Consider submanifolds in the nested space. For a compact pseudoumbilical submanifold with parallel mean curvature vector of a Riemannian submanifold with constant curvature immersed in a quasi-constant curvature Riemannian manifold, two sufficient conditions are given to let the pseudo-umbilical submanifold become a totally umbilical submanifold.
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An initial entire graph with bounded second fundamental form in Rn+1 over some hyperplane is evolving under a general flow defined in the paper. For an additionally suitable condition in the main theorem, we obtain gradient and curvature estimates, leading to long-time existence of the flow, and convergence to an entire graph in the limit.
The study aimed to compare Mspl polymorphisms in the 3rd intron of the porcine gene encoding the pituitary-1 transcription factor (Pit-1, renamed as POU1F1) among 5 breeds and to determine the associations between its genotypes and growth performance in a commercial pig population by using the PCR-RFLP technique. Significant differences in genotypie and allelic frequencies were found between the meat-type and fat-type breeds (P < 0.05), and between miniature pigs and others (P < 0.05). No breed deviated from the Hardy-Weinberg equilibrium (verified by chi-square test). The general linear model analysis revealed that higher body weight on day 180 (BW180) and average daily gain (ADG) were significantly associated with POU1F1 DD genotype (P < 0.05). The differences in BW180 and ADG between DD pigs and both CD and CC pigs were significant (P < 0.05), and the DD pigs had a significantly higher body weight on day 45 (BW45) and on day 70 (BW70) than CC pigs (P < 0.05). All measured growth traits, except for body weight at birth (BWB), showed higher values in DD pigs. The D allele had a favorable positive effect on growth traits. Thus POU1F1 is a potential major gene or marker for growth traits.
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