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Cnoidal, snoidal, dnoidal wave solutions of the first extended 3D Vakhnenko–Parkes equation together with its conservation laws and various life applications 第一个扩展三维Vakhnenko-Parkes方程的余弦、滑弦、齿状波解及其守恒定律和各种寿命应用
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2025.12.041
Chaudry Masood Khalique , Oke Davies Adeyemo
This paper significantly provides various analytical examinations of the first extended Vakhnenko–Parkes equation, which has never been explored before. To this model, abundant structures of various exact periodic solutions to this equation through the use of the extended Jacobi elliptic function expansion technique is abundantly computed for the first time. This approach employs three different auxiliary nonlinear differential equations to generate the solutions. Consequently, various cnoidal, snoidal, dnoidal, and complex snoidal wave solutions of notes were obtained. We further explore the wave dynamics of these periodic solutions in three and two dimensions using computer software. Moreover, Lie group analysis is utilized to generate the symmetries of the equation. Thereafter, conserved vectors associated with the equation are constructed through the application of Ibragimov’s conserved theorem using the formal Lagrangian of the model. The results, whose significance is demonstrated in physical sciences and technology in this research, can be very useful for researchers in relevant fields for further analysis and applications. All these results are new and unique, and they complement the work previously done on the model, thus underscoring the originality of this research.
本文对第一个从未被探索过的扩展Vakhnenko-Parkes方程提供了各种分析检验。对于该模型,利用扩展Jacobi椭圆函数展开技术,首次大量计算了该方程的各种精确周期解的丰富结构。该方法采用三个不同的辅助非线性微分方程来生成解。因此,得到了音符的各种弦波解、弦波解、弦波解和复弦波解。我们利用计算机软件进一步探讨了这些周期解在三维和二维中的波动动力学。此外,利用李群分析生成了方程的对称性。然后,利用模型的形式拉格朗日,应用Ibragimov守恒定理,构造了与方程相关的守恒向量。本研究结果在物理科学和技术领域具有重要意义,可供相关领域的研究人员进一步分析和应用。所有这些结果都是新的和独特的,它们补充了以前在模型上所做的工作,从而强调了本研究的原创性。
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引用次数: 0
Zero-shot attack detection in UAV networks using foundation models 基于基础模型的无人机网络零弹攻击检测
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2025.12.065
Adel Alshamrani , Ahmed M. Alghamdi
Traditional intrusion detection systems require extensive training data for each attack type, creating vulnerabilities in UAV networks where novel threats frequently emerge. We present ZeroUAV, a zero-shot attack detection framework using foundation models to identify unseen attack patterns without labeled examples. Our transformer-based architecture employs cross-modal attention to align network traffic with semantic attack descriptions, enabling classification based on conceptual similarity. The framework incorporates attack ontology, contrastive learning, and meta-learning for rapid adaptation. Evaluation on UAV-NIDD dataset shows 87.3 % zero-shot accuracy and 94.6 % accuracy with five examples per attack type, significantly outperforming supervised methods. The system achieves under 10 ms inference latency for real-time UAV deployment. Our contributions include the first foundation model for UAV cybersecurity, a novel zero-shot learning framework, and validation demonstrating practical viability for evolving threat landscapes.
传统的入侵检测系统需要针对每种攻击类型的大量训练数据,这在无人机网络中造成了漏洞,而新威胁经常出现。我们提出了ZeroUAV,这是一个零攻击检测框架,使用基础模型来识别未见过的攻击模式,而不需要标记示例。我们基于变压器的体系结构采用跨模态关注来将网络流量与语义攻击描述对齐,从而实现基于概念相似性的分类。该框架结合了攻击本体、对比学习和元学习,以实现快速适应。对无人机- nidd数据集的评估显示,每种攻击类型有5个样本,零射击准确率为87.3 %,准确率为94.6 %,显著优于监督方法。该系统实现了10 ms以下的实时无人机部署推理延迟。我们的贡献包括无人机网络安全的第一个基础模型,一个新的零射击学习框架,以及对不断变化的威胁景观的实际可行性的验证。
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引用次数: 0
MSDD-Net: A lightweight multi-scale defect detection network for industrial lead frame inspection MSDD-Net:用于工业引线框架检测的轻量级多尺度缺陷检测网络
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2026.01.017
Mingyue Wei, Weidong Zhao, Ning Jia, Xianhui Liu, Zhen Xu
Lead frames are key components in semiconductor packaging, where undetected surface defects may lead to reliability issues and economic losses. Existing surface defect detection methods are limited by large variations in defect scale, resulting in reduced accuracy and continued dependence on manual inspection. To address these challenges, a lightweight multi-scale defect detection network (MSDD-Net) is proposed for automated lead frame inspection. The network employs a dual-branch dynamic hierarchical fusion backbone (DDHFNet) to extract discriminative multi-scale texture features. A cross-scale feature amalgamation module (GSMD-CFA) is introduced, which integrates gated sampling with multi-dilation convolution to enhance both long-range and short-range feature interactions. A customized loss function is further designed to improve robustness by emphasizing hard samples during training. The proposed network contains 19.68 million parameters, meeting the deployment constraints of industrial real-time inspection while preserving high detection accuracy. A lead frame surface defect dataset comprising 43 defect categories is constructed to reflect real industrial conditions. On this dataset, the proposed method achieves a mean Average Precision (mAP) of 86.8%, with performance improvements of 6.7, 4.0, and 0.9 percentage points for small, medium, and large defects, respectively, compared with the baseline. Experiments on a public steel surface defect dataset further demonstrate the generalization capability of the proposed method.
引线框架是半导体封装中的关键部件,未检测到的表面缺陷可能导致可靠性问题和经济损失。现有的表面缺陷检测方法受到缺陷规模变化较大的限制,导致精度降低,继续依赖于人工检测。为了解决这些问题,提出了一种用于引线框架自动检测的轻量级多尺度缺陷检测网络(MSDD-Net)。该网络采用双分支动态层次融合主干网(DDHFNet)提取判别性多尺度纹理特征。介绍了一种跨尺度特征融合模块(GSMD-CFA),该模块将门控采样与多重膨胀卷积相结合,增强了远程和短程特征的相互作用。进一步设计了定制的损失函数,通过在训练过程中强调硬样本来提高鲁棒性。该网络包含1968万个参数,满足工业实时检测的部署约束,同时保持较高的检测精度。构建了包含43个缺陷类别的引线框架表面缺陷数据集,以反映真实的工业条件。在该数据集上,该方法的平均精度(mAP)达到86.8%,在小缺陷、中缺陷和大缺陷上的性能分别比基线提高6.7、4.0和0.9个百分点。在公共钢表面缺陷数据集上的实验进一步验证了该方法的泛化能力。
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引用次数: 0
Brain tumor segmentation and classification: A CVAE-UNETR-ResNet50-VGG16 hybrid deep learning approach 脑肿瘤分割与分类:一种cvae - unetra - resnet50 - vgg16混合深度学习方法
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2026.01.003
Wessam M. Salama , Moustafa H. Aly
This paper introduces a new hybrid DL framework, CVAE-UNETR-ResNet50-VGG16, for accurate brain tumor segmentation and classification from MRI and BraTS2021 scans. The proposed model integrates a Convolutional Variational Autoencoder (CVAE) for synthetic MRI and BraTS2021 data generation, a UNET Transformer (UNETR) for enhanced spatial segmentation through global self-attention, and ResNet50 and VGG16 networks for robust multi-scale feature classification. Moreover, data augmentation technique is proposed based on both CVAE and diffusion technique. Experimental results on the BraTS2021 dataset demonstrate a 2.57 % overall improvement in segmentation and classification performance compared to conventional UNET-based approaches. The model achieved a Dice Similarity Coefficient (DSC) of 97.45 %, Intersection over Union (IoU) of 95.67 %, and a classification accuracy of 99.35 %, representing a 3.1 % reduction in segmentation error and a 2.4 % increase in classification accuracy over benchmark models. The inference time per image is 1.6541 s on a system with 13 GB RAM, confirming its computational efficiency for clinical deployment. By effectively combining generative modeling, transformer-based segmentation, and deep feature classification, the proposed CVAE-UNETR-ResNet50-VGG16 framework establishes a new performance benchmark for automated brain tumor analysis, offering a quantifiable step forward, 2.5–3 % improvement, in diagnostic precision, computational efficiency, and medical imaging reliability. Thus, the CVAE-UNETR-ResNet50-VGG16 model offers a measurable 2–3 % performance improvement over current techniques, creating a basis for AI-assisted brain tumor diagnosis and treatment planning. This advancement supports the broader goal of AI-driven healthcare, enhancing early diagnosis and treatment planning for neurological disorders. This hybrid design bridges the gap between data-driven inference and structural MRI priors, enhancing both interpretability and precision in clinical decision-making.
本文介绍了一种新的混合深度学习框架cvae - unetre - resnet50 - vgg16,用于从MRI和BraTS2021扫描中准确分割和分类脑肿瘤。该模型集成了用于合成MRI和BraTS2021数据生成的卷积变分自编码器(CVAE),通过全局自关注增强空间分割的UNET变压器(UNETR),以及用于鲁棒多尺度特征分类的ResNet50和VGG16网络。在此基础上,提出了基于CVAE和扩散技术的数据增强技术。在BraTS2021数据集上的实验结果表明,与传统的基于unet的方法相比,分割和分类性能总体提高了2.57 %。该模型的Dice Similarity Coefficient (DSC)为97.45 %,Intersection over Union (IoU)为95.67 %,分类准确率为99.35 %,与基准模型相比,分割误差降低了3.1 %,分类准确率提高了2.4 %。在13 GB RAM的系统上,每张图像的推理时间为1.6541 s,证实了其临床部署的计算效率。通过有效地结合生成建模、基于变压器的分割和深度特征分类,所提出的cvae - unetre - resnet50 - vgg16框架为自动化脑肿瘤分析建立了新的性能基准,在诊断精度、计算效率和医学成像可靠性方面提供了可量化的进步,提高了约2.5 - 3%。因此,cvae - unetre - resnet50 - vgg16模型比现有技术的性能提高了2 - 3%,为人工智能辅助脑肿瘤诊断和治疗计划奠定了基础。这一进展支持人工智能驱动的医疗保健的更广泛目标,加强对神经系统疾病的早期诊断和治疗计划。这种混合设计弥合了数据驱动推理和结构MRI先验之间的差距,增强了临床决策的可解释性和准确性。
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引用次数: 0
Predictive analysis of Hajj and Umrah performance using key performance indicators (KPIs) and machine learning (ML) 利用关键绩效指标(kpi)和机器学习(ML)对朝觐和朝圣表现进行预测分析
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2025.12.032
Ahmed M. Alghamdi , Adel Bahaddad , Khalid Almarhabi , Asmaa A. Al-Zobidi
Hajj and Umrah services annually attract millions of pilgrims to Saudi Arabia, making their efficient management crucial to achieving Vision 2030’s objectives. This paper explores the use of artificial intelligence (AI) and machine learning to predict and optimize key performance indicators for these services. We propose an AI-driven framework that processes vast datasets to enhance decision making, improve service provision, and optimize the pilgrimage experience. Our results demonstrate significant improvements in KPI prediction accuracy, supporting Saudi Arabia’s efforts to advance the quality of Hajj and Umrah services while aligning with Vision 2030’s goals.
朝觐和朝圣活动每年吸引数百万朝圣者前往沙特阿拉伯,因此有效管理这些活动对于实现《2030年愿景》的目标至关重要。本文探讨了使用人工智能(AI)和机器学习来预测和优化这些服务的关键性能指标。我们提出了一个人工智能驱动的框架,该框架可以处理大量数据集,以增强决策,改善服务提供,并优化朝圣体验。我们的研究结果表明,关键绩效指标预测的准确性有了显著提高,支持沙特阿拉伯努力提高朝觐和朝圣服务的质量,同时与2030年愿景目标保持一致。
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引用次数: 0
Fly ash carbon composites: A breakthrough in CO2 capture and energy efficiency 粉煤灰碳复合材料:二氧化碳捕获和能源效率的突破
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2025.11.049
Jih-Hsing Chang , S. Selvaraj , S. Manikandan , S. Nagarani , Saiful Islam , Mohd Shkir , Arun Kumar Senthilkumar , Ashwini J. John , Selvarajan Ethiraj , Sambasivam Sangaraju , Mohanraj Kumar
Carbon composites made from fly ash represent a significant innovation in environmentally friendly construction materials. These composites offer multiple advantages, including CO2 capture and improved energy efficiency, which leads to a circular economy. Fly ash, which is a by-product of coal combustion, has been integrated into carbon-based materials to create composites that enhance concrete's structural performance while also supporting environmental sustainability. Given that a high surface area and porosity are crucial for CO2 adsorption, these composites are expected to serve as an environmentally friendly alternative for producing construction materials with minimal greenhouse gas emissions. Carbon materials intermixed in fly ash composites increase concrete mechanical strength and service life, help construction projects last longer, and extend their useful lives more cost-effectively. Besides incorporating QWR into composites, this approach reduces the energy required for processing since, unlike conventional materials, they are manufactured at lower temperatures and with less energy-demanding processes. CO2 adsorption capacity of fly ash carbon composites can be increased due to the synergistic effects between carbon and fly ash via higher CO2 capture efficiency by research. Moreover, the use of industrial waste fly ash is in line with the principles of circular economy, lessening waste and promoting resource efficiency. The fly ash carbon composites could enhance the performance of construction materials, at the same time, it can solve problems related to CO2 emission and energy production. Adoption of the same by the construction industry can be useful in achieving sustainability goals SDG11 and reducing the carbon footprint (SDG13) of infrastructure projects to attract greener, more energy-efficient building practices.
粉煤灰碳复合材料是环保建筑材料的重大创新。这些复合材料具有多种优势,包括二氧化碳捕获和提高能源效率,从而实现循环经济。粉煤灰是煤燃烧的副产品,已被整合到碳基材料中,以制造复合材料,增强混凝土的结构性能,同时也支持环境的可持续性。考虑到高表面积和孔隙度对二氧化碳吸附至关重要,这些复合材料有望成为一种环保的建筑材料替代品,同时减少温室气体排放。在粉煤灰复合材料中掺入碳材料,可提高混凝土的机械强度和使用寿命,延长建筑工程的使用寿命,更经济有效地延长其使用寿命。除了将QWR整合到复合材料中,这种方法还减少了加工所需的能量,因为与传统材料不同,它们在更低的温度下制造,耗能更少。研究表明,粉煤灰炭复合材料具有较高的CO2捕集效率,可通过碳与粉煤灰的协同作用提高其对CO2的吸附能力。此外,利用工业废粉煤灰符合循环经济的原则,减少浪费,提高资源效率。粉煤灰碳复合材料在提高建筑材料性能的同时,还可以解决与二氧化碳排放和能源生产相关的问题。建筑行业采用同样的标准有助于实现可持续发展目标11和减少基础设施项目的碳足迹(可持续发展目标13),以吸引更环保、更节能的建筑实践。
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引用次数: 0
ASTUNN: An enhanced spatiotemporal uncertainty guided neural network for flood management in mountainous areas 基于增强时空不确定性的山区洪水管理神经网络
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2025.12.069
Wei Liu, Dexian Li
Mountain flood disasters in rugged terrains pose significant challenges due to rapid onset, complex spatiotemporal dynamics, and data scarcity, where traditional hydrological models and pairwise graph neural networks struggle to capture multi-scale dependencies and uncertainty in propagation patterns. This study proposes the Adaptive Spatiotemporal Uncertainty-Guided Neural Network (ASTUNN), a hybrid framework that synergistically combines Bidirectional Gated Recurrent Units (BiGRU) for temporal modeling, Spherical Manifold Graph Learning (SMGL) for non-Euclidean spatial analysis, Fractional-Order Dynamic Attention (FODA) for long-memory patterns, Stochastic Variational Inference (SVI) for uncertainty quantification, and Adaptive Feature Synthesis (AFS) for multi-scale fusion. Key innovations include: (1) hyperedge-aware spatiotemporal message passing with fractional-order attention to model higher-order interactions and long-range dependencies in river networks and terrain gradients; and (2) stochastic variational uncertainty estimation to provide calibrated probabilistic forecasts and prevention capability rankings. These contributions overcome limitations of static graphs and deterministic models under rapid environmental changes. Validated on multi-source hydrological datasets from seven high-risk mountainous regions in southwest China, ASTUNN achieves an AUC-ROC of 0.947, MAE of 0.103 for prevention capability rankings, and ECE of 0.029, outperforming state-of-the-art baselines by 15–25 % while reducing false alarms by 18 % and enabling early warnings up to 48 h ahead.
起伏地形的山洪灾害由于其快速发作、复杂的时空动态和数据稀缺性带来了重大挑战,传统的水文模型和两两图神经网络难以捕捉多尺度依赖关系和传播模式的不确定性。本研究提出了自适应时空不确定性引导神经网络(ASTUNN),这是一个混合框架,它协同结合了双向门控循环单元(BiGRU)用于时间建模,球面流形图学习(SMGL)用于非欧几里得空间分析,分数阶动态注意(FODA)用于长记忆模式,随机变分推理(SVI)用于不确定性量化,自适应特征合成(AFS)用于多尺度融合。关键创新包括:(1)基于分数阶关注的超边缘感知时空信息传递,以模拟河流网络和地形梯度中的高阶相互作用和长期依赖关系;(2)随机变分不确定性估计,提供校准的概率预测和预防能力排名。这些贡献克服了静态图和确定性模型在快速环境变化下的局限性。在西南7个高风险山区的多源水文数据集上验证,ASTUNN的AUC-ROC为0.947,预防能力排名的MAE为0.103,ECE为0.029,优于最先进的基线15-25 %,同时减少了18 %的误报,并实现了提前48 h的预警。
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引用次数: 0
A dynamic reinforcement feedback network-based intelligent feedback mechanism in online learning platforms 基于动态强化反馈网络的在线学习平台智能反馈机制
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2026.01.005
Yang Xia , Yu Wang , Peng Yu
Online learning platforms’ intelligent feedback mechanisms suffer from static strategies and inadequate content adaptability, failing to meet learners’ dynamic needs. This paper proposes the Dynamic Reinforcement Feedback Network (DRF-Net), integrating Dynamic State Perception, PPO decision-making, and LLaMA 3 generation modules. Experiments on the KDD Cup and OpenEdX datasets show that DRF-Net achieves a learning effect improvement rate of 0.35±0.05 (34.6% higher than traditional models) and a cumulative reward of 56.8±4.2 (33.6% higher than single reinforcement learning models). Ablation experiments confirm the necessity of each module — removing the Dynamic State Perception module reduces the learning effect improvement rate by 22.9%. Future work will expand datasets, optimize adaptability to extreme states, and promote the model’s application in real scenarios.
在线学习平台的智能反馈机制存在静态策略和内容适应性不足的问题,无法满足学习者的动态需求。本文提出了动态强化反馈网络(DRF-Net),该网络集成了动态状态感知、PPO决策和LLaMA 3生成模块。在KDD Cup和OpenEdX数据集上的实验表明,DRF-Net的学习效果提升率为0.35±0.05(比传统模型高34.6%),累积奖励为56.8±4.2(比单一强化学习模型高33.6%)。消融实验证实了每个模块的必要性——去掉动态感知模块后,学习效果提升率降低了22.9%。未来的工作将扩展数据集,优化对极端状态的适应性,并促进模型在实际场景中的应用。
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引用次数: 0
MGHNM: A multi-granularity based on hybrid network model for postpartum hemorrhage prediction MGHNM:基于多粒度混合网络的产后出血预测模型
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2025.12.026
Xiaodan Li , Yue Zhou , Fengchun Gao , Di Cheng , Wushan Li , Kaijian Xia , Hongsheng Yin
Precise prediction of postpartum hemorrhage (PPH) is of great significance for early identification of high-risk pregnant women, optimizing medical resource allocation, and reducing maternal mortality. However, existing PPH prediction methods suffer from limitations such as coarse prediction granularity, and single-stage prediction processes, leading to insufficient prediction accuracy. This has made prediction methods based on hybrid network architectures an important research direction in current PPH studies. This paper proposes a Multi-Granularity Hybrid Network Model (MGHNM) for PPH prediction, which integrates advanced methods such as ensemble learning, convolutional neural networks (CNN), and variational autoencoders (VAE). By leveraging multi-level feature extraction, the model effectively suppresses interference from secondary information, thus significantly enhancing prediction accuracy. The MGHNM model introduces a learnable control switch mechanism to achieve dynamic feature selection, significantly enhancing the model's discriminative ability. By organically combining the CatBoost classifier, CNN feature extractor, VAE representation learning module, and Vision Transformer (ViT), the hybrid network prediction model achieves a significant improvement in prediction accuracy for the three-level classification task of PPH severity (mild, moderate, and severe). The experimental data in this paper is derived from a PPH dataset constructed from the electronic medical record (EMR) system of the Maternal and Child Health Hospital in Jinan, Shandong Province, China. Three experiments were designed: First, the hyperparameters of the prediction model were optimized and analyzed. Second, a multi-model comparative experiment was conducted. Finally, an ablation study was performed. The experimental results demonstrate the significant superiority of the proposed MGHNM model for PPH prediction. It achieves an overall mean accuracy of 89.50 % with a standard deviation of 0.0045 %, substantially outperforming both the baseline and state-of-the-art (SOTA) methods.
准确预测产后出血(PPH)对早期发现高危孕妇、优化医疗资源配置、降低孕产妇死亡率具有重要意义。然而,现有的PPH预测方法存在预测粒度粗、预测过程单阶段等局限性,导致预测精度不足。这使得基于混合网络架构的预测方法成为当前PPH研究的一个重要研究方向。本文提出了一种用于PPH预测的多粒度混合网络模型(MGHNM),该模型集成了集成学习、卷积神经网络(CNN)和变分自编码器(VAE)等先进方法。该模型通过多级特征提取,有效地抑制了二次信息的干扰,显著提高了预测精度。MGHNM模型引入了可学习的控制切换机制,实现了动态特征选择,显著提高了模型的判别能力。混合网络预测模型通过将CatBoost分类器、CNN特征提取器、VAE表示学习模块和Vision Transformer (ViT)有机结合,对PPH严重程度(轻度、中度、重度)三级分类任务的预测精度有了显著提高。本文的实验数据来源于中国山东省济南市妇幼保健院电子病历(EMR)系统构建的PPH数据集。设计了三个实验:首先,对预测模型的超参数进行了优化和分析。其次,进行了多模型对比实验。最后,进行消融研究。实验结果表明,所提出的MGHNM模型在PPH预测方面具有显著的优越性。它的总体平均准确度为89.50 %,标准差为0.0045 %,大大优于基线和最先进的(SOTA)方法。
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引用次数: 0
New oscillation results for nonlinear delay differential equations of third-order in the canonical case 三阶非线性时滞微分方程在典型情况下的新的振荡结果
IF 6.8 2区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2026-01-01 DOI: 10.1016/j.aej.2025.12.036
Feryal Abdullah Aladsani , Ali Muhib
In this paper, we focus on finding new oscillation criteria for third-order differential equations. We used a variety of analytical techniques and combined them with new relationships to address some of the problems that have hindered previous studies. As a result, and by using comparability principles, we were able to obtain results that improve and extend some of the previous results published in the literature. We provide some examples to illustrate the effectiveness of the obtained results.
本文主要研究三阶微分方程的新的振动判据。我们使用了各种分析技术,并将它们与新的关系相结合,以解决阻碍以前研究的一些问题。因此,通过使用可比性原则,我们能够获得改进和扩展先前在文献中发表的一些结果的结果。通过算例说明所得结果的有效性。
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引用次数: 0
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