Correcció a l'article "Anàlisi formalment recursiva"

En l'article citat en el títol, publicat en aquesta mateixa revista [1], es demostren, basats en el formalisme AFR (aritmética formalment recursiva), els teoremes de Bolzano-Weierstrass [4 .8, pp. 63-68] i els teoremes del máxim i del mínim i de Bolzano per a funcions contínues [5 .9 i 5.10, pp. 71-74]. Peró en les demostracions d'aquests teoremes s'utilitza sistemáticament, ja sigui de manera explícita o implícita, una forma del metateorema de minimització (p. 40) que no está justificada

Terrorismo, derecho internacional público y derecho de la Unión Europea

Ponencia recogida en las actas de los Cursos de Derecho Internacional y Relaciones Internacionales de Vitoria-Gasteiz organizados por la Facultad de Derecho de la Universidad del País Vasco.Los acontecimientos internacionales de los últimos años revelan que el terrorismo es el problema fundamental a resolver por el Estado de Derecho en las democracias occidentales. El terrorismo intenta desestabilizar regímenes democráticos extendiendo la consideración de víctima potencial a todos los integrantes de una sociedad. Los hechos tristemente han demostrado que no hay Estado invulnerable frente al terrorismo2 . La necesidad de una respuesta está fuera de toda duda. Ahora bien, dentro de las democracias occidentales existen modelos de respuesta diferentes. En este curso intentaré defender la tesis de que el modelo europeo es más sensato, más ajustado a la regla de derecho, y a la larga más eficaz que el modelo norteamericano de los últimos años.The international events of recent years reveal that terrorism is the fundamental problem to be solved by the rule of law in democracies Western Terrorism tries to destabilize democratic regimes by extending the consideration of potential victim to all the members of a society. The facts sadly they have shown that there is no invulnerable state against terrorismo. The need for an answer is beyond doubt. Now, within the democracies Western countries there are different response models. In this course I will try to defend the thesis that the European model is more sensible, more adjusted to the rule of law, and to the long more effective than the North American model of recent years

Asymmetric trehalose analogues to probe disaccharide processing pathways in mycobacteria

The uptake and metabolism of the disaccharide trehalose by Mycobacterium tuberculosis is essential for the virulence of this pathogen. Here we describe the chemoenzymatic synthesis of new azido-functionalised asymmetric trehalose probes that resist degradation by mycobacterial enzymes and are used to probe trehalose processing pathways in mycobacteria

Crab cavity option for LHC IR upgrade

Crab cavities, initially proposed by Palmer, are used to impart a z-dependent transverse kick to rotate particle bunches. An appropriate rotation of the bunch ensures head-on collisions to recover the geometric luminosity from the presence of a finite crossing angle of the IR

CRAB-CAVITY BEAM DYNAMICS ISSUES FOR AN LHC UPGRADE

Modern colliders bring into collision a large number of bunches per pulse or per turn to achieve a high luminosity. The long-range beam-beam effects arising from parasitic encounters at such colliders are mitigated by introducing a crossing angle. Under these conditions, crab cavities can be used to restore effective head-on collisions and thereby to increase the geometric luminosity. The crab cavities have been proposed for both linear and circular colliders. The crab cavities are rf cavities operated in a transverse dipole mode, which imparts on the beam particles a transverse kick that varies with the longitudinal position along the bunch. The use of crab cavities in the LHC may not only raise the luminosity, but it could also complicate the beam dynamics, e.g. crab cavities might not only cancel synchro-betatron resonances excited by the crossing angle but they could also excite new ones, they could reduce the dynamic aperture for off-momentum particles, they could degrade the collimation cleaning efficiency, and so on. In this note, we summarize the results of several preliminary studies of beam-dynamics challenges associated with crab cavities in the LHC

BPM calibration independent LHC optics correction

The tight mechanical aperture for the LHC imposes severe constraints on both the beta and dispersion beating. Robust techniques to compensate these errors are critical for operation of high intensity beams in the LHC. We present simulations using realistic errors from magnet measurements and alignment tolerances in the presence of BPM noise. Correction reveals that the use of BPM calibration and model independent observables are key ingredients to accomplish optics correction. Experiments at RHIC to verify the algorithms for optics correction are also presented

Measurement of Resonance Driving Terms at SPS at 26 GeV

In 2001 a series of experiments has been performed at the SPS at an energy of 26 GeV to measure resonance driving terms. Theory predicts that these terms can be determined by harmonic analysis of BPM data recorded after applying single kicks. This analysis works equally well for linear and non–linear diagnostics of accelerators. Results of the experiments are presented, including a direct measurement of resonance driving terms and a comparison to the theory

Tune Shift Due to Crossing Collision and CRAB Collision

The use of crab cavities in the LHC may not only raise the luminosity, but it could also complicate the beam dynamics, e.g. crab cavities might not only cancel synchrobetatron resonances excited by the crossing angle but they could also excite new ones. In this paper, we use weakstrong beam-beam model to study the incoherent linear tune shift of the weak beam, for the crossing collision case and crab collision case with a nite crossing angle. The tune shift is also compared among the head-on collision, crossing collision and crab collision cases, both analytically and numerically