Mathematics

16 pages, 430 KB

Open AccessArticle

Stability Analysis of T-S Fuzzy Systems via Delay-Dependent Lyapunov–Krasovskii Functionals and Linear Switching Method

by Chang-Ho Lee, Yeong-Jae Kim, Yong-Gwon Lee, Seung-Hoon Lee and Oh-Min Kwon

Mathematics 2026, 14(10), 1609; https://doi.org/10.3390/math14101609 (registering DOI) - 9 May 2026

This paper investigates the problem of stability analysis for Takagi–Sugeno fuzzy systems with time-varying delays. By integrating an augmented delay-dependent Lyapunov–Krasovskii functional (LKF) structure, a refined LKF based on auxiliary function-based integral inequalities, and utilizing a linear switching method, this paper proposes less [...] Read more.

This paper investigates the problem of stability analysis for Takagi–Sugeno fuzzy systems with time-varying delays. By integrating an augmented delay-dependent Lyapunov–Krasovskii functional (LKF) structure, a refined LKF based on auxiliary function-based integral inequalities, and utilizing a linear switching method, this paper proposes less conservative stability criteria that effectively enhance fuzzy membership characteristics. The proposed stability criteria are formulated in the framework of linear matrix inequalities. Through three numerical examples, the effectiveness and superiority of the proposed approach are demonstrated by achieving significantly improved maximum delay bounds compared to the existing literature. Full article

14 pages, 485 KB

Open AccessArticle

Rebalancing Curriculum Learning via In-Batch Difficulty Reallocation for Neural Machine Translation

by Sugyeong Eo and Chanjun Park

Mathematics 2026, 14(10), 1607; https://doi.org/10.3390/math14101607 (registering DOI) - 9 May 2026

Abstract

The advent of large language models has reshaped the landscape of artificial intelligence, yet their learning dynamics remain constrained by rigid training strategies. Curriculum learning (CL), inspired by the human learning process, improves model performance over conventional randomly shuffled training while incurring no [...] Read more.

The advent of large language models has reshaped the landscape of artificial intelligence, yet their learning dynamics remain constrained by rigid training strategies. Curriculum learning (CL), inspired by the human learning process, improves model performance over conventional randomly shuffled training while incurring no additional computational overhead. However, its competence-conservative mechanism often leads to diminished learning stimuli and suboptimal performance plateaus. Inspired by the flow theory in psychology, this study proposes in-batch hard sample injection curriculum learning (DACL), a learning strategy that dynamically balances stability and challenge. DACL regulates sample selection by aligning the model’s competence with the intrinsic complexity of the data, allocating the

R_{e a s y}

proportion of each batch to instances within the competence range and the remaining

(1 - R_{e a s y})

to higher-difficulty samples that stimulate adaptive learning. Experiments on the English–Vietnamese pair demonstrate that DACL achieves superior performance over curriculum learning baselines across multiple difficulty evaluation criteria. Further experiments reveal the effectiveness of the similarity-based difficulty standard, demonstrating the ability to capture task complexity with greater precision. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

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15 pages, 1095 KB

Open AccessArticle

Stability and Weakly Nonlinear Dynamics of Rotating Convection of a Casson Fluid with Helical Force

by S. Suresh Kumar Raju and Gundlapally Shiva Kumar Reddy

Mathematics 2026, 14(10), 1606; https://doi.org/10.3390/math14101606 (registering DOI) - 9 May 2026

Abstract

Linear and weakly nonlinear instabilities in thermosolutal rotating convection of a Casson fluid, incorporating the effects of helical forcing, are investigated. The governing equations, expressed in non-dimensional form, are solved by employing the normal mode method. We have shown the effect of various [...] Read more.

Linear and weakly nonlinear instabilities in thermosolutal rotating convection of a Casson fluid, incorporating the effects of helical forcing, are investigated. The governing equations, expressed in non-dimensional form, are solved by employing the normal mode method. We have shown the effect of various key parameters on convective regions and presented them graphically. The parameter regimes corresponding to the onset of stationary and oscillatory instabilities are systematically delineated. The effect of different key parameters on linear theory is obtained. The Taylor number, helical force parameter, and solute Rayleigh number have a stabilizing effect, whereas the Lewis number and Casson parameter have a destabilizing effect on the system. Within the framework of weakly nonlinear analysis, an amplitude equation is derived using the method of multiple scales. The amplitude equation is solved numerically to calculate the convective amplitude. Using the Nusselt and Sherwood numbers, the heat and mass transfer are analyzed. Full article

(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)

36 pages, 1794 KB

Open AccessArticle

When Does Domination Matter? A Structural and Computational Study of Spanning and Dominating Trees in Geometric Networks

by Pablo Adasme

Mathematics 2026, 14(10), 1605; https://doi.org/10.3390/math14101605 (registering DOI) - 9 May 2026

Abstract

In geometric communication networks, a backbone is useful only if it is inexpensive to build and, at the same time, close enough to the demand points it must serve. This paper studies a backbone design problem in geometric communication networks that explicitly captures [...] Read more.

In geometric communication networks, a backbone is useful only if it is inexpensive to build and, at the same time, close enough to the demand points it must serve. This paper studies a backbone design problem in geometric communication networks that explicitly captures this trade-off between connectivity and user coverage. Two classical combinatorial optimization paradigms—the minimum spanning tree (MST), which promotes low-cost connectivity, and the dominating tree (DT), which additionally enforces that every node either belongs to the backbone or is adjacent to an active backbone node—are considered. To compare both paradigms within a common framework, this paper proposes a unified mixed-integer optimization model that balances backbone-construction and user-assignment costs. Three classes of exact formulations, namely MTZ, single-flow, and cut-set formulations, are developed. In particular, the single-flow model with valid inequalities and root-aware connectivity cuts is strengthened. For larger instances, the exact approach is complemented with a local branching matheuristic. Finally, theoretical results on computational complexity, formulation structure, and dominance relations between the MST and DT models are provided. Computational experiments show that the single-flow formulation achieves the best scalability. Furthermore, a sensitivity analysis with respect to the communication radius and the weighting parameter

α

reveals a structural transition: as the network becomes denser or the objective becomes more coverage-oriented, MST and DT solutions tend to converge. The results give a concrete way to identify when domination constraints are worth imposing and when a simpler spanning tree design already captures the relevant structure. Full article

(This article belongs to the Special Issue Mathematical Advances in Combinatorial Optimization: Theory, Methods, and Applications)

33 pages, 449 KB

Open AccessArticle

On the Structure of Uncertainty Inequalities for the Novel Quadratic-Phase Deformed Hankel Transform

by Saifallah Ghobber and Hatem Mejjaoli

Mathematics 2026, 14(10), 1604; https://doi.org/10.3390/math14101604 (registering DOI) - 9 May 2026

Abstract

Quadratic-phase (deformed) transforms are a recent extension within the class of linear canonical transformations and have attracted increasing interest in signal analysis and related fields. Motivated by the fundamental role of uncertainty principles in theoretical analysis and practical applications, this article presents a [...] Read more.

Quadratic-phase (deformed) transforms are a recent extension within the class of linear canonical transformations and have attracted increasing interest in signal analysis and related fields. Motivated by the fundamental role of uncertainty principles in theoretical analysis and practical applications, this article presents a thorough study of the uncertainty inequalities associated with the quadratic-phase deformed Hankel transform (QPDHT), which has recently been introduced into the literature. We first establish qualitative results. We then derive several forms of the Heisenberg’s uncertainty inequality using different analytical approaches, highlighting the interplay between spatial and frequency localization. Finally, we complete our study by proving local uncertainty inequalities, which provide refined quantitative bounds on the concentration of the transform. These results contribute to a deeper understanding of the localization properties of the QPDHT and extend classical uncertainty principles to a broader analytical framework. Full article

(This article belongs to the Section C: Mathematical Analysis)

26 pages, 1517 KB

Open AccessArticle

A Semi-Empirical Model for the Stress Reduction Factor Incorporating Soil Plasticity and Random Vibration Theory

by Kaveh Dehghanian

Mathematics 2026, 14(10), 1603; https://doi.org/10.3390/math14101603 (registering DOI) - 8 May 2026

Abstract

This study presents a physics-informed semi-empirical formulation for the stress reduction factor (r_d) that integrates random vibration theory with nonlinear soil behavior and plasticity-dependent attenuation. The model incorporates depth, effective stress ratio, normalized shear modulus, and Plasticity Index (PI) within a [...] Read more.

This study presents a physics-informed semi-empirical formulation for the stress reduction factor (r_d) that integrates random vibration theory with nonlinear soil behavior and plasticity-dependent attenuation. The model incorporates depth, effective stress ratio, normalized shear modulus, and Plasticity Index (PI) within a unified analytical framework, enabling representation of frequency-dependent seismic stress attenuation. A synthetic dataset comprising approximately 3600 realizations was generated using physically consistent constraints based on spectral attenuation and modulus reduction relationships, in which the target r_d values represent hybrid responses derived from random vibration theory and calibrated empirical trends. Model parameters were optimized using a global calibration procedure, improving predictive performance from an initial R² ≈ 0.31 to R² = 0.914. Validation was conducted by comparing the model with established empirical models and by independent evaluation using real earthquake records (Chi-Chi, Kobe, and Kocaeli), demonstrating the model’s ability to capture variations in seismic frequency content and energy distribution. Although direct field measurement of r_d is inherently limited, the agreement with multiple independent seismic datasets and widely accepted empirical relationships provides strong indirect validation of the model’s physical reliability. Global sensitivity analysis using Sobol indices confirms that the effective stress ratio is the dominant controlling parameter, while soil plasticity influences r_d primarily through interaction effects. The proposed model offers an interpretable and computationally efficient alternative to conventional approaches for seismic site response and liquefaction assessment. Full article

(This article belongs to the Special Issue Advanced Geostatistics and Data Analysis: Novel Mathematical Methods and Their Applications)

25 pages, 2586 KB

Open AccessArticle

Non-Singular Fast Terminal Sliding Mode Control Based Trajectory Tracking Control of Cable-Driven Manipulators Subject to Lumped Mismatched Uncertainties

by Tran Buu Thach Nguyen, Hoai Vu Anh Truong and Kyoung Kwan Ahn

Mathematics 2026, 14(10), 1602; https://doi.org/10.3390/math14101602 (registering DOI) - 8 May 2026

Abstract

Cable-driven manipulators have emerged as a compelling alternative to traditional manipulators (driven by either electrical, hydraulic, or pneumatic motors), especially for operations in constrained and complex environments. Despite offering many advantages, they still pose significant control challenges. Therefore, this paper presents a novel [...] Read more.

Cable-driven manipulators have emerged as a compelling alternative to traditional manipulators (driven by either electrical, hydraulic, or pneumatic motors), especially for operations in constrained and complex environments. Despite offering many advantages, they still pose significant control challenges. Therefore, this paper presents a novel position tracking control framework for an n-DOF cable-driven manipulator subject to lumped mismatched uncertainties arising from unknown dynamic errors and external disturbances. The proposed approach is built upon non-singular fast terminal sliding mode control (NFTSMC), which provides robustness, high-precision tracking, fast finite-time convergence, chattering-free torque input, and complete elimination of singularity issues. To further enhance control performance, an extended state observer (ESO) is incorporated to accurately estimate unmeasured states and suppress lumped uncertainties. The stability of the closed-loop system under the proposed method is rigorously proven by the Lyapunov theorem. Finally, the superiority of the proposed method over existing controllers is demonstrated by comparative simulations to highlight its potential for practical implementation in complex robotic environments. Full article

(This article belongs to the Special Issue Mathematics Methods of Robotics and Intelligent Systems)

15 pages, 1616 KB

Open AccessFeature PaperArticle

Oil Market Volatility Forecasting Under Uncertainty Theory: A Joint Modeling Framework via Uncertain Vector Autoregression

by Chenyu Gao and Piwei Chen

Mathematics 2026, 14(10), 1601; https://doi.org/10.3390/math14101601 (registering DOI) - 8 May 2026

Abstract

Oil price volatility forecasting remains a central challenge in financial risk management and macroeconomic policy, particularly when market uncertainty stems from expert judgment, geopolitical assessments, or imprecisely quantified fundamentals rather than statistical frequencies. We propose a bivariate uncertain vector autoregressive (UVAR) model to [...] Read more.

Oil price volatility forecasting remains a central challenge in financial risk management and macroeconomic policy, particularly when market uncertainty stems from expert judgment, geopolitical assessments, or imprecisely quantified fundamentals rather than statistical frequencies. We propose a bivariate uncertain vector autoregressive (UVAR) model to jointly forecast crude oil realized volatility (RV) and the Overall Equity Market Volatility (EMV) tracker within the framework of uncertainty theory, using 204 monthly observations from January 2008 to December 2024. Three cross-validation schemes consistently identify UVAR(1) as optimal, and least-squares estimation reveals an asymmetric bidirectional relationship between the two variables. Residual analysis and uncertain hypothesis testing confirm the adequacy of the fitted model at both

α = 0.05

and

α = 0.10

, the conventional significance levels reported in the empirical literature. Relative to a univariate UAR benchmark, UVAR(1) yields lower residual variance and, on average, narrower 95% confidence intervals for both variables and remedies the hypothesis-test failure of UAR(1) for realized volatility; while its fixed-origin ATE is marginally higher on the EMV tracker, this is more than offset by substantial gains on realized volatility, the primary economic variable of interest. Against a probabilistic VAR(1) benchmark, UVAR(1) attains marginally lower out-of-sample sum of squared mean errors while uniquely supporting principled uncertain-statistical inference under non-frequentist data-generating mechanisms. These results provide principled inputs for value-at-risk assessment and portfolio hedging in oil-dependent economies. Full article

(This article belongs to the Special Issue Mathematical Problems in Financial Fluctuations and Forecasting)

30 pages, 3409 KB

Open AccessArticle

Bayesian Analysis of Tuberculosis Spread Scenarios in Regions of Russian Federation

by Olga Krivorotko, Andrei Neverov, Yakov Schwartz, Grigoriy Kaminskiy, Nikolay Zyatkov and Zhanna Laushkina

Mathematics 2026, 14(10), 1600; https://doi.org/10.3390/math14101600 (registering DOI) - 8 May 2026

Abstract

Understanding the heterogeneous spread of tuberculosis (TB), particularly multidrug-resistant (MDR) forms and the role of subclinical infection, is critical for achieving the WHO End TB strategy. This study develops a novel compartmental model that explicitly incorporates incipient and subclinical TB together with MDR [...] Read more.

Understanding the heterogeneous spread of tuberculosis (TB), particularly multidrug-resistant (MDR) forms and the role of subclinical infection, is critical for achieving the WHO End TB strategy. This study develops a novel compartmental model that explicitly incorporates incipient and subclinical TB together with MDR forms, and links them to case detection and treatment pathways. The key innovation lies in integrating a sensitivity-based identifiability analysis with a Bayesian MCMC framework to quantify parameter uncertainty and correlations directly from regional surveillance data. Applied to five high-burden regions of the Russian Federation (2009–2020), the approach reveals strong heterogeneity in epidemic drivers: wide credible intervals for contagiousness, the rate of progression to bacterio-positive (BE+) states, and detection rates. The probabilistic forecasts up to 2025 are validated against 2021–2023 data. The region-specific differences in these correlated parameters dictate transmission dynamics, and improving detection of BE+ cases is the most effective lever for control. Full article

(This article belongs to the Special Issue Recent Advances in Mathematical Epidemiology and Applications)

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Graphical abstract

30 pages, 950 KB

Open AccessArticle

Complexity-Aware Progressive Data Error Correction with Distilled Language Models and Conformal Reliability Control

by Chao Liu, Hong Mu, Jingjing Zhou, Enliang Wang and Xuejian Zhao

Mathematics 2026, 14(10), 1599; https://doi.org/10.3390/math14101599 (registering DOI) - 8 May 2026

Abstract

Reliable tabular data correction is a prerequisite for trustworthy analytics in enterprise information systems. Tabular data in such environments frequently contain formatting errors, semantic conflicts, missing values, and cross-field inconsistencies that degrade downstream analytics and machine learning performance. Rule-based methods efficiently handle structural [...] Read more.

Reliable tabular data correction is a prerequisite for trustworthy analytics in enterprise information systems. Tabular data in such environments frequently contain formatting errors, semantic conflicts, missing values, and cross-field inconsistencies that degrade downstream analytics and machine learning performance. Rule-based methods efficiently handle structural violations but miss context-dependent errors, whereas large language models (LLMs) offer strong semantic-correction capability at inference costs prohibitive for enterprise-scale deployment. This paper formulates data error correction as a progressive decision process and proposes a complexity-aware framework with three processing stages. The first stage applies deterministic rules for low-complexity structural errors. The second stage employs a task-specialized distilled language model for medium-complexity semantic correction. The third stage performs neural probabilistic–logical reasoning on a factor graph for high-complexity cross-field errors. A learnable routing mechanism assigns each record to the appropriate stage based on a lightweight complexity score. Layer-wise conformal prediction is further introduced to construct calibrated prediction sets with coverage guarantees at each stage, together with a rejection mechanism for low-confidence corrections. The framework is evaluated on one enterprise dataset and two public benchmarks (Hospital and Flights). It improves the record-level complete repair rate by 2.1 to 3.1 percentage points over the strongest baseline (GPT-4o-Direct) and by up to 16.8 points over purely rule-based repair, while reducing average inference latency by approximately 80% relative to direct GPT-4o invocation. Ablation studies confirm the critical role of complexity-aware routing and rule-trigger features, and reliability analyses show that hierarchical conformal calibration maintains tighter coverage than single-level alternatives across varying confidence requirements. These results indicate that complexity-aware progressive routing coupled with hierarchical conformal calibration provides a practical path toward high-throughput, auditable, and reliability-controlled data cleaning suitable for enterprise deployment. Full article

24 pages, 387 KB

Open AccessArticle

New Families of Asymmetric Quantum MDS Codes via Affine and Projective Partitions

by Sami H. Saif and Shayea Aldossari

Mathematics 2026, 14(10), 1598; https://doi.org/10.3390/math14101598 (registering DOI) - 8 May 2026

Abstract

We construct three new families of asymmetric quantum MDS codes from nested Hermitian self-orthogonal generalized Reed–Solomon and extended generalized Reed–Solomon codes over

F_{q^{2}}

. The construction is developed in three settings: affine partitions of

F_{q^{2}}

, projective norm partitions [...] Read more.

We construct three new families of asymmetric quantum MDS codes from nested Hermitian self-orthogonal generalized Reed–Solomon and extended generalized Reed–Solomon codes over

F_{q^{2}}

. The construction is developed in three settings: affine partitions of

F_{q^{2}}

, projective norm partitions of

F_{q^{2}}^{*}

, and extended affine configurations obtained by adjoining the point at infinity. In each case, the Hermitian orthogonality conditions are reduced to explicit linear systems over

F_{q}

, whose solvability follows from structured moment identities and Vandermonde-type arguments. This yields nested classical MDS codes satisfying the Hermitian dual-containment condition required in the Hermitian construction of asymmetric quantum codes. As a consequence, we obtain three explicit families of asymmetric quantum MDS codes with fully determined lengths, dimensions, and asymmetric distances

d_{z}

and

d_{x}

. Our results show that affine and projective partition techniques provide a natural and effective framework for constructing optimal asymmetric quantum codes with flexible parameters. Full article

21 pages, 941 KB

Open AccessArticle

MQ Quasi-Interpolation Operators: Adaptive Construction and Rigorous Approximation Bound Estimations

by Lixia Gao

Mathematics 2026, 14(10), 1597; https://doi.org/10.3390/math14101597 (registering DOI) - 8 May 2026

Abstract

This paper focuses on constructing four novel multiquadric (MQ) quasi-interpolation operators. We conduct a comprehensive analysis of the essential properties of the proposed operators and further derive rigorous optimal upper and lower bounds for the approximation error. Numerical experiments are performed to verify [...] Read more.

This paper focuses on constructing four novel multiquadric (MQ) quasi-interpolation operators. We conduct a comprehensive analysis of the essential properties of the proposed operators and further derive rigorous optimal upper and lower bounds for the approximation error. Numerical experiments are performed to verify the theoretical results, and the numerical outcomes are in excellent agreement with our theoretical analysis. Full article

(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications in Science and Engineering, 4th Edition)

19 pages, 440 KB

Open AccessFeature PaperArticle

A MAP/PH/1/K Queueing Model with N-Policy for Optimal Regeneration of a Diesel Particulate Filter

by Dmitry Efrosinin, Natalia Stepanova, Zóltan Gál and Janos Sztrik

Mathematics 2026, 14(10), 1596; https://doi.org/10.3390/math14101596 (registering DOI) - 8 May 2026

Abstract

This paper analyzes a

M A P / P H / 1 / K

queue with N-policy, setup, interruptions, reset, and a random environment. Arrivals are the MAP; service, setup, interruption, and reset times are PH-distributed. Under the N-policy, the server [...] Read more.

This paper analyzes a

M A P / P H / 1 / K

queue with N-policy, setup, interruptions, reset, and a random environment. Arrivals are the MAP; service, setup, interruption, and reset times are PH-distributed. Under the N-policy, the server idles until the queue length is equal to N, and then performs setup. Interruptions return the system to idle and re-enable the N-policy. At capacity K, a reset empties the system. The random environment modulates parameters for different regimes. Motivated by Diesel Particulate Filter (DPF) regeneration, soot accumulation is mapped to arrivals, burning to service, regeneration triggers to N-policy, heating to setup, engine changes to interruptions, and cleaning to reset. Environmental states represent driving patterns. Regeneration succeeds if either the system empties via service or an interruption occurs with remaining soot less than or equal to level L. We derive the block-structured generator, obtain stationary probabilities via matrix-analytic methods, and optimize the threshold N via average cost. Numerical results quantify how correlation and driving conditions affect performance and costs, offering tools to balance fuel consumption, engine performance, and filter longevity. Full article

(This article belongs to the Special Issue Advances in Queueing Theory and Applications, 2nd Edition)

23 pages, 5358 KB

Open AccessArticle

A Finite Integral Transform-Based Generalized Eigenvalue Solution for Free Vibration of Anisotropic Rectangular Plates with Rotationally Restrained Edges

by Yongming Cai, Changshu Zhao, Tiancai Tan, Liang Chen, Yan Wang, Yifan Li, Chen Tang and Dongqi An

Mathematics 2026, 14(10), 1595; https://doi.org/10.3390/math14101595 (registering DOI) - 8 May 2026

Abstract

A generalized eigenvalue formulation is developed for the free vibration analysis of anisotropic rectangular plates with rotationally restrained edges using the finite integral transform method. For free vibration problems, casting the governing equations into a generalized eigenvalue problem is particularly advantageous because it [...] Read more.

A generalized eigenvalue formulation is developed for the free vibration analysis of anisotropic rectangular plates with rotationally restrained edges using the finite integral transform method. For free vibration problems, casting the governing equations into a generalized eigenvalue problem is particularly advantageous because it enables the direct and systematic extraction of multiple natural frequencies and their associated mode shapes within a unified framework, while avoiding the need for assumed trial functions or solution searching near initial guesses. In the present study, a two-dimensional sine integral transform is introduced into the governing equation of anisotropic plates with bending-twisting coupling, and the mechanical description of rotationally restrained boundary conditions is incorporated simultaneously, thereby converting the original partial differential boundary value problem into a generalized eigenvalue problem. The corresponding analytical solution is then established through the finite integral transform framework. The accuracy and reliability of the proposed method are verified through comparisons with finite element results and published data. Based on the obtained analytical solution, the effects of boundary conditions, rotational stiffness coefficients, aspect ratio, and key stiffness components on the vibration characteristics of anisotropic rectangular plates are further examined. The present study provides an effective analytical framework for free vibration analysis of anisotropic plates with nonclassical rotational restraints and offers theoretical support for the dynamic design and optimization of advanced composite plate structures. Full article

(This article belongs to the Special Issue Mathematical Modeling in Structural Mechanics)

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53 pages, 893 KB

Open AccessArticle

Who Bears Green Costs in Competitive Supply Chains

by Yudong Li and Yan Chen

Mathematics 2026, 14(10), 1594; https://doi.org/10.3390/math14101594 (registering DOI) - 8 May 2026

Abstract

Green investment is increasingly important in sustainable supply chain management, but it remains unclear whether the associated costs should be borne by manufacturers or retailers in competitive markets. To address this issue, this study develops a two-tier green supply chain model with one [...] Read more.

Green investment is increasingly important in sustainable supply chain management, but it remains unclear whether the associated costs should be borne by manufacturers or retailers in competitive markets. To address this issue, this study develops a two-tier green supply chain model with one manufacturer and two competing retailers, where demand depends on retail prices and product greenness. A Stackelberg game framework is used to compare two green cost-bearing structures: manufacturer-borne green cost (MBG) and retailer-borne green cost (RBG). The results show that neither mode is universally superior. When green investment costs are low, both modes lead to the maximum feasible green level. When costs are higher, their relative performance depends on product substitutability and green cost sensitivity. Stronger substitutability increases the strategic value of greenness and may favor RBG, whereas higher green cost sensitivity tends to favor MBG because manufacturers can recover green investment through wholesale pricing. This study contributes by clarifying how green cost allocation affects pricing, demand, and profit distribution under retail competition, and it provides guidance for designing green investment arrangements in practice. Full article

(This article belongs to the Special Issue Applied Mathematics in Modern Supply Chain and Logistics)

38 pages, 2249 KB

Open AccessArticle

A Coupled Mathematical Model of Groundwater Dynamics and Salt Transport in a Two-Layer Porous Medium

by Ergashevich Halimjon Khujamatov, Sherzod Daliev, Sherzod Urakov, Sirojiddin Elmonov, Abdinabi Mukhamadiyev and Razvan Craciunescu

Mathematics 2026, 14(10), 1593; https://doi.org/10.3390/math14101593 (registering DOI) - 8 May 2026

Abstract

Understanding the coupled dynamics of groundwater flow and salinity transport is essential for the sustainable management of aquifer systems, particularly in irrigated and semi-arid regions where evaporation, recharge variability, and groundwater abstraction strongly influence hydrogeological regimes. In multilayer porous media, groundwater-level fluctuations and [...] Read more.

Understanding the coupled dynamics of groundwater flow and salinity transport is essential for the sustainable management of aquifer systems, particularly in irrigated and semi-arid regions where evaporation, recharge variability, and groundwater abstraction strongly influence hydrogeological regimes. In multilayer porous media, groundwater-level fluctuations and salt migration processes are closely interconnected, since hydraulic gradients control solute transport while salinity variations may affect flow behaviour through density-related mechanisms. In this study, a nonlinear mathematical model is developed to describe groundwater-level evolution and salt transport within a two-layer porous medium consisting of a phreatic layer and an underlying confined aquifer. The model accounts for filtration processes, interlayer hydraulic exchange, density-dependent effects, and external forcing factors including surface recharge, evaporation, and pumping. For numerical implementation, the governing equations are discretized using a finite-difference scheme with central spatial approximations and an implicit Crank–Nicolson-type temporal formulation. A hybrid second-order time approximation is introduced for the main-layer equation to improve numerical smoothness and stability. The resulting tridiagonal algebraic systems are solved using the Thomas algorithm within an iterative quasi-linearization framework, ensuring both computational efficiency and numerical robustness. Simulation results reveal a clear difference in the dynamical behaviour of the two layers. The phreatic aquifer exhibits rapid and high-amplitude responses to external forcing, whereas the confined aquifer demonstrates slower and smoother hydraulic and geochemical adjustments. Sensitivity analysis further identifies the filtration coefficient, transmissivity, porosity, density-related parameters, surface flux, and pumping intensity as the dominant factors governing groundwater dynamics and salinity redistribution. The proposed modelling framework provides a reliable tool for analysing coupled groundwater–salinity processes and offers a scientifically grounded basis for groundwater monitoring, salinization risk assessment, and sustainable aquifer management. Full article

(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 3rd Edition)

16 pages, 264 KB

Open AccessArticle

Nonlinear Mixed Left Bi-Skew Jordan and Right Jordan-Type Derivations on -Algebra^*

by Amal S. Alali and Md Arshad Madni

Mathematics 2026, 14(10), 1592; https://doi.org/10.3390/math14101592 (registering DOI) - 8 May 2026

Abstract

Consider a unital *-algebra

A

defined over the complex field

C

. In this work, we establish that a mapping, referred to as a nonlinear mixed left bi-skew Jordan and right Jordan n-derivation, reduces to an additive *-derivation under certain conditions. As [...] Read more.

Consider a unital *-algebra

A

defined over the complex field

C

. In this work, we establish that a mapping, referred to as a nonlinear mixed left bi-skew Jordan and right Jordan n-derivation, reduces to an additive *-derivation under certain conditions. As applications, we further investigate special classes of unital *-algebras, namely, prime *-algebras and factor von Neumann algebras using our main result. Full article

(This article belongs to the Section A: Algebra and Logic)

21 pages, 874 KB

Open AccessArticle

Mathematical Formalization of Zero-Distance Interaction: An Optimization and Control-Theoretic Reformulation of Fitts’s Law

by Aleksandra Ivanov, Lazar Stošić, Olja Krčadinac, Vladimir Đokić and Dragana Đokić

Mathematics 2026, 14(10), 1591; https://doi.org/10.3390/math14101591 (registering DOI) - 8 May 2026

Abstract

This paper presents a mathematical formalization of human–computer interaction under a zero-distance constraint, introducing a degenerate formulation of Fitts’s Law. In classical models, movement time depends logarithmically on spatial distance and target size. By enforcing D → 0, the Index of Difficulty converges [...] Read more.

This paper presents a mathematical formalization of human–computer interaction under a zero-distance constraint, introducing a degenerate formulation of Fitts’s Law. In classical models, movement time depends logarithmically on spatial distance and target size. By enforcing D → 0, the Index of Difficulty converges to zero, and movement time reduces to a constant equal to the physiological intercept, yielding a constant-time interaction model. A rigorous ε–δ limit analysis proves convergence, while an optimization formulation shows that zero-distance interaction achieves the global minimum of latency. From a control-theoretic perspective, the model eliminates nonlinear dependencies and produces a time-invariant system. The framework is empirically validated on a teleoperated mobile robotic platform using a haptic Touch–Release protocol. Experimental results show a reduction in total response latency from approximately 1040 ms to 450 ms (≈56%). Cryptographically secured telemetry (AES-256) ensures data integrity and reproducibility. The proposed model establishes a new paradigm of constant-time human–computer interaction, with implications for optimization and control in cyber–physical systems and safety-critical applications. Full article

(This article belongs to the Special Issue Human–Computer Interaction: Techniques, Algorithms and Real-World Impact)

31 pages, 1621 KB

Open AccessArticle

A Conservative Runge–Kutta Discontinuous Galerkin ConRKDG Method for Inviscid Compressible Flows in One-Dimensional Computational Fluid Dynamics Simulations

by Thien Binh Nguyen and Nguyen Minh Hieu Pham

Mathematics 2026, 14(10), 1590; https://doi.org/10.3390/math14101590 (registering DOI) - 8 May 2026

Abstract

This article proposes a novel conservative ConRKDG method for one-dimensional hyperbolic conservation laws with applications in computational fluid dynamics simulations. A DG local solution is reconstructed over each element based on the sub-cell solution averages with a newly proposed set of shape functions. [...] Read more.

This article proposes a novel conservative ConRKDG method for one-dimensional hyperbolic conservation laws with applications in computational fluid dynamics simulations. A DG local solution is reconstructed over each element based on the sub-cell solution averages with a newly proposed set of shape functions. In this virtue, the conservation property of the problem is naturally imposed for the numerical DG solution. In addition, the availability of finite-volume sub-cell solution averages without any DG-to-FV transformation or vice versa facilitates a direct and robust technique for detecting troubled elements, in which the unlimited DG local solution is deemed unstable. A new WENO-type smoothness measurement based on sub-cell solution averages is introduced to assess whether a DG local solution is admissible or unstable, thereby determining whether an element is good or troubled. For the latter case, a secondary finite-volume WENO method is invoked in an a posteriori phase to recalculate the sub-cell averages to sustain numerical stability by essentially suppressing non-physical spurious oscillations in the vicinity of shocks or discontinuities at troubled elements. The performance of the ConRKDG method with different secondary finite-volume WENO methods is compared for both problems with smooth solutions and those with shocks and discontinuities. Full article

(This article belongs to the Special Issue Numerical Methods for Fluid Dynamics)

30 pages, 2038 KB

Open AccessArticle

A Multi-Objective Drone Routing Problem for On-Demand Delivery Considering Hybrid Delivery Modes

by Shuxuan Li, Teng Ren and Guohua Wu

Mathematics 2026, 14(10), 1589; https://doi.org/10.3390/math14101589 (registering DOI) - 8 May 2026

Abstract

This paper investigates the multi-objective drone routing problem for on-demand delivery considering hybrid delivery modes. Unlike previous studies that assume a single delivery strategy or statically bind modes to heterogeneous drone types, real-world operations require a hybrid framework where homogeneous drones dynamically switch [...] Read more.

This paper investigates the multi-objective drone routing problem for on-demand delivery considering hybrid delivery modes. Unlike previous studies that assume a single delivery strategy or statically bind modes to heterogeneous drone types, real-world operations require a hybrid framework where homogeneous drones dynamically switch between exclusive and sharing modes to accommodate orders with distinct logics. We formulate a multi-objective mixed-integer programming model that minimizes operational costs while maximizing order revenue, explicitly accounting for dynamic order arrivals, drone battery swapping, and resource conflicts at shared lockers. To solve this problem under dynamic conditions, we propose an online optimization framework, the reinforcement learning knowledge-driven multi-objective evolutionary algorithm based on decomposition (RL-KMD-MOEA/D), which integrates Q-learning for adaptive operator selection within a rolling-horizon scheme. Comprehensive experiments demonstrate that RL-KMD-MOEA/D achieves competitive performance on small-scale instances and exhibits superior scalability and robustness on large-scale, highly constrained dynamic scenarios, outperforming other compared algorithms. Full article

(This article belongs to the Section D: Statistics and Operational Research)

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26 pages, 603 KB

Open AccessArticle

A Weighted Multi-Objective Intelligent Grey Target Decision Model for Optimal Natural Rubber Selection in Aircraft Tires

by Kun Jiang and Baoling Wang

Mathematics 2026, 14(10), 1588; https://doi.org/10.3390/math14101588 (registering DOI) - 8 May 2026

Abstract

In response to the bottleneck issue of natural rubber selection in aircraft tire formulation design, this study proposes a data-driven screening methodology that integrates a simulated performance database with grey system theory. A multidimensional performance simulation database was constructed, encompassing representative NR brands [...] Read more.

In response to the bottleneck issue of natural rubber selection in aircraft tire formulation design, this study proposes a data-driven screening methodology that integrates a simulated performance database with grey system theory. A multidimensional performance simulation database was constructed, encompassing representative NR brands from six major global producing regions: Malaysia, Indonesia, Thailand, Vietnam, Hainan (China), and Yunnan (China). This repository encompasses critical metrics, including raw rubber constitution, molecular characteristics, and the static/dynamic mechanical behaviors of vulcanizates. Utilizing this foundation, a novel material selection protocol was formulated, grounded in a multi-objective weighted intelligent grey target decision framework. The Analytic Hierarchy Process (AHP) was applied to ascertain differentiated performance criteria and assign corresponding weights, specifically tailored to the functional necessities of distinct aircraft tire sections. To substantiate the model’s efficacy, the primary tire of the ubiquitous Boeing 737-800 served as a validation case. The optimal Natural Rubber (NR) grade identified by the algorithm was cross-referenced with the empirical expertise and engineering practices of premier global tire manufacturers, thereby confirming the framework’s robustness and predictive accuracy. Consequently, this investigation establishes a comprehensive intelligent decision-making architecture, spanning data construction to engineering deployment, offering a quantitative and referential pathway for NR material screening in aviation applications. Full article

(This article belongs to the Special Issue Advanced Mathematical Models in Engineering Design Optimization)

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18 pages, 1318 KB

Open AccessArticle

A Quantization-Adaptive Early Termination Method for Fast Coding Unit Partitioning in VVC

by Donggeon Jo and Dongsan Jun

Mathematics 2026, 14(10), 1587; https://doi.org/10.3390/math14101587 (registering DOI) - 7 May 2026

Abstract

Versatile Video Coding (VVC) achieves higher compression efficiency than the previous High Efficiency Video Coding (HEVC) standard by employing advanced coding tools, including Quad Tree (QT) and Multi-Type Tree (MTT) block partitioning, extended intra prediction modes, and affine motion compensation. Among these tools, [...] Read more.

Versatile Video Coding (VVC) achieves higher compression efficiency than the previous High Efficiency Video Coding (HEVC) standard by employing advanced coding tools, including Quad Tree (QT) and Multi-Type Tree (MTT) block partitioning, extended intra prediction modes, and affine motion compensation. Among these tools, the QT-MTT hierarchical partitioning structure significantly increases encoder complexity, since Rate-Distortion Optimization (RDO) must be performed over an exponentially growing number of partition candidates. To mitigate this complexity, a quantization-adaptive early termination method is proposed that combines neural network-based and rule-based partitioning strategies. The proposed decision mechanism significantly reduces the number of Coding Unit (CU) partition candidates, which directly lowers the number of required RDO evaluations and overall encoder complexity. Experimental results demonstrate that the proposed method achieves a 38.28% reduction in encoding time with only a 0.85% increase in Bjøntegaard Delta Bitrate (BD-BR) under the VVC common test conditions. These results indicate that the proposed method effectively balances computational complexity and rate-distortion performance. Full article

(This article belongs to the Special Issue Coding Theory and the Impact of AI)

17 pages, 709 KB

Open AccessReview

A Review of Inverse Scattering Imaging Methods Based on Transmission Eigenfunctions

by Youzi He

Mathematics 2026, 14(10), 1586; https://doi.org/10.3390/math14101586 - 7 May 2026

Abstract

Designing imaging methods is one of the important issues in inverse scattering problems. In recent years, some studies have shown that the transmission eigenfunctions contain important qualitative and quantitative information about the unknown scatterers. These spectral properties are closely related to the intrinsic [...] Read more.

Designing imaging methods is one of the important issues in inverse scattering problems. In recent years, some studies have shown that the transmission eigenfunctions contain important qualitative and quantitative information about the unknown scatterers. These spectral properties are closely related to the intrinsic nature of the scatterers and provide a connection between the scattering data and the geometry and the material characteristics of the target objects. This paper reviews recent developments in inverse scattering imaging methods that utilize local and global geometric structures of the transmission eigenfunctions. We first summarize the theoretical properties of these eigenfunctions, and then discuss the imaging algorithms based on them. Particular emphasis is placed on the theoretical justification of these imaging methods, including comparisons between them and traditional qualitative reconstruction methods. Finally, we discuss the current challenges and open problems, such as issues related to the theoretical explanation of super-resolution effect, limited-aperture data, and the extension to more complex physical models. Full article

(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 3rd Edition)

51 pages, 9569 KB

Open AccessArticle

A Multi-Strategy Enhanced Farthest Better or Nearest Worse Optimizer for Complex Optimization Problems

by Xiaojie Tang, Chengfen Jia, Pengju Qu and Pan Zhang

Mathematics 2026, 14(10), 1585; https://doi.org/10.3390/math14101585 (registering DOI) - 7 May 2026

Abstract

An enhanced Farthest Better or Nearest Worse Optimizer (EFNO) is developed to overcome the limitations of the original FNO, including insufficient population diversity, and slow and premature convergence. To achieve a more effective balance between exploration and exploitation, three complementary strategies are incorporated: [...] Read more.

An enhanced Farthest Better or Nearest Worse Optimizer (EFNO) is developed to overcome the limitations of the original FNO, including insufficient population diversity, and slow and premature convergence. To achieve a more effective balance between exploration and exploitation, three complementary strategies are incorporated: an adaptive weighted Euclidean distance mechanism to improve solution selection, an elite-guided archive reinforcement strategy for stage-wise differentiated population guidance, and a nearest-worse-individual-based reverse-reinforcement mechanism to enhance diversity. The effectiveness of EFNO is evaluated on the CEC2017 and CEC2022 benchmark suites under different dimensional settings. Comparative experiments with eleven State-of-the-Art algorithms, including a benchmark-winning method, are conducted to assess convergence behavior and optimization accuracy. The results indicate that EFNO consistently achieves superior performance and obtains the best overall ranking. To further demonstrate its applicability, EFNO is applied to two real-world engineering optimization problems and a robot path-planning task. In the path-planning experiments, six random grid-based environments with different sizes (20 × 20, 30 × 30, and 50 × 50) and obstacle densities (20% and 40%) are constructed. Experimental results show that EFNO outperforms all competing algorithms in terms of solution quality and robustness, confirming its effectiveness and strong generalization capability. Full article

21 pages, 10667 KB

Open AccessArticle

MRF-SA: Multi-Receptive Field Spatial–Angular Framework for Light Field Angular Super-Resolution

by Ebrahem Elkady, Ahmed Salem, Hyun-Soo Kang and Jae-Won Suh

Mathematics 2026, 14(10), 1584; https://doi.org/10.3390/math14101584 (registering DOI) - 7 May 2026

Abstract

Light field angular super-resolution (LFASR) aims to reconstruct densely sampled views from sparse inputs by exploiting spatial–angular correlations, thereby producing rich spatial–angular representations and enabling applications such as 3D reconstruction, refocusing, and virtual reality. In this paper, we propose a multi-receptive field spatial–angular [...] Read more.

Light field angular super-resolution (LFASR) aims to reconstruct densely sampled views from sparse inputs by exploiting spatial–angular correlations, thereby producing rich spatial–angular representations and enabling applications such as 3D reconstruction, refocusing, and virtual reality. In this paper, we propose a multi-receptive field spatial–angular (MRF-SA) framework that jointly captures fine-grained details and long-range dependencies through complementary spatial and angular branches. This design enables effective modeling of disparity-aware interactions without relying on computationally expensive attention mechanisms. In addition, we introduce a lightweight variant based on depth-wise separable convolutions to achieve a favorable tradeoff between reconstruction accuracy and computational efficiency. Extensive experiments on both real-world and synthetic datasets demonstrate that the proposed method achieves competitive performance compared to state-of-the-art approaches. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

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19 pages, 484 KB

Open AccessArticle

Classification of Topological Contacts Between Phases in 3D Multiphase Systems by Betti Number Dynamics

by Andrey O. Kalashnikov and Diana V. Manukovskaya

Mathematics 2026, 14(10), 1583; https://doi.org/10.3390/math14101583 - 7 May 2026

Abstract

A methodological approach to the quantitative description of the spatial relations between phases in multicomponent systems is developed, based on the comparison of Betti numbers of united phases. Two disjoint phases Xⁱ and X^j in three-dimensional space are considered, each consisting [...] Read more.

A methodological approach to the quantitative description of the spatial relations between phases in multicomponent systems is developed, based on the comparison of Betti numbers of united phases. Two disjoint phases Xⁱ and X^j in three-dimensional space are considered, each consisting of a finite number of connected components. Reference points R₁ (absolute minimum), R₂ = min (β_k), R₃ = max (β_k), and R₄ = ∑β_k are introduced, with respect to which the value β_k(Xⁱ ∪ X^j) is analyzed. For each Betti number (k = 0,1,2) the possible types of topological contacts (unifying, filling, generating) are defined, and rigorous interpretation rules are established, linking the position of β_k(Xⁱ ∪ X^j) relative to the reference points to the presence and quantity of contacts. All interpretations are proved and summarized in tables. The obtained results create a theoretical basis for automated analysis of any three-dimensional distributed data, e.g., the tomographic, material science, and biomedical images, where it is necessary to characterize the spatial arrangement of phases without exhaustive pairwise comparison of objects. The ways of adaptation to real data (accounting for discreteness, boundary effects, and segmentation uncertainty) and directions for further development (generalization to more than two phases, use of persistent homology, and relation to physical properties) are outlined. The approach will widen and automatize the interpretation of a 3D structure of any volume of images in medical, geological, and material sciences. Full article

(This article belongs to the Special Issue Advances in Design Theory, Combinatorial Algebraic Geometry and Applications)

16 pages, 267 KB

Open AccessArticle

ESOP Expression Minimization for Multi-Valued Functions Using Nonlinear Integer Programming

by George Papakonstantinou and Konstantinos G. Papakonstantinou

Mathematics 2026, 14(10), 1582; https://doi.org/10.3390/math14101582 - 7 May 2026

Abstract

The minimization of Exclusive-OR Sum-of-Products (ESOP) expressions in the case of multi-valued input, multi-output binary, and certain types of multi-valued output functions (MVESOP) is approached in this work through a novel nonlinear integer programming methodology. The devised method is applicable to both completely [...] Read more.

The minimization of Exclusive-OR Sum-of-Products (ESOP) expressions in the case of multi-valued input, multi-output binary, and certain types of multi-valued output functions (MVESOP) is approached in this work through a novel nonlinear integer programming methodology. The devised method is applicable to both completely and incompletely specified functions and has the capacity to provide exact solutions of global optimality. A key general transformation converts the minimization problem from the MVESOP to the classical algebraic domain, resulting in a nonlinear integer program. Notably, for the challenging cases of incompletely specified functions, the problem becomes significantly simpler after this mapping. Several illustrative, analytical, and numerical examples are provided to demonstrate the implementation and performance of the approach. Full article

(This article belongs to the Special Issue Mathematical Programming and Optimization Algorithms)

25 pages, 1945 KB

Open AccessFeature PaperArticle

Mission-Oriented Multirotor UAV Design Using Multi-Stage Battery Detachment for Extended Range and Endurance

by Hyojun Kim and Chankyu Son

Mathematics 2026, 14(10), 1581; https://doi.org/10.3390/math14101581 - 7 May 2026

Abstract

Multi-stage battery detachment is an effective approach for extending the endurance of multirotor UAVs. However, mission-dependent design guidelines remain insufficient. An optimization framework was developed to estimate the weight margin over an entire mission profile and extend the main mission duration by utilizing [...] Read more.

Multi-stage battery detachment is an effective approach for extending the endurance of multirotor UAVs. However, mission-dependent design guidelines remain insufficient. An optimization framework was developed to estimate the weight margin over an entire mission profile and extend the main mission duration by utilizing the estimated weight margin. The framework was applied to a 7 kg-class quadcopter and evaluated for three scenarios at different forward flight speeds: maximum-range flight, reconnaissance, and maritime search-and-rescue missions. The results showed that the optimal number of detachment stages strongly depended on flight speed. Under hovering conditions and at speeds of 10 m/s or lower, a 13-stage configuration was optimal whereas, at 20 m/s, a 9-stage configuration was optimal because of the higher required power. For the maximum-range scenario, the proposed approach achieved 64.8 km at 10 m/s, representing a 111.8% improvement over the single-battery configuration. In addition, reconnaissance loiter time increased by 183–290%, and the maritime search-and-rescue operational radius increased by 39%. These results provide a practical design methodology for multi-stage battery detachment. Full article

(This article belongs to the Section E: Applied Mathematics)

20 pages, 294 KB

Open AccessArticle

Higher-Order Nonlinear Multivariable Isometric Transformations on Normed Spaces

by Hadi Obaid Alshammari and Sid Ahmed Ould Ahmed Mahmoud

Mathematics 2026, 14(10), 1580; https://doi.org/10.3390/math14101580 - 7 May 2026

Abstract

In this paper, we investigate fundamental properties of

(m, p)

-isometric tuples

((m, p) - I . T .)

in normed spaces. We first establish conditions under which the product of two [...] Read more.

In this paper, we investigate fundamental properties of

(m, p)

-isometric tuples

((m, p) - I . T .)

in normed spaces. We first establish conditions under which the product of two

(m, p) - I . T .

remains in the same class, providing a framework for composing such tuples. Next, we derive necessary conditions for an

(m, p) - I . T .

to become a

(2, p) - I . T .

, characterizing when higher-order isometric behavior can change under parameter adjustments. We also show that any

(m, p) - I . T .

that is power-bounded reduces to a

(1, p) - I . T .

, revealing a structural collapse from higher-order to first-order isometries under boundedness constraints. Furthermore, we prove that if a tuple

(N_{1}, \dots, N_{d})

is simultaneously an

(m, p) - I . T .

and an

(m, \infty)

-isometry, then

(N_{1}^{m}, \dots, N_{d}^{m})

is a

(1, p) - I . T .

, providing a link between different isometric classes. These results provide a systematic understanding of the stability, transformation behavior, and interrelations of

(m, p) - I . T .

, extending classical operator-theoretic concepts to tuples of commuting linear or nonlinear transformations in normed and Banach spaces. Full article

14 pages, 1597 KB

Open AccessArticle

Physics-Informed POD-PINN for Fast Wake Prediction of Twin Vertical-Axis Hydroturbine Arrays

by Ai Shan, Hu Chao and Ma Yong

Mathematics 2026, 14(10), 1579; https://doi.org/10.3390/math14101579 - 7 May 2026

Abstract

Accurate prediction of wake interactions in twin vertical-axis hydroturbine (VAHT) arrays is important for dense tidal-farm layout assessment but remains computationally expensive when based directly on Computational Fluid Dynamics (CFD) reference simulations. While simplified analytical models offer speed, they fail to capture the [...] Read more.

Accurate prediction of wake interactions in twin vertical-axis hydroturbine (VAHT) arrays is important for dense tidal-farm layout assessment but remains computationally expensive when based directly on Computational Fluid Dynamics (CFD) reference simulations. While simplified analytical models offer speed, they fail to capture the non-axisymmetric wake characteristics of VAHT arrays, and standard Physics-Informed Neural Networks (PINNs) often struggle with convergence in small-sample, high-dimensional flow settings. To address this challenge, this study proposes a Physics-Informed POD-PINN framework for predicting configuration-wise time-averaged wake fields. The hybrid architecture combines Proper Orthogonal Decomposition (POD) for dimensionality reduction with a dual-branch neural network: a global POD branch captures dominant flow structures, while a lightweight spatial correction branch acts as a continuity-informed regularization on the predicted field. Trained on CFD-generated reference data covering diverse longitudinal and lateral spacing configurations, the model learns to map geometric parameters to a three-component wake field represented on a regularized 3D grid. Results show that the proposed framework achieves the lowest mean streamwise error among the tested surrogate models while maintaining millisecond-level inference speed. This study provides an efficient and physics-aware surrogate tool for repeated wake-field evaluation in twin-hydroturbine configuration exploration. Full article

(This article belongs to the Topic AI and Data-Driven Advancements in Industry 4.0, 2nd Edition)

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Mathematics, Volume 14, Issue 10 (May-2 2026) – 33 articles

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