This research focuses on enhancing the understanding and evaluation of the Fourier series approximation of discontinuous periodic signals, with a particular emphasis on square waves. It is an important work because Fourier analysis is required by so many fields, such as signal processing, communications, physics, and applied mathematics. But it is sometimes inadequately visualized and quantitatively evaluated in its teaching and its practical exploration. The research comes into play to fill the gap in the literature, whereby the current ways of approach are either overly theoretical without systematic demonstration or interactive yet deficient in accuracy analysis. A possible solution to this is a computationally reproducible visualization and error-analysis model combining signal synthesis, Fourier series approximation, and multi-perspective evaluation. The method involves generating ideal square wave signals, systematically varying the number of harmonic terms, constructing time-domain and frequency-domain visualizations, and computing error metrics including Mean Squared Error (MSE), pointwise error distributions, spectral energy analysis, and statistical error histograms. The framework is tested in a controlled computational environment with high-resolution simulations (1000–4000 samples, up to 150 harmonics). Results demonstrate rapid global convergence of the Fourier series, with MSE decreasing from 0.1902 (N = 1) to 0.0032 (N = 100), while also confirming the persistence of the Gibbs phenomenon, with overshoot stabilizing at about 9
Paper cultural relics are precious historical and cultural resources that are highly susceptible to microbial damage, particularly mold infection, during storage and conservation. Conventional mold detection methods are often time-consuming, subjective, and unsuitable for rapid, non-destructive assessment, creating the need for an accurate hyperspectral imaging-based detection approach. This paper investigates mold spot detection in paper cultural relics using hyperspectral imaging and proposes an attention-based dimensionality reduction method for hyperspectral images. First, under the guidance of professional museum staff, Aspergillus niger mold spot samples were created on paper cultural relics, and hyperspectral data were collected using an imaging hyperspectral spectrometer for spectral analysis. The experimental dataset comprised 20 hyperspectral images, including 450 training spectral samples and 150 testing spectral samples for model development and evaluation. Two preprocessing methods and three classification methods were applied for mold spot identification. Subsequently, the proposed attention mechanism and two conventional dimensionality reduction methods were evaluated using four semantic segmentation models, namely U-Net, SegNet, DeepLabV3 + , and PSPNet. Experimental results demonstrate that channel attention-based dimensionality reduction improves segmentation performance over conventional PCA and ICA methods. The proposed approach achieved the best performance with the U-Net model, obtaining a mildew spot detection accuracy of 89.49
This research proposes a novel framework for sugarcane leaf disease classification by integrating Swin-GAN U-Net, DenseNet-201 with Triple Attention, Salmon Salar Optimization (SSO), and an agricultural knowledge-based large language model (LLM). The proposed framework achieves an accuracy of 93.89
In this paper, a hybrid optimization approach to allocating resources in IoT networks with the help of SDN and NFV is developed. Resource allocation for IoT networks with SDN and NFV technologies is optimized simultaneously in terms of VNF placement, load balancing, resource consolidation, and network slicing. The cooperation of LP and GA is structured in a two-level way. At first, LP calculates a feasible allocation of VNFs that meets the constraints on server capacity and link bandwidth and provides a minimum of communication overhead, excess server capacity, and service response cost. The obtained allocation is further submitted to GA to find another feasible allocation to improve energy efficiency, resource utilization, and performance. Thus, LP provides a deterministic initial solution that meets all the constraints, while GA performs a global optimization inside the combinatorial space. It was found that the proposed algorithm decreased server utilization by 15
Increasing use of artificial intelligence (AI) in English language learning has created the need for reliable predictive models that can evaluate learner outcomes in adaptive educational settings. This study introduces a hybrid Bidirectional Encoder Representation from Transformer-Gated Recurrent Unit (BERT- GRU) framework that combines BERT-based contextual semantic embedding with GRU-based temporal sequence modeling to predict personalized learning effectiveness. The model is trained on the Adaptive English Learning Dataset, which contains 4,931 classroom interaction sessions and 26 multimodal features, including learner behavior, instructor attributes, and environmental conditions. The dataset captures various learning-related signals like engagement patterns, performance indicators, and instructional context, allowing for thorough modeling of learner progress. The proposed architecture merges deep contextual language representations with sequential learning dynamics to improve prediction reliability and strength. BERT extracts rich contextual embeddings from learner interactions, while GRU captures time dependencies across sequential learning sessions. The main technical contributions of this study include a hybrid embedding, sequence fusion strategy, a structured feature engineering pipeline, and an optimized BERT, GRU architecture for educational outcome prediction. These elements work together to effectively combine semantic and temporal information, enhancing predictive performance in adaptive learning environments. Experimental results show strong performance with an accuracy of 95.17
