• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.201-211
• /
• 2010

We investigate the number of the nontrivial solutions of the nonlinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the nonlinear biharmonic problem. We prove this result by the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• Korean Journal of Mathematics
• /
• v.17 no.1
• /
• pp.103-112
• /
• 2009

We show the existence of the solutions for the following nonlinear elliptic problem under the Dirichlet boundary condition. To show the existence of the solutions we use the variational formulation.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.281-290
• /
• 2024

We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.

• Clean Technology
• /
• v.11 no.3
• /
• pp.147-152
• /
• 2005

For estblishing the best technique for the micronization of Ibuprofen using supercritical fluids, the solubility should be known. The solubility of Ibuprofen in supercritical carbon dioxide was measured by observing the cloud point. The cloud point was observed using high pressure equipment equipped a variable volume view cell between temperature of 35, 40 and $45^{\circ}C$. The solubility data was correlated by the Peng-Robinson equation of state Solute physical properties, such as critical temperature (Tc), critical pressure (Pc) and acentric factor (${\omega}$) were estimated by the some group contribution method. As pressure was increased, the solubility increased at constant temperature. The retrograde phenomenon by a solute vapor pressure and a density of solvent was observed at the pressure of around 150bar. It was found that $CO_2$ can be used as a supercritical solvent in micronization of ibuprofen by RESS.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.15 no.2
• /
• pp.630-643
• /
• 1991

The hydrodynamic stability equations are formulated for buoyancy-induced flows adjacent to a vertical, planar, isothermal surface in cold pure water. The resulting stability equations, when reduced to ordinary differential equation by a similarity transformation, constitute a two-point boundary-value(eigenvalue) problem, which was numerically solved for various values of the density extremum parameter R=( $T_{m}$ - $T_.inf./) / ( $T_{o}$ - $T_.inf./). These stability equations have been solved using a computer code designed to accurately solve two-point boundary-value problems. The present numerical study includes neutral stability results for the region of the flows corresponding to 0.0.leq. R. leq.0.15, where the outside buoyancy force reversals arise. The results show that a small amount of outside buoyancy force reversal causes the critical Grashof number $G^*/ to increase significantly. A further increase of the outside buoyancy force reversal causes the critical Grashof number to decrease. But the dimensionless frequency parameter $B^*/ at $G^*/ is systematically decreased. When the stability results of the present work are compared to the experimental data, the numerical results agree in a qualitative way with the experimental data.erimental data.

• Journal of the Korean Chemical Society
• /
• v.35 no.5
• /
• pp.487-492
• /
• 1991

$[P+a(b/v)^n]$ = RT / (V - b) Above equation of state had been derived from Roulette theory. Three parameters-a, b, n are estimated from the critical point and the inversion temperature. When it is applied to 52 materials and to the regions of high density such as dense gas and supercritical gas, the results are good.

• Fire Science and Engineering
• /
• v.25 no.3
• /
• pp.113-118
• /
• 2011

The flash point is an important indicator of the flammability of a chemical. The minimum flash point behaviour (MFPB) is exhibited when the flash point of a mixture is below the flash points of the individual components. The identification of this behaviour is critical, because a hazardous situation results from taking the lowest component flash point value as the mixture flash point. In this study, the flash points for the n-butanol + n-decane and n-octane + n-propanol systems which exhibit MFPB, were measured by Tag open-cup apparatus. The experimental data were compared with the alues calculated by the Raoult's law, the van Laar equation and the Wilson equation. The calculated values based on the van Laar and Wilson equations were found to be better than those based on the Raoult's law. It was concluded that the van Laar and Wilson equations were more effective than the Raoult' law at describing the activity coefficients for non-ideal solution such as the n-butanol + n-decane and n-octane + n-propanol systems. The predictive curve of the flash point prediction model based on the Wilson equation described the experimentally-derived data more effectively than was the case when the prediction model was based upon the van Laar equation.

• Proceedings of the KSR Conference
• /
• 2003.05a
• /
• pp.755-761
• /
• 2003

The dynamic analysis of the KTX can predict the dynamic motions which occurred in test drive. In this study an analytical model of the KTX is developed to find the critical speed. The numerical analysis for the nonlinear equation motions of 17 degrees of freedom show the running stability and the critical speed due to the hunting motion of the KTX. Also, the vibration modes of the KTX are calculated using the ADAMS/RAIL software, which show that the critical speed occurs for the yawing modes of the car body and the bogie. Finally, this paper shows that the critical speed of the KTX could be changed with the modifications of the design parameters of wheel conicity and wheel contact point.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2005.11a
• /
• pp.785-788
• /
• 2005

In this paper, the influence of many factors related to the concrete mixture and the weather condition on plastic shrinkage cracking are analyzed through parametric studies using the numerical models introduced in the companion paper. First of all, through a systematic calculation of bleeding, the relationship between the bleeding constants and concrete mixture is proposed on the basis of the experimental data obtained by many researchers. Moreover, an equation, which can directly determine a critical point at which the evaporation and bleeding is balanced, is introduced, and the efficiency of the introduced equation is verified through the correlation study between the obtained results by the introduced equation and those by the rigorous analyses. The introduced equation can effectively be used to predict and to prevent plastic shrinkage cracking without any rigorous analysis and, in advance, to cope with the sudden changes in the concrete mixture and/or weather condition.

• Journal of the Korean Magnetics Society
• /
• v.20 no.2
• /
• pp.75-82
• /
• 2010

A recent progress on the prediction of the thermal stability of a nanostructured exchange-coupled trilayer is reviewed. An analytical/numerical combined method is used to calculate its magnetic energy barrier and hence the thermal stability parameter. An important feature of the method is the use of an analytical equation for the total energy that contains the magnetostatic fields. Under an assumption of the single domain state, the effective values of all the magnetostatic fields can be obtained by averaging their nonuniform values over the entire magnetic volume. In an equilibrium state, however, it is not easy to calculate the magnetostatic fields at the saddle point due to the absence of suitable methods of the accessing its magnetic configuration. This difficulty is overcome with the use of equations that link the magnetostatic fields at the saddle point and critical fields. Since the critical fields can readily be obtained by micromagnetic simulation, the present method should provide accurate results for the thermal stability of a nanostructured exchange-coupled trilayer.