Mathematics

29 pages, 4367 KB

Open AccessArticle

Aircraft Takeoff Mass Estimation Method Based on Historical Flight Parameters in the Stable Climb Segments

by Xiangling Zhao, Haorun Qi, Shengqi He, Runping Gu and Bo Han

Mathematics 2026, 14(17), 3067; https://doi.org/10.3390/math14173067 (registering DOI) - 26 Aug 2026

Aircraft mass is a fundamental input for aircraft performance calculations, and estimation errors may degrade trajectory-prediction accuracy and affect operational safety. To improve the reliability of aircraft mass estimation, this study proposes a takeoff mass estimation method based on flight parameters from stable [...] Read more.

Aircraft mass is a fundamental input for aircraft performance calculations, and estimation errors may degrade trajectory-prediction accuracy and affect operational safety. To improve the reliability of aircraft mass estimation, this study proposes a takeoff mass estimation method based on flight parameters from stable climb segments. First, the phase characteristics of Quick Access Recorder (QAR) data are analyzed, and a sliding-window-based screening method is developed to identify stable climb segments. A takeoff mass estimation model is then established using the Total Energy Model (TEM), and an improved differential evolution algorithm is designed to solve the resulting nonlinear optimization problem through iterative search. Validation using historical A320 flight data shows that the proposed method produces takeoff mass estimates with relatively small discrepancies from the QAR-recorded reference values. Batch experiments involving A320 and B737 flights further show that the DE algorithm achieves absolute percentage errors of 1.64% and 2.60%, respectively. These results demonstrate the applicability of the proposed method to the two aircraft types considered in this study and indicate its potential to support aircraft performance monitoring and trajectory prediction. Full article

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25 pages, 1243 KB

Open AccessArticle

Sharp Coefficient Bounds for a Disk-Starlike Preimage Class Defined by an Algebraically Damped Hadamard Operator

by A. Alameer

Mathematics 2026, 14(17), 3066; https://doi.org/10.3390/math14173066 (registering DOI) - 26 Aug 2026

Abstract

Coefficient operators provide a natural way to reshape an analytic function before testing its geometry. This paper develops a two-parameter algebraically damped Hadamard-product operator and investigates the functions whose transformed images satisfy a disk-starlikeness condition. The construction retains a visible contribution from the [...] Read more.

Coefficient operators provide a natural way to reshape an analytic function before testing its geometry. This paper develops a two-parameter algebraically damped Hadamard-product operator and investigates the functions whose transformed images satisfy a disk-starlikeness condition. The construction retains a visible contribution from the first coefficients while allowing the higher-order tail to be attenuated at an adjustable algebraic rate. The geometric conclusion concerns the transformed function; it does not automatically imply that the original function is starlike or univalent. Sharp initial-coefficient estimates, a corrected Fekete–Szegö inequality, and corresponding extremal functions are obtained. The multiplier is compared quantitatively with several established coefficient operators, and the effects of its parameters on damping and coefficient flexibility are examined. A weighted-coefficient criterion yields transparent perturbation and convex-combination consequences, while explicit examples illustrate both membership and failure of the criterion. The practical profiles included in the paper are conceptual visualizations rather than empirically validated models. Full article

(This article belongs to the Special Issue Advances in Convex Analysis and Inequalities)

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19 pages, 412 KB

Open AccessArticle

Efficient Quadrature Rules for Cauchy Principal Value Integrals with Highly Oscillatory Bessel Kernel

by Bin Li, Yibo Liu and Jinjun Yong

Mathematics 2026, 14(17), 3065; https://doi.org/10.3390/math14173065 (registering DOI) - 26 Aug 2026

Abstract

In this paper, we address the fast computation of highly oscillatory Bessel transforms involving algebraic-type singularities and Cauchy principal value integrals. By modifying the numerical steepest-descent method, we propose a new efficient quadrature rule. We first divide the considered integrals into two parts [...] Read more.

In this paper, we address the fast computation of highly oscillatory Bessel transforms involving algebraic-type singularities and Cauchy principal value integrals. By modifying the numerical steepest-descent method, we propose a new efficient quadrature rule. We first divide the considered integrals into two parts

I_{ω}^{1} [f, s]

and

I_{ω}^{2} [f, s]

, which can be transformed into the infinite integrals on

[0, \infty)

by the Cauchy residue theorem. Based on the asymptotic properties of the kernel function, we construct suitable Gaussian quadrature rules to enable efficient evaluation of the resulting infinite integrals. We next develop two new quadrature rules for this transform, applicable regardless of whether the endpoint a is zero or nonzero. Error bounds are established for both methods, and their effectiveness is validated through several numerical experiments. Full article

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

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26 pages, 656 KB

Open AccessArticle

Prescribing Decisions Using AI-Based Prescriptive Analytics: Procedure, Challenge, and Validation Pathways

by Yunxiang Shu, Ran Yan, Feng Tian and Shuaian Wang

Mathematics 2026, 14(17), 3064; https://doi.org/10.3390/math14173064 (registering DOI) - 26 Aug 2026

Abstract

Prescriptive analytics uses predictions to recommend decisions, but its superiority over the current approach is commonly evaluated on historical data in which only the cost of the implemented decision is observed. When a prescribed decision differs from the historical decision, its actual cost [...] Read more.

Prescriptive analytics uses predictions to recommend decisions, but its superiority over the current approach is commonly evaluated on historical data in which only the cost of the implemented decision is observed. When a prescribed decision differs from the historical decision, its actual cost is a counterfactual outcome and is unavailable, so the conventional comparison between predicted and actual costs does not establish superiority. This study formalizes the conditions under which this fundamental challenge arises and develops a four-case classification according to the dimensions of the feature and decision spaces, the existence of an intermediate random variable vector enabling closed-form cost evaluation, and the observability of its components. Each case is assigned a validation pathway: Cases 1 and 2 permit direct prescription or evaluation from sufficient historical observations or fully observable intermediate variables; Case 3 constructs test sets with fully observable intermediate variables through restriction or sampling; Case 4 uses domain-specific explicit rules to approximate the unobservable costs of alternative decisions. The conditions under which a lower evaluated cost supports a conclusion about the actual cost ordering are established. Three freight transport examples illustrate the classification and the validation pathways. Full article

(This article belongs to the Special Issue Decision-Making, Artificial Intelligence and Data Analytics in Logistics and Scheduling)

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17 pages, 335 KB

Open AccessArticle

The Independent Bondage Number of Planar Graphs Without Short Cycles

by Pongpat Sittitrai and Wannapol Pimpasalee

Mathematics 2026, 14(17), 3063; https://doi.org/10.3390/math14173063 (registering DOI) - 26 Aug 2026

Abstract

An independent dominating set I of a graph G is an independent set such that every vertex in

V (G) - I

has at least one neighbor in I. The independent domination number of G is the minimum cardinality of [...] Read more.

An independent dominating set I of a graph G is an independent set such that every vertex in

V (G) - I

has at least one neighbor in I. The independent domination number of G is the minimum cardinality of an independent dominating set of G. The independent bondage number of a graph G, denoted by

b_{i} (G)

, is the minimum cardinality of an edge set whose removal increases the independent domination number of G. In 2025, Gamlath et al. proved that for planar graphs G with

δ (G) \geq 2

, the following holds:

b_{i} (G) \leq 5

if G does not contain cycles of lengths 3 and 4, and

b_{i} (G) \leq 4

if G does not contain cycles of lengths 3, 4, 5, and 6. This motivates us to investigate the independent bondage number of planar graphs with

δ (G) \geq 2

without cycles of lengths 4 and 5, or cycles of lengths 4, 5, 6, and 7. In this paper, we prove the following bounds for planar graphs G with

δ (G) \geq 2

:

b_{i} (G) \leq 5

if G does not contain cycles of lengths 4 and 5, and

b_{i} (G) \leq 4

if G does not contain cycles of lengths 4, 5, 6, and 7. Full article

(This article belongs to the Special Issue Advances in Combinatorics, Tropical Geometry and Geometry of Matroids)

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19 pages, 387 KB

Open AccessArticle

Evolutionary Variational Inequalities and Long-Run Growth Equilibria with Transaction Costs

by Andrey L. Bulgakov, Igor Yu. Panarin, Anna V. Aleshina, Rasul A. Musaev, Aleksei E. Granukhin and Aleksandra A. Batskikh

Mathematics 2026, 14(17), 3062; https://doi.org/10.3390/math14173062 - 25 Aug 2026

Abstract

We study a class of evolutionary variational inequalities in a Hilbert space that models the long-run balanced-growth equilibrium of a competitive economy with transaction costs, time-dependent production and infrastructure constraints, and exogenous price dynamics. The paper makes four contributions. First, we introduce [...] Read more.

We study a class of evolutionary variational inequalities in a Hilbert space that models the long-run balanced-growth equilibrium of a competitive economy with transaction costs, time-dependent production and infrastructure constraints, and exogenous price dynamics. The paper makes four contributions. First, we introduce a parametrized monotonicity functional

μ_{α} (t; F; u, v; p)

and prove an exact equivalence theorem: the inequality

μ_{α} \geq β {∥u - v∥}^{2}

holds if and only if the operator F is strongly monotone with the explicitly computed constant

m = β - α (1 + {∥p∥}_{\infty})

. This turns the growth parameter

α

and the price level into explicit terms of a single admissibility threshold and, for

β < α (1 + {∥p∥}_{\infty})

, produces a scale of conditions that covers operators which are not monotone, i.e., economies with a bounded degree of increasing returns. Second, we prove well-posedness: for every admissible initial state there is exactly one Lipschitz equilibrium trajectory

u^{*} (\cdot)

, obtained through Moreau’s catching-up algorithm for the associated perturbed sweeping process, together with the explicit velocity bound

∥{\dot{u}}^{*}∥ \leq L_{K} + 2 C_{F}

. Third, we derive one comparison estimate from which global exponential stability, the convergence rate

∥u (t) - u^{*} (t)∥ \leq r e^{- m t} + L_{p} m^{- 1} \sup ∥Δ p∥ + ε m^{- 1}

, and robustness with respect to perturbations of prices and of the operator all follow; we also show that, when the constraint sets stabilize, the trajectory converges to the stationary equilibrium of the limit problem. Fourth, we prove that strong monotonicity implies the c-covering property with

c = m

, so that the shock-absorbing capacity of the economy is governed by the same constant as the speed of convergence. Two examples—a two-resource system and an n-market network with nonlinear transaction costs—are worked out with a complete verification of every hypothesis and with explicit numerical constants. Full article

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

21 pages, 3656 KB

Open AccessArticle

A Deep Learning Segmentation Method for Analyzing Intraventricular Hemorrhage Secondary to Hypertension

by Guoyu Tong and Zhaoshuo Diao

Mathematics 2026, 14(17), 3061; https://doi.org/10.3390/math14173061 - 25 Aug 2026

Abstract

Background and Objective: When hypertensive cerebral hemorrhage causes secondary intraventricular hemorrhage, it usually significantly increases the complexity of the patient’s condition and the risk of poor prognosis. Deep learning methods can automatically and quickly segment intraparenchymal hemorrhage and intraventricular hemorrhage, and quantitatively analyze [...] Read more.

Background and Objective: When hypertensive cerebral hemorrhage causes secondary intraventricular hemorrhage, it usually significantly increases the complexity of the patient’s condition and the risk of poor prognosis. Deep learning methods can automatically and quickly segment intraparenchymal hemorrhage and intraventricular hemorrhage, and quantitatively analyze hematoma-related properties to provide auxiliary information for subsequent diagnosis and treatment. Methods: We retrospectively enrolled 351 patients with hypertensive cerebral hemorrhage, 219 of whom had secondary intraventricular hemorrhage. All patients underwent computed tomography within 1 week after diagnosis. Based on 3D U-Net, we developed a deep learning network with a multi-scale deformable convolution module and a softened anatomical consistency loss. The multi-scale deformable convolution module can enhance the learning ability of multi-deformation features and increase the receptive field of the network. The anatomical consistency loss, built upon softened labels, can alleviate the impact of label noise. Results: We evaluated our model at pixel, volume, and morphology levels. It achieved Dice of 0.8990 ± 0.1169 for intraparenchymal hemorrhage and 0.7124 ± 0.1227 for intraventricular hemorrhage, both higher than that of the comparison model. Compared with the Coniglobus method, our model has a narrower consistency limit and more concentrated predicted values. Additionally, in segmenting irregular and different-sized hematomas, it generates the smallest centroid, volume, position, and morphology deviations. Conclusions: The proposed model can automatically and accurately segment two types of hematomas and quantify multiple attributes, is robust in multi-deformation and label noise scenarios, and has the potential to assist in clinical diagnosis and treatment; its actual impact on clinical decision-making and patient outcomes requires prospective validation. Full article

(This article belongs to the Special Issue Advances in Deep Learning in Medical Image Analysis)

21 pages, 554 KB

Open AccessFeature PaperArticle

Stability Properties of Neutral Delay Fractional Systems with Caputo Derivatives Due to the Perron Condition

by Mariyan Milev

Mathematics 2026, 14(17), 3060; https://doi.org/10.3390/math14173060 - 25 Aug 2026

Abstract

In this article, we consider a class of nonhomogeneous neutral linear systems with Caputo-type fractional derivatives, having incommensurate orders of differentiation and distributed delays. The main goal is to investigate the influence of the Perron condition on the stability properties of the corresponding [...] Read more.

In this article, we consider a class of nonhomogeneous neutral linear systems with Caputo-type fractional derivatives, having incommensurate orders of differentiation and distributed delays. The main goal is to investigate the influence of the Perron condition on the stability properties of the corresponding homogeneous neutral linear system, when the nonhomogeneous system satisfies this condition. We first prove that, for any partially absolutely continuous initial functions, the investigated nonhomogeneous system has a unique global absolutely continuous solution. Furthermore, if the nonhomogeneous system satisfies the Perron condition, we establish that the fundamental and the extended fundamental matrices of the corresponding homogeneous system are uniformly bounded under certain boundedness conditions, which are also used in the classical case for systems with first-order derivatives. This uniform boundedness implies that the zero solution of the homogeneous system is uniformly stable. Finally, it is proved that the extended fundamental matrix Q(t,s) tends to zero as t → ∞, thereby demonstrating that the zero solution of the investigated homogeneous system is uniformly asymptotically stable. Full article

(This article belongs to the Special Issue Stability Analysis of Fractional Systems, 3rd Edition)

24 pages, 9361 KB

Open AccessArticle

An Uncertainty-Guided Evidential Deep Learning Framework for Reliability-Aware Multimodal Fusion in Cancer Prognosis

by Yalu Huang, Yushuai Yuan, Wenbin Ye and Wenlong Ming

Mathematics 2026, 14(17), 3059; https://doi.org/10.3390/math14173059 - 25 Aug 2026

Abstract

Background: Reliability-aware integration of heterogeneous data sources remains a fundamental challenge in multimodal deep learning: prevailing fusion strategies assume uniform reliability across sources and instances, limiting their responsiveness to data-dependent trustworthiness. Methods: We introduce REM-Fuse (Reliability-aware Evidential Multimodal Fusion), an evidential deep learning [...] Read more.

Background: Reliability-aware integration of heterogeneous data sources remains a fundamental challenge in multimodal deep learning: prevailing fusion strategies assume uniform reliability across sources and instances, limiting their responsiveness to data-dependent trustworthiness. Methods: We introduce REM-Fuse (Reliability-aware Evidential Multimodal Fusion), an evidential deep learning (EDL) framework in which per-source Dirichlet uncertainty adaptively weights each source through dual-channel weighting, asymmetric cross-scale enhancement, and Dempster–Shafer-inspired evidence accumulation. As a case study for cancer prognosis, REM-Fuse integrates multi-scale histopathology (10×, 20×) and RNA-seq on TCGA-BRCA (n = 831) via five-fold cross-validation with subtype- and stage-stratified analyses. Results: REM-Fuse attained a concordance index of 0.715 and a 60-month time-dependent AUC of 0.729, indicating moderate discrimination and significant risk separation (log-rank p < 0.001). Adaptive source weights and per-patient uncertainty varied significantly across molecular subtypes (Kruskal–Wallis p = 0.010 and p = 0.007), indicating patient-specific rather than fixed multimodal integration. Conclusions: REM-Fuse provides a compact reliability-aware fusion strategy for cancer prognosis, although external validation is needed before broader clinical or cross-cohort generalization. Full article

(This article belongs to the Special Issue Knowledge-Enhanced Computational Intelligence for Complex Real-World Problems)

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15 pages, 297 KB

Open AccessArticle

A New Density Hierarchy Based on Riesz and Hölder Summability

by János T. Tóth, Ferdinánd Filip and József Bukor

Mathematics 2026, 14(17), 3058; https://doi.org/10.3390/math14173058 - 25 Aug 2026

Abstract

Let

f (n)

be an Erdős–Ulam function satisfying

f (n + 1) / f (n) \to 1

as

n \to \infty

, and let

A_{f}

denote the associated Riesz matrix. Furthermore, let

A_{f^{*}}

be [...] Read more.

Let

f (n)

be an Erdős–Ulam function satisfying

f (n + 1) / f (n) \to 1

as

n \to \infty

, and let

A_{f}

denote the associated Riesz matrix. Furthermore, let

A_{f^{*}}

be the Riesz matrix generated by the weights

f (n) / (f (1) + f (2) + \dots + f (n))

,

n \geq 1

. The main result establishes that the matrix density induced by an arbitrary power of

A_{f}

—or, equivalently, by a generalized Hölder mean of arbitrary order—is stronger than the matrix density induced by

A_{f^{*}}

. Full article

15 pages, 290 KB

Open AccessArticle

Second Order Nonlinear Differential Equations with Riccati-Type Solutions

by Corina N. Babalic and Radu Constantinescu

Mathematics 2026, 14(17), 3057; https://doi.org/10.3390/math14173057 - 25 Aug 2026

Abstract

Solutions to complex nonlinear ordinary differential equations (NODEs) are often obtained by seeking them in the form of series expansions of known solutions to an auxiliary equation. This paper presents an exhaustive study of a general class of second-order NODEs with polynomial coefficients [...] Read more.

Solutions to complex nonlinear ordinary differential equations (NODEs) are often obtained by seeking them in the form of series expansions of known solutions to an auxiliary equation. This paper presents an exhaustive study of a general class of second-order NODEs with polynomial coefficients and identifies the necessary, but not sufficient, conditions on the polynomial degrees of these coefficients for the equation to admit solutions expressible in terms of solutions of the Riccati equation. From this perspective, “Go/No-Go” criteria are formulated for numerous models of practical interest, such as the well-known Burgers, Korteweg–de Vries, Schrödinger, Klein–Gordon, Dodd–Bullough–Mikhailov, Fisher and Chaffee–Infante equations. As a case study, explicit solutions for a generalized model of the Hunter–Saxton equation are presented. The results summarized in the tables provide a useful criterion for assessing, prior to solving, whether a given second-order equation admits solutions in terms of an auxiliary Riccati equation, and indicate the expected form of such solutions. Full article

(This article belongs to the Section C1: Difference and Differential Equations)

33 pages, 1869 KB

Open AccessArticle

Bayesian Estimation for the Single Coefficient of Variation of Zero-Inflated Two-Parameter Rayleigh Distribution

by Sasipong Kijsason, Sa-Aat Niwitpong and Suparat Niwitpong

Mathematics 2026, 14(17), 3056; https://doi.org/10.3390/math14173056 - 25 Aug 2026

Abstract

Real data such as road traffic mortality rates and lifetime observations are often zero-inflated and right-skewed. The zero-inflated two-parameter Rayleigh (ZITR) distribution is employed to model such data in this study. The coefficient of variation (CV) is a statistical measure that is used [...] Read more.

Real data such as road traffic mortality rates and lifetime observations are often zero-inflated and right-skewed. The zero-inflated two-parameter Rayleigh (ZITR) distribution is employed to model such data in this study. The coefficient of variation (CV) is a statistical measure that is used to quantify the relative dispersion of a population, by comparing the standard deviation with the mean. It is widely used to evaluate variability and facilitate comparisons among datasets with different scales or measurement units. This study develops and evaluates seven methods for constructing confidence intervals for the single CV of the ZITR distribution. Three proposed approaches, including Bayesian Markov chain Monte Carlo (MCMC), Bayesian highest posterior density (HPD), and approximate normal (AN) methods, are compared with three existing approaches: generalized confidence interval (GCI), percentile bootstrap (PB), and bootstrap with standard error (BS). Monte Carlo simulations are employed to assess the efficacy of these methods in terms of expected length (EL) and coverage probability (CP). The simulation results show that the HPD method gives acceptable CP with shorter interval lengths than other methods. Moreover, the proposed methods are illustrated with road traffic mortality rates per 100,000 population collected in January 2026 from the Phichit, Suphan Buri, and Prachuap Khiri Khan provinces in Thailand. The results indicate the applicability of the proposed methods for analyzing zero-inflated and right-skewed data in this real-data example. Full article

(This article belongs to the Special Issue Advances of Applied Probability and Statistics, 2nd Edition)

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52 pages, 615 KB

Open AccessArticle

A Perron–Volterra Lyapunov Function for Mathematical Epidemiology Models with Non-Interacting Rank-One Strains

by Rim Adenane, Florin Avram, Miruna Beldiman and Andrei-Dan Halanay

Mathematics 2026, 14(17), 3055; https://doi.org/10.3390/math14173055 - 25 Aug 2026

Abstract

Persistence, coexistence, competitive exclusion, and global asymptotic stability (GAS) are closely related problems in mathematical epidemiology that are often treated by model-specific arguments. We develop a unified approach to GAS based on Perron–Volterra Lyapunov functions

L_{p}

, for multi-strain epidemic reaction networks. [...] Read more.

Persistence, coexistence, competitive exclusion, and global asymptotic stability (GAS) are closely related problems in mathematical epidemiology that are often treated by model-specific arguments. We develop a unified approach to GAS based on Perron–Volterra Lyapunov functions

L_{p}

, for multi-strain epidemic reaction networks. For bilinear m-strain models with irreducible rank-one infection blocks and block-diagonal next-generation structure, these functions yield a generic competitive-exclusion partition of parameter space into at most

m + 1

regions: either the disease free equilibrium is GAS, or exactly one dominant strain persists and its boundary endemic equilibrium is GAS; see non-generic tie surfaces on which the corresponding reproduction numbers coincide. We also prove a second complete GAS partition, for two-strain models with increasing concave incidence and scalar, non-interacting strain blocks, extending the Rahman–Zou result beyond rational saturating incidence. In this class, the disease-free, single-strain, and coexistence equilibria may all occur, and explicit Lyapunov functions provide the full exclusion/coexistence partition among the four possible equilibrium supports. The construction combines five ingredients: siphons, which determine forward-invariant boundary faces; triangular Jacobian structure on siphon faces; the Metzler property of transversal Jacobians and their Perron eigenvectors; regular next-generation splittings, whose spectral radii determine invasibility; and boundary transcritical invasion relays linking eigenvalue crossings to the emergence of equilibria on adjacent faces. The resulting Perron–Volterra functions combine Volterra entropy terms for resident variables with Perron-weighted linear functionals for absent strain blocks. These constructions are implemented in the Mathematica package EpidCRN, which computes siphons, transversal blocks, invasion data, Perron weights, and candidate Lyapunov functions. For the two model classes considered here, these candidates are proved to be genuine Lyapunov functions and yield complete generic GAS partitions. Full article

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

26 pages, 5916 KB

Open AccessArticle

A Novel Expanding-Window Tensor TOPSIS (EWTT) Approach for Dynamic Sustainability Ranking of Countries

by Ali Özarslan and Orhan Balcı

Mathematics 2026, 14(17), 3054; https://doi.org/10.3390/math14173054 - 25 Aug 2026

Abstract

This study proposes the Expanding-Window Tensor TOPSIS method, a novel dynamic multi-criteria decision analysis framework that integrates temporal feature extraction with an expanding-window estimation scheme. The method structures panel data as a third-order tensor and extracts three time-series features—linear trend, mean, and standard [...] Read more.

This study proposes the Expanding-Window Tensor TOPSIS method, a novel dynamic multi-criteria decision analysis framework that integrates temporal feature extraction with an expanding-window estimation scheme. The method structures panel data as a third-order tensor and extracts three time-series features—linear trend, mean, and standard deviation—from rolling windows for each alternative-criterion pair. These features are retained as distinct dimensions of the decision matrix. At each target year, normalization bounds, entropy weights, and ideal solutions are calculated based on the information accumulated up to that year, thereby avoiding look-ahead bias. A burn-in threshold prevents unreliable early estimates, while complementary diagnostics assess the convergence of weights and sensitivity to the window width. The method yields a dynamic score matrix representing the evolution of the relative position of each alternative over time. The proposed framework is applied to the ND-GAIN Country Index, which includes data for 152 countries from 2000 to 2024. The dynamic rankings have high face validity, almost perfect robustness to the choice of window width and burn-in threshold, fast convergence of the entropy weights, and robustness to changes in the alternative set. Extensive robustness checks—including Monte Carlo weight-uncertainty analysis, comparisons with alternative weighting (CRITIC, standard-deviation-based, equal weighting) and aggregation (VIKOR) methods, and benchmarks against Dynamic TOPSIS-Entropy and a rolling-window variant—confirm the insensitivity of the findings to the choice of weighting and aggregation strategy. The methodology is not domain-specific and offers a transparent and diagnostically rich tool for dynamic performance evaluation. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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56 pages, 87040 KB

Open AccessArticle

Logistics-Supply-Chain-Enhanced Human Urbanization Algorithm for Global Optimization and Engineering Applications

by Zheming Zhang and Fan Liu

Mathematics 2026, 14(17), 3053; https://doi.org/10.3390/math14173053 - 25 Aug 2026

Abstract

Cloud task scheduling is a critical component of cloud computing systems because it directly affects resource allocation, workload distribution, execution efficiency, and service cost. However, many metaheuristic algorithms suffer from population diversity loss, premature convergence, and an inadequate balance between global exploration and [...] Read more.

Cloud task scheduling is a critical component of cloud computing systems because it directly affects resource allocation, workload distribution, execution efficiency, and service cost. However, many metaheuristic algorithms suffer from population diversity loss, premature convergence, and an inadequate balance between global exploration and local exploitation when solving complex and large-scale optimization problems. To address these limitations, this study develops an Enhanced Human Urbanization Algorithm (EHUA) for numerical optimization and cloud task scheduling. Inspired by the collaborative resource-allocation behavior of modern logistics networks, three coordinated mechanisms are reformulated within the adventurer–city–citizen structure of the original Human Urbanization Algorithm: a logistics-hub-guided adaptive exploration mechanism, a supply–demand-based dynamic redistribution mechanism, and a cooperative logistics delivery exploitation mechanism. These mechanisms reduce excessive dependence on a single capital, adaptively regulate city search ranges, and strengthen citizen-level solution refinement. The performance of EHUA is evaluated on the CEC2014 and CEC2020 benchmark suites using convergence analysis, box plots, numerical statistics, Wilcoxon signed-rank tests, Friedman rankings, and ablation experiments. EHUA obtains the best mean fitness values on 20 of the 30 CEC2014 functions under both 30- and 50-dimensional settings, on 8 of the 10 CEC2020 functions at 10 dimensions, and on all 10 functions at 20 dimensions, demonstrating strong overall competitiveness and repeatability without implying universal superiority on every problem. EHUA is further applied to cloud task scheduling under workload scales ranging from 100 to 10,000 tasks. Considering comprehensive cost, monetary cost, execution time, and load cost, the proposed method consistently achieves low comprehensive scheduling costs and maintains favorable trade-offs among individual objectives as the workload increases. These results indicate that EHUA provides an effective and scalable optimization framework for complex benchmark problems and cloud task scheduling applications. Full article

(This article belongs to the Special Issue Application of Mathematical Methods in Multi-Objective Optimization and Evolutionary Algorithms)

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21 pages, 310 KB

Open AccessArticle

A Weak Condition for Limited Augmented Zarankiewicz Numbers

by Liqun Qi, Chunfeng Cui and Yi Xu

Mathematics 2026, 14(17), 3052; https://doi.org/10.3390/math14173052 - 25 Aug 2026

Abstract

This paper introduces the weak augmented Zarankiewicz number

z_{w A} (m, n)

and the weak limited augmented Zarankiewicz number

z_{w L} (m, n)

, which relax the admissibility conditions for augmented bipartite graphs. We show [...] Read more.

This paper introduces the weak augmented Zarankiewicz number

z_{w A} (m, n)

and the weak limited augmented Zarankiewicz number

z_{w L} (m, n)

, which relax the admissibility conditions for augmented bipartite graphs. We show that the weak framework still guarantees irreducibility of the associated doubly simple biquadratic forms, with SOS rank equal to the total number of edges. This yields

BSR (m, n) \geq z_{w A} (m, n) \geq z_{w L} (m, n) \geq z_{L} (m, n) \geq z (m, n) .

We give three complementary strict improvements. A

5 \times 3

weak admissible limited augmented graph with two row-degenerate 2-edges gives

z_{w L} (5, 3) \geq 10 > 9 = z_{L} (5, 3)

, and hence

BSR (5, 3) \geq 10

. A

6 \times 3

weak admissible limited augmented graph with a mutually complementary pair of nondegenerate 2-edges gives

z_{w L} (6, 3) \geq 12 > 11 = z_{L} (6, 3)

, and hence

BSR (6, 3) \geq 12

. A

15 \times 6

construction on the incidence graph of

K_{6}

with 14 nondegenerate 2-edges gives

z_{w L} (15, 6) \geq 44 > 43

. Finally, a

4 \times 4

reducible example shows that (W3), like (W2′), cannot be omitted. Full article

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

31 pages, 414 KB

Open AccessArticle

Adaptive Sparrow Search Algorithm with Dynamic Penalty and Repair Operators for Constrained Disposal Scheduling

by Yuxiao Peng and Wenfei Lan

Mathematics 2026, 14(17), 3051; https://doi.org/10.3390/math14173051 - 25 Aug 2026

Abstract

Solid waste disposal scheduling coordinates waste generation, facility capacities, fleet resources, treatment compatibility, disposal priorities, and environmental costs over multiple periods. The deterministic model considered in this study is a continuous linear program with a convex polyhedral feasible region. To provide a domain-specific [...] Read more.

Solid waste disposal scheduling coordinates waste generation, facility capacities, fleet resources, treatment compatibility, disposal priorities, and environmental costs over multiple periods. The deterministic model considered in this study is a continuous linear program with a convex polyhedral feasible region. To provide a domain-specific population-search framework for this constraint-intensive setting, this paper proposes an Adaptive Sparrow Search Algorithm with Dynamic Penalty and Repair Operators (ADP-SSA). Its distinctive feature is a closed-loop design: population diversity, feasibility ratio, violation type, and stagnation jointly regulate sparrow roles, penalty pressure, and schedule repair. The repair stage performs compatibility correction, capacity redistribution, fleet-resource adjustment, priority-preserving backlog control, terminal clearance, and feasible local refinement. Experiments on six benchmark instances constructed from public New York City and Philadelphia municipal-waste records compare ADP-SSA with SSA, PSO, GA, GWO, and DE under a common evaluation budget. The reported aggregate results indicate lower mean feasible cost and stronger feasibility for ADP-SSA. Friedman and repeated-measures ANOVA tests computed from the six matched instance means identify a global algorithm effect, while exact pairwise Wilcoxon tests are reported with multiplicity correction. The present formulation and evidence do not establish superiority over commercial linear-programming solvers or unexecuted recent optimizers; these comparisons are identified as limitations and priorities for future work. Full article

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

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30 pages, 1604 KB

Open AccessArticle

How Tax–Subsidy Policies Shape Battery Recycling Strategies Under the Extended Producer Responsibility System

by Yuling Sun, Siyu Yao, Shihan Qian and Shuting Wei

Mathematics 2026, 14(17), 3050; https://doi.org/10.3390/math14173050 - 24 Aug 2026

Abstract

To address the increasing volume of end-of-life power batteries, governments leverage Extended Producer Responsibility (EPR) regulations to encourage battery suppliers to increase recycling. We develop a Stackelberg game model for a closed-loop supply chain (CLSC) that includes a government, a battery supplier, an [...] Read more.

To address the increasing volume of end-of-life power batteries, governments leverage Extended Producer Responsibility (EPR) regulations to encourage battery suppliers to increase recycling. We develop a Stackelberg game model for a closed-loop supply chain (CLSC) that includes a government, a battery supplier, an NEV manufacturer, and a third-party recycler. The model endogenizes tax–subsidy decisions while incorporating cascade utilization, competitive intensity, and environmental damage from informal channels. We compare three recycling modes: manufacturer–supplier competition (MSC), manufacturer–third-party competition (MTC), and manufacturer–third-party alliance (MTA). Our analysis addresses three main issues. First, the structure of recycling modes affects the equilibrium decisions of CLSC members: pricing under MSC is governed by a threshold effect of cascade utilization, whereas pricing under MTC depends on relative cost differences. Second, higher cascade utilization strengthens the supplier’s pricing power under MSC, whereas intensified competition reduces the profits of the supplier and government under MSC and MTC; by contrast, the profits of the supplier and government under MTA remain stable. Third, environmental damage encourages the government to raise the subsidy level provided to suppliers for battery recycling. These findings offer practical guidance for designing adaptive EPR policies that balance economic and environmental objectives. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain, 2nd Edition)

26 pages, 1061 KB

Open AccessArticle

A Hybrid Algorithm Approach to Designing a Three-Echelon Supply Chain Network Model

by Xuyang Wang, Wenfei Zhang and Shuhai Fan

Mathematics 2026, 14(17), 3049; https://doi.org/10.3390/math14173049 - 24 Aug 2026

Abstract

This study addresses a large-scale location–allocation problem in a three-echelon automotive supply chain comprising 382 suppliers, candidate distribution centers, and six assembly plants. The planning task is to redesign the inbound consolidation network while minimizing transportation and distribution center operating costs, enforcing a [...] Read more.

This study addresses a large-scale location–allocation problem in a three-echelon automotive supply chain comprising 382 suppliers, candidate distribution centers, and six assembly plants. The planning task is to redesign the inbound consolidation network while minimizing transportation and distribution center operating costs, enforcing a 480 km supplier-to-center service radius, and achieving at least 90% demand-weighted coverage. We formulate a mixed discrete-continuous model with supplier-to-center assignment, center location, throughput, and flow decisions. A feasibility-oriented hybrid algorithm uses a genetic algorithm as the main search engine, ant colony construction to seed solutions near the feasible region, adaptive mutation and simulated annealing to preserve exploration and refine elite solutions, and an online neural surrogate to avoid a subset of costly exact fitness evaluations. The design differs from a simple collection of metaheuristics: all components share one variable-length encoding, the same feasibility metrics, and periodic exact reevaluation of candidate solutions. Using the competition case data, the redesigned network reduces total cost by 27.0% relative to the six-center baseline, decreases the demand-weighted average supplier-to-center distance from 461.3 km to 53.0 km, lowers the maximum distance from 2807.22 km to 441.78 km, and raises coverage from 45.0% to 100%. Across ten independent runs, the hybrid method obtains a mean cost 10.3% below that of a standard genetic algorithm, with lower run-to-run dispersion. The results show that feasibility-aware initialization, adaptive search, and selective surrogate evaluation can support practical redesign of a strongly constrained, national-scale inbound logistics network. The directly attached reproducibility package provides the MATLAB implementation and the seven supplied input workbooks used by the reported model. The evidence is limited to one deterministic competition instance, a fixed cost schedule, and fixed-topology sensitivity calculations; generalization under demand uncertainty, facility disruption, and alternative road conditions remains to be tested. Full article

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