Mathematics

13 pages, 260 KiB

Open AccessEditorial

Editorial: New Advances in High-Dimensional and Non-Asymptotic Statistics

by Huiming Zhang and Xiaowei Yang

Mathematics 2025, 13(14), 2267; https://doi.org/10.3390/math13142267 (registering DOI) - 14 Jul 2025

This editorial paper reviews the Special Issue “New Advances in High-Dimensional and Non-asymptotic Statistics” and summarizes the ten collected papers [...] Full article

(This article belongs to the Special Issue New Advances in High-Dimensional and Non-asymptotic Statistics)

31 pages, 4652 KiB

Open AccessArticle

A Delayed Malware Propagation Model Under a Distributed Patching Mechanism: Stability Analysis

by Wei Zhang, Xiaofan Yang and Luxing Yang

Mathematics 2025, 13(14), 2266; https://doi.org/10.3390/math13142266 (registering DOI) - 14 Jul 2025

Abstract

Antivirus (patch) is one of the most powerful tools for defending against malware spread. Distributed patching is superior to its centralized counterpart in terms of significantly lower bandwidth requirement. Under the distributed patching mechanism, a novel malware propagation model with double delays and [...] Read more.

Antivirus (patch) is one of the most powerful tools for defending against malware spread. Distributed patching is superior to its centralized counterpart in terms of significantly lower bandwidth requirement. Under the distributed patching mechanism, a novel malware propagation model with double delays and double saturation effects is proposed. The basic properties of the model are discussed. A pair of thresholds, i.e., the first threshold

R_{0}

and the second threshold

R_{1}

, are determined. It is shown that (a) the model admits no malware-endemic equilibrium if

R_{0} \leq 1

, (b) the model admits a unique patch-free malware-endemic equilibrium and admits no patch-endemic malware-endemic equilibrium if

1 < R_{0} \leq R_{1}

, and (c) the model admits a unique patch-free malware-endemic equilibrium and a unique patch-endemic malware-endemic equilibrium if

R_{0} > R_{1}

. A criterion for the global asymptotic stability of the malware-free equilibrium is given. A pair of criteria for the local asymptotic stability of the patch-free malware-endemic equilibrium are presented. A pair of criteria for the local asymptotic stability of the patch-endemic malware-endemic equilibrium are derived. Using cybersecurity terms, these theoretical outcomes have the following explanations: (a) In the case where the first threshold can be kept below unity, the malware can be eradicated through distributed patching. (b) In the case where the first threshold can only be kept between unity and the second threshold, the patches may fail completely, and the malware cannot be eradicated through distributed patching. (c) In the case where the first threshold cannot be kept below the second threshold, the patches may work permanently, but the malware cannot be eradicated through distributed patching. The influence of the delays and the saturation effects on malware propagation is examined experimentally. The relevant conclusions reveal the way the delays and saturation effects modulate these outcomes. Full article

(This article belongs to the Special Issue Mathematical Epidemiological Models: Classical and Interdisciplinary Applications)

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14 pages, 380 KiB

Open AccessArticle

Stability Analysis of a Mathematical Model for Infection Diseases with Stochastic Perturbations

by Marina Bershadsky and Leonid Shaikhet

Mathematics 2025, 13(14), 2265; https://doi.org/10.3390/math13142265 - 14 Jul 2025

Abstract

A well-known model of infectious diseases, described by a nonlinear system of delay differential equations, is investigated under the influence of stochastic perturbations. Using the general method of Lyapunov functional construction combined with the linear matrix inequality (LMI) approach, we derive sufficient conditions [...] Read more.

A well-known model of infectious diseases, described by a nonlinear system of delay differential equations, is investigated under the influence of stochastic perturbations. Using the general method of Lyapunov functional construction combined with the linear matrix inequality (LMI) approach, we derive sufficient conditions for the stability of the equilibria of the considered system. Numerical simulations illustrating the system’s behavior under stochastic perturbations are provided to support the thoretical findings. The proposed method for stability analysis is broadly applicable to other systems of nonlinear stochastic differential equations across various fields. Full article

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12 pages, 355 KiB

Open AccessArticle

A Goodness-of-Fit Test for Log-Linearity in Cox Proportional Hazards Model Under Monotonic Covariate Effects

by Huan Chen and Chuan-Fa Tang

Mathematics 2025, 13(14), 2264; https://doi.org/10.3390/math13142264 - 14 Jul 2025

Abstract

The Cox proportional hazards (PH) model is widely used because it models the covariates to the hazard through a log-linear effect. However, exploring flexible effects becomes desirable within the Cox PH framework when only a monotonic relationship between covariates and the hazard is [...] Read more.

The Cox proportional hazards (PH) model is widely used because it models the covariates to the hazard through a log-linear effect. However, exploring flexible effects becomes desirable within the Cox PH framework when only a monotonic relationship between covariates and the hazard is assumed. This work proposes a partial-likelihood-based goodness-of-fit (GOF) test to assess the log-linear effect assumption in a univariate Cox PH model. Rejection of log-linearity suggests the need to incorporate monotonic and non-log-linear covariate effects on the hazard. Our simulation studies show that the proposed GOF test controls type I error rates and exhibits consistency across various scenarios. We illustrate the proposed GOF test with two datasets, breast cancer data and lung cancer data, to assess the presence of log-linear effects in the Cox PH model. Full article

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

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13 pages, 314 KiB

Open AccessArticle

Application-Oriented Study of Next-Generation Alternant Codes over Gaussian Integers for Secure and Efficient Communication

by Muhammad Sajjad and Nawaf A. Alqwaifly

Mathematics 2025, 13(14), 2263; https://doi.org/10.3390/math13142263 - 13 Jul 2025

Abstract

This paper presents the construction and analysis of a novel class of alternant codes over Gaussian integers, aimed at enhancing error correction capabilities in high-reliability communication systems. These codes are constructed using parity-check matrices derived from finite commutative local rings with unity, specifically [...] Read more.

This paper presents the construction and analysis of a novel class of alternant codes over Gaussian integers, aimed at enhancing error correction capabilities in high-reliability communication systems. These codes are constructed using parity-check matrices derived from finite commutative local rings with unity, specifically

Z_{n} [i],

where

i^{2} = - 1

. A detailed algebraic investigation of the polynomial

x^{n} - 1

over these rings is conducted to facilitate the systematic construction of such codes. The proposed alternant codes extend the principles of classical BCH and Goppa codes to complex integer domains, enabling richer algebraic structures and greater error-correction potential. We evaluate the performance of these codes in terms of error correction capability, and redundancy. Numerical results show that the proposed codes outperform classical short-length codes in scenarios requiring moderate block lengths, such as those applicable in certain segments of 5G and IoT networks. Unlike conventional codes, these constructions allow enhanced structural flexibility that can be tuned for various application-specific parameters. While the potential relevance to quantum-safe communication is acknowledged, it is not the primary focus of this study. This work demonstrates how extending classical coding techniques into non-traditional algebraic domains opens up new directions for designing robust and efficient communication codes. Full article

(This article belongs to the Special Issue Mathematics for Algebraic Coding Theory and Cryptography)

38 pages, 1773 KiB

Open AccessArticle

Pricing and Emission Reduction Strategies of Heterogeneous Automakers Under the “Dual-Credit + Carbon Cap-And-Trade” Policy Scenario

by Chenxu Wu, Yuxiang Zhang, Junwei Zhao, Chao Wang and Weide Chun

Mathematics 2025, 13(14), 2262; https://doi.org/10.3390/math13142262 - 13 Jul 2025

Abstract

Against the backdrop of increasingly severe global climate change, the automotive industry, as a carbon-intensive sector, has found its low-carbon transformation crucial for achieving the “double carbon” goals. This paper constructs manufacturer decision-making models under an oligopolistic market scenario for the single dual-credit [...] Read more.

Against the backdrop of increasingly severe global climate change, the automotive industry, as a carbon-intensive sector, has found its low-carbon transformation crucial for achieving the “double carbon” goals. This paper constructs manufacturer decision-making models under an oligopolistic market scenario for the single dual-credit policy and the “dual-credit + carbon cap-and-trade” policy, revealing the nonlinear impacts of new energy vehicle (NEV) credit trading prices, carbon trading prices, and credit ratio requirements on manufacturers’ pricing, emission reduction effort levels, and profits. The results indicate the following: (1) Under the “carbon cap-and-trade + dual-credit” policy, manufacturers can balance emission reduction costs and NEV production via the carbon trading market to maximize profits, with lower emission reduction effort levels than under the single dual-credit policy. (2) A rise in credit trading prices prompts hybrid manufacturers (producing both fuel vehicles and NEVs) to increase NEV production and reduce fuel vehicle output; higher NEV credit ratio requirements raise fuel vehicle production costs and prices, suppressing consumer demand. (3) An increase in carbon trading prices raises production costs for both fuel vehicles and NEVs, leading to decreased market demand; hybrid manufacturers reduce emission reduction efforts, while others transfer costs through price hikes to boost profits. (4) Hybrid manufacturers face high carbon emission costs due to excessive actual fuel consumption, driving them to enhance emission reduction efforts and promote low-carbon technological innovation. Full article

(This article belongs to the Special Issue Intelligent Operations, Game Analysis and Decision Making in Platform-Based Supply Chains)

22 pages, 9035 KiB

Open AccessArticle

Chirped Soliton Perturbation and Benjamin–Feir Instability of Chen–Lee–Liu Equation with Full Nonlinearity

by Khalil S. Al-Ghafri and Anjan Biswas

Mathematics 2025, 13(14), 2261; https://doi.org/10.3390/math13142261 - 12 Jul 2025

Abstract

The objective of the present study is to detect chirped optical solitons of the perturbed Chen–Lee–Liu equation with full nonlinearity. By virtue of the traveling wave hypothesis, the discussed model is reduced to a simple form known as an elliptic equation. The latter [...] Read more.

The objective of the present study is to detect chirped optical solitons of the perturbed Chen–Lee–Liu equation with full nonlinearity. By virtue of the traveling wave hypothesis, the discussed model is reduced to a simple form known as an elliptic equation. The latter equation, which is a second-order ordinary differential equation, is handled by the undetermined coefficient method of two forms expressed in terms of the hyperbolic secant and tangent functions. Additionally, the auxiliary equation method is applied to derive several miscellaneous solutions. Various types of chirped solitons are revealed such as W-shaped, bright, dark, gray, kink and anti-kink waves. Taking into consideration the existence conditions, the dynamical behaviors of optical solitons and their corresponding chirp are illustrated. The modulation instability of the perturbed CLL equation is examined by means of the linear stability analysis. It is found that all solutions are stable against small perturbations. These entirely new results, compared to previous works, can be employed to understand pulse propagation in optical fiber mediums and dynamic characteristics of waves in plasma. Full article

(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 2nd Edition)

20 pages, 568 KiB

Open AccessArticle

Non-Parametric Inference for Multi-Sample of Geometric Processes with Application to Multi-System Repair Process Modeling

by Ömer Altındağ

Mathematics 2025, 13(14), 2260; https://doi.org/10.3390/math13142260 - 12 Jul 2025

Abstract

The geometric process is a significant monotonic stochastic process widely used in the fields of applied probability, particularly in the failure analysis of repairable systems. For repairable systems modeled by a geometric process, accurate estimation of model parameters is essential. The inference problem [...] Read more.

The geometric process is a significant monotonic stochastic process widely used in the fields of applied probability, particularly in the failure analysis of repairable systems. For repairable systems modeled by a geometric process, accurate estimation of model parameters is essential. The inference problem for geometric processes has been well-studied in the case of single-sample data. However, multi-sample data may arise when the repair processes of multiple systems are observed simultaneously. This study addresses the non-parametric inference problem for geometric processes based on multi-sample data. Several non-parametric estimators are proposed using the linear regression method, and their asymptotic properties are established. In addition, test statistics are introduced to assess sample homogeneity and to evaluate the significance of the trend observed in the process. The performance of the proposed estimators is evaluated through a comprehensive simulation study under small-sample settings. An artificial data analysis is conducted to model the repair processes of multiple repairable systems using the geometric process. Furthermore, a real-world dataset consisting of multi-sample failure data from two shared memory processors of the Blue Mountain supercomputer is analyzed to demonstrate the practical applicability of the method in multi-sample failure data analysis. Full article

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

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33 pages, 12259 KiB

Open AccessFeature PaperArticle

A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems

by Lin Zhang, Dongming Li, Cen-Ying Liao and Li-Rui Tian

Mathematics 2025, 13(14), 2259; https://doi.org/10.3390/math13142259 - 12 Jul 2025

Abstract

A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation [...] Read more.

A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation in sequence. The quasi-convex reproducing kernel approximation proposed by Wang et al. to construct almost positive reproducing kernel shape functions with relaxed monomial reproducing conditions is applied to improve the positivity of the thermal matrixes in the final discreated equations. Two numerical examples are given to verify the effectiveness of the developed method. The numerical results show that the solutions obtained by the quasi-convex reproducing kernel particle method agree well with the analytical ones, with a slightly better-improved numerical accuracy than the element-free Galerkin method and the reproducing kernel particle method. The effects of different parameters, i.e., the scaling parameter, the penalty factor, and node distribution on computational accuracy and efficiency, are also investigated. Full article

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17 pages, 2527 KiB

Open AccessArticle

An Adaptive Prescribed Performance Position Tracking Controller for Hydraulic Systems

by Junqiang Shi, Xiaowei Yang, Jinjun Wu and Jingcheng Gao

Mathematics 2025, 13(14), 2258; https://doi.org/10.3390/math13142258 - 12 Jul 2025

Abstract

Unknown time-varying parameters, along with mismatched and matched disturbances, exist in hydraulic systems, worsening position tracking performance and even destabilizing systems. To address this issue, this article proposes an adaptive full-state prescribed performance position tracking control for hydraulic systems subject both to unknown [...] Read more.

Unknown time-varying parameters, along with mismatched and matched disturbances, exist in hydraulic systems, worsening position tracking performance and even destabilizing systems. To address this issue, this article proposes an adaptive full-state prescribed performance position tracking control for hydraulic systems subject both to unknown time-varying parameters and to mismatched and matched disturbances. First, a smooth nonlinear term is skillfully introduced into the controller design so that it can simultaneously cope with both unknown time-varying parameters and disturbances. Next, by integrating the adaptive technique and the prescribed performance function, an adaptive full-state prescribed performance position tracking controller is developed for hydraulic systems in which both the transient and steady performance of all the control errors can be prescribed. A stability analysis then confirms both the prescribed transient performance and the asymptotic steady performance of all the control errors. Finally, the superiority of the proposed controller is also validated by comparison with simulation results. Full article

(This article belongs to the Special Issue High-Performance Advanced Control for Electromechanical and Hydraulic Systems)

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30 pages, 2843 KiB

Open AccessArticle

Survey on Replay-Based Continual Learning and Empirical Validation on Feasibility in Diverse Edge Devices Using a Representative Method

by Heon-Sung Park, Hyeon-Chang Chu, Min-Kyung Sung, Chaewoon Kim, Jeongwon Lee, Dae-Won Kim and Jaesung Lee

Mathematics 2025, 13(14), 2257; https://doi.org/10.3390/math13142257 - 12 Jul 2025

Abstract

The goal of on-device continual learning is to enable models to adapt to streaming data without forgetting previously acquired knowledge, even with limited computational resources and memory constraints. Recent research has demonstrated that weighted regularization-based methods are constrained by indirect knowledge preservation and [...] Read more.

The goal of on-device continual learning is to enable models to adapt to streaming data without forgetting previously acquired knowledge, even with limited computational resources and memory constraints. Recent research has demonstrated that weighted regularization-based methods are constrained by indirect knowledge preservation and sensitive hyperparameter settings, and dynamic architecture methods are ill-suited for on-device environments due to increased resource consumption as the structure scales. In order to compensate for these limitations, replay-based continuous learning, which maintains a compact structure and stable performance, is gaining attention. The limitations of replay-based continuous learning are (1) the limited amount of historical training data that can be stored due to limited memory capacity, and (2) the computational resources of on-device systems are significantly lower than those of servers or cloud infrastructures. Consequently, designing strategies that balance the preservation of past knowledge with rapid and cost-effective updates of model parameters has become a critical consideration in on-device continual learning. This paper presents an empirical survey of replay-based continual learning studies, considering the nearest class mean classifier with replay-based sparse weight updates as a representative method for validating the feasibility of diverse edge devices. Our empirical comparison of standard benchmarks, including CIFAR-10, CIFAR-100, and TinyImageNet, deployed on devices such as Jetson Nano and Raspberry Pi, showed that the proposed representative method achieved reasonable accuracy under limited buffer sizes compared with existing replay-based techniques. A significant reduction in training time and resource consumption was observed, thereby supporting the feasibility of replay-based on-device continual learning in practice. Full article

(This article belongs to the Special Issue Computational Intelligence in Systems, Signals and Image Processing)

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18 pages, 15177 KiB

Open AccessArticle

Optimization-Driven Reconstruction of 3D Space Curves from Two Views Using NURBS

by Musrrat Ali, Deepika Saini, Sanoj Kumar and Abdul Rahaman Wahab Sait

Mathematics 2025, 13(14), 2256; https://doi.org/10.3390/math13142256 - 12 Jul 2025

Abstract

In the realm of 3D curve reconstruction, Non-Uniform Rational B-Splines (NURBSs) offer a versatile mathematical tool due to their ability to precisely represent complex geometries. However, achieving high fitting accuracy in stereo-based applications remains challenging, primarily due to the nonlinear nature of weight [...] Read more.

In the realm of 3D curve reconstruction, Non-Uniform Rational B-Splines (NURBSs) offer a versatile mathematical tool due to their ability to precisely represent complex geometries. However, achieving high fitting accuracy in stereo-based applications remains challenging, primarily due to the nonlinear nature of weight optimization. This study introduces an enhanced iterative strategy that leverages the geometric significance of NURBS weights to incrementally refine curve fitting. By formulating an inverse optimization problem guided by model deformation principles, the proposed method progressively adjusts weights to minimize reprojection error. Experimental evaluations confirm the method’s convergence and demonstrate its superiority in fitting accuracy when compared to conventional optimization techniques. Full article

(This article belongs to the Special Issue Advances in Deep Learning, Computer Vision, and Engineering Applications)

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89 pages, 695 KiB

Open AccessArticle

An Improvement of Least Squares Theory: Theory of Least p-Variances Approximation and p-Uncorrelated Functions

by Mohammad Masjed-Jamei

Mathematics 2025, 13(14), 2255; https://doi.org/10.3390/math13142255 - 11 Jul 2025

Abstract

We establish a theory whose structure is based on a fixed variable and an algebraic inequality and which improves the well-known least squares theory. The mentioned fixed variable plays a basic role in creating such a theory. In this direction, some new concepts, [...] Read more.

We establish a theory whose structure is based on a fixed variable and an algebraic inequality and which improves the well-known least squares theory. The mentioned fixed variable plays a basic role in creating such a theory. In this direction, some new concepts, such as p-covariances with respect to a fixed variable, p-correlation coefficients with respect to a fixed variable, and p-uncorrelatedness with respect to a fixed variable, are defined in order to establish least p-variance approximations. We then obtain a specific system, called the p-covariances linear system, and apply the p-uncorrelatedness condition on its elements to find a general representation for p-uncorrelated variables. Afterwards, we apply the concept of p-uncorrelatedness for continuous functions, particularly for polynomial sequences, and we find some new sequences, such as a generic two-parameter hypergeometric polynomial of the

_{4} F_{3}

type that satisfies a p-uncorrelatedness property. In the sequel, we obtain an upper bound for 1-covariances, an improvement to the approximate solutions of over-determined systems and an improvement to the Bessel inequality and Parseval identity. Finally, we generalize the concept of least p-variance approximations based on several fixed orthogonal variables. Full article

81 pages, 20908 KiB

Open AccessArticle

Image Inpainting with Fractional Laplacian Regularization: An L^p Norm Approach

by Hongfang Yuan, Weijie Su, Xiangkai Lian, Zheng-An Yao and Dewen Hu

Mathematics 2025, 13(14), 2254; https://doi.org/10.3390/math13142254 - 11 Jul 2025

Abstract

This study presents an image inpainting model based on an energy functional that incorporates the

L^{p}

norm of the fractional Laplacian operator as a regularization term and the

H^{- 1}

norm as a fidelity term. Using the properties of the fractional [...] Read more.

This study presents an image inpainting model based on an energy functional that incorporates the

L^{p}

norm of the fractional Laplacian operator as a regularization term and the

H^{- 1}

norm as a fidelity term. Using the properties of the fractional Laplacian operator, the

L^{p}

norm is employed with an adjustable parameter p to enhance the operator’s ability to restore fine details in various types of images. The replacement of the conventional

L^{2}

norm with the

H^{- 1}

norm enables better preservation of global structures in denoising and restoration tasks. This paper introduces a diffusion partial differential equation by adding an intermediate term and provides a theoretical proof of the existence and uniqueness of its solution in Sobolev spaces. Furthermore, it demonstrates that the solution converges to the minimizer of the energy functional as time approaches infinity. Numerical experiments that compare the proposed method with traditional and deep learning models validate its effectiveness in image inpainting tasks. Full article

(This article belongs to the Special Issue Numerical and Computational Methods in Engineering)

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23 pages, 3874 KiB

Open AccessArticle

Optimal Media Control Strategy for Rumor Propagation in a Multilingual Dual Layer Reaction Diffusion Network Model

by Guiyun Liu, Haozhe Xu, Yu Zhu, Yiyang Ma and Zhipeng Chen

Mathematics 2025, 13(14), 2253; https://doi.org/10.3390/math13142253 - 11 Jul 2025

Abstract

The rapid advancement of Internet of Things technologies has significantly enhanced cross-regional communication among geographically and linguistically diverse populations on social platforms yet simultaneously accelerated the propagation of rumors across multilingual networks at unprecedented velocity. Therefore, this study focuses on investigating the spatiotemporal [...] Read more.

The rapid advancement of Internet of Things technologies has significantly enhanced cross-regional communication among geographically and linguistically diverse populations on social platforms yet simultaneously accelerated the propagation of rumors across multilingual networks at unprecedented velocity. Therefore, this study focuses on investigating the spatiotemporal propagation dynamics and cross-lingual diffusion characteristics of rumors. Distinguished from conventional approaches, we innovatively formulate a hybrid dual-layer rumor containment model through a reaction–diffusion framework that explicitly incorporates the coupling control effects of media layers with independent propagation dynamics. Furthermore, we rigorously prove the differentiability of control-to-state mappings, which enables the derivation of necessary optimality conditions for the optimal control problem. Finally, comprehensive simulations validate both the adaptability and effectiveness of our media-based spatiotemporal control strategies in multilingual environments. Full article

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16 pages, 284 KiB

Open AccessArticle

Initial Coefficient Bounds for Bi-Close-to-Convex and Bi-Quasi-Convex Functions with Bounded Boundary Rotation Associated with q-Sălăgean Operator

by Prathviraj Sharma, Srikandan Sivasubramanian, Adriana Catas and Sheza M. El-Deeb

Mathematics 2025, 13(14), 2252; https://doi.org/10.3390/math13142252 - 11 Jul 2025

Abstract

In this article, through the application of the q-Sălăgean operator associated with functions characterized by bounded boundary rotation, we propose a few new subclasses of bi-univalent functions that utilize the q-Sălăgean operator with bounded boundary rotation in the open unit disk [...] Read more.

In this article, through the application of the q-Sălăgean operator associated with functions characterized by bounded boundary rotation, we propose a few new subclasses of bi-univalent functions that utilize the q-Sălăgean operator with bounded boundary rotation in the open unit disk

E

. For these classes, we establish the initial bounds for the coefficients

| a_{2} |

and

| a_{3} |

. Additionally, we have derived the well-known Fekete–Szegö inequality for this newly defined subclasses. Full article

(This article belongs to the Special Issue Geometric Function Theory and Applications―Festschrift for Grigore-Stefan Salagean's 75th Birthday)

41 pages, 20897 KiB

Open AccessArticle

Voltage and Frequency Regulation in Interconnected Power Systems via a (1+PDD²)-(1+TI) Cascade Controller Optimized by Mirage Search Optimizer

by Kareem M. AboRas, Ali M. Elkassas, Ashraf Ibrahim Megahed and Hossam Kotb

Mathematics 2025, 13(14), 2251; https://doi.org/10.3390/math13142251 - 11 Jul 2025

Abstract

The combined application of Load Frequency Control (LFC) and Automatic Voltage Regulation (AVR), known as Automatic Generation Control (AGC), manages active and reactive power to ensure system stability. This study presents a novel hybrid controller with a (1+PDD²)-(1+TI) structure, optimized using [...] Read more.

The combined application of Load Frequency Control (LFC) and Automatic Voltage Regulation (AVR), known as Automatic Generation Control (AGC), manages active and reactive power to ensure system stability. This study presents a novel hybrid controller with a (1+PDD²)-(1+TI) structure, optimized using the Mirage Search Optimization (MSO) algorithm. Designed for dual-area power systems, the controller enhances both LFC and AVR by coordinating voltage and frequency loops. MSO was chosen after outperforming five algorithms (ChOA, DOA, PSO, GTO, and GBO), achieving the lowest fitness value (ITSE = 0.028). The controller was tested under various challenging conditions: sudden load disturbances, stochastic variations, nonlinearities like Generation Rate Constraints (GRC) and Governor Dead Band (GDB), time-varying reference voltages, and ±20% to ±40% parameter deviations. Across all scenarios, the (1+PDD²)-(1+TI) controller consistently outperformed MSO-tuned TID, FOPID, FOPI-PIDD², (1+PD)-PID, and conventional PID controllers. It demonstrated superior performance in regulating frequency, tie-line power, and voltage, achieving approximately a 50% improvement in dynamic response. MATLAB/SIMULINK results confirm its effectiveness in enhancing overall system stability. Full article

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

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15 pages, 281 KiB

Open AccessArticle

Reciprocal Theorems for Multi-Cost Problems with S-Type I Functionals

by Savin Treanţă, Valeria Cîrlan and Omar Mutab Alsalami

Mathematics 2025, 13(14), 2250; https://doi.org/10.3390/math13142250 - 11 Jul 2025

Abstract

In this paper, for the considered multi-cost variational problem (P), we associate a dual model (D) in order to study and state the connections between the solution sets of these control problems. Thus, under S-type I assumptions associated with the integral functionals [...] Read more.

In this paper, for the considered multi-cost variational problem (P), we associate a dual model (D) in order to study and state the connections between the solution sets of these control problems. Thus, under S-type I assumptions associated with the integral functionals involved, we formulate and prove various reciprocal results, such as weak, strong, and converse-type dualities. Full article

17 pages, 624 KiB

Open AccessArticle

Parallel Simulation Multi-Sample Task Scheduling Approach Based on Deep Reinforcement Learning in Cloud Computing Environment

by Yuhao Xiao, Yping Yao and Feng Zhu

Mathematics 2025, 13(14), 2249; https://doi.org/10.3390/math13142249 - 11 Jul 2025

Abstract

Complex scenario analysis and evaluation simulations often involve multiple sets of simulation applications with different combinations of parameters, thus resulting in high computing power consumption, which is one of the factors that limits the efficiency of multi-sample parallel simulations. Cloud computing provides considerable [...] Read more.

Complex scenario analysis and evaluation simulations often involve multiple sets of simulation applications with different combinations of parameters, thus resulting in high computing power consumption, which is one of the factors that limits the efficiency of multi-sample parallel simulations. Cloud computing provides considerable amounts of cheap and convenient computing resources, thus providing efficient support for multi-sample simulation tasks. However, traditional simulation scheduling methods do not consider the collaborative parallel scheduling of multiple samples and multiple entities under multi-objective constraints. Deep reinforcement learning methods can continuously learn and adjust their strategies through interactions with the environment, demonstrating strong adaptability in response to dynamically changing task requirements. Therefore, herein, a parallel simulation multi-sample task scheduling method based on deep reinforcement learning in a cloud computing environment is proposed. The method collects cluster load information and simulation application information as state inputs in the cloud environment, designs a multi-objective reward function to balance the cost and execution efficiency, and uses deep Q-networks (DQNs) to train agents for intelligent scheduling of multi-sample parallel simulation tasks. In a real cloud environment, the proposed method demonstrates runtime reductions of 4–11% and execution cost savings of 11–22% compared to the Round-Robin algorithm, Best Fit algorithm, and genetic algorithm. Full article

(This article belongs to the Special Issue Advanced Optimization Modeling and Algorithms for Planning and Scheduling)

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