6,278 research outputs found
Nonlinear Electromagnetic Quasinormal Modes and Hawking Radiation of A Regular Black Hole with Magnetic Charge
Based on a regular exact black hole (BH) from nonlinear electrodynamics (NED)
coupled to General Relativity, we investigate its stability of such BH through
the Quasinormal Modes (QNMs) of electromagnetic (EM) field perturbation and its
thermodynamics through Hawking radiation. In perturbation theory, we can deduce
the effective potential from nonlinear EM field. The comparison of potential
function between regular and RN BHs could predict their similar QNMs. The QNMs
frequencies tell us the effect of magnetic charge , overtone , angular
momentum number on the dynamic evolution of NLED EM field. Furthermore we
also discuss the cases near extreme condition of such magnetically charged
regular BH. The corresponding QNMs spectrum illuminates some special properties
in the near-extreme cases. For the thermodynamics, we employ Hamilton-Jacobi
method to calculate the near-horizon Hawking temperature of the regular BH and
reveal the relationship between classical parameters of black hole and its
quantum effect
Fermions Tunneling from Higher-Dimensional Reissner-Nordstr\"om Black Hole: Semiclassical and Beyond Semiclassical Approximation
Based on semiclassical tunneling method, we focus on charged fermions
tunneling from higher-dimensional Reissner-Nordstr\"{o}m black hole. We first
simplify the Dirac equation by semiclassical approximation, and then a
semiclassical Hamilton-Jacobi equation is obtained. Using the Hamilton-Jacobi
equation, we study the Hawking temperature and fermions tunneling rate at the
event horizon of the higher-dimensional Reissner-Nordstr\"{o}m black hole
spacetime. Finally, the correct entropy is calculation by the method beyond
semiclassical approximation.Comment: 7 page
The tools related to mathematics teachers’ pedagogical reasoning: critical review
[EN] Shulman (1987) introduced pedagogical reasoning in his model of pedagogical reasoning and action, refers to the phases of activities involving comprehension, transformation, instruction, evaluation, and reflection. The present study aims at a critical review on the tools for investigating the phases of pedagogical reasoning and action for mathematics teachers. Based on a focused search in the database Scopus, 13 articles were reviewed. Findings showed three categories included mathematical tasks, teaching materials and videos. We further classified each category and connected it with Shulman’s phases of pedagogical reasoning. Mathematical tasks are classified as pure mathematical tasks and mathematical pedagogical tasks which can be connected to comprehension and transformation phases. Teaching materials are classified into three sub-categories, including materials in planning session, in implementation session, and after implementation which can be connected to comprehension and transformation, instruction, and evaluation and reflection phases, respectively. Lastly, videos are classified into three subcategories including video of self-teaching, others teaching, and movie which connected to evaluation and reflection phases. Two findings are highlighted including (1) the correspondence between the tools for pedagogical reasoning and Shulman’s phases of pedagogical reasoning and (2) the features of each sub-category of the tools related to pedagogical reasoning.This research was funded by the Ministry of Science and Technology (MOST), Taiwan, R.O.C., under the grant number MOST 107-2511-H-003 -004 -MY3.Yang, K.; Tambunan, S. (2021). The tools related to mathematics teachers’ pedagogical reasoning: critical review. En 7th International Conference on Higher Education Advances (HEAd'21). Editorial Universitat Politècnica de València. 129-136. https://doi.org/10.4995/HEAd21.2021.12698OCS12913
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