For weighted L space on the unit sphere of R, in which the weight functions are invariant under finite reflection groups, a maximal function is introduced and used to prove the almost everywhere convergence of orthogonal expansions in h-harmonics. The result applies to various methods of summability, including the de la Vallée Poussin means and the Cesàro means. Similar results are also establi...

Let u(x; t) be the solution to the free time-dependent Schrr odinger equation at the point (x; t) in space-time R n+1 with initial data f. We characterize the size of u in terms L p (L q)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces _ H s (R n). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interpo...

This study introduces a method for estimating the model parameters of plucked string instruments using artiicial neural networks (ANN's). The system consists of a preprocessor and an ANN model. The prepro-cessor computes the time-varying harmonics of recorded sounds and this data is fed into the ANN model to implement the nonlinear mapping to the parameter space. The main advantage of this meth...

Gravimetric quantities are commonly represented in terms of high degree surface or solid spherical harmonics. After EGM2008, such expansions routinely extend to spherical harmonic degree 2190, which makes the computation of gravimetric quantities at a large number of arbitrarily scattered points in space using harmonic synthesis, a very computationally demanding process. We present here the dev...

We show that a moving vortex lattice, as it comes to a crystal edge, radiates into a free space the harmonics of the washboard frequency, omega(0)=2pi v/a, up to a superconducting gap, Delta/variant Planck's over 2pi. Here v is the velocity of the vortex lattice and a is the intervortex spacing. We compute radiation power and show that this effect can be used for the generation of terahertz rad...

In [1] a method of decomposing a 3D wave field into spherical harmonics (’eigen-beams’) by using spherical microphone arrays was introduced. It was further shown how the eigen-beams can be used for beamforming applications by means of a modal beamformer structure. This paper introduces a method for the unambiguous localization of multiple wideband acoustic sources in 3D space using the eigen-be...

In this paper we propose a suitable reference wave for Pulse Width Modulation (PWM) AC Drives. Staircase reference waves whose levels are calculated to eliminate certain harmonics are studied and a certain staircase reference waveform with L levels is constructed. When L is made very large in limit, this staircase waveform approaches a continuous one which is called Quasine (Quasi + Sine). This...