‎in this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎we show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a lie groupoid‎. ‎using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the lie algebra of all vector fields on the smooth...

This article presents a new compact multiplexer structure and its design approach, based on novel resonant manifold. Different from typical transmission-line-based manifold multiplexers, the proposed junction is formed of coupled resonators, so that also contributes to filtering poles selectivity in passbands. The all-resonator configuration achieves more footprint than conventional multiport n...