The bifurcations of multiple limit cycles for a rotor-active magnetic bearings (AMB) system with the time-varying stiffness are considered in this paper. The governing nonlinear equation of motion is established for the rotor-AMB system with single-degree-of-freedom and parametric excitation. Using the method of multiple scales, the governing nonlinear equation of motion is first transformed to the averaged equation, which is in the form of a Z2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, the bifurcation theory of planar dynamical system and the method of detection function are utilized to analyze the bifurcations of multiple limit cycles of the averaged equation. Four groups of parametric controlling conditions are given to obtain the configurations of compound eyes. It is found that there exist respectively at least 17, 19, 21 and 22 limit cycles in the rotor-AMB system with the time-varying stiffness under the different controlling conditions.
Tropomyosin receptor kinase (TRK) inhibition is an effective therapeutic approach for treatment of a variety of cancers. Despite the use of first-generation TRK inhibitor (TRKI) larotrectinib (1) resulting in significant therapeutic response in patients, acquired resistance develops invariably. The emergence of secondary mutations occurring at the solvent-front, xDFG, and gatekeeper regions of TRK represents a common mechanism for acquired resistance. However, xDFG mutations remain insensitive to second-generation macrocyclic TRKIs selitrectinib (3) and repotrectinib (4) designed to overcome the resistance mediated by solvent-front and gatekeeper mutations. Here, we report the structure-based drug design and discovery of a next-generation TRKI. The structure−activity relationship studies culminated in the identification of a promising drug candidate 8 that showed excellent in vitro potency on a panel of TRK mutants, especially TRKA G667C in the xDFG motif, and improved in vivo efficacy than 1 and 3 in TRK wild-type and mutant fusion-driven tumor xenograft models, respectively.
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