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In this paper, we focus on a general n-dimension system of k-Hessian equations. By introducing some new suitable growth conditions, the existence results of radial k-admissible solutions of the k-Hessian system are obtained. Our approach is largely based on the well-known fixed-point theorem. [ABSTRACT FROM AUTHOR]

Objective: We want to investigate the effect of aquaporin-4 (AQP4) on cerebral edema induced by ischemic stroke in rats and explore whether inhibiting the expression of AQP4 through acetazolamide (AZA) could attenuate brain edema and protect cerebral function. Methods: The Sprague Dawley (SD) rats were randomly divided into four groups: sham + saline group, sham + AZA group, AZA intervention group, and nonintervention group. Each group was divided into five subgroups according to the time of cerebral ischemia (6 h, 1 day, 3 days, 5 days, and 7 days). The model of cerebral infarction in rats was adopted by means of the bilateral carotid arteries ligation (2-VO) method. The rats in intervention group were given intraperitoneal injection of AZA (35 mg/kg/day). Hematoxylin–eosin staining was performed for pathological analysis of the infarcted area. The brain water content was calculated to evaluate the degree of brain edema. The messenger RNA (mRNA) and protein expressions of AQP4 in the brain were measured by quantitative real-time polymerase chain reaction and immunohistochemistry, respectively. Results: Significant cerebral pathological damages were found in ischemic stroke rats. The brain water content, protein, and mRNA expression of AQP4 of the intervention and nonintervention groups were markedly higher than those of the sham groups. By contrast, AZA administration reduced the brain water content, whereas improved cerebral dysfunction was induced by ischemic stroke. Moreover, AZA obviously reduced the protein and mRNA expression of AQP4 after ischemic stroke in rats' brains. Conclusions: The expression of AQP4 was closely related to cerebral edema induced by ischemic stroke. Decreasing the expression of AQP4 mRNA by AZA administration can effectively relieve cerebral edema and decrease cerebral pathological damage. [ABSTRACT FROM AUTHOR]