This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara...This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.展开更多
The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering model is established and the existence ...The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach. The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated. Result on the uniqueness of the inverse problem is proved.展开更多
This paper describes a new method which has been developed for the solution of direct and inverse problems of 3-D compressible flows in turbomachinery.Two types of streamfunctions are proposed in the paper and the str...This paper describes a new method which has been developed for the solution of direct and inverse problems of 3-D compressible flows in turbomachinery.Two types of streamfunctions are proposed in the paper and the streamfunction-coordinate system is applied in numerical computations.The algorithm is applied to stator blades and the results are compared with experimental data,It is shown that the comparisons are very satis- factory.展开更多
基金supported by the Tianjin Municipal Science and Technology Program of China(No.23JCZDJC00070)。
文摘This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.
基金Supported by the Key Project of Chinese Ministry of Education(102088)the NNSF of China(10431030).
文摘The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach. The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated. Result on the uniqueness of the inverse problem is proved.
基金Project supported by the National Natural Science Fundation of China
文摘This paper describes a new method which has been developed for the solution of direct and inverse problems of 3-D compressible flows in turbomachinery.Two types of streamfunctions are proposed in the paper and the streamfunction-coordinate system is applied in numerical computations.The algorithm is applied to stator blades and the results are compared with experimental data,It is shown that the comparisons are very satis- factory.
