• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1141-1158
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• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.783-792
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• 2007

We consider estimation of reliability P(Y

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.187-194
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• 2015

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Inspired by the excellent work of Jin and Lee (2014), we present certain characterizations of gamma distribution based on the concept of sub-independence.

• Journal of Korea Water Resources Association
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• v.36 no.2
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• pp.223-235
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• 2003

An indirect or supplementary approach is proposed for determining the parameters of the Clark's model in order to improve existing defect in estimating the parameters. The gamma-distribution type function is employed to represent the Clark's model, which takes the same form as the Nash's model, so that parameter estimation is not difficult since it can be performed with a simple optimization process. Analytic forms of Clark's models parameters are introduced using parameters of the proposed methodology to give traditional form of Clark's. An application to a watershed has shown that the proposed approach can preserve the properties of observed data. Based the application, the new approach is recommended as an alternative to the existing parameter estimating methodology.

• Journal of the Korean Society of Propulsion Engineers
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• v.16 no.4
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• pp.33-41
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• 2012

The aim of the study is to investigate the method to estimate a shelf life of KM6 single base propellant by stochastic gamma process model. The state failure level is assumed that the degradation content of stabilizer is below 0.8%. The constant of time dependent shape function and the scale parameter of stationary gamma process are estimated by moment method. The state distribution at each storage time can be shown from probability density function of deterioration. It is estimated that the $B_{10}$ life, a time at which the cumulative failure probability is 10%, is 25 years and the $B_{50}$ life is 36 years from cumulative failure distribution function curve. The $B_{50}$ life can be treated as the average shelf life from the practical viewpoint and the lifetime can be expressed as distribution curve by using stochastic process theory.

• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.265-279
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• 1999

In this study, one of the techniques on the extension of low flow series has been developed, in which the daily streamflows were simulated by the Tank model with the input of extended daily rainfall series which were stochastically generated by the Markov chain model. The annual lowest flow serried for each of the given durations were formulated form the simulated daily streamflow sequences. The frequency of the estimated annual lowest flow series was analyzed. The distribution types to be used for the frequency analysis were two-parameter and three-parameter log-normal distribution, two-parameter and three-parameter Gamma distribution, three-parameter log-Gamma distribution, Gumbel distribution, and Weibull distribution, of which parameters were estimated by the moment method and the maximum likelihood method. The goodness-of-fit test for probability distribution is evaluated by the Kolmogorov-Sminrov test. The fitted distribution function for each duration series is applied to frequency analysis for developing duration-low flow-frequency curves at Yongdam Dam station. It was shown that the purposed technique in this study is available to generate the daily streamflow series with fair accuracy and useful to determine the probabilistic low flow in the watersheds having the poor historic records of low flow series.

• Journal of Korea Multimedia Society
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• v.24 no.11
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• pp.1461-1471
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• 2021

This paper presents a light exposure correction algorithm for less pleasant images, acquired with a light metering failure. Since conventional tone mapping and gamma correction methods adopt a function mapping with the same range of input and output, the results are pleasurable for almost symmetric distributions to their intensity average. However, their corrections gave insufficient outputs for asymmetric cases at either bright or dark regions. Also, histogram modification approaches show good results on varied pattern images, but these generate unintentional noises at flat regions because of the compulsive shift of the intensity distribution. Therefore, in order to sufficient corrections for both bright and dark areas, the proposed algorithm calculates the gamma coefficients using primary parameters extracted from the global distribution. And the fusion weights are adaptively determined with complementary parameters, considering the classification information of a binary segmentation. As the result, the proposed algorithm can obtain a good output about both the symmetric and the asymmetric distribution images even with severe exposure values.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2003.10a
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• pp.62-63
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• 2003

The inter-particle distance between diamonds on the segment surface of sawing blade predicted theoretically and measured experimentally followed a Gamma or Weibull function, rather than a normal distribution function. These results suggest that random dispersion of diamond particles in the segment may not be an efficient way of improving cutting efficiency of the blade.

• Journal of Korean Society for Quality Management
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• v.41 no.1
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• pp.135-148
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• 2013

Purpose: This paper presents a method to evaluate the stockpile reliability of propelling charge for performance and storage safety with storage time. Methods: We consider a performance failure level is the amount of muzzle velocity drop which is the maximum allowed standard deviation multiplied by 6. The lifetime for performance is estimated by non-linear regression analysis. The state failure level is assumed that the content of stabilizer is below 0.2%. Because the degradation of stabilizer with storage time has both distribution of state and distribution of lifetime, it must be evaluated by stochastic process method such as gamma process. Results: It is estimated that the lifetime for performance is 59 years. The state distribution at each storage time can be shown from probability density function of degradation. It is estimated that the average lifetime as $B_{50}$ life is 33 years from cumulative failure distribution function curve. Conclusion: The lifetime for storage safety is shorter than for performance and we must consider both the lifetime for storage safety and the lifetime performance because of variation of degradation rate.

• Korean Journal of Remote Sensing
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• v.21 no.2
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• pp.99-111
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• 2005

A fuzzy logic based data integration was applied for geothermal potential mapping in Jeju Island. Several data sets, such as geological map, the density of drainage system, the distribution density of cinder cones, density of lineaments, aerial survey map for total magnetic intensity and total gamma ray, were collected as thematic map for the integration. Fuzzy membership function for all thematic maps were compared to the locations of the spa, which were used as ground-truth control points. The older geology, the lower density of drainage, cinder cones and lineaments, and the lower intensity of magnetic and gamma ray were showed the higher fuzzy membership function values, respectively. After integrating all thematic maps, the results of gamma operator with the gamma value of 0.75 was the highest success rate, and new geothermal potential zone is prospected in western north part of Jeju Island.