In this paper,we prove the existence of the scattering operator for the fractional magnetic Schrodinger operators.In order to do this,we construct the fractional distorted Fourier transforms with magnetic potentials.A...In this paper,we prove the existence of the scattering operator for the fractional magnetic Schrodinger operators.In order to do this,we construct the fractional distorted Fourier transforms with magnetic potentials.Applying the properties of the distorted Fourier transforms,the existence and the asymptotic completeness of the wave operators are obtained.Furthermore,we prove the absence of positive eigenvalues for fractional magnetic Schrodinger operators.展开更多
With the development of molecular imaging,Cherenkov optical imaging technology has been widely concerned.Most studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the stead...With the development of molecular imaging,Cherenkov optical imaging technology has been widely concerned.Most studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion equation.In this paper,time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic process.Based on the original steady-state diffusion equation,we first propose a stochastic partial differential equationmodel.The numerical solution to the stochastic partial differential model is carried out by using the finite element method.When the time resolution is high enough,the numerical solution of the stochastic diffusion equation is better than the numerical solution of the steady-state diffusion equation,which may provide a new way to alleviate the problem of Cherenkov luminescent imaging quality.In addition,the process of generating Cerenkov and penetrating in vitro imaging of 18 F radionuclide inmuscle tissue are also first proposed by GEANT4Monte Carlomethod.The result of the GEANT4 simulation is compared with the numerical solution of the corresponding stochastic partial differential equations,which shows that the stochastic partial differential equation can simulate the corresponding process.展开更多
文摘In this paper,we prove the existence of the scattering operator for the fractional magnetic Schrodinger operators.In order to do this,we construct the fractional distorted Fourier transforms with magnetic potentials.Applying the properties of the distorted Fourier transforms,the existence and the asymptotic completeness of the wave operators are obtained.Furthermore,we prove the absence of positive eigenvalues for fractional magnetic Schrodinger operators.
基金National Science Foundation of China(NSFC)(61671009,12171178).
文摘With the development of molecular imaging,Cherenkov optical imaging technology has been widely concerned.Most studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion equation.In this paper,time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic process.Based on the original steady-state diffusion equation,we first propose a stochastic partial differential equationmodel.The numerical solution to the stochastic partial differential model is carried out by using the finite element method.When the time resolution is high enough,the numerical solution of the stochastic diffusion equation is better than the numerical solution of the steady-state diffusion equation,which may provide a new way to alleviate the problem of Cherenkov luminescent imaging quality.In addition,the process of generating Cerenkov and penetrating in vitro imaging of 18 F radionuclide inmuscle tissue are also first proposed by GEANT4Monte Carlomethod.The result of the GEANT4 simulation is compared with the numerical solution of the corresponding stochastic partial differential equations,which shows that the stochastic partial differential equation can simulate the corresponding process.
