Mathematics doi: 10.3390/math14173211

Authors: Yumei Li Qier Lan Zhe Zhang Huina Zhang Xianbing Cao Xin Wang Shuai Liu

High average-utility itemset mining is a significant research direction in data mining. The traditional average-utility (AU) measure employs itemset length as the normalization benchmark, which mitigates the bias toward long itemsets; however, it does not adequately account for the discrepancies between unit profit and actual sales volume. This paper introduces two novel measures: the weighted average utility based on external utility (E_WAU) and that based on internal utility (I_WAU), and examines the theoretical relationships among AU, E_WAU, and I_WAU. Subsequently, we establish a three-dimensional evaluation framework, namely, “category average–profit conversion–unit profitability”. Based on this framework, we develop classification decision matrices for pairwise comparisons of AU, E_WAU, and I_WAU. Within these matrices, products are grouped according to combinations of any two measures, yielding distinct product classifications that support customized marketing strategies. This approach further underscores the practical value of E_WAU and I_WAU in facilitating real-world decision-making. Finally, we conduct empirical validation and analysis on three real-world datasets. Experimental results demonstrate that, compared with using AU alone, the combined use of E_WAU and I_WAU is more effective in identifying product categories and devising appropriate sales strategies.

Mathematics doi: 10.3390/math14173209

Authors: İbrahim Demir Soley Ersoy Mahpeyker Öztürk

In this paper, we investigate the antiholomorphic counterpart of bicomplex quadratic dynamics by introducing bicomplex Mandelbar sets associated with the three natural involutive conjugations of the bicomplex algebra. For each conjugation †m, m∈{1,2,3}, we study the iteration (Fm)C(η)=(η†m)2+C on BC and define the associated parameter set via the boundedness of the orbit of the origin. Using the idempotent decomposition, we obtain a conjugation-dependent classification of the dynamics: †3 yields the idempotent product of two classical Mandelbar sets, whereas †2 and †1 generate cross-coupled quadratic systems, holomorphic and antiholomorphic in one step, respectively. We further prove that the †1- and †2-dynamics are equivalent up to complex conjugation of an idempotent parameter; consequently, the principal three-dimensional slices of the corresponding Mandelbar sets are congruent, mirror-symmetric copies of one another, although neither possesses this diagonal symmetry individually. We visualize these slices and rigorously establish their reflection symmetries. The results clarify the role of bicomplex conjugations in antiholomorphic dynamics and reveal structural phenomena absent from the holomorphic bicomplex Mandelbrot setting.

Mathematics doi: 10.3390/math14173210

Authors: Zhiyue Gao Xu Yang

Particle swarm optimization (PSO) is a classical metaheuristic algorithm that has been widely used to solve continuous optimization problems. However, it still suffers from inherent drawbacks, such as being prone to premature convergence and an imbalance between exploration and exploitation. To address these problems, a Multi-swarm Collaborative Particle Swarm Optimization with Adaptive Learning Strategy (MCPSO-ALS) is proposed in this paper. Firstly, an Adaptive Population Division Strategy (APDS) is designed to realize effective information interaction among particles. At each iteration, the overall population is dynamically divided and reorganized, based on the fitness values of all the particles. Specifically, particles with high fitness form an elite population focusing on local search; particles with low fitness form a poor population focusing on global search; and ordinary particles form a general population aiming to achieve a balance between exploration and exploitation. Secondly, an Adaptive Learning Mechanism (ALM) is introduced. In this mechanism, particles with different roles adopt distinct updating strategies, which productively guarantees the dynamic equilibrium between exploration and exploitation. To validate the outstanding performance of the proposed algorithm, comprehensive experiments are conducted on CEC2013 and CEC2017. The experimental results demonstrate that the proposed method exhibits significant advantages in convergence speed, solving accuracy, and comprehensive optimization capabilities compared with several state-of-the-art algorithms.

Mathematics doi: 10.3390/math14173208

Authors: David Díaz-León Santiago Lain Diego Garzón-Alvarado Carlos Duque-Daza

Persistent late-time variation can remain in physics-informed neural network (PINN) solutions after the governing transient has effectively decayed, while conventional error norms do not reveal whether this variation has a systematic temporal–frequency structure. This study develops an offline temporal–spectral diagnostic and postprocessing workflow for a one-dimensional advection–diffusion benchmark. A high-accuracy analytical reference and three fixed-resolution finite-difference baselines are used to assess a PINN whose architecture is selected by a fully supervised neural architecture search and whose parameters are trained with progressive temporal windowing. Candidate late-time intervals are selected without using the reference solution by applying the Bayesian information criterion (BIC) to a breakpoint model for the inter-reconstruction sensitivity; the selected field is subsequently reconstructed by retaining a prescribed fraction of its temporal spectral energy and is evaluated independently through reference-error and physics-consistency measures. For [tcut,tmax]=[1.8,5], the zero-frequency component contains 0.9999996 of the raw-field energy, so the q=0.95 reconstruction retains only the temporal mean. This projection reduces the final-time spatial error norm from 2.70×10−3 to 1.06×10−3, a factor of approximately 2.5, while changing the discrete governing-equation residual by less than 0.3% over the filtered window. Mean-removed tests for q=0.90,0.95,0.99 show that the discarded fluctuation is dominated by low-frequency approximation error rather than high-frequency noise. The result supports the proposed selection–validation workflow for this controlled benchmark but does not establish a universally transferable filter.

Mathematics doi: 10.3390/math14173205

Authors: Bozhi Zhang Mingxing Shao Tiancheng Zhang Shenyu Xu

Image aesthetic assessment (IAA) has progressed from handcrafted visual features to deep neural models, yet fine-art evaluation remains difficult because aesthetic judgment depends on style, historical context, and formal composition. Large Vision-Language Models (LVLMs) offer strong multimodal reasoning capabilities, but their direct application to art critique can produce generic descriptions, unstable scores, and weakly interpretable judgments. We therefore propose the Aesthetic Expert Knowledge Injection (AEKI) framework, which translates formal art principles into structured, machine-executable instructions. AEKI operationalizes four dimensions—Contrast & Harmony, Rhythm & Flow, Symmetry & Balance, and Variety & Unity—and assigns style-dependent weights w* across 16 artistic categories. The resulting three-stage pipeline performs style anchoring, expert-weight allocation, and structured instruction compilation before LVLM inference. We evaluate the framework on a multi-category painting collection and a balanced subset annotated by human evaluators. Comparisons with zero-shot LVLM baselines show improved alignment in both numerical scoring and critique professionalism, while ablation experiments clarify the contributions of style anchoring and dynamic weighting. These results indicate that domain knowledge can be incorporated into LVLM evaluation through a transparent rule-based layer, supporting applications in digital curation, computational aesthetics, and art education.

Mathematics doi: 10.3390/math14173207

Authors: Qianxin Xie Jinfeng Xu Yuchen Lu Yuxuan Zhang

Accurate traffic-flow forecasting remains challenged by abrupt and irregular states even after dominant periodic patterns are captured. Existing predictors model the resulting difficult errors implicitly through their parameters and cannot explicitly reuse specific historical errors at inference. We find that multi-horizon base-prediction errors recur conditionally across similar de-cycled node-local states. Based on this observation, we propose De-Cycled Residual Memory with Utility-Gated Retrieval (DeCyReM). It constructs queries from de-cycled residuals, spatial context, and temporal information, retrieves historical base errors from a node-local difficult-and-diverse memory, and uses a utility gate to control their contribution as forecast corrections. Across PeMS03, PeMS04, PeMS07, and PeMS08, DeCyReM records the numerically lowest reported value in seven of the twelve dataset–metric combinations and ranks within the top three in eleven. Ablation and mechanism analyses show that retrieval improves error alignment and mainly benefits difficult samples; similarity alone cannot determine correction utility, whereas gate values track helpful retrievals. Case and robustness analyses further characterize successful correction, safe attenuation, and mismatch-induced failure, identifying reliable key–value correspondence as essential. Overall, DeCyReM converts reusable historical error experience into selective forecast corrections, providing an error-centric approach to forecasting abrupt and irregular traffic states.

Mathematics doi: 10.3390/math14173206

Authors: Jining Wang Gengchen Zhao Lei Wang Han Sun

From the executive risk preference–policy uncertainty interaction perspective, this paper constructs a CA-SHIRD model by leveraging complex network theory and cellular automata, and further analyzes the liquidity risk contagion mechanism and dynamic evolutionary characteristics in the high-carbon manufacturing industry. In summary, this paper yields several key findings: (1) An increase in infection probability intensifies liquidity risk contagion, while a higher transition probability mainly accelerates short-term risk exposure. A higher recovery probability mitigates the contagion process and increases the proportion of recovered enterprises, whereas a higher default probability also weakens contagion but leads to a larger proportion of defaulted enterprises. (2) The liquidity risk contagion threshold in the high-carbon manufacturing industry is positively correlated with policy sensitivity, policy target ambiguity, and policy change frequency; negatively correlated with green preference, long-term orientation, and policy coordination; and exhibits a U-shaped relationship with risk perception and an inverted U-shaped relationship with policy instrument predictability. (3) When policy sensitivity interacts with policy change frequency, it exerts a risk resonance effect; when policy target ambiguity interacts with green preference and long-term orientation, a risk hedging effect is generated; when policy change frequency interacts with green preference and long-term orientation, the risk amplification effect of policy change frequency dominates the risk mitigation effect of green preference and long-term orientation.

Mathematics doi: 10.3390/math14173204

Authors: Tabinda Rasheed Sania Asif Yao Wang

Let G be a finite simple graph, let I(G) denote its edge ideal, and let m be the homogeneous maximal ideal of the corresponding polynomial ring. We introduce the notion of shadow-compatible regular powers: for every p,q≥0 with p+q>0, the mixed ideal mpI(G)q admits a linear-quotient order with a regular decomposition function, and these orders are compatible under the adjacent inclusions mpI(G)q⊆mp+1I(G)q−1,q≥1. For graphs with this property, every such mixed ideal has a (p+2q)-linear resolution. Moreover, for every k≥1 and i≥0, the homological shift ideal HSi(I(G)k), whenever nonzero, is generated in degree 2k+i. For i≥2, this generating-degree statement does not imply a linear resolution in general; by contrast, HS1(I(G)k) has linear quotients and a (2k+1)-linear resolution. We prove that shadow-compatible regular powers are preserved under adjoining a dominating vertex and hence under joins with complete graphs. Finally, we show that every Ferrers edge ideal has this property. Consequently, for every Ferrers graph Fλ and every r≥1, the edge ideal of Fλ*Kr provides a family with linear mixed powers and homological shift ideals generated in the expected degrees.

Mathematics doi: 10.3390/math14173203

Authors: Hleil Alrweili Fatimah A. Almulhim

The availability of auxiliary information has encouraged the development of increasingly efficient estimators for population mean estimation under systematic sampling. Motivated by this, the present study introduces a new family of mean-based estimators by combining power transformations with an exponential adjustment mechanism. The proposed family offers considerable flexibility through different choices of transformation parameters, enabling it to adapt to a variety of population characteristics. Approximate expressions for the bias and mean squared error are derived using first-order approximations, and the unknown constants are determined by minimizing the mean squared error. In addition, theoretical efficiency conditions are established to compare the proposed family with several existing estimators available in the systematic sampling literature. The performance of the proposed estimators is investigated through a systematic sensitivity analysis using three generated populations and three real populations with different characteristics. The findings show that the proposed sub-classes consistently achieve lower mean squared errors and higher percent relative efficiencies than the competing estimators across the parameter combinations considered. Furthermore, the results demonstrate that increasing the value of the exponential adjustment parameter generally improves estimation efficiency, while several sub-classes maintain superior performance under different population settings. Overall, the proposed family provides a flexible and effective approach for improving population mean estimation in systematic sampling.

Mathematics doi: 10.3390/math14173202

Authors: Xiuzhen Li Ruoxi He Yalan Zhang Guodong Shi

(1) Background: Hom-type algebras, proposed by Yau, generalize classical algebras via twisting maps. Dendriform and tridendriform algebras, introduced by Loday and Vallette, decompose associative multiplications and play significant roles in algebraic K-theory and operad theory. Rota–Baxter operators, originating from analysis and probability, have become a vital bridge connecting multiple disciplines. The π-graded structure, a classical tool in algebra, decomposes algebraic objects into direct sums indexed by a monoid π. (2) Methods: We systematically investigate constructive approaches for Rota–Baxter operators on Hom-π-algebras, establish the stepwise structural derivation chain among Hom-tridendriform, Hom-dendriform, and Hom-associative π-algebras, and characterize the equivalence between generalized Rota–Baxter systems and dendriform structures in the Hom-π framework. (3) Results: We present several systematic constructive methods for Rota–Baxter Hom-π-algebras, including Yau twists, iterative endomorphism twisting, centroid element modifications, and monoid tensor lifting. We prove the structural equivalence between Rota–Baxter Hom-π-systems and Hom-dendriform π-algebras, and further extend the study to Hom-quadri-π-algebras with corresponding induction results. (4) Conclusions: The established structural equivalence and derivation relations provide a unified framework for these π-graded Hom-type algebraic structures, covering Rota–Baxter operators and various dendriform-derived algebras.

Mathematics doi: 10.3390/math14173201

Authors: Jeza Allohibi

We study prediction intervals for the semi-functional partial linear model (SFPLM) under stationary, geometrically β-mixing dependence. We analyze a split conformal procedure based on a three way data partition with buffer gaps, a functional principal component projection semi-metric on the functional covariate, profiled least squares estimation of the parametric component, kernel estimation of the nonparametric component and of the conditional standard deviation, and a studentized absolute residual score. Marginal validity of split conformal prediction with a trained score under β-mixing is available from generic results of Oliveira et al. and of Barber and Pananjady, without any buffer and without accuracy requirements on the fitted estimators. Our main result is complementary to those guarantees: a finite sample marginal lower coverage bound whose theoretical finite-sample coverage penalty decomposes additively into seven interpretable components expressed in the structural primitives of the SFPLM, quantifying the price of replacing the ideal SFPLM score by the estimated score inside the proof. The penalty plays no role in the computation of the interval, involves unknown structural constants, and is not an operational correction. The bound requires no parametric error model, but it is not assumption free; it holds under explicit structural conditions, including geometric β-mixing, conditionally centered sub-Gaussian errors, a fractal small ball regime for the projected functional covariate, and local regularity of the score distribution. Simulations under a protocol frozen before outcome computation, spanning mild and strong dependence, a misspecification stress test, and a dependent-score design with exactly quantified score autocorrelation, show near nominal coverage for all methods, with the gapped and contiguous variants statistically indistinguishable in coverage. Studentization showed no systematic coverage advantage, while interval-length differences were systematic. The value of the analysis lies in the explicit model-specific estimation layer of the coverage decomposition, not in a numerical gain over naive split conformal.

Mathematics doi: 10.3390/math14173200

Authors: Junchao Zhou Fang Xu Min Deng

Plateaued Boolean functions play an important role in sequence design and cryptography due to their favorable properties such as high nonlinearity, resilience and low additive autocorrelation. In this paper, by modifying the support of certain quadratic functions, we propose a generic construction of plateaued Boolean functions. Additionally, we analyze the algebraic normal form of the newly constructed functions. As applications of the proposed construction, we obtain infinite families of near-bent and semi-bent functions.

Mathematics doi: 10.3390/math14173199

Authors: Daya K. Nagar Edwin Zarrazola Santiago Echeverri-Valencia

In this article, we propose a new bivariate generalization of the inverted Topp–Leone distribution. First, we express its joint cumulative distribution and survival functions in series forms using special functions, which yields the bivariate hazard rate, reversed hazard rate, and the exact distributions of min{X,Y}. We then establish several essential properties, such as marginal and conditional distributions, joint moments, entropy, and the Fisher information matrix. After proving that the distribution exhibits positive likelihood ratio dependence, we derive the exact distributions for the transformations X+Y, X/(X+Y), and XY when X and Y follow an inverted bivariate Topp–Leone distribution. Finally, we round out the statistical framework by presenting parameter estimation techniques, a simulation study, and Bayesian inference.

Mathematics doi: 10.3390/math14173198

Authors: Jingwen Chen Xianyi Li

This paper investigates the local dynamics of a discrete predator–prey system incorporating an Allee effect and a Holling-IV functional response. After nondimensionalization, a positivity-preserving discrete model is obtained by the semi-discretization method. The non-negative fixed points are classified and their local stability is established. The center manifold theorem and local bifurcation theory are then used to prove two transcritical bifurcations at the boundary fixed points E1 and E2 and a saddle-node bifurcation at the positive critical fixed point E*. Numerical equilibrium branch diagrams and phase portraits illustrate these local results. The possible Neimark–Sacker bifurcation at E3 and flip bifurcation at E4 are beyond the present scope of this study.

Mathematics doi: 10.3390/math14173197

Authors: Plamen Stanchev Nikolay Hinov Polya Gocheva Valeri Gochev

Bidirectional DC–DC converters are key interfaces in battery energy storage systems, electric vehicles, fuel cell vehicles, and DC microgrids, where transparent mathematical models are required for simulation, controller evaluation, and energy-flow analysis. This paper presents a hybrid index matrix framework for the Python-based modeling of a bidirectional buck–boost converter coupled to a first-order Thevenin battery model. In contrast to a classical state-space formulation, the index matrix is used as a label-aware model-assembly layer: component equations are aligned by explicit row and column identifiers and subsequently projected into ordered numerical matrices for solution. Charging, idle, and discharging equations are solved using a fixed-step backward-Euler procedure, and a PI current controller with duty-cycle saturation and anti-windup regulates the power-flow direction. A conventional switched ODE implementation is retained only as a software-level numerical-consistency check between two implementations of the same assumptions; it is not presented as experimental validation or as an independent physical benchmark. For the reported 60 s current profile, the model gives a current RMSE of 0.0863 A and a peak current of 4.3684 A, corresponding to 9.2094% overshoot at the idle-to-discharge transition. The power-integration balance is 1.6091 Wh input, 1.5868 Wh output, and 0.0223 Wh estimated loss under the adopted conduction-oriented loss model. The conditional one-step sensitivity matrices have a spectral radius of 1.00000 in all three modes; the unit eigenvalue is consistent with the slowly varying SOC state, while the remaining electrical eigenvalues lie inside the unit circle. These eigenvalue results are interpreted as local non-divergence diagnostics rather than proof of asymptotic closed-loop or switched-system stability. The framework provides a transparent and reproducible numerical workflow, while experimental validation, detailed switching-level loss modeling, step-size convergence, and formal closed-loop/switched-system stability analysis remain necessary future work.

Mathematics doi: 10.3390/math14173193

Authors: Mahammad Khuddush Saleh S. Almuthaybiri

In this paper, we study the existence of positive solutions for a nonlinear fifth-order boundary value problem arising from fully developed couple-stress fluid flow through a porous channel. Under a natural restriction relating the couple-stress and permeability parameters, the associated linear operator factorizes into two positive second-order operators; we construct the corresponding Green function, show that it is strictly positive, and obtain it in an explicit closed form. By reformulating the problem as a completely continuous operator on a cone in C[0,1] and applying Krasnosel’skiĭ’s fixed point theorem of cone compression–expansion type, sufficient conditions for the existence of positive solutions are established in terms of the load parameter. The positivity of the velocity further yields a strictly positive cumulative-flow solution on (0,1]. Several examples and a numerically calibrated application are given to illustrate the main results.

Mathematics doi: 10.3390/math14173196

Authors: Guangzong Ding Erpeng Wang Yun Zhang Linxiao Ma

To investigate the marketing cooperation and decision equilibrium mechanism of a dual-channel supply chain under the premium effect of animal welfare labels, this paper constructs a dual-channel supply chain model consisting of one manufacturer and one retailer. The manufacturer invests in animal welfare and adopts animal welfare certification labels to obtain product premiums, and the retailer implements local advertising campaigns to boost offline market demand. Within this framework, we study equilibrium outcomes under two decentralized decision modes, including the Nash non-cooperative game and the Stackelberg leader–follower game, as well as the centralized decision mode corresponding to the fully cooperative game. We compare the optimal advertising investment, animal welfare investment and supply chain members’ profits in different scenarios. The findings indicate that the manufacturer offers no advertising cost-sharing under the Nash non-cooperative equilibrium. Under the Stackelberg leader–follower game, the manufacturer is willing to cover part of the retailer’s advertising cost if the manufacturer’s marginal profit ρ1 satisfies 2ρ1 > ρ2, and both firms achieve higher profits than those under the Nash equilibrium. When  2ρ1 ≤ ρ2, the optimal sharing ratio equals zero, and the Stackelberg equilibrium degenerates into the Nash equilibrium. The total supply chain profit under centralized decision-making is consistently higher than that under the two decentralized decision modes. Serving as a theoretical benchmark, centralized decision-making reveals the boundary of efficiency loss arising from decentralized decisions. Numerical simulations further validate the above findings and uncover how the advertising cost-sharing ratio and channel preference influence the profits of all participants.

Mathematics doi: 10.3390/math14173195

Authors: Fátima Ferreira António Pacheco Helena Ribeiro

We derive the joint probability-generating function of the number of customers served and the number of customers lost in busy periods of MX/M/1/n queueing systems with balking. Capitalizing on the Markov-regenerative nature of these systems, we propose an efficient recursive procedure to compute this joint distribution. The model incorporates customer impatience, where the admission of customers is modulated by the number of customers in the system at arrival instants. Specifically, customers arriving in batches that find a place in the system may opt to join or balk, depending on the number of customers already in the system. The performance analysis of such systems is an important issue for business management, as customer impatience may result in the loss of potential customers, thus reducing the number of served customers. In addition, we perform a sensitivity analysis of the corresponding joint probability function of the numbers of customers served and lost in busy periods and other performance measures, considering both partial and total customer batch blocking policies, across various batch size distributions and balking probability profiles.

Mathematics doi: 10.3390/math14173194

Authors: Yang Kyu Lim Hyeon Gyu Kim

The F1 score depends on the positive-class prevalence (π), which complicates comparisons across datasets. Our previous work proposed F1* as an equal-weight composite of F1 and accuracy and derived auxiliary estimation functions. The present study evaluates that previously defined index using 12 text datasets and four models under RepeatedKFold with five folds and five repeats (25 held-out cross-validation evaluations per dataset–model pair). All 1200 runs used identical persisted splits across models, fold-local recurrent preprocessing, and raw-prediction audit. Mean F1 values across datasets were 0.9571 for BERT, 0.9263 for LSTM, 0.9244 for GRU, and 0.9235 for RNN. Mean absolute differences for the auxiliary reconstructions were 0.0012 for F1 and 0.0012 for accuracy. The evaluation also includes MCC, a controlled-prevalence analysis, and an evaluation-sample-size sensitivity analysis using fixed out-of-fold (OOF) predictions from all four models. The evidence remains bounded to binary text datasets and does not establish universal metric superiority.

Mathematics doi: 10.3390/math14173192

Authors: Guadalupe Eunice Campirán García

Efron’s double bootstrap and hierarchical Bayesian nonparametric methods have largely developed along separate paths. This paper connects them and uses that connection to motivate a new resampling procedure. We show that a suitable two-level Dirichlet construction, with base measures matched to the data, can approach the classical double bootstrap when its concentration parameters become large, while the hierarchical Dirichlet process of Teh et al. does not share this limit. This distinction identifies the double bootstrap as the endpoint of a construction of hierarchical Dirichlet type—though not of the hierarchical Dirichlet process itself—and as the boundary of a broader family of two-level resampling methods. Moving away from that boundary leads to the Informative Bayesian Double Bootstrap (IBDB). The method introduces prior information at the first stage while keeping the second stage focused on calibration, as in the classical double bootstrap. We also establish finite-concentration bounds describing how the proposed construction differs from its classical counterpart and when it can move beyond the support of the observed data. In simulations against four competing methods, the IBDB performs best for tail-sensitive quantities and heavy-tailed settings, while it tends to over-cover simple location parameters. Similar patterns appear in the Danish fire-insurance and Siemens equity-loss examples. Its main advantage is improved calibration through interval repositioning rather than simply wider intervals. The gains are most relevant when sample information is limited.

Mathematics doi: 10.3390/math14173191

Authors: Abdul Mateen Wali Haider Mehrun Nisa Ghada AlNemer

This study presents new Boole-type integral inequalities for convex functions within the framework of quantum calculus. First, a quantum integral identity involving the left and right q-integral operators is established and subsequently used to derive several Boole-type inequalities under suitable convexity assumptions. Numerical examples, together with graphical representations, are provided to illustrate the theoretical results and to verify the derived bounds for different parameter values. This work broadens the understanding of quantum mechanics and mathematical inequalities, encouraging further research in this area.

Mathematics doi: 10.3390/math14173189

Authors: Xiaotong Ma Wei Li

Matrix differential equations with time delay are crucial to the modeling of complex multivariate systems. However, the existing semi-analytic Laplace residual power series method (LRPSM) literature mainly focuses on scalar or no-delay problems, and lacks rigorous theoretical guarantees for matrix-valued time delay systems. This study systematically generalizes LRPSM to the linear time-delay matrix differential equation X′(t)=AX(t)+BX(t−τ)+F(t) , where X(t)∈Rn×n, A and B are constant matrices, τ>0 is a constant delay, and the forcing term F(t) and the history function Φ(t) are analytic. The method of steps is employed to construct the solution piecewise: on each local interval, the solution is expanded asymptotically in the Laplace domain, and the coefficients are determined recursively via the Laplace residual function. We establish local error bounds on the initial interval and derive a global error propagation bound across successive delay interfaces using a variation-of-constants framework. Numerical experiments, including non-diagonal matrices, non-zero history functions, and multi-interval tests, illustrate the effectiveness of the approach. The proposed method reduces exactly to the standard LRPSM for scalar cases, demonstrating its validity as a natural and rigorous generalization of the existing semi-analytical framework.

Mathematics doi: 10.3390/math14173190

Authors: Wenbo Zhang Xinyi He Yueting Gao Jiajie Cao

Comparing metro-station service at national scale is hindered by the scarcity of consistent ridership or mobile-phone data across cities. We propose MetroVFE, a topology-based framework for diagnosing metro-station structural service potential. It combines three coupled subsystems—vitality (network centrality, transfer capacity, and feeder-bus connectivity), function (route-type diversity, destination reachability, directional coverage, and operator diversity), and spatial coverage equity (station-spacing uniformity). All indicators are derived from publicly available transit-network topology. Each subsystem is aggregated by entropy weighting, and the three are combined through a coupling coordination degree (CCD) model that penalizes unbalanced development. We instantiate the framework on the CPTOND-2025 national bus–metro vector dataset, computing indicators for 7057 unique metro stations in 45 Chinese cities, with 42,796 feeder bus routes spatially joined to 500 m station catchments. The empirical analysis yields four main findings: (i) Coupling coordination is moderate and has positive skew: the mean station CCD is 0.46, with 58.5% of stations in antagonistic or transitional bands and only 1.5% highly coordinated. (ii) vitality is the dominant lagging subsystem (66.4% of stations), and this share rises monotonically from large to small networks (63.7%→69.3%→78.2%). (iii) Unsupervised clustering recovers five interpretable diagnostic typologies, dominated by vitality-deficient (48.3%) and function-developing (24.8%) stations, with only 12.3%balanced–coordinated. (iv) Spatial coverage equity modestly moderates the function→vitality relationship (interaction p=1×10−4, robust to controls): the marginal contribution of functional diversity to vitality is about 25% larger in high-coverage-equity than low-coverage-equity station areas (0.207 vs. 0.165). Mean coordination does not differ significantly across network-size tiers (ANOVA p=0.12), but typology composition does (χ2p<10−58). Ablation and sensitivity analyses confirm that the coordination feature and the full V-F-E feature set are necessary for stable typologies. MetroVFE is fully reproducible from open data and provides an actionable, mathematically grounded tool for prioritizing station-level interventions.

Mathematics doi: 10.3390/math14173188

Authors: A. Nihal Tuncer Ayça Cemile Akgün

In this study, the concept of Riesz summability for interval-valued series is introduced, and the corresponding interval-valued Riesz-summable series space RIcs is constructed. In contrast to the sequence setting, Riesz summability of an interval-valued series is defined by applying the Riesz transformation to its sequence of partial sums. A metric based on the Hausdorff metric is defined on RIcs, and the resulting metric space is proved to be complete. It is also shown that every convergent interval-valued series is Riesz-summable to the same interval and that the inclusion of the convergent series space in RIcs is proper. Furthermore, RIcs is proved to be a quasilinear space and, when equipped with an appropriate norm, a normed quasilinear space. The metric associated with this norm is shown to coincide with the previously defined metric. In addition, the solid-floored property of RIcs is established. These results provide a systematic theoretical framework for the metric, algebraic, topological, and order-related analysis of interval-valued Riesz-summable series and contribute to the further development of summability theory in interval-valued settings.

Mathematics doi: 10.3390/math14173187

Authors: Lateef Ahmad Wani Francesco Aldo Costabile Saiful R. Mondal Shahid Ahmad Wani

In this paper, we introduce and systematically study a new two-parameter family of affine (q,η)-Gould–Hopper-based Appell polynomials. These polynomials arise by fusing the affine (q,η)-exponential Gould–Hopper kernel with an invertible Appell multiplier. A central contribution is the affine quasi-monomial construction: an explicit raising operator obtained from a logarithmic-difference quotient of the combined kernel, together with the lowering operator and the resulting q-commutation structure. An explicit double-sum series representation and an affine diffusion equation of order j connecting differences in the two variables, and the full quasi-monomial framework identifying the operator pair (Pq,η+,Pq,η−) are developed. Additional results include a governing difference equation, a converse characterisation, a determinantal representation, an affine addition formula, and an order recursion. Further, the Bernoulli and Euler sub-families are obtained as invertible specialisations, while the Genocchi family is treated separately as a derived noninvertible family through its exact relation with the Euler family. The corresponding structural results are stated with these hypotheses made explicit. Surface plots, numerical value tables, and a numerical illustration of real zeros accompany the theoretical development. The diffusion relation provides a discrete affine analogue of a higher-order evolution equation; no claim of a fully developed physical model is made in the present work.

Mathematics doi: 10.3390/math14173186

Authors: Ishtiaq Ali

This paper investigates a distributed-order fractional SEIRS epidemic model with temporary immunity, vaccination, disease-induced mortality, and density-dependent natural mortality. The distributed-order formulation provides a flexible framework for incorporating heterogeneous memory effects into epidemic dynamics. The basic reproduction number is derived, the disease-free and endemic equilibria are characterized, and their local stability properties are investigated through the distributed-order characteristic equation. In addition, a sufficient global disease extinction criterion is established using a distributed-order Lyapunov argument, yielding global asymptotic stability of the disease-free equilibrium under an explicit transmission bound. Numerical spectral analysis shows that no oscillatory stability transition occurs within the considered parameter ranges and that the endemic equilibrium remains asymptotically stable within these ranges. Numerical simulations examine the effects of the memory interval and memory density shape on epidemic transients. Broadening the memory interval toward lower fractional orders slows convergence and increases transient persistence. For a fixed memory interval, densities concentrated near lower fractional orders produce the slowest relaxation, whereas those concentrated near higher orders, closer to the classical first-order limit, yield the fastest decay. These results show that distributed-order memory primarily regulates transient epidemic dynamics while preserving endemic equilibrium stability within the investigated parameter regimes, providing new insight into heterogeneous memory effects in fractional epidemic models.

Mathematics doi: 10.3390/math14173185

Authors: Pengwei Zhu Shengjie Chen

This paper studies candidate intermediary node deployment for influence diffusion under the linear threshold model (LTM). Given fixed diffusion sources, target nodes, and a budget, the decision maker selects candidate intermediary nodes to maximize the expected total weight of activated targets. Once deployed, a candidate node enables its associated potential arcs whose other endpoints belong to the effective network. Using the LTM live-arc representation, we establish distributional equivalence between sampling on the potential graph and then restricting each scenario to the deployed induced network, and sampling directly on the deployed network. This leads to a finite-scenario sample-average approximation (SAA) mixed-integer formulation based on canonical live paths; the resulting deployment objective is monotone and supermodular but is generally not submodular, so the classical greedy-approximation guarantee for monotone submodular maximization does not apply in general. Since the compact SAA formulation contains many scenario–target variables and covering constraints, solving the formulation directly can be computationally demanding. We therefore propose a scenario-decomposed branch-and-Benders-cut algorithm that solves the finite-scenario SAA model to optimality. Each scenario subproblem is separable by target and has a closed-form dual optimum, so Benders cuts are separated by scanning required-node sets rather than solving linear programs inside callbacks. On five real networks and 225 SAA instances, the algorithm solves all instances within one hour, averaging 27.46 s; the compact SAA formulation solves 172 instances, with an average capped time of 1444.11 s.

Mathematics doi: 10.3390/math14173184

Authors: Li Chen Ran Gao Yun Wang Jinman He

In this paper, an efficient numerical method is presented for solving the generalized time-fractional Boussinesq equation. The Caputo fractional derivative is approximated by the L1 formula and the space is discretized by using the Fourier spectral method. The a priori estimates, solvability and convergence of the numerical scheme are rigorously established. The presented numerical results demonstrate the effectiveness of the Fourier spectral method.

Mathematics doi: 10.3390/math14173183

Authors: Haifa Bin Jebreen

In this work, we introduce an efficient spectral Galerkin method for solving one-dimensional time-fractional reaction–subdiffusion equations. Traditional fractional operators often pose severe computational challenges and exhibit weak singularities near the initial time. To address these issues, we analytically transform the governing differential equation into a weakly singular Volterra integral equation. The numerical solution is then constructed in a two-dimensional tensor-product space using orthogonal Legendre cardinal functions on both Gauss and Gauss–Lobatto grids. A major computational advantage of this cardinal basis is that it eliminates the need for expensive numerical quadratures when assembling the operational matrices. From a theoretical view, we establish a rigorous a priori error bound and a fully computable a posteriori error estimator based on the residual. The analysis confirms that the convergence rate is governed algebraically by the Sobolev regularity of the exact solution, naturally accelerating to exponential (spectral) convergence for sufficiently smooth profiles. Extensive numerical experiments validate these theoretical claims, demonstrating that the proposed framework offers significant improvements in accuracy and efficiency.

Mathematics doi: 10.3390/math14173182

Authors: Slim Dhahri Sultan M. Alzahrani Hafedh Rguigui Omar Naifar Abdellatif Ben Makhlouf

We study the asymptotic behavior of multi-order fractional cooperative systems in which each component carries a Caputo tempered fractional derivative of its own order αi∈(0,1) with a common tempering parameter λ≥0. For cooperative vector fields that are homogeneous of degree p≥1 and admit a vector v≻0 with f(v)≺0, we prove that every solution starting in the nonnegative orthant is global, remains nonnegative, and satisfies 0≤Φi(t,ω)≤∥ω∥vvie−λt; for λ>0, this expresses decay at the rate of the free tempered evolution, that is, of the profile w0e−λt obtained when the tempered derivative vanishes identically, while for λ=0, it reduces to the known invariant-norm bound. When p=1, the estimate is sharpened to the tempered Mittag–Leffler rate e−λtEα̲(−ηtα̲), where α̲ is the smallest order. When p>1 and the tempering is strictly positive, λ>0, we derive the first-order asymptotic expansion eλtΦi(t,ω)=ωi+Ci(ω)tαi−1+o(tαi−1), in which Ci(ω) is given by an explicit convergent integral; hence, every component with positive initial value attains both the exact exponent and the exact amplitude of the free tempered profile, and a two-sided envelope for a scalar model problem, valid under an explicit smallness condition on the initial datum, makes this optimality quantitative for all times. As an application, we prove extinction at a tempered Mittag–Leffler rate for a class of tempered fractional Kolmogorov systems with net mortality. Numerical experiments with a predictor–corrector scheme support the theoretical findings.

Mathematics doi: 10.3390/math14173181

Authors: Jae-Hyeong Bae Won-Gil Park

In this paper, we characterize the general solution to a system of functional equations with respect to the multi-quadratic mappings by proving that any such mapping can be uniquely represented via a 2n-additive pairwise symmetric mapping. And we prove the stability results with respect to multi-quadratic mappings in two different algebraic settings.

Mathematics doi: 10.3390/math14173180

Authors: Lijun Liu Fei Ren Jiahao Liu Zuhua Jiang Guobin Pei

Shipbuilding task packages are commonly defined from professional experience, which can produce heterogeneous work content within packages, dense coordination interfaces across packages, and uneven labor-time allocation. This study formulates task-package partitioning as a multi-objective combinatorial optimization problem with multi-dimensional engineering features and labor-time constraints. Four features of ship intermediate products—construction stage, structural type, spatial area, and functional system—are used to construct a model that increases intra-package cohesion, reduces inter-package coupling, and improves workload balance. A collaborative method combines genetic-algorithm global search with budget-constrained branch-and-bound refinement of boundary tasks. In a case containing 68 construction tasks from an 11,000 DWT bulk carrier, GA-B&B achieved a mean composite evaluation of 0.8403 over five independent runs, improvements of 18.9%, 3.4%, and 3.0% over a manual-rule baseline, pure GA, and NSGA-II, respectively. Its hypervolume was 0.6% higher than that of NSGA-II, while the number of nondominated solutions was reduced by 97.1%. The method improved partition quality and reduced the number of candidate schemes requiring engineering review, although local refinement increased computational cost. It therefore provides quantitative support for task release, crew organization, and labor-time allocation.

Mathematics doi: 10.3390/math14173179

Authors: Linhai Wei Liangliang Miao Yijun Hu

In this paper, by proposing a new risk measure called CoRVaR, we explore the risk spillover effect within a financial system consisting of the banking, security and insurance industries. To be precise, we examine the risk spillover effect from each industry to the other. Moreover, we also examine the risk spillover effect from each industry to the system. The dependence structure between industries is modeled using the vine copula. By employing the Monte Carlo simulation technique, an empirical study via data from Chinese financial markets is implemented. Finally, backtesting and comparisons with existing results are also performed. It turns out that the proposed risk measure can well quantify the risk spillover effect. In addition, the copula employed can also well reveal the interdependence structure of the financial system.

Mathematics doi: 10.3390/math14173178

Authors: Abdul Karim Marco Carratù In cheol Jeong

Reliable finite-horizon forecasting of chaotic dynamics is challenging because small approximation errors grow rapidly during recursive prediction. This study presents a controlled comparison of data-driven and physics-regularized forecasting methods for the Lorenz and Rössler systems. The proposed Hybrid Physics-Informed Feedforward Neural Network (Hybrid PI-FNN) learns a discrete state-transition map from a ten-state observation window through a five-step recursive rollout. Unlike conventional continuous-coordinate physics-informed neural networks, physical consistency is imposed using fourth-order Runge–Kutta transition targets derived from the known governing equations. The physics weight is selected using chronological recursive validation and evaluated against an architecturally identical multi-step FNN with λ=0. Conventional FNN, LSTM, Echo State Network (ESN), Autoregressive AR(10), and Dynamic Mode Decomposition baselines are also evaluated using untouched test trajectories. For the 1000-step Lorenz test rollout, the ESN achieved the lowest mean squared error (MSE) of 0.1701, followed by the LSTM with 22.9962. The Hybrid PI-FNN produced an MSE of 95.8157, compared with 87.9260 for its λ=0 ablation; therefore, physics regularization did not improve Lorenz test MSE, although their forecast horizons at a 10% normalized-error threshold were similar (273 and 272 steps, respectively). For the Rössler system, the Hybrid PI-FNN reduced recursive MSE from 0.2202 for the λ=0 ablation to 0.0834, corresponding to a 62.11% reduction, while both models completed the maximum evaluated 1000-step forecast horizon. Nevertheless, the ESN again achieved the lowest Rössler MSE of approximately 8.04×10−5. Finite-horizon correlation-dimension analysis, exact governing-equation Lyapunov spectra, computational-cost comparisons, and five-seed paired experiments were additionally conducted. The exact spectra confirmed one positive, one approximately neutral, and one negative exponent for each system, indicating chaotic but not hyperchaotic behavior. The paired multi-seed analysis did not establish a statistically significant forecasting advantage from physics regularization. These findings show that higher-order physics consistency can benefit particular systems and configurations, but it does not guarantee universal superiority in recursive chaotic forecasting.

Mathematics doi: 10.3390/math14173177

Authors: Mousa J. Huntul Yashar T. Mehraliyev Muhammad K. Iqbal

This work is concerned with an inverse problem for the second-order hyperbolic PDE, in which extra data are imposed. The time-varying coefficient is not known a priori. We begin by introducing the notion of a classical solution for the problem at hand. The primary aim is to recover both the solution θ(κ,τ) and the unknown coefficient s(τ). To analyze the well-posedness of the problem, we introduce an auxiliary inverse formulation. We establish its parity with the primary one in an appropriate sense. Employing the Fourier method, we prove that the auxiliary problem admits a unique solution. This equivalence then allows us to establish uniqueness and existence for the classical solution of the original inverse problem. The numerical solution of the inverse problem is obtained using a CB-spline method in conjunction with Tikhonov regularization. The CB-spline approach reduces the PDE to a system of ODEs, discretized in time by a Crank–Nicolson scheme. The regularization stabilizes the ill-posed reconstruction. Numerical experiments with two test problems, one smooth and one non-smooth in s(τ), confirm the accuracy and stability of the suggested procedure. These results are cross-validated against an independently implemented finite-difference discretization. The unconditional stability and second-order convergence of the numerical method are both established theoretically and confirmed numerically.

Mathematics doi: 10.3390/math14173176

Authors: Youn Su Kim In Hong Chang Kwang Yoon Song

Many software systems currently under development exhibit numerous new types of failure due to their structural complexity. This suggests the need for research on structures capable of representing convex patterns in the fault-detection rate over time. This paper proposes a non-homogeneous Poisson process (NHPP) software reliability model (SRM) incorporating a convex fault-detection rate. To validate this, we compared 13 SRMs with different forms using three datasets to evaluate the effectiveness and applicability of the proposed model. Furthermore, the performance of the proposed model was evaluated through comparisons with multiple models, and a deep-learning-based parameter estimation (DL-BPE) was introduced as an alternative estimation framework. The proposed DL-BPE provides a competitive and flexible parameter estimation framework, showing improved predictive performance in several datasets while preserving the structural interpretability of the proposed NHPP SRM. Based on the results, we propose new assumptions for enhancing the reliability of increasingly complex software packages. The DL-BPE framework may provide a basis for integrating interpretable reliability-model structures into deep-learning architectures for software reliability analysis.

Mathematics doi: 10.3390/math14173175

Authors: Yoshiyuki Kitaoka

Let f(x) be a monic integral polynomial of degree n and p a prime number for which f(x) is the fully decomposable modulo p. Let integers r1,…,rn be the roots of f(x)modp with 0≤r1≤⋯≤rn<p. In this series of papers, we have investigated the distribution of the points (r1,…,rn). In the present paper, we present several conjectures concerning the distribution of polynomials in the roots ri.

Mathematics doi: 10.3390/math14173174

Authors: Suha Wazzan

In previous work, Wazzan, together with Gilbert, established a connection between the λ-Zappa–Szép product of bands and groups and Billhardt’s λ-semidirect product of inverse semigroups using automata-theoretic methods. Motivated by the need for a structural and transparent interpretation of this correspondence, we present an alternative proof based on the Ehresmann–Schein–Nambooripad theorem. The approach reformulates the construction through the associated inductive groupoid and makes the matched-pair actions explicit, so that the interaction between the band component and the group component can be followed directly at the level of arrows, identities, and composition. Within this framework, several structural features of the resulting product are clarified, including regularity, idempotents, inverse-type behavior, orthodoxness, L-unipotence, and the connection with semidirect products. The paper also consolidates related intermediate results into a unified proof route and illustrates the construction by examples and schematic figures. This groupoid-based viewpoint provides a conceptually motivated treatment of the λ-Zappa–Szép product and highlights its role as a bridge between matched-pair decompositions, bands and groups, and inverse semigroup theory.

Mathematics doi: 10.3390/math14173173

Authors: Omid Nikan Mehdi Alaeiyan Suhad Yousef

The time-fractional Black–Scholes model (TFBSM) is used to describe option price dynamics within a fractional diffusion model. It provides a mathematical model for valuing European and American call and put options on non-dividend-paying stocks. In this paper, the TFBSM is solved numerically for European and American option pricing using a local meshless interpolation approach. The time-fractional derivative is approximated by a finite difference scheme with accuracy of order 2−α for 0<α<1, while the spatial derivatives are discretized using the local radial point interpolation method (LRPIM). Theoretical analysis establishes the unconditional stability and convergence of the time-semi-discrete scheme in the L2 norm. Numerical examples are presented to confirm the theoretical results and demonstrate the accuracy and performance of the proposed method for fractional option pricing problems.

Mathematics doi: 10.3390/math14173172

Authors: Snezhana Gocheva-Ilieva

Interest in statistical modeling of complex systems and large-scale phenomena using data about them continues to actively excite the scientific community [...]

Mathematics doi: 10.3390/math14173171

Authors: Yiqing Zhang Zimo Chen

Against the background of increasing styling convergence in the new energy vehicle (NEV) market, rear-end styling has gradually become a key visual interface for communicating brand identity, shaping product differentiation, and eliciting users’ Kansei cognition. However, existing Kansei design studies on automotive styling have mainly focused on whole-vehicle forms or front-face morphology, while systematic modeling methods for local rear-end styling remain limited. Under small-sample conditions, the nonlinear mapping between the Kansei semantic space and styling parameters also faces the risk of overfitting. To address these issues, this study proposes a data-driven Kansei Engineering (KE) framework integrating non-negative matrix factorization (NMF), grey relational analysis (GRA), and deep feedforward neural network (DFNN), aiming to achieve a continuous translation from Kansei need identification to parametric scheme generation for rear-end styling. First, the original seven-dimensional Kansei evaluations were aggregated into three latent Kansei dimensions through the non-negative low-rank decomposition of NMF. Second, GRA was used to screen key morphological features and reduce modeling complexity at the feature level. Third, DFNN and random forest (RF) were constructed as prediction models, and DFNN showed better average test RMSE and R2 than RF. Finally, the optimal codes predicted by the DFNN were transformed into design schemes constrained by morphological coding, and their consistency in expressing the target Kansei images was verified, thereby establishing an engineering constraint-oriented and interpretable decoding pathway distinct from free-association-based Kansei design. The ablation experiment indicates that the performance advantage of the proposed framework does not arise solely from DFNN, but from the mathematical coupling among NMF-based semantic aggregation, GRA-based feature screening, and DFNN-based nonlinear mapping. This framework reformulates Kansei design as a hierarchical decomposition and modeling process, establishing a data-driven decision-support tool jointly driven by mathematical algorithms and artificial intelligence for NEV rear-end styling design.

Mathematics doi: 10.3390/math14173170

Authors: Qihui Hu Aoxue Sun Huijuan Wang

Mean curvature flow (MCF) is an effective tool for investigating the geometry and topology of submanifolds under suitable curvature pinching conditions. While most existing convergence results in complex projective spaces rely on pointwise curvature assumptions, much less is known about the case of integral curvature constraints. In this paper, we consider the MCF of smooth closed submanifolds of small codimension immersed in CPn+k2. We establish our main theorem under an explicit integral curvature pinching condition: the Lp-norm of the second fundamental form of the initial submanifold is bounded above by a small constant depending only on the dimension and the exponent p. The proofs are based on evolution equations for geometric quantities, Sobolev inequalities, and Moser iteration, which together yield uniform curvature estimates and preserve the required integral pinching condition along the flow. These estimates allow us to reduce the problem to previously established convergence criteria under pointwise curvature pinching conditions. Consequently, the MCF either shrinks to a round point in finite time or converges smoothly to a totally geodesic submanifold as t→∞. As a consequence, we obtain a differentiable sphere theorem: any such submanifold satisfying the same integral curvature pinching condition is diffeomorphic to either the standard sphere Sn or the complex projective space CPn2.

Mathematics doi: 10.3390/math14173169

Authors: Saira Batool Muhammad Imran Brett McKinney

This study develops and analyzes a nonlinear tumor–immune–chemotherapy model to investigate how chemotherapy influences tumor suppression in the presence of heterogeneous tumor subpopulations and immune responses. The model incorporates two tumor cell populations with different immunogenic characteristics, innate and adaptive immune responses, and a dynamic chemotherapy effect. We analytically identify the equilibrium points and assess the conditions for their stability in the presence of chemotherapy. A bifurcation analysis with respect to the chemotherapy tumor killing rate of the less immunogenic tumor reveals Hopf bifurcations, indicating transitions to oscillatory behavior and complex tumor–immune dynamics under varying treatment intensities. The effects of chemotherapy dosing and drug potency are investigated through six-month numerical treatment simulations to evaluate tumor suppression and long-term system behavior under different treatment scenarios. An optimal control problem is then formulated to determine chemotherapy schedules that reduce tumor burden while limiting drug exposure. Numerical results indicate that the optimal chemotherapy protocol produces faster and more efficient tumor reduction than a constant-dose treatment strategy. Overall, this study provides a treatment-focused dynamical framework for understanding how chemotherapy interacts with tumor heterogeneity and immune response, providing theoretical insight into treatment-dependent tumor–immune dynamics and chemotherapy scheduling.

Mathematics doi: 10.3390/math14173166

Authors: Xilong Ye Chenglong Miao Weiwei Jia Xinyi Huang Maofa Wang Jun Tan

The safe and stable operation of coal-fired generating units is of critical strategic importance for ensuring the reliable supply of power systems. However, the fault evolution of industrial thermal systems exhibits the characteristics of strong nonlinearity and a long incubation period, coupled with the extreme scarcity of key fault samples (Few-shot) in actual production, which severely limits the engineering application of traditional data-driven diagnostic methods. Existing deep learning models, which are highly dependent on massive and balanced labeled data, not only struggle to overcome the overfitting bottleneck in scenarios with scarce fault samples, but also frequently introduce severe label noise (Label Noise) by ignoring the physical incubation period of faults, resulting in the degradation of the model’s decision boundary. To address the above challenges, this paper proposes a novel fault diagnosis framework integrating multi-scale spatiotemporal feature engineering and the Tabular Prior-Data Fitted Network (TabPFN). Starting from the physical mechanism of the system, this paper develops a dynamic label cleaning strategy based on multivariate statistical deviation, which accurately defines the fault divergence point to eliminate the noise in the incubation period. The constructed multi-scale spatiotemporal feature engineering integrating first-order difference and sliding window statistics can effectively map the transient mutation and steady-state evolution trend of the system. The introduced pre-trained TabPFN model based on the Transformer architecture, relying on its Bayesian inference capability and in-context learning (In-Context Learning) mechanism, can realize parameter-tuning-free and efficient classification for scarce samples. Experiments based on high-fidelity dynamic simulation data from GE Steam Power show that under the strict setting of limiting the training set to only 2000 samples, the proposed method achieves a comprehensive diagnostic accuracy of up to 99.29% and an F1-score of 0.9929 for seven typical operating conditions. Multi-dimensional comparative experiments and ablation studies confirm that the proposed framework comprehensively outperforms six mainstream baseline models, including XGBoost and SVM, in terms of precision, recall, and anti-interference robustness, and also delivers outstanding performance when benchmarked against deep learning models. This provides a brand-new theoretical perspective and technical paradigm for equipment health management in the context of industrial big data.

Mathematics doi: 10.3390/math14173168

Authors: Yimin Liu Qike Ji Shengbo Lu Jianliang Chen

To mitigate high expert-annotation costs, domain-preference misalignment, and the inherent trade-off between sensitive-data protection and training utility in petrochemical dataset construction, an iterative framework combining human-feedback-aligned reinforcement learning (RLHF) with post hoc data de-identification is proposed. Direct scoring and pairwise preference feedback are generated using two high-capability language models. A reward model is subsequently trained via a joint Bradley–Terry and mean-squared-error loss, followed by three rounds of closed-loop proximal policy optimization (PPO) constrained by a fixed supervised fine-tuning reference model. Retained high-quality samples are then processed through a four-stage post-RLHF de-identification pipeline. Experimental results demonstrate that the PPO-V3 model achieves a reward score increase of 1.183 over the baseline alongside a 96.2% pairwise win rate, while the sensitivity-aware adaptive differential privacy with context-aware token-level injection (SA-ADP-CTI) post-RLHF de-identification method attains a composite score of 0.9636. The reliability of both the automated feedback and privacy-preservation mechanisms is further validated through blind expert review and manual spot checks.

Mathematics doi: 10.3390/math14173167

Authors: Christian Camacho Morales Oscar Camacho Marco Herrera Juan Pablo Vásconez Brayan Durán Toconás Alvaro Prado-Romo

Reinforcement learning (RL) has become an effective paradigm for enabling autonomous robots to acquire navigation policies directly from interaction with complex and uncertain environments. Nevertheless, autonomous path planning for Skid-Steer Mobile Manipulators (SSMMs) remains a challenging problem because it requires the coordinated control of the non-holonomic mobile base and the manipulator while simultaneously accounting for obstacle avoidance and wheel–terrain interaction effects. This paper presents and evaluates RL-based path planning strategies for SSMMs, explicitly incorporating coupled dynamics of the mobile platform and manipulator to generate collision-free trajectories under varying terrain conditions. The proposed framework incorporates a slip-aware reward formulation that penalizes discrepancies between commanded and measured robot motion while accounting for longitudinal and lateral slip resulting from wheel–terrain interaction. The main contributions are (i) a unified RL-based framework based on actor–critic techniques for SSMM path planning, integrating the mobile base and manipulator dynamics within a coupled system representation; (ii) a physics-aware multi-objective reward formulation that incorporates wheel–terrain interaction into policy learning; and (iii) the implementation via simulation and field validation of the proposed policies under progressively complex navigation conditions and real underground mining scenarios. The framework is evaluated using four RL algorithms across multiple environments and maps from real mining scenarios, encompassing diverse navigation conditions and start-to-goal configurations. The evaluated methods include Deep Deterministic Policy Gradient (DDPG), Proximal Policy Optimization (PPO), Soft Actor–Critic (SAC), and Twin Delayed DDPG (TD3). Experimental field results show that SAC achieves the lowest planning time, reducing the planning time by 127.3%, 24.1%, and 2.52% compared with PPO, TD3, and DDPG, respectively. SAC also achieves the shortest path, reducing the average path length by 20.32%, 8.58%, and 1.90% compared with PPO, DDPG, and TD3, respectively. Moreover, SAC generates smoother control profiles for both the mobile base and the manipulator arm, while TD3 exhibits competitive performance across several navigation metrics. The proposed framework demonstrates the potential of slip-aware RL for coordinated SSMM navigation, providing a practical foundation for improving the safety, energy efficiency, and operational autonomy of mobile manipulators exposed to complex mining environments.

Mathematics doi: 10.3390/math14173165

Authors: Remus-Daniel Ene Romeo Negrea Rodica Badarau Nicolina Pop

This paper investigates the damped and periodical oscillations of a specific system that depends on four physical parameters. Exact parametric solutions are established based on a smooth function. The system is explicitly integrated without admitting prime integrals. The influence of the physical parameters is examined semi-analytically through the Multistage Optimal Parametric Iteration Method (MOPIM). A key advantage of this method is that it used only one iteration, owing to an appropriate choice of auxiliary functions for convergence control. There is accuracy between MOPIM solutions and corresponding numerical results, highlighted qualitatively through figures, quantitatively through tables, and by statistical tests of the residuals. The damped or periodical behaviors of the system’s solutions lead to their application on electronic circuits or other technological application fields.

Mathematics doi: 10.3390/math14173164

Authors: Omar Kahouli Nadjette Debbouche Adel Ouannas Sulaiman Almohaimeed Lilia El Amraoui Mohamed Ayari

This paper presents the nonlinear chaotic dynamics of a power system model within an incommensurate fractional-order framework. Equilibrium points are derived and analyzed using Jacobian-based local stability theory adapted to fractional-order systems. Furthermore, bifurcation analysis is employed to examine how variations in system parameters and incommensurate fractional orders influence the emergence of period-doubling cascades and chaotic motion. The study investigates multistability phenomena characterized by the coexistence of multiple attractors under identical system parameters. The simulation is run in MATLAB R2020a, and nonlinear tools such as time series, bifurcation diagrams, Lyapunov exponents, and phase portraits in 2D and 3D projections are used to visualize the findings.

Mathematics doi: 10.3390/math14173163

Authors: Ayman A. Amin Shuhrah A. Alghamdi

Autoregressive models with exogenous variables (ARX) constitute a fundamental family of time series tools with broad applicability across engineering, environmental science, and finance. A persistent limitation of standard Bayesian treatments is the Gaussian error assumption, which frequently proves inadequate when dealing with real data displaying heavy tails or occasional extreme observations. To overcome this shortcoming, the present paper develops a complete Bayesian inferential framework for ARX models under the scale-mixtures of normal (SMN) error distribution, integrating model identification, parameter estimation, and multi-step-ahead prediction within a unified scheme. A stochastic search variable selection (SSVS) procedure is adapted to perform simultaneous selection of the autoregressive order and the active exogenous regressors by assigning binary latent indicators to each candidate coefficient. Mixture-of-normals priors are specified for the dynamic and exogenous coefficients and an inverse-gamma prior for the error scale, while Bernoulli priors govern the latent selection indicators. These choices yield tractable full conditional posterior distributions: multivariate normal for the complete coefficient vector, inverse-gamma for the scale, and Bernoulli for the indicators. The conditional predictive distribution of future observations is also multivariate normal. For SMN-specific mixing parameters whose conditionals lack standard forms, Metropolis–Hastings steps are embedded within the Gibbs sampler. An extensive simulation study evaluates recovery accuracy across three SMN distributions and several ARX configurations. The methodology is then applied to the forecasting of daily global horizontal irradiance (GHI) in Najran, southwestern Saudi Arabia, using clear-sky GHI as an exogenous covariate, demonstrating the practical value of the proposed framework in a renewable energy context.

Mathematics doi: 10.3390/math14173162

Authors: Jean-Luc Boulnois

The classical Lotka–Volterra predator–prey system is often used in modeling species competition. The two-species nonlinear system is expressed in terms of a single positive coupling parameter λ. Based on a standard functional transformation, a novel λ-invariant Hamiltonian yields a system of two partially uncoupled first-order hybrid-function ODEs, albeit with one being linear. An exact single quadrature solution that is valid for any value of λ and the system’s energy is derived. In the particular case of λ=1, the ODE system completely uncouples. One ODE is autonomous. An exact analytic quadrature solution is derived that is predicated on the exact turning-point solutions. It is expressed in terms of the Lambert W function and must be evaluated numerically. Exact time-dependent solutions are presented for each individual species separately. In the case of λ≠1 an accurate practical approximation uncoupling the nonlinear system is proposed and solutions are provided in terms of explicit quadratures together with high-energy asymptotic solutions. An exact analytic expression for the system’s oscillation period that is valid for any value of λ and orbital energy is derived in terms of a dimensionless energy function.

Mathematics doi: 10.3390/math14173161

Authors: Salha Altharwi Mohd Tahir Ismail

Return predictability on the Saudi Arabian Stock Exchange (Tadawul), the largest equity market in the Middle East, remains underexplored relative to its structural distinctiveness as an oil-linked, retail-dominated emerging market. We compare 11 predictive models spanning five linear (regularised) regressors, three tree-based ensembles, and three stacked hybrid architectures. This comparison quantifies the improvement that nonlinear and ensemble methods offer over linear benchmarks for daily return prediction in this setting and identifies which method delivers the best accuracy-versus-cost trade-off for practical deployment. Using 28,750 daily observations (January 2015–December 2025), we constructed a 40-feature technical signal space spanning six families and evaluated all 11 models under a strict chronological train–validate–test protocol with an 18-month sealed holdout. A Lasso–XGBoost stacked ensemble achieves the lowest test RMSE of 0.906 and an out-of-sample Information Coefficient of 0.133, outperforming linear benchmarks by 15–27% in forecast error. Translated into a long-short strategy subject to 0.6% round-trip transaction costs, the optimal model delivers a Sharpe ratio of 0.587, an 81.1% win rate and a maximum drawdown of −5.53% across 758 trades. Sensitivity analysis confirms robustness across hyperparameter grids and rolling estimation windows. Bollinger Band Width, cross-sectional stock identity and lagged MACD signals collectively dominate feature importance rankings.

Mathematics doi: 10.3390/math14173160

Authors: Jianfeng Ren Yingying Jia Guo Sun

Allocating elective patients to operating rooms (ORs) under uncertain surgery durations and limited historical data requires balancing, opening costs against overtime risk. We develop a data-driven distributionally robust optimization model (DDRO) that jointly determines OR openings and patient assignments, with room-level risk measured by worst-case expected overtime over a Delage–Ye moment-based ambiguity set. We derive exact semidefinite reformulations under box and nonnegative ellipsoidal supports. OR homogeneity and separable risk yield an equivalent set-partitioning model, solved by a tailored column-generation algorithm (DDRO-CG) using exact full-enumeration pricing for small instances and heuristic candidate-pool pricing for larger ones. Experiments using the MSS-Adjusted Surgery Data validate DDRO-CG on small instances and show empirical tractability on the larger tested instances, although candidate-pool pricing provides no global optimality certificate. Out-of-sample evaluations and paired tests under controlled distributional shift show that DDRO reduces cost variability and upper-tail risk relative to deterministic and SAA benchmarks at a small average-cost premium over SAA.

Mathematics doi: 10.3390/math14173156

Authors: Long Lin Yue Qi

Our environment deteriorates primarily due to the emissions of carbon dioxide. Scientists and entrepreneurs promote carbon offset to reduce the emissions. Scientists and investors explore the investments of carbon offset. Some scientists encouragingly construct portfolio selection models but do not completely optimize them. Some scientists encouragingly construct capital asset pricing models (CAPM) but do not completely justify them. Under such contexts, this paper proposes a model of multiple-objective portfolio selection (MOPS) and preliminarily explores multiple-objective capital asset pricing models (MOCAPM). By the classical transition from portfolio selection to CAPM, we introductorily conjecture the extended transition from MOPS to MOCAPM. Specifically, we prove mathematical properties for the model. For instance, its minimum-variance surface is convex, and its feasible region is bounded by the convex surface. We examine whether a point on the minimum-variance surface is nondominated. By the properties, we heuristically prove different tangent planes for MOCAPM (instead of the unique tangent line for CAPM). We tentatively hint the conditions for a unique tangent plane. This paper acts as a footstep of the introductory conjecture.

Mathematics doi: 10.3390/math14173159

Authors: Hadil Alhazmi Mohamed Kharrat Asma Al-Jaser Paolo Mercorelli

This paper proposes an adaptive fuzzy prescribed-time output feedback control approach for strict-feedback nonlinear cyber–physical systems (CPSs) subjected to malicious attacks, output constraints, and backlash-like hysteresis. To approximate unknown system nonlinearities, fuzzy logic systems (FLSs) are employed. A practical prescribed-time stability condition is introduced, based on which a prescribed-time output feedback control scheme is constructed using Lyapunov-based analysis and the backstepping technique. The proposed control strategy guarantees that both the tracking error and the observation error converge to small neighborhoods around zero within a prescribed time. Furthermore, all signals within the closed-loop system remain bounded, and the tracking error is driven to a constrained target region near the origin. The effectiveness and robustness of the proposed method are validated through a practical example.

Mathematics doi: 10.3390/math14173158

Authors: Patrizio Vanella Julian Ernst

Reliable regional mortality rates are crucial for public health monitoring and planning. However, their estimation is often complicated by data limitations, with data being published only in broad age groups or affected by systematic errors. This is particularly relevant in intercensal periods, when population estimates may increasingly diverge from the true population structure. Using the German federal states as a case study, we develop and evaluate models for estimating and nowcasting age-, sex-, and nationality-specific rates under the outlined data issues. The analysis covers 1995–2023 and accounts for heterogeneous data availability, changing age groups, missing regional information on sex and nationality in recent years, and census-related revisions of population estimates. We first compare negative binomial regression models of increasing complexity. We then propose a state-specific generalized additive model based on a penalized splines framework, using national mortality schedules as a reference and explicitly modeling deviations associated with sex, nationality, calendar time, and time since the last population revision. The final model substantially outperforms the directly specified regression models based on in-sample, semi- and full-out-of-sample prediction compared with unadjusted regional estimates and national reference rates. The approach produces plausible, bias-adjusted mortality schedules despite limited regional data and can be used both to revise historical estimates and to nowcast mortality during intercensal periods. Although developed for Germany, the framework is applicable to other countries and small-area settings with incomplete or error-prone demographic data.

Mathematics doi: 10.3390/math14173157

Authors: Nueraminaimu Maihemuti Yimamujiang Aisan Jiayin Peng Jiangang Tang

We propose two multi-layer controlled multi-output remote state preparation (RSP) schemes for arbitrary single-qubit and single-qudit states. Twelve-particle entangled channels are constructed in two-dimensional and d-dimensional Hilbert spaces, and a hierarchical authorization mechanism is introduced to enable controllers with different permission levels to jointly and selectively regulate the reconstruction of quantum states at multiple receivers. First, based on a twelve-qubit maximally entangled channel, we design a deterministic three-layer controlled multi-output RSP protocol in which one sender assists three receivers in preparing their respective target single-qubit states. In this protocol, the controllers are assigned high-, medium-, and low-level permissions. Under different multi-layer control conditions, the three receivers can reconstruct their respective original single-qubit states by performing appropriate local unitary operations. The results show that the protocol achieves unit success probability, exhibits good universality and provides a structured basis for extension to larger multi-user settings, and enforces hierarchical access control by preventing unauthorized receivers from deterministically reconstructing the target states. Subsequently, we replace the maximally entangled channel with a non-maximally entangled twelve-qubit state. After the sender performs two specific three-qubit projective measurements, the receivers can probabilistically reconstruct their respective target states under the same three-layer control structure by introducing auxiliary qubits, applying controlled-U gates, and measuring the auxiliary systems. Finally, by employing positive operator-valued measurements, the above scheme is generalized from qubit systems to arbitrary d-dimensional qudit systems, providing a theoretical basis for exploring larger multi-user quantum communication settings with hierarchical authorization.

Mathematics doi: 10.3390/math14173155

Authors: Zhiqiang Guo Yulin Hu Yuwei Liu Yihang Ye

Full-vehicle active suspension control requires coordinated regulation of ride comfort, body posture, suspension travel, tire road holding, and control effort. To improve the adaptability of fixed-weight MPC while retaining model-based interpretability, this paper proposes a TD3-MPC posture-feedback controller for a seven-degree-of-freedom full-vehicle active suspension system. The TD3 Actor is trained offline and deployed with fixed network parameters to generate five bounded actions for online MPC weight regulation rather than directly outputting actuator forces. The MPC layer calculates the constrained four-wheel baseline forces, after which posture feedback compensates for vehicle-body vertical, pitch, and roll responses. A composite reward balances body acceleration, suspension deflection, tire deformation, energy control, force variation, and action smoothness. The controller is evaluated through time-domain, frequency-domain, parameter-perturbation, ablation, and Monte Carlo analyses. Under the nominal Class-D Road condition at 20 m/s, it reduced the RMS values of body vertical, pitch, and roll angular accelerations by 13.24%, 4.77%, and 10.68%, respectively, and reduced control energy by 3.06% relative to fixed-weight MPC. Across 360 paired cases covering ISO Class-B-D roads and speeds of 10–25 m/s, the corresponding mean reductions were 9.55%, 6.30%, and 8.37%, respectively.

Mathematics doi: 10.3390/math14173154

Authors: Yong Wu Huainian Zhu

With the increasing power of institutional investors, in order to compete for more investment agency business, the competition among institutional investors has become increasingly fierce. This paper studies a non-zero-sum game between two competing institutional investors who adopt mean–variance preferences and account for model uncertainty in order to derive robust optimal portfolios. The ambiguity-averse institutional investors can invest in a financial market with one risk-free bond and one individual stock. The objective of each institutional investor is to maximize the mean–variance utility of his terminal wealth relative to that of his competitor under the worst-case scenario of the alternative measures. By means of stochastic dynamic programming, we obtain closed-form expressions for the robust Nash equilibrium strategies and prove a verification theorem. Numerical simulations are finally presented to examine how model parameters influence the equilibrium strategies and to extract associated economic interpretations.

Mathematics doi: 10.3390/math14173153

Authors: Egemen Özkan

The estimation of the uncertainty of random variables or the entropy of stochastic processes has attracted considerable attention in many studies. In this study, we focus on obtaining estimators for the Shannon, Rényi, Tsallis, and Havrda–Charvat entropy measures of the Kumaraswamy distribution. Maximum likelihood and Bayesian estimation methods are employed to obtain entropy estimators under progressive Type-II censoring schemes with binomial removals. The Tierney–Kadane approximation is used to obtain the Bayesian estimators. The consistency and asymptotic normality of the maximum likelihood estimators are also stated under standard regularity conditions, and approximate confidence intervals for the entropy measures are constructed accordingly. The behavior of the proposed estimators under various sample sizes and censoring schemes is investigated through an extensive Monte Carlo simulation study. Finally, the Kumaraswamy distribution is fitted to two real datasets from the fields of economics and agricultural hydrology. In both applications, the Kumaraswamy distribution is shown to provide a better fit than the three competing unit distributions. Under different progressive Type-II censoring schemes, maximum likelihood and TK-based Bayesian estimates of the four entropy measures are obtained, while Markov chain Monte Carlo is additionally used to construct Bayesian credible intervals. The resulting credible intervals are found to be similar to the corresponding maximum likelihood-based confidence intervals, supporting the practical applicability of the proposed estimation procedures for entropy measures under censored data.

Mathematics doi: 10.3390/math14173152

Authors: Jin-Ho Chung Dongsup Jin Daehwan Kim

In this paper, we derive complete weight distributions and solve constrained optimization problems for affine-half coordinate extensions of a known family of partial-spread minimal binary codes. The extended code has length 2m+2m−1−1 and dimension m+1, and it remains minimal. The repetition step and its preservation of minimality are elementary; the principal results instead consist of an affine Walsh-sum identity, exact translation incidence counts, and the resulting complete weight distributions when the affine normal lies inside or outside the union of the dual-spread components. The construction and weight distributions hold for 2≤r≤2t−1. In the principal range 2≤r≤2t−2, where m=2t, we characterize every optimal coordinate set for each prescribed extension size and solve the affine-half optimization exactly.

Mathematics doi: 10.3390/math14173150

Authors: Elif Segah Öztaş Merve Bulut Yılgör

This paper focuses on the construction and analysis of codes over the Frobenius ring T. By exploiting the idempotent structure of the ring, codes over T are decomposed into direct sums of component codes over a related local Frobenius non-chain ring. A gray map is constructed and shown to be bijective and distance-preserving, allowing code parameters to be determined from their gray images. Linear codes and cyclic codes over the considered ring are completely characterized, and explicit descriptions of their generating sets and cardinalities are obtained. The duals of cyclic codes are also examined, and the gray map is shown to preserve orthogonality and self-duality. Well-parameterized codes were obtained over the ring T.

Mathematics doi: 10.3390/math14173151

Authors: Gizem Nur Bulanık Durmuş

This study develops a single-level energy management optimization model that evaluates hourly electricity market data and hourly dynamic emission factors (DEF) within a grid-connected photovoltaic (PV) system. The model uses hourly PV production data for 2025, hourly market clearing price (MCP) data from the EPİAŞ day-ahead market, and hourly dynamic emission factors. The aim is to maximize total benefit by considering both the revenue from electricity sales and the carbon credits associated with the estimated avoided emissions resulting from PV energy exported to the grid during periods of high grid carbon intensity. To represent real grid operating conditions, a quota constraint for annual energy sales to the grid is defined, and the model is tasked with distributing this quota to the most optimal hours throughout the year. According to the baseline scenario results, where 60% of annual PV production is allowed to be sold to the grid and the carbon credit price is set at USD 15/tCO2, 8062.04 MWh was curtailed due to quota restrictions. As a result of the optimum hourly sales plan, electricity sales revenue of USD 1,007,770.44 and carbon credits of USD 81,460.01 were obtained. The estimated quantity of avoided emissions, calculated according to dynamic emission factors, was 5430.67 tons of CO2. In this study, comprehensive sensitivity analyses were conducted to evaluate the effects of different grid sales quota levels, carbon credit prices, and hourly emission factor reduction scenarios, representing the long-term decarbonization of the grid in line with Türkiye’s 2053 Net Zero Emissions Target. The findings suggest that dynamic emission factors are one of the key elements determining the economic and environmental performance of PV systems under different sales limits, carbon credit prices, and emission reduction scenarios.

Mathematics doi: 10.3390/math14173148

Authors: Ahad Fatahi Mohamed Fouad Benkhoris Djamel Ziane Mohamed Assaad Hamida

Multi-phase permanent magnet synchronous generators (PMSGs) are increasingly adopted in renewable energy systems and isolated microgrids due to their improved fault tolerance, reduced per-phase current stress, and enhanced power density compared to conventional three-phase machines. This article presents a systematic performance comparison between 15-phase and 9-phase PMSGs under four distinct operating conditions: healthy mode, single-phase open-circuit fault (Phase 1), and two fault-tolerant control (FTC) strategies. The first FTC technique involves opening a second phase with approximately 90-degree phase displacement from the faulty phase to attenuate power oscillations and reduce current amplitude imbalances. The second technique involves isolating a complete three-phase set containing the faulty phase without adapting the machine model. Both machines are modeled using the vector space decomposition (VSD) approach under field-oriented control (FOC), and simulations are performed in MATLAB/Simulink. Performance metrics include power efficiency, power losses, power ripple factor, electromagnetic power ripple, stator RMS current evolution, and stator current balance. Results demonstrate that the 15-phase PMSG consistently exhibits lower power ripple (6.5% vs. 15.54% under open-circuit fault), higher efficiency (89.02% vs. 87.44%), and reduced power losses across all fault scenarios. The first fault-tolerant strategy improves performance in both machines but is more effective in the 15-phase configuration. To validate the findings beyond offline simulation, hardware-in-the-loop (HIL) experiments are conducted on an OPAL-RT real-time platform, where the complete system—the PMSG and converter models together with the FOC and fault-tolerant control algorithms—is implemented within its FPGA framework. The HIL results for electromagnetic power and d–q axis stator currents show close agreement with the MATLAB/Simulink results across all operating conditions, confirming the FPGA implementability of the proposed control strategies under real-time constraints. These findings provide actionable insights for the design and control of high-phase-count generators in grid-connected and isolated power systems.

Mathematics doi: 10.3390/math14173149

Authors: Nawal Louzi Mohammad Q. Al-Jamal Mahmoud AlJamal Ayoub Alsarhan Nayef H. Alshammari Khalid Hamad Alnafisah Mohammed Kamel Aleinzi Sami Aziz Alshammari

This study presents a mathematical modeling and simulation framework for pavement crack maintenance under limited work zone energy availability. The framework combines crack evolution, thermal repair, interface behavior, and maintenance decision-making within a unified structural–thermal–energy formulation. A three-dimensional multilayer flexible pavement model is developed with an XFEM-enriched region in the aged asphalt surface layer, a localized repair zone, cohesive interface behavior, and wheel-loading stages before and after maintenance. Rather than assuming constant heating, the repair heat flux is governed by a photovoltaic battery-dependent amplitude function, allowing the model to reflect practical variations in available energy. The simulation generated a dataset containing crack geometry, pavement properties, repair zone dimensions, loading conditions, heat flux intensity, heating duration, bonding quality, XFEM damage status, stress response, temperature distribution, interface damage, energy feasibility, durability, and service life gain. These variables were used to develop the Crack–Energy–Repair Interaction Graph Network (CERIG-Net), which represents each maintenance case as a physics-guided heterogeneous graph and ranks delayed repair, crack sealing, localized patching, thin overlay, and deep repair. The thin overlay strategy reduced final crack length from 94.7 mm to 53.8 mm, lowered maximum stress from 3.85 MPa to 2.22 MPa, achieved a durability index of 0.86, and extended service life by 6.7 years.

Mathematics doi: 10.3390/math14173147

Authors: Houshi Yu Shikui Zhao Yuqi Zhang

Early dropout prediction requires models that integrate heterogeneous educational records without information leakage. We propose multi-view neural risk augmentation (MVNRA), a cross-fitted framework that separates early-warning predictors into academic, contextual, and digital-engagement views. View-specific encoders and a gated fusion module produce four supervised risk scores. We evaluated MVNRA on a public longitudinal dataset from a Spanish technological university containing 464,739 student–course records and 81 predictors available by December. Within each outer student-level GroupKFold split, the neural risk generator was trained through inner student-grouped cross-fitting. Its out-of-fold fused, academic, contextual, and digital risk scores were then appended to the original predictors before six conventional classifiers were fitted. MVNRA increased mean area under the receiver operating characteristic curve (AUC) for all six classifiers. The largest gains occurred for AdaBoost (0.7717 to 0.9240), linear discriminant analysis (0.8701 to 0.9176), Gaussian Naive Bayes (0.7313 to 0.7786), and Logistic Regression (0.9139 to 0.9352). MVNRA + Random Forest achieved the highest absolute discrimination (AUC =0.9577), with increases of 0.0191 in precision–recall AUC and 0.0112 in F1 score. SHAP analysis ranked the fused and academic neural risk scores above the cumulative academic-progress indicators. These findings show that cross-fitted, view-specific neural risk scores can transfer nonlinear structure to conventional tabular classifiers while preserving a SHAP-compatible decision layer and strict student-level separation.

Mathematics doi: 10.3390/math14173146

Authors: Mingxu Li Sherry Zhefang Zhou

This paper develops a generalized autoregressive conditional heteroskedasticity–mixed data sampling model with continuous and jump components (GARCH-MIDAS-CJ). It aligns the continuous–jump (CJ) decomposition of realized volatility with the long-run–short-run multiplicative structure. The model places block-smoothed daily continuous variation in the long-run mixed-data-sampling term and demeaned jump variation in the short-run Glosten–Jagannathan–Runkle GARCH (GJR-GARCH) recursion. Using high-frequency data for the Standard & Poor’s 500 (S&P 500), we find a positive jump coefficient under both the Corsi–Pirino–Renò (CPR) and Andersen–Bollerslev–Dobrev (ABD) decompositions, supported by one-sided Wald, boundary-adjusted likelihood-ratio, and parametric-bootstrap tests. Relative to return- and realized-measure benchmarks, the forecasting value of the CJ allocation is competitive for multi-day and cumulative variance forecasts and in high-volatility periods, whereas established benchmarks can perform better for one-day and low-volatility forecasts. Under the CPR decomposition, the h=22 average cumulative forecasts reduce the mean squared error (MSE) and QLIKE relative to the aggregate-realized-variance benchmark by 8.2% and 3.3%, respectively. One-day-ahead value-at-risk (VaR) results are strongest at the 1% and 0.5% tails; the 5% forecasts have exceedance rates above the nominal level. Across alternative information-timing conventions, forecast windows, and United States equity assets, the clearest gains remain concentrated at multi-day horizons, although their magnitude varies across settings. The findings support a persistence-based allocation of continuous and jump variation within the GARCH-MIDAS structure.

Mathematics doi: 10.3390/math14173145

Authors: Kyungsik Min Do-Yup Kim

Symbiotic radio (SR) has emerged as a spectral-efficient paradigm for Internet-of-Things networks. However, simultaneously optimizing coexisting primary and secondary transmissions remains a challenge. To address this, a joint precoding and RIS phase shift design is proposed to maximize the sum-rate in the reconfigurable intelligent surface (RIS)-aided multiple-input single-output SR system. Specifically, based on an optimization problem that maximizes the sum-rate of primary and secondary data, an iterative algorithm that sequentially updates the precoder and the RIS phase shift matrix is developed. To address practical aspects, channel training overhead and minimum signal-to-interference-plus-noise ratio (SINR) constraints are also considered in the precoder design. Simulation results verify that the precoder design based on perfect successive interference cancellation achieves the highest sum-rate. The results also highlight the necessity of the proposed SINR-constrained precoding schemes in guaranteeing data rates of the primary and secondary links under various channel environments, proving the practical validity of our joint precoder and RIS phase shift design.

Mathematics doi: 10.3390/math14173144

Authors: Yu Zhang Huimin Zhu Chi Li Shiyan Sun Weige Liang

Formations of fixed-wing unmanned aerial vehicles (UAVs) must maintain mission-level coordination despite actuator degradation, bias faults, model uncertainty, wind disturbances, and command limits. This study presents a mission-oriented formation-recovery framework. Acceptable relative position and velocity performance is represented by an ellipsoidal tolerance set, and resilient formation recovery time (RFRT) is the elapsed time from fault onset to the first permanent re-entry into that set. The controller generates relative demand commands that are reconstructed from the parent limited command and then clipped componentwise. A second-order edge-based extended state observer, driven by the relative limited command, estimates the physical edge fault–disturbance mismatch, while the command-saturation residual is retained explicitly in the closed-loop analysis. A distributed fault-tolerant controller combines linear recovery feedback, observer-based compensation, and a continuous robust term. The analysis uses a finite Lyapunov energy-jump inequality at step-fault instants and an upper-right Dini derivative at saturation breakpoints to establish uniform ultimate boundedness, a sufficient recovery-set inclusion condition, and an RFRT upper bound. In the one-leader–four-follower baseline simulation, permanent re-entry occurs at 22.3313 s, corresponding to an RFRT of 2.3313 s. Relative to Edge-ESO-FTC, the proposed method reduces the post-fault peak metric by 61.2%, RFRT by 25.2%, cumulative position deviation by 54.6%, and out-of-bounds duration by 67.7%.

Mathematics doi: 10.3390/math14173143

Authors: Najaya Al-Hajri Mohammad Taghi Darvishi Silvia Noschese Lothar Reichel

Complex systems of interacting components often can be modeled by a graph that consists of a set of n nodes and a set of m edges. Such a graph can be represented by an adjacency matrix A∈Rn×n, whose (ij)th entry is one if there is an edge pointing from node i to node j, and is zero otherwise. The matrix A and its low-order powers reveal important properties of the graph and allow the enumeration of short paths and cycles that are important for determining short-range communication in the graph as well as node clustering. Closed-form expressions for path matrices of length up to four are derived, and a novel indicator of the structural propensity of the graph to form clusters is proposed. Numerical examples illustrate our analysis.

Mathematics doi: 10.3390/math14173137

Authors: Riaman Monika Hidayanti Julita Nahar Sukono Moch Panji Agung Saputra Hasna Kamilah Faishal Nazla Aqira Maghfirani Heri Kurniawan Alim Jaizul Wahid

Economic evaluation of Battery Energy Storage Systems (BESSs) integrated with solar photovoltaic (PV) systems requires the consideration of financial performance, operational behavior, battery degradation, reliability, and uncertainty. This PRISMA-based systematic review synthesizes mathematical and decision-making approaches relevant to Fuzzy Soft Set-based PV–BESS evaluation. Searches in Scopus, ScienceDirect, SpringerLink, and Taylor & Francis Online identified 789 records published between 2015 and 2026, and 74 studies were included. All studies were coded by theme, method, and economic and technical criteria, while 15 representative studies were analyzed at the equation level. Six model families were identified: techno-economic valuation, multi-objective planning, operational energy management, reliability assessment, fuzzy and multi-criteria decision-making, and degradation-aware optimization or control. Most studies appeared in 2024–2026 (57/74; 77.0%), while keyword analysis highlighted decision making and battery storage. Common formulations included NPV, NPC, LCOE, IRR, payback period, market revenue, battery capacity fade, equivalent full cycles, degradation cost, LPSP, LOLE, EENS, Monte Carlo simulation, and fuzzy ranking methods. These components remain fragmented across separate frameworks. Fuzzy Soft Set is therefore positioned as a potential parameterized decision-support layer for integrating heterogeneous outputs, subject to further theoretical development and empirical validation. This direction is relevant to Sustainable Development Goal 7 (Affordable and Clean Energy).

Mathematics doi: 10.3390/math14173142

Authors: Won-Kwang Park

This paper concerns the application of the Bifocusing Method (BFM) for imaging small, well-separated dielectric objects within a two-dimensional homogeneous domain using an zero-padded incomplete multi-static response (MSR) matrix. A core challenge in this constrained measurement setup is the presence of an interference term that could obscure target localization. To address this, we theoretically prove that the disturbing term of the imaging function is strictly bounded above by 0.2438, thereby guaranteeing the unique identification of targets without the interference overshadowing the dominant localization term. Extensive numerical simulations across various frequencies and diverse target properties validate these theoretical findings. The results demonstrate that the BFM-based imaging function robustly localizes targets despite substantial missing data.

Mathematics doi: 10.3390/math14173141

Authors: Yupeng Liang Yihe Zhang Kenan Li Zhang Tao

With the rapid development of internet technology, live-streaming sales have emerged as a new form of online shopping and gradually become an important channel for consumer purchases. This paper investigates the decision-making problem in a dual-channel supply chain under the live-streaming sales model, focusing on the optimal decisions and profit distribution between the retailer and live-streamer when a Valuation Adjustment Mechanism (VAM) is in place. We construct a dual-channel supply chain model consisting of a retailer and a live-streamer, then analyze the decision-making and profits under three scenarios: centralized decision-making, decentralized decision-making without VAM, and decentralized decision-making with VAM. The results show that the proper use of a VAM can increase the profits of all supply chain participants; furthermore, different sales target-setting methods should be adopted for products with different price levels. The sales target serves as the core of the incentive mechanism and directly influences the streamer’s effort and pricing strategies. When formulating sales strategies, retailers and live-streamers should comprehensively consider the decision-making structure, the incentives and risks associated with using a VAM, and the coordinated development of multiple channels to maximize overall supply chain profits.

Mathematics doi: 10.3390/math14173139

Authors: Lingxue Zhu

We study the linear continuous interior penalty finite element method (CIP-FEM) for the two-dimensional Helmholtz equation on nonconvex polygonal obstacle domains with mixed Dirichlet and impedance boundary conditions. Re-entrant corners reduce the global regularity below H2(Ω) and require a corner-sensitive treatment of the CIP stabilization term. Using a wavenumber-explicit regular–singular decomposition, we establish exact consistency of the CIP formulation under this reduced regularity. We also prove the critical-order penalty-seminorm estimate |IhSj|J ≲ hαj for the Scott–Zhang quasi-interpolant of the cut-off corner singular functions. Combining this estimate with endpoint Scott–Zhang approximation and wavenumber-explicit bounds for the regular and singular components yields infvh ∈ Vh∥u−vh∥h,k ≲ (kh + kα−1/2hα)∥f∥0,Ω. A Schatz-type duality argument then yields the corresponding quasi-optimal error estimate ∥u−uh∥h,k ≲ (kh + kα−1/2hα)∥f∥0,Ω under the sufficient resolution condition k2h ≤ δ, where δ is independent of k and h. Discrete uniqueness is proved independently of this condition. Numerical experiments support the predicted corner-singularity behavior; for the tested problems with the fixed penalty value γ = 0.1, they show smaller errors than the standard FEM on some relatively coarse meshes in the high-wavenumber pre-asymptotic regime. The present analysis does not separately identify an additive pollution error term.

Mathematics doi: 10.3390/math14173140

Authors: Daniel López-Rodríguez Jorge Jordán-Núñez Bàrbara Micó-Vicent Macarena Boix-García

We study prediction-to-decision certification for inverse design with vector-valued response surfaces. An unknown response map is estimated from data, a target response is prescribed, and a decision is obtained by minimizing a target-loss function. The main question is how statistical prediction error and approximate global optimization error propagate to the true decision quality. We prove an end-to-end certificate showing that a high-probability uniform response bound and a certified global-search tolerance imply a high-probability bound on the true excess risk of the selected decision. Under a growth condition, the same event also yields an explicit distance-to-argmin bound. We provide finite-sample ordinary least squares response certificates, conditional ridge certificates with explicit bias decomposition, certified Lipschitz branch-and-bound, and polynomial sum-of-squares formulations. The formal certificate is demonstrated on a controlled synthetic benchmark. A clay-coloration example illustrates the workflow, while the pilot measurements are treated only as local forward-color checks.

Mathematics doi: 10.3390/math14173138

Authors: Jie Zhang Hang Li Jun Deng Songtao Ji Mohan Ren Jianjun Feng Jurij Karlovšek

External loads acting on shield tunnel linings in service are difficult to determine, while existing back analysis methods often require multiple monitoring quantities and repeated numerical calculations. This study develops an analytical method for identifying the equivalent horizontal load and lateral pressure coefficient from a single rotation measurement. The lining is modelled as a continuous Euler–Bernoulli curved beam on a radial Winkler foundation, with circumferential compression and bending considered. The radial components of the vertical and horizontal loads are decomposed into uniform and second-order terms. Closed-form solutions are obtained for displacement, rotation, and internal forces, followed by an explicit inverse relation between rotation at one circumferential position and the load difference. The analytical responses agree closely with an independent plane-frame finite element model. Prescribed horizontal loads and lateral pressure coefficients are also recovered accurately from finite element rotations. A FLAC3D model of the complete ring with continuous elastic ground further shows that the circumferential response pattern is retained and that the equivalent horizontal load can still be estimated when the Winkler ground representation is relaxed. The method identifies the load difference from one rotation measurement, and when the vertical load is independently estimated, determines the equivalent horizontal load. It provides a basis for assessing lining ovalization, bending response, and abnormal loading states.

Mathematics doi: 10.3390/math14173136

Authors: Yifei Wang Xiaojun Wang

Accurate identification of complex crack networks with branching and intersecting topologies remains a challenge in aerospace and civil engineering. Conventional non-destructive testing techniques are constrained by limited coverage and equipment access requirements, while model-based inverse methods face the curse of dimensionality and high computational cost when characterizing intricate crack morphologies. To address these limitations, a Binary-encoded Transformable Modular Component (BTMC) method is proposed, which abstracts complex crack morphologies into combinations of modular components representing elementary crack topological operations and encodes their parameters into a unified binary genotype. This representation converts the high-dimensional continuous inverse problem into a discrete combinatorial optimization task over a bounded search space, and the extended finite element method is coupled with a genetic algorithm for forward analysis and parameter optimization. Numerical simulations covering non-intersecting cracks, intersecting networks, and irregular morphologies beyond the component library demonstrate that the method maintains stable identification accuracy under measurement noise up to 10%. Experimental verification on a metal tensile plate and a wing surface curved-shell structure confirms that the identified configurations are mechanically consistent with the measurements, with the strain-response error on the wing surface reduced from 8.67% for the traditional genetic algorithm to 2.27% for BTMC. Across all test cases, the BTMC method converges in fewer generations with a total identification time of approximately 16 min on average, which provides a computationally efficient framework for online structural health monitoring of aircraft structures.

Mathematics doi: 10.3390/math14173134

Authors: Anil Thapa Jonathan Washburn

We study a conditional finite-dimensional operator construction based on two imported Recognition-Science inputs: a continuous comparison cost satisfying a multiplicative coherence axiom and equilibrium calibration, and a three-coordinate, eight-tick ledger schedule. The first input uniquely determines the reciprocal cost J(x)=12(x+x−1)−1. A cyclic Gray traversal of the configuration graph Q3 fixes the cyclic ordering of an assumed eight-sample register with shift P. The additional half-cycle antiperiodicity criterion selects the odd Fourier sector V=ker(P4+I); unitarity alone does not select this sector because P is unitary on the full register. On the realification of V, P2 defines an additional complex structure, and, after assigning an independent beat duration, the principal logarithm defines one self-adjoint stroboscopic interpolation, unique only after imposing the principal-zone convention. We distinguish the exact reciprocal action from a local adapter hypothesis needed to relate its mismatch coordinates to Hilbert-space defect coordinates. For the regular shift, the rational cyclotomic decomposition identifies V as the minimal faithful Φ8-block. Under the stated relative normalization of the local bridge, leading cost–defect agreement is equivalent to an isometric adapter tangent, while a positive self-adjoint single-filter commit that commutes with the beat has at most three non-negative mode factors on the minimal register; defect descent restricts them to [0,1]. The relaxed commit is a contraction and, in a normalized quantum interpretation, represents a trace-nonincreasing accepted branch whose complementary trace weight is recorded by a measurement outcome or environment; the in-sector component nevertheless evolves exactly and unitarily. For coupled ququart cores, adjoining the standard conjugate Weyl shift to the clock inherited from P spans the full finite-dimensional operator algebra. This proves algebraic representability of arbitrary finite-dimensional Hermitian dynamics, not a physical rule selecting their coefficients.

Mathematics doi: 10.3390/math14173135

Authors: Majeed Ahmad Yousif Karwan S. Mohammed Faraidun K. Hamasalh Pshtiwan Othman Mohammed

This paper presents a modified non-polynomial fractional cubic spline (MNPFCS) method for solving fractional Lotka–Volterra prey–predator systems governed by the Caputo fractional derivative. The proposed method integrates non-polynomial spline interpolation with fractional calculus to obtain accurate numerical approximations for nonlinear coupled systems. The stability and convergence of the method are established theoretically. To further verify its effectiveness, the numerical solutions are compared with those predicted by a feed-forward artificial neural network (ANN). Two benchmark examples demonstrate excellent agreement between the numerical and ANN solutions, while the MSE, MAE, and R2 metrics confirm the high predictive accuracy of the ANN. The obtained results show that the proposed MNPFCS method is an accurate, stable, and efficient approach for solving nonlinear fractional dynamical systems.

Mathematics doi: 10.3390/math14173133

Authors: Tianhao Gao Ke Zhang Xu Bai Xiaotong Li Xinguo Yan Nan Wang Shijie Wang

In unmanned aerial vehicle inspection of transmission lines, insulators often exhibit arbitrary orientations and elongated shapes and are frequently embedded in complex backgrounds. Horizontal bounding boxes tend to include substantial redundant regions. Meanwhile, existing oriented object detection methods still suffer from angular discontinuities at periodic boundaries, insufficient geometric supervision for rotated bounding boxes, and difficulties in lightweight deployment. To address these issues, this paper proposes a lightweight oriented object detection model, termed R-YOLOv8-PSGH, which integrates dual-frequency phase-shift encoding and Gaussian geometric supervision. Based on a lightweight R-YOLOv8 architecture, a rotated detection head is developed to decouple the predictions of object categories, bounding-box locations, and orientation angles. To improve the periodic continuity of angle representations and strengthen the geometric constraints on rotated bounding boxes, a dual-frequency phase-shift angle encoding strategy and a Gaussian geometric localization loss are designed. Specifically, the complementary relationship between periodic signals with periods of 180°and 90° is exploited to map orientation angles into continuous phase responses, thereby improving the stability of orientation prediction. Moreover, the spatial structure of each rotated bounding box is modeled as a two-dimensional Gaussian distribution, and overlap consistency, center distance, and shape discrepancy are jointly optimized. In this manner, the orientation representation and bounding-box-level geometric supervision are collaboratively enhanced. Experimental results demonstrate that the proposed method improves the detection accuracy and localization stability of rotated objects while maintaining favorable lightweight deployment capability, providing a new solution for lightweight object detection in complex scenarios.

Mathematics doi: 10.3390/math14173132

Authors: Yuhao Song Yiyuan Liu Chang Wang Haiyan Li

Multivariate long-term forecasting requires deciding how much cross-channel structure can be exploited reliably, yet existing architectures fix this decision by design, from no exchange at all to unrestricted mixing. We argue that the amount should instead be selected from data, and propose CLOC (Controlled Local–Global Channel Communication), a framework in which it becomes an explicit operating point with an exact zero-communication endpoint; setting the residual scales to zero recovers the channel-independent model within the same family. Local grouped attention restricts exchange through group size g, while K learnable prototypes mediate global context and the residual scales α and β control message strength. Operating points are selected on validation data under a stated rule and fixed before testing. Across eight benchmarks under a unified 720-step lookback, validation selects qualitatively different regimes, from full suppression on the four ETT datasets to local–global communication on Electricity and Solar-Energy. CLOC attains the best or tied-best result on 50 of 64 horizon-level metrics and a mean rank of 1.45 among eleven models, against 3.73 for the next best, while dense mixing runs out of memory at 862 channels. Thus, forecasting quality depends on matching communication to the structure a dataset can reliably support, not on maximizing it.

Mathematics doi: 10.3390/math14173131

Authors: Qian Li Xin Xiang Hu Mao Yuan Liang

Synthesizing realistic radio-frequency signals is important for data augmentation in wireless systems, yet labeled in-phase/quadrature (I/Q) measurements are expensive to collect, and diffusion models typically demand large per-class training sets. This paper studies whether a diffusion model trained on one modulation scheme can be transferred to unseen schemes with minimal data and a minimal parameter budget. We formulate the adaptation as a minimal-cardinality parameter-increment problem and adapt a conditional diffusion transformer, pretrained on QPSK signals from the RML2018.01a corpus, to three target modulations (OQPSK, 16PSK, and 32QAM) through low-rank adaptation (LoRA) of its attention projections under a composite objective that couples waveform reconstruction with spectral and autocorrelation constraints, updating only 0.496% of the 9.9-million-parameter backbone. With only 50 target signals, the adapted models attain a periodogram cosine similarity of 0.985 against 0.705 for from-scratch training and match from-scratch models given 1000 signals: a twenty-fold gain in sample efficiency. The transferred models also match or exceed reference target experts trained on up to 333 times more target data on every spectral and autocorrelation metric. Ablations on two target schemes show that sources with dense phase manifolds transfer best irrespective of family labels and that the generation quality is insensitive to the LoRA rank between 1 and 16, pointing to a low-dimensional adaptation subspace. Downstream classifier experiments confirm that the synthetic signals help few-shot modulation classification, and they also bound the claim: conventional label-preserving transforms remain stronger at very small sample sizes, downstream utility does not track spectral fidelity, and the generated signals under-represent the noise floor in the low-SNR regime. The main study uses RML2018.01a; a cross-corpus check on the independently generated Sig53 corpus reproduces the transfer advantage with compressed margins, and validation on over-the-air recordings remains future work.

Mathematics doi: 10.3390/math14173130

Authors: Mingyu Shi Fan Zhang

Normalizing-flow Markov chain Monte Carlo (MCMC), such as flowMC, augments local moves with a learned global flow proposal; a natural reliability idea is to pool samples from several such samplers. On 6 targets in 20 and 50 dimensions, a 5-member diverse flowMC ensemble appeared to reduce the average marginal Jensen–Shannon (JS) distance by about 18% relative to a single flowMC run. Matching the returned sample counts—our “equal budget”: wall-clock costs differ and are reported separately—reverses this verdict: the ensemble draws five times as many samples, and even a perfect sampler’s histogram JS estimate has a closed root-mean-square finite-sample floor c(1/N+1/M), with c a fitted coefficient set by the binning, which explains the apparent gain almost entirely. At a matched 10,000-sample budget, a single flowMC run matches or beats this ensemble on all eleven configurations and runs about six times faster. Applied to exact draws, the uncorrected reweight-and-resample aggregation reproduces about 93% of the ensemble’s elevation above the floor, separating a genuine law shift (coverage and tempering reweighting) from an estimator-level loss (resampling). On two real Bayesian posteriors scored against long NUTS references, uniform pooling improved on the sample-count-matched single run under marginal JS, energy distance, and MMD2 in every recorded run (a descriptive comparison at three and two repetitions), while the aggregation’s deficit is confined to the biased marginal metric. We recommend matched sample counts and floor reporting for histogram divergences, unbiased joint metrics alongside, and uniform pooling instead of uncorrected reweighting and resampling.

Mathematics doi: 10.3390/math14173128

Authors: Wenjie Zhao Chengpeng Li

To address the limitations of the original Honey Badger Algorithm (HBA), including premature convergence, limited search directionality, and insufficient local escape capability in high-dimensional complex optimization problems, this paper proposes an improved Honey Badger Algorithm based on a traffic-driven strategy, namely the Traffic-driven Covariance Honey Badger Algorithm (TCHBA). The proposed algorithm introduces three synergistic evolutionary mechanisms. First, Elite Covariance Rotation Guidance learns correlated search directions from the current elite subset and injects a truncated covariance-based step into the HBA update. Second, Urban Traffic-Inspired Search uses population density and an iteration-dependent signal to regulate attraction and diversion. Third, Stagnation-Aware Lens Opposition Mutation is activated after unsuccessful updates and combines lens opposition with a heavy-tailed Cauchy perturbation to restore search mobility. Extensive experiments are conducted on the CEC2017 (100-dimensional) and CEC2022 (10- and 20-dimensional) benchmark suites. The results demonstrate that TCHBA significantly outperforms nine state-of-the-art optimization algorithms, including VPPSO, EGWO, GJO, RIME, ALA, HBO, MO, PWO, and the original HBA, in terms of solution accuracy, convergence speed, and statistical robustness. Furthermore, TCHBA is applied to the problem of Taiwanese enterprise bankruptcy prediction, a representative financial risk classification task. By optimizing the key parameters of the K-nearest neighbors (KNN) classifier, a TCHBA-KNN prediction model is constructed. Experimental results on real-world datasets show that the proposed model achieves superior performance in terms of accuracy, Matthews correlation coefficient (MCC), recall, and F1-score, thereby validating the effectiveness and practical potential of the proposed algorithm for real-world engineering and financial decision-making problems.

Mathematics doi: 10.3390/math14173129

Authors: Mohammed Alkinidri

Exceptional points are parameter values at which two eigenvalues and their corresponding eigenfunctions coalesce, rendering the wave operator defective. They arise widely in non-Hermitian wave physics and disrupt the modal expansions on which semi-analytic scattering methods rely. For lined acoustic waveguides, an augmented mode-matching ansatz that restores completeness at such a degeneracy—by adjoining the generalised eigenfunction obtained from the derivative of the parametrised duct mode with respect to its transverse spectral parameter—has been established for junctions between duct sections with discrete modal sets. This article extends that ansatz to an open, radiating configuration: a rigid feed duct communicates through an impedance-lined throat, tuned to an order-two exceptional point, with a half-space bounded by a rigid flange. The radiating mouth replaces the discrete modal closure by a continuous spectrum, so the augmented basis must be matched against an improper spectral integral. The half-space field is generated by the aperture velocity, which builds the rigid-flange condition into the representation exactly, and the resulting improper integrals are rendered analytic by branch-aware substitutions whose cutoff is tied to the retained modal content. The formulation is validated on the matching and boundary conditions themselves: pointwise continuity of pressure and of normal velocity at the internal junction, pointwise pressure continuity at the radiating mouth, the vanishing of the normal velocity on the rigid flange, and the recovery of the classical flanged-duct radiation problem in the rigid limit, cross-checked against an independent implementation. The full lined problem, including the defective case, has been further verified against an independent finite-volume solution of the same boundary-value problem, whose grid-converged fractions agree with the mode-matching values to within 8×10−5. A conserved-power identity is monitored as a necessary but not sufficient check. Numerical experiments confirm the known breakdown of the standard expansion at the exceptional point and the well-conditioned convergence of the augmented one in this radiating setting, and a scan of the complex admittance plane, refined by local optimisation and repeated across throat lengths and frequencies, shows that flange radiation detunes the absorption optimum away from the exceptional point, by an amount that grows with the radiated share of the power budget and vanishes as the throat lengthens.

Mathematics doi: 10.3390/math14173127

Authors: Deyu Wu Yuheng Ding Peng Miao

Real-time inter-vehicle distance estimation is a critical component of autonomous driving perception systems, directly influencing collision avoidance and trajectory planning. This paper proposes a novel fixed-time zeroing neural network (FXTZNN) for solving the time-varying quadratic programming (TVQP) problem formulated for inter-vehicle distance estimation. Unlike conventional finite-time zeroing neural network (ZNN) models whose convergence time depends on the initial conditions, the proposed model guarantees convergence within a uniform upper bound independent of initial errors. A specially designed piecewise activation function is embedded into the ZNN framework, which not only accelerates network convergence but also yields a significantly tighter upper bound compared with existing lemmas as all the intermediate terms are explicitly retained during derivation. A comprehensive parameter sensitivity analysis is conducted, and practical tuning guidelines are provided to balance convergence speed and numerical stability. Numerical simulations in a realistic autonomous driving scenario validate that the proposed model converges within the derived theoretical bound and outperforms existing FXTZNN variants in both convergence speed and accuracy. The results demonstrate the potential of the proposed approach for reliable real-time deployment in dynamic and complex driving environments.

Mathematics doi: 10.3390/math14173126

Authors: Xintong Chen Qiangfei Chai Zelin Wang Bangyi Li

As the global stockpile of end-of-life electric vehicle batteries grows, subsidies have become a primary policy tool to stimulate recycling. However, recyclers can exploit private information about a battery’s State of Health to inflate quality claims and obtain excessive subsidies. This paper develops a Stackelberg game model encompassing a manufacturer and a recycler under three policy scenarios—no subsidy, subsidizing the manufacturer, and subsidizing the recycler—and extends the analysis to a hybrid subsidy scheme that optimally allocates a fixed subsidy budget between the two parties. The results deliver three explicit findings. First, subsidies exhibit a dual effect: while incentivizing recycling, excessively high subsidy levels can instead induce recycler misreporting and fail to improve environmental benefits, particularly for batteries with high reusable value. Second, the expected net value of recycled batteries is a pivotal parameter. When it is high, Pareto improvements for both supply chain members are achieved even with minimal subsidies, regardless of the subsidy recipient. Third, the proposed hybrid subsidy scheme, with an optimally derived allocation ratio, aligns the incentives of the manufacturer and the recycler, mitigates misreporting risk, and coordinates the supply chain more effectively than static, one-size-fits-all policies. The contribution of this study is twofold: it characterizes how subsidy allocation interacts with recycler misreporting in a battery recycling supply chain, and it provides policymakers with actionable guidance for designing differentiated and robust subsidy contracts that advance a sustainable battery ecosystem.

Mathematics doi: 10.3390/math14173125

Authors: Ivan Tikshaev Anatoly Sidorov

This paper considers the task of assessing the relevance of a procurement procedure for a supplier under conditions of growing volumes of open procurement data and increasing complexity of electronic publication services. It is shown that, for a supplier, relevance cannot be reduced to a match between a procurement notice and a search query or classifier code. In the European procurement context, procedure assessment requires consideration of the procurement object, lot structure, selection and award criteria, European Single Procurement Document requirements, procedure language, place of performance, participation through a specific legal entity, contract terms, data-protection requirements, service obligations, risk signals, and retrospective context. A formal mathematical representation of relevance assessment is developed, and on this basis a cascade agent model is proposed in which relevance is defined as the result of matching a procurement procedure, a supplier profile, and a set of evaluation rules. The model includes specialized agents for query normalization, procedure search, primary filtering, documentation preparation, fact extraction, constraint identification, procurement-object identification, customer analysis, contract-terms analysis, supplier-profile matching, dossier checking, relevance calculation, result interpretation, and final-card generation. The key intermediate result is an analytical procurement dossier containing structured facts, constraints, risk signals, matching results, and evidential links to sources. The proposed model is implemented as a research prototype and evaluated on an active stream of procurement procedures published through TED. The prototype evaluation shows that the cascade can transform a broad and heterogeneous set of retrieved procedures into a multilevel operational funnel comprising a shortlist, comparison pool, manual-review routes, and a monitoring layer. Within the reported case, these outputs demonstrate execution of the intended cascade sequence and generation of explainable user-specific assessments; they are not presented as evidence of ranking accuracy, superiority over simpler alternatives, or generalizability.

Mathematics doi: 10.3390/math14173124

Authors: Miloš S. Pešić Vladimir Lj. Dunić Vladimir P. Milovanović Aleksandar S. Bodić Miroslav M. Živković

This paper presents an analytical and numerical benchmark verification framework for explicit time integration procedures applied to the one-dimensional wave equation. The study combines an exact analytical solution, a closed-form discrete central-difference solution, and explicit finite element models implemented in LS-DYNA and in the in-house academic FEM code PAK-Multiphysics. Two benchmark problems with the same first sinusoidal spatial mode and homogeneous Dirichlet boundary conditions are considered. The first problem, defined by sinusoidal initial displacement and zero initial velocity, is used to analyse the central-difference discretization and its convergence behaviour. The closed-form discrete response enables direct comparison with the analytical solution and confirms the expected second-order accuracy under coupled mesh and time-step refinement at a fixed Courant number. The second problem, defined by zero initial displacement and sinusoidal initial velocity, introduces a phase-shifted temporal response suitable for explicit finite element verification. Four meshes are analysed over five periods of the first longitudinal mode. The numerical responses are assessed using displacement histories, maximum absolute errors, RMS errors, relative RMS errors, amplitude errors, and an energy check. The PAK-Multiphysics results show very close agreement with the analytical solution and a systematic reduction of the error measures, consistent with the lumped-mass central-difference formulation. The LS-DYNA results provide an independent commercial-code comparison, showing decreasing displacement errors under refinement and bounded total-energy variation. The proposed framework provides a transparent and reproducible benchmark for verifying one-dimensional explicit wave propagation models.

Mathematics doi: 10.3390/math14173123

Authors: Daoyuan Sun Ruosong Bu Guohui Zhang Quan Jiang Xiao Li Chenliang Hao Jian Wang

To achieve the optimal balance between structural safety and stripping economy for the rock slopes of a specific open-pit iron mine, a rigorous mathematical modeling and computational framework was established. In contrast to traditional simplified pseudo-static evaluations, authentic monitored seismic and blasting waveforms were integrated within an explicit dynamic strength reduction model to ensure that transient stress wave propagation and progressive failure paths of rock slopes were accurately captured. Furthermore, a constrained multi-objective optimization model was established so that the nonlinear trade-off between dynamic safety margins and stripping volumes could be quantitatively resolved. Based on the application to the studied open-pit slopes, it was revealed that severe deep plastic yielding and topological shear band coalescence were caused by transient dynamic stress waves when the slope angle was steepened to 45°. Consequently, the factor of safety (FS) was abruptly reduced to an unsafe range of 1.01 to 1.20. Through the effective exclusion of this high-risk 45° configuration, a global optimal mining slope angle of 42° was rigorously established. At this optimal angle, a robust factor of safety ranging from 1.45 to 1.98 was consistently maintained across all extreme multi-field coupled conditions. Ultimately, from an engineering perspective, dynamic shear failure paths were successfully interrupted, and the need for expensive structural reinforcement was eliminated. Economically, waste rock stripping volumes were significantly minimized, whereby the overall stripping ratio was optimized, and life-cycle excavation efficiency was maximized.

Mathematics doi: 10.3390/math14173122

Authors: Srđan Kostić Nebojša Vasović

Earthquake sequences can affect slope stability before recovery from an earlier event is complete, yet reduced-order models commonly treat successive earthquakes as independent inputs or prescribe cumulative damage through event-based increments. We introduce a bounded, response-generated memory state into a delayed two-block landslide model. The state reduces incremental friction, evolves exclusively through computed dissipative response, and heals continuously between earthquakes. Its critical value is derived independently from the characteristic roots of the delayed mechanical subsystem. Paired aftershock-only and mainshock–aftershock experiments use corrected accelerograms from the 2011 Redcliffs sequence as recorded inputs rather than calibration data. Across 1255 admissible deterministic comparisons, a subcritical mainshock reduced the aftershock activation threshold in every parameter cell; 1235 threshold intervals were strictly separated, while 20 converged to the aftershock-only limit under strong healing. Threshold reduction was almost entirely determined by retained memory (Spearman rank coefficient ρS = 0.9997). Under stochastic forcing, all 33 primary parameter cells showed the same direction of reduction, and 32 paired 95% bootstrap confidence intervals excluded zero. Independent 4096-realisation ensembles yielded reductions of 18.0–26.2% under white-noise and Ornstein–Uhlenbeck forcing. Resetting memory reproduced the aftershock-only response exactly, whereas removing displacement delay eliminated delayed activation. These results identify a causal mechanism by which a non-activating earthquake can transiently lower the activation threshold of a subsequent event, while distinguishing dimensionless model activation from physical landslide failure.

Mathematics doi: 10.3390/math14173120

Authors: Ghadah Alomani Amer Ibrahim Al-Omari

In this paper, we propose a new flexible modification of the Lomax distribution within the Bilal-G family generated through the T-X framework, referred to as the Lomax–Bilal distribution. The proposed model offers greater flexibility for modeling-skewed and heavy-tailed phenomena that frequently arise in survival and reliability studies. A comprehensive set of statistical properties is derived, as moments, order statistics, reliability measures, the quantile function, stochastic ordering, and maximum likelihood estimation. Furthermore, several information measures are obtained to characterize the uncertainty structure of the distribution, namely Shannon entropy, Rényi entropy, extropy, cumulative residual extropy, and generalized weighted extropy. Also, the Lorenz, Bonferroni, Zenga curves and Gini index are presented. The practical applicability and effectiveness of the proposed distribution are illustrated through analyses of two real datasets: survival times of patients with head and neck cancer treated with chemotherapy and radiation therapy, and repair times of an airborne communication transceiver. The empirical results showed that the Lomax–Bilal distribution consistently provides a better fit than several well-established lifetime distributions according to goodness-of-fit statistics and information criteria, particularly in modeling tail behavior. These findings suggest that the Lomax–Bilal distribution constitutes a flexible and competitive alternative for analyzing complex lifetime data in reliability engineering and medical survival studies.

Mathematics doi: 10.3390/math14173121

Authors: Paramahansa Pramanik Michael Bowdin

We develop a stochastic-control and mean field game framework for catastrophe insurance under stochastic replacement-cost risk. Insurer surplus follows a controlled jump diffusion in which catastrophe losses are scaled by an exogenous mean-reverting replacement-cost factor and attenuated through physical hedging. We establish well-posedness and stability of the controlled state process, derive a stopping-time dynamic programming principle, and characterize the value function as the unique viscosity solution of the associated nonlocal Hamilton–Jacobi–Bellman (HJB) equation. We then formulate strategic interaction among insurers through a coupled nonlocal HJB–Kolmogorov system and establish existence and uniqueness of mean field equilibrium under regularity and monotonicity conditions. The analysis quantifies how elevated replacement costs amplify catastrophe-loss exposure while physical hedging reduces it. Numerical results indicate stronger optimal hedging under high replacement-cost states and weak capitalization and quantify the equilibrium effects of industry-wide vulnerability.

Mathematics doi: 10.3390/math14173119

Authors: Jernej Jerebic Miha Ravber Luka Mernik Marjan Mernik

Differential Evolution (DE) is one of the most successful population-based optimization algorithms, and numerous adaptive variants, such as JADE, L-SHADE, and jDElscop, have been proposed to improve its search performance. Although these methods consistently outperform classical DE variants, whether they genuinely improve the balance between exploration and exploitation remains largely unexamined, since prior evaluations relied on imprecise diversity-based measures. This paper presents a detailed study of DE variants using the recently proposed attraction basin-based measures that distinguish between different types of exploration (successful, failed, deceptive, and successful rejection) and exploitation (successful and unsuccessful). The exploration and exploitation behavior of JADE, L-SHADE, and jDElscop is compared with four classical DE strategies: DE/best/1/bin, DE/best/1/exp, DE/rand/1/bin, and DE/rand/1/exp. The results show that adaptive DE variants prolong the exploration phase and improve the balance between successful and unsuccessful exploitation compared with the classical strategies, though each achieves this through a distinct mechanism. The presented findings improve the understanding of adaptive DE search behavior and demonstrate the usefulness of attraction basin-based measures for analyzing evolutionary optimization algorithms.

Mathematics doi: 10.3390/math14173118

Authors: Bo Lei Panshi Xie Ding Lang Bosheng Hu Haiyan Liu

Understanding the failure behavior of cylindrical-hole hard rocks is essential for rockburst prevention in deep underground engineering. In this study, fractal–statistical analysis was combined with true triaxial testing and discrete element modeling to quantify the rate-dependent failure and crack-network evolution of holed granodiorite. The results showed that, with an increasing loading rate, the peak axial stress increased from 143 to 190 MPa, the peak axial strain decreased from 1.24% to 0.86%, and the post-peak brittleness index increased from 0.83 to 1.19. The final failure pattern evolved from multi-crack tension–shear coupled failure to localized dominant fracture and intense hole-wall exfoliation. The mass fractal dimension of rockburst fragments increased with loading rate, reflecting a transition toward finer and more dispersed fragmentation. To extend the experimentally observed hole-wall failure mechanism to adjacent openings, a calibrated PFC3D double-hole model was further established. The numerical results revealed that crack interaction was governed by stress-concentration superposition and progressive rock-bridge damage, and the hole-spacing ratio controlled the connectivity and complexity of the crack network. As S/2R increased from 1.25 to 2.00, the dominant fracture-band inclination increased from 27° to 54°, reflecting a transition from steep inter-hole coalescence to more inclined and spatially dispersed fracture development.

Mathematics doi: 10.3390/math14173117

Authors: Zameddin I. Ismailov Pembe Ipek Al Mohammad Sababheh

In this paper, a new sequential joint (f,δ,q)-numerical radius is introduced for sequences of bounded linear operators on Hilbert spaces, motivated by recent generalizations of the numerical radius. Firstly, several fundamental properties of the sequential joint (f,δ,q)-numerical radius function are established. Subsequently, lower and upper bounds for the sequential joint (f,δ,q)-numerical radius function are derived, yielding generalizations of several known inequalities. Finally, the sequential joint (f,δ,q)-numerical radius function is investigated for operator sequences whose coordinate operators are sectorial, leading to further estimates and properties. The obtained results extend and unify a variety of existing results on numerical radius inequalities and provide new contributions to the theory of operator sequences on Hilbert spaces.

Mathematics doi: 10.3390/math14173116

Authors: Deva Putra Setyawan Diah Chaerani Sukono Sukono Nurfadhlina Abdul Halim

Portfolio optimization models are highly sensitive to estimation errors in expected returns and covariance matrices, often resulting in unstable allocations. Robust optimization mitigates parameter uncertainty by optimizing against worst-case realizations within a specified uncertainty set, whose construction critically determines the effectiveness of the approach. This paper proposes a data-driven framework for constructing polyhedral uncertainty sets that integrates Gaussian mixture models (GMMs) to identify heterogeneous distributional components and ARIMA-GARCH models to capture time-varying volatility dynamics. The construction proceeds in three stages. First, ARIMA-GARCH filters remove serial dependence and volatility clustering. Second, GMM clustering applied to the standardized residuals identifies latent market regimes. Third, convex hulls of observations lying within a Mahalanobis distance threshold form component-wise polyhedral sets, which are aggregated into a global convex uncertainty set. The robust counterpart is derived via linear programming duality, transforming the robust constraint into a tractable quadratic program that preserves convexity and polyhedrality. We prove that the constructed sets are convex and polyhedral, establish probabilistic coverage guarantees under mild regularity conditions, and analyze the computational complexity of the framework. Empirical analysis of Indonesian equity data confirms heavy tails and volatility clustering, with GMM identifying three distinct regimes of approximately equal proportions. Controlled synthetic experiments show that uncertainty set geometry fundamentally influences portfolio outcomes: overlapping clusters yield stable allocations across regimes, whereas well-separated clusters reveal that convex hull aggregation introduces conservatism that masks regime distinctions. Rolling window backtests demonstrate that the proposed approach produces economically higher Sharpe ratios than standard uncertainty set formulations in the reported out-of-sample period, although statistical significance is limited by the small number of independent rebalancing periods (18 quarterly events). The practical advantage should therefore be interpreted as conditional on moderate transaction costs and manageable turnover. These findings provide a statistically grounded, geometrically faithful, and computationally tractable methodology for practical implementation, contributing to financial resilience and sustainable economic growth with broader implications for stable capital markets.

Mathematics doi: 10.3390/math14173115

Authors: Shiyuan Huang Ziwei Chen

Major recommendation systems have considered multifaceted user profiles. However, their heavy reliance on questionnaire surveys makes it difficult to extend their application, and also renders recommendation outcomes susceptible to interference from biases. Addressing these issues, this paper proposes a multidimensional decision-fusion major recommendation framework for university applicants. A large language model was innovatively utilized to generate participant responses, constructing a simulated dataset (SimuCareer-25) to overcome the low efficiency and high bias of traditional survey methods. Building upon this, the framework integrates three key decision dimensions: preference, capability, and experience. It then employs fuzzy theory and XGBoost to process multidimensional user features encompassing personality, interests, subject literacy, and skills. Simultaneously, it leverages collaborative filtering to mine group experience. An Analytic Hierarchy Process module is used to perform adjustable weighted fusion of these three dimensions. Through experiments on SimuCareer-25 and real-world data, it was indicated that integrating preference, capability, and historical experience is conducive to generating robust and reliable major recommendations, and that despite structural deviations from real-world samples, the simulated data provides effective feature transferability to support the framework’s practical utility.

Mathematics doi: 10.3390/math14173114

Authors: Asifa Tassaddiq Muhammad Sajjad Shabbir Rabab Alharbi Youngsoo Seol Dalal Khalid Almutairi Rizwan Ahmed

The factorial Mathieu multiplier used in the nearest bi-univalent model is substituted with a gamma-shifted family using deformation parameter τ≥0. In this case, one differential operator describes all class operators introduced previously, whereas the function and inverse subordination can be controlled by two different generalized Ma–Minda functions. Explicit bounds for |a2|, |a3| and the Fekete–Szegő functional follow from identities involving exact second-order coefficients. These are sharpened by using the full Schwarz–Pick estimate |ω2| ≤ |1−|ω1|2. The estimates continue to hold even when Q=0. The positive-real-part, strongly starlike, Janowski, mixed Mathieu, and phase-dependent Noshiro families are included with explicit admissibility criteria, except for the Noshiro family, which has its phase limited to −π<ϕ<π, since Δ2 vanishes at the excluded endpoint. The numerical analysis compares the gamma deformation with the factorial case, partitions parameter space according to the active coefficient estimate, locates Q=0, and shows how unequal targets displace the center of the Fekete–Szegő bound. The auxiliary Schwarz inequalities are sharp, but simultaneous equality within the full bi-univalent class is not established.

Mathematics doi: 10.3390/math14173113

Authors: Woorim Shin Kyungwoon Cho Jiyoon Kim Siyeon Kang Hyokyung Bahn

The rapid proliferation of AI-enabled Industrial Internet of Things (IIoT) applications has significantly increased the energy consumption of shared edge computing infrastructures. Despite this sustainability challenge, contemporary resource pricing models in edge computing environments remain largely anchored in coarse-grained physical resource allocations rather than the actual energy consumed during workload execution. To support energy-aware resource management in industrial edge computing, this article formalizes an energy attribution model for AI workloads executed in shared edge nodes, where multi-tenant workloads concurrently share computing resources. The primary challenge in such environments stems from the inherent non-separability of localized power consumption among co-located workloads due to dynamic resource sharing and execution interference. To address this technical hurdle without introducing prohibitive monitoring or instrumentation overheads to the industrial environment, our model partitions aggregate system-level energy metrics into baseline platform elements and resource-specific functional components. It then formulates energy shares to individual workloads by solving consistent attribution functions based on observable resource allocation and utilization variables. By categorizing infrastructure hardware into utilization-driven, allocation-centric, and hybrid behavior profiles, the model precisely approximates workload-level energy responsibility within a practical error margin in shared IIoT edge computing environments.

Mathematics doi: 10.3390/math14173112

Authors: Cunyuan Yang Ken Nah Zhe Qian Guangliang Sang

Impressionist artworks, marked by distinctive brushstrokes and light effects, pose challenges for holistic deep learning models. Existing classification methods often lack interpretability and mathematical rigor. To address this, we propose an explainable AI framework for Impressionist painting classification based on feature disentanglement. The framework uses Fourier transform to decompose images into magnitude and phase spectra and then applies frequency filtering to separate high-frequency components (brushstroke textures, edges) from mid-to-low frequencies (global composition, color transitions). A state space model captures long-range dependencies within frequency representations. Disentangled features are fused with the original image features via a dual-branch injection mechanism. Experiments show that a lightweight model with 10M parameters, using this injection strategy, outperforms conventional baselines with 25M parameters. Moreover, the approach provides interpretability by explicitly linking classification decisions to brushstroke organization, frequency energy distribution, and semantic composition. This work offers a unified, computationally efficient, and mathematically rigorous solution for feature disentanglement in artistic image analysis, laying a theoretical foundation for explainable computational aesthetics and human–AI collaborative appreciation.