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

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

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

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

Search for collectivity with azimuthal J/psi-hadron correlations in high multiplicity p-Pb collisions at ,root s(NN)=5.02 and 8.16 TeV

We present a measurement of azimuthal correlations between inclusive J/psi and charged hadrons in p-Pb collisions recorded with the ALICE detector at the CERN LHC. The J/psi are reconstructed at forward (p-going, 2.03 <y <3.53) and backward (Pb-going, -4.46 <y <-2.96) rapidity via their mu(+)mu(-) decay channel, while the charged hadrons are reconstructed at mid-rapidity (vertical bar eta vertical bar <1.8). The correlations are expressed in terms of associated charged-hadron yields per W . trigger. A rapidity gap of at least 1.5 units is required between the trigger J/psi and the associated charged hadrons. Possible correlations due to collective effects are assessed by subtracting the associated per-trigger yields in the low-multiplicity collisions from those in the high-multiplicity collisions. After the subtraction, we observe a strong indication of remaining symmetric structures at Delta phi approximate to 0 and Delta phi approximate to pi), similar to those previously found in two-particle correlations at middle and forward rapidity. The corresponding second-order Fourier coefficient (v(2) ) in the transverse momentum interval between 3 and 6 GeV/c is found to be positive with a significance of about 5 sigma. The obtained results are similar to the J/psi v(2) coefficients measured in Pb-Pb collisions at root s(NN) = 5.02 TeV, suggesting a common mechanism at the origin of the J/psi v(2) . (C) 2018 The Author. Published by Elsevier B.V.Peer reviewe

Measurement of jet radial profiles in Pb\u2013Pb collisions at 1asNN = 2.76 TeV

The jet radial structure and particle transverse momentum (pT) composition within jets are presented in centrality-selected Pb\u2013Pb collisions at 1asNN = 2.76 TeV. Track-based jets, which are also called charged jets, were reconstructed with a resolution parameter of R = 0.3 at midrapidity |\u3b7ch jet| < 0.6 for transverse momenta pT, ch jet = 30\u2013120 GeV/c. Jet\u2013hadron correlations in relative azimuth and pseudorapidity space (\u3c6,\u3b7) are measured to study the distribution of the associated particles around the jet axis for different pT,assoc-ranges between 1 and 20 GeV/c. The data in Pb\u2013Pb collisions are compared to reference distributions for pp collisions, obtained using embedded PYTHIA simulations. The number of high-pT associate particles (4 < pT,assoc < 20 GeV/c) in Pb\u2013Pb collisions is found to be suppressed compared to the reference by 30 to 10%, depending on centrality. The radial particle distribution relative to the jet axis shows a moderate modification in Pb\u2013Pb collisions with respect to PYTHIA. High-pT associate particles are slightly more collimated in Pb\u2013Pb collisions compared to the reference, while low-pT associate particles tend to be broadened. The results, which are presented for the first time down to pT, ch jet = 30 GeV/c in Pb\u2013Pb collisions, are compatible with both previous jet\u2013hadron-related measurements from the CMS Collaboration and jet shape measurements from the ALICE Collaboration at higher pT, and add further support for the established picture of in-medium parton energy loss

Study of the \u39b\u2013\u39b interaction with femtoscopy correlations in pp and p\u2013Pb collisions at the LHC

This work presents new constraints on the existence and the binding energy of a possible \u39b\u2013\u39b bound state, the H-dibaryon, derived from \u39b\u2013\u39b femtoscopic measurements by the ALICE collaboration. The results are obtained from a new measurement using the femtoscopy technique in (Figure presented.) collisions at s=13 TeV and p\u2013Pb collisions at sNN=5.02 TeV, combined with previously published results from (Figure presented.) collisions at s=7 TeV. The \u39b\u2013\u39b scattering parameter space, spanned by the inverse scattering length f0 121 and the effective range d0, is constrained by comparing the measured \u39b\u2013\u39b correlation function with calculations obtained within the Lednick\ufd model. The data are compatible with hypernuclei results and lattice computations, both predicting a shallow attractive interaction, and permit to test different theoretical approaches describing the \u39b\u2013\u39b interaction. The region in the (f0 121,d0) plane which would accommodate a \u39b\u2013\u39b bound state is substantially restricted compared to previous studies. The binding energy of the possible \u39b\u2013\u39b bound state is estimated within an effective-range expansion approach and is found to be B\u39b\u39b=3.2 122.4+1.6(stat) 121.0+1.8(syst) MeV