We consider closed, Weyl-transitive groups of automorphisms of thick buildings. For each element of such a group, we derive a combinatorial formula for its scale and establish the existence of a tidy subgroup for it that equals the stabilizer of a simplex. Simplices whose stabilizers are tidy for some element of the group are characterized in terms of the minimal set of the isometry induced by ...

We employ WKB approximation up to the third order to determine the low-lying quasinormal modes for Weyl neutrino field in R-N black holes, which are the most relevant to the evolution of the field around a black hole in the intermediate stage. It is showed that the quasinormal mode frequencies for Weyl neutrino field in R-N black holes are different from those in Schwartzchild black holes ownin...

We attempt to a physical interpretation of some known static vacuum solutions of Einstein’s equations, namely, the A and B metrics of Ehlers and Kundt. All of them have axial symmetry, so they can be transformed to the Weyl form. In Weyl coordinates ln √ −g44 obeys a Laplace equation, and from this a source, called The Newtonian image source can be identified. We use the image sources to interp...

This note investigates the possibility of converses of the Weyl theorems that two conformally related metrics on a manifold have the same Weyl conformal tensor and that two projectively related connections on a manifold have the same Weyl projective tensor. It shows that, in all relevant cases, counterexamples to each of Weyl’s theorems exist except for his conformal theorem in the 4-dimensiona...

The aim of the paper is to extend the class of generalized Weyl algebras to a larger class of rings (they are also called generalized Weyl algebras) that are determined by two ring endomorphisms rather than one as in the case of ‘old’ GWAs. A new class of rings, the diskew polynomial rings, is introduced that is closely related to GWAs (they are GWAs under a mild condition). The, so-called, amb...

Recently orthonormal Wilson bases with good time–frequency localization have been constructed by Daubechies, Jaffard, and Journé. We extend this construction to Wilson sets and frames with arbitrary oversampling (or redundancy). We state conditions under which dual Weyl–Heisenberg (WH) sets induce dual Wilson sets, and we formulate duality conditions in the time domain and frequency domain. We ...

Let A be a subspace arrangement and let (A; t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(Bn), where Bn is the type B Weyl arrangement, then (A; t) counts a certain set of lattice points. This is the only known combinatorial interpretation of this polynomial in the subspace case. One can use this result to study the par...