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Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is α-inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem. Our method of proof is of independent interest. Finally, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

The purpose of the paper is to predict the aerodynamic performance of a complete scale model H-Darrieus vertical axis wind turbine (VAWT) with end plates at different operating conditions. This paper aims at understanding the flow physics around a model VAWT for three different tip speed ratios corresponding to three different flow regimes.

This study achieves a first three-dimensional hybrid lattice Boltzmann method/very large eddy simulation (LBM-VLES) model for a complete scaled model VAWT with end plates and mast using the solver PowerFLOW. The power curve predicted from the numerical simulations is compared with the experimental data collected at Erlangen University. This study highlights the complexity of the turbulent flow features that are seen at three different operational regimes of the turbine using instantaneous flow structures, mean velocity, pressure iso-contours, blade loading and skin friction plots.

The power curve predicted using the LBM-VLES approach and setup provides a good overall match with the experimental power curve, with the peak and drop after the operational point being captured. Variable turbulent flow structures are seen over the azimuthal revolution that depends on the tip speed ratio (TSR). Significant dynamic stall structures are seen in the upwind phase and at the end of the downwind phase of rotation in the deep stall regime. Strong blade wake interactions and turbulent flow structures are seen inside the rotor at higher TSRs.

The computational cost and time for such high-fidelity simulations using the LBM-VLES remains expensive. Each simulation requires around a week using supercomputing facilities. Further studies need to be performed to improve analytical VAWT models using inputs/calibration from high fidelity simulation databases. As a future work, the impact of turbulent and nonuniform inflow conditions that are more representative of a typical urban environment also needs to be investigated.

The LBM methodology is shown to be a reliable approach for VAWT power prediction. Dynamic stall and blade wake interactions reduce the aerodynamic performance of a VAWT. An ideal operation close to the peak of the power curve should be favored based on the local wind resource, as this point exhibits a smoother variation of forces improving operational performance. The 3D flow features also exhibit a significant wake asymmetry that could impact the optimal layout of VAWT clusters to increase their power density. The present work also highlights the importance of 3D simulations of the complete model including the support structures such as end plates and mast.

Accurate predictions of power performance for Darrieus VAWTs could help in better siting of wind turbines thus improving return of investment and reducing levelized cost of energy. It could promote the development of onsite electricity generation, especially for industrial sites/urban areas and renew interest for VAWT wind farms.

A first high-fidelity simulation of a complete VAWT with end plates and supporting structures has been performed using the LBM approach and compared with experimental data. The 3D flow physics has been analyzed at different operating regimes of the turbine. These physical insights and prediction capabilities of this approach could be useful for commercial VAWT manufacturers.

The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued ρ-quasi-contractive mappings in modular function spaces. We approximate fixed points of this class of nonlinear multivalued mappings in modular function spaces. Moreover, we extend the concepts of T-stability, almost T-stability and summably almost T-stability to modular function spaces and give some results.

The purpose of this study is to show that closure-based classification and regression models provide both high accuracy and interpretability.

Pattern structures allow one to approach the knowledge extraction problem in case of partially ordered descriptions. They provide a way to apply techniques based on closed descriptions to non-binary data. To provide scalability of the approach, the author introduced a lazy (query-based) classification algorithm.

The experiments support the hypothesis that closure-based classification and regression allow one to both achieve higher accuracy in scoring models as compared to results obtained with classical banking models and retain interpretability of model results, whereas black-box methods grant better accuracy for the cost of losing interpretability.

This is an original research showing the advantage of closure-based classification and regression models in the banking sphere.