On the equivalence between MV-algebras and ll-groups with strong unit

In "A new proof of the completeness of the Lukasiewicz axioms"} (Transactions of the American Mathematical Society, 88) C.C. Chang proved that any totally ordered $MV$-algebra $A$ was isomorphic to the segment $A \cong \Gamma(A^*, u)$ of a totally ordered $l$-group with strong unit $A^*$. This was done by the simple intuitive idea of putting denumerable copies of $A$ on top of each other (indexed by the integers). Moreover, he also show that any such group $G$ can be recovered from its segment since $G \cong \Gamma(G, u)^*$, establishing an equivalence of categories. In "Interpretation of AF $C^*$-algebras in Lukasiewicz sentential calculus" (J. Funct. Anal. Vol. 65) D. Mundici extended this result to arbitrary $MV$-algebras and $l$-groups with strong unit. He takes the representation of $A$ as a sub-direct product of chains $A_i$, and observes that $A \overset {} {\hookrightarrow} \prod_i G_i$ where $G_i = A_i^*$. Then he let $A^*$ be the $l$-subgroup generated by $A$ inside $\prod_i G_i$. He proves that this idea works, and establish an equivalence of categories in a rather elaborate way by means of his concept of good sequences and its complicated arithmetics. In this note, essentially self-contained except for Chang's result, we give a simple proof of this equivalence taking advantage directly of the arithmetics of the the product $l$-group $\prod_i G_i$, avoiding entirely the notion of good sequence.Comment: 6 page

Effective theories and constraints on new phyhsics

Anomalous moments of the top quark arises from one loop corrections to the vertices $\bar t t g$ and $\bar t t \gamma$. We study these anomalous couplings in different frameworks: effective theories, Standard Model and 2HDM. We use available experimental results in order to get bounds on these anomalous couplings.Comment: 8 pages, 2 figures, talk presented by R. Martinez at the X Mexican School of Particles and Fields, Playa del Carmen, Mexico, 200

Detector Developments for the LHC: CMS TOB Silicon Detector Modules and ATLAS TileCal Read-Out Driver

This Research Report is divided in two different parts corresponding to two different periods of time working in different collaborations. First, a general approach to the framework where this work is set is presented at the Introduction: the CERN laboratory near Geneva, the LHC accelerator and its two general purpose experiments CMS and ATLAS. The first part of this report consists in the study of the performance of the silicon strip detectors specifically designed for the Tracker Outer Barrel (TOB) of the CMS Tracker detector. Results of the performance of CMS TOB silicon detector modules mounted on the first assembled double-sided rod at CERN are presented. These results are given in terms of noise, noise occupancies, signal to noise ratios and signal efficiencies. The detector signal efficiencies and noise occupancies are also shown as a function of threshold for a particular clustering algorithm. Signal efficiencies versus noise occupancy plots as a function of the threshold level, which could also be used to grade detector modules in rods during production, are presented. In the second part the standalone software developments for the characterization and system tests of the pre-production ATLAS TileCal Read-Out Driver (ROD) prototypes are presented. The XTestROD and XFILAR programs, specifically written for the TileCal ROD characterisation and system tests, are presented and all their functionalities are discussed in detail. These programs allow to write/read the registers and configure the different operation modes of all the modules in the ROD crate and the ROS computer. Using this software standalone data acquisition runs can also be performed through the VMEbus or standard read-out cards in ATLAS

Averaging in a Class of Stochastic Hybrid Dynamical Systems with Time-Varying Flow Maps

We present stability and recurrence results for a class of stochastic hybrid dynamical systems with oscillating flow maps. These results are developed by introducing averaging tools that parallel those already existing for ordinary differential equations and deterministic hybrid dynamical systems. Such tools can be used to examine the stability properties of the original dynamics based on the properties of a simpler dynamical system constructed from the average of the original oscillating vector field. In this work, we focus on a class of systems for which global stability and recurrence results are achievable under suitable smoothness assumptions on the dynamics. By studying the average stochastic hybrid dynamics using Lyapunov-Foster functions, we derive similar stability and recurrence results for the original stochastic hybrid system