In this paper, we generalize some integral inequalities to more general situations, and the inequalities of Pachpatte type are corollaries of our's. We establish bounds on the solutions, and we show the usefulness of our results in investigating the asymptotic behavior and the stability on the solutions of integral equations, differential equations and integrodifferential equations with time delay.

Background The 2019 Coronavirus (COVID-19) pandemic poses a huge threat internationally; however, the role of the host immune system in the pathogenesis of COVID-19 is not well understood. Methods Cytokine and chemokine levels and characterisation of immune cell subsets from 20 COVID-19 cases after hospital admission (17 critically ill and 3 severe patients) and 16 convalescent patients were determined using a multiplex immunoassay and flow cytometry, respectively. Results IP-10, MCP-1, MIG, IL-6, and IL-10 levels were significantly higher in acute severe/critically ill patients with COVID-19, whereas were normal in patients who had reached convalescence. CD8+ T cells in severe and critically ill COVID-19 patients expressed high levels of cytotoxic granules (granzyme B and perforin)and was hyperactivated as evidenced by the high proportions of CD38. Furthermore, the cytotoxic potential of natural killer (NK) cells, and the frequencies of myeloid dendritic cells and plasmacytoid dendritic cells was reduced in patients with severe and critical COVID-19; however, these dysregulations were found to be restored in convalescent phases. Conclusion Thus, elicitation of the hyperactive cytokine-mediated inflammatory response, dysregulation of CD8+ T and NK cells, and deficiency of host myeloid and plasmacytoid DCs, may contribute to COVID-19 pathogenesis and provide insights into potential therapeutic targets and strategies.

A set of eight geochemical standard reference samples of stream sediments was prepared. The original purpose was to use these samples as primary standards for the data quality monitoring of a nation‐wide regional geochemical survey program in China. But their use has been soon extended to other fields. Forty‐one laboratories in China have joined in a collaborative venture to analyse these samples, using a variety of analytical procedures. Recommended values for over 50 trace and minor elements were derived by a method of repetitive elimination of outliers and calculation of central “tendency” from several central values.

The objective of this paper is to study some dynamic integral inequalities on time scales, which provide explicit bounds on unknown functions. Our results include many known ones in the literature and can be used as tools in the study of qualitative theory of certain classes of dynamic equations with mixed nonlinearities on time scales. MSC: Primary 26D10; 26D15; secondary 34C11; 34N05