Gongcheng Kexue Yu Jishu/Advanced Engineering Science

Abstract : We construct the triple difference sequence spaces Γ^3 (p∇^3 q)=(Γ^3 )_(p∇^3 q), where p=(θ_uvw^mnk ) is an infinite three-dimensional matrix of Padovan numbers θ_mnk defined by (θ_uvw^mnk )={■(θ_mnk/(θ_(u+5,v+5,w+5)-2),&m≤u,n≤v,k≤w,@0,&m>u,n>v,k>w)┤ and ∇_q^3 is a q-difference operator of third order. We obtain some inclusion relations, topological properties, Schauder basis and α-,β- and γ- duals of the newly defined space. We examine some geometric properties. We introduce and study some basic properties of rough I_λ-statistical convergent of weight g(A),where g:N^3→[0,∞) is a function satisfying g(m,n,k)→∞ and g(m,n,k)↛0 as m,n,k→∞ of triple sequence of Padovan q-difference matrix, where A represent the RH-regular matrix and also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence of weight g(A) limits of a triple sequence of Padovan q-difference matrix and also have proved Korovkin approximation theorem by using the notion of weight g(A) limits of a triple sequence space of Padovan q-difference matrix. All the results will certainly motivate the young researchers..
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Abstract : Recent breakthroughs in deep learning have contributed to this area of glyph classification, script recognition, and even multi-lingual Optical Character Recognition. Several deep learning architectures-from the conventional Convolutional Neural Network to the recent Vision Transformer and even their combination-have been proposed in the past for performing the mentioned tasks. Each of these deep learning architectures has varying strengths and weaknesses w.r.t. accuracy, complexity, scalability, and applicability. This paper presents a clear, comparative study of recent deep learning-based architectures on existing standard benchmarks like EMNIST, Omniglot, and multi-lingual script datasets. The study has brought forth the relevance of different architectures with respect to accuracy, complexity of calculations, execution speed, and practical applicability in applications related to a few-shot learning problem and edge computing..
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Abstract : In the e-commerce industry, where keeping current customers is frequently more cost-effective than recruiting new ones, customer churn is a major problem. In order to improve the precision and interpretability of churn prediction, this paper presents proposed hybrid framework that blends probabilistic modeling, deep learning, and stacked ensemble learning. SMOTE and ADASYN oversampling approaches are used to correct class imbalance in a real-world e-commerce dataset that includes demographic, transactional, and behavioral data. While deep learning models like CNN, RNN, and FCNN showed better recall and validation accuracy, with CNN reaching up to 83% following Keras-Tuner optimization, traditional models like Random Forest and Logistic Regression only managed baseline accuracies of about 79%. Individual models exceeded by 2.2% to 5.3%, a model that is proposed, used Gradient Boosting, CatBoost, XGBoost and SVM with Logistic Regression as a meta-classifier, reached 96% of high test accuracy post-ADASYN. Hidden Markov Models (HMMs) with 2, 4, and 6 latent states were used to further examine its churn probabilities that reflected the temporal dynamics of consumer behavior. HMM framework's ability to track dynamic states and identify churn-prone pathways supported the Individualized risk assessments and focused retention efforts. The suggested proposed model framework provides a scalable and interpretable solution, for real-world churn management, with excellent predictive performance and useful insights..
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Abstract : Contamination of water by hexavalent chromium [Cr(VI)] has garnered considerable attention because this ion is highly toxic and carcinogenic, posing serious threats to human health. In this work, we present an easy and effective method to eliminate Cr(VI) pollutants by reusing red mud. The prepared adsorbents were examined using XRD, FT-IR, FE-SEM, and XRF techniques. Red mud exhibited greater adsorption performance than synthetic goethite. Both materials are simple to operate and have the potential to be regenerated for repeated Cr(VI) removal. The key benefit of red mud lies in its wide availability and functional properties, making it a readily obtainable and efficient material for sorption studies. Therefore, this mining residue offers a practical option for treating wastewater containing hexavalent chromium..
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Abstract : Mobile Edge Computing (MEC) has emerged as a disruptive paradigm for supporting computation intensive and latency critical applications on resource constrained mobile devices. By offloading tasks to proximate edge servers, MEC reduces communication delay and energy consumption compared to conventional cloud computing. However, dynamic radio access conditions, heterogeneous server capacities, and user mobility make efficient task offloading highly challenging. Recent advances in deep learning provide promising alternatives by enabling adaptive, data driven decision making. This survey presents a comprehensive review of deep learning approaches for MEC task offloading. A novel dual taxonomy is proposed, jointly classifying existing works by learning methodology—supervised, unsupervised, reinforcement, and distributed learning—and by optimization objectives including deadline satisfaction, energy efficiency, cost reduction, and scalability. Representative neural architectures such as multilayer perceptrons, convolutional networks, recurrent models, and reinforcement learning agents are analyzed for their suitability in dynamic MEC environments. Distributed learning paradigms including federated and split learning are further examined to highlight privacy preserving and scalable edge intelligence. Key lessons and limitations are distilled, emphasizing the strengths of deep learning in feature extraction, data driven modeling, online adaptation, and distributed coordination, while acknowledging challenges such as training complexity, lack of transparency, and communication overhead. Finally, future research directions are outlined, including hybrid optimization frameworks, adaptive federated learning, explainable AI, sustainable edge intelligence, transformer based architectures, multi agent reinforcement learning, and emerging applications such as vehicular edge computing and IoT driven smart cities. By explicitly highlighting novelty and providing a forward looking roadmap, this survey advances the state of knowledge in deep learning enabled MEC offloading and serves as both a reference for established scholars and a guide for new researchers entering the field..
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