• The Bulletin of The Korean Astronomical Society
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• 제39권2호
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• pp.74.2-74.2
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• 2014

Magnetohydrodynamics(MHD) dynamo depends on many factors such as viscosity ${\gamma}$, magnetic diffusivity ${\eta}$, magnetic Reynolds number $Re_M$, external driving source, or magnetic Prandtl number $Pr_M$. $Pr_M$, the ratio of ${\gamma}$ to ${\eta}$ (for example, galaxy ${\sim}10^{14}$), plays an important role in small scale dynamo. With the high PrM, conductivity effect becomes very important in small scale regime between the viscous scale ($k_{\gamma}{\sim}Re^{3/4}k_fk_f$:forcing scale) and resistivity scale ($k_{\eta}{\sim}PrM^{1/2}k_{\gamma}$). Since ${\eta}$ is very small, the balance of local energy transport due to the advection term and nonlocal energy transfer decides the magnetic energy spectra. Beyond the viscous scale, the stretched magnetic field (magnetic tension in Lorentz force) transfers the magnetic energy, which is originally from the kinetic energy, back to the kinetic eddies leading to the extension of the viscous scale. This repeated process eventually decides the energy spectrum of the coupled momentum and magnetic induction equation. However, the evolving profile does not follow Kolmogorov's -3/5 law. The spectra of EV (${\sim}k^{-4}$) and EM (${\sim}k^0$ or $k^{-1}$) in high $Pr_M$ have been reported, but our recent simulation results show a little different scaling law ($E_V{\sim}k^{-3}-k^{-4}$, $EM{\sim}k^{-1/2}-k^{-1}$). We show the results and explain the reason.

• Communications for Statistical Applications and Methods
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• 제26권5호
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• pp.431-443
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• 2019

Goodness-of-fit techniques are an important topic in statistical analysis. Censored data occur frequently in survival experiments; therefore, many studies are conducted when data are censored. In this paper we mainly consider test statistics based on the empirical distribution function (EDF) to test normal distributions with unknown location and scale parameters when data are randomly censored. The most famous EDF test statistic is the Kolmogorov-Smirnov; in addition, the quadratic statistics such as the $Cram{\acute{e}}r-von$ Mises and the Anderson-Darling statistic are well known. The $Cram{\acute{e}}r-von$ Mises statistic is generalized to randomly censored cases by Koziol and Green (Biometrika, 63, 465-474, 1976). In this paper, we generalize the Anderson-Darling statistic to randomly censored data using the Kaplan-Meier estimator as it was done by Koziol and Green. A simulation study is conducted under a particular censorship model proposed by Koziol and Green. Through a simulation study, the generalized Anderson-Darling statistic shows the best power against almost all alternatives considered among the three EDF statistics we take into account.

• Journal of the Earthquake Engineering Society of Korea
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• 제24권5호
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• pp.219-232
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• 2020

The slip-weakening model developed by Ohnaka and Yamashita is extended over the breakdown zone by equating the scaling relationships for the breakdown zone and the whole rupture area. For the extension, the study uses the relationship between rupture velocity and radiation efficiency, which was derived in the theory of linear elastic fracture mechanics, and the definition of f_max given in the specific barrier model proposed by Papageorgiou and Aki. The results clearly show that the extended scaling relationship is governed by the ratio of rupture velocity to S wave velocity, and the velocity ratio can be determined by the ratio of characteristic frequencies of a Fourier amplitude spectrum, which are corner frequency, f_c, and source-controlled cut-off frequency, f_max, or vice versa. The derived relationship is tested by using the characteristic frequencies extracted from previous studies of more than 130 shallow crustal events (focal depth less than 25 km, M_W 3.0~7.5) that occurred in Japan. Under the assumption of a dynamic similarity, the rupture velocity estimated from f_max/f_c and the modified integral timescale give quite similar scale-dependence of the rupture area to that given by Kanamori and Anderson. Also, the results for large earthquakes show good agreement to the values from a kinematic inversion in previous studies. The test results also indicate the unavailability of the spectral self-similarity proposed by Aki because of the scale-dependent rupture velocity and the rupture velocity-dependent f_max/f_c; however, the results do support the local similarity asserted by Ohnaka. It is also remarkable that the relationship between the rupture velocity and f_max/f_c is quite similar to Kolmogorov's hypothesis on a similarity in the theory of isotropic turbulence.

• Journal of Mechanical Science and Technology
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• 제20권2호
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• pp.262-270
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• 2006

Direct numerical simulations (DNS) of turbulent channel flows up to $Re_{\tau}=1270$ are performed to investigate an elliptic feature and strain rate field on cross sections of coherent fine scale eddies (CFSEs) in wall turbulence. From DNS results, the CFSEs are educed and the strain rate field around the eddy is analyzed statistically. The principal strain rates (i.e. eigenvalues of the strain rate tensor) at the CFSE centers are scaled by the Kolmogorov length $\eta$ and velocity $U_k$. The most expected maximum (stretching) and minimum (compressing) eigenvalues at the CFSE centers are independent of the Reynolds number in each $y^+$ region (i. e. near-wall, logarithmic and wake regions). The elliptic feature of the CFSE is observed in the distribution of phase-averaged azimuthal velocity on a plane perpendicular to the rotating axis of the CFSE $(\omega_c)$. Except near the wall, phase-averaged maximum $(\gamma^{\ast}/\gamma_c^{\ast})$ and minimum $(\alpha^{\ast}/\alpha_c^{\ast})$ an eigenvalues show maxima on the major axis around the CFSE and minima on the minor axis near the CFSE center. This results in high energy dissipation rate around the CFSE.

• Journal of the Korean Data and Information Science Society
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• 제27권2호
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• pp.373-380
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• 2016

Even though Likert type data is ordinal scale, many researchers who regard Likert type data as interval scale adapt as parametric methods. In this research, simulations have been used to find out a proper analysis of Likert type data. The locations and response distributions of five point Likert type data samples having diverse distribution have been evaluated. In estimating samples' locations, we considered parametric method and non-parametric method, which are t-test and Mann-Whitney test respectively. In addition, to test response distribution, we employed Chi-squared test and Kolmogorov-Smirnov test. In this study, we assessed the performance of the four aforementioned methods by comparing Type I error ratio and statistical power.

• Communications for Statistical Applications and Methods
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• 제24권5호
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• pp.481-492
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• 2017

This paper investigates a convergence rate of a test statistics given by two scale sampling method based on $A\ddot{i}t$-Sahalia and Jacod (Annals of Statistics, 37, 184-222, 2009). This statistics tests for longitudinal data having the existence of long memory dependence driven by fractional Brownian motion with Hurst parameter $H{\in}(1/2,\;1)$. We obtain an upper bound in the Kolmogorov distance for normal approximation of this test statistic. As a main tool for our works, the recent results in Nourdin and Peccati (Probability Theory and Related Fields, 145, 75-118, 2009; Annals of Probability, 37, 2231-2261, 2009) will be used. These results are obtained by employing techniques based on the combination between Malliavin calculus and Stein's method for normal approximation.

• Microbiology and Biotechnology Letters
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• 제23권5호
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• pp.499-505
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• 1995

Immobilization of anchorage-dependent animal cells was investigated using macroporous gelatin microcarriers developed in our laboratory. For the observation of the distribution of cells in macroporous beads, Vero-6 cells and CHO cells were cuttured and their distribution in macroporous beads was observed using a confocal microscope. In results, the final concentration of Vero-6 cells and CHO cells on macroporous beads was 2-3 times higher than that on commercial solid microcarriers (Cytodex-3). Also, macroporous microcarriers could hold cells in their macropores. Consequently, the pores protected cells against hydrodynamic shear. Based on Kolmogorov eddy length scale, the smaller eddies (80 $\mu $m) showed the detrimental effect on cells in macroporous beads as compared with 160 $\mu $m of eddies in conventional solid microcarriers.

• Wind and Structures
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• 제31권5호
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• pp.419-430
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• 2020

Weibull distribution is a conspicuous distribution known for its accuracy and its usage for wind energy analysis. The two and three parameter Weibull distributions are adopted in this study to fit wind speed data. The daily mean wind speed data of Ennore, Tamil Nadu, India has been used to validate the procedure. The parameters are estimated using maximum likelihood method, least square method and moment method. Four statistical tests namely Root mean square error, R2 test, Kolmogorov-Smirnov test and Anderson-Darling test are employed to inspect the fitness of Weibull probability density functions. The value of shape factor, scale factor, wind speed and wind power are determined at a height of 100m using extrapolation of numerical equations. Also, the value of capacity factor is calculated mathematically. This study provides a way to evaluate feasible locations for wind energy assessment, which can be used at any windy site throughout the world.

• Transactions of the Korean Society of Mechanical Engineers A
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• 제24권9호
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• pp.2353-2360
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• 2000

Statistical fatigue properties of metallic materials are increasingly required for reliability design purpose. In this study, static and fatigue tests were conducted and the normal, log-normal, two -parameter Weibull distributions at the 5% significance level are compared using the Kolmogorov-Smirnov goodness-of-fit test. Parameter estimation were compared with experimental results using the maximum likelihood method and least square method. It is found that two-parameter Weibull distribution and maximum likelihood method provide a good fit for static and fatigue life data. Therefore, it is applicable to the static and fatigue life analysis of the spheroidal graphite cast iron. The P-S-N curves were evaluated using log-normal distribution, which showed fatigue life behavior very well.

• Journal of the Korean Data and Information Science Society
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• 제21권2호
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• pp.345-354
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• 2010

The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.