• 대한수학회지
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• 제56권1호
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• pp.91-111
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• 2019

We give a direct proof of the sharp two-sided estimates, recently established in [4, 9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1,1}$ open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be $C^{1,{\theta}}$ for some ${\theta}{\in}({\alpha}/2,1]$.

• Asian Pacific Journal of Cancer Prevention
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• 제17권5호
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• pp.2565-2571
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• 2016

A cross-sectional survey was conducted among 730 participants from 4 rural districts of Nakhon Ratchasima province, Thailand, with a reported high incidence of liver fluke infection. This study was aimed to examine and evaluate the nutritional status in relation to Opisthorchis viverrini infection. Participants were purposive selected from Chum Phuang, Mueang Yang, Bua Yai, and Kaeng Sanam Nang districts. Stool samples were prepared by Kato Katz technique and then assessed by microscopy. Anthropometry was evaluated according to the body mass index from weight and height. Descriptive statistics and Spearman rank correlation coefficients were used to evaluate the association between the nutritional status and O. viverrini infection. Of 1.64% infected with O. viverrini the highest proportions were found in age groups ${\geq}61$ and 41-50 years old, Mueang Yang district. The majorities of participants had normal weight (32.2%), followed by class II obesity (28.1 %), class I obesity (21.8%), underweight (10.3%), and class III obesity (8.63%). Nutritional status with class II obesity (rS=0.639, p<0.01) and class I obesity (rS=0.582, p<0.05), had moderately statistical significant correlations with O. viverrini infection. Meanwhile, normal weight (rS=0.437, p<0.05) and class III obesity (rS=0.384, p<0.05) demonstrated lower statistical significance. These findings raise the possibility that infection with O. viverrini may contribute to fat deposition and thereby have long-term consequences on human health. Further studies are needed to better understand whether O. viverrini contributes directly to fat deposition and possible mechanisms.