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1
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Kolmogorov-Smirnov isometries and affine automorphisms of spaces of distribution functions

100%
Molnár L.
Open Mathematics
|
2011
|
tom 9
|
nr 4
789-796
EN
In this paper we describe the structure of surjective isometries of the spaces of all absolutely continuous, singular, or discrete probability distribution functions on R equipped with the Kolmogorov-Smirnov metric. We also study the structure of affine automorphisms of the space of all distribution functions.
2
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Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions

84%
Dimov I., Georgieva R., Ostromsky T., Zlatev Z.
Open Mathematics
|
2013
|
tom 11
|
nr 8
1531-1545
EN
The influence of emission levels on the concentrations of four important air pollutants (ammonia, ozone, ammonium sulphate and ammonium nitrate) over three European cities (Milan, Manchester, and Edinburgh) with different geographical locations is considered. Sensitivity analysis of the output of the Unified Danish Eulerian Model according to emission levels is provided. The Sobol’ variance-based approach for global sensitivity analysis has been applied to compute the corresponding sensitivity measures. To measure the influence of the variation of emission levels over the pollutants concentrations the Sobol’ global sensitivity indices are estimated using efficient techniques for small sensitivity indices to avoid the effect of loss of accuracy. Theoretical studies, as well as, practical computations are performed in order to analyze efficiency of various variance reduction techniques for computing small indices. The importance of accurate estimation of small sensitivity indices is analyzed. It is shown that the correlated sampling technique for small sensitivity indices gives reliable results for the full set of indices. Its superior efficiency is studied in details.
3
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A rough curvature-dimension condition for metric measure spaces

84%
Bonciocat A.-I.
Open Mathematics
|
2014
|
tom 12
|
nr 2
362-380
EN
We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as well. For spaces that satisfy a rough curvature-dimension condition we prove a generalized Brunn-Minkowski inequality and a Bonnet-Myers type theorem.
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