Anisotropic weakly over-penalised symmetric interior penalty method for the Stokes equation

In this study, we investigate an anisotropic weakly over-penalised symmetric interior penalty method for the Stokes equation. Our approach is a simple discontinuous Galerkin method similar to the Crouzeix--Raviart finite element method. As our primary contribution, we show a new proof for the consistency term, which allows us to obtain an estimate of the anisotropic consistency error. The key idea of the proof is to apply the relation between the Raviart--Thomas finite element space and a discontinuous space. While inf-sup stable schemes of the discontinuous Galerkin method on shape-regular mesh partitions have been widely discussed, our results show that the Stokes element satisfies the inf-sup condition on anisotropic meshes. Furthermore, we also provide an error estimate in an energy norm on anisotropic meshes. In numerical experiments, we compare calculation results for standard and anisotropic mesh partitions, and the results show the effectiveness of using anisotropic meshes for problems with boundary layers.Comment: 41 pages, 9 figures, 11 table

Anisotropic Raviart-Thomas interpolation error estimates using a new geometric parameter

We present precise Raviart-Thomas interpolation error estimates on anisotropic meshes. The novel aspect of our theory is the introduction of a new geometric parameter of simplices. It is possible to obtain new anisotropic Raviart-Thoma error estimates using the parameter. We also include corrections to an error in "General theory of interpolation error estimates on anisotropic meshes" (Japan Journal of Industrial and Applied Mathematics, 38 (2021) 163-191), in which Theorem 3 was incorrect.Comment: 26 pages, 2 figures. arXiv admin note: text overlap with arXiv:2106.0333

Introduction of The Competency Based Approach in Teaching and Learning Mathematics at Elementary School Level in Senegal : Successes And Challenges

In Senegal, the generalization of the new curriculum 2013, has triggered profound changes and raised new challenges in the teaching and learning system in elementary schools. From Content and Objectives Based Approaches, teachers have been experimenting nowadays, the Competency Based Approach (CBA) which focuses not only on the transfer of knowledge, but also on the mastering of the core competencies. Based on the theories of constructivism and social-constructivism, this system of instruction promotes learner centered activity, creativity, critical thinking, problem solving and collaborative learning. Despite the eff orts of the Senegalese government in reforming the teaching and learning system, the quality of education is still a big issue for MoE. Assessment studies made at the national, regional and international levels, have shown that Senegalese elementary school students are lacking performances in reading and mathematics as indicated in the SNERS and PASEC, reports respectively in 2013 and 2014. This study proposes an analysis of the introduction of the new curriculum in Senegal through the model of Competency Based Approach (CBA) in teaching and learning mathematics. The methodology used to collect data was the questionnaire administrated to teachers, classroom visits and the exploitation of reports produced by the MoE. The fi ndings globally show that the implementation of the CBA is confronted with serious issues like the big gap between the intended and the implemented curriculum, the absence of integrative activities and feedbacks to students without forgetting the students\u27 lack of performances in reading and mathematics. These issues open the door of many challenges that need to be overcome by Senegalese education system stakeholders for a successful implementation of the reform

Anisotropic interpolation error estimates using a new geometric parameter

We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the diameter of a simplex and the geometric parameter. Imposing additional assumptions makes it possible to obtain anisotropic error estimates. This paper also includes corrections to an error in Theorem 2 of our previous paper, "General theory of interpolation error estimates on anisotropic meshes" (Japan Journal of Industrial and Applied Mathematics, 38 (2021) 163-191).Comment: 36 pages, 12 figure

Effectiveness and Issues of ESMATE (Project of Making New Mathematics Textbooks for Primary and Secondary Schools) : Contextualization of the Japanese Teaching Style Materials to Current Learning Situation in El Salvador

The low performance in mathematic skills is common in El Salvador, several results in several assessments and evaluations make this fl agrant. Since 2016 in El Salvador a curriculum reform has been developed including new textbooks, for whole grades of primary and secondary school with the technical support of Japan. The national implementation has been held in 2018 and 2019 by proposing a curricular development strategy with the use of textbook. In order to measure the eff ectiveness of textbook and national strategy, an impact evaluation was carried out in 2018, fi rst results showed the improvement of the mathematic performance of Salvadoran students and teachers\u27 practices

論理プログラム学習における汎化と述語発見

1 Introduction 2 Preliminaries 3 Least Generalization in Learning Logic Programs 4 Learning Primitive Prologs from Positive Facts 5 Model Inference with Predicate Invention 6 Learning Regular Languages 7 Learning Simple Deterministic Languages 8 ConclusionMade available in DSpace on 2012-07-04T00:19:08Z (GMT). No. of bitstreams: 2 ishizaka1.pdf: 8030405 bytes, checksum: 86eb04c3fd068627be8f98000a43fa0d (MD5) ishizaka2.pdf: 8852675 bytes, checksum: dee2c3b524970361131007dacbf79349 (MD5) Previous issue date: 1993-03-19主1-参

Possibility of Utilizing Inquiry-Based Learning as a Pedagogy to Foster 5E Model in Mathematics Education in Jamaica

This paper examines the development of Jamaica’s formal education system from when it was first established to its progression in the 21st century era. Since its first development, Jamaica has strived to provide quality education moving from a framework of segregated ideology to inclusiveness. However, further development for quality education is of great concern as over the years, many students have failed to meet the national standards and competencies for Mathematics; especially in reasoning. Reasoning comprises of critical thinking and problem -solving skills which are critical 21st century skills necessary for solving real-world situations. The major finding is that Jamaica has begun to utilize Inquiry-Based Learning (IBL) in its formal education system through the use of the 5E model as a means to achieve these key competencies. Examination of its use suggests a gap between the theory and its implementation which means there is a need for further development of contextualization of the model and continued evaluation of its use in order to enhance the possibility of achieving key competencies as well as logical reasoning and rational thinking learning outcomes