In this paper,we study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary ...In this paper,we study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary condition for the temperature with small viscosityνand small thermal diffusionμ.We establish that if the initial perturbation velocity and initial perturbation temperature satisfy ||u_(0)||H^(2)≤ε_(0) min{μ,ν}1/2, and ||θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||_(H^(1))≤εi min{μ,ν}^(5/6),for some smallε0 andε1 independent ofμ,ν,then the solution of the two-dimensional NavierStokes Boussinesq system does not transition away from the Couette flow for any time.展开更多
This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium...This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R〉1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence ,sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.展开更多
Recently,water extraction based on the indices method has been documented in many studies using various remote sensing data sources.Among them,Landsat satellites data have certain advantages in spatial resolution and ...Recently,water extraction based on the indices method has been documented in many studies using various remote sensing data sources.Among them,Landsat satellites data have certain advantages in spatial resolution and cost.After the successful launch of Landsat 8,the Operational Land Imager(OLI)data from the satellite are getting more and more attention because of its new improvements.In this study,we used the OLI imagery data source to study the water extraction performance based on the Normalized Difference Vegetation Index,Normalized Difference Water Index,Modified Normalized Water Index(MNDWI),and Automated Water Extraction Index(AWEI)and compared the results with the Thematic Mapper(TM)imagery data.Two test sites in Tianjin City of north China were selected as the study area to verify the applicability of OLI data and demonstrate its advantages over TM data.We found that the results of surface water extraction based on OLI data are slightly better than that based on TM in the two test sites,especially in the city site.The AWEI and MNDWI indices performs better than the other two indices,and the thresholds of water indices show more stability when using the OLI data.So,it is suitable to combine OLI imagery with other Landsat sensor data to study water changes for long periods of time.展开更多
In this study,we observe that there are two threshold speeds(stability threshold speed and second threshold speed)for the long journal bearing,which is different for the short bearing.When the rotating speed is below ...In this study,we observe that there are two threshold speeds(stability threshold speed and second threshold speed)for the long journal bearing,which is different for the short bearing.When the rotating speed is below the stability threshold speed,the stability boundary nearly coincides with the clearance circle,and the journal center gradually returns to the equilibrium point after being released at an initial point.If the rotating speed is between the stability threshold speed and the second threshold speed,after being released at an initial point,the journal center converges to a contour containing the equilibrium point.In this situation,for a higher rotating speed,the corresponding contour is also larger.When the rotating speed exceeds the second threshold speed,the journal gradually moves towards the bearing surface after being released at an initial point.展开更多
By monotone methods and invariant region theory, a reaction-diffusion equations D-SIS epidemic model with bilinear rate is studied. The existence and uniqueness of the solution of the model are proved. The basic repro...By monotone methods and invariant region theory, a reaction-diffusion equations D-SIS epidemic model with bilinear rate is studied. The existence and uniqueness of the solution of the model are proved. The basic reproductive number which determines whether the disease is extinct or not is found. The globally asymptotical stability of the disease-free equilibrium and the endemic equilibrium are obtained. Some results of the ordinary differential equations model are extended to the present partial differential equations model.展开更多
文摘In this paper,we study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary condition for the temperature with small viscosityνand small thermal diffusionμ.We establish that if the initial perturbation velocity and initial perturbation temperature satisfy ||u_(0)||H^(2)≤ε_(0) min{μ,ν}1/2, and ||θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||_(H^(1))≤εi min{μ,ν}^(5/6),for some smallε0 andε1 independent ofμ,ν,then the solution of the two-dimensional NavierStokes Boussinesq system does not transition away from the Couette flow for any time.
文摘This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R〉1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence ,sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.
基金The authors would like to thank the support by the Key Research Program of the Chinese Academy of Science[grant number KZZD–EW–14]the Visiting Scholar Foundation of Chinese Academy of Science.The authors would like to thank USGS for processing and providing Landsat data and the reviewers for their constructive comments and suggestions.The authors especially thank Prof Xiangming Xiao in the Earth Observation and Modeling Facility,University of Oklahoma,for his useful suggestions to this paper.
文摘Recently,water extraction based on the indices method has been documented in many studies using various remote sensing data sources.Among them,Landsat satellites data have certain advantages in spatial resolution and cost.After the successful launch of Landsat 8,the Operational Land Imager(OLI)data from the satellite are getting more and more attention because of its new improvements.In this study,we used the OLI imagery data source to study the water extraction performance based on the Normalized Difference Vegetation Index,Normalized Difference Water Index,Modified Normalized Water Index(MNDWI),and Automated Water Extraction Index(AWEI)and compared the results with the Thematic Mapper(TM)imagery data.Two test sites in Tianjin City of north China were selected as the study area to verify the applicability of OLI data and demonstrate its advantages over TM data.We found that the results of surface water extraction based on OLI data are slightly better than that based on TM in the two test sites,especially in the city site.The AWEI and MNDWI indices performs better than the other two indices,and the thresholds of water indices show more stability when using the OLI data.So,it is suitable to combine OLI imagery with other Landsat sensor data to study water changes for long periods of time.
基金This research is supported by doctoral research fund of Hubei University of Arts and Science(No.2059023)the Project of Hubei University of Arts and Science(No.XK2020005)+2 种基金National Science and Technology Major Project(No.2019ZX04001024)Central Government Guides Local Science and Technology Development Projects of Hubei Province(No.2018ZYYD016)start-up program for excellent young and middle-aged scientific and technological innovation team of Hubei Provincial Department of Education(No.T201919).
文摘In this study,we observe that there are two threshold speeds(stability threshold speed and second threshold speed)for the long journal bearing,which is different for the short bearing.When the rotating speed is below the stability threshold speed,the stability boundary nearly coincides with the clearance circle,and the journal center gradually returns to the equilibrium point after being released at an initial point.If the rotating speed is between the stability threshold speed and the second threshold speed,after being released at an initial point,the journal center converges to a contour containing the equilibrium point.In this situation,for a higher rotating speed,the corresponding contour is also larger.When the rotating speed exceeds the second threshold speed,the journal gradually moves towards the bearing surface after being released at an initial point.
基金Supported by the National Natural Science Foundation of China(10371097 10531030)the National Fifteenth Research of Medicinal Sciences and Technologies(2004BA719A01).
文摘By monotone methods and invariant region theory, a reaction-diffusion equations D-SIS epidemic model with bilinear rate is studied. The existence and uniqueness of the solution of the model are proved. The basic reproductive number which determines whether the disease is extinct or not is found. The globally asymptotical stability of the disease-free equilibrium and the endemic equilibrium are obtained. Some results of the ordinary differential equations model are extended to the present partial differential equations model.
