• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.401-408
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• 2009

Let {$Y_i,-{\infty}<i<{\infty}$} be a doubly infinite sequence of identically distributed and ${\rho}^*$-mixing random variables and {$a_i,-{\infty}<i<{\infty}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence of $\{\sum\limits_{k=1}^n\;\sum\limits_{n=-\infty}^\infty\;a_{i+k}Y_i/n^{1/t};\;n{\geq}1\}$ under suitable conditions.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.127-136
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• 2010

For the maximum partial sum of linear process generated by a doubly infinite sequence of identically distributed $\rho$-mixing random variables with mean zeros, a complete convergence is obtained under suitable conditions.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.597-606
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• 2008

Let {$Y_{ij}-{\infty}\;<\;i\;<\;{\infty}$} be a doubly infinite sequence of identically distributed and ${\rho}^*$-mixing random variables with zero means and finite variances and {$a_{ij}-{\infty}\;<\;i\;<\;{\infty}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {${\sum}^n_{k=1}\;{\sum}^{\infty}_{i=-{\infty}}\;a_{i+k}Y_i/n^{1/p}$; $n\;{\geq}\;1$} under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191.197.] to the ${\rho}^*$-mixing case.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.479-486
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• 2008

Let {${\Omega}$, F, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. We study the Hajeck-Renyi-type inequality for p..mixing random variable sequences and obtain the strong law of large numbers by using this inequality. We also consider the strong law of large numbers for weighted sums of ${\tilde{\rho}}$-mixing sequences.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.321-328
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• 1995

Ibragimov(1975) showed the central limit theorem and the invariance principle for $\rho$-mixing random variables satisfying $\sigma^2(n) = nh(n) \longrightarrow \infty$ and $E$\mid$\zeta_0$\mid$^{2+\delta} < \infty$ for some $\delta > 0$ where $\sigma^2(n)$ denotes the variance of the partial sum $S_n$ and h(n) is a slowly varying function.

• Journal of ILASS-Korea
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• v.4 no.3
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• pp.8-14
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• 1999

The characteristics of the breakup process in supercritical spray is investigated during the injection of supercritical sulfur hexafluoride into dissimilar gases at supercritical pressures and subcritical temperature of the injected fluid. The visualization techniques used are backlighting and shadowgraph methods. The spray angles are measured and the breakup and mixing process are observed at near and supercritical conditions. The results show that spray angles are decreased with the in..ease of the ratio of density $(\frac{\rho_f}{\rho_g})$. At the supercritical temperature, the spray angles in atomization region are kept nearly constant such as the typical spray angle in gas injection. The mixing process is changed radically at the temperature where $\frac{d\rho}{dT}=\frac{1}{2}[\frac{d\rho}{dT}]_{max}$ at given pressure.

• Journal of the Korean Society of Industry Convergence
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• v.2 no.2
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• pp.73-81
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• 1999

Shake mixing has been widely used in cell culture. The mixing performance for shake mixing, however, has not been reported quantitatively. The critical circulating frequency and the power consumption for complete suspension of particles, based on the definition of Zwietering, were measured in a shaking vessel containing a solid-liquid system. The critical suspension frequency was correlated by the equation from Baldi's particle suspension model modified with the physical properties of the particles. Critical suspension frequency was correlated as following ; $$N_{JS}={\frac{0.58\;d{_p}^{0.06}(g{\Delta}{\rho}/{\rho}_L)^{0.004}X^{0.03}}{D^{0.35}d^{0.17}{\upsilon}^{0.04}}}$$ The power consumption at the critical suspension condition in the shaking vessel was less than that in an agitated vessel with impeller.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.525-536
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• 2010

Let $X_1,X_2,\cdots$ be identically distributed $\rho$-mixing random variables with mean zeros and positive finite variances. In this paper, we prove $$\array{\lim\\{\in}\downarrow0}{\in}^2 \sum\limits_{n=3}^\infty\frac{1}{nlogn}P({\mid}S_n\mid\geq\in\sqrt{nloglogn}=1$$, $$\array{\lim\\{\in}\downarrow0}{\in}^2 \sum\limits_{n=3}^\infty\frac{1}{nlogn}P(M_n\geq\in\sqrt{nloglogn}=2 \sum\limits_{k=0}^\infty\frac{(-1)^k}{(2k+1)^2}$$ where $S_n=X_1+\cdots+X_n,\;M_n=max_{1{\leq}k{\leq}n}{\mid}S_k{\mid}$ and $\sigma^2=EX_1^2+ 2\sum\limits{^{\infty}_{i=2}}E(X_1,X_i)=1$.

• Journal of the Korean Society of Safety
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• v.13 no.3
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• pp.112-118
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• 1998

This work has been carried out to study the mixing characteristics of solid in vibrating feeder for stable operations of fluidized bed combustion. The system consisted of two particles such that fine particles were located on the top of the coarse particles before vibratory mixing had started. Effect of particle size, particle densities, vibration amplitude and vibration frequency were experimentally obtained. Also, a diffusion model was applied in interpreting the experimental results. From these results, the following empirical equation for the diffusivity was obtained. $0.87{(\frac{d_c}{d_f})}^{0.73}\;{(\frac{\rho_f}{\rho_c})}^{0.53}(A^2f)$.

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.125-135
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• 2001

In this article we investigate the dependence between components of the random vector which is given as an asymptotic limit of an array of random vectors with interlaced mixing conditions. We discuss the cross covariance of the limiting vector process and give a stronger condition to have a central limit theorem for an array of random vectors with mixing conditions.