Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square order, then N must act semi-regularly on P. In addition we prove that if a finite non-Desarguesian projective plane P admits more than one nilpotent group which is regular on the points of P then P has non-square order a...

We are given a large integer N , and a fixed basis {ei : 1 ≤ i ≤ N} for the space H = C . We are also given an N -by-N matrix H that has all its diagonal entries zero, and has norm one. If σ ⊆ {1, 2, . . . , N}, let Pσ be the projection onto the space Hσ := ∨{ei : i ∈ σ}. Call such a projection basic, and the range of a basic projection a basic subspace. For each constant 0 < γ < 1, we want to ...

The Woods Hole fixed point theorem is a farreaching extension of the classical Lefschetz fixed point theorem to vector bundles. It has as corollaries a holomorphic Lefschetz formula for complex manifolds and the Weyl character formula for the irreducible representations of a compact Lie group. Apart from its importance in its own right, the Woods Hole fixed point theorem is crucial in the histo...

In some historical opera halls there are boxes located around the proscenium, commonly called proscenium or "director" boxes. These boxes have a certain influence on the initial part of the impulse response of an opera hall on the singer-auditorium, singer-singer, and singer-orchestra pit paths. During the reconstruction of the Ljubljana opera hall, measurement of a scaled model was performed t...

This study presents an effective technique for automatically identifying the singer of a music recording. Since the vast majority of popular music contains background accompaniment during most or all vocal passages, directly acquiring isolated solo voice data for extracting the singer’s vocal characteristics is usually infeasible. To eliminate the interference of background music for singer ide...