Synchronized abandonments in a single server unreliable queue

We consider a single server unreliable queue represented by a 2-dimensional continuous-time Markov chain. At failure times, the present customers leave the system. Moreover, customers become impatient and perform synchronized abandonments, as long as the server is down. We analyze this model and derive the main performance measures using results from the basic q-hypergeometric series.     

Bridging the Gap Between the Dense and the Discrete: The Number Line and the “Rubber Line” Bridging Analogy

In two experiments we explored the instructional value of a cross‐domain mapping between “number” and “line” in secondary school students' understanding of density. The first experiment investigated the hypothesis that density would be more accessible to students in a geometrical context (infinitely many points on a straight line segment) compared to a numerical context (infinitely many numbers in an interval). The participants were 229 seventh to eleventh graders. The results supported this hypothesis but also showed that students' conceptions of the line segment were far from that of a dense array of points. We then designed a text-based intervention that attempted to build the notion of density in a geometrical context, making explicit reference to the number-to-points correspondence and using the “rubber line” bridging analogy (the line as an imaginary unbreakable rubber band) to convey the no-successor principle. The participants were 149 eighth and tenth graders. The text intervention improved student performance in tasks regarding the infinity of numbers in an interval; the “rubber line” bridging analogy further improved performance successfully conveying the idea that these numbers can never be found one immediately next to the other.     

Polyhedral models for generalized associahedra via Coxeter elements

Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin, and A. Zelevinsky associated to each finite type root system a simple convex polytope, called generalized associahedron. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram. In the first part of this paper, using the parametrization of cluster variables by their g-vectors explicitly computed by S.-W. Yang and A. Zelevinsky, we generalize the original construction to any orientation. In the second part we show that our construction agrees with the one given by C. Hohlweg, C. Lange, and H. Thomas in the setup of Cambrian fans developed by N. Reading and D. Speyer.     

Running of neutrino parameters and the Higgs self-coupling in a six-dimensional UED model

We investigate a six-dimensional universal extra-dimensional model in the extension of an effective neutrino mass operator. We derive the β  -functions and renormalization group equations for the Yukawa couplings, the Higgs self-coupling, and the effective neutrino mass operator in this model. Especially, we focus on the renormalization group running of physical parameters such as the Higgs self-coupling and the leptonic mixing angles. The recent measurements of the Higgs boson mass by the ATLAS and CMS Collaborations at the LHC as well as the current three-flavor global fits of neutrino oscillation data have been taken into account. We set a bound on the six-dimensional model, using the vacuum stability criterion, that allows five Kaluza–Klein modes only, which leads to a strong limit on the cutoff scale. Furthermore, we find that the leptonic mixing angle _θ12${\theta }_{12}$ shows the most sizeable running, and that the running of the angles _θ13${\theta }_{13}$ and _θ23${\theta }_{23}$ are negligible. Finally, it turns out that the findings in this six-dimensional model are comparable with what is achieved in the corresponding five-dimensional model, but the cutoff scale is significantly smaller, which means that it could be detectable in a closer future.     

Quelques consequences de la locale nilpotence des boucles de moufang commutatives

It is well-known that any finitely generated commutative Moufang loop (CML) is centrally nilpotent and has a finite derived subloop. Consequently such a loop possesses all the classical properties of noethe-rianity: any subloop is finitely generated too, any surjective endomorphism is an automorphism, etc. Besides we prove that, in any CML E(finitely generated or not) the maximal subloops are normal of prime index ; thus the Frattini quotient E_/Φ(E) is an abelian group, sub-direct product of groups of prime order. We shall study also some dual notion of the Frattini subloop, namely the subloop φ^*(E) generated by the minimal normal subloops ; it turns out that φ^*(E) is made up by the products of the prime order central elements.     

Targeting Vacancies in Nitridosilicates: Aliovalent Substitution of M2+ (M=Ca,Sr) by Sc3+ and U3+

Based on the known linking options of their fundamental building unit, that is the SiN₄ tetrahedron, nitridosilicates belong to the inorganic compound classes with the greatest structural variability. Although facilitating the discovery of novel Si–N networks, this variability represents a challenge when targeting non‐stoichometric compounds. Meeting this challenge, a strategy for targeted creation of vacancies in highly condensed nitridosilicates by exchanging divalent M²⁺ for trivalent M³⁺ using the ion exchange approach is reported. As proof of concept, the first Sc and U nitridosilicates were prepared from α‐Ca₂Si₅N₈ and Sr₂Si₅N₈. Powder X‐ray diffraction (XRD) and synchrotron single‐crystal XRD showed random vacancy distribution in Sc_0.2Ca_1.7Si₅N₈, and partial vacancy ordering in U_0.5xSr_2?0.75xSi₅N₈ with x≈1.05. The high chemical stability of U nitridosilicates makes them interesting candidates for immobilization of actinides.     

Direct and Regioselective Di-α-fucosylation on the Secondary Rim of β-Cyclodextrin

A straightforward glycosylation method is described to regio- and stereoselectively introduce two α-l -fucose moieties directly to the secondary rim of β-cyclodextrin. Using NMR and MS fragmentation studies, the nonasaccharide structure was determined, which was also visualized using molecular dynamics simulations. The reported glycosylation method proved to be robust on gram-scale, and may be generally applied to directly glycosylate β-cyclodextrins to make well-defined multivalent glycoclusters.     

Versatile vacuum chamber for in situ surface X‐ray scattering studies

A compact portable vacuum‐compatible chamber designed for surface X‐ray scattering measurements on beamline ID01 of the European Synchrotron Radiation Facility, Grenoble, is described. The chamber is versatile and can be used for in situ investigation of various systems, such as surfaces, nanostructures, thin films etc., using a variety of X‐ray‐based techniques such as reflectivity, grazing‐incidence small‐angle scattering and diffraction. It has been conceived for the study of morphology and structure of semiconductor surfaces during ion beam erosion, but it is also used for the study of surface oxidation or thin film growth under ultra‐high‐vacuum conditions. Coherent X‐ray beam experiments are also possible. The chamber is described in detail, and examples of its use are given.     

Cu-Doped ZnO Nanoparticles for Non-Enzymatic Glucose Sensing

Copper-doped zinc oxide nanoparticles (NPs) Cu_xZn_1−xO (x = 0, 0.01, 0.02, 0.03, and 0.04) were synthesized via a sol-gel process and used as an active electrode material to fabricate a non-enzymatic electrochemical sensor for the detection of glucose. Their structure, composition, and chemical properties were characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), Fourier-transform infrared (FTIR) and Raman spectroscopies, and zeta potential measurements. The electrochemical characterization of the sensors was studied using cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), and differential pulse voltammetry (DPV). Cu doping was shown to improve the electrocatalytic activity for the oxidation of glucose, which resulted from the accelerated electron transfer and greatly improved electrochemical conductivity. The experimental conditions for the detection of glucose were optimized: a linear dependence between the glucose concentration and current intensity was established in the range from 1 nM to 100 μM with a limit of detection of 0.7 nM. The proposed sensor exhibited high selectivity for glucose in the presence of various interfering species. The developed sensor was also successfully tested for the detection of glucose in human serum samples.     

Interface Fluctuations for the D = 1 Stochastic Ginzburg–Landau Equation with Nonsymmetric Reaction Term

We consider a Ginzburg–Landau equation in the interval [?ε^?1, ε^?1], ε>0, with Neumann boundary conditions, perturbed by an additive white noise of strength $\sqrt {\varepsilon } $ and reaction term being the derivative of a function which has two equal–depth wells at ±1, but is not symmetric. When ε=0, the equation has equilibrium solutions that are increasing, and connect ?1 with +1. We call them instantons, and we study the evolution of the solutions of the perturbed equation in the limit ε→0⁺, when the initial datum is close to an instanton. We prove that, for times that may be of the order of ε^?1, the solution stays close to some instanton whose center, suitably normalized, converges to a Brownian motion plus a drift. This drift is known to be zero in the symmetric case, and, using a perturbative analysis, we show that if the nonsymmetric part of the reaction term is sufficiently small, it determines the sign of the drift.