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In this paper, we estimate the number of limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3, when they are perturbed inside the class of piecewise smooth polynomial systems of degree n. By using the first-order averaging method, we give the upper and lower bounds on the maximal number of limit cycles which can bifurcate from the period annuluses. Our results indicate that the nonsmooth systems can have more limit cycles than the smooth ones. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the number of limit cycles of a near-Hamiltonian system under Z 4-equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we found that the perturbed system can have 13 limit cycles. [Copyright &y& Elsevier]

Postoperative complications at the anastomosis site following tracheal resection are a prevalent and substantial concern. However, most existing solutions primarily focus on managing symptoms, with limited attention given to proactively preventing the underlying pathological processes. To address this challenge, we conducted a drug screening focusing on clinically-relevant polyphenolic compounds, given the growing interest in polyphenolic compounds for their potential role in tissue repair during wound healing. This screening led to the identification of resveratrol as the most promising candidate for mitigating tracheal complications, as it exhibited the most significant efficacy in enhancing the expression of vascular endothelial growth factor (VEGF) while concurrently suppressing the pivotal fibrosis factor: transforming growth factor-beta 1 (TGF-β1), showcasing its robust potential in addressing these issues. Building upon this discovery, we further developed an innovative photosensitive poly-L-lysine gel integrated with a resveratrol-magnesium metal polyphenol network (MPN), named Res-Mg/PL-MA. This design allows for the enables sustained release of resveratrol and synergistically enhances the expression of VEGF and also promotes resistance to tensile forces, aided by magnesium ions, in an anastomotic tracheal fistula animal models. Moreover, the combination of resveratrol and poly-L-lysine hydrogel effectively inhibits bacteria, reduces local expression of key inflammatory factors, and induces polarization of macrophages toward an anti-inflammatory phenotype, as well as inhibits TGF-β1, consequently decreasing collagen production levels in an animal model of post-tracheal resection. In summary, our novel Res-Mg/PL-MA hydrogel, through antibacterial, anti-inflammatory, and pro-vascularization mechanisms, effectively prevents complications at tracheal anastomosis, offering significant promise for translational applications in patients undergoing tracheal surgeries., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors. Published by Elsevier Ltd.)