We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary i...We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.展开更多
In this paper,we consider numerical methods for two-sided space variable-order fractional diffusion equations(VOFDEs)with a nonlinear source term.The implicit Euler(IE)method and a shifted Grünwald(SG)scheme are ...In this paper,we consider numerical methods for two-sided space variable-order fractional diffusion equations(VOFDEs)with a nonlinear source term.The implicit Euler(IE)method and a shifted Grünwald(SG)scheme are used to approximate the temporal derivative and the space variable-order(VO)fractional derivatives,respectively,which leads to an IE-SG scheme.Since the order of the VO derivatives depends on the space and the time variables,the corresponding coefficient matrices arising from the discretization of VOFDEs are dense and without the Toeplitz-like structure.In light of the off-diagonal decay property of the coefficient matrices,we consider applying the preconditioned generalized minimum residual methods with banded preconditioners to solve the discretization systems.The eigenvalue distribution and the condition number of the preconditioned matrices are studied.Numerical results show that the proposed banded preconditioners are efficient.展开更多
Developing dynamic color-tunable ultra-long room temperature phosphorescence(URTP)polymers with afterglow of over 1 s,photo-chromism,and multi-stimuli response for practical anti-counterfeiting and information securit...Developing dynamic color-tunable ultra-long room temperature phosphorescence(URTP)polymers with afterglow of over 1 s,photo-chromism,and multi-stimuli response for practical anti-counterfeiting and information security applications is attractive but very challenging.Herein,by doping multicolor phosphorescence pyri-dinium bromide L block or viologen-based photo-chromic V block into polyvinyl alcohol matrixes,the water-stimuli-responsive color-tunable URTP polymerfilms with afterglow of up to 8 s and the reversible viologen-based photochromic polymerfilms have been developed.More significantly,a series of dynamic color-tunable URTP polymerfilms with ultra-long afterglow of over 6 s,photo-chromism,and water-stimuli response have been successfully exploited by integrating L and V blocks into one polymer system.Mechanistic investigations have revealed that their photo-chromism mainly comes from the photo-generated viologen free radicals.Furthermore,their dynamic multilevel anti-counterfeiting applications have been demonstrated.These results pave the way to develop smarter multifunctional URTP materials for anti-counterfeiting and optical sensing.展开更多
文摘We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.
文摘In this paper,we consider numerical methods for two-sided space variable-order fractional diffusion equations(VOFDEs)with a nonlinear source term.The implicit Euler(IE)method and a shifted Grünwald(SG)scheme are used to approximate the temporal derivative and the space variable-order(VO)fractional derivatives,respectively,which leads to an IE-SG scheme.Since the order of the VO derivatives depends on the space and the time variables,the corresponding coefficient matrices arising from the discretization of VOFDEs are dense and without the Toeplitz-like structure.In light of the off-diagonal decay property of the coefficient matrices,we consider applying the preconditioned generalized minimum residual methods with banded preconditioners to solve the discretization systems.The eigenvalue distribution and the condition number of the preconditioned matrices are studied.Numerical results show that the proposed banded preconditioners are efficient.
基金Priority Academic Program Development of Jiangsu Higher Education InstitutionsApplied Basic Research Programs of Science and Technology Commission Foundation of Jiangsu Province,Grant/Award Number:BK20231340+4 种基金Changzhou Introduction Program of Innovative Leading Talents,Grant/Award Number:CQ20220111Natural Science Foundation of Jiangsu Province,Grant/Award Number:BK20170290Natural Science Foundation of the Higher Education Institutions of Jiangsu Province,Grant/Award Number:17KJB150002Opening Project of Zhejiang Engineering Research Center of Fat-soluble Vitamin,Grant/Award Number:202107National Natural Science Foundation of China,Grant/Award Numbers:51803143,。
文摘Developing dynamic color-tunable ultra-long room temperature phosphorescence(URTP)polymers with afterglow of over 1 s,photo-chromism,and multi-stimuli response for practical anti-counterfeiting and information security applications is attractive but very challenging.Herein,by doping multicolor phosphorescence pyri-dinium bromide L block or viologen-based photo-chromic V block into polyvinyl alcohol matrixes,the water-stimuli-responsive color-tunable URTP polymerfilms with afterglow of up to 8 s and the reversible viologen-based photochromic polymerfilms have been developed.More significantly,a series of dynamic color-tunable URTP polymerfilms with ultra-long afterglow of over 6 s,photo-chromism,and water-stimuli response have been successfully exploited by integrating L and V blocks into one polymer system.Mechanistic investigations have revealed that their photo-chromism mainly comes from the photo-generated viologen free radicals.Furthermore,their dynamic multilevel anti-counterfeiting applications have been demonstrated.These results pave the way to develop smarter multifunctional URTP materials for anti-counterfeiting and optical sensing.
