Mathematical Simulators for the Study of the Integral Calculus of Engineering Students

Currently, technological tools have positioned themselves in the first places of human development, and higher education has not been the exception. This research aims to improve academic performance with the application of mathematical simulators (Wólfram Alpha, GeoGebra, Derive, and Matlab) as a didactic strategy for the study of integral calculus in engineering students. This research has a quantitative approach, which allows for the investigation of the data from academic activities; likewise, it includes an explanatory study with the purpose of verifying the relationship that exists between the dependent and independent variables. In addition, the method of the questionnaire technique with raised exercises was used, and then the qualification averages of the groups were taken. Similarly, the perspective provided a solid base to analyze the data objectively and establish statistical relationships between the variables involved. The methodology used in this study was to obtain precise and measurable information on the impact of mathematical simulators on learning integral calculus. The questionnaire technique with posed exercises made it possible to collect data directly from the participants, providing detailed information on their understanding and performance in relation to integral calculus. The exercises posed in the questionnaire served as a structured way to assess the knowledge and skills acquired by students. The design applied in the study is made up of two control and experimental groups, applying the pretest and posttest methods. For the analysis and interpretation of data, the parametric statistical student’s T-test was used for related samples, where the simulators significantly influenced the learning of integral calculus, at a significance level of 5%. The results of the analysis indicated that the mathematical simulators significantly influenced the learning of integral calculus. That is, statistically significant improvements were observed in the academic performance of the students after the intervention with the simulators. Briefly, the study used a two-group (control and experimental) design, applied pretest and posttest methods to assess academic performance, and used the Student’s T-test for related samples in data analysis. Therefore, the importance of the role of the teacher in the learning process of higher mathematics is exemplified. Keywords: mathematical simulators, integral calculus, Derive, GeoGebra, Wolfram, Matlab. Resumen Actualmente, las herramientas tecnológicas se han posicionado en los primeros lugares del desarrollo humano, y la Educación Superior no ha sido la excepción, el presente trabajo de investigación tiene como finalidad mejorar el rendimiento académico con la aplicación de los simuladores matemáticos (Wólfram Alpha, GeoGebra, Derive y Matlab), como estrategia didáctica del estudio del cálculo integral en los estudiantes de ingeniería. La investigación tiene un enfoque cuantitativo, el cual, permitió indagar los datos de actividades académicas, así mismo, comprende un estudio de tipo explicativo con el propósito de comprobar la relación que existe entre las variables dependiente e independiente. Además, se utilizó el método de la técnica del cuestionario con ejercicios planteados, luego, se tomó los promedios de calificación de los grupos. Así mismo, la perspectiva proporcionó una base sólida para analizar los datos de manera objetiva y establecer relaciones estadísticas entre las variables involucradas. En este estudio, se ha utilizado esta metodología para obtener información precisa y medible sobre el impacto de los simuladores matemáticos en el aprendizaje del cálculo integral. La técnica del cuestionario con ejercicios planteados ha permitido recopilar datos directamente de los participantes, brindando información detallada sobre su comprensión y desempeño en relación con el cálculo integral. Los ejercicios planteados en el cuestionario sirven como una forma estructurada de evaluar el conocimiento y las habilidades adquiridas por los estudiantes. El diseño aplicado en el estudio está constituido por dos grupos control y experimental, aplicando la prueba del pretest y postest. Para el análisis e interpretación de datos se utilizó la prueba estadística paramétrica T - Student para muestras relacionadas, donde, los simuladores influyeron de manera significativa en el aprendizaje del cálculo integral, a un nivel de significancia del 5%. Los resultados del análisis indicaron que los simuladores matemáticos influyeron de manera significativa en el aprendizaje del cálculo integral. Es decir, se observaron mejoras estadísticamente significativas en el rendimiento académico de los estudiantes después de la intervención con los simuladores. En pocas palabras, el estudio utilizó un diseño con dos grupos (control y experimental), aplicó pruebas de pretest y postest para evaluar el rendimiento académico, y empleó la prueba estadística T-Student para muestras relacionadas en el análisis de los datos. Los resultados mostraron que los simuladores matemáticos tuvieron un impacto significativo en el aprendizaje del cálculo integral, demostrando mejoras estadísticamente significativas en el rendimiento académico de los estudiantes. Por consiguiente, se ejemplifica la importancia del rol del docente en el proceso de aprendizaje de la matemática superior. Palabras Clave: simuladores matemáticos, Cálculo Integral, Derive, GeoGebra, Wólfram, Matlab

Search for a common baryon source in high-multiplicity pp collisions at the LHC

We report on the measurement of the size of the particle-emitting source from two-baryon correlations with ALICE in high-multiplicity pp collisions at s=13 TeV. The source radius is studied with low relative momentum p–p, p‾–p‾, p–Λ, and p‾–Λ‾ pairs as a function of the pair transverse mass mT considering for the first time in a quantitative way the effect of strong resonance decays. After correcting for this effect, the radii extracted for pairs of different particle species agree. This indicates that protons, antiprotons, Λ s, and Λ‾ s originate from the same source. Within the measured mT range (1.1–2.2) GeV/c2the invariant radius of this common source varies between 1.3 and 0.85 fm. These results provide a precise reference for studies of the strong hadron–hadron interactions and for the investigation of collective properties in small colliding systems. © 2020 CERN for the benefit of the ALICE CollaborationPeer reviewe

Long- and short-range correlations and their event-scale dependence in high-multiplicity pp collisions at 1as = 13 TeV

Two-particle angular correlations are measured in high-multiplicity proton-proton collisions at s = 13 TeV by the ALICE Collaboration. The yields of particle pairs at short-( 06\u3b7 3c 0) and long-range (1.6 < | 06\u3b7| < 1.8) in pseudorapidity are extracted on the near-side ( 06\u3c6 3c 0). They are reported as a function of transverse momentum (pT) in the range 1 < pT< 4 GeV/c. Furthermore, the event-scale dependence is studied for the first time by requiring the presence of high-pT leading particles or jets for varying pT thresholds. The results demonstrate that the long-range \u201cridge\u201d yield, possibly related to the collective behavior of the system, is present in events with high-pT processes as well. The magnitudes of the short- and long-range yields are found to grow with the event scale. The results are compared to EPOS LHC and PYTHIA 8 calculations, with and without string-shoving interactions. It is found that while both models describe the qualitative trends in the data, calculations from EPOS LHC show a better quantitative agreement for the pT dependency, while overestimating the event-scale dependency. [Figure not available: see fulltext.

Global baryon number conservation encoded in net-proton fluctuations measured in Pb–Pb collisions at √sNN = 2.76 TeV

Experimental results are presented on event-by-event net-proton fluctuation measurements in Pb–Pb collisions at √SNN=2.76 TeV, recorded by the ALICE detector at the CERN LHC. These measurements have as their ultimate goal an experimental test of Lattice QCD (LQCD) predictions on second and higher order cumulants of net-baryon distributions to search for critical behavior near the QCD phase boundary. Before confronting them with LQCD predictions, account has to be taken of correlations stemming from baryon number conservation as well as fluctuations of participating nucleons. Both effects influence the experimental measurements and are usually not considered in theoretical calculations. For the first time, it is shown that event-by-event baryon number conservation leads to subtle long-range correlations arising from very early interactions in the collisions.publishedVersio

Evidence of Spin-Orbital Angular Momentum Interactions in Relativistic Heavy-Ion Collisions

The first evidence of spin alignment of vector mesons (K^{*0} and ϕ) in heavy-ion collisions at the Large Hadron Collider (LHC) is reported. The spin density matrix element ρ_{00} is measured at midrapidity (|y|<0.5) in Pb-Pb collisions at a center-of-mass energy (sqrt[s_{NN}]) of 2.76 TeV with the ALICE detector. ρ_{00} values are found to be less than 1/3 (1/3 implies no spin alignment) at low transverse momentum (p_{T}<2  GeV/c) for K^{*0} and ϕ at a level of 3σ and 2σ, respectively. No significant spin alignment is observed for the K_{S}^{0} meson (spin=0) in Pb-Pb collisions and for the vector mesons in pp collisions. The measured spin alignment is unexpectedly large but qualitatively consistent with the expectation from models which attribute it to a polarization of quarks in the presence of angular momentum in heavy-ion collisions and a subsequent hadronization by the process of recombination

ϒ production in p–Pb collisions at sNN=8.16 TeV

ϒproduction in p–Pbinteractions is studied at the centre-of-mass energy per nucleon–nucleon collision √sNN=8.16TeV with the ALICE detector at the CERN LHC. The measurement is performed reconstructing bottomonium resonances via their dimuon decay channel, in the centre-of-mass rapidity intervals 2.03 &lt;3.53and −4.46 &lt;−2.96, down to zero transverse momentum. In this work, results on the ϒ(1S) production cross section as a function of rapidity and transverse momentum are presented. The corresponding nuclear modification factor shows a suppression of the ϒ(1S) yields with respect to ppcollisions, both at forward and backward rapidity. This suppression is stronger in the low transverse momentum region and shows no significant dependence on the centrality of the interactions. Furthermore, the ϒ(2S) nuclear modification factor is evaluated, suggesting a suppression similar to that of the ϒ(1S). A first measurement of the ϒ(3S) has also been performed. Finally, results are compared with previous ALICE measurements in p–Pbcollisions at √sNN=5.02TeV and with theoretical calculations

Measurement of the non-prompt D-meson fraction as a function of multiplicity in proton-proton collisions at s \sqrt{s} = 13 TeV

The fractions of non-prompt (i.e. originating from beauty-hadron decays) D0 and D+ mesons with respect to the inclusive yield are measured as a function of the charged-particle multiplicity in proton-proton collisions at a centre-of-mass energy of √s = 13 TeV with the ALICE detector at the LHC. The results are reported in intervals of transverse momentum (pT) and integrated in the range 1 < pT < 24 GeV/c. The fraction of non-prompt D0 and D+ mesons is found to increase slightly as a function of pT in all the measured multiplicity intervals, while no significant dependence on the charged- particle multiplicity is observed. In order to investigate the production and hadronisation mechanisms of charm and beauty quarks, the results are compared to PYTHIA 8 as well as EPOS 3 and EPOS 4 Monte Carlo simulations, and to calculations based on the colour glass condensate including three-pomeron fusion

Inclusive and multiplicity dependent production of electrons from heavy-flavour hadron decays in pp and p-Pb collisions

Measurements of the production of electrons from heavy-flavour hadron decays in pp collisions at root s = 13 TeV at midrapidity with the ALICE detector are presented down to a transverse momentum (p(T)) of 0.2 GeV/c and up to p(T) = 35 GeV/c, which is the largest momentum range probed for inclusive electron measurements in ALICE. In p-Pb collisions, the production cross section and the nuclear modification factor of electrons from heavy-flavour hadron decays are measured in the p(T) range 0.5 < p(T) < 26 GeV/c at root s(NN) = 8.16 TeV. The nuclear modification factor is found to be consistent with unity within the statistical and systematic uncertainties. In both collision systems, first measurements of the yields of electrons from heavy-flavour hadron decays in different multiplicity intervals normalised to the multiplicity-integrated yield (self-normalised yield) at midrapidity are reported as a function of the self-normalised charged-particle multiplicity estimated at midrapidity. The self-normalised yields in pp and p-Pb collisions grow faster than linear with the self-normalised multiplicity. A strong p(T) dependence is observed in pp collisions, where the yield of high-p(T) electrons increases faster as a function of multiplicity than the one of low-p(T) electrons. The measurement in p-Pb collisions shows no p(T) dependence within uncertainties. The self-normalised yields in pp and p-Pb collisions are compared with measurements of other heavy-flavour, light-flavour, and strange particles, and with Monte Carlo simulations