In this contribution we define a new class of non-linear integrals based on decomposition integrals. These integrals are motivated by greediness of many real-life situations. Another view on this new class of integrals is that it is a generalization of both the Shilkret and PAN integrals. Moreover, it can be seen as an iterated Shilkret integral. Also, an example in time-series analysis is prov...

This paper employs one-dimensional numerical ground response analysis models to investigate seismic response of shallow cohesive and non-cohesive soil deposits on vertical propagation of horizontal shear waves. Soil response is modelled by traditional equivalent-linear (EL) frequency-domain analysis using DEEPSOIL software and nonlinear (NL) time-domain analysis using OPENSEES software. The ana...

An artificial neural network can be used as an intelligent controller to control non-linear, dynamic system through learning. It can easily accommodate non-linearities and time dependencies. Most common multi-layer feed-forward neural networks have the drawbacks of large number of neurons and hidden layers required to deal with complex problems and require large training time. To overcome these...

Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a partial differential equation, providing possibilities for accelerating computation its solution. While parallelisation in time has allowed remarkable speed-ups applications involving parabolic equations, effectiveness hyperbolic framework remains debatable: growth instabilities and slow convergence are bo...