In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic functions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectral-Galerkin method is proposed and analyzed for ellipti...

It is common practice to spatially smooth fMRI data prior to statistical analysis and a number of different smoothing techniques have been proposed (e.g., Gaussian kernel filters, wavelets, and prolate spheroidal wave functions). A common theme in all these methods is that the extent of smoothing is chosen independently of the data, and is assumed to be equal across the image. This can lead to ...

We find a close relationship between the discrete KarhunenLoeve transform (KLT) and the discrete prolate spheroidal wave functions (DPSWF). We show that the DPSWF form a natural basis for an expansion of the eigenfunctions of the KLT in the frequency domain, and then determine more general conditions that any set of functions must obey to be a valid basis. We also present approximate solutions ...

0885–3010/$25.00 © 2014 IEEE Abstract—Across a range of spectral estimation problems and beam focusing problems, it is necessary to constrain the properties of a function and its Fourier transform. In many cases, compact functions in both domains are desired, within the theoretical bounds of the uncertainty principle. Recently, a hyperbolic sine function of modified argument and power was found...

Pollen morphology of ten (10) species representing nine (9) genera, two (2) varieties in the family Cucurbitaceae from Nigeria has been examined under light microscope. The pollen grains are largely monads. Exine wall ornamentation is most often reticulate all studied with exception pollens Cucurbita maxima Duch. which echinate, this a diagnostic character for species. Cell thickness least vari...

A composite dust grain model which is consistent with the observed interstellar extinction and linear polarization is presented. The composite grain is made up of a host silicate spheroid and graphite inclusions. The extinction efficiencies of the composite spheroidal grains for three axial ratios are computed using the discrete dipole approximation (DDA). The interstellar extinction curve is e...

The new representation of the Coulomb three-body wave function via the well-known solutions of the separable Coulomb two-centre problem φj(ξ, η) = Xj(ξ)Yj(η) is obtained, where Xj(ξ) and Yj(η) are the Coulomb spheroidal functions. Its distinguishing characteristic is the coordination with the boundary conditions of the scattering problem below the three-particle breakup. That is, the wave funct...

We report the discovery of a significant old population in the dwarf spheroidal (dSph) galaxy Leo I as a result of a wide-area search with the ESO New Technology Telescope. Studies of the stellar content of Local Group dwarf galaxies have shown the presence of an old stellar population in almost all of the dwarf spheroidal galaxies. The only exception was Leo I, which alone appeared to have del...

An analytical solution is presented for the problem of magnetic diffusion into and scattering from a permeable, highly but not perfectly conducting prolate spheroid under axial excitation, expressed in terms of an infinite matrix equation. The spheroid is assumed to be embedded in a homogeneous nonconducting medium as appropriate for low-frequency, highcontrast scattering governed by magnetoqua...

Of 35 tuco-tucos (Ctenomys opimus) collected in Bolivia, South America, 31 (88%) had eimerian oocysts in their feces at the time they were examined. Eighteen (58%) of the 31 infected animals were concurrently infected with 2 or 3 eimerian species. Four species of Eimeria were recovered and are described as new species based on the characteristics of sporulated oocysts. Oocysts of Eimeria granif...