Evidences of World`s Technical Revolution 4.0

Over last three centuries industry as it is now has dramatically changed and developed from global urbanization and steam machines to invention of PC with variety of digital devices and spreading of the Internet. The Fourth Industrial Revolution marked by emerging technology breakthroughs in a number of fields, including robotics, artificial intelligence, nanotechnology, biotechnology, the Internet of Things (IoT), 3D printing and autonomous vehicles. The Fourth Industrial Revolution was declared in Davos on “World Economic Forum” in 2016. This statement was built on the Digital Revolution, representing new ways in which technology becomes embedded within societies and even the human body

Formal completions of N\'eron models for algebraic tori

We calculate the formal group law which represents the completion of the N\'eron model of an algebraic torus over the rationals that splits in a tamely ramified abelian extension. As a tools in the proof, we define and give criterions to compute the Weil restriction of a formal group law and the analog of the fixed part of a formal group law with respect to the action of a (finite) group.Comment: 35 pages. New version with new functoriality results. Final version in the Proceedings of the London Mathematical Society, link: http://plms.oxfordjournals.org/cgi/content/abstract/pdp039?ijkey=NVyJlz51HbzrzxM&keytype=re

Localized Electron States Near a Metal-Semiconductor Nanocontact

The electronic structure of nanowires in contact with metallic electrodes of experimentally relevant sizes is calculated by incorporating the electrostatic polarization potential into the atomistic single particle Schr\"odinger equation. We show that the presence of an electrode produces localized electron/hole states near the electrode, a phenomenon only exhibited in nanostructures and overlooked in the past. This phenomenon will have profound implications on electron transport in such nanosystems. We calculate several electrode/nanowire geometries, with varying contact depths and nanowire radii. We demonstrate the change in the band gap of up to 0.5 eV in 3 nm diameter CdSe nanowires and calculate the magnitude of the applied electric field necessary to overcome the localization.Comment: 11 pages 4 figure