Ergodic stationary distribution and practical application of a hybrid stochastic cholera transmission model with waning vaccine-induced immunity under nonlinear regime switching

Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine-induced immunity and nonlinear telegraph perturbations. First, we derive a critical value ${?}_0^C$ related to the basic reproduction number ${?}_0$ of the deterministic model. The key aim of this paper is to generalize the θ-stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ-stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under ${?}_0^C>1$. Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper.     

System scan of the multiplicity correlation between forward and backward rapidities in relativistic heavy-ion collisions using a multi-phase transport model

A systematic study on forward–backward (FB) multiplicity correlations from large systems to small ones through a multi-phase transport model (AMPT) has been performed and the phenomenon that correlation strength increases with centrality can be explained by taking the distribution of events as the superposition of a series of Gaussian distributions. It is also found that correlations in the \begin{document}$ \eta -\phi $\end{document} plane can imply the shape of the event. Furthermore, long-range correlations originate from the fluctuations associated with the source information. FB correlations allow us to decouple long-range correlations from short-range correlations, and may provide a chance to investigate the α-clustering structure in initial colliding light nuclei as well. It seems the tetrahedron ¹⁶O + ¹⁶O collision gives a more uniform and symmetrical fireball, that emits the final particles more isotropically or independently in the longitudinal direction, indicating that the forward–backward multiplicity correlation could be used to identify the pattern of α-clustered ¹⁶O in future experiments.     

环加成反应、环合反应、电环化反应与环化反应的区别*

环加成反应、环合反应、电环化反应与环化反应都是合成有机环状化合物的成环反应,它们描述的反应类型完全不同。但是,它们却经常被误用或者混用。阐述了这4类反应的区别,希望能够从教学上明确这4类反应,从源头为将来的有机化学工作者建立起准确的概念。     

An improved generalized predictive control algorithm based on the difference equation CARIMA model for the SISO system with known strong interference

ABSTRACT

The single input single output (SISO) system with known strong interference is widely used in various occasions. Due to its strong interference, the control accuracy is hard to guarantee. To solve this problem, an improved generalized predictive control (IGPC) algorithm is developed. The IGPC firstly builds the difference equation CARIMA (Controlled Auto-Regressive Integrated Moving-Average) model of the SISO system and then treats the system as a two input single output (TISO) system and calculates its predictive vector, then transforms it into a SISO system and uses the TISO system predictive vector to calculate the SISO system control increment. A new parameter called phase coefficient is added to inhibit the control lag. Simulations are performed to make the comparison among the traditional GPC, PID control, velocity synchronization control (VSC), fuzzy adaptive PID control (FAPID), model-based robust PID control (BPID) and the IGPC. Results show that IGPC has best performance compared to the others. Finally, experiments are developed which proved that the IGPC algorithm has a higher accuracy in the SISO system with known strong interference than that of VSC.