Mathematical Approach Research Articles

Mathematical Approach for Directly Solving Air–Water Interfaces in Water Emptying Processes

Emptying processes are operations frequently required in hydraulic installations by water utilities. These processes can result in drops to sub-atmospheric pressure pulses, which may lead to pipeline collapse depending on soil characteristics and the stiffness of a pipe class. One-dimensional mathematical models and 3D computational fluid dynamics (CFD) simulations have been employed to analyse the behaviour of the air–water interface during these events. The numerical resolution of these models is challenging, as 1D models necessitate solving a system of algebraic differential equations. At the same time, 3D CFD simulations can take months to complete depending on the characteristics of the pipeline. This presents a mathematical approach for directly solving air–water interactions in emptying processes involving entrapped air, providing a predictive tool for water utilities. The proposed mathematical approach enables water utilities to predict emptying operations in water pipelines without needing 2D/3D CFD simulations or the resolution of a differential algebraic equations system (1D model). A practical application is demonstrated in a case study of a 350 m long pipe with an internal diameter of 350 mm, investigating the influence of air pocket size, friction factor, polytropic coefficient, pipe diameter, resistance coefficient, and pipe slope. The mathematical approach is validated using an experimental facility that is 7.36 m long, comparing it with 1D mathematical models and 3D CFD simulations. The results confirm that the derived mathematical expression effectively predicts emptying operations in single water installations.

Analysis of Gender Issues in Computational Thinking Approach in Science and Mathematics Learning in Higher Education

In the contemporary era, Computational Thinking has emerged as a crucial skill for individuals to possess in order to thrive in the 21st century. In this context, there is a need to develop a methodology for cultivating these skills within a science and mathematics content education framework, particularly among pre-service teachers. This study aimed to investigate the impact of Educational Robotics on the development of Computational Thinking skills, with a particular focus on the role of gender, through a scientific and mathematical content teaching approach. A pre-experimental design with a quantitative approach was employed, and it was implemented with a total of 116 pre-service teachers, 38 males and 78 females. The results demonstrated a notable enhancement between the pre-test (8.11) and post-test (9.63) scores, emphasising specific concepts such as simple functions, while, and compound conditional. With respect to gender, statistically significant differences were identified prior to the intervention, but not following its implementation. The high level of Computational Thinking exhibited by both genders was comparable (53.85% in females and 55.26% in males) following the intervention. This indicates that the intervention is a promising approach for enhancing Computational Thinking proficiency, independent of gender and initial proficiency levels. The implementation of Educational Robotics in the teaching of science and mathematics enables the enhancement of Computational Thinking abilities among pre-service teachers, while reducing the observed gender disparity in this area of skill development.

Equilibria of large random Lotka–Volterra systems with vanishing species: a mathematical approach

Equilibria of large random Lotka–Volterra systems with vanishing species: a mathematical approach

Analysis of the air gap magnetic field in cylindrical magnetic couplings based on mathematical and finite element approach

The air gap magnetic field of a magnetic coupling plays a crucial role in the examination of its static torque and eddy current losses. Precise characterization of the air gap magnetic field is essential for ensuring the accuracy of performance assessments of the magnetic coupling. This study focuses on the cylindrical magnetic coupling as the subject of investigation, employing mathematical analysis and finite element methods to evaluate and quantify the magnetic field properties. The study establishes a mathematical model of the magnetic field of a magnetic coupling based on electromagnetic field principles and the superposition theorem. An analytical formula for the magnetic flux density distribution of the air-gap magnetic field is derived. Subsequently, a three-dimensional magnetic field finite element model is created using the finite element method to numerically calculate the air gap magnetic field and validate the analytical formula. The research also explores the periodic distribution characteristics of the magnetic field in the air gap, analyzing axial differences in magnetic flux density value and direction distribution influenced by end effects.

A Review on the Mathematical Modelling of the Grain Storage Ecosystemin Storage Structures and Bags

The grain storage ecosystem comprises of biotic and abiotic factors that interact during grain storage, and their interaction affects the quality of the stored grains over time. The understanding and management of the complex interaction of the biotic and abiotic factors in the stored grain ecosystem is crucial to decision-making and in the development of management strategies for grain farmers and elevators. Mathematical modelling has emerged as an essential approach in tackling complex systems such as the stored grain ecosystem. This review explores the application of mathematical modelling in the grain storage ecosystem and synthesizes the existing literature, highlighting the various mathematical models and approaches to solving issues relating to the grain storage ecosystem. The review will be helpful to researchers and stored grain experts in the grain industry on the various mathematical modelling approaches and equations that can be employed to solve problems associated with grain storage in order to better manage the quality of stored grain.

Mathematical crystal chemistry: A mathematical programming approach to crystal structures of inorganic compounds

Mathematical crystal chemistry: A mathematical programming approach to crystal structures of inorganic compounds

Short-term forecast of solar irradiance components using an alternative mathematical approach for the identification of cloud features

Solar energy technologies require precise solar forecasting to reduce power generation losses and protect equipment from irradiance fluctuations. This study introduces an alternative methodology for short-term forecasting of direct normal irradiance (DNI) and global horizontal irradiance (GHI) utilizing ground-based sky images captured by a single device. A low-cost all-sky imager (ASI) was developed, which implements an angular transformation and an optical flow technique to extract cloud features such as shape and velocity. A mathematical model calculates cloud transmittance based on pixel intensity, eliminating complex training steps. Results from a 30-day experimental campaign, incorporating diverse meteorological conditions, were compared against a secondary standard solarimetric station, a smart persistence model, and state-of-the-art approaches. The DNI forecast achieved an RMSE (relative error) of 46.79 W/m2 (11.99%) for 1-min intervals and 90.21 W/m2 (17.54%) for 10-min intervals, while GHI ranged from 31.73 W/m2 (4.68%) to 75.02 W/m2 (13.63%). Pearson correlation coefficients exceeded 0.9 overall, reaching 0.98 and 0.99 for the 1-min DNI and GHI forecasts, and 0.91 and 0.96 for the 10-min DNI and GHI forecasts, respectively, underscoring the system’s accuracy and robustness in complex meteorological scenarios.

Dynamic signatures: a mathematical approach to analysis

Abstract This study evaluates mathematical tools (principal component analysis, dynamic time warping, and the Kolmogorov–Smirnov hypothesis test) to analyse global and local data from dynamic signatures to reduce subjectivity and increase the reproducibility of handwriting examination using a two-step approach. A data set composed of 1800 genuine signature samples, 870 simulated signatures, and 60 disguises (30 formally similar or ‘autosimulated’ and 30 random but different from usual) provided by 30 volunteers was collected. The first step involved global data analysis using principal component analysis and a hypothesis test performed for 62 global characteristics, and associations of these characteristics were analysed through calculations of multivariate distance followed by a hypothesis test. The second step involved the analysis of local characteristics including vertical and horizontal positions, speed, pressure gradient, acceleration, and jerk point-to-point, by using dynamic time warping followed by a hypothesis test. Optimization of sensitivity and specificity metrics of the hypothesis test was explored by varying its stringency and observing accuracy rates for the simulated and genuine groups. A P-value threshold of 1 × 10−10 was found to be optimal, making the test more restrictive and yielding accuracy rates of 96.7% for genuine global data and 88.9% for simulated data. The same cutoff value for local characteristics provided an average accuracy rate of 95.4% for genuine samples and 94.7% for simulated samples, demonstrating high accuracy for both simulated and genuine samples. However, the method did not offer reasonable accuracy rates for disguises, consistent with observations in traditional handwriting examination. Our approach provided satisfactory results for forensic examination use. The visualization of graphs and signatures and analysis of all identifying elements of handwriting by the examining expert are still essential. In future studies, we plan to perform blind tests to validate our approach and propose a rigorous methodology.

Mixture-of-Experts Based Dissociation Kinetic Model for De Novo Design of HSP90 Inhibitors with Prolonged Residence Time.

The dissociation rate constant (koff) significantly impacts the drug potency and dosing frequency. This work proposes a powerful optimization-based framework for de novo drug design guided by koff. First, a comprehensive database containing 2,773 unique koff values is created. Based on the database, a novel generic dissociation kinetic model is developed with a mixture-of-experts architecture, enabling high-throughput predictions of koff with high accuracy. The developed model is then integrated with an optimization-based mathematical programming approach to design drug candidates with low koff. Finally, the τ-RAMD method is utilized to rigorously verify the designed potential drug candidates. In a case study, the framework successfully identified numerous new potential HSP90 inhibitor candidates, achieving a maximum 45.7% improvement in residence time (τ = 1/koff) compared to that of a known exceptional HSP90 inhibitor. These findings demonstrate the feasibility and effectiveness of the kinetics-guided optimization-based de novo drug design framework in designing drug candidates with prolonged τ.

Computational Math Modeling and AI Optimization for Better Decision-Making: Applications in Machine Learning

The integration of computational mathematical modeling, optimization, machine learning (ML), data analysis, and artificial intelligence (AI) offers transformative opportunities to solve complex problems across diverse fields. This paper delves into the development and application of advanced modeling techniques that blend traditional mathematical approaches with advanced AI algorithms to enhance predictive accuracy, optimize resource allocation, and improve decision-making processes in areas such as logistics, finance, engineering, and healthcare. By leveraging data-driven insights, these models can simulate real-world scenarios and identify optimal solutions more effectively than conventional methods. The paper also explores how AI-enhanced modeling can impact broader systems by reshaping industry practices, influencing frameworks, and potentially challenging established societal norms. Eventually, the paper argues for a balanced and informed deployment of AI-driven modeling techniques to maximize their benefits while addressing potential risks and limitations.

Energy Efficiency and Mathematical Modeling of Shrimp Pond Oxygenation: A Multiple Regression Experimental Study

Aquaculture is one of the key economic activities to reduce food shortages worldwide. Water recirculation systems using pumps are crucial to maintain oxygenation and water quality, consuming about 35% of the total energy in this economic activity. This research proposes a multiple linear regression mathematical model to optimize oxygenation systems in intensive shrimp aquaculture by reducing energy consumption and minimizing water changes in ponds. The proposed model is key to optimizing the operation of pumping systems, allowing us to significantly reduce water turnover without compromising dissolved oxygen levels as a function of key variables such as water turnover volume, biomass, solar radiation (0–1200 W/m2), water temperature (20 °C–32 °C), phytoplankton levels (0–1,000,000 cells/ml), zooplankton (0–500,000 cells/ml), and wind speed (0–15 m/s). These variables are integrated into the model, managing to explain 94.02% of the variation in dissolved oxygen, with an R2 of 92.9%, which adjusts the system conditions in real time, reducing the impact of environmental fluctuations on water quality. This leads to an estimated annual energy savings of 106,397.5 kWh, with a total consumption of 663.8 MWh. The research contributes to the development of a mathematical approach that not only improves oxygenation prediction, but also minimizes the use of water resources, improving the sustainability and profitability of shrimp farming systems, and is a robust tool that maximizes operational efficiency in intensive aquaculture, particularly where water and energy management are critical.

Modified Shooting with Discretization Validation for Non-Standard Optimal Control Problem: Case Study for Four-Stage Royalty Payment Problem

A modified shooting method augmented by discretization validation is presented in this paper to address the challenges inherent in non-standard optimal control problems. Specifically, a specific case study involving four-stage royalty payment functions is focused on, with the aim of effectively optimizing these complex, non-differentiable functions. The shooting method is adapted and enhanced to compute optimal solutions, and its accuracy is rigorously confirmed through discretization techniques. The primary objectives involve maximizing the performance index and determining optimal control strategies for scenarios where the final state variable remains unknown. In this study, the royalty payment is defined as a four-stage piecewise function. The incorporation of piecewise royalty functions introduces non-differentiability at specific time intervals, necessitating innovative approaches for finding optimal solutions. This, in turn, leads to the utilization of the continuous hyperbolic tangent (tanh) function to address the non-differentiability issue. A hybrid shooting method, combining the Newton and Golden Section Search methods, is employed in the C++ programming language to compute the unknown final state value. A new natural boundary condition, based on established theory, is introduced to further facilitate the investigation. Discretization methods such as Euler, Runge-Kutta, Trapezoidal, and Hermite-Simpson approximations are employed for validation. The validation process entails the use of the AMPL programming language with the MINOS solver. Comparative analyses reveal that the modified shooting method yields more accurate optimal results than discretization methods, thus demonstrating the method’s effectiveness in addressing non-standard optimal control problems. The significance of fundamental theories in addressing real-world challenges is underscored by this research, providing valuable insights for future researchers exploring mathematical approaches in similar contexts. The study contributes to the continued relevance of the academic field, particularly in science and mathematics education.

Transmission Dynamics of Typhoid Fever Outbreak: A Mathematical Modelling and Optimal Control Approach

In this paper, we propose and analyze a deterministic mathematical model for the control of typhoid fever. This model incorporates five effective control strategies, including vaccination, booster vaccination, personal hygiene, treatment, and bacteria sterilization, in order to effectively stop the spread of the disease in the population. The model consists of seven compartments, each representing a different stage in the disease’s progression: vaccinated, susceptible, carrier, infected, recovered, booster vaccinated, and bacterial. Using the next-generation matrix approach, we calculated the reproduction number , which measures the disease’s potential for spreading. Our stability analysis, using the Routh-Hurwitz criteria, revealed that the disease-free equilibrium point is locally asymptotically stable when is less than 1, among other conditions. This means that typhoid can be completely eradicated if the rate of secondary infection is kept below a certain threshold. Further sensitivity analyses were conducted to determine the key parameters that impact . Based on our findings, we formulated an optimal control problem and utilized Pontryagin’s Maximum Principle to determine the most effective strategy for controlling and eliminating the disease. Our results show that a combination of vaccination, booster vaccination, personal hygiene, treatment, and bacteria sterilization is the most optimal approach. With our comprehensive model and effective control strategies, we are one step closer to wiping out typhoid fever for good.

Spatiotemporal Moisture Field

For monitoring capillary moisture conduction, the most important parameter is the moisture conductivity coefficient, which is a material characteristic; however, its use in practical calculations is not very common. For further development in the field of liquid moisture propagation, an automated measuring apparatus has been developed and granted a European patent. Its essence lies in detecting the liquid water content based on a well-known physical phenomenon: electromagnetic radiation in the microwave range. The determination of the spatiotemporal moisture field is the first and fundamental step for describing transportation phenomena. The moisture field thus created allows for the viewing of the moisture conductivity coefficient, which is one of the most important parameters in describing transportation phenomena as a function of moisture. The presence of water in building materials can significantly affect their physical properties, such as mechanical or thermal–technical characteristics. This may lead to unacceptable consequences, which might only manifest after a certain period of time. In the case of multi-layered structures, moisture can transfer from one material to another. Therefore, it is essential to address this process. The advantage of the software solution described by the methodology is the use of an open communication protocol in the form of a synchronized array, which is not common in typical applications of this type. The principle of separating hardware modules is also unusual for devices of this type, as it requires the independent communication of each module with the control software. Mutual communication is handled exclusively at the software level, making it possible to modify, optimize, or parameterize the procedures as needed. Upon closer examination of the wetting curves of various materials, anomalies were revealed in some of their structures. This can be advantageously utilized in the research of newly developed composite materials. The assembled system of measuring instruments, their software integration, and control provide a foundation for the practical application of the described procedures and methods for determining the moisture field of building materials. The parameterization of individual processes, as well as the open access to data, allows for the optimization of the methodology, as materials of entirely different characteristics may require an individual approach, which will certainly contribute to the advancement of science and research in this area. Currently, this work is being followed by further extensive studies, not yet published by the authors, focusing on the application of the described moisture field to evaluate the moisture conductivity coefficient as a function dependent on the material’s mass moisture content. Their application requires specific mathematical and programming approaches due to the significant volume of data involved.

Setting priorities for police operations by using a multicriteria decision approach with partial information

Abstract The paper presents a real-world decision-making problem in the context of the Brazilian Federal Police (BFP), which consists of establishing priorities for Police Operations. This study deals with allocating resources to trigger police operations that, while demanding more resources and specialized techniques, also promote the effectiveness of police actions more conspicuously and directly. Driven by the Value Focused Thinking methodology, the objectives and values of the Federal Police were structured and represented by criteria, which let police operations be evaluated and prioritized. The FITradeoff method was applied to rank the operations, with an innovative methodological perspective, which integrates two different paradigms for preference modelling: elicitation by decomposition and holistic evaluations. A mathematical modelling approach is presented to deal with the combination of both types of information obtained by the Decision Maker (DM), in order to search for dominance relations between alternatives. This study shows how incorporating holistic judgments in the process can be useful for tightening the decision process, since the inequalities obtained with holistic judgments have a high impact on the space of weights compatible with the DM’s preferences. A clear conceptual framework is presented for the analysis, showing how the application of such a combined approach to prioritizing special police operations adds a step to the decision-making processes and policies of the BFP, thereby broadening the managerial implications of tackling public security issues by seeking to solve them using management mathematics.

Conceptualizing Mathematics Student Teachers' Approaches towards Responding to Availability of Tools and Resources in the Context of Knowledge Quartet

The purpose of this study is to conceptualize the approaches of secondary mathematics student teachers towards contingencies encountered during the teaching process within the context of responding to availability of tools and resources. In order to achieve the goal of the study based on the grounded theory, the nine secondary mathematics student teachers’ lessons were observed, and recorded using a video camera, and semi-structured interviews were performed. The data collection process ended after 54 lesson hours of observation, that is, when code saturation was reached. As a result, four sub-codes in the context of responding to availability of tools and resources were identified within the approaches of participants in relation to contingent moments. It is thought that conceptualizing the approaches of participants towards unplanned situations encountered during lessons in real class environment would prove to be beneficial in teacher training.

Thermal Oxidation Characteristics and Kinetics of Micron Aluminum Powder in Different Ambient Oxygen Concentration Atmospheres

This paper examines the effect of oxygen concentration on the oxidation process and properties of aluminum particles, providing valuable insights for production and storage. Micron-grade aluminum powders were tested at heating rates of 5, 7.5, 10, and 15 K/min under oxygen concentrations of 7, 11, 15, 21, and 30 vol%. Results indicate a two-step mass gain oxidation process, with less pronounced mass gain at lower oxygen concentrations. SEM and XRD characterized the morphological and crystalline changes during oxidation. Lowering oxygen concentration from 30 vol% to 7 vol% increased the onset oxidation temperature by 17.1 °C. Increasing the proportion of inert gas in the atmosphere increases the ignition temperature of aluminum powder. The mathematical modeling approach of AKTS was used to decouple and analyze the thermal effects of simultaneous melting and oxidation, using the Friedman method to show that the apparent activation energy is about 350 kJ/mol in low-oxygen atmospheres (7 vol% and 11 vol%). The kinetics of aluminum oxidation were found to be closely related to the oxygen concentration, and based on the kinetics parameter, it is possible to predict a minimum limiting oxygen concentration.

Uncertain multi‐objective programming approach for planning supplementary irrigation areas in rainfed agricultural regions

AbstractRainfed agriculture is crucial for ensuring global food and water security, and supplementary irrigation is an effective means of improving the economic benefits in rainfed agricultural regions. This study proposes a novel uncertain optimization approach to optimize supplementary irrigation areas in rainfed agricultural regions. The approach incorporates multi‐objective linear programming, interval linear programming, fuzzy goal programming and stochastic expected value programming. In the proposed interval multi‐fuzzy goal stochastic expected‐value programming, uncertainties are expressed in the form of discrete intervals, probability distributions and fuzzy goals. This approach, which considers the randomness of precipitation during the optimization process and allocates limited irrigation water resources to different subareas and crops, was applied to a case study of crop irrigation area planning in Guyuan City, Ningxia Hui Autonomous Region, northwestern China. The maximum economic benefits and the minimum sum of the Gini coefficients among the different subareas and crops were regarded as the planning objectives, and a series of optimal irrigation areas with different crops and subareas under different water levels were obtained. The optimization results revealed that vegetables and fruits consumed large amounts of irrigation water to increase their economic benefits. In addition, allocating a large amount of irrigation water to wheat is essential to decrease the Gini coefficient and meet food security constraints, particularly at extremely low water levels. Compared with current management, the optimized irrigation area decreased by 30%, the crop water deficit index increased by 9%, the economic benefits increased by 3% and the total Gini coefficient of crops decreased by 17%, indicating that the optimization approach could fairly and reasonably allocate irrigation water resources. Our research provides a mathematical approach for decision‐makers to plan supplementary irrigation areas in rainfed agricultural regions.

A Novel Centralized Allocation Data Envelopment Analysis Model for Carbon Emission Allocation Under a Heterogeneous Abatement Cost: Application Within the Chinese Industrial Sector

This paper presents a mathematical approach to analyzing carbon abatement costs and the allocation of carbon emission allowances in China’s industrial sectors. We utilize input–output data from 30 Chinese provinces between 2009 and 2018 to estimate carbon abatement costs by applying the slack-based measure (SBM) efficiency model and its dual form. The SBM model captures inefficiencies and offers a rigorous framework for measuring abatement costs. Using these costs, we develop a centralized allocation data envelopment analysis (DEA) model, which maximizes sectoral benefits through optimal reallocation. This DEA model is formalized as a linear programming problem, with the aim of determining the efficient allocations of carbon allowances while maintaining the system’s economic productivity. Furthermore, we construct intertemporal, interregional, and spatiotemporal allocation DEA models to examine the dynamics of carbon emission allowance allocation over time, space, and combined spatiotemporal dimensions. These models offer insights into the efficiency of carbon markets under varying conditions. Our proposed new mathematical formulations reveal optimal allocation strategies that can balance emission reductions with industrial productivity. This study also provides novel mathematical frameworks for analyzing the carbon allowance distribution and contributions to both the theory and application of mathematical optimization in environmental policy design. Our findings reveal that China’s industrial carbon abatement costs exhibit significant interprovincial and regional differences. Developed provinces with higher levels of industrial development have higher carbon abatement costs, while provinces with less-developed industrial sectors have lower costs. Under the interregional allocation scenario of carbon emission allowances that consider abatement costs, developed provinces have smaller industrial carbon emission reductions, whereas less-developed provinces have larger reductions. In the intertemporal allocation scenario, provinces with larger industrial economies face greater emission reduction tasks. Under the combined interregional and intertemporal allocation scenario, industrial sectors in coastal developed provinces have lower carbon emission reductions, while those in inland less-developed provinces have higher reductions, mirroring the spatial allocation results of carbon emission allowances.

Mathematical approaches to fisheries quota management: ensuring sustainable practices in U.S. commercial fishing

Fisheries quota management plays a critical role in ensuring the sustainability of commercial fishing practices, particularly in the United States, where overfishing and resource depletion pose significant challenges to marine ecosystems. This review explores the mathematical approaches utilized to manage fisheries quotas effectively and sustainably. The paper examines key mathematical models, including population dynamics, bioeconomic models, game theory, and Catch-per-Unit-Effort (CPUE) models, highlighting their role in maintaining fish stock levels and regulating fishing activities. Through case studies from U.S. fisheries, such as the New England groundfish and Alaska pollock fisheries, the review assesses the effectiveness of these models in real-world applications. Additionally, it explores how advances in technology, such as satellite tracking, big data, and artificial intelligence, are enhancing the accuracy and adaptability of fisheries management models. The review concludes with insights into future directions for mathematical approaches in fisheries management, emphasizing the need for continuous innovation to support sustainable commercial fishing practices. By integrating advanced mathematical techniques and data-driven models, this paper aims to provide a pathway for policymakers and fisheries managers to achieve long-term sustainability in U.S. commercial fisheries.