Exact Traveling Wave Solutions for Generalized Camassa-Holm Equation by Polynomial Expansion Methods

We formulate efficient polynomial expansion methods and obtain the exact traveling wave solutions for the generalized Camassa-Holm Equation. By the methods, we obtain three types traveling wave solutions for the generalized Camassa-Holm Equation: hyperbolic function traveling wave solutions, trigonometric function traveling wave solutions, and rational function traveling wave solutions. At the same time, we have shown graphical behavior of the traveling wave solutions.

A Kind of Time-Delayed COVID-19 Dynamical Model with Vaccination

In the paper, we study a kind of time-delayed novel coronavirus pneumonia dynamical model with vaccination. This model considers that people are vaccinated, and the human immune system has a series of processes, which need a certain time. We first obtain the disease-free equilibrium and the basic reproduction number R0, and the system has a unique endemic equilibrium when R0 > 1. Then we discuss the stability of the disease-free equilibrium and the endemic equilibrium with different delays τ. For τ = 0, using the Lyapunov function approach, we obtained the stability of disease-free equilibrium and the endemic equilibrium, respectively. For any delay τ ≠ 0, using the Routh-Hurwitz Criteria, we obtained that the disease-free equilibrium is locally asymptotically stable. We also find the critical value τ0 at the endemic equilibrium, and obtain the condition that the system has a Hopf bifurcation at the endemic equilibrium. Finally, with the suitable choices of the parameters, some numerical simulations are presented in order to verify the effectiveness of the obtained theoretical results.

Study of C parity violating and strangeness changing J/ψ→ PP weak decays

Although J/ψ weak decays are rare,they are possible within the standard model of elementary particles.Inspired by the potential prospects of the future intensity frontier,the C parity violating J/ψ→πη^(′),ηη′decays and the strangeness changing J/ψ→πK,Kη^(′)decays are studied via the perturbative QCD approach.It is determined that the J/ψ→ηη^(′) decays have relatively large branching ratios,approximately on the order of 10^(11),which might be within the measurement capability and sensitivity of the future STCF experiment.

Etherified dicyandiamide condensation copolymer as a wet-end additive for papermaking

Dicyandiamide-formaldehyde condensation copolymer was synthesized and used as a wet-end additive for papermaking.The retention of fibers and fines was used as a performance index.Factors were evaluated governing the performance of the polymer,including polymer dosage,pH and mixing time.The optimum dosage of the polymer was found to be 0.03%under the conditions.Overall,the polymer was effective in improving the drainage,as well as the retention of fibers and fines in papermaking process。