In this work, we study the numerical simulation of the one‐dimensional reaction‐diffusion system known as the Gray‐Scott model. This model is responsible for the spatial pattern formation, which we often meet in nature as the result of some chemical reactions. We have used the trigonometric quartic B‐spline (T4B) functions for space discretization with the Crank‐Nicolson method for time integration to integrate the nonlinear reaction‐diffusion equation into a system of algebraic equations. The solutions of the Gray‐Scott model are presented with different wave simulations. Test problems are chosen from the literature to illustrate the stationary waves, pulse‐splitting waves, and self‐replicating waves.
Recommender systems provide personalized suggestions by processing user and item information and interactions. Personalized product recommendations make it easier for users to access products that interest them. Course recommendation systems, on the other hand, aim to guide students to fields of interest in which they can succeed. On e-learning sites, there are many courses and students from different fields. Also, students can select courses from other than the fields they are studying. However, students in educational institutions must follow a curriculum. Since each educational institution has distinct constraints on course selection, a specific approach to the problem is required to develop a course recommender system. Due to the restrictive nature of the problem, developing a recommendation system for institutions is considered challenging. Therefore, students consult a faculty member when selecting a course for enrollment. In this study, a hybrid recommender system is proposed using student and course information with collaborative filtering and content-based filtering models. The proposed system provides consistent recommendations by using explicit and implicit data, without predefined association rules. The collaborative filtering algorithms use grades as rating values. The content-based filtering algorithms utilize text-based information about students and courses by converting them into feature vectors using natural language processing methods. In the combination phase of the hybrid recommender system, only one of the collaborative filtering and one of the content-based filtering models are used with different ensembling methods. It is found that the suggested hybrid recommender system can achieve outperforming results for all evaluation metrics. The results show the values of the rank-aware metrics Precision@N, AP@N, mAP@N, and NDCG@N for the individual models and the hybrid models with different combinations. In particular, for content-based filtering with Bayesian personalized ranking, the hybrid model performs better than any algorithm in practice.
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