• Communications for Statistical Applications and Methods
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• 제22권3호
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• pp.277-283
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• 2015

Pickands constant $H_{\alpha}$ appears in the classical result about tail probabilities of the extremes of Gaussian processes and there exist several different representations of Pickands constant. However, the exact value of $H_{\alpha}$ is unknown except for two special Gaussian processes. Significant effort has been made to find numerical approximations of $H_{\alpha}$. In this paper, we attempt to compute numerically $H_{\alpha}$ based on its representation derived by $H{\ddot{u}}sler$ (1999) and Albin and Choi (2010). Our estimates are compared with the often quoted conjecture $H_{\alpha}=1/{\Gamma}(1/{\alpha})$ for 0 < ${\alpha}$ ${\leq}$ 2. This conjecture does not seem compatible with our simulation result for 1 < ${\alpha}$ < 2, which is also recently observed by Dieker and Yakir (2014) who devised a reliable algorithm to estimate these constants along with a detailed error analysis.

• Journal of the Korean Statistical Society
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• 제27권2호
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• pp.165-187
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• 1998

Shin and Sarkar (1993, 1994) studied the problem of testing for a unit root in an AR(p) signal observed with MA(q) noise when the MA parameters are known. In this paper we consider the case when the MA parameters are unknown and to be estimated. Test statistics are defined using unit root parameter estimates based on three different estimation methods of Hannan and Rissanen (1982), Kohn (1979) and Shin and Sarkar (1995). An AR(p) process contaminated by MA(q) noise is a .estricted ARMA model, for which Shin and Sarkar (1995) derived an easy-to-compute Newton- Raphson estimator The two-stage estimation p.ocedu.e of Hannan and Rissanen (1982) is used to compute initial parameter estimates in implementing the iterative estimation methods of both Shin and Sarkar (1995) and Kohn (1979). In a simulation study we compare the relative performance of these unit root tests with respect to both size and power for p=q=1.

• Asian Journal of Atmospheric Environment
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• 제8권2호
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• pp.96-107
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• 2014

Extreme recovery of the thermal energy from the combustion of flue gas may bring about early gas condensation resulting in the increased formation of nitric acid vapor. The behavior of the nitric acid formed inside the stack and in the atmosphere was investigated through a computer-aided simulation in this study. Low temperatures led to high conversion rates of the nitrogen oxide to nitric acid, according to the Arrhenius relationship. Larger acid plumes could be formed with the cooled flue gas at $40^{\circ}C$ than the present exiting gas at $115^{\circ}C$. The acid vapor plume of 0.1 ppm extended to 25 m wide and 200 m high. The wind, which had a seasonal local average of 3 m/s, expanded the influencing area to 170 m along the ground level. Its tail stretched 50 m longer at $40^{\circ}C$ than at $115^{\circ}C$. The emission concentration of the acid vapor in the summer season was a little lower than in the winter. However, a warm atmosphere facilitated the Brownian motion of the discharged flue gas, finally leading to more vigorous dispersion.

• Korea-Australia Rheology Journal
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• 제19권3호
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• pp.99-107
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• 2007

A nanofluid is a mixture of solid nanoparticles and a common base fluid. Nanofluids have shown great potential in improving the heat transfer properties of liquids. However, previous studies on the characteristics of nanofluids did not adequately explain the enhancement of heat transfer. This study examined the distribution of particles in a fluid and compared the mechanism for the enhancement of heat transfer in a nanofluid with that in a general microparticle suspension. A theoretical model was formulated with shear-induced particle migration, viscosity-induced particle migration, particle migration by Brownian motion, as well as the inertial migration of particles. The results of the simulation showed that there was no significant particle migration, with no change in particle concentration in the radial direction. A uniform particle concentration is very important in the heat transfer of a nanofluid. As the particle concentration and effective thermal conductivity at the wall region is lower than that of the bulk fluid, due to particle migration to the center of a microfluid, the addition of microparticles in a fluid does not affect the heat transfer properties of that fluid. However, in a nanofluid, particle migration to the center occurs quite slowly, and the particle migration flux is very small. Therefore, the effective thermal conductivity at the wall region increases with increasing addition of nanoparticles. This may be one reason why a nanofluid shows a good convective heat transfer performance.