19 research outputs found

    The Pogorelov estimates for degenerate curvature equations

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    We establish the Pogorelov type estimates for degenerate prescribed k-curvature equations as well as k-Hessian equations. Furthermore,we investigate the interior C1,1 regularity of the solutions for Dirichlet problems. These techniques also enable us to improve the existence theorem for an asymptotic Plateau type problem in hyperbolic space

    A geometric flow on noncompact affine Riemannian manifolds

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    In this paper, we obtain the existence criteria for a geometic flow on noncompact affine Riemannian manifolds. Our results can be regarded as a real version of Lee-Tam [19]. As an application, we prove that a complete noncompact Hessian manifold with nonnegative Hessian sectional curvature and bounded geometry is diffeomorphic to Rn\mathbb{R}^n if its tangent bundle has maximal volume growth.Comment: arXiv admin note: text overlap with arXiv:math/0504422, arXiv:1708.00141 by other author

    SECOND ORDER ESTIMATES FOR HESSIAN TYPE FULLY NONLINEAR ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS

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    Abstract. We derive a priori estimates for second order derivatives of solutions to a wide calss of fully nonlinear elliptic equations on Riemannian manifolds. The equations we consider naturally appear in geometric problems and other applications such as optimal transportation. There are some fundamental assumptions in the literature to ensure the equations to be elliptic and that one can apply EvansKrylov theorem once the C 2 estimates are derived. However, in previous work one needed extra assumptions which are more technical in nature to overcome various difficulties. In this paper we are able to remove most of these technical assumptions. Indeed, we derive the estimates under conditions which are almost optimal, and prove existence results for the Dirichlet problem which are new even for bounded domains in Euclidean space. Moreover, our methods can be applied to other types of nonlinear elliptic and parabolic equations, including those on complex manifolds

    Design and Stability Analysis of Six-Degree-of-Freedom Hydro-Pneumatic Spring Wheel-Leg

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    Traditional hydro-pneumatic spring suspensions are limited to a single vertical degree of freedom, which cannot accommodate the significant technological changes introduced by the new in-wheel motor drive mode. Integrating the motor into the vehicle’s hub creates a direct motor drive mode, replacing the traditional engine–transmission–drive shaft configuration. Together with the dual in-wheel motor wheelset structure, this setup can achieve both drive and differential steering functions. In this study, we designed a six-arm suspension wheel-leg device based on hydro-pneumatic springs, and its structural composition and functional characteristics are presented herein. The external single-chamber hydro-pneumatic springs used in the six-arm structure suspension were analyzed and mathematically modeled, and the nonlinear characteristic curves of the springs were derived. To overcome the instability caused by inconsistent extension lengths of the hydro-pneumatic springs during horizontal steering, the spring correction force, horizontal rotational torque, consistency, and stiffness of the six-degree-of-freedom hydro-pneumatic spring wheel-leg device were analyzed. Finally, with the auxiliary action of tension springs, the rotational torque of the hydro-pneumatic springs and the tension resistance torque of the tension spring counterbalanced each other, keeping the resultant torque on the wheelset at approximately 0 N∙m. The results suggest that the proposed device has excellent self-stabilizing performance and meets the requirements for straight-line driving and differential steering applications. This device provides a new approach for the drive mode and suspension design of the dual in-wheel motor wheelset

    Nanomaterial-Based Drug Delivery Systems for Pain Treatment and Relief: From the Delivery of a Single Drug to Co-Delivery of Multiple Therapeutics

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    The use of nanomaterials in drug delivery systems for pain treatment is becoming increasingly common. This review aims to summarize how nanomaterial-based drug delivery systems can be used to effectively treat and relieve pain, whether via the delivery of a single drug or a combination of multiple therapeutics. By utilizing nanoformulations, the solubility of analgesics can be increased. Meanwhile, controlled drug release and targeted delivery can be realized. These not only improve the pharmacokinetics and biodistribution of analgesics but also lead to improved pain relief effects with fewer side effects. Additionally, combination therapy is frequently applied to anesthesia and analgesia. The co-encapsulation of multiple therapeutics into a single nanoformulation for drug co-delivery has garnered significant interest. Numerous approaches using nanoformulation-based combination therapy have been developed and evaluated for pain management. These methods offer prolonged analgesic effects and reduced administration frequency by harnessing the synergy and co-action of multiple targets. However, it is important to note that these nanomaterial-based pain treatment methods are still in the exploratory stage and require further research to be effectively translated into clinical practice

    Endoplasmic reticulum stressed HNSCC cell-derived exosomal miR-26a-5p promotes PD-L1 expression in macrophage through PTEN/AKT signaling pathway

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    Objective To investigate the impact of exosomal miRNAs derived from endoplasmic reticulum-stressed (ERS) head and neck squamous cell carcinoma (HNSCC) cells on macrophages. Methods This study was reviewed and approved by the Ethics Committee. The expression levels of ERS-associated proteins, including protein kinase R-like endoplasmic reticulum kinase (PERK) and glucose-regulated protein 78 (GRP78), in HNSCC tissues and para-tumor tissues were detected by Western blot (WB) and quantitative real-time PCR (RT-qPCR). HN4 human laryngeal squamous cell carcinoma cells were treated with 500 U/mL interferon-γ (IFN-γ) for 48 h to induce ER stress, and exosomes secreted by ER-stressed HN4 cells were collected and identified. The types of miRNAs in exosomes were identified through bioinformatics analysis, and the target genes of miRNAs were predicted. Macrophages were transfected with miRNA, co cultured with collected exosomes, and the expression of PTEN in macrophages was knocked down. The downstream signaling pathway regulated by exosomal miRNAs was studied by WB and RT-qPCR. Results Compared with that in para-tumor tissues, the expression level of ER stress-associated proteins in HNSCC tissues was increased (P<0.05). RNA-seq analysis revealed that miR-26a-5p was highly upregulated in ER-stressed HN4 cell-derived exosomes (P<0.05). PTEN is the target gene for miR-26a-5p. miR-26a-5p increased the expression level of PD-L1 in macrophages and downregulated the expression of PTEN (P<0.05). Macrophages co cultured with ERS extracellular vesicles showed an increase in miR-26a-5p and PD-L1 expression, a decrease in PTEN expression, and an increase in p-AKT expression (P<0.05). Knock down the expression of PTEN in macrophages and increase the expression of PD-L1 (P<0.01). Conclusion ERS HNSCC cell-derived exosomal miR-26a-5p promotes the expression of PD-L1 in macrophages through the PTEN/AKT signaling pathway
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