The emerging technology of interacting systems calls for new verification methods to ensure their reliability. Concurrent Game Structures are expressive abstract models for which several logics have been studied. Yet, these logics are not sufficiently expressive to support certain strategic situation which arise naturally. We propose a second-order mu-calculus enabling a straightforward specifi...

We prove a finite model theorem and infinitary completeness result for the propositional μ-calculus. The construction establishes a link between finite model theorems for propositional program logics and the theory of wellquasi-orders.

The double-controlled metric-type space (X,D) is a metric in which the triangle inequality has form D(η,μ)≤ζ1(η,θ)D(η,θ)+ζ2(θ,μ)D(θ,μ) for all η,θ,μ∈X. maps ζ1,ζ2:X×X→[1,∞) are called control functions. In this paper, we introduce novel generalization of double-composed space, where D(η,μ)≤αD(η,θ)+βD(θ,μ) our new functions α,β:[0,∞)→[0,∞) composed D inequality, multiplied with D. We establish s...

The aim of these notes is to illustrate a proof of the following remarkable Theorem of Alberti (first proved in [1]). Here, when μ is a Radon measure on Ω ⊂ R, we denote by μ its absolutely continuous part (with respect to the Lebesgue measure L ), by μ := μ− μ its singular part, and by |μ| its total variation measure. Clearly, |μ|a = |μa| and |μ|s = μ. When μ = Du for some u ∈ BV (Ω,R), we wil...

Reactions of [MoReCp(μ-PMes*)(CO)6] with internal alkynes RC≡CR yielded the phosphapropenylidene-bridged complexes [MoReCp(μ-κ2P,C:η3-PMes*CRCR)(CO)5] (Mes* = 2,4,6-C6H2tBu3; R CO2Me, Ph). Terminal HC≡CR1 gave mixtures isomers [MoReCp(μ-κ2P,C:η3-PMes*CHCR1)(CO)5] and [MoReCp(μ-κ2P,C:η3-PMes*CR1CH)(CO)5], first isomer being major (R1 CO2Me) or unique tBu), indicating relevance steric repulsions ...