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Item type:Publication, Mathematical processes for the development of algebraic reasoning in geometrical situations with in-service secondary school teachers(Modestum LTD, 2024-01-01)This paper starts from the hypothesis that algebraic reasoning can be used as an axis between different mathematical domains at school. This is relevant given the importance attributed to mathematical connections for curriculum development and the algebraic reasoning makes it possible to articulate it in a coherent manner. A definition of generalized algebraic reasoning is proposed, based on the notion of elementary algebraic reasoning of the onto-semiotic approach, and it is used to highlight the presence of typical algebraic processes in problem solving in geometrical contexts. To develop these ideas, a training course is designed and implemented with in-service secondary school teachers. Based on design-based research, the results obtained are contrasted with the expected answers. In this way, relevant information is obtained on how teachers mobilize different typically algebraic processes, that is, particularization-generalization, representation-signification, decomposition-reification and modelling. Actually, it is clear to affirm that teachers need specific training to improve their skills about how algebraic reasoning can help them to develop mathematical connections with their students. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Berglund–Hübsch transpose and Sasaki–Einstein rational homology 7-spheres(Springer Science and Business Media Deutschland GmbH, 2024-08-01)We show that links of isolated hypersurface singularities defined by invertible polynomials coming from the Johnson and Kollár list of Kähler-Einstein 3-folds that are rational homology 7-spheres remain rational homology 7-spheres under the so-called Berglund-Hübsch transpose rule coming from classical mirror symmetry constructions. Actually, this rule produces twins, that is, links with same degree, Milnor number and homology H3, with the exception of iterated Thom-Sebastiani sums of singularities of chain and cycle type, where the torsion and the Milnor number vary. The Berglund-Hübsch transpose rule not only gives a framework to better understand the existence of Sasaki-Einstein twins but also gives a mechanism for producing new examples of Sasaki-Einstein twins in the rational homology 7-sphere setting. We also give reasonable conditions for a Sasaki-Einstein rational homology 7-sphere to remain Sasaki-Einstein under the Berglund-Hübsch transpose rule. In particular, we found 75 new examples of Sasaki-Einstein rational homology 7-spheres arising as links of not well-formed hypersurface singularities.2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, On the Zariski invariant of plane branches(Polish Academy of Sciences::will be referenced::ROR-ID, 2026-03-16)We show how to obtain the Zariski invariant of a plane branch employing the contact order or the intersection multiplicity with elements in a particular family of curves, and we present some consequences of this result.2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, In-service teachers' mathematical work on quadrilaterals and their technological knowledge(Modestum Limited, 2025-01-01)This article aims to analyze the mathematical work of teachers, associated with their technological knowledge (TK) of quadrilaterals teaching. The research subjects are secondary mathematics teachers. The study uses as a basis the technological pedagogical content knowledge model and the theory of mathematical working spaces. It follows a qualitative research methodology and a case study method. Mathematics teachers interact with digital artifacts to increase their TK in the development of their mathematical work by solving a task on quadrilaterals as their students would. This study presents the analysis of a task involving the construction of a quadrilateral by using GeoGebra. The study revealed that the mathematical work of teachers was favored by developing their TK and their confidence in the use of GeoGebra since using this digital technology implies recognizing the importance of exploring and visualizing representations of mathematical objects.5 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Charged-particle multiplicity distributions over a wide pseudorapidity range in p–Pb collisions at √ˢɴɴ=5.02 TeV(Springer Nature, 2025)This paper presents the primary charged-particle multiplicity distributions in proton–lead collisions at a centre-of-mass energy per nucleon–nucleon collision of √ˢɴɴ = 5.02 TeV. The distributions are reported for non-single diffractive collisions in different pseudorapidity ranges. The measurements are performed using the combined information from the Silicon Pixel Detector and the Forward Multiplicity Detector of ALICE. The multiplicity distributions are parametrised with a double negative binomial distribution function which provides satisfactory descriptions of the distributions for all the studied pseudorapidity intervals. The data are compared to models and analysed quantitatively, evaluating the first four moments (mean, standard deviation, skewness, and kurtosis). The shape evolution of the measured multiplicity distributions is studied in terms of KNO variables and it is found that none of the considered models reproduces the measurements. This paper also reports on the average charged-particle multiplicity, normalised by the average number of participating nucleon pairs, as a function of the collision energy. The multiplicity results are then compared to measurements made in proton–proton and nucleus–nucleus collisions across a wide range of collision energies.3 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Measurements of differential two-particle number and transverse momentum correlation functions in pp collisions at s = 13 TeV(Springer Nature, 2025)Differential two-particle normalized cumulants (R₂) and transverse momentum correlations (P₂) are measured as a function of the relative pseudorapidity and azimuthal angle difference (Δ η , Δ φ) of charged particle pairs in minimum bias pp collisions at √s = 13 TeV. The measurements use charged hadrons in the pseudorapidity region of |η| < 0.8 and the transverse momentum range 0.2 < pT < 2.0 GeV/c in order to focus on soft multiparticle interactions and to complement prior measurements of these correlation functions in p–Pb and Pb–Pb collisions. The correlation functions are reported for both unlike-sign and like-sign pairs and their charge-independent and charge-dependent combinations. Both the R₂ and P₂ measured in pp collisions exhibit features qualitatively similar to those observed in p–Pb and Pb–Pb collisions. The Δη and Δφ root mean square widths of the near-side peak of the correlation functions are evaluated and compared with those observed in p–Pb and Pb–Pb collisions and show smooth evolution with the multiplicity of charged particles produced in the collision. The comparison of the measured correlation functions with predictions from PYTHIA8 shows that this model qualitatively captures their basic structure and characteristics but feature important differences. In addition, the R₂ᶜᶛ is used to determine the charge balance function of hadrons produced within the detector acceptance of the measurements. The integral of the balance function is found to be compatible with those reported by a previous measurement in Pb–Pb collisions.1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, System size and energy dependence of the mean transverse momentum fluctuations at the LHC(Springer Nature, 2025)Event-by-event fluctuations of the event-wise mean transverse momentum, ⟨Pᴛ⟩, of charged particles produced in proton–proton (pp) collisions at √s = 5.02 TeV, Xe–Xe collisions at √ˢɴɴ = 5.44 TeV, and Pb–Pb collisions at √ˢɴɴ = 5.02 TeV are studied using the ALICE detector based on the integral correlator ⟨⟨ΔPᴛ ΔPᴛ⟩⟩ . The correlator strength is found to decrease monotonically with increasing produced charged-particle multiplicity measured at midrapidity in all three systems. In Xe–Xe and Pb–Pb collisions, the multiplicity dependence of the correlator deviates significantly from a simple power-law scaling as well as from the predictions of the HIJING and AMPT models. The observed deviation from power-law scaling is expected from transverse radial flow in semicentral to central Xe–Xe and Pb–Pb collisions. In pp collisions, the correlation strength is also studied by classifying the events based on the transverse spherocity, S₀ , of the particle production at midrapidity, used as a proxy for the presence of a pronounced back-to-back jet topology. Low-spherocity (jetty) events feature a larger correlation strength than those with high spherocity (isotropic). The strength and multiplicity dependence of jetty and isotropic events are well reproduced by calculations with the PYTHIA 8 and EPOS LHC models.1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Multiplicity-dependent jet modification from di-hadron correlations in pp collisions at √s = 13 TeV(Springer Science and Business Media Deutschland GmbH, 2025)Short-range correlations between charged particles are studied via two-particle angular correlations in pp collisions at √s = 13 TeV. The correlation functions are measured as a function of the relative azimuthal angle ∆φ and the pseudorapidity separation ∆η for pairs of primary charged particles within the pseudorapidity interval |η| < 0.9 and the transverse-momentum range 1 < Pᴛ < 8 GeV/c. Near-side (|∆φ| < 1.3) peak widths are extracted from a generalised Gaussian fitted over the correlations in full pseudorapidity separation (|∆η| < 1.8), while the per-trigger associated near-side yields are extracted for the short-range correlations (|∆η| < 1.3). Both are evaluated as a function of charged-particle multiplicity obtained by two different event activity estimators. The width of the near-side peak decreases with increasing multiplicity, and this trend is reproduced qualitatively by the Monte Carlo event generators PYTHIA 8, AMPT, and EPOS. However, the models overestimate the width in the low transverse-momentum region (Pᴛ < 3 GeV/c). The per-trigger associated near-side yield increases with increasing multiplicity. Although this trend is also captured qualitatively by the considered event generators, the yield is mostly overestimated by the models in the considered kinematic range. The measurement of the shape and yield of the short-range correlation peak can help us understand the interplay between jet fragmentation and event activity, quantify the narrowing trend of the near-side peak as a function of transverse momentum and multiplicity selections in pp collisions, and search for final-state jet modification in small collision systems.2