• 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.

• 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.

• 한국화재소방학회논문지
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• 제22권4호
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• pp.65-69
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• 2008

인화점의 정보를 확보하는 것은 화재 및 폭발의 예방을 위해 대단히 중요하다. 본 연구에서는 n-propanol+formic acid 계의 하부 인화점을 Penskey-Martens 밀폐식 장치를 이용하여 측정하였다. 이성분계 혼합물은 최소 인화점 현상(MFPB)을 보였다. 실험값은 Raoult의 법칙과 최적화 기법에 의해 추산된 값과 비교하였다. 그 결과, 최접화 기법에 의한 추산값이 Raoult의 법칙에 의한 추산값 보다 실험값에 더욱 근접하였다.

• 한국가스학회지
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• 제16권5호
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• pp.41-46
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• 2012

인화점은 공기 속 가연성 증기의 농도가 연소하한계(lower flammability limit)에 도달할 때의 최저 온도이며, 산업현장에서 사용하는 물질들의 화재와 폭발의 위험성을 결정하는 중요한 물성치이다. 단일 성분의 인화점 정보는 여러 문헌에서 얻을 수 있으나, 이성분계 혼합물의 인화점은 충분히 제공되어 있지 않다. 본 연구에서는 tert-pentanol+n-decanel 계의 인화점을 Tag 개방식 장치를 이용하여 측정하였다. 실험값은 Raoult의 법칙과, Wilson 식과 NRTL 식을 활용한 최적화 기법에 의해 계산된 값들과 비교되었다. 최적화 기법에 의한 계산값이 Rauolt의 법칙에 의한 계산값 보다 실험값에 더욱 근접하였다.

• 충청수학회지
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• 제35권4호
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• pp.315-327
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• 2022

In this paper, we investigate the transferred superstability for the p-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from the p-radical functional equations: $$f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)g(y),\;\\f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)h(y),$$ where p is an odd positive integer, λ is a positive real number, and f is a complex valued function. Furthermore, the results are extended to Banach algebras. Therefore, the obtained result will be forced to the pre-results(p=1) for this type's equations, and will serve as a sample to apply it to the extension of the other known equations.

• 대한화학회지
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• 제53권6호
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• pp.663-670
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• 2009

논랜덤 혼합의 2-성분 격자용액에서 특정상호작용을 갖는 경우의 수에 대한 분포를 난수 모의실험을 통하여 구하였다. 이 분포로부터 2-성분격자용액의 과잉깁스에너지 $G^E$에 대한 근사식을 유도하였다. 이 식을 사용하여 15개의 2-성분용액에 대한 일정압력에서의 액체-증기 상평형 계산을 하였고 Wilson식, Van Laar식, Redlich-Kister식의 계산 결과와 비교하여 보았다.

• 한국안전학회지
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• 제31권6호
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• pp.39-44
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• 2016

Suitable design and operation of distillation process is very dependent on vapor-liquid equilibrium calculation. The usual calculation method is use binary interaction parameter. Flash points of n-propanol+n-butanol and 2-butanol+n-butanol were measured by Seta-flash closed cup tester. Experimental Flash points were compared with those calculated by the method based on Raoult's law and the optimization method using Wilson equation. The binary interaction parameters obtained by the optimization method are then used to calculate the bubble points of n-propanol+n-butanol and 2-butanol+n-butanol.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 춘계학술대회논문집; 부산수산대학교, 10 May 1996
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• pp.80-85
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• 1996

Predictions of vibration induced by subway operation has been studied through comparison between the measurement values and the estimated values which proposed by other scientists to determine the adequacy of each equation. It was found from this study that the Wilson's prediction equation gives the best overall approximation value although the peak frequency band lies somewhat higher than that obtained from measurement.

• 대한화학회지
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• 제57권5호
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• pp.540-546
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• 2013

van der Waals식의 자유부피항, 강체구형입자에 대한 Carnahan-Starling식, 용액의 논랜덤 혼합을 고려한 Wilson식, NRTL식과 본 연구자의 식등을 사용하여 기체에 대한 여러 개의 새로운 상태방정식을 만들었다. 이 식들을 이용하여 순수 기체에 대한 압축인자를 계산하였고 이를 실험적인 Nelson-Obert 압축인자도표와 비교하였다. 분자의 논랜덤 분포를 고려하여 유도된 상태방정식들이 랜덤분포를 가정한 상태방정식보다 더 좋은 결과가 나왔다. 이를 통하여 분자의 논랜덤 분포가 상태방정식에 상당한 영향을 미친다는 것을 알 수 있다.