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On the basis of the skewed pole model, this study uses the elite opposition-based golden-sine whale optimization algorithm to carry out the multi-objective optimization design of the frameless external rotor permanent magnet synchronous motor of the robot arm and achieve high torque density and low torque ripple. First, the key parameters affecting the torque ripple and torque density of the motor are analyzed. Second, the angle of the oblique pole is studied to reduce torque ripple. On the basis of the oblique pole model of the motor, the sample library is established according to the key parameters, the K-nearest neighbor algorithm is introduced for regression fitting, and the high-precision and fast calculation model of the motor is established. Third, the elite opposition-based golden-sine whale optimization algorithm (EGWOA) is introduced to optimize the key parameters of the fitting model with the objective of reducing torque ripple and increasing torque density, and the non dominated sorting and crowding degree calculation methods are used to improve it. Finally, a prototype is made to prove the effectiveness of the optimized design. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an SVEIR epidemic model with reaction–diffusion and nonlinear incidence. We establish the well-posedness of the solutions and the basic reproduction number R 0 . Moreover, we show that the disease-free steady state is globally asymptotically stable when R 0 < 1 , whereas the disease will be persistent when R 0 > 1 . Furthermore, using the method of Lyapunov functional, we prove the global stability of the positive steady state for the spatial homogeneous model. [ABSTRACT FROM AUTHOR]

In this paper, we derive a discretized multi-group epidemic model with time delay by using a nonstandard finite difference (NSFD) scheme. A crucial observation regarding the advantage of the NSFD scheme is that the positivity and boundedness of solutions of the continuous model are preserved. Furthermore, we show that the discrete model has the same equilibria, and the conditions for their stability are identical in case of both the discrete and the corresponding continuous models. Specifically, if $\mathfrak{R}_{0}\leq1$ , then the disease-free equilibrium $P_{0}$ is globally asymptotically stable; if $\mathfrak{R}_{0}>1$ , then the infection equilibrium $P_{*}$ is globally asymptotically stable. The results imply that the discretization scheme can efficiently preserve the global dynamics of the original continuous model. [ABSTRACT FROM AUTHOR]