Assimilation into numerical weather models of the refractivity, Abel-retrieved from radio occultations, as the local refractivity at ray tangent point may result in large errors in the presence of strong horizontal gradients (atmospheric fronts, strong convection). To reduce these errors, other authors suggested modeling the Abel-retrieved refractivity as a nonlocal linear function of the 3D re...

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...

An Abel di erential equation y p x y q x y is said to have a center at a pair of complex numbers a b if y a y b for any its solution y x with the initial value y a small enough Let p q be polynomials and let P R p Q R q P and Q satisfy Polynomial Composition condition if there exist polynomials P Q and W such that P x P W x Q x Q W x and W a W b The main result of this paper is that for a xed p...

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