In this study, an impulsive boundary value problem, generated by Sturm-Liouville differential equation with the eigenvalue parameter contained in one boundary condition is considered. It is shown that the coefficients...In this study, an impulsive boundary value problem, generated by Sturm-Liouville differential equation with the eigenvalue parameter contained in one boundary condition is considered. It is shown that the coefficients of the problem are uniquely determined either by the Weyl function or by two given spectra.展开更多
In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem an...In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.展开更多
In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known...In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known conjecture due to Polya, its connections to Weyl's asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed.展开更多
We study a family of ＂symmetric＂ multiparameter quantized Weyl alge- bras A-q,A n（K） and some related algebras. We compute the Nakayama automorphism of A-q,A n（K）, give a necessary and sufficient condition for A...We study a family of ＂symmetric＂ multiparameter quantized Weyl alge- bras A-q,A n（K） and some related algebras. We compute the Nakayama automorphism of A-q,A n（K）, give a necessary and sufficient condition for A-q,A n（K） to be Calabi-Yau, and prove that A-q,A n（K） is cancellative. We study the automorphisms and isomorphism problem for A-q,A n（K） and .A-q,A n（K[t]）. Similar results are established for the Maltsiniotis multiparam- eter quantized Weyl algebraA-q,A n（K） and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization （A-q,A n（K））z and determine its automorphism group.展开更多
In this work,we study boundary value problems for second-order differential equations with singularities of second kind inside an interval.First,we investigate properties of the spectrum,then prove a theorem on comple...In this work,we study boundary value problems for second-order differential equations with singularities of second kind inside an interval.First,we investigate properties of the spectrum,then prove a theorem on completeness of eigenfunctions,and study the inverse problem of reconstructing the differential equation from spectral characteristics.展开更多
基金supported by Cumhuriyet University Scientific Research Project (CUBAP) No: F-371
文摘In this study, an impulsive boundary value problem, generated by Sturm-Liouville differential equation with the eigenvalue parameter contained in one boundary condition is considered. It is shown that the coefficients of the problem are uniquely determined either by the Weyl function or by two given spectra.
文摘In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.
文摘In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known conjecture due to Polya, its connections to Weyl's asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed.
文摘We study a family of ＂symmetric＂ multiparameter quantized Weyl alge- bras A-q,A n（K） and some related algebras. We compute the Nakayama automorphism of A-q,A n（K）, give a necessary and sufficient condition for A-q,A n（K） to be Calabi-Yau, and prove that A-q,A n（K） is cancellative. We study the automorphisms and isomorphism problem for A-q,A n（K） and .A-q,A n（K[t]）. Similar results are established for the Maltsiniotis multiparam- eter quantized Weyl algebraA-q,A n（K） and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization （A-q,A n（K））z and determine its automorphism group.
基金supported by the University of Kashan under grant number 464151/7
文摘In this work,we study boundary value problems for second-order differential equations with singularities of second kind inside an interval.First,we investigate properties of the spectrum,then prove a theorem on completeness of eigenfunctions,and study the inverse problem of reconstructing the differential equation from spectral characteristics.
