A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that all delta-functions and their derivatives are automatically generated, and insures that the Gauss theorem is correct for any distribution with a finite number of isolated point-like singularities.The method is applied to the Coulomb field, and to show the intrinsic differences between the dipole and dimonopole fields in classical electrodynamics.In all cases the method directly leads to the general expressions required by the internal consistency of classical electrodynamics.

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A straightforward introduction to the theory of Colombeau generalized functions is given with an emphasis on the underlying concepts in view of their applications to applied and theoretical problems by physicists who do not need to know all the mathematical intricacies of that theory. As an application the meaning of the square of the delta function is discussed in some detail.

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The amplitude of K s regeneration by electrons, f 2 i e /k = --(a/3) (R 2 ) ((R 2 ) is the K 6 charge radius), can be determined by comparing the rates of coherent (transmission) regeneration and of diffraction regeneration at q 2 = 0. We made a determination from 30 to 100 GeV/c, using a novel approach: Two distinct Pb regenerators, of optimized thicknesses, were exposed to a double beam, and interchanged every burst. We find (i? 2 ) = -(0.054 ± 0.026) fm 2 . The sign, magnitude, and p independence agree with predictions.