1,551 research outputs found
A general conservative extension theorem in process algebras with inequalities
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc
Quantum Mechanics and Stochastic Mechanics for compatible observables at different times
Bohm Mechanics and Nelson Stochastic Mechanics are confronted with Quantum
Mechanics in presence of non-interacting subsystems. In both cases, it is shown
that correlations at different times of compatible position observables on
stationary states agree with Quantum Mechanics only in the case of product wave
functions. By appropriate Bell-like inequalities it is shown that no classical
theory, in particular no stochastic process, can reproduce the quantum
mechanical correlations of position variables of non interacting systems at
different times.Comment: Plain Te
Free holomorphic functions on the unit ball of B(H)^n
We develop a theory of holomorphic functions in several noncommuting (free)
variables and thus provide a framework for the study of arbitrary n-tuples of
operators. The main topics are the following: Free holomorphic functions and
Hausdorff derivations; Cauchy, Liouville, and Schwartz type results for free
holomorphic functions; Algebras of free holomorphic functions; Free analytic
functional calculus and noncommutative Cauchy transforms; Weierstrass and
Montel theorems for free holomorphic functions; Free pluriharmonic functions
and noncommutative Poisson transforms; Hardy spaces of free holomorphic
functions.Comment: 51 page
- …