Motivated by the work of Pólya, Schur, and Turán, a complete characterization of multiplier sequences for the Hermite polynomial basis is given. Laguerre's theorem and a remarkable curve theorem due to Pólya are generalized. ...

An important and long-standing open problem in universal algebra asks whether every finite lattice is isomorphic to the congruence lattice of a finite algebra. Until this problem is resolved, our understanding of finite ...

Let T : R [x] → R [x] be a linear operator such that T[ xk] = gammakxk for all k = 0, 1, 2, ..., where gamma k ∈ R . The real sequence gkinfinity k=0 is called a multiplier sequence if for any p ∈ R [x], ...

This dissertation introduces the concept of Q-Witt rings and SQ-Witt rings. A Q-Witt ring is defined as a finite quotient of a torsion free abstract Witt ring for an elementary 2-group G. Local Q-Witt rings are characterized ...

We give a complete characterization of degree two rational maps on P1 with potential good reduction over local fields. We show this happens exactly when the map corresponds to an integral point in the moduli space M2. The ...

This dissertation introduces triple gluing lattices and proves that a triple gluing lattice is small if the key subcomponents are small. Then attention is turned to triple gluing irreducible small lattices. The triple ...