• 대한교통학회지
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• 제9권2호
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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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• 제16권3호
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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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• 제62권1호
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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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• 제29권4호
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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.

• 분석과학
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• 제30권6호
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• pp.405-410
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• 2017

고 에너지 물질은 폭약이나 로켓의 추진체와 같은 군사적 목적뿐만 아니라 연료, 토목 및 건축 등의 민간 분야에도 사용되고 있다. 새로운 고에너지 물질의 개발을 위해 필수적인 단계는 물질의 폭발성능을 정확하게 계산하는 것이다. 여러 수식들 중에서 폭발 성능을 계산하는데 가장 대표적인 수식은 Kamlet-Jacobs (K-J) 식 이다. K-J 식에서는 폭발 시 기체 생성물의 몰수와 이들 기체의 평균 분자량, 그리고 폭발열 과 같은 인자가 폭발 성능에 크게 영향을 미치고, 이것들은 폭발반응에서 생성된 생성물 조성에 좌우되게 된다. 본 연구에서는 4가지 화학 양론적 규칙(Kamlet-Jacobs, Kistiakowsky-Wilson, modified Kistiakowsky-Wilson, Springall-Roberts 규칙)을 통해 65종 고에너지물질의 폭발 생성물 조성을 계산하였고, 이를 K-J, Rothstein, Xiong, Stine, Keshavarz등이 제안한 폭발속도식에 적용하였다. 각 계산된 방법별로 실험값에 대한 평균절대오차와 평균제곱근오차를 얻었다. 다소 복잡한 K-J와 Xiong식은 간단한 Keshavarz 식과 Rothstein식보다 더 낮은 평균절대오차를 나타내었다. 또한 mod-KW규칙으로 생성물을 계산하여 Xiong의 식에 적용하였을 때, 폭발속도들이 가장 정확했다. 이 연구는 고에너지물질의 정확한 성능을 얻기 위하여 폭발속도를 계산하는 다양한 방법을 비교하였다.

• 한국가스학회지
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• 제13권5호
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• pp.20-25
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• 2009

혼합물의 폭발하한계는 Raoult의 법칙, Dalton의 법칙, Le Chatelier 법칙 그리고 활동도계수 모델식을 이용하여 예측될 수 있다. 본 연구에서는 ethylacetate-ethanol 계와 ethanol+toluene 계의 폭발하한계를 예측하기 위해 Raoult의 법칙 그리고 활동도계수 모델식인 van Laar 식과 Wilson 식을 이용하였다. 계산값과 문헌값을 비교한 결과, Raoult의 법칙에 의한 계산값이 활동도 모델식에 의한 계산값 보다 모사성이 뛰어남을 확인하였다.

• 설비공학논문집
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• 제27권1호
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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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• 제5권5호
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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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• 제1권4호
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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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• 제16권1호
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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.