4,412 research outputs found

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

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    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 MVMV-algebra AA was isomorphic to the segment AΓ(A,u)A \cong \Gamma(A^*, u) of a totally ordered ll-group with strong unit AA^*. This was done by the simple intuitive idea of putting denumerable copies of AA on top of each other (indexed by the integers). Moreover, he also show that any such group GG can be recovered from its segment since GΓ(G,u)G \cong \Gamma(G, u)^*, establishing an equivalence of categories. In "Interpretation of AF CC^*-algebras in Lukasiewicz sentential calculus" (J. Funct. Anal. Vol. 65) D. Mundici extended this result to arbitrary MVMV-algebras and ll-groups with strong unit. He takes the representation of AA as a sub-direct product of chains AiA_i, and observes that AiGiA \overset {} {\hookrightarrow} \prod_i G_i where Gi=AiG_i = A_i^*. Then he let AA^* be the ll-subgroup generated by AA inside iGi\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 ll-group iGi\prod_i G_i, avoiding entirely the notion of good sequence.Comment: 6 page

    Effective theories and constraints on new phyhsics

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    Anomalous moments of the top quark arises from one loop corrections to the vertices tˉtg\bar t t g and tˉtγ\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

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    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