1.5V fully programmable CMOS Membership Function Generator Circuit with proportional DC-voltage control

A Membership Function Generator Circuit (MFGC) with bias supply of 1.5 Volts and independent DC-voltage programmable functionalities is presented. The realization is based on a programmable differential current mirror and three compact voltage-to-current converters, allowing continuous and quasi-linear adjustment of the center position, height, width and slopes of the triangular/trapezoidal output waveforms. HSPICE simulation results of the proposed circuit using the parameters of a double-poly, three metal layers, 0.5 μm CMOS technology validate the functionality of the proposed architecture, which exhibits a maximum deviation of the linearity in the programmability of 7 %

Integrability from an abelian subgroup of the diffeomorphism group

It has been known for some time that for a large class of non-linear field theories in Minkowski space with two-dimensional target space the complex eikonal equation defines integrable submodels with infinitely many conservation laws. These conservation laws are related to the area-preserving diffeomorphisms on target space. Here we demonstrate that for all these theories there exists, in fact, a weaker integrability condition which again defines submodels with infinitely many conservation laws. These conservation laws will be related to an abelian subgroup of the group of area-preserving diffeomorphisms. As this weaker integrability condition is much easier to fulfil, it should be useful in the study of those non-linear field theories.Comment: 13 pages, Latex fil