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.

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.

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.

ON THE INVERSE PROBLEM OF LAGRANGIAN SUPERMECHANICS

1993 ◽  
Vol 08 (20) ◽  
pp. 3565-3576 ◽  
Author(s):  
L. A. IBORT ◽  
G. LANDI ◽  
J. MARÍN-SOLANO ◽  
G. MARMO
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lagrangian Function ◽  
Necessary And Sufficient Conditions ◽  
Recursion Operators ◽  
Second Order Differential Equations ◽  
Necessary And Sufficient

The inverse problem of Lagrangian supermechanics is investigated. A set of necessary and sufficient conditions for a system of second order differential equations in superspace to derive from a (possibly nonregular) super-Lagrangian function are given. The harmonic superoscillator is revisited and a family of even and odd alternative super-Lagrangians are constructed for it. Finally, we comment on the existence of recursion operators.

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