• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.289-302
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• 2004

The asymptotic dependence between the central quasi-ranges and empirical quantiles was studied. The asymptotic dependence are obtained when the sample size is a positive integer valued random variable (r. v.). The dependence conditions and limit forms are obtained under generl conditions such as : the interrelation of the basic variables (the original random sample) and the random sample size is not restricted. In additition the normalizing constants do not depend on the random size.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.335-337
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• 2015

We modify the normalizing constants of the functions in the orthonormal basis for the Bergman space and restate their consequences in the paper that was published in Honam Math. J. 36 (2014), no. 4, pp. 777-786.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.454-460
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• 1998

The vibration behavior of fuel rods has been analyzed by FEM in consideration of axial force and support spring constants. The axial compression force on the fuel rod in reactor decreases with the fuel rod burnup, and its decrease makes the natural frequencies of fuel rod considerably increase. The change of support spring constant can contribute to the remarkable change of the mode shapes, but not greatly to the natural frequencies. The reaction forces of support springs are obtained from normalizing the lst mode with the max. 0.2 mm displacement. The calculated reaction forces are larger than the previous results obtained by disregarding the deflections of the support springs.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.145-153
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• 2003

In this Paper, we examine the limiting distributional behaviour of extreme values of mixed Erlang random variables. We show that, in the finite mixture of Erlang distributions, the component distribution with an asymptotically dominant tail has a critical effect on the asymptotic extreme behavior of the mixture distribution and it converges to the Gumbel extreme-value distribution. Normalizing constants are also established. We apply this result to characterize the asymptotic distribution of maxima of sojourn times in M/M/s queuing system. We also show that Erlang mixtures with continuous mixing may converge to the Gumbel or Type II extreme-value distribution depending on their mixing distributions, considering two special cases of uniform mixing and exponential mixing.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.879-895
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• 2022

This paper establishes the Baum-Katz type theorem and the Marcinkiewicz-Zymund type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors {X, X_n, n ≥ 1} taking values in a Hilbert space H with general normalizing constants $b_n=n^{\alpha}{\tilde{L}}(n^{\alpha})$, where ${\tilde{L}}({\cdot})$ is the de Bruijn conjugate of a slowly varying function L(·). The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.400-405
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• 2004

In this study, the optimal welding condition of the input power was selected experimentally through the ERW simulator, which is equal to welding status of ERW part in pipe. This condition is the input power 250kW in the heat treatment of the $900^{\circ}C$ normalizing derived from the nondestructive technique and impact energy. In order to evaluate the variation of the fatigue life in the pipe, fatigue surface crack growth test of base and optimal welded metal were performed statistically. As stress intensity factor range (${\Delta}K_s$) increases, the fatigue crack propagation rate (da/aN) of the base metal is faster than that of the welded joint. The variation of the fatigue life in the ERW pipe was estimated statistically using Monte-Carlo simulation with the standard deviation of material constants (C and m) of the paris law in the specimen.