We explore the relationship between limit linear series and fibers of Abel maps in the case of curves with two smooth components glued at a single node. To an r-dimensional limit linear series satisfying a certain exactness property (weaker than the refinedness property of Eisenbud and Harris) we associate a closed subscheme of the appropriate fiber of the Abel map. We then describe this closed...

We discuss how the 1'st order speci cation and programming language ABEL could be extended with higher order functions. Several issues arise, related to subtyping, parameterization, strictness of generators and de ned functions, and to the choice between lambda expressions and currying. The paper can be regarded as an exercise in language design: how to introduce higher order functions under th...

When electrical magnetic wave passes through the ionosphere, it is reflected and disturbed. This feature will bring: 1) beneficial results i.e. as a media for radio signal long distance propagation; and 2) disadvantage results i.e. causing Global Positioning System (GPS) inaccuracy. Therefore it is necessary to build up an accurate ionospheric model for use in various applications. Because elec...

The problem of downward continuation of the gravity field from the Earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying Stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the Earth’s surface. Downward continuation is a...