Measures induced by units

The half-open real unit interval (0,1] is closed under the ordinary multiplication and its residuum. The corresponding infinite-valued propositional logic has as its equivalent algebraic semantics the equational class of cancellative hoops. Fixing a strong unit in a cancellative hoop -equivalently, in the enveloping lattice-ordered abelian group- amounts to fixing a gauge scale for falsity. In this paper we show that any strong unit in a finitely presented cancellative hoop H induces naturally (i.e., in a representation-independent way) an automorphism-invariant positive normalized linear functional on H. Since H is representable as a uniformly dense set of continuous functions on its maximal spectrum, such functionals -in this context usually called states- amount to automorphism-invariant finite Borel measures on the spectrum. Different choices for the unit may be algebraically unrelated (e.g., they may lie in different orbits under the automorphism group of H), but our second main result shows that the corresponding measures are always absolutely continuous w.r.t. each other, and provides an explicit expression for the reciprocal density.Comment: 24 pages, 1 figure. Revised version according to the referee's suggestions. Examples added, proof of Lemma 2.6 simplified, Section 7 expanded. To appear in the Journal of Symbolic Logi

Mixing for suspension flows over skew-translations and time-changes of quasi-abelian filiform nilflows

We consider suspension flows over uniquely ergodic skew-translations on a $d$-dimensional torus $\mathbb{T}^d$, for $d \geq 2$. We prove that there exists a set $\mathscr{R}$ of smooth functions, which is dense in the space $\mathscr{C}(\mathbb{T}^d)$ of continuous functions, such that every roof function in $\mathscr{R}$ which is not cohomologous to a constant induces a mixing suspension flow. We also construct a dense set of mixing examples which is explicitly described in terms of their Fourier coefficients. In the language of nilflows on nilmanifolds, our result implies that, for every uniquely ergodic nilflow on a quasi-abelian filiform nilmanifold, there exists a dense subspace of smooth time-changes in which mixing occurs if and only if the time-change is not cohomologous to a constant. This generalizes a theorem by Avila, Forni and Ulcigrai (J. Diff. Geom., 2011) for the classical Heisenberg group.Comment: 25 pages, 3 figures. Minor corrections, revised expositio

Studio della risposta di dosimetri a stato solido da utilizzare per la misura dei campi di radiazione nell'esperimento CMS a LHC

In the CMS experiment at the Large Hadron Collider (LHC) intense radiation fields are expected during p-p collisions. To guarantee the correct functioning of CMS for many years, an on-line dosimetric system will be required to check the energy deposed (via ionizing and non-ionizing energy losses) in the detectors during collisions. In the present work, two types of solid-state dosimeters, p+/n/n+ diodes for fluence measurement and RadFETs for absorbed dose measurement, were tested in neutrons, protons, and positive pions beams. The analysis include the study of the response of the devices compared with the field intensities expected in CMS, as well as the study of different instabilities that could affect the measure of the absorbed dose for RadFETs dosimeters only

Mixing for Smooth Time-Changes of General Nilflows

We consider irrational nilflows on any nilmanifold of step at least $2$. We show that there exists a dense set of smooth time-changes such that any time-change in this class which is not measurably trivial gives rise to a mixing nilflow. This in particular reproves and generalizes to any nilflow (of step at least $2$) the main result proved in [AFU] for the special class of Heisenberg (step $2$) nilflows, and later generalized in [Rav2] to a class of nilflows of arbitrary step which are isomorphic to suspensions of higher-dimensional linear toral skew-shifts.Comment: 36 pages, 1 figur

Development and Characterisation of Radiation Monitoring Sensors for the High Energy Physics Experiments of the CERN LHC Accelerator

The Radiation monitoring at the High Energy Physic experiments of the LHC, the next CERN particle accelerator, will be a challenge for the existing dosimetry technologies. The radiation environment generated by the high-energy proton collisions will be complex reaching locally very high levels. The measurement of the energy deposition, in the IEL and NIEL channels, for semiconductor materials will therefore help to insure the reliability of the electronic systems during the LHC operation. In this work, the qualification of RadFET and p-i-n diode dosimeters, suitable for the measurements in the LHC radiation field, is presented. A series of two RadFETs and two p-i-n diodes have been then selected and characterized in detail in view of their installation at the LHC. Sensors integration issues, supported by Monte Carlo simulations studies, are also presented. Finally, the applicability of OSL materials for the dosimetry of the mixed fields at the LHC has been also discussed here