ThispaperinvestigatesseveralformsofSylvester-typeoperatorequationsininfinite-dimensional Hilbertspaces, focusingonboththeclassicalequation AX−XB = CanditsgeneralizedversionAX−YB = C, which involves two unknowns. We establish new necessary and sufficient conditions for the existence of solutions by employing generalized inverses under novel structuralassumptions. Specialattentionisgiven to the behavior of these equations when restricted to subspaces such asker(A+I)andker(B+I), andtocases involving two distinct subspaces. The study highlights how operator properties-such as involution and pseudo-inverses-govern solvability and solution structure. The results offer a unified theoretical frame work that encompasses both classical and generalized operator equations, with potential applications in control theory, perturbation analysis, and related areas. Illustrative examples are provided to demonstrate the applicability and relevance of the theoretical developments.

ThispaperinvestigatesseveralformsofSylvester-typeoperatorequationsininfinite-dimensional Hilbertspaces, focusingonboththeclassicalequation AX−XB = CanditsgeneralizedversionAX−YB = C, which involves two unknowns. We establish new necessary and sufficient conditions for the existence of solutions by employing generalized inverses under novel structuralassumptions. Specialattentionisgiven to the behavior of these equations when restricted to subspaces such asker(A+I)andker(B+I), andtocases involving two distinct subspaces. The study highlights how operator properties-such as involution and pseudo-inverses-govern solvability and solution structure. The results offer a unified theoretical frame work that encompasses both classical and generalized operator equations, with potential applications in control theory, perturbation analysis, and related areas. Illustrative examples are provided to demonstrate the applicability and relevance of the theoretical developments.

Fixed point theory stands as a fundamental pillar in nonlinear functional anal ysis, being essential for proving the existence of solutions for nonlinear dif ferential and integral equations. Krasnoselskii’s hybrid fixed point theorem, which combines the Banach contraction principle with Schauder’s theorem, is a pivotal contribution. Recent efforts have focused on refining and relaxing the conditions of this theorem. This study aims to extend the theoretical frame work of Krasnoselskii-type fixed point theorems to address a broader and more general class of nonlinear operator equations within a Banach algebra setting. It also seeks to establish rigorous conditions for the existence (and uniqueness, where possible) of solutions. The approach involves developing local variants of the classic Krasnoselskii fixed point theorems. We performed a comparative analysis of previous studies, introduced modifications to the operator equations to relax restrictive assumptions, and theoretically generalized the theorems to accommodate a complex structure involving four operators. To validate the results, they were applied to a nonlinear functional integral equation within the Banach space C[0,1]. We successfully generalized existing results by in corporating the H¨older continuity condition, which is less restrictive than the standard Lipschitz condition. The unified theoretical framework led to the es tablishment of a comprehensive set of theorems and corollaries covering a wide class of operator equations such as : Ax(ρ2)Bxρ1 + Cx(ρ3)Dxρ1 = x. Our re sults provide less restrictive local existence conditions and wider applicability in the analysis of complex mathematical systems.

Fixed point theory stands as a fundamental pillar in nonlinear functional anal ysis, being essential for proving the existence of solutions for nonlinear dif ferential and integral equations. Krasnoselskii’s hybrid fixed point theorem, which combines the Banach contraction principle with Schauder’s theorem, is a pivotal contribution. Recent efforts have focused on refining and relaxing the conditions of this theorem. This study aims to extend the theoretical frame work of Krasnoselskii-type fixed point theorems to address a broader and more general class of nonlinear operator equations within a Banach algebra setting. It also seeks to establish rigorous conditions for the existence (and uniqueness, where possible) of solutions. The approach involves developing local variants of the classic Krasnoselskii fixed point theorems. We performed a comparative analysis of previous studies, introduced modifications to the operator equations to relax restrictive assumptions, and theoretically generalized the theorems to accommodate a complex structure involving four operators. To validate the results, they were applied to a nonlinear functional integral equation within the Banach space C[0,1]. We successfully generalized existing results by in corporating the H¨older continuity condition, which is less restrictive than the standard Lipschitz condition. The unified theoretical framework led to the es tablishment of a comprehensive set of theorems and corollaries covering a wide class of operator equations such as : Ax(ρ2)Bxρ1 + Cx(ρ3)Dxρ1 = x. Our re sults provide less restrictive local existence conditions and wider applicability in the analysis of complex mathematical systems.

Fixed point theory stands as a fundamental pillar in nonlinear functional anal ysis, being essential for proving the existence of solutions for nonlinear dif ferential and integral equations. Krasnoselskii’s hybrid fixed point theorem, which combines the Banach contraction principle with Schauder’s theorem, is a pivotal contribution. Recent efforts have focused on refining and relaxing the conditions of this theorem. This study aims to extend the theoretical frame work of Krasnoselskii-type fixed point theorems to address a broader and more general class of nonlinear operator equations within a Banach algebra setting. It also seeks to establish rigorous conditions for the existence (and uniqueness, where possible) of solutions. The approach involves developing local variants of the classic Krasnoselskii fixed point theorems. We performed a comparative analysis of previous studies, introduced modifications to the operator equations to relax restrictive assumptions, and theoretically generalized the theorems to accommodate a complex structure involving four operators. To validate the results, they were applied to a nonlinear functional integral equation within the Banach space C[0,1]. We successfully generalized existing results by in corporating the H¨older continuity condition, which is less restrictive than the standard Lipschitz condition. The unified theoretical framework led to the es tablishment of a comprehensive set of theorems and corollaries covering a wide class of operator equations such as : Ax(ρ2)Bxρ1 + Cx(ρ3)Dxρ1 = x. Our re sults provide less restrictive local existence conditions and wider applicability in the analysis of complex mathematical systems.

Detecting arrhythmias via electrocardiograms (ECGs) is vital for healthcare. While deep learning has advanced classification, capturing critical patterns in complex data remains challenging. We propose Res_Bi-LSTM_MHA, a novel model integrating a multi-head self-attention (MHA) mechanism to selectively focus on relevant signal segments. This enhances the capture of subtle features often missed by conventional methods. By combining Residual Networks (ResNet) for robust feature extraction with Bidirectional Long Short-Term Memory (Bi-LSTM) for temporal dependencies, our approach significantly improves accuracy. We evaluated the model at subject and record levels using the China Physiological Signal Challenge (CPSC 2018), St. Petersburg Institute of Cardiological Technics (INCART), and Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) databases. The model achieved an F1 score of 98.01% and 99.42% accuracy on the MIT-BIH dataset. Our results demonstrate that effectively utilizing attention mechanisms offers a substantial improvement in arrhythmia classification.

Detecting arrhythmias via electrocardiograms (ECGs) is vital for healthcare. While deep learning has advanced classification, capturing critical patterns in complex data remains challenging. We propose Res_Bi-LSTM_MHA, a novel model integrating a multi-head self-attention (MHA) mechanism to selectively focus on relevant signal segments. This enhances the capture of subtle features often missed by conventional methods. By combining Residual Networks (ResNet) for robust feature extraction with Bidirectional Long Short-Term Memory (Bi-LSTM) for temporal dependencies, our approach significantly improves accuracy. We evaluated the model at subject and record levels using the China Physiological Signal Challenge (CPSC 2018), St. Petersburg Institute of Cardiological Technics (INCART), and Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) databases. The model achieved an F1 score of 98.01% and 99.42% accuracy on the MIT-BIH dataset. Our results demonstrate that effectively utilizing attention mechanisms offers a substantial improvement in arrhythmia classification.

Detecting arrhythmias via electrocardiograms (ECGs) is vital for healthcare. While deep learning has advanced classification, capturing critical patterns in complex data remains challenging. We propose Res_Bi-LSTM_MHA, a novel model integrating a multi-head self-attention (MHA) mechanism to selectively focus on relevant signal segments. This enhances the capture of subtle features often missed by conventional methods. By combining Residual Networks (ResNet) for robust feature extraction with Bidirectional Long Short-Term Memory (Bi-LSTM) for temporal dependencies, our approach significantly improves accuracy. We evaluated the model at subject and record levels using the China Physiological Signal Challenge (CPSC 2018), St. Petersburg Institute of Cardiological Technics (INCART), and Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) databases. The model achieved an F1 score of 98.01% and 99.42% accuracy on the MIT-BIH dataset. Our results demonstrate that effectively utilizing attention mechanisms offers a substantial improvement in arrhythmia classification.

Global solutions to a Gierer-Meinhardt model of two substances defined by reaction-diffusion equations are shown in this article. By employing Lyapunov functionals and investigating the regularizing properties inherent to parabolic equations, we rigorously establish the existence and asymptotic behavior of solutions under appropriate assumptions. Numerical simulations are used to corroborate the analytical findings. This research differs from previous work because it relies on spatial domains that vary over time, rather than being static.

Information and communication technology clearly affects regional development in several aspects, most notably facilitating access to services. This has led to its widespread adoption, which faces significant geographical and social obstacles that limit it s efficiency. This study aims to assess the state of information and communication technology in the Aurès Mountains of Algeria, with a particular focus on the structure of telephone services in order to illustrate the challenges that hinder regional development. The current situation of telephone communication infrastructure in the area was analysed using geographic information systems, in addition to the construction of a weighted spatial regression model to demonstrate the relationship between the efficiency of telephone services and network coverage variables. The findings revealed that the existi ng infrastructure is constrained by the challenges of terrain and by social factors related to unequal population density and distribution. Based on these aspects, solutions were proposed to improve the effectiveness of telephone services, with an emphasis on addressing the identified gaps to enhance regional development through strategic actions by decision-makers, thereby improving access to services and contri buting to bridging the digital divide in the future.

Information and communication technology clearly affects regional development in several aspects, most notably facilitating access to services. This has led to its widespread adoption, which faces significant geographical and social obstacles that limit it s efficiency. This study aims to assess the state of information and communication technology in the Aurès Mountains of Algeria, with a particular focus on the structure of telephone services in order to illustrate the challenges that hinder regional development. The current situation of telephone communication infrastructure in the area was analysed using geographic information systems, in addition to the construction of a weighted spatial regression model to demonstrate the relationship between the efficiency of telephone services and network coverage variables. The findings revealed that the existi ng infrastructure is constrained by the challenges of terrain and by social factors related to unequal population density and distribution. Based on these aspects, solutions were proposed to improve the effectiveness of telephone services, with an emphasis on addressing the identified gaps to enhance regional development through strategic actions by decision-makers, thereby improving access to services and contri buting to bridging the digital divide in the future.

Information and communication technology clearly affects regional development in several aspects, most notably facilitating access to services. This has led to its widespread adoption, which faces significant geographical and social obstacles that limit it s efficiency. This study aims to assess the state of information and communication technology in the Aurès Mountains of Algeria, with a particular focus on the structure of telephone services in order to illustrate the challenges that hinder regional development. The current situation of telephone communication infrastructure in the area was analysed using geographic information systems, in addition to the construction of a weighted spatial regression model to demonstrate the relationship between the efficiency of telephone services and network coverage variables. The findings revealed that the existi ng infrastructure is constrained by the challenges of terrain and by social factors related to unequal population density and distribution. Based on these aspects, solutions were proposed to improve the effectiveness of telephone services, with an emphasis on addressing the identified gaps to enhance regional development through strategic actions by decision-makers, thereby improving access to services and contri buting to bridging the digital divide in the future.

Information and communication technology clearly affects regional development in several aspects, most notably facilitating access to services. This has led to its widespread adoption, which faces significant geographical and social obstacles that limit it s efficiency. This study aims to assess the state of information and communication technology in the Aurès Mountains of Algeria, with a particular focus on the structure of telephone services in order to illustrate the challenges that hinder regional development. The current situation of telephone communication infrastructure in the area was analysed using geographic information systems, in addition to the construction of a weighted spatial regression model to demonstrate the relationship between the efficiency of telephone services and network coverage variables. The findings revealed that the existi ng infrastructure is constrained by the challenges of terrain and by social factors related to unequal population density and distribution. Based on these aspects, solutions were proposed to improve the effectiveness of telephone services, with an emphasis on addressing the identified gaps to enhance regional development through strategic actions by decision-makers, thereby improving access to services and contri buting to bridging the digital divide in the future.

Objectives: Traffic accidents cause severe social and economic impacts, demanding fast and reliable detection to minimize secondary collisions and improve emergency response. However, existing cloud-dependent detection systems often suffer from high latency and limited scalability, motivating the need for an edge-centric and consensus-free accident detection framework in IoV environments. 

Methods: This study presents a real-time accident detection framework tailored for Internet of Vehicles (IoV) environments. The proposed system forms an integrated IoV architecture combining on-vehicle inference, RSU-based validation, and asynchronous cloud reporting. The system integrates a lightweight ensemble of Vision Transformer (ViT) and EfficientNet models deployed on vehicle nodes to classify video frames. Accident alerts are generated only when both models agree (vehicle-level ensemble consensus), ensuring high precision. These alerts are transmitted to nearby Road Side Units (RSUs), which validate the events and broadcast safety messages without requiring inter-vehicle or inter-RSU consensus. Structured reports are also forwarded asynchronously to the cloud for long-term model retraining and risk analysis. 

Results: Evaluated on the CarCrash and CADP datasets, the framework achieves an F1-score of 0.96 with average decision latency below 60 ms, corresponding to an overall accuracy of 98.65% and demonstrating measurable improvement over single-model baselines. 

Conclusions: By combining on-vehicle inference, edge-based validation, and optional cloud integration, the proposed architecture offers both immediate responsiveness and adaptability, contrasting with traditional cloud-dependent approaches.

Objectives: Traffic accidents cause severe social and economic impacts, demanding fast and reliable detection to minimize secondary collisions and improve emergency response. However, existing cloud-dependent detection systems often suffer from high latency and limited scalability, motivating the need for an edge-centric and consensus-free accident detection framework in IoV environments. 

Methods: This study presents a real-time accident detection framework tailored for Internet of Vehicles (IoV) environments. The proposed system forms an integrated IoV architecture combining on-vehicle inference, RSU-based validation, and asynchronous cloud reporting. The system integrates a lightweight ensemble of Vision Transformer (ViT) and EfficientNet models deployed on vehicle nodes to classify video frames. Accident alerts are generated only when both models agree (vehicle-level ensemble consensus), ensuring high precision. These alerts are transmitted to nearby Road Side Units (RSUs), which validate the events and broadcast safety messages without requiring inter-vehicle or inter-RSU consensus. Structured reports are also forwarded asynchronously to the cloud for long-term model retraining and risk analysis. 

Results: Evaluated on the CarCrash and CADP datasets, the framework achieves an F1-score of 0.96 with average decision latency below 60 ms, corresponding to an overall accuracy of 98.65% and demonstrating measurable improvement over single-model baselines. 

Conclusions: By combining on-vehicle inference, edge-based validation, and optional cloud integration, the proposed architecture offers both immediate responsiveness and adaptability, contrasting with traditional cloud-dependent approaches.

Objectives: Traffic accidents cause severe social and economic impacts, demanding fast and reliable detection to minimize secondary collisions and improve emergency response. However, existing cloud-dependent detection systems often suffer from high latency and limited scalability, motivating the need for an edge-centric and consensus-free accident detection framework in IoV environments. 

Methods: This study presents a real-time accident detection framework tailored for Internet of Vehicles (IoV) environments. The proposed system forms an integrated IoV architecture combining on-vehicle inference, RSU-based validation, and asynchronous cloud reporting. The system integrates a lightweight ensemble of Vision Transformer (ViT) and EfficientNet models deployed on vehicle nodes to classify video frames. Accident alerts are generated only when both models agree (vehicle-level ensemble consensus), ensuring high precision. These alerts are transmitted to nearby Road Side Units (RSUs), which validate the events and broadcast safety messages without requiring inter-vehicle or inter-RSU consensus. Structured reports are also forwarded asynchronously to the cloud for long-term model retraining and risk analysis. 

Results: Evaluated on the CarCrash and CADP datasets, the framework achieves an F1-score of 0.96 with average decision latency below 60 ms, corresponding to an overall accuracy of 98.65% and demonstrating measurable improvement over single-model baselines. 

Conclusions: By combining on-vehicle inference, edge-based validation, and optional cloud integration, the proposed architecture offers both immediate responsiveness and adaptability, contrasting with traditional cloud-dependent approaches.

Objectives: Traffic accidents cause severe social and economic impacts, demanding fast and reliable detection to minimize secondary collisions and improve emergency response. However, existing cloud-dependent detection systems often suffer from high latency and limited scalability, motivating the need for an edge-centric and consensus-free accident detection framework in IoV environments. 

Methods: This study presents a real-time accident detection framework tailored for Internet of Vehicles (IoV) environments. The proposed system forms an integrated IoV architecture combining on-vehicle inference, RSU-based validation, and asynchronous cloud reporting. The system integrates a lightweight ensemble of Vision Transformer (ViT) and EfficientNet models deployed on vehicle nodes to classify video frames. Accident alerts are generated only when both models agree (vehicle-level ensemble consensus), ensuring high precision. These alerts are transmitted to nearby Road Side Units (RSUs), which validate the events and broadcast safety messages without requiring inter-vehicle or inter-RSU consensus. Structured reports are also forwarded asynchronously to the cloud for long-term model retraining and risk analysis. 

Results: Evaluated on the CarCrash and CADP datasets, the framework achieves an F1-score of 0.96 with average decision latency below 60 ms, corresponding to an overall accuracy of 98.65% and demonstrating measurable improvement over single-model baselines. 

Conclusions: By combining on-vehicle inference, edge-based validation, and optional cloud integration, the proposed architecture offers both immediate responsiveness and adaptability, contrasting with traditional cloud-dependent approaches.

Objectives: Traffic accidents cause severe social and economic impacts, demanding fast and reliable detection to minimize secondary collisions and improve emergency response. However, existing cloud-dependent detection systems often suffer from high latency and limited scalability, motivating the need for an edge-centric and consensus-free accident detection framework in IoV environments. 

Methods: This study presents a real-time accident detection framework tailored for Internet of Vehicles (IoV) environments. The proposed system forms an integrated IoV architecture combining on-vehicle inference, RSU-based validation, and asynchronous cloud reporting. The system integrates a lightweight ensemble of Vision Transformer (ViT) and EfficientNet models deployed on vehicle nodes to classify video frames. Accident alerts are generated only when both models agree (vehicle-level ensemble consensus), ensuring high precision. These alerts are transmitted to nearby Road Side Units (RSUs), which validate the events and broadcast safety messages without requiring inter-vehicle or inter-RSU consensus. Structured reports are also forwarded asynchronously to the cloud for long-term model retraining and risk analysis. 

Results: Evaluated on the CarCrash and CADP datasets, the framework achieves an F1-score of 0.96 with average decision latency below 60 ms, corresponding to an overall accuracy of 98.65% and demonstrating measurable improvement over single-model baselines. 

Conclusions: By combining on-vehicle inference, edge-based validation, and optional cloud integration, the proposed architecture offers both immediate responsiveness and adaptability, contrasting with traditional cloud-dependent approaches.

Objectives: Traffic accidents cause severe social and economic impacts, demanding fast and reliable detection to minimize secondary collisions and improve emergency response. However, existing cloud-dependent detection systems often suffer from high latency and limited scalability, motivating the need for an edge-centric and consensus-free accident detection framework in IoV environments. 

Methods: This study presents a real-time accident detection framework tailored for Internet of Vehicles (IoV) environments. The proposed system forms an integrated IoV architecture combining on-vehicle inference, RSU-based validation, and asynchronous cloud reporting. The system integrates a lightweight ensemble of Vision Transformer (ViT) and EfficientNet models deployed on vehicle nodes to classify video frames. Accident alerts are generated only when both models agree (vehicle-level ensemble consensus), ensuring high precision. These alerts are transmitted to nearby Road Side Units (RSUs), which validate the events and broadcast safety messages without requiring inter-vehicle or inter-RSU consensus. Structured reports are also forwarded asynchronously to the cloud for long-term model retraining and risk analysis. 

Results: Evaluated on the CarCrash and CADP datasets, the framework achieves an F1-score of 0.96 with average decision latency below 60 ms, corresponding to an overall accuracy of 98.65% and demonstrating measurable improvement over single-model baselines. 

Conclusions: By combining on-vehicle inference, edge-based validation, and optional cloud integration, the proposed architecture offers both immediate responsiveness and adaptability, contrasting with traditional cloud-dependent approaches.