Mathematics

34 pages, 14577 KB

Open AccessArticle

Effective Alternator Voltage Control Based on Computational Intelligence Using Dream Optimizer

by Wajdi M. Alghamdi and Madini O. Alassafi

Mathematics 2026, 14(11), 1796; https://doi.org/10.3390/math14111796 (registering DOI) - 22 May 2026

Controller performance is strongly influenced by its parameters. Estimating these parameters requires an effective estimation approach for obtaining the best possible response. This study proposes a novel methodology for the estimation of controller parameters, utilizing the dream optimization algorithm (DOA) and a new [...] Read more.

Controller performance is strongly influenced by its parameters. Estimating these parameters requires an effective estimation approach for obtaining the best possible response. This study proposes a novel methodology for the estimation of controller parameters, utilizing the dream optimization algorithm (DOA) and a new objective function. The proposed method is employed to determine the optimal parameters of various PID controllers used in the automatic voltage regulator (AVR) system. Thus, the suggested objective function consists of transient response metrics and the stability index “integral of time-weighted absolute error (

I T A E

)”. Three different PID controllers are used, which are cascaded PIPD with filter (CPIPDF), cascaded fractional-order PI fractional-order PDF (CFOPIFOPDF), and PIDF. The DOA’s performance is compared with famous and recent optimizers and shows more reliable performance. For example, based on the statistical analysis, the DOA obtained a standard deviation of 0.0042, while the closest competitor obtained 0.0089. Furthermore, the CPIPDF, CFOPIFOPDF, and PIDF controllers are compared under a wide variety of operating conditions. Based on ITAE, the CPIPDF controller achieved lower values than the CFOPIFOPDF and PIDF controllers. Also, the results show that the CPIPDF controller achieves better performance than other published controllers. For instance, the CPIPDF controller improves AVR performance by approximately 45.3% compared to the fireworks whale optimization algorithm-based PIDD² controller in the case of varying load condition impact. Moreover, scenarios that remain insufficiently addressed in the literature, such as communication delays, restricted excitation voltages, and external disturbances, are considered. Full article

(This article belongs to the Section E2: Control Theory and Mechanics)

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21 pages, 1003 KB

Open AccessArticle

Bias Evaluation in Large Language Model Summaries Using Financial Crimes Data

by Shegufta Tasneem, Hanna Courtot, Katherine Fullowan and Patrick Hall

Mathematics 2026, 14(11), 1795; https://doi.org/10.3390/math14111795 (registering DOI) - 22 May 2026

Abstract

Large language models (LLMs) are being adopted rapidly in financial institutions for applications including customer communication, compliance review, fraud detection, and agentic workflows, but without bias evaluation, they risk reinforcing systemic biases that may lead to unethical or unlawful decisions. To address potential [...] Read more.

Large language models (LLMs) are being adopted rapidly in financial institutions for applications including customer communication, compliance review, fraud detection, and agentic workflows, but without bias evaluation, they risk reinforcing systemic biases that may lead to unethical or unlawful decisions. To address potential systemic bias in LLMs in regulated settings like financial services, we present a statistical analysis framework and structured, reproducible methodology for evaluating whether LLM outputs vary significantly across demographic groups. Using financial fraud stories from the CNN/DailyMail dataset, we employ substitution-based identity variations across protected demographic classes, generate summaries via three proprietary language models, and perform statistical analysis on common metrics (ROUGE, BERTScore, Adverse Impact Ratio (AIR), and Standardized Mean Difference (SMD)). Statistical approaches such as MANOVA and ANOVA reveal small but significant differences in output metric values (e.g., for White female, Black male, and Asian male identities in our analysis), while sentiment analysis and human evaluation confirm disparities in tone and framing. Our results also indicate that measured disparities appear to decrease across subsequent model generations. Full article

(This article belongs to the Special Issue Advanced Statistical and Machine Learning Methods for High-Dimensional and Big Data Analysis)

8 pages, 4756 KB

Open AccessArticle

The Exact Solutions of the Kundu–Eckhaus Equation Using the Dbar Method

by Lili Wen

Mathematics 2026, 14(11), 1794; https://doi.org/10.3390/math14111794 (registering DOI) - 22 May 2026

Abstract

In this paper, we investigate high-order soliton solutions of the Kundu–Eckhaus equation using the Dbar method. As a key technique in the field of integrable systems, the Dbar method occupies an important position in the study of exact solutions due to its unique [...] Read more.

In this paper, we investigate high-order soliton solutions of the Kundu–Eckhaus equation using the Dbar method. As a key technique in the field of integrable systems, the Dbar method occupies an important position in the study of exact solutions due to its unique advantages. Exact solutions for first-order to fifth-order solitons are presented under the zero-background condition. The nonlinear dynamics of the solitons are also discussed, including their interaction behaviors. The results are also depicted graphically in both 3D and 2D for different values of associated parameters. Full article

(This article belongs to the Section C2: Dynamical Systems)

54 pages, 10762 KB

Open AccessArticle

Controllability of Prabhakar Fractional System of Integro-Differential Equations of Order η∈(1,2) with Nonlocal Conditions: Application to Viscoelastic Mechanical Systems

by Suganya Palanisamy, Mallika Arjunan Mani, Kavitha Velusamy, Sowmiya Ramasamy and Seenith Sivasundaram

Mathematics 2026, 14(11), 1793; https://doi.org/10.3390/math14111793 (registering DOI) - 22 May 2026

Abstract

This paper advances a comprehensive controllability framework for Prabhakar fractional differential systems (

PFDS

s) of order

η \in (1, 2)

with nonlocal initial conditions, where the second-order setting requires the joint specification of both an initial state and an [...] Read more.

This paper advances a comprehensive controllability framework for Prabhakar fractional differential systems (

PFDS

s) of order

η \in (1, 2)

with nonlocal initial conditions, where the second-order setting requires the joint specification of both an initial state and an initial velocity. Explicit solution representations for four structurally distinct classes of second-order Prabhakar systems are derived via the Laplace transform method and Neumann series expansions, revealing that the placement of the forcing term directly in the system or under the Prabhakar fractional integral operator produces fundamentally different convolution kernels. For linear integro-differential systems, necessary and sufficient controllability conditions are established through a Gramian rank criterion with an explicit norm-bounded control law, while for nonlinear systems, sufficient conditions are obtained via the Schauder fixed-point theorem under an asymptotic growth condition. Three numerical examples validate the theory: a three-dimensional linear system and a two-dimensional nonlinear integro-differential system achieve terminal errors of order

10^{- 12}

and

10^{- 7}

, respectively, and a Prabhakar fractional mass–spring–damper system with viscoelastic hereditary damping demonstrates direct physical relevance, with all theoretical conditions verified and a terminal error of

7.42 \times 10^{- 5}

confirming precise rest-position steering by the Gramian-based control law. Full article

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

26 pages, 749 KB

Open AccessFeature PaperArticle

Generalized Finite Difference Methods for Risk-Averse Optimal Investment in Mean-Field Type Control

by Yuzu Wang, Le Xu, SingRu (Celine) Hoe and Zhongfeng Yan

Mathematics 2026, 14(11), 1792; https://doi.org/10.3390/math14111792 - 22 May 2026

Abstract

This work studies a finite-time mean-field type control problem arising from optimal investment under uncertainty with risk management. The problem leads to a nonlinearly coupled system of parabolic equations with temporal and nonlocal interactions. An explicit characterization of the solution to the system [...] Read more.

This work studies a finite-time mean-field type control problem arising from optimal investment under uncertainty with risk management. The problem leads to a nonlinearly coupled system of parabolic equations with temporal and nonlocal interactions. An explicit characterization of the solution to the system is obtained, and a generalized finite difference method (GFDM) combined with an iterative scheme is developed to ensure global temporal consistency of the mean-field feedback during backward computation. Numerical experiments illustrate the accuracy and effectiveness of the proposed approach.In addition, sensitivity studies with respect to the volatility and risk-aversion parameters demonstrate the robustness of the proposed numerical framework under parameter perturbations. Full article

(This article belongs to the Special Issue Advances in Mathematical Finance and Insurance)

18 pages, 607 KB

Open AccessArticle

Time-Varying Rare Disasters, Model Uncertainty, and the Equity Premium Puzzle

by Yuzhuo Ren and Weiqi Liu

Mathematics 2026, 14(11), 1791; https://doi.org/10.3390/math14111791 - 22 May 2026

Abstract

This study develops a production-based asset pricing model that incorporates time-varying disaster risk together with model uncertainty. Within an extended relative-entropy framework, agents’ distorted beliefs and ambiguity aversion are characterized, and the corresponding Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation is derived under a stochastic robust-control setting. [...] Read more.

This study develops a production-based asset pricing model that incorporates time-varying disaster risk together with model uncertainty. Within an extended relative-entropy framework, agents’ distorted beliefs and ambiguity aversion are characterized, and the corresponding Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation is derived under a stochastic robust-control setting. The framework implies that the equity premium can be decomposed into three components: diffusion and jump risk premiums associated with conventional risk aversion and an additional rare-event premium generated by ambiguity aversion. Numerical experiments show that ambiguity aversion reduces the equilibrium risk-free rate, whereas aversion to rare disasters significantly raises compensation for bearing risk, helping reconcile both the equity premium puzzle and the risk-free rate puzzle. In addition, equity return volatility increases with the probability of disaster events, but at a diminishing rate. Overall, the results underscore the importance of model uncertainty and time-varying disaster risk in the determination of asset prices and risk premia. Full article

41 pages, 536 KB

Open AccessFeature PaperArticle

Four-Dimensional CR Submanifolds of the Homogeneous Nearly Kähler Product Manifold S³×S³

by Nataša Djurdjević

Mathematics 2026, 14(11), 1790; https://doi.org/10.3390/math14111790 - 22 May 2026

Abstract

This article presents results on four-dimensional CR submanifolds of the homogeneous nearly Kähler product manifold

S^{3} \times S^{3}

. In the research of CR submanifolds of

S^{3} \times S^{3}

, the most important role in the classification is played [...] Read more.

This article presents results on four-dimensional CR submanifolds of the homogeneous nearly Kähler product manifold

S^{3} \times S^{3}

. In the research of CR submanifolds of

S^{3} \times S^{3}

, the most important role in the classification is played by the action of the almost product structure P. Here, the investigation of the action of the almost product structure on the tangent bundle of four-dimensional CR submanifolds of

S^{3} \times S^{3}

is extended. Classifications are obtained for certain types of submanifolds whose almost complex distribution is almost product invariant, such as the class characterized by a special type of angle functions, as well as those whose tangent bundle is almost product invariant. The previously mentioned classes of four-dimensional CR submanifolds lead to the classification of those submanifolds that are locally usual product manifolds of Lagrangian submanifolds of

S^{3} \times S^{3}

and curves. Full article

(This article belongs to the Special Issue Submanifolds in Metric Manifolds, 2nd Edition)

20 pages, 367 KB

Open AccessArticle

On the Distribution of αp² + β Modulo One and r-Free Integers

by Tatiana L. Todorova and Atanaska Georgieva

Mathematics 2026, 14(11), 1789; https://doi.org/10.3390/math14111789 - 22 May 2026

Abstract

Let

α

be an irrational number,

β

a real number, and

a_{1}, \dots, a_{s}

a set of distinct positive integers that do not form a reduced residue system modulo

p^{r}

for any prime p. In this work, [...] Read more.

Let

α

be an irrational number,

β

a real number, and

a_{1}, \dots, a_{s}

a set of distinct positive integers that do not form a reduced residue system modulo

p^{r}

for any prime p. In this work, we establish that there are infinitely many prime numbers p that satisfy the condition

| | α p^{2} + β | | < p^{- θ}

for a suitable

θ

, and at the same time each of the numbers

p + a_{1}, \dots

,

p + a_{s}

is r-free. Full article

(This article belongs to the Special Issue Analytic Methods in Number Theory and Allied Fields)

20 pages, 542 KB

Open AccessArticle

Time-Series Forecasting by Statistical State-Dependent Reconstruction of Coefficients of Itô-Type Processes

by Mikhail Ivanov, Victor Korolev and Alexander Vakshin

Mathematics 2026, 14(11), 1788; https://doi.org/10.3390/math14111788 - 22 May 2026

Abstract

We consider the problem of time-series forecasting via statistical reconstruction of the coefficients of the Itô representation of the underlying stochastic process

X (t)

. The reconstructed coefficients are obtained using techniques that account for their dependence on the current value [...] Read more.

We consider the problem of time-series forecasting via statistical reconstruction of the coefficients of the Itô representation of the underlying stochastic process

X (t)

. The reconstructed coefficients are obtained using techniques that account for their dependence on the current value of the process. We augmented the basic linear autoregressive model with the estimated Itô drift coefficients: 1st order

\hat{a} (t, X_{t})

and 2nd order

\hat{\hat{a}} (t, \hat{a} (t, X_{t}))

that can be treated as the 1st and 2nd quasi-derivatives of the original time series that is assumed to be a realization of

X (t)

. The predictive techniques used in this paper are based on a kind of statistical analog of the Taylor expansion for the time series. The proposed predictive algorithms demonstrate higher accuracy as compared to other autoregressive algorithms applied to forecasting a big set of time series. Full article

(This article belongs to the Special Issue Time Series Analysis: Methods and Applications)

23 pages, 711 KB

Open AccessArticle

Self-Triggered Impulsive Control for Exponential Synchronization of Complex Networks Subject to Cyber Attacks

by Xin Liu, Da Wang, Xichao Ma, Yan Gao and Yu Cheng

Mathematics 2026, 14(11), 1787; https://doi.org/10.3390/math14111787 - 22 May 2026

Abstract

The exponential synchronization in mean square for complex networks by using two self-triggered impulsive control mechanisms under denial-of-service (DoS) and deception attacks is studied in this paper. These proposed control mechanisms include both static and dynamic forms. Meanwhile, under these control mechanisms, Zeno [...] Read more.

The exponential synchronization in mean square for complex networks by using two self-triggered impulsive control mechanisms under denial-of-service (DoS) and deception attacks is studied in this paper. These proposed control mechanisms include both static and dynamic forms. Meanwhile, under these control mechanisms, Zeno behavior is effectively avoided, which contributes to improved system stability. Additionally, two independent Bernoulli random sequences are introduced for integrating the denial-of-service (DoS) and deception attacks into a common modeling structure. Further, sufficient conditions for achieving exponential stability in mean square are derived by constructing the Lyapunov functional. Ultimately, the reliability and accuracy of the derived results are validated through simulation experiments. It is observed from the numerical experiments that dynamic self-triggered control enables more efficient utilization of the communication resources. Full article

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26 pages, 52806 KB

Open AccessArticle

RF-GoatDet: An Occlusion-Aware Instance Segmentation Framework for Dairy Goats with an Adaptive Receptive Field Encoder

by Yongliang Zhang, Yue Yang, Ronggeng Guo and Nan Geng

Mathematics 2026, 14(11), 1786; https://doi.org/10.3390/math14111786 - 22 May 2026

Abstract

Accurate instance segmentation is essential for precision livestock farming, as it supports individual tracking, posture analysis, body-shape measurement, and other downstream visual monitoring tasks. However, dairy goat segmentation in dense barn scenes remains challenging because frequent mutual occlusion, instance adhesion, partial visibility, and [...] Read more.

Accurate instance segmentation is essential for precision livestock farming, as it supports individual tracking, posture analysis, body-shape measurement, and other downstream visual monitoring tasks. However, dairy goat segmentation in dense barn scenes remains challenging because frequent mutual occlusion, instance adhesion, partial visibility, and non-rigid posture variation often lead to incomplete masks and ambiguous instance boundaries. To address these challenges, this study develops RF-GoatDet, a real-time instance segmentation framework for dairy goats built upon RT-DETR. The main component of the proposed framework is an Adaptive Receptive Field Encoder (ARFE), which enhances feature encoding by adapting the effective receptive field to irregular goat contours, scale variation, and partially visible body regions. In addition, Coordinate Attention is introduced to strengthen direction-aware spatial representation, while a Query-Conditioned Dynamic Mask Head is used to generate instance-specific masks and improve the separation of adjacent goats. A dairy goat instance segmentation dataset containing 2288 annotated images was constructed, and a two-stage cleaning procedure was applied to reduce redundancy and visual anomalies. Experimental results show that RF-GoatDet achieves 46.5% mask AP and 62 FPS on this dataset, improving the RT-DETR baseline by 4.2 percentage points in mask AP while maintaining real-time inference. These results demonstrate that the proposed ARFE-centered framework effectively improves mask quality and instance discrimination in dense dairy goat scenes, providing a robust and efficient solution for real-time visual monitoring in precision livestock farming. Full article

(This article belongs to the Special Issue Machine Learning Applications in Image Processing and Computer Vision)

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20 pages, 1600 KB

Open AccessArticle

DiT1dLnet: A Fast and Accurate Diffusion Model Structure Based on Robot Behavior Imitation

by Jiaxin Liao, Weiyuan He, Qing Yu and Fei Chen

Mathematics 2026, 14(11), 1785; https://doi.org/10.3390/math14111785 - 22 May 2026

Abstract

A novel robot behavior generation method combining imitation learning with diffusion models elegantly addresses multi-modal action distributions, adapts to high-dimensional action spaces, and demonstrates impressive training stability. It significantly improves success rates across nine diverse tasks on three different robot simulation benchmarks, but [...] Read more.

A novel robot behavior generation method combining imitation learning with diffusion models elegantly addresses multi-modal action distributions, adapts to high-dimensional action spaces, and demonstrates impressive training stability. It significantly improves success rates across nine diverse tasks on three different robot simulation benchmarks, but comes with longer training times and slower inference speed. This paper proposes a novel architecture, DiT1dLnet, applied to DDPM for training and inference. DiT1dLnet improves accuracy across various robotic simulation tasks while accelerating training and inference speed by 50–100%. We benchmarked its performance on nine different tasks using three distinct robots. Full article

(This article belongs to the Special Issue Advances in Artificial Intelligence, Machine Learning and Optimization, 2nd Edition)

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Mathematics, Volume 14, Issue 11 (June-1 2026) – 12 articles

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