• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.547-567
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• 2007

We obtain spatial-temporal decay rates of weak solutions of incompressible flows in exterior domains. When a domain has a boundary, the pressure term yields difficulties since we do not have enough information on the pressure term near the boundary. For our calculations we provide an idea which does not require any pressure information. We also estimated the spatial and temporal asymptotic behavior for strong solutions.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.619-634
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• 2023

This paper considers a parabolic-hyperbolic-hyperbolic type chemotaxis system in ℝ^d, d ≥ 3, describing tumor-induced angiogenesis. The global existence result and temporal decay estimate for a unique mild solution are established under the assumption that some Sobolev norms of initial data are sufficiently small.

• Journal of Environmental Science International
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• v.27 no.7
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• pp.499-507
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• 2018

Agricultural meteorological information is an important resource that affects farmers' income, food security, and agricultural conditions. Thus, such data are used in various fields that are responsible for planning, enforcing, and evaluating agricultural policies. The meteorological information obtained from automatic weather observation systems operated by rural development agencies contains missing values owing to temporary mechanical or communication deficiencies. It is known that missing values lead to reduction in the reliability and validity of the model. In this study, the hierarchical Bayesian spatio-temporal model suggests replacements for missing values because the meteorological information includes spatio-temporal correlation. The prior distribution is very important in the Bayesian approach. However, we found a problem where the spatial decay parameter was not converged through the trace plot. A suitable spatial decay parameter, estimated on the bias of root-mean-square error (RMSE), which was determined to be the difference between the predicted and observed values. The latitude, longitude, and altitude were considered as covariates. The estimated spatial decay parameters were 0.041 and 0.039, for the spatio-temporal model with latitude and longitude and for latitude, longitude, and altitude, respectively. The posterior distributions were stable after the spatial decay parameter was fixed. root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and bias were calculated for model validation. Finally, the missing values were generated using the independent Gaussian process model.

• Journal of the Korean Society of Safety
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• v.33 no.4
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• pp.78-83
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• 2018

Previous researches on the analysis of algae concentration were restricted to applying single-valued decay coefficient during simulation period, and the accuracy as well as the applicability were severely challenged. In this study, an equivalent tracking method of decay coefficient was proposed by introducing the time-series decay coefficients and restart option. Dye module in EFDC model was employed to route the temporal variation of Chl-a concentration. It was shown that the simulation results can be significantly improved up to 46% when the equivalent tracking method was activated.

• 한국정보디스플레이학회:학술대회논문집
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• 2008.10a
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• pp.377-380
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• 2008

In this work, we measured the spatiotemporal surface charge distribution by the longitudinal electro-optic amplitude modulation method with BSO single crystal to investigate the decay and diffusion characteristics of surface charges in three types of MgO. The speed of decay and diffusion of two different kinds doped MgO is compared with those of pure MgO. The difference in the characteristics of the decay and diffusion between the electron and ion surface charges is investigated separately. We found that the rate of ion decay is the major factor that makes the difference of the temporal variation of wall voltage among different types doped MgO.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.2
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• pp.76-107
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• 2022

In this paper, we study the temporal decay of global weak solutions to the inhomogeneous Hall-magnetohydrodynamic (Hall-MHD) equations. First, an approximation problem and its weak solutions are obtained via the Caffarelli-Kohn-Nirenberg retarded mollification technique. Then, we prove that the approximate solutions satisfy uniform decay estimates. Finally, using the weak convergence method, we construct weak solutions with optimal decay rates to the inhomogeneous Hall-MHD equations.

• Journal of Korean Society of Water and Wastewater
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• v.26 no.6
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• pp.861-869
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• 2012

The chlorine's residual concentration prevents the regrowth of microorganism in water transport along the pipeline system. Precise prediction of chlorine concentration is important in determining disinfectant injection for the water distribution system. In this study, a pilot scale water distribution system was designed and fabricated to measure the temporal variation of chlorine concentration for three flow conditions (V = 0.88, 1.33, 1.95 m/s). Various kinetic models were applied to identify the relationship between hydraulic condition and chlorine decay. Genetic Algorithm (GA) was integrated into five kinetic models and time series of chlorine were used to calibrate parameters. Model fitness was compared by Root Mean Square Error (RMSE) between measurement and prediction. Limited first order model and Parallel first order showed good fitness for prediction of chlorine concentration.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.1
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• pp.47.1-47.1
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• 2013

Supersonic turbulence is believed to decay rapidly within a flow crossing time irrespective of the degree of magnetization. However, this consensus of decaying magnetohydrodynamic (MHD) turbulence relies on local isothermal simulations, which are unable to investigate the role of global magnetic fields and structures. Utilizing three-dimensional MHD simulations including interstellar cooling and heating, we investigate decaying MHD turbulence within cold neutral medium sheets embedded in warm neutral medium. Early evolution is consistent with previous studies characterized rapid decay of turbulence with the decaying time shorter than a flow crossing time and power-law temporal decay of turbulent kinetic energy with slope of -1. If initial magnetic fields are strong and perpendicular to the sheet, however long term evolutions of kinetic energy shows that a significant amount of turbulent energy still remains even after ten flow crossing times, and decaying rate is reduced as field strengths increase. We analyse power spectra of remaining turbulence to show that incompressible, in-plane motions dominate.

• Journal of Environmental Science International
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• v.24 no.10
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• pp.1273-1283
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• 2015

In present study, the temporal characteristics of nine selected volatile organic compounds (VOCs), including four alcohol, 2 aldehyde, and 3 ketone compounds, in high-stories urban apartments over a 2-y period were investigated. The indoor VOC concentrations had generally a decreasing trend over the 2-y follow-up period. For examples, the 2E1H indoor concentration decreased from $10.8{\mu}g/m^3$ for the first two months to $5.1{\mu}g/m^3$ for the last two months. In addition, the DCA and ACT indoor concentrations decreased from 5.0 and $14{\mu}g/m^3$ for the first two months to 2.2 and $6.4{\mu}g/m^3$, respectively, for the last two months. The indoor-to outdoor concentration ratios over the 2-y period were much greater than 1, indicating that indoor VOC concentrations were higher than the outdoor VOC concentrations. Similar to those of the individual VOCs, the indoor-to-outdoor concentration ratios of all three VOC groups were higher than 1 over the 2-y follow-up period, suggesting higher indoor concentrations of the three VOC groups than outdoor concentrations. In consistence with the results of VOC indoor concentrations, the VOC emission rates decreased gradually as time passed, due to the decreased VOC emission strengths of indoor sources. Finally, there was an initial sharp decrease in the indoor VOC concentrations followed by a slower decrease, indicating a multi-exponential decay model for the target VOCs, which was demonstrated by comparison of the residuals and the adjusted coefficient of determination associated with the one and two-exponential fits of each data set.

• Bulletin of the Korean Chemical Society
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• v.24 no.11
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• pp.1675-1679
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• 2003

The photodynamics of excited-state intramolecular proton transfer reaction of 1-hydroxyanthraquinone (1-HAQ) and 1-deuterioanthraquinone was investigated in toluene with time-resolved emission and femtosecond transient transmittance techniques at room temperature. The temporal profiles of transient transmittance of 1-HAQ could be well described with multi-decaying time constants. The ultrafast time constant within ca. 260 fs reflects the dynamics of proton transfer. The decay component of 2 ps is assigned to an additional proton translocation process induced by the intramolecular vibrational relaxation, whereas the decay component of 18 ps is assigned to the vibrational cooling process, while the long component (200 ps) can be explained in terms of the relaxation from excited-state keto-tautomer to its ground state. Time-resolved anisotropy decay dynamics and isotope effects on the photodynamics reveals that the ESIPT from enol-tautomer to keto-one of 1-HAQ is barrierless reaction and coupled to a vibrational relaxation process.