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THE STABILITY OF WEAK SOLUTIONS TO AN ANISOTROPIC POLYTROPIC INFILTRATION EQUATION
Zhan, Huashui Korean Mathematical Society 2021 대한수학회지 Vol.58 No.5
This paper considers an anisotropic polytropic infiltration equation with a source term $$u_t={\sum\limits_{i=1}^{N}}{\frac{{\partial}}{{\partial}x_i}}\(a_1(x){\mid}u{\mid}^{{\alpha}_i}{\mid}u_{x_i}{\mid}^{p_i-2}u_{x_i}\)+f(x,t,u)$$, where p<sub>i</sub> > 1, α<sub>i</sub> > 0, a<sub>i</sub>(x) ≥ 0. The existence of weak solution is proved by parabolically regularized method. Based on local integrability $u_{x_i}{\in}W_{loc}^{1,p_i}(\Omega)$, the stability of weak solutions is proved without boundary value condition by the weak characteristic function method. One of the essential characteristics of an anisotropic equation different from an isotropic equation is found originally.
Tang, Jianhong,Zhang, Zhiyan,Yang, Bin,Guo, Yuanmei,Ai, Huashui,Long, Yi,Su, Ying,Cui, Leilei,Zhou, Liyu,Wang, Xiaopeng,Zhang, Hui,Wang, Chengbin,Ren, Jun,Huang, Lusheng,Ding, Nengshui Asian Australasian Association of Animal Productio 2017 Animal Bioscience Vol.30 No.1
Objective: Three genome-wide association studies (GWAS) and a meta-analysis of GWAS were conducted to explore the genetic mechanisms underlying variation in pig teat number. Methods: We performed three GWAS and a meta-analysis for teat number on three pig populations, including a White Duroc${\times}$Erhualian $F_2$ resource population (n = 1,743), a Chinese Erhualian pig population (n = 320) and a Chinese Sutai pig population (n = 383). Results: We detected 24 single nucleotide polymorphisms (SNPs) that surpassed the genome-wide significant level on Sus Scrofa chromosomes (SSC) 1, 7, and 12 in the $F_2$ resource population, corresponding to four loci for pig teat number. We highlighted vertnin (VRTN) and lysine demethylase 6B (KDM6B) as two interesting candidate genes at the loci on SSC7 and SSC12. No significant associated SNPs were identified in the meta-analysis of GWAS. Conclusion: The results verified the complex genetic architecture of pig teat number. The causative variants for teat number may be different in the three populations
Wang, Wenjun,Huang, Lusheng,Chen, Kefei,Gao, Jun,Ren, Jun,Ai, Huashui,Lin, Wanhua Asian Australasian Association of Animal Productio 2002 Animal Bioscience Vol.15 No.10
The polymorphism of insulin-like growth factor-I (IGF-I) in 13 pig breeds (total n=559) was detected by PCR-Hha I- RFLP, and allele A (151 bp and 28 bp) or allele B (116 bp, 35 bp and 28 bp) were observed. In these pig breeds, it was found that European pig breeds carried high frequencies of allele B, while Chinese native pig breeds carried high frequencies of allele A. Meanwhile the role of porcine IGF-I was investigated in 117 Nanchang White pigs and 360 Large Yorkshire pigs. Eight traits about growth and carcass were recorded for analyzing the associations between IGF-I gene polymorphism and performance quantitative traits. In the Nanchang White pigs, those with AA genotype generally had higher birth weight than those with AB genotype (p<0.05), but all these genotypes had no significant effect on the other traits which had been analyzed. In Large Yorkshire pigs, those with BB genotype had higher 2 months and 6 months body weight than those with AA genotype (p<0.05), and had a thicker hind-back-fat thickness and mid-back-thickness than those with AB and BB genotypes (p<0.05). And those with BB genotype were the thinnest in Large Yorkshire. Furthermore, pigs with AA genotype had a lower lean percentage than those with AB and BB genotypes (p<0.01), and the lean percentage of those with BB genotype was the highest. Based on these results, it is possible to make the IGF-I gene locus into the application of marker-assisted selection programmes.