In this paper, we investigate some kind of Dynkin game under $g$-expectation induced by backward stochastic differential equation (shortly for BSDE). We define the lower and upper value functions $\underline{V}_t=ess\sup\limits_{\tau\in{\mathcal{T}_t}} ess\inf\limits_{\sigma\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$ and $\overline{V}_t=ess\inf\limits_{\sigma\in{\mathcal{T}_t}}ess\sup\limits_{\tau\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$, respectively. Under some regular assumptions, a pair of saddle point is obtained and the value function of Dynkin game $V(t)=\underline{V}_t=\overline{V}_t$ follows. Furthermore, the constrained case of Dynkin game is also considered.

Pulmonary arterial hypertension (PAH) is a pathophysiological condition characterized by pulmonary vascular remodeling and elevated vascular resistance, which may ultimately result in cardiovascular failure and sudden cardiac death. In recent years, the occurrence of pregnancy complicated by pulmonary arterial hypertension has witnessed a notable increase, whereas the incidence of postpartum pulmonary arterial hypertension is comparatively rare. This study presents a case involving a 39-year-old female who exhibited severe pulmonary arterial hypertension, finally diagnosed as idiopathic pulmonary arterial hypertension, within 2 days postpartum. The diagnosis was made following a thorough clinical examination. This case report emphasizes the significance of promptly initiating targeted therapy as an initial step in effectively managing patients and the criticality of conducting a thorough assessment of multidisciplinary collaboration in postpartum management. Furthermore, the report has the potential to enhance awareness and education regarding the future management of similarly intricate conditions.

Research has shown that the consumption of herbal teas is linked with positive effects on the regulation of postprandial blood glucose level. In this study, a comparative analysis of aqueous and ethanol extractions is performed on four herbal teas (Mallotus, Cyclocarya, Rubus, Vine) to evaluate their phytochemical profiles and functional activities. Investigations of phytochemical contents, antioxidant activities, α-glucosidase inhibitory activities and chemical compositions are carried out through colorimetric analyses and UPLC-Q-Orbitrap HRMS/MS, respectively. Results showed that among the studied herbal teas, Vine exhibited the highest glucose re-gulating abilities under both aqueous and ethanol extractions. Overall, ethanol extracted samples yielded higher phytochemicals content, but the compositions of the phytochemicals varied. Meanwhile, aqueous extracts showed surprisingly strong antioxidant activities and comparable α-glucosidase inhibitory activities with ethanol extracts. Phytochemicals contents presented a positive correlation with antioxidant activities and α-glucosidase inhibitory activities. Nevertheless, antioxidant activities displayed a weak positive correlation with α-glucosidase inhibitory activities. Results from this study provided evidence that aqueous extracts from herbal teas possessed valuable phytochemicals composition for antioxidants and the hyperglycemic populations, and are promising candidates for potential applications as functional ingredients with health promoting effects and as natural additives to boost the nutritional value of herbal food products.