An inverse problem of scattering theory for the perturbed Stark operator on the semiaxis

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Aynur R. Ahmedova
Keyword(s):  
Inverse Problem ◽  
Scattering Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Scattering Data ◽  
Stark Operator ◽  
Necessary And Sufficient

AbstractIn the present paper, we consider the inverse problem for the perturbed Stark operator. We obtain necessary and sufficient conditions on the set of values, which could serve as scattering data for the considered operator, and we prove their sufficiency.

Inverse problem about two-spectra for finite Jacobi matrices with zero diagonal

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Adil Huseynov
Keyword(s):  
Inverse Problem ◽  
Finite Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Jacobi Matrices ◽  
The Matrix ◽  
Explicit Procedure ◽  
Necessary And Sufficient

AbstractThe necessary and sufficient conditions for solvability of the inverse problem about two-spectra for finite order real Jacobi matrices with zero-diagonal elements are established. An explicit procedure of reconstruction of the matrix from the two-spectra is given.

Metrizability problem for spray on Lie algebroids

2016 ◽  
Vol 13 (09) ◽  
pp. 1650115
Author(s):  
Zahra Pirbodaghi ◽  
Morteza Mir Mohammad Rezaii
Keyword(s):  
Inverse Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lie Algebroids ◽  
Jacobi Endomorphism ◽  
Necessary And Sufficient

In this paper, we study inverse problem for sprays on Lie algebroids. We obtain necessary and sufficient conditions, based on semi-basic forms, for a spray to be Lagrangian. Then we discuss the Finsler metrizability of a spray and obtain some equations on the Jacobi endomorphism.

scholarly journals Re-nnd SOLUTIONS OF THE MATRIX EQUATION AXB=C

2008 ◽  
Vol 84 (1) ◽  
pp. 63-72 ◽  
Author(s):  
DRAGANA S. CVETKOVIĆ-ILIĆ
Keyword(s):  
Inverse Problem ◽  
Linear Algebra ◽  
Matrix Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Explicit Solutions ◽  
Matrix Inverse ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Special Case

AbstractIn this article we consider Re-nnd solutions of the equation AXB=C with respect to X, where A,B,C are given matrices. We give necessary and sufficient conditions for the existence of Re-nnd solutions and present a general form of such solutions. As a special case when A=I we obtain the results from a paper of Groß (‘Explicit solutions to the matrix inverse problem AX=B’, Linear Algebra Appl.289 (1999), 131–134).

scholarly journals An inverse problem for the second-order integro-differential pencil

2019 ◽  
Vol 50 (3) ◽  
pp. 223-231 ◽  
Author(s):  
Natalia P. Bondarenko
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Spectral Parameter ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Uniqueness Of Solution ◽  
Convolution Kernel ◽  
Sturm Liouville ◽  
Necessary And Sufficient

We consider the second-order (Sturm-Liouville) integro-differential pencil with polynomial dependence on the spectral parameter in a boundary condition. The inverse problem is solved, which consists in reconstruction of the convolution kernel and one of the polynomials in the boundary condition by using the eigenvalues and the two other polynomials. We prove uniqueness of solution, develop a constructive algorithm for solving the inverse problem, and obtain necessary and sufficient conditions for its solvability.

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