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E-raamat: Transport Equation and Tomography [De Gruyter e-raamatud]

  • De Gruyter e-raamatud
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This monograph deals with the results of the authors' research on both the study of the transport equation (the linear Boltzmann equation) and its applications in X-ray tomography. The introduction contains an outline of the text and deals with certain aspects of the methodology. The first part of the volume is devoted to the investigation of known and new problems for the stationary transport equation of a general form. New problems are treated as problems of tomography. The second part deals with the monoenergetic transport equation.

Main designations 1(2)
Introduction 3(10)
Part
1. Direct and inverse problems for the transport equation with energy dependence
13(64)
Derivation of the radiation transport equation
13(5)
Formulation and investigation of the direct problem for the transport equation
18(10)
Continuity of solutions to the direct problem
28(5)
Determination of the total attenuation coefficient for discontinuous density of the input flux
33(6)
Description of a source with discontinuous radiation density
39(5)
A boundary value problem with a parameter for the transport equation
44(9)
Determining the total interaction coefficient by multiple irradiation
53(2)
Providing special boundary conditions for multiple irradiation
55(10)
Testing the algorithms for determining unknown media
65(12)
Part
2. The tomography problem in the monoenergetic case
77(116)
The direct problem for the monoenergetic transport equation
77(8)
Additional restrictions
85(4)
A formula for the gradient of a solution to the transport equation
89(13)
Auxiliary statements
102(20)
The indicator of heterogeneity in the tomography problem, and the measure of visibility
122(19)
Invisibility media in tomography
141(7)
Computerized testing of the indicator of heterogeneity
148(12)
Some contradictions between two mathematical models of transport theory
160(15)
Comparing two models in transport theory in the plane-parallel case
175(11)
Prospective investigation
186(7)
Bibliography 193