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In this thesis, I study the connections between extremal eigenvalue problems and the existence of extremal function for the $generalized$ Moser-Trudinger type functional. Using the method of blow-up analysis, we prove that if $(M, g)$ is a closed Riemann surface which is not diffeomorphic to the sphere, then the generalized Moser-Trudinger type functional could attain its minimum by a smooth function. This result implies the first extremal eigenvalue of $M$ in the conformal class of $g$ is greater than $8\pi$. We also consider surface with boundary. Under the Dirichlet boundary condition, we prove the existence of extremal function for the generalized Moser-Trudinger type functional. Under the Neumann boundary condition, if the generalized Moser-Trudinger type functional has no minimizer, we give a specific lower bound of the functional.

Up to now, facile and pollution-free routes for catalyst preparation are in high demand. In this study, a green and cost-effective strategy was successfully developed to construct platinum/graphene aerogel (Pt/GA) nanocomposites by the co-reduction of graphene oxides (GO) and chloroplatinic acid (H2PtCl6·6H2O) with the assists of γ-ray irradiation in the absence of any other reductants. Characterization studies indicated that the energy of γ-ray irradiation and the hole scavenger isopropanol (IPA) played a vital role in forming small Pt nanoparticles with uniform size of ∼3 nm on the surface of graphene aerogel (GA). Furthermore, Pt/GA synthesized with a mass ratio of 2:1 (Pt/GA-2) exhibited a lowest activation energy value and outstanding catalytic properties for the reduction of 4-nitrophenol (4-NP). The excellent catalytic and cycling performance suggest that Pt/GA-2 catalyst has a promising prospect for the reduction of nitroaromatic compounds in wastewater treatment and other industrial applications.

The pharmacodynamic effect of longan leaves was attributed to various components, especially the flavonoids. In this paper, a new strategy of quantitative analysis of multicomponents by a single marker (QAMS) method was first established to synchronously determine 5 components (ethyl gallate (C1), astragalin (C2), quercetin (C3), luteolin (C4), and kaempferol (C5)) in Dimocarpus longan by ultra-performance liquid chromatography (UPLC) and high-performance liquid chromatography (HPLC). Quercetin (C3) was chosen as the internal reference. Relative correction factors (RCFs, ƒs/i) of the other 4 components were calculated by two correction methods (multipoint correction and slope correction) to effectuate QAMS. At the same time, the difference between the results measured by the QAMS and external standard methods was compared to verify the accuracy of QAMS. Within the linear range, the results showed that all ƒs/i values were obtained with good durability under diverse chromatographic conditions (RSD Dimocarpus longan collected from 10 producing areas by different chromatographic systems and quantitative methods were significantly correlated (Pearson’s r > 97.0%). The applicability and feasibility of the QAMS method established in this study were evaluated to be favorable for quality control of the leaves of Dimocarpus longan. As a new model of quality control, it can provide one more choice of multicomponent quality-control method in the absence of standard substances or instruments.

Background: Sepiapterin reductase (SPR) is an important regulator of the biosynthesis of tetrahydrobiopterin (BH(4)), which has been shown to be a promoter of different kinds of tumors. This study aims to investigate the role of SPR in breast cancer and to explore its molecular mechanism. Methods: SPR expressions in breast cancer tissues with different pathological stages were compared with the corresponding pericarcinomatous tissues and were analyzed using immunohistochemical staining and western blot. SPR knockdown was performed in MDA-MB-231 and MDA-MB-468 triple-negative breast cancer cells using specific siRNAs. Quantitative real-time PCR and western blot were used to determine the efficiency of the SPR knockdown. The intracellular BH(4) levels were measured using HPLC, and the intracellular ROS levels were measured using an ROS detection kit. Clone formation and cell proliferation assays were used to study the effect of the SPR knockdown on cell proliferation. Annexin V/PI double staining, cell mitochondria isolation, and western blot were performed to study the effect of the SPR knockdown on cell apoptosis. ROS scavenger NAC was used to inhibit increased ROS caused by the SPR knockdown. Results: SPR is highly expressed in breast cancer tissues compared with the pericarcinomatous tissues and positively correlated with the pathological stages. The knockdown of SPR causes decreased intracellular BH(4) and increased intracellular ROS and inhibits the proliferation of MDA-MB-231 and MDA-MB-468 cells. The knockdown of SPR also induces mitochondrial pathway-mediated apoptosis. NAC suppresses the SPR knockdown-caused cell apoptosis and cell death. Conclusions: SPR promotes the proliferation of breast cancer cells. The knockdown of SPR suppresses the proliferation of breast cancer cells by inducing ROS-mediated apoptosis.