Search Results (22,618)

Background and Objectives: Determining the mechanical stability of osteosynthesis in pertrochanteric fractures remains a critical challenge in orthopedic biomechanics. The aim of this study was to develop a mathematical model for quantifying the stability of osteosynthesis and to establish criteria for its evaluation under physiological loading conditions. Materials and Methods: A mathematical model describing the biomechanical behavior of a proximal femur with a pertrochanteric fracture stabilized using a cephalomedullary nail (CMN) was developed. The model integrates force equilibrium, stress–strain relationships, and loading conditions representative of early functional rehabilitation. The theoretical framework was implemented in MATLAB/Simulink R2025b and complemented by finite element analysis to determine stress distribution, deformation patterns, and stability-related parameters of the bone–implant system. Results: The developed mathematical model enabled a quantitative assessment of osteosynthesis stability through the evaluation of key mechanical indicators, including displacement, stress distribution, and safety factor within the fixation system. Critical stress zones in the implant and surrounding bone were identified, allowing analysis of load transfer mechanisms. Finite element simulations showed that improved fixation mechanics reduced peak implant stresses, limited displacement at the fracture site, and increased the safety factor of the fixation construct, resulting in a more uniform load distribution in the surrounding bone and enhanced overall stability of the osteosynthesis system. Conclusions: The proposed mathematical model provides a systematic approach for determining the stability of osteosynthesis in pertrochanteric fractures. It offers a theoretical basis for optimizing implant design and fixation strategies, with potential applications in preclinical evaluation and surgical planning. Full article

This study stems from the need to investigate how GenAI tools, particularly ChatGPT-4o, can support the professional development of mathematics teachers. It explores how Blum’s modeling cycle can serve as a conceptual and operational framework for mathematics teachers’ instructional design when supported by ChatGPT-4o. Drawing on a qualitative case study within a teacher professional development program, the research analyzes how two upper secondary school teachers engaged with ChatGPT-4o to redesign a mathematical task involving probability and real-world contexts. Data include responses to three modeling-related tasks, teachers’ prompts and interactions with ChatGPT-4o, and the final mathematical activity they designed. These materials were analyzed qualitatively according to the modeling cycle and its sub-competencies. The results indicate that the modeling cycle provided teachers with a cognitive and methodological scaffold to guide their interaction with ChatGPT-4o, allowing them to structure, validate, and refine AI-generated ideas through all stages of modeling—from understanding and mathematizing to interpreting and validating. These findings suggest that the modeling cycle can be reinterpreted as a design-oriented framework for integrating ChatGPT-4o in mathematics teacher education. Implications for teacher professional development and future research directions are discussed. Full article

This paper presents an integrated mathematical model to improve the safety and operational efficiency of train traffic in centralised railway dispatching systems. The proposed approach combines the alternative graph model with a Mealy automaton to synchronously address route planning, delay minimisation, and strict compliance with safety requirements. Formal control theory based on finite-state automata is employed to describe routing logic and signal control through state transitions, while the alternative graph model represents scheduling constraints and resource conflicts. To enhance real-time adaptability, a tabu search algorithm is implemented for train schedule optimisation, enabling dynamic rescheduling under changing operational conditions. The mathematical formulation incorporates blocking time parameters, a system of discrete constraints, and automaton-based safety conditions governing train movements and route authorisation. The integrated model explicitly formalises the processes of block section occupation and release, ensuring consistency between control logic and scheduling decisions. Practical testing and computational experiments demonstrate that the proposed approach effectively reduces train delays, improves the reliability of dispatch control, and increases system resilience to dynamic disturbances. The results confirm that the developed model can be implemented within existing centralised dispatching infrastructures without requiring a complete system overhaul. Overall, the proposed framework expands the functional capabilities of centralised dispatch systems by enabling efficient schedule generation, minimising the propagation of delays, and ensuring reliable command exchange between central control posts and field-level railway infrastructure. Full article

Personalized instruction remains a major bottleneck in higher education, especially in large classes where timely, individualized feedback is difficult to achieve. Existing automation typically relies on rigid rule-based pipelines or computationally heavy deep learning models, making it difficult to simultaneously achieve interpretability, instructional usability, and scalable deployment. In this study, we present CalcTutor, a generative-AI-based assessment and feedback system designed to support open-ended handwritten calculus problem solving. The system organizes instructional support through three coordinated components: (1) a multi-agent large language model (LLM) mechanism that evaluates solution processes and produces diagnostic feedback, (2) a retrieval-augmented generation (RAG) pipeline that links diagnosed difficulties to aligned instructional materials, and (3) real-time learner analytics for both students and instructors, forming an integrated instructional support workflow rather than an automated answer-checking tool. In offline evaluation and a pilot classroom deployment, the multi-agent grader achieved a weighted agreement accuracy of 0.931 and an F1-score of 0.934 on 1055 handwritten solutions. Participant feedback and workflow testing indicated that CalcTutor can be stably integrated into routine classroom use and enables students to interpret and act upon the provided feedback. These results indicate that automated assessment, diagnostic feedback, and targeted review can operate coherently within a single instructional process that supports instructor-led assessment practices. Using undergraduate calculus as an application domain for open-ended handwritten mathematical assessment, the study demonstrates the operational feasibility of a closed-loop assessment–feedback–revision workflow and provides a deployable instructional infrastructure for formative instructional support in real classroom contexts. Full article

The control of surface residual stress is paramount for ensuring the mechanical performance and longevity of machined GH2132 superalloy bolts. However, direct measurement of residual stress remains challenging. This study introduces a novel, efficient approach by establishing a quantitative correlation between Vickers hardness and residual stress based on the energy indentation method. The core hypothesis leverages the principle that residual stress modifies the indentation work; the difference in energy dissipation between stressed and stress-free states provides a direct measure of residual stress. A mathematical model relating hardness (HV) to residual stress (σ) was derived. To validate the model and unravel the underlying microstructural mechanisms, orthogonal cutting experiments were conducted. Comprehensive microstructural characterization using SEM, XRD, and metallography revealed a synchronous relationship between hardness and residual stress. Both properties increased concurrently with greater grain refinement and higher volume fraction/distribution density of carbides and γ’ phases, which impede dislocation motion and introduce micro-strain. The model predictions showed excellent agreement (R² = 92.5%) with X-ray diffraction measurements, confirming its reliability. Furthermore, the influence of cutting parameters (speed V_c, feed f, depth of cut a_p) on residual stress was analyzed. Cutting depth was identified as the most significant factor. An optimal parameter combination (V_c = 20 m × min⁻¹, f = 1 mm × rev⁻¹, a_p = 1.2 mm) was identified to maximize beneficial compressive residual stress, corresponding to the most refined microstructure. This work presents a validated, hardness-based model for residual stress assessment in GH2132 and provides a microstructure-guided pathway for optimizing machining processes to enhance component life. Full article

This study addresses the problem of improving the efficiency of fine grinding of bulk materials in a spring-rotor mill. The objective is to determine technologically sound operating parameters based on mathematical modeling, design of experiments, and multi-objective optimization. The methodology relies on a full-factorial experimental design according to the Hartley plan, with five control factors: rotor rotational speed, material loading ratio, overlap of the working zones, grinding chamber clearance, and grinding duration. The analyzed responses include grinding fineness, throughput, power consumption, specific energy consumption, and specific metal intensity. Based on experimental data, adequate second-order polynomial regression models were obtained for all response variables using the least-squares method. Statistical analysis showed that grinding time and rotational speed had the most significant influence on the process. Multi-objective optimization using the weighted-sum method enabled the identification of optimal operating conditions that balance product quality, throughput, and energy consumption. Verification experiments confirmed the adequacy of the developed models. Practical implementation of the optimized regimes increases throughput by 15–20% while simultaneously reducing energy consumption by 8–12% compared with empirically selected operating conditions. The proposed models and recommendations provide a quantitative basis for tuning and controlling grinding equipment in processing industries. Full article

Background: Gestational diabetes mellitus (GDM) affects many pregnancies worldwide and is associated with adverse maternal and fetal outcomes. Current screening at 24–28 weeks limits opportunities for early intervention. We evaluated whether machine learning (ML) models using first-trimester clinical and dietary data can predict GDM risk before the standard oral glucose tolerance test. Methods: We analyzed data from 797 pregnant women enrolled in the BORN2020 prospective cohort study (Thessaloniki, Greece). Ten ML algorithms were evaluated across five class-imbalance handling strategies using stratified 5-fold cross-validation, with final evaluation on an independent 20% held-out test set. Features included maternal demographics, obstetric history, lifestyle factors, and 22 dietary micronutrient intakes from the pre-pregnancy period assessed by Food Frequency Questionnaire. Results: The best-performing model (Logistic Regression without resampling) achieved an AUC-ROC of 0.664 (95% CI: 0.542–0.777), with sensitivity of 0.783 and NPV of 0.932 at the pre-specified threshold. The high NPV should be interpreted in the context of the low GDM prevalence (14.7%), as NPV is mathematically dependent on disease prevalence. A reduced nine-feature model using only routine clinical and demographic variables achieved a numerically higher AUC of 0.712 (95% CI: 0.589–0.825), with overlapping confidence intervals, indicating that detailed FFQ-derived micronutrient data did not improve prediction. Maternal age and pre-pregnancy BMI were the strongest individual predictors by SHAP analysis. No model reached the AUC >0.80 threshold for good discrimination. Substantial miscalibration was observed (slope: 0.56; intercept: −1.83), limiting use for absolute risk estimation. Conclusions: This exploratory study demonstrates that first-trimester ML models achieve modest discriminative ability for early GDM prediction, with routine clinical variables performing comparably to models incorporating detailed dietary assessment. These findings should be interpreted with caution, as no external validation cohort was available and the low events-per-variable ratio (~3.8) constrains the reliability of individual model estimates. Substantial miscalibration further limits use for absolute risk estimation. Accordingly, these models should be regarded as exploratory risk-ranking tools only and require external validation and recalibration before any clinical implementation. Full article

This paper introduces the New Bipolar Intuitionistic Fuzzy Metric Space (NBIFM-space)—a mathematical framework that extends intuitionistic and previously proposed bipolar intuitionistic structures by providing a complete three-component formulation based on positive similarity, negative similarity, and indeterminacy. Unlike earlier bipolar intuitionistic models, the NBIFM-space employs normalized metric components and coordinated triangular norms denoted by t-norm/t-conorm interactions, yielding a fully consistent topological and analytic setting. We have developed the basic properties of this structure and have demonstrated its effectiveness in image processing, where the explicit separation of attraction, repulsion, and uncertainty leads to robust edge-preserving filtering. Furthermore, a Banach-type fixed point theorem is established in the full NBIFM framework. Full article

Document Layout Analysis (DLA) is a critical step in intelligent document processing and is essential for accurately reconstructing the hierarchical structure of pages. While modern convolutional neural networks exhibit high performance, their effectiveness heavily depends on the quality and representativeness of training data, limiting their application in scenarios where labeled datasets are scarce. This paper proposes a method for enhancing DLA through synthetic generation of training data. A formalized mathematical model for generating document layouts has been developed, allowing control over element placement density, sizes, and spatial distribution. An experimental study investigated the impact of various data generation strategies on the training of the YOLO11m model, including median and threshold-based element splitting as well as different block sampling schemes. The experiments showed that employing median element splitting combined with random sampling from a large shuffled pool of synthetic data yields consistent improvements of 2–4% across all key metrics: precision, recall, mAP@50, and mAP@50:95, as compared with simple data generation strategies. These results demonstrate that targeted optimization of the data preparation process can enhance the performance of convolutional models in DLA tasks without increasing architectural complexity. The practical applicability of the method is validated through integration into the MinerU system. Future research will focus on extending the proposed model to complex layouts in scientific journals, technical reports, and handwritten documents. Full article

Climate change leads to less water in forest ecosystems and higher evapotranspiration during the growing season, increasing the risk of drought. This study evaluates microclimate and soil hydrology at two different sites in the Dobroč Primeval Forest (National Nature Reserve, NATURA 2000): a near-natural fir–beech buffer zone and a managed Norway spruce monoculture. Measurements cover two hydrological years with very different climatic conditions. The Climatic Water Balance (CWB) was used to assess precipitation deficit, and soil moisture dynamics were simulated with the GLOBAL mathematical model. In 2021, precipitation was 223.7 mm below the long-term average, and the cumulative CWB deficit from March to September was 224 mm. Drought risk peaked in summer 2021. The spruce stand’s A/B horizon was 197 days below the point of decreased availability (PDA), compared to 179 days in the beech buffer zone. Drought moved through the soil profile with a 3–4-day lag between horizons at both sites. Results confirm that Norway spruce monocultures are more drought-vulnerable than near-natural beech stands under identical conditions, supporting active forest conversion in Central European mountain regions. Full article

In this study, we examine the effectiveness of combining interleukin-2 (IL-2) with highly active antiretroviral therapy (HAART) in controlling HIV replication. A mathematical model of the immune system is developed to analyze immune recovery when IL-2 is administered alongside HAART. We investigate the stability of the endemic equilibrium and Hopf bifurcation and determine the direction and stability of periodic solutions using center manifold theory. Numerical simulations are conducted to support the theoretical findings. The results show that the disease-free equilibrium is stable when the basic reproduction number $R_0<1$, while the endemic equilibrium exists when $R_0>1$. Our results also reveal the presence of a subcritical Hopf bifurcation in the system. An optimal control problem is also studied, showing that the combined therapy of IL-2 and HAART improves treatment outcomes, reduces side effects, and has a unique optimal control pair. Sensitivity analysis further highlights the importance of system parameters in influencing treatment effectiveness. Full article

Atomic charges play a central role in the analysis of molecular electronic structure and are widely used in the development of computational models. We introduce a simple and computationally efficient extension of Hirshfeld’s 1977 stockholder partitioning method, called scaled Hirshfeld, in which neutral proatom densities are scaled to construct a promolecular density better adapted to the molecular electron density. We present a fixed-point iterative algorithm to compute the proatom scaling coefficients and show that this formulation is equivalent to the information-theoretic additive variational Hirshfeld method with a minimal basis. This equivalence establishes a rigorous mathematical foundation for the scaled Hirshfeld method and ensures size consistency as well as the existence of a unique solution. Numerical results demonstrate that the proposed approach yields charges larger than those obtained with the original Hirshfeld method, while retaining computational efficiency and providing an improved description of molecular dipole moments and electrostatic potentials. Full article

To address the issue of cable force optimization during the cantilever casting stage of reinforced concrete arch bridge construction, this study proposes a cable force optimization method based on an Improved Whale Optimization Algorithm (IWOA) combined with a Support Vector Machine (SVM) model. First, the standard Whale Optimization Algorithm is enhanced through Tent chaotic mapping, a nonlinear iterative control parameter, adaptive weight factors, and adaptive threshold strategies. The improved algorithm is then used to optimize key parameters (C, g) in the SVM model, constructing a parameter-optimized cable force combination-structure response prediction model for the arch bridge. Next, with the average tensile stress of the arch ring’s top and bottom slabs during construction and the bending strain energy after bridge completion as target variables, a multi-objective optimization mathematical model for cable forces during the construction stage of reinforced concrete arch bridges based on IWOA-SVM was established. Finally, the feasibility of the method was validated using the Shatuo Bridge project as a case study. The results indicate that compared to the finite element optimization method, the IWOA-SVM cable force optimization method significantly improved computational efficiency while ensuring optimization effectiveness. After optimization, the peak tensile stress and vertical displacement of each arch segment were significantly reduced, leading to improved internal force distribution and alignment, thereby enhancing the overall structural safety and reliability of reinforced concrete arch bridges. Full article

This paper investigates the fractal dynamical behavior of a discrete Caputo fractional-order hepatitis C virus model. First, we analyze the stability of the system by using spectral radius and design the fractional-order controller based on coordinate transformation. Then, a nonlinear coupling controller is constructed to achieve synchronization between two fractional-order models with different parameters and different fractional orders, and the synchronization is supported by rigorous mathematical proof. Numerical simulations are used to verify the effectiveness of control and synchronization. Full article

Doubly periodic tangles, or DP tangles, are embeddings of curves in the thickened plane that are periodically repeated in two directions. They are defined as universal covers of their generating cells, the flat motifs, which represent knots and links in the thickened torus, and which can be chosen in infinitely many ways. DP tangles are used in modeling materials and physical systems of entangled filaments. In this paper, we establish the complete mathematical framework of the topological theory of DP tangles. We present an exhaustive analysis of DP tangle isotopies. These are distinguished in local isotopies and global isotopies. Our analysis yields the characterization of DP isotopy as an equivalence relation on the level of their (flat) motifs, called DP tangle equivalence. Along the way, we also discuss motif minimality. We further generalize our results to other diagrammatic categories, namely framed, virtual, welded, singular, pseudo, tied and bonded DP tangles, which could be used in novel applications. Full article