Motivated by the research on social opinion dynamics over large networks, a general framework for verifying the Monotonicity Property of multi-agent dynamics is introduced. This allows a derivation of sociologically meaningful sufficient conditions for monotonicity that are tailor-made for social opinion dynamics, which typically have high non-linearity. A key part of this framework is the defi...

Let K be a field having prime characteristic p. The following conditions on a subfield k of K are equivalent: (i) || K" (k) = k and K/k is separable, (ii) k is the field of constants of an infinite higher derivation defined in K. (iii) k is the field of constants of a set of infinite higher derivations defined in K. If K/k is separably generated and k is algebraically closed in K, then k is the...

We demonstrate that spin-orbit coupled electrons in a magnetically doped system exert a spin torque on the local magnetization, without a flowing current, when the chemical potential is modulated in a magnetic field. The spin torque is proportional to the anomalous Hall conductivity, and its effective field strength may overcome the Zeeman field. Using this effect, the direction of the local ma...

The derivation of a local mobility model for symmetrical ultra-thin DGSOI nMOSFETs is outlined. A local-field variant is found to reproduce the dependencies of the quantummechanical mobility on silicon slab thickness and normal field with a maximum error of 10%. The model can be used with the density-gradient approach.