Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gauss-type quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a sign-variable measure, which arises in connection with Gauss-Kronrod quadrature, and power (or implicit) orthogonality enc...

A unified electrodynamic approach to the guided-wave excitation theory is generalized to the waveguiding structures containing a hypothetical space-dispersive medium with drifting charge carriers possessing simultaneously elastic, piezoelectric and magnetic properties. Substantial features of our electrodynamic approach are: (i) the allowance for medium losses and (ii) the separation of potenti...

0. Introduction In a rst course in representation theory one usually learns that there are two important relations for characters of a nite group, the rst orthogonality relation and the second orthogonality relation. When one moves on to study algebras which are not necessarily group algebras it is not clear, apriori, that the study of characters would be fruitful, and one encounters various pr...

Throughout, we work in the Euclidean vector space V = R, the space of column vectors with n real entries. As inner product, we will only use the dot product v ·w = vw and corresponding Euclidean norm ‖v ‖ = √v · v . Two vectors v,w ∈ V are called orthogonal if their inner product vanishes: v ·w = 0. In the case of vectors in Euclidean space, orthogonality under the dot product means that they m...

In this paper we design space-time multiuser transceivers suitable for coping with frequency-selective multipath channels (downlink or uplink). Relying on symbol blocking, space-time codes are derived in the frequency-domain and MUI is eliminated without destroying the orthogonality of space-time block codes. The system is shown capable of providing transmit diversity while guaranteeing symbol ...

In this paper, we study the broadcasting performance of urban Vehicle-to-everything (V2X) communications at road intersections. such environments, dense buildings obstruct radio channel between vehicles in adjacent segments and Non-Line-Of-Sight (NLOS) signal propagation reduces received power level. Therefore, messages that originate from roads traveling a non-parallel direction usually have w...

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.