Abstract Consider a proper, isometric action by unimodular locally compact group $G$ on Riemannian manifold $M$ with boundary, such that $M/G$ is compact. For an equivariant, elliptic operator $D$ $M$, and element $g \in G$, we define numerical index ${\operatorname {index}}_g(D)$, in terms of parametrix for trace associated to $g$. We prove equivariant Atiyah–Patodi–Singer theorem this index. ...

In this study, a compact semi-circular metamaterial-inspired dual-band antenna is presented. The total antenna size is 0.22 o × 0.19 o × 0.02 o. Simulation results show dual-band operation with an impedance bandwidth of 2.7% for first band (resonant at 4.1 GHz) and 25.7% for second band (resonant at 6.15 GHz). The proposed compact metamaterialinspired antenna shows monopole-like radiation patte...

We propose a triplexer in a low temperature co-fired ceramic substrate for ultra-wideband (UWB) and 2.4GHz wireless systems. This triplexer can be applied to the band of 2.4GHz wireless systems (2.4 2.5GHz), the band group 1 (3.168 4.752GHz) of multiband orthogonal frequency-division multiplexing UWB wireless systems, and the band groups 3 and 4 (6.336 9.504GHz) of the same systems. The triplex...

This article reports on monolithically integrated and low form-factor vertically-stacked coaxial resonator-based single-/multi-band filters radio frequency (RF) diplexers using stereolithography apparatus (SLA) additive manufacturing (AM). The proposed RF filtering/diplexer concepts exhibit the following unique features: 1) due to use of vertically stacked low-profile capacitively-loaded cavity...

The estimation of the underlying probability density of n i.i.d. random objects on a compact Riemannian manifold without boundary is considered. The proposed methodology adapts the technique of kernel density estimation on Euclidean sample spaces to this non-Euclidean setting. Under sufficient regularity assumptions on the underlying density, L 2 convergence rates are obtained. Index Terms — No...