In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study h...In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data.展开更多
In this note, we consider the following Navier-Stokes equations （n≥2）: where t≥0,x=（x<sub>1</sub>,…,x<sub>n</sub>）,ρ,density,u=（u<sub>1</sub>,…,u<sub>n</sub>）...In this note, we consider the following Navier-Stokes equations （n≥2）: where t≥0,x=（x<sub>1</sub>,…,x<sub>n</sub>）,ρ,density,u=（u<sub>1</sub>,…,u<sub>n</sub>）,velocity,μ,μ’,coefficient of viscosity,μ】0,μ’+2/3μ≥0,P（ρ）,pressure,P’（ρ）】0,ρ】0,1≤i≤n,is a constant,展开更多
We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic variational wave equation with nonnegative L^2(R) initial data.
文摘In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data.
基金Project supported by the National Natural Science Foundation of China.
文摘In this note, we consider the following Navier-Stokes equations （n≥2）: where t≥0,x=（x<sub>1</sub>,…,x<sub>n</sub>）,ρ,density,u=（u<sub>1</sub>,…,u<sub>n</sub>）,velocity,μ,μ’,coefficient of viscosity,μ】0,μ’+2/3μ≥0,P（ρ）,pressure,P’（ρ）】0,ρ】0,1≤i≤n,is a constant,
基金The work of Ping Zhang is supported by the Chinese postdoctor's foundation,and that of Yuxi Zheng is supported in part by NSF DMS-9703711 and the Alfred P.Sloan Research Fellows award
文摘We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic variational wave equation with nonnegative L^2(R) initial data.
