Module white noise calculus

Itô calculus and quantum white noise calculus

Itô calculus has been generalized in white noise analysis and in quantum stochastic calculus. Quantum white noise calculus is a third generalization, unifying the two above mentioned ones and bringing some unexpected insight into some old problems studied in different fields, such as the renormalization problem in physics and the representation theory of Lie algebras. The present paper is an at...

White Noise Calculus and Hamiltonian of a Quantum Stochastic Process

Abstract. A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick’s and Ito’s theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and the conditions for unitarity have been proven. The Hamiltonian of the associated one parameter strongly continuous group has been calculated expli...

An Applicative Module Calculus

The SML-like module systems are small typed languages of their own. As is, one would expect a proof of their soundness following from a proof of subject reduction. Unfortunately, the subject-reduction property and the preservation of type abstraction seem to be incompatible. As a consequence, in relevant module systems, the theoretical study of reductions is meaningless, and for instance, the q...

A calculus of module systems

A Calculus with Lazy Module Operators

Modern programming environments such as those of Java and C# support dynamic loading of software fragments. More in general, we can expect that in the future systems will support more and more forms of interleaving of reconfiguration steps and standard execution steps, where the software fragments composing a program are dynamically changed and/or combined on demand and in different ways. Howev...