AppliedMath doi: 10.3390/appliedmath6090154

Authors: Obiora Cornelius Collins Oludolapo Akanni Olanrewaju

Malaria and typhoid fever co-infection produces severe illness affecting public health, especially in countries where both diseases coexist. A mathematical model that considers the critical factors influencing the transmission dynamics and control interventions of malaria and typhoid fever co-infection is developed. The essential epidemiological features of the model, such as the basic reproduction number and disease-free equilibrium, are determined and analysed. A dynamical systems analysis of the model reveals the conditions under which the disease can be eradicated or persists. Numerical simulations are conducted using real data from Nigeria as a case study. By fitting the model to the real data, essential parameter values are estimated and model prediction that reveals the possible long-term dynamics of the model is determined. The impact of the various control interventions are investigated. These findings are anticipated to aid in improving the management of malaria–typhoid co-infection in endemic regions for expeditious disease eradication.

AppliedMath doi: 10.3390/appliedmath6090153

Authors: David Shituula Iiyambo

Lumpy skin disease (LSD) is a rapidly spreading viral disease of cattle that threatens livestock productivity and agricultural trade across Africa, the Middle East, and Asia. Despite effective vaccines being available, evidence-based guidance on allocating limited veterinary budgets across competing interventions remains lacking, and no LSD study has yet combined dynamic transmission modelling with a hard budget constraint and formal cost-effectiveness analysis. We develop a deterministic ShVhEhIhRh–SvIv (SVEIRSI) compartmental model for LSD, embedded within a budget-constrained optimal control framework with three time-dependent controls—vaccination (u1), vector control (u2), and movement restriction (u3)—evaluated across all eight strategy combinations. The basic reproduction number is R0=2.7899. Pontryagin’s Maximum Principle characterises the optimality conditions. The resulting two-point boundary value problem is solved via forward–backward sweep with budget bisection over a 180-day horizon at three budget levels (WL=NAD5000, WM=NAD15,000, WH=NAD40,000). Vaccination dominates the optimal allocation at every budget, reducing peak infectious prevalence by 54–57% and averting 15,645–17,970 animal-days of cumulative burden relative to the uncontrolled baseline (I0=97,313 animal-days). Shadow-price analysis reveals that the budget constraint is non-binding across all three policy budget levels (actual optimal spend ≈ NAD 572), indicating that logistical (rather than financial) barriers are the true bottleneck, with the shadow price dropping to zero at W≈NAD1862. Incremental cost-effectiveness analysis places vaccination alone (S1), vaccination plus vector control (S12), and the combined strategy (S123) on the efficiency frontier, with ICERs of NAD 0.012, 0.015, and 0.166 per animal-day averted, respectively. One-way sensitivity analysis identifies vaccine efficacy ε as the dominant driver of cases averted (swing ≈85,601 animal-days), while global sensitivity analysis via Latin Hypercube Sampling identifies the midge biting rate a as the strongest driver of cumulative infectious burden (PRCC=0.926, p<0.001). These results provide actionable, quantitative guidance for LSD outbreak response in Namibia and comparable resource-limited settings.

AppliedMath doi: 10.3390/appliedmath6090152

Authors: Lu Zou Qin Yue

Low adult density can suppress recruitment through mate limitation or cooperative reproductive failure, even when a host improves adult survival. Motivated by this ecological tension, we introduce a fecundity-related component Allee effect into a stage-structured commensalism model with a Holling type II host benefit. The nonlinear recruitment term is f(x2)=αx22/(x2+A), and the independently growing host converges to its carrying capacity, yielding an asymptotically autonomous commensal subsystem. We obtain a complete analytical classification. If the long-term host benefit D exceeds mature mortality δ2, a unique coexistence equilibrium attracts every nontrivial commensal population. If the benefit is insufficient, fecundity limitation can instead create two positive equilibria: a low-density saddle whose stable set is the basin boundary and a stable high-density coexistence state. Thus, extinction and coexistence are both possible, depending on initial stage composition and host abundance. Stronger fecundity limitation enlarges the extinction region, whereas greater recruitment, maturation or host benefit promotes persistence. At the critical boundary, the positive equilibria merge in a non-degenerate saddle-node bifurcation. Rigorous global arguments and numerical comparisons with the linear-recruitment model show how a component Allee effect can induce strong-Allee-type demographic behavior, including bistability and threshold-mediated extinction.

AppliedMath doi: 10.3390/appliedmath6090151

Authors: Nacim Nait Mohand Hocine Lehouche

This paper addresses loop-wise PI/PID controller structure selection in a coupled two-tank hydraulic system. Existing studies generally prescribe controller architectures or compare predefined configurations after synthesis, leaving this problem insufficiently explored when each choice depends energetically on the neighboring loop. Although exact feedback linearization decouples the auxiliary tracking dynamics, the reconstructed physical pump inputs retain nonlinear hydraulic coupling. Consequently, reducing the control energy of one loop may increase the effort required by the other, creating conflicting local objectives that motivate a non-cooperative game-theoretic formulation. The plant is feedback-linearized, PI and PID controllers are parameterized by pole placement, and their assignment is posed as a finite static game in which each player minimizes pump energy cost. For the nominal symmetric configuration, (PID, PID) is the unique Nash equilibrium, although (PI, PI) yields a lower aggregate control energy cost (291.4134 vs. 291.8184), showing that unilateral optimality does not coincide with collective energy minimization. PID reduces settling time from 5.253 s to 3.422 s (34.9%) but increases maximum overshoot from 13.55% to 20.82% (53.7%). Sensitivity analyses show that tuning, leakage, coupling, and initial conditions can reverse best responses, while a ±10% parametric mismatch analysis preserves convergent tracking with small steady-state errors, although the equilibrium may change.

AppliedMath doi: 10.3390/appliedmath6090150

Authors: Song-Yi Song Wookjae Heo

We develop a predictive–prescriptive decision-support framework for football squad composition under budget and positional constraints, in which mixed-integer optimization is the central methodological contribution. The framework integrates four components: (i) construction of a Sports Performance Index (SPI) via principal component analysis (PCA) of standardized per-90 performance features; (ii) leakage-free, player-wise, five-fold cross-fitted prediction of seasonal goals plus assists using ordinary least squares (OLS) as the primary input model, regularized linear models as additional baselines, and gradient boosting (XGBoost) as a nonlinear benchmark and uncertainty-estimation component, with each player-season receiving an out-of-fold prediction; (iii) a mixed-integer linear program (MILP) that selects a player-season portfolio under budget, position composition, squad-size, and duplicate-player constraints, with a tunable weight balancing predicted attacking output against the performance index; and (iv) a robust counterpart that incorporates prediction uncertainty into the optimization. The framework is implemented on English Premier League data covering the 2023–2024 and 2024–2025 seasons (N = 218 forward and midfielder player-seasons with at least 1800 min of playing time). Cross-fitted OLS attains a five-fold mean R2 = 0.76 ± 0.03 with stable performance across folds. The exact MILP outperforms a benefit-to-cost greedy heuristic by up to 9.4% and the best of 1000 random feasible rosters by 41.0–53.0% in objective value, while guaranteeing feasibility of all composition and budget constraints. Sensitivity analyses across budget tightness, position bounds, squad size, and cost proxy demonstrate qualitative robustness. The robust counterpart with risk-aversion parameter κ ∈ {0, 0.5, 1.0} produces a Jaccard roster overlap of 0.75 relative to the nominal solution and reduces average selected-player prediction uncertainty from 2.65 to 2.49. The contribution is a mathematically rigorous, integer-programming-centered decision-support framework that integrates machine learning with optimization for sports business analytics and is directly applicable to club-level squad planning.

AppliedMath doi: 10.3390/appliedmath6090149

Authors: Saifon Chaturantabut Jatupat Chanakul

This work introduces efficient signal denoising methods based on wavelet thresholding (WT) and Hankel matrix-based Singular Value Decomposition (HSVD) with a randomized algorithm. The sequential hybrid frameworks of these techniques are investigated—both WT followed by HSVD (WT-HSVD) and HSVD followed by WT (HSVD-WT)—across varying noise levels. Numerical tests are performed through different benchmark signals, including dual harmonic, damped sine, and dual frequency signals, as well as a natural phonocardiogram recording. Different types of corrupted noises, including white Gaussian, colored (brown), and impulsive noises, are considered in the numerical tests. For moderate and high noise levels, hybrid frameworks can significantly improve the final accuracy of the denoised signals, as measured by reconstruction error metrics and Signal-to-Noise Ratio. These hybrid frameworks are also shown to be advantageous in compensating for suboptimal parameter selections that may occur when using either method individually. Furthermore, to mitigate the computational burden inherent to exact SVD, this work employs a randomized Singular Value Decomposition (rSVD) algorithm. Depending on the signal size, the proposed hybrid frameworks with rSVD achieve a 30% to 80% reduction in CPU execution time while maintaining denoised signal reconstruction accuracy across test cases.

AppliedMath doi: 10.3390/appliedmath6090148

Authors: Joshua Kay Zilong Song

Friction stir welding (FSW) is a solid-state manufacturing process widely used in joining aluminum and other metal workpieces. The FSW process can be modeled by a coupled system of non-Newtonian Navier–Stokes and heat-transfer equations. However, solving this non-linear system with high accuracy requires significant computational power. This work refines the system by introducing corrected coefficients and new treatments for boundary conditions near the tool. Then, model order reduction, including the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), is applied to efficiently solve the FSW system in a low-dimensional space. To enhance accuracy and effectiveness, two novel treatments have been adopted for the POD and DEIM models: the introduction of preconditioner matrices to avoid large condition numbers and the use of indicator matrices to generate the non-linear data. For different cases regarding operating parameters, the results show that the DEIM model dramatically speeds up the computation (e.g., over 250 times faster compared with the full model) while maintaining accuracy. This makes simulations of the FSW process more accessible and easily combined with machine learning techniques in future study.

AppliedMath doi: 10.3390/appliedmath6090147

Authors: Mahmoud Moustafa

Mastitis remains one of the most important infectious diseases affecting dairy cows, with substantial consequences for animal health, milk production, and farm profitability. In this study, we extend a nonlinear SIRS–P compartmental model for mastitis transmission in dairy cows by incorporating sensitivity analysis, optimal control, and cost-effectiveness analysis. The model consists of susceptible, infected, and recovered cow populations together with an environmental pathogen compartment, and accounts for direct cow-to-cow transmission, indirect transmission through environmental contamination, recovery, recurrence of infection, recruitment, and culling. A sensitivity analysis of the basic reproduction number R0 is performed to identify the parameters that most strongly influence mastitis transmission. An optimal control problem is then formulated using time-dependent controls that reduce direct transmission, reduce environmental contamination, and enhance recovery. Pontryagin’s Maximum Principle is applied to derive the optimality system, which is solved numerically using the forward–backward sweep method. Seven intervention strategies are compared through numerical simulations and cost-effectiveness analysis using ACER and ICER. The results indicate that the fully integrated strategy S7, which combines prevention and screening, environmental sanitation, and treatment, provides the largest overall disease reduction. However, Strategy S1, based on direct transmission reduction, offers the most cost-effective allocation of resources for reducing the mastitis infection burden.

AppliedMath doi: 10.3390/appliedmath6090146

Authors: Edmundo Rubén Vergara Moreno Juana María González Moreno Rafael Marcel Asmat Uceda Juan Carlos Ponte Bejarano Yoni Mateo Valiente Saldaña

This paper applies the updated fuzzy model proposed by Belhadj and Bounani in 2023 to microdata from the National Household Survey (ENAHO) for the province of Trujillo, La Libertad, Peru, to measure monetary poverty. The study demonstrates that this framework offers a more detailed, continuous assessment of poverty levels than traditional binary classifications. By assigning degrees of deprivation to various poverty indicators, the fuzzy approach captures the full intensity of deprivation, uncovering intermediate socioeconomic states that conventional methods systematically overlook. While the official binary classification by INEI categorizes 94.62% of Trujillo’s population as “non-poor,” the fuzzy methodology reveals that only 22.18% experience complete non-deprivation. Crucially, it exposes that 49.94% of the population resides in a state of “mild poverty”—a highly vulnerable segment rendered invisible by standard metrics. District-level disaggregation highlights sharp territorial disparities, ranging from severe structural vulnerability in Florencia de Mora (Fuzzy Poverty Index = 0.428) to consolidated stability in Víctor Larco Herrera (0.288). Ultimately, the fuzzy approach provides a more nuanced and realistic representation of poverty dynamics. This offers crucial insights for policymakers designing targeted poverty-reduction interventions.

AppliedMath doi: 10.3390/appliedmath6090145

Authors: Shankun Zhao Qifan Zeng Zhenguo Su Taoying Liu

Deep mining operations in metal mines face escalating challenges from high in situ stress environments, where conventional single-method ground control approaches often prove insufficient. This study proposes an innovative combined protection technology integrating four synergistic components: (i) prestressed rock bolt and plate support for immediate roadway reinforcement, (ii) hydraulic fracturing-based shielding to create fracture zones isolating the orebody from surrounding high-stress regimes, (iii) destress blasting at the orebody crown to form a stress-transfer barrier, and (iv) subsequent cemented paste backfill to provide long-term regional stability. Theoretical formulations are derived for each component: a bolt–rock composite bearing model quantifies the confinement provided by prestressed support; a fracture mechanics-based model characterizes the stress-shielding efficiency of hydraulic fracture networks; controlled blasting theory predicts the stress redistribution achieved through crown destressing; and a backfill arching model evaluates the long-term load-bearing capacity of cemented paste fill. A three-dimensional FLAC3D numerical model was established to simulate six working conditions: no protection, support-only, shield-only, pressure relief-only, backfilling-only, and the integrated four-component system combining support, shield, pressure relief and backfilling. The numerical results reveal that the integrated composite protection system reduces roadway subsidence by 86%. Furthermore, the synergistic effect among all components exceeds the sum of individual contributions, which verifies the necessity of adopting the comprehensive protection strategy under deep high in situ stress conditions. The research findings provide theoretical basis and engineering design references for safe and efficient mining in deep metal mines.

AppliedMath doi: 10.3390/appliedmath6090144

Authors: Carlo Bianca Luca Guerrini Stefania Ragni

A delayed malware dissemination model for wireless sensor networks is extended by replacing the single fixed anti-virus cycle time with distributed recovery memories. Two normalized gamma kernels are considered: a one-stage exponential memory (weak kernel) and a two-stage gamma memory (strong kernel), both representing heterogeneous anti-virus removal times across carrier and infectious nodes. The linear chain trick transforms the corresponding integro-differential systems into six- and eight-dimensional ordinary differential equation models. For these distributed-delay formulations, we derive the common disease-free equilibrium and its local stability conditions, prove that the endemic equilibrium and the basic reproduction number are preserved, and show that the inherited delayed-removal mechanism does not generate a positively invariant nonnegative orthant; in its place, we establish the strongest valid conditional boundedness and continuation result. Local endemic stability is reduced to a Routh–Hurwitz problem, and Hopf thresholds are obtained from simple purely imaginary roots together with transversality. For the reference parameter set, full spectral verification and first-Lyapunov-coefficient evaluation show that the first weak- and strong-kernel Hopf points are subcritical. Numerical simulations illustrate convergence below threshold and loss of equilibrium stability above it, while comparison with the discrete-delay benchmark shows that a broader recovery-time distribution postpones instability.

AppliedMath doi: 10.3390/appliedmath6090143

Authors: Anurag Dutta S. Shanmuga Priya A. Ramamoorthy Pijush Kanti Kumar

Large language models (LLMs) have recently improved their problem-solving abilities and can solve complex mathematical problems with an increasing accuracy, necessitating the development of more challenging benchmarks. Over the years, the performance of LLMs on several benchmark datasets has also improved, motivating the development of evaluation frameworks that emphasize deeper algorithmic reasoning. This research presents Bench of Euler, a benchmark comprising 954 challenging mathematical and computational puzzles from the “Project Euler” collection, designed to evaluate complex multi-step mathematical reasoning. Solving these puzzles requires in-depth algorithmic deduction, as solutions based on brute force enumeration are mathematically infeasible. The benchmark is further classified into bands with respect to the problem difficulty to enable structured evaluation. Several existing open-source and proprietary, as well as base and reasoning, models have been evaluated on Bench of Euler, among which the highest-performing gpt-4o model by OpenAI achieved the highest accuracy of 43.21%. To evaluate the algorithmic efficiency, the models were prompted to generate Python code, which was subsequently executed in an isolated sandbox with strict timeout constraints. A failure analysis of the top-performing models revealed their inability to effectively optimize solutions, resulting in time-limit exceeded (TLE) errors during execution and outputs that often remained incomplete or approximate. Additionally, second-pass evaluations yielded an average performance improvement of approximately 2.09%, indicating limited gains from a second stochastic sample under the adopted decoding protocol.

AppliedMath doi: 10.3390/appliedmath6090142

Authors: Mujahid Abbas Muhammad Waseem Asghar

In this work, we prove the strong convergence of an inertial iterative scheme to approximate solutions of the equilibrium fixed point problem associated with nonexpansive mappings in Hilbert spaces. Numerical simulations are carried out to examine the performance of the proposed approach. The results indicate that the proposed inertial approach achieves faster convergence when compared with existing comparable iterative schemes. We also investigate how different choices of initial values influence the convergence behavior of our algorithms and we compare these effects with those observed in classical iterative schemes through graphical illustrations. In applications, we used our approach to solve the signal processing problem. We also apply it to a mathematical model describing the spread of an infectious disease, which illustrates its relevance to real-world dynamical systems. Finally, we show that the proposed method can be applied in solving constrained optimization, variational inequality and split feasibility problems which highlight its flexibility and wide applicability.

AppliedMath doi: 10.3390/appliedmath6090141

Authors: Kunle Adegoke Robert Frontczak Taras Goy

We develop a unified method for transforming and evaluating infinite series involving products of terms of second-order linear recurrences in the denominator. The approach is based on a discrete Abel-type summation formula (summation by parts), which converts reciprocal series with three or more factors into expressions exhibiting a partial telescoping structure. As a consequence, we obtain general transformation formulas for series of the form ∑k=1∞(±1)kwrk+lwmk+swm(k+1)+s, together with extensions to products of four or more terms. These formulas provide a systematic framework that unifies and extends many known identities for Fibonacci and Lucas numbers. In addition, the method leads to explicit evaluations and identities involving several classical combinatorial sequences, including Catalan numbers, harmonic numbers, and Stirling numbers of both kinds. A key feature of the approach is that it naturally distinguishes between even and odd values of the parameter m, leading to structurally different representations. The results show that summation by parts is an effective and flexible tool for reducing multi-factor reciprocal sums to simpler forms.

AppliedMath doi: 10.3390/appliedmath6080140

Authors: Sultan Shoaib Muhammad Zahid Riqza Khattak Waleed Amjad Awan Zia Ur Rehman Yasar Amin

A Lyapunov-based framework for stability analysis and synthesis of adaptive neural-network (NN) controllers for a class of uncertain second-order nonlinear systems (SNS) with bounded external perturbations and unmodelled dynamics is presented. Online learning is employed for the reconstruction of the plant nonlinearity with the use of a radial-basis-function (RBF) network whose weights are adapted using a direct adaptation law deduced from a single composite Lyapunov function. The proposed controller couples the weight update to a persistent robustifying action, while the closed-loop stability is guaranteed throughout the learning transient, in contrast to schemes that guarantee stability after learning has converged. Using a composite Lyapunov function in the filtered tracking error and the weight-estimation error, we prove that all closed-loop signals are uniformly ultimately bounded (UUB) and that the tracking error converges to an explicitly characterized residual set whose radius is governed by the network reconstruction accuracy, the disturbance bound and the design gains. A σ-modification ensures parameter boundedness without persistency of excitation, and a robustness theorem shows that bounded parametric perturbations of the plant preserve stability and enlarge the ultimate bound only gradually (a graceful degradation, rather than a loss of the guarantee). The open-loop plant (a forced double-well Duffing oscillator) is characterized by means of equilibrium and Jacobian analyses. A bifurcation diagram and the largest Lyapunov exponent are presented, which show a chaotic regime (with λ1≈0.17). Numerical experiments indicate that the proposed controller is able to suppress the chaotic motion with a small value of the ultimate bound, and maintain a smooth reference motion with a small and constant RMS error of order 10−3, which is approximately 26 times less than the RMS error obtained with a tuned fixed-gain baseline, and the theoretical dependence of the ultimate bound on the disturbance and the design gains is confirmed by sensitivity sweeps.

AppliedMath doi: 10.3390/appliedmath6080139

Authors: Akeem Olarewaju Yunus Oludolapo Akanni Olanrewaju

Meningitis is a significant public health problem despite the availability of effective vaccination programs, especially in children and young people. The memory-dependent features of disease transmission, immunity and vaccination dynamics are not often represented in classical integer-order epidemic models. This study proposes a fractional-order model of meningitis transmission with memory using the Atangana–Baleanu–Caputo fractional derivative. The model features susceptible, vaccinated, exposed, infectious, treated, and recovered populations to assess the impact of vaccination coverage, vaccine effectiveness, loss of vaccine immunity, and treatment on the spread of meningitis. The basic mathematical characteristics of the model, such as positivity, existence, uniqueness, and stability of solution are proven. The Laplace–Adomian Decomposition Method (LADM) is used to obtain the approximate analytical solutions, and a numerical simulation is used to analyze the influence of the fractional-order memory and epidemiological parameters on the epidemic process. The most important parameters that influence the basic reproduction number are found in sensitivity analysis to be the transmission rate and the vaccination-related parameters. The results show that simply increasing the vaccination coverage and vaccine effectiveness can substantially decrease the number of disease transmissions, and vaccine coverage can produce memory effects to change the timing and duration of outbreaks. The suggested fractional-order computational framework is a framework that is vital for studying the dynamics of meningitis and can be used for the design of long-term vaccination and disease-control strategies.

AppliedMath doi: 10.3390/appliedmath6080138

Authors: Vasileios Charilogis Ioannis G. Tsoulos Anna Maria Gianni

SPARQ is an advanced global optimization algorithm, the direct evolution of an earlier method called ARQ2. It searches efficiently for the best solution to problems where the space of options is too vast to check exhaustively, such as tuning antenna arrays or planning fuel-efficient spacecraft trajectories. Like its predecessor, it works with a population of candidate solutions that improve generation after generation, alternating between two complementary search strategies. What sets SPARQ apart is that it makes nearly every part of this process adaptive. Its population shrinks intelligently as the search matures. Its internal settings draw from a memory of many past successful configurations, not a single average. Its escape-from-stagnation mechanisms come in graduated strength, from a gentle nudge to a deeper partial restart. It also adds capabilities its predecessor never had, including a dedicated phase that locally polishes the current best solution using its own memory of productive directions. Every addition is kept only where it showed an overall benefit during development, though a subsequent component-wise analysis shows this benefit varies markedly in size and statistical significance across mechanisms. The result is more reliable than its predecessor on the large majority of tested problems, while staying grounded in the same battle-tested core.

AppliedMath doi: 10.3390/appliedmath6080137

Authors: Aicha Ait Bakrim Khalid Benmoussa

This paper presents a new algorithm based on splitting methods for the numerical solution of the Navier–Stokes equations coupled with the heat equation. This work is set in a context where viscosity and thermal conductivity depend explicitly on temperature We propose an extension of the Coupled Prediction Scheme based on a rotational projection formulation, noted as the Rotational Coupled Prediction Scheme (RCPS). The accuracy and effectiveness of the proposed numerical scheme are demonstrated through a series of numerical tests, and the results obtained are compared with those already existing in the literature. In particular, the Rayleigh–Bénard convection (RBC) problem was used as a reference benchmark.

AppliedMath doi: 10.3390/appliedmath6080136

Authors: Yara Althurwi Saddah Alkhateeb Nada Almuallem

Electron–positron pair production is one of the fundamental quantum electrodynamical (QED) processes and provides an important framework for investigating photon–matter interactions. In this work, the influence of linear photon polarization on electron–positron pair production in the electromagnetic field of the Be49 nucleus is investigated using both the conventional Bethe–Heitler formalism and its polarization-dependent extension. The differential cross sections are evaluated deterministically in Wolfram Mathematica 13.3 over the intermediate photon-energy range of 400–600 MeV and emission angles between 30° and 90°. The numerical results show that the largest differential cross sections are obtained at an incident photon energy of 400 MeV and an emission angle of 30°. A detailed examination of the angular distributions reveals a local change in the vicinity of 60°, which is interpreted because of the kinematic structure of the Bethe–Heitler formalism rather than a distinct production mechanism. A direct comparison with the conventional Bethe–Heitler model demonstrates that linear photon polarization consistently enhances the differential cross section throughout the investigated kinematic range. These leading-order theoretical results provide a systematic analysis of the combined energy and angular dependence of polarized pair production in the Be49 nucleus and contribute to a deeper understanding of polarization effects in intermediate-energy QED processes.

AppliedMath doi: 10.3390/appliedmath6080135

Authors: Bi Youan Désiré Youan Thibaut K. Kouakou Nabongo Diabaté

We study a delayed semilinear evolution equation with a Caputo time derivative and the spectral fractional Dirichlet Laplacian on a bounded connected domain. The model separates two forms of memory: the Caputo operator retains the distributed Volterra history, whereas the nonlinear production samples the single past state u(t−τ). Working in the strongly continuous phase space C0(Ω), we prove local well-posedness, positivity, a sup-norm continuation criterion, and a compatible weak formulation. In the delayed-source case with μ=0, the solution exists globally and remains bounded on every finite time interval, while the first Dirichlet mode admits an explicit recursive sequence of positive lower bounds across successive delay windows. In the dissipative case μ>0, p>q>1, histories satisfying the explicit smallness conditions remain in an invariant order interval and the L2-energy decays at a Mittag–Leffler rate. The scalar computations are presented only as heuristic first-mode surrogate experiments. In addition, an independent spatially resolved sine spectral-Galerkin/L1 computation of the PDE, with temporal and spectral refinement studies, is included as a numerical illustration.

AppliedMath doi: 10.3390/appliedmath6080134

Authors: Nyatuga Gideon Nyakundi John Ndiritu Ivivi Joseph Mwaniki Timothy Kevin Kamanu

Missing data remain a major challenge in breast cancer research because they can introduce bias, reduce statistical efficiency, and compromise the performance of predictive models. Although numerous imputation techniques have been proposed, their comparative performance under different missing-data mechanisms and their impact on downstream classification remain inadequately understood. This study systematically compared statistical and machine learning-based imputation methods using two publicly available breast cancer datasets representing complementary clinical settings. The methods were evaluated under simulated Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) mechanisms using both reconstruction accuracy and downstream classification performance. The results showed that no single imputation method consistently achieved the best performance across both datasets. Regularized regression and machine learning-based methods generally outperformed conventional statistical approaches, although the optimal method depended on the characteristics of the dataset. Furthermore, the best-performing imputation methods preserved downstream classification performance despite the introduction of missing data, demonstrating that reconstruction accuracy alone is insufficient for selecting imputation strategies intended for predictive modelling. Overall, the findings highlight the importance of considering dataset characteristics, missing-data mechanisms, and the intended analytical objective when selecting imputation methods. The proposed evaluation framework provides a robust approach for assessing missing-data handling strategies in breast cancer prediction studies and other biomedical machine learning applications.

AppliedMath doi: 10.3390/appliedmath6080133

Authors: Salman Ghazal

Suppose that T is a normal spanning tree (depth-first search tree) of a graph G. If e=xy and e′=uv are edges of G, satisfying x≺Tu≺Ty≺Tv, then they are called secant edges of G with respect to T. Suppose that G has no secant edges with respect to T. If T is a path, Ghazal and Al-Mniny proved that the chromatic number is at most 3. We conjecture that there is a positive constant γ such that, for any graph G that has no secant edges with respect to a normal spanning tree T, then χ(G)≤γ. We pose the problem of whether γ=4 suffices. We establish a positive answer in the case where T has at most one node.

AppliedMath doi: 10.3390/appliedmath6080132

Authors: Amit Kulkarni Varun Dogra

Financial contagion—the propagation of shocks across markets, sectors, and time—remains one of the central questions in empirical finance, and yet most computational approaches model it at the wrong granularity. Existing work captures contagion at the asset level by measuring realised return or volatility comovements between specific securities, which conflates a structural pattern with its surface manifestation. We argue that the genuine causal regularity in contagion is between event types (rate decisions, default announcements, regulatory actions) rather than between individual assets. This paper introduces TECG, a framework that learns time-stamped causal-temporal association edges—predictive dependencies rather than identified causal effects—between abstract financial event types from news text and uses them to forecast multi-step contagion cascades. Methodologically, TECG can be read as a neural impulse response function (IRF) for event sequences: where the canonical structural-VAR IRF traces the dynamic response of one continuous variable to a shock in another, TECG traces the conditional intensity with which one event type fires after a shock to another event type, at a learned and possibly multi-modal lag. The framework couples LLM-based event extraction with a multivariate neural Hawkes process whose intensity functions are parameterised by a temporal graph neural network. The resulting graph has interpretable, time-stamped edges of the form “event-type A triggers event-type B with lag distribution L and conditional intensity κ.” We evaluated TECG on an aggregated corpus of approximately 482,000 financial news items spanning 2007–2023 and report three findings. First, the learned edges recover associations consistent with known causal relationships in finance—central-bank announcements preceding sector-level earnings revisions, default events at one institution preceding due-diligence events at competitors—without supervision on these relationships. Second, edges learned from data up to 2018 transfer to held-out cascades from 2020 (COVID equity crash) and 2023 (US regional banking stress) with substantially better fidelity than baselines that ignore temporal structure or operate at the asset level. Third, the framework supports generalised impulse response analysis: given a hypothetical seed event, it produces a distribution over downstream event chains that an analyst can interrogate, time-stamp, and entity-resolve. We are explicit that the empirical validation is observational and that the causal interpretation rests on assumptions we discuss at length. All headline comparisons are supported by paired-bootstrap significance tests; the extraction front end is independently evaluated on a manually annotated benchmark, with an explicit error-propagation analysis; and additional comparisons against recent temporal point-process and temporal-graph baselines are reported. The framework’s principal limitation is that it does not separately identify endogenous fire-sale or leverage-spiral dynamics; we point to where these gaps could be closed.

AppliedMath doi: 10.3390/appliedmath6080131

Authors: Dor Mizrahi Inon Zuckerman Ilan Laufer

Task-evoked EEG can reveal individual differences in cognitive processing, but it also creates a machine-learning challenge: many epochs are recorded from relatively few participants, and evaluation can be misleading if within-subject dependence is ignored. This study compared handcrafted, ROCKET, and EEGNet representations under subject-wise validation for classifying questionnaire-derived Dark Triad profiles from task-onset EEG. Dark Triad traits were assessed with the Dirty Dozen and clustered into four exploratory multivariate profiles using k-means. EEG was recorded during a visual speeded decision task, and epochs were extracted from −200 to 1000 ms around task onset. The final dataset included 1780 retained task-onset epochs from 30 participants. Three representations were evaluated under identical five-fold subject-wise cross-validation: XGBoost with handcrafted EEG features, XGBoost with ROCKET-derived time-series features, and compact EEGNet. All performance estimates were based only on predictions from held-out participants. The handcrafted model achieved balanced accuracy of 60.9%, whereas ROCKET and EEGNet improved performance to 74.3% and 76.2%, respectively, with only a modest difference between the waveform-based representations. A participant-level label-shuffling analysis of the out-of-fold predictions indicated that prediction–label alignment exceeded chance for all models. Across models, the mean probability assigned to the true cluster increased with psychometric cluster centrality, suggesting that borderline profiles were harder to classify. Signed channel-wise ablation of EEGNet suggested distributed model sensitivity, with the largest positive effects over posterior/parietal electrodes. The findings highlight the importance of participant-level validation, EEG signal representation, and psychometric label structure, while emphasizing the need for external validation in larger independent cohorts.

AppliedMath doi: 10.3390/appliedmath6080130

Authors: Clement Atachegbe Onate Matthew Olanrewaju Oluwayemi Olumide Oyewale Ajani

This study obtained the energy levels and examined the partition function (Z) of a quantum system described by an Eckart-like potential model. By adopting the Greene–Aldrich approximation scheme for the centrifugal term, the radial Schrödinger equation (SE) is solved and the analytic expression of the energy eigenvalues is obtained. The ro-vibrational Z is computed by explicitly incorporating the rotational quantum number, a feature often neglected or misapplied in many studies. This result is used to evaluate the key thermodynamic properties (TP), including the Gibbs free energy (G), entropy (S), and enthalpy (H). Numerical analysis reveals that the Z increases monotonically with temperature, while the G decreases in accordance with statistical thermodynamics. The S exhibits saturation-like behaviour at higher temperatures, while the H displays convex growth with increasing thermal energy. Parametric studies demonstrate that the Eckart-like potential allows for the controlled tuning of TP, with variations in the potential parameters, including the screening parameter, having distinct effects. The results generalise existing models, reproduce the Hulthén potential under specific conditions, show the effect of the rotational quantum number of TP, and provide new insights into the ro-vibrational statistical mechanics of exponential-type potentials.

AppliedMath doi: 10.3390/appliedmath6080129

Authors: Artan F. Alidema Atanas Ilchev Diana Nedelcheva Boyan Zlatanov

We introduce finite-observation conditional guarded language operators on the complete length-based ultrametric space of formal languages over a finite alphabet. A finite observation map selects a guarded branch according to the membership of prescribed test words. Although each branch is Banach-contractive, branch switching may destroy global Banach contractivity. We derive depth–residual conditions yielding a max-type Kannan inequality with an explicit constant α<1/2. Consequently, the operator has a unique fixed language, and the Picard iteration converges from every initial language. We also construct multi-branch operators that are Kannan-contractive but not Banach contractive and obtain residual error estimates, explicit convergence bounds, finite-depth certification, and eventual stabilization of the selected branch.

AppliedMath doi: 10.3390/appliedmath6080128

Authors: Ayse Bugatekin Mine Dogan

The Rayleigh–Logarithmic distribution provides a useful framework for modelling lifetime data by combining continuous lifetime variability with a logarithmic compounding mechanism. This study introduces a three-parameter Alpha Power Rayleigh–Logarithmic (APRL) distribution by applying the Alpha Power transformation to the classical Rayleigh–Logarithmic model. The additional transformation parameter allows the distributional shape, skewness, tail behaviour, and rate of increase in the hazard function to be adjusted while retaining the underlying structure of the baseline model. Several mathematical and reliability properties of the APRL distribution are derived, including the probability density and cumulative distribution functions, survival and hazard rate functions, quantile function, moments, order statistics, and mean residual life function. Model parameters are estimated by maximum likelihood using a multiple-start numerical optimization procedure, and the finite-sample performance of the estimators is investigated through Monte Carlo simulations under different parameter configurations and sample sizes. The simulation results show that estimation accuracy generally improves with increasing sample size, as reflected by decreasing bias, MSE, and RMSE, although estimation of the transformation parameter may exhibit greater variability for more extreme parameter settings. The practical performance of the APRL distribution is examined using the Aircraft Windshield Failure Times and Breaking Stress of Carbon Fibres datasets. Model comparisons based on information criteria, bootstrap-based goodness-of-fit assessment, and graphical diagnostics show that the APRL distribution provides competitive fits relative to several established lifetime distributions. In addition, mean time to failure and mean residual life analyses illustrate the practical interpretation of the reliability measures derived for the proposed model. Overall, the results support the APRL distribution as a useful alternative for the statistical analysis of lifetime and reliability data.

AppliedMath doi: 10.3390/appliedmath6080127

Authors: Mohammad Ali Yousefi Majid Monajjemi Seyed Javad Mirabedini Nayereh Zaghari Fatemeh Mollaamin

Fractional Brownian motion (fBm) provides a powerful stochastic framework for modeling long-range temporal dependence that cannot be represented by classical Brownian motion. This study presents a numerical and theoretical investigation of constrained fractional Brownian motion with applications to stochastic financial systems. An efficient simulation framework combining Fast Fourier Transform (FFT)-based circulant embedding and Markov Chain Monte Carlo (MCMC) sampling is developed to generate long correlated trajectories under absorbing boundary conditions. The proposed algorithm enables simulations with trajectory lengths up to L = 107 while reducing the computational complexity from O (L3) for direct covariance decomposition to approximately O(L log L). Numerical results accurately reproduce the theoretical autocorrelation function of fBm and confirm the expected persistence behavior governed by the Hurst exponent. Super-diffusive regimes (H > 0.5) exhibit persistent long-range correlations and enhanced survival probabilities, whereas sub-diffusive regimes (H < 0.5) display anti-persistent dynamics and increased boundary absorption. The fractional stochastic volatility formulation captures important characteristics associated with long-memory financial systems, including persistent volatility dynamics and implied-volatility structures. The proposed biophysical-based FFT–MCMC methodology provides an accurate, scalable, and computationally efficient framework for studying constrained fractional stochastic processes and offers a foundation for future investigations of fractional volatility models and related financial applications. A conceptual Adaptive Hurst Momentum framework is briefly discussed as a possible direction for future research.

AppliedMath doi: 10.3390/appliedmath6080126

Authors: Samer Israwi Charbel Geryes Aoun Bassam A. Y. Alqaralleh

We study a Camassa–Holm-type equation with a prescribed, time-independent bottom profile, mt+(u+h(x))mx+2uxm+12hx(x)m=0,m=(1−∂x2)u. The model is considered here as a mathematically motivated bottom-modified Camassa–Holm equation. The bottom modifies the transport velocity and the lower-order term is chosen so that the basic momentum balance keeps the same cancellation structure as in the flat-bottom case. We clarify the meaning of a gentle bottom in terms of bounded multiplier norms of the prescribed profile and do not claim a complete asymptotic derivation from the Euler equations. Under suitable regularity assumptions on h, we prove local well-posedness in Sobolev spaces by verifying the hypotheses of Kato’s quasilinear semigroup theorem. We also derive an L2 momentum identity and a continuation criterion based on the integrability of ∥ux∥L∞. The proof of the continuation criterion is strengthened by combining the momentum bound with a high-order Hs energy estimate.

AppliedMath doi: 10.3390/appliedmath6080125

Authors: Mohamed Shenify Janet Kez Fokrul Alom Mazarbhuiya

Complex interval-valued fuzzy sets are powerful tools for representing uncertainty and periodicity that occur in many real-life problems. They not only take both periodicity semantics and uncertainty into account but also describe the information using interval-valued membership grades, which gives experts more freedom to solve complex real-life problems effectively. Complex interval-valued fuzzy sets have been successfully employed many times in medical diagnosis and pattern recognition problems. In this article, two novel methods for computing the correlation coefficient and weighted correlation coefficient of complex interval-valued fuzzy sets are proposed. The methods employed fuzzy statistical parameters such as mean, variance, and covariance of complex interval-valued fuzzy sets. Several important mathematical properties are rigorously established. In order to establish the efficacy and implementation of the methods, a real-life application related to pattern recognition for mineral identification is discussed in detail. Furthermore, based on the proposed correlation and weighted correlation, a classification algorithm is developed. The time and space complexities of the proposed algorithm are analyzed. The proposed algorithm is validated through experiments conducted on two real benchmark datasets. The results demonstrate that the proposed approaches are more reliable and accurate than several existing approaches by achieving classification accuracies exceeding 98%.

AppliedMath doi: 10.3390/appliedmath6080124

Authors: Juanita Castro-Chica Diógenes de Jesus Ramirez-Ramirez Cristian David Correa-Álvarez

Acetaldehyde is routinely monitored in neutral alcohol, but pooled precision summaries can obscure changes in performance across the working range. This study evaluated 446 valid GC–FID verification results obtained by three anonymized analysts on two gas chromatographic systems (GC 8890 and GC 7890B) at 0.6, 2.5, and 9.0 mg L−1. The analysis included measured concentration, recovery, relative bias, relative standard deviation (RSD), confidence intervals, and fixed-effect factorial analysis of variance (ANOVA). Mean recoveries for the GC 8890 and GC 7890B systems were 48.7% and 157.2% at 0.6 mg L−1, 92.1% and 124.8% at 2.5 mg L−1, and 92.0% and 103.1% at 9.0 mg L−1, respectively. Recovery RSD decreased from 47.8% and 18.4% at the lowest level to 4.2% and 3.0% at the highest level. Type III ANOVA identified significant verification-level, analyst, GC-system, and interaction effects. A contextual comparison with concentration-matched AOAC Appendix F targets classified both systems as outside the recovery and RSD benchmarks at the lowest level, showed system-specific partial conformity at the middle level, and placed both systems within the screening benchmarks at the highest level. The contribution of the study is an integrated decision framework in which predefined recovery and RSD targets are interpreted together with factorial interactions to determine when results may be pooled and when level- or system-specific control is required.

AppliedMath doi: 10.3390/appliedmath6080123

Authors: Muhammad Amer Latif Ayesha Shabbir

This paper establishes new Fejér and Hermite–Hadamard-type inequalities for functions of two variables whose mixed second-order partial derivatives satisfy coordinated GA-convexity or coordinated GA-quasi-convexity on a rectangle in the positive quadrant. Our main results are formulated for non-negative continuous weight functions that are not necessarily symmetric with respect to the geometric means of the interval endpoints, thereby extending the classical framework to genuinely asymmetric weights. However, to obtain explicit and sharp integral bounds in certain cases, we also employ a technical lemma that assumes a special symmetric setting where the weight function is symmetric on each coordinate with respect to h1h2 and k1k2. We clearly distinguish which theorems hold for general asymmetric weights and which depend on this symmetry condition. Our findings unify and extend numerous previously known results for both symmetric and non-symmetric weight functions.

AppliedMath doi: 10.3390/appliedmath6080122

Authors: Ashenafi Kelemu Mengistu Elias Merkebu Adamu Getachew Tilahun Affesa Yeshambel Azene Belay Peter Joseph Witbooi

In this study, we propose a mathematical model for the dynamics of atmospheric carbon dioxide (CO2) with human population growth and an age-structured vehicle population. The positivity and boundedness of the model’s solutions are verified, and the global stability of an interior equilibrium point is proved. We calibrate the model parameters using the least-squares method. Simulations of the model show good alignment with the reported atmospheric CO2 data. Moreover, the sensitivity analysis shows that human-related emission factors and emissions from old vehicles are the main contributors to CO2 accumulation. The results of this study recommend that reducing anthropogenic emissions, accelerating the retirement of old vehicles, and strengthening carbon sequestration initiatives be considered to mitigate future atmospheric CO2 accumulation.

AppliedMath doi: 10.3390/appliedmath6080121

Authors: Wilson Chango José Espinosa

This study investigates the efficacy of early multimodal data fusion for identifying academic performance profiles and predicting academic risk in specialized postgraduate education under small-sample constraints (n=51 graduate students distributed across three independent cohorts). Student numerical grades and multi-source qualitative faculty evaluations (self-, peer-, and hetero-evaluation) were integrated at the feature level prior to modeling. To overcome the limitations of traditional small-sample validation, a multi-layered framework was deployed, combining non-linear Kernel Principal Component Analysis (KPCA), multi-method clustering consensus, bootstrap resampling (1000 iterations), stratified nested cross-validation, and an external cohort validation strategy. The analysis revealed a bimodal distribution of academic risk (low-risk: 71.4%, high-risk: 28.6%) with high consensus across unsupervised algorithms (Adjusted Rand Index values spanning 0.922–1.000). Supervised predictive models yielded an unbiased nested cross-validation accuracy of 0.980±0.040, while external cohort validation demonstrated generalizability with a mean cross-cohort accuracy of 0.970±0.052 and a mean AUC of 0.997±0.001 (95% CI: 0.996–0.998). SHAP feature importance analysis identified Machine Learning (28.68%), Artificial Intelligence (17.93%), and Big Data (16.66%) as the primary drivers of risk differentiation. This study contributes a methodologically rigorous, moderately stable, and reproducible workflow for educational data mining in sample-constrained environments, providing actionable insights for evidence-based curriculum design and early pedagogical interventions. However, given the limited sample size, results should be interpreted as exploratory evidence rather than definitive population-level conclusions.

AppliedMath doi: 10.3390/appliedmath6080120

Authors: Bing Yao Jianjian Sun Zhexing Wang Wanli Cheng Qiang Han Jinjun Guo Yuanyuan Cheng Kun Wang

External sulfate attack constitutes a major durability challenge for structural concrete, yet the influence of mechanical loads on sulfate transport remains incompletely understood. This study develops a coupled sulfate–water transport model that embeds the effects of axial static loads and fatigue loads into the effective sulfate diffusion coefficient through physically motivated correction factors, without explicitly resolving chemical reactions or physical crystallization. Numerical simulations were performed for coupled scenarios of static loading, fatigue loading, and drying–wetting cycles. Three principal findings emerge. First, drying–wetting cycles produce a stable convection enrichment peak at 1 to 3 mm from the exposed surface, rather than a monotonic decay profile. Second, axial static loads exhibit pronounced tension–compression asymmetry: tensile stress enhances sulfate transport, while compressive stress exerts a comparatively weak inhibition effect. Third, fatigue loading introduces time-dependent accumulation and nonlinear acceleration driven by the dynamic evolution of microcrack connectivity. The tensile zone consistently exhibits markedly higher sulfate enrichment and deeper penetration than the compressive zone, identifying it as the dominant region for coupled deterioration. These findings provide a quantitative foundation for durability assessment of concrete structures under complex loading environments.

AppliedMath doi: 10.3390/appliedmath6080119

Authors: George A. Anastassiou Seda Karateke Metin Zontul

This paper studies symmetrized neural network (SNN) operators generated by an adjustable half-hyperbolic tangent activation function. The construction is based on the paired density kernels ℵt and ℵ1/t, whose average defines the symmetric kernel F. This kernel is positive, even, normalized, and preserves the partition of unity. Using F, we define finite-interval and whole-line SNN operators in the Banach space-valued setting. Pointwise and uniform convergence estimates are obtained through the first modulus of continuity. Higher-order and fractional approximation estimates are also derived, the latter using Caputo–Bochner fractional derivatives. The numerical part compares the nonsymmetrized operator Ln and the symmetrized operator Lns. For n=80, the uniform error decreases from 0.010463 to 0.003479, the root mean square error (RMSE) decreases from 0.006530 to 0.000826, and the coefficient of determination (R2) improves from 0.999675 to 0.999995. This improvement is accompanied by an increase in central processing unit (CPU) time from 0.014161 s to 0.027088 s. The parameter tests further show that the performance depends on the joint choice of n, t, and ξ. Overall, the results indicate that symmetrization improves approximation accuracy, while parameter tuning remains necessary.

AppliedMath doi: 10.3390/appliedmath6070118

Authors: Ronobir Chandra Sarker Shelly Arora Atiqur Rahman Mahede- Ul-Hassan Sharandeep Singh Pandher

The generalized Burgers–Huxley (gBH) equation arises as a canonical model in nerve-pulse propagation (generalizing the Hodgkin–Huxley/FitzHugh–Nagumo excitable-media framework), in population dynamics with Allee-threshold reaction kinetics, and in nonlinear wave propagation in dispersive media; accurate benchmark solutions are essential for quantitative predictions in these domains. We couple the fourth-order exponential time differencing scheme ETDRK4 with a Chebyshev collocation spatial discretization and a linear boundary-lifting procedure to solve the gBH equation on a bounded interval with non-homogeneous Dirichlet data. On the canonical Ismail–Raslan–Rabboh travelling-wave benchmark the scheme attains L∞ errors at the level of floating-point round-off (∼10−19 absolute, ∼10−15 relative) with as few as N=2 collocation points and a single time step of size Δt=1.0—that is, three total nodes and one ETDRK4 advance. In strongly nonlinear regimes (γ=0.1, 0.3, 0.5, 0.9) the scheme exhibits approximately O(Δt2.45) temporal convergence across all four parameter values, consistent with the classical Hochbruck–Ostermann order reduction for exponential integrators on parabolic PDEs with non-homogeneous Dirichlet data. Used as a high-accuracy probe, the scheme provides a diagnostic of independent interest: the wave-speed formula of Wang, Zhu and Lu, still appearing as the exact-solution benchmark in numerical studies as recently as 2020, does not satisfy the partial differential equation. The corrected formula stated by Deng and verified symbolically by Appadu and Tijani is the unique value that makes the travelling-wave ansatz a genuine solution. We derive the residual associated with Wang’s formula in closed form, R=γA12(A2−A2W)(1−v2), and show both analytically and numerically that reported errors for schemes benchmarked against Wang’s formula coincide with the analytical wave-profile gap γA12|A2−A2W| rather than with true scheme accuracy. At the Ismail benchmark this gap equals 3.748×10−7, which matches the N- and Δt-independent plateau observed when the scheme is measured against Wang’s profile. In the nerve-pulse and excitable-media interpretation, the two formulas correspond to action-potential propagation speeds of opposite sign at the Ismail benchmark, underscoring that the correction is not a mere algebraic curiosity but changes the qualitative physical prediction of the model.

AppliedMath doi: 10.3390/appliedmath6070117

Authors: Yumu Lu Su Hoe Yeak

Many applications in finance and biology involve multiplicative noise geometric Brownian motion (GBM)-type stochastic differential equations (SDEs) whose drift carries a single dominant periodic component. Such structures arise in seasonal Black–Scholes option pricing, commodity derivatives with annual price cycles, and stochastic biological oscillators driven by a known frequency; the primary contribution of this paper is a high-precision numerical scheme validated on GBM-type test problems with periodic drift. This paper proposes a Strang operator splitting scheme within the Logarithmic Drift-Diffusion Splitting (LDDS) framework, which splits the SDE in y-space into a deterministic drift ODE sub-step (Step A) and an exactly solvable multiplicative diffusion sub-step (Step B). Step A employs the Periodically Fitted Adams–Bashforth–Moulton fourth-order predictor–corrector method (PABM4), which achieves zero local truncation error for trigonometric forcing terms by introducing additional shift terms and simultaneously imposing polynomial exactness conditions and trigonometric fitting conditions. When the Step A forcing belongs to the PABM4 exact function class Fω=span{1,t,t2,sinωt,cosωt}, the Strang+PABM4 scheme achieves floating-point precision saturation. We investigate three test problems: the cosine-drift GBM (Test Problem 1), the polynomial–trigonometric mixed drift GBM (Test Problem 2), and a dual-frequency drift applicability test (Test Problem 3). Monte Carlo strong error experiments (M=1000 paths) validate that Strang+PABM4 achieves saturation at machine precision (≈10−15) on Test Problems 1 and 2, improving precision by ≈102× over the best algebraically convergent reference. Test Problem 3 identifies the method’s applicability boundary: when the drift contains a second frequency outside Fω, Strang+PABM4 degrades gracefully to order ≈ 4 without catastrophic failure. The floating-point saturation of Strang+PABM4 is contingent on the drift belonging to F^ω; when this condition is violated, the method degrades gracefully to algebraic order ≈ 4, as demonstrated in Test Problem 3.

AppliedMath doi: 10.3390/appliedmath6070116

Authors: Darija Semenoja Minna Sinkkonen Patrik Eklund

The focus of this paper is the semi-quantitative approach to risk analysis in HACCP (Hazard Analysis and Critical Control Points), where we show how alternative computations in the risk matrix, combining probability and impact, can be provided based on algebraic and many-valued logical techniques. Doing so, we further show how applying such computations requires being formal concerning underlying information structures, which in turn enables being formal concerning functional representation of mappings between information structures appearing within risk analysis in risk management. Our mathematical algebraic framework also enables a more formal treatment of the duality between threat and opportunity.

AppliedMath doi: 10.3390/appliedmath6070115

Authors: Guojin Wang Wei Yao

Cruise ships, characterized by high density, enclosed environments and shared facilities, have become amplifiers for infectious disease outbreaks; however, predicting transmission in such settings remains challenging due to small initial case numbers. In this study, a mathematical modeling framework—including compartmental, small-world (SW), and scale-free (SF) network models—was developed to analyze the dynamics of hantavirus and norovirus transmission on recent cruise ship outbreaks. The results show that when the initial number of exposed or infected individuals is extremely small (e.g., 1–2 persons), disease spread is dominated by stochasticity, causing substantial variation between individual simulations and mean model predictions. Notably, SF networks exhibited lower transmission risk under these conditions, contradicting the theoretical expectation that when the population is large, SF networks facilitate the spread of disease. The compartmental model, while consistent with average simulation outcomes, failed to reliably predict any single outbreak event. In conclusion, for closed environments such as cruise ships with very few initial cases, stochastic variability is essential, and single-outbreak outcomes should be understood as highly contingent rather than deterministically predictable.

AppliedMath doi: 10.3390/appliedmath6070114

Authors: Bojana Stojčetović

This paper presents a procedure for constructing a matrix A⊗A* of a size 3×3 in max-plus algebra. The max-algebraic product of a matrix A and its conjugate (negative transpose) matrix A* always yields a pseudo skew-symmetric matrix. We address the inverse problem: given a matrix A˜ of this type, can one determine a matrix A such that A⊗A*=A˜? A particular case involving 3×3 matrices is examined, and one procedure is explained in detail. The method illustrates how such a matrix A can be constructed column by column while also indicating directions for further generalization and computational exploration.

AppliedMath doi: 10.3390/appliedmath6070113

Authors: Ioannis Kosmas Theofanis Papadopoulos Christos Michalakelis

The operationalization of machine learning (ML) introduces distinct engineering and lifecycle management challenges—such as extreme data dependence, silent model degradation (concept drift), and inherent non-determinism—which traditional software engineering workflows fail to adequately address. This systematic literature review provides a rigorous, comprehensive mapping of the ML lifecycle domain between 2015 and 2025 using the PRISMA protocol. Out of an initial pool of 12,450 articles, a highly specialized cohort of 22 primary studies was extracted, classified, and synthesized to map out contemporary Machine Learning Operations (MLOps) patterns, technical debt structures, governance models, and security vulnerabilities. To address the documented “production gap,” this paper formalizes the findings into a synthesized operational mapping and introduces a preliminary conceptual layout for an Adaptive Lifecycle Framework (ALF), juxtaposing it with legacy paradigms like CRISP-DM. Furthermore, we expand the scope to investigate domain-specific lifecycle complexities in healthcare systems and Large Language Model (LLM) pipelines, providing an essential evolutionary baseline for sustainable MLOps.

AppliedMath doi: 10.3390/appliedmath6070112

Authors: Ndivhuwo Ndou

This study presents a comparative numerical investigation of second-order and fourth-order Runge–Kutta methods for solving chaotic dynamical systems. The Lorenz, Genesio–Tesi, and Rössler systems are considered because of their nonlinear behavior and high sensitivity to initial conditions. The numerical schemes investigated include the Midpoint, Improved Euler, Ralston, and fourth-order Runge–Kutta (RK4) methods. The performance of the methods is evaluated in terms of convergence behavior, numerical accuracy, stability characteristics, and computational cost. A stability analysis of each chaotic system is carried out through equilibrium point determination and Jacobian eigenvalue analysis. Numerical simulations are implemented in MATLAB 2023 version, and comparisons are performed using different step sizes. The results indicate that all numerical methods converge as the step size decreases; however, the RK4 method consistently provides significantly smaller errors and improved stability properties compared with the second-order schemes. The findings further demonstrate that higher-order numerical integration methods provide superior performance for highly sensitive chaotic systems where accuracy and reliability are essential.

AppliedMath doi: 10.3390/appliedmath6070111

Authors: Yung-Ning Cheng Ching-Wen Yeh Kuo-Chen Hung

This paper solves the open problem mentioned by Lin that was published in 2026 of Algorithms to prove the uniqueness property for the solution procedure proposed by Lin. The developed mathematical verification fulfills the research gap left by Lin. Moreover, for the local maximum point near the starting point (denoted as 3×10−7) of the amelioration inventory model, this study presents an alternative explanation to help researchers execute their numerical methods with confidence such that, without the analytical procedure developed by Lin, only a rough numerical method can help researchers locate two local maximum points.

AppliedMath doi: 10.3390/appliedmath6070110

Authors: Jiazheng Du Bing Lin Hongling Ye Zhichao Guo

To address jagged boundaries in conventional fixed-mesh topology optimization and the discontinuous transfer of topology information after remeshing, this study proposes an improved Movable Morphable Smooth-Boundary (MMSB) method for displacement-constrained continuum topology optimization. A topology optimization model is established using the Independent Continuous Mapping (ICM) method, with structural weight minimization as the objective and displacement as the constraint. In the proposed framework, a triangular mesh is adopted as the current analysis mesh, threshold boundary points are identified using a holographic scanning strategy, and a fixed background mesh is introduced as an intermediate carrier for topology-variable transfer before and after remeshing. Three numerical examples are used to validate the proposed method and to compare it with the original MMSB method. The results show that the proposed method produces clearer boundary representations and more distinct load-transfer paths. In Examples 1–3, the number of result analyses is reduced from 60 to 24, from 144 to 36, and from 112 to 24, respectively. The number of boundary movements is also reduced from 5 to 4, from 8 to 6, and from 7 to 4, respectively. Meanwhile, the final structural weights are 22.0 kg, 101.4 kg, and 1.64 kg, which are close to or slightly lower than those obtained by the original MMSB method. These results indicate that the proposed method improves topology-information continuity and boundary representation while maintaining structural performance.

AppliedMath doi: 10.3390/appliedmath6070109

Authors: Ahmed Nuino Omar Bahou Senhaji Yassine Mustapha Ez-zaiym Karim El Moutaouakil Savin Treanta

Complex-valued knowledge graph embedding (KGE) models like ComplEx effectively capture asymmetric relations but are fundamentally constrained by integer-order transformations. This restriction limits their ability to model multi-scale interactions, hierarchical correlations, and non-local semantic dependencies inherent in heterogeneous graphs. To address these limitations, this paper introduces FracComplEx, a novel fractional-order extension that embeds fractional calculus into the complex latent space. By leveraging fractional operators, the framework introduces non-local dynamics and memory-aware mechanisms to continuously generalize standard linear transformations. The core architecture employs a fractional-order parameter α as a controllable scaling mechanism that balances local relational details with global topology, optimizing representation smoothness and flexibility. We provide rigorous theoretical findings demonstrating that fractional transformations enhance the embedding’s expressive capacity, spectral characteristics, and perturbation robustness beyond conventional integer-order benchmarks. Extensive experiments on FB15k-237, WN18RR, and CoDEx-M establish the empirical superiority of FracComplEx, yielding significant improvements in Mean Reciprocal Rank (MRR) and Hits@K metrics over classical baselines, particularly under severe structural data sparsity.

AppliedMath doi: 10.3390/appliedmath6070108

Authors: Ahmadjan Muhammadhaji Hui Zhang

This study constructs a novel fractional-order eco-epidemiological predator–prey model, in which disease spreads among predators through environmental transmission, and both cooperative hunting behavior and disease latency delay are incorporated simultaneously. Different from classical integer-order predator–prey models, fractional derivative is adopted to describe the memory-dependent mechanism of ecological populations, and the infection can alter the hunting strategy of diseased predators. The existence, non-negativity, and boundedness of system solutions are proved theoretically. The local stability of all equilibrium points is analyzed, and the conditions for the occurrence of Hopf bifurcation induced by latency delay are derived. Numerical simulations further verify the theoretical results, and quantitatively reveal the separate and combined effects of the fractional order, cooperative hunting coefficient, and latency delay on the dynamical evolution of the population system.

AppliedMath doi: 10.3390/appliedmath6070107

Authors: Aayush Samant Alexander Y. Klimenko Yuanshen Lu Mayank Kumar

This study presents an ideal-cycle thermodynamic analysis of an advanced compressed air energy storage (A-CAES) system with single thermal energy storage (TES) and an external heat boost. The additional heat is represented by a solar heat source, although the analysis is equally applicable to other forms of externally supplied thermal energy. Following the classical thermodynamic approach used for ideal cycles such as the Brayton, Otto and Diesel cycles, the objective is to establish analytical relationships and performance bounds for the integrated system rather than to model a specific engineering configuration. Three principal performance measures are examined: the electrical round-trip coefficient of performance (CoP), the marginal thermal coefficient of performance associated with external heat addition, and the overall second-law efficiency. Closed-form analytical expressions are derived for these quantities under idealised but still practically relevant assumptions. The analysis identifies distinct operating regimes governed by the level of external heat input and establishes analytical transition conditions between them. It is shown that external heat addition can substantially increase the round-trip coefficient of performance and lead to high marginal heat-utilisation effectiveness. A rigorous upper bound on the second-law efficiency is also obtained from a complete-cycle exergy analysis, demonstrating consistency with the laws of thermodynamics. The results provide analytical insight into the fundamental thermodynamic structure of solar-assisted A-CAES systems and establish performance bounds that are independent of any particular engineering implementation.

AppliedMath doi: 10.3390/appliedmath6070106

Authors: Ibrahim Sadok Hennia Douini Saqer Abdullah Faqih Ramy A. Aldallal

The rapid growth of high-dimensional predictive models in science and industry has intensified the need for statistically rigorous interpretability tools. Although model-agnostic feature importance methods are widely used to explain black-box models, they lack formal uncertainty quantification, leading to unreliable conclusions in high-dimensional settings where spurious correlations are common. We propose a Bootstrap-of-Bootstrap (BoB) inference framework that enables valid uncertainty quantification and hypothesis testing for any model-agnostic feature importance measure. To overcome the high computational cost of nested resampling, we develop an efficient analytical approximation based on influence function theory. The proposed approach provides calibrated confidence intervals and a stability score for each feature, strengthening the statistical foundations of explainable AI. Simulation studies and real-world applications in cancer genomics and credit risk modeling demonstrate its effectiveness, providing reliable, auditable explanations for high-stakes decision-making.

AppliedMath doi: 10.3390/appliedmath6070105

Authors: Teng Long

Viscous effects play an important role in the mechanical characterization of soft biological tissues under high-strain-rate loading. Accurate modeling of these behaviors is important for impact biomechanics, injury prediction, and crash safety analysis, in which biological tissues may experience high-strain-rate deformation. To describe the dynamic mechanical responses of soft tissues, a reliable constitutive framework is therefore needed to represent the dynamic response of soft tissues under high-strain-rate loading. The objective of this study is to develop and evaluate a viscohyperelastic constitutive framework for describing the dynamic compressive responses of multiple soft tissues. The proposed formulation is constructed within a continuum mechanics framework, in which the viscous contribution is expressed using objective invariant functions, namely J2, J6, and J7. The developed analytical formulations are calibrated against high-strain-rate experimental data from different soft biological tissues, namely porcine meniscus, bovine liver, and ovine brain tissues. To find the material model parameters, genetic algorithm optimization is used to identify the material parameters and assess the robustness of the fitting procedure. In order to assess the robustness of the proposed constitutive framework across different loading rates, a multi-objective optimization strategy is used to calibrate the model parameters by fitting multiple strain-rate-dependent responses at the same time. This approach enables the model predictive capability to be evaluated over a range of high-strain-rate conditions. These results show that the proposed framework can reasonably describe the nonlinear and rate-dependent mechanical responses of different soft tissues under dynamic compression.

AppliedMath doi: 10.3390/appliedmath6070104

Authors: Sangsung Park Sunghae Jun

This study proposes a transformed two-part bootstrap confidence interval (TTB-CI) for zero-inflated count data. The method combines a standard zero-inflated mixture formulation, parametric bootstrap, and monotone transformations to improve inference for practically meaningful estimands, including the marginal mean, zero probability, and positive-part mean. Simulation studies under zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) data-generating processes show that the proposed method maintains nominal or near-nominal coverage while reducing interval width, particularly for the positive-part mean. Compared with conventional Poisson- and negative binomial-based confidence intervals, the proposed TTB-CI provides a more favorable coverage and width tradeoff and yields more informative intervals for positive count inference. These results indicate that the proposed method offers a practical and efficient confidence interval framework for zero-inflated count data.

AppliedMath doi: 10.3390/appliedmath6070103

Authors: Janet Kez Mohamed Shenify Fokrul Alom Mazarbhuiya

Bipolar fuzzy sets provide an effective framework for representing both positive and negative aspects of information. The necessity of a mathematically rigorous and valid distance measure in bipolar fuzzy environments motivates us to introduce a new real-valued function on the set of bipolar fuzzy sets defined over both discrete and continuous universes of discourse. The proposed function is shown to define a valid metric on the set of bipolar fuzzy sets, as it satisfies all the metric axioms. The metric induced by the real-valued function is inspired by the Canberra distance, and it can effectively quantify the dissimilarity between bipolar fuzzy sets in a normalized and interpretable manner. The practical utility of the proposed metric is demonstrated in a pattern recognition problem, where it successfully recognizes an unknown pattern using known bipolar fuzzy patterns. Using the proposed metric, a bipolar fuzzy C-means clustering algorithm is developed for sentiment analysis. The time complexity of the aforementioned algorithm is also analysed. Experiments conducted on the IMDb Movie Review Dataset demonstrate that the proposed algorithm outperforms k-means, fuzzy C-means, and intuitionistic fuzzy C-means algorithms. The proposed bipolar fuzzy C-means algorithm achieves an accuracy of 90.04%, a precision of 90.51%, a recall of 89.01%, an F1-score of 89.75%, a Root mean square error of 0.1191, and a Silhouette score of 0.75. The findings establish that the proposed metric and the associated bipolar fuzzy clustering approach provide a robust and effective framework of handling sentiment data associated with simultaneous positive and negative opinions.

AppliedMath doi: 10.3390/appliedmath6070102

Authors: Danail Brezov

Reference Replacement [...]

AppliedMath doi: 10.3390/appliedmath6070101

Authors: Yasser A. Davizon Alexander Mendoza-Acosta Rafael García-Martinez Aureliano Quiñonez-Ruiz Jaime Sanchez-Leal Eric D. Smith Neale R. Smith

This technical note aims to present a theoretical analysis for cybertronics engineering (CE) for a class of dynamic supply chains for artificial intelligence (AI)-based products, services or hybrid solutions. The cybertronics-based analysis encompasses three classes of supply chains: (1) energy-based dynamic supply chains (DSC); (2) semiconductor manufacturing and quantum supply chains; and (3) retailing of the AI-based DSC solutions generated. Considering the nonlinear nature of DSC, to provide solutions for products and services based on AI-chained supply chains, novel robust control is addressed via sliding mode control (SMC) with proper stability analysis for the DSC.

AppliedMath doi: 10.3390/appliedmath6060100

Authors: Gabriela Vasileva Dilyana Karova Mariyan Milev Penko Mitev

We compare classical and modern regression models for next-day cryptocurrency forecasting on 14 USD-denominated coins across three liquidity tiers from 2018 through 2025, and we use the resulting panel to formally test three pre-specified hypotheses. The features are a strictly past-only 28-element set; the evaluation uses expanding-window walk-forward cross-validation with nested hyperparameter tuning, stationary block-bootstrap 95% confidence intervals, and pairwise Diebold–Mariano tests. Methodologically, we derive a bias-variance bound that turns the ‘no model beats the mean’ observation from a null finding into a predicted outcome under weak-form market efficiency. Empirically, (H1) the threshold–effect interaction is not supported (slope −1.7 × 10−4, 95% CI [−4.8 × 10−4, +1.4 × 10−4], p = 0.25). (H2) Statistical loss minimisation is decoupled from risk-adjusted economic outcome: the cluster-bootstrapped 95% CI for the Spearman rank correlation between the within-ticker MAE rank and within-ticker post-cost Sharpe rank is [−0.39, +0.10] overall, lies *strictly below zero* on the mid-cap (CI [−0.71, −0.04]) and long-tail (CI [−0.26, −0.09]) tiers, and decisively rejects perfect alignment (ρ = +1) on every tier. None of the seven (ticker, model) pairs with annualised Sharpe ≥ 0.5 has a hit rate significantly different from 0.5; high-Sharpe outcomes reflect return skew, not directional skill—formally predicted by a closed-form Sharpe–MSE decoupling proposition we derive in Section 3.6 under non-zero return skewness. (H3) Lo–MacKinlay variance ratio tests show top-tier coins are indistinguishable from a random walk (|z| ≤ 1.5 at q ∈ {2, 5, 10}), while mid- and long-tail tiers reject the random-walk null at q = 2 (z = −2.36, z = −2.60). The findings extend across two robustness layers. An AR(1)-GARCH(1,1) baseline produces R2 ≈ −0.005 on every tier and is indistinguishable from Lasso, supporting the bias-variance bound; Giacomini–White conditional predictive ability tests reject equal predictive ability between Lasso and tree-based models on every coin in every tier, complicating naive DM interpretations; and a forward-walking 2026-Q1 holdout—83 daily observations per coin entirely outside the training window—confirms that H1 is even more decisively null on unseen data and that the H3 efficiency conclusion holds. Together, these results give a formally tested EMH-style picture for daily crypto: no model meaningfully forecasts log-returns; statistical accuracy and trading P&L are decoupled by an analytically derived mechanism; and weak-form efficiency is approximately satisfied in most liquid coins and in the convergence across the cross-section.

AppliedMath doi: 10.3390/appliedmath6060099

Authors: Darko Tomaš Bojan Baškot Andrej Ševa Dalibor Tomaš

This paper presents a methodological framework for anomaly detection in child benefit administration based on Long Short-Term Memory (LSTM) neural networks. The content of this analysis, in general, is situated within the social (S) pillar of the environmental, social, and governance (ESG) accountability framework. We construct a framework applied to 305,338 child allowance claim records from the Fund for Child Protection of Republika Srpska, Bosnia and Herzegovina (February 2017 to December 2025), construct behavioural and demographic features at the applicant and household level, encode sequential claim histories as three-dimensional tensors, and conduct a systematic architecture sweep across six LSTM configurations. The target variable, the guardianship anomaly flag, identifies 172 anomalous records (0.056%) among 305,338 claims, and yields a class weighting ration of approximately 1515:1. Across all six configurations, ROC-AUC values range from 0.706 to 0.870 and PR-AUC from 0.002 to 0.071. The reference configuration (L1_U10_T20_he_normal, ROC-AUC = 0.870) flags 170 applications (0.37% of the test set) for priority manual review at the operational audit threshold of τ=0.05. The highest-risk application identified (anomaly probability 0.935) is characterised by a four-child household with below-poverty declared income, elevated benefit-to-income ratios, home delivery payment method, and a persistent high-risk sequential claim pattern not previously flagged by the Fund’s rule-based administrative system. The results confirm that LSTM-based sequential anomaly detection is a viable and principled complement to rule-based eligibility screening in public social transfer administration.

AppliedMath doi: 10.3390/appliedmath6060098

Authors: Fatma Al-Musalhi Nasser Al-Salti Erkinjon Karimov

A non-homogeneous fractional differential equation with a variable coefficient involving a Caputo fractional derivative is considered. The equation is first transformed into an integral equation and then solved using the method of successive approximations. The obtained general solution involves a generalized Mittag–Leffler-type function and Meijer G-functions. Example solutions corresponding to particular choices of the non-homogeneous term are presented. As an application of the considered non-homogeneous equation, direct and inverse source problems are studied. The solutions are expressed in the form of series expansions using an orthogonal basis obtained through separation of variables. Illustrative examples for the direct and inverse problems are also presented for specific choices of the initial and final time data and the source function.

AppliedMath doi: 10.3390/appliedmath6060097

Authors: Qingli Luo Zhe Wang Yufeng Zhang

This paper investigates recursion operators and nonlocal symmetry structures for the modified Veronese web equation. The novelty of the work lies in the explicit construction of a direct recursion operator and its inverse in the tangent-covering framework. Starting from a compatible linear covering with a spectral parameter, we derive both operators and interpret them as auto-Bäcklund transformations for the corresponding linearized equation. We also determine the contact symmetry algebra and compute the action of the two recursion operators on its infinitesimal generators. In particular, the inverse recursion operator produces shadows of nonlocal symmetries associated with conservation-law coverings. These results provide a concrete recursive mechanism for the symmetry space of the modified Veronese web equation and clarify its covering-based nonlocal geometric structure.

AppliedMath doi: 10.3390/appliedmath6060096

Authors: Tarikul Islam Marco Martins Afonso Sílvio Gama

This study investigates the thermal optimization of unsteady nanofluid natural convection within a quarter-circular domain with an inner wavy boundary under inclined periodic magnetic forcing. A combined finite-element method (FEM) and central composite design-based response surface methodology (RSM) is employed for optimizing both the geometric configuration and the parametric setting. For the geometric optimization, we find that the wavy-wall amplitude is the key parameter to determine the optimal configuration, followed by the inner radius and undulation number. The parametric analysis shows that strong magnetic effects suppress convection, while increasing the Rayleigh number and the nanoparticle volume fraction significantly enhances heat transport. Additionally, rising magnetic field wavelength and/or inclination angle result in a reduction in heat transmission under strong magnetic intensity. A statistical quadratic correlation equation with the help of the RSM method between Rayleigh number, Hartmann number, and nanoparticle volume fraction, and the mean Nusselt number is formulated, which gives a good match with numerical FEM analysis results in which about 99% of the variation in the response variable is predicted (R2 = 0.9975). The results obtained in this study offer valuable information along with computational efficiency in predicting the behavior of such advanced thermal systems.

AppliedMath doi: 10.3390/appliedmath6060095

Authors: C. Jeeva Jose Aneesh P. Baiju Riya Roy A. Harikrishnan Rahul Sanju P. B. Vinod Kumar K. K. Sherly Rinku Jacob G. Sreekumar

In this study, a layer-wise point cloud representation of CT scan images is proposed, from which persistence diagrams are constructed and persistent entropy is computed as a compact topological feature for three-class lung tumor classification. Two parallel approaches are investigated: the direct computation of persistence diagrams from CT images, and computation from subsampled point clouds derived from image intensity layers. The proposed method is evaluated on the publicly available IQ-OTH/NCCD lung cancer dataset, comprising 1097 CT scan images from 110 individuals, annotated by expert oncologists and radiologists. Classification is performed using K-Nearest Neighbors (KNN), Random Forest, Support Vector Machine, and eXtreme Gradient Boosting, and compared against Convolutional Neural Network (CNN) and traditional image feature-based methods. The persistent entropy approach applied to layer-wise subsampled point clouds achieves 97.67% accuracy, a Precision–Recall AUC of 96.63%, and a ROC-AUC of 99.46% using KNN, outperforming direct image-based analysis (95.91%) and achieving comparable accuracy to the CNN method (97.21%) with a computational speedup of approximately 478×. These results demonstrate that persistent homology applied to subsampled point clouds provides an accurate, mathematically interpretable, and computationally efficient alternative to deep learning for lung tumor classification.

AppliedMath doi: 10.3390/appliedmath6060094

Authors: Adam Dudáš Peter Babic

Graphical methods of correlation analysis, such as correlation n-ptychs or hotspots, focus on the identification of the strength and direction of functional relationships between sets of attributes in multidimensional datasets. Since these correlation structures only take into account values of the attributes, situations arise when the relationship is coincidental, meaning that there is no real-world causality between the values of the observed attributes but these values still exhibit significant correlation. This problem of correlation analysis as a whole motivates the need for semantic evaluation of significant relationships identified using its methods—a task that could potentially be time- and resource-intensive when conducted manually. However, modern results in the large language model area provide tools for the automatization of such tasks. Hence, this work focuses on the design and implementation of a novel large language model-based method for semantic evaluation of correlation structures embedded in a correlation graph, specifically correlation n-ptychs for n∈{3, 4, 5} and correlation hotspots. In the method, the large language model is automatically prompted to assess the semantic nature of relationships in the set of correlation substructures of the dataset, identify their real-world relevance, and visualize the result in the form of a Semantic evaluation card. The proposed approach is evaluated using two benchmarking datasets focusing on the visualization method used in the model, large language model interaction with the correlation substructures, and comparative analysis with previously used tools in the area.

AppliedMath doi: 10.3390/appliedmath6060093

Authors: Sonja Orlić José Luis Palacios Aleksandar Petojević

Thehitting time index HT(G) is a recently introduced topological descriptor based on expected hitting times of a random walk on a graph. In this paper, we derive a closed-form formula for HT(G) for broom graphs Bn,d that holds for all parameters 2≤d≤n−1, HT(Bn,d)=S1+S2+S3+(n−d)∑i=1d−1max{A(i),B(i)}, where S1,S2,S3,A(i),B(i) are explicitly defined. For d≥2 and n≥4d−8 we derive a simpler cubic polynomial formula in n, HT(Bn,d)=n3+adn2+bdn+cd, with explicitly given coefficients ad,bd,cd depending only on d. We also consider quartic polynomial formulas for special cases.

AppliedMath doi: 10.3390/appliedmath6060092

Authors: Khadijetou Maaloum Din Rabii El Maani Ahmed Tchvagha Zeine Rachid Ellaia

Multi-objective optimization plays a fundamental role in solving complex engineering design problems characterized by conflicting objectives and nonlinear constraints. In this study, a novel hybrid optimization algorithm, named Multi-objective Lemurs Optimizer-Backtracking Search Algorithm (MOLOBSA), is proposed to improve the exploration and exploitation capabilities of existing metaheuristic methods. The proposed approach integrates the global exploration ability of the Lemurs Optimizer (LO) with the efficient mutation and crossover mechanisms of the Backtracking Search Algorithm (BSA) within a multi-objective optimization framework. The effectiveness of the proposed algorithm is evaluated using the CEC2020 multimodal multi-objective benchmark suite, where its performance is assessed using the PSP and IGDX performance indicators. In addition, the proposed method was successfully applied to the multi-objective design optimization of an I-beam structure, where the objectives were to minimize the structural weight and the maximum displacement under mechanical constraints. The obtained Pareto solutions exhibit better diversity and improved trade-off characteristics compared with those produced by the baseline algorithm.

AppliedMath doi: 10.3390/appliedmath6060091

Authors: Wafa Louafi Houda Tadjer Yacine Lafifi

The adaptive regulation of student productivity remains a challenging problem in technology-enhanced learning environments due to the continuous and uncertain nature of cognitive effort, attention, and behavioral fluctuations. While existing educational intervention models are predominantly based on discrete-time decision frameworks, they often provide limited support for the representation of stochastic productivity dynamics and continuous effort adaptation. This paper proposes a continuous-time stochastic optimal control framework for adaptive effort allocation in student productivity regulation. The learner productivity level is modeled as a bounded stochastic diffusion process evolving on the interval ([0, 1]), where the drift and diffusion coefficients depend on both effort allocation and learner-specific psychological characteristics. The control objective is formulated as the maximization of an expected cumulative productivity reward penalized by excessive cognitive effort over a finite study horizon. Using the Hamilton–Jacobi–Bellman (HJB) framework, we derive an optimal state-dependent feedback policy that dynamically adjusts effort allocation according to the current productivity level, the remaining study horizon, and the learner profile. We establish the well-posedness of the controlled stochastic dynamics and show that the productivity state remains invariant within the admissible interval. The resulting HJB equation is solved numerically using a semi-implicit finite-difference approximation combined with iterative feedback updates. Simulation experiments conducted on synthetic learner profiles illustrate the qualitative behavior of the proposed controller under heterogeneous psychological configurations. Compared with constant-effort and threshold-based heuristic strategies, the adaptive feedback policy produces smoother productivity trajectories and more stable effort allocation patterns under stochastic perturbations. The proposed framework provides a mathematically grounded approach for studying adaptive productivity regulation under uncertainty and establishes a foundation for future data-driven calibration and personalized intervention systems.

AppliedMath doi: 10.3390/appliedmath6060090

Authors: Kaloyan N. Vitanov Nikolay K. Vitanov

We present a review on the application of the mathematical models for research on social processes, social structures, and actors in social systems. The scope of the review is not restricted to the classical applications of mathematics such as theory of probability, statistics, stochastic processes, differential equations, and game theory. We also discuss applications of the theory of networks for social network analysis and the numerical research on dynamics of social systems. The number of these applications has increased very fast in recent years. Special attention is given to the results from the area of sociophysics, where mathematical methodology is used to analyze social systems in cooperation with the models and concepts of physics. Another special topic in his review is connected to the results from econophysics, where the mathematical methodology and theories and methods of physics are used in the studies on the dynamics of economic systems. In addition, we give several examples for the application of mathematical methods to social systems: (a) application of difference equations to model the flow of substances in channels of networks; (b) analytical solution of nonlinear equations connected to the model of waves of popularity; (c) numerical results of the waves of popularity in a model that accounts for the change in the opinion of the supporters of the ideas for positive or negative popularity of a person, material item, or a piece of information (idea, theory, ideology, etc.) In the last case, we illustrate the effectiveness of the numerical analysis to discover new effects on the studied social system. The review ends with a large list of references. These references can be used as a guide of the way of new researchers to the large field of mathematical social dynamics.

AppliedMath doi: 10.3390/appliedmath6060089

Authors: Adjété Lionel Wilson Toyo Koffi Edarh Bossou

We introduce a mathematical model describing a dynamical system made up of interdependent compartments subject to intrinsic fragility and cross-support. The dynamics are driven by the competition between hierarchical sublinear dissipation and cyclic coupling, enabling a natural interpretation of transitions between distinct regimes (e.g., resilience versus degradation, vulnerability and crisis/extinction in finance or biology). We establish the existence, uniqueness, positivity, and global continuation of solutions. We also investigate the qualitative behavior of the system by studying the stability of equilibrium points and deriving threshold conditions characterizing increasing, decreasing, and stationary regimes. Numerical simulations are provided to illustrate the theoretical results and the transition phenomena between extinction and self-sustained dynamics.

AppliedMath doi: 10.3390/appliedmath6060088

Authors: Stathis Hadjidemetriou

The classical Regiomontanus problem asks for the position that maximizes the angle subtended by a fixed line segment, a problem originating in Euclidean geometry and observational astronomy. This work extends the problem to observers constrained to move along a circular path. The solution uses the geometric fact that the optimal viewpoint occurs precisely where the trajectory is tangent to an isoangle circle. This framework unifies configurations both exterior and interior to the circular path. The analytical solution is validated against direct numerical optimization, with agreement exceeding ten decimal places, and the subtended angle is shown to attain a unique maximum along each half of the circular trajectory. In the limit as the radius becomes large, the analytical result reduces to the classical linear case. Beyond its historical interest, a potential extension illustrates how this simple geometric condition can govern optimal viewing and highlights connections to modern imaging and vision systems.

AppliedMath doi: 10.3390/appliedmath6060087

Authors: Wiam Zeid Haissam Chehade Issam Kaddoura Yahia Awad

Let k be a positive integer. A polynomial A∈F2[x] is called k-unitary perfectif the sum of the k-th powers of its distinct unitary divisors equals Ak. In this paper, we study the case k=2n and prove that every 2n-unitary perfect polynomial over F2 is even. Moreover, we completely classify all even 2n-unitary perfect polynomials having at most three distinct irreducible factors. In particular, we characterize all such polynomials of the form A=xa(x+1)bPh, where P is a Mersenne prime over F2 and a,b,h∈N. As a consequence, several explicit infinite families of k-unitary perfect polynomials over F2 are obtained.

AppliedMath doi: 10.3390/appliedmath6060086

Authors: Rekha Panicker Rahul Shukla

This paper investigates common fixed point theorems for (β,α)-generalized enriched contractions in Banach spaces. We provide a corrected proof of an existing theorem on enriched contractions, thereby strengthening the reliability of results in this area. Our analysis further shows that a previously published illustrative example does not satisfy the proposed enriched contraction condition, since the condition fails for x=0, y=18, and b=45. We then introduce a generalized pair of mappings and prove two common fixed point theorems for single-valued (β,α)-generalized enriched contractions under weak commutativity and compatibility conditions. Strong convergence to the unique common fixed point is established through a Mann-type iteration process, and an example is provided to validate the proposed generalizations.

AppliedMath doi: 10.3390/appliedmath6060085

Authors: Mathias Wagner Thomas Harweg Roland Linder Frank Weichert

In this paper, we introduce an agent-based pedestrian simulation with aerosol modeling, which we use for analyzing the risk of infection with airborne diseases, with special attention to indoor scenarios and the corresponding geometry. For our analysis, we simulate a realistic supermarket scenario, and analyze the influence of geometric factors for the risk of infection regarding aerosol concentration. Using such a defined set of geometry allows for a targeted analysis of risk factors. Specifically, we examine if angular structures bear higher viral loads than flat structures, which is confirmed by our experiments. An artificial neural network (ANN) specifically trained on simulation data is able to identify adjacent geometric structures based on aerosol concentration with up to 94% accuracy.

AppliedMath doi: 10.3390/appliedmath6060084

Authors: Olga Kozlovska Felix Sadyrbaev

The system of ordinary differential equations that arises in models of genetic networks is considered. This system has both nonlinear and linear parts. As a nonlinear part, we use a piecewise linear function. This allows us to treat systems with multiple (up to ten) equations. Special attention is paid to the four-dimensional systems that have an attractor in the form of a periodic solution. In the final part, the 10th-dimensional system is considered, which describes a subnetwork of a larger network that arises in a practical biomedical problem.

AppliedMath doi: 10.3390/appliedmath6060083

Authors: Sapna Amit Sharma Naveen Mani Rahul Shukla

This study determines the time period of vibrational modes for a non-uniform orthotropic parallelogram plate, featuring a one-dimensional circular thickness variation and subjected to clamped (CCCC) edges. The authors make assumptions about the material; they assume a one-dimensional circular density variation and incorporate Poisson’s ratio to address material non-uniformity. The motivation to choose circular variation in the plate parameter was due to its numerous applications in engineering and real-life applications like engine covers, rotor blades, etc. The authors also account for a parabolic temperature gradient across the plate. Utilizing the Rayleigh–Ritz technique, they derive the frequency equation and solve it to determine the vibration mode time periods. This study includes a convergence analysis of the plate across (CCCC) edge conditions. The primary aim is to demonstrate the advantage of selecting a variable (circular) density and Poisson’s ratio simultaneously over solely varying the density parameter. The secondary aim is to show that the variable Poisson’s ratio is a much better choice in comparison to variable density as a non-homogeneity parameter.

AppliedMath doi: 10.3390/appliedmath6060082

Authors: César Catalán José M. Calabuig Luis M. García-Raffi Enrique A. Sánchez-Pérez

This study introduces a novel physics-inspired framework to quantify defensive pressure in football from tracking data. We model defender–attacker interactions as a variable-mass dynamical system, translating Newtonian mechanics into operational metrics that combine spatial configuration and motion. From this formulation we derive interpretable quantities at dyad, player, and team level, including a Center of Pressure (CP), Defensive Momentum, Defensive Force, and Defensive Work. We illustrate the framework in a single-match proof-of-concept using professional optical tracking data, analysing both full-match behaviour and football-specific phases such as counter-pressing, set-pieces, and throw-ins. Results show how the proposed metrics separate persistent spatial constraint (pressure) from energetically demanding defensive actions (work), enable identification of high-cost match-ups and workload concentration, and support time-resolved descriptions of coordinated pressing sequences. The framework provides a transferable, mechanically grounded toolkit for applied defensive performance analysis and motivates future validation on larger datasets.

AppliedMath doi: 10.3390/appliedmath6050081

Authors: Daniel B. Wright Sage N. Stafford

Count outcomes are commonly analyzed using Poisson regression, but empirical data often exhibit overdispersion, excess ties, heaping, or other departures from the Poisson distribution. This paper evaluates a rank-Poisson transformation, denoted poisrank, designed to map observed counts onto Poisson quantiles before fitting a Poisson regression model. Our goal is to test whether a rank-Poisson transformation offers a useful general-purpose strategy when count data do not satisfy Poisson assumptions. Using an empirical example and a Monte Carlo simulation study with Poisson, overdispersed, rounded, and gapped count distributions, we compared Poisson regression on raw counts, Poisson regression after the poisrank transformation, quasi-Poisson regression, and additional comparison approaches. Although the transformation made the marginal distribution more similar to a Poisson distribution, it generally did not outperform standard alternatives for inference. In particular, quasi-Poisson regression more consistently maintained appropriate rejection rates with overdispersion whereas poisrank tended to be conservative and often reduced power. These findings suggest that the rank-Poisson transformation is better understood as an exploratory robustness device than as a preferred replacement for established count-data methods.

AppliedMath doi: 10.3390/appliedmath6050080

Authors: Danail Brezov

This paper builds upon a previous study suggesting an optimization procedure for rotation sequences by introducing a fourth factor in Euler-type decompositions, thus allowing for an additional degree of freedom used both as a variational parameter and a means to avoid the gimbal lock singularity. Here, an analogous result is derived for generic rigid motions, which is of potential interest in 3D robot manipulators, aircraft, and spacecraft using gimbals to navigate in space. The idea is based on Kotelnikov’s principle of transference, which extends the properties of pure rotations to arbitrary Galilean transformations, interpreted as screw motions. To do that in practice, it is convenient to use dual quaternions or their projective version, referred to as dual Rodrigues’ vectors. With this approach, the explicit solutions are easy to extend and therefore optimization is rather straightforward: we show, both analytically and with numerical examples, that factorizing motion into sequences of four consecutive screws is, in general, significantly more energy-efficient compared to using three.

AppliedMath doi: 10.3390/appliedmath6050079

Authors: Daniel O. Aikhuele Shahryar Sorooshian Harold U. Nwosu

This study develops a stochastic degradation-based reliability framework for mechanical systems subject to interacting operational stresses and imperfect maintenance. The degradation dynamics are formulated in cumulative damage space and modeled using a geometric Itô diffusion process, in which the drift term incorporates a multiplicative degradation kernel representing the combined influence of load, speed, misalignment, and environmental exposure. Imperfect maintenance is represented through a continuous attenuation functional embedded within the drift structure, allowing maintenance actions to reduce degradation growth without restoring the system to an as-good-as-new condition. Using a logarithmic transformation, the multiplicative stochastic differential equation is converted into an additive diffusion process, enabling analytical treatment via Itô’s lemma. A closed-form reliability expression is then obtained through first-passage analysis, yielding a lognormal survival function governed directly by the degradation dynamics. Numerical evaluation demonstrates physically consistent wear-out behavior and confirms the stability of the derived reliability formulation. The model further enables reliability-based maintenance optimization through preventive replacement analysis. Sensitivity results indicate that system reliability is strongly influenced by the degradation growth parameter governing the stochastic drift. The proposed framework provides a mathematically tractable connection between stochastic degradation modeling, reliability theory, and maintenance optimization. Beyond its application to conveyor belt systems, the formulation offers a general analytical structure for reliability assessment of degrading engineering systems governed by multiplicative stochastic dynamics.

AppliedMath doi: 10.3390/appliedmath6050078

Authors: Mario Alberto Sandoval-Hernandez Arturo Sarmiento-Reyes Fernando Ivan Molina-Herrera Hugo Jimenez-Islas Uriel Antonio Filobello-Nino Gerardo Ulises Diaz-Arango Francisco Marroquin-Gutierrez Rogelio Alejandro Callejas-Molina Sandra Ysabel Campos-Dominguez Cristian Dumay Hernandez-Garcia Hector Vazquez-Leal

This paper presents analytical approximations for the inverse error function, its complementary inverse, and the cumulative distribution function using the Power Series Extender Method (PSEM). The proposed expressions exhibit high accuracy over a wide portion of the domain, particularly in the central region, while maintaining a compact structure based on elementary functions. This formulation ensures practical implementation and computational efficiency without the need for specialized numerical algorithms. The use of strategically selected cancellation points further enhances the accuracy of the approximations, especially in regions of interest. As expected for this class of elementary approximations, a gradual loss of accuracy is observed near the boundaries of the domain due to the asymptotic behavior of the inverse functions. To demonstrate the effectiveness and practical relevance of the proposed expressions, two case studies are presented, involving applications in statistical analysis and engineering contexts.

AppliedMath doi: 10.3390/appliedmath6050077

Authors: Dinis Pestana Maria Luísa Rocha

Rising temperatures in industrial processes are a serious alert that the system can be shifting from an In Control (InC) to an Out of Control (OutC) state, causing waste, financial losses and, eventually, disaster. Consultation in a case study analyzing the Statistical Quality Control (SQC) routines in a potato chip factory revealed that laymen dealing with data may naively spoil and misuse traditional SQC tools, downgrading the interval-scale temperature data to a simple nominal classification, true or false Negative (N) or Positive (P) symptoms that the production line is InC or OutC. Appropriate scores, negative for true N and false P, and positive for false N and true P, were designed so that their moving averages upcrossing 0 detect clusters of suspicious temperature deregulation, in order to effectively salvage the InC/OutC prognostic value of data.

AppliedMath doi: 10.3390/appliedmath6050076

Authors: Remo Pacella Angelo Di Egidio

A reduced analytical formulation for the linear elastic behavior of axisymmetric shells subjected to axisymmetric load distributions is presented. The mechanical response of the shell is interpreted through the interaction between two families of one–dimensional structural elements, namely meridian fibers and circumferential fibers, whose kinematic coupling emerges naturally from the compatibility relations of the classical Reissner–Mindlin shell theory. By exploiting a geometric reinterpretation of the shell kinematics in terms of auxiliary curvature radii, a simplified mechanical model is derived by neglecting the kinematic contributions associated with one of these radii, which become negligible for shells sufficiently far from the degenerative planar membrane/plate configuration. The resulting formulation leads to a reduced set of compatibility, equilibrium, and constitutive equations that preserve the essential mechanical features of the shell response while significantly simplifying the mathematical structure of the problem. Two internally constrained variants of the reduced model are introduced, corresponding, respectively, to shear–indeformable and inextensible meridian fibers. Within this framework, the governing equations reduce to ordinary differential equations that, for specific shell geometries such as spherical and conical shells, admit closed-form analytical solutions. Based on these reduced models, two approximate solution strategies are developed. The first relies directly on the reduced shear–indeformable shell formulation to describe the overall structural behavior, whereas the second combines membrane solutions with the more internally constrained shell model to capture boundary effects through a superposition procedure. The effectiveness of the proposed approaches is assessed through comparison with numerical solutions obtained from the classical Reissner–Mindlin axisymmetric shell model. The results show that the proposed formulations provide an accurate approximation of both displacements and stress resultants for a sufficiently large range of spherical and conical shell configurations under distributed loads.

AppliedMath doi: 10.3390/appliedmath6050075

Authors: Rajai S. Alassar Mohammed Abushoshah Husain Al-Attas Said Algarni

An analytical solution is presented for transient heat conduction in a two-layer composite cylinder subjected to outer-surface convection with a general time-dependent ambient temperature. Using Duhamel’s principle, closed-form series expressions are derived and then specialized to harmonic ambient fluctuations, recovering the classical constant-ambient solution in the zero-frequency limit. A parametric study shows that the ratio of the inner layer conductivity to the conductivity of the outer layer strongly shapes interfacial gradients and mean-temperature evolution, with sensitivity concentrated at small ratios and diminishing when the ratio is larger than 0.1. Increasing Biot number accelerates the heat transfer and approaches the isothermal-surface limit as it becomes extremely large. The geometric aspect ratio is most influential when the inner layer is resistive, and becomes weak for large conductivity ratio, supporting thin-coating approximations. Under harmonic ambient fluctuations, the response rapidly reaches a periodic steady state; higher frequency decreases amplitude and increases phase lag, while larger Biot numbers amplify oscillations and reduce delay. The coupled effects of the aspect ratio and the conductivity ratio govern penetration and phase behavior.

AppliedMath doi: 10.3390/appliedmath6050074

Authors: Julian Allagan Vladimir Deriglazov Kevin Pereyra Matthew Hill

Adversarial perturbations measured by ℓp norms do not reflect key structural constraints in tabular security data, including anisotropic geometry, feature dependence, and distributional plausibility. We introduce a composite attacker cost functional Catk(x,x′)=τmax{0,m(x′)}+λ1δ⊤G⊥(γ)(x)δ+λ∑jωj|δj|+λ2δ⊤LHδ+λ3logf^1(ϵ)(x)−logf^1(ϵ)(x′)+∑j∈supp(δ)cj+β|M(supp(δ))|ν, which integrates a spectrally truncated geometric term, a graph-based coherence penalty, a smooth copula density barrier, and a superlinear module-spread term. Under spectral degeneracy of the legitimate-class covariance, we establish nonnegativity under density dominance, exact zero self-cost, lower semicontinuity, and λ3κK-weak convexity of the continuous component on compact convex sets, for both affine and ρm-weakly convex scoring functions. These properties yield existence of constrained minimizers. The continuous component is locally Lipschitz, whereas the full functional is not due to the support-counting term. A component feasibility result shows that each term eliminates a distinct class of degenerate perturbations. Limiting regimes and refined evasion cost bounds are derived. An empirical instantiation on PHIUSIIL indicates that perturbations with identical ℓ2 norm can incur costs differing by an order of magnitude.

AppliedMath doi: 10.3390/appliedmath6050073

Authors: Saba N. Al-Khafaji Emad Kadhim Mouajeeb

Bazilevič mappings are considered very important in the theory of geometric mappings because they provide a way to generalize and study the properties of important classes of univalent mappings. Their importance is not only in the deepening of the theory, but also in the practical means of modeling phenomena in applied science and engineering, physics, and differential equations. This paper, in this sense, provides a new subclass of bi-Bazilevič mappings with the use of advanced analytical methods, Chebyshev polynomials on one side, and a Miller–Ross-type Poisson distribution on the other side. The Poisson distribution is considered one of the most important models of probability distributions with a large scope of application in the various sciences. The main components of this study are the definition and the study of this new class of functions, in which the initial Taylor–Maclaurin coefficients, in particular, q2 and q3, are determined and estimated for mappings in this subclass. Also, the classical Fekete–Szegö problem is solved and the first-order limits of this important functional are obtained with respect to the newly introduced bi-Bazilevič mappings. The outcomes contribute to expanding both the theoretical and practical aspects of this type of mapping.

AppliedMath doi: 10.3390/appliedmath6050072

Authors: Noppanon Teangthae Dawud Thongtha

A warrant is a financial derivative that grants the holder the right to purchase company shares at a predetermined price within a specified period. Generally, upon exercise, the total number of outstanding shares increases because of the issuance of new shares, reducing the stock price. In this study, an analytical formula for warrant valuation is developed without relying on the restrictive assumptions of log-normal asset return distributions or constant volatility. The model incorporates key financial variables, including the current asset price, the strike price, the risk-free interest rate, the time to maturity, and the dilution factor. To capture dynamic market conditions, asset return volatility is estimated using GARCH-type models. The performance of this analytical approach is evaluated by comparing its numerical results with those obtained using alternative methods, such as Monte Carlo simulations and the conventional warrant valuation framework. An empirical analysis based on data from the Stock Exchange of Thailand indicates that the proposed method yields improved pricing accuracy with lower estimation errors than existing benchmarks.

AppliedMath doi: 10.3390/appliedmath6050071

Authors: Van Thanh Phan Duc Trien Nguyen Ngoc Xuan Quynh Nguyen Xuan Hau Huynh

Energy consumption demand forecasting plays a critical role in the planning and development of national energy security, which underpins the Vietnam’s Eighth National Power Development Plan (PDP VIII) and Vietnam’s ambitious Net-Zero 2050 commitment. However, this task becomes more difficult because the big data environment is filled with a lot of noise and highly fluctuating data. In order to deal with the problem, this paper evaluates five models: Linear Regression, Holt’s Exponential Smoothing, PSO-GM (1,1), Support Vector Regression (SVR), and Random Forest as a benchmark to conduct a rigorous comparative analysis to identify the most accurate forecasting model. The performance was evaluated by MAE, RMSE, and MAPE indexes based on Vietnam’s total primary energy demand data from 1986 to 2024. To check the accuracy of the forecasting model, this study split the data into two periods: first time for the training data (1986–2016), and second for the testing data set (2017–2024). Furthermore, a five-fold rolling-window time-series cross-validation method and Diebold–Mariano tests were employed to ensure the statistical robustness of the findings on the small-sample datasets (n = 39). The results decisively identified that the Holt’s model as the superior framework, maintaining high stability and achieving a testing MAPE of 7.19% (training MAPE of 5.52%), while the complex machine learning benchmark shows severe over-fitting. Applying this model, Vietnam’s energy demand will reach 1528.08 TWh and 1882.55 TWh in 2025 and 2030, respectively. Furthermore, this study provides empirical evidence that simpler, well-chosen statistical models can surpass complex alternatives in small-sample scenarios, offering a reliable quantitative baseline for policymakers to navigate infrastructure development and decarbonization challenges.

AppliedMath doi: 10.3390/appliedmath6050070

Authors: Rakhal Das Satyendra Narayan

In this paper, we introduce and systematically study the class of interpolative Geraghty-type contractive mappings within the framework of complete bicomplex-valued metric spaces (bi-CVMS). We prove seven new results: (i) a fixed point theorem for a single interpolative Geraghty contraction; (ii) a common fixed point theorem for a pair of such mappings; (iii) a fixed point theorem for interpolative Reich–Rus–Ćirić type contractions in bi-CVMS; (iv) a coincidence point and common fixed point theorem for weakly compatible maps; (v) a fixed point theorem for Jaggi-type hybrid contractions in bi-CVMS; (vi) a stability result for the Picard iteration associated with the main contraction; and (vii) an application theorem establishing the existence and uniqueness of solutions to a boundary value problem governed by a Caputo fractional differential equation. All results are furnished with complete proofs and non-trivial illustrative examples. Several well-known theorems—including those of Banach, Kannan, Reich, Geraghty, and their complex-valued analogues—follow as special cases. The paper significantly advances the fixed point theory in bicomplex-valued metric spaces.

AppliedMath doi: 10.3390/appliedmath6050069

Authors: Alexandru-Dragoș Adam Alina Nirvana Popescu Jair Gonzalez

This paper presents a proposed architecture for an artificial intelligence-driven unmanned aerial vehicle (UAV) system intended for tactical intelligence, surveillance, and reconnaissance (ISR) missions. The architecture brings together electro-optical imaging, long-wave infrared sensing, two-dimensional light detection and ranging (LiDAR), inertial navigation support, onboard edge computing, and resilient communication links within a unified system-level framework. Unlike many existing approaches that treat perception, autonomy, communication, and safety as loosely coupled functions, the proposed architecture combines multi-modal sensing, operator-supervised autonomy, and a safety-oriented decision validation layer intended for future integration with Ansys SCADE. The system is structured around operational and sensor-performance requirements used to justify the selection and interaction of the main onboard subsystems. At the architectural level, the proposed framework is intended to support target detection, tracking, environment awareness, and mission-level decision support under degraded visibility, constrained communication, and contested operating conditions. The paper therefore contributes a requirement-driven and safety-aware ISR UAV architecture that provides a scalable basis for future implementation, validation, and multi-UAV extension.

AppliedMath doi: 10.3390/appliedmath6050068

Authors: Mudassir Shams Bruno Carpentieri

This paper presents a hybrid two-stage implicit scheme for the numerical solution of fractional initial value problems involving Caputo derivatives. The proposed formulation incorporates the nonlinear source term directly into the time-stepping procedure, leading to improved stability and accuracy compared with classical fractional implicit schemes. The resulting nonlinear systems are solved using a parallel iterative strategy based on the Weierstrass-type method, combined with OpenMP-style parallelization to ensure efficient workload distribution and accelerated convergence. In addition, a data-driven module is introduced to generate high-quality initial guesses, thereby enhancing the robustness and efficiency of the nonlinear solver. The main contributions include the development of a unified fractional-parallel-data-driven framework, improved stability properties with enlarged real-axis stability regions, and reduced computational cost through parallel implementation and informed initialization. A theoretical analysis establishes consistency, boundedness, and convergence under standard Lipschitz assumptions. Numerical experiments on representative fractional models demonstrate that the proposed schemes achieve higher accuracy and improved efficiency compared with classical implicit methods, with significant reductions in error and iteration counts. The ANN-enhanced variant further attains near machine-precision accuracy for a range of fractional orders. Overall, the proposed approach provides a robust and scalable computational framework for the efficient solution of nonlinear fractional dynamical systems.

AppliedMath doi: 10.3390/appliedmath6050067

Authors: B. Divya K. Ganesan A. Selvam

This research presents a fractional-order formulation and mathematical analysis of the Rössler chaotic attractor. By utilizing the Nabla discrete Atangana–Baleanu fractional difference derivative in the Caputo sense, the classical integer-order attractor is extended into the fractional domain. The existence and uniqueness of solutions for the resulting fractional system are established via the fixed-point theorem, thereby ensuring that the recommended attractor is well-posed. Furthermore, the Ulam–Hyers stability is investigated within the Nabla discrete Atangana–Baleanu fractional difference derivative in the Caputo sense framework. For numerical investigations, an Euler numerical scheme adapted to the fractional difference derivative is developed and implemented, yielding high-quality phase portraits of a chaotic attractor. The results highlight the effectiveness of fractional-order modeling and numerical methods in capturing the dynamics and stability of the Rössler chaotic system.

AppliedMath doi: 10.3390/appliedmath6050066

Authors: Ali Shojaei-Fard

The article applies the working platform of topological Hopf algebra of renormalization to address a new construction program for the fabric of space-time from the perspective of Feynman graphon models.

AppliedMath doi: 10.3390/appliedmath6050065

Authors: V. L. Stass

The problem that this study is concerned with is the ontogenetic growth of humans and animals. The aim of this research is to analyze a model of the ontogenetic growth of animals. The target of the analyses is to show a link between growth and longevity. This model has implications for modelling the growth of humans as well. In this study, pigs were considered model animals for humans. Humans and pigs have a number of comparable physiological features as well as a few analogous aspects of growth. The resemblance of the biological functions leads us to think that by modelling the growth of pigs, one can gain a better look into the growth of humans. In this research, we model growth, which is operationalized as weight gain; weight loss was not considered. In this study, a discussion of the translation of the results to the growth and longevity of humans was provided. The lifespan or longevity of animals was not modelled explicitly; predictions were made in accordance with the results of the growth model. The main result of the model is that growth promotes, if not causes, longevity.

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.