• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1463-1481
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• 2018

Let $X=\{X_t\}_{t{\geq}0}$ be a $L{\acute{e}}vy$ process in ${\mathbb{R}}^d$ and ${\Omega}$ be an open subset of ${\mathbb{R}}^d$ with finite Lebesgue measure. The quantity $H_{\Omega}(t)={\int_{\Omega}}{\mathbb{P}}^x(X_t{\in}{\Omega})$ dx is called the heat content. In this article we consider its generalized version $H^{\mu}_g(t)={\int_{\mathbb{R}^d}}{\mathbb{E}^xg(X_t){\mu}(dx)$, where g is a bounded function and ${\mu}$ a finite Borel measure. We study its asymptotic behaviour at zero for various classes of $L{\acute{e}}vy$ processes.

• Korean Journal of Agricultural Science
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• v.46 no.4
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• pp.941-953
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• 2019

Biodiesels are being explored as a clean energy alternative to regular diesel, which causes pollution. In this study, the optimum conditions for producing biodiesel (BD) by combining beef tallow, an animal waste resource with a high saturated fatty acid content, and corn oil, a vegetable oil with a high unsaturated fatty acid content, were investigated, and the fuel properties were analyzed. Furthermore, Multivariate Analysis of Variance (MANOVA) was used to verify the optimum conditions for producing biodiesel. The influences of control factors, such as the oil blend ratio and methanol to oil molar ratio, on the fatty acid methyl ester and biodiesel production yield were investigated. As a result, the optimum condition for producing blended biodiesel was verified to be tallow to corn oil blend ratio of 7 : 3 (TACO7) and a methanol to oil molar ratio of 14 : 1. Moreover, the interaction between the oil blend ratio and the methanol to oil molar ratio has the most crucial effects on the production of oil blended biodiesel. In conclusion, the analysis results of the fuel properties of TACO7 BD satisfied the BD quality standard, and thus, the viability of BD blended with waste tallow as fuel was verified.