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  • 1. Brännström, Niklas
    et al.
    Persson, Leif A.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A measure theoretic approach to linear inverse atmospheric dispersion problems2015In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 31, no 2, article id 025009Article in journal (Refereed)
    Abstract [en]

    Using measure theoretic arguments, we provide a general framework for describing and studying the general linear inverse dispersion problem where no a priori assumptions on the source function has been made (other than assuming that it is indeed a source, i.e. not a sink). We investigate the source-sensor relationship and rigorously state solvability conditions for when the inverse problem can be solved using a least-squares optimization method. That is, we derive conditions for when the least-squares problem is well-defined.

  • 2.
    Persson, Leif
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Swedish Defence Research Agency, FOI CBRN Defence and Security, SE-901 82 Umeå, Sweden.
    Boso, Jonas
    Nylén, Torbjörn
    Ramebäck, Henrik
    Application of a Monte Carlo method to the uncertainty assessment in in situ gamma-ray spectrometry2018In: Journal of Environmental Radioactivity, ISSN 0265-931X, E-ISSN 1879-1700, Vol. 187, p. 1-7Article in journal (Refereed)
    Abstract [en]

    In situ gamma-ray spectrometry has since the introduction of portable germanium detectors been a widely used method for the assessment of radionuclide ground deposition activity levels. It is, however, a method that is most often associated with fairly large and, more important, poorly known combined measurement uncertainties. In this work an uncertainty analysis of in situ gamma ray spectrometry in accordance with the Guide to the Expression of Uncertainty in Measurements is presented. The uncertainty analysis takes into account uncertainty contributions from the calibration of the detector system, the assumed activity distribution in soil, soil density, detector height and air density. As a result, measurement results from in situ gamma spectrometry will serve as a better basis for decision-making in e.g. radiological emergencies.

  • 3.
    Åhag, Per
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Czyz, Rafal
    Persson, Leif
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Radially symmetric plurisubharmonic functions2012In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 106, p. 1-17Article in journal (Refereed)
    Abstract [en]

    In this note we consider radially symmetric plurisubharmonic functions and the complex Monge–Ampère operator. We prove among other things a complete characterization of unitary invariant measures for which there exists a solution of the complex Monge–Ampère equation in the set of radially symmetric plurisubharmonic functions. Furthermore, we prove in contrast to the general case that the complex Monge–Ampère operator is continuous on the set of radially symmetric plurisubharmonic functions. Finally we characterize radially symmetric plurisubharmonic functions among the subharmonic ones using merely the laplacian.

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