The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses considered along with some other properties which generalize those that guarantee harmonicity.

Audio classification is very important in many audio applications so that different audio signal can be processed appropriately. We propose an audio classification scheme which will categorise audio based on a number of audio features. These features include silence ratio, spectral centroid, harmonicity and pitch. Our preliminary experiments with silence ratio feature produce very promising cla...

‎We consider four-dimensional lie groups equipped with‎ ‎left-invariant Lorentzian Einstein metrics‎, ‎and determine the harmonicity properties ‎of vector fields on these spaces‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional ‎restricted to vector fields‎. ‎We also classify vector fields defining harmonic maps‎, ‎and calculate explicitly the energy of t...

‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...