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 general method for common intervals

Given an elementary chain of vertex set V, seen as a labelling of V by the set {1, ...,n=|V|}, and another discrete structure over $V$, say a graph G, the problem of common intervals is to compute the induced subgraphs G[I], such that $I$ is an interval of [1, n] and G[I] satisfies some property Pi (as for example Pi= "being connected"). This kind of problems comes from comparative genomic in bioinformatics, mainly when the graph $G$ is a chain or a tree (Heber and Stoye 2001, Heber and Savage 2005, Bergeron et al 2008). When the family of intervals is closed under intersection, we present here the combination of two approaches, namely the idea of potential beginning developed in Uno, Yagiura 2000 and Bui-Xuan et al 2005 and the notion of generator as defined in Bergeron et al 2008. This yields a very simple generic algorithm to compute all common intervals, which gives optimal algorithms in various applications. For example in the case where $G$ is a tree, our framework yields the first linear time algorithms for the two properties: "being connected" and "being a path". In the case where $G$ is a chain, the problem is known as: common intervals of two permutations (Uno and Yagiura 2000), our algorithm provides not only the set of all common intervals but also with some easy modifications a tree structure that represents this set

A differentiable monoid of smooth maps on Lie groupoids

In this article we investigate a monoid of smooth mappings on the space of arrows of a Lie groupoid and its group of units. The group of units turns out to be an infinite-dimensional Lie group which is regular in the sense of Milnor. Furthermore, this group is closely connected to the group of bisections of the Lie groupoid. Under suitable conditions, i.e. the source map of the Lie groupoid is proper, one also obtains a differentiable structure on the monoid and can identify the bisection group as a Lie subgroup of its group of units. Finally, relations between groupoids associated to the underlying Lie groupoid and subgroups of the monoid are obtained. The key tool driving the investigation is a generalisation of a result by A. Stacey which we establish in the present article. This result, called the Stacey-Roberts Lemma, asserts that pushforwards of submersions yield submersions between the infinite-dimensional manifolds of mappings.Comment: 35 pages, v3: Step 4 in the proof of Lemma C.4 was critically flawed, added explanation and reference to P. Steffens work arXiv:2404.07931 where a correct argument is contained in Lemma 3.2.18. All results thus remain vali

On some simplicial elimination schemes for chordal graphs

We present here some results on particular elimination schemes for chordal graphs, namely we show that for any chordal graph we can construct in linear time a simplicial elimination scheme starting with a pending maximal clique attached via a minimal separator maximal (resp. minimal) under inclusion among all minimal separators

Algebraic Optimization of Binary Spatially Coupled Measurement Matrices for Interval Passing

We consider binary spatially coupled (SC) low density measurement matrices for low complexity reconstruction of sparse signals via the interval passing algorithm (IPA). The IPA is known to fail due to the presence of harmful sub-structures in the Tanner graph of a binary sparse measurement matrix, so called termatiko sets. In this work we construct array-based (AB) SC sparse measurement matrices via algebraic lifts of graphs, such that the number of termatiko sets in the Tanner graph is minimized. To this end, we show for the column-weight-three case that the most critical termatiko sets can be removed by eliminating all length-12 cycles associated with the Tanner graph, via algebraic lifting. As a consequence, IPA-based reconstruction with SC measurement matrices is able to provide an almost error free reconstruction for significantly denser signal vectors compared to uncoupled AB LDPC measurement matrices.Comment: 5 pages, 2 figures, To appear in the Proceedings of 2018 IEEE Information Theory Workshop, Guangzhou, Chin