Eigenvalues of the basic Dirac operator on quaternion-Kahler foliations

In this paper, we give an optimal lower bound for the eigenvalues of the basic Dirac operator on a quaternion-Kahler foliation. The limiting case is characterized by the existence of quaternion-Kahler Killing spinors. We end this paper by giving some examples

Directive ultra wideband antenna for medical applications

Since the acceptance of unlicensed band of Ultra-Wideband (UWB) technology in the range between 3.1 and 10.6 GHz, the realization of low-cost UWB wireless systems is considered a fundamental research goal both for military and commercial applications. The possible use and benefits of UWB technology are significant among its potential applications, high-resolution radar and short-range ultra-high speed data transmission. However, one of the most critical challenging task of the UWB system is the designing of a compact size antenna that possess a good gain and high directivity. Thus, the aim of this project is to design and develop a directive and miniaturized antenna for UWB applications. The antenna is designed and fabricated on a Flame Retardant (FR4) laminated substrate with dielectric constant, ԑr of 4.3 and thickness of 1.6mm. Several numbers of antennas have been carried out throughout the completion of the project. Firstly, an antenna with slots on radiator has been designed. Subsequently, Ground Defected Structure (DGS) is implemented. For increasing bandwidth and impedance matching of the first antenna, thus an antenna with compact dimension of 25×45mm2 has been resulted. Finally, a reflector structure with the distance of 18mm is added for directivity and gain enhancement. The antenna with reflector has been fabricated using etching technique and being measured for the reflection coefficient. As the result, by applying reflector, the directivity and gain of the antenna has increased significantly, from 5.81dBi to 7.06dBi. This showed 21.52% gain improvement of the proposed antenna by implementing reflector. Therefore, the proposed antenna which has compact size and high gain is seen as a suitable candidate for the use of UWB applications

A brief note on the spectrum of the basic Dirac operator

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation $(M,\mathcal{F})$ with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on spin flows in terms of the O'Neill tensor and the first eigenvalue of the Dirac operator on $M$. We discuss examples and also define a new version of the basic Laplacian whose spectrum does not depend on the choice of bundle-like metric

Geometric aspects of transversal Killing spinors on Riemannian flows

We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those Riemannian flows $M$ carrying non-trivial solutions to that equation in case $M$ is a local Riemannian product, a Sasakian manifold or 3-dimensional