In Bulgaria there is a century-long tradition of radon measurements [8]. Since 1907 with hardly any interruption radon and later also radon progeny have been measured in mineral spas, in underground mines, in the human environment and in laboratory research. Experience from all these fields was gathered in the Faculty of Physics at St. Kliment Ohridski University of Sofia. Nowadays, exposure to...

We consider the cluster of problems raised by the relation between the notion of time, gravitational theory, quantum theory and thermodynamics; in particular, we address the problem of relating the ”timelessness” of the hypothetical fundamental general covariant quantum field theory with the ”evidence” of the flow of time. By using the algebraic formulation of quantum theory, we propose a unify...

At the core of this paper is a simple geometric object, namely the risk set of a statistical testing problem on the one hand and f -divergences, which were introduced by Csiszár (1963) on the other hand. f -divergences are measures for the hardness of a testing problem depending on a convex real valued function f on the interval [0,∞). The choice of this parameter f can be adjusted so as to mat...

In this paper we give simpler proofs of the classical continuity and lower semicontinuity theorems of Reshetnyak. 1. Main result In 1968, Reshetnyak [20] proved two important results concerning the continuity and lower semicontinuity of functionals with respect to weak-star convergence of measures. These theorems are used in a variety of areas in the calculus of variations, ranging from problem...

Existence and uniqueness of complex geodesics joining two points of a convex bounded domain in a Banach space X are considered. Existence is proved for the unit ball of X under the assumption that X is 1-complemented in its double dual. Another existence result for taut domains is also proved. Uniqueness is proved for strictly convex bounded domains in spaces with the analytic Radon-Nikodym pro...

We consider the dynamics of semi-hyperbolic semigroups generated by finitely many rational maps on the Riemann sphere. Assuming that the nice open set condition holds it is proved that there exists a geometric measure on the Julia set with exponent h equal to the Hausdorff dimension of the Julia set. Both h-dimensional Hausdorff and packing measures are finite and positive on the Julia set and ...

Conditional probability distributions seem to have a bad reputation when it comes to rigorous treatment of conditioning. Technical arguments are published as manipulations of Radon-Nikodym derivatives, although we all secretly perform heuristic calculations using elementary deenitions of conditional probabilities. In print, measurability and averaging properties substitute for intuitive ideas a...

Abstract For a pair of bounded linear Hilbert space operators A and B one considers the Lebesgue type decompositions with respect to into an almost dominated part singular part, analogous decomposition for measures in which case speaks absolutely continuous part. complete parametrization all will be given, uniqueness such characterized. In addition, it shown that has abstract Radon–Nikodym deri...

Ilias Garnier Ecole Normale Supérieure Paris [email protected] Alexandra Silva University College London [email protected] Abstract This paper introduces a categorical framework to study the exact and approximate semantics of probabilistic programs. We construct a dagger symmetric monoidal category of Borel kernels where the dagger-structure is given by Bayesian inversion. We show fu...

Radon concentrations were measured using passive dosimeters SSNTD CR-39inIllar region, Tulkarem, Palestine. The dosimeters were installed in living rooms, bedrooms, bathrooms and kitchens, which were selected randomly in the surveyed area. Indoor radon levels and the annual effective dose in houses were found to be from 4.9-116.0 Bq m and 0.11-1.73 mSv y, respectively, with average values of 38...