Emotional intelligence is the automatic detection of human emotions using various intelligent methods. Several studies have been conducted on emotional intelligence, and only a few have been adopted in education. Detecting student emotions can significantly increase productivity and improve the education process. This paper proposes a new deep learning method to detect student emotions. The main aim of this paper is to map the relationship between teaching practices and student learning based on emotional impact. Facial recognition algorithms extract helpful information from online platforms as image classification techniques are applied to detect the emotions of student and/or teacher faces. As part of this work, two deep learning models are compared according to their performance. Promising results are achieved using both techniques, as presented in the Experimental Results Section. For validation of the proposed system, an online course with students is used; the findings suggest that this technique operates well. Based on emotional analysis, several deep learning techniques are applied to train and test the emotion classification process. Transfer learning for a pre-trained deep neural network is used as well to increase the accuracy of the emotion classification stage. The obtained results show that the performance of the proposed method is promising using both techniques, as presented in the Experimental Results Section.

This paper introduces a new symmetric fractional-order discrete system. The dynamics and symmetry of the suggested model are studied under two initial conditions, mainly a comparison of the commensurate order and incommensurate order maps, which highlights their effect on symmetry-breaking bifurcations. In addition, a theoretical analysis examines the stability of the zero equilibrium point. It proves that the map generates typical nonlinear features, including chaos, which is confirmed numerically: phase attractors are plotted in a two-dimensional (2D) and three-dimensional (3D) space, bifurcation diagrams are drawn with variations in the derivative fractional values and in the system parameters, and we calculate the Maximum Lyapunov Exponents (MLEs) associated with the bifurcation diagram. Additionally, we use the $C_0$ algorithm and entropy approach to measure the complexity of the chaotic symmetric fractional map. Finally, nonlinear 3D controllers are revealed to stabilize the symmetric fractional order map’s states in commensurate and incommensurate cases.

The preliminary idea of statistical weighted B-summability was introduced by Kadak et al. [27]. Subsequently, deferred weighted statistical B-summability has recently been studied by Pradhan et al. [38]. In this paper, we study statistical versions of deferred weighted B-summability as well as deferred weighted B-convergence with respect to the difference sequence of order r (> 0) involving (p,q)-integers and accordingly established an inclusion between them. Moreover, based upon our proposed methods, we prove an approximation theorem (Korovkin-type) for functions of two variables defined on a Banach space CB(D) and demonstrated that, our theorem effectively improves and generalizes most (if not all) of the existing results depending on the choice of (p,q)-integers. Finally, with the help of the modulus of continuity we estimate the rate of convergence for our proposed methods. Also, an illustrative example is provided here by generalized (p,q)-analogue of Bernstein operators of two variables to demonstrate that our theorem is stronger than its traditional and statistical versions.

In this paper, a set of conditions under which the absolute Nörlund summability method include in the absolute weighted mean method have been established. Three non-trivial examples to show that this inclusion holds have been given, and other three examples to show that even if both and are regular, the inclusion fails to holds have been constructed. The paper give two non-trivial examples to show that the equivalence of these two methods may holds. Finally, we give two examples to show that inclusion may holds in only one way without the other.