In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-...In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.展开更多
Adjoint-free calculation method is proposed to compute conditional nonlinear optimal perturbations(CNOP) combined with initial perturbations and model parameter perturbations. The new approach avoids the use of adjoin...Adjoint-free calculation method is proposed to compute conditional nonlinear optimal perturbations(CNOP) combined with initial perturbations and model parameter perturbations. The new approach avoids the use of adjoint technique in the optimization process. CNOPs respectively generated by ensemble-based and adjoint-based methods are compared based on a simple theoretical model.展开更多
基金The author is partially supported by the Nature Science Foundation of Guangdong(5012285)the"Thousand,Hundred,Ten"Science Foundation of Guangdong(Q02052)the Nature Science Foundation of Education Bureau of Guangdong(Z02075)
文摘In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.
基金supported by National Natural Science Foundation of China(Grant No.11201265)Shandong Natural Science Foundation(Grant No.ZR2012AM003)China Postdoctoral Science Foundation(Grant No.20110490564)
文摘Adjoint-free calculation method is proposed to compute conditional nonlinear optimal perturbations(CNOP) combined with initial perturbations and model parameter perturbations. The new approach avoids the use of adjoint technique in the optimization process. CNOPs respectively generated by ensemble-based and adjoint-based methods are compared based on a simple theoretical model.
