We investigate the concept of Abel continuity. A function f defined on a subset of ℝ, the set of real numbers, is Abel continuous if it preserves Abel convergent sequences. Some other types of continuities are also studied and interesting result is obtained. It turned out that uniform limit of a sequence of Abel continuous functions is Abel continuous and the set of Abel continuous functions is...

We sharpen the two main tools used to treat the compactified Jacobian of a singular curve: Abel maps and presentation schemes. First we prove a smoothness theorem for bigraded Abel maps. Second we study the two complementary filtrations provided by the images of certain Abel maps and certain presentation schemes. Third we study a lifting of the Abel map of bidegree (m, 1) to the corresponding p...

Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey’s 6ψ6 bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the 6ψ6 sum. We present a systematic approach to compute Abel pairs for bilateral and unilateral basic hypergeometric summation formulas by using the q-Gosper algorithm. It is demo...

We give a combinatorial characterization of nodal curves admitting a natural (i.e. compatible with and independent of specialization) d-th Abel map for any d ≥ 1. Let X be a smooth projective curve and d a positive integer; the classical d-th Abel map of X , αX : X d −→ PicX , associates to (p1, . . . , pd) ∈ X the class of the line bundle OX(p1 + . . .+ pd) in Pic d X . Such a morphism has goo...

A Riemann surface is associated with its Jacobian through the Abel map. Using a plane algebraic curve representation of the Riemann surface, we provide an algorithm for the numerical computation of the Abel map. Since our plane algebraic curves are of arbitrary degree and may have arbitrary singularities, the Abel map of any connected compact Riemann surface may be obtained in this way.

Using a corollary to Karamata’s main theorem [Math. Z. 32 (1930), 319—320], we prove that if a slowly decreasing sequence of real numbers is Abel summable, then it is convergent in the ordinary sense. Subjclass [2010] : 40A05; 40E05; 40G10.

Today, different formalisms exist to solve reasoning problems under uncertainty. For most of the known formalisms, corresponding computer implementations are available. The problem is that each of the existing systems has its own user interface and an individual language to model the knowledge and the queries. This paper proposes ABEL, a new and general language to express uncertain knowledge a...

In this paper, we present a method for solving the rst kind Abel integral equation. In thismethod, the rst kind Abel integral equation is transformed to the second kind Volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. By using Sidi's sinm - transformation and modied Navot-Simpson'sintegration rule, an algorithm for solving this...

1Instituto de Ciências Biomédicas Abel Salazar, Universidade do Porto, Rua Jorge Viterbo Ferreira, no 228, 4050-313 Porto, Portugal 2Paediatric Gastroenterology Service, Department of Child and Adolescent, Centro Hospitalar do Porto, Largo Abel Salazar, 4099-001 Porto, Portugal 3Paediatric Service, Unidade Hospitalar de Famalicao, Centro Hospitalar do Médio Ave, Rua de Cupertino de Miranda, 476...

In [14], Walter and Shen use an Abel summation technique to construct a positive scaling function Pr, 0 < r < 1, from an orthonormal scaling function φ that generates V0. A reproducing kernel can in turn be constructed using Pr. This kernel is also positive, has unit integral, and approximations utilitizing it display no Gibbs’ phenomenon. These results were extended to scaling vectors and mult...