Mathematical and Computational Applications

39 pages, 747 KB

Open AccessArticle

Impacts and Spatial Spillover Effects of Artificial Intelligence Development on Government Governance Performance—Evidence from China

by Jia Yuan

Math. Comput. Appl. 2026, 31(4), 167; https://doi.org/10.3390/mca31040167 - 21 Aug 2026

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Abstract

With the advancement of a new round of technological revolution and industrial transformation, regional AI development has become increasingly relevant to changes in government governance performance (GGP). However, existing research has predominantly concentrated on a single dimension or static effects of AI development [...] Read more.

With the advancement of a new round of technological revolution and industrial transformation, regional AI development has become increasingly relevant to changes in government governance performance (GGP). However, existing research has predominantly concentrated on a single dimension or static effects of AI development on GGP, lacking systematic investigations into the short-term and long-term effects as well as spatial spillover effects. To address these research gaps, using panel data from 286 prefecture-level cities in China from 2009 to 2023, this study empirically examines the short-term and long-term effects, threshold effects, and spatial spillover effects of AI development on GGP. The research findings indicate that regional AI technological capacity is significantly and positively associated with GGP. The short-term and long-term effect tests reveal a negative association between AI development and GGP in the short term and a positive association in the long term. In the short term, this association may be constrained by the “creative destruction” effect, whereas in the long term, the positive association becomes stronger as regional technological capacity increasingly supports the integration of AI-related technologies into governance scenarios. There is a single-threshold effect between the institutional environment and the intensity of AI funding. Beyond the threshold value, the positive association between AI development and GGP becomes significantly stronger. Regional AI technological capacity is positively associated not only with local GGP but also with GGP in neighboring regions, potentially through technological spillovers and cross-regional collaboration. This study provides empirical evidence and theoretical support for the modernization of government governance empowered by AI. Full article

(This article belongs to the Section Social Sciences)

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48 pages, 691 KB

Open AccessArticle

On a New Class of Power-Transformed Bimodal Exponential Distributions with Inferential Procedures and Applications

by Ibrahim Hassan Alkhairy, Jondeep Das, Laxmi Prasad Sapkota, Hassan Alsuhabi, Md Moyazzem Hossain, Eslam Hussam and A. M. A. Gemeay

Math. Comput. Appl. 2026, 31(4), 166; https://doi.org/10.3390/mca31040166 - 20 Aug 2026

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Abstract

In this paper, we introduce a new three-parameter lifetime distribution that is obtained via a power transformation of the modified bimodal exponential model. The inclusion of an additional shape parameter significantly enhances the flexibility of the baseline distribution, allowing it to capture a [...] Read more.

In this paper, we introduce a new three-parameter lifetime distribution that is obtained via a power transformation of the modified bimodal exponential model. The inclusion of an additional shape parameter significantly enhances the flexibility of the baseline distribution, allowing it to capture a wide range of distributional characteristics, including skewness, heavy tails, and varying hazard rate shapes such as increasing, decreasing, and non-monotonic forms. Several important structural properties of the proposed model are derived, including explicit expressions for the probability density function, cumulative distribution function, moments, and moment generating function. Entropy measures such as Rényi entropy, Shannon entropy, and cumulative residual entropy are also obtained. Key reliability characteristics, including the survival function, hazard rate function, cumulative hazard function, reversed hazard rate, and mean residual life function, are investigated in detail. A theoretical result on the modality of the distribution is established, demonstrating its ability to exhibit both unimodal and bimodal shapes. Parameter estimation is carried out using maximum likelihood estimation along with several alternative methods. A comprehensive simulation study is conducted to evaluate the performance of the estimators under different parameter settings. Finally, the applicability and effectiveness of the proposed distribution are demonstrated through the analysis of real datasets from reliability and environmental studies. Comparative results based on goodness-of-fit measures indicate that the proposed model provides a superior fit compared to several existing competing distributions. Full article

(This article belongs to the Section Natural Sciences)

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35 pages, 907 KB

Open AccessArticle

A General Transformation Framework from 3-Point Relaxed Binary Subdivision Schemes to 4-Point Relaxed Quaternary Subdivision Schemes for Efficient Curve Modeling

by Rabia Hameed, Jihad Younis, Maryam Salem Alatawi, Sidra Nosheen and Shahnaz Sharif

Math. Comput. Appl. 2026, 31(4), 165; https://doi.org/10.3390/mca31040165 - 15 Aug 2026

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Abstract

Subdivision schemes are widely used in computer-aided geometric design and computer graphics for generating smooth curves from discrete control polygons. This paper presents a general transformation framework for constructing the corresponding 4-point relaxed quaternary subdivision schemes from 3-point relaxed binary subdivision schemes. The [...] Read more.

Subdivision schemes are widely used in computer-aided geometric design and computer graphics for generating smooth curves from discrete control polygons. This paper presents a general transformation framework for constructing the corresponding 4-point relaxed quaternary subdivision schemes from 3-point relaxed binary subdivision schemes. The proposed framework requires only the subdivision mask of the binary scheme and is applicable to both parametric and non-parametric subdivision schemes. The resulting quaternary schemes preserve the fundamental properties of their binary counterparts, including continuity, polynomial generation, polynomial reproduction, and shape-preserving characteristics. In many cases, they also possess an enlarged continuity parameter range and increased Hölder regularity. Several examples are presented to demonstrate the applicability of the proposed framework and to illustrate the relationship between the binary subdivision schemes and their corresponding quaternary subdivision schemes. The graphical results show that the transformed quaternary schemes preserve the geometric behavior of their binary counterparts while producing smoother limit curves with fewer subdivision iterations. The proposed framework provides a systematic and efficient approach for establishing the connection between binary and quaternary subdivision schemes and for constructing quaternary schemes directly from existing binary schemes. Full article

(This article belongs to the Section Engineering)

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22 pages, 6688 KB

Open AccessArticle

Enhanced Concept-Based Exploration of Manipulators’ Design Spaces with Kinematics, Dynamics and Control Co-Design

by Dithoto Modungwa

Math. Comput. Appl. 2026, 31(4), 164; https://doi.org/10.3390/mca31040164 - 15 Aug 2026

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Abstract

Determining the parameters of a manipulator for optimal performance is a challenging task. This is primarily due to possible conflicting objectives, various tasks that should be considered, and the highly non-linear behavior that is involved. This work proposes an enhanced version of the [...] Read more.

Determining the parameters of a manipulator for optimal performance is a challenging task. This is primarily due to possible conflicting objectives, various tasks that should be considered, and the highly non-linear behavior that is involved. This work proposes an enhanced version of the concept-based design space exploration (C-DSE) approach for the design of manipulators. According to the C-DSE approach, prior to the search, the designers divide the set of feasible solutions into meaningful subsets, which are termed concepts. The design space exploration involves a simultaneous search for optimal solutions within each of the pre-defined concepts. This enhanced framework integrates the following: (1) kinematics, dynamics, and control co-design, and the simultaneous optimization of manipulator morphology and controller parameters; (2) surrogate-assisted optimization using Gaussian process (GP) and neural network (NN) models to reduce computational cost; (3) approximately 30 performance metrics spanning kinematic, dynamic, structural, control, and task performance domains; (4) task-aware feasibility verification applying a multi-level hierarchy; (5) a generative AI integration pathway using diffusion models and LLM-guided concept generation (proposed in this preliminary investigation). The results demonstrate a 95.7% reduction in high-fidelity function evaluations (50,000 to 2150), corresponding to a 23.3 times reduction in evaluation count and a 6.6 times reduction in wall-clock computation time (25 h to 3.8 h). Co-design yields up to a 35% improvement in energy efficiency and a 28% reduction in tracking error compared to sequential morphology-only optimization. Full article

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

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11 pages, 266 KB

Open AccessArticle

Recent Results on Nonlinear Retarded Integral Inequalities with Applications

by Abdul Shakoor, Mahvish Samar, Ifra Kalsoom and Samad Wali

Math. Comput. Appl. 2026, 31(4), 163; https://doi.org/10.3390/mca31040163 - 14 Aug 2026

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Abstract

This article establishes new retarded nonlinear integral inequalities that extend and generalize several known results in the literature, including recently reported estimates. These inequalities are used to derive explicit bounds for the unknown functions. These bounds are shown to be sharper and more [...] Read more.

This article establishes new retarded nonlinear integral inequalities that extend and generalize several known results in the literature, including recently reported estimates. These inequalities are used to derive explicit bounds for the unknown functions. These bounds are shown to be sharper and more general than existing ones, recovering earlier results as special cases. As an application, the derived inequalities are used to study the boundedness, uniqueness, and global existence of solutions to an initial value problem for a class of nonlinear integro-differential equations with delay. An illustrative example is presented to illustrate the applicability and effectiveness of the results. Full article

(This article belongs to the Section Natural Sciences)

23 pages, 901 KB

Open AccessArticle

A Robust High-Order Haar Wavelet Collocation Method for Linear and Nonlinear Delay Differential Equations: Theoretical Analysis and Numerical Validation

by Naveed Khan, Muhammad Asif, Muhammad Ahsan, Naveed Ullah and Ioan-Lucian Popa

Math. Comput. Appl. 2026, 31(4), 162; https://doi.org/10.3390/mca31040162 - 14 Aug 2026

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Abstract

Delay differential equations form a distinct class of differential equations in which the derivative of the dependent variable depends on its value at an earlier time. This unique structure makes them particularly suitable for modeling phenomena in areas such as population dynamics, epidemiology, [...] Read more.

Delay differential equations form a distinct class of differential equations in which the derivative of the dependent variable depends on its value at an earlier time. This unique structure makes them particularly suitable for modeling phenomena in areas such as population dynamics, epidemiology, and the spread or control of diseases. In this study, a high-order Haar wavelet collocation method (HoHWCM) is proposed for the numerical solution of second-order delay differential equations (SoDDEs). The delay term is approximated using a Taylor expansion, transforming the SoDDE into a standard second-order differential equation (SoDE). The nonlinear terms are linearized through an innovative Taylor series-based approach, which also serves as an efficient iterative scheme. The resulting SoDE is then discretized using Haar wavelet basis functions, yielding a system of linear algebraic equations that is solved iteratively. This strategy eliminates the need for Newton’s or Broyden’s methods, thereby reducing computational cost and improving time efficiency. A variety of linear and nonlinear benchmark problems are solved to evaluate the accuracy and efficiency of the proposed method. Comparative results with established approaches from the literature demonstrate that the HoHWCM achieves higher accuracy, faster convergence, and reduced computational time, making it a highly effective alternative for solving such problems. Full article

(This article belongs to the Special Issue Mathematical Modeling, Computational Methods, and AI-Driven Applications in Industrial and Applied Mathematics)

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31 pages, 2980 KB

Open AccessArticle

Dynamic Stability Analysis of Grooved Rubber Hydrodynamic Journal Bearings Considering Elastic Deformation of the Liner

by Mahdi Zare Mehrjardi, Ahmad Golzar Shahri and Asghar Dashti Rahmatabadi

Math. Comput. Appl. 2026, 31(4), 161; https://doi.org/10.3390/mca31040161 - 12 Aug 2026

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Abstract

This study investigates the influence of liner elastic deformation on the static performance and dynamic stability of grooved rubber journal bearings (GRJBs) using the finite element method (FEM) in conjunction with a Winkler elastic foundation model. The formulation is validated through comparison with [...] Read more.

This study investigates the influence of liner elastic deformation on the static performance and dynamic stability of grooved rubber journal bearings (GRJBs) using the finite element method (FEM) in conjunction with a Winkler elastic foundation model. The formulation is validated through comparison with the limiting case of a plain circular bearing. Increasing the effective liner stiffness (

\hat{k}

) reduces liner compliance and consequently shifts the overall system response toward that of a rigid bearing. For configurations with 6, 9, and 12 grooves, raising the effective liner stiffness from 0.4 to 4 GPa/mm increases the maximum hydrodynamic pressure by approximately 8–15% and enhances the load-carrying capacity by about 5–8%. The variation in key performance indicators becomes progressively less sensitive beyond an approximate threshold, entering a low-sensitivity region near 1.5 GPa/mm. Dynamic stability is assessed through linear perturbation of the journal center about its static equilibrium position. The stiffness and damping matrices are derived from the perturbed lubricant-film pressure response, capturing both restoring forces and squeeze-film effects. The results indicate that increasing effective liner stiffness generally strengthens the direct stiffness and damping behavior and raises the dimensionless critical mass, suggesting an improved stability margin under the investigated conditions. The influence of groove number on dynamic response is also significant. Fewer grooves tend to promote a more favorable balance between restoring and damping actions, whereas higher groove counts can reduce the stability margin despite improvements in lubricant supply characteristics. Among the studied cases, the 6-groove bearing yields the highest predicted critical mass and linear stability margin, while the 9-groove configuration provides the highest vertical direct stiffness coefficient. Overall, the findings emphasize that the groove number and effective liner stiffness should be optimized jointly, as static performance improvements do not necessarily translate into proportional gains in dynamic stability. Full article

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

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21 pages, 3032 KB

Open AccessArticle

Bridge-Net: Boundary-Ambiguity Guided Residual Injection for MRI-Based Brain Tumor Segmentation

by Haoran Gu, Shuo Guo, Yuhan Ying, Zhijian Zhu and Guoli Song

Math. Comput. Appl. 2026, 31(4), 160; https://doi.org/10.3390/mca31040160 - 10 Aug 2026

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Abstract

Encoder-decoder segmentation networks use skip connections to recover spatial detail, but direct feature transfer can also propagate irrelevant high-frequency responses into the decoder. This problem is pronounced at weak or irregular tumor margins, where contour evidence is useful but should not modify semantically [...] Read more.

Encoder-decoder segmentation networks use skip connections to recover spatial detail, but direct feature transfer can also propagate irrelevant high-frequency responses into the decoder. This problem is pronounced at weak or irregular tumor margins, where contour evidence is useful but should not modify semantically reliable features indiscriminately. We propose Bridge-Net, a boundary-ambiguity guided residual injection framework for two-dimensional brain tumor MRI segmentation. Bridge-Net formulates boundary enhancement as a conditional feature-correction problem. A structural boundary prior is coupled multiplicatively with an ambiguity map obtained from an auxiliary foreground logit. The ambiguity cue is deterministic and probability-based, rather than a Bayesian or calibrated uncertainty estimate. The overlap between the two cues identifies locations that are both boundary-like and prediction-ambiguous. A level-specific gated residual branch then injects the resulting cue into each skip feature, while a zero-initialized bounded scaling factor preserves an identity-like main pathway at the start of optimization. Experiments were conducted on TCGA-LGG and BRISC2025 under dataset-specific protocols, including patient-level partitioning for TCGA-LGG and the official image-level split for BRISC2025. Bridge-Net achieved Dice/IoU/HD95 values of 84.16%/73.65%/15.38 on TCGA-LGG and 87.26%/77.63%/8.68 on BRISC2025. Patient-level paired analysis on TCGA-LGG and image-level paired analysis on BRISC2025 further supported the improvements over UCTransNet. Ablation results support the complementary roles of structural boundary and probability-ambiguity cues, and a same-seed repeated-run comparison across reproduced models supports the stability of the observed performance trend under the tested setting. Relative to UCTransNet, the proposed mechanism increases the parameter count from 7.982 M to 7.988 M and FLOPs from 24.083 G to 24.196 G at

256 \times 256

resolution. These results indicate that ambiguity-filtered boundary residual fusion introduces only a small increase in parameter count and FLOPs for boundary-ambiguous MRI segmentation, although broader patient-level and volumetric validation remains necessary. Full article

(This article belongs to the Topic Machine Learning, Optimization, and Computational Methods in Biomedical Informatics)

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24 pages, 1756 KB

Open AccessArticle

On the Background Driving Lévy Density Associated with the General Tempered Stable Distribution: Theoretical Properties and Financial Applications

by Aubain Nzokem and Daniel Maposa

Math. Comput. Appl. 2026, 31(4), 159; https://doi.org/10.3390/mca31040159 - 7 Aug 2026

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Abstract

This paper identifies and characterizes the background driving Lévy process (BDLP) associated with the Generalized Tempered Stable (GTS) distribution, a flexible seven-parameter family of infinitely divisible distributions with applications in physics and quantitative finance. We show that the corresponding BDLP is a finite-variation, [...] Read more.

This paper identifies and characterizes the background driving Lévy process (BDLP) associated with the Generalized Tempered Stable (GTS) distribution, a flexible seven-parameter family of infinitely divisible distributions with applications in physics and quantitative finance. We show that the corresponding BDLP is a finite-variation, infinite-activity Type B Lévy process and derive its explicit background driving characteristic exponent function (BDCEF). The resulting BDLP provides a unified representation that encompasses several important special cases, including the bilateral stable, bilateral Gamma, and Variance Gamma distributions. Building on these results, we develop a simulation framework based on a stationary Ornstein–Uhlenbeck (OU)-type process driven by the GTS BDLP. The mean-reversion speed parameter of the OU process is calibrated using maximum likelihood estimation applied to daily return data from the SPY ETF and Ethereum over the period 2010–2024. The proposed simulation methodology produces realistic daily cumulative return trajectories, and comprehensive numerical error analyses demonstrate the accuracy and efficiency of the resulting discretization scheme. These findings provide both a theoretical extension of Lévy-driven OU models and a practical framework for simulating complex financial return dynamics. Full article

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

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40 pages, 4454 KB

Open AccessArticle

Bayesian Spike-and-Slab Finite Mixture with Adaptive Tail Regularisation for Robust Volatility Regime Identification: Evidence from the Johannesburg Stock Exchange

by Ntebogang Dinah Moroke and Sharon Nwanamidwa

Math. Comput. Appl. 2026, 31(4), 158; https://doi.org/10.3390/mca31040158 - 6 Aug 2026

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Abstract

Volatility regime identification underpins risk management and portfolio allocation in quantitative finance, yet standard mixture models fail in heavy-tailed environments: components are consumed by outliers rather than genuine persistent regimes. We propose the Bayesian Spike-and-Slab Finite Mixture with Adaptive Tail Regularisation (BSS-FM-ATR), which [...] Read more.

Volatility regime identification underpins risk management and portfolio allocation in quantitative finance, yet standard mixture models fail in heavy-tailed environments: components are consumed by outliers rather than genuine persistent regimes. We propose the Bayesian Spike-and-Slab Finite Mixture with Adaptive Tail Regularisation (BSS-FM-ATR), which resolves this at the component level via a spike-and-slab prior on the degrees-of-freedom parameter

ν_{k}

. A latent binary indicator assigns each component to a slab state (data-driven tail adaptation for genuine regimes) or a spike state (inert heavy-tail absorber for artefacts). Applied to 19 JSE blue-chip securities over December 2019 to December 2025—spanning the COVID-19 crash and Eskom load-shedding episodes—BSS-FM-ATR achieves the highest silhouette score (0.3809 on the full dataset), regime persistence (0.9391), and interpretability (0.800) across nine standard baselines, including Gaussian HMM, MS-AR, MS-GARCH(1,1), and Bayesian Changepoint detection, plus three outlier-component comparators (Contaminated–Normal Mixture, TCLUST, and robust Bayesian mixture). A complete rerun after removing the contaminated observations confirms that ARI (

Δ = - 0.0283

) and persistence (

Δ = + 0.0105

) remain stable; the silhouette reduction (from 0.3809 to 0.3773) is a positive finding: it confirms that the spike-state component R3 was correctly identified as a compact, well-separated artefact cluster whose removal reveals the genuine regime structure. This dual validation establishes BSS-FM-ATR’s role as both a regime identifier and a data quality filter. The method isolates a Yahoo Finance data-contamination artefact (

n = 21

, January–February 2025) through a principled spike-and-slab mechanism, providing an explicit posterior probability

p (γ_{3} = 0 ∣ X) > 0.99

of artefact status: a structural identifier that contaminated-normal and robust Bayesian alternatives cannot supply, establishing its value as both a regime identifier and a data quality filter for financial monitoring systems. Full article

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21 pages, 3253 KB

Open AccessArticle

Adaptive Fuzzy Control Without Feasibility Conditions for Fractional-Order Nonlinear State-Constrained Systems: A Bounded Virtual Controller Design Method

by Xiaobing Han, Ziyun Zhao, Zhiyao Ma and Hao Wang

Math. Comput. Appl. 2026, 31(4), 157; https://doi.org/10.3390/mca31040157 - 6 Aug 2026

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Abstract

This paper addresses adaptive fuzzy tracking control for fractional-order nonlinear systems (FONSs) subject to asymmetric state constraints without imposing separate feasibility conditions on intermediate virtual controllers. Fuzzy logic systems are used to approximate the unknown nonlinear functions. By exploiting the boundedness of the [...] Read more.

This paper addresses adaptive fuzzy tracking control for fractional-order nonlinear systems (FONSs) subject to asymmetric state constraints without imposing separate feasibility conditions on intermediate virtual controllers. Fuzzy logic systems are used to approximate the unknown nonlinear functions. By exploiting the boundedness of the hyperbolic tangent function, a coordinate transformation and an asymmetric fractional barrier Lyapunov function (AFBLF) are developed to construct bounded virtual control signals. Within a backstepping framework, an adaptive fuzzy controller is designed. Fractional-order Lyapunov analysis establishes semi-global uniform ultimate boundedness of all closed-loop signals and preservation of the prescribed asymmetric constraints. Comparative and benchmark simulations demonstrate constraint satisfaction, moderate control effort, and suppression of high-frequency chattering-like oscillations. Full article

(This article belongs to the Topic Dynamics Modeling, Chaos Theories and Nonlinear Control of Complex Systems: Complexity and AI-Driven to Hybrid and Distributed Computing Approaches)

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19 pages, 1023 KB

Open AccessArticle

Accurate Treatment of Solution and Flux Discontinuities in 2D Time-Dependent Interface Problems via Meshless Method

by Muhammad Asif, Ruqia Khan, Mehnaz Shakeel and Ioan-Lucian Popa

Math. Comput. Appl. 2026, 31(4), 156; https://doi.org/10.3390/mca31040156 - 5 Aug 2026

Viewed by 356

Abstract

Interface problems frequently arise in applications including heat conduction with composite materials, fluid flow in porous media, and diffusion–reaction processes across heterogeneous domains. This paper presents a numerical method that combines radial basis functions with a finite difference method to solve two-dimensional linear [...] Read more.

Interface problems frequently arise in applications including heat conduction with composite materials, fluid flow in porous media, and diffusion–reaction processes across heterogeneous domains. This paper presents a numerical method that combines radial basis functions with a finite difference method to solve two-dimensional linear and nonlinear parabolic-type interface problems. In the proposed approach, spatial derivatives are approximated using multi-quadric radial basis functions, while the time derivative is discretized via a finite difference method. The method is applied to both linear and nonlinear problems. Gaussian elimination is used to solve the resulting algebraic equation in linear cases, while a quasi-Newton linearization technique is used to handle the nonlinear terms in nonlinear cases. Several numerical experiments are performed to assess the performance of the proposed method. The results are compared with the Haar wavelet collocation method, demonstrating the improved accuracy, computational efficiency, and straightforward implementation of the method. Full article

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

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20 pages, 1097 KB

Open AccessArticle

Rotary Burnishing of Cylindrical Surfaces: Kinematic Layout, Relative Curvature Tensor, and Contact-Conformity Classification

by Kirill A. Bashmur, Alexander V. Zagulyaev and Ivan S. Nekrasov

Math. Comput. Appl. 2026, 31(4), 155; https://doi.org/10.3390/mca31040155 - 4 Aug 2026

Viewed by 319

Abstract

Rotary and vibro-rotary burnishing create regular arrays of imprints whose geometric interaction depends on the pitch, indentation depth, and relative curvature of the tool–workpiece pair. This paper develops a unified kinematic–curvature model that maps machine settings to an imprint layout on the unwrapped [...] Read more.

Rotary and vibro-rotary burnishing create regular arrays of imprints whose geometric interaction depends on the pitch, indentation depth, and relative curvature of the tool–workpiece pair. This paper develops a unified kinematic–curvature model that maps machine settings to an imprint layout on the unwrapped cylindrical surface and constructs the relative curvature tensor. The tensor state and full normalized neighbor metric assign the contact state to one of four mutually exclusive categories: non-elliptic, cell-limited, near-conformal (warning), or isolated elliptic. The tensor formulation is invariant under rotation of the tangent basis and provides a common geometric mapping for external cylinders and internal tubes. The kinematic map and tensor classification are independent of the rigid-plastic mean-pressure approximation and are verified by the factor relation between the center-line slope and imprint orientation, tensor invariance, limiting cases, and a closed-form identity. The calibrated approximation is used solely to estimate the maximum-load penetration and an equivalent projected footprint. At a fixed normal force and effective hardness, the projected area is identical in all curvature cases, whereas the curvature changes the penetration and footprint aspect ratio. Neglecting the workpiece curvature underestimates the external cylinder indentation depth by about 5.8% relative to the full tensor calculation; this ratio is independent of the force and effective hardness within the approximation. For the stated internal tube row pitch and hardness, the axis-aligned cell-limited transition force is 5–8 N. Evaluation with the full metric shows that the consecutive-event vectors are separated well; the periodic-row neighbor nevertheless places the reference case in the cell-limited class. A closed-form expression for this transition force is derived. The model provides a transition criterion verified by analytical identity and consistency checks; residual geometry and post-threshold pressure redistribution require unloading calibration and a periodic unilateral contact formulation, respectively. Full article

(This article belongs to the Section Engineering)

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24 pages, 2166 KB

Open AccessArticle

On the Numerical Solution of the Multiscale Models Characterising Noroviral Infectious Disease Systems Using the Multistage Spectral the Relaxation Method and the Nonstandard Finite Difference Method

by Kizito Muzhinji

Math. Comput. Appl. 2026, 31(4), 154; https://doi.org/10.3390/mca31040154 - 3 Aug 2026

Viewed by 394

Abstract

Multiscale models for infectious disease systems are highly nonlinear. This presents substantial difficulties for both analysis and computation. Consequently, there is a continuous demand for the development of efficient numerical methods that provide reliable solutions. Over time, various numerical techniques have been developed [...] Read more.

Multiscale models for infectious disease systems are highly nonlinear. This presents substantial difficulties for both analysis and computation. Consequently, there is a continuous demand for the development of efficient numerical methods that provide reliable solutions. Over time, various numerical techniques have been developed for single-scale models. However, multiscale models have increasingly relied on built-in solvers and, more recently, the nonstandard finite difference method. The primary aim of this study is to offer an in-depth examination of the multistage spectral relaxation method (MSRM) applied to the multiscale model characterising norovirus infection. This study also provides a comprehensive comparison with the nonstandard finite difference method (NSFDM) in terms of convergence and accuracy, as well as their handling of highly nonlinear systems of ordinary differential equations. Both schemes were validated against an adaptive ODE45 scheme in MATLAB2025a, which served as the reference solver. The numerical outcomes indicate that the MSRM achieves a better accuracy level, with relative

L^{2}

errors ranging from

10^{- 9}

to

10^{- 7}

for

Δ τ \leq 0.10

and

N_{ch} = 8

. In contrast, the NSFDM provides solid first-order accuracy, yielding

L^{2}

errors around

10^{- 4}

, while ensuring strict unconditional positivity and stability across all tested step sizes from

h = 0.01

to

2.0

. This study features a parameter sensitivity analysis that varies

β_{H}, δ_{H}, α_{h}, μ_{V}, μ_{H}

, as well as semi-log error graphs, convergence rate visuals, and CPU performance benchmarks. The MSRM costs about 24 times more per run, but it offers better accuracy for between-host variables. This makes it the preferred method for high-fidelity applications. In contrast, the NSFDM is the best option for quick parameter sweeps and long simulations that require guaranteed positivity. Full article

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3 pages, 480 KB

Open AccessCorrection

Correction: Umegaki et al. Mathematical Structure of RelB Dynamics in the NF-κB Non-Canonical Pathway. Math. Comput. Appl. 2024, 29, 62

by Toshihito Umegaki, Naoya Hatanaka and Takashi Suzuki

Math. Comput. Appl. 2026, 31(4), 153; https://doi.org/10.3390/mca31040153 - 3 Aug 2026

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Abstract

In the original publication [...] Full article

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20 pages, 8821 KB

Open AccessArticle

Numerical Approximation of a Smoking Dynamics Model Using a Hybrid Deep Neural Network Architecture

by Allah Dad, Shumaila Javeed, Mansoor Shaukat Khan, Atif Jameel and Dumitru Baleanu

Math. Comput. Appl. 2026, 31(4), 152; https://doi.org/10.3390/mca31040152 - 2 Aug 2026

Viewed by 469

Abstract

Despite the fact that smoking is still a significant global public health concern, current mathematical models of smoking dynamics primarily depend on conventional numerical solvers. A particular five-compartment smoking dynamics model has not yet been solved using deep neural network (DNN) techniques. In [...] Read more.

Despite the fact that smoking is still a significant global public health concern, current mathematical models of smoking dynamics primarily depend on conventional numerical solvers. A particular five-compartment smoking dynamics model has not yet been solved using deep neural network (DNN) techniques. In order to fill this research gap, this work creates a unique DNN framework that can simulate nonlinear smoking dynamics in a computationally efficient manner. The Levenberg–Marquardt backpropagation technique is used to improve a dual-hidden-layer network consisting of 20 radial basis activation function (RBAF) neurons and 40 log-sigmoid activation function (LSAF) neurons. With a minimum mean squared error (MSE) of

1.865 \times 10^{- 6}

and a coefficient of determination

R^{2}

equal to or near unity across all model variables, the trained DNN offers instantaneous predictions while maintaining superior accuracy, in contrast to traditional numerical methods that necessitate the explicit re-solving of differential equations for each parameter change. Crucially, our DNN-based framework is appropriate for automated public health decision-support systems since it functions independently and does not require human intervention during the prediction phase. Key smoking behaviors, such as initiation, quitting efforts, relapse dynamics, and long-term recovery patterns, are successfully replicated by the framework, while relapse dynamics are captured through the recovered-to-potential smoker pathway, consistent with the original model formulation. These findings show that the proposed DNN approach not only closes the methodological gap in the application of deep learning to smoking dynamics but also offers a dependable and computationally effective tool for quick evaluation of intervention scenarios, supporting evidence-based public health decision making without compromising accuracy. Full article

(This article belongs to the Section Natural Sciences)

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20 pages, 3699 KB

Open AccessArticle

Optimizing Traffic Signal Control Using Reinforcement Learning Methods: Hybrid Approach

by Azzeddine Ben Moussa and Adil Khazari

Math. Comput. Appl. 2026, 31(4), 151; https://doi.org/10.3390/mca31040151 - 1 Aug 2026

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Abstract

Urban traffic congestion remains a major challenge for modern cities, requiring intelligent traffic signal control (TSC) strategies capable of adapting to dynamic traffic conditions. This paper proposes a hybrid reinforcement learning approach for traffic signal control that combines the complementary learning mechanisms of [...] Read more.

Urban traffic congestion remains a major challenge for modern cities, requiring intelligent traffic signal control (TSC) strategies capable of adapting to dynamic traffic conditions. This paper proposes a hybrid reinforcement learning approach for traffic signal control that combines the complementary learning mechanisms of Q-learning, SARSA, and Monte Carlo algorithms to improve both learning efficiency and control performance. The proposed approach is implemented and evaluated using the Simulation of Urban MObility (SUMO) simulator on a realistic road network corresponding to the “Route de Sefrou” in Fez, Morocco. The traffic signal controller is trained through continuous interaction with the simulated environment and compared with the three individual reinforcement learning algorithms under identical experimental conditions. The experimental results demonstrate that the proposed hybrid approach provides more efficient traffic management, faster convergence, and greater learning stability than the individual algorithms. These findings demonstrate the potential of hybrid reinforcement learning as an effective solution for adaptive traffic signal control in realistic urban environments. Full article

(This article belongs to the Topic Dynamics Modeling, Chaos Theories and Nonlinear Control of Complex Systems: Complexity and AI-Driven to Hybrid and Distributed Computing Approaches)

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28 pages, 2646 KB

Open AccessArticle

Hybridizing of Multi-Objective Coronavirus Herd Immunity Optimizer with Lévy Flight for Time Scheduling of Internet of Things Appliances in Smart Homes

by Husam Jasim Mohammed, Nabeel Salih Ali, Sharif Naser Makhadmeh, Zaid Abdi Alkareem Alyasseri, Riyadh Rahef Nuiaa Al Ogaili and Zuraida Abal Abas

Math. Comput. Appl. 2026, 31(4), 150; https://doi.org/10.3390/mca31040150 - 1 Aug 2026

Viewed by 404

Abstract

With the rapid deployment of Internet of Things appliances in smart homes, making efficient energy scheduling is a critical necessity to satisfy their exponentially increased residential energy demand. The problem of optimizing appliance operational times in smart homes is known as the Appliance [...] Read more.

With the rapid deployment of Internet of Things appliances in smart homes, making efficient energy scheduling is a critical necessity to satisfy their exponentially increased residential energy demand. The problem of optimizing appliance operational times in smart homes is known as the Appliance Energy Scheduling Problem, which is a complex, NP-hard multi- objective challenge. Various metaheuristic algorithms have been utilized by researchers to address this problem; existing methods often struggle with slow convergence rates and are trapped in local optima. To overcome these limitations and produce a superior solution, this study proposes a new hybrid framework that integrates the Coronavirus Herd Immunity Optimizer (CHIO) with Lévy Flight (LF). By strategically embedding LF into the CHIO framework, the proposed method effectively balances exploration and exploitation search capabilities to achieve true global optimization. In the evaluation stage, three structural variations in hybrid CHIO models are evaluated against the standard appliance energy scheduling problem to determine the robust model and compare its performance with prominent existing methods in the literature. The experimental results demonstrate the superiority of the optimized CHIOLF-2 approach among other hybrid CHIO models. The CHIOLF-2 successfully navigates the trade-off between grid efficiency and user experience by achieving a reduction in electricity bills and the Peak-to-Average Ratio while maximizing user comfort through minimized appliance waiting times. Eventually, this research produces a highly efficient scheduling framework for modern smart homes and offers a versatile algorithmic design that can be readily adapted to address other complex real-world optimization problems. Full article

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35 pages, 2975 KB

Open AccessArticle

Adaptive Chaotic Golden Jackal Optimization for the Multi-Objective Optimal Design of Three-Element Dynamic Vibration Absorbers

by Eslam F. Kelash, Doaa A. Hammad, Mohamed A. El Sayed, Ragab A. El-Sehiemy and Mohamed A. Elsisy

Math. Comput. Appl. 2026, 31(4), 149; https://doi.org/10.3390/mca31040149 - 1 Aug 2026

Viewed by 366

Abstract

The optimal design of a three-element dynamic vibration absorber (TEDVA) involves a fundamental trade-off between minimizing the peak amplitude magnification (

H_{\infty}

norm) and the broadband energy absorption (

H_{2}

proxy), a conflict that is further complicated by the lack of [...] Read more.

The optimal design of a three-element dynamic vibration absorber (TEDVA) involves a fundamental trade-off between minimizing the peak amplitude magnification (

H_{\infty}

norm) and the broadband energy absorption (

H_{2}

proxy), a conflict that is further complicated by the lack of closed-form solutions, even for undamped primary systems. In this paper, we present an algorithm that extends the golden jackal optimizer with dynamic multi-map chaotic initialization, a Pareto-guided two-leader search structure driven by crowding distance, and a Pareto-gated self-adaptive differential evolution mutation to jointly ensure convergence and diversity. The algorithm is validated on the benchmark TEDVA case with mass ratio

μ = 0.1

and primary damping

ζ_{1} = 0.3

, and benchmarked against standard multi-objective algorithms (NSGA-II and MOPSO) as well as the single-objective AM-PSO baseline. Simulation results indicate that MODCGJO achieves a 7.3% reduction in peak amplitude compared to the state-of-the-art single-objective adaptive multi-swarm particle swarm optimization (AM-PSO), while maintaining a competitive

H_{2}

performance and converging to the same Pareto-optimal region as NSGA-II and MOPSO. Comprehensive Pareto metrics—hypervolume, generational distance, spread, and spacing—are adopted, validating the front’s superior quality and uniform distribution. Sensitivity analyses on both physical design parameters (spring and damping ratios) and algorithmic control parameters (population size, iteration count, and archive size) confirm the robustness of the obtained solution and the stability of MODCGJO’s performance across varying configurations. The results show that MODCGJO is an effective and reliable tool for the multi-objective design of vibration absorbers, providing a superior trade-off between conflicting performance criteria, with the Pareto front offering engineers flexible design choices for different application requirements. Full article

(This article belongs to the Section Engineering)

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17 pages, 394 KB

Open AccessArticle

An Application of Fractional Calculus to Column Theory

by José Villa-Morales and Manuel Ramírez-Aranda

Math. Comput. Appl. 2026, 31(4), 148; https://doi.org/10.3390/mca31040148 - 1 Aug 2026

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Abstract

In this article, we employ a fractional version of the radius of curvature in Euler’s equation for column buckling, enabling us to derive a fractional differential equation in the Caputo sense. We solve this equation and demonstrate that for certain values of the [...] Read more.

In this article, we employ a fractional version of the radius of curvature in Euler’s equation for column buckling, enabling us to derive a fractional differential equation in the Caputo sense. We solve this equation and demonstrate that for certain values of the fractional parameter, there exists a critical buckling force. Additionally, we provide a numerical scheme for accurately approximating this critical force. Full article

(This article belongs to the Section Engineering)

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15 pages, 451 KB

Open AccessArticle

DEA Cross-Efficiency Evaluation Considering Interval Efficiency with Aggressive–Benevolent Formulation

by Yingting Shu and Ke Gong

Math. Comput. Appl. 2026, 31(4), 147; https://doi.org/10.3390/mca31040147 - 1 Aug 2026

Viewed by 231

Abstract

In DEA cross-efficiency, information aggregation of self-evaluation and peer-evaluation has been one of the main concerns. The inherent variability of decision-makers’ preferences in peer-evaluation, whether expressed aggressively or benevolently within the secondary goal programming, can yield divergent peer-efficiency scores. Therefore, interval efficiency for [...] Read more.

In DEA cross-efficiency, information aggregation of self-evaluation and peer-evaluation has been one of the main concerns. The inherent variability of decision-makers’ preferences in peer-evaluation, whether expressed aggressively or benevolently within the secondary goal programming, can yield divergent peer-efficiency scores. Therefore, interval efficiency for considering different preferences of decision-makers and group opinions is used to represent the variable efficiency range. In this paper, comparison norms for the advantage degree between any two interval efficiencies are defined, and a pairwise advantage-degree matrix is developed. By aggregating this matrix through a dominance score, a unique ranking of DMUs can be obtained. Subsequently, a synthetic evaluation model, ICE-AB, is proposed for DEA cross-efficiency evaluation. To demonstrate the effectiveness, discriminatory capability, and practical applicability of ICE-AB, a benchmark numerical example, a differentiating numerical case, and an empirical application to major Chinese new energy vehicle manufacturers are provided. Comparative analysis and ranking results show that the new model not only preserves different peer-evaluation information but also obtains the unique ranking results of DMUs under uncertain attitudes of decision-makers. Full article

(This article belongs to the Section Engineering)

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31 pages, 5084 KB

Open AccessArticle

A Digital Twin for Brake Wear Predictive Maintenance

by Luke van Eyk, Johannes Moes, Brian Ellis, Stephan Schmidt and Stephan Heyns

Math. Comput. Appl. 2026, 31(4), 146; https://doi.org/10.3390/mca31040146 - 1 Aug 2026

Viewed by 657

Abstract

Brake pad wear is governed by coupled thermo-mechanical interactions in which degradation alters braking behaviour. This altered braking behaviour, in turn, affects vehicle dynamics, which, in turn, influences future wear evolution. Existing diagnostic and prognostic approaches typically neglect this dynamics–wear coupling, potentially limiting [...] Read more.

Brake pad wear is governed by coupled thermo-mechanical interactions in which degradation alters braking behaviour. This altered braking behaviour, in turn, affects vehicle dynamics, which, in turn, influences future wear evolution. Existing diagnostic and prognostic approaches typically neglect this dynamics–wear coupling, potentially limiting their ability to accurately predict remaining useful life under evolving operating conditions. This work proposes a digital-twin framework for brake wear prognosis that integrates state estimation, parameter adaptation, and dynamics-aware degradation modelling. The approach combines brake pad volume estimation from vehicle operational data, online identification of the brake wear coefficient through inverse modelling, and forward propagation of degradation using a wear-dependent dynamics model. The proposed digital-twin predictive maintenance framework is evaluated using simulated run-to-failure datasets for a mining load-haul-dumper and compared against data-driven and physics-based predictive maintenance models. Results show that the digital-twin approach improves the accuracy and stability of remaining useful life prediction, particularly under anomalous degradation conditions, and achieves earlier convergence to practically useful predictions. These findings demonstrate that accurate brake wear prognosis requires integrating degradation modelling with vehicle dynamics and online parameter updating. The proposed digital twin provides a practical pathway towards more reliable predictive maintenance in systems where degradation and system behaviour are strongly coupled. Full article

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

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23 pages, 2668 KB

Open AccessArticle

The Inertial Proximal Algorithm for the Split Variational Inclusion Problem

by Qiaoling Zhang and Xiaojun Ma

Math. Comput. Appl. 2026, 31(4), 145; https://doi.org/10.3390/mca31040145 - 1 Aug 2026

Viewed by 231

Abstract

In this work, we propose an inertial proximal splitting algorithm for the split variational inclusion problem in real Hilbert space, in which a new stepsize rule is provided for avoiding the case that the original stepsize equals to zero, It also helps enlarge [...] Read more.

In this work, we propose an inertial proximal splitting algorithm for the split variational inclusion problem in real Hilbert space, in which a new stepsize rule is provided for avoiding the case that the original stepsize equals to zero, It also helps enlarge the value range of the stepsize parameter. A weak and strong convergence theorem is established under mild conditions. Additionally, our obtained result is extended to split feasibility problems and split minimization problems. Finally, some numerical experiments are conducted to illustrate and compare. Full article

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15 pages, 360 KB

Open AccessArticle

Ulam’s Type Stability of a Discrete Matrix Equation with Second-Order Difference and Single Delay

by Maosong Yang, Guanli Xiao, Yumei Liao and Adan Ding

Math. Comput. Appl. 2026, 31(4), 144; https://doi.org/10.3390/mca31040144 - 1 Aug 2026

Viewed by 217

Abstract

In this paper, we investigate the Ulam stability problem for a second-order discrete matrix difference equation with a single delay. The primary aim of this work is to establish rigorous Ulam-type stability criteria for this class of delayed matrix difference systems. Firstly, we [...] Read more.

In this paper, we investigate the Ulam stability problem for a second-order discrete matrix difference equation with a single delay. The primary aim of this work is to establish rigorous Ulam-type stability criteria for this class of delayed matrix difference systems. Firstly, we formally define Hyers–Ulam stability (HUS) and Hyers–Ulam–Rassias stability (HURS) tailored to delayed discrete matrix equations, and derive an essential norm estimate for the delayed discrete matrix function (DDMF). Relying on this critical norm inequality, we further derive sufficient conditions to guarantee the Hyers–Ulam and Hyers–Ulam–Rassias stability of the addressed equation, which constitute the core theoretical contributions of this study. Compared with the existing literature, the obtained stability judgments are less conservative and applicable to second-order matrix delayed difference models rarely discussed in previous works. Finally, several numerical examples are presented to demonstrate the correctness and effectiveness of the derived theoretical conclusions. Full article

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19 pages, 12459 KB

Open AccessArticle

A Spectral Numerical Investigation of Hybrid Nanoliquid Flow over a Porous Wedge: Effects of Heat Transfer, Brownian Motion, and Activation Energy

by Anwar Shahid, Yumei Lin, Habib Khan, Mian Muhammad Kamal and Muhammad Shafique

Math. Comput. Appl. 2026, 31(4), 143; https://doi.org/10.3390/mca31040143 - 27 Jul 2026

Viewed by 284

Abstract

This investigation meticulously examines the influence of activation energy, thermophoresis, Brownian motion, and magnetic fields on the flow dynamics and heat transfer characteristics of a non-Newtonian hybrid nanofluid comprising aluminum oxide (Al₂O₃), copper (II) oxide (CuO), and ethylene glycol [...] Read more.

This investigation meticulously examines the influence of activation energy, thermophoresis, Brownian motion, and magnetic fields on the flow dynamics and heat transfer characteristics of a non-Newtonian hybrid nanofluid comprising aluminum oxide (Al₂O₃), copper (II) oxide (CuO), and ethylene glycol over a horizontally stretching porous wedge. This research addresses the imperative need for enhancing energy transfer and thermal management systems, which possess considerable technical significance and industrial relevance. The flow equations were formulated into ordinary differential equations through the use of similarity transformations, which in turn were solved numerically by employing the spectral relaxation (SR) scheme. The findings indicate that the Brownian motion, activation energy, wedge angle, and magnetic field intensity are pivotal determinants of the system’s flow and thermal behavior. In particular, an increase in the wedge angle correlates with an augmentation of the Nusselt number while concurrently diminishing the thermal and diffusion profiles. A comparative analysis of the current investigation and earlier scrutiny revealed that hybrid nanofluids enhance mass and energy transfer rates in both studies. The novelty of this investigation is anchored in its comprehensive exploration of magneto-flow dynamics and the characteristics of hybrid nanofluids within the context of porous wedge-shaped geometries and external magnetic influences. The findings of this study extend previous research by offering quantitative elucidation regarding how pivotal parameters, such as wedge angles, activation energy, thermophoresis, and Brownian motion, affect heat and mass transfer phenomena, thus laying a robust groundwork for the optimization of hybrid nanofluid applications in engineering and industrial environments. The results are in robust agreement with the existing body of literature, thereby affirming the contributions of this study to the academic discourse in the field. Full article

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35 pages, 2194 KB

Open AccessArticle

Physics-Constrained Neural Identification of Fragmentation Kernels: From Synthetic Recovery to Effective Daughter-Volume-Fraction Estimation in Droplet Breakup

by Joseph El Maalouf, Alain Ajami and Candy Abboud

Math. Comput. Appl. 2026, 31(4), 142; https://doi.org/10.3390/mca31040142 - 20 Jul 2026

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Abstract

Fragmentation processes arise in many physical systems, including droplet breakup, aerosols, sprays, comminution, and granular media. A central difficulty in fragmentation modeling is the identification of the breakup law from observed particle-size distributions. In this work, we propose a physics-constrained neural framework for [...] Read more.

Fragmentation processes arise in many physical systems, including droplet breakup, aerosols, sprays, comminution, and granular media. A central difficulty in fragmentation modeling is the identification of the breakup law from observed particle-size distributions. In this work, we propose a physics-constrained neural framework for the inverse identification of fragmentation laws. Starting from a size-structured binary fragmentation equation, the kernel is decomposed into a breakup rate

B (s)

, depending on the parent size s, and a daughter-size distribution

κ (z)

, depending on the normalized daughter-size fraction z. The unknown functions B and

κ

are represented by neural networks designed to satisfy physical constraints, including non-negativity of the breakup rate, non-negativity and normalization of the daughter distribution, and first-moment conservation in the symmetric binary setting. The direct fragmentation equation is solved using a first-moment-conserving quadrature discretization, and the inverse problem is formulated as a regularized optimization problem constrained by the fragmentation dynamics. Synthetic experiments, generated independently of the inverse solver, show that the proposed method can recover B and

κ

from simulated particle-size distributions, with accurate recovery in the unimodal case and reasonable performance in the more challenging bimodal case. Robustness tests indicate stability with respect to moderate observational noise and highlight the importance of multiple observation times. For experimental droplet-breakup measurements without time-resolved particle-size distributions, the same constrained neural daughter-density representation is used to estimate effective marginal daughter-volume-fraction distributions from normalized daughter-to-parent volume fractions. The resulting distributions distinguish rim and node fragments and different breakup modes, while stratified cluster-bootstrap confidence bands quantify their sampling uncertainty. The experimental analysis is therefore interpreted as constrained density estimation from final fragment measurements rather than as full validation of the PDE-constrained inverse recovery. Full article

(This article belongs to the Section Natural Sciences)

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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

Viewed by 555

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

Viewed by 285

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

Cited by 1 | Viewed by 301

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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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

Viewed by 341

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))

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