Improving Online Education Using Big Data Technologies

In a world in full digital transformation, where new information and communication technologies are constantly evolving, the current challenge of Computing Environments for Human Learning (CEHL) is to search the right way to integrate and harness the power of these technologies. In fact, these environments face many challenges, especially the increased demand for learning, the huge growth in the number of learners, the heterogeneity of available resources as well as the problems related to the complexity of intensive processing and real-time analysis of data produced by e-learning systems, which goes beyond the limits of traditional infrastructures and relational database management systems. This chapter presents a number of solutions dedicated to CEHL around the two big paradigms, namely cloud computing and Big Data. The first part of this work is dedicated to the presentation of an approach to integrate both emerging technologies of the big data ecosystem and on-demand services of the cloud in the e-learning field. It aims to enrich and enhance the quality of e-learning platforms relying on the services provided by the cloud accessible via the internet. It introduces distributed storage and parallel computing of Big Data in order to provide robust solutions to the requirements of intensive processing, predictive analysis, and massive storage of learning data. To do this, a methodology is presented and applied which describes the integration process. In addition, this chapter also addresses the deployment of a distributed e-learning architecture combining several recent tools of the Big Data and based on a strategy of data decentralization and the parallelization of the treatments on a cluster of nodes. Finally, this article aims to develop a Big Data solution for online learning platforms based on LMS Moodle. A course recommendation system has been designed and implemented relying on machine learning techniques, to help the learner select the most relevant learning resources according to their interests through the analysis of learning traces. The realization of this system is done using the learning data collected from the ESTenLigne platform and Spark Framework deployed on Hadoop infrastructure

The first eigencurve for a Neumann boundary problem involving p-Laplacian with essentially bounded weights

This article is intended to prove the existence and uniqueness of the first eigencurve, for a homogeneous Neumann problem with singular weights associated with the equation $$-\Delta_{p} u=\alpha m_{1}|u|^{p-2}u+\beta m_{2}|u|^{p-2}u$$ in a bounded domain $\Omega \subset \mathbb{R}^{N}$. We then establish many properties of this eigencurve, particularly the continuity, variational characterization, asymptotic behavior, concavity and the differentiability

Real quadratic number fields with metacyclic Hilbert 22-class field tower

summary:We begin by giving a criterion for a number field $K$ with 2-class group of rank 2 to have a metacyclic Hilbert 2-class field tower, and then we will determine all real quadratic number fields $\mathbb Q(\sqrt d)$ that have a metacyclic nonabelian Hilbert $2$-class field tower

On the spectrum of one dimensional p-Laplacian for an eigenvalue problem with Neumann boundary conditions

This work deals with an indefinite weight one dimensional eigenvalue problem of the p-Laplacian operator subject to Neumann boundary conditions. We are interested in some properties of the spectrum like simplicity, monotonicity and strict monotonicity with respect to the weight. We also aim the study of zeros points of eigenfunctions