A Mathematical Approach to Empirical Astrophysics with Applications.

A set of consistent and optimal mathematical techniques which are well-suited for many problems incurred in observational astrophysics is presented. These methods are first derived and then their generality is demonstrated by applying them to two fundamental and diverse astronomical problems. The first is the derivation of the form of interstellar extinction in the visible and ultraviolet. It is found that two, and only two, distinct forms exist. These forms place important new restrictions on the possible physical processes effecting the interstellar grains. The second is the determination of euclidian distance measures from galactic images. It is shown that the currently available data contain serious systematic errors. An approach capable of avoiding these errors is suggested.