Mathematics doi: 10.3390/math14101647

Authors: Chayapat Sudprasert Suphawat Asawasamrit Sotiris K. Ntouyas Jessada Tariboon

This paper investigates a new class of mixed impulsive fractional boundary value problems (BVPs) in which the mixing occurs both in the governing fractional differential equations—through the combined presence of ψ-Caputo and quantum (q-difference) fractional derivatives—and in the boundary conditions formulated via fractional integral constraints. By incorporating two distinct operators within the same dynamical framework, the proposed model is capable of capturing both memory effects and discrete-scale behaviors inherent in complex hybrid systems. Using the Banach contraction mapping principle and the Leray–Schauder nonlinear alternative, sufficient conditions ensuring the existence and uniqueness of solutions are established. The theoretical results unify and extend several known fractional models. Owing to its flexible structure, the proposed framework may serve as a useful mathematical tool for modeling impulsive phenomena in systems where non-local memory and scale-transition mechanisms coexist, such as in engineering, physics, and applied sciences. Finally, numerical examples are provided to illustrate the applicability and qualitative behavior of the solutions.

Mathematics doi: 10.3390/math14101646

Authors: Linzi Ouyang Yuling Lai Raman Kumar Yao Chen

This study addresses the challenge of prioritizing Virtual Reality (VR) and Augmented Reality (AR) applications in Product Lifecycle Management (PLM) under multiple conflicting criteria. A comprehensive fuzzy Multi-Criteria Decision-Making (FMCDM) framework is proposed to support robust and unbiased decision-making. The methodology integrates multiple objective weighting techniques, including Entropy, Criteria Importance Through Intercriteria Correlation (CRITIC), Method based on the Removal Effects of Criteria (MEREC), and Standard Deviation, which are aggregated using the Bonferroni operator to obtain balanced criterion weights. The Fuzzy Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method is employed as the primary ranking approach, supported by comparative methods such as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VIšekriterijumsko KOmpromisno Rangiranje (VIKOR), Evaluation based on Distance from Average Solution (EDAS), Weighted Aggregated Sum Product Assessment (WASPAS), and Multi-Objective Optimization on the basis of Ratio Analysis (MOORA) for validation. The results indicate that Virtual Reality Digital Prototyping and Design Review (A3) is the most preferred alternative, achieving the highest utility value (0.95267), followed by Augmented Reality-Assisted Assembly and Inspection Guidance (A1) and Augmented Reality-Supported Maintenance and Operator Training (A4). A high Stability Index of 0.9133 confirms robustness, and sensitivity analysis shows stable rankings. The framework provides a reliable and scalable decision-support system for smart manufacturing.

Mathematics doi: 10.3390/math14101644

Authors: Hristo Hristov Atanas Ilchev Hristina Kulina Boyan Zlatanov

We study a class of wrapping operators acting on the space of formal languages over a fixed finite alphabet. The underlying space is equipped with a length-based ultrametric, in which two languages are close whenever they coincide on all sufficiently short words. We prove that every wrapping operator generated by a finite family of guards with positive total guard length is a contraction. As a consequence, Banach’s contraction principle yields existence and uniqueness of a fixed point for the corresponding recursive language equation, together with convergence of the Picard iteration from an arbitrary initial language. We also obtain an explicit quantitative estimate for the rate of convergence. This makes it possible to determine how many iterations are sufficient to recover the fixed point correctly on all words up to a prescribed length. Several examples illustrate the theory, including operators with different guard lengths and a case showing that convergence in the length-based ultrametric does not coincide with set-theoretic convergence. An application to recursive structures and document validation is also presented, including recursive data formats, abstract syntax trees, and a restricted fragment of JSON schemas. The results provide a formal foundation for validation together with explicit bounds for correctness on inputs of bounded length.

Mathematics doi: 10.3390/math14101645

Authors: Yihui Xu Xi Xi

Antiviral pulse dosing is shaped by discrete dosing events, two-compartment pharmacokinetics, nonlinear pharmacodynamics, and resistance evolution. To characterize sustained suppression, resistance accumulation, and risk-cost tradeoffs within a unified framework, this study formulates a two-compartment pharmacokinetic-viral dynamic pulse-dosing model with competition between drug-sensitive and drug-resistant strains. Nonlinear metabolic terms, safety constraints, and a mutant selection window (MSW) residence metric are incorporated. Rather than merely superimposing standard logistic growth, Emax pharmacodynamics, and Dirac-delta impulses, the proposed framework couples cross-compartment exposure, MSW residence, resistance ratio feedback, and finite-time stability diagnostics in a discrete-control setting. Pontryagin’s minimum principle is used to derive marginal optimality conditions for impulsive dosing, whereas the numerical implementation adopts a safety-constrained grid search over a finite set of candidate dose intensities. Scenario simulations for SARS-CoV-2 and HIV suggest that, under the assumed mechanisms and parameter ranges examined, high-intensity or high-frequency dosing may improve short-term viral suppression but may also increase MSW crossings and tail residence, thereby amplifying resistance accumulation and finite-time sensitivity risk. The stratified results should therefore be interpreted as a theoretical sensitivity analysis rather than as direct clinical prescribing guidance. The framework may provide a basis for subsequent individualized PK/PD calibration and resistance monitoring.

Mathematics doi: 10.3390/math14101642

Authors: Funian Hu Bin Xie

The battery management system (BMS) is the core of ensuring the safety and performance of new energy vehicles, and real-time high-precision estimation of battery state of charge (SOC) is its key function, which directly affects battery safety, endurance, and service life. Faced with the challenges brought by high energy density and ultra-fast charging technology, lithium-ion batteries exhibit strong nonlinear and time-varying characteristics, making it difficult for existing SOC estimation methods to balance computational efficiency and accuracy. This study proposes a Bayesian-based Hammerstein multi-model (MM) fusion algorithm for accurate lithium battery SOC estimation across a wide temperature range, especially under low-temperature conditions. First, two Hammerstein SOC submodels are constructed: a traditional polynomial Hammerstein model and a TPA-Hammerstein model incorporating the temporal pattern attention mechanism. Second, KV-ADAM is employed for parameter training and identification of the submodels. Finally, a Bayesian weighted fusion strategy is used to dynamically integrate the outputs of the two submodels. The experimental results show that this method significantly improves the accuracy and robustness of SOC estimation, overcomes the limitations of a single model under complex dynamic conditions, provides an effective solution for lithium battery SOC estimation, and helps the safe operation of electric vehicles and the sustainable development of the industry.

Mathematics doi: 10.3390/math14101643

Authors: Yinghui Liu Yinhua Xie Jiancheng Lyu

This study examines how bank financing and direct financing provided by a third-party logistics (3PL) firm affect the operational and financing decisions of a capital-constrained retailer. It focuses on a dual-channel financing setting in which both funding sources are available and investigates whether the retailer uses them simultaneously, how creditor priority affects equilibrium outcomes, and how procurement cost and logistics pricing shape financing choices. A Stackelberg game model is developed for a supply chain comprising a retailer, a 3PL firm, and a bank. Two benchmark settings, namely bank financing only and direct 3PL financing only, are first analyzed. The study then examines the dual-channel financing equilibrium when the 3PL firm acts as the senior creditor and further extends the model to consider bank seniority and endogenous logistics pricing. When the 3PL firm is the senior creditor, the retailer does not use both funding sources simultaneously in equilibrium; instead, it chooses either bank financing only or direct 3PL financing only. The 3PL firm prefers bank financing when logistics pricing is low and procurement cost is high, whereas it prefers direct financing when logistics pricing is high or when both logistics pricing and procurement cost are low. When logistics pricing is endogenous, the optimal lending rate set by the 3PL firm is zero. This study extends the literature on 3PL financing by explicitly incorporating a dual-channel financing structure that includes both bank credit and direct 3PL lending. It highlights the strategic role of creditor priority and shows how procurement cost and logistics pricing jointly shape the financing equilibrium, thereby providing managerial insights into financing design and operational decision-making in capital-constrained supply chains.

Mathematics doi: 10.3390/math14101641

Authors: Kai Zhang Lingfei Chen Xinmiao Zhou Yuanxin Li Pingling Cai Zhihong Wang

The Black–Scholes model laid the mathematical foundation for modern option pricing; however, its assumptions—stationary, independent, and Gaussian returns—are frequently violated in real markets, where long-memory volatility and sudden price jumps are well-documented. Two issues remain open: (1) Few option pricing models comprehensively incorporate long-memory and jump features. (2) The equivalence of the hedging, risk-neutral, and actuarial pricing methods, well-established under the standard Black–Scholes framework, has not been examined under jump–diffusion models. To address these gaps, we developed a sub-mixed fractional Brownian motion with Jumps (smfBm-J) model that jointly captures long memory, nonstationary increments, and jumps and derives a closed-form European call option pricing formula under the smfBm-J framework, highlighting the impact of model choice on valuation in incomplete markets.

Mathematics doi: 10.3390/math14101640

Authors: Nguyet Nguyen

Insurance pricing plays a central role in risk management and financial decision-making, as accurate premium estimation directly impacts portfolio stability and profitability. This study investigates insurance pure premium estimation by integrating classical actuarial models with modern machine learning techniques. We compare the traditional frequency–severity decomposition framework with direct modeling approaches, including XGBoost and Tweedie models. For claim frequency, we evaluate Poisson-based models, generalized additive models, and XGBoost. For claim severity, we compare a Gamma generalized linear model with XGBoost. The results show that XGBoost improves predictive performance for both components based on the evaluation metrics considered. Within the decomposition framework, the XGBoost–XGBoost model achieves the lowest prediction error among the models considered. However, lift-based analysis reveals that the XGBoost–Gamma model provides superior risk segmentation, highlighting a trade-off between prediction accuracy and risk ranking. Direct modeling approaches, while competitive, do not consistently achieve lower error than the decomposition framework across the evaluation metrics considered. Overall, the findings demonstrate that machine learning enhances predictive performance, but its effectiveness is maximized within the frequency–severity framework. The results highlight the importance of both frequency and severity modeling in insurance pricing, while suggesting that their relative contributions to risk segmentation depend on model specification and evaluation criteria. These findings have important implications for risk management and pricing strategies in insurance portfolios.

Mathematics doi: 10.3390/math14101639

Authors: Nataša Ošep Ferš Aleš Zamuda

This paper introduces a new single-objective formulation of the mixed-integer Cassini2 interplanetary trajectory problem (Cassini2-MINLP), extending the GTOPX benchmark library. The formulation introduces four additional decision variables that determine the sequence of intermediate planetary flybys, expanding the set of feasible trajectories and increasing the dimensionality, flexibility, and structural complexity of the trajectory design problem. The resulting search space is 26-dimensional, consisting of 22 continuous trajectory variables and four variables encoding the discrete flyby sequence. The mission scenario assumes a fixed departure from Earth and arrival at Saturn, while the intermediate flyby planets are selected from the set of major Solar System planets. The encounter sequence is modeled using discrete variables derived from a relaxed continuous encoding through rounding and bounding operations, resulting in a mixed-integer nonlinear programming (MINLP) problem. The objective is to minimize the total ΔV, representing propellant consumption and overall energetic efficiency. To evaluate algorithmic performance on this challenging benchmark, eight well-established and recent optimization algorithms from three methodological families (ACO, DE, and CMA-ES) are evaluated under a consistent experimental setup with fixed random seeds to ensure reproducibility. Statistical analyses based on the 30 independent runs using the Friedman test confirm highly significant differences among the algorithms, with the DISHr algorithm achieving the best average rank at value 1.567 and statistically outperforming several other competing methods according to the Nemenyi post-hoc test. The results demonstrate that the Cassini2-MINLP formulation provides a challenging and practically relevant benchmark for trajectory optimization and establishes a foundation for future research on multi-objective formulations and advanced optimization strategies for complex interplanetary missions.

Mathematics doi: 10.3390/math14101638

Authors: Nikolay Hinov Reni Kabakchieva Plamen Stanchev

This paper develops a unified α-cut optimization framework for modular electric vehicle (EV) fast-charging station design under fuzzy uncertainty. Uncertain peak demand, annual delivered energy, electricity price, ambient temperature, arrival rate, and energy per session are represented by triangular or trapezoidal fuzzy numbers and reformulated through α-cut bounds. The resulting design problem is expressed as a hybrid discrete–continuous model in which the number of modules, the selected catalog module rating, installed power, cooling provision, and a station-volume proxy are jointly optimized. An aggregated representation of interchangeable modules is adopted to remove permutation-equivalent descriptions and preserve a compact search space. Three planning views are examined: minimum CAPEX at a prescribed α-cut level, minimum loss-driven OPEX under a CAPEX budget, and a service-oriented admissibility/coverage analysis that avoids interpreting larger α values as greater robustness. The strengthened numerical study includes a deterministic nominal benchmark, peak demand sensitivity regimes, feasibility threshold and budget sweep results, explicit service stress scenarios, and a queueing sensitivity check against Erlang-C and discrete-event simulation indicators. The results show that baseline CAPEX designs may be dominated by catalog thresholds, whereas OPEX and service-oriented conclusions become informative once budget and traffic regimes are varied. The proposed framework is therefore positioned as a tractable α-cut-based design screening and comparative optimization tool for representative modular EV charging station scenarios, rather than as a universally validated operational design rule.

Mathematics doi: 10.3390/math14101637

Authors: Jovana Lj. Jović Dragan S. Domazet Nenad O. Vesić Branislav M. Ranđelović Dušan J. Simjanović

The use of large language models (LLMs) in higher education has increased significantly, and their potential for supporting teaching and learning is considerable. However, their reliability and suitability for generating educational content remain open questions, particularly in technically demanding fields such as software engineering. This paper proposes a multi-criteria framework for assessing the quality of educational content generated by LLMs. The framework is based on existing open educational resource (OER) evaluation rubrics, which were adapted for the assessment of LLM-generated content and further refined based on expert evaluation and consultation. The evaluation was conducted by a panel of eight experts from software engineering, artificial intelligence, education, and related fields, using predefined criteria and pairwise comparisons. The framework was applied to five contemporary LLMs across three selected topics in software engineering. The relative importance of the criteria was determined using the Analytic Hierarchy Process (AHP) and its fuzzy extension (FAHP). The results show that accuracy and professional correctness represent the most important criterion, while visual presentation and language style have the least influence. The findings also indicate differences across models and a high level of agreement between AHP and FAHP rankings.

Mathematics doi: 10.3390/math14101636

Authors: Jie Wen Nan Jiang Yajie He

The remarkably developed graph neural networks (GNNs) are extensively applied to specific tasks in online social networks (OSNs), especially in the vital domain of social trust. Meanwhile, the vulnerability of GNN applied in trust assessment can be exposed leveraging the deployment of subtly designed adversarial attacks. However, the predominant adversarial attack strategies targeting GNN are manipulating graph structure, which is not well-suited for social trust prediction tasks. In this article, we craft a novel black-box attack strategy, T-Attack, aimed at trust evaluation tasks, without tampering with the network structure of the specific trust prediction models. Specifically, a surrogate model is initially established to replicate trust prediction models based on GNN. The attack strategy on the surrogate model is formulated by adding unnoticed perturbations to user features related to network structure and manipulating the existing trust rating based on prior knowledge of social trust propagation, thereby avoiding a traditional attack against the GNN-based trust prediction model via modifying graph structure. By leveraging transferable attacks, our attack strategy can also distort the predictions of GNN-based trust prediction models. Through implementing extensive experiments in untargeted attack scenarios, we demonstrate the predictive performance of our crafted surrogate model and verify the effectiveness of the attack strategy on various GNN-based trust prediction models.

Mathematics doi: 10.3390/math14101635

Authors: Pedro Luis González Rodríguez David Sánchez-Wells José Miguel León-Blanco Marcos Calle Suárez José Luis Andrade Pineda

Truck–multiple-drone routing problems involve conflicting operational criteria and are therefore naturally suited to multiobjective analysis. In practical settings, however, decision makers may also specify aspiration levels for the considered criteria, which call for a target-oriented perspective. This paper studies a bi-criterion truck–multiple-drone routing problem through a goal-induced deviation framework in which the original objectives are transformed to normalized positive deviations with respect to prescribed targets. First, a general mathematical framework is introduced, and several structural properties are established, including dominance preservation, invariance under positive weighting, equivalence with the original Pareto structure when all the targets are violated, and the loss of discrimination when the targets are attainable. To address this latter effect, an enhanced goal-programming scalarization is proposed and shown to preserve consistency with the Pareto efficiency. The framework is then specialized to a truck–multiple-drone routing problem with truck time and makespan as criteria and evaluated on representative benchmark instances together with a broader attainable-target benchmark battery, using a common agent-based metaheuristic search framework adapted from literature. This search framework is employed both to estimate a reference Pareto frontier and to solve the GP and EGP scalarizations under the same computational scheme. The computational results illustrate two target regimes: When the targets are unattainable, both formulations are mainly driven by the minimization of positive deviations; when they are attainable, classical goal programming may return satisfactory but dominated solutions, whereas the enhanced formulation preserves discrimination and selects Pareto-efficient alternatives.

Mathematics doi: 10.3390/math14101634

Authors: Amira Bouhali Zeineb Ounissi Ali Moussaoui Slimane Ben Miled Amira Kebir

Human papillomavirus (HPV) is one of the most widespread sexually transmitted infections globally, whose persistent infection plays a major role in causing cervical cancer. Vaccination is therefore a key prevention strategy. Using a gender-stratified dynamic transmission model tailored to a Tunisian case, we investigate the impact of bivalent HPV vaccination. The proposed model accounts for partial cross-immunity and captures both direct and indirect effects of female-only vaccination. We derive the basic reproduction number and the corresponding herd immunity threshold, and a global sensitivity analysis shows that vaccine coverage, efficacy, and cross-protection are strong drivers of transmission reduction. Their combined effects on disease spread are quantified by varying these parameters across biologically relevant ranges. An optimal control problem was formulated and analyzed using Pontryagin’s Maximum Principle to minimize persistent infections and cancer cases while limiting vaccination effort. Three vaccination scenarios are compared: an ideal case with full vaccine availability and two resource-constrained cases with respective maximum coverage rates of 100% and 80%. The numerical simulations revealed that the optimal strategy under unconstrained conditions can achieve significant suppression of infection, persistence, and cancer. Under constrained effort, the optimal control still achieves substantial reductions in disease burden, with minor differences in dynamics and speed of immunity buildup. Our results highlight the effectiveness of female-only HPV vaccination in providing both direct and indirect protection. They also emphasize the importance of sustained coverage in constrained settings.

Mathematics doi: 10.3390/math14101631

Authors: Aybeyan Selim Muzafer Saracevic Omer Aydin

Classical enumeration of triangulations and angulations of convex polygons is governed by the Catalan and Fuss–Catalan families. In this paper, we introduce a Lucas-inspired symbolic encoding framework for a restricted subclass of triangulations, called Lucas-compatible triangulations. The purpose of the framework is not to replace classical Catalan enumeration, but to provide a complementary structural layer that records admissible local reductions through two canonical operations. Within this restricted setting, the geometric objects remain Catalan-based, whereas the associated encoding space satisfies a Fibonacci-type recurrence. We formalize the reduction model, define admissible Lucas words, and prove structural properties of the encoding map. We further present recursive generation algorithms, analyze their output-sensitive complexity, and compare the size of the encoding space with the size of the full triangulation space. In addition, we discuss geometric constraints, equivalence phenomena, and potential uses of the encoding in compact representation, constrained enumeration, and recursion-guided generation of polygon dissections. Computational experiments support the theoretical predictions and illustrate how the proposed encoding yields a compressed symbolic view of a restricted but mathematically meaningful class of dissections.

Mathematics doi: 10.3390/math14101633

Authors: Vasudevan Tharakeswari Meenakshi Sundaram Kameswari Shanmugavel Krishnaprakash

Over the past few decades, extensive attention has been given by researchers and practitioners to the development and application of multi-criteria decision-making (MCDM) methods within intuitionistic fuzzy environments across a wide range of fields and disciplines. This challenging research area has emerged as one of the most prominent topics, and its importance and popularity are expected to continue growing in the future. The elliptic intuitionistic fuzzy set (EIFS) addresses complex, multidimensional, non-symmetrical vagueness and uncertainty more effectively than other traditional intuitionistic fuzzy sets (IFSs). Sustainable renewable energy source selection is a critical decision-making (DM) process aiming to identify the most suitable energy alternative. The process of selecting sustainable renewable energy sources necessitates a comprehensive assessment of numerous criteria, which encompass environmental ramifications, economic feasibility, and societal acceptance. Contemporary research suggests novel methodologies to enhance this selection process, highlighting the need for an MCDM framework that integrates a variety of factors. This study presents an innovative DM framework for sustainable renewable energy source selection based on EIFS and a newly developed aggregation operator, the Elliptic Intuitionistic Fuzzy Weighted Muirhead Mean Aggregation (EIFWMMA) operator. These mechanisms expand upon conventional intuitionistic fuzzy frameworks by employing an elliptical portrayal of membership and non-membership degrees, facilitating a more accurate and lifelike representation of uncertainty and hesitation in evaluations by experts. To enhance computational efficiency, the framework weaves together machine learning-driven dimensionality reduction and weight optimization strategies of principal component analysis (PCA) for DM. The suggested operators are employed in an MCDM scenario centered around the selection of sustainable renewable energy sources, where the hierarchy of alternatives is established through score values derived from EIFWMMA. A comparative exploration of Circular Intuitionistic Fuzzy Sets (C-IFSs) and Interval-Valued Intuitionistic Fuzzy Sets (IVIFSs) uncovers that the elliptical formulation yields consistently reliable, precise, and geometrically comprehensible results. The findings affirm that EIFS-based operators offer a resilient, adaptable, and broadly applicable strategy for tackling MCDM challenges amidst uncertainty. The Min–Max normalization method is employed to validate our proposed methodology for identifying alternatives within the MCDM paradigm. It also improves accuracy, stability, and scalability in comparison to conventional approaches.

Mathematics doi: 10.3390/math14101632

Authors: Lu Yan Hailun Pan Jing Sun Mengyuan Cui Shuanggen Liu

Under the paradigm of the Internet of Things (IoT), the processing of large-scale data not only imposes higher demands on data-sharing efficiency but also increases the risk of user privacy leakage. To address these challenges, this paper proposes a blockchain-assisted traceable and revocable broadcast encryption scheme for preventing malicious encryptors (BATR). To resist trapdoor attacks by malicious encryptors, the scheme utilizes the uniform distribution property of hash function outputs to generate the random numbers required for the encryption algorithm. To block malicious users from leaking private keys, which attackers could exploit to construct piracy decoders with decryption capabilities, the scheme enhances the traditional broadcast encryption system by incorporating public tracing and revocation mechanisms. The scheme employs personalized transmission technology, allowing data owners to share public data with a set of authorized users while also sharing personalized data with specific authorized users. Additionally, users communicate using pseudonyms to ensure that their real identities are not accessible to third parties, thereby meeting privacy protection requirements. With the assistance of blockchain, trusted authorities and users can invoke smart contract interfaces to trigger blockchain peer nodes to execute smart contracts, thereby acquiring or updating identity authentication information stored on the blockchain to achieve secure authentication. This paper provides an analysis of the correctness and security of BATR, demonstrating that BATR satisfies chosen-ciphertext security under the Random Oracle Model. We also present performance evaluations and describe the experimental setup used to obtain operation-time baselines. Finally, this paper conducts a performance analysis of the BATR scheme, which exhibits high computational efficiency and compact communication bandwidth, resulting in significant performance improvements.

Mathematics doi: 10.3390/math14101630

Authors: Bin Ji Jing Liu Samson S. Yu

With the expansion of offshore oil and gas exploration into deep-water regions, the efficient scheduling of platform supply vessels (PSVs) is critical to offshore operations. The platform supply vessel routing and scheduling problem (PSVRSP) is an NP-hard combinatorial optimization problem, which is further complicated by uncertainty in offshore demand. Existing studies reveal a methodological gap: exact optimization algorithms have rarely been applied to this problem, as most prior research relies on heuristic methods that cannot guarantee optimality. To address this gap, this study proposes a novel enhanced branch-and-price (B&P) algorithm for the platform supply vessel routing and scheduling problem with uncertain demand (PSVRSP-UD). The proposed approach integrates NG-route labeling, a group-representative label mechanism, and a two-level branching strategy to efficiently obtain globally optimal solutions under demand uncertainty. A scenario-based mixed-integer linear programming (MILP) model is formulated, in which demand uncertainty is captured using Latin hypercube sampling (LHS) combined with Cholesky decomposition and sample-based reduction (SBR). Based on Dantzig–Wolfe decomposition, the proposed B&P algorithm integrates NG-route labeling and a two-level branching strategy to achieve global optimization. Computational experiments show that the B&P algorithm outperforms CPLEX in both computational efficiency and solution quality. Sensitivity analyses examine the impacts of scenario number, demand fluctuation, time window tightness, and weight coefficients on the results. The new results in this study can provide a practical decision-support tool for offshore logistics operations.

Mathematics doi: 10.3390/math14101629

Authors: Daniel Rothbaum

This paper studies a realization-theoretic problem inside the standard Lorentz-covariant Fourier-dual framework on L2(R3,1): whether position-space and momentum-space geometric translations can be placed on equal structural footing without leaving the ordinary X- and K-polarized realizations. Working on the common Schwartz core S(R3,1), we first isolate a Fourier-compatibility obstruction: Fourier transform exchanges geometric translations with character actions, while the Poincaré algebra contains at most one Lorentz-covariant abelian translation ideal. The main result is that, within the resulting Fourier-compatible realization class, the minimal operator-generated Lie algebra is the Lorentz–Heisenberg algebra. We then determine the full center of its universal enveloping algebra, derive the normalized Lorentz-bivector invariants, orbit data, and connected stabilizers in nondegenerate sectors, and show that the orbit variable is a normalized Lorentz bivector rather than a momentum vector. Finally, for fixed spectral elements in the dual translation sectors, we derive the associated scalar, Dirac, and vector equations in position and momentum space and show that, in the regular polarized realizations, the represented Heisenberg sector induces dual local abelian phase groups, compatible covariant derivatives, curvatures, and primary Dirac–Maxwell systems.

Mathematics doi: 10.3390/math14101628

Authors: Ruben Rodriguez-Cardos Jose A. Olivas

Elastic Patterns are presented as a novel approach to prototype-based pattern classification that integrates concepts from cognitive psychology, fuzzy logic, and physics. Traditional prototypes are revisited through their different formulations: psychological prototypes as central category elements, Fuzzy Prototypes addressing vagueness, and Deformable Prototypes incorporating elasticity to adapt to data variability. Elastic Patterns extend these ideas by representing each parameter as an independent elastic component, conceptualized as springs, which deform to fit new cases while minimizing deformation energy. Elastic Patterns operate at two levels: parameter-level deformation, measured through axial strain, and pattern-level deformation, expressed as cumulative deformation energy. This structure enables a transparent and adaptive recognition process, where classification is achieved by selecting the pattern requiring the least energy to deform. A case study on the MNIST dataset validates the proposal, achieving approximately 80% accuracy and reducing the need for extensive preprocessing. These results indicate that Elastic Patterns offer a promising alternative to conventional methods, combining interpretability, adaptability, and physical grounding in pattern recognition tasks.

Mathematics doi: 10.3390/math14101625

Authors: Omiros Ragos Angela E. Perdiou Efstathios A. Perdios Vassilis S. Kalantonis

Hill’s problem plays an important role in analyzing the local dynamics of an infinitesimal body under the gravitational influence of a distant massive primary and a nearby secondary body of smaller mass. When radiation pressure is included, the resulting model becomes particularly relevant for studying the motion of dust particles and solar-sail spacecraft in the vicinity of minor celestial bodies, such as planets or asteroids. This inclusion breaks the symmetry with respect to the Oy axis that characterizes the configurations of motion in the classical Hill’s problem. Thus, the location of the collinear equilibrium points, and the evolution of the Lyapunov families must be studied independently. Although the planar dynamics of the photogravitational Hill’s problem have been extensively investigated, its three-dimensional structure remains largely unexplored. The present study undertakes a systematic numerical investigation of branches of spatial periodic orbits that bifurcate from the planar Lyapunov families. Specifically, we compute all three-dimensional bifurcations up to multiplicity four and classify them according to their symmetry properties. The analysis reveals that these families exhibit distinct evolutionary patterns in the space of initial conditions, with most of them terminating in collision orbits with the secondary body.

Mathematics doi: 10.3390/math14101627

Authors: Jose L. Salmeron

This research presents the architecture, implementation, and validation of a novel Agentic Large Model (ALM) framework for in silico patient simulation, synergistically combining pharmacokinetic modeling with autonomous clinical reasoning. The multi-agent architecture enables emerging collaboration between specialized components for physiological simulation, medication management, and safety monitoring, coordinated through a central orchestrator to ensure behavioral alignment. Leveraging LLaMA3 via Ollama, the system demonstrates clinically plausible strategic planning across 12 diverse patient scenarios while maintaining trustworthiness through structured JSON-constrained outputs. Key innovations include a modular agent design with clear separation of concerns, integrated drug interaction checking with hierarchical severity assessment, and multi-layer safety assurance. Rigorous evaluation demonstrates effective pain management (39–58% reduction) with appropriate safety flagging in complex cases, particularly for geriatric and polypharmacy patients. The system achieves an average decision latency of 2.1 s while maintaining 98.7% structured output compliance, advancing the foundations of reliable agentic systems in critical healthcare domains.

Mathematics doi: 10.3390/math14101626

Authors: Limu Qiu

Real-time fraud detection has become a critical component in ensuring the security and stability of the digital financial ecosystem. However, existing methods struggle to adapt to the highly dynamic and adversarial nature of modern financial fraud, where malicious actors constantly evolve their strategies to evade detection. To address the dual challenges of complex topological relationships and severe concept drift, we propose the Augmented-Driven Graph Network with Adaptive Exploration (AGNAE). First, this paper introduces an augmented graph neural network tailored for financial transaction graphs, which dynamically models the heterogeneous interactions between transacting entities to capture complex, hidden fraud rings. Second, rather than relying on static classifiers, we rigorously formulate the real-time detection process as a sequential decision-making problem. This paper introduces a deep reinforcement learning agent equipped with an adaptive exploration mechanism to continuously update detection strategies, striking an optimal balance between exploiting known fraud patterns and exploring emerging mutations. Furthermore, a novel joint loss function is designed to synergize topological representation learning with the agent’s long-term financial reward optimization. Extensive experiments on the real-world for IEEE-CIS and FDAD-20 datasets demonstrate that AGNAE significantly outperforms state-of-the-art baselines. Crucially, despite its sophisticated architecture, AGNAE maintains an inference latency of 1.12 ms per transaction, fully satisfying the stringent computational requirements of real-world financial infrastructures.

Mathematics doi: 10.3390/math14101624

Authors: Zhi Yi Zhongmin Wu Yongming Xie Ming Chen Yinglong Dai

In Reinforcement Learning (RL), the agent cannot distinguish between exploratory and exploitative experience. Not all sequential experiences contribute equally to the agent’s optimization, and the same experience holds different importance at different learning stages. We propose the Extractor for Adaptive Tradeoff Between Exploration and Exploitation (EATBEE), a task-oriented tool that tightly couples with the agent’s current knowledge and enables adaptive knowledge acquisition. We compare the originally sampled data with the task-driven data distribution to clearly illustrate their deviation. Then, we show how EATBEE identifies and extracts beneficial data for the agent. The monotonic improvement policy is theoretically validated under the assumption that the experience trajectory keeps a high degree of trajectory similarity after extraction. EATBEE serves as an independent module that can be seamlessly integrated with most existing RL algorithms. We substantiate the efficacy and practical applicability of the EATBEE method through experiments conducted in both discrete and continuous environments.

Mathematics doi: 10.3390/math14101623

Authors: Yajin Chen Hongwei Gao Yanshan Liu Zhonghao Jiang

This paper investigates the optimal control problem of opinion dynamics within complex networks. By introducing a state transformation, the original problem is reformulated within a discounted Linear Quadratic Regulator (LQR) framework, establishing a connection between opinion control and classical control theory. Within this unified framework, the optimal control law can be obtained by solving the discrete-time algebraic Riccati equation, thereby circumventing the complexity of dealing with linear terms inherent in traditional dynamic programming approaches. Numerical experiments validate the effectiveness of the algorithm in a benchmark case, a 20-node complete network, and complex topologies. They also reveal the influence mechanisms of network heterogeneity on convergence speed and control energy consumption, providing a theoretical basis for public opinion guidance strategies under different network structures.

Mathematics doi: 10.3390/math14101622

Authors: Jose Luis Menaldi

A definition of identifiable-sets is used with sequential analysis to establish a realm of mathematics. Within this imaginary world, a specific consonant between infinite sets and sequentiality is reached. This consonant allows some mathematical constructions to model pieces of the reality, based on dual philosophy and physics itself. There is an effort made to render this understandable for the scientific community.

Mathematics doi: 10.3390/math14101621

Authors: Yuhang Du Yuhan Zhao

This paper presents a Multi-Strategy Market Dynamics Analysis (MSMDA) framework for agent-based economic modeling with reinforcement learning. The primary methodological contribution is an integrated strategy–stability–macro inference pipeline that links population-level strategy evolution to dynamic market stability and model-internal counterfactual policy analysis. The framework is organized into six analytical components: Strategy Temporal Pattern Recognition (STPR), Strategy Transition Detection and Analysis (STDA), Strategy-Macro Causality Analysis (SMCA), the Dynamic Market Stability Index (DMSI), the Adaptive Rationality Equilibrium (ARE), and the Information Asymmetry Propagation (IAP) metric. The method is evaluated within a simulation dataset comprising 447,129 records across four experimental scenarios, 1500 discrete time periods, and 200 heterogeneous firms governed by proximal policy optimization. Results show that competitive strategies dominate market emergence patterns at 60.8% of all observations and achieve superior average profitability of 28.07 monetary units per period, compared with −4.49 for dumping strategies and 7.83 for market power strategies. The DMSI reveals a mean stability of 0.372 with standard deviation 0.097, peaking at 0.780 during strategic consolidation and collapsing to zero during a major demand shock. Within the simulated economy, doubly-robust counterfactual analysis projects a 28.4% GDP increase from a market power-to-competition intervention and a 31.2% increase under full ARE optimization at ρ*=0.6. The ARE further identifies a Pareto-optimal market configuration that jointly maximizes per-firm profit at 229.82 monetary units per period and systemic stability at DMSI =0.67, indicating that efficiency and resilience need not conflict in the calibrated simulation environment. To address time-series autocorrelation in bootstrap inference throughout the framework, we employ a moving block bootstrap with data-adaptive block length selection based on the spectral density at frequency zero, providing finite-sample confidence intervals for the reported test statistics and counterfactual projections.

Mathematics doi: 10.3390/math14101620

Authors: Kadioglu Karaca

This paper investigates fixed point results in convex double-controlled metric-type spaces. By introducing a convex structure on double-controlled metric-type spaces, we study the convergence of the Mann iteration process for contractive mappings in this framework. Under suitable conditions on the control functions, we establish the existence and uniqueness of fixed points and prove that the Mann iterative sequence converges to the fixed point. In addition, we investigate the stability of the Mann iteration process and establish a data dependence result. Finally, an application to a Fredholm integral equation is presented to illustrate the applicability of the obtained results.

Mathematics doi: 10.3390/math14101619

Authors: Khurram Ashfaq Muhammad Tariq Mahmood

Shape from Focus (SFF) estimates scene depth by analyzing focus variations across a sequence of images captured at different focal settings. Traditional SFF methods rely on handcrafted focus operators that preserve local structural details, but they are often sensitive to noise and perform poorly in textureless regions. In contrast, deep learning-based methods are more robust and can exploit semantic and contextual cues, yet they may lose fine structural information due to feature abstraction and spatial downsampling. To address these complementary limitations, we propose a dual-branch SFF framework that integrates deep and traditional focus cues within a unified architecture. The first branch generates a deep focus volume using a multi-scale encoder-decoder network, while the second branch computes a traditional focus volume using a directional dilated Laplacian (DDL) operator to capture structural focus responses. These two volumes are progressively combined through an iterative gated fusion module, producing a more discriminative fused focus representation. From this fused volume, an initial depth map is estimated through a softmax-based slice aggregation strategy. To further improve spatial consistency and reduce residual artifacts, we introduce a lightweight depth refinement module guided by the mean RGB image of the focal stack. This refinement stage enhances boundary quality and improves the overall depth structure. Extensive experiments on synthetic and real-world datasets demonstrate that the proposed framework produces accurate and reliable depth maps.

Mathematics doi: 10.3390/math14101618

Authors: Juanjuan Li

This paper studies European option pricing in a Heston–Hull–White model with a stochastic long-run variance mean. Within this setting, a semi-analytical pricing formula is derived using a change of numeraire together with characteristic-function and Fourier-transform methods. The model is examined with SSE 50ETF option data from 1 January 2024 to 1 January 2025 through rolling-window calibration and a deep-learning-guided joint calibration scheme. The empirical results show that the proposed model reduces overall pricing errors relative to several standard benchmark models, while the deep-learning hybrid specification delivers the strongest out-of-sample pricing performance among the models considered.

Mathematics doi: 10.3390/math14101617

Authors: Yue Gu Shuanhong Wang

In this paper, we mainly introduce the notion of a braided algebraic group, which unifies the notions of a braided Hopf algebra with an integral, a Hopf group-coalgebra with a group-integral and an algebraic quantum group. For this, we introduce the notion of braided multiplier rings and study their properties. Then we study some structural properties of a braided multiplier algebra with a nontrivial example.

Mathematics doi: 10.3390/math14101616

Authors: Xianghui Wen Di Zhao Hongyi Li Chengwei Pan

Assuming the coefficient matrix is a nonzero singular matrix, we demonstrate that the invertible solutions of the Yang–Baxter-like matrix equation must possess at least two elementary divisors. This establishes a necessary condition for an invertible matrix to satisfy the Yang–Baxter-like matrix equation. Building on this finding, we derive several meaningful corollaries. Additionally, we provide some examples to illustrate our results.

Mathematics doi: 10.3390/math14101615

Authors: Salim Lahmiri Stelios Bekiros

We propose various hybrid predictive systems to forecast the Bitcoin next-day price. In particular, we combine the decomposition methods based on signal processing techniques including maximum overlap discrete wavelet transform (MODWT), empirical wavelet transform (EWT), empirical mode decomposition (EMD), and variational mode decomposition (VMD) for feature extraction from original price series. Then, the extracted features are fed to the machine learning models for training and forecasting. We implemented five machine learning models, including regression Gaussian process (RGP), support vector regression (SVR), k-nearest neighbors algorithm (kNN), regression trees (RT), and feedforward neural networks (FFNN). The grey wolf optimization (GWO) algorithm is employed for hyperparameter optimization of the machine learning models. The root mean squared error (RMSE) is used for the evaluation and comparison of 20 hybrid predictive systems. The simulation results show that the RGP-GWO-VMD hybrid predictive system achieved the lowest forecasting error. In addition, RGP-GWO yielded on average the lowest forecasting error across all of the machine learning systems. Furthermore, among signal decomposition methods, the lowest forecasting error is generally achieved under the EWT. Hence, we presented the best results in forecasting Bitcoin prices from 20 hybrid prediction systems to serve as the baseline for future work and to guide traders, investors, and portfolio managers.

Mathematics doi: 10.3390/math14101614

Authors: Zhuo Du Xu Wang

Indirect methods based on Pontryagin’s Maximum Principle (PMP) offer theoretical rigor for nonlinear optimal control but suffer from extreme sensitivity to costate initialization. Physics-Informed Neural Networks (PINNs) provide a promising data-free approach to globally approximate trajectories and overcome this initialization barrier. However, they often lack strict numerical precision due to their reliance on soft penalty constraints. To bridge this gap, this paper proposes a hybrid framework that synergizes the global search capability of a structurally modified PINN with the rigorous precision of high-order Chebyshev–Gauss–Lobatto (CGL) spectral discretization. Within this framework, we first introduce a novel neural architecture that enforces the PMP stationarity condition as a hard constraint by analytically eliminating control inputs via costates, thereby reducing the optimization search space and ensuring strict optimality during training. The neural-generated trajectories subsequently provide a high-quality warm start for a CGL pseudospectral solver, transforming the problem into a single-shot convex quadratic programming formulation. Numerical experiments on the Van der Pol oscillator and elliptic PDE optimal control problems demonstrate that this strategy effectively mitigates the initialization sensitivity of indirect methods. The results show that the proposed method achieves superior accuracy and convergence stability compared to standalone PINN solvers, providing a robust initialization-free approach for complex nonlinear optimal control.

Mathematics doi: 10.3390/math14101613

Authors: Bo-Jun Yuan Jia-Jin Wang

Let G be a simple graph. The sum of the α-th degree powers of G, denoted by Mα(G), is obtained by summing the α-th powers of all vertex degrees. We use Gn,m to denote the set of all graphs having n vertices and m edges. Extremal problems concerning M2(G) have a long history in combinatorics and graph theory. In 1971, Katz (Israel J. Math., 1971) first initiated the study of maximizing M2(G) within Gn,m. After nearly 40 years, Ábrego et al. (J. Inequal. Pure and Appl. Math., 2009) completely resolved this problem. In this paper, we extend the power exponent from α=2 to α>2, investigating the problem of determining the graph that maximizes the value of Mα(G) within Gn,m. We show that the graph that maximizes Mα(G) when α>2 and 1≤m≤14n2 is the quasi-star graph, which belongs to a special class of threshold graphs (defined in the Introduction).

Mathematics doi: 10.3390/math14101612

Authors: Jicheng Li Guangjun Liao Yufei Wang Xing Liu Beibei Liu

Generalizable deepfake detection is essential for trustworthy visual understanding in real-world computer vision applications. This paper presents a dynamic spatial-temporal inconsistency learning algorithm designed to achieve high generalization in deepfake video detection. Current video-based detection approaches tend to either isolate spatial artifacts or merely exploit coarse temporal inconsistencies when identifying deepfake videos, which impedes the acquisition of fine-grained spatial-temporal clues and consequently limits their generalization capability. To this end, we propose the dynamic spatial-temporal network (DST-Net), a deep architecture that systematically mines comprehensive inconsistency cues through three synergistic modules. The short-term temporal modality extraction (STME) module captures temporal dynamics from adjacent frames. The short-term spatial-temporal inconsistency extraction (SSTIE) module with pixel-wise supervision learns semantically meaningful inconsistency features resistant to perturbations. The dynamic-term spatial-temporal inconsistency extraction (DSTIE) module adaptively aggregates these features across timescales, building robust multi-scale representations. This design ensures that the learned representations capture intrinsic forgery patterns, enhancing generalization and robustness. Comprehensive evaluations conducted on five widely adopted benchmark datasets reveal that our method surpasses nine representative competitors, with superior robustness to common image perturbations. This work advances the application of deep learning algorithms to reliable visual understanding in multimedia forensics.

Mathematics doi: 10.3390/math14101611

Authors: Pingan Peng Xuhe Li Kaixuan Cheng Shuangwei Gong Haoyue Zhang

This study demonstrates how structured algorithmic optimization can enhance intelligent visual measurement systems in mining engineering. Real-time visual measurement of mining conveyor belts is critical for operational safety, yet achieving high-precision anomaly detection under complex environmental conditions remains a significant challenge. Conventional approaches often struggle to balance detection accuracy with computational efficiency due to inefficient feature representation and optimization strategies. To address this, this study proposes FDSE-DETR, a lightweight end-to-end framework designed for real-time anomaly evaluation. The framework eliminates Non-Maximum Suppression (NMS) to streamline inference. Specifically, this study introduces a deformation-aware sampling mechanism to enhance feature representation of irregular hazards, alongside a cost-effective multi-scale aggregation strategy to preserve fine cues within strict device budgets. Furthermore, a reformulated loss objective is developed to rebalance hard samples under severe class imbalance, improving the detection confidence. Experimental results on mining conveyor belt foreign object datasets show a 4.5% improvement in mean average precision (mAP), a 3.9% improvement in overall recall and a 22.5% reduction in computational cost, achieving 120.7 FPS. This study aims to address the problems of insufficient accuracy and low efficiency in real-time material flow measurements on mining conveyor belts under high-dust and low-illumination conditions.

Mathematics doi: 10.3390/math14101610

Authors: Baoyi Zhang Xi Yu Wuyi Cai Xian Zhou Binhai Wang Tongyun Zhang

Triangular mesh is one of the most widely used representations for 3D surfaces. However, high-resolution mesh models often contain a large number of triangles, leading to significant burdens in storage, transmission, and real-time rendering. Mesh simplification aims to reduce model complexity while preserving geometric fidelity and structural features. Classical methods, such as quadric error metrics (QEM), rely solely on local geometric errors, making them difficult to distinguish between redundant regions and structurally important features, often resulting in feature loss and topological degradation. To address these limitations, this study proposes a structure-aware triangular mesh simplification framework based on graph neural networks (GNNs)-guided QEM. GNNs are employed as a structural importance estimator to predict geometric saliencies of mesh edges. The predicted importances are incorporated into the classical QEM edge collapse cost through a soft modulation mechanism. Furthermore, a geometry-saliency-driven dynamic cost modulation strategy is designed, enabling the simplification process to prioritize critical features in early stages and gradually transition to global error minimization in later stages, without compromising the geometric optimality of QEM. In terms of model design, hybrid structural representation GNNs are constructed by integrating spectral geometry and a dual-branch architecture. Laplacian positional encoding is introduced to capture global topological information, while 1-hop and 2-hop message passing branches enable multi-scale representation of complex geometric structures. In addition, a staged inference strategy is adopted to dynamically update graph structural features during simplification, effectively mitigating topological drift. Experimental results on the TOSCA dataset demonstrate that the proposed method achieves stable performance across various simplification ratios. It consistently outperforms FQMS and QEM in terms of geometric error (\({P_{CD}}\)) and normal consistency (\({P_{NE}}\)). For structural preservation (\({P_{LE}}\)), the method shows advantages, with win-rates generally exceeding 90%. Moreover, it significantly improves the preservation of local geometric details at low to moderate simplification ratios. In summary, the proposed method effectively enhances local structural preservation while maintaining global geometric topology, providing an interpretable and practical solution for integrating learning-based structural awareness with classical geometric optimization in mesh simplification.

Mathematics doi: 10.3390/math14101608

Authors: Muhammed Yusuf Küçükkara Furkan Atban Cüneyt Bayılmış

The rapid expansion of the Internet of Things (IoT) has increased the risk of large-scale Distributed Denial-of-Service (DDoS) attacks. In high-availability IoT environments, the operational costs of false positives and false negatives are asymmetric, whereas conventional deep learning models usually optimize static accuracy-based objectives. To address this, we propose CDRL-QNN, a cost-aware and chaos-driven reinforcement learning quantum neural network framework in which a parameterized quantum circuit serves as the action-value function approximator within a Deep Q-Network (DQN) agent. The framework incorporates asymmetric operational penalties through both the reward function and sample-wise weighted Bellman optimization, while a logistic-map-based deterministic perturbation mechanism is used to promote exploration under constrained quantum-circuit training conditions. Evaluated on a computationally constrained balanced subset of the CIC-DDoS2019 dataset, the proposed framework reduced false negatives from 49 to 33 without increasing false positives, improving recall from 0.9673 to 0.9780 and F1-score from 0.9738 to 0.9793 while lowering operational cost. These findings suggest that hybrid quantum representations can be integrated into cost-sensitive reinforcement learning pipelines for IoT intrusion detection under constrained experimental conditions.

Mathematics doi: 10.3390/math14101606

Authors: S. Suresh Kumar Raju Gundlapally Shiva Kumar Reddy

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

Mathematics doi: 10.3390/math14101609

Authors: Chang-Ho Lee Yeong-Jae Kim Yong-Gwon Lee Seung-Hoon Lee Oh-Min Kwon

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

Mathematics doi: 10.3390/math14101607

Authors: Sugyeong Eo Chanjun Park

The advent of large language models has reshaped the landscape of artificial intelligence, yet their learning dynamics remain constrained by rigid training strategies. Curriculum learning (CL), inspired by the human learning process, improves model performance over conventional randomly shuffled training while incurring no additional computational overhead. However, its competence-conservative mechanism often leads to diminished learning stimuli and suboptimal performance plateaus. Inspired by the flow theory in psychology, this study proposes in-batch hard sample injection curriculum learning (DACL), a learning strategy that dynamically balances stability and challenge. DACL regulates sample selection by aligning the model’s competence with the intrinsic complexity of the data, allocating the Reasy proportion of each batch to instances within the competence range and the remaining (1−Reasy) to higher-difficulty samples that stimulate adaptive learning. Experiments on the English–Vietnamese pair demonstrate that DACL achieves superior performance over curriculum learning baselines across multiple difficulty evaluation criteria. Further experiments reveal the effectiveness of the similarity-based difficulty standard, demonstrating the ability to capture task complexity with greater precision.

Mathematics doi: 10.3390/math14101605

Authors: Pablo Adasme

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

Mathematics doi: 10.3390/math14101604

Authors: Saifallah Ghobber Hatem Mejjaoli

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

Mathematics doi: 10.3390/math14101603

Authors: Kaveh Dehghanian

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

Mathematics doi: 10.3390/math14101602

Authors: Tran Buu Thach Nguyen Hoai Vu Anh Truong Kyoung Kwan Ahn

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

Mathematics doi: 10.3390/math14101599

Authors: Chao Liu Hong Mu Jingjing Zhou Enliang Wang Xuejian Zhao

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

Mathematics doi: 10.3390/math14101601

Authors: Chenyu Gao Piwei Chen

Oil price volatility forecasting remains a central challenge in financial risk management and macroeconomic policy, particularly when market uncertainty stems from expert judgment, geopolitical assessments, or imprecisely quantified fundamentals rather than statistical frequencies. We propose a bivariate uncertain vector autoregressive (UVAR) model to jointly forecast crude oil realized volatility (RV) and the Overall Equity Market Volatility (EMV) tracker within the framework of uncertainty theory, using 204 monthly observations from January 2008 to December 2024. Three cross-validation schemes consistently identify UVAR(1) as optimal, and least-squares estimation reveals an asymmetric bidirectional relationship between the two variables. Residual analysis and uncertain hypothesis testing confirm the adequacy of the fitted model at both α=0.05 and α=0.10, the conventional significance levels reported in the empirical literature. Relative to a univariate UAR benchmark, UVAR(1) yields lower residual variance and, on average, narrower 95% confidence intervals for both variables and remedies the hypothesis-test failure of UAR(1) for realized volatility; while its fixed-origin ATE is marginally higher on the EMV tracker, this is more than offset by substantial gains on realized volatility, the primary economic variable of interest. Against a probabilistic VAR(1) benchmark, UVAR(1) attains marginally lower out-of-sample sum of squared mean errors while uniquely supporting principled uncertain-statistical inference under non-frequentist data-generating mechanisms. These results provide principled inputs for value-at-risk assessment and portfolio hedging in oil-dependent economies.

Mathematics doi: 10.3390/math14101600

Authors: Olga Krivorotko Andrei Neverov Yakov Schwartz Grigoriy Kaminskiy Nikolay Zyatkov Zhanna Laushkina

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

Mathematics doi: 10.3390/math14101598

Authors: Sami H. Saif Shayea Aldossari

We construct three new families of asymmetric quantum MDS codes from nested Hermitian self-orthogonal generalized Reed–Solomon and extended generalized Reed–Solomon codes over Fq2. The construction is developed in three settings: affine partitions of Fq2, projective norm partitions of Fq2*, and extended affine configurations obtained by adjoining the point at infinity. In each case, the Hermitian orthogonality conditions are reduced to explicit linear systems over Fq, whose solvability follows from structured moment identities and Vandermonde-type arguments. This yields nested classical MDS codes satisfying the Hermitian dual-containment condition required in the Hermitian construction of asymmetric quantum codes. As a consequence, we obtain three explicit families of asymmetric quantum MDS codes with fully determined lengths, dimensions, and asymmetric distances dz and dx. Our results show that affine and projective partition techniques provide a natural and effective framework for constructing optimal asymmetric quantum codes with flexible parameters.

Mathematics doi: 10.3390/math14101597

Authors: Lixia Gao

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

Mathematics doi: 10.3390/math14101595

Authors: Yongming Cai Changshu Zhao Tiancai Tan Liang Chen Yan Wang Yifan Li Chen Tang Dongqi An

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

Mathematics doi: 10.3390/math14101596

Authors: Dmitry Efrosinin Natalia Stepanova Zóltan Gál Janos Sztrik

This paper analyzes a MAP/PH/1/K queue with N-policy, setup, interruptions, reset, and a random environment. Arrivals are the MAP; service, setup, interruption, and reset times are PH-distributed. Under the N-policy, the server idles until the queue length is equal to N, and then performs setup. Interruptions return the system to idle and re-enable the N-policy. At capacity K, a reset empties the system. The random environment modulates parameters for different regimes. Motivated by Diesel Particulate Filter (DPF) regeneration, soot accumulation is mapped to arrivals, burning to service, regeneration triggers to N-policy, heating to setup, engine changes to interruptions, and cleaning to reset. Environmental states represent driving patterns. Regeneration succeeds if either the system empties via service or an interruption occurs with remaining soot less than or equal to level L. We derive the block-structured generator, obtain stationary probabilities via matrix-analytic methods, and optimize the threshold N via average cost. Numerical results quantify how correlation and driving conditions affect performance and costs, offering tools to balance fuel consumption, engine performance, and filter longevity.

Mathematics doi: 10.3390/math14101594

Authors: Yudong Li Yan Chen

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

Mathematics doi: 10.3390/math14101593

Authors: Ergashevich Halimjon Khujamatov Sherzod Daliev Sherzod Urakov Sirojiddin Elmonov Abdinabi Mukhamadiyev Razvan Craciunescu

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

Mathematics doi: 10.3390/math14101592

Authors: Amal S. Alali Md Arshad Madni

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

Mathematics doi: 10.3390/math14101591

Authors: Aleksandra Ivanov Lazar Stošić Olja Krčadinac Vladimir Đokić Dragana Đokić

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

Mathematics doi: 10.3390/math14101590

Authors: Thien Binh Nguyen Nguyen Minh Hieu Pham

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

Mathematics doi: 10.3390/math14101589

Authors: Shuxuan Li Teng Ren Guohua Wu

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

Mathematics doi: 10.3390/math14101588

Authors: Kun Jiang Baoling Wang

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

Mathematics doi: 10.3390/math14101584

Authors: Ebrahem Elkady Ahmed Salem Hyun-Soo Kang Jae-Won Suh

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

Mathematics doi: 10.3390/math14101587

Authors: Donggeon Jo Dongsan Jun

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

Mathematics doi: 10.3390/math14101585

Authors: Xiaojie Tang Chengfen Jia Pengju Qu Pan Zhang

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

Mathematics doi: 10.3390/math14101586

Authors: Youzi He

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

Mathematics doi: 10.3390/math14101583

Authors: Andrey O. Kalashnikov Manukovskaya

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

Mathematics doi: 10.3390/math14101582

Authors: George Papakonstantinou Konstantinos G. Papakonstantinou

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

Mathematics doi: 10.3390/math14101581

Authors: Hyojun Kim Chankyu Son

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

Mathematics doi: 10.3390/math14101580

Authors: Hadi Obaid Alshammari Sid Ahmed Ould Ahmed Mahmoud

In this paper, we investigate fundamental properties of (m,p)-isometric tuples ((m,p)−I.T.) in normed spaces. We first establish conditions under which the product of two (m,p)−I.T. remains in the same class, providing a framework for composing such tuples. Next, we derive necessary conditions for an (m,p)−I.T. to become a (2,p)−I.T., characterizing when higher-order isometric behavior can change under parameter adjustments. We also show that any (m,p)−I.T. that is power-bounded reduces to a (1,p)−I.T., revealing a structural collapse from higher-order to first-order isometries under boundedness constraints. Furthermore, we prove that if a tuple (N1,…,Nd) is simultaneously an (m,p)−I.T. and an (m,∞)-isometry, then (N1m,…,Ndm) is a (1,p)−I.T., providing a link between different isometric classes. These results provide a systematic understanding of the stability, transformation behavior, and interrelations of (m,p)−I.T., extending classical operator-theoretic concepts to tuples of commuting linear or nonlinear transformations in normed and Banach spaces.

Mathematics doi: 10.3390/math14101579

Authors: Ai Shan Hu Chao Ma Yong

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

Mathematics doi: 10.3390/math14101578

Authors: Ömer Küsmüş

Characterizing specific types of units in group rings in terms of the Jacobson radical constitutes a frequently investigated problem in the theory of group rings. In this study, since R is a commutative ring with unity and G is a finite Abelian group, Uft(RG) as the set of feckly trivial units in the group ring RG, consisting of units that are congruent modulo J(RG) to some g∈G, where J(RG) denotes the Jacobson radical of RG, is defined. Secondly, some necessary and sufficient conditions are given for the group U(RG) of units of the group ring RG to be feckly trivial under the assumption that supp(G)∩jp(R)=∅ where P is the set of all prime integers, supp(G)={p∈P:Gp≠eG}, jp(R)={p∈P:∃r∈R∖{0R},pr∈J(R)} and Gp is the p-primary component in G. Finally, two open problems related to this notion are introduced.

Mathematics doi: 10.3390/math14101577

Authors: Yan Su Jiawen Liu Ran Zhong

This paper investigates the optimal dynamic policies of time-inhomogeneous unreliable multi-server queueing systems with multiple customer sources and differentiated maintenance speeds. Under the criterion of global revenue optimality, we first elaborate the existence of bias-optimal policies and rigorously prove the existence of optimal time-inhomogeneous multi-threshold policies. We further derive two sufficient conditions to solve the monotonicity problem of the optimal time-inhomogeneous multi-threshold policies. Finally, to reduce the computational complexity of deriving optimal policies under the global optimization objective, we propose a heuristic algorithm based on the above theoretical results. The numerical examples not only demonstrate the strong performance of the proposed algorithm, but also indicate that the assumption of the monotonicity of production loss cost with respect to service states is no longer valid when the preset thresholds are differentiated by customer types.

Mathematics doi: 10.3390/math14101576

Authors: Junyan Hu Wei Luo Tong Chen Xiaobao Yang Zhiqiang Hou

For image generation, denoising diffusion probabilistic models (DDPMs) have shown strong performance. Nevertheless, under class-imbalanced training data, many existing models tend to overfit head classes, which degrades image quality for tail classes. To mitigate this issue, we propose a new generation method, PD-CBDM (perceptual distinguish loss–class-balancing diffusion models). As a first step, PD-CBDM revises the target-label distribution used for label sampling in the baseline pipeline, so tail classes are sampled more frequently during training; this improves the diversity of generated images while keeping fidelity high. Next, we introduce a perceptual distinguish loss that enlarges the separation (measured by the KL divergence in the reverse process) between the data distributions of head and tail classes, which helps suppress head-class overfitting and improves generation quality across classes. Additionally, we propose a timestep-dependent Self-Attention (TSA) module that injects timestep cues into the self-attention mechanism to model temporal and spatial dependencies together, thereby enhancing noise estimation accuracy and image generation quality. Experiments show that PD-CBDM improves FID from 5.81 to 4.96 on CIFAR100-LT and from 5.46 to 5.03 on CIFAR10-LT, and it is competitive with representative recent methods such as BPA and NoisyTwins.

Mathematics doi: 10.3390/math14091575

Authors: Xiongfei Wang Hua Xu Yuanyuan Song Zhirong Sheng Minggang Wang

Technological progress reduces carbon emissions by promoting energy structure optimization while fostering new industries and improving efficiency, thus achieving a win–win situation for economic growth and low-carbon development. From the perspective of mechanism analysis, this paper constructs a new dynamic system model of technological progress–carbon emissions–economic growth–energy structure based on the interdependent and mutually restrictive causal relationships among technological progress, carbon emissions, economic growth and energy structure within an economic period. The dynamical behaviors of the system and its subsystems are analyzed using Lyapunov exponents, bifurcation diagrams, equilibrium point stability theory and other methods. Numerical simulations show that the system parameter a2 (the driving coefficient of economic growth on carbon emissions) determines the threshold of state transition. With the increase in a2, the system exhibits a clear evolutionary path from stable equilibrium to periodic state and then to chaotic state. The system enters chaos when a2 falls within the interval [0.741, 0.79]. Model parameters are estimated based on real data, the evolutionary relationships of technological progress, carbon emissions, energy structure and economic growth over time are presented, and the impacts of different regulation strategies on carbon emission reduction and economic growth are analyzed.

Mathematics doi: 10.3390/math14091574

Authors: Peipei Zhang Yusen Luo

The synergistic development of digitalization and greening is an important lever for China to accelerate the formation of new quality productive forces. This study adopted the global entropy method and coupling coordination degree model to measure the level of coordinated development between digitalization and greening with the panel data of Chinese cities from 2011 to 2022. Spatio-temporal evolution characteristics were explored through kernel density estimation, the Dagum Gini coefficient, and spatial autocorrelation methods. This study further tested the convergence characteristics of coordinated development through a two-way fixed effect model and spatial econometric model. The results show the following: (1) The overall level of coordinated development of digitalization and greening in China is on the rise, with the development level in the eastern region being significantly higher than that in the central and western regions. The degree of differentiation in coordinated development shows a trend of decreasing first and then increasing, mainly due to regional differences. (2) The level of coordinated development between digitalization and greening in China shows a significant positive spatial autocorrelation feature, with a clustering pattern dominated by “low–low” clustering. (3) It is found that the coordinated development of digitalization and greening in China has significant characteristics of σ convergence, spatial β convergence and club convergence.

Mathematics doi: 10.3390/math14091573

Authors: Jinsong Yang Jie Luo Xiaozhen Zhang Chengguang Fan

Accurate impact localization on spacecraft structural panels subjected to contact loading by on-orbit servicing robots is critical for real-time structural health monitoring (SHM), yet remains challenging due to heterogeneous elastic wave propagation in complex aluminum structures with stiffener ribs and bonded joints. Conventional Received Signal Strength Indicator (RSSI)-based weighted centroid methods rely on fixed path-loss exponents that cannot accommodate spatially varying wave attenuation, resulting in position-dependent localization errors that worsen significantly near structural discontinuities. This paper proposes a Crow Search Algorithm (CSA)-optimized adaptive weighted centroid algorithm using distributed Fiber Bragg Grating (FBG) sensors, featuring three principal innovations: (i) a novel FBG wavelength-shift-to-RSSI amplitude mapping derived from elastic wave attenuation theory, bridging optical fiber sensing with centroid localization; (ii) per-event online weight optimization via CSA that adapts sensor contributions to each individual impact’s strain-wave signature; and (iii) a multi-objective fitness function simultaneously optimizing localization accuracy, noise robustness, and temporal consistency. The proposed method is validated across 200 impact events distributed over five representative positions on a 1 m3 Al6061 satellite-like structure with 64 FBG sensors (8 × 8 grid, 125 mm pitch), under three Gaussian noise levels (σ = 1%, 3%, 5% of signal RMS), and benchmarked against classical weighted centroid (WC), PSO-WC, GA-WC, DE-WC, and GWO-WC using paired t-tests (p < 0.01). CSA-WC achieves a mean localization error of 4.63 mm—an 83.29% improvement over classical WC and the lowest error among all five compared algorithms—with an average computation time of 0.14 s per event, satisfying real-time monitoring requirements.

Mathematics doi: 10.3390/math14091571

Authors: Jian Li Zhengbang Zha Ziran Tu

Complete permutation polynomials have many applications in mathematics and cryptography. In this paper, we study the complete permutation property of polynomial xh(xq−1)q+1 over Fq2, where h(x)=h1(x+xq)+h2(x+xq)xk. Based on the trace functions and Dickson polynomials, we present several new constructions of such complete permutations by choosing suitable h1(x), h2(x), and k.

Mathematics doi: 10.3390/math14091572

Authors: Sajedeh Norozpour

We propose a unified additive–multiplicative optimization framework, termed hybrid multiplicative gradient decomposition (HMGD), for training machine learning models. Unlike conventional gradient-based methods that rely solely on additive parameter updates, the proposed approach decomposes the gradient into complementary additive and multiplicative components, where the multiplicative term is defined through logarithmic derivative transformations to capture geometric scaling effects. This formulation enables the simultaneous modeling of linear and exponential parameter dynamics, which is particularly relevant in non-convex optimization settings and in models involving multiplicative interactions. The HMGD framework introduces separate momentum mechanisms for additive and multiplicative components, along with norm-based regularization to improve stability and promote structured sparsity in gradient updates. The method can be integrated into standard backpropagation by extending the chain rule to incorporate geometric derivatives. Empirical evaluations on multiple benchmark datasets demonstrate that HMGD achieves consistently faster convergence, improved robustness under multiplicative noise, and competitive or slightly improved performance compared to widely used optimizers such as Adam and RMSProp. Additional analysis shows that the proposed framework induces higher gradient sparsity and maintains stable optimization behavior across training. These results suggest that HMGD provides a flexible and theoretically grounded alternative for optimization in complex learning systems, particularly in scenarios involving nonlinear and multiplicative dynamics.

Mathematics doi: 10.3390/math14091570

Authors: Yue He Shishun Cheng Zhuo Xie Shaowen Yao Lijun Wei

This paper proposes an efficient algorithm that integrates a variable neighborhood search (VNS) framework with an adaptive voxel discretization for the three-dimensional irregular packing problem. The problem arises in additive manufacturing, logistics loading, and other fields, especially in strip packing scenarios where the filling length in a virtual container with a fixed cross-section and infinite length is to be minimized. The algorithm first discretizes continuous three-dimensional geometric models into Boolean voxel matrices, thereby transforming complex geometric interference detection into efficient logical operations. An initial solution is generated using a greedy “largest-volume-first” strategy. An innovative adaptive voxel precision adjustment mechanism is introduced to dynamically modify the discretization granularity according to the current filling rate, realizing a hierarchical solution strategy of “coarse-grained fast search + fine-grained precise optimization”. On this basis, a variable-neighborhood iterative framework based on tabu search (TS-VNS) is constructed. Three complementary neighborhood operators are designed: single-item reinsertion, block exchange, and rotation perturbation, together with an adaptive operator selection mechanism driven by historical contributions. Experiments on multiple standard instances of varying scales and complexities (e.g., miniature chess pieces and engine components) show that the proposed algorithm outperforms comparative methods in both packing height and average height, achieving a favorable balance between solution efficiency and stability. Thus, it provides a reliable and efficient approach for the practical engineering application of three-dimensional irregular packing.

Mathematics doi: 10.3390/math14091569

Authors: Fengbing Li Jiaxiang Tao Haitao Huang Qinlong Wang

In this paper, a sugarcane pokkah boeng SEIR model with time delay due to removal or chemical treatment of diseased sugarcane plants is investigated. By analyzing the characteristic equations, the stability of each feasible equilibrium of the system is discussed, and the existence of a Hopf bifurcation at the positive equilibrium is established. Furthermore, by choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can occur as τ crosses some critical values. Meanwhile, we adopt a hierarchical Bayesian model to conduct statistical inference on time delay and combine it with the former to carry out an empirical analysis on the prevention and control of sugarcane pokkah boeng. These provide a more comprehensive and effective theoretical basis for decision-making in the prevention and control of sugarcane pokkah boeng. Numerical simulations are carried out to illustrate the main theoretical results.

Mathematics doi: 10.3390/math14091568

Authors: Shiwei Huang Shunxin Xiao Xu-Yao Zhang Shunzhi Zhu Luoqi Liu Da-Han Wang

Text-attributed graphs (TAGs) require models to jointly exploit node text and graph structure, yet doing so effectively remains difficult when node text is sparse and the structural context is large. Here, we propose STAGE (Semantic and Topological Augmented Graph Embedding), a two-stage framework for representation learning on TAGs. In Stage I, a frozen large language model is used offline to generate explanatory text that enriches compressed node attributes without introducing online LLM training cost. In Stage II, STAGE performs structure-aware representation learning under a fixed global token budget by combining random-walk-based structural context with graph-conditioned token reduction before PLM encoding. This design preserves informative semantic content while preventing unconstrained sequence expansion. Experiments on seven benchmark datasets show that STAGE consistently outperforms strong baselines under the same evaluation setting and maintains favorable efficiency under bounded input-length constraints.

Mathematics doi: 10.3390/math14091567

Authors: Yu Fu Fan Zhang Zhou Li

The visible light and infrared thermal multimodal images in autonomous driving provide a wealth of information for pedestrian detection, and its challenge lies in utilizing the complementary information across modalities to obtain an optimal joint representation. This study proposes a light-aware modality balancing network (LMB-Net) for pedestrian detection by fusing visible light and infrared thermal images. We designed an alignment complementary fusion module across modalities to exchange target information. Deformable convolutions are employed to automatically perform spatial deformation on features, thereby eliminating perception biases caused by misalignment. Furthermore, as the contribution of different modalities to pedestrian detection varies under different lighting conditions, we designed a light-aware module to utilize the distinct advantages of visible light and infrared thermal images. Extensive experiments on the KAIST and LLVIP datasets demonstrate that our method achieves the best detection performance compared to some other methods.

Mathematics doi: 10.3390/math14091566

Authors: Ohud A. Alqasem Ahmed Elshahhat

Researchers often develop ordinal hazard distributions, whether increasing or decreasing, into multi-parameter distributions to derive various forms of the hazard function. This process necessitates the formulation of a multi-parameter hazard function, which involves a more complex mathematical expression. In contrast, this study introduces a new one-parameter lifetime model, termed the Inverted Z–Lindley (IZL) distribution, which is capable of capturing an upside-down bathtub-shaped failure rate without sacrificing analytical simplicity. Fundamental distributional properties of the IZL model are rigorously established, including closed-form expressions for the probability density, cumulative distribution, reliability, and hazard rate functions. Theoretical analysis shows that the density is strictly positive, unimodal, positively skewed, and heavy-tailed, while the hazard rate is unimodal with vanishing limits at both extremes. Fractional moments are obtained, and the non-existence of classical moments is formally justified, motivating the use of quantile-based and inactivity-time reliability measures. Besides the quantile function, several key reliability measures, including the mean inactivity time and strong mean inactivity time functions, and order statistics, are also developed. Inferential procedures are constructed under Type-II censoring using both likelihood-based and Bayesian frameworks. The existence and uniqueness of the frequentist estimator are established, while Bayesian estimation is implemented via Markov chain Monte Carlo methods under informative gamma priors. Several interval estimation techniques—including asymptotic, bootstrap, Bayesian credible, and highest posterior density intervals—are developed and compared through extensive Monte Carlo simulations. The practical relevance of the proposed model is demonstrated using real datasets from environmental health and communication engineering, where the IZL distribution consistently outperforms fifteen well-established inverted lifetime models according to likelihood-based criteria, information measures, and goodness-of-fit diagnostics. Overall, the IZL model offers a powerful, interpretable, and computationally efficient alternative for modeling heavy-tailed lifetime data with non-monotone failure behavior, contributing meaningfully to modern distribution theory and applied reliability analysis.

Mathematics doi: 10.3390/math14091565

Authors: Hailong Sun Shenbing Fei Mengdi Ma Zhiqi Yan Wei Wang

Currently, the research on academic early warning assessment and prediction for college students under the credit system in colleges and universities is mainly based on methods such as machine learning. However, the existing prediction models often have problems such as difficulty in network structure, parameter selection, and extraction of context time series information. In response to these issues, this study, based on students’ historical academic performance, proposes LTBoost, a novel framework of the XGBoost classification prediction model. The proposed model framework integrates the BiLSTM module to handle the time series information in the original data. It also integrates the proposed Enhanced Transformer module to perceive global information and obtain enhanced features. Through experiments, the LTBoost prediction model was compared with four other machine learning algorithms. The accuracy of the proposed LTBoost classification prediction model increased by 0.7% to 99.4%, demonstrating a good prediction effect on whether students are at risk of prolonging their studies. It provides a new paradigm and path for the construction of talent cultivation plans in credit-based universities.

Mathematics doi: 10.3390/math14091564

Authors: Jiahui Dai Peng Hou

Active disturbance rejection control (ADRC) is attractive because it estimates and compensates a lumped “total disturbance” with limited plant information, but privacy-sensitive networked deployment, measurement-noise amplification, and actuator saturation remain insufficiently addressed together. This paper proposes a Differentially Private Probabilistic ADRC (DP-PADRC) framework for nonlinear SISO systems under saturation. In contrast to adaptive ADRC schemes that schedule gains from raw residuals, and unlike model-based differentially private filters that rely on explicit stochastic plant models, the proposed method combines a linear ESO with a lightweight uncertainty surrogate computed from clipped and privatized innovations. The resulting controller is not Bayesian; rather, it is probabilistic in the sense that second-moment information from the released innovation stream is explicitly used to calibrate observer bandwidth and disturbance compensation. We further incorporate a saturation-aware gate so that scheduling remains well behaved when the commanded and applied inputs differ. An ISS-type mean-square bound is derived for the closed loop, making the dependence on the disturbance derivative, measurement-noise variance, clipping level, and privacy parameters (ε,δ) explicit. We also discuss the composition of privacy loss across repeated tuning windows and quantify the privacy-induced perturbation of the scheduling signal. Simulation-based nonlinear servo benchmarks show improved tracking/noise robustness over fixed-gain LADRC and a nonlinear ADRC baseline, while clarifying the privacy–performance trade-off and the scope of the method.

Mathematics doi: 10.3390/math14091563

Authors: Ji Lin Zonghui Zhang Yuhui Zhang Jun Lu

This paper presents a meshless collocation technique for the fourth-order transient stream function formulation of the Navier–Stokes equations. The technique employs a hybrid kernel function and is augmented by the ghost point method and Picard iteration. The reduction in unknowns inherent in this stream function approach simplifies the solution process. Introducing vorticity and stream functions enables mathematical reformulation of the coupled, time-dependent Navier–Stokes system as a fourth-order partial differential equation in one variable. The Gaussian–cubic backward substitution method and time difference method are used to solve the corresponding equation, in which the nonlinear part is generally transformed into linear equations through Picard iteration methods. This paper simulates three flows to prove the feasibility of the scheme.

Mathematics doi: 10.3390/math14091562

Authors: Zhiwei Bi Yunfang Tang

The strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they are incident to a common edge or share an endpoint. The strong chromatic index of a graph G, denoted by χs′(G), is the minimum number of colors needed for a strong edge coloring of G. In this paper, we prove the following two theorems: (1) If G=T∪C is a complete Halin graph with Δ=4 that contains adjacent vertices of maximum degree, then χs′(G)≤χs′(T)+1=2Δ. In particular, when T is a regular tree, χs′(G)=χs′(T)+1=2Δ. (2) If G=T∪C is a complete Halin graph with Δ≥5 and G≠Wn, then χs′(G)=χs′(T)=2Δ−1 when T is a regular tree. We extend the strong edge coloring results for complete cubic regular Halin graphs studied by W.C. Shiu and W.K. Tam, and improve the upper bound on the strong chromatic index of general Halin graphs established by Wei Yang and Baoyindureng Wu.

Mathematics doi: 10.3390/math14091561

Authors: Linyan Zhang Yumeng Zhang Kun Yang Jian Zhang

In recent years, China’s digital economy has become a key engine for high-quality development. Assessing the operational efficiency of leading digital enterprises is crucial for optimizing resource allocation and promoting sectoral growth. However, existing research largely remains at regional or industry levels and typically reports efficiency scores without diagnosing the root sources of inefficiency. To fill this gap, this study measures the operational efficiency of 99 firms selected from China’s Top 100 Digital Economy list (2017–2022) using the BCC-DEA model, and analyzes their dynamic evolution via kernel density estimation. The findings reveal a fluctuating upward trend in overall efficiency, and that the gap in overall technical efficiency primarily originates from scale efficiency rather than pure technical efficiency. The kernel density peak exhibits a “rise–decline–rise” pattern, indicating existing but narrowing efficiency differences among firms. By decomposing efficiency, this study further classifies firms into four types, revealing that inefficiency is heterogeneous. This paper makes three main contributions. First, it identifies scale efficiency as the main source of efficiency gaps. Second, it classifies firms into four types, revealing that inefficiency is heterogeneous. Third, it uses kernel density estimation to track the dynamic evolution of efficiency, showing a narrowing efficiency gap but a persistent superstar effect. Two policy implications follow: firms with low pure technical efficiency should focus on management training and technology adoption, while firms with low scale efficiency should pursue scale expansion through mergers or partnerships.

Mathematics doi: 10.3390/math14091560

Authors: Juan D. Vélez Carlos Cadavid

We study truncation-compatible families F=(Fm)m≥1 over Q[z] through an inverse-limit formalism, and we evaluate them at the punctured cyclotomic cosine points αk,n=cos(2πk/n) with the specialization z=n−1. For symmetric families of uniformly bounded total x-degree ≤d, we prove a stable-range rigidity theorem: for all n≥d+2, the cosine-point evaluation factors through the finitely many punctured cosine power sums P1(n),…,Pd(n). In the purely polynomial case, this implies eventual polynomiality in n. We then extend the framework to include fixed-product factors and package their cosine-point contribution in multiplicative invariants MQ(n). In the stable range, the bounded-degree symmetric part collapses as before; any remaining cyclotomic dependence occurs only through these explicit product terms. Finally, we show that coefficient extraction from such products produces further bounded-degree symmetric families, and we apply this to complete symmetric functions hr evaluated at cosine points.

Mathematics doi: 10.3390/math14091559

Authors: Ji Shi Demetrio Labate

Deep neural networks have been remarkably successful in high-dimensional learning and scientific computing, often succeeding where classical discretization methods fail due to the curse of dimensionality. This efficacy is often explained by their approximation properties combined with the manifold hypothesis: the idea that although data are embedded in dimension D, the effective degrees of freedom are governed by a much smaller intrinsic dimension d≪D. Under this hypothesis, data are concentrated near a low-dimensional manifold that neural networks can approximate efficiently. While the approximation theory for fully-connected ReLU networks on manifolds is well established, a comparable theory for transformer architectures, the dominant model class in modern foundation models, is still emerging. In this paper, we prove a new non-asymptotic, uniform approximation theorem for a class of single-head ReLU-transformers acting on vector inputs, where the approximation error depends only on the intrinsic dimension d rather than on the ambient dimension D. To the best of our knowledge, this is the first transformer approximation result that combines an intrinsic-dimensional rate with an ambient-dimension-independent multiplicative constant. We include a numerical experiment using a circle embedded in ambient dimensions of various sizes, showing that the observed error remains nearly unchanged as D varies, in agreement with the predicted ambient-dimension independence.

Mathematics doi: 10.3390/math14091558

Authors: Zhuo-Heng He Yu-Fei Jiang Mei-Ling Deng Shao-Wen Yu

This paper extends the theory of equivalence canonical forms from quaternion matrices to quaternion tensors under the Einstein product. Motivated by recent results on the simultaneous decomposition of two specific configurations of five quaternion matrices, we establish a comprehensive framework for the corresponding configurations of five quaternion tensors. The core approach leverages bijective transformation maps that establish isomorphisms between quaternion tensor spaces and matrix spaces, allowing us to systematically construct invertible transformation tensors that simultaneously reduce the given tensor quintuples to canonical forms consisting solely of binary entries (0 and 1). A detailed structural analysis of the resulting canonical tensor forms is provided, including explicit dimension formulas for all identity blocks derived from precise rank conditions. To demonstrate practical utility, we integrate the proposed tensor decomposition with the discrete wavelet transform to construct a color video encryption and decryption system. Experimental results confirm perfect reconstruction (PSNR exceeding 300 dB, SSIM equal to 1) and strong security performance: NPCR of 49.8%, UACI of 49.6%, information entropy of 0.9986 bits per pixel, adjacent pixel correlation below 0.03 in absolute value, and a key space exceeding 2512. The developed theory significantly extends the existing literature on quaternion tensor decompositions and provides powerful tools for multidimensional signal processing.

Mathematics doi: 10.3390/math14091556

Authors: Rashad M. EL-Sagheer Mohamed H. El-Menshawy Mahmoud E. Bakr Noha A. Tashkandi Oluwafemi Samson Balogun Mahmoud M. Ramadan

An adaptive progressive first-failure censoring scheme is used to enhance the efficiency of statistical analyses and minimize test time in life-testing experiments. This paper focuses on statistical inferences for the unknown parameters, survival, and hazard rate functions of the Burr XII distribution under this censoring scheme. Since the maximum likelihood estimates for the model parameters and reliability characteristics cannot be obtained explicitly, the Newton–Raphson method is employed for numerical derivation. The delta method is used to determine the variances of reliability characteristics and is applied to construct confidence intervals. Bayesian estimates of the unknown parameters and reliability characteristics are derived under the squared error and linear exponential loss functions. As these estimates are not explicitly obtainable, the Lindley and Markov chain Monte Carlo methods are used as approximation techniques. Additionally, asymptotic confidence intervals and highest posterior density credible intervals are developed for the parameters and reliability characteristics. A Monte Carlo simulation is performed to evaluate the proposed estimators, and the methodology is validated through a real dataset analysis on arthritic patients.

Mathematics doi: 10.3390/math14091557

Authors: Fozaiyah Alhubairah Adem Kiliçman Maryam F. Alshammari Altaf Alshuhail

In this paper, we study the homotopy theory of single intersection graphs arising from acting spaces over topological semigroups. An acting space (S,B) is defined as a topological space B equipped with a continuous action of a topological semigroup S, generalizing the notion of algebraic actions in a topological setting. To connect this structure with graph theory, we associate to each acting space a single intersection graph GSB, whose vertices are proper SB-subacting spaces, and two vertices are adjacent if their intersection is a singleton set. This graph construction encodes both algebraic and topological interactions between subacting spaces and provides a framework to study connectivity and homotopical properties via combinatorial methods. We then work within a categorical framework, where objects are graphical acting semigroups and morphisms are S-acting maps, allowing us to systematically study structural properties and their invariance under morphisms. In this setting, we introduce the notion of acting fibrations and formulate the corresponding lifting problem. Our main result establishes that an S-acting map is an acting fibration if and only if it admits an A-lifting function, providing a characterization analogous to classical fibration theory. Furthermore, we introduce A-regular lifting functions and analyze their role in preserving homotopical structures, including a natural homotopy extension property.

Mathematics doi: 10.3390/math14091555

Authors: Sabit Igissinov Gulmira Nigmetova Talgat Akhazhanov Dauren Matin Manat Shomanbayeva

This paper investigates a class of third-order partial differential equations with an unbounded lower-order coefficient in the Hilbert space L2(R2). The study is motivated by the wide use of third-order equations, particularly of Korteweg–de Vries type, in mathematical physics and wave theory, as well as by the limited development of the corresponding theory in the presence of unbounded coefficients. The main focus is on the existence, uniqueness, and maximal regularity of solutions. Within a functional-analytic framework, the well-posedness of the problem is established in natural function spaces under minimal assumptions on the coefficients. In particular, a priori estimates ensuring maximal regularity are derived.

Mathematics doi: 10.3390/math14091554

Authors: Fernando Rojas Axa Tapia Hilda Espinoza

We develop a design-aware framework that combines penalized prediction and causal inference for finite populations observed through complex survey designs. The framework integrates survey-weighted pseudo-likelihoods, ℓ1-penalized estimation, Neyman-orthogonal moment functions, and a bootstrap procedure that resamples primary sampling units within strata. Methodologically, the contribution is an explicit pipeline that supports design-based inference while separating predictive associations from structurally adjusted effects in high-dimensional, clustered data. We illustrate the framework using data from the Chilean National Health Survey (ENS) 2016–2017 to study the relationship between chronic kidney disease (CKD) and high cardiovascular (CV) risk. In the ENS adult population, the survey-weighted prevalence of CKD was 3.1% (95% CI: 2.4–3.8), and the prevalence of high CV risk was 23.9% (95% CI: 21.5–26.3). High CV risk was markedly more frequent among individuals with CKD than among those without CKD (90.9% versus 21.5%). Predictive and associational analyses combined survey-weighted penalized logistic regression (LASSO) with refitted unpenalized models. In conventional survey-weighted logistic regressions, CKD showed a strong association with high CV risk (odds ratio = 5.66; 95% CI: 2.71–11.82; p<0.001), and effect sizes remained stable after LASSO-based variable selection. To assess causal relevance under confounding and potential endogeneity, we implemented two endogeneity-aware estimators: two-stage residual inclusion (2SRI) and double/debiased machine learning (DML). The DML estimator, defined as the primary causal estimand, reports an orthogonalized estimate of the average treatment effect of CKD on the probability of high CV risk. After adjustment for age and major cardiometabolic comorbidities, the DML estimate was attenuated and statistically non-significant (average treatment effect = −0.094; 95% CI: [−0.409,0.220]). The 2SRI approach yielded unstable estimates with wide confidence intervals, consistent with the limited effective sample size of CKD cases (nCKD≈190 in a sample with n ≈ 6233) and weak identification conditions under low-prevalence settings. Simulation experiments under ENS-like complex sampling suggest that naive predictive associations may overestimate the structural contribution of CKD under confounding, whereas orthogonalized estimators yield more conservative estimates when identification holds. The causal interpretation relies on a conditional mean independence assumption given observed covariates and survey design, while control-function specifications are treated as diagnostic sensitivity analyses due to the absence of credible exclusion-based instruments. Overall, the results demonstrate a fundamental divergence between predictive relevance and causal importance in finite-population settings, underscoring the need for design-aware and endogeneity-robust methods in statistical modeling.

Mathematics doi: 10.3390/math14091553

Authors: Andrea Torrejón-Fontana Luis Silva-Llanca Sonia Montecinos Charles Meneveau

Global reliance on wind energy continues to grow, leading to an increasing number of wind farms implemented in complex topographies. However, there remains a significant research gap on how the terrain’s features affect the wake recovery, especially when the irregularities scale with the wind turbine’s size. This study uses field data and Reynolds-averaged simulations to quantify the influence of topographical features on a wind farm’s wake recovery and power generation. To characterize the terrain surrounding the turbines, this study introduces two parameters—the Downwind Slope and the surface complexity length ζ—which quantify the local average terrain unevenness. The findings demonstrate that turbines in terrains with streamwise positive slopes exhibit faster wake recovery, averaging 6.35D in length (D = turbine diameter), followed by complex-flat terrain (8.7D on average), then descending terrains with the least beneficial wake recovery (9.2D on average). A terrain with a higher surface complexity also improves wake recovery owing to the turbulent entrainment that enhances momentum transport exchange into the wake. Additionally, simulations of the same turbine distribution, but in a completely flat terrain, showed that the complex terrain may lead to lower performance compared to the idealized flat terrain: 11.5% of power generation decrease in our case. The latter highlights the importance of considering topographic effects when planning wind energy projects.

Mathematics doi: 10.3390/math14091552

Authors: Liqun Qi Chunfeng Cui Yi Xu

This paper introduces the concepts of the augmented Zarankiewicz number zA(m,n) and the limited augmented Zarankiewicz number zL(m,n), which are natural combinatorial extensions of the classical Zarankiewicz number. These numbers arise from augmented bipartite graphs that may contain both standard edges (1-edges) and pairs of edges representing squares of binomials (2-edges). The main theoretical result establishes the inequality chain BSR(m,n)≥zA(m,n)≥zL(m,n)≥z(m,n), linking the maximum biquadratic sum-of-squares (SOS) rank to these extremal graph parameters. We determine the exact values of zL(m,n) for the cases (m,2), (3,3), (4,3), and (4,4) and provide new lower bounds for the cases (5,3), (5,4), and (5,5). These results yield improved lower bounds for the maximum SOS rank of biquadratic forms, demonstrating that zL(m,n) can exceed the classical Zarankiewicz number, thereby offering a refined combinatorial perspective on the SOS rank problem.

Mathematics doi: 10.3390/math14091551

Authors: Shuai Li Yaya Yan Yue Yu Qishui Zhong Lanfeng Hua Daixi Liao

In research on electro-hydraulic servo systems, nonlinearity deeply affects dynamic performance, such as the output of hydraulic actuators and the generation of control signals, leading to response hysteresis and control complexity. Moreover, during the control process, changes in the external environment and component loss lead to model parameter distort, which reduces control capability. To address these challenges, this paper conducts a structural transformation on the traditional dynamic surface controller in combination with the fast finite-time stability theorem and proposes a novel finite-time dynamic surface control strategy, which can not only overcome the differential explosion phenomenon in the recursive backstepping iterative process but also enhance the transient dynamic response speed. Furthermore, the neural network adaptive algorithm is adopted to handle the negative dynamic effect caused by parametric uncertainty. The theoretical results are verified by the Lyapunov stability method and numerical simulation.

Mathematics doi: 10.3390/math14091550

Authors: Tom Huang Shu Su Nuttanan Wichitaksorn Kirsten Spencer

In this study, we propose a general mathematical modelling framework based on the characteristics of elite athletes’ movements in the touch rugby matches to investigate the dynamic relationship between physical workload and injury risk over time. Our framework extends the Cox-based model in the context of touch rugby by incorporating a time-scaling component and cluster-specific heterogeneity simultaneously. In addition, we allow for the inclusion of covariates (e.g., velocity variation) to capture their effects. We applied our model to high-frequency wearable sensor data collected from 27 elite athletes (15 men and 12 women). The empirical study results show that our model, time-scaled frailty model (TSFM), demonstrates better goodness-of-fit than traditional frailty and Andersen–Gill models. The results reveal that higher velocity variation, particularly during high-intensity phases, and longer time of continuous exposure to the workload spike state significantly increased overload risk, ultimately resulting in injury. It also highlights the importance of individual differences, even under the same exercise intensity. These insights provide coaches with an evidence-based framework for athlete monitoring, allowing for more personalized training loads, tactical deployment, and injury prevention strategies in elite touch rugby environments.

Mathematics doi: 10.3390/math14091549

Authors: Alexander Robitzsch

Comparison of two or multiple groups based on dichotomous items is a central task in item response theory (IRT) linking. This article considers the two-parameter logistic scaling model under sparse differential item functioning (DIF) in item intercepts and DIF-free item discriminations. Robust-mean-geometric-mean (RMGM) and robust Haberman (RHAB) linking are compared across several loss functions and under scaling models with noninvariant or invariant item discriminations. Two simulation studies show that invariant item discriminations improve the precision of estimated group means. In addition, the L0 loss function is generally preferable to the L1 and L0.5 loss functions when DIF proportions or sample sizes are large. Several empirical examples illustrate the proposed specifications.

Mathematics doi: 10.3390/math14091548

Authors: Na Li Fen Wang

In this paper, we continue to investigate the norm inequality for three real matrices that was recently conjectured by L. László. We establish the validity of the conjecture for the case where n=2 and one of the matrices is normal.