For any positive integer n, a new family of periodic functions in power series form and of period n is used to solve in closed form a class of polynomial equations of order n. The n roots are the values of the appropriate function from that family taken at 0, 1, ..., n − 1. 1 Background For centuries mathematicians have sought closed-form expressions for the roots of polynomial equations of arb...

Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone-beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. In this paper, a new stable algorithm based on shifted Chebyshev polynomial approxima...

We present an Anti-Brownian Electrokinetic trap (ABEL trap) capable of trapping individual fluorescently labeled protein molecules in aqueous buffer. The ABEL trap operates by tracking the Brownian motion of a single fluorescent particle in solution, and applying a time-dependent electric field designed to induce an electrokinetic drift that cancels the Brownian motion. The trapping strength of...

Normal-hearing subjects show improved speech understanding when they wear conventional passive hearing protectors in noisy surroundings. In contrast, hearing-impaired subjects are at a disadvantage. Sound attenuation exacerbates the handicap from hearing loss (Abel et al., 1982). Level-dependent (active) hearing protectors which provide limited amplification of sounds below 85 dBA have the oppo...

The present paper is an attempt to apply the authors’ experiences of their work in validation of rule based systems (of. (Knauf, Abel, Jantke ~nd Gonzalez 1998). (Knauf, .lantke, Abd anti Philippow 1997), (Abel, Knauf, and Gonzalez 1996), (Abel Gonzalez 1997b), (Herrmann, .lantkc, and Knauf 1997), and (,lantke, Knauf and Abel 1997),t:.g.) c~e based systems. The objective of this work is both to...

Compton scatter tomography is an emerging technique with attractive applications in several fields imaging such as non-destructive testing and medical scanning. In this paper, we introduce a novel modality three dimensions fixed source single detector that moves on spherical surface. We also study the Radon transform modeling data consists integrals toric surfaces. Using harmonics arrive to gen...

The direct radiative effect of biomass burning aerosols over southern Africa S. J. Abel , E. J. Highwood, J. M. Haywood, and M. A. Stringer Department of Meteorology, University of Reading, UK Met Office, Exeter, UK Received: 8 November 2004 – Accepted: 20 November 2004 – Published: 7 March 2005 Correspondence to: S. J. Abel ([email protected]) © 2005 Author(s). This work is licensed...

The transmission of an electromagnetic field produced by a current loop finite radius through coaxial circular aperture in perfectly conducting plate is evaluated rapidly convergent formulation exact form. By applying the equivalence principle, problem first formulated Hankel transform domain, obtaining set dual integral equations which equivalent surface magnetic density defined on not known. ...