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Let X₁,…,Xₙ be independent and identically distributed random variables with distribution F. Assuming that there are measurable functions f:R²→R and g:R²→R characterizing a family F of distributions on the Borel sets of R in the way that the random variables f(X₁,X₂),g(X₁,X₂) are independent, if and only if F∈F, we propose to treat the testing problem H:F∈F,K:F∉F by applying a consistent nonparametric independence test to the bivariate sample variables (f(Xᵢ,Xⱼ),g(Xᵢ,Xⱼ)),1⩽i,j⩽n,i≠j. A parametric bootstrap procedure needed to get critical values is shown to work. The consistency of the test is discussed. The power performance of the procedure is compared with that of the classical tests of Kolmogorov–Smirnov and Cramér–von Mises in the special cases where F is the family of gamma distributions or the family of inverse Gaussian distributions.
Booster stations can fulfill a varying pressure demand with high energy-efficiency, because individual pumps can be deactivated at smaller loads. Although this is a seemingly simple approach, it is not easy to decide precisely when to activate or deactivate pumps. Contemporary activation controls derive the switching points from the current volume flow through the system. However, it is not measured directly for various reasons. Instead, the controller estimates the flow based on other system properties. This causes further uncertainty for the switching decision. In this paper, we present a method to find a robust, yet energy-efficient activation strategy.
Data-driven prediction and prevention of extreme events in a spatially extended excitable system
(2015)
The sterilization of packages in aseptic food processes is highly significant to maintain a consumer-safe product with extended shelf-life. Today, the sterilization of food packages is predominantly accomplished by gaseous hydrogen peroxide (H2O2) in combination with heat. In order to monitor this sterilization process, calorimetric gas sensors as differential set-up of two platinum temperature sensors representing a catalytically active (additionally deposition of MnO2) and a passive segment have been recently developed. The temperature rise of the exothermic decomposition serves as an indicator of the present H2O2 concentration. In the present work, a theoretical approach considering the sensor’s thermochemistry and physical transport phenomena was formulated to evaluate the temperature rise based on the energy content of gaseous H2O2. In a further part of this work, three polymers have been analyzed with respect to their application as passivation materials. The examined polymers are photoresist SU-8, perfluoroalkoxy (PFA) and fluorinated ethylene propylene (FEP). Thermal analyses by means of differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) have been conducted to determine the operation limits of the polymers. The overall chemical resistance and stability of the polymers against the harsh environmental conditions during the sterilization process have been examined by attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR).