Transport equation and tomography

Main designations introduction direct and inverse problems for the transport equation with energy dependence derivation of the radiation transport equation formulation and investigation of the direct problem for the transport equation continuity of solutions to the direct problem determination of the total attenuation coefficient for discontinuous density of the input flux description of a source with discontinuous radiation density a boundary value problem with a parameter for the transport equation determining the total interaction coefficient by multiple irradiation providing special boundary conditions for multiple irradiation testing the algorithms for determining unknown media the tomography problem in the monoenergetic case the direct problem for the monoenergetic transport equation additional restrictions a formula for the gradient of a solution to the transport equation auxiliary statements the indicator of heterogeneity in the tomography problem, and the measure of visibility invisibility media in tomography computerized testing of the indicator of heterogeneity some contradictions between two mathematical models of transport theory comparing two models in transport theory in the plane-parallel case prospective investigation.