Mathematical and Computational Applications

23 pages, 512 KB

Open AccessArticle

Toeplitz and Hankel Determinants for Certain Subclasses Associated with Sakaguchi Type Functions

by Mohammed Ali Alamri, Adriana Catas, Bushra Kanwal, Arooj Iman, Fethiye Müge Sakar and Saqib Hussain

Math. Comput. Appl. 2026, 31(4), 141; https://doi.org/10.3390/mca31040141 - 20 Jul 2026

Abstract

In this work, we establish bounds for Hermitian Toeplitz determinants of orders two and three for distinct subclasses of symmetric starlike functions associated with balloon-, limaçon-, and bean-shaped domains. Using subordination theory, we derive explicit upper and lower bounds for Toeplitz determinants of [...] Read more.

In this work, we establish bounds for Hermitian Toeplitz determinants of orders two and three for distinct subclasses of symmetric starlike functions associated with balloon-, limaçon-, and bean-shaped domains. Using subordination theory, we derive explicit upper and lower bounds for Toeplitz determinants of order two and three for each class. Our results reveal a clear geometric hierarchy: the bean-shaped domain imposes the tightest restrictions, while the limaçon- domain permits the widest variation. The analysis is further extended to 2-fold and 3-fold symmetric functions, for which bounds for the third Hankel determinant are obtained. This work demonstrates how symmetry and domain geometry jointly govern coefficient estimates, offering new insights into the interplay between shape and analytic structure. Full article

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30 pages, 1793 KB

Open AccessArticle

Parameter Estimation for Modeling and Simulation of Multimodal Membrane Chromatography

by Hannah Shead and Anastasia B. Wilson

Math. Comput. Appl. 2026, 31(4), 140; https://doi.org/10.3390/mca31040140 - 17 Jul 2026

Abstract

Protein chromatography, the process of separating desired proteins from other elements in a chemical solution, is used widely in the manufacturing of biotherapeutics. Many parameters involved in this process must be tested extensively during process development, which results in higher costs of the [...] Read more.

Protein chromatography, the process of separating desired proteins from other elements in a chemical solution, is used widely in the manufacturing of biotherapeutics. Many parameters involved in this process must be tested extensively during process development, which results in higher costs of the biotherapeutics. Modeling and simulation of the chromatography process could reduce the amount of time and resources spent on running live experiments, potentially lowering therapeutic costs. In this work, we consider the transport equation coupled with adsorption isotherm equations to model the process using a porous membrane as the medium for protein adsorption. For the adsorption isotherm models, we consider both an explicit function and an implicitly defined relationship. We use a semi-implicit, finite element solution implemented in FEniCS to solve the modeling equations and simulate the adsorption phase of membrane chromatography. We conduct an initial parameter space investigation to establish acceptable ranges on each parameter and then apply numerical optimization methods to determine optimal parameter values for the modeling equations. We solve the single-parameter optimization problem by applying a line search algorithm and a multi-parameter optimization problem using built-in functionality in FEniCS which applies the adjoint method. The single-parameter optimization algorithm is applied with an explicit adsorption model while the multi-parameter optimization algorithm is applied to both the explicitly and implicitly defined adsorption models. Both algorithms yield optimal parameter values that provide much more accurate simulation results. Last, we conduct a sensitivity analysis to establish which parameters most affect the model solution in an effort to reduce computational effort in the multi-parameter optimization problem. Results indicate that two parameters most affect the optimization results and suggest that the multi-objective optimization could be modified to adjust certain parameter values at different simulation times to reduce the computation time. Full article

(This article belongs to the Section Engineering)

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31 pages, 4193 KB

Open AccessArticle

Invariant-Based Analysis of Transient Gas Flow and Optimal Valve Spacing in Pipelines

by Ilgar G. Aliyev and Elkhan Karimov

Math. Comput. Appl. 2026, 31(4), 139; https://doi.org/10.3390/mca31040139 - 16 Jul 2026

Abstract

Leakage-induced transients in natural gas transmission pipelines can significantly affect operational safety and emergency response. This study develops a physics-based analytical framework for predicting transient pressure evolution, leakage dynamics, and emergency valve response in high-pressure gas pipelines while deriving a closed-form criterion for [...] Read more.

Leakage-induced transients in natural gas transmission pipelines can significantly affect operational safety and emergency response. This study develops a physics-based analytical framework for predicting transient pressure evolution, leakage dynamics, and emergency valve response in high-pressure gas pipelines while deriving a closed-form criterion for optimal valve spacing. The governing equations of compressible gas flow are reduced to a diffusion-type model incorporating acoustic wave propagation and frictional attenuation. A dynamic Robin-type boundary condition is introduced to describe valve–pipeline interactions, and closed-form analytical solutions are obtained using the Laplace transform method. An analytical leakage function and an explicit valve spacing criterion are derived directly from the governing equations and boundary conditions. Parametric investigations under representative transmission pipeline operating conditions demonstrate that the optimal valve spacing depends systematically on attenuation characteristics, activation thresholds, and allowable response times. The analytical solution further predicts a narrow quasi-invariant valve activation interval of approximately 112–116 s, which is theoretically explained through the dominant acoustic–diffusive balance of the proposed model. Verification against an independent finite difference solution shows excellent agreement, with the maximum relative deviation remaining below 1%, thereby confirming the accuracy and numerical consistency of the analytical formulation. The proposed framework provides a physically interpretable and computationally efficient tool for leakage assessment, emergency valve design, and safety-oriented analysis of conventional natural gas transmission pipelines. Full article

(This article belongs to the Section Engineering)

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Graphical abstract

24 pages, 408 KB

Open AccessArticle

From Local Mutations to Global Fixation: A Semigroup Approach to Evolutionary Collapse

by Marshal I. Sampson, Reny George, Rafiat B. Abubakar and Julie S. George

Math. Comput. Appl. 2026, 31(4), 138; https://doi.org/10.3390/mca31040138 - 16 Jul 2026

Abstract

In a previous paper the authors initiated a study of mutation semigroups, where elementary mutation operations were encoded as total maps on finite sets and analyzed through structural, algebraic, and computational methods. Here we address several of the open problems raised therein. First, [...] Read more.

In a previous paper the authors initiated a study of mutation semigroups, where elementary mutation operations were encoded as total maps on finite sets and analyzed through structural, algebraic, and computational methods. Here we address several of the open problems raised therein. First, we investigate the algebraic characterization of generator sets that force the existence of constant or low-rank maps, linking these conditions to classical results on synchronizing automata. Second, we analyze the computational complexity of contraction-based heuristics, identifying cases where polynomial-time criteria are achievable and others where hardness results emerge. Finally, we discuss connections with quasispecies models in biology and interpret image contractions as mechanisms of error suppression and genomic stability, while noting that rigorous extension to infinite state spaces remains future work. By combining algebraic definitions, structural theorems, and algorithmic analyses, we provide a refined toolkit for understanding mutation collapse and its theoretical implications, with potential applications that require empirical validation beyond the scope of this paper. Full article

(This article belongs to the Special Issue Celebrate the 30th Anniversary of Mathematical and Computational Applications (MCA))

19 pages, 507 KB

Open AccessArticle

Qualitative Analysis and Numerical Approximation of Nonlinear Caputo–Hadamard Fractional Boundary Value Problems

by Fangfang Hu, Weimin Hu and Xiaoxiao Cui

Math. Comput. Appl. 2026, 31(4), 137; https://doi.org/10.3390/mca31040137 - 16 Jul 2026

Abstract

This paper investigates a class of nonlinear fractional differential equations with boundary value problems involving Caputo–Hadamard-type derivatives. By relaxing the monotonicity constraints on the nonlinear terms and considering more general nonlinear structures, the paper extends the theoretical framework and application scope of the [...] Read more.

This paper investigates a class of nonlinear fractional differential equations with boundary value problems involving Caputo–Hadamard-type derivatives. By relaxing the monotonicity constraints on the nonlinear terms and considering more general nonlinear structures, the paper extends the theoretical framework and application scope of the relevant fractional models. Using the upper-lower solution method in conjunction with Schauder’s fixed-point theorem, we establish the existence of exact solutions; furthermore, by applying the Banach contraction mapping principle, we prove the uniqueness of the solutions. Concurrently, we construct a convergent iterative approximation scheme and provide a priori and a posteriori error estimates for numerical solution. Furthermore, the robustness of the solutions to perturbations is characterised via Ulam–Hyers stability analysis, ensuring the reliability of the approximate solutions. Finally, numerical examples are employed to validate all theoretical results. The qualitative theory and numerical analysis methods for Caputo–Hadamard-type fractional boundary value problems have been improved. Full article

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23 pages, 404 KB

Open AccessArticle

A Novel Shrinkage Class for the Negative Binomial Regression Model: Theory, Simulation, and Healthcare Application in Saudi Arabia

by Eslam Hussam, A. M. A. Gemeay, M. M. Abd El-Raouf, Ramy Aldallal, M. S. Mohamed and A. T. A. Hammad

Math. Comput. Appl. 2026, 31(4), 136; https://doi.org/10.3390/mca31040136 - 15 Jul 2026

Abstract

Count data are widely encountered in many scientific fields, particularly in healthcare and epidemiology. One of the most commonly used approaches for analyzing such data is the negative binomial regression model (NBRM), due to its simplicity and effectiveness in modeling event frequencies. Despite [...] Read more.

Count data are widely encountered in many scientific fields, particularly in healthcare and epidemiology. One of the most commonly used approaches for analyzing such data is the negative binomial regression model (NBRM), due to its simplicity and effectiveness in modeling event frequencies. Despite its popularity, the presence of severe multicollinearity among explanatory variables can substantially inflate the variance of parameter estimates and reduce the reliability of statistical inference. To address this issue, this study proposes an improved shrinkage estimator for the NBRM, referred to as a novel class of negative binomial Liu-type estimator. The proposed estimator combines the advantages of ridge regression and the Liu estimator, aiming to reduce estimation variance while maintaining stable parameter estimates under conditions of multicollinearity. The proposed estimator is compared with the traditional maximum likelihood estimator, as well as existing ridge and Liu-type estimators, using performance measures such as mean squared error. Its performance is evaluated through extensive Monte Carlo simulation experiments under different levels of multicollinearity and sample sizes. The simulation results demonstrate that the proposed estimator provides more accurate and stable estimates than the competing methods, particularly in the presence of high multicollinearity. To illustrate the practical applicability of the proposed approach, the method is applied to a real-world healthcare dataset related to COVID-19 cases in the Kingdom of Saudi Arabia. The empirical results confirm the effectiveness of the proposed estimator in improving estimation accuracy and model stability when modeling multivariate healthcare count data. Overall, the proposed estimator offers a useful alternative for modeling multicollinear healthcare count data and enhances the reliability of statistical analysis in applied health research. Full article

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22 pages, 1044 KB

Open AccessArticle

Statistical Properties and Actuarial Measures of Exponentiated Type II Topp-Leone-G Family of Distributions with Insurance Applications

by Ibrahim Sule, Olalekan Akanji Bello and Mogiveny Rajkoomar

Math. Comput. Appl. 2026, 31(4), 135; https://doi.org/10.3390/mca31040135 - 14 Jul 2026

Abstract

In this work, a type II Topp-Leone-G family of distributions is parametrically transformed to create a new flexible family of continuous probability distributions called exponentiated type II Topp-Leone-G distribution through exponentiation. A variety of density shapes and hazard rate behaviors, such as increasing, [...] Read more.

In this work, a type II Topp-Leone-G family of distributions is parametrically transformed to create a new flexible family of continuous probability distributions called exponentiated type II Topp-Leone-G distribution through exponentiation. A variety of density shapes and hazard rate behaviors, such as increasing, decreasing, bathtub, inverted bathtub-shaped, and unimodal forms, can be captured by the proposed family, which generalizes several current lifetime models. In addition to discussing significant special cases that correspond to well-known distributions, explicit expressions for the cumulative distribution function, probability density function, survival function, hazard rate function, quantile function, actuarial measures, and linear representation of the probability density function are derived. The maximum likelihood approach is used for parameter estimation, and the simulation study provides a brief discussion of the estimator’s asymptotic characteristics. Kolmogorov–Smirnov and Cramer–Von Mises goodness-of-fit metrics and their p-values, along with information criteria like Akaike Information Criterion, Bayesian Information Criterion, Consistent Akaike Information Criterion, and Hannan–Quinn Information Criterion, are used to evaluate the appropriateness of the model. Furthermore, to visually assess model performance, graphical diagnostic techniques, such as density and distribution function overlays, quantile–quantile plots, and probability–probability plots, are used. Real-life datasets are analyzed to show the applicability of the exponentiated type II Topp-Leone-G family using Weibull distribution as the baseline, and its performance is compared with some other competing distributions. The findings demonstrate the potential utility of the proposed model in the areas of insurance and related applied domains by showing that it fits better than the competing models considered. Full article

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25 pages, 504 KB

Open AccessArticle

A Projection-Based Framework for Exact Partial Controllability of Semilinear Stochastic Fractional Evolution Equations with State-Dependent Delays, Impulses, and Q-Wiener Perturbations

by Thwiba A. Khalid, Nidal E. Taha, Manal Yagoub Juma, Manahil A. M. Ashmaig, Mona Elmahi, Khdija O. Taha and Khadiga Wadi Nahar Tajer

Math. Comput. Appl. 2026, 31(4), 134; https://doi.org/10.3390/mca31040134 - 13 Jul 2026

Abstract

We study the exact partial controllability of a semilinear stochastic fractional evolution equation of Caputo order

α \in (1, 2)

in a separable Hilbert space, subject to a genuine state-dependent delay [...] Read more.

We study the exact partial controllability of a semilinear stochastic fractional evolution equation of Caputo order

α \in (1, 2)

in a separable Hilbert space, subject to a genuine state-dependent delay

y (t - ρ (t, y_{t}))

, impulsive effects, and Q-Wiener perturbations. To accommodate the state-dependent delay, we work in a Sobolev-type prehistory space that restores the local Lipschitz property lost in the space of continuous functions, and to accommodate the impulses, we use a piecewise-continuous mean-square path space; two initial data points are prescribed, as required for

α \in (1, 2)

. The existence and uniqueness of mild solutions are established by the Banach contraction principle on a Lipschitz ball equipped with a Bielecki-type weighted norm, which removes the smallness conditions of the contraction-based literature. The stochastic convolution is treated rigorously by the Da Prato factorization realized through the subordination of the fractional resolvent family, with the Burkholder inequality applied only to the genuine Itô integral and never to the non-martingale convolution itself. For controllability, we adopt the correct stochastic notion: the target is an

F_{T}

-measurable random variable, and the adapted control is constructed through the martingale representation theorem, together with the projected controllability Gramian, yielding

P y (T) = η

almost surely. A numerical study on a stochastic fractional wave equation verifies the main controllability theorem, driving the projected terminal state to the prescribed

F_{T}

-measurable target at machine precision, and confirms the observability requirement. Full article

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42 pages, 2811 KB

Open AccessArticle

GWS-STNet: A Contractive Spatio-Temporal Architecture with Metabolic Saliency for Systemic Stress Detection in JSE Equity Markets

by Ntebogang Dinah Moroke

Math. Comput. Appl. 2026, 31(4), 133; https://doi.org/10.3390/mca31040133 - 11 Jul 2026

Abstract

Predicting systemic stress in high-dimensional equity markets remains challenging, owing to non-stationarity, heavy tails, and regime shifts. This paper introduces GWS-STNet (Gaussian-Weighted Swin Spatio-Temporal Network), a deep learning architecture grounded in functional analysis and thermodynamic analogy. A Gaussian-Weighted Swin Operator (

G^{σ}

[...] Read more.

Predicting systemic stress in high-dimensional equity markets remains challenging, owing to non-stationarity, heavy tails, and regime shifts. This paper introduces GWS-STNet (Gaussian-Weighted Swin Spatio-Temporal Network), a deep learning architecture grounded in functional analysis and thermodynamic analogy. A Gaussian-Weighted Swin Operator (

G^{σ}

) replaces the standard shifted-window attention mechanism with a kernel-regularised counterpart on the Hilbert space (

H

) of financial spatio-temporal voxels. The principal theoretical contribution is a proof, via the Banach Fixed-Point Theorem, that the window-level attention operator (

G^{σ}

) is a strict contraction (Lipschitz constant of

κ < 1

) under a bandwidth of

σ < {(2 π)}^{- 1 / 2}

, guaranteeing convergence of internal network representations to a unique fixed point. Metabolic Saliency (

S_{ms}

), derived from the exact Jacobian of the Power Mapping Network (PMNet) weighted by pairwise transfer entropy, provides intrinsic, post hoc-free attribution of sector-level stress contributions. Empirical validation on 15 large-capitalisation JSE securities (

T = 2857

trading days, January 2015–December 2025) with Eskom load-shedding stages as exogenous stress injectors shows that GWS-STNet outperforms nine baselines, including classical benchmarks (Random Walk and AR(1)) and state-of-the-art Transformers across RMSE, MAE, the Gaussian Calibration Score (GCS), and the Metabolic Efficiency Ratio (MER), with Diebold–Mariano

p < 0.001

. Full article

(This article belongs to the Special Issue Celebrate the 30th Anniversary of Mathematical and Computational Applications (MCA))

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28 pages, 7168 KB

Open AccessArticle

A Regularized Numerical Solution to an Inverse Coefficient Problem for the Forced Vibrations of a Cantilever Beam Equation Under Nonlocal Conditions

by Qabas Kadhem Jawad and M. S. Hussein

Math. Comput. Appl. 2026, 31(4), 132; https://doi.org/10.3390/mca31040132 - 10 Jul 2026

Abstract

This study tackles a fourth-order inverse problem involving a cantilever beam with nonlocal conditions to simultaneously calculate the beam’s displacement and an unknown time-dependent coefficient. A finite difference approach is suggested to discretize the hyperbolic fourth-order equation. A stability analysis for the proposed [...] Read more.

This study tackles a fourth-order inverse problem involving a cantilever beam with nonlocal conditions to simultaneously calculate the beam’s displacement and an unknown time-dependent coefficient. A finite difference approach is suggested to discretize the hyperbolic fourth-order equation. A stability analysis for the proposed scheme is also provided. The indirect problem is the minimization of the misfit function. The goal of the minimization algorithm is to reduce the gap between the measured (noisy) data and the numerical computed solution provided by the model. To achieve stable results, Tikhonov’s regularization technique is employed, and two numerical test examples are shown to illustrate the suggested scheme’s reliability. The unknown potential terms are successfully reconstructed, and stability and accuracy are maintained even in the presence of noise following the application of the Tikhonov regularization method. A trial-and-error strategy and the L-curve method are employed to obtain the optimal value for the regularization parameter. Full article

(This article belongs to the Special Issue Celebrate the 30th Anniversary of Mathematical and Computational Applications (MCA))

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31 pages, 21566 KB

Open AccessArticle

Thermofluid Design and Performance Evaluation of a Natural Draft Air-Cooled Condenser Towards Annual Performance Modeling of Concentrated Solar Power Plants

by Tristan O. Nel, Johannes P. Pretorius and Pieter G. Rousseau

Math. Comput. Appl. 2026, 31(4), 131; https://doi.org/10.3390/mca31040131 - 10 Jul 2026

Abstract

This paper presents the sizing and performance evaluation of a natural draft air-cooled condenser, with a nominal heat rejection rate of 75 MW_th, for implementation at a concentrated solar power plant in the Northern Cape province of South Africa. Initial sizing [...] Read more.

This paper presents the sizing and performance evaluation of a natural draft air-cooled condenser, with a nominal heat rejection rate of 75 MW_th, for implementation at a concentrated solar power plant in the Northern Cape province of South Africa. Initial sizing and optimization of the tower geometry is done with the aid of a one-dimensional thermofluid model at design point conditions. A high-density Latin hypercube sampling-based parametric sweep was conducted that covers the geometric design envelope, which is defined via the tower and heat exchanger heights, and the tower base and outlet diameters. Following this, the performance of the best-performing tower geometry is verified via detailed three-dimensional computational fluid dynamics (CFD), and the geometry adjusted slightly to achieve the desired heat rejection rate. This process includes refinement and validation of the CFD model compared to previous work, with the heat rejection rate matching the previous results within 0.1%, as well as performing grid convergence studies to ensure mesh independence. The refinements include a more direct coupling with the solver continuity equation, improving the accuracy of the heat exchanger integration via porous media, and a decrease in computational overhead to reduce the time required for parametric studies. The best-performing geometry implemented in the CFD model features a tower height of 80 m, base diameter of 58 m, outlet diameter of 40.15 m, heat exchanger height of 11.25 m and heat exchanger width of 3.551 m, with the model predicting a conservative heat rejection rate of 76 MW_th at the design point. Finally, a methodology is presented to evaluate the performance of the system over the full range of ambient conditions encountered during an annual operating cycle. The methodology will be applied in further work to develop a reduced-order surrogate model for application in annual performance studies. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics (AfriComp7))

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28 pages, 1329 KB

Open AccessArticle

Bayesian Prediction of Future Network Latency Times Under Two-Parameter Exponential Current Records

by Ramy A. Aldallal and Metwally R. Alseedy

Math. Comput. Appl. 2026, 31(4), 130; https://doi.org/10.3390/mca31040130 - 10 Jul 2026

Abstract

Modeling and predicting extreme observations in network latency data is an important task for monitoring the performance and reliability of communication systems. In this paper, we develop a comprehensive inferential and predictive framework for network latency times using upper and lower current record [...] Read more.

Modeling and predicting extreme observations in network latency data is an important task for monitoring the performance and reliability of communication systems. In this paper, we develop a comprehensive inferential and predictive framework for network latency times using upper and lower current record values from the two-parameter exponential distribution. First, explicit expressions for the probability density functions and cumulative distribution functions of the lower and upper current records are derived. Closed-form expressions for the r-th moments of these records are also obtained. Parameter estimation for the location and scale parameters is then investigated using both maximum likelihood estimation and Bayesian estimation. Because the Bayesian estimators do not admit closed-form solutions, a Markov Chain Monte Carlo approach based on the Metropolis–Hastings algorithm is employed to compute the posterior summaries. To forecast future latency behavior, classical predictive intervals and Bayesian predictive procedures are developed for future upper and lower current records as well as for future record ranges. The Bayesian framework additionally provides Bayesian predictive values and Bayesian predictive intervals that incorporate parameter uncertainty. The performance of the proposed procedures is evaluated through a simulation study. Finally, the methodology is applied to real network latency time data from Saudi Arabia. The results demonstrate that record-based inference combined with Bayesian prediction provides effective tools for modeling and forecasting extreme latency observations in modern communication networks. Full article

(This article belongs to the Special Issue Computational Mathematics and Applied Statistics, 2nd Edition)

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13 pages, 1305 KB

Open AccessArticle

Radiative Transport in Concentrated Viscoelastic Flow of HNF (Cu–Fe₃O₄/C₂H₆O₂) with the Cattaneo–Christov Model: Applications to Advanced Energy and Thermal Management Technologies

by Rajab Alsayegh

Math. Comput. Appl. 2026, 31(4), 129; https://doi.org/10.3390/mca31040129 - 9 Jul 2026

Abstract

Hybrid nanofluids with enhanced thermal conductivity have emerged as promising candidates for efficient heat removal in advanced energy systems and next-generation thermal management technologies. In particular, the use of viscoelastic base fluids embedded with radiatively active nanoparticles enables improved thermal regulation in solar [...] Read more.

Hybrid nanofluids with enhanced thermal conductivity have emerged as promising candidates for efficient heat removal in advanced energy systems and next-generation thermal management technologies. In particular, the use of viscoelastic base fluids embedded with radiatively active nanoparticles enables improved thermal regulation in solar collectors, electronic cooling units, and high-temperature industrial processes. This study presents a comparative thermal investigation of mono- and hybrid nanofluids comprising the ferro-oxide (Fe₃O₄) and copper (Cu) metallic particles dispersed in ethylene glycol (C₂H₆O₂), under magnetohydrodynamic (MHD) viscoelastic flow over a stretched surface. Accurate modeling of heat and mass phenomena in such fluids arises from their growing application in advanced thermal systems, including cooling technologies, electronic devices, and renewable energy modules. Unlike conventional models, the current analysis incorporates the Cattaneo–Christov heat flux framework to capture non-Fourier thermal relaxation effects, alongside the influence of thermal radiation and solutal transport. The developed system is truncated into dimensionless form with the proper choice of appropriate quantities, whose solution methodology is based on the implementation of a Runge–Kutta scheme. Compiled observations suggest that the hybrid nanomaterial exhibits more pronounced thermal recovery, while mono nanofluid attributes lower impact. Moreover, increasing the viscoelastic and magnetic parameters leads to notable variations in temperature and concentration distributions. This work advances the current literature by simultaneously integrating viscoelastic rheology, dual nanoparticle suspensions, and non-classical heat conduction laws, providing new insights for optimizing thermal performance in engineering applications. Full article

(This article belongs to the Special Issue Advances in Computational and Applied Mechanics (SACAM))

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26 pages, 9259 KB

Open AccessArticle

Parameter Estimation of Laplace Distribution Using Quantum-Inspired QMLE Method

by Amna Riaz and Rehan Ahmad Khan Sherwani

Math. Comput. Appl. 2026, 31(4), 128; https://doi.org/10.3390/mca31040128 - 8 Jul 2026

Abstract

Quantum computing has emerged as a revolutionary technology in recent years, with wide-ranging applications across many fields. It provides a significant advantage in terms of exponential speedups, leading researchers to believe that classical computing cannot overcome this gap. However, its true potential has [...] Read more.

Quantum computing has emerged as a revolutionary technology in recent years, with wide-ranging applications across many fields. It provides a significant advantage in terms of exponential speedups, leading researchers to believe that classical computing cannot overcome this gap. However, its true potential has not yet been thoroughly investigated in statistics. In the present study, we incorporate quantum dynamics into the statistical estimation method and propose a quantum-based estimation approach, i.e., quantum maximum likelihood estimation. The proposed method leverages quantum principles and dynamics to estimate the unknown parameters of probability distributions. This study implements the proposed method to estimate the Laplace location parameter. Simulation studies and real-world analyses are performed to evaluate the performance of the QMLE estimate of the Laplace parameter compared to the MLE estimate. The validity of the QMLE estimate is also assessed through variance and convergence analyses. All the findings validate the potential computational advantages of the QMLE approach as a competitive and promising method for parameter estimation of the Laplace parameter. QMLE provides more accurate, precise, efficient, less uncertain, and better-fitting estimates than MLE. Overall, the results indicate that statistical estimation theory can be improved by incorporating quantum dynamics into the classical estimation process. Full article

(This article belongs to the Special Issue Advances in Computational and Applied Mechanics (SACAM))

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29 pages, 10959 KB

Open AccessArticle

A Unified Framework for Optimization and Analysis of Fractional-Order Chaotic Systems

by Massoud M. Aboukhalaf, Mohamed A. El-Beltagy, Ahmed G. Radwan and Amr M. AbdelAty

Math. Comput. Appl. 2026, 31(4), 127; https://doi.org/10.3390/mca31040127 - 8 Jul 2026

Abstract

Maximizing the dominant Lyapunov exponent

λ_{1}

of an incommensurate fractional-order chaotic system, while respecting the dynamical conditions for a strange attractor, is a non-convex, gradient-free problem on a history-dependent landscape. Existing metaheuristic studies typically use hard-cutoff penalties that distort the fitness landscape [...] Read more.

Maximizing the dominant Lyapunov exponent

λ_{1}

of an incommensurate fractional-order chaotic system, while respecting the dynamical conditions for a strange attractor, is a non-convex, gradient-free problem on a history-dependent landscape. Existing metaheuristic studies typically use hard-cutoff penalties that distort the fitness landscape and integer-order Lyapunov estimators that can be biased for strongly fractional regimes. This paper presents a constraint-faithful optimization framework combining (i) subtractive-hinge penalties that vanish on the feasible set, (ii) a memory-consistent Grünwald–Letnikov variational Lyapunov estimator with adaptive tail-sum truncation, (iii) joint search over parameters and incommensurate orders by the Marine Predators Algorithm, and (iv) a fractional conditional Lyapunov exponent (FCLE) that recovers the integer-order limit. Applied with a fixed configuration to the fractional-order Lorenz, Ma–Chen financial, Iqbal–Wang, and Hyper–Chen systems, the framework converges to feasible attractors with enlarged Lyapunov spectra. Dissipativity is rigorously verified; all selected optima have strictly negative Lyapunov trace at the reported precision. FCLE analysis on the optimized Lorenz attractor recovers the integer-order identity

c_{min} = λ_{1}

under full-state coupling, and shows that single-state x-coupling raises the threshold to ≈9

λ_{1}^{*}

. The optimized fractional-order Lorenz attractor is employed as the random-number generator of a recent chaos-based image-encryption scheme, where it yields strong statistical results across standard benchmarks. Full article

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33 pages, 2733 KB

Open AccessArticle

Exploring Nonlinear Dynamics and Chaos in the Modified Korteweg–de Vries–Zakharov–Kuznetsov Equation with NARX Neural Networks

by Muhammad Ghulam Abbas Malik, Muhammad Mudassir and Zia Bashir

Math. Comput. Appl. 2026, 31(4), 126; https://doi.org/10.3390/mca31040126 - 7 Jul 2026

Abstract

This work examines the nonlinear dynamics of a generalized Korteweg–de Vries–Zakharov–Kuznetsov equation, a model that appears in plasma physics, shallow water flows, and nonlinear wave propagation. By applying a solitary-wave transformation, the governing partial differential equation is reduced to an autonomous dynamical system, [...] Read more.

This work examines the nonlinear dynamics of a generalized Korteweg–de Vries–Zakharov–Kuznetsov equation, a model that appears in plasma physics, shallow water flows, and nonlinear wave propagation. By applying a solitary-wave transformation, the governing partial differential equation is reduced to an autonomous dynamical system, enabling a direct study of its phase portraits and equilibrium behavior. Stability of the fixed points is assessed through Jacobian matrices and eigenvalue classification, revealing parameter regimes that admit saddle states, centers, and oscillatory structures. The system’s richer behavior is explored by varying key parameters, with phase-space trajectories exhibiting periodic, quasiperiodic, and irregular wave patterns. To probe the onset of complexity, we employ several diagnostic tools, including time-series evolution, Lyapunov exponents, bifurcation analysis, sensitivity tests, and Poincaré sections, which together indicate transitions to chaotic motion. The resulting dynamics are further captured using a nonlinear autoregressive neural network, which accurately reproduces the observed trajectories. The combination of analytical and computational perspectives provides a clear framework for understanding this generalized equation and offers a practical approach for investigating other nonlinear systems with a similar structure. Full article

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43 pages, 1365 KB

Open AccessArticle

A Modular and Reproducible Pipeline for Generating Physically Coherent Synthetic Benchmarks for the EV-STSP

by Juan Carlos Hernandez-Marin, Laura Cruz-Reyes, Bernabé Dorronsoro, Patricia Ruiz, Norberto Castillo-Garcia and Hector Joaquin Fraire-Huacuja

Math. Comput. Appl. 2026, 31(4), 125; https://doi.org/10.3390/mca31040125 - 7 Jul 2026

Abstract

The evaluation of optimization algorithms for electric vehicle routing problems depends strongly on the quality of the benchmark instances used during experimentation. However, many synthetic instances simplify the joint effects of geometry, topography, operation, and energy, which can distort algorithmic assessment. This article [...] Read more.

The evaluation of optimization algorithms for electric vehicle routing problems depends strongly on the quality of the benchmark instances used during experimentation. However, many synthetic instances simplify the joint effects of geometry, topography, operation, and energy, which can distort algorithmic assessment. This article proposes a modular and reproducible pipeline for generating synthetic instances of the Electric Vehicle Steiner Traveling Salesman Problem (EV-STSP), calibrated from a real urban reference network based on publicly available Madrid data. The pipeline combines directed graph construction, geometric control, attribute enrichment, charging-infrastructure placement, structured export, and explicit traceability mechanisms. To assess the realism of the generated instances, a three-level validation protocol is introduced, covering marginal distributional similarity, physical coherence among dependent variables, and structural–operational consistency. A controlled ablation design is then used to quantify the contribution of individual modules to overall benchmark realism. Within the experimental domain explored here, the results show that benchmark realism is not supported uniformly by all modules; instead, it depends primarily on arc-length generation, topographic alignment, and energy modeling. The proposed framework therefore offers not only a reproducible way to generate EV-STSP benchmarks, but also an explicit methodology for verifying whether such benchmarks are suitable for comparative algorithmic experimentation. Full article

(This article belongs to the Section Engineering)

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Open AccessArticle

Impulsive Antibody Therapy and Hopf Bifurcation Analysis in SARS-CoV-2 Dynamics

by Fahad Al Basir, Khalid Aldawsari and Yahya AlQahtani

Math. Comput. Appl. 2026, 31(4), 124; https://doi.org/10.3390/mca31040124 - 7 Jul 2026

Abstract

In this article, we formulated a mathematical model to describe SARS-CoV-2 development in humans, accounting for the dynamics of susceptible and infected epithelial cells, viral particles, ACE2 receptors, cytotoxic T lymphocytes (CTLs), and antibodies. The basic reproduction number and equilibrium points are derived, [...] Read more.

In this article, we formulated a mathematical model to describe SARS-CoV-2 development in humans, accounting for the dynamics of susceptible and infected epithelial cells, viral particles, ACE2 receptors, cytotoxic T lymphocytes (CTLs), and antibodies. The basic reproduction number and equilibrium points are derived, with stability analysis showing that the disease-free equilibrium is maintained when

R_{0} < 1

, while an endemic equilibrium arises for

R_{0} > 1

. Additionally, Hopf bifurcating periodic solutions are observed under elevated viral replication and infection rates. To capture therapeutic intervention, an impulsive control framework based on antibody-mediated drug administration is introduced. The existence and stability of a disease-free periodic orbit are established through the impulsive reproduction number

R_{0}^{i m p}

, with stability ensured when

R_{0}^{i m p} < 1

. The findings from numerical simulations support the analytical outcomes, proving the efficacy of impulsive control in suppressing viral persistence. The current research work offers important knowledge on the interaction between immune system and impulsive control mechanisms, which serves as a basis to develop therapies against SARS-CoV-2. Full article

(This article belongs to the Section Natural Sciences)

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16 pages, 2922 KB

Open AccessArticle

Mathematical Modeling for Tumor–Immune Dynamics with Clinical Validation

by Mohsin Kamran, Johari Yap Abdullah and Abdul Majeed

Math. Comput. Appl. 2026, 31(4), 123; https://doi.org/10.3390/mca31040123 - 6 Jul 2026

Abstract

Pituitary adenoma is a clinically important brain tumor whose progression and therapeutic outcomes are influenced by intricate interactions between tumor development and the host immune response. Globally, pituitary adenomas account for approximately 15% of all intracranial tumors. This study aims to investigate clinical [...] Read more.

Pituitary adenoma is a clinically important brain tumor whose progression and therapeutic outcomes are influenced by intricate interactions between tumor development and the host immune response. Globally, pituitary adenomas account for approximately 15% of all intracranial tumors. This study aims to investigate clinical MRI data obtained from a patient who recovered from a pituitary adenoma. The collected data provide measurements of tumor volume (mm) at several time points throughout the treatment period. The patient received vaccine-based therapy accompanied by regular clinical assessments, and achieved recovery after nearly twenty-two months. Motivated by the clinical observations and the underlying treatment mechanism, a mathematical model describing tumor–immune–vaccine interactions is developed. The proposed ordinary differential equation (ODE) framework incorporates tumor cells, immune cells, and vaccine components to characterize the temporal evolution of tumor volume during treatment. Fundamental dynamical properties of the model, including positivity, boundedness, existence of solutions, and equilibrium stability, are established through analytical techniques. In addition, numerical simulations are performed using the fourth-order Runge–Kutta (RK4) method and validated against the available clinical measurements. The numerical results exhibit close agreement between the observed and simulated data, yielding a minimal root mean square error (RMSE). Furthermore, sensitivity analysis highlights the significant role of immune- and vaccine-related parameters in regulating tumor suppression. The findings suggest that a relatively simple mechanistic framework can effectively capture the reduction in pituitary adenoma under vaccine-based therapy. Full article

(This article belongs to the Special Issue Latest Research in Mathematical Modeling in Cancer Research)

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