We introduce the notion of well-founded recursive order-sorted equational logic (OS) theories modulo axioms. Such theories de ne functions by well-founded recursion and are inherently terminating. Moreover, for well-founded recursive theories important properties such as con uence and su cient completeness are modular for so-called fair extensions. This enables us to incrementally check these p...

This paper introduces an analysis technique, commutativity analysis, for automatically parallelizing computations that manipulate dynamic, pointer-based data structures. Commutativity analysis views computations as composed of operations on objects. It then analyzes the program to discover when operations commute, i.e. leave the objects in the same state regardless of the order in which they ex...

After introducing the concept of commutativity for continuous-time linear time-varying systems, the related literature and the results obtained so far are presented. For a simple introduction of the commutativity of discrete-time linear time-varying systems, the problem is formulated for first-order systems. Finally, explicit necessary and sufficient conditions for the commutativity of first-or...

A ring satisfying x = x is necessarily commutative. We consider a variety of weaker forms of this condition and show that many but not all of them imply commutativity. We also present a variety of elementary proofs of the fact that x = x implies commutativity.

We obtain a criterion on the commutativity of polynomials in the enveloping algebra of a Lie algebra in terms of an involution condition with respect to the Berezin bracket. As an application, it is shown that the commutativity requirement of missing label operators for reduction chains in the missing label problem can be solved analytically. PACS numbers: 02.20Sv, 21.60Fw

We examine magnetic and electric near horizon regions of maximally supersymmetric D– brane and NS5–brane bound states and find transformations between near horizon regions with worldvolume dual magnetic and electric fluxes. These point to dual formulations of NCYM, NCOS and ODp theories in the limit of weak coupling and large spatial or temporal non-commutativity length scale in terms of weakly...