Search Results (989)

This study builds on Davis’ TAM by integrating environmental and psychological variables relevant to AI medical diagnostics. This study developed a mathematical theoretical model called the “AI medical diagnosis-acceptance evaluation model” (AMD-AEM) to better understand acceptance behavior intention. Using mathematical modeling, we established reflective measurement model indicators and structural equation relationships, where linear structural equations illustrate the interactions among latent variables. In 2025, we collected empirical data from 2380 patients and medical staff who have experience with AI diagnostic systems in teaching hospitals in central Taiwan. Smart PLS 3 was employed to validate the AMD-AEM model. The results reveal that perceived usefulness (PU) and information quality (IQ) are the primary predictors of acceptance behavior intention (ABI). Additionally, perceived ease of use (PE) indirectly influences ABI through PU and attitude toward use (ATU). AI emotional perception (AEP) notably shows a significant positive relationship with ATU, highlighting that warm and positive human–AI interactions are crucial for user acceptance. IQ was identified as a mediating variable, with variance accounted for (VAF) coefficient analysis confirming its complete mediation effect on the path from ATU to ABI. This indicates that information quality enhances user attitudes and directly increases acceptance behavior intention. The AMD-AEM model demonstrates an excellent fit, providing valuable insights for academia and the healthcare industry. Full article

The use of augmented reality (AR) tools and innovative learning environments in education have increased over the last few years due to the rapid advancement of technology. In this study, an AR mathematics learning intervention has been proposed which consisted of the creation of 3D multibase blocks to perform AR arithmetic calculations conducted through active methodologies in the future classroom lab (FCL). The aim of this study was to analyze pre-service teachers’ (PSTs) affective domain (emotion, self-efficacy, and attitude), engagement, motivation, and confidence. The sample consisted of 97 PSTs enrolled on the second year of the Primary Education degree, who were attending the “Mathematics and its Didactics” subject. The findings revealed a significant increase in PSTs’ satisfaction, fun, confidence, and pride, and a decrease in uncertainty, nervousness, and concern. Regarding PSTs’ self-efficacy, a significant improvement was observed in knowing the necessary steps to teach mathematical concepts and work in the FCL. No significant differences were found in attitude, engagement, and motivation; however, the PSTs showed a high disposition in all of them before starting the intervention. Additionally, the PSTs reported to be more confident, and it enhanced their knowledge in the use of 3D design and AR applications to create multibase blocks to support the teaching–learning content of arithmetic operations. Full article

This paper calculates the expected cost of uncertainty in solar and wind energy using the uncertainty cost function (UCF), with a primary focus on computational processing time. The comparison of processing time for the uncertainty cost quantification (UCQ) is conducted through three methods: the Monte Carlo simulation method (MC), numerical integration method, and analytical method. The MC simulation relies on random simulations, while numerical integration employs established numerical formulations. These methods are commonly used for solving cost optimization problems in power systems. However, the analytical method is a less conventional approach. The analytical method for calculating uncertainty costs is closely related to the UCF, as it relies on a mathematical representation of the impact of uncertainty on costs, which is modeled through the UCF. A multi-objective approach was employed for scheduling an energy management system, that is to say, thermal–wind–solar energy systems, proposing a simplified method for modeling controllable renewable generation through UCF with an analytical method, instead of the complex probability distributions typically used in traditional methods. This simplification reduces complexity and computational processing time in optimization problems, offering greater accuracy in approximating real distributions and adaptability to various scenarios. The simulations performed yielded positive results in improving cost estimation and computational efficiency, making it a promising tool for enhancing economic distribution and grid operability. Full article

The problem of the conversion of diesel buses to electric ones in connection with the inevitable introduction of the EURO 7 emission standards entails an automatic requirement to follow several additional United Nations Economic Commission for Europe rules, like R100 regulations. They regulate the preservation of battery units at longitudinal 12 g and transverse 10 g accelerations without penetrating into the elements of the bus body. Three models (12 modes in total) of battery units with frames made of S235 steel were analysed. The maximum stress value varies between 364.89 MPa and 439.08 MPa in 10 g and 12 g modes, respectively, which is beyond the tensile strength (360 MPa) and provokes plastic deformations. The max deformations were recorded in the models with the highest average stress: 63.04 mm in the 12 g mode with an average stress of 83.18 MPa. The minimum deformations of 6.95 and 7.95 mm were found in the 10 g modes (left and right acceleration direction, respectively), which meet the manufacturer’s requirements (45–50 mm maximum). The study’s primary contribution lies in developing a practical method for assessing battery unit integrity and structural behaviour during the conversion of diesel buses to electric propulsion, fully compliant with R100 regulations. By combining transient structural simulation, mathematical centre modelling of acceleration propagation, and centre of gravity prediction, the proposed approach enables engineers to evaluate electric conversions’ safety and certification feasibility without modifying the existing bus body. Full article

Metacognition and self-regulated learning are widely understood to offer significant benefits for pupils’ mathematical problem solving; however, the existing literature highlights that the under-representation of these concepts in curriculum, policy, and teacher professional development means that their potential for impact remains unfulfilled. This article, therefore, examines the potential value of an innovative fading professional development programme—“Stepping Stones”—in enhancing teachers’ understanding and use of metacognitive strategies for mathematical problem solving. Adopting a convergent mixed methods design, this pilot evaluation involved Year 2 teachers across five primary schools. The results from both qualitative and quantitative data demonstrate that, as the scaffolding provided by programme materials faded and teachers assumed greater responsibility for session planning, they incorporated metacognitive strategies into their planning and delivery with increased independence. The results also indicate the acceptability of this professional development model, suggesting that, when combined with peer collaboration, the fading design was associated with improvements in knowledge and confidence regarding both metacognition and mathematical problem solving, alongside increased ownership and buy in. The conclusions advocate further examination and implementation of fading models of professional development to promote the understanding and use of metacognition for mathematical problem solving and recommend exploration into different professional development contexts. Full article

This paper presents a detailed kinematic analysis of a double-toggle jaw crusher used for the primary crushing of hard and bulky materials. The study introduces an innovative mathematical modeling method for the motion of the mechanism’s components, eliminating the need for traditional decomposition into structural groups. General equations are developed to determine the positions, linear velocities, and angular displacements of the moving elements, providing a solid foundation for equipment design and study. The generated mathematical model was validated using real-world dimensions of an SMD-117-type jaw crusher and by comparison with simulation results obtained from Mathcad, Linkage, Roberts Animator, and GIM software. The results demonstrated a high degree of agreement between the calculated and simulated trajectories and linear velocities. The analysis of angular displacements and linear velocities confirmed the cyclic nature of the mechanism’s motion, characterized by sinusoidal variations and low oscillations, which are relevant for assessing variable loads. Through its rigorous approach and multi-source validation, the research makes a significant contribution to the development of more efficient, durable, and adaptable jaw crushers for modern industrial requirements. Full article

Trapezoidal-valued fermatean fuzzy numbers (TpVFFNs) are essential for handling daily decision-making issues in the engineering and management fields. Accumulation processes on the set of TpVFFN are used to address decision-making problems described in this environment as necessary. The primary goal of this paper is to provide the concept of Dombi t-norm $\left(D_{tn}\right)$- and Dombi t-conorm $\left(D_{tcn}\right)$-based accumulation operators on the class of TpVFFN, emphasizing how they behave symmetrically in aggregation processes to maintain consistency and fairness. To use s to illustrate mathematical circumstances, we first create a trapezoidal-valued fermatean fuzzy Dombi’s weighted geometric operator, hexagonal hybird geometric operator, fermatean fuzzy order weighted geometric operator. Second, we use a multi-attribute group decision-making (MAGDM) approach to compute the recommended accumulation operators. Finally, we demonstrate the potential practical application of the proposed decision-making problem related to the pink cab. Full article

This study investigates the performance of medium-power wind turbines (within kilowatt range) in response to substantial fluctuations in wind speed. The wind turbines utilize induction generators that have a short-circuited rotor and are controlled by a power converter within the stator circuit. This configuration facilitates the adjustment of the stator frequency, thereby allowing the desired rotational speed to be achieved and guaranteeing that the turbine operates at the maximum power point (MPP). Specific mathematical models for the turbine and generator have been developed using technical data from an operational wind turbine. The study demonstrated that utilizing a power converter within the stator circuit enhances the turbine’s operation at its maximum power point. A crucial aspect of effective MPP operation is the accurate determination of the relationship between wind speed and the corresponding optimal angular mechanical speed. Precise understanding and implementation of the interdependence among the primary generator parameters—namely power, frequency, current, and power factor—in relation to wind speed is essential for maximizing power generation and achieving grid stability for wind turbines operating in variable wind speed. Full article

Non-unique fixed-point theorems play a pivotal role in the mathematical modeling to solve certain typical equations, which admit more than one solution. In such situations, traditional outcomes fail due to uniqueness of fixed points. The primary aim of the present article is to investigate a non-unique fixed-point theorem in the framework of a metric space endowed with a local class of transitive binary relations. To obtain our main objective, we introduce a new nonlinear contraction-inequality that subsumes the ideas involved in four noted contraction conditions, namely: almost contraction, Boyd–Wong contraction, Pant contraction and relational contraction. We also establish the corresponding uniqueness theorem for the proposed contraction under some additional hypotheses. Several examples are furnished to illustrate the legitimacy of our newly proved results. In particular, we deduce a fixed-point theorem for almost Boyd–Wong contractions in the setting of abstract metric space. Our results generalize, enhance, expand, consolidate and develop a number of known results existing in the literature. The practical relevance of the theoretical findings is demonstrated by applying to study the existence and uniqueness of solution of a specific periodic boundary value problem. Full article

The focus of this paper is placed on Oscillating Water Column (OWC) systems. The primary aim is to analyze, through both mathematical modeling and numerical simulations, a single module (chamber) of an OWC plant which, in addition to energy production, offers the dual advantage of large-scale integration into port infrastructures or coastal defense structures such as breakwaters, etc. The core challenge lies in optimizing the geometry of the OWC chamber and its associated ducts. A trapezoidal cross-section is adopted, with various front wall inclinations ranging from $90°$ to $45°$. This geometric parameter significantly affects both the internal compression ratio and the hydrodynamic behavior of incoming and outgoing waves. Certain inclinations revealed increased turbulence and notable interference with waves reflected from the chamber bottom which determined an unexpected drop in efficiency. The optimal performance occurred at an inclination of approximately $55°$, yielding an efficiency of around 12.8%, because it represents the most advantageous and balanced compromise between counter-trend phenomena. A detailed analysis is carried out on several key parameters for the different configurations (e.g., internal and external wave elevations, crest phase shifts, pressures, hydraulic loads, efficiency, etc.) to reach the most in-depth analysis possible of the complex phenomena that come into play. Lastly, the study also discusses the additional structural and functional benefits of inclined walls over traditional parallelepiped-shaped chambers, both from a structural and construction point of view, and for the possible use for coastal defense. Full article

The study of neuronal electrical activity and spatial organization is essential for uncovering the mechanisms that regulate neuronal electrophysiology and function. Mathematical models have been utilized to analyze the structural properties of neuronal networks, predict connectivity patterns, and examine how morphological changes impact neural network function. In this study, we aimed to explore the role of the actin cytoskeleton in neuronal signaling via primary cilia and to elucidate the role of the actin network in conjunction with neuronal electrical activity in shaping spatial neuronal formation and organization, as demonstrated by relevant mathematical models. Our proposed model is based on the polygamma function, a mathematical application of ramification, and a geometrical definition of the actin cytoskeleton via complex numbers, ring polynomials, homogeneous polynomials, characteristic polynomials, gradients, the Dirac delta function, the vector Laplacian, the Goldman equation, and the Lie bracket of vector fields. We were able to reflect the effects of neuronal electrical activity, as modeled by the Van der Pol equation in combination with the actin cytoskeleton, on neuronal morphology in a 2D model. In the next step, we converted the 2D model into a 3D model of neuronal electrical activity, known as a core-shell model, in which our generated membrane potential is compatible with the neuronal membrane potential (in millivolts, mV). The generated neurons can grow and develop like an organoid brain based on the developed mathematical equations. Furthermore, we mathematically introduced the signal transduction of primary cilia in neurons. Additionally, we proposed a geometrical model of the neuronal branching pattern, which we described as ramification, that could serve as an alternative mathematical explanation for the branching pattern emanating from the neuronal soma. In conclusion, we highlighted the relationship between the actin cytoskeleton and the signaling processes of primary cilia. We also developed a 3D model that integrates the geometric organization unique to neurons, which contains soma and branches, such that the mathematical model represents the interaction between the actin cytoskeleton and neuronal electrical activity in generating action potentials. Next, we could generalize the model into a cluster of neurons, similar to an organoid brain model. This mathematical framework offers promising applications in artificial intelligence and advancements in neural networks. Full article

This paper analyzes a mathematical model to investigate the complex interactions between tumor cells, immune cells (natural killer (NK) cells and CD8+ cytotoxic T lymphocytes (CTLs)) and chemotherapy. The primary objectives are to analyze tumor–immune interactions without and under treatment, identify critical thresholds for tumor eradication, and evaluate how chemotherapy parameters influence therapeutic outcomes. The model integrates NK cells and CTLs as effector cells, combining their dynamics linearly for simplicity. Tumor growth follows a logistic function, while immune–tumor interactions are modeled using a Hill function for fractional cell death. Stability and bifurcation analysis are employed to identify equilibria (tumor-free, high-tumor, and a novel middle steady state), bistability regimes, and critical parameter thresholds. Numerical simulations use experimentally validated parameter values from the literature. This mathematical analysis provides a framework for assessing the efficacy of chemotherapy by examining the dynamic interplay between tumor biology and treatment parameters. Our findings reveal that treatment outcomes are sensitive to the balance between the immune system’s biological parameters and chemotherapy-specific factors. The model highlights scenarios where chemotherapy may fail due to bistability and identifies critical thresholds for successful tumor eradication. These insights can guide clinical decision making in dosing strategies and suggest combination therapies such as immunotherapy–chemotherapy synergies to shift the system toward favorable equilibria. Full article

This paper presents a spectral method to solve nonlinear distributed-order diffusion equations with both time-distributed-order and two-sided space-fractional terms. These are highly challenging to solve analytically due to the interplay between nonlinearity and the fractional distributed-order nature of the time and space derivatives. For this purpose, Hexic-kind Chebyshev polynomials (HCPs) are used as the backbone of the method to transform the primary problem into a set of nonlinear algebraic equations, which can be efficiently solved using numerical solvers, such as the Newton–Raphson method. The primary reason of choosing HCPs is due to their remarkable recurrence relations, facilitating their efficient computation and manipulation in mathematical analyses. A comprehensive convergence analysis was conducted to validate the robustness of the proposed method, with an error bound derived to provide theoretical guarantees for the solution’s accuracy. The method’s effectiveness is further demonstrated through two test examples, where the numerical results are compared with existing solutions, confirming the approach’s accuracy and reliability. Full article

This study introduces a novel subclass of q-starlike functions that is defined by the application of the q-difference operator and q-analogue of hyperbolic secant function. By making certain variations to the parameter “q”, the geometric interpretation of the domain hyperbolic secant function has also been discussed. The primary objective is to investigate and establish key results on the differential subordination of various orders within this newly defined class. Furthermore, convolution properties are explored and coefficient bounds are derived for these functions. A deeper analysis of these coefficients bounds unveils intriguing geometric insights and significant mathematical problems. Full article

Compliant mechanisms are often utilized in precise positioning systems but have not been thoroughly examined in vibration-aided fine CNC machining. This study aims to develop a new 02-DOF flexure stage for vibration-aided fine CNC milling. A hybrid displacement amplifier, featuring a two-lever mechanism, two Scott–Russell mechanisms, and a parallel leading mechanism, was integrated into a symmetric perpendicular series configuration to create an innovative design. The pseudo-rigid body model (PRBM), Lagrangian approach, finite element analysis (FEA), and Firefly optimization algorithm were employed to develop, verify, and optimize the quality response of the new positioner. The PRBM and Lagrangian methods were used to construct an analytical model, while finite element analysis was used to validate the theoretical solution. The primary natural frequency results from theoretical and FEM methods were 318.16 Hz and 308.79 Hz, respectively. The difference between these techniques was 3.04%, demonstrating a reliable modelling strategy. The Firefly optimization approach applied mathematical equations to enhance the key design factors of the mechanism. The prototype was then built, revealing an error of 7.23% between the experimental and simulated frequencies of 331.116 Hz and 308.79 Hz, respectively. The specimen was subsequently mounted on the fabricated optimization positioner, and vibration-assisted fine CNC milling was performed at 100–1000 Hz. At 400 Hz, the specimen achieved ideal surface roughness with a Ra value of 0.187 µm. The developed design is a potential structure that generates non-resonant frequency power for vibration-aided fine CNC milling. Full article