NUKLEONIKA 2010, 55(4):433-437
## INVERSION OF THE JACOBI-PORSTENDORFER ROOM MODEL FOR THE RADON PROGENY
**Josef Thomas**^{1}, **Karel Jílek**^{1}, **Martin Brabec**^{2}
^{1} *National Radiation Protection Institute, 28 Bartoškova Str., Praha 4-140 00, Czech Republic*
^{2} *Institute of Computer Science, Academy of Sciences of the Czech Republic, *
28 Bartoškova Str., Praha 4-140 00, Czech Republic
The Jacobi-Porstendörfer (J-P) room model describes the behaviour of radon progeny in the atmosphere of a room. It distinguishes between free and attached radon progeny in air. It has been successfully used without substantial changes for nearly 40 years. There have been several attempts to invert the model approximately to determine the parameters describing the physical processes. Here, an exact solution is aimed at as an algebraic inversion of the system of six linear equations for the five unknown physical parameters *k*, *X*, *R*, *q*_{f}, *q*_{a} of the room model. Two strong linear dependencies in this system, unfortunately do not allow to obtain a general solution (especially not for the ventilation coefficient *k*), but only a parameterized one or for reduced sets of unknown parameters. More, the impossibility to eliminate one of the two linear dependencies and the departures of the measured concentrations forces to solve a set of allowed combinations of equations of the algebraic system and to accept its mean values (therefore with variances) as a result of the algebraic inversion. These results are in agreement with results of the least squares method as well as of a sophisticated modern statistical approach. The algebraic approach provides, of course, a lot of analytical relations to study the mutual dependencies between the model parameters and the measurable quantities.
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