasticity, along with Rayleigh and Bishop theories (higher-order theories) are established to justify the nonlocal behavior of constitutive relations. The governing equation and the related boundary conditions are derived from Hamilton's principle. The assumed modes method is adopted to solve the equation of motion. For the free axial vibration, the natural frequencies are calculated for the various values of the nonlocal parameter only based on Eringen's theory. The effects of the nonlocal parameter, thickness, length, and ratio of the excitation frequency to the natural frequency over time in dimensional and non-dimensional axial displacements are investigated for the first time.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.2
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• pp.252-263
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• 1997

Steady-state two-dimensional natural convective heat transfer in horizontal cylindrical annuli was studied by solving the governing equations based on the primitive variables. Emphasis was put on the occurrence of the multiple solutions at a given set of parameter values, and on the determination of the bifurcation points at which those multiple solutions begin to branch out. The multicellular flow pattern from the results of melting process in an isothermally heated horizontal cylinder for high Rayleigh numbers, was used as initial guesses for the field variables. This was succeeded in new bifurcation point to tetracellular solutions for an identical set of parameter variables of previous works. The close examination of flow pattern transition around bifurcation point was also conducted. It was found that the mechanisms of flow transition are different depending on the critical Rayleigh number of bifurcation point.