With a change of variables the Abel transform gives the projection of a 2-D distribution with circular symmetry. Thus the Abel inversion formula allows one to determine the radial dependence of such a distribution from its projection. However, this inversion formula is very sensitive to noise in the projection data. When the projection data are derived from radiographic measurements, further di...

We consider a cell sorting process based on negative dielectrophoresis. The goal is to optimize the shape of an electrode network to speed up the positioning. We first show that the best electric field to impose has to be radial in order to minimize the average time for a group of particles. We can get an explicit formula in the specific case of a uniform distribution of initial positions, thro...

We discuss Stochastic Quantization of d=3 dimensional non-Abel-ian Chern-Simons theory. We demonstrate that the introduction of an appropriate regulator in the Langevin equation yields a well-defined equilibrium limit, thus leading to the correct propagator. We also analyze the connection between d=3 Chern-Simons and d=4 Topolog-ical Yang-Mills theories showing the equivalence between the corre...

We investigate the Hadamard function, the vacuum expectation values of the field square and the energy-momentum tensor of a scalar field with general curvature coupling parameter in de Sitter spacetime compactified along one of spatial dimensions. By using the Abel-Plana summation formula, we have explicitly extracted from the vacuum expectation values the part due to the compactness of the spa...

Recently, the first Abel map for a stable curve of genus g ≥ 2 has been constructed. Fix an integer d ≥ 1 and let C be a stable curve of compact type of genus g ≥ 2. We construct two d-th Abel maps for C, having different targets, and we compare the fibers of the two maps. As an application, we get a characterization of hyperelliptic stable curves of compact type with two components via the 2-n...

A simple model is presented for the analysis of inviscid flow fields over slender bodies accompanied by high rates of surface mass transfer. This model assumes a thin, inviscid injectant layer, which is separated from the outer flow by a contact discontinuity. Inviscid boundary-layer equations are shown to be applicable within the injectant layer, and the pressure gradient is found by matching ...

Through a suitable ad hoc assumption, a nonlinear PDE governing a three-dimensional weak, irrotational, steady vector field is reduced to a system of two nonlinear ODEs: the first of which corresponds to the two-dimensional case, while the second involves also the third field component. By using several analytical tools as well as linear approximations based on the weakness of the field, the fi...

Radio occultation (RO) has been proven to be a powerful technique for ionospheric electron density profile (EDP) retrieval. The Abel inversion currently used in RO EDP retrieval has degraded performance in regions with large horizontal gradients because of an assumption of spherical symmetry as indicated by many studies. Some alternative methods have been proposed in the past; the global ionosp...

We study nonparametric maximum likelihood estimation for the distribution of spherical radii using samples containing a mixture of one-dimensional, two-dimensional biased and three-dimensional unbiased observations. Since direct maximization of the likelihood function is intractable, we propose an expectation-maximization algorithm for implementing the estimator, which handles an indirect measu...

Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind Ab-1 equations . Based on the results of a previous work, concerning a closed-form solution of a general Ab-1 equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of ...