We provide exact expressions for the electrostatic energy of uniformly charged prolate and oblate spheroidal shells. We find that uniformly charged prolate spheroids of eccentricity greater than 0.9 have lower Coulomb energy than a sphere of the same area. For the volume-constrained case, we find that a sphere has the highest Coulomb energy among all spheroidal shells. Further, we derive the ch...

Background: Sheroidal degeneration , reported as a rare entity in western literature is a common ocular morbidity in our parts of India. It is commonly seen in persons who are exposed to intense sun light (excess UV radiation) reflected off the surface of the sea, snow and sand. Hence, its prevalence is more in fishermen. Clinically, it is characterised by the presence of amber coloured spherul...

Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the truncated Fourier transform, restricted to D-dimensional balls in the spatial domain and frequency domain. Despite their useful properties in many applications, GPSFs are often replaced by crude approximations. The purpose of this paper is to review the elements of computing GPSFs and associated eigenvalues. This pape...