A B-spline with the symplectic algorithm method for the solution of time-dependent Schrodinger equations （TDSEs） is introduced. The spatial part of the wavefunction is expanded by B-spline and the time evolution is ...A B-spline with the symplectic algorithm method for the solution of time-dependent Schrodinger equations （TDSEs） is introduced. The spatial part of the wavefunction is expanded by B-spline and the time evolution is given in a symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSEs. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atoms in comparison with other references.展开更多
A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and l...A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and local Morrey spaces is discussed. As an application of the duality results, one obtains the boundedness of the singular integral operators, the Hardy-Littlewood maximal operators and the fractional integral operators, as well as the commutators generated by the bounded mean oscillation(BMO) and the singular integral operators.What is new in this paper is that we do not have to depend on the specific structure of the operators. The results on the boundedness of operators are formulated in terms of B_σ-spaces and B_σ-spaces together with the detailed comparison of the ones in Herz spaces and local Morrey spaces. Another application is the nonsmooth atomic decomposition adapted to B_σ-spaces.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10374119, and the 0ne-Hundred-Talents Project of Chinese Academy of Science. ACKN0WLEDGMENTS： We gratefully acknowledge Professors Ding Peizhu and Liu Xueshen for their hospitality and help with the symplectic al- gorithm.
文摘A B-spline with the symplectic algorithm method for the solution of time-dependent Schrodinger equations （TDSEs） is introduced. The spatial part of the wavefunction is expanded by B-spline and the time evolution is given in a symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSEs. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atoms in comparison with other references.
基金supported by Grant-in-Aid for Scientific Research(C)(Grant No.16K05209)the Japan Society for the Promotion of Science
文摘A predual of B_σ-spaces is investigated. A predual of a predual of B_σ-spaces is also investigated,which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and local Morrey spaces is discussed. As an application of the duality results, one obtains the boundedness of the singular integral operators, the Hardy-Littlewood maximal operators and the fractional integral operators, as well as the commutators generated by the bounded mean oscillation(BMO) and the singular integral operators.What is new in this paper is that we do not have to depend on the specific structure of the operators. The results on the boundedness of operators are formulated in terms of B_σ-spaces and B_σ-spaces together with the detailed comparison of the ones in Herz spaces and local Morrey spaces. Another application is the nonsmooth atomic decomposition adapted to B_σ-spaces.
