Geometrically Convex Function and Estimation of Remainder Terms in Taylor Series Expansion of Some Functions

In this paper, two integral inequalities of geometrically convex functions are proved

Similar but Not Identical Resuscitation Trajectories of the Soil Microbial Community Based on Either DNA or RNA after Flooding

Both drought and flooding are unfavorable for soil microorganisms, but nevertheless, are highly relevant to the extreme weather events that have been predicted to increase in the future. The switch of soil water status from drought to flooding can happen rapidly and microbial activity might be either stimulated or further inhibited, but we have insufficient understanding of the underlying microbial processes. Here, we tracked the changes in soil bacterial and fungal abundance and their community structures, assaying the total (DNA-based) and potentially active (RNA-based) communities in response to abrupt flooding of dry soil. Also, rates of soil respiration and enzyme activity were measured after flooding. Results showed that the bacterial community was found to be more responsive than the fungal community to flooding. The bacterial community responses were clearly classified into three distinct patterns in which the intermediate pattern displayed highly phylogenetic clustering. A transient flourish of Bacilli which belongs to Firmicutes was detected at 8–48 h of flooding, suggesting its potential importance in the microbial assemblage and subsequent ecosystem functioning. Finally, the accumulative amount of CO2 released was more closely related than enzyme activity to the change in structure of the bacterial community after flooding. In conclusion, these findings extended our understanding of the underlying soil microbial processes following abrupt water condition changes

Nlrp9b inflammasome restricts rotavirus infection in intestinal epithelial cells

Rotavirus, a leading cause of severe gastroenteritis and diarrhoea in young children, accounts for around 215,000 deaths annually worldwide. Rotavirus specifically infects the intestinal epithelial cells in the host small intestine and has evolved strategies to antagonize interferon and NF-κB signalling, raising the question as to whether other host factors participate in antiviral responses in intestinal mucosa. The mechanism by which enteric viruses are sensed and restricted in vivo, especially by NOD-like receptor (NLR) inflammasomes, is largely unknown. Here we uncover and mechanistically characterize the NLR Nlrp9b that is specifically expressed in intestinal epithelial cells and restricts rotavirus infection. Our data show that, via RNA helicase Dhx9, Nlrp9b recognizes short double-stranded RNA stretches and forms inflammasome complexes with the adaptor proteins Asc and caspase-1 to promote the maturation of interleukin (Il)-18 and gasdermin D (Gsdmd)-induced pyroptosis. Conditional depletion of Nlrp9b or other inflammasome components in the intestine in vivo resulted in enhanced susceptibility of mice to rotavirus replication. Our study highlights an important innate immune signalling pathway that functions in intestinal epithelial cells and may present useful targets in the modulation of host defences against viral pathogens