The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections in the case of non graded associative unital algebras with involution. We extend this framework to the case of Z2-graded unital involutive algeb...

Abstract. If M is a compact oriented 3-manifold, let S(M) denote the Homflypt skein module of M. We show that S(M1#M2) is isomorphic to S(M1)⊗ S(M2) modulo torsion. In fact, we show that S(M1#M2) is isomorphic to S(M1) ⊗ S(M2) if we are working over a certain localized ring. We show a similar result holds for relative skein modules. If M contains a separating 2-sphere, we give conditions under ...

Connections of KP, qKP, and Moyal type dKP constructions are developed. Some expansion of the Moyal KP constructions of Kemmoku-Saito is given with clarification of the role of spectral variables as a phase space.

Abstract. Let k be a subring of the field of rational functions in α, s which contains α, s. Let M be a compact oriented 3-manifold, and let K(M) denote the Kauffman skein module of M over k. Then K(M) is the free k-module generated by isotopy classes of framed links in M modulo the Kauffman skein relations. In the case of k = Q(α, s), the field of rational functions in α, s, we give a basis fo...

We discuss the amazing interconnections between normal form theory, classical invariant theory and transvectants, modular forms and Rankin–Cohen brackets, representations of the Heisenberg algebra, differential invariants, solitons, Hirota operators, star products and Moyal brackets and coherent states. † Supported in part by NSF Grant DMS 98–03154.

One of the most common areas of ceramic bracket fracture is within the tie-wing complex. When an archwire is ligated into position, tensile forces are placed under the tie wing. However, no study, to date, has focused specifically on the fracture resistance of the tie-wing complex. The aim of this study is to compare the tensile fracture strength of seven currently available ceramic brackets (I...