Abstract We derive the fast convergence rates of a deep neural network (DNN) classifier with rectified linear unit (ReLU) activation function learned using hinge loss. consider three cases for true model: (1) smooth decision boundary, (2) conditional class probability, and (3) margin condition (i.e., probability inputs near boundary is small). show that DNN loss achieves rate convergences all p...

Wear is a complicated phenomenon caused by the relative movement of two contacting surfaces compressed together by a normal force. Prediction of the wear, in most cases, requires various experiments and microstructural characterization of the contacting surfaces. Mathematical models based on physical concepts could provide considerable help in understanding the physical behavior and hence the p...

Wear is a complicated phenomenon caused by the relative movement of two contacting surfaces compressed together by a normal force. Prediction of the wear, in most cases, requires various experiments and microstructural characterization of the contacting surfaces. Mathematical models based on physical concepts could provide considerable help in understanding the physical behavior and hence the p...

In the present study, an analytical investigation on the entropy generation examination for viscoelastic fluid flow involving inclined magnetic field and non-linear thermal radiation aspects with the heat source and sink over a stretching sheet has been done. The boundary layer governing partial differential equations were converted in terms of appropriate similarity transformations to non-line...

The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...

Based on calculations of activation process parameters for gold, it is shown that if the energy required to create a defect (vacancy or diffusing atom) less than certain value (h i <h si ), resulting has volume (v < v then this negative entropy, i. e. orders crystal. The changes in functions h and with increasing pressure been studied. Keywords: vacancy, self-diffusion, enthalpy, ...

the method of entropy production minimization for finding energy efficient paths of operation of process equipment is first presented using an instructive example with optimal control theory. with refer-ence to the earlier investigations, the researchers present some design rules that relate to the designs’ en-tropy production. minimum entropy production is not obtained in special cases, not ge...

Energetic acetone cations decay by methane or methyl radical loss. Although the methane-loss barrier to form the ketene cation is higher and the activation entropy is lower, it has a significant branching ratio at low energies thanks to quantum tunnelling. H-atom tunnelling can be selectively quenched and the methane-loss channel suppressed quantitatively by deuteration.