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Full-Text Articles in Physical Sciences and Mathematics
Numerical And Analytical Solutions Of The Integral Geometry Problem On The Families Of Parabola And Broken Lines, N.U Uteuliev, Gafur Djaykov, Seidullaev Abat
Numerical And Analytical Solutions Of The Integral Geometry Problem On The Families Of Parabola And Broken Lines, N.U Uteuliev, Gafur Djaykov, Seidullaev Abat
Karakalpak Scientific Journal
In this paper, the problem of reconstructing the function in the strip on the known integrals from it with a given weight function on the family of parabola and broken lines. Inversion formulas for the family of broken lines were obtained, on their basis the theorems of uniqueness and existence of the solution were proved. Estimations of stability of problem solving in Sobolev spaces are obtained, from which weak ill-posed of problems follows. For the problems of integral geometry on the parabola family we obtained a regularized solution. On the basis of these obtained results the numerical results of experiments …
The Problem Of Integral Geometry In A Strip With Weight Function, A. X. Begmatov, A. S. Ismoilov
The Problem Of Integral Geometry In A Strip With Weight Function, A. X. Begmatov, A. S. Ismoilov
Scientific Journal of Samarkand University
In this work we consider the problem of reconstructing a function from a family of parabolas in the upper half-plane with a weight function having a singularity. The uniqueness of theorem for the solution of equation is proved and the inversion formula is derived. It is shown that the solution of the problem posed is weakly ill-posed, that is, stability estimates are obtained in spaces of finite smoothness.