We present some necessary and/or sufficient conditions for the positivity problem of three-term recurrence sequences. As applications we show the positivity of diagonal Taylor coefficients of some rational functions in a unified approach. We also establish a criterion for the positivity and log-convexity of such sequences.

We investigate coordination numbers of the cubic lattices with emphases on their analytic behaviors, including the total positivity of the coordination matrices, the distribution of zeros of the coordination polynomials, the asymptotic normality of the coefficients of the coordination polynomials, the logconcavity and the log-convexity of the coordination numbers.

Crohn's disease (CD) is a chronic inflammatory illness of the digestive system with unknown etiology, and its incidence is increasing worldwide. However, there are currently no effective treatments or medications available for individuals with CD. Therefore, novel therapeutic strategies are urgently needed. The bioactive compounds and targets associated with compounds of Qinghua Xiaoyong Formula (QHXYF) were examined using The Traditional Chinese Medicine Systems Pharmacology database, and 5 disease target databases were also used to identify CD-related disease targets. A total of 166 overlapping targets were identified from QHXYF-related and CD-related disease targets and they were found to be enriched in oxidative stress-related pathways and the PI3K/AKT signaling pathway. Molecular docking was then used to predict how the bioactive compounds would bind to the hub targets. It was found that quercetin could be the core bioactive compound and had good binding affinity to the top 5 hub targets. Finally, animal experiments were performed to further validate the findings, and the results revealed that QHXYF or quercetin inhibited 2,4,6-trinitrobenzenesulfonic acid-induced inflammation and oxidative stress processes by inhibiting the PI3K/AKT pathway, thereby improving CD symptoms. These findings suggest that QHXYF and quercetin may be potential novel treatments for CD.

No abstract