The Xiaolangdi Reservoir has entered the later sediment-retaining period, and new sediment transport phenomena and channel re-estab- lishing behaviors are appearing. A physical model test was used to forecast the scou...The Xiaolangdi Reservoir has entered the later sediment-retaining period, and new sediment transport phenomena and channel re-estab- lishing behaviors are appearing. A physical model test was used to forecast the scouring and silting trends of the lower Yellow River. Based on water and sediment data from the lower Yellow River during the period from 1960 to 2012, and using a statistical method, this paper analyzed the sediment transport in sediment-laden flows with different discharges and sediment concentrations in the lower Yellow River. The results show that rational water-sediment regulation is necessary to avoid silting in the later sediment-retaining period. The combination of 3 000 m^3/s 〈 Q 〈 4 000 m^3/s and 20 kg/m^3 〈 S 〈 60 kg/m^3 （where Q is the discharge and S is the sediment concentration） at the Huayuankou section is considered an optimal combination for equilibrium sediment transport in the lower Yellow River over a long period of time.展开更多
We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has ...We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details.展开更多
In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform ...In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.展开更多
In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the...In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.展开更多
基金supported by the National Natural Science Foundation of China(Grants No.51039004 and No.51079055)the High-Level Personnel Research Start-Up Funds of North China University of Water Resources and Electric Power(Grant No.201403)the Science and Technology Research Project of the Education Department of Henan Province(Grant No.14A570001)
文摘The Xiaolangdi Reservoir has entered the later sediment-retaining period, and new sediment transport phenomena and channel re-estab- lishing behaviors are appearing. A physical model test was used to forecast the scouring and silting trends of the lower Yellow River. Based on water and sediment data from the lower Yellow River during the period from 1960 to 2012, and using a statistical method, this paper analyzed the sediment transport in sediment-laden flows with different discharges and sediment concentrations in the lower Yellow River. The results show that rational water-sediment regulation is necessary to avoid silting in the later sediment-retaining period. The combination of 3 000 m^3/s 〈 Q 〈 4 000 m^3/s and 20 kg/m^3 〈 S 〈 60 kg/m^3 （where Q is the discharge and S is the sediment concentration） at the Huayuankou section is considered an optimal combination for equilibrium sediment transport in the lower Yellow River over a long period of time.
基金Supported by the National Natural Science Foundation of China
文摘We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details.
文摘In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.
基金supported by the National Natural Science Foundation of China (No.12231008 and No.11971185)。
文摘In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.
