• 한국화재소방학회논문지
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• 제21권4호
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• pp.32-37
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• 2007

인화점의 정보를 확보하는 것은 화재 및 폭발의 예방을 위해 대단히 중요하다. 본 연구에서는 2-propanol+acetic acid 계와 2-propanol+n-propionic acid 계의 하부 인화점을 클리브랜드 개방식 장치를 이용하여 측정하였다. 실험값은 Raoult의 법칙, Wilson 식과 NRTL 식에 의해 계산된 값과 비교하였다. 그 결과, Wilson 식과 NRTL 식에 의한 예측값이 Raoult의 법칙에 의한 예측값 보다 실험값에 더욱 근접하였다. 또한, NRTL 식의 실험값에 대한 모사성이 Wilson 식의 그것 보다 우수하였다.

• 한국안전학회지
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• 제22권2호
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• pp.47-52
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• 2007

The flash points and the fire points for the m-xylene+n-propionic acid and n-butanol+n-pentanol systems were measured by using Tag open-cup apparatus(AS1M D 1310-86). The experimental flash points of two binary systems were compared with the values calculated by the Raoult's law, Van Laar equation and Wilson equation. The calculated values based on the Raoult's law on m-xylene+n-propionic acid system were found to be better than those based on Van Laar and Wilson equations. The calculated values based on Van Laar equation on n-butanol+n-pentanol system were found to be better than those based on the Raoult's law and Wilson equation. The the fire points for the m-xylene+n-propionic acid system were about $7{\sim}8^{\circ}C$ above the flash points. In the case of n-butanol+n-pentanol system, the flash points and the fire points had been found to be identical.

• 한국화재소방학회논문지
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• 제25권3호
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• pp.113-118
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• 2011

인화점은 화학물질의 연소성의 중요한 지표이다. 최소인화점 현상은 혼합물의 인화점이 개별 성분의 인화점보다 작은 값을 보이는 현상을 의미한다. 이 현상에 대한 정보를 인지하는 것은 매우 중요하다. 혼합물의 특정 조성에서 매우 낮은 인화점을 가질 때 위험한 상황이 발생할 수 있기 때문이다. 본 연구에서는 최소인화점 현상을 보이는 n-butanol + n-decane 계와 n-octane + n-propanol 계의 인화점을 Tag 개방식장치 (ASTM D1310-86)를 이용하여 측정하였다. 실험값은 Raoult의 법칙, van Laar 모델식과 Wilson 모델식에 의해 계산된 값들과 비교되었다. 그 결과 van Laar 모델식과 Wilson 모델식에 의한 예측값이 Rauolt의 법칙에 의한 예측값보다 실험값에 더욱 근접 하였다. 이는 n-butanol + n-decane 계와 n-octane + n-propanol 계와 같은 비이상 용액의 활동도 계수값을, van Laar 및 Wilson 모델식이 Raoult의 법칙보다 정확하게 계산하기 때문이다. 또한 Wilson 모델식의 실험값에 대한 모사성이 van Laar 모델식의 그것보다 우수하였다.

• Journal of the Korean Wood Science and Technology
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• 제37권2호
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• pp.128-136
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• 2009

Curved glued laminated timber (glulam) is rapidly coming into the domestic modern timber frame buildings and predominant in building construction. The radial stress is frequently occurred in curved beams and is a critical design parameter in curved glulam. Three models, Wilson equation, Exact solution and Approximation equation were introduced to determine the radial stress of curved glulam under pure bending condition. It is obvious that radial stress distribution between small radius and large radius was different due to slight change of neutral plane location to center line. If the beam design with extremely small radius, it should be considered to determine the exact location of maximum radial stress. The current standard KSF 3021 was reviewed and would be considered some adjustment determining the optimum radius in curved glulam. Current design principle is that the stress factor is given by the curvature term only in constant depth of the beam, but like tapered or small radius of beams, the stress factor by Wilson equation was underestimated. So current design formula should be considered to improvement for characterizing the radial stress factor under pure bending condition.

• 대한수학회논문집
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• 제39권3호
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• pp.785-802
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• 2024

Given M a monoid with a neutral element e. We show that the solutions of d'Alembert's functional equation for n × n matrices Φ(pr, qs) + Φ(sp, rq) = 2Φ(r, s)Φ(p, q), p, q, r, s ∈ M are abelian. Furthermore, we prove under additional assumption that the solutions of the n-dimensional mixed vector-matrix Wilson's functional equation $$\begin{cases}f(pr, qs) + f(sp, rq) = 2\phi(r, s)f(p, q),\\Φ(p, q) = \phi(q, p),{\quad}p, q, r, s {\in} M\end{cases}$$ are abelian. As an application we solve the first functional equation on groups for the particular case of n = 3.

• International Journal of Safety
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• 제10권1호
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• pp.5-9
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• 2011

Two popular activity coefficient models, Wilson and NRTL equations have been used to correlate the published flash point data on the n-propanol + propionic acid and n-butanol + propionic acid systems through the optimization method. The results of these correlation were compared with the results calculated by Raoult's law. The optimization method were found to be better than those based on the Raoult's law. The optimization method based on the Wilson equation described the published data more effectively than was the case when the optimization method was based upon the NRTL equation.

• 대한수학회보
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• 제53권4호
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• 한국화재소방학회논문지
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• 제17권2호
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• pp.50-55
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• 2003

The lower flash points for the binary system, n-butanol+n-decane, were measured by Pensky-Martens closed cup tester. The experimental results showed the minimum in the flash point versus composition curve. The experimental data were compared with the values calculated by the reduced model under an ideal solution assumption and the flash point-prediction models based on the Van Laar and Wilson equations. The predictive curve based upon the reduced model deviated form the experimental data for this system. The experimental results were in good agreement with the predictive curves, which use the Van Laar and Wilson equations to estimate activity coefficients. However, the predictive curve of the flash point prediction model based on the Willson equation described the experimentally-derived data more effectively than that of the flash point prediction model based on the Van Laar equation.

• 대한수학회논문집
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• 제35권3호
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• pp.711-722
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• 2020

Given a semigroup S generated by its squares equipped with an involutive automorphism 𝝈 and a multiplicative function 𝜇 : S → ℂ such that 𝜇(x𝜎(x)) = 1 for all x ∈ S, we determine the complex-valued solutions of the following functional equations f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S and f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(y)g(x), x, y ∈ S.

• 대한수학회논문집
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• 제38권4호
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• pp.1063-1074
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• 2023

Let S be a semigroup. We determine the complex-valued solutions of the following functional equation f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S, where 𝜎 : S → S is an automorphism, and 𝜇 : S → ℂ is a multiplicative function such that 𝜇(x𝜎(x)) = 1 for all x ∈ S.