AppliedMath, Volume 5, Issue 4 (December 2025) – 55 articles

This article presents a deterministic model describing the joint dynamics of canine and human rabies in a cross-border context. This model explicitly integrates dog mobility between two neighboring countries and allows us to assess the impact of these movements on disease persistence. We analyze the basic reproduction number ${\mathcal{R}}_0$, study the local and global stability of equilibrium points, identify the most influential parameters through sensitivity analysis, and perform numerical simulations to test the effectiveness of different vaccination and movement control strategies. Full article

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

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

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

Tumor angiogenesis models based on coupled nonlinear parabolic partial differential equations require solving stiff systems where explicit time-stepping methods impose severe stability constraints on the time step size. Implicit–Explicit (IMEX) schemes relax this constraint by treating diffusion terms implicitly and reaction–chemotaxis terms explicitly, reducing each time step to a single linear system solution. However, standard Gaussian elimination with partial pivoting exhibits cubic complexity in the number of spatial grid points, dominating computational cost for realistic discretizations in the range of 400–800 grid points. This work presents a CUDA-based parallel algorithm that accelerates the IMEX scheme through GPU implementation of three core computational kernels: pivot finding via atomic operations on double-precision floating-point values, row swapping with coalesced memory access patterns, and elimination updates using optimized two-dimensional thread grids. Performance measurements on an NVIDIA H100 GPU demonstrate speedup factors, achieving speedup factors from 3.5× to 113× across spatial discretizations spanning $M\in [25,800]$ grid points relative to sequential CPU execution, approaching 94.2% of the theoretical maximum speedup predicted by Amdahl’s law. Numerical validation confirms that GPU and CPU solutions agree to within twelve digits of precision over extended time integration, with conservation properties preserved to machine precision. Performance analysis reveals that the elimination kernel accounts for nearly 90% of total execution time, justifying the focus on GPU parallelization of this component. The method enables parameter studies requiring $\sim {10}^4$ PDE solves, previously computationally prohibitive, facilitating model-driven investigation of anti-angiogenic therapy design. Full article

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

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

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

This paper considers a continuous review inventory system for two interconnected product types, 1 and 2. Product type 1 is purchased from an external agency, whereas type 2 is manufactured in-house through a sequential batching process. The maximum stock position attainable by type 1 is $S_1$ and that of type 2 is $S_2$. Unit demands arise independently for the two products, where type 1 demand arrives following a Poisson process with rate ${\lambda }_1$ and that for product B also follows a Poisson process with rate ${\lambda }_2$. At the instance of the stock level of type 1 dropping to zero, it is replenished instantaneously to the maximum level $S_1$, such that the stock level is never zero, and hence all demands for type 1 product are satisfied. The production machine attached to type 2 stops manufacturing immediately when its stock level reaches $S_2$, and resumes immediately when the stock level drops to $S_2-1$. In the event of the type 2 product not being available when demand arrives, it is substituted with the type 1 product with probability p. The production time for a single unit of type 2 is exponentially distributed with mean ${\displaystyle \frac{1}{\gamma }}$. We identify the underlying Markov process and analyse the performance of the interconnected inventory system. Full article

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

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

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

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

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

This study introduces and analyzes several new functionals defined on the interval $[0,1]$, which are associated with weighted integral inequalities for geometrically–arithmetically ($GA$) convex functions. Building upon the classical Hermite–Hadamard and Fejér inequalities, we define mappings such as $\mathcal{G}\left(u\right)$, ${\mathcal{H}}_y\left(u\right)$, ${\mathcal{K}}_y\left(u\right)$, $\mathcal{N}\left(u\right)$, $\mathcal{L}\left(u\right)$, ${\mathcal{L}}_y\left(u\right)$, and ${\mathcal{S}}_y\left(u\right)$, which incorporate a $GA$-convex function x and a non-negative, integrable weight function y that is symmetric about the geometric mean $\sqrt{s_1{s}_2}$. Under these conditions, we establish novel Fejér-type inequalities that connect these functionals. Furthermore, we investigate essential properties of these mappings, including their $GA$-convexity, monotonicity, and symmetry. The validity of our main results is demonstrated through detailed examples. The findings presented herein provide significant refinements and weighted generalizations of known results in the literature. Full article

We establish a modular-space framework for the study of tripled fixed points and tripled best proximity points. Under suitable assumptions on the underlying modular (convexity, the ${\Delta }_2$ property, uniform continuity, and uniform convexity-type properties), we prove that Banach theorems guarantee the existence, uniqueness, and convergence of modular iterative schemes. In particular, we develop results for cyclic $\rho$–Kannan contraction maps and pairs, showing that both tripled fixed points and tripled best proximity points arise uniquely and attract all iterative trajectories. An illustrative example in the space $L^2[0,1]$ with integral operators demonstrates the applicability of the theory and the predicted rate of convergence. These results extend classical fixed point methods to a broader modular setting and open the way for applications in nonlinear functional equations. Full article

Geospatial–statistical integration remains a persistent bottleneck for official statistics and applied spatial analysis. The GISINTEGRATION R package provides a modular, reproducible workflow for preprocessing, harmonizing, and linking heterogeneous GIS and non-GIS datasets, with export utilities that are compatible with common desktop GIS. This paper outlines the package architecture and demonstrates its use in two applications. The first integrates population statistics with newly introduced statistical output geographies for Northern Ireland, enabling rapid preparation of analysis-ready layers such as all usual residents and population density at Super Data Zones. The second links daily PM_2.5 measurements from the U.S. EPA Air Quality System with county boundaries for California (July 2020) to produce policy-relevant indicators; spatial aggregation yielded valid monthly means for 46 of 58 counties (79.31%) and reduced variance from 40.716 (monitor level) to 5.777 (county means), improving signal stability and comparability. Across both cases, the workflow standardizes variable names, supports user-controlled overrides, identifies common keys, and performs quality checks, thereby reducing manual effort while increasing transparency and reproducibility. The results illustrate how standardized integration facilitates official statistical production, environmental monitoring, and evidence-based decision-making. Full article

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

Fisheries worldwide exhibit puzzling boom-and-bust cycles despite regulatory efforts, raising questions about what drives these oscillations. We investigate whether temporal delays in monitoring and decision-making contribute to system instability. Our model uses delay differential equations to track an exploiting population and its renewable resources, incorporating two distinct delays: one for perceiving resource status (${\tau }_2$) and another for implementing management responses (${\tau }_1$). We establish the existence, uniqueness, and positivity of solutions, then analyze equilibrium stability through linearization and Lyapunov–Razumikhin functions. The characteristic equation reveals Hopf bifurcations at critical delay thresholds. Numerical simulations across 1600 parameter combinations using MATLAB R2023b’s DDE23 algorithm quantify these transitions. The results show a critical threshold near 1.64 years (20 months): below this value, systems converge to a stable equilibrium, while above it, persistent oscillations emerge within 20–26 year periods. Unexpectedly, one large delay destabilizes less than two moderate delays summing to the same total, contradicting uniform improvement strategies. Convergence to limit cycles requires roughly 40 years, exceeding typical management horizons and potentially masking true system dynamics. The critical threshold lies within realistic administrative timescales, suggesting that institutional delays may substantially contribute to observed population fluctuations. These findings indicate that accelerating either monitoring or decision processes rather than providing modest improvements to both could better stabilize exploited resources. Full article

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

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

In this study, we consider and analyze an inhomogeneous Whittaker-type differential equation of the form ${\displaystyle \frac{d^{2}y\left(x\right)}{d{x}^2}}+{\displaystyle \frac{1}{x}}{\displaystyle \frac{dy\left(x\right)}{dx}}-{\alpha }^2\left(x^2-{\beta }^2\right)y\left(x\right)=g\left(x\right)$, where $\alpha$ and $\beta$ are given parameters. We investigate the analytical structure of its solution through the application of the Whittaker integral representation. The analysis encompasses both initial value problems (IVPs) and boundary value problems (BVPs), wherein appropriate conditions are imposed within a unified analytical framework. Furthermore, a systematic methodology is developed for constructing explicit solutions within the framework of Whittaker function theory. This approach not only elucidates the functional behaviour of the solutions but also provides a foundation for extending the analysis to more general classes of second-order linear differential equations. Full article

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

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

We introduce and analyze a subclass of analytic functions with negative coefficients, denoted by ${\mathcal{P}}_{q,\sigma }^{m,\ell ,p}(\alpha ,\eta )$, constructed through a generalized q-calculus operator in combination with a multiplier-type transformation. For this class, we obtain sharp coefficient bounds, growth and distortion estimates, and closure results. The radii of close-to-convexity, starlikeness, and convexity are determined, and further consequences, such as integral means inequalities and neighborhood characterizations, are derived. The results presented provide a broad framework that incorporates and extends several earlier families of analytic and geometric function classes. Full article

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

In this work, we obtain an iterative formula that can be used for computing digits of $\pi$ and nested radicals of kind $c_n/\sqrt{2-c_{n-1}}$, where $c_0=0$ and $c_n=\sqrt{2+c_{n-1}}$. We also show how with the help of this iterative formula, the two-term Machin-like formulas for $\pi$ can be generated and approximated. Some examples with Mathematica codes are presented. Full article

Rankings drive consequential decisions in science, sports, medicine, and business. Conventional evaluation methods typically analyze rank concordance, dispersion, and extremeness in isolation, inviting biased inference when these properties co-move. We introduce the Concordance–Dispersion–Extremeness Framework (CDEF), a copula-based audit that treats dependence among these properties as the object of interest. The CDEF automatically detects forced versus non-forced ranking regimes, then screens dispersion mechanics via ${\chi }^2$ tests that distinguish independent multinomial structures from without-replacement structures and, for forced dependent data, compares Mallows structures against appropriate baselines. The framework estimates upper-tail agreement between raters by fitting pairwise Gumbel copulas to mid-rank pseudo-observations, summarizing tail co-movement alongside Kendall’s W and mutual information, then reports likelihood-based summaries and decision rules that distinguish genuine from phantom agreement. Applied to pre-season college football rankings, the CDEF reinterprets apparently high concordance by revealing heterogeneity in pairwise tail dependence and dispersion patterns that inflate agreement under univariate analyses. In simulation, traditional Kendall’s W fails to distinguish scenarios, whereas the CDEF clearly separates Phantom from Genuine and Clustered agreement settings, clarifying when agreement stems from shared tail dependence rather than stable consensus. Rather than claiming probabilities from a monolithic trivariate model, the CDEF provides a transparent, regime-aware diagnosis that improves reliability assessment, surfaces bias, and supports sound decisions in settings where rankings carry real stakes. Full article

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

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