GeoGebra as learning tool for the search of the roots of functions in numerical methods

Physics is capable of describing, through equations, phenomena on a micro and macroscopic scale. However, most of these equations are non-linear and the identification of their roots requires the use of approximation methods, with numerical methods being a proposal based on a systematic and iterative process, that conclude only when a pre-established tolerance is satisfied. Traditional teaching of numerical methods involves the memorization of algorithms. However, this hinders student’s ability to understand the important aspects and then apply them for solving applied problems in subjects such as kinematics, dynamics, electromagnetism, etc. Therefore, this work proposes the use of GeoGebra, as a didactic tool to illustrate the functioning of single root searching algorithms. By using the dynamical graphic’s view of GeoGebra, a series of abstract and applied problems where solved by engineering students taking a numerical methods course. The scores of this test group was then compared to a test group, taught trough algorithm memorization. Results show can improve their understanding of how the bisection, false position, secant, and Newton-Raphson methods are able to find approximated solutions to polynomial and trigonometric equations. The results are compared against traditional learning, based on memorizing the steps of the algorithm for each method and the representation of the convergence of successive roots by numerical tables

Testing GeoGebra as an effective tool to improve the understanding of the concept of limit on engineering students

The impact GeoGebra on the teaching of the concept of limit was analyzed. Two groups of engineering students, studying differential calculus, served as control and test groups. The traditional teaching, based on examples solved by hand, was given to the control group while a series of activities involving the usage of the mathematical software GeoGebra were applied in an attempt of improving the degree of assimilation on the concept of limits

Learning the concept of integral through the appropriation of the competence in Riemann sums

It is proposed that the difficulty of engineering students into understanding the concept of the integral, as a way for calculating the area under a curve, can be overcame if students are taught how to translate it into the problem of calculating a Riemann sum. A series of applied problems are proposed to provide a frame that required to calculate the area under a curve to two groups of students. For one of these groups, Geogebra was proposed as a tool that could be used to maintain the focus of students into the concepts, by providing ways to easily calculate and visualize the solutions, while the other group reached to the solutions by analytically making all the calculations. Evidence was found that, to a confidence level of 95%, Riemann sums calculated with Geogebra reduce the score difference in context problems requiring the calculation of integrals, helping students to reach a better understanding on the concept of the integral as the area under the curve of a given function

Neuronas en espejo. Otra forma de aprendizaje para el ser humano. Revisión sistemática de la literatura

Resumen Introducción: Las neuronas espejo conocidas solo en el ser humano y en monos, se activan cuando el individuo realiza una acción y cuando observa una acción similar realizada por otro individuo, esto pertenece al campo de la percepción-ejecución-intención y forma parte de la teoría de la mente. Gracias a las técnicas de imagen cerebral, se han identificado algunas zonas cerebrales donde las neuronas espejo son activas, especialmente en el lóbulo parietal, área 40 de Brodman y en el lóbulo frontal posterior, área 44 de Brodman, junto al área de Broca. Por lo que el propósito de este trabajo es realizar una revisión sistemática de la literatura para correlacionar si hay problema en las neuronas espejo en los desórdenes psiquiátricos severos como la esquizofrenia y en desórdenes conductuales como la falta de empatía que se ha asociado a una “falta” de inteligencia emocional. Material y métodos: Se buscaron revisiones sistemáticas, metaanálisis y artículos doble ciego con grupo control de las revistas The New England Journal of Medicina, The Lancet y la Revista Neurology, Journal of Apply Physiology,así como Anales de Psicología, utilizando las bases de datos de Pubmed, Medline,SciELO, www.mdconsult.com, www.aha.com, www.online.ca/medline. El estudio se llevó a cabo de Marzo de 2019 a Agosto de 2019 y se realizó en el Departamento de Farmacología de la Facultad de Medicina de la propia UAEMéx. Resultados y Discusión: De 75 artículos publicados en el presente siglo XXI se extrajo la información que a manera abreviada se presenta a continuación: Existió una relación en la enfermedad autismo y la falla de las neuronas espejo en los sujetos estudiados. En pacientes epilépticos con focalización temporal presentan dificultad en las pruebas neuropsicológicas del lenguaje y de memoria, y no se puede demostrar activación de las neuronas espejo. En el caso de las psicosis esta se asocia también a disfunciones en los mecanismos de predicción del cerebro normal. Y el déficit de cognición en especial social se presentan aún más en los psicópatas. La imagen corporal se aprende de la experiencia durante el desarrollo pre y post natal con la participación de las neuronas espejo. A futuro la terapia espejo podría emplearse como adyuvante en el manejo del dolor crónico incluso en dolor por infarto miocárdico. Conclusiones: Las neuronas espejo podrían participar en la génesis y desarrollo de los síntomas en caso de pacientes autistas. Las alteraciones en la relación sustancia gris/sustancia blanca en determinadas zonas cerebrales participa en la génesis y desarrollo de los trastornos psiquiátricos. Las crisis epilépticas focalizadas en las regiones relacionadas con las neuronas espejo afectan su función. Niños y adultos con psicopatías se caracterizan por déficits emocionales. La terapia espejo ha sido usada con éxito en pacientes que han presentado amputaciones de brazos o piernas y quizá podría ayudar en el infarto y en el dolor crónico. Abstract Introduction: Mirror neurons known only in humans and monkeys, are activated when the individual performs an action and when observes a similar action performed by another individual, this belongs to the field of perception-execution-intention and is part of the theory of mind. So the purpose of this work is to perform a systematic review of the literature to correlate if there is a problem in mirror neurons in severe psychiatric disorders such as schizophrenia and behavioral disorders such as lack of empathy that has been associated with a “lack “ emotional intelligence. Material and methods: We searched systematic reviews, meta-analyzes and double-blind articles with control group of The New England Journal of Medicine, The Lancet and the Neurology Magazine, Journal of Apply Physiology, as well as Anales de Psicología, using the databases of Pubmed, Medline, SciELO, www.mdconsult.com, www.aha.com, www.online.ca/medline. The study was carried out from March 2019 to August 2019 and was carried out in the Pharmacology Department of the Faculty of Medicine of UAEMex itself. Results and Discussion: Of the 75 articles published in the 21st century, the following information was extracted: There was a relationship in the autism disease and the failure of the mirror neurons in the subjects studied. In epileptic patients with temporal focalization they present difficulty in neuropsychological tests of language and memory, and activation of mirror neurons can not be demonstrated. In the case of psychoses this is also associated with dysfunctions in the prediction mechanisms of the normal brain. And the deficit of cognition especially social appear even more in psychopaths.Body image is learned from experience during pre and post natal development with the participation of mirror neurons. In the future, mirror therapy could be used as an adjuvant in the management of chronic pain even in pain due to myocardial infarction. Conclusions: Mirror neurons could participate in the genesis and development of symptoms in autistic patients. Alterations in the gray matter / white substance ratio in certain brain areas participate in the genesis and development of psychiatric disorders. Epileptic seizures focused on regions related to mirror neurons affect their function. Children and adults with psychopathies are characterized by emotional deficits. The mirror therapy has been used successfully in patients who have had arm or leg amputations and could perhaps help in the infarction and in the chronic pain

Neuronas en espejo. Otra forma de aprendizaje para el ser humano. Revisión sistemática de la literatura

Resumen Introducción: Las neuronas espejo conocidas solo en el ser humano y en monos, se activan cuando el individuo realiza una acción y cuando observa una acción similar realizada por otro individuo, esto pertenece al campo de la percepción-ejecución-intención y forma parte de la teoría de la mente. Gracias a las técnicas de imagen cerebral, se han identificado algunas zonas cerebrales donde las neuronas espejo son activas, especialmente en el lóbulo parietal, área 40 de Brodman y en el lóbulo frontal posterior, área 44 de Brodman, junto al área de Broca. Por lo que el propósito de este trabajo es realizar una revisión sistemática de la literatura para correlacionar si hay problema en las neuronas espejo en los desórdenes psiquiátricos severos como la esquizofrenia y en desórdenes conductuales como la falta de empatía que se ha asociado a una “falta” de inteligencia emocional. Material y métodos: Se buscaron revisiones sistemáticas, metaanálisis y artículos doble ciego con grupo control de las revistas The New England Journal of Medicina, The Lancet y la Revista Neurology, Journal of Apply Physiology,así como Anales de Psicología, utilizando las bases de datos de Pubmed, Medline,SciELO, www.mdconsult.com, www.aha.com, www.online.ca/medline. El estudio se llevó a cabo de Marzo de 2019 a Agosto de 2019 y se realizó en el Departamento de Farmacología de la Facultad de Medicina de la propia UAEMéx. Resultados y Discusión: De 75 artículos publicados en el presente siglo XXI se extrajo la información que a manera abreviada se presenta a continuación: Existió una relación en la enfermedad autismo y la falla de las neuronas espejo en los sujetos estudiados. En pacientes epilépticos con focalización temporal presentan dificultad en las pruebas neuropsicológicas del lenguaje y de memoria, y no se puede demostrar activación de las neuronas espejo. En el caso de las psicosis esta se asocia también a disfunciones en los mecanismos de predicción del cerebro normal. Y el déficit de cognición en especial social se presentan aún más en los psicópatas. La imagen corporal se aprende de la experiencia durante el desarrollo pre y post natal con la participación de las neuronas espejo. A futuro la terapia espejo podría emplearse como adyuvante en el manejo del dolor crónico incluso en dolor por infarto miocárdico. Conclusiones: Las neuronas espejo podrían participar en la génesis y desarrollo de los síntomas en caso de pacientes autistas. Las alteraciones en la relación sustancia gris/sustancia blanca en determinadas zonas cerebrales participa en la génesis y desarrollo de los trastornos psiquiátricos. Las crisis epilépticas focalizadas en las regiones relacionadas con las neuronas espejo afectan su función. Niños y adultos con psicopatías se caracterizan por déficits emocionales. La terapia espejo ha sido usada con éxito en pacientes que han presentado amputaciones de brazos o piernas y quizá podría ayudar en el infarto y en el dolor crónico. Abstract Introduction: Mirror neurons known only in humans and monkeys, are activated when the individual performs an action and when observes a similar action performed by another individual, this belongs to the field of perception-execution-intention and is part of the theory of mind. So the purpose of this work is to perform a systematic review of the literature to correlate if there is a problem in mirror neurons in severe psychiatric disorders such as schizophrenia and behavioral disorders such as lack of empathy that has been associated with a “lack “ emotional intelligence. Material and methods: We searched systematic reviews, meta-analyzes and double-blind articles with control group of The New England Journal of Medicine, The Lancet and the Neurology Magazine, Journal of Apply Physiology, as well as Anales de Psicología, using the databases of Pubmed, Medline, SciELO, www.mdconsult.com, www.aha.com, www.online.ca/medline. The study was carried out from March 2019 to August 2019 and was carried out in the Pharmacology Department of the Faculty of Medicine of UAEMex itself. Results and Discussion: Of the 75 articles published in the 21st century, the following information was extracted: There was a relationship in the autism disease and the failure of the mirror neurons in the subjects studied. In epileptic patients with temporal focalization they present difficulty in neuropsychological tests of language and memory, and activation of mirror neurons can not be demonstrated. In the case of psychoses this is also associated with dysfunctions in the prediction mechanisms of the normal brain. And the deficit of cognition especially social appear even more in psychopaths.Body image is learned from experience during pre and post natal development with the participation of mirror neurons. In the future, mirror therapy could be used as an adjuvant in the management of chronic pain even in pain due to myocardial infarction. Conclusions: Mirror neurons could participate in the genesis and development of symptoms in autistic patients. Alterations in the gray matter / white substance ratio in certain brain areas participate in the genesis and development of psychiatric disorders. Epileptic seizures focused on regions related to mirror neurons affect their function. Children and adults with psychopathies are characterized by emotional deficits. The mirror therapy has been used successfully in patients who have had arm or leg amputations and could perhaps help in the infarction and in the chronic pain

All-particle cosmic ray energy spectrum measured by the HAWC experiment from 10 to 500 TeV

We report on the measurement of the all-particle cosmic ray energy spectrum with the High Altitude Water Cherenkov (HAWC) Observatory in the energy range 10 to 500 TeV. HAWC is a ground based air-shower array deployed on the slopes of Volcan Sierra Negra in the state of Puebla, Mexico, and is sensitive to gamma rays and cosmic rays at TeV energies. The data used in this work were taken from 234 days between June 2016 to February 2017. The primary cosmic-ray energy is determined with a maximum likelihood approach using the particle density as a function of distance to the shower core. Introducing quality cuts to isolate events with shower cores landing on the array, the reconstructed energy distribution is unfolded iteratively. The measured all-particle spectrum is consistent with a broken power law with an index of $-2.49\pm0.01$ prior to a break at $(45.7\pm0.1$) TeV, followed by an index of $-2.71\pm0.01$. The spectrum also respresents a single measurement that spans the energy range between direct detection and ground based experiments. As a verification of the detector response, the energy scale and angular resolution are validated by observation of the cosmic ray Moon shadow's dependence on energy.Comment: 16 pages, 11 figures, 4 tables, submission to Physical Review

Observation of the Crab Nebula with the HAWC Gamma-Ray Observatory

The Crab Nebula is the brightest TeV gamma-ray source in the sky and has been used for the past 25 years as a reference source in TeV astronomy, for calibration and verification of new TeV instruments. The High Altitude Water Cherenkov Observatory (HAWC), completed in early 2015, has been used to observe the Crab Nebula at high significance across nearly the full spectrum of energies to which HAWC is sensitive. HAWC is unique for its wide field-of-view, nearly 2 sr at any instant, and its high-energy reach, up to 100 TeV. HAWC's sensitivity improves with the gamma-ray energy. Above $\sim$1 TeV the sensitivity is driven by the best background rejection and angular resolution ever achieved for a wide-field ground array. We present a time-integrated analysis of the Crab using 507 live days of HAWC data from 2014 November to 2016 June. The spectrum of the Crab is fit to a function of the form $\phi(E) = \phi_0 (E/E_{0})^{-\alpha -\beta\cdot{\rm{ln}}(E/E_{0})}$. The data is well-fit with values of $\alpha=2.63\pm0.03$, $\beta=0.15\pm0.03$, and log$_{10}(\phi_0~{\rm{cm}^2}~{\rm{s}}~{\rm{TeV}})=-12.60\pm0.02$ when $E_{0}$ is fixed at 7 TeV and the fit applies between 1 and 37 TeV. Study of the systematic errors in this HAWC measurement is discussed and estimated to be $\pm$50\% in the photon flux between 1 and 37 TeV. Confirmation of the Crab flux serves to establish the HAWC instrument's sensitivity for surveys of the sky. The HAWC survey will exceed sensitivity of current-generation observatories and open a new view of 2/3 of the sky above 10 TeV.Comment: Submitted 2017/01/06 to the Astrophysical Journa

Very high energy particle acceleration powered by the jets of the microquasar SS 433

SS 433 is a binary system containing a supergiant star that is overflowing its Roche lobe with matter accreting onto a compact object (either a black hole or neutron star). Two jets of ionized matter with a bulk velocity of $\sim0.26c$ extend from the binary, perpendicular to the line of sight, and terminate inside W50, a supernova remnant that is being distorted by the jets. SS 433 differs from other microquasars in that the accretion is believed to be super-Eddington, and the luminosity of the system is $\sim10^{40}$ erg s$^{-1}$. The lobes of W50 in which the jets terminate, about 40 pc from the central source, are expected to accelerate charged particles, and indeed radio and X-ray emission consistent with electron synchrotron emission in a magnetic field have been observed. At higher energies (>100 GeV), the particle fluxes of $\gamma$ rays from X-ray hotspots around SS 433 have been reported as flux upper limits. In this energy regime, it has been unclear whether the emission is dominated by electrons that are interacting with photons from the cosmic microwave background through inverse-Compton scattering or by protons interacting with the ambient gas. Here we report TeV $\gamma$-ray observations of the SS 433/W50 system where the lobes are spatially resolved. The TeV emission is localized to structures in the lobes, far from the center of the system where the jets are formed. We have measured photon energies of at least 25 TeV, and these are certainly not Doppler boosted, because of the viewing geometry. We conclude that the emission from radio to TeV energies is consistent with a single population of electrons with energies extending to at least hundreds of TeV in a magnetic field of $\sim16$~micro-Gauss.Comment: Preprint version of Nature paper. Contacts: S. BenZvi, B. Dingus, K. Fang, C.D. Rho , H. Zhang, H. Zho