• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.529-534
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• 1997

Even though the Shannon wavelet is a prototype of wavelets are assumed to have. By providing a sufficient condition to compute the size of Gibbs phe-nomenon for the Shannon wavelet series we can see the overshoot is propotional to the jump at discontinuity. By comparing it with that of the Fourier series we also that these two have exactly the same Gibbs constant.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.19 no.12
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• pp.883-888
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• 2007

As a starting point of investigating what molecular dynamic simulations can reveal about the nature of atomic level of heating and cooling process, argon described by the LJ potential is considered. Stepwise heating and cooling of constant rates are simulated in the NPT (constant number, pressure and temperature) ensemble. Hysteresis is found due to the superheating and supercooling. Drastic change of volume and energy is involved with phase change, but the melting point can not be obtained by simply observing the changes of these quantities. Since liquid and solid phases can co-exist at the same temperature, Gibbs free energy should be calculated to find the temperature where the Gibbs free energy of liquid is equal to that of the solid since the equilibrium state is the state of minimum Gibbs free energy. The obtained melting temperature, $T^*=0.685$, is close to that of the experiment with only 2% error.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.9-19
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• 1994

Beta-binomial model, which is reparametrized in terms of the mean probability $\mu$ of a positive deagnosis and the $\kappa$ of agreement, is widely used in psychology. When $\mu$ is close to 0, inference about $\kappa$ become difficult because likelihood function becomes constant. We consider Bayesian approach in this case. To apply Bayesian analysis, Gibbs sampler is used to overcome difficulties in integration. Marginal posterior density functions are estimated and Bayesian estimates are derived by using Gibbs sampler and compare the results with the one obtained by using numerical integration.

• Journal of the Korean Applied Science and Technology
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• v.36 no.4
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• pp.1143-1152
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• 2019

In order to study the solubilization of aniline by cationic surfactants (DTAB, TTAB and CTAB), the solubilization constant (K_s) and thermodynamic functions were measured and calculated by using the UV-Vis method. The solubilization constants of aniline with the change of temperature were measured, and the effects of addition of ionic salts and organics on the solubilization constants were investigated. These effects of additives and temperature changes were compared and analyzed for each type of surfactant, and the solubilization of aniline was analyzed microscopically by comparing and evaluating the thermodynamic functions obtained from the solubilization constants. As a result, the Gibbs free energy and enthalpy changes were both negative and the entropy changes were positive within the measured range for the solubilization of aniline by cationic surfactants. The solubilization constant value decreased with increasing temperature and increased with increasing carbon chain length of the surfactant. As the concentration of ionic salts increased, the Gibbs free energy change increased at first and then decreased. In n-butanol solution, the Gibbs free energy change tended to increase continuously with increasing the concentration of n-butanol.

• Journal of the Korean Chemical Society
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• v.53 no.6
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• pp.663-670
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• 2009

Performing random number simulations, we obtained an approximate distribution of the number of ways arranging molecules in a binary lattice solution of nonrandom mixing with a specific interaction. From the distribution an approximate equation of excess Gibbs energy for a binary lattice solution was derived. Using the equation, liquid-vapor equilibrium at constant pressure for 15 binary solutions were calculated and compared with the result from Wilson equation, Van Laar equation and Redlich-Kister equation.

• Journal of the Mineralogical Society of Korea
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• v.9 no.1
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• pp.17-25
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• 1996

Usual experimental adsorption isotherms as a function of relative humidity were constructed from adsorbed water contents in soils, which were kept more than 2 days in vacuum desiccators with constant humidities controlled by sulfuric acids of various concentrations. From the experimental data, the adsorption surface areas were calculated on the basis of the existing adsorption theory, such as Langmuir, BET, and Aranovich. Based on the Gibbs function describing chemical potential of perfect gas, the relative humidities in the desiccators were transformed into their chemical potentials, which were assumed to be the same as the potentials of equilibratedly adsorbed water in soils. Moreover, the water potentials were again transformed into the equivalent capillary pressures, heads of capillary rise, and equivalent radius of capillary pores, on the basis of Laplace equation for surface tension pressure of spherical bubbles in water. Adsorption quantity distributions were calculated on the profile of chemical potentials of the adsorbed water, equivalent adsorption and/or capillary pressures, and equivalent capillary radius. The suggested theories were proved through its application for the prediction of temperature rise of sulfuric acid due to hydration heat. Adsorption heat calculated on the basis of the potential difference was dependant on various factors, such as surface area, equilibrium constants in Langumuir, BET, etc.

• Korean Chemical Engineering Research
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• v.52 no.4
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• pp.486-491
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• 2014

In this paper, the adsorption behavior and kinetic characteristics of cibacron brilliant red 3B-A from aqueous solution using granular activated carbon were investigated. The effect of various parameters such as adsorbent dose, pH, initial concentration, contact time and temperature on the adsorption system were studied. Base on the estimated Langmuir constant ($R_L$) and Freundlich constant (1/n), This process could be employed as effective treatment method. From the Temkin constant (B) and Dubinin-Radushkevich constant (E), This adsorption process is physical adsorption. From kinetic experiments, the adsorption process followed the pseudo second order model with good correlation. Base on the Gibbs free energy and enthalpy, the adsorption of cibacron brilliant red 3B-A onto granular activated carbon was physisorption and endothermic in nature.

• Korean Chemical Engineering Research
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• v.56 no.2
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• pp.222-228
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• 2018

Benzene is one of the most widely used basic materials in the petrochemical industry. Generally, benzene exists as a mixture with alcohols rather than as a pure substance. Further, the alcohols-added mixtures usually exhibit an azeotropic composition. In this context, knowledge of the phase equilibrium behavior of the mixture is essential for its separation and purification. In this study, the vapor-liquid equilibrium data were measured in favor of a recirculating VLE apparatus under constant pressure for the 1 - propanol / benzene system. The measured vapor - liquid equilibrium data were also correlated by using the UNIQUAC and WILSON models and the thermodynamic consistency test based on the Gibbs/Duhem equation was followed. The results of the phase equilibrium experiment revealed RMSEs (Root Mean Square Error) and AADs (Average Absolute Deviation) of less than 0.05 for both models, indicating a good agreement between the experimental value and the calculated value. The results of the thermodynamic consistency test also confirmed through the residual term within ${\pm}0.2$.

• Bulletin of the Korean Chemical Society
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• v.24 no.6
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• pp.751-756
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• 2003

We have investigated the solvent effects on Δlog $K_s$ (the difference of stability constant of binding) and the relative free energies of binding of $La^{3+} and Nd^{3+}$ ions to 18-crown-6 by a Monte Carlo simulation of statistical perturbation theory (SPT) in diverse solvents. We compared relative binding Gibbs free energies and the differences in stability constant (Δlog $K_s$) of binding of $La^{3+} and Nd^{3+}$ ions to 18-crown-6 in $CH_3OH$ in this study with the experimental. There is a good agreement between our study and the experimental. We noted that Borns function of the solvents, the electron pair donor properties of the solvent, the radii of host and guest and the differences in solvation dominate the differences in the stability constant (Δlog $K_s$) as well as the relative free energies of binding of TEX>$La^{3+} to Nd^{3+}$ ions to 18-crown-6. The results of this study appear promising for providing the association properties of crown ethers with alkaline earth metals among polar solvents and the less polar or non-polar solvents.

• Bulletin of the Korean Chemical Society
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• v.29 no.2
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• pp.431-437
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• 2008

The solvent effects on the relative free energies of binding of K+ and Na+ ions to 12-crown-4 and Dlog Ks (the difference of stability constant of binding) have been investigated by a Monte Carlo simulation of statistical perturbation theory (SPT) in several solvents. Comparing the relative free energies of binding of K+ and Na+ ions to 12-crown-4, in CH3OH of this study with experimental works, there is a good agreement among the studies. We have reported here the quantitative solvent-polarity relationships (QSPR) studied on the solvent effects the relative free energies of binding of K+ and Na+ ions to 12-crown-4. We noted that DN(donor number) dominates the differences in relative solvation Gibbs free energies of K+ and Na+ ions and DN dominates the negative values in differences in the stability constant (Dlog Ks) as well as the relative free energies of binding of K+ and Na+ ions to 12-crown-4 and p* (Kamlet-Tafts solvatochromic parameters) dominates the positive values in differences in the stability constant (Dlog Ks) as well as the relative free energies of binding of K+ and Na+ ions to 12-crown-4.