GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE HYPERBOLIC GEOMETRY FLOW WITH TIME-DEPENDENT DISSIPATION

In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation（δ2 gij）/δt2＋μ/（（1 ＋ t）λ）（δ gij）/δt=-2 Rij,on Riemann surface. On the basis of the energy method, for 0 〈 λ ≤ 1, μ 〉 λ ＋ 1, we show that there exists a global solution gij to the hyperbolic geometry flow with time-dependent dissipation with asymptotic flat initial Riemann surfaces. Moreover, we prove that the scalar curvature R（t, x） of the solution metric gij remains uniformly bounded.

Symmetry Reduction and Exact Solutions of a Hyperbolic Monge-Ampère Equation

By means of the classical symmetry method,a hyperbolic Monge-Ampère equation is investigated.The symmetry group is studied and its corresponding group invariant solutions are constructed.Based on the associated vector of the obtained symmetry,the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampère equation,from which two interesting classes of solutions to the hyperbolic Monge-Ampère equation are obtained successfully.

Application of computer-aided diagnosis of congenital heart disease in four-chamber view of fetal heart basic screening

To the Editor:Congenital heart disease(CHD)is the most common severe congenital malformation which threatens the health of the fetus and the primary factor of intrauterine death.Prenatal detection of severe CHD could reduce the neonatal mortality and morbidity.The detection rate ranges between 25.0%and 59.7%in the prenatal ultrasonographic examination.^([1])We need to identify new strategies to improve detection rates of CHD prenatally.Deep-learning(DL)-based computer-aided diagnosis(CAD)has been highly and rapidly developed in recent years.

A Primal-Dual Hybrid Gradient Algorithm to Solve the LLT Model for Image Denoising

We propose an efficient gradient-type algorithm to solve the fourth-order LLT denoising model for both gray-scale and vector-valued images.Based on the primal-dual formulation of the original nondifferentiable model,the new algorithm updates the primal and dual variables alternately using the gradient descent/ascent flows.Numerical examples are provided to demonstrate the superiority of our algorithm.

Suspected Close Contacts as the Pilot Indicator of the Growth Trend of Confirmed Population During the COVID-19 Pandemic: A Simulation Approach

Regarding to the actual situation of the new coronavirus disease 2019 epidemic,social factors should be taken into account and the increasing growth trend of confirmed populations needs to be explained.A proper model needs to be established,not only to simulate the epidemic,but also to evaluate the future epidemic situation and find a pilot indicator for the outbreak.The original susceptible-infectious-recover model is modified into the susceptible-infectious-quarantine-confirm-recover combined with social factors(SIDCRL)model,which combines the natural transmission with social factors such as external interventions and isolation.The numerical simulation method is used to imitate the change curve of the cumulative number of the confirmed cases and the number of cured patients.Furthermore,we investigate the relationship between the suspected close contacts(SCC)and the final outcome of the growth trend of confirmed cases with a simulation approach.This article selects four representative countries,that is,China,South Korea,Italy,and the United States,and gives separate numerical simulations.The simulation results of the model fit the actual situation of the epidemic development and reasonable predictions are made.In addition,it is analyzed that the increasing number of SCC contributes to the epidemic outbreak and the prediction of the United States based on the population of the SCC highlights the importance of external intervention and active prevention measures.The simulation of the model verifies its reliability and stresses that observable variable SCC can be taken as a pilot indicator of the coronavirus disease 2019 pandemic.