In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it...

In this paper, we show some applications to algebraic cycles by using higher Abel-Jacobi maps which were defined in [the author: Motives and algebraic de Rham cohomology]. In particular, we prove that the Beilinson conjecture on algebraic cycles over number fields implies the Bloch conjecture on zero-cycles on surfaces. Moreover, we construct a zero-cycle on a product of curves whose Mumford in...

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...

The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation x 7→ x−1, and there are many results available in the literature for the first kind equation. However, the equivalence breaks down when one seeks for solutions with nonconstant sign. Th...

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...

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 Anti-Brownian Electrophoretic trap (ABEL trap) allows a user to trap and manipulate individual fluorescent molecules in solution. The heart of the ABEL trap is a microfluidic cell. In previous incarnations of the ABEL trap, the microfluidic cell was formed from a polydimethylsiloxane (PDMS) stamp and a glass coverslip. Here we present an improved microfluidic cell, made entirely out of glas...

This section deals with the definition, terminologies, and properties of the Sumudu transform and the Abel integral equation. In Section 2, solution of Abel integral equation is obtained by the application of the Sumudu transform, and in Section 3, the Sumudu transform is proved for distribution spaces, and the solution of Abel integral equation in the sense of distribution is obtained. The Sum...

Previous empirical work has suggested that performance in using the Web as an information resource deteriorates when the cognitive load imposed by the content of Web pages exceeds the cognitive capacity of the user [3], [7]. This problem is particularly pronounced in users with below average cognitive capacity. The work reported in this paper describes the design, rationale and development of a...