Compact Multi-Mode Filtering Power Divider with High Selectivity, Improved Stopband and In-band Isolation

This letter presents a new compact multi-mode filtering power divider (FPD) design based on co-shared FPD topology with sharp frequency selectivity, improved out-of-band harmonic rejection and port-to-port isolation. Power splitting and quasi-elliptic filtering functions are achieved by masterly integrating only one triple-mode resonator. By loading different open-circuited stubs at the input/output ports, multiple additional transmission zeros (TZs) are generated at both lower and upper stopband, resulting in an improved stopband performance. Meanwhile, a better port-to-port isolation is obtained by adopting frequency-dependent resistor-capacitor parallel isolation network. The proposed multi-mode FPD design stands out from those in the literature by both nice operation performance and compact topology with only one resonator. For demonstration purposes, one triple-mode FPD prototype and its improved one are implemented, respectively. Measured results exhibit the superiority of the FPD design.

RECOVERING THE BOUNDARY PATH SPACE OF A TOPOLOGICAL GRAPH USING POINTLESS TOPOLOGY

First, we generalize the definition of a locally compact topology given by Paterson and Welch for a sequence of locally compact spaces to the case where the underlying spaces are $T_{1}$ and sober. We then consider a certain semilattice of basic open sets for this topology on the space of all paths on a graph and impose relations motivated by the definitions of graph C*-algebra in order to recover the boundary path space of a graph. This is done using techniques of pointless topology. Finally, we generalize the results to the case of topological graphs.

Locally compact groups with totally disconnected space of subgroups

The closed subsets {\mathcal{F}(X)} of any topological space can be given a topology, called the Chabauty–Fell topology, in which {\mathcal{F}(X)} is quasi-compact. If X is a locally compact space, then {\mathcal{F}(X)} is Hausdorff. If {X=G} is a locally compact group, then the subset {\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)} of closed subgroups is closed in {\mathcal{F}(G)} , and the set of closed subgroups inherits its own compact topology, called the Chabauty topology. We develop some of the important properties of this topology. More precisely, the results contained in this paper deal with the following question: Given a locally compact topological group, when is {\mathcal{F}(G)} (resp. {\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)} ) a totally disconnected space?