Search Results (47)

Water scarcity and soil salinization pose significant challenges to sustainable agricultural development in arid and semi-arid regions globally. This study applies Positive Mathematical Programming (PMP) to analyze agricultural water resource management in the Hetao Irrigation District (HID), China. The research constructs a comprehensive multi-stress-factor integrated PMP model to evaluate the compound impacts of water resource constraints, pricing policies, and environmental stress on agricultural production systems. The model incorporates crop-specific salinity tolerance thresholds and simulates farmer decision-making behaviors under various scenarios including water supply reduction (0–100%), water pricing increases (0.2–1.0 CNY/m³), and soil salinity stress (0–10 dS/m). The results reveal that the agricultural system exhibits significant vulnerability characteristics with critical thresholds concentrated in the 60–70% water resource utilization interval. Water pricing policies show limited effectiveness in low-price ranges, with wheat demonstrating the highest price sensitivity (−23.8% elasticity). Crop salinity tolerance analysis indicates that wheat–sunflower rotation systems maintain an 85% planting proportion even under extreme salinity conditions (10 dS/m), significantly outperforming individual crops. The study proposes a hierarchical water resource quota allocation system based on vulnerability thresholds and recommends promoting salt-tolerant rotation systems to enhance agricultural resilience. These findings provide scientific evidence for sustainable water resource management and agricultural adaptation strategies in water-stressed regions, contributing to both theoretical advancement of the PMP methodology and practical policy formulation for irrigation districts facing similar challenges. Full article

This paper investigates the structural properties of solutions of vector equilibrium systems and mixed variational inequalities in topological vector spaces. Based on Himmelberg-type fixed point theorem, combined with the analysis of set-valued mapping and quasi-monotone conditions, the existence criteria of solutions for two classes of generalized equilibrium problems with weak compactness constraints are constructed. This work introduces an innovative application of the measurable selection theorem of semi-continuous function space to eliminate the traditional compactness constraints, and provides a more universal theoretical framework for game theory and the economic equilibrium model. In the analysis of mixed variational problems, the topological stability of the solution set under the action of generalized monotone mappings is revealed by constructing a new KKM class of mappings and introducing the theory of pseudomonotone operators. In particular, by replacing the classical compactness assumption with pseudo-compactness, this study successfully extends the research boundary of scholars on variational inequalities, and its innovations are mainly reflected in the following aspects: (1) constructing a weak convergence analysis framework applicable to locally convex topological vector spaces, (2) optimizing the monotonicity constraint of mappings by introducing a semi-continuous asymmetric condition, and (3) in the proof of the nonemptiness of the solution set, the approximation technique based on the family of relatively nearest neighbor fields is developed. The results not only improve the theoretical system of variational analysis, but also provide a new mathematical tool for the non-compact parameter space analysis of economic equilibrium models and engineering optimization problems. This work presents a novel combination of measurable selection theory and pseudomonotone operator theory to handle non-compact constraints, advancing the theoretical framework for economic equilibrium analysis. Full article

This feature paper explores the comparative pedagogical roles of concrete and virtual manipulatives in preservice mathematics teacher education. Based on a design-based research (DBR) methodology, this study investigates the effects of tangible tools (e.g., base-ten blocks, fraction circles) and digital applications (e.g., GeoGebra Classic 6, Polypad) on preservice teachers’ problem solving, conceptual understanding, engagement, and instructional reasoning. Data were collected through surveys (n = 53), semi-structured interviews (n = 25), and classroom observations (n = 30) in a Spanish university’s teacher education program. Key findings show that both forms of manipulatives significantly enhance engagement and conceptual clarity, but are affected by logistical and digital access barriers. This paper further proposes a theoretically grounded model for simulating manipulatives through ICT-based environments, enabling scalable and adaptive mathematics teacher training. By linking constructivist learning theory, the Technologically Enhanced Learning Environment (TELE) framework, and simulation-based pedagogy, this model aims to replicate the cognitive, affective, and collaborative affordances of manipulatives in virtual contexts. Distinct from prior work, this study contributes an integrated theoretical and practical framework, contextualized through empirical classroom data, and presents a clear plan for real-world ICT-based implementation. The findings provide actionable insights for teacher educators, edtech developers, and policymakers seeking to expand equitable and engaging mathematics education through simulation and blended modalities. Full article

Traditional coal quality assessment methods rely exclusively on the laboratory testing of physical samples, which impedes detailed stratigraphic evaluation and limits the integration of intelligent precision mining technologies. To resolve this challenge, this study investigates geophysical logging as an innovative method for coal quality prediction. By integrating scanning electron microscopy (SEM), X-ray analysis, and optical microscopy with interdisciplinary methodologies spanning mathematics, mineralogy, and applied geophysics, this research analyzes the coal quality and mineral composition of the Shanxi Formation coal seams in northern Jiangsu, China. A predictive model linking geophysical logging responses to coal quality parameters was established to delineate relationships between subsurface geophysical data and material properties. The results demonstrate that the Shanxi Formation coals are gas coal (a medium-metamorphic bituminous subclass) characterized by low sulfur content, low ash yield, low fixed carbon, high volatile matter, and high calorific value. Mineralogical analysis identifies calcite, pyrite, and clay minerals as the dominant constituents. Pyrite occurs in diverse microscopic forms, including euhedral and semi-euhedral fine grains, fissure-filling aggregates, irregular blocky structures, framboidal clusters, and disseminated particles. Systematic relationships were observed between logging parameters and coal quality: moisture, ash content, and volatile matter exhibit an initial decrease, followed by an increase with rising apparent resistivity (LLD) and bulk density (DEN). Conversely, fixed carbon and calorific value display an inverse trend, peaking at intermediate LLD/DEN values before declining. Total sulfur increases with density up to a threshold before decreasing, while showing a concave upward relationship with resistivity. Negative correlations exist between moisture, fixed carbon, calorific value lateral resistivity (LLS), natural gamma (GR), short-spaced gamma-gamma (SSGG), and acoustic transit time (AC). In contrast, ash yield, volatile matter, and total sulfur correlate positively with these logging parameters. These trends are governed by coalification processes, lithotype composition, reservoir physical properties, and the types and mass fractions of minerals. Validation through independent two-sample t-tests confirms the feasibility of the neural network model for predicting coal quality parameters from geophysical logging data. The predictive model provides technical and theoretical support for advancing intelligent coal mining practices and optimizing efficiency in coal chemical industries, enabling real-time subsurface characterization to facilitate precision resource extraction. Full article

In order to explore the optimal vibration parameters for the selective harvesting of coffee fruits, a high-velocity dynamic photography monitoring system was developed to analyze the vibration-assisted harvesting process. This system identified the optimal vibration position on coffee branches and facilitated theoretical energy transfer analysis, obtaining a mathematical formula for calculating the total kinetic energy of coffee branches. A single-factor experiment was conducted with the vibration position as the experimental factor and the total kinetic energy of coffee branches as the response variable. The results showed that the total kinetic energy of the branches was the highest at Vibration Position 2 (the position between the third and the fourth Y-shaped bud tips on the branch). Therefore, Vibration Position 2 was determined as the optimal vibration position. Further analysis established a mathematical model linking coffee cherry motion parameters to theoretical detachment force. A factorial experiment was conducted with vibration frequency and amplitude as test factors, using detachment rates of green, semi-ripe, and ripe cherries as indicators. The results showed that at 55 Hz and 10.10 mm amplitude, the detachment rate of ripe cherries was highest (83.33%), while green and semi-ripe cherries detached at 16.67% and 33.33%, respectively. A field validation experiment, with Vibration Position 2, 55 Hz frequency, 10.10 mm amplitude, and 1 s vibration duration, yielded actual detachment rates of 15.86%, 35.17%, and 89.50% for green, semi-ripe, and ripe cherries, respectively. The error margins compared with the theoretical values were all below 10%. These results confirm the feasibility of optimizing vibration harvesting parameters through high-velocity photography dynamic analysis. Full article

This study establishes a mathematical model for analyzing pulsed laser target echo signals in non-uniform smoke environments, thereby enabling evaluations of the target echo characteristics of laser detection systems under various smoke conditions. A semi-analytical Monte Carlo method for laser reception is developed by integrating the T-matrix scattering phase function rejection method with the characteristics of the non-uniform smoke environment. The effects of the pulse width, smoke concentration, target reflectance, and target distance on the laser echo signal waveform are studied in detail. The results indicate that when the pulse width is small (τ = 5 ns), the echo signal exhibits a dual-peak profile due to the signals from the backscattered smoke particles and the target echo. Moreover, the smoke concentration significantly affects the amplitude of the backscatter signal. When the pulse width is large (τ ≥ 40 ns), the echo signal peak is a combination of both signals, where the amplitude increases with increasing pulse width but decreases with the increasing smoke concentration. Additionally, the target echo signal amplitude is positively correlated with the target reflectance and negatively correlated with the target distance. The accuracy of the proposed model is verified by comparing the simulation results with the experimental data. Overall, this study provides a theoretical foundation for target identification and detection in smoky environments for laser fuze applications and the analysis of laser detection characteristics in smoky environments. Full article

Arid and semi-arid environments are characterized by highly variable and unpredictable rainfall patterns, which significantly affect the structure and function of natural ecosystems. Understanding the interconnected relationship between climate variability, forage availability, and livestock dynamics in these regions is crucial to ensure sustainable management. This study provides novel insights into the effects of rainfall variability on natural forage resources and livestock populations in Botswana. In this arid region, traditional livestock farming remains a key economic and food security pillar. By employing a mathematical model based on plant–herbivore interactions, this article quantitatively evaluates the impact of changes in rainfall timing and intensity on forage biomass and, subsequently, livestock populations. A robust analysis of critical threshold values for ecosystem sustainability is possible when real-world climate data are incorporated. This study examines the effects of harvesting and rainfall variability on livestock dynamics across different locations in Botswana. Delayed rainfall leads to a sharp decline in livestock, while Sehitlwa sees biomass loss without a notable reduction in herd size. In Kgagodi, for example, livestock numbers decline by 37% without harvesting, but they remain stable with controlled harvesting. Conversely, Letlhakeng experiences a 6% increase in livestock numbers despite delayed rainfall, which results in a biomass decline. Both Mabutsane and Letlhakeng maintain stable livestock numbers. The findings confirm that early and intense rainfall enhances livestock productivity, while delayed or reduced rainfall leads to population decline, aligning with observed trends in historical data. Additionally, the study underscores the potential of adaptive livestock harvesting strategies as a viable approach to mitigating climate-related risks in grazing systems. As this work integrates theoretical modeling with empirical climate data, it contributes to understanding arid land dynamics, providing a predictive method for assessing ecosystem responses to climate variability. These insights are invaluable for policymakers, conservationists, and local farmers seeking sustainable livestock management practices in the face of changing climatic conditions. Full article

Developing robust and reliable models for Named Entity Recognition (NER) in the Russian language presents significant challenges due to the linguistic complexity of Russian and the limited availability of suitable training datasets. This study introduces a semi-automated methodology for building a customized Russian dataset for NER specifically designed for literary purposes. The paper provides a detailed description of the methodology employed for collecting and proofreading the dataset, outlining the pipeline used for processing and annotating its contents. A comprehensive analysis highlights the dataset’s richness and diversity. Central to the proposed approach is the use of a voting system to facilitate the efficient elicitation of entities, enabling significant time and cost savings compared to traditional methods of constructing NER datasets. The voting system is described theoretically and mathematically to highlight its impact on enhancing the annotation process. The results of testing the voting system with various thresholds show its impact in increasing the overall precision by 28% compared to using only the state-of-the-art model for auto-annotating. The dataset is meticulously annotated and thoroughly proofread, ensuring its value as a high-quality resource for training and evaluating NER models. Empirical evaluations using multiple NER models underscore the dataset’s importance and its potential to enhance the robustness and reliability of NER models in the Russian language. Full article

The concept of symmetry under various transformations of quantities describing basic natural phenomena is one of the fundamental principles in the mathematical formulation of physical laws. Starting with Noether’s theorems, we highlight some well–known examples of global symmetries and symmetry breaking on the particle level, such as the separation of strong and electroweak interactions and the Higgs mechanism, which gives mass to leptons and quarks. The relation between symmetry energy and charge symmetry breaking at both the nuclear level (under the interchange of protons and neutrons) and the particle level (under the interchange of u and d quarks) forms the main subject of this work. We trace the concept of symmetry energy from its introduction in the simple semi-empirical mass formula and liquid drop models to the most sophisticated non-relativistic, relativistic, and ab initio models. Methods used to extract symmetry energy attributes, utilizing the most significant combined terrestrial and astrophysical data and theoretical predictions, are reviewed. This includes properties of finite nuclei, heavy-ion collisions, neutron stars, gravitational waves, and parity–violating electron scattering experiments such as CREX and PREX, for which selected examples are provided. Finally, future approaches to investigation of the symmetry energy and its properties are discussed. Full article

This paper presents a study of the vibration isolation properties of pneumatic suspension systems for work machinery seats, with a particular focus on adjustable stiffness. It highlights the contribution that semi-active seat suspension systems make to vibration reduction, ultimately leading to improved passenger comfort levels and increased safety for vehicle users. The primary objectives of the research were twofold: firstly, to identify the key parameters of the apneumatic vibration isolation system; and secondly, to evaluate its performance in improving vibration damping. This entailed the development of a mathematical model that would foreground the movement through simulations based on different initial pressures, thus enabling the accurate prediction of real-life scenarios concerning the vibration-damping characteristics of the seating system, taking into account the different design options available for working machine technology applied at the test bed level, of which the pneumatic isolator is an integral component. In the cognitive process, the verification and validation of the formulated theoretical model play an important role. This approach enables the behaviour of the actual system to be inferred from the results of simulation studies, thus allowing the design of an appropriate vibration control system. By simulating different air bellow pressures, the characteristics of the seat suspension system can be assessed. This study provides valuable insights into optimising the vibration-damping capability of the air suspension system. Full article

Hard milling is being increasingly used as an alternative to EDM due to its high productivity. The present paper presents the results of theoretical-experimental research on the face milling of hard steel 55NiCrMoV7. A comprehensive analysis of cutting temperatures and forces during single-tooth milling and a morphological examination of the resulting chips are conducted for roughing and semi-finishing operations. The temperature is analyzed in the chip formation area, and the detached chips and the cutting force are analyzed through their tangential, radial, and penetration components, depending on the contact angle of the cutter tooth with the workpiece. The analysis of chip morphology is carried out based on the dimensional and angular parameters of chip segmentation and their degree of segmentation. Based on the central composite design and the response surface method, it is shown that it is possible to mathematically model the dependence of the macroscopic dimensions of the detached chips on the cutting parameters. The determined process functions, the maximum chip curling diameter, and the maximum chip height allow for establishing the influence of the cutting parameters’ values on the chips’ macroscopic dimensions and, thus, guiding the cutting process in the desired direction. Full article

This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples. Full article

The continuous deterioration of the ecological environment and the increasing scarcity of resources have posed a serious challenge to the survival and development of human beings, and the implementation of green supply chain management (GSCM) in this context is an effective means to ensure the sustainable development of society and the economy. In order to seek the optimal strategy of evolutionary game in the implementation of green supply chain management and explore the influence of environmental regulation intensity and public preference degree on the evolution process of green supply chain management diffusion development, this paper takes the study of green supply chain management diffusion as the core innovation point, and under the premise of environmental regulation, selects the government, the core enterprise, and the public as the participating bodies of green supply chain management diffusion, and uses the theory of evolutionary game to construct a diffusion model of green supply chain management. Using evolutionary game theory to construct a diffusion model, and with the help of MATLAB and other mathematical tools for numerical simulation analysis, we discuss the diffusion of the green supply chain and derive the optimal combination strategy. The results of the study show that: (1) there are four evolutionary stable states in the process of green supply chain management diffusion: preliminary diffusion, extinction, semi-diffusion, and full diffusion; (2) it will be beneficial for the government to promote the evolutionary diffusion of green supply chain management by implementing a higher intensity of pollution tax policy while implementing green supply chain incentive strategies; (3) the government, while implementing environmental regulation policies, should also pay attention to the guidance of the public’s awareness of environmental friendliness and greenness, and focus on the role of the comprehensive strategy selection of the three parties of the game in reaching the optimal state. The conclusions of the study provide theoretical guidance and decision support for the implementation and diffusion of green supply chain management under environmental regulation. Full article

Faced with the problem of incompatibility between traditional information acquisition mode and spaceborne earth observation tasks, starting from the general mathematical model of compressed sensing, a theoretical model of block compressed sensing was established, and a full-process adaptive coding and decoding compressed sensing framework for remote sensing images was proposed, which includes five parts: mode selection, feature factor extraction, adaptive shape segmentation, adaptive sampling rate allocation and image reconstruction. Unlike previous semi-adaptive or local adaptive methods, the advantages of the adaptive encoding and decoding method proposed in this paper are mainly reflected in four aspects: (1) Ability to select encoding modes based on image content, and maximizing the use of the richness of the image to select appropriate sampling methods; (2) Capable of utilizing image texture details for adaptive segmentation, effectively separating complex and smooth regions; (3) Being able to detect the sparsity of encoding blocks and adaptively allocate sampling rates to fully explore the compressibility of images; (4) The reconstruction matrix can be adaptively selected based on the size of the encoding block to alleviate block artifacts caused by non-stationary characteristics of the image. Experimental results show that the method proposed in this article has good stability for remote sensing images with complex edge textures, with the peak signal-to-noise ratio and structural similarity remaining above 35 dB and 0.8. Moreover, especially for ocean images with relatively simple image content, when the sampling rate is 0.26, the peak signal-to-noise ratio reaches 50.8 dB, and the structural similarity is 0.99. In addition, the recovered images have the smallest BRISQUE value, with better clarity and less distortion. In the subjective aspect, the reconstructed image has clear edge details and good reconstruction effect, while the block effect is effectively suppressed. The framework designed in this paper is superior to similar algorithms in both subjective visual and objective evaluation indexes, which is of great significance for alleviating the incompatibility between traditional information acquisition methods and satellite-borne earth observation missions. Full article

Mathematical models and numerical simulations are necessary to understand the functions of biological rhythms, to comprehend the transition from simple to complex behavior and to delineate the conditions under which they arise. The aim of this work is to investigate the R$\ddot{\mathrm{o}}$ssler-type system. This system could be proposed as a theoretical model for biological rhythms, generalizing this formula for chaotic behavior. It is assumed that the R$\ddot{\mathrm{o}}$ssler-type system has a Hamilton–Poisson realization. To semi-analytically solve this system, a Bratu-type equation was explored. The approximate closed-form solutions are obtained using the Optimal Parametric Iteration Method (OPIM) using only one iteration. The advantages of this analytical procedure are reflected through a comparison between the analytical and corresponding numerical results. The obtained results are in a good agreement with the numerical results, and they highlight that our procedure is effective, accurate and usefully for implementation in applicationssuch as an oscillator with cubic and harmonic restoring forces, the Thomas–Fermi equation and the Lotka–Voltera model with three species. Full article