• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.949-957
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• 2005

For weighted sum of a sequence {X, X$\_{n}$, n $\geq$ 1} of identically distributed, negatively orthant dependent random variables such that |r| > 0, has a finite moment generating function, a strong law of large numbers is established.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1987.04a
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• pp.184-187
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• 1987

The method of Conjugate Gradient(C.G.M) is applied to the solution of current distribution from body of revolution (B.O.R).Using the C.G.M it is possible to analyze electrically large arbtrarily oriented B.O.R. The fundamental differences between C.G.M and moment method are outlined. This method converges for any initial guess and this techniqe gurantees a monotonic convergence. Numerical results are presented for electromagnetic case which show good agreement with moment solution.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.99-106
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• 2004

Let {X, $X_{n}, n\;{\geq}\;1$} be a sequence of identically distributed, negatively associated (NA) random variables and assume that $│X│^{r}$, r > 0, has a finite moment generating function. A strong law of large numbers is established for weighted sums of these variables.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.369-380
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• 2009

Let $X,X_1,X_2,\;{\cdots}$ be identically distributed and negatively associated random variables with mean zeros and positive, finite variances. We prove that, if $E{\mid}X_1{\mid}^r$ < ${\infty}$, for 1 < p < 2 and r > $1+{\frac{p}{2}}$, and $lim_{n{\rightarrow}{\infty}}n^{-1}ES^2_n={\sigma}^2$ < ${\infty}$, then $lim_{{\epsilon}{\downarrow}0}{\epsilon}^{{2(r-p}/(2-p)-1}{\sum}^{\infty}_{n=1}n^{{\frac{r}{p}}-2-{\frac{1}{p}}}E\{{{\mid}S_n{\mid}}-{\epsilon}n^{\frac{1}{p}}\}+={\frac{p(2-p)}{(r-p)(2r-p-2)}}E{\mid}Z{\mid}^{\frac{2(r-p)}{2-p}}$, where $S_n\;=\;X_1\;+\;X_2\;+\;{\cdots}\;+\;X_n$ and Z has a normal distribution with mean 0 and variance ${\sigma}^2$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.585-592
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• 2010

Let {$\varepsilon_i:-{\infty}$$\infty$} be a strictly stationary sequence of linearly positive quadrant dependent random variables and $\sum\limits\frac_{i=-{\infty}}^{\infty}|a_i|$<$\infty$. In this paper, we prove the precise asymptotics in the law of iterated logarithm for the moment convergence of moving-average process of the form $X_k=\sum\limits\frac_{i=-{\infty}}^{\infty}a_{i+k}{\varepsilon}_i,k{\geq}1$

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.679-698
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• 2018

In this paper, with optimal normalized constants, the asymptotic expansions of the distribution and density of the normalized maxima from generalized Maxwell distribution are derived. For the distributional expansion, it shows that the convergence rate of the normalized maxima to the Gumbel extreme value distribution is proportional to 1/ log n. For the density expansion, on the one hand, the main result is applied to establish the convergence rate of the density of extreme to its limit. On the other hand, the main result is applied to obtain the asymptotic expansion of the moment of maximum.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.1
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• pp.43-51
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• 2000

The response statistics of a hinged-clamped beam under broad-band random excitation is investigated. The random excitation is applied at the nodal point of the second mode. By using Galerkin's method the governing equation is reduced to a system of nonautonomous nonlinear ordinary differential equations. A method based upon the Markov vector approach is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. The analytical results for two and three mode interactions are also compared with results obtained by Monte Carlo simulation.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.2
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• pp.141-147
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• 2000

The nonlinear response statistics of an autoparameteric system under broad-band random excitation is investigated. The specific system examined is a vibration absorber system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The jump phenomenon was found by Gaussian closure method under random excitation.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.35-42
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• 2003

This paper provides the first known flexural vibration data for thick (Mindlin) rectangular plates having V-notches. The V-notch has bending moment and shear force singularities at its sharp corner due to the transverse vibratory bending motion. Based upon Mindlin plate theory, in which transverse shear deformation and rotary inertia effects are considered, the Ritz procedure is employed with a hybrid set of admissible functions assumed for the rotational and transverse vibratory displacements. This set includes: (1) a mathematically complete set of admissible algebraic-trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained; and (2) an admissible set of Mindlin corner functions which account for the bending moment and shear force singularities at the sharp corner of the V-notch. Extensive convergence studies demonstrate the necessity of adding the Mindlin corner functions to achieve accurate frequencies for rectangular plates having sharp V-notches.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.2
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• pp.133-139
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• 2001

The nonlinear response statistics of an spring-pendulum system with internal resonance under narrow band random excitation is investigated analytically- The center frequency of the filtered excitation is selected to be close to natural frequency of directly excited spring mode. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The nonlinear phenomena, such as jump and multiple solutions, under narrow band random excitation were found by Gaussian closure method.