Narrow Results

This paper presents a class comprising three series of Ohmic switches, elucidating their design principles, simulation outcomes and the findings derived from measuring the initial batch of manufactured samples. The design of the membranes employs meandered beams to achieve a small actuation voltage. Initial electro-mechanical simulations, conducted within the Ansys Workbench environment, projected actuation voltages ranging from 5 to 8 Volts, whereas the measured values were marginally higher. The electromagnetic behavior of these devices demonstrated a generally qualitative concordance with simulations performed in the Ansys HFSS environment, exhibiting satisfactory performance in terms of return loss ($<-20.22$dB) and isolation ($<-14.86$dB) across the 5–30GHz frequency spectrum.

We present two families of knots which have straight number higher than crossing number. In the case of the second family, we have computed the straight number explicitly. We also give a general theorem about alternating knots that states adding an even number of crossings to a twist region will not change whether the knots are perfectly straight or not perfectly straight.

The problem concerning which Gauss diagrams can be realized by knots is an old one and has been solved in several ways. In this paper, we present a direct approach to this problem. We show that the needed conditions for realizability of a Gauss diagram can be interpreted as follows “the number of exits = the number of entrances” and the sufficient condition is based on the Jordan curve theorem. Further, using matrices, we redefine conditions for realizability of Gauss diagrams and then we give an algorithm to construct meanders.