AppliedMath doi: 10.3390/appliedmath6050064

Authors: Elvira Rolón José G. Méndez Roberto Pichardo

Crime forecasting in heterogeneous urban contexts remains challenging due to the combined effects of territorial heterogeneity and complex temporal dynamics. However, a large portion of the existing literature tends to address territorial segmentation and predictive modeling separately, or to combine them within unified workflows that may obscure their distinct analytical roles. This study presents a modular spatial–temporal analytical approach that treats territorial segmentation and short-term crime prediction as complementary but methodologically independent components. Unsupervised segmentation captures territorial heterogeneity, while a supervised ensemble model estimates short-term crime occurrence. A chronological expanding-window validation scheme is implemented, reserving the most recent period as a blind test set to prevent temporal leakage. Across municipalities, recall values in 2022 range from 0.36 to 0.77, with corresponding F1-scores ranging from 0.174 to 0.696, while blind-test recall ranges from 0.184 to 0.856, with F1-scores ranging from 0.000 to 0.784, and AUC values up to 0.88, indicating that predictive performance is context-dependent rather than uniform. The proposed approach provides a replicable and context-aware analytical approach for spatially differentiated crime risk estimation under strict forward-looking evaluation.

AppliedMath doi: 10.3390/appliedmath6040063

Authors: Amna M. Grgar Lucy J. Campbell

Asymptotic solutions are derived to model the development of atmospheric internal gravity waves generated by latent heating in a two-dimensional configuration involving a vertically-sheared background flow. The mathematical model comprises nonlinear partial differential equations derived from the conservation laws of fluid dynamics under the anelastic approximation where the background density and temperature vary with altitude. The latent heating is represented by a horizontally-periodic but vertically-localized nonhomogeneous forcing term in the energy conservation equation. This generates gravity waves that are considered as perturbations to the background flow and are expressed as perturbation series, with the leading-order contributions being the solutions of linearized equations. Taking into account the nonlinear terms at the next order gives expressions for the effects of the waves on the background mean flow. Due to the vertical shear, there is a critical level where momentum and energy are transferred from the wave modes to the mean flow. The asymptotic solutions show that the wave–mean-flow interaction is nonlocal and occurs over the range of altitudes from the thermal forcing level up the critical level. This is in contrast to what occurs in the case of waves forced by an oscillatory lower boundary, where the interaction is typically localized around the critical level. It is found that the wave drag is negative above the thermal forcing level, making the mean flow velocity more negative, but it becomes positive as the waves approach the critical level, indicating wave absorption in this region. There is wave transmission through the critical level, as well as absorption, and the extent of transmission depends on the depth of the latent heating profile. The mean potential temperature is reduced above the thermal forcing level and enhanced at the critical level, a situation that could ultimately lead to the development of convective instabilities.

AppliedMath doi: 10.3390/appliedmath6040062

Authors: Mahmoud B. Mahmoud Amira M. Salama Mustafa AL-Tawfiq Khaled H. Ibrahim Eslam M. Abd Elaziz

Harmonic distortion in power systems, primarily caused by nonlinear loads, leads to significant power quality issues such as increased losses, reduced power factor, and equipment malfunctions. To mitigate these effects, passive power filters (PPFs) are widely employed due to their cost-effectiveness and simplicity. This paper presents an optimized design of a single-tuned passive filter (STPF) using the Firefly Algorithm (FFA) and its multi-objective extension, the Multi-Objective Firefly Algorithm (MOFA). The optimization aims to minimize both voltage total harmonic distortion (VTHD) and power loss and to maximize the power factor (PF) while complying with IEEE 519-2014 standards. The study evaluates the proposed method under two different industrial case studies with varying system parameters and harmonic profiles. Simulation results demonstrate that the proposed FFA-based optimization outperforms the Mixed Integer Distributed Ant Colony Optimization (MIDACO) method, achieving superior VTHD reduction, power loss minimization, and power factor enhancement. The MOFA approach provides a Pareto-optimal front, offering trade-offs among competing objectives. Comparative analysis confirms the efficiency, robustness, and faster convergence of FFA-based optimization, making it a promising approach for optimal filter design in power systems.

AppliedMath doi: 10.3390/appliedmath6040061

Authors: Stelios Arvanitis Pantelis Argyropoulos Spyros Vassilakis

We develop a categorical framework for modeling recursive uncertainty over preferences in decision theory. Classical models of ambiguity allow for uncertainty over outcomes or beliefs but usually rely on finite or exogenously truncated representations when agents face uncertainty about their own evaluative criteria. Given that such recursive preference formation generates an infinite hierarchy that may not stabilize at any finite level, we introduce a contractive von Neumann–Morgenstern utility functor on a category of compact metric spaces enriched over complete metric spaces, and establish the existence and uniqueness of its canonical fixed point. This fixed point is interpreted as a universal preference space that contains all levels of recursive ambiguity in a consistent and metrically stable form. We further extend the construction to multi-utility representations and discuss its relation to existing models of ambiguity and universal choice spaces. This framework offers a minimal unified representation of recursive preference structures.

AppliedMath doi: 10.3390/appliedmath6040060

Authors: Meriem Keddali Hamida Talhi Mohammed Amine Meraou Ali Slimani

A novel flexible single-parameter polynomial distribution is presented in this study. The forms of hazard rate and density functions are examined. Additionally, exact formulas for a number of numerical characteristics of distributions are obtained. Stochastic ordering, the moment technique, the maximum likelihood, and a Bayesian analysis of this novel distribution based on type II censored data are used to derive the extreme order statistics. We construct Bayes estimators and the associated posterior risks using a variety of loss functions, such as the generalized quadratic, entropy, and Linex functions. Since tractable analytical formulations of these estimators are unattainable, we suggest using a simulation technique based on Markov chain Monte-Carlo (MCMC) to examine their performance. Furthermore, we construct maximum likelihood estimators given initial values for the model’s parameters. Additionally, we use integrated mean square error and Pitman’s proximity criteria to compare their performance with that of the Bayesian estimators. Lastly, we apply the new family to many real-world datasets to show its versatility, and we model cancer survival data using this new distribution to explain our methodology.

AppliedMath doi: 10.3390/appliedmath6040059

Authors: Obiora Cornelius Collins Oludolapo Akanni Olanrewaju

Substance abuse addictions and hepatitis B infections are two major public health problems facing humanity globally, especially in areas where the two problems co-exist. A mathematical model was used in this work to study the co-dynamics of substance abuse addictions and hepatitis B infections and investigate their possible control strategies. The mathematical features of the model, such as the disease-free equilibrium, endemic equilibrium, and basic reproduction number, were computed. The stability analysis of the disease-free equilibrium and endemic equilibrium was conducted analytically. The impact of multiple control measures, including public enlightenment, rehabilitation of individuals with substance abuse disorders, treatment of persons infected with hepatitis B, and vaccination of susceptible individuals, was examined numerically. The study reveals how co-existence fundamentally alters system behavior and control effectiveness and offers new insights for designing effective control management strategies.

AppliedMath doi: 10.3390/appliedmath6040058

Authors: Douglas Kwasi Boah Suleman Abudu Fiele Christian John Etwire

This study introduces a deterministic fractional-penalty refinement of Vogel’s Approximation Method (VAM) for generating high-quality initial basic feasible solutions (IBFS) in classical transportation problems. Unlike the traditional additive regret measure employed in VAM, the proposed method uses a multiplicative contrast ratio between the two smallest admissible costs in each row and column. This modification preserves the allocation structure of VAM while introducing scale-invariant prioritization that improves sensitivity to relative cost differences.The method was evaluated on thirty-four benchmark transportation problems drawn from the literature and self-constructed large-scale instances (up to 10×20). Performance was assessed using percentage optimality gaps relative to optimal solutions obtained via the Stepping–Stone and MODI procedures. Across all instances, the proposed approach achieved a mean optimality gap of 2.78%, compared to 5.22% for classical VAM, 14.97% for the Least Cost Method (LCM), and 45.78% for the Northwest Corner Method (NWCM). Dispersion of deviations was also reduced, indicating improved robustness across heterogeneous cost structures Statistical validation confirms the improvement over VAM: the paired t-test yielded t=−3.17 (p=0.00163, one-sided), and the Wilcoxon signed-rank test produced p=6.10×10−5. Computational experiments further show that the refinement does not increase runtime relative to classical IBFS procedures.The proposed method therefore constitutes a structured enhancement of VAM that improves initial solution quality while maintaining computational simplicity.

AppliedMath doi: 10.3390/appliedmath6040057

Authors: Senne Aerts Eleonora Iachini Urszula Kochanska Eleni Koutrouli Polychronis Manousopoulos

Crypto-asset markets have been rapidly evolving during the past years, being under the spotlight of a diverse set of actors in the financial ecosystem, including investors, financial institutions, regulators and academics. Their potential interconnections with the traditional financial markets are important, and identifying them can provide useful insight in a diversity of areas such as risk contagion and mitigation, price formation, portfolio management and regulatory framework design. In order to identify such interconnections, various lines of research are followed. Specifically, the correlation between prominent stock market indices and crypto-assets from 2018 to 2025 is examined, while their volatility is also evaluated. Furthermore, the relevant effect of news, events and announcements is explored. The results are based on both daily and high-frequency datasets, with the use of the latter focusing on intra-day variation. The analysis of the results identifies existing interconnections between 2020 and 2025, as well as the important respective impact of news and announcements. An additional generic outcome is the usefulness of high-frequency datasets in the crypto-asset context. The conclusions are useful for all actors in the financial ecosystem. Future work can focus on the extension of the research to additional markets or crypto-assets.

AppliedMath doi: 10.3390/appliedmath6040056

Authors: Salvador E. Ayala-Raggi Manuel Rendón-Marín

The exact perimeter of an ellipse involves the complete elliptic integral of the second kind, which lacks a closed-form expression in elementary functions. As a result, analytical approximations have been proposed for applications requiring fast and accurate evaluation of elliptical geometries. In this study, we present a new ultra-accurate and compact closed-form approximation for the ellipse perimeter based on an exponential correction applied to Ramanujan’s second formula. The proposed expression preserves simplicity—using only three exponential functions and six constants—while achieving a maximum relative error of approximately 0.57 ppm observed over the tested grids covering the full eccentricity range. This represents a significant accuracy improvement over classical and modern approximations while maintaining a single-line analytical form with low computational cost. Due to its robustness, quasi-exact behavior at both circular and highly eccentric limits, and its suitability for numerical algorithms and embedded implementations, the proposed approximation is particularly useful in engineering computations involving elliptical boundaries.

AppliedMath doi: 10.3390/appliedmath6040055

Authors: Daniel López-Rodríguez Jorge Jordán-Núñez Bàrbara Micó-Vicent Antonio Belda

Sectional warping requires selecting a final operating length when only a small sample of residual cone masses can be measured. This paper proposes a Bayesian chance-constrained planning rule that combines a conjugate log-space model with fast posterior predictive simulation of the population minimum to recommend a risk-limited band length. The method provides a transparent risk parameter, efficient computation, and direct comparison with heuristic, bootstrap, distribution-free, and tail-model baselines. In an industrial-like synthetic study, the Bayesian policy reduced the mean remainder relative to a tuned sample-minimum rule while maintaining controlled shortage risk, and the results clarify why fully distribution-free guarantees are impractical under typical sampling budgets.

AppliedMath doi: 10.3390/appliedmath6040054

Authors: Kadrzhan Shiyapov Zhanars Abdiramanov Zhuldyz Issa Aruzhan Zhumaseyitova

We develop a fast numerical method for solving nonlinear diffusion equations with memory phenomena, a class of problems arising within viscoelastic materials, anomalous transport, and hereditary systems. The primary computational problem is the nonlocal temporal dependence captured by Volterra-type memory operators, which makes direct evaluation scale quadratically with the number of time steps (O(Nt2)), rendering prolonged simulations prohibitively expensive. To address this bottleneck, we develop a novel synthesis that combines a high-order spectral method for spatial discretization with a fast memory algorithm based on a sum-of-exponentials approximation. The spectral method obtains exponential spatial convergence for smooth solutions. At the same time, the fast memory algorithm reduces memory usage and computational complexity to O(Nt), yielding computational speedups exceeding 414x for prolonged simulations. We rigorously prove that the proposed scheme preserves the discrete energy dissipation law of the continuous system under mild assumptions on the memory kernel, thereby ensuring unconditional stability. Error analysis verifies spectral accuracy in space and first-order temporal convergence. Extensive numerical experiments using exponentially decaying and weakly singular kernels validate the theoretical results and illustrate the method’s effectiveness for modeling viscoelastic transport phenomena and irregular diffusion in complex systems.

AppliedMath doi: 10.3390/appliedmath6040053

Authors: Gorenc Mateja

This paper studies subsidy allocation in interconnected industrial systems using the spectral theory of positive matrices. The allocation is characterized by the Perron eigenvector of a cost matrix describing inter-factory interactions. We show that convergence to equilibrium is exponential and governed by the spectral ratio. A systemic resilience index based on spectral separation is introduced to quantify both stability and robustness under perturbations. The results demonstrate that stability and fairness arise from the spectral structure of the system.

AppliedMath doi: 10.3390/appliedmath6040052

Authors: Rajendra Prasad Najwa Mohammed Al-Asmari Abdul Haseeb Sushmita Sen

The main object of this work is to study the generalized B-curvature tensor in an n-dimensional Lorentzian para-Kenmotsu (briefly, (LPK)n) manifold along a semi-symmetric metric connection ∇¯. First, in an (LPK)n-manifold, we explore certain flatness conditions, namely, B¯(Y,Z)X=0, B¯(Y,Z)ζ=0, g(B¯(φY,φZ)φX,φW)=0, and B¯(Y,Z)·φ=0 conditions, which all result in an η-Einstein manifold. Furthermore, in an (LPK)n-manifold, we study the curvature conditions B¯.Q=0 and B¯.Q¯ = 0, which provide the scalar curvature. The generalized B-curvature tensor blends the features of different curvature tensors, allowing researchers to study conditions like semi-symmetry, pseudo-symmetry in a unified framework. Conditions like B-semi-symmetry correspond to conservation laws or stability properties in physical systems.

AppliedMath doi: 10.3390/appliedmath6030051

Authors: Stefan Brock

Time delays are inherent in modern motion-control and electric-drive loops due to sensing, filtering, sampling and computation, communication, and actuation scheduling. When such delays are only partially known, they can markedly reduce stability margins and narrow the admissible range of state-feedback gains, especially in high-bandwidth servo applications. This paper develops a design-oriented state-feedback framework for delay-affected plants based on the Manabe polynomial concept and the Coefficient Diagram Method (CDM). The plant is represented as a chain of integrators of order two to four with an effective input gain, and the feedback gain is synthesized for the nominal delay-free model by matching a standard Manabe/CDM characteristic polynomial using the classical CDM stability-index pattern. When an unmodeled input delay is present, the closed loop is governed by a delay-dependent characteristic equation. By introducing a normalized representation, the analysis yields explicit delay-stability limits that directly translate into a lower bound on the equivalent time constant used for tuning. The degradation of the phase margin and gain margin with increasing normalized delay is quantified as design charts, and a simple phase-margin-based inequality is proposed for selecting the tuning time constant, with gain-margin checks recommended as a verification step.

AppliedMath doi: 10.3390/appliedmath6030050

Authors: Sunil Kumar Yadav Najwa Mohammed Al-Asmari Abdul Haseeb

The objective of this work is to characterize certain geometric aspects of LP-Sasakian (LPS) manifolds admitting a generalized almost Schouten soliton (GASS) and to prove that a such manifold with GASS is of constant scalar curvature. Initially, we examine the solitonic behavior of ϕ-recurrent LPS manifolds with GASS in view of certain curvature conditions. Moreover, we also deliberate the geometric properties of a perfect fluid LPS spacetime with a unit torse-forming vector field (UTVF) in connection with a GASS. Also, the behavior of a GASS is studied in the broader framework of special types of perfect fluid LPS spacetime such as dust fluid, dark fluid, and radiation era. Overall, the main novelty of this work is its study of the geometrical phenomena and characteristics of a GASS on LPS manifolds and their application in a perfect fluid LPS spacetime.

AppliedMath doi: 10.3390/appliedmath6030049

Authors: Abdul-Mumin Khalid Musah Sulemana Wahab Abdul Iddrisu

Multimodal epileptic seizure detection using physiological biosignals remains challenging due to signal noise, inter-subject variability, weak cross-modal alignment, and the limited interpretability of many machine learning models. To address these challenges, this study proposes a parameterized multimodal feature-fusion framework that unifies normalization, modality weighting, and nonlinear cross-modal interaction within a single mathematical representation. Four fusion parameters, the fusion exponent ρ, interaction weight (δ), normalization factor (λ), and the cross-modal interaction term (η), are introduced at the feature-fusion level, while all classifiers retain their original learning mechanisms. The framework is evaluated using synchronized EEG, ECG, EMG, and accelerometer signals from 120 subjects, segmented into 2 s windows at 512 Hz and analyzed using twelve classical and deep learning classifiers. Principal Component Analysis (PCA) applied to the fused feature space reveals improved class separability compared to unimodal representations, with EEG exhibiting the strongest intrinsic discrimination and peripheral modalities contributing complementary structure when fused. SHapley Additive exPlanations (SHAP) further identify entropy as the most influential feature across all modalities, followed by RMS and energy, yielding physiologically coherent attributions. Quantitative performance evaluation and ablation analysis confirm that the observed improvements arise from the proposed representation design rather than classifier-specific modifications. Unlike existing architecture-dependent fusion strategies, the proposed method introduces a mathematically parameterized feature-space formulation that enhances separability and interpretability without modifying classifier architectures, thereby establishing a representation-driven paradigm for explainable multimodal seizure detection. These results demonstrate that mathematically principled feature-space modeling can simultaneously enhance predictive performance and interpretability, providing a transparent and robust foundation for explainable multimodal seizure detection.

AppliedMath doi: 10.3390/appliedmath6030048

Authors: Rinaldi (Unciuleanu) Oana Costin-Gabriel Chiru

This paper develops a rigorous mathematical and computational framework for four-dimensional chess defined on the discrete hypercubic lattice {1,…, 8}4. We formalize piece movement using displacement sets in Z4, define adjacency via the Chebyshev metric, and analyze the resulting move graphs for rooks, bishops, knights, queens, and kings. We establish exact mobility formulas, parity invariants, and connectivity properties, consolidating known product-graph results for rooks and kings while introducing a boundary-sensitive analysis of the four-dimensional knight verified by exhaustive enumeration. The mathematical framework is complemented by a fully implemented 4D chess engine and interactive visualization environment rendering all 64 (z,w)-slices of the hypercube simultaneously. The system supports full move legality, generalized special rules, multi-king checkmate detection, and reproducible state enumeration. Performance measurements and exploratory branching-factor estimates are obtained through reproducible random playouts using the publicly available implementation. We contextualize this ruleset within existing work on move graphs on Znm, higher-dimensional leapers, spectral properties of grid graphs, toroidal analogs, and multidimensional visualization. Exploratory qualitative feedback (N = 18) is included to examine whether the visualization design is interpretable and navigable in practice, providing feasibility-oriented observations on how slice-based 4D projection and layered board rendering are perceived by non-expert users in an exploratory context. Together, the mathematical results, implemented engine, and visualization form a coherent foundation for the study of strategy, complexity, and human interaction in four-dimensional game systems. The framework provides a basis for future investigations into spectral analysis of move graphs, symmetry-aware search, hierarchical planning, and educational applications in high-dimensional geometry.

AppliedMath doi: 10.3390/appliedmath6030047

Authors: Tatsuya Sekiguchi Hiroyuki Hamada Masahiro Okamoto

Parameter estimation for biochemical reaction networks is computationally demanding, especially for systems with oscillatory nonlinear dynamics, where standard iterative optimization strategies, including genetic algorithms, often struggle with prohibitive computational costs. We introduce an efficient parameter estimation framework that combines a real-coded genetic algorithm with a novel adaptive simulation termination strategy. This strategy defines a time-dependent termination boundary based on population quantiles, which is permissive during early transients and becomes progressively stricter as simulations advance, explicitly accounting for the temporal structure of oscillatory behavior. Crucially, this mechanism facilitates the efficient identification and early simulation termination of poor parameter candidates, thus avoiding the computational expense of full-horizon simulations. The framework further integrates global exploration with the modified Powell method for rapid local refinement. Numerical experiments on two benchmark oscillatory models—the Lotka–Volterra and Goodwin oscillators—demonstrate that the framework reduces computational cost by approximately 30–50% compared to a baseline GA without this strategy. For the parameter-sensitive Goodwin model, the framework efficiently identifies candidates evolving toward damped oscillations caused by subtle parameter variations. Sensitivity analysis also confirms robustness across diverse hyperparameter settings, indicating that adaptive simulation termination provides a practical acceleration mechanism for inverse problems in systems biology where iterative objective function evaluation dominates runtime.

AppliedMath doi: 10.3390/appliedmath6030046

Authors: Seweryn Lipiński Łukasz Dziubiński Paweł Chwietczuk

The paper presents a mathematical validation and a local sensitivity analysis of a reduced-order thermal balance model designed to predict nighttime heat losses from an above-ground outdoor pool. The model expresses the total heat flux as a linear function of the water–air temperature difference through an effective overall heat-transfer coefficient aggregating convective, evaporative, and radiative mechanisms, as well as cover-related effects. The analysis is explicitly restricted to quasi-steady nighttime conditions. Field data were segmented into 13 independent nighttime realizations (∆T ≈ 5.5–26.9 °C, wind ≈ 0.00–1.32 m∙s−1). Across the entire dataset, the model achieved a mean relative error of 0.39% and a maximum absolute deviation of 3.72%, with no monotonic error growth versus ∆T or wind speed. Normalized local sensitivities reveal that the convective (hc) and evaporative (he) components dominate the response, whereas the radiative contribution is smaller under typical nighttime boundaries; the cover-permeability factor gains influence as wind speed increases. The additive structure limits independent identifiability of individual mechanisms, supporting an interpretation in terms of effective parameters. The results delineate the domain where the reduced-order formulation is predictive without refitting and provide a compact, interpretable reference for analyzing energy-balance models of open-water systems under nighttime operation.

AppliedMath doi: 10.3390/appliedmath6030045

Authors: Tristan Guillaume

This paper investigates the finite-horizon survival probability for a system of correlated arithmetic Brownian motions with heterogeneous drifts and volatilities, focusing on the event in which one component remains strictly below all others. Using a whitening transformation of the covariance structure, we reduce the problem to the survival of a standard Brownian motion in a simplicial cone, characterized by its spherical cross-section. While explicit solutions are available in low dimensions, we address the computationally challenging tetrahedral angular case. We derive a semi-analytic formula for the survival probability via an eigenfunction expansion of the Dirichlet Laplace–Beltrami operator on this curved domain. For efficient implementation, we construct a diffeomorphism from the spherical tetrahedron to a fixed Euclidean tetrahedron, enabling the computation of angular eigenpairs through a stable finite-element scheme. For higher-dimensional regimes, we also introduce a covariance-based difficulty index and geometric bounds based on an inscribed spherical cap to assess spectral convergence and estimate long-time decay rates. Numerical experiments show that this offline–online approach achieves high accuracy and substantial speedups relative to Monte Carlo benchmarks.

AppliedMath doi: 10.3390/appliedmath6030044

Authors: Vicente Peña Caballero Abraham Efraim Rodríguez-Mata Pablo Antonio López-Pérez Dulce J. Hernández-Melchor Víctor Alejandro González-Huitrón

This work proposes an integral-enhanced nonlinear PI2 state observer for the robust estimation of unmeasured states in nonlinear dynamic systems, with experimental validation on a flat-panel photobioreactor. The observer is designed as a virtual sensor to reconstruct key biological variables using a reduced set of online measurements and known operating conditions. Compared with a conventional extended Luenberger observer, the proposed structure improves estimation accuracy and robustness against constant disturbances and model mismatch, which are common in bioprocess applications. The experimental results show a clear performance advantage during transient growth phases while highlighting that the method relies on a locally valid model structure and appropriate gain tuning. Overall, the proposed observer provides a practical and scalable monitoring tool for nonlinear systems where the direct measurement of critical state is not feasible.

AppliedMath doi: 10.3390/appliedmath6030043

Authors: Mudassir Shams Bruno Carpentieri

Nonlinear systems with multiple roots arise frequently in biomedical and engineering models, yet their reliable numerical solution remains a challenging task. Many classical methods suffer from sensitivity to initial guesses, reduced convergence rates, and loss of accuracy in the presence of multiple or clustered solutions. In addition, the exploitation of parallelism to improve robustness and computational efficiency has received limited attention. In this work, we propose a high-accuracy parallel numerical framework of fourth-order convergence for the simultaneous approximation of all solutions of nonlinear systems with multiple roots. The proposed scheme is derivative-free and structurally decoupled, enabling efficient parallel implementation and robust convergence even when reliable initial approximations are unavailable. The effectiveness of the method is demonstrated on representative biomedical engineering models, including a glucose–insulin–glucagon regulatory network and a multi-compartment pharmacokinetic system, both exhibiting strong nonlinearity and multistability. Numerical experiments confirm stable convergence toward distinct solution clusters, machine-level accuracy, reduced residual norms, and improved computational performance when compared with existing approaches. These results indicate that the proposed framework provides a reliable and efficient alternative for solving nonlinear systems with multiple roots in complex applied settings.

AppliedMath doi: 10.3390/appliedmath6030042

Authors: Chih-Chiang Hong

An advanced frequency study in thick-walled functionally graded material (FGM) spherical shells is investigated with advanced shear correction. The values of advanced shear correction can be greater than one, be a negative value, and be affected by a nonlinear term of third-order shear deformation theory (TSDT) of displacements, FGM power law index, and temperature. It is novel and interesting to consider using TSDT and advanced shear correction to derive a simple homogeneous equation with reasonable simplifications into a symmetrical sparse matrix subjected to free vibration. The zero determinant of the symmetrical sparse matrix can be expressed to calculate the natural frequency by Newton’s method. The parameter effects of advanced shear correction, a nonlinear TSDT term, temperature, and the FGM power-law index on the natural frequencies of thick-walled FGM spherical shells are presented. The natural-frequency data for the axial and circumferential mode shapes are obtained. This is a new finding, as the assumed simplification in a sparse matrix causes a numerical truncation error; the natural-frequency values of the presented sparse matrix are much greater than those in a full matrix for thick-walled FGM spherical shells.

AppliedMath doi: 10.3390/appliedmath6030041

Authors: Felipe J. Torres Israel Martínez Antonio J. Balvantín Edgar H. Robles

Professors, students, and researchers from universities around the world use software distributed under licenses for numerical simulation purposes, which requires a computer with considerable hardware capabilities. This implies a high cost of simulations in engineering applications that require dynamic modeling using numerical methods, particularly in robotics and nonlinear control. This article compares and analyzes the performance of a frugal simulation scheme based on the use of low-cost, free, and open-source technology, specifically a low-power, single-board minicomputer (Raspberry Pi) in conjunction with GNU-Octave software. The benchmark is a numerical simulation of trajectory tracking control in the joint space of a Selective Conformal Assembly Robot Arm (SCARA). To perform this task, a system of coupled nonlinear differential equations is solved in matrix form using a numerical method known as an ODE solver. This solution includes the control law and the dynamic system model derived from Euler–Lagrange formalism. The time complexity and accuracy are analyzed to compare the performance of the frugal simulation tool with that of a conventional simulation setup consisting of a personal computer and MATLABTM running the same simulation code. The analysis shows minimal deviations in the numerical solutions and reasonable time complexity. Moreover, the frugality score of this approach and the low acquisition cost of the simulation tool enable the creation of simulation laboratories at universities with limited budgets for education and research.

AppliedMath doi: 10.3390/appliedmath6030040

Authors: Yanhui Ding Qiong Tang Sijia Tang

The paper utilizes the continuous finite element method to solve stiff ordinary differential equations and proves that the linear finite element method and the quadratic finite element method have A-stability in solving autonomous ordinary differential equations, and exponential dichotomy in solving non-autonomous ordinary differential equations. In the numerical experiments of nonlinear autonomous and non-autonomous strongly and moderately stiff ordinary differential equations, a relatively large step size of h=0.1 was adopted over a longer period of time, with the numerical solution accuracy reaching 10−4. The superconvergence order maintained the theoretical order. A new approach is provided for solving stiff ordinary differential equations.

AppliedMath doi: 10.3390/appliedmath6030039

Authors: Fotini Sereti Dimitrios Georgiou Theodoros Karakasidis

Genetic sequences play a central role in biological and medical research, and mathematics provides powerful means for their representation and analysis. Conventional approaches, such as the fuzzy polynucleotide space [0, 1]12, model codons as 12-dimensional vectors, but this comes at the cost of high dimensionality. In this study, we introduce two new models, Vector-Fuzzy-I and Vector-Fuzzy-II, that map codons and genetic sequences into the 4-dimensional Euclidean space ℝ4 using vector algebra and fuzzy set theory. In the first model, sequence structure is represented by successive vector addition, while in the second, it is represented by positional frequencies normalized by nucleotide locations. These low-dimensional representations are unique, preserve sequence order, and allow effective measurement of similarity and difference via Euclidean metrics. Compared with the fuzzy polynucleotide space, the proposed models achieve dimensionality reduction while enhancing the resolution of sequence differentiation. Our approach offers new mathematical perspectives for sequence analysis in theoretical biology.

AppliedMath doi: 10.3390/appliedmath6030038

Authors: Tahmineh Azizi

The complex and heterogeneous nature of cancer necessitates advanced modeling techniques to better understand tumor dynamics and inform treatment strategies. This paper explores the application of stochastic modeling in cancer research, focusing on five key areas: tumor growth kinetics, evolutionary dynamics of cancer, treatment response and resistance, spatial modeling of tumor progression, and clinical applications of stochastic models. We first examine how stochastic models capture the randomness in tumor growth and proliferation, providing insights into cellular behaviors that deterministic models may overlook. Next, we investigate the evolutionary dynamics that govern tumor heterogeneity and the emergence of resistance, highlighting the role of genetic mutations and environmental pressures. The paper also discusses how stochastic modeling can improve predictions of treatment responses, elucidating mechanisms behind therapy resistance in various tumor subpopulations. Furthermore, we address the significance of spatial modeling in understanding tumor interactions within their microenvironment, shedding light on processes such as metastasis. Finally, we emphasize the translational potential of these mathematical frameworks, demonstrating how they can enhance personalized medicine approaches in oncology. By integrating stochastic modeling into cancer research, this work contributes to a deeper understanding of cancer biology and paves the way for improved patient outcomes.

AppliedMath doi: 10.3390/appliedmath6030037

Authors: Chengxi Zhang

This paper addresses the consensus problem in multi-agent systems via a self-learning control scheme that directly reuses prior control information to accelerate transient coordination while maintaining robustness. I study agents with linear dynamics and external disturbances, and design a lightweight self-learning consensus control law for the distributed consensus domain, formulated as ui(t)=k1ui(t−τ)+k2si(t) with learning intensity k1 and learning interval τ. I provide a Lyapunov-based stability proof showing uniform ultimate boundedness of the consensus error under bounded disturbances. Compared to non-learning consensus laws, the proposed strategy achieves faster agreement with reduced long-term effort and retains simplicity suitable for resource-constrained multi-agent platforms, while also achieving decent performance against external disturbances. Simulations validate the improved transient speed and steady accuracy. The full-version-source code is open-sourced.

AppliedMath doi: 10.3390/appliedmath6030036

Authors: Calisto B. Marime Justin B. Munyakazi

Standard numerical methods such as Runge–Kutta and Euler methods have been widely used to approximate solutions to nonlinear systems. These methods converge to the solution only for small step sizes; for larger time steps, they generally generate spurious or chaotic solutions. In this paper, we consider a malaria propagation model with control for which we construct a second-order nonstandard finite difference scheme that preserves the important mathematical properties of the continuous model, which are positivity, boundedness, and stability of solutions irrespective of the step size. Moreover, we show that the equilibrium points of the discrete model are the same as those of the continuous model. By applying the double mesh principle, we provide evidence that the second-order NSFD scheme approximates the true solution with small errors. Theoretical assertions and numerical results show the advantages of the developed second-order nonstandard finite difference method.

AppliedMath doi: 10.3390/appliedmath6030035

Authors: Shi-Chu Li Hong-Yu Ma Bo-Wen Zhang Li-Yong Shen

Triangular mesh surface representation is widely adopted in geometric design and reverse engineering applications. However, in high-precision Computer Numerical Control (CNC) machining, significant limitations persist in automated Computer-Aided Manufacturing (CAM) tool path generation for such representations. Conventional CAM workflows heavily rely on manual engineering interventions, such as creating drive surfaces or tuning extensive parameters—a dependency that becomes particularly acute for generic free-form models. To address this critical challenge, this paper proposes a novel end-to-end single-step end-milling tool path generation methodology for triangular mesh surfaces in high-precision five-axis CNC machining. The framework includes clustering analysis for optimal workpiece orientation, normal vector distribution analysis to identify shallow and steep regions, Graphics Processing Unit (GPU)-accelerated collision detection for feasible tool orientation domains, and iso-planar tool path generation with Traveling Salesman Problem (TSP) optimization for efficient tool lifting and movement. Experimental validation confirms the framework ensures machining quality and algorithmic robustness.

AppliedMath doi: 10.3390/appliedmath6020034

Authors: Olugbade Ezekiel Faniyi Mark Ifeanyi Modebei Matthew Olanrewaju Oluwayemi Ikechukwu Jackson Otaide

This paper addresses the numerical integration of first-order ordinary differential equations by developing a continuous linear multistep block method. The method is constructed through the approximation of the exact solution using a linear combination of shifted Vieta–Lucas polynomials defined on the interval [0, 4]. The use of this polynomial basis extends traditional approximation approaches and provides improved stability while maintaining high-order accuracy. Theoretical analysis shows that the proposed method attains sixth-order convergence and possesses an extended stability interval of [−19.5,0], ensuring reliable performance for moderately stiff problems. Numerical experiments confirm that the method achieves lower errors and higher computational efficiency than conventional methods. These results demonstrate the suitability of the proposed approach for scientific computing applications, including engineering simulations and mathematical modeling, where accurate numerical integration of first-order differential equation is required.

AppliedMath doi: 10.3390/appliedmath6020033

Authors: Elsayed M. E. Zayed Mona El-Shater Ahmed H. Arnous Lina S. Calucag Anjan Biswas

The paper retrieves quiescent dispersive solitons in dispersion-flattened optical fibers having nonlinear chromatic dispersion and the Kerr law of self-phase modulation. The platform model is the Schrödinger–Hirota equation. The enhanced direct algebraic method has made this retrieval possible. The intermediary functions are Jacobi’s elliptic function and Weierstrass’ elliptic function. The final results appear with parameter constraints for the existence of such solitons.

AppliedMath doi: 10.3390/appliedmath6020032

Authors: Wullianallur Raghupathi

Modeling legal reasoning with artificial intelligence and machine learning presents formidable challenges. Legal decisions emerge from a complex interplay of factual circumstances, statutory interpretation, case precedent, jurisdictional variation, and human judgment—including the behavioral characteristics of judges and juries. This paper takes an exploratory approach to investigating how contemporary ML techniques might capture aspects of this complexity. Using pharmaceutical patent litigation as an illustrative domain, we develop a multi-layer analytical pipeline integrating text mining, clustering, topic modeling, and classification to analyze 698 U.S. federal district court decisions spanning January 2016 through December 2018, comprising substantive validity and infringement rulings under the Hatch-Waxman regulatory framework. Results demonstrate that the pipeline achieves 85–89% prediction accuracy—substantially exceeding the 42% baseline majority-class rate and comparing favorably with prior legal prediction studies—while producing interpretable intermediate outputs: clusters that correspond to recognized doctrinal categories (Abbreviated New Drug Application—ANDA litigation, obviousness, written description, claim construction) and topics that capture recurring legal themes. We discuss what these findings reveal about both the possibilities and limitations of computational approaches to legal reasoning, acknowledging the significant gap between statistical prediction and genuine legal understanding.

AppliedMath doi: 10.3390/appliedmath6020031

Authors: Edoardo Ballico

In Algebraic Statistics, M.A. Cueto, J. Morton and B. Sturmfels introduced a statistical model, the Restricted Boltzmann Machine, which introduced the Hadamard product of two or more vectors of an affine or projective space, i.e., the componentwise product of their entries, forcing Algebraic Geometry to enter. The Hadamard product X⋆Y of two subvarieties X,Y⊂Pn is defined as the Zariski closure of the Hadamard product of its elements. Recently, D. Antolini and A. Oneto introduced and studied the definition of Hadamard rank, and we prove some results on it. Moreover, we prove some theorems on the dimension and shape of the Hadamard powers of X. The aim is to describe the images of the Hadamard products without taking the Zariski closure. We also discuss several scenarios describing the case in which some of the data, i.e., the variety X, is wrong or it is not possible to recover it.

AppliedMath doi: 10.3390/appliedmath6020030

Authors: Moritz Sohns Ali Zakaria Idriss

This paper presents a topology-based approach to the general vector-valued stochastic integral for predictable integrands and semimartingale integrators. The integral is defined as a unique mapping that achieves closure under the semimartingale topology. While the topology and the closedness of the integral operator are well known, the method of defining the integral via this mapping is new and offers a significantly more efficient path to understanding the general stochastic integral compared to existing techniques. Instead of defining a basic integral and then extending it through a sequence of case distinctions, our construction performs a single topological closure: we define the vector stochastic integral as the unique continuous extension of the simple-predictable integral under the Émery topology, within the predictable σ-algebra. This single step yields the general predictable, vector-valued integral without invoking semimartingale decompositions, Doob–Meyer, or detours through H2/quasimartingale frameworks and without re-engineering from the componentwise to the vector case.

AppliedMath doi: 10.3390/appliedmath6020029

Authors: Preet Mishra Shyam Kumar Sorokhaibam Cha Captain Vyom R. K. Brojen Singh

Evolutionary changes can significantly impact interactions among populations and disrupt ecosystems by driving extinctions or collapsing population oscillations, posing substantial challenges to biodiversity conservation. This study addresses the ecological rescue of a predator population threatened by a mutant prey population using the optimal control method. To study this, we study a model that incorporates a genotypically structured prey population comprising wild-type, heterozygous, and mutant prey types, as well as the predator population. We prove that this model has both local and global existence and uniqueness of solutions, ensuring the model’s robustness. Then, we applied the optimal control method, incorporating Pontryagin’s Maximum Principle, to introduce a control input into the model and minimize the mutant population, thereby stabilizing the ecosystem. We utilize a reproduction number and a control efficacy measure to numerically demonstrate that the undesired dynamics of the model can be controlled, leading to the suppression of the mutant and the restoration of the oscillatory dynamics of the system. These findings demonstrate the applicability of optimal control strategies and provide a mathematical framework for managing such ecological disruptions.

AppliedMath doi: 10.3390/appliedmath6020028

Authors: Len Meas Chhaunny Chhum Phichhang Ou Mara Mong

This paper explores the intersection of three foundational areas—partial differential equations, financial mathematics, and probability—by providing a rigorous framework for the classical Black-Scholes–Merton option pricing model and its generalized extensions. For the classical model, a change in variables is employed to transform the Black-Scholes partial differential equation into the linear heat equation. The resulting formulation enables the use of Fourier transform techniques and the fundamental solution (heat kernel) to derive the closed-form Black-Scholes–Merton formula. To extend the classical setting, the interest rate in the discount factor and the stock’s rate of return are modeled using a multifactor Vasicek process, leading to a more sophisticated and realistic option pricing framework. In addition, a complementary derivation based on probabilistic methods, using a change in measure, yields an alternative explicit pricing formula. Numerical experiments based on Monte Carlo simulation show excellent agreement with the closed-form solutions and illustrate notable gains in computational efficiency. The comparative analysis further demonstrates that stochastic interest rates systematically produce lower option prices than the classical constant-rate model, underscoring the importance of accurate interest-rate modeling in practical valuation.

AppliedMath doi: 10.3390/appliedmath6020027

Authors: Jené Mercia van Schalkwyk Peter Joseph Witbooi Sibaliwe Maku Vyambwera Mozart Umba Nsuami

This article introduces and thoroughly examines a novel deterministic compartmental model of COVID-19 dynamics. The model uniquely incorporates compartments for symptomatic and asymptomatic individuals alongside an environmental reservoir for the pathogen. It also accounts for a steady inflow of infected visitors and a steady outflow from the removed class. The mathematical soundness of the model is established by identifying the invariant region and ensuring positivity of solutions. Notably, during surges of infected visitors, certain classes maintain positive minimum values. We analytically determine endemic equilibrium points and prove the global stability of the disease-free equilibrium. Sensitivity analysis highlights the significant roles of transmission rates and asymptomatic individuals in disease spread. Simulation results corroborate the theoretical findings and provide additional insights into the model’s predictive capabilities.

AppliedMath doi: 10.3390/appliedmath6020026

Authors: Muhammad Azam Imran Shabir Chuhan Muhammad Shafiq Ahmed Kaleem Arshid

Recent advances in physics-informed neural networks (PINN) have highlighted the need for systematic criteria for selecting appropriate algorithms to solve differential equations. This paper presents a numerical comparison between standard PINNs and gradient-enhanced PINNs (gPINNs) used to solve a high-order partial differential equations (PDE). To verify the accuracy and convergence behavior of all the methods, we solve a fourth-order PDE whose analytical solution is known. gPINN is recommended for problems requiring high accuracy in gradient fields or operating with sparse data, whereas standard PINN is advised for strongly nonlinear or computationally constrained scenarios. We synthesize our findings into a practical selection guide; gPINN is recommended for problems requiring high accuracy in gradient fields or operating with sparse data, whereas standard PINN is advised for strongly nonlinear or computationally constrained scenarios. This framework provides a clear, evidence-based policy for algorithm choice in SciML. Beyond numerical comparison, we provide an analytical interpretation linking solver performance to the spectral and stiffness properties of each PDE class, offering a principled basis for algorithm selection.

AppliedMath doi: 10.3390/appliedmath6020025

Authors: Sroor M. Elnady Mohamed A. El-Beltagy Mohammed E. Fouda Ahmed G. Radwan

The chain rule is a foundational concept in calculus, critical for differentiating composite functions, especially those appearing in modern AI techniques. Its extension to fractional calculus presents challenges due to the integral-based nature and intrinsic memory effects of these fractional operators. This survey provides a review of chain-rule formulations across major known FDs, including Riemann-Liouville (RL), Caputo, Caputo-Fabrizio (CF), Atangana-Baleanu-Riemann (ABR), Atangana-Baleanu-Caputo (ABC), and Caputo-Fabrizio with Gaussian kernel (CFG). The main contribution here is the introduction of a unified criterion, denoted as C, which synthesizes and extends previous classification frameworks for systematically formulating the chain rule across different operators. Each chain rule is examined in terms of its derivation, operator structure, and scope of applicability. In addition, the survey analyzes series-based approximations that appear in computing these derivatives, highlighting the minimum number of terms required to achieve acceptable mean absolute error (MAE). By consolidating theoretical developments, derivation methods, and numerical strategies, this paper provides a comprehensive resource for researchers and practitioners working with fractional-order models.

AppliedMath doi: 10.3390/appliedmath6020024

Authors: Pablo Ramos-Ruiz Antonio Miguel Fuentes-Jiménez José E. Ramos-Ruiz Inmaculada Jiménez-Manchado

In recent years, several quantum algorithms have been proposed for addressing combinatorial optimization problems. Among them, the Quantum Approximate Optimization Algorithm (QAOA) has become a widely used approach. However, reported limitations of QAOA have motivated the development of multiple algorithmic variants, including recursive hybrid methods such as the Recursive Quantum Approximate Optimization Algorithm (RQAOA), as well as the Quantum-Informed Recursive Optimization (QIRO) framework. In this work, we integrate the Quantum Alternating Operator Ansatz within the QIRO framework in order to improve its quantum inference stage. Both the original and the enhanced versions of QIRO are applied to the Minimum Vertex Cover problem, an NP-complete problem of practical relevance. Performance is evaluated on a benchmark of Erdös-Rényi graph instances with varying sizes, densities, and random seeds. The results show that the proposed modification leads to a higher number of successfully solved instances across the considered benchmark, indicating that refinements of the variational layer can improve the effectiveness of the QIRO framework.

AppliedMath doi: 10.3390/appliedmath6020023

Authors: Ioannis G. Tsoulos Vasileios Charilogis Dimitrios Tsalikakis

Artificial neural networks are reliable machine learning models that have been applied to a multitude of practical and scientific applications in recent decades. Among these applications, there are examples from the areas of physics, chemistry, medicine, etc. To effectively apply them to these problems, it is necessary to adapt their parameters using optimization techniques. However, in order to be effective, optimization techniques must know the range of values for the parameters of the artificial neural network, so that they can adequately train the artificial neural network. In most cases, this is not possible, as these ranges are also significantly affected by the inputs to the artificial neural network from the objective problem it is called upon to solve. This situation usually results in artificial neural networks becoming trapped in local minima of the error function or, even worse, in the phenomenon of overfitting, where although the training error achieves low values, the artificial neural network exhibits low performance in the corresponding test set. To address this limitation, this work proposes a novel two-stage training approach in which a simulated annealing (SA)-based preprocessing stage is employed to automatically identify optimal parameter value intervals before the application of any optimization method to train the neural network. Unlike similar approaches that rely on fixed or heuristically selected parameter bounds, the proposed preprocessing technique explores the parameter space probabilistically, guided by a temperature-controlled acceptance mechanism that balances global exploration and local refinement. The proposed method has been successfully applied to a wide range of classification and regression problems and comparative results are presented in detail in the present work.

AppliedMath doi: 10.3390/appliedmath6020022

Authors: Luisa Carracciuolo Ugo D’Amora Raffaele Dubbioso Ines Fasolino

Amyotrophic Lateral Sclerosis (ALS) is a progressive neurodegenerative disorder for which despite its severity, no validated biomarker currently exists to support early diagnosis, limiting therapeutic effectiveness and patient survival. In this context, mathematical modeling therefore becomes essential: it allows us to maximize the information obtainable from a limited number of samples, identify patterns that may not be directly observable, and estimate the relative contribution of different molecular markers to ALS progression. In this work, we propose methods for qualitatively and quantitatively evaluating the relevance of selected biomarkers in ALS classification and disease-state identification and laying the foundations for the definition of a protocol useful for constructing “digital twins” of the entire process of study, diagnosis, and treatment of the disease from the perspective of innovative precision medicine.

AppliedMath doi: 10.3390/appliedmath6020021

Authors: Ibrahim Mohammed Dibal Yeak Su Hoe

This study introduces a novel single-step hybrid block method with three intra-step points that attains fifth-order accuracy, offering an accurate and computationally economical tool for solving first-order differential equations. The method is specifically designed to handle first-order differential equations with efficiency and precision while employing a constant step size throughout the computation. To further enhance accuracy, interpolation techniques are incorporated to approximate function values at specific positions, addressing the fundamental properties of the method and verifying its mathematical soundness. These analyses confirm that the scheme satisfies the essential requirements of stability, consistency, and convergence, ensuring reliability in practical applications. In addition, the method demonstrates strong adaptability, making it suitable for a broad spectrum of problem settings that involve both stiff and non-stiff systems. Numerical experiments are carried out, and the results consistently demonstrate that the proposed method is robust and effective under various test cases. The outcomes further reveal that it frequently outperforms several existing numerical approaches in terms of both accuracy and computational efficiency.

AppliedMath doi: 10.3390/appliedmath6020020

Authors: Vasiliki Pantoula Vasileios Mandikas Tryfon Daras

The analysis of multivariate data is a central issue in biomedical research, where the accurate classification of patients and the extraction of reliable conclusions are of critical importance. Linear Discriminant Analysis (LDA) remains one of the most established methods for both dimensionality reduction and classification of data. In this paper, we examine in detail the theoretical foundations, assumptions, and statistical properties of LDA, and apply the method step by step to real data from the Breast Cancer Wisconsin (Diagnostic) database, which includes cellular features from breast biopsy samples with the aim of distinguishing benign from malignant tumors. Emphasis is placed on the importance of the method’s assumptions, such as multivariate normality, equality of covariance matrices, and absence of multicollinearity, demonstrating that their fulfillment leads to significant improvements in model performance. Specifically, careful preprocessing and strict adherence to these assumptions increase classification accuracy from 95.6% (94.7% cross-validated) to 97.8% (97.4% cross-validated). To our knowledge, this study is the first to demonstrate the dual use of LDA as both a dimensionality-reduction tool and a predictive classification model for this medical database within the same biomedical analysis framework. Moreover, we provide, for the first time, a systematic comparison between our assumption-aware LDA model and related studies employing the most accurate machine-learning classifiers reported in the literature for this dataset, showing that classical LDA achieves accuracy comparable to these more complex methods. The resulting discriminant model, which uses 13 variables out of the original 30, can be applied easily by clinical researchers to classify new cases as benign or malignant, while simultaneously providing interpretable coefficients that reveal the underlying relationships among variables. The implementation is carried out in the SPSS environment, following the theoretical steps described in the paper, thus offering a user-friendly and reproducible framework for reliable application. In addition, the study establishes a structured and transparent workflow for the proper application of LDA in biomedical research by explicitly linking assumption verification, preprocessing, dimensionality reduction, and classification.

AppliedMath doi: 10.3390/appliedmath6020019

Authors: Hening Huang

In many scientific and engineering fields (e.g., measurement science), a probability density function often models a system comprising a signal embedded in noise. Conventional measures, such as the mean, variance, entropy, and informity, characterize signal strength and uncertainty (or noise level) separately. However, the true performance of a system depends on the interaction between signal and noise. In this paper, we propose a novel measure, called “inforpower”, for quantifying the system’s informational power that explicitly captures the interaction between signal and noise. We also propose a new measure of central tendency, called “information-energy center”. Closed-form expressions for inforpower and information-energy center are provided for ten well known continuous distributions. Moreover, we propose a maximum inforpower criterion, which can complement the Akaike information criterion (AIC), the minimum entropy criterion, and the maximum informity criterion for selecting the best distribution from a set of candidate distributions. Two examples (synthetic Weibull distribution data and Tana River annual maximum streamflow) are presented to demonstrate the effectiveness of the proposed maximum inforpower criterion and compare it with existing goodness-of-fit criteria.

AppliedMath doi: 10.3390/appliedmath6010018

Authors: Jaume de Haro Emilio Elizalde

The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant ds2, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued that Albert Einstein initially sought a dynamical formulation in which ds2 encoded the gravitational effects, without invoking curvature as a physical entity. The now more familiar geometrical interpretation—identifying gravitation with spacetime curvature—gradually emerged through his collaboration with Marcel Grossmann and the adoption of the Ricci tensor in 1915. Anyhow, in his 1920 Leiden lecture, Einstein explicitly reinterpreted spacetime geometry as the state of a physical medium—an “ether” endowed with metrical properties but devoid of mechanical substance—thereby actually rejecting geometry as an independent ontological reality. Building upon this mature view, gravitation is reconstructed from the Weak Equivalence Principle, understood as the exact compensation between inertial and gravitational forces acting on a body under a uniform gravitational field. From this fundamental principle, together with an extension of Fermat’s Principle to massive objects, the invariant ds2 is obtained, first in the static case, where the gravitational potential modifies the flow of proper time. Then, by applying the Lorentz transformation to this static invariant, its general form is derived for the case of matter in motion. The resulting invariant reproduces the relativistic form of Newton’s second law in proper time and coincides with the weak-field limit of General Relativity in the harmonic gauge. This approach restores the operational meaning of Einstein’s theory: spacetime geometry represents dynamical relations between physical measurements, rather than the substance of spacetime itself. By deriving the gravitational modification of the invariant directly from the Weak Equivalence Principle, Fermat Principle and Lorentz invariance, this formulation clarifies the physical origin of the metric structure and resolves long-standing conceptual issues—such as the recurrent hole argument—while recovering all the empirical successes of General Relativity within a coherent and sound Machian framework.

AppliedMath doi: 10.3390/appliedmath6010017

Authors: Elena Sánchez Arnau Antonia Ferrer Sapena Maria Carmen Cárcel-Mas Claudia Sánchez Arnau Enrique A. Sánchez Pérez

Parcel size strongly influences agricultural production costs, and combining spatial and economic information within a mathematical setting helps to clarify this relationship. In this study, we introduce a Gamma-based stochastic framework to integrate actual parcel size distributions into cost estimates, an approach that, to our knowledge, has not been applied in this context. Using a representative traditional orchard system as a case study, parcel sizes (characterized by strong right skewness) are modelled with a Gamma distribution; for highly fragmented landscapes, a truncated Gamma on (0.01,1] ha yields a mean parcel area of about 0.255 ha. Results show that parcel-size heterogeneity substantially affects expected per-parcel costs; for example, calibrating ploughing at 800 EUR/ha leads to an average of ∼160 EUR/parcel, whereas intensive vegetable harvesting at 5000 EUR/ha reaches ∼2100 EUR/parcel. In our simulation, in which the main parameters have been roughly fixed with the aim of showing the methodology, results are given on an expected costs scale relative to parcel area and operation intensity. Overall, the framework shows how parcel-size distributions condition cost estimates and provides a transferable basis for comparative analyses, while acknowledging limitations related to the area-only specification.

AppliedMath doi: 10.3390/appliedmath6010016

Authors: Vesna Antoska Knights Marija Prchkovska Luka Krašnjak Jasenka Gajdoš Kljusurić

Uncertainty-aware decision-making increasingly relies on multimodal sensing pipelines that must fuse correlated measurements, propagate uncertainty, and trigger reliable control actions. This study develops a unified mathematical framework for multimodal data fusion and Bayesian decision-making under uncertainty. The approach integrates adaptive Covariance Intersection (aCI) for correlation-robust sensor fusion, a Gaussian state–space backbone with Kalman filtering, heteroskedastic Bayesian regression with full posterior sampling via an affine-invariant MCMC sampler, and a Bayesian likelihood-ratio test (LRT) coupled to a risk-sensitive proportional–derivative (PD) control law. Theoretical guarantees are provided by bounding the state covariance under stability conditions, establishing convexity of the aCI weight optimization on the simplex, and deriving a Bayes-risk-optimal decision threshold for the LRT under symmetric Gaussian likelihoods. A proof-of-concept agro-environmental decision-support application is considered, where heterogeneous data streams (IoT soil sensors, meteorological stations, and drone-derived vegetation indices) are fused to generate early-warning alarms for crop stress and to adapt irrigation and fertilization inputs. The proposed pipeline reduces predictive variance and sharpens posterior credible intervals (up to 34% narrower 95% intervals and 44% lower NLL/Brier score under heteroskedastic modeling), while a Bayesian uncertainty-aware controller achieves 14.2% lower water usage and 35.5% fewer false stress alarms compared to a rule-based strategy. The framework is mathematically grounded yet domain-independent, providing a probabilistic pipeline that propagates uncertainty from raw multimodal data to operational control actions, and can be transferred beyond agriculture to robotics, signal processing, and environmental monitoring applications.

AppliedMath doi: 10.3390/appliedmath6010015

Authors: Xiaojie Dou Jin-San Cheng Junyi Wen

This paper presents a Maple implementation of an interval verification method for identifying isolated simple zeros in square polynomial systems. Compared to the known MATLAB (R2019b) implementation, the Maple-based approach achieves significantly higher numerical accuracy. The implementation enables polynomial evaluation at specific points to yield results with very small absolute values—sufficiently precise to reach error bounds computed through theoretical formulations for moderate-sized systems. This advancement allows the deterministic certification of isolated simple zeros in over-determined polynomial systems containing approximately 10,000 complex zeros. As a practical demonstration, the method is further applied to rigorously verify isolated multiple zeros in smaller-scale polynomial systems.

AppliedMath doi: 10.3390/appliedmath6010014

Authors: Eldar Sultanow Anja Jeschke Amir Darwish Tfiha Madjid Tehrani William J. Buchanan

We investigate a special family of elliptic curves, namely Ep,q:y2=x3−pqx, where p<q are odd primes. We study sufficient conditions for p and q so that the corresponding elliptic curve has non-trivial rational points. The number of sufficient conditions reduces to six. These six sufficient conditions relate to Polignac’s conjecture, to the prime gap problem, the twin prime conjecture, and to results from Green and Sawhney and Friedlander and Iwaniec. Additionally, we analyze the structures of the sufficient conditions for p and q by their graphical visualizations of the six sufficient conditions for p,q≤6997. The graphical structures for the six sufficient conditions exhibit arc structures, quasi-linear arc segments, tile structures, and sparsely populated structures.

AppliedMath doi: 10.3390/appliedmath6010013

Authors: Alexander Robitzsch

The Rasch model has the desirable property that item parameter estimation can be separated from person parameter estimation. This implies that no assumptions about the ability distribution are required when estimating item difficulties. Pairwise estimation approaches in the Rasch model exploit this principle by estimating item difficulties solely from sample proportions of respondents who answer item i correctly and item j incorrectly. A recent contribution by Tutz introduced Tutz’s pairwise separation estimator (TPSE) for the more general class of homogeneous monotone (HM) models, extending the idea of pairwise estimation to this broader setting. The present article examines the asymptotic behavior of the TPSE within the Rasch model as a special case of the HM framework. It should be emphasized that both analytical derivations and a numerical illustration show that the TPSE yields asymptotically biased item parameter estimates, rendering the estimator inconsistent, even for a large number of items. Consequently, the TPSE cannot be recommended for empirical applications.

AppliedMath doi: 10.3390/appliedmath6010012

Authors: Oussama Boufares Mohamed Boussif Noureddine Aloui

In this paper, we present a novel method for background estimation and updating in video sequences, utilizing an innovative approach that combines an intelligent truncated mean, the stationary wavelet transform (SWT), and advanced thresholding techniques. This method aims to significantly enhance the accuracy of moving object detection by mitigating the impact of outliers and adapting background estimation to dynamic scene conditions. The proposed approach begins with a robust initial background estimation, followed by moving object detection through frame subtraction and gamma correction. Segmentation is then performed using SWT, coupled with adaptive thresholding methods, including hard and soft thresholding. These techniques work in tandem to effectively reduce noise while preserving critical details. Finally, the background is selectively updated to integrate new information from static regions while excluding moving objects, ensuring a precise and robust detection system. Experimental evaluation on the CDnet 2014 and SBI 2015 datasets demonstrates that the proposed method improves the F1 score by 12.5 percentage points (from 0.7511 to 0.8765), reduces false positives by up to 65%, and achieves higher PSNR values compared to GMM_Zivk, SuBSENSE, and SC_SOBS. These results confirm the robustness of the hybrid approach based on truncated mean and SWT in dynamic and challenging environments.

AppliedMath doi: 10.3390/appliedmath6010011

Authors: Wullianallur Raghupathi Jie Ren Tanush Kulkarni

As artificial intelligence systems proliferate across critical societal domains, understanding the nature, patterns, and evolution of AI-related harms has become essential for effective governance. Despite growing incident repositories, systematic computational analysis of AI incident discourse remains limited, with prior research constrained by small samples, single-method approaches, and absence of temporal analysis spanning major capability advances. This study addresses these gaps through a comprehensive multi-method text analysis of 3494 AI incident records from the OECD AI Policy Observatory, spanning January 2014 through October 2024. Six complementary analytical approaches were applied: Latent Dirichlet Allocation (LDA) and Non-negative Matrix Factorization (NMF) topic modeling to discover thematic structures; K-Means and BERTopic clustering for pattern identification; VADER sentiment analysis for emotional framing assessment; and LIWC psycholinguistic profiling for cognitive and communicative dimension analysis. Cross-method comparison quantified categorization robustness across all four clustering and topic modeling approaches. Key findings reveal dramatic temporal shifts and systematic risk patterns. Incident reporting increased 4.6-fold following ChatGPT’s (5.2) November 2022 release (from 12.0 to 95.9 monthly incidents), accompanied by vocabulary transformation from embodied AI terminology (facial recognition, autonomous vehicles) toward generative AI discourse (ChatGPT, hallucination, jailbreak). Six robust thematic categories emerged consistently across methods: autonomous vehicles (84–89% cross-method alignment), facial recognition (66–68%), deepfakes, ChatGPT/generative AI, social media platforms, and algorithmic bias. Risk concentration is pronounced: 49.7% of incidents fall within two harm categories (system safety 29.1%, physical harms 20.6%); private sector actors account for 70.3%; and 48% occur in the United States. Sentiment analysis reveals physical safety incidents receive notably negative framing (autonomous vehicles: −0.077; child safety: −0.326), while policy and generative AI coverage trend positive (+0.586 to +0.633). These findings have direct governance implications. The thematic concentration supports sector-specific regulatory frameworks—mandatory audit trails for hiring algorithms, simulation testing for autonomous vehicles, transparency requirements for recommender systems, accuracy standards for facial recognition, and output labeling for generative AI. Cross-method validation demonstrates which incident categories are robust enough for standardized regulatory classification versus those requiring context-dependent treatment. The rapid emergence of generative AI incidents underscores the need for governance mechanisms responsive to capability advances within months rather than years.

AppliedMath doi: 10.3390/appliedmath6010010

Authors: Huiying Wang Chengwei Yu Jiahuan Wang

Forest fires pose escalating threats to ecological security and public safety in Guangdong Province. This study presents a novel machine learning framework for fire occurrence prediction by synergistically integrating multi-source geospatial data. Utilizing Moderate-resolution Imaging Spectroradiometer (MODIS) active fire detections from 2014 to 2023, we quantified historical fire patterns and incorporated four categories of predisposing factors: meteorological variables, topographic attributes, vegetation characteristics, and anthropogenic activities. Spatiotemporal clustering dynamics were characterized via kernel density estimation and spatial autocorrelation analysis. An XGBoost classifier, hyperparameter-optimized through the Sparrow Search Algorithm (SSA), achieved a predictive accuracy of 90.4%, with performance evaluated through precision, recall, and F1-score. Risk zoning maps generated from predicted probabilities were validated against independent fire records from 2019 to 2024. Results reveal pronounced spatial heterogeneity, with high-risk zones concentrated in northern and western mountainous areas, constituting 29% of the provincial territory. Critical driving factors include slope gradient, proximity to roads and rivers, temperature, population density, and elevation. This robust predictive framework furnishes a scientific foundation for spatially-explicit fire prevention strategies and optimized resource allocation in key high-risk jurisdictions, notably Qingyuan, Shaoguan, Zhanjiang, and Zhaoqing.

AppliedMath doi: 10.3390/appliedmath6010009

Authors: Dragana Cvetković Ernest Šanca

It is well known that the position of the Jacobian matrix spectrum in the left-half complex plane provides the local asymptotic stability of a nonlinear dynamical system, but it is also well known that for large matrices, computing its eigenvalues just to see their position is computationally prohibitive. Instead, it is recommended to check if a given matrix belongs to the H-matrix class and has negative diagonal entries. Since confirming the H-matrix property is computationally costly, the preference is to work with its subclasses, which are defined by simpler conditions. In this paper, we develop and investigate a new subclass of H-matrices via the Frobenius matrix norm, which generalizes the recently introduced classes. We support its significance with real-life examples and clarify its relationship to some well-known block H-matrices based on the Euclidean matrix norm. The main novelty in this paper is that when a fast and inexpensive answer about the stability of a dynamical system is required, and the system matrix has a natural block structure, we develop a simple tool to check whether this structure, along with the additional condition of negative diagonal elements, ensures stability. This is especially important when the matrix does not belong to any previously known H-matrix subclasses.

AppliedMath doi: 10.3390/appliedmath6010008

Authors: David de Oliveira Costa Cleyton Mário de Oliveira Rodrigues Ana Claudia Souza Carlo Marcelo Revoredo da Silva Andrei Bonamigo Miguel Ângelo Lellis Moreira Marcos dos Santos Carlos Francisco Simões Gomes Daniel Augusto de Moura Pereira

This study proposes a structured multicriteria approach to assist professionals in the selection of appropriate computing platforms for children diagnosed with Autism Spectrum Disorder, particularly those between 4 and 6 years of age. Recognizing the learning limitations and reduced attention span typical of this group, the study addresses a gap in the current selection process, which is often based on professional experience rather than objective and measurable criteria. A Systematic Literature Review (SLR), protocol analysis, and problem-structuring methods identified essential evaluation criteria that incorporated key dimensions of development and behavior. These include personalization and adaptation, interactivity and engagement, monitoring and feedback, communication and language, cognitive and social development, usability and accessibility, and security and privacy. Based on these dimensions, a multicriteria method was applied to rank the alternatives represented by the technologies in question. The proposed framework enables a rigorous and axiomatic comparison of platforms based on structured criteria aligned with established intervention protocols, such as ABA, DIR/Floortime, JASPER, and SCERTS. The results validate the model’s effectiveness in highlighting the most appropriate technological tools for this audience. Although the scope is limited to children aged 4 to 6 years, the proposed methodology can be adapted for use with broader age groups. This work contributes to inclusive education by providing a replicable, justifiable framework for selecting digital learning tools that may influence clinical recommendations and family engagement.

AppliedMath doi: 10.3390/appliedmath6010007

Authors: Francisco J. Esteban Eva Vargas

Fractal geometry offers a mathematical framework to quantify the complexity of brain structure and function. The fractal dimension (FD) captures self-similarity and irregularity across spatial and temporal scales, surpassing the limits of traditional Euclidean metrics. In neuroscience, FD serves as a key descriptor of the brain’s hierarchical organization—from dendritic arborization and cortical folding to neural dynamics measured by diverse neuroimaging techniques. This review summarizes theoretical foundations and methodological advances in FD estimation, including the box-counting approach for imaging, and Higuchi’s and Katz’s algorithms for electrophysiological data, addressing reliability and reproducibility issues. In addition, we illustrate how fractal analysis characterizes brain complexity in health and disease. Clinical applications include detecting white matter alterations in multiple sclerosis, atypical maturation in intrauterine growth restriction, reduced cortical complexity in Alzheimer’s disease, and altered neuroimaging patterns in schizophrenia. Emerging evidence highlights FD’s potential for distinguishing consciousness states and quantifying neural integration and differentiation. Bridging mathematics, physics, and neuroscience, fractal analysis provides a quantitative lens on the brain’s multiscale organization and pathological deviations. FD thus stands as both a theoretical descriptor and a translational biomarker whose standardization could advance precision diagnostics and understanding of neural dynamics.

AppliedMath doi: 10.3390/appliedmath6010006

Authors: Teng Long Leyu Wang Cing-Dao Kan James D. Lee

Effective identification of strain-hardening parameters is essential for predictive plasticity models used in automotive applications. However, the performance of Bayesian optimization depends strongly on kernel hyperparameters in the Gaussian-process surrogate, which are often kept fixed. In this work, we propose a likelihood-based online hyperparameter strategy within Bayesian optimization to identify strain-hardening parameters in plasticity. Specifically, we used the rational polynomial strain-hardening scheme for the plasticity model to fit the force vs. displacement response of automotive structural steel in tension. An in-house Bayesian optimization framework was first developed, and an online hyperparameter tuning algorithm was further incorporated to advance the optimization scheme. The optimization histories obtained from the fixed and online-tuning hyperparameters were compared. For the same number of iterations, the online hyperparameter adaptation reduced the final residual by approximately 20.4%, 24.0%, and 3.8% for Specimens 1–3, respectively. These results demonstrate that the proposed strategy can significantly improve the efficiency and quality of strain-hardening parameter identification. The results show that the online tuning scheme improved the optimization efficiency. This proposed strategy may be readily extensible to other materials and identification problems where enhancing optimization efficiency is needed.

AppliedMath doi: 10.3390/appliedmath6010005

Authors: Muhammad Zakria Javed Muhammad Uzair Awan Dafang Zhao Awais Gul Khan Lorentz Jäntschi

The main goal of this study is to explain the idea of generalized interval-valued (I.V) convexity on a fractal set. We first define the basic operations for a generalized interval of Rs with 0<s≤1. Then, we expand the idea of (I.V) Riemann integration to (I.V) local fractal integration, which sets the stage for further research. This is followed by the proof of new Jensen, Hermite, Hadamard, Pachpatte, and Fejer inequalities that are (I.V) and have to do with the generalized class of (I.V) convexity defined over the fractal domain. We furnish validation through visual and comparative approaches. Our outcomes are the refinement of many existing results, indicating that they are fruitful. In fractal settings, this is the first paper to work on (I.V) convexity and some set-valued versions of Hermite–Hadamard-type containments.

AppliedMath doi: 10.3390/appliedmath6010004

Authors: Neveen Ali Eshtewy Shahid Zaman Shumaila Noreen

Machine learning (ML) is a powerful tool in drug design, enabling the rapid analysis of large and complex molecular graphs that represent the structural and chemical properties of medications. It enhances the precision and speed with which molecular interactions are predicted, drug candidates are refined, and potential therapeutic targets are identified. When combined with graph theory, ML allows for the prediction of structural properties, molecular behaviour, and the performance of chemical compounds. This integration promotes drug development, reduces costs, and increases the likelihood of producing effective medicines. In this study, we focus on the efficacy of medications used in the treatment of coronary artery disease (CAD) using graph-theoretical methodologies, such as topological indices. We computed several degree-based topological descriptors from chemical graphs, capturing essential connectivity and structural properties. These variables were incorporated into a machine learning framework to develop predictive models that identify structural factors influencing medication performance. Our study explores a dataset of known CAD drugs using supervised learning techniques to estimate their potential efficacy and support improved molecular design. The findings highlight the utility of graph-theoretical descriptors in enhancing prediction accuracy and providing insights into fundamental structural elements related to drug efficacy. Furthermore, this work emphasises the synergy between chemical graph theory and machine learning in accelerating drug development for CAD, offering a scalable and interpretable framework for future pharmaceutical applications.

AppliedMath doi: 10.3390/appliedmath6010003

Authors: Thomas E. Woolley

Turing patterns, characterised by spatial self-organisation in reaction–diffusion systems, exhibit sensitivity to initial conditions. This sensitivity, known as the robustness problem, results in different final patterns emerging even from small initial perturbations. In this paper, we introduce a mechanism of pattern mode isolation, where we investigate parameter regimes that promote the isolation of bifurcation branches, thereby delineating the conditions under which distinct pattern modes emerge and evolve independently. Pattern mode isolation can provide a means of enhancing the predictability of Turing pattern mode transitions and enhance the robustness and reproducibility of the patterning outputs.

AppliedMath doi: 10.3390/appliedmath6010002

Authors: Chunhua Feng

In this paper, an economic competition–cooperation model is examined, which has one core enterprise and four satellite enterprises. This extends previous smaller models in the literature mathematically. The unique positive solution to the original solution after a change of variables corresponds to a trivial equilibrium of a linearized system. The instability of this linearized solution implies the instability of the positive solution to the original system. The instability of the positive solution and boundedness will force this system to have a periodic solution. Some sufficient conditions to guarantee the periodic oscillation of the solutions for this model are provided, and computer simulations are given to support the present criteria.

AppliedMath doi: 10.3390/appliedmath6010001

Authors: Sanja Atanasova Slavica Gajić Smiljana Jakšić Snježana Maksimović

Fractional transforms have emerged as powerful analytical tools that bridge the time, frequency, and scale domains by introducing a fractional-order parameter into the kernel of classical transforms. This survey provides an overview of the mathematical foundations and distributional frameworks of several key fractional transforms, with emphasis on their formulation within appropriate spaces of generalized functions. Particular attention is devoted to the quasiasymptotic behavior of distributions in relation to the asymptotic properties of their corresponding fractional transforms. We demonstrate how individual transforms map illustrative signals into their corresponding domains and identify the values of the parameter α for which they produce the best results.

AppliedMath doi: 10.3390/appliedmath5040182

Authors: Abdramane Saad Mahamat Daoussa Haggar

This article presents a deterministic model describing the joint dynamics of canine and human rabies in a cross-border context. This model explicitly integrates dog mobility between two neighboring countries and allows us to assess the impact of these movements on disease persistence. We analyze the basic reproduction number R0, study the local and global stability of equilibrium points, identify the most influential parameters through sensitivity analysis, and perform numerical simulations to test the effectiveness of different vaccination and movement control strategies.

AppliedMath doi: 10.3390/appliedmath5040181

Authors: Kapya Tshinangi Olufemi Adetunji Sarma Yadavalli

Inventory models have evolved to incorporate a wide range of realistic factors, including growing items, imperfect quality, deterioration, and sustainability concerns. While these areas have received significant individual attention, no model has yet integrated the complexities of growing items, imperfect quality, deterioration, and carbon emissions. This study addresses this gap by introducing an economic order quantity (EOQ) model for growing items that simultaneously accounts for imperfect quality, deterioration, carbon emissions, and a demand rate that is influenced by both stock levels and the freshness condition. The goal is to determine the replenishment cycle and the optimal order quantity that will maximise profit. A numerical example is presented to illustrate the model’s feasibility. A sensitivity analysis on key parameters is also conducted to provide critical managerial insights. The results reveal that the shelf life of items and the scaling parameter of demand are among the most influential factors of profit, causing up to 150% and 112% increase in profit, respectively. The findings also indicate that deterioration significantly impacts system profitability by up to −45%. Another critical insight is that profit decreases by up to 80% when the weight of the growing items increases. Furthermore, emissions can be most effectively reduced by focusing on the feeding process, which represents the most impactful factor for improving sustainability, whereas emissions from the screening process, purchasing, deterioration, and storage hold minimal financial consequence.

AppliedMath doi: 10.3390/appliedmath5040180

Authors: Mapule Pheko Sicelo P. Goqo Salma Ahmedai Letlhogonolo Moleleki

This paper investigates the flow of a second-grade hybrid nanofluid through a Darcy–Forchheimer porous medium under Cattaneo–Christov heat and mass flux models. The hybrid nanofluid, composed of alumina and copper nanoparticles in water, enhances thermal and mass transport, while the second-grade model captures viscoelastic effects, and the Darcy–Forchheimer medium accounts for both linear and nonlinear drag. Using similarity transformations and the spectral quasilinearisation method, the nonlinear governing equations are solved numerically and validated against benchmark results. The results show that hybrid nanoparticles significantly boost heat and mass transfer, while Cattaneo–Christov fluxes delay thermal and concentration responses, reducing the near-wall temperature and concentration. The distributions of velocity, temperature, concentration, and microorganism density are markedly affected by porosity, the Forchheimer number, the bio-convection Peclet number, and relaxation times. The results illustrate that hybrid nanoparticles significantly increase heat and mass transfer, whereas thermal and concentration relaxation factors delay energy and species diffusion, thickening the associated boundary layers. Viscoelasticity, porous medium resistance, Forchheimer drag, and bio-convection all have an influence on flow velocity and transfer rates, highlighting the subtle link between these mechanisms. These breakthroughs may be beneficial in establishing and enhancing bioreactors, microbial fuel cells, geothermal systems, and other applications that need hybrid nanofluids and non-Fourier/non-Fickian transport.

AppliedMath doi: 10.3390/appliedmath5040179

Authors: Edney Dias Batista André Cristiano Silva Melo Manoel Tavares de Paula Seidel Ferreira dos Santos Altem Nascimento Pontes Flávia Cristina Araújo Lucas Vitor William Batista Martins

This study aimed to identify and validate the main challenges to be overcome for the promotion of sustainability in the Brazilian from the perspective of mining professionals. The research strategies employed were a systematic review of the literature and a survey. The data collected was processed using Lawshe’s quantitative method. The questionnaire was answered by 53 experts, and 8 of the 11 challenges identified in the literature were validated. The results highlight insufficient water resource management, a lack of technology, difficulties in implementing Corporate Social Responsibility (CSR) practices, and misalignment with the Sustainable Development Goals (SDGs). Global challenges, such as emissions control and renewable energy integration, were not validated, indicating a possible disconnect between international priorities and local realities. Therefore, the findings reinforce the need for robust public policies, technological innovation, and participatory governance, adapted to the Brazilian context. The study contributes to literature by incorporating the views of industry professionals, providing input for corporate and regulatory strategies.

AppliedMath doi: 10.3390/appliedmath5040178

Authors: Pasquale De Luca Giuseppe Fiorillo Livia Marcellino

Tumor angiogenesis models based on coupled nonlinear parabolic partial differential equations require solving stiff systems where explicit time-stepping methods impose severe stability constraints on the time step size. Implicit–Explicit (IMEX) schemes relax this constraint by treating diffusion terms implicitly and reaction–chemotaxis terms explicitly, reducing each time step to a single linear system solution. However, standard Gaussian elimination with partial pivoting exhibits cubic complexity in the number of spatial grid points, dominating computational cost for realistic discretizations in the range of 400–800 grid points. This work presents a CUDA-based parallel algorithm that accelerates the IMEX scheme through GPU implementation of three core computational kernels: pivot finding via atomic operations on double-precision floating-point values, row swapping with coalesced memory access patterns, and elimination updates using optimized two-dimensional thread grids. Performance measurements on an NVIDIA H100 GPU demonstrate speedup factors, achieving speedup factors from 3.5× to 113× across spatial discretizations spanning M∈[25,800] grid points relative to sequential CPU execution, approaching 94.2% of the theoretical maximum speedup predicted by Amdahl’s law. Numerical validation confirms that GPU and CPU solutions agree to within twelve digits of precision over extended time integration, with conservation properties preserved to machine precision. Performance analysis reveals that the elimination kernel accounts for nearly 90% of total execution time, justifying the focus on GPU parallelization of this component. The method enables parameter studies requiring ∼104 PDE solves, previously computationally prohibitive, facilitating model-driven investigation of anti-angiogenic therapy design.

AppliedMath doi: 10.3390/appliedmath5040177

Authors: Tassaddaq Hussain Mohammad Shakil Mohammad Ahsanullah

A novel statistical model, the Bounded Gamma–Gompertz Distribution (BGGD), is presented alongside a full characterization of its properties. Our investigation identifies maximum-likelihood estimation (MLE) as the most effective fitting procedure, proving it to be more consistent and efficient than alternative approaches like L-moments and Bayesian estimation. Empirical validation on Tesla (TSLA) financial records—spanning open, high, low, close prices, and trading volume—showcased the BGGD’s superior performance. It delivered a better fit than several competing heavy-tailed distributions, including Student-t, Log-Normal, Lévy, and Pareto, as indicated by minimized AIC and BIC statistics. The results substantiate the distribution’s robustness in capturing extreme-value behavior, positioning it as a potent tool for financial modeling applications.

AppliedMath doi: 10.3390/appliedmath5040176

Authors: Sebastian Thomas Lynch Parisa Derakhshan Stephen Lynch

Forecasting stock prices remains a central challenge in financial modelling, as markets are influenced by market sentiment, firm-level fundamentals and complex interactions between macroeconomic and microeconomic factors, for example. This study evaluates the predictive performance of both classical statistical models and advanced attention-based deep learning architectures for daily stock price forecasting. Using a dataset of major U.S. equities and Exchange Traded Funds (ETFs) covering 2012–2024, we compare traditional statistical approaches, Seasonal Autoregressive Integrated Moving Average (SARIMA) and Exponential Smoothing (ES) in the Error, Trend, Seasonal (ETS) framework, with deep learning architectures such as the Temporal Fusion Transformer (TFT), and a novel hybrid model, the TFT-Graph Neural Network (TFT-GNN), which incorporates relational information between assets. All models are assessed under consistent experimental conditions in terms of forecast accuracy, computational efficiency, and interpretability. Our results indicate that while statistical models offer strong baselines with high stability and low computational cost, the TFT outperforms them in capturing short-term nonlinear dependencies. The hybrid TFT-GNN achieves the highest overall predictive accuracy, demonstrating that relational signals derived from inter-asset connections provide meaningful enhancements beyond traditional temporal and technical indicators. These findings highlight the advantages of integrating relational learning into temporal forecasting frameworks and emphasise the continued relevance of statistical models as interpretable and efficient benchmarks for evaluating deep learning approaches in high-frequency financial prediction.

AppliedMath doi: 10.3390/appliedmath5040175

Authors: Ibrahim Elmojtaba Mariam Al-Moqbali Nasser Al-Salti

In this paper, we incorporate a new type of fear effect into a predator–prey time-delay model to study their combined impact on the system’s dynamics. Without time delay, our results show that the prey-only and coexistence equilibrium points are globally asymptotically stable under certain conditions. We also find that a transcritical bifurcation occurs near the prey-only equilibrium, while a Hopf bifurcation arises near the coexistence equilibrium. The fear effect plays a crucial role in the system’s behavior, as it can lead to predator extinction or near-extinction of the prey. Moreover, the inclusion of time delay influences the coexistence equilibrium, potentially destabilizing it and giving rise to a stable limit cycle.

AppliedMath doi: 10.3390/appliedmath5040174

Authors: Venkata S. S. Yadavalli Kapya Tshinangi Olufemi Adetunji

This paper considers a continuous review inventory system for two interconnected product types, 1 and 2. Product type 1 is purchased from an external agency, whereas type 2 is manufactured in-house through a sequential batching process. The maximum stock position attainable by type 1 is S1 and that of type 2 is S2. Unit demands arise independently for the two products, where type 1 demand arrives following a Poisson process with rate λ1 and that for product B also follows a Poisson process with rate λ2. At the instance of the stock level of type 1 dropping to zero, it is replenished instantaneously to the maximum level S1, such that the stock level is never zero, and hence all demands for type 1 product are satisfied. The production machine attached to type 2 stops manufacturing immediately when its stock level reaches S2, and resumes immediately when the stock level drops to S2−1. In the event of the type 2 product not being available when demand arrives, it is substituted with the type 1 product with probability p. The production time for a single unit of type 2 is exponentially distributed with mean 1γ. We identify the underlying Markov process and analyse the performance of the interconnected inventory system.

AppliedMath doi: 10.3390/appliedmath5040173

Authors: Shi-Dong Liang

Based on noncommutative relations and the Dirac canonical dequantization scheme, I generalize the canonical Poisson bracket to a deformed Poisson bracket and develop a non-canonical formulation of the Poisson, Hamilton, and Lagrange equations in the deformed Poisson and symplectic spaces. I find that both of these dynamical equations are the coupling systems of differential equations. The noncommutivity induces the velocity-dependent potential. These formulations give the Noether and Virial theorems in the deformed symplectic space. I find that the Lagrangian invariance and its corresponding conserved quantity depend on the deformed parameters and some points in the configuration space for a continuous infinitesimal coordinate transformation. These formulations provide a non-canonical framework of classical mechanics not only for insight into noncommutative quantum mechanics, but also for exploring some mysteries and phenomena beyond those in the canonical symplectic space.

AppliedMath doi: 10.3390/appliedmath5040172

Authors: Galya Georgieva-Tsaneva

Background: Realistic simulation of ECG signals is essential for validating signal-processing algorithms and training artificial intelligence models in cardiology. Many existing approaches model either waveform morphology or heart rate variability (HRV), but few achieve both with high accuracy. This study proposes a hybrid method that combines morphological accuracy with physiological variability. Methods: We developed a mathematical model that integrates Gaussian mesa functions (GMF) for waveform generation and a chaotic Rössler attractor to simulate RR-interval variability. The GMF approach allows fine control over the amplitude, width, and slope of each ECG component (P, Q, R, S, T), while the Rössler system introduces dynamic modulation through the use of seven parameters. Spectral and statistical analyses were applied, including power spectral density (PSD) computed via the Lomb–Scargle, STFT, CWT, and histogram analyses. Results: The synthesized signals demonstrated physiological realism in both the time and frequency domains. The LF/HF ratio was 1.5–2.0 when simulating a normal rhythm and outside these limits in a simulated stress rhythm, consistent with typical HRV patterns. PSD analysis captured clear VLF (0.003–0.04 Hz), LF (0.04–0.15 Hz), and HF (0.15–0.4 Hz) bands. Histogram distributions showed amplitude ranges consistent with real ECGs. Conclusions: The hybrid GMF–Rössler approach enables large-scale ECG synthesis with controllable morphology and realistic HRV. It is computationally efficient and suitable for artificial intelligence training, diagnostic testing, and digital twin modeling in cardiovascular applications.

AppliedMath doi: 10.3390/appliedmath5040171

Authors: Fahad Mostafa Kannon Hossain Dip Das Hafiz Khan

Early and accurate diagnosis of Alzheimer’s disease is critical for effective clinical intervention, particularly in distinguishing it from mild cognitive impairment, a prodromal stage marked by subtle structural changes. In this study, we propose a hybrid deep learning ensemble framework for Alzheimer’s disease classification using structural magnetic resonance imaging. Gray and white matter slices are used as inputs to three pretrained convolutional neural networks: ResNet50, NASNet, and MobileNet, each fine-tuned through an end-to-end process. To further enhance performance, we incorporate a stacked ensemble learning strategy with a meta-learner and weighted averaging to optimally combine the base models. Evaluated on the Alzheimer’s Disease Neuroimaging Initiative dataset, the proposed method achieves state-of-the-art accuracy of 99.21% for Alzheimer’s disease vs. mild cognitive impairment and 91.02% for mild cognitive impairment vs. normal controls, outperforming conventional transfer learning and baseline ensemble methods. To improve interpretability in image-based diagnostics, we integrate Explainable AI techniques by Gradient-weighted Class Activation Mapping, which generates heatmaps and attribution maps that highlight critical regions in gray and white matter slices, revealing structural biomarkers that influence model decisions. These results highlight the framework’s potential for robust and scalable clinical decision support in neurodegenerative disease diagnostics.

AppliedMath doi: 10.3390/appliedmath5040170

Authors: Cristian Staii

Neuronal circuits arise as axons and dendrites extend, navigate, and connect to target cells. Axonal growth, in particular, integrates deterministic guidance from substrate mechanics and geometry with stochastic fluctuations generated by signaling, molecular detection, cytoskeletal assembly, and growth cone dynamics. A comprehensive quantitative description of this process remains incomplete. We review stochastic models in which Langevin dynamics and the associated Fokker–Planck equation capture axonal motion and turning under combined biases and noise. Paired with experiments, these models yield key parameters, including effective diffusion (motility) coefficients, speed and angle distributions, mean-square displacement, and mechanical measures of cell–substrate coupling, thereby linking single-cell biophysics and intercellular interactions to collective growth statistics and network formation. We further couple the Fokker–Planck description to a mechanochemical actin–myosin–clutch model and perform a linear stability analysis of the resulting dynamics. Routh–Hurwitz criteria identify regimes of steady extension, damped oscillations, and Hopf bifurcations that generate sustained limit cycles. Together, these results clarify the mechanisms that govern axonal guidance and connectivity and inform the design of engineered substrates and neuroprosthetic scaffolds aimed at enhancing nerve repair and regeneration.

AppliedMath doi: 10.3390/appliedmath5040169

Authors: John D. Clayton

Material failure by adiabatic shear is analyzed in viscoplastic metals that can demonstrate up to three distinct softening mechanisms: thermal softening, ductile fracture, and melting. An analytical framework is constructed for studying simple shear deformation with superposed static pressure. A continuum power-law viscoplastic formulation is coupled to a ductile damage model and a solid–liquid phase transition model in a thermodynamically consistent manner. Criteria for localization to a band of infinite shear strain are discussed. An analytical–numerical method for determining the critical average shear strain for localization and commensurate stress decay is devised. Averaged results for a high-strength steel agree reasonably well with experimental dynamic torsion data. Calculations probe possible effects of ductile fracture and melting on shear banding, and vice versa, including influences of cohesive energy, equilibrium melting temperature, and initial defects. A threshold energy density for localization onset is positively correlated to critical strain and inversely correlated to initial defect severity. Tensile pressure accelerates damage softening and increases defect sensitivity, promoting shear failure. In the present steel, melting is precluded by ductile fracture for loading conditions and material properties within realistic protocols. For this steel, if conduction, fracture, and damage softening are artificially suppressed, melting is confined to a narrow region in the core of the band. However, for other metals with vastly different physical properties, or for more diverse loading conditions, melting has not been unequivocally ruled out, even if fracture and conduction are permitted.

AppliedMath doi: 10.3390/appliedmath5040168

Authors: Muhammad Amer Latif

This study introduces and analyzes several new functionals defined on the interval [0,1], which are associated with weighted integral inequalities for geometrically–arithmetically (GA) convex functions. Building upon the classical Hermite–Hadamard and Fejér inequalities, we define mappings such as G(u), Hyu, Kyu, Nu, L(u), Ly(u), and Syu, which incorporate a GA-convex function x and a non-negative, integrable weight function y that is symmetric about the geometric mean s1s2. Under these conditions, we establish novel Fejér-type inequalities that connect these functionals. Furthermore, we investigate essential properties of these mappings, including their GA-convexity, monotonicity, and symmetry. The validity of our main results is demonstrated through detailed examples. The findings presented herein provide significant refinements and weighted generalizations of known results in the literature.

AppliedMath doi: 10.3390/appliedmath5040167

Authors: Aynur Ali Miroslav Hristov Atanas Ilchev Diana Nedelcheva Boyan Zlatanov

We establish a modular-space framework for the study of tripled fixed points and tripled best proximity points. Under suitable assumptions on the underlying modular (convexity, the Δ2 property, uniform continuity, and uniform convexity-type properties), we prove that Banach theorems guarantee the existence, uniqueness, and convergence of modular iterative schemes. In particular, we develop results for cyclic ρ–Kannan contraction maps and pairs, showing that both tripled fixed points and tripled best proximity points arise uniquely and attract all iterative trajectories. An illustrative example in the space L2[0,1] with integral operators demonstrates the applicability of the theory and the predicted rate of convergence. These results extend classical fixed point methods to a broader modular setting and open the way for applications in nonlinear functional equations.

AppliedMath doi: 10.3390/appliedmath5040166

Authors: Hossein Hassani Leila Marvian Mashhad Sara Stewart Steve MacFeely

Geospatial–statistical integration remains a persistent bottleneck for official statistics and applied spatial analysis. The GISINTEGRATION R package provides a modular, reproducible workflow for preprocessing, harmonizing, and linking heterogeneous GIS and non-GIS datasets, with export utilities that are compatible with common desktop GIS. This paper outlines the package architecture and demonstrates its use in two applications. The first integrates population statistics with newly introduced statistical output geographies for Northern Ireland, enabling rapid preparation of analysis-ready layers such as all usual residents and population density at Super Data Zones. The second links daily PM2.5 measurements from the U.S. EPA Air Quality System with county boundaries for California (July 2020) to produce policy-relevant indicators; spatial aggregation yielded valid monthly means for 46 of 58 counties (79.31%) and reduced variance from 40.716 (monitor level) to 5.777 (county means), improving signal stability and comparability. Across both cases, the workflow standardizes variable names, supports user-controlled overrides, identifies common keys, and performs quality checks, thereby reducing manual effort while increasing transparency and reproducibility. The results illustrate how standardized integration facilitates official statistical production, environmental monitoring, and evidence-based decision-making.

AppliedMath doi: 10.3390/appliedmath5040165

Authors: Saeed Mirzajani Gholam Hosein Askarirobati Majid Roohi

The design of a control system becomes more complex with the advancement of technology, and this requires optimization techniques to be developed. In particular, multi-objective optimal control (MOC) is a method that can be used to achieve a scheme for control system that coordinates several design objectives that can be in conflict with each other. In this study, a new hybrid scheme is presented that is a combination of non-dominated sorting genetic algorithm-II (NSGA-II) and the simple cell mapping (SCM) method. The combined method first starts a random search using the genetic algorithm and then proceeds by using the SCM method for a neighborhood-based search and recovery algorithm. An evaluation of the proposed method’s efficiency and performance was conducted on two benchmark problems and two multi-objective optimal control problems. We utilized two performance indicators (generational distance (GD) and a diversity metric) to assess the convergence to the Pareto front and the diversity of the solution set, respectively. The results demonstrated that the proposed method not only achieved superior efficiency but also produced a more uniform distribution of solutions along the Pareto front compared to the SCM and NSGA-II algorithms.

AppliedMath doi: 10.3390/appliedmath5040164

Authors: Malicki Zorom Mansourou Cisse Maïmouna Bologo (Traore) Sina Thiam Harouna Karambiri

Fisheries worldwide exhibit puzzling boom-and-bust cycles despite regulatory efforts, raising questions about what drives these oscillations. We investigate whether temporal delays in monitoring and decision-making contribute to system instability. Our model uses delay differential equations to track an exploiting population and its renewable resources, incorporating two distinct delays: one for perceiving resource status (τ2) and another for implementing management responses (τ1). We establish the existence, uniqueness, and positivity of solutions, then analyze equilibrium stability through linearization and Lyapunov–Razumikhin functions. The characteristic equation reveals Hopf bifurcations at critical delay thresholds. Numerical simulations across 1600 parameter combinations using MATLAB R2023b’s DDE23 algorithm quantify these transitions. The results show a critical threshold near 1.64 years (20 months): below this value, systems converge to a stable equilibrium, while above it, persistent oscillations emerge within 20–26 year periods. Unexpectedly, one large delay destabilizes less than two moderate delays summing to the same total, contradicting uniform improvement strategies. Convergence to limit cycles requires roughly 40 years, exceeding typical management horizons and potentially masking true system dynamics. The critical threshold lies within realistic administrative timescales, suggesting that institutional delays may substantially contribute to observed population fluctuations. These findings indicate that accelerating either monitoring or decision processes rather than providing modest improvements to both could better stabilize exploited resources.

AppliedMath doi: 10.3390/appliedmath5040163

Authors: Handika Lintang Saputra Moch. Fandi Ansori

This study proposes an SVEIR with a reinfection model of tuberculosis disease spread to examine the impact of saturated infection and imperfect vaccination. Vaccinated individuals are considered vulnerable, as they are still likely to be reinfected. As the recovered individuals still have bacteria in their bodies, they are likely to return to their latent class. The dynamic behavior of the proposed model was analyzed to understand both the local and global stability equilibrium points. To analyze the disease-free and endemic equilibrium stability, the Routh–Hurwitz Criterion and Center Manifold theorems were used, respectively. The local and global stability equilibrium state is entirely dependent on the effective reproduction number. If the effective reproduction number is less than one, the disease-free equilibrium point is locally and globally asymptotically stable, whereas if it is greater than one, the endemic equilibrium point is locally asymptotically stable. Numerical simulations show the time series of the solution of the model, phase-plane trajectory, elasticity indices, bifurcation diagram, partial rank correlation coefficients, and the sensitivity of the infected class to variations in the transmission rate represented both in the peak value and a heatmap. Furthermore, the contour plot illustrates that the disease transmission rate affects the effective reproduction number and the stability of equilibrium points.

AppliedMath doi: 10.3390/appliedmath5040162

Authors: Carlo Bianca Luca Guerrini Stefania Ragni

The stability of energy demand–supply systems is often affected by delayed feedback caused by regulatory inertia, communication lags, and heterogeneous agent responses. Conventional models typically assume discrete delays, which may oversimplify real dynamics and reduce controller effectiveness. This work addresses this limitation by introducing a novel class of nonlinear energy models with distributed delay feedback governed by gamma-distributed memory kernels. Specifically, we consider both weak (exponential) and strong (Erlang-type) kernels to capture a spectrum of memory effects. Using the linear chain trick, we reformulate the resulting integro-differential model into a higher-dimensional system of ordinary differential equations. Analytical conditions for local asymptotic stability and Hopf bifurcation are derived, complemented by Lyapunov-based global stability criteria. The related numerical analysis confirms the theoretical findings and reveals a distinct stabilization regime. Compared to fixed-delay approaches, the proposed framework offers improved flexibility and robustness, with implications for delay-aware energy control and infrastructure design.

AppliedMath doi: 10.3390/appliedmath5040161

Authors: M. S. Abu Zaytoon Hannah Al Ali M. H. Hamdan

In this study, we consider and analyze an inhomogeneous Whittaker-type differential equation of the form d2y(x)dx2+1xdy(x)dx−α2x2−β2y(x)=g(x), where α and β are given parameters. We investigate the analytical structure of its solution through the application of the Whittaker integral representation. The analysis encompasses both initial value problems (IVPs) and boundary value problems (BVPs), wherein appropriate conditions are imposed within a unified analytical framework. Furthermore, a systematic methodology is developed for constructing explicit solutions within the framework of Whittaker function theory. This approach not only elucidates the functional behaviour of the solutions but also provides a foundation for extending the analysis to more general classes of second-order linear differential equations.

AppliedMath doi: 10.3390/appliedmath5040160

Authors: Sree Pradip Kumer Sarker Md. Mahmud Alam

Efficient management of heat transfer and entropy generation in nanofluid enclosures is essential for the development of high-performance thermal systems. This study employs the finite element method (FEM) to numerically analyze the effects of wall corrugation and base inclination on magnetohydrodynamic (MHD)-assisted natural convection of Cu–H2O nanofluid in a trapezoidal cavity containing internal heat-generating obstacles. The governing equations for fluid flow, heat transfer, and entropy generation are solved for a wide range of Rayleigh numbers (103–106), Hartmann numbers (0–50), and geometric configurations. Results show that for square obstacles, the Nusselt number increases from 0.8417 to 0.8457 as the corrugation amplitude rises (a = 0.025 L–0.065 L) at Ra = 103, while the maximum heat transfer (Nu = 6.46) occurs at Ra = 106. Entropy generation slightly increases with amplitude (15.46–15.53) but decreases under stronger magnetic fields due to Lorentz damping. Higher corrugation frequencies (f = 9.5) further enhance convection, producing Nu ≈ 6.44–6.47 for square and triangular obstacles. Base inclination significantly influences performance: γ = 10° yields maximum heat transfer (Nu ≈ 6.76), while γ = 20° minimizes entropy (St ≈ 0.00139). These findings confirm that optimized corrugation and inclination, particularly with square obstacles, can effectively enhance convective transport while minimizing irreversibility, providing practical insights for the design of energy-efficient MHD-assisted heat exchangers and cooling systems.

AppliedMath doi: 10.3390/appliedmath5040159

Authors: Tomohiro Hayashida Shinya Sekizaki Kosuke Shimoyoshi Ichiro Nishizaki

In high-dimensional optimization, particle swarm optimization (PSO) algorithms often suffer from premature convergence due to stagnation in certain dimensions. This study proposes an enhanced variant, ELPSO-C, which integrates dimension-wise convergence detection with adaptive exploration mechanisms. By applying agglomerative clustering to inter-particle velocity diversity, ELPSO-C identifies dimensions showing signs of stagnation and selectively reintroduces diversity through targeted mutation strategies. The algorithm preserves global search capability while reducing unnecessary perturbation in well-explored dimensions. Experimental results on a suite of 18 benchmark functions across various dimensions demonstrate that ELPSO-C consistently achieves superior performance compared to existing PSO variants, especially in high-dimensional and complex landscapes. These findings suggest that dimension-aware adaptation is an effective strategy for improving PSO’s robustness and convergence quality.

AppliedMath doi: 10.3390/appliedmath5040158

Authors: Mohamed Illafe Feras Yousef

We introduce and analyze a subclass of analytic functions with negative coefficients, denoted by Pq,σm,ℓ,p(α,η), constructed through a generalized q-calculus operator in combination with a multiplier-type transformation. For this class, we obtain sharp coefficient bounds, growth and distortion estimates, and closure results. The radii of close-to-convexity, starlikeness, and convexity are determined, and further consequences, such as integral means inequalities and neighborhood characterizations, are derived. The results presented provide a broad framework that incorporates and extends several earlier families of analytic and geometric function classes.

AppliedMath doi: 10.3390/appliedmath5040157

Authors: Aghalaya S. Vatsala Govinda Pageni

The computation of solutions of Caputo fractional differential equations is paramount in modeling to establish its benefits over the corresponding integer order models. In the literature so far, in order to compute the solution of Caputo fractional differential equations, the solution is typically assumed to be a Cn function, which is a sufficient condition for the Caputo derivative to exist. In this work, we assume the necessary condition for the Caputo derivative of order nq,(n−1)<nq<n, to exist, which means that we assume it to be a Cnq function. Recently, it has been established that the Caputo derivative of order nq is sequential of order q. As such, we assume the fractional initial conditions. In our work, we have obtained an analytical solution for the Caputo fractional differential equation of order nq with fractional initial conditions by two different methods. Namely, the approximation method and the Laplace transform method. The application of our main results is illustrated with examples.

AppliedMath doi: 10.3390/appliedmath5040156

Authors: Sanjar M. Abrarov Rehan Siddiqui Rajinder Kumar Jagpal Brendan M. Quine

In this work, we obtain an iterative formula that can be used for computing digits of π and nested radicals of kind cn/2−cn−1, where c0=0 and cn=2+cn−1. We also show how with the help of this iterative formula, the two-term Machin-like formulas for π can be generated and approximated. Some examples with Mathematica codes are presented.

AppliedMath doi: 10.3390/appliedmath5040155

Authors: Lawrence Fulton Arvind Sharma Aleksandar Tomic Ramalingam Shanmugam

Rankings drive consequential decisions in science, sports, medicine, and business. Conventional evaluation methods typically analyze rank concordance, dispersion, and extremeness in isolation, inviting biased inference when these properties co-move. We introduce the Concordance–Dispersion–Extremeness Framework (CDEF), a copula-based audit that treats dependence among these properties as the object of interest. The CDEF automatically detects forced versus non-forced ranking regimes, then screens dispersion mechanics via χ2 tests that distinguish independent multinomial structures from without-replacement structures and, for forced dependent data, compares Mallows structures against appropriate baselines. The framework estimates upper-tail agreement between raters by fitting pairwise Gumbel copulas to mid-rank pseudo-observations, summarizing tail co-movement alongside Kendall’s W and mutual information, then reports likelihood-based summaries and decision rules that distinguish genuine from phantom agreement. Applied to pre-season college football rankings, the CDEF reinterprets apparently high concordance by revealing heterogeneity in pairwise tail dependence and dispersion patterns that inflate agreement under univariate analyses. In simulation, traditional Kendall’s W fails to distinguish scenarios, whereas the CDEF clearly separates Phantom from Genuine and Clustered agreement settings, clarifying when agreement stems from shared tail dependence rather than stable consensus. Rather than claiming probabilities from a monolithic trivariate model, the CDEF provides a transparent, regime-aware diagnosis that improves reliability assessment, surfaces bias, and supports sound decisions in settings where rankings carry real stakes.

AppliedMath doi: 10.3390/appliedmath5040154

Authors: Javier Flores Méndez Gustavo M. Minquiz Alfredo Morales-Sánchez Mario Moreno Zaira Jocelyn Hernández Simón José Alberto Luna López Francisco Severiano Carrillo Luis Hernández Martínez Nancy E. González Sierra Ana Cecilia Piñón Reyes

This paper presents research and theoretical development of a mathematical model that, first, allows us to understand how the positional exactitude of the output link of a four-bar mechanism depends on the manufacturing dimensional tolerances. To find this dependence, the total differentials of the kinematic constraint functions that govern the field of positions must be determined for each kinematic cycle of the mechanism under consideration. These total differentials lead to a system of equations whose solution gives the positional errors of the movable output links as a function of the manufacturing dimensional errors and an incidence matrix that varies with each one of the positions of the input element. On the other hand, the theoretical transmission ratio between the output velocities with respect to the input velocity of the articulated kinematic chain is defined, and for determining the total errors in each ratio, the total differential of each one of them is calculated, showing a clear dependence with respect to the positional errors of the output links (previously defined) of the mechanism. The sum of the theoretical transmission ratio and its respective error provides the real transmission ratio. Furthermore, the described methodology allows for determining the sensitivity (influence coefficients) in the transmission ratios due to errors inherent in the link lengths. Finally, the presented analytical approach is numerically implemented through an example of articulated parallelogram design, principally characterizing in graphic form the transmission ratios in their regions of permitted movements and blocking positions, for a specific IT degree of precision of the bilateral dimensional tolerances of their functional geometric parameters, with the objective of analyzing every aspect related to the performance of the mechanisms. This formalism is validated through three particular design cases using a CAD model in a simulation module of kinematic motion analysis; additionally, the evolution of the transmission angle is discussed. The methods and conclusions proposed in this document also leave open the way as future work to study separately the magnitudes and signs of the positional errors and the transmission ratio, or even the influence coefficients themselves, in order to assign the most convenient degree of IT precision for each link in the mechanism with the purpose of reducing errors in the designs and obtain better efficiency in the transmission ratio.

AppliedMath doi: 10.3390/appliedmath5040153

Authors: Seshu Kumar Damarla Madhusree Kundu

This paper presents a novel and computationally efficient numerical method for solving systems of fractional-order differential equations using orthogonal hybrid functions (HFs). The proposed HFs are constructed by combining piecewise constant orthogonal sample-and-hold functions with piecewise linear orthogonal right-handed triangular functions, resulting in a flexible and accurate approximation basis. A central innovation of the method is the derivation of generalized one-shot operational matrices that approximate the Riemann–Liouville fractional integral, enabling direct integration of differential operators of arbitrary order. These matrices act as unified integrators for both integer and non-integer orders, enhancing the method’s applicability and scalability. A rigorous convergence analysis is provided, establishing theoretical guarantees for the accuracy of the numerical solution. The effectiveness and robustness of the approach are demonstrated through several benchmark problems, including fractional-order models related to smoking dynamics, lung cancer progression, and Hepatitis B infection. Comparative results highlight the method’s superior performance in terms of accuracy, numerical stability, and computational efficiency when applied to complex, nonlinear, and high-dimensional fractional-order systems.

AppliedMath doi: 10.3390/appliedmath5040152

Authors: Ioannis Sitzimis Irini Dimou George Xanthos Ioannis Passas

This study examines how sentiments and perceptions in Greece relate to seaplane adoption, building on prior work on Greek users’ emotions and attitudes toward seaplane services. Using survey data from N = 443 respondents (N = 373 used in the logistic model), we estimate a binary logistic regression for the intention to choose a seaplane. Perceived comfort and safety (F3) is the dominant predictor, substantially increasing the odds of adoption (e.g., OR = 6.67, 95% CI [4.09, 11.35]; robust under Firth penalization). In the full MLE model, emotion dummies (Freedom, No feelings) are not statistically significant relative to Joy; Fear exhibits quasi-complete separation, so its MLE coefficient is not interpretable (penalized results are provided as sensitivity). Model performance indicates acceptable discrimination (AUC = 0.782, 95% CI [0.734, 0.829]). Better perceived comfort and safety are critical for broader seaplane use in island and coastal regions.

AppliedMath doi: 10.3390/appliedmath5040151

Authors: Md Sadikur Rahman

In inventory management, business organizations gradually face challenges due to the complexities of managing perishable goods whose value diminishes over time. In such circumstances, interval’s bounds estimated business policy can be adopted to study a non-deterministic inventory model incorporating decay, preservation technology, and financial incentives, viz. advanced payments and fixed discounts. This study explores an interval Economic Order Quantity (EOQ) model incorporating advanced payment with discount options under preservation technology framework in interval environment. In this model, the demand rate is expressed as a convex combination of linear and power patterns of the selling price. The present model is formulated mathematically using interval differential equations and interval mathematics. Then, the corresponding interval-valued average profit of the model is obtained. In order to optimize the corresponding interval optimization problem, C-U optimization technique is developed. Employing the C-U optimization technique, the said interval optimization problem is converted into crisp optimization problems. Then, these problems are solved numerically by Wolfrom MATHEMATICA-11.0 software and validated with the help of two numerical examples. Finally, sensitivity analyses have been performed to study the impact of known inventory parameters on optimal policy.

AppliedMath doi: 10.3390/appliedmath5040150

Authors: Said Choufi Lakhdar Djeffal

In this paper, we consider a general quadratic problem (P) with linear constraints that are not necessarily linear independent. To resolve this problem, we use a new algorithm based on the Inertia-Controlling method while replacing the condition of the Lagrange multiplier vector μ by resolution of a linear system obtained thanks to the Kuruch–Kuhn–Tuker matrix (KKT-matrix) in order to determine the minimizing direction of (P) and so calculate the steep length in general cases, as follows: indefinite, concave, and convex cases. This paper has an interesting topic and meaningful results.

AppliedMath doi: 10.3390/appliedmath5040149

Authors: Mohamed Ilyas El Harrak Karim El Moutaouakil Nuino Ahmed Eddakir Abdellatif Vasile Palade

This study introduces Itô-RMSProp, a novel extension of the RMSProp optimizer inspired by Itô stochastic calculus, which integrates adaptive Gaussian noise into the update rule to enhance exploration and mitigate overfitting during training. We embed this optimizer within Gated Recurrent Unit (GRU) networks for stock price forecasting, leveraging the GRU’s strength in modeling long-range temporal dependencies under nonstationary and noisy conditions. Extensive experiments on real-world financial datasets, including a detailed sensitivity analysis over a wide range of noise scaling parameters (ε), reveal that Itô-RMSProp-GRU consistently achieves superior convergence stability and predictive accuracy compared to classical RMSProp. Notably, the optimizer demonstrates remarkable robustness across all tested configurations, maintaining stable performance even under volatile market dynamics. These findings suggest that the synergy between stochastic differential equation frameworks and gated architectures provides a powerful paradigm for financial time series modeling. The paper also presents theoretical justifications and implementation details to facilitate reproducibility and future extensions.

AppliedMath doi: 10.3390/appliedmath5040148

Authors: Hamza Mihoubi Awatif Muflih Alqahtani

In the present study, we aimed to derive analytical solutions of the homotopy analysis method (HAM) for the time-fractional Navier–Stokes equations in cylindrical coordinates in the form of a rapidly convergent series. In this work, we explore the time-fractional Navier–Stokes equations by replacing the standard time derivative with the Katugampola fractional derivative, expressed in the Caputo form. The homotopy analysis method is then employed to obtain an analytical solution for this time-fractional problem. The convergence of the proposed method to the solution is demonstrated. To validate the method’s accuracy and effectiveness, two examples of time-fractional Navier–Stokes equations modeling fluid flow in a pipe are presented. A comparison with existing results from previous studies is also provided. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathematics.

AppliedMath doi: 10.3390/appliedmath5040147

Authors: Miriam Di Ianni

Phenomena from a variety of disciplines, including biology, computer science and sociology, can be modeled by graph dynamics in which nodes are associated with states and the node-state association changes in time. Although general k-state dynamics have been considered, most of the research in this area refers to binary dynamics especially as far as deterministic dynamics are regarded. In this paper 3-state deterministic dynamics are studied from the computational complexity perspective. A tractability result is proved when the third state is a state of neutrality, adopted by any node unable to establish a preference between the two remaining states. Subsequently, two hardness results are proved for two cases where each of the three states represents a semantically distinct state: the case in which a state change occurs in a node only if the most preferred state among the remaining two receives a suitable number of preferences, and the case in which a state change occurs in a node only if its current state lacks sufficient preferences and the most preferred state among the remaining two receives a suitable number of preferences. Finally, the relation of the last two results and a conjecture from the 1980s is discussed and it is shown that the conjecture is contradicted in both cases.