We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditi...We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.展开更多
We extend our previous analysis and consider the interacting holographic Ricci dark energy (IRDE) model in non-flat universe. We study astrophysical constraints on this model using the recent observations including th...We extend our previous analysis and consider the interacting holographic Ricci dark energy (IRDE) model in non-flat universe. We study astrophysical constraints on this model using the recent observations including the type Ia supernovae (SNIa), the baryon acoustic oscillation (BAO), the cosmic microwave background (CMB) anisotropy, and the Hubble parameter. It is shown that the allowed parameter range for the fractional energy density of the curvature is ?in the presence of the interactions between dark energy and matter. Without the interaction, the flat universe is observationally disfavored in this model.展开更多
Compounds selectively binding and stabilizing G-quadruplex structures could inhibit the telomerase or down- regulate the oncogenes and may act as anti-cancer drugs. An alkaloid with non-flat structure, fangchinoline, ...Compounds selectively binding and stabilizing G-quadruplex structures could inhibit the telomerase or down- regulate the oncogenes and may act as anti-cancer drugs. An alkaloid with non-flat structure, fangchinoline, showed to strongly stabilize the intermolecular and intramolecular parallel stranded G-quadruplex structure, increasing melting temperature by 20 and 23℃, respectively. The binding mode was investigated by using NMR and molec- ular modelling methods. Four human cell lines （HL-60, BGC-823, Be1-7402 and KB） were taken to test the an- ti-proliferation effects of fangchinoline and the IC50 values were ranged from 16 to 32 μmol/L. These results showed that the fangchinoline or related moiety derivatives may represent a class of telomere-targeted agents as po- tential anti-cancer drugs.展开更多
基金supported in part by the National Science Foundation under Grants DMS-0807551, DMS-0720925, and DMS-0505473the Natural Science Foundationof China (10728101)supported in part by EPSRC grant EP/F029578/1
文摘We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.
文摘We extend our previous analysis and consider the interacting holographic Ricci dark energy (IRDE) model in non-flat universe. We study astrophysical constraints on this model using the recent observations including the type Ia supernovae (SNIa), the baryon acoustic oscillation (BAO), the cosmic microwave background (CMB) anisotropy, and the Hubble parameter. It is shown that the allowed parameter range for the fractional energy density of the curvature is ?in the presence of the interactions between dark energy and matter. Without the interaction, the flat universe is observationally disfavored in this model.
基金We thank the National Natural Science Foundation of China （Nos. 21472197, 91027033, 81072576, 21205121, 21305145 and 31200576）, the Major National Basic Research Projects （973） （No. 2013CB733701）, the ＂Strategic Priority Research Program＂ of the Chinese Academy of Sciences （No. XDA09030307）, and the Key Program of the Chinese Academy of Sciences （No. KJCX2-EW-N06-01）.
文摘Compounds selectively binding and stabilizing G-quadruplex structures could inhibit the telomerase or down- regulate the oncogenes and may act as anti-cancer drugs. An alkaloid with non-flat structure, fangchinoline, showed to strongly stabilize the intermolecular and intramolecular parallel stranded G-quadruplex structure, increasing melting temperature by 20 and 23℃, respectively. The binding mode was investigated by using NMR and molec- ular modelling methods. Four human cell lines （HL-60, BGC-823, Be1-7402 and KB） were taken to test the an- ti-proliferation effects of fangchinoline and the IC50 values were ranged from 16 to 32 μmol/L. These results showed that the fangchinoline or related moiety derivatives may represent a class of telomere-targeted agents as po- tential anti-cancer drugs.
