Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payo (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall t, i.e. the t of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young (1985)'s axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models

Measurements and CFD modeling of a pulverized coal flame with emphasis on ash deposition

Measurements of fly ash deposition in a 15 kW pulverized coal jet flame and CFD-based mathematical modeling have been performed. The deposits have been collected at two ports at particle Stokes numbers in the 0.02–0.34 range and particle kinetic energies not larger than 2×10-92×10-9 J. Inertial impaction and thermophoresis have been identified as main mechanisms of particle transport towards the deposition surfaces. Deposition rates on air-cooled probes (View the MathML source600–700°C surface temperature) have been measured to be 24% (Port 2) and 79.4% (Port 3) larger than those measured on uncooled probes (View the MathML source1150°C surface temperature) due to the enhanced role of thermophoresis. Complex dependencies of the deposition rate on the probe surface temperature and the probe location have been observed. The CFD-model predictions are able to reproduce these dependencies after adjustments to the particle sticking sub-model. The paper contains estimations of both the impaction and sticking efficiencies