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The outbreak of a novel coronavirus (COVID-19) generated an outbreak of public opinions in the Chinese Sina-microblog. To help in designing effective communication strategies during a major public health emergency, we propose a multiple-information susceptible-discussing-immune (M-SDI) model in order to understand the patterns of key information propagation on social networks. We develop the M-SDI model, based on the public discussion quantity and take into account of the behavior that users may re-enter another related topic or Weibo after discussing one. Data fitting using the real data of COVID-19 public opinion obtained from Chinese Sina-microblog can parameterize the model to make accurate prediction of the public opinion trend until the next major news item occurs. The reproduction ratio has fallen from 1.7769 and maintained around 0.97, which reflects the peak of public opinion has passed but it will continue for a period of time.

By using Monte Carlo simulations, we investigated a triangle double-layer graphene nanoisland with mixed-spin (3/2, 2) configuration. We focused on the effects of crystal-fields, exchange couplings, longitudinal magnetic fields, and temperature on the magnetic properties of the system. Various curves of magnetization, susceptibility, and internal energy as a function of temperature were obtained. We plotted the phase diagrams of blocking temperature in the different parameter planes. We found that increasing |Jab/JZ|,Jbb/JZ, and h/JZ or weakening |Db/JZ| is beneficial to improving the TB/JZ, but the TB/JZ is very insensitive to changes in the Da/JZ and Jaa/JZ. In addition, it is worth noting that the system can exhibit abundant multiple-loops hysteresis behaviors for certain physical parameters, such as triple, quadruple, quintuple, septuple hysteresis loops.

The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to solve this practical problem efficiently, this paper constructs a continuation method with the trusty time-stepping scheme for the linearly equality-constrained optimization problem at every sampling time. At every iteration, the new method only solves a system of linear equations other than the traditional optimization method such as the sequential quadratic programming (SQP) method, which needs to solve a quadratic programming subproblem. Consequently, the new method can save much more computational time than SQP. Numerical results show that the new method works well for this problem and its consumed time is about one fifth of that of SQP (the built-in subroutine fmincon.m of the MATLAB2018a environment) or that of the traditional dynamical method (the built-in subroutine ode15s.m of the MATLAB2018a environment). Furthermore, we also give the global convergence analysis of the new method.