Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac’s light-cone coordinate system, Lorentz boosts are squeeze transformatio...

Recently there has been interest in the collective instability regime of the free electron laser (FEL) [ 1,2]. There is also some work on the collective regime appearing in the Russian literature [3,4]. Bonifacio, Narducci and Pellegrini [5] (referred to hereafter as BNP) have discussed the collective instability regime of an FEL studying the growth of the radiation field from noise and the sat...

for transforming Legendre polynomial expansions, but it appears not to generalize to the spherical case. This paper introduces a fast algorithm for obtaining a uniform resolution representation of a function known at a latitude– Swarztrauber [12] has reviewed other transformation algolongitude grid on the surface of a sphere, equivalent to a triangular, rithms. isotropic truncation of the spher...

A large amount of 2D drawings have been produced in engineering fields. To reuse and share the available drawings efficiently, we propose two methods in this paper, namely 2.5D spherical harmonics transformation and 2D shape histogram, to retrieve 2D drawings by measuring their shape similarity. The first approach represents a drawing as a spherical function by transforming it from a 2D space i...

We show that in an optical waveguide with no material losses at wavelengths near the second-order Bragg condition, there exists two pairs of modes. One pair has identical propagation constants but have different attenuation coefficients, while a second (different from first pair) and coefficients. The four coefficients may either positive value, representing power leaking out mode or negative e...

Weak lensing of CMB anisotropies and polarization for the power spectra and higher order statistics can be handled directly in harmonic-space without recourse to real-space correlation functions. For the power spectra, this approach not only simplifies the calculations but is also readily generalized from the usual flat-sky approximation to the exact all-sky form by replacing Fourier harmonics ...

Permanent Magnet Machines (PMM) with a phase number (m) higher than three allow redundancy and lower torque ripple compared to their three phase counterparts. In this paper, a six phase permanent magnet machine with surface rotor magnets, designed with fractional slot tooth winding is proposed. A stator design with fractional slot tooth winding allows the design of a compact machine through sho...

A fundamental characteristic of spontaneous brain activity is coherent oscillations covering a wide range of frequencies. Interestingly, these temporal oscillations are highly correlated among spatially distributed cortical areas forming structured correlation patterns known as the resting state networks, although the brain is never truly at "rest." Here, we introduce the concept of harmonic br...

The Selective Harmonic Elimination (SHE) technique is the fundamental switching frequency scheme which is used to eliminate specific order harmonics. In this paper, the elimination of low order harmonics in cascaded multilevel inverter with equal DC sources is proposed. The modulation strategy used here is SHEPWM in which non linear equations that characterize the low order harmonics are obtain...