Search Results (613)

The use of vibrational transport for granular materials has significantly increased in the technological industry due to its reliability, operational efficiency, cost-effectiveness, and relatively uncomplicated technological setup. These transportation methods typically utilize various forms of asymmetry, such as kinematic, temporal (time), wave, and power asymmetry, to induce controlled motion on oscillating surfaces. This study analyses the motion of the granular materials on an inclined plane, where the central innovation lies in the creation of an additional system asymmetry of frictional conditions that enables the granular materials to move upward. This asymmetry is created by introducing dry friction dynamic manipulations. A mathematical model has been developed to describe the motion of particles under these conditions. The modelling results proved that in an inclined transportation system, the asymmetry of frictional conditions during the oscillation cycle—created through dynamic dry friction manipulations—generates a net frictional force exceeding the gravitational force, thereby enabling the upward movement of granular particles. Additionally, the findings highlighted the key control parameters governing the motion of granular particles. λ, which represents the segment of the sinusoidal period over which the friction is dynamically louvered, serves as a parameter that controls the velocity of a moving particle on an inclined surface. The phase shift ϕ serves as a parameter that controls the direction of the particle’s motion at various inclination angles. Experimental investigations were conducted to assess the practicality of this method. The experimental results confirmed that the granular particles can be transported upward along the inclined surface with an inclination angle of up to 6 degrees, as well as provided both qualitative and quantitative validation of the model by illustrating that motion parameters exhibit comparable responses to the control parameters, and strongly agree with the theoretical findings. The primary advantage of the proposed vibrational transport method is the capacity for precise control of both the direction and velocity of granular particle transport using relatively simple mechanical setups. This method offers mechanical simplicity, low cost, and high reliability. It is well-suited to assembly line and manufacturing environments, as well as to industries involved in the processing and handling of granular materials, where controlled transport, repositioning, or recirculation of granular materials or small discrete components is required. Full article

Modal decomposition, introduced by Fourier, expresses complex functions, such as sums of symmetric basis modes. However, convergence alone does not ensure structural fidelity. Discontinuities, sharp gradients, and localized features often lie outside the chosen basis’s symmetry class, producing artifacts such as the Gibbs overshoot. This study introduces a unified geometric framework for assessing when modal representations remain faithful by defining three symbolic invariants—curvature (κ), strain (τ), and compressibility (σ)—and their diagnostic ratio Γ = κ/τ. Together, these quantities measure how closely the geometry of a function aligns with the symmetry of its modal basis. The condition Γ < σ identifies the domain of structural closure: this is the region in which expansion preserves both accuracy and symmetry. Analytical demonstrations for Fourier, polynomial, and wavelet systems show that overshoot and ringing arise precisely where this inequality fails. Numerical illustrations confirm the predictive value of the invariants across discontinuous and continuous test functions. The framework reframes modal analysis as a problem of geometric compatibility rather than convergence alone, establishing quantitative criteria for closure-preserving transforms in mathematics, physics, and applied computation. It provides a general diagnostic for detecting when symmetry, curvature, and representation fall out of alignment, offering a new foundation for adaptive and structure-aware transform design. In practical terms, the invariants (κ, τ, σ) offer a diagnostic for identifying where modal systems preserve geometric structure and where they fail. Their link to symmetry arises because curvature measures structural deviation, strain measures representational effort within a given symmetry class, and compressibility quantifies efficiency. This geometric viewpoint complements classical convergence theory and clarifies why adaptive spectral methods, edge-aware transforms, multiscale PDE solvers, and learned operators benefit from locally increasing strain to restore the closure condition Γ < σ. These applications highlight the broader analytical and computational relevance of the closure framework. Full article

Background/Objectives: Employee engagement is fundamental for the quality and sustainability of the Slovak healthcare sector. While the concept is critical, its operational challenges lie in the differentiated perception of its drivers across the highly heterogeneous workforce. This study aimed to empirically identify and structure the key antecedent factors of engagement and examine their perception based on structural and sociodemographic characteristics among healthcare workers in Slovakia. Methods: This research employed a quantitative, cross-sectional design, utilizing a self-administered questionnaire distributed widely among healthcare providers throughout Slovakia. To achieve the study’s objectives, several advanced mathematical and statistical methods were applied: the Kaiser-Meyer-Olkin (KMO) Measure and Bartlett’s Test for sample adequacy, Principal Component Analysis (PCA) for empirical factor structuring and Analysis of Variance (ANOVA). Results: Three common antecedent factors for healthcare workers’ engagement and well-being were identified: Factor 1—Organizational Commitment and Identity; Factor 2—Meaningful Involvement and Job Satisfaction; and Factor 3—Organizational Citizenship and Retention Intent. Factor 1 was evaluated positively in public (state-owned) and mixed organizations but negatively in private healthcare providers, confirming a statistically significant difference. Factor 2 also exhibited significant differences based on work position: it was negatively rated by management, physicians, and nurses, but positively by other staff categories. Conclusions: The contribution of this study lies in the empirical confirmation that a universal managerial approach to increasing employee engagement in Slovak healthcare is ineffective. A differentiated managerial approach based on organizational type and work position directly supports the transition from blanket, expensive, and ineffective HR policies to strategic and targeted engagement management, which is essential for the long-term sustainability and improvement of care quality in Slovak healthcare. Full article

Aerobic methanotrophs mediate methane oxidation contributing to a major biological sink that limits CH₄ release to the atmosphere in oxygenated environments and serve as promising platforms for biotechnological applications. In natural and engineered environments, these bacteria rarely exist in isolation but form stable associations with heterotrophic satellites that utilize methanotrophic metabolites, remove inhibitory intermediates, and provide essential growth factors. Such interactions enhance methane oxidation efficiency and community stability, yet the metabolic mechanisms underlying them remain poorly resolved. This review summarizes current knowledge on both natural and synthetic aerobic methanotrophic consortia, focusing on the composition, functions, and biotechnological relevance of satellite microorganisms. We systematically examine available mathematical frameworks—from ecological and statistical models to genome-scale metabolic reconstructions and dynamic flux balance analysis—applied to methanotrophs and their satellites. Our analysis reveals that while genome-scale metabolic models have been developed for model heterotrophic species, only a few correspond to experimentally identified methanotroph satellites, and community-level reconstructions remain limited. The lack of curated and experimentally validated models restricts the predictive power of current approaches. Addressing these limitations will require not only targeted reconstruction of satellite metabolism, but also the combined use of complementary computational methods followed by experimental verification. Such an integrative strategy will be essential for understanding methanotrophic community organization and function and, more broadly, other microbial consortia with complex metabolic interactions. Addressing these limitations through targeted reconstruction of satellite metabolism and integration of existing models will be key to advancing quantitative understanding of methanotrophic community organization and function. Full article

Dendritic cell (DC) immunotherapy is a promising approach for treating cancers such as melanoma and prostate cancer. Although DC-based vaccines can elicit potent anti-tumor immune responses, dosing schedules in both preclinical and clinical settings are often chosen empirically rather than through quantitative optimization. In this work, we develop an enhanced mathematical model of tumor-immune dynamics that incorporates a more realistic tumor growth law and an estimated immune-response delay, enabling the systematic design of DC vaccination protocols. Tumor-growth and immunotherapy parameters were calibrated using experimental melanoma data and two metaheuristic optimization methods: Genetic Algorithm and Particle Swarm Optimization. Using the calibrated model, we derived vaccination schedules consisting of three injections totaling $2.4 \times {10}^6$ DCs. Despite using the same total dose as the baseline four-injection protocol, the optimized schedules reduced tumor burden by approximately $52\%$ over a 5000-h window, as measured by the area under the tumor-time curve, while also lowering the number of administrations. These results demonstrate that effective tumor control can be achieved without increasing treatment intensity and with substantially fewer vaccinations than previously assumed. Prior optimization studies often required cumulative doses exceeding $1 \times {10}^7$ cells to obtain comparable therapeutic effects. In contrast, our findings show that metaheuristic algorithms can produce dose-efficient and biologically grounded schedules that significantly enhance treatment performance. This work highlights the value of computational optimization as a decision-support tool for designing efficient and clinically meaningful DC immunotherapy protocols. Full article

Based on existing models, this paper incorporates some key ecological factors, thereby obtaining a class of eco-epidemiological models that can more objectively reflect natural phenomena. This model simultaneously integrates disease dynamics within the prey population and the Beddington–DeAngelis functional response, thus achieving an organic combination of ecological dynamics, epidemic transmission, and spatial movement under time-varying environmental conditions. The proposed framework significantly enhances ecological realism by simultaneously accounting for spatial dispersal, predator–prey interactions, disease transmission within prey species, and seasonal or temporal variations, providing a comprehensive mathematical tool for analyzing complex eco-epidemiological systems. The theoretical results obtained from this study can be summarized as follows: Firstly, the existence and uniqueness of globally positive solutions for any positive initial data are rigorously established, ensuring the well-posedness and biological feasibility of the model over extended temporal scales. Secondly, analytically tractable sufficient conditions for uniform population persistence are derived, which elucidate the mechanisms of species coexistence and biodiversity preservation even under sustained epidemiological pressure. Thirdly, by employing innovative applications of differential inequalities and fixed point theory, the existence and uniqueness of a positive spatially homogeneous periodic solution in the presence of time-periodic coefficients are conclusively demonstrated, capturing essential rhythmicities inherent in natural systems. Fourthly, through a sophisticated combination of the upper and lower solution method for parabolic partial differential equations and Lyapunov stability theory, the global asymptotic stability of this periodic solution is rigorously established, offering a powerful analytical guarantee for long-term predictive modeling. Beyond theoretical contributions, these research findings provide actionable insights and quantitative analytical tools to tackle pressing ecological and public health challenges. They facilitate the prediction of thresholds for maintaining ecosystem stability using real-world data, enable the analysis and assessment of disease persistence in spatially structured environments, and offer robust theoretical support for the planning and design of wildlife management and conservation strategies. The derived criteria support evidence-based decision-making in areas such as controlling zoonotic disease outbreaks, maintaining ecosystem stability, and mitigating anthropogenic impacts on ecological communities. A representative numerical case study has been integrated into the analysis to verify all of the theoretical findings. In doing so, it effectively highlights the model’s substantial theoretical value in informing policy-making and advancing sustainable ecosystem management practices. Full article

This paper introduces a similarity index aimed at modeling psychological well-being through a set-theoretic formalization of self–ideal alignment. Inspired by Tversky’s feature-based model of similarity, the proposed index quantifies the degree of overlap and divergence between the current self-perception and the ideal self, each represented as a vector of signed attributes. The formulation extends traditional approaches in Personal Construct Psychology by incorporating directional and magnitude-based comparisons across constructs, and its mathematical properties can be expressed within a fuzzy similarity space that ensures boundedness and internal coherence. Unlike standard correlational methods commonly used in psychological assessment, this model provides an alternative framework that allows for asymmetric weighting of discrepancies and non-linear representations of similarity. Developed within the WimpGrid formalism—a graph-theoretical extension of constructivist assessment—the index offers potential applications in clinical modeling, idiographic measurement, and the mathematical analysis of dynamic self-concept systems. We discuss its relevance as a generalizable tool for quantitative psychology, and its potential for integration into computational models of personality and self-organization. Full article

In order to obtain a damage assessment method that can clearly express the influence mechanism of defect characteristics on fatigue damage, an integrated analytical framework combining the Shapley Additivity Interpretation (SHAP) method with the Extreme Gradient Boosting (XGBoost) model is established. Based on this framework, a high-accuracy fatigue damage prediction model was first established using the XGBoost model. Its accuracy and reliability are rigorously evaluated using the coefficient of determination R² and root mean square error RMSE. Results demonstrate that the model performs exceptionally well on both the training and test datasets (R² values of 0.999 and 0.846, respectively, with RMSE values of 0.0136 and 0.3727), establishing a reliable foundation for subsequent damage mechanism interpretation. Furthermore, by comparing defect feature importance between the XGBoost model and the SHAP interpretability model, it is revealed and cross-validated that the dominance order of defect features affecting the stress concentration factor k is S_max > P > S_area > N > V_max, confirming the physical stability of this dominance relationship. Additionally, leveraging the powerful local interpretability of the SHAP method, the contribution of each defect feature to the value in any sample was quantitatively analyzed, establishing a mathematical relationship between defect feature variables and the stress concentration factor k. Ultimately, based on the results of interpretability analysis and guided by fracture mechanics theory, the damage variable D is constructed by coupling multiple defect characteristics. This approach quantitatively reveals the intrinsic relationship between this variable and material fatigue damage. It provides a scientific basis for maintenance and repair decisions of aluminum alloy components in engineering applications, significantly enhancing their safety and reliability during use. Full article

This study develops a semi-discretized time system from the continuous-time Rosenzweig–-MacArthur model via the method of piecewise constant argument—a discretization approach that preserves both mathematical rigor and biological interpretability. For the proposed system incorporating constant-effort harvesting on both prey and predator populations, we present rigorous quantitative derivations for the existence and local stability of non-negative equilibrium. Furthermore, we investigate complex dynamical behaviors, including transcritical and Neimark–Sacker bifurcations, induced by parameter variations. We specifically focus on calculating the first Lyapunov coefficient to determine the stability of closed orbits emerging from the Neimark–Sacker bifurcation. Numerical validation of chaotic dynamics is conducted using the computed Maximum Lyapunov Exponent spectrum. Numerical simulations not only confirm consistency with analytical results but also reveal key ecological dynamics of the system: (i) the paradox of enrichment—a classic ecological phenomenon—persists even under constant-effort harvesting; (ii) appropriate tuning of harvesting parameters enables the coexistence of prey and predator populations in a stable closed orbit, resulting in cyclic coexistence. Full article

Monte Carlo methods offer a fast, cost-effective approach for modeling environmental systems influenced by random variability. This study applied them to three abiotic cases: (I) water quality in a lentic surface water source, (II) sizing of a homogenization chamber for solid waste treatment, and (III) removal of atmospheric particulate matter by rain. Deterministic models produced wide and inconsistent estimates: BOD₅ concentrations from 5.28 to 19.81 mg/L (275% relative difference), chamber volumes from 24.12 to 116.53 m³, and particulate matter reductions with up to 60 µg/m³ per month variation. Monte Carlo simulations, by contrast, captured system variability and provided more robust outputs: a design value of 94.84 m³ for the homogenization chamber, narrower ranges for BOD₅, and realistic distributions of atmospheric PM concentrations. Results show that reliance on average values introduces strong biases and mathematical incompatibilities, while the Monte Carlo approach yields quantitative predictions that are both accurate and operationally useful. This confirms its relevance as a practical tool for analyzing and designing environmental systems under uncertainty. Full article

The paper proposes a multi-objective approach for optimizing the structure of electric power generation amid tightening requirements for the energy efficiency and environmental safety of power systems. The study identifies relevant directions for improving advanced natural gas-fired power plants. An algorithm for the multi-objective optimization of the power generation structure has been developed, based on the sequential application of mathematical tools such as principal component analysis, Pareto optimization, and the entropy-based TOPSIS method. It has been established that under the model’s given constraints, the share of highly efficient energy complexes in Pareto-optimal generation structures typically does not exceed 40% of the total generating capacity, while the share of low-carbon complexes does not exceed 60%. Furthermore, as the energy planning horizon extends, the share of carbon-free energy complexes in the most efficient generation structures increases, reaching 51% with the introduction of generating capacity in 2031, and 92% with a system commissioning date in 2035. The proposed methodology enables a quantitative analysis of the evolution of the optimal electric power generation structure over time, highlighting a priority pathway for the development of sustainable energy. Full article

Background/Objectives: Myasthenia gravis (MG) is a rare autoimmune neuromuscular disease. Clinical trials with rigorously collected data provide valuable opportunities for mathematical modeling of patient outcomes over time. However, for rare diseases such as MG, combining data across multiple trials presents challenges due to heterogeneity in outcome measures. This study aims to address these challenges by investigating relationships among commonly used MG outcome measures to support the development of a standardized “Myasthenia Gravis Portrait.” Methods: We integrated three primary data types from multiple clinical studies: (i) laboratory and medication data, (ii) Electronic Health Record (EHR) data (e.g., age, sex, years since diagnosis, BMI), and (iii) disease severity scores. We examined the relationships among several MG-specific scoring systems, including Activities of Daily Living (MG-ADL), Quantitative Myasthenia Gravis (QMG), MG Composite (MG-CE), and MG Quality of Life-15 (MGQOL-15), to evaluate consistency and comparability across studies. Results: Preliminary analyses revealed variable correlations among the different scoring systems, indicating that, while some measures capture overlapping aspects of disease progression, others reflect distinct patient- or clinician-centered perspectives. These findings highlight the need for a harmonized framework that captures both functional and clinical dimensions of MG severity. Conclusions: The proposed “Myasthenia Gravis Portrait” provides a standardized approach for representing patient outcomes across diverse clinical datasets. This framework will facilitate the creation of virtual populations of digital twins, enabling a machine-learning-based modeling of MG progression and prediction of individualized disease trajectories. Full article

Background: Systemic inflammatory factors may be altered by periodontitis and/or COVID-19, potentially increasing the risk of adverse pregnancy outcomes, a relationship that remains unclear. Objective: This study aimed to identify associations between periodontitis and COVID-19 during pregnancy, evaluating the influence of dental care on obstetric variables through set theory and probability. Methods: A quantitative, cross-sectional, and correlational study was conducted in two phases. The first phase analyzed 156 medical records from 5 institutions, including gynecological and periodontal data; the second phase examined 104 records from a single institution selected for data completeness (2020–2021). Descriptive statistics, bivariate analysis, chi-square tests, and odds ratios were applied. Set operations (union, intersection) and relative probabilities were calculated using R and Excel. Sets represented dental care, dental disease, COVID-19 diagnosis, gestational age, neonatal weight, and complications. Results: In Phase 1, 37% of pregnant women were COVID-19-positive, 44% vaccinated, 51.9% underwent cesarean section, and 5.12% had periodontitis. In Phase 2, 76 pregnant women did not receive dental care, while 28 did; among them, 6 were COVID-19-positive. Mean neonatal weight ranged from 2336 g (dental care) to 2271 g (no dental care). COVID-19-positive pregnant women showed fewer complications and a higher proportion of normal-weight neonates. Gingivitis was the most frequent periodontal condition (75%). No statistically significant differences were observed between the analyzed sets. Conclusions: no direct relationship was found between periodontitis and neonatal weight in COVID-19-positive cases. Dental care did not influence maternal–fetal outcomes. The methodology provides an innovative framework for clinical analysis through mathematical abstraction. Full article

This study introduces a Fuzzy–AHP–based analytical model for the quantitative assessment of authenticity loss in adaptive reuse practices, addressing a persistent gap in heritage research—the lack of reproducible mathematical frameworks capable of linking authenticity evaluation with sustainability indicators. Unlike previous studies that approach authenticity conceptually or qualitatively, this research develops a hybrid decision-support system that translates both intangible and tangible heritage attributes into measurable linguistic variables, enabling systematic and comparable authenticity assessments. The model was applied to ten traditional houses in Alanya, Türkiye, representing different adaptive reuse types (residential, cultural, commercial, and touristic). A total of 17 experts contributed to the Analytic Hierarchy Process (AHP) weighting stage, producing a Consistency Ratio of 0.0156 (<0.10), and 8 experts provided scoring inputs for the fuzzy system. The fuzzy inference system was implemented in MATLAB R2023a, incorporating seven main criteria and three subcriteria, nine input variables, five linguistic categories, and a rule base of 3400 fuzzy rules. Membership functions were defined within the 0–100 numerical range, and the centroid defuzzification method was used to compute final authenticity values. Model reliability was confirmed through Kendall’s W = 0.87, demonstrating strong inter-rater agreement. Results show that buildings retaining their original residential function achieved the highest authenticity scores (Final Score ≈ 86), while structures converted into boutique hotels or restaurants exhibited substantial authenticity losses (Final Score range: 25–45), especially within Group 2 criteria (environment, function, spirit, and intangible cultural heritage). This divergence illustrates a sustainability paradox: although adaptive reuse prolongs building life cycles and reduces embodied carbon, it may simultaneously undermine cultural sustainability when authenticity is significantly compromised. The proposed Fuzzy–AHP authenticity model provides a replicable, transparent, and empirically validated tool for evaluating the effects of functional transformation within a sustainability framework. By quantifying the relationship between adaptive reuse types and authenticity retention, the study contributes to sustainable heritage management research and supports the implementation of SDG 11—Sustainable Cities and Communities. Full article

Urban flood disasters have become one of the most significant natural hazards under the dual pressures of rapid urbanization and intensified climate change. With the increasing interconnection among urban subsystems, these disasters often evolve into urban flood disaster chains, characterized by cascading failures across infrastructure, environment, and society. Current research hotspots mainly focus on three key aspects: the formation mechanisms, identification methods, and risk assessment approaches of urban flood disaster chains. In terms of formation mechanisms, most studies qualitatively describe the triggering and transmission processes of cascading events, revealing how interactions among hazard-inducing factors, disaster-formative environments, and disaster receptor generate chain reactions. Identification methods are categorized into four paradigms: qualitative identification based on experiential reasoning, semantic identification driven by data, structural identification through model inference, and behavioral identification using simulation modeling. Risk assessment approaches include historical disaster analysis, indicator-based evaluation models, uncertainty models, numerical simulation models, and intelligent algorithm models that integrate machine learning with physical simulations. The review finds that, due to the scarcity and heterogeneity of disaster chain event data, existing studies lack a unified quantitative framework to represent the mechanisms of urban flood disaster chains, as well as dynamic identification and assessment methods that can adapt to their evolutionary processes. Future research should focus on developing integrated mathematical paradigms, enhancing multisource data fusion and causal reasoning, and constructing hybrid models to support real-time risk assessment for urban flooding disaster chains. Full article