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Mathematics, Volume 14, Issue 2 (January-2 2026) – 24 articles

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31 pages, 1573 KB  
Article
When Does Platform Private-Label Advertising Work? The Role of Quality and Supply Chain Structure
by Yunrong Zhang, Shuyan Pan and Mengyang Li
Mathematics 2026, 14(2), 227; https://doi.org/10.3390/math14020227 - 7 Jan 2026
Abstract
Advertising is often viewed as an effective strategy for platforms to boost the sales of their private-label (PL) products. Nevertheless, not all platforms adopt PL advertising strategies, and the drivers of these heterogeneous advertising practices across platforms, which differ in PL product quality [...] Read more.
Advertising is often viewed as an effective strategy for platforms to boost the sales of their private-label (PL) products. Nevertheless, not all platforms adopt PL advertising strategies, and the drivers of these heterogeneous advertising practices across platforms, which differ in PL product quality and supply chain structures (agency (A) vs. reselling (R) modes), remain unclear. Our analysis shows that, without advertising, an increase in PL quality does not necessarily deter the manufacturer from competition under mode A. When advertising is introduced, however, increasing PL quality may sometimes amplify the negative effect of advertising on the manufacturer-branded products’ price under mode A. Moreover, contrary to common belief that advertising always benefits the platform, we identify conditions under which PL advertising leads to a lose–lose outcome for both the manufacturer and the platform, regardless of PL quality. Finally, we find that an appropriately designed advertising effort allows the platform to align the manufacturer’s channel preference with its own—toward either Mode A or Mode R structure. Overall, our findings uncover the strategic interplay between PL advertising, product quality, and supply chain structure, thereby explaining the diversity of platform advertising behaviors in practice, such as JD.com and Taobao. Full article
(This article belongs to the Special Issue Computation and Optimization for Emerging Topics in Operations and Supply Chain Management)
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28 pages, 570 KB  
Article
Direct Transformation of Laplace Equation’s Solution from Spherical to Cartesian Representation
by Gibárt Gilányi
Mathematics 2026, 14(2), 226; https://doi.org/10.3390/math14020226 - 7 Jan 2026
Abstract
The description of the Earth’s gravitational field, governed by the fundamental potential equation (the Laplace equation), is conventionally expressed using spherical harmonics, yet the Cartesian formulation, using a Taylor series representation, offers significant algebraic advantages. This paper proposes a novel Direct Cartesian Method [...] Read more.
The description of the Earth’s gravitational field, governed by the fundamental potential equation (the Laplace equation), is conventionally expressed using spherical harmonics, yet the Cartesian formulation, using a Taylor series representation, offers significant algebraic advantages. This paper proposes a novel Direct Cartesian Method for generating spherical basis functions and coefficients directly within the Cartesian coordinate system, utilising the partial derivatives of the inverse distance (1/R) function. The present study investigates the structural correspondence between the Cartesian form of spherical basis functions and the high-order partial derivatives of 1/R. The study reveals that spherical basis functions can be categorised into four distinct groups based on the parity of the degree n and order m. It is demonstrated that each spherical basis function is equivalent to a weighted summation of the partial derivatives of the inverse distance (1/R) with respect to Cartesian coordinates. Specifically, the basis functions are combined with those derivatives that share the same order of Z-differentiation and possess matching parities in their orders of differentiation with respect to X and Y. In order to facilitate the practical calculation of these high-degree derivatives, a recursive numerical algorithm has been developed. The method generates the polynomial coefficients for the numerator of the 1/R derivatives. A pivotal innovation is the implementation of a step-wise normalization scheme within the recursive relations. The integration of the recursive ratios of global normalization factors (including full Schmidt normalization) into each step of the algorithm effectively neutralises factorial growth, rendering the process immune to numerical overflow. The validity and numerical stability of the proposed method are demonstrated through a detailed step-by-step derivation of a sectorial basis function (n=8,m=2). Full article
29 pages, 12826 KB  
Article
PLB-GPT: Potato Late Blight Prediction with Generative Pretrained Transformer and Optimizing
by Peisen Yuan, Ye Xia, Mengjian Dong, Cheng He, Dingfei Liu, Yixi Tan and Suomeng Dong
Mathematics 2026, 14(2), 225; https://doi.org/10.3390/math14020225 - 7 Jan 2026
Abstract
Potato late blight is a devastating disease and threatening global potato production, necessitating accurate early prediction for effective management and yield enhancement.This paper presents the PLB-GPT, a novel generative pre-trained transformer-based model built on GPT-2 architecture, designed to forecast late blight outbreaks using [...] Read more.
Potato late blight is a devastating disease and threatening global potato production, necessitating accurate early prediction for effective management and yield enhancement.This paper presents the PLB-GPT, a novel generative pre-trained transformer-based model built on GPT-2 architecture, designed to forecast late blight outbreaks using meteorological data. Our method is trained and evaluated on a real-world dataset encompassing temperature, humidity, atmospheric pressure, and other climatic variables from diverse regions of China; PLB-GPT demonstrates state-of-the-art performance. The framework of PLB-GPT employs advanced fine-tuning strategies, including Linear Probing, Full Fine-Tuning, and a novel two-stage method, effectively applied across different time windows (1-day, 3-day, 5-day, 7-day). The model achieves an accuracy of 0.8746, a precision of 0.8915, and an F1 score of 0.8472 in the 5-day prediction window, surpassing baseline methods such as CARAH, ARIMA, LSTM, and Informer. These results highlight PLB-GPT as a robust tool for early disease outbreak prediction, with significant implications for agricultural disease management. Full article
(This article belongs to the Special Issue Computational Intelligence for Bioinformatics)
27 pages, 2225 KB  
Article
Qualitative Analysis and Applications of Fractional Stochastic Systems with Non-Instantaneous Impulses
by Muhammad Imran Liaqat and Abdelhamid Mohammed Djaouti
Mathematics 2026, 14(2), 224; https://doi.org/10.3390/math14020224 - 7 Jan 2026
Abstract
Fractional stochastic differential Equations (FSDEs) with time delays and non-instantaneous impulses describe dynamical systems whose evolution relies not only on their current state but also on their historical context, random fluctuations, and impulsive effects that manifest over finite intervals rather than occurring instantaneously. [...] Read more.
Fractional stochastic differential Equations (FSDEs) with time delays and non-instantaneous impulses describe dynamical systems whose evolution relies not only on their current state but also on their historical context, random fluctuations, and impulsive effects that manifest over finite intervals rather than occurring instantaneously. This combination of features offers a more precise framework for capturing critical aspects of many real-world processes. Recent findings demonstrate the existence, uniqueness, and Ulam–Hyers stability of standard fractional stochastic systems. In this study, we extend these results to include systems characterized by FSDEs that incorporate time delays and non-instantaneous impulses. We prove the existence and uniqueness of the solution for this system using Krasnoselskii’s and Banach’s fixed-point theorems. Additionally, we present findings related to Ulam–Hyers stability. To illustrate the practical application of our results, we develop a population model that incorporates memory effects, randomness, and non-instantaneous impulses. This model is solved numerically via the Euler–Maruyama method, and graphical simulations effectively depict the dynamic behavior of the system. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 2nd Edition)
22 pages, 394 KB  
Article
A Fractional Calculus Approach to Energy Balance Modeling: Incorporating Memory for Responsible Forecasting
by Muath Awadalla and Abulrahman A. Sharif
Mathematics 2026, 14(2), 223; https://doi.org/10.3390/math14020223 - 7 Jan 2026
Abstract
Global climate change demands modeling approaches that are both computationally efficient and physically faithful to the system’s long-term dynamics. Classical Energy Balance Models (EBMs), while valuable, are fundamentally limited by their memoryless exponential response, which fails to represent the prolonged thermal inertia of [...] Read more.
Global climate change demands modeling approaches that are both computationally efficient and physically faithful to the system’s long-term dynamics. Classical Energy Balance Models (EBMs), while valuable, are fundamentally limited by their memoryless exponential response, which fails to represent the prolonged thermal inertia of the climate system—particularly that associated with deep-ocean heat uptake. In this study, we introduce a fractional Energy Balance Model (fEBM) by replacing the classical integer-order time derivative with a Caputo fractional derivative of order α(0<α≤1), thereby embedding long-range memory directly into the model structure. We establish a rigorous mathematical foundation for the fEBM, including proofs of existence, uniqueness, and asymptotic stability, ensuring theoretical well-posedness and numerical reliability. The model is calibrated and validated against historical global mean surface temperature data from NASA GISTEMP and radiative forcing estimates from IPCC AR6. Relative to the classical EBM, the fEBM achieves a substantially improved representation of observed temperatures, reducing the root mean square error by approximately 29% during calibration (1880–2010) and by 47% in out-of-sample forecasting (2011–2023). The optimized fractional order α=0.75±0.03 emerges as a physically interpretable measure of aggregate climate memory, consistent with multi-decadal ocean heat uptake and observed persistence in temperature anomalies. Residual diagnostics and robustness analyses further demonstrate that the fractional formulation captures dominant temporal dependencies without overfitting. By integrating mathematical rigor, uncertainty quantification, and physical interpretability, this work positions fractional calculus as a powerful and responsible framework for reduced-order climate modeling and long-term projection analysis. Full article
(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics—In Memory of Prof. Dr. Ravi P. Agarwal)
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45 pages, 589 KB  
Article
Mixed Parity Variants of Apéry-Type Binomial Series and Level Four Colored Multiple Zeta Values
by Ce Xu and Jianqiang Zhao
Mathematics 2026, 14(2), 222; https://doi.org/10.3390/math14020222 - 7 Jan 2026
Abstract
In this paper, we study an Apéry-type series involving the central binomial coefficients ∑n1>…>nd>014n12n1n1n1−s1…nd−sd [...] Read more.
In this paper, we study an Apéry-type series involving the central binomial coefficients ∑n1>…>nd>014n12n1n1n1−s1…nd−sd and its variations where the summation indices may have mixed parities and some or all “>” are replaced by “≥”, as long as the series are defined. These sums have naturally appeared in the calculation of massive Feynman integrals by the work of Jegerlehner, Kalmykov, and Veretin. We show that all these sums can be expressed as Q-linear combinations of the real and/or imaginary parts of the colored multiple zeta values at level four, i.e., special values of multiple polylogarithms at fourth roots of unity. For example, our main theorem shows that when n1−s1 is replaced by (2n1)−s1 and other nj−sj’s are replaced by either (2nj)−sj or (2nj+1)−sj, then all the colored multiple zeta values can be chosen to have the same weight s1+…+sd, but the weights of these values are only bounded by s1+…+sd for general variant Apéry-type series of mixed parities. We also show that the corresponding series where 2n1n1/4n1 is replaced by 2n1n12/16n1 can be expressed in a similar way except for a possible extra factor of 1/π, with the weight of the colored multiple zeta values similarly bounded. Full article
(This article belongs to the Section A: Algebra and Logic)
30 pages, 4550 KB  
Article
Robust Controller Design Based on Sliding Mode Control Strategy with Exponential Reaching Law for Brushless DC Motor
by Seyfettin Vadi
Mathematics 2026, 14(2), 221; https://doi.org/10.3390/math14020221 - 6 Jan 2026
Abstract
This study presents a comprehensive performance analysis of four different control strategies, Proportional–Integral (PI), classical Sliding Mode Control (SMC), Super-Twisting SMC (ST-SMC), and Exponential Reaching Law SMC (ERL-SMC), applied to the speed regulation of a Hall-effect sensored Brushless DC (BLDC) motor. A mathematically [...] Read more.
This study presents a comprehensive performance analysis of four different control strategies, Proportional–Integral (PI), classical Sliding Mode Control (SMC), Super-Twisting SMC (ST-SMC), and Exponential Reaching Law SMC (ERL-SMC), applied to the speed regulation of a Hall-effect sensored Brushless DC (BLDC) motor. A mathematically detailed BLDC motor model, three-phase inverter structure with safe commutation logic, and a high-frequency PWM switching scheme were implemented in the MATLAB/Simulink-2024a environment to provide a realistic simulation framework. The control strategies were evaluated under multiple test scenarios, including variations in supply voltage, mechanical load disturbances, reference speed transitions, and steady-state operation. The comparative results reveal that the classical SMC and PI controllers suffer from significant oscillations, overshoot, and limited disturbance rejection capability, especially during voltage and load transients. The ST-SMC algorithm improves robustness and reduces the chattering effect inherent to first-order SMC but still exhibits noticeable oscillations near the sliding surface. In contrast, the proposed ERL-SMC controller demonstrates superior performance across all scenarios, achieving the lowest steady-state ripple, the shortest settling time, and the most stable transition response while significantly mitigating chattering. These results indicate that ERL-SMC is the most effective and reliable control strategy among the evaluated methods for BLDC speed regulation, which requires high dynamic response and disturbance robustness. The findings of this study contribute to the advancement of SMC-based BLDC motor control, providing a solid foundation for future research that integrates observer-based schemes, adaptive tuning, or real-time hardware implementation. Full article
(This article belongs to the Special Issue Advances in Mathematical Modeling for Robotic Systems: Dynamics, Stability, Optimization and Control)
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22 pages, 759 KB  
Article
Research on Risk Contagion and Risk Early Warning of China’s Fintech and Banking Industry from the Perspective of Complex Networks
by Peng Sun, Xin Xiang and Kaiyue Ye
Mathematics 2026, 14(2), 220; https://doi.org/10.3390/math14020220 - 6 Jan 2026
Abstract
This study selects daily data from 27 fintech companies and 16 listed commercial banks between January 2015 and December 2024 as research samples. Based on complex network theory, we construct an integrated analytical framework encompassing risk measurement, regime identification, and early warning system [...] Read more.
This study selects daily data from 27 fintech companies and 16 listed commercial banks between January 2015 and December 2024 as research samples. Based on complex network theory, we construct an integrated analytical framework encompassing risk measurement, regime identification, and early warning system construction through HD-TVP-VAR model coupled with the Elastic Net algorithm, MS-AR model, and dynamic Logit model. The findings reveal that the total risk spillover rate between fintech and banking ranges from 73.09% to 95.18%, demonstrating significant time-varying and event-driven characteristics in risk contagion. The risk contagion evolution is characterized by three distinct phases: net risk absorption by the banking sector, bidirectional equilibrium contagion, and net risk dominance by the fintech sector. Joint-stock commercial banks and city commercial banks exhibit higher sensitivity to fintech risks compared to state-owned large commercial banks. Key hubs for risk contagion include institutions like Yinxin Technology and Huaxia Bank, with concentrated risk contagion within industry clusters. The MS-AR model accurately delineates low-, medium-, and high-risk zones, showing strong alignment between high-risk periods and major events. The dynamic Logit model incorporating total risk correlation indices demonstrates high consistency between early warning signals and risk evolution trajectories, providing theoretical and practical references for cross-industry systemic financial risk prevention. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
25 pages, 3274 KB  
Article
Understanding the Impact of Flight Restrictions on Epidemic Dynamics: A Meta-Agent-Based Approach Using the Global Airlines Network
by Alexandru Topîrceanu
Mathematics 2026, 14(2), 219; https://doi.org/10.3390/math14020219 - 6 Jan 2026
Abstract
In light of the current advances in computational epidemics and the need for improved epidemic governance strategies, we propose a novel meta-agent-based model (meta-ABM) constructed using the global airline complex network, using data from openflights.org, to establish a configurable framework for monitoring epidemic [...] Read more.
In light of the current advances in computational epidemics and the need for improved epidemic governance strategies, we propose a novel meta-agent-based model (meta-ABM) constructed using the global airline complex network, using data from openflights.org, to establish a configurable framework for monitoring epidemic dynamics. By integrating our validated SICARQD complex epidemic model with global flights and airport information, we simulate the progression of an airborne epidemic, specifically reproducing the resurgence of COVID-19. In terms of originality, our meta-ABM considers each airport node (i.e., city) as an individual agent-based model assigned to its own independent SICARQD epidemic model. Agents within each airport node engage in probabilistic travel along established flight routes, mirroring real-world mobility patterns. This paper focuses primarily on investigating the effect of mobility restrictions by measuring the total number of cases, the peak infected ratio, and mortality caused by an epidemic outbreak. We analyze the impact of four key restriction policies imposed on the airline network, as follows: no restrictions, reducing flight frequencies, limiting flight distances, and a hybrid policy. Through simulations on scaled population systems of up to 1.36 million agents, our findings indicate that reducing the number of flights leads to a faster and earlier decrease in total infection cases, while restricting maximum flight distances results in a slower and much later decrease, effective only after canceling over 80% of flights. Notably, for practical travel restriction policies (e.g., 25–75% of flights canceled), epidemic control is significantly more effective when limiting flight frequency. This study shows the critical role of reducing global flight frequency as a public health policy to control epidemic spreading in our highly interconnected world. Full article
(This article belongs to the Special Issue Mathematical Epidemiological Models: Classical and Interdisciplinary Applications)
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28 pages, 6394 KB  
Article
Prediction of Blade Root Loads for Wind Turbine Based on RBMO-VMD and TCN-BiLSTM-Attention
by Yifan Liu and Jing Cheng
Mathematics 2026, 14(2), 218; https://doi.org/10.3390/math14020218 - 6 Jan 2026
Abstract
Addressing the challenges associated with wind turbine blade root loads—including nonlinearity, strong coupling effects, high computational complexity, and the limitations of conventional mathematical-physical modeling approaches. This paper proposes a wind turbine blade root load prediction model that integrates Variational Mode Decomposition (VMD) optimized [...] Read more.
Addressing the challenges associated with wind turbine blade root loads—including nonlinearity, strong coupling effects, high computational complexity, and the limitations of conventional mathematical-physical modeling approaches. This paper proposes a wind turbine blade root load prediction model that integrates Variational Mode Decomposition (VMD) optimized by the Red-billed Blue Magpie Algorithm (RBMO) and a combined Temporal Convolutional Network (TCN)—Bidirectional Long Short-Term Memory (BiLSTM)—Attention mechanism. First, the RBMO algorithm optimizes VMD parameters. VMD decomposes data into multiple sub-sequences, which are combined with environmental and operational parameters to form input components for the TCN-BiLSTM-Attention ensemble prediction model. Finally, the RBMO algorithm determines the optimal hyperparameter configuration for the combined model. Prediction outputs from each component are then aggregated and reconstructed to yield the final blade root load prediction. Predictions are compared against actual data and results from other forecasting models. Results demonstrate superior predictive performance for the proposed model, effectively enhancing the accuracy of blade root load prediction for wind turbines. Full article
(This article belongs to the Collection Applied Mathematics for Emerging Trends in Mechatronic Systems)
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13 pages, 384 KB  
Article
Investigation into Thermoelastic Issues Arising from Temperature Shock in Spacecraft Solar Panels
by Andrey V. Sedelnikov and Alexandra S. Marshalkina
Mathematics 2026, 14(2), 217; https://doi.org/10.3390/math14020217 - 6 Jan 2026
Abstract
This paper investigates the thermal shock response of a spacecraft solar panel. The panel is represented as a thin homogeneous plate. The governing equations are derived from the coupled thermoelasticity theory for a homogeneous medium, combining the heat equation with compressibility effects and [...] Read more.
This paper investigates the thermal shock response of a spacecraft solar panel. The panel is represented as a thin homogeneous plate. The governing equations are derived from the coupled thermoelasticity theory for a homogeneous medium, combining the heat equation with compressibility effects and the Lamé equations for the displacement vector. The aim of the paper is to analyze new properties of a specific formulation of the coupled thermoelasticity problem and to establish a justified simplification. New properties follow from a specific formulation of the thermoelasticity problem for a real physical object (a solar panel). They are subjective properties of this formulation and allow, in particular, to reduce the coupled thermoelasticity problem to a simpler, uncoupled problem, with certain limitations. This simplification is driven by the physics of the thermal shock process and the resulting plate deformation, which allows the thermal problem to be reduced to a one-dimensional formulation. The main result is a simplified thermoelasticity model that reveals several new properties. Notably, in the region where longitudinal displacements are negligible, the coupled problem generates into an uncoupled one. This result can be applied to model disturbances caused by thermal shock on spacecraft. Full article
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30 pages, 593 KB  
Review
On Intensively Criticizing and Envisioning the Research on Multiple-Objective Portfolio Selection from the Perspective of Capital Asset Pricing Models
by Yue Qi, Jianing Huang and Yixuan Zhu
Mathematics 2026, 14(2), 216; https://doi.org/10.3390/math14020216 - 6 Jan 2026
Abstract
Nobel Laureate Markowitz originates portfolio selection as the birth of modern finance. Nobel Laureate Sharpe implements portfolio selection and originates capital asset pricing models. Nobel Laureate Fama also implements portfolio selection and originates zero-covariance capital asset pricing models. After these feats, researchers have [...] Read more.
Nobel Laureate Markowitz originates portfolio selection as the birth of modern finance. Nobel Laureate Sharpe implements portfolio selection and originates capital asset pricing models. Nobel Laureate Fama also implements portfolio selection and originates zero-covariance capital asset pricing models. After these feats, researchers have gradually realized additional objectives and have promisingly extended portfolio selection into multiple-objective portfolio selection. However, there hardly exists research to leap from multiple-objective portfolio selection to multiple-objective capital asset pricing models (as initiated by Markowitz and Sharpe in finance). Moreover, the extension is basically confined to the branches of mathematics, operations research, optimization, and computer sciences. Many researchers sufficiently review multiple-objective portfolio selection. However, the reviews are extensive. Instead, we intensively criticize and envision the research on multiple-objective portfolio selection from the perspective of capital asset pricing models by crystallizing the research limitations and heralding future directions. Specifically, we emphasize seven research limitations for multiple-objective portfolio optimization, multiple-objective capital asset pricing models, and multiple-objective zero-covariance capital asset pricing models. We also generalize from common three-objective portfolio selection to k-objective portfolio selection. Visually, we orchestrate figures to delineate the complexity. Theoretically, this paper heralds challenging but encouraging future directions. Pragmatically, this paper proposes a formulation for the multiple-objective nature of practical convolution in finance. Full article
(This article belongs to the Special Issue Applications of Mathematics Analysis in Financial Marketing)
39 pages, 504 KB  
Article
Zappa–Szép Skew Braces: A Unified Framework for Mutual Interactions in Noncommutative Algebra
by Suha Wazzan and David A. Oluyori
Mathematics 2026, 14(2), 215; https://doi.org/10.3390/math14020215 - 6 Jan 2026
Abstract
This paper introduces and systematically develops the theory of Zappa–Szép skew braces, a novel algebraic structure that provides a unified framework for bidirectional group interactions, thereby generalizing the classical constructions of semidirect skew braces and matched-pair factorizations (ZS1–ZS4, BC1–BC2). We establish the [...] Read more.
This paper introduces and systematically develops the theory of Zappa–Szép skew braces, a novel algebraic structure that provides a unified framework for bidirectional group interactions, thereby generalizing the classical constructions of semidirect skew braces and matched-pair factorizations (ZS1–ZS4, BC1–BC2). We establish the complete axiomatic foundation for these objects, characterizing them through necessary and sufficient compatibility conditions that encode mutual actions between two digroups. Central results include a semidirect embedding theorem, explicit constructions of nontrivial examples—notably a fully mutual brace of order 12 built from V4 and C3—and a detailed analysis of key structural invariants such as the socle, center, and automorphism groups. The framework is further elucidated via universal properties and categorical adjunctions, positioning Zappa–Szép skew braces as fundamental objects within noncommutative algebra. Applications to representation theory, cohomology, and the construction of set-theoretic solutions to the Yang–Baxter equation are derived, demonstrating both the generality and utility of the theory. Full article
(This article belongs to the Special Issue Non-associative Structures and Their Applications in Physics and Geometry)
11 pages, 290 KB  
Article
Optimal One-Coincidence Sequence Sets with a Large Alphabet and Prime Length
by Jin-Ho Chung, Duehee Lee and Dongsup Jin
Mathematics 2026, 14(2), 214; https://doi.org/10.3390/math14020214 - 6 Jan 2026
Abstract
The performance of a frequency-hopping spread-spectrum system is mainly dependent on the mathematical properties of its hopping sequences, which are designed to minimize interference between different users. The one-coincidence sequence frequency-hopping sequence (OC-FHS) set is one of the primary types, because it achieves [...] Read more.
The performance of a frequency-hopping spread-spectrum system is mainly dependent on the mathematical properties of its hopping sequences, which are designed to minimize interference between different users. The one-coincidence sequence frequency-hopping sequence (OC-FHS) set is one of the primary types, because it achieves the lowest possible values regarding Hamming auto- and cross-correlation. In this work, we propose an OC-FHS set of a prime length p and alphabet size pq for two primes p and q using a block structure modulo pq. In particular, when p=q, our construction provides a significantly larger set size compared with a previously known OC-FHS set with the same length and the same alphabet size. Moreover, the set size is optimal with respect to the bound established by Cao, Ge, and Miao. This extended set size can be applied to FHMA systems that need to accommodate a large number of users. Full article
(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)
28 pages, 1280 KB  
Article
Two-Stage Genetic-Based Optimization for Resource Provisioning and Scheduling of Multiple Workflows on the Cloud Under Resource Constraints
by Feng Li, Wen Jun Tan, Moongi Seok and Wentong Cai
Mathematics 2026, 14(2), 213; https://doi.org/10.3390/math14020213 - 6 Jan 2026
Abstract
Resource provisioning and scheduling are essential challenges in handling multiple workflow requests within cloud environments, particularly given the constraints imposed by limited resource availability. Although workflow scheduling has been extensively studied, few methods effectively integrate resource provisioning with scheduling, especially under cloud resource [...] Read more.
Resource provisioning and scheduling are essential challenges in handling multiple workflow requests within cloud environments, particularly given the constraints imposed by limited resource availability. Although workflow scheduling has been extensively studied, few methods effectively integrate resource provisioning with scheduling, especially under cloud resource limitations and the complexities of multiple workflows. To address this challenge, we propose an innovative two-stage genetic-based optimization approach. In the first stage, candidate cloud resources are selected for the resource pool under the given resource constraints. In the second stage, these resources are provisioned and task scheduling is optimized on the selected resources. A key advantage of our approach is that it reduces the search space in the first stage through a novel encoding scheme that enables a caching strategy, in which intermediate results are stored and reused to enhance optimization efficiency in the second stage. The proposed solution is evaluated through extensive simulation experiments, assessing both resource selection and task scheduling across a diverse range of workflows. The results demonstrate that the proposed approach outperforms existing algorithms, particularly for highly parallel workflows, highlighting its effectiveness in managing complex workflow scheduling under resource-constrained cloud environments. Full article
(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)
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35 pages, 454 KB  
Article
Topological Powerset Theories in Context of Fuzzy Topological Concepts
by Jiří Močkoř and David Hynar
Mathematics 2026, 14(2), 212; https://doi.org/10.3390/math14020212 - 6 Jan 2026
Abstract
This study explores the role of powerset theory as a unifying framework within fuzzy set theory, particularly in the context of fuzzy topological concepts. We extend the definition of the topological powerset theory and examine the transformation processes between the categories of fuzzy [...] Read more.
This study explores the role of powerset theory as a unifying framework within fuzzy set theory, particularly in the context of fuzzy topological concepts. We extend the definition of the topological powerset theory and examine the transformation processes between the categories of fuzzy topological concepts, fuzzy topological spaces, and topological powerset theory. Using categorical tools, we define functors among these categories that handle both morphisms based on mappings and fuzzy relational morphisms. We introduce a morphism between topological powerset theories and demonstrate examples of this morphism. We also show how various fuzzy topological concepts can be approximated by topological powerset theory. Full article
(This article belongs to the Section B: Geometry and Topology)
25 pages, 3250 KB  
Article
Optical Mirage–Based Metaheuristic Optimization for Robust PEM Fuel Cell Parameter Estimation
by Hashim Alnami, Badr M. Al Faiya, Sultan Hassan Hakmi and Ghareeb Moustafa
Mathematics 2026, 14(2), 211; https://doi.org/10.3390/math14020211 - 6 Jan 2026
Abstract
The parameter extraction of proton exchange membrane fuel cells (PEMFCs) has been an active area of study over the past few years, relying on metaheuristic optimizers and experimental datasets to achieve accurate current/voltage (I/V) curves. This work develops a mirage search optimizer (MSO) [...] Read more.
The parameter extraction of proton exchange membrane fuel cells (PEMFCs) has been an active area of study over the past few years, relying on metaheuristic optimizers and experimental datasets to achieve accurate current/voltage (I/V) curves. This work develops a mirage search optimizer (MSO) to precisely estimate the PEMFC model parameters. The MSO employs two search techniques based on the physical phenomena of light bending caused by atmospheric refractive index gradients: a superior mirage for global exploration and an inferior mirage for local exploitation. The MSO employs optical physics to direct search behavior, in contrast to conventional optimization approaches, allowing for a dynamic balance between exploration and exploitation. Convergence efficiency is increased by its iteration-dependent control and fitness-based influence. Using two common PEMFC modules, a comparison study with previously published methodologies and new, recently developed optimizers—the Educational Competition Optimizer (ECO), basketball team optimization (BTO), the fungal growth optimizer (FGO), and the naked mole rat optimizer (NMRO)—was conducted to evaluate the proposed MSO for parameter identification. Furthermore, the two models were tested under various temperatures and pressures. For the three examples studied, the MSO achieved the best sum of squared errors (SSE) values with an intriguing overall standard deviation (STD). It is undeniable that the STD and cropped SSE values, among other difficult techniques, are quite competitive and display the fastest convergence. According to the MSO, the BCS 500W, Ballard Mark V, and Modular SR-12 each have MSO values of 0.011697781, 0.852056, and 1.42098181379214 × 10−4, respectively. Additionally, the comparison results demonstrate that the proposed MSO can be successfully used to quickly and accurately define the PEMFC model. Full article
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35 pages, 2401 KB  
Article
Literary Language Mashup: Curating Fictions with Large Language Models
by Gerardo Aleman Manzanarez, Raul Monroy, Jorge Garcia Flores and Hiram Calvo
Mathematics 2026, 14(2), 210; https://doi.org/10.3390/math14020210 - 6 Jan 2026
Abstract
The artificial generation of text by computers has been a field of study in computer science since the beginning of the twentieth century, from Markov chains to Turing tests. This has evolved into automatic summarization and marketing chatbots. The generation of literary texts [...] Read more.
The artificial generation of text by computers has been a field of study in computer science since the beginning of the twentieth century, from Markov chains to Turing tests. This has evolved into automatic summarization and marketing chatbots. The generation of literary texts by Large Language Models (LLMs) has also been an area of scholarly inquiry for over six decades. The literary quality of AI-generated text can be evaluated with GrAImes, an evaluation protocol grounded in literary theory and inspired by the editorial process of book publishers. This evaluation can also be framed as part of broader editorial practices within publishing, emphasizing both theoretical grounding and applied assessment. This protocol necessitates the involvement of human judges to validate the texts generated, a process that is often resource-intensive in terms of both time and financial investment, primarily due to the specialized credentials and expertise required of these evaluators. In this paper, we propose an alternative approach by employing LLMs themselves as evaluators within the GrAImes framework. We apply this methodology to assess human-written and AI-generated microfictions in Spanish, to five PhD professors in literature and sixteen literary enthusiasts, and to short stories in both Spanish and English. By comparing the evaluations performed by LLMs with those of human judges, we examine the degree of alignment and divergence between both perspectives, thereby assessing the feasibility of LLMs as auxiliary literary evaluators. Our analysis focuses on the alignment of responses from LLMs with those of human evaluators, providing insights into the potential of LLMs in literary assessment. The conducted experiments reveal that while LLMs cannot be regarded as substitutes for human judges in the evaluation of literary microfictions and short stories, with a Krippendorff’a alpha reliability coefficient less than 0.66, they can serve as a valuable tool that offers an initial perspective on the editorial quality of the texts in question. Overall, this study contributes to the ongoing discourse on the role of artificial intelligence in literature, underlining both its methodological constraints and its potential as a complementary resource for literary evaluation. Full article
(This article belongs to the Special Issue Advances in Computational Intelligence and Applications)
24 pages, 412 KB  
Article
Square Root of a Multivector of Clifford Algebras in 3D: A Game with Signs
by Arturas Acus and Adolfas Dargys
Mathematics 2026, 14(2), 209; https://doi.org/10.3390/math14020209 - 6 Jan 2026
Abstract
An algorithm is presented to extract the square root from a multivector (MV) in real Clifford algebras Clp,q, where n=p+q≤3, in radicals. It is shown that in Cl3,0, [...] Read more.
An algorithm is presented to extract the square root from a multivector (MV) in real Clifford algebras Clp,q, where n=p+q≤3, in radicals. It is shown that in Cl3,0, Cl1,2, and Cl0,3 algebras, there are up to four isolated square roots in a case of the most general (generic) MV. The algebra Cl2,1 is an exception and, there, the MV can have up to 16 isolated roots. In addition, a continuum of roots has been found in all Clifford algebras except p+q=1. Examples which clarify computations are provided to illustrate the properties of roots in all n=3 algebras. The results may be useful in solving nonlinear equations, like for example, the Clifford–Riccati equation. Full article
23 pages, 3158 KB  
Article
Fast Model-Free Image Dehazing via Haze-Density-Driven Fusion
by Jeonghyeon Son, Dat Ngo, Suhun Ahn and Bongsoon Kang
Mathematics 2026, 14(2), 208; https://doi.org/10.3390/math14020208 - 6 Jan 2026
Abstract
This paper presents a fast and model-free image dehazing algorithm based on haze-density-driven image fusion. Instead of relying on explicit physical haze models, the proposed approach restores visibility by fusing the input image with its dehazed estimate using spatially adaptive weights derived from [...] Read more.
This paper presents a fast and model-free image dehazing algorithm based on haze-density-driven image fusion. Instead of relying on explicit physical haze models, the proposed approach restores visibility by fusing the input image with its dehazed estimate using spatially adaptive weights derived from a haze-density map. The dehazed estimate is produced by blending multiple synthetically under-exposed versions of the input, where local fusion weights promote stronger enhancement in dense-haze regions while preserving appearance in mild-haze areas. This model-free formulation avoids the limitations inherent to traditional scattering-based models and ensures robust performance under spatially nonuniform haze conditions. The overall framework is lightweight and suitable for embedded, real-time imaging systems due to its reliance on simple local operations. Experimental evaluations demonstrate that the proposed method achieves competitive results compared to state-of-the-art dehazing algorithms in both visual quality and quantitative metrics. A hardware prototype further shows that the method can process high-resolution imagery at real-time rates, achieving 271.74 megapixels per second, or 30.69 frames per second at DCI 4K (4096×2160) resolution. These results establish haze-density-driven fusion as an effective and efficient model-free solution for real-time image dehazing. Full article
(This article belongs to the Special Issue Machine Learning Applications in Image Processing and Computer Vision)
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20 pages, 802 KB  
Article
CNL-Diff: A Nonlinear Data Transformation Framework for Epidemic Scale Prediction Based on Diffusion Models
by Boyu Ma and Yifei Du
Mathematics 2026, 14(2), 207; https://doi.org/10.3390/math14020207 - 6 Jan 2026
Abstract
In recent years, the complexity and suddenness of infectious disease transmission have posed significant limitations for traditional time-series forecasting methods when dealing with the nonlinearity, non-stationarity, and multi-peak distributions of epidemic scale variations. To address this challenge, this paper proposes a forecasting framework [...] Read more.
In recent years, the complexity and suddenness of infectious disease transmission have posed significant limitations for traditional time-series forecasting methods when dealing with the nonlinearity, non-stationarity, and multi-peak distributions of epidemic scale variations. To address this challenge, this paper proposes a forecasting framework based on diffusion models, called CNL-Diff, aimed at tackling the prediction challenges in complex dynamics, nonlinearity, and non-stationary distributions. Traditional epidemic forecasting models often rely on fixed linear assumptions, which limit their ability to accurately predict the incidence scale of infectious diseases. The CNL-Diff framework integrates a forward–backward consistent conditioning mechanism and nonlinear data transformations, enabling it to capture the intricate temporal and feature dependencies inherent in epidemic data. The results show that this method outperforms baseline models in metrics such as Mean Absolute Error (MAE), Continuous Ranked Probability Score (CRPS), and Prediction Interval Coverage Probability (PICP). This study demonstrates the potential of diffusion models in complex-distribution time-series modeling, providing a more reliable probabilistic forecasting tool for public health monitoring, epidemic early warning, and risk decision making. Full article
(This article belongs to the Special Issue AI-Driven Innovations in Healthcare: Advances in Machine Learning and Computer Vision)
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13 pages, 289 KB  
Article
The Weighted k-Search Problem
by Michael Schwarz and Robert Dochow
Mathematics 2026, 14(2), 206; https://doi.org/10.3390/math14020206 - 6 Jan 2026
Abstract
In the uni-directional conversion problem, the objective is to convert wealth from one asset into another while maximizing its value at the end of the investment horizon. In the k-preemptive variant of this problem, also known as the k-search problem, the [...] Read more.
In the uni-directional conversion problem, the objective is to convert wealth from one asset into another while maximizing its value at the end of the investment horizon. In the k-preemptive variant of this problem, also known as the k-search problem, the wealth is divided into k equally-sized units that cannot be converted simultaneously. In this work the weighted k-search problem is introduced. The weighted k-search problem is a generalization of the k-search problem, since the problem setting is changed in a way in which the given number of units to convert is not limited to one. In the weighted k-search problem, the k units are grouped into l groups of variable size. Instead of one unit, each group has to be converted at once, and each group has to be converted separately. The online algorithm lRPP is presented and its competitive ratio is determined. It is shown that no deterministic algorithm can achieve a lower competitive ratio. Thus, lRPP solves the weighted k-search problem optimally. Both variants of the weighted k-search problem, i.e., min-search and max-search, are solved separately. Full article
21 pages, 311 KB  
Article
The Predictive Power of Managerial Confidence: A Dynamic Mechanism of Attention and Reliability in China’s Stock Market
by Jiang Hu, Yong Wang and Di Gao
Mathematics 2026, 14(2), 205; https://doi.org/10.3390/math14020205 - 6 Jan 2026
Abstract
Based on the “Future Outlook” sections of annual and semi-annual reports from Chinese A-share-listed companies (2011–2024), we construct a novel measure of managerial confidence by quantifying the intertemporal shifts in textual sentiment. Using a sample of 76,923 observations, our analysis reveals that this [...] Read more.
Based on the “Future Outlook” sections of annual and semi-annual reports from Chinese A-share-listed companies (2011–2024), we construct a novel measure of managerial confidence by quantifying the intertemporal shifts in textual sentiment. Using a sample of 76,923 observations, our analysis reveals that this measure exhibits dynamic predictive power for expected stock returns. Specifically, in the short term, managerial confidence serves as a valid predictor. A long-short portfolio sorted by managerial confidence yields a 7.05% cumulative return spread over the five post-disclosure trading days. Mechanism analysis suggests that this short-term predictability stems from high managerial confidence effectively attracting investor attention. Over the medium term (six months), however, its predictive power hinges on the reliability of the confidence signal: For managers whose historical confidence has aligned with fundamental performance, high confidence predicts positive expected excess returns; for those who are chronically overoptimistic, it becomes an inverse predictor of firm value. These findings indicate that financial markets dynamically assess both the intensity and the reliability of signals within managerial disclosures, offering a new perspective on the predictive power of managerial psychological traits in capital markets. Full article
(This article belongs to the Special Issue Mathematical and Quantitative Methods in Finance and Forecasting)
13 pages, 1261 KB  
Article
The Self-Adjoint Fractional Heun Operator and Its Spectral Properties
by Muath Awadalla
Mathematics 2026, 14(2), 204; https://doi.org/10.3390/math14020204 - 6 Jan 2026
Abstract
This paper introduces a rigorously defined fractional Heun operator constructed through a symmetric composition of left and right Riemann–Liouville fractional derivatives. By deriving a compatible fractional Pearson-type equation, a new weight function and Hilbert space setting are established, ensuring the operator’s self-adjointness under [...] Read more.
This paper introduces a rigorously defined fractional Heun operator constructed through a symmetric composition of left and right Riemann–Liouville fractional derivatives. By deriving a compatible fractional Pearson-type equation, a new weight function and Hilbert space setting are established, ensuring the operator’s self-adjointness under natural fractional boundary conditions. Within this framework, we prove the existence of a real, discrete spectrum and demonstrate that the corresponding eigenfunctions form a complete orthogonal system in Lωα2(a,b). The central theoretical result shows that the fractional eigenpairs (λn(α),un(α)) converge continuously to their classical Heun counterparts (λn(1),un(1)) as α→1−. This provides a rigorous analytic bridge between fractional and classical spectral theories. A numerical study based on the fractional Legendre case confirms the predicted self-adjointness and spectral convergence, illustrating the smooth deformation of the classical eigenfunctions into their fractional counterparts. The results establish the fractional Heun operator as a mathematically consistent generalization capable of generating new families of orthogonal fractional functions. Full article
(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics—In Memory of Prof. Dr. Ravi P. Agarwal)
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