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12 pages, 615 KB  
Article
Factors Affecting Axillary Lymph Node Involvement Based on Permanent Section Evaluation of the Excised Sentinel Lymph Nodes in Early-Stage Breast Cancer Patients: A Single-Center Retrospective Study
by Hakan Baysal, Tunc Eren, Kubra Kargici, Ozge Kapar, Begumhan Baysal and Orhan Alimoglu
Medicina 2026, 62(1), 213; https://doi.org/10.3390/medicina62010213 - 20 Jan 2026
Abstract
Background and Objectives: Sentinel lymph node (LN) biopsy (SLNB) remains to be the standard approach for surgical axillary staging of breast cancer (BC) patients. The aim of this study was to investigate the factors that affect axillary LN involvement in early BC patients. [...] Read more.
Background and Objectives: Sentinel lymph node (LN) biopsy (SLNB) remains to be the standard approach for surgical axillary staging of breast cancer (BC) patients. The aim of this study was to investigate the factors that affect axillary LN involvement in early BC patients. Materials and Methods: Clinically node negative early stage (cT1-2N0) BC patients having undergone breast conserving surgery (BCS) between February 2021 and January 2024 were included. During axillary exploration of all cases, sentinel LNs were excised and reserved for permanent section pathological examination (PS) only. Historical records of patients including clinicopathological features, surgical outcomes as well as pathological results were recorded and analyzed retrospectively. p < 0.05 indicated statistically significant results. Results: The study group consisted of 150 women with cT1-2N0 BC having undergone BCS with a median age of 59 (range: 25–81) years. According to the PS results of the sentinel LNs, the need for reoperation to complete axillary lymph node dissection was present in three (2%) patients. Tumors of the Luminal B subtype were significantly associated with increased sentinel LN positivity (p = 0.014). The risk of sentinel LN metastasis was found to be 5.2 times greater in patients with a Ki-67 ≥ %14 [OR: 5.224 (%95 CI:1.73–15.82, p = 0.003)] and the Ki-67 proliferation index was determined as an independent risk factor. Conclusions: In early-stage BC patients, PS of the excised sentinel LN offers sufficient axillary LN staging. On the other hand, a more careful clinical assessment is necessary for early BC patients harboring tumors with an elevated Ki-67 index and/or tumors of the Luminal B subtype. Full article
(This article belongs to the Section Surgery)
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27 pages, 2933 KB  
Article
The iPSM-SD Framework: Enhancing Predictive Soil Mapping for Precision Agriculture Through Spatial Proximity Integration
by Peng-Tao Guo, Wen-Tao Li, Mao-Fen Li, Pei-Sheng Yan, Yan Liu and Ju Zhao
Agronomy 2026, 16(2), 231; https://doi.org/10.3390/agronomy16020231 - 18 Jan 2026
Viewed by 40
Abstract
A key challenge in precision agriculture is acquiring reliable spatial soil information under varying sampling densities, from sparse surveys to intensive monitoring. The individual predictive soil mapping (iPSM) method performs well in data-scarce conditions but neglects spatial proximity, limiting its predictive accuracy where [...] Read more.
A key challenge in precision agriculture is acquiring reliable spatial soil information under varying sampling densities, from sparse surveys to intensive monitoring. The individual predictive soil mapping (iPSM) method performs well in data-scarce conditions but neglects spatial proximity, limiting its predictive accuracy where spatial autocorrelation exists. To overcome this, we developed an enhanced framework, iPSM-Spatial Distance (iPSM-SD), which systematically integrates spatial proximity through multiplicative (MUL) and additive (ADD) strategies. The framework was validated using two contrasting cases: sparse soil organic carbon density data from Yunnan Province (n = 118) and dense soil organic matter data from Bayi Farm (n = 2511). Results show that the additive model (iPSM-ADD) significantly outperformed the original iPSM and benchmark models, including random forest, regression kriging, geographically weighted regression, and multiple linear regression, under sufficient sampling, achieving an R2 of 0.86 and reducing RMSE by 46.6% at Bayi Farm. It also maintained robust accuracy under sparse sampling conditions. The iPSM-SD framework thus provides a unified and adaptive tool for digital soil mapping across a wide range of data availability, supporting scalable soil management decisions from regional assessment to field-scale variable-rate applications in precision agriculture. Full article
(This article belongs to the Section Precision and Digital Agriculture)
24 pages, 3250 KB  
Article
CYPOR Variability as a Biomarker of Environmental Conditions in Bream (Abramis brama), Roach (Rutilus rutilus), Perch (Perca flavescens), and Pike-Perch (Sander lucioperca) from Lake Ladoga
by Vladimir Ponamarev, Olga Popova, Elena Semenova, Evgeny Mikhailov and Alexey Romanov
Vet. Sci. 2026, 13(1), 94; https://doi.org/10.3390/vetsci13010094 - 18 Jan 2026
Viewed by 34
Abstract
The fish liver, as the main detoxification organ, is highly susceptible to xenobiotic exposure, often resulting in various hepatopathies. The cytochrome P450 system plays a central role in xenobiotic metabolism, with cytochrome P450 reductase (CYPOR) supplying the electrons required for CYP enzyme activity. [...] Read more.
The fish liver, as the main detoxification organ, is highly susceptible to xenobiotic exposure, often resulting in various hepatopathies. The cytochrome P450 system plays a central role in xenobiotic metabolism, with cytochrome P450 reductase (CYPOR) supplying the electrons required for CYP enzyme activity. This study aimed to evaluate the relationship between the ecological state of a reservoir and fish health, including CYPOR levels, through hematological, bacteriological, and histological analyses. Samples of water and fish were collected from 12 littoral sites of Lake Ladoga. A total of 1360 specimens of fish from carp (Cyprinidae) and perch (Percidae) families were examined. For histological examination and CYPOR level determination, we selected 40 specimens using a blind randomization method. This sample size was sufficient for statistical analyses. Hematological smears were stained with azure eosin; bacteriological cultures were grown on multiple media; liver samples were stained with hematoxylin and eosin and Sudan III. CYPOR levels in liver homogenates were measured by ELISA-test. Physical and hydrochemical analyses indicated a high pollution level in the littoral zones. Isolated bacterial species were non-pathogenic but exhibited broad antibiotic resistance. Hematological evaluation revealed erythrocyte vacuolization and anisocytosis. Histological analysis showed marked fatty degeneration in hepatocytes, indicating toxic damage. CYPOR concentrations ranged from 0.3–0.4 ng/mL in healthy fish to 5–6 ng/mL in exposed specimens, showing strong correlation between environmental influence and enzyme activity. These findings demonstrate the potential of CYPOR as a sensitive biomarker for biomonitoring programs. The integrated methodological approach provides a model for assessing aquatic ecosystem health and identifying zones requiring priority remediation. Full article
(This article belongs to the Section Anatomy, Histology and Pathology)
20 pages, 1905 KB  
Article
Feasibility Study of School-Centred Peer-to-Peer Energy Trading with Households and Electric Motorbike Loads
by Lerato Paulina Molise, Jason Avron Samuels and Marthinus Johannes Booysen
Sustainability 2026, 18(2), 978; https://doi.org/10.3390/su18020978 - 18 Jan 2026
Viewed by 74
Abstract
South Africa faces high energy costs, highlighting the urgent need for sustainable and cost-effective energy solutions. This study investigates the design of a cost-effective photovoltaic energy system that maximises savings and revenue for the school through energy trading. In this study, the school [...] Read more.
South Africa faces high energy costs, highlighting the urgent need for sustainable and cost-effective energy solutions. This study investigates the design of a cost-effective photovoltaic energy system that maximises savings and revenue for the school through energy trading. In this study, the school trades with 14 neighbouring households and 125 electric motorbikes. This research first applies Latin Hypercube Sampling to explore the solution space and determine which system parameters have a significant impact on supply reliability, investment costs, revenue and savings. Optimal solutions are generated using Non-Dominated Sorting Genetic Algorithm II for a range of system scenarios. Following this, the most promising scenario is selected and applied to 53 schools in the Western Cape. The results show that number of panels strongly correlates with both supply reliability and revenue, thus reducing the break-even years, while battery capacity affects investment costs and, to some extent, break-even years. Among the configurations tested, scenarios where schools traded with both households and electric motorbikes, particularly when both included their own battery systems, achieved the most favourable financial performance for the school, with break-even periods of less than five years under sufficient roof area and improved reliability for the external entities, with an average improvement of 60%. These findings demonstrate that peer-to-peer energy trading between schools and communities can enhance the financial feasibility and sustainability of decentralised solar systems, offering a scalable model for improving energy access and affordability in South Africa and possibly other developing countries. Full article
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25 pages, 32460 KB  
Article
Physically Consistent Radar High-Resolution Range Profile Generation via Spectral-Aware Diffusion for Robust Automatic Target Recognition Under Data Scarcity
by Shuai Li, Yu Wang, Jingyang Xie and Biao Tian
Remote Sens. 2026, 18(2), 316; https://doi.org/10.3390/rs18020316 - 16 Jan 2026
Viewed by 100
Abstract
High-Resolution Range Profile (HRRP) represents the electromagnetic backscattering distribution of targets and plays a pivotal role in remote-sensing-based Automatic Target Recognition (RATR). However, in non-cooperative sensing scenarios, acquiring sufficient measured data is severely constrained by operational costs and physical limitations, leading to data [...] Read more.
High-Resolution Range Profile (HRRP) represents the electromagnetic backscattering distribution of targets and plays a pivotal role in remote-sensing-based Automatic Target Recognition (RATR). However, in non-cooperative sensing scenarios, acquiring sufficient measured data is severely constrained by operational costs and physical limitations, leading to data scarcity that hampers model robustness. To overcome this, we propose SpecM-DDPM, a spectral-aware Denoising Diffusion Probabilistic Models (DDPM) tailored for generating high-fidelity HRRPs that preserve physical scattering properties. Unlike generic generative models, SpecM-DDPM incorporates radar signal physics into the diffusion process. Specifically, a parallel multi-scale block is designed to adaptively capture both local scattering centers and global target resonance structures. To ensure spectral fidelity, a spectral gating mechanism serves as a physics-constrained filter to calibrate the energy distribution in the frequency domain. Furthermore, a Frequency-Aware Curriculum Learning (FACL) strategy is introduced to guide the progressive reconstruction from low-frequency structural components to high-frequency scattering details. Experiments on measured aircraft data demonstrate that SpecM-DDPM generates samples with high physical consistency, significantly enhancing the generalization performance of radar recognition systems in data-limited environments. Full article
9 pages, 6264 KB  
Article
A 4.7–8.8 GHz Wideband Switched Coupled Inductor VCO for Dielectric Spectroscopy Sensors
by Kiho Lee, Hapsah Aulia Azzahra, Muhammad Fakhri Mauludin, Dong-Ho Lee, Jusung Kim and Songcheol Hong
Electronics 2026, 15(2), 388; https://doi.org/10.3390/electronics15020388 - 15 Jan 2026
Viewed by 118
Abstract
The miniaturization of dielectric sensing has driven the development of both oscillator- and receiver-based sensors. Wide-frequency-range and low-power-consumption voltage-controlled oscillators (VCOs) are required as a reference clock for receiver-based dielectric spectroscopy. In this paper, we propose a switched coupled inductor VCO offering sufficiently [...] Read more.
The miniaturization of dielectric sensing has driven the development of both oscillator- and receiver-based sensors. Wide-frequency-range and low-power-consumption voltage-controlled oscillators (VCOs) are required as a reference clock for receiver-based dielectric spectroscopy. In this paper, we propose a switched coupled inductor VCO offering sufficiently wide bandwidth in a power-efficient manner. The proposed switched coupled inductor offers higher coupling factor and mutual inductance compared to direct switched inductor schemes along with a higher quality factor and tuning range. The proposed switched coupled inductor improved the frequency tuning range by 21% compared to the conventional VCO. The measurement results show that the proposed VCO oscillates from 4.7 to 8.8 GHz frequency, suitable for dielectric spectroscopy sensors. With only 4.5 mW power consumption, the proposed VCO can achieve −103.3 dBc/Hz phase noise at 1 MHz offset, with a resulting tuning range figure-of-merit (FOMT) of −187.4 dBc/Hz. Full article
17 pages, 4231 KB  
Article
The Impact of Soil Tillage Systems and Fertilization Strategies on Winter Wheat Yield Under the Variable Weather Conditions of the Transylvanian Plain
by Felicia Chețan, Cornel Chețan, Alina Șimon, Ovidiu Adrian Ceclan, Diana Hirișcău, Raluca Rezi, Alin Popa, Marius Bărdaș, Camelia Urdă, Roxana Elena Călugăr, Paula Ioana Moraru and Teodor Rusu
Nitrogen 2026, 7(1), 12; https://doi.org/10.3390/nitrogen7010012 - 15 Jan 2026
Viewed by 66
Abstract
Agronomic systems that can guarantee consistent and sufficient crop yields must be developed and implemented in order to address the problems presented by climate change, especially the increase in average annual temperatures and the unequal distribution of precipitation. Over the course of five [...] Read more.
Agronomic systems that can guarantee consistent and sufficient crop yields must be developed and implemented in order to address the problems presented by climate change, especially the increase in average annual temperatures and the unequal distribution of precipitation. Over the course of five successive growing seasons (2019–2024), a Poly-Factorial field experiment was carried out at the Agricultural Research and Development Station (ARDS) Turda, Romania, which is situated in the hilly region of the Transylvanian Plain. The study investigated the combined effects of soil tillage system (conventional tillage—CS; no-tillage—NT) and fertilization strategies (N48P48K48 at sowing vs. N48P48K48 at sowing + N40.5CaO10.5MgO7 applied in early spring at the growth resumption) on the quantitative and qualitative performance of winter wheat (Triticum aestivum L.). Results showed a modest yield difference of 206 kg ha−1 between the two tillage systems, favoring conventional tillage. However, the application of additional early-spring fertilization resulted in a significant average yield increase of 338 kg ha−1. Yield variability across the five years ranged from 262 to 1797 kg ha−1, highlighting the strong influence of climatic conditions on crop performance and emphasizing the need for adaptive management practices under changing environmental conditions. Full article
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18 pages, 2246 KB  
Article
Reliability of Joint Position Sense and Force Sense Measurements in Children with Developmental Coordination Disorder
by Anna Gogola, Piotr Woźniak, Zenta Piscova, Anna Rubika, Liene Lukjaņenko, Irēna Kaminska and Rafał Gnat
J. Funct. Morphol. Kinesiol. 2026, 11(1), 35; https://doi.org/10.3390/jfmk11010035 - 15 Jan 2026
Viewed by 108
Abstract
Background: Quantitative assessment of proprioception in children with Developmental Coordination Disorder (DCD) is limited by methodological variability and the lack of developmentally appropriate protocols. Joint position sense (JPS) and force sense (FS) assessments are commonly used in adults; however, their reliability in pediatric [...] Read more.
Background: Quantitative assessment of proprioception in children with Developmental Coordination Disorder (DCD) is limited by methodological variability and the lack of developmentally appropriate protocols. Joint position sense (JPS) and force sense (FS) assessments are commonly used in adults; however, their reliability in pediatric populations has not been sufficiently established. The objective of this study was to evaluate the intra- and inter-rater reliability of adapted JPS and FS protocols in children with DCD and to determine whether the observed reliability supports the use of these methods in experimental research. Methods: A repeated-measurements reliability research design was employed. Twenty-eight children aged 10–15 years (mean age 12.86 years), with a mean body mass of 43.68 kg and a mean height of 149.32 cm, and with medically confirmed DCD, completed four proprioceptive tests: joint angle reproduction and differentiation, and force reproduction and differentiation. Absolute errors were calculated for each trial. Reliability was assessed using intraclass correlation coefficients (ICC2,k), standard error of measurement, and smallest detectable difference. Bland–Altman plots were used to evaluate agreement. Results: Reliability across all tests and movement directions ranged from good to excellent. Most ICC values exceeded 0.90, with only a small number falling between 0.86 and 0.90. Although differentiation tasks produced larger absolute errors than reproduction tasks, their reliability remained excellent. Bland–Altman analyses demonstrated acceptable bias, reasonable clustering around the mean difference, and only occasional outliers beyond the limits of agreement. Conclusions: The adapted JPS and FS protocols demonstrated high intra- and inter-rater reliability in children with DCD, supporting their use in experimental research. Full article
(This article belongs to the Section Functional Anatomy and Musculoskeletal System)
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45 pages, 32626 KB  
Article
Estimation of Sea State Parameters from Measured Ship Motions with a Neural Network Trained on Experimentally Validated Model Simulations
by Jason M. Dahl, Annette R. Grilli, Stephanie C. Steele and Stephan T. Grilli
J. Mar. Sci. Eng. 2026, 14(2), 179; https://doi.org/10.3390/jmse14020179 - 14 Jan 2026
Viewed by 123
Abstract
The use of ships and boats as sea-state (SS) measurement platforms has the potential to expand ocean observations while providing actionable information for real-time operational decision-making at sea. Within the framework of the Wave Buoy Analogy (WBA), this work develops an inverse approach [...] Read more.
The use of ships and boats as sea-state (SS) measurement platforms has the potential to expand ocean observations while providing actionable information for real-time operational decision-making at sea. Within the framework of the Wave Buoy Analogy (WBA), this work develops an inverse approach in which efficient simulations of wave-induced motions of an advancing vessel are used to train a neural network (NN) to predict SS parameters across a broad range of wave climates. We show that a reduced set of novel motion discriminant variables (MDVs)—computed from short time series of heave, roll, and pitch motions measured by an onboard inertial measurement unit (IMU), together with the vessel’s forward speed—provides sufficient and robust information for accurate, near-real-time SS estimation. The methodology targets small, barge-like tugboats whose operations are SS-limited and whose motions can become large and strongly nonlinear near their upper operating limits. To accurately model such responses and generate training data, an efficient nonlinear time-domain seakeeping model is developed that includes nonlinear hydrostatic and viscous damping terms and explicitly accounts for forward-speed effects. The model is experimentally validated using a scaled physical model in laboratory wave-tank tests, demonstrating the necessity of these nonlinear contributions for this class of vessels. The validated model is then used to generate large, high-fidelity datasets for NN training. When applied to independent numerically simulated motion time series, the trained NN predicts SS parameters with errors typically below 5%, with slightly larger errors for SS directionality under relatively high measurement noise. Application to experimentally measured vessel motions yields similarly small errors, confirming the robustness and practical applicability of the proposed framework. In operational settings, the trained NN can be deployed onboard a tugboat and driven by IMU measurements to provide real-time SS estimates. While results are presented for a specific vessel, the methodology is general and readily transferable to other ship geometries given appropriate hydrodynamic coefficients. Full article
(This article belongs to the Section Ocean Engineering)
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22 pages, 2627 KB  
Article
FANET Routing Protocol for Prioritizing Data Transmission to the Ground Station
by Kaoru Takabatake and Tomofumi Matsuzawa
Network 2026, 6(1), 7; https://doi.org/10.3390/network6010007 - 14 Jan 2026
Viewed by 120
Abstract
In recent years, with the improvement of unmanned aerial vehicle (UAV) performance, various applications have been explored. In environments such as disaster areas, where existing infrastructure may be damaged, alternative uplink communication for transmitting observation data from UAVs to the ground station (GS) [...] Read more.
In recent years, with the improvement of unmanned aerial vehicle (UAV) performance, various applications have been explored. In environments such as disaster areas, where existing infrastructure may be damaged, alternative uplink communication for transmitting observation data from UAVs to the ground station (GS) is critical. However, conventional mobile ad hoc network (MANET) routing protocols do not sufficiently account for GS-oriented traffic or the highly mobile UAV topology. This study proposed a flying ad hoc network (FANET) routing protocol that introduces a control option called GS flood, where the GS periodically disseminates routing information, enabling each UAV to efficiently acquire fresh source routes to the GS. Evaluation using NS-3 in a disaster scenario confirmed that the proposed method achieves a higher packet delivery ratio and practical latency compared to the representative MANET routing protocols, namely DSR, AODV, and OLSR, while operating with fewer control IP packets than existing methods. Furthermore, although the multihop throughput between UAVs and the GS in the proposed method plateaued at approximately 40% of the physical-layer maximum, it demonstrated performance exceeding realistic satellite uplink capacities ranging from several hundred kbps to several Mbps. Full article
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24 pages, 5067 KB  
Article
Collision Avoidance Strategy by Utilizing Safety Envelope for Automated Driving System: Hazardous Situation Case
by Mingwei Gao and Hidekazu Nishimura
Systems 2026, 14(1), 89; https://doi.org/10.3390/systems14010089 - 14 Jan 2026
Viewed by 191
Abstract
Autonomous vehicles (AVs) must dynamically maintain sufficient safe distances from surrounding vehicles to ensure safety. Many existing studies have focused on collisions avoidance, such as the safety ranges in a rectangular shape that consider only longitudinal safe distance. A safety envelope is proposed [...] Read more.
Autonomous vehicles (AVs) must dynamically maintain sufficient safe distances from surrounding vehicles to ensure safety. Many existing studies have focused on collisions avoidance, such as the safety ranges in a rectangular shape that consider only longitudinal safe distance. A safety envelope is proposed herein, which is geometrically constructed from four quarter ellipses that account for longitudinal and lateral safe distances. The origin of the safety envelope is placed at the AV’s center of gravity. Using the safety envelope, a potential collision is identified when any surrounding vehicle enters it. To sustain the safety envelope even under hazardous situations, a collision avoidance strategy is introduced. In this strategy, the AV dynamically adjusts its velocity or changes lanes with velocity adjusting by assessing the risk level, complexity level, and riding comfort. For the lane-changing maneuvers, a virtual vehicle is introduced to be placed in the target lane to guide the AV’s movement. The efficacy of this strategy is verified via a simulation under a hazardous situation involving an AV and six human-driven vehicles driving on a highway. Results show that the proposed collision avoidance strategy utilizing safety envelope effectively ensures the safety of AV and surrounding vehicles, even under hazardous situations. Full article
(This article belongs to the Special Issue Application of the Safe System Approach to Transportation)
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21 pages, 699 KB  
Review
Low-Cost Sensors in 5G RF-EMF Exposure Monitoring: Validity and Challenges
by Phoka C. Rathebe and Mota Kholopo
Sensors 2026, 26(2), 533; https://doi.org/10.3390/s26020533 - 13 Jan 2026
Viewed by 159
Abstract
The deployment of 5G networks has transformed the landscape of radiofrequency electromagnetic field (RF-EMF) exposure patterns, shifting from high-power macro base stations to dense networks of small, beamforming cells. This review critically assesses the validity, challenges, and research gaps of low-cost RF-EMF sensors [...] Read more.
The deployment of 5G networks has transformed the landscape of radiofrequency electromagnetic field (RF-EMF) exposure patterns, shifting from high-power macro base stations to dense networks of small, beamforming cells. This review critically assesses the validity, challenges, and research gaps of low-cost RF-EMF sensors used for 5G exposure monitoring. An analysis of over 60 studies covering Sub-6 GHz and emerging mmWave systems shows that well-calibrated sensors can achieve measurement deviations of ±3–6 dB compared to professional instruments like the Narda SRM-3006, with long-term calibration drift less than 0.5 dB per month and RMS reproducibility around 5%. Typical outdoor 5G FR1 exposure levels range from 0.01 to 0.5 W/m2 near small cells, while personal device use can cause transient exposures 10–30 dB higher. Although mmWave (24–100 GHz) and Wi-Fi 7/8 (~60 GHz) are underrepresented due to antenna and component limitations, Sub-6 GHz sensing platforms, including software-defined radio (SDR)-based and triaxial isotropic designs, provide sufficient sensitivity for both citizen and institutional monitoring. Major challenges involve calibration drift, frequency band gaps, data interoperability, and ethical management of participatory networks. Addressing these issues through standardized calibration protocols, machine learning-assisted drift correction, and open data frameworks will allow affordable sensors to complement professional monitoring, improve spatial coverage, and enhance public transparency in 5G RF-EMF exposure governance. Full article
(This article belongs to the Special Issue Electromagnetic Sensing and Its Applications)
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19 pages, 287 KB  
Article
Existence, Uniqueness, and Hyers–Ulam’s Stability of the Nonlinear Bagley–Torvik Equation with Functional Initial Conditions
by Chenkuan Li, Wenyuan Liao and Ying-Ying Ou
Mathematics 2026, 14(2), 286; https://doi.org/10.3390/math14020286 - 13 Jan 2026
Viewed by 101
Abstract
The nonlinear Bagley–Torvik equation is of fundamental importance, as it captures a realistic and intricate interplay among memory effects, nonlinearity, and functional dependence—making it a powerful model for a wide range of natural and engineered systems. Its analysis contributes significantly to both the [...] Read more.
The nonlinear Bagley–Torvik equation is of fundamental importance, as it captures a realistic and intricate interplay among memory effects, nonlinearity, and functional dependence—making it a powerful model for a wide range of natural and engineered systems. Its analysis contributes significantly to both the theoretical development of fractional differential equations and their practical applications across science and technology. In this paper, we employ the inverse operator method, the multivariate Mittag-Leffler function, and several classical fixed-point theorems to establish sufficient conditions for the existence, uniqueness, and Hyers–Ulam stability of solutions to the nonlinear Bagley–Torvik equation with functional initial conditions. Finally, we present several examples by explicitly computing values of the multivariate Mittag-Leffler functions to illustrate the main results. Full article
22 pages, 4957 KB  
Article
Machine Learning-Based Algorithm for the Design of Multimode Interference Nanodevices
by Roney das Mercês Cerqueira, Vitaly Félix Rodriguez-Esquerre and Anderson Dourado Sisnando
Nanomanufacturing 2026, 6(1), 3; https://doi.org/10.3390/nanomanufacturing6010003 - 13 Jan 2026
Viewed by 195
Abstract
Multimode interference photonic nanodevices have been increasingly used due to their broad functionality. In this study, we present a methodology based on machine learning algorithms for inverse design capable of providing the output port position (x-axis coordinate) and MMI region length [...] Read more.
Multimode interference photonic nanodevices have been increasingly used due to their broad functionality. In this study, we present a methodology based on machine learning algorithms for inverse design capable of providing the output port position (x-axis coordinate) and MMI region length (y-axis coordinate) for achieving higher optical signal transfer power. This is sufficient to design Multimode Interference 1 × 2, 1 × 3, and 1 × 4 nanodevices as power splitters in the wavelength range between 1350 and 1600 nm, which corresponds to the E, S, C, and L bands of the optical communications window. Using Multilayer Perceptron artificial neural networks, trained with k-fold cross-validation, we successfully modeled the complex relationship between geometric parameters and optical responses with high precision and low computational cost. The results of this project meet the requirements for photonic device projects of this nature, demonstrating excellent performance and manufacturing tolerance, with insertion losses ranging from 0.34 dB to 0.58 dB. Full article
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15 pages, 14065 KB  
Article
Design and Verification of Ladder Sleepers Suitable for Rail Joints in Ballasted Tracks
by Tsutomu Watanabe, Keiichi Goto, Tomoya Yamashita and Daisuke Mimura
Appl. Sci. 2026, 16(2), 769; https://doi.org/10.3390/app16020769 - 12 Jan 2026
Viewed by 140
Abstract
Ladder sleepers were originally developed to reduce maintenance requirements in ballasted tracks by improving load distribution along the rail direction. In Japan, their design generally follows the method used for prestressed concrete sleepers, where dynamic and impact effects induced by train passage are [...] Read more.
Ladder sleepers were originally developed to reduce maintenance requirements in ballasted tracks by improving load distribution along the rail direction. In Japan, their design generally follows the method used for prestressed concrete sleepers, where dynamic and impact effects induced by train passage are accounted for using an impact factor. However, the impact factor and the length of the unsupported section—which compensates for ballast settlement over time—have not been sufficiently verified for ladder sleeper applications at rail joints, where the load environment is more severe. In this study, ladder sleepers designed following the criteria for general track sections were installed at rail joints in an operating ballasted track. Field measurements of bending moments under train passage were collected over 13 months, and numerical analyses were performed to evaluate the applicability of key design parameters. The impact factor at rail joints remained within a range comparable to that of general sections, confirming that a value of 2 is appropriate. In contrast, the unsupported section tended to extend over time and should be set to ~1.5 times the conventional design length. Accordingly, new ladder sleeper structures suitable for the load environment at rail joints were designed. Full article
(This article belongs to the Section Civil Engineering)
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