Mathematics

27 pages, 938 KB

Open AccessArticle

Optimal Job Choice, Consumption, and Investment Under Subsistence-Consumption Constraints

by Geonwoo Kim and Junkee Jeon

Mathematics 2026, 14(13), 2451; https://doi.org/10.3390/math14132451 - 7 Jul 2026

Viewed by 303

This paper extends a benchmark reversible job-choice framework by imposing a subsistence-consumption constraint. The agent chooses consumption, portfolio allocation, and one of two jobs in continuous time. The first job provides low income and high leisure, whereas the second job provides high income [...] Read more.

This paper extends a benchmark reversible job-choice framework by imposing a subsistence-consumption constraint. The agent chooses consumption, portfolio allocation, and one of two jobs in continuous time. The first job provides low income and high leisure, whereas the second job provides high income and low leisure. We focus on the case in which the coefficient of relative risk aversion satisfies

γ > 1

, so that the transformed risk-aversion parameter also satisfies

γ_{1} > 1

. Consumption must satisfy the lower bound

c_{t} \geq \underset{̲}{c}

under both jobs. The constraint changes both the natural solvency boundary and the job-switching rule. In the dual problem, each job generates a subsistence-adjusted reward whose form depends on whether the consumption floor is binding. The optimal job is selected by the upper envelope of the two dual rewards. We prove that, when

γ > 1

, the resulting dual switching function has a unique positive zero. We also characterize the location of this zero explicitly in terms of the income gap

Y_{1} - Y_{0}

and the subsistence level

\underset{̲}{c}

. Hence the optimal job policy remains a one-threshold rule: the agent chooses the high-income job at low wealth and the high-leisure job at high wealth. The consumption floor shifts this boundary and implies that near the solvency boundary the agent necessarily consumes at the subsistence level and works in the high-income job. We provide a complete closed-form representation of the dual value function in all possible regimes. Full article

(This article belongs to the Special Issue Portfolio Optimization and Risk Management In Financial Markets )

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20 pages, 699 KB

Open AccessArticle

Stochastic First Passage to Institutional Distrust Under Informational Turbulence

by Dimitri Volchenkov

Mathematics 2026, 14(13), 2450; https://doi.org/10.3390/math14132450 - 7 Jul 2026

Viewed by 302

Abstract

Institutional distrust is treated here not as a low value of trust but as a positive social disposition, the settled expectation that formal procedures and official explanations no longer carry their stated public meaning. The paper studies the consolidation of that disposition as [...] Read more.

Institutional distrust is treated here not as a low value of trust but as a positive social disposition, the settled expectation that formal procedures and official explanations no longer carry their stated public meaning. The paper studies the consolidation of that disposition as a threshold event. Building on a stochastic trust-phase model, it applies the same multiplicative-noise mechanism to a delegitimating assertion, so the bounded state variable is the probability of adopting institutional distrust. A logit transformation maps the inherited nonlinear diffusion exactly onto Brownian motion with drift and yields closed-form first-passage formulas for the crossing of operational distrust thresholds. The endpoints of the bounded variable are limiting consolidated regimes rather than finite-time targets, so observable institutional failure is a threshold passage and not literal absorption at zero trust. The drift-to-turbulence ratio fixes the shape of the crossing probabilities and the noise scale fixes the time scale. The same coordinate measures the distance between social layers facing one assertion. In United States partisan survey data, this inter-layer logit distance is large and, on consolidated assertions, stationary, the empirical signature of a completed passage, while valence assertions reset with the change in incumbent. The empirical section illustrates the coordinate rather than calibrating or validating the dynamics: the drift and turbulence parameters are not estimated, as that would require matched longitudinal items with recorded field dates and published subsample sizes. Full article

(This article belongs to the Special Issue Mathematical Models in Sociology: Dynamics, Networks, and Decision Processes)

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23 pages, 3138 KB

Open AccessArticle

Research on the Spillover Effects Among Artificial Intelligence, New Energy Industry, and High-Carbon-Emission Industries from a Time–Frequency Perspective

by Ruijie Song, Xuebing Li, Mengzao Wang and Soonhu Soh

Mathematics 2026, 14(13), 2449; https://doi.org/10.3390/math14132449 - 7 Jul 2026

Viewed by 419

Abstract

Artificial intelligence (AI) technology has become the core force driving industrial transformation in today’s world. In-depth exploration of the spillover effects between artificial intelligence and new energy, as well as high-carbon-emission industries is of great significance for optimizing the industrial structure, preventing systemic [...] Read more.

Artificial intelligence (AI) technology has become the core force driving industrial transformation in today’s world. In-depth exploration of the spillover effects between artificial intelligence and new energy, as well as high-carbon-emission industries is of great significance for optimizing the industrial structure, preventing systemic risks in the industrial system, and achieving high-quality development. Based on the DY and BK spillover index model under the TVP-VAR framework, this paper analyzes the spillover effects between artificial intelligence and new energy, as well as high-carbon-emission industries from a time–frequency perspective, and constructs a spillover network to analyze the risk spillover transmission path. Finally, it explores the optimal investment portfolio weights and investment hedging strategies in the financial market. The results show that there is a significant static spillover effect between artificial intelligence and new energy, as well as high-carbon-emission industries. The intensity of this effect follows the pattern of “short-term > medium-term > long-term”. Moreover, new energy and some high-carbon-emission industries (such as the non-ferrous metals industry, the petrochemical industry, and the chemical industry) are the net spillover sources, while artificial intelligence and some high-carbon-emission industries (such as the power industry, the building materials industry, and the aerospace industry) are the net receiving parties. The dynamic spillover effect exhibits significant time-varying characteristics, being significantly impacted by major events such as environmental protection policies, the COVID-19 pandemic, and technological innovations. The chemical industry is the largest spillover outputter in all frequency domains, while the building materials industry is the largest receiver. From the perspective of the spillover network, the artificial intelligence industry, as a key node of the spillover network, plays a crucial role in the transmission of risk spillover. From the perspective of investment practice, the minimum connectedness portfolio (MCoP) performs well in terms of risk hedging effectiveness and return performance and may be the best choice for investors to balance risk and return. Full article

(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data, 2nd Edition)

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42 pages, 3047 KB

Open AccessArticle

Fuzzy Comprehensive Evaluation of the Geological Environment of Abandoned Open-Pit Mines Based on IRBMO-G1-EWM Combined Weighting

by Liangxing Jin, Xinqi Zhang, Pingting Liu, Zhonghe Yao and Hao Li

Mathematics 2026, 14(13), 2448; https://doi.org/10.3390/math14132448 - 7 Jul 2026

Viewed by 234

Abstract

The geological environment evaluation of abandoned open-pit mines frequently encounters challenges, including the reliance of subjective weighting on judgment matrices, the complexity of weight adjustment, and the inadequate interpretation of systematic evaluation results. Addressing these limitations in existing AHP/FAHP and their combinatory weighting [...] Read more.

The geological environment evaluation of abandoned open-pit mines frequently encounters challenges, including the reliance of subjective weighting on judgment matrices, the complexity of weight adjustment, and the inadequate interpretation of systematic evaluation results. Addressing these limitations in existing AHP/FAHP and their combinatory weighting models, this study proposes the IRBMO-G1-EWM-FCE framework. This framework embeds the Improved Red Billed Blue Magpie Optimizer (IRBMO) into the improved G1 method to optimize indicator contribution rates, and subsequently integrates EWM, game theory combinatory weighting, and Fuzzy Comprehensive Evaluation (FCE) to evaluate three abandoned quarries in the Yellow River Basin of Shaanxi Province. The results demonstrate that across 20 independent runs, IRBMO yields a mean fitness value of 1.6496, lower than the 1.7732 of RBMO, with a 63.8% reduction in standard deviation, thereby indicating superior convergence accuracy and stability. The comprehensive membership degrees of the three quarries are A = [0.405,0.143,0.452], B = [0.405,0.450,0.145], and C = [0.742,0.077,0.181], corresponding to evaluation grades of Grade III, Grade II, and Grade I, respectively. While circumventing the construction of complete judgment matrices and consistency modifications, this method incorporates both expert experience and data discreteness into the evaluation, thereby providing an interpretable quantitative tool for geological environment classification, governance priority identification, and restoration decision-making for abandoned open-pit mines. Full article

(This article belongs to the Special Issue Sensitivity Analysis and Decision Making)

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18 pages, 1278 KB

Open AccessArticle

Power Rayleigh Accelerated Life Model Inference with Censoring: Methods and Applications

by Abdelfattah Mustafa, Areej Almuneef, Zuhur Alqahtani, Raga Hassan Ali Shiekh and Samah M. Ahmed

Mathematics 2026, 14(13), 2447; https://doi.org/10.3390/math14132447 - 7 Jul 2026

Viewed by 332

Abstract

In reliability engineering research, obtaining accurate information about the life expectancy of products or materials is essential. However, collecting such data under normal operating conditions is often challenging, particularly for highly reliable items. This paper addresses the problem of statistical inference for lifetime [...] Read more.

In reliability engineering research, obtaining accurate information about the life expectancy of products or materials is essential. However, collecting such data under normal operating conditions is often challenging, particularly for highly reliable items. This paper addresses the problem of statistical inference for lifetime data following the power Rayleigh distribution. To reduce experimental cost and time, a partially step-stress-accelerated life test is employed under a Type-I generalized hybrid censoring scheme (GHCS). Point estimators of the model parameters, as well as the acceleration factor, are derived using both maximum likelihood and Bayesian approaches. Furthermore, interval estimation is developed based on the asymptotic normality of maximum likelihood estimators, in addition to a bootstrap method and Markov-chain Monte Carlo techniques. A real-life dataset is analyzed to demonstrate the applicability of the proposed model. Finally, a Monte Carlo simulation study is conducted to evaluate and compare the performance of the suggested model and estimation procedures. Full article

(This article belongs to the Special Issue Advanced Mathematical and Statistical Methods for Modern Data Science and Scientific Machine Learning)

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30 pages, 887 KB

Open AccessArticle

A Maturity-Aware Proximal ADMM with NG-Route Relaxation for Dynamic Inventory Reallocation in a Multi-Echelon Mandarin Cold-Chain Network

by Baowen Liang, Linjie Ma, Yiran Zhang, Yuxuan Su, Haoyu Wang and Yiping Jiang

Mathematics 2026, 14(13), 2446; https://doi.org/10.3390/math14132446 - 7 Jul 2026

Viewed by 311

Abstract

The Vehicle Routing Problem with Time Windows (VRPTW) takes on a structurally distinct form when the goods being routed undergo first-order quality decay during transport. In this setting, distance minimisation alone underestimates the true economic cost. A per-customer minimum-quality acceptance constraint further introduces [...] Read more.

The Vehicle Routing Problem with Time Windows (VRPTW) takes on a structurally distinct form when the goods being routed undergo first-order quality decay during transport. In this setting, distance minimisation alone underestimates the true economic cost. A per-customer minimum-quality acceptance constraint further introduces a non-linear feasibility condition that does not appear in the classical formulation. This paper addresses such a setting in the context of loose-skin citrus fruit (e.g., mandarins) distribution, where stock has already undergone several days of cold storage at the origin warehouse, and remaining shelf life makes retail time windows binding rather than decorative. We formulate a Maturity-Aware Multi-Echelon Dynamic Reallocation Vehicle Routing Problem with Time Windows (MA-MEDR-VRPTW) on a three-echelon network (origin warehouse → distribution centres → stores) over a seven-day rolling horizon. A first contribution shows that the minimum-quality acceptance constraint admits an analytic transformation into a time-window tightening, which removes per-extension exponential evaluations from the subproblem solver. The algorithmic contribution is a proximal alternating direction method of multipliers (ADMM) with NG-route relaxation (padmm-ma) whose quality-loss weight is updated by a residual-balancing rule and is decoupled from the outer reallocation linear program (LP) through approximate dynamic-programming-style marginal costs. On twelve Solomon-derived mandarin instances (72 feasible algorithm–instance combinations), padmm-ma returns a mean seven-day cost of 12,638 CNY against 11,753 CNY for a subgradient baseline (

+ 7.5 %

) at statistically indistinguishable arrival quality (paired Wilcoxon

p = 0.077

for

{\bar{q}}_{arr}

), while cutting mean wall-clock time from 350 to 23 s (about

15 \times

). The method, therefore, reads as a fast operational heuristic for daily re-planning. An ablation, an exact-MIP benchmark on tractable subproblems, and a scale extension to

n = 100

customers round out the validation. Full article

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43 pages, 25846 KB

Open AccessArticle

An Economic Investment Strategy: Enhanced Golden Sine Optimization Algorithm for Global Optimization and Practical Engineering Applications

by Zheming Zhang and Hui Zhang

Mathematics 2026, 14(13), 2445; https://doi.org/10.3390/math14132445 - 7 Jul 2026

Viewed by 229

Abstract

Cloud task scheduling is a critical optimization problem in cloud computing environments, aiming to allocate computational tasks to appropriate virtual machines while reducing execution time, balancing resource load, and minimizing scheduling cost. However, due to the high dimensionality, nonlinear characteristics, and complex constraints [...] Read more.

Cloud task scheduling is a critical optimization problem in cloud computing environments, aiming to allocate computational tasks to appropriate virtual machines while reducing execution time, balancing resource load, and minimizing scheduling cost. However, due to the high dimensionality, nonlinear characteristics, and complex constraints of cloud scheduling scenarios, traditional optimization methods often struggle to obtain high-quality solutions efficiently. To address these challenges, this paper proposes a Multi-strategy Improved Golden Sine Optimization Algorithm (MIGoldSA) for global optimization and cloud task scheduling problems. First, an adaptive chaotic opposition initialization strategy is incorporated to improve the distribution quality and diversity of the initial population. Second, a dynamic elite-guided sine evolution strategy is designed to reduce the dependence on a single best individual and improve the coordination between global exploration and local exploitation. Third, an Economic Investment Strategy is introduced to adaptively allocate search efforts according to the optimization potential of individuals. To verify the effectiveness of MIGoldSA, extensive experiments are conducted on the IEEE CEC2017 and CEC2022 benchmark suites and compared with nine advanced optimization algorithms. The results show that MIGoldSA obtains the best or tied-best mean fitness values on 60 out of 84 benchmark cases, accounting for 71.43% of all test cases. In the Wilcoxon signed-rank test, MIGoldSA achieves 662 wins, 57 ties, and 37 losses among 756 pairwise comparisons, corresponding to an overall win rate of 87.57% and a non-inferiority rate of 95.11%. In addition, the Friedman mean ranks of MIGoldSA are 1.47, 2.00, 3.98, and 4.17 under the four benchmark settings, which are reduced by 85.26%, 79.94%, 45.25%, and 42.32%, respectively, compared with the original GoldSA. Furthermore, the proposed algorithm is applied to cloud task scheduling problems under different task scales. The experimental results show that MIGoldSA maintains competitive time-cost performance and achieves clear reductions in load cost, price cost, and comprehensive scheduling cost. Compared with the original GoldSA, the normalized comprehensive scheduling cost is reduced by approximately 9–14% in small-scale scenarios and approximately 18–21% in large-scale scenarios. Meanwhile, the normalized load cost and price cost are reduced by about 18–25% and 10–18%, respectively, and the time cost shows an approximately 8–12% reduction in large-scale scheduling scenarios. These quantitative results demonstrate that MIGoldSA can improve the optimization accuracy, statistical robustness, and overall scheduling cost efficiency of the original GoldSA on most tested problems. Full article

(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)

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25 pages, 8119 KB

Open AccessArticle

A Bee Colony Optimization Framework with Fuzzy Softmax Confidence Modeling for Multiclass Brain Tumor MRI Classification

by Nebojša Ralević, Nataša Milosavljević, Zoran Ovcin and Ljubo Nedović

Mathematics 2026, 14(13), 2444; https://doi.org/10.3390/math14132444 - 7 Jul 2026

Viewed by 303

Abstract

Brain tumor classification from magnetic resonance imaging (MRI) remains challenging in settings where only image-level labels are available and tumor classes exhibit overlapping visual characteristics. In this study, we consider the publicly available Brain Tumor MRI Dataset from Kaggle, a four-class dataset composed [...] Read more.

Brain tumor classification from magnetic resonance imaging (MRI) remains challenging in settings where only image-level labels are available and tumor classes exhibit overlapping visual characteristics. In this study, we consider the publicly available Brain Tumor MRI Dataset from Kaggle, a four-class dataset composed of 2D MRI slices belonging to the categories glioma, meningioma, pituitary tumor, and no tumor. Accordingly, the proposed framework is formulated as a slice-based multiclass classification approach rather than a volumetric 3D analysis pipeline. We propose a lightweight and interpretable framework that integrates handcrafted multiscale MRI descriptors, an artificial neural network (ANN), Bee Colony Optimization (BCO)-based neural architecture search, and fuzzy softmax confidence modeling. Each MRI slice is represented by a compact 9-dimensional feature vector derived from intensity, local entropy, and gradient magnitude computed globally and over non-overlapping spatial blocks. The ANN design problem is formulated as a discrete–continuous optimization task, where BCO is employed to optimize network architecture and training hyperparameters by maximizing validation macro-

F_{1}

. To quantify predictive reliability, the softmax outputs are interpreted as fuzzy class memberships and further analyzed using maximum membership, normalized entropy, decision margin, and ambiguity measures, enabling confidence-aware reliability assessment. These fuzzy confidence descriptors enable confidence-threshold-based selective classification and rejection of low-confidence predictions. Across repeated runs, the optimized BCO-ANN achieved a mean test accuracy of

0.781 \pm 0.009

, mean macro-

F_{1}

of

0.775 \pm 0.010

, mean Brier score of

0.319 \pm 0.012

, and mean Expected Calibration Error (ECE) of

0.0273 \pm 0.0080

, compared with

0.748 \pm 0.011

,

0.738 \pm 0.013

,

0.352 \pm 0.010

, and

0.0446 \pm 0.0071

for the baseline ANN, respectively. Under confidence-threshold-based rejection, selective macro-

F_{1}

increased to

0.820 \pm 0.009

at

τ = 0.55

and to

0.874 \pm 0.020

at

τ = 0.85

, with the expected reduction in coverage. These results indicate that the proposed framework provides a transparent and reproducible approach for optimization-aware and confidence-aware multiclass brain tumor MRI classification in a lightweight handcrafted feature setting. Full article

(This article belongs to the Special Issue Evolutionary Algorithms for Engineering Optimization, Fuzzy Control, and Decision Systems)

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33 pages, 1435 KB

Open AccessArticle

Tripartite Evolutionary Game Analysis of Digital Transformation in Sports Equipment Manufacturing Industry

by Mingcan Xu and Jian Yang

Mathematics 2026, 14(13), 2443; https://doi.org/10.3390/math14132443 - 7 Jul 2026

Viewed by 346

Abstract

With the widespread application of IoT and AI technologies in the sports equipment manufacturing sector, traditional sports equipment manufacturers are facing challenges such as financial pressures, technological integration barriers, and the gradual reduction in government subsidies during digital transformation. To investigate the intrinsic [...] Read more.

With the widespread application of IoT and AI technologies in the sports equipment manufacturing sector, traditional sports equipment manufacturers are facing challenges such as financial pressures, technological integration barriers, and the gradual reduction in government subsidies during digital transformation. To investigate the intrinsic mechanism of multi-stakeholder collaborative transformation, this paper, based on the bounded rationality assumption, incorporates the government, sports equipment manufacturers, and third-party digital service providers into a unified analytical framework. A tripartite evolutionary game model is constructed, systematically deriving the replication dynamic equations for each stakeholder under different strategies, and analyzing the stability of the system equilibrium point using the Jacobian matrix. This study shows that the sustainability of government subsidies depends on the trade-off between social benefits, administrative costs, and subsidy expenditures; whether manufacturers choose to cooperate is mainly influenced by the cost of self-purchased equipment, digital service fees, operation and maintenance risks, and residual value recovery; and the investment willingness of digital service providers depends on infrastructure construction costs, service revenue, and government support. Further simulation analysis shows that a higher initial willingness to cooperate can accelerate system convergence, a moderate capital interest rate helps balance the incentives of both supply and demand sides, excessively high core equipment prices will inhibit manufacturers’ willingness to cooperate, and reasonable digital service fees are key to achieving stable collaboration. This paper provides a theoretical basis for policy optimization, service pricing, and industrial collaborative governance in the digital transformation of the sports manufacturing industry. Full article

(This article belongs to the Special Issue Mathematical Modeling for Digital and Intelligent Supply Chains)

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27 pages, 667 KB

Open AccessArticle

A Structured Reconstruction of Identity Proofs in Wu’s Method for Automated Geometric Theorem Proving

by Siran Lei, Qixin Zhou, Hao Guan, Yongsheng Rao and Jingzhong Zhang

Mathematics 2026, 14(13), 2442; https://doi.org/10.3390/math14132442 - 7 Jul 2026

Viewed by 407

Abstract

Although Wu’s method has achieved remarkable success in automated geometric theorem proving, its proving process relies heavily on complex algebraic elimination operations, making it difficult to directly reveal the reasoning relationships between hypotheses and conclusions, thereby reducing the interpretability and readability of the [...] Read more.

Although Wu’s method has achieved remarkable success in automated geometric theorem proving, its proving process relies heavily on complex algebraic elimination operations, making it difficult to directly reveal the reasoning relationships between hypotheses and conclusions, thereby reducing the interpretability and readability of the resulting proofs. To address this issue, this paper presents a theoretical reconstruction of the proving mechanism of Wu’s method from the perspective of identity proofs. By establishing an identity representation between the conclusion polynomial and the hypothesis polynomials, the algebraic elimination process of Wu’s method is transformed into a structured proof representation with explicit logical semantics. To this end, a Remainder Tracking Matrix (RTM) is introduced, and a systematic method is designed for the joint construction of the characteristic sequence and its RTM during the ascending process, thereby providing a structured and traceable algebraic representation for the elimination procedure of Wu’s method. Furthermore, we realize a mechanized construction of identity proofs within Wu’s method, demonstrating its capability in constructing readable proofs. Additionally, we demonstrate the effectiveness and feasibility of the proposed approach via machine-assisted verification of several representative geometric theorems. This study offers a new pathway toward the structured representation of geometric proofs in Wu’s method and lays a theoretical foundation for the algebraic characterization of geometric invariants as well as for enhancing the explainability of automated geometric theorem proving. Full article

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31 pages, 1702 KB

Open AccessArticle

Strategic Choices of Carbon Trading Modes for Competing Manufacturers Under the Cap-and-Trade Policy

by Xuemei Zhang, Qiang Hu, Xiao Jiang and Tingyuan Lou

Mathematics 2026, 14(13), 2441; https://doi.org/10.3390/math14132441 - 7 Jul 2026

Viewed by 405

Abstract

Confronted with the constraints of global carbon reduction mandates and the widespread implementation of cap-and-trade (CAT) policy, competing manufacturers face critical choices in carbon quota trading, such as engaging in external markets or internal agreements. We develop a duopolistic game model comprising a [...] Read more.

Confronted with the constraints of global carbon reduction mandates and the widespread implementation of cap-and-trade (CAT) policy, competing manufacturers face critical choices in carbon quota trading, such as engaging in external markets or internal agreements. We develop a duopolistic game model comprising a low-carbon manufacturer (M_G) and a traditional manufacturer (M_T) under a CAT framework. In a perfect carbon quota trading market, manufacturers simultaneously cooperate and compete, facing a strategic choice between external trading through the open carbon market and internal trading agreements. We investigate how the low-carbon development level, carbon quota surplus, and internal carbon price affect their choices of carbon quota trading modes. Analytical results indicate that in the scenario where M_G’s quota surplus is insufficient to fully meet M_T’s demand, both manufacturers can achieve Pareto improvement in their respective profits within a certain range of internal carbon prices. Otherwise, the internal trading agreements may only guarantee an increase in their aggregate profits. A numerical analysis based on the actual situation of China’s steel industry verifies the theoretical conclusions. Full article

(This article belongs to the Special Issue Applications of Mathematical Methods in Economics and Finance)

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34 pages, 811 KB

Open AccessArticle

Analysis of a Fourth-Order Conservative Compact Finite Difference Method for Benjamin–Bona–Mahony–Burgers Equation

by Morrakot Khebchareon, Nattapol Ploymaklam, Natchanan Prabhong, Keerati Buchatip and Supanut Chaidee

Mathematics 2026, 14(13), 2440; https://doi.org/10.3390/math14132440 - 7 Jul 2026

Viewed by 272

Abstract

This study presents a fourth-order implicit compact finite difference scheme for the Benjamin–Bona–Mahony–Burgers (BBMB) equation, a nonlinear long-wave equation describing the dynamics of various wave phenomena. By employing an order-reduction framework via an auxiliary variable, we construct a compact difference scheme that yields [...] Read more.

This study presents a fourth-order implicit compact finite difference scheme for the Benjamin–Bona–Mahony–Burgers (BBMB) equation, a nonlinear long-wave equation describing the dynamics of various wave phenomena. By employing an order-reduction framework via an auxiliary variable, we construct a compact difference scheme that yields a nonlinear algebraic system with a narrowly banded structure. Because the continuous BBMB model is governed by an underlying conservation law, the proposed numerical method is designed to preserve this structural property in the discrete sense. The discrete conservation, boundedness, and unique solvability of the scheme are firmly established, and an optimal discrete maximum norm error estimate is derived. Finally, comprehensive numerical experiments are conducted to validate both the conservative properties and the theoretical order of accuracy of the proposed scheme. Full article

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

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8 pages, 209 KB

Open AccessArticle

New Interpretations for the Riemann Curvature and the Landsberg Property in Homogeneous Finsler Geometry

by Ming Xu and Xiaoyang Wang

Mathematics 2026, 14(13), 2439; https://doi.org/10.3390/math14132439 - 7 Jul 2026

Viewed by 296

Abstract

In this paper, we provide a new Riemann curvature formula in homogeneous Finsler geometry. Meanwhile, we prove that a homogeneous Finsler metric is Landsberg if and only if its connection operator induces Killing vector fields for a Hessian metric. As an application, we [...] Read more.

In this paper, we provide a new Riemann curvature formula in homogeneous Finsler geometry. Meanwhile, we prove that a homogeneous Finsler metric is Landsberg if and only if its connection operator induces Killing vector fields for a Hessian metric. As an application, we prove that any homogeneous Landsberg sphere with dimension bigger than 1 and constant flag curvature must be Riemannian. Full article

33 pages, 507 KB

Open AccessFeature PaperArticle

Observable Degrees of Freedom in Programmable Electromagnetic Environments

by Carlos Bousoño-Calzón

Mathematics 2026, 14(13), 2438; https://doi.org/10.3390/math14132438 - 7 Jul 2026

Viewed by 251

Abstract

Programmable electromagnetic environments, including reconfigurable intelligent surface (RIS)-assisted systems, are often described in terms of physical or controllable degrees of freedom. Such counts, however, do not determine which channel or operator directions can actually be distinguished by a finite measurement architecture. This paper [...] Read more.

Programmable electromagnetic environments, including reconfigurable intelligent surface (RIS)-assisted systems, are often described in terms of physical or controllable degrees of freedom. Such counts, however, do not determine which channel or operator directions can actually be distinguished by a finite measurement architecture. This paper develops an operator-space formulation of observable degrees of freedom for programmable propagation systems. We distinguish three nested layers: the physical operator space generated by the family of physically admissible propagation operators, the effective operator space selected by architectural constraints, and the observable subspace induced by a finite probing architecture. Once the effective space is fixed, observability is characterized by the spectrum of the associated measurement Gram operator. To remove arbitrary amplitude scaling, we introduce a common probe-energy normalization and define the resolution-dependent observable dimension

N_{obs} (η)

from the normalized Gram spectrum. The same spectrum also yields an observability condition number, which quantifies the stability of the visible subspace. We then extend the construction to symmetry-resolved operator spaces, showing how invariant probing can create sectorial blind subspaces and how controlled symmetry breaking produces second-order restricted visibility inside the original blind subspace. The mathematical ingredients are standard finite-dimensional tools from operator theory, frame theory, representation theory, and matrix concentration; the contribution is their integration into a measurement-oriented degrees-of-freedom framework for programmable electromagnetic environments. Numerical experiments with normalized probing families, sectorial decompositions, controlled symmetry breaking, and a canonical narrowband RIS-inspired model illustrate that architectures with the same effective dimension and probing budget can exhibit substantially different observable dimensions and conditioning. The results support the view that practical electromagnetic design should optimize not only the number of accessible modes or control states, but also the Gram geometry through which those directions are measured. Full article

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

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23 pages, 769 KB

Open AccessArticle

A Unified Multi-Modal Framework for Intelligent Financial Systems: Integrating Reinforcement Learning, High-Frequency Trading, and Game-Theoretic Approaches with Cross-Modal Sentiment Analysis

by Yuwei Zhang, Fanrong Liu, Chang-An Xu and Mingni Luo

Mathematics 2026, 14(13), 2437; https://doi.org/10.3390/math14132437 - 7 Jul 2026

Viewed by 448

Abstract

The rapid evolution of financial technology demands sophisticated artificial intelligence systems capable of handling diverse challenges across multiple domains simultaneously. This paper presents a unified framework that integrates Proximal Policy Optimization (PPO) for robo-advisory systems, multi-scale time-series prediction models for high-frequency trading, in-context [...] Read more.

The rapid evolution of financial technology demands sophisticated artificial intelligence systems capable of handling diverse challenges across multiple domains simultaneously. This paper presents a unified framework that integrates Proximal Policy Optimization (PPO) for robo-advisory systems, multi-scale time-series prediction models for high-frequency trading, in-context learning mechanisms for dynamic investment advisory, game-theoretic reasoning for competitive banking scenarios, and unified embeddings for cross-modal financial sentiment analysis. Our comprehensive framework addresses the critical gap in the existing literature where these technologies have been developed in isolation, failing to leverage their synergistic potential. Through extensive experimentation across multiple financial datasets and real-world scenarios, we demonstrate that our integrated approach achieves superior performance compared to specialized single-domain systems. Specifically, our framework shows a 23.7% improvement in portfolio optimization metrics, reduces prediction error in high-frequency trading by 31.2%, enhances investment recommendation accuracy by 18.9%, optimizes competitive banking strategies with a 27.4% increase in Nash equilibrium convergence speed, and improves sentiment analysis accuracy by 15.6% through cross-modal fusion. The theoretical foundation of our work establishes convergence guarantees for the integrated optimization problem, while our empirical results validate the practical applicability across diverse financial institutions. This research not only advances the state-of-the-art in financial AI but also provides a blueprint for developing comprehensive intelligent systems that can adapt to the complex, interconnected nature of modern financial markets. Full article

(This article belongs to the Special Issue Advanced Algorithms for Multi-Modal Learning, Knowledge Graphs, and Trustworthy AI)

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15 pages, 292 KB

Open AccessArticle

Weighted Simpson-Type Quantum Integral Inequalities for h-Convex Functions

by Tuncay Köroğlu, Muhammet Yazıcı, Bahadır Özgür Güler and Abdul Wakil Baidar

Mathematics 2026, 14(13), 2436; https://doi.org/10.3390/math14132436 - 7 Jul 2026

Viewed by 283

Abstract

This paper establishes a weighted Simpson-type identity on the parameter domain associated with quantum integral operators. Using this identity together with Hölder’s inequality and the power mean inequality, we derive new estimates for classes of functions whose associated parameter-domain q-derivatives satisfy h [...] Read more.

This paper establishes a weighted Simpson-type identity on the parameter domain associated with quantum integral operators. Using this identity together with Hölder’s inequality and the power mean inequality, we derive new estimates for classes of functions whose associated parameter-domain q-derivatives satisfy h-convexity assumptions. Additional bounds are obtained under boundedness and Lipschitz conditions. Applications to the s-moment of a random variable and to several special means are derived in the classical limit

q \to 1^{-}

. Full article

(This article belongs to the Special Issue Mathematical Inequalities and Fractional Calculus)

22 pages, 4826 KB

Open AccessArticle

The Impact of Neutral Subpopulations on Cooperation in Two-Layer Coupled Networks

by Pan Zhao, Xiaopeng Wan, Jun Feng and Linjiang Yang

Mathematics 2026, 14(13), 2435; https://doi.org/10.3390/math14132435 - 7 Jul 2026

Viewed by 326

Abstract

Sustaining cooperation under severe social dilemmas is a fundamental challenge in complex systems. This paper proposes a two-layer coupled network model integrating three neutral subpopulations, combining an upper human layer (Fermi rule) and a lower agent layer (Bush–Mosteller reinforcement learning). The core scientific [...] Read more.

Sustaining cooperation under severe social dilemmas is a fundamental challenge in complex systems. This paper proposes a two-layer coupled network model integrating three neutral subpopulations, combining an upper human layer (Fermi rule) and a lower agent layer (Bush–Mosteller reinforcement learning). The core scientific contribution is revealing that the three-subpopulation structure induces closed invasion cycles. This cross-subpopulation reciprocal suppression effectively halts the global expansion of defectors. Monte Carlo simulations demonstrate that under a severe dilemma

(b = 1.8

), optimizing the coupling strength boosts the cooperation persistence probability (

P_{C C}

) by 91% and reduces defection persistence (

P_{D D}

) by 55%, stabilizing the global cooperation rate at approximately 50%. Furthermore, for

b > 1.26

, this model consistently outperforms the canonical BM model. Practically, these findings provide a theoretical foundation and a quantitative reference for designing cooperative mechanisms in human–machine collaboration and public governance. Full article

(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)

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36 pages, 701 KB

Open AccessArticle

Operator-Blind Secret Mediation for AI Agents: A Formal Model and FHE Construction for Credential Derivation on Untrusted Infrastructure

by Shutong Jin, Ruiyi Guo and Ray C. C. Cheung

Mathematics 2026, 14(13), 2434; https://doi.org/10.3390/math14132434 - 7 Jul 2026

Viewed by 484

Abstract

Artificial intelligence (AI) agents increasingly need credentials such as application programming interface (API) keys and Secure Shell (SSH) credentials, but placing those secrets in the agent process exposes them to prompt injection, tool misuse, and exfiltration through ordinary agent outputs. We present CapSeal, [...] Read more.

Artificial intelligence (AI) agents increasingly need credentials such as application programming interface (API) keys and Secure Shell (SSH) credentials, but placing those secrets in the agent process exposes them to prompt injection, tool misuse, and exfiltration through ordinary agent outputs. We present CapSeal, a capability-based broker that replaces direct secret access with session-bound, non-exportable handles. Agents request policy-evaluated actions, while the broker performs credential-bearing Hypertext Transfer Protocol (HTTP) and SSH execution through typed executors with schema validation, replay protection, revocation epochs, and tamper-evident audit logging. We extend this design to hosted settings where the broker operator is not trusted with tenant secrets. Our main contribution is operator-blind secret mediation: a split-broker architecture in which a small trusted tenant gateway cooperates with an untrusted operator service that stores the master secret only as a fully homomorphic encryption (FHE) ciphertext and evaluates per-request derivations without decrypting it. We formalize the model and prove computational operator blindness from indistinguishability under chosen-plaintext attack (IND-CPA) security of the FHE scheme, together with conditional capability binding for any secure pseudorandom function/message authentication code (PRF/MAC) instantiation. We implement an end-to-end TFHE-rs prototype that exercises split-broker derivation, multi-tenant revocation and rate limiting, audit integration, and HTTP/SSH mediation. The prototype uses a non-cryptographic homomorphic stand-in and measures the cost of crossing the operator-untrusted boundary at about 9 s per request, roughly 17 million times slower than the plaintext path. We also give LowMC and Rasta transciphering designs and compare FHE with trusted execution environment (TEE)- and secure multiparty computation (MPC)-based alternatives, positioning each trust boundary by assurance and performance. Full article

(This article belongs to the Special Issue Next-Generation Quantum Security: Algorithms, Cryptography, and Computational Breakthroughs)

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21 pages, 289 KB

Open AccessArticle

Some Rigidity Results Related to Conformal Vector Fields

by Hanan Alohali and Sharief Deshmukh

Mathematics 2026, 14(13), 2433; https://doi.org/10.3390/math14132433 - 7 Jul 2026

Viewed by 358

Abstract

This article explores properties of conformal vector fields on a Riemannian manifold, focusing on conditions that lead to the manifold being isometric to the Euclidean space. Given a conformal vector

ζ

with conformal factor

σ

on a Riemannian manifold

(N, g)

, [...] Read more.

This article explores properties of conformal vector fields on a Riemannian manifold, focusing on conditions that lead to the manifold being isometric to the Euclidean space. Given a conformal vector

ζ

with conformal factor

σ

on a Riemannian manifold

(N, g)

, there is naturally associated a skew-symmetric tensor

χ

to

ζ

called the essential tensor of

ζ

. It is shown that the essential tensor

χ

plays a vital role in our study. We intend to analyze when a conformal vector field becomes a Killing vector field. In a first result of this article, we obtain a necessary and sufficient geometric condition on a complete and connected Riemannian manifold

(N, g)

admitting a conformal vector field

ζ

so that

ζ

is a Killing vector field. In the rest of the article, we obtain characterizations of a Euclidean space using conformal vector fields. In the first such result, it is shown that an n-dimensional complete and connected Riemannian manifold

(N, g)

,

n > 2

admits a conformal vector field

ζ

with conformal factor

σ \neq 0

and essential tensor

χ

such that the affinity tensor of

\nabla σ

is zero, the function

ζ (σ)

is a constant, and

ζ

annihilates

χ

if and only if

(N, g)

is isometric to the Euclidean space

E^{n}

. Similarly, in a second characterization of the Euclidean space

E^{n}

using a conformal vector field

ζ

, we use the following conditions:

ζ

annihilates the Ricci operator S,

\nabla σ

annihilates

χ

, and the vector field

χ (ζ)

is incompressible. Finally, we consider a conformal vector field

ζ

with conformal factor

σ \neq 0

and essential tensor

χ

on a complete and connected Riemannian manifold

(N, g)

such that the Hessian operator

H_{σ}

is invariant under the local flow of

ζ

so that the function

ζ (σ) - σ^{2}

is a subharmonic function and

ζ

annihilates

χ

, and show that

(N, g)

is isometric to the Euclidean space

E^{n}

. The converse holds as well. Full article

(This article belongs to the Section B: Geometry and Topology)

21 pages, 945 KB

Open AccessFeature PaperArticle

Fractional Brownian Vector Field in the Framework of Euclidean Geometry

by Leonidas Sakalauskas and Neringa Urbonaitė

Mathematics 2026, 14(13), 2432; https://doi.org/10.3390/math14132432 - 7 Jul 2026

Viewed by 338

Abstract

A new fractional Brownian vector field (FBVF) is created for modeling multidimensional and multivariate fractal data. It is shown that the FBVF is a multidimensional and multivariate generalization of the classical Kolmogorov–Wiener process, allowing the distribution of field increments to be defined solely [...] Read more.

A new fractional Brownian vector field (FBVF) is created for modeling multidimensional and multivariate fractal data. It is shown that the FBVF is a multidimensional and multivariate generalization of the classical Kolmogorov–Wiener process, allowing the distribution of field increments to be defined solely through fractal Euclidean distances between observation points. Conditions are established under which the family of field distributions satisfies the Kolmogorov consistency theorem. Maximum likelihood and variogram-based methods are developed to analytically estimate the mean and covariance of the FBVF, while the Hurst parameter is computed using an one-variable optimization algorithm. A kriging method is constructed for solving prediction problems using observations of fractal data. For computer simulation of field realizations, recursive and kriging-based algorithms are applied. A computational Monte Carlo experiment confirms the reliability of the proposed methods, particularly in accurately estimating the Hurst parameter. Applications to heavy metal concentrations in soil and climate data analysis demonstrate the effectiveness of the model in representing and analyzing multifractal, multidimensional processes. Full article

(This article belongs to the Section D1: Probability and Statistics)

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10 pages, 722 KB

Open AccessArticle

First Integral and General Solution of the Reduced Nonlinear Third-Order Differential Equation with a Nonlinear Source

by Nikolay A. Kudryashov

Mathematics 2026, 14(13), 2431; https://doi.org/10.3390/math14132431 - 7 Jul 2026

Viewed by 358

Abstract

We consider a generalization of the modified Korteweg–de Vries–Burgers equation with a nonlinear source. Using the Painlevé test for partial differential equation with the Kruskal variable, we show that the corresponding Cauchy problem cannot be solved by the inverse scattering transform. However, the [...] Read more.

We consider a generalization of the modified Korteweg–de Vries–Burgers equation with a nonlinear source. Using the Painlevé test for partial differential equation with the Kruskal variable, we show that the corresponding Cauchy problem cannot be solved by the inverse scattering transform. However, the equation admits a two-wave solution, which is obtained by means of the Cole–Hopf transformation. Taking into account the traveling wave reduction, we derive the resulting nonlinear ordinary differential equation and determine the parameter conditions under which it passes the Painlevé test. This finding suggests the possible existence of the general solution for the ordinary differential equation, which can be reduced to the linear third-order equation. The general solution of the resulting linear equation is expressed in terms of the hypergeometric function. Full article

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

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16 pages, 331 KB

Open AccessArticle

Zero-Cost Enhancement of the Steffensen Method for Nonlinear Equations

by Avram Sidi

Mathematics 2026, 14(13), 2430; https://doi.org/10.3390/math14132430 - 7 Jul 2026

Viewed by 261

Abstract

The Steffensen method is a very effective root-finding procedure used for solving nonlinear equations of the form

f (x) = 0

numerically. When the root of

f (x)

is simple, this method converges with order 2. Following a critical [...] Read more.

The Steffensen method is a very effective root-finding procedure used for solving nonlinear equations of the form

f (x) = 0

numerically. When the root of

f (x)

is simple, this method converges with order 2. Following a critical review of its convergence analysis, in this work, we provide a modification with memory of the Steffensen method, which achieves an order substantially higher than 2, without increasing the number of function evaluations per iteration. Specifically, with an arbitrary fixed integer

k \geq 1

and with initial approximations

x_{0}, x_{1}, \dots, x_{k}

, the modified method generates a sequence of approximations to the solution of

f (x) = 0

via

x_{n + 1} = x_{n} - f (x_{n}) / f [c_{n}, x_{n}]

,

n = k, k + 1, \dots,

where

c_{n} = x_{n} - f (x_{n}) / p_{n, k}^{'} (x_{n})

and

p_{n, k} (x)

is the polynomial of interpolation to

f (x)

at the points

x_{n}, x_{n - 1}, \dots, x_{n - k}

. Just as in the original method, the modified method makes use of only

f (x)

; no derivatives of

f (x)

are needed. We prove that the order of this method is

1 + \sqrt{2} \dot{=} 2.414

for

k = 1

and it can be increased towards

(3 + \sqrt{5}) / 2 \dot{=} 2.618

by increasing k. (For example, the order of the method is

2.617 \dots

already for

k = 6

.) Full article

(This article belongs to the Special Issue Numerical Analysis of Partial Differential Equations and Their Application)

32 pages, 6329 KB

Open AccessFeature PaperArticle

Dynamics of Perceived Risk in Risk-Sharing by Exogenous Information: A Non-Hermitian Hamiltonian Quantum Approach

by Miwaka Yamashita

Mathematics 2026, 14(13), 2429; https://doi.org/10.3390/math14132429 - 6 Jul 2026

Viewed by 283

Abstract

This paper introduces quantum risk measurement models focusing on the evolution of risk observation over time triggered by the arrival of information. These models address the contextuality of risk-related decision-making with greater flexibility and greater coherence than conventional approaches. A typical example of [...] Read more.

This paper introduces quantum risk measurement models focusing on the evolution of risk observation over time triggered by the arrival of information. These models address the contextuality of risk-related decision-making with greater flexibility and greater coherence than conventional approaches. A typical example of such information is the commencement of external support for a risk-sharing pool. This paper investigates the amplification and attenuation of perceived risk within risk-sharing pools, driven by the arrival of exogenous information using open system quantum theory models. Rather than adopting a closed system framework—where the quantum model employs a Hermitian Hamiltonian resulting in unitary time evolution—an open system approach is implemented utilizing a non-Hermitian Hamiltonian and non-unitary time evolution to describe the dynamics of risk observation. The perceived risk is measured by a quantum risk measure operator. While unitary time evolution preserves the sum of the eigenvalues of this operator, keeping the magnitude of the expectation value under strict constraints, our proposed open system framework breaks these limitations. By employing a non-Hermitian Hamiltonian and non-unitary transformations, the model captures the risk dynamics of amplification or attenuation of the size more realistically, allowing exogenous information to alter the scale of observed risk fundamentally, flexibly, and significantly. Agent-based models provide less structural insight, and the jump diffusion models do not treat mind state interactions. Numerical simulations demonstrate that this model successfully accounts for both risk amplification and attenuation—phenomena that occur naturally in the real world but cannot be explained by unitary transformations. The time evolution described by the Schrödinger equation shows step-by-step effects of perceived risk size changes and risk-based interactions. Practical applications include scenarios where new informational shocks alter the perceived severity of risk, such as the formalization of risk pooling rules or the establishment of new regulatory frameworks. Full article

(This article belongs to the Special Issue Advances in Mathematical Modeling for Insurance and Risk Management)

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37 pages, 3387 KB

Open AccessArticle

A Locality-Activated Matrix Reordering Framework for SpMV

by Qi Zhang, Zhengan Yao, Zhenglu Jiang and Zanbo Zhang

Mathematics 2026, 14(13), 2428; https://doi.org/10.3390/math14132428 - 6 Jul 2026

Viewed by 316

Abstract

Sparse Matrix-Vector Multiplication (SpMV) is a fundamental kernel in many scientific and graph applications, and its performance is often limited by the poor locality of input-vector accesses. Matrix reordering is an efficient approach for improving such locality; however, existing methods, such as GOrder, [...] Read more.

Sparse Matrix-Vector Multiplication (SpMV) is a fundamental kernel in many scientific and graph applications, and its performance is often limited by the poor locality of input-vector accesses. Matrix reordering is an efficient approach for improving such locality; however, existing methods, such as GOrder, suffer from two major limitations: they are applied without estimating whether a matrix has sufficient relabeling headroom, and they can incur substantial preprocessing overhead on large graphs. To address these issues, we propose a locality-activated parallel matrix reordering framework consisting of two components. First, we introduce a reuse-distance-based locality headroom predictor that estimates the potential SpMV speedup after applying matrix reordering; reordering is activated only when the expected benefit is sufficiently large. Second, we propose a two-phase parallel matrix reordering algorithm, termed pGOrder. It decomposes the sequential greedy process of GOrder into global coarse-grained batch generation and local fine-grained refinement. In the first phase, reuse-aware vertex batches are generated on the GPU according to global reuse signals. In the second phase, the ordering within each batch is refined concurrently on multi-core CPUs. Experimental results show that the proposed predictor effectively identifies matrices with meaningful locality headroom, and pGOrder preserves most of the locality benefit of GOrder while substantially reducing order-generation overhead. On the selected matrices, pGOrder retains over 95% of GOrder’s average SpMV speedup while requiring less than 5% of its order-generation time. Full article

(This article belongs to the Special Issue Numerical and Computational Methods in Engineering, 2nd Edition)

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31 pages, 5268 KB

Open AccessArticle

Modelling South African Macroeconomic and Financial Time Series: A Comparative Analysis of Vector Autoregressive Moving Average and Asymmetric Generalised Autoregressive Conditional Heteroskedasticity Frameworks

by Thatoyaone Johannes Modise, Johannes Tshepiso Tsoku and Tshegofatso Botlhoko

Mathematics 2026, 14(13), 2427; https://doi.org/10.3390/math14132427 - 6 Jul 2026

Viewed by 401

Abstract

This study examines the modelling and forecasting of South African macroeconomic and financial time series using a comparative framework based on Vector Autoregressive (VAR), Vector Autoregressive Moving Average (VARMA), and GARCH-type models. Quarterly data spanning 1970 to 2024 were analysed to determine GDP [...] Read more.

This study examines the modelling and forecasting of South African macroeconomic and financial time series using a comparative framework based on Vector Autoregressive (VAR), Vector Autoregressive Moving Average (VARMA), and GARCH-type models. Quarterly data spanning 1970 to 2024 were analysed to determine GDP growth, exchange rates, interest rates, and household consumption expenditure. VAR and VARMA models were employed to capture conditional mean dynamics, while GARCH, EGARCH, and GJR-GARCH models, including ARMA-GARCH extensions, were used to model volatility behaviour. Optimal model specifications were selected using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Hannan–Quinn Criterion (HQ), and the Extended Cross-Correlation Matrix (ECCM), resulting in the estimation of VAR (4) and VARMA (1,1) models. The results reveal strong dynamic interdependencies among the variables. However, diagnostic tests indicate that the VAR (4) and VARMA (1,1) models do not fully capture the underlying data-generating process, as evidenced by residual autocorrelation, heteroskedasticity, and non-normality. Although the VARMA (1,1) model improved forecasting performance relative to the VAR (4) model, important nonlinear and higher-order dynamics remained unexplained. Volatility modelling revealed substantial persistence and clustering, particularly in exchange rates and interest rates. Initial GARCH, EGARCH, and GJR-GARCH specifications exhibited residual autocorrelation and remaining ARCH effects, suggesting model misspecification. The incorporation of an ARMA (1,1) term into the asymmetric GARCH models significantly improved model adequacy by eliminating residual autocorrelation and heteroskedasticity. Limited evidence of asymmetric volatility effects was found. Overall, the findings demonstrate that GARCH-ARMA specifications provide a more robust framework for modelling South Africa’s macroeconomic and financial dynamics. This study recommends future research incorporating nonlinear, regime-switching, and exogenous-variable models to enhance forecasting accuracy and policy relevance. Full article

(This article belongs to the Special Issue Application of Statistical Analysis and Models in Economics and Management)

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18 pages, 383 KB

Open AccessArticle

Viscous Current Induced by Kelvin Force in Ordinary Fluids with Magnetic Susceptibility Contrasts

by Mutabe Aljaghtham, Kannan Premnath and Radi A. Alsulami

Mathematics 2026, 14(13), 2426; https://doi.org/10.3390/math14132426 - 6 Jul 2026

Viewed by 303

Abstract

The magnetic susceptibilities of various electrically insulating ordinary fluids depend on their local states, such as their density and temperature. When such fluids, which can be characterized as either paramagnetic or diamagnetic and occur commonly in nature, are subjected to magnetic field gradients, [...] Read more.

The magnetic susceptibilities of various electrically insulating ordinary fluids depend on their local states, such as their density and temperature. When such fluids, which can be characterized as either paramagnetic or diamagnetic and occur commonly in nature, are subjected to magnetic field gradients, it induces an effective body force—the Kelvin force. This force, which depends on the susceptibility and the gradient of the square of the magnetic field strength, can become one of the effective mechanisms for modulating the flow and transport, particularly where terrestrial gravity becomes negligible, such as in free space or under microgravity conditions. For the first time, we developed a theoretical model demonstrating that a viscous current can be generated due to the contrasts between the magnetic susceptibilities of the intruding and ambient fluids in the presence of gradients in magnetic fields, analogous to the viscous gravity current in terrestrial situations. We derived similarity solutions for the two-dimensional and axisymmetric currents arising from a balance between the Kelvin buoyancy and viscous forces with a prescribed power law for the magnetic field strength. These determine the shape and various spreading relationships of the viscous current. For a prescribed time variation in the source flux, it is shown that a family of scaling laws exists for the spreading rate and the thickness of the current, which depend on the steepness of the magnetic field gradient. Unlike gravity, since the driving horizontal buoyancy arising from the Kelvin force is externally specified, it potentially offers a mechanism to control the characteristic shape and the rate of motion of the viscous current. Full article

(This article belongs to the Special Issue Mathematical Fluid Dynamics: Theory, Analysis and Emerging Trends)

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21 pages, 576 KB

Open AccessArticle

Quartic Rational Iterations for the Matrix Sign with Applications to Principal Square Roots and Inverse Square Roots

by Haifa Bin Jebreen

Mathematics 2026, 14(13), 2425; https://doi.org/10.3390/math14132425 - 6 Jul 2026

Viewed by 291

Abstract

This paper develops a new rational fixed-point iteration for

sign (M)

whose scalar prototype enjoys half-plane global convergence and a quartic local error contraction. By embedding M into a block matrix and exploiting the classical sign–square root identity, the proposed iteration [...] Read more.

This paper develops a new rational fixed-point iteration for

sign (M)

whose scalar prototype enjoys half-plane global convergence and a quartic local error contraction. By embedding M into a block matrix and exploiting the classical sign–square root identity, the proposed iteration yields

M^{1 / 2}

and

M^{- 1 / 2}

within a single iterative run under standard spectral admissibility conditions. A norm-balancing scaling strategy is also incorporated to accelerate the initial phase without changing the asymptotic order. Numerical experiments in a unified implementation demonstrate that the method reduces iteration counts and time compared with Newton-type and Padé-based competitors. Full article

(This article belongs to the Special Issue Advanced Numerical Linear Algebra)

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36 pages, 431 KB

Open AccessArticle

Closed-Form Equations for the Reorder Point and Order-Up-To Level in a Lost-Sales Periodic-Review (R, s, S) Inventory Policy

by Samir Žic and Jasmina Žic

Mathematics 2026, 14(13), 2424; https://doi.org/10.3390/math14132424 - 6 Jul 2026

Viewed by 379

Abstract

This paper develops explicit equations for setting the reorder point s and the order-up-to level S in a periodic-review (R, s, S) inventory policy in a lost-sales environment. The objective is to support direct policy parameterization from demand level, [...] Read more.

This paper develops explicit equations for setting the reorder point s and the order-up-to level S in a periodic-review (R, s, S) inventory policy in a lost-sales environment. The objective is to support direct policy parameterization from demand level, demand variability, review period, lead time, and type-II unit fill-rate target. A long-horizon discrete-event simulation was combined with exhaustive enumeration of integer policy pairs to construct a policy-consistent reference dataset of five million observations. Symbolic regression was then used to convert this simulation-derived reference map into compact closed-form equations for both policy parameters. Over the full tested domain, the equations achieved R² = 0.941 for the reorder point s and R² = 0.989 for the order-up-to level S. On the common domain where analytical comparison is possible, the proposed equations reduced mean absolute error by approximately 65% for the reorder point and 85% for the order-up-to level. The equations also remain directly evaluable at the finite-horizon zero-lost-sales boundary corresponding to a 100% fill rate, where standard normal-loss logic has no finite safety-factor solution. The study provides an interpretable, auditable equation system for initial estimation of policy parameters for periodic-review lost-sales inventory policies within the tested normal-demand domain. Full article

33 pages, 14316 KB

Open AccessArticle

IMU-Sequence-Based GNSS Short Outage Compensation and Hybrid Positioning Strategy

by Ziyong Lei, Luyao Du and Zelong Lian

Mathematics 2026, 14(13), 2423; https://doi.org/10.3390/math14132423 - 6 Jul 2026

Viewed by 855

Abstract

Pure inertial dead reckoning during short GNSS outages causes rapid drift on low-cost MEMS GNSS/IMU platforms. Most learning-based compensators upgrade a single predictor and rarely address late-outage drift or cross-domain bias mismatch. This paper proposes two enhancements over a Transformer baseline (TF-Base) plus [...] Read more.

Pure inertial dead reckoning during short GNSS outages causes rapid drift on low-cost MEMS GNSS/IMU platforms. Most learning-based compensators upgrade a single predictor and rarely address late-outage drift or cross-domain bias mismatch. This paper proposes two enhancements over a Transformer baseline (TF-Base) plus a lightweight inference-time fusion strategy. MGTR (Motion-Guided Transformer with Tail-aware Readout) adds residual motion gating and a tail-aware readout for hard-segment and late-outage response. TAMS (Temporal Attention Multi-Scale) replaces global average pooling with learnable temporal attention and a short-window dual head. Delayed-Switch selects among TF-Base, MGTR, and TAMS without retraining backbones; its classifier needs a one-pass target-domain calibration, so it is not zero-shot. On real 5 Hz GNSS/IMU recordings under a three-tier protocol, where dead reckoning yields a 40.02 m mean RMSE on cross-domain segments, MGTR cuts the 90th-percentile 2D-RMSE by 20.3% over TF-Base, and Delayed-Switch reaches 30.32 m mean RMSE (24.2% below dead reckoning, 9.5% below TF-Base), within 0.51 m of the better-of-two upper bound. Against two recent baselines under the same protocol, only the AT-LSTM gain is significant after multiple-comparison correction; the margins over the strongest predictors are numerically favorable but not significant at this sample size, with gains concentrated on a few hard segments. Full article

(This article belongs to the Special Issue Advances in Perception, Control and Optimization Methods in Intelligent Transportation Systems)

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17 pages, 374 KB

Open AccessArticle

WAVE: Interpretable High-Dimensional Change Point Detection via Adaptive Weighted Variable Selection

by Hui Lan, Luyue Qi, Jianyuan Xue and Qijing Yan

Mathematics 2026, 14(13), 2422; https://doi.org/10.3390/math14132422 - 6 Jul 2026

Viewed by 347

Abstract

High-dimensional change point detection is a fundamental problem in modern statistical learning, particularly when distributional changes are driven by a small and unknown subset of variables. In heterogeneous settings, uniform aggregation across coordinates may suffer from signal dilution, because stable or noisy variables [...] Read more.

High-dimensional change point detection is a fundamental problem in modern statistical learning, particularly when distributional changes are driven by a small and unknown subset of variables. In heterogeneous settings, uniform aggregation across coordinates may suffer from signal dilution, because stable or noisy variables can mask the evidence carried by structurally unstable coordinates. Moreover, many existing procedures primarily focus on temporal localization and provide limited information about the variables responsible for a detected structural break. To address these challenges, we propose WAVE, a weighted adaptive variable selection procedure for interpretable change point detection. WAVE constructs variance-standardized global CUSUM evidence and locally standardized exponentially weighted evidence for each coordinate and then adaptively maps intervalwise coordinate evidence into a continuous weight vector. The learned weights strengthen coordinates with persistent or local evidence of change while downweighting nuisance coordinates with weak evidence. The resulting weighted scan statistic is calibrated by a residual moving block bootstrap that preserves temporal and cross-sectional dependence and re-applies the weighting rule within bootstrap samples to account for data-adaptive aggregation. Detected change points are further equipped with coordinate-level attribution through a multi-criteria fusion rule combining adaptive weights, local standardized effect sizes, and marginal testing evidence. Simulation studies show that WAVE achieves accurate localization and reliable support recovery in both single and multiple change point settings, particularly under sparse and heterogeneous alternatives. An empirical analysis of S&P 100 stock returns in 2020 further demonstrates that WAVE identifies economically meaningful market regime shifts with interpretable coordinate-level attribution. Full article

(This article belongs to the Special Issue Mathematical Statistics and Nonparametric Inference)

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