Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from the direct product of k copies of G to G), where G is an arbitrary finite group. We call w measure preserving if given uniform measure on G x G x ... x G, w induces uniform measure on G (for every finite G). This is the second criterion we investigate: it is not hard to see that primitivity implies measure preservation and it was conjectured that the two properties are equivalent. Our combinatorial approach to primitivity allows us to make progress on this problem and in particular prove the conjecture for k=2. It was asked whether the primitive elements of F_k form a closed set in the profinite topology of free groups. Our results provide a positive answer for F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I: A New Algorithm", and "On Primitive Words II: Measure Preservation". 42 pages, 14 figures. Some parts of the paper reorganized towards publication in the Israel J. of Mat

Photostimulated desorption performance of the future circular hadron collider beam screen

Synchrotron radiation (SR) originated at superconducting bending magnets is known to be at the origin of several beam detrimental effects related to vacuum instabilities. One of the major challenges in the design of the vacuum beam pipes of high-energy hadron colliders is the SR coping strategy. In the case of the future circular hadron collider (FCC-hh), a Cu-coated beam screen (BS) operating in the range of 40–60 K has been designed with the aim of protecting the superconducting magnet cold bores from direct synchrotron irradiation. In order to experimentally study the FCC-hh BS vacuum and cryogenic performance, two sample prototypes were manufactured and installed in the beam screen test-bench experiment (BESTEX) at the Karlsruhe Research Accelerator (KARA) at the Karlsruhe Institute of Technology (KIT). The emitted SR has a critical energy of 6.2 keV, very similar to the 4.6 keV of FCC-hh. Irradiation at both room (RT) and cryogenic (77 K) temperatures showed a significant reduction of the molecular photostimulated desorption yields (η) of the FCC-hh beam screen compared to those of Cu samples. A first approximation of η and its evolution with the photon dose accumulated on the FCC-hh BS prototype at 77 K allows to estimate that a machine conditioning period of ∼1.2 months would be needed to reduce the photostimulated molecular density at the necessary levels to ensure a 100 h beam lifetime at nominal FCC-hh operation

Commissioning of a beam screen test bench experiment with a future circular hadron collider type synchrotron radiation beam

Coping with synchrotron radiation (SR) that originated at superconducting bending magnets is one of the major challenges in the design of the vacuum beam pipes of hadron colliders. In the case of the Future Circular hadron Collider (FCC-hh), similarly as for the LHC, a beam screen, operating at higher temperatures than the cold mass, has been designed in order to preserve the superconducting magnet cold bores from direct synchrotron irradiation. The quality of the beam screen vacuum can be severely compromised by the absorption of SR into its walls, enhancing the risk for numerous beam detrimental effects to arise. In order to experimentally study such effects and develop strategies for their minimization, a beam screen test bench experiment (BESTEX) has been conceived and installed in the Karlsruhe Research Accelerator storage ring at the Karlsruhe Institute for Technology. The BESTEX has been designed to explore photon stimulated desorption, photon reflectivity, photon heat loads, and photoelectron generation originated on beam screen prototypes under irradiation of the FCC-hh-like SR spectrum. A detailed description of the BESTEX, its commissioning, and its functionality is hereby presented

Commissioning of a beam screen test bench experiment with a future circular hadron collider type synchrotron radiation beam

TesisElpresente trabajo de investigación tuvo como principalobjetivo: Determinar lasprincipales características dela gestión de calidad en atenciónalclientede lasmypedel sector comercio rubro BoticasAv. Bolognesi del distrito de Tacna, año2018, el nivel de investigación fue no experimental”descriptivo. Para la recolección de información por estrategia, se llevó al 100% de la población a quienesse les aplicó una encuesta de 22 preguntas., el cual se obtuvo los siguientes resultados: que el 80% de las mypetiene menos de 6 años en el mercado. El 50% de los colaboradores de la empresa viene laborando menos de 4 años. El 70% de los emprendedores si tienen registrados a sus colaboradores en planilla. El 60% de los emprendedores tienedefinidosu plande negocio.El 70% de los emprendedores cuenta con instalaciones propias. El 50% de los emprendedores están por programar capacitaciones para brindar un buen servicio y atención al cliente.Finalmente se concluye que la mayoría de los emprendedores si tiene yadefinido modelos estratégicos de un plan de negocios; por otro lado,falta de capacitación para atender al público, no tienen diseñado un protocolo de atención al cliente y que la prioridad de las boticas es la rentabilidad más que mejorar laexperiencia de servicio

Coxeter Groups as Beauville Groups

We generalize earlier work of Fuertes and Gonzalez-Diez as well as earlier work of Bauer, Catanese and Grunewald by classifying which of the irreducible Coxeter groups are (strongly real) Beauville groups. We also make partial progress on the much more difficult question of which Coxeter groups are Beauville groups in general as well as discussing the related question of which Coxeter groups can be used in the construction of mixed Beauville groups

Generators and commutators in finite groups; abstract quotients of compact groups

Let N be a normal subgroup of a finite group G. We prove that under certain (unavoidable) conditions the subgroup [N,G] is a product of commutators [N,y] (with prescribed values of y from a given set Y) of length bounded by a function of d(G) and |Y| only. This has several applications: 1. A new proof that G^n is closed (and hence open) in any finitely generated profinite group G. 2. A finitely generated abstract quotient of a compact Hausdorff group must be finite. 3. Let G be a topologically finitely generated compact Hausdorff group. Then G has a countably infinite abstract quotient if and only if G has an infinite virtually abelian continuous quotient.Comment: This paper supersedes the preprint arXiv:0901.0244v2 by the first author and answers the questions raised there. Latest version corrects erroneous Lemma 4.30 and adds new Cor. 1.1

Purely (Non-)Strongly Real Beauville Groups

We discuss Beauville groups whose corresponding Beauville surfaces are either always strongly real or never strongly real producing several infinite families of examples

HE-LHC: The High-Energy Large Hadron Collider – Future Circular Collider Conceptual Design Report Volume 4

In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100 km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100 TeV. Its unprecedented centre-of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries