On Legendrian Embbeddings into Open Book Decompositions

We study Legendrian embeddings of a compact Legendrian submanifold $L$ sitting in a closed contact manifold $(M,\xi)$ whose contact structure is supported by a (contact) open book $\mathcal{OB}$ on $M$. We prove that if $\mathcal{OB}$ has Weinstein pages, then there exist a contact structure $\xi'$ on $M$, isotopic to $\xi$ and supported by $\mathcal{OB}$, and a contactomorphism $f:(M,\xi) \to (M,\xi')$ such that the image $f(L)$ of any such submanifold can be Legendrian isotoped so that it becomes disjoint from the closure of a page of $\mathcal{OB}$.Comment: 14 pages, 4 figures. Major corrections made. arXiv admin note: substantial text overlap with arXiv:1003.220

Existence of compatible contact structures on G₂ -manifolds

In this paper, we show the existence of (co-oriented) contact structures on certain classes of G(2)-manifolds, and that these two structures are compatible in certain ways. Moreover, we prove that any seven-manifold with a spin structure (and so any manifold with G(2)-structure) admits an almost contact structure. We also construct explicit almost contact metric structures on manifolds with G(2)-structures

Multipath Separation-Direction of Arrival (MS-DOA) with Genetic Search Algorithm for HF channels

Cataloged from PDF version of article.Direction-of-Arrival (DOA) defines the estimation of arrival angles of an electromagnetic wave impinging on a set of sensors. For dispersive and time-varying HF channels, where the propagating wave also suffers from the multipath phenomena, estimation of DOA is a very challenging problem. Multipath Separation-Direction of Arrival (MS-DOA), that is developed to estimate both the arrival angles in elevation and azimuth and the incoming signals at the output of the reference antenna with very high accuracy, proves itself as a strong alternative in DOA estimation for HF channels. In MS-DOA, a linear system of equations is formed using the coefficients of the basis vector for the array output vector, the incoming signal vector and the array manifold. The angles of arrival in elevation and azimuth are obtained as the maximizers of the sum of the magnitude squares of the projection of the signal coefficients on the column space of the array manifold. In this study, alternative Genetic Search Algorithms (GA) for the maximizers of the projection sum are investigated using simulated and experimental ionospheric channel data. It is observed that GA combined with MS-DOA is a powerful alternative in online DOA estimation and can be further developed according to the channel characteristics of a specific HF link. (C) 2009 COSPAR. Published by Elsevier Ltd. All rights reserve