• Journal of Korean Society of Transportation
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• v.9 no.2
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• pp.121-126
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• 1991

Wilson made an importent contribution to develop a trip distribution model with the general form of gravity model which is an entropy maximization program. Also Wilson suggested a technique which is called the "iterative balancing method" for soving the model. This te-chnique however is not stable to find solution because it is a heuristic method and sometimes does not converge to the correct solution. In this paper a new solution method using a numerical method for solving the non-linear simultaneous equation system is developed and evaluated in both computers VAX 8700 and PC/AT 286 The result of this method and Wilson's method are compared with each other. Wilson's method resulted in inferior solutions measured by the final norm of residuals.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.369-378
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• 2008

The aim of this paper is to study the stability problem for the pexider type trigonometric functional equation f(x + y) − f(x−y) = 2g(x)h(y), which is related to the d'Alembert, the Wilson, the sine, and the mixed trigonometric functional equations.

• Korean Chemical Engineering Research
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• v.62 no.1
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• pp.53-69
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• 2024

The solubility of Cloxacillin sodium in ethanol, 1-propanol, isopropanol, and acetone solutions was measured at different temperatures. The melting property was also tested by using a differential scanning calorimeter (DSC). Then, the solubility data were fitted using Apelblat equation and λh equation, respectively. The Wilson model and NRTL model were not utilized to correlate the test data, since Cloxacillin sodium will decompose directly after melting. For comparison purposes, the four empirical models, i.e., Apelblat equation, λh equation, Wilson model and NRTL Model, were evaluated by using 1155 solubility curves of 103 solutes tested under different monosolvents and temperatures. The comparison results indicate that the Apelblat equation is superior to the others. Furthermore, a new method (named the calculation method) for determining the Apelblat equation using only three data points was proposed to solve the problem that there may not be enough solute in the determination of solubility. The log-logistic distribution function was used to further capture the trend of the correlation and to make better quantitative comparison between predicted data and the experimental ones for the Apelblat equation determined by different methods (fitting method or calculation method). It is found that the proposed calculation method not only greatly reduces the number of test data points, but also has satisfactory prediction accuracy.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.765-774
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• 2021

In this paper, we solve and investigate the superstability of the p-radical functional equations $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}f(x)g(y),\\f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)f(y),$$ which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebras.

• Analytical Science and Technology
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• v.30 no.6
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• pp.405-410
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• 2017

High energetic materials (HEMs) have been used in fuels, civil engineering and architecture as well as military purposes such as explosives and propellants. The essential process for the development of new energetic compounds is to accurately calculate its detonation performances. The most typical equation for calculating the explosive performance is the Kamlet-Jacobs (K-J) equation. In the K-J equation, the parameter such as the number of moles of gaseous products at the explosion, the average molar mass of gas products, and the explosion heat greatly affect the explosion performance. These depend on the product composition for the detonation reaction. In this study, detonation products of 65 high energetic molecules (HEMs) were calculated from the various rules such as Kamlet-Jacobs, Kistiakowsky-Wilson, modified Kistiakowsky-Wilson, Springall-Roberts rules to calculate more accurate detonation velocity (Dv). In addition, they were applied to five kinds of detonation velocity equations proposed by K-J, Rothstein, Xiong, Stine and Keshavarz. The mean absolute error and root mean square error of HEMs were obtained from experimental and calculated velocity value for each method. The K-J and Xiong equation that is slightly complex showed a lower mean absolute error than the simple Rothstein and Keshavarz equation. When the mod-KW rule was applied to the Xiong equation, the detonation velocities were the most accurate. This study compared the various method of calculating the detonation velocity of HEMs to obtain accurate HEMs performance.

• Journal of the Korean Institute of Gas
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• v.13 no.5
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• pp.20-25
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• 2009

Low explosion limits of flammable liquid mixtures can be calculated with the appropriate use of the fundamental laws of Raoult, Dalton, Le Chatelier and activity coefficient models. In this paper, Raoult's law, van Laar equation and Wilson equation are shown to be applicable for the prediction of the lower explosion limits for ethylacetate+ethanol and ethanol+toluene systems. The calculated values based on Raoult's law were found to be better than those based on van Laar and Wilson equations.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.27 no.1
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• pp.8-13
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• 2015

The objective of this paper is to provide design data of fin-tube heat exchanger which have a large diameter oval tube for dryer application. In this study, the heat transfer and pressure drop performance characteristics of the fin-tube heat exchanger were compared with Dittus-Boelter and a new correlation equation using Wilson plot method. The simulation results based on section by section method were compared with experimental results. These results showed that a new correlation equation using Wilson plot method provided better prediction, about 3 to 12%, than the Dittus-Boelter equation, from the experiment comparison. Also, the pressure drop of simulation results showed much more deviation with the experimental results.

• Earthquakes and Structures
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• v.5 no.5
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• pp.589-605
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• 2013

The effect of dead loads on dynamic responses of a uniform elastic beam subjected to moving loads is examined by means of a governing equation which takes into account initial bending stresses due to dead loads. First, the governing equation of beams which includes the effect of dead loads is briefly presented from the author's paper (1990, 1991, 2010). The effect of dead loads is considered by a strain energy produced by conservative initial stresses caused by the dead loads. Second, the effect of dead loads on dynamical responses produced by moving loads in simply supported beams is confirmed by the results of numerical computations using the Galerkin method and Wilson-${\theta}$ method. It is shown that the dynamical responses by moving loads are decreased remarkably on a heavyweight beam when the effect of dead loads is included. Third, an approximate solution of dynamic deflections including the effect of dead loads for a uniform beam subjected to moving loads is presented in a closed-form for the case without the additional mass due to moving loads. The proposed solution shows a good agreement with results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. Finally it is clarified that the effect of dead loads on elastic uniform beams subjected to moving loads acts on the restraint of the transverse vibration for the both cases without and with the additional mass due to moving loads.

• Earthquakes and Structures
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• v.1 no.4
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• pp.411-425
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• 2010

The effect of dead loads on dynamic responses of uniform elastic beams is examined by means of a governing equation which takes into account initial bending stress due to dead loads. First, the governing equation of beams which includes the effect of dead loads is briefly presented from the author's paper (Takabatake 1990). In the formulation the effect of dead loads is considered by strain energy produced by conservative initial stresses produced by the dead loads. Second, the effect of dead loads on dynamical responses produced by live loads in simply supported beams and clamped beams is confirmed by the results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. It is shown that the dynamical responses, like dynamic deflections and bending moments produced by dynamic live loads, are decreased in a heavyweight beam when the effect of dead loads is included. Third, an approximate solution for dynamic deflections including the effect of dead loads is presented in closed-form. The proposed solution shows good in agreement with results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. Finally, a method reflecting the effect of dead loads for dynamic responses of beams on the magnitude of live loads is presented by an example.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.103-114
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• 2008

In this paper, we investigate the superstability problem for the pexiderized cosine functional equations f(x+y) +f(x−y) = 2g(x)h(y), f(x + y) + g(x − y) = 2f(x)g(y), f(x + y) + g(x − y) = 2g(x)f(y). Consequently, we have generalized the results of stability for the cosine($d^{\prime}Alembert$) and the Wilson functional equations by J. Baker, $P.\;G{\check{a}}vruta$, R. Badora and R. Ger, and G.H. Kim.