It is shown that every regular Krein-Feller eigenvalue problem can be transformed to a semidefinite Sturm-Liouville problem introduced by Atkinson. This makes it possible to transfer results between the corresponding theories. In particular, Prüfer angle methods become available for Krein-Feller problems.

A combinatorial bijection between k-edge colored trees and colored Prüfer codes for labelled trees is established. This bijection gives a simple combinatorial proof for the number k(n − 2)!(nk−n n−2 ) of k-edge colored trees with n vertices.

H-local domains arise in a variety of moduleand ideal-theoretic applications. In the first half of the paper, we survey some of these applications, and collect a number of characterizations and examples of h-local domains. In the second half, we show how diverse examples of h-local Prüfer domains arise as overrings of Noetherian domains and polynomial rings in finitely many variables.

In this article, we employ a modified Prüfer substitution acting on a coupled system involving one-dimensional p-Laplacian equations. The basic properties for the initial valued problem and some estimates are obtained. We also derive an analogous Sturmian theory and give a reconstruction formula for the potential function.

In his 1974 text, Commutative Ring Theory, Kaplansky states that among the examples of non-Dedekind Prüfer domains, the main ones are valuation domains, the ring of entire functions and the integral closure of a Prüfer domain in an algebraic extension of its quotient field [Kap74, p.72]. A similar list today would likely include Kronecker function rings, the ring of integervalued polynomials an...