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In this paper, we prove the existence and uniqueness of mild solutions for the impulsive fractional differential equations for which the impulses are not instantaneous in a Banach space H. The results are obtained by using the analytic semigroup theory and the fixed points theorems.

We propose a hierarchy of low-dimensional proper orthogonal decomposition (POD) models for the transient and post-transient flow around a high-lift airfoil with unsteady Coanda blowing over the trailing edge. The modal expansion comprises actuation modes as a lifting method for wall actuation following Graham et al. (Intl J. Numer. Meth. Engng, vol. 44 (7), 1999, pp. 945–972) and Kasnakoğlu et al. (Intl J. Control, vol. 81 (9), 2008, pp. 1475–1492). A novel element is separate actuation modes for different frequencies. The structure of the dynamic model rests on a Galerkin projection using the Navier–Stokes equations, simplifying mean-field considerations, and a stochastic term representing the background turbulence. The model parameters are identified with a data assimilation (4D-Var) method. We propose a model hierarchy from a linear oscillator explaining the suppression of vortex shedding by blowing to a fully nonlinear model resolving unactuated and actuated transients with steady and high-frequency modulation of blowing. The models’ accuracy is assessed through the mode amplitudes and an estimator for the lift coefficient. The robustness of the model is physically justified, and then observed for the training and the validation dataset.

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This chapter presents an algorithm to train radial basis function neural networks (RBFN) in a semi-online manner. It employs the online, evolving clustering algorithm of Kasabov and Song (2002) in the unsupervised training part of the RBFN and the ordinary least squares estimation technique for the supervised training part. Its effectiveness is demonstrated on two problems related to bankruptcy prediction in financial engineering. In all the cases, 10-fold cross validation was performed. The present algorithm, implemented in two variants, yielded more sensitivity compared to the multi layer perceptron trained by backpropagation (MLP) algorithm over all the problems studied. Based on the results, it can be inferred that the semi-online RBFN without linear terms is better than other neural network techniques. By taking the Area Under the ROC curve (AUC) as the performance metric, the proposed algorithms viz., semi-online RBFN with and without linear terms are compared with classifiers such as ANFIS, TreeNet, SVM, MLP, Linear RBF, RSES and Orthogonal RBF. Out of them TreeNet outperformed both the variants of the semi-online RBFN in both data sets considered here.

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