Mechanical milling of aluminum powders with two immiscible liquids, acetonitrile and hexane, produced roughly spherical particles increased flowability sizes in the range tens to hundreds microns specific surface areas 15 – 30 m2/g. The near shapes comprised agglomerated flakes. Samples were milled from 0.5 2 hours a planetary mill. Longer times led reduced sizes, while porosity area peaked at ...

For xed c, Prolate Spheroidal Wave Functions (PSWFs), denoted by ψn,c, form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith c. They have been largely studied and used after the seminal work of D. Slepian and his co-authors. In several applications, uniform estimates of the ψn,c in n and c, are needed. To progress in this direction, we push fo...

An important problem in communication engineering is the energy concentration problem, that is the problem of finding a signal bandlimited to [−σ, σ] with maximum energy concentration in the interval [−τ, τ ], 0 < τ, in the time domain, or equivalently, finding a signal that is time limited to the interval [−τ, τ ] with maximum energy concentration in [−σ, σ] in the frequency domain. This probl...

We examine the merits of using prolate spheroidal wave functions (PSWFs) as basis functions when solving hyperbolic PDEs using pseudospectral methods. The relevant approximation theory is reviewed and some new approximation results in Sobolev spaces are established. An optimal choice of the band-limit parameter for PSWFs is derived for single-mode functions. Our conclusion is that one might gai...

Many systems of orthogonal polynomials and functions are bases of a variety of function spaces, such as the Hermite and Laguerre functions which are orthogonal bases of L2(−∞,∞) and L2(0,∞), and the Jacobi polynomials which are an orthogonal basis of a weighted L2(−1, 1). The associated Legendre functions, and more generally, the spheroidal wave functions are also an orthogonal basis of L2(−1, ...

The estimation of radiative modes is a central problem in gravitational wave theory, with essential applications signal modeling and data analysis. This complicated by most astrophysically relevant systems not having that are analytically tractable. A ubiquitous workaround to use modes, but multipole moments defined spin-weighted spherical harmonics. However, only related the without angular mo...

Clifford's geometric algebra has enjoyed phenomenal development over the last 60 years by mathematicians, theoretical physicists, engineers, and computer scientists in robotics, artificial intelligence data analysis, introducing a myriad of different often confusing notations. The Euclidean 3-space, natural generalization both well-known Gibbs-Heaviside vector Hamilton's quaternions, is used he...

Granato et al. (2004) have elaborated a physically grounded model exploiting the mutual feedback between starforming spheroidal galaxies and the active nuclei growing in their cores to overcome, in the framework of the hierarchical clustering scenario for galaxy formation, one of the main challenges facing such scenario, i.e. the fact that massive spheroidal galaxies appear to have formed much ...