Mathematics

24 pages, 5413 KiB

Open AccessArticle

System Identification of a Servo-Valve Controlled Hydraulic Cylinder Operating Under Variable Load

by Daniel Catalin Stroita, Dorin Bordeasu and Florin Dragan

Mathematics 2025, 13(3), 341; https://doi.org/10.3390/math13030341 (registering DOI) - 22 Jan 2025

This work presents an in-depth study on the system identification of a servo-valve controlled hydraulic cylinder operating under variable load. This research addresses the growing demand for improved control systems (enhancing time response, settling time, and precision) in variable load hydraulic actuators, such [...] Read more.

This work presents an in-depth study on the system identification of a servo-valve controlled hydraulic cylinder operating under variable load. This research addresses the growing demand for improved control systems (enhancing time response, settling time, and precision) in variable load hydraulic actuators, such as those used in blade pitching systems of wind turbines. The paper begins by detailing the experimental setup, followed by the development of the system’s mathematical model, a fourth-order transfer function (TF). The experimental data collected by a proposed data acquisition system are used for the dynamic identification of the hydraulic setup using periodical signals as commands. All possible combinations of TFs up to order 8 are identified. After an initial visual preselection of the 15 most accurate ones, analyses comparing quality indicators between the measured (experimental) and the TF (simulated) step and sinusoidal responses are conducted to determine the most accurate TF. The paper concludes with the presentation and analysis of the dynamic model, identified as being a fourth-order TF, which replicates the system dynamics with the greatest fidelity. It provides an identification methodology with significant potential for industry practitioners aiming to improve, optimize, and enhance control strategies for variable load hydraulic actuators. Full article

(This article belongs to the Special Issue Mathematical Applications in Industrial Engineering)

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23 pages, 3204 KiB

Open AccessArticle

An Improved Whale Optimization Algorithm for the Integrated Scheduling of Automated Guided Vehicles and Yard Cranes

by Shuaishuai Gong, Ping Lou, Jianmin Hu, Yuhang Zeng and Chuannian Fan

Mathematics 2025, 13(3), 340; https://doi.org/10.3390/math13030340 (registering DOI) - 22 Jan 2025

Abstract

With the rapid development of global trade, the cargo throughput of automated container terminals (ACTs) has increased significantly. To meet the demands of large-scale, high-intensity, and high-efficiency ACT operations, the seamless integration of various terminal facilities has become crucial, particularly the collaboration between [...] Read more.

With the rapid development of global trade, the cargo throughput of automated container terminals (ACTs) has increased significantly. To meet the demands of large-scale, high-intensity, and high-efficiency ACT operations, the seamless integration of various terminal facilities has become crucial, particularly the collaboration between yard cranes (YCs) and automated guided vehicles (AGVs). Therefore, an integrated scheduling problem for YCs and AGVs (YAAISP) is proposed and formulated in this paper, considering stacking containers and bidirectional transport of AGVs. As the YAAISP is an NP-hard problem, an Improved Whale Optimization Algorithm (IWOA) is proposed in which a reverse learning strategy is used for the population to enhance population diversity; a random difference variation strategy is employed to improve individual exploration capabilities; and a nonlinear convergence factor alongside an adaptive weighting mechanism to dynamically balance global exploration and local exploitation. For container tasks of size 100, the objective function value (OFV) of the IWOA was reduced by 9.25% compared to the standard Whale Optimization Algorithm. Comparisons with other algorithms, such as the Genetic Algorithm, Particle Swarm Optimization, and Grey Wolf Optimizer, showed an OFV reduction of 9.61% to 11.75%. This validates the superiority of the proposed method. Full article

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13 pages, 268 KiB

Open AccessArticle

A Note on Mutation Equivalence

by Siyang Liu and Jie Pan

Mathematics 2025, 13(3), 339; https://doi.org/10.3390/math13030339 - 21 Jan 2025

Abstract

We focus on the necessary conditions for two totally sign-skew-symmetric matrices B and

B^{'}

to be mutation equivalent, obtaining two specific conditions: the equality of their column greatest common divisor vectors and the equality of

| B |

and [...] Read more.

We focus on the necessary conditions for two totally sign-skew-symmetric matrices B and

B^{'}

to be mutation equivalent, obtaining two specific conditions: the equality of their column greatest common divisor vectors and the equality of

| B |

and

| B^{'} |

, up to a relabeling of indices, when both matrices are acyclic. As a byproduct, the former condition confirms a conjecture on cluster automorphisms for totally sign-skew-symmetric cluster algebras. Full article

19 pages, 1844 KiB

Open AccessArticle

Prediction of Projectile Interception Point and Interception Time Based on Harris Hawk Optimization–Convolutional Neural Network–Support Vector Regression Algorithm

by Zhanpeng Gao and Wenjun Yi

Mathematics 2025, 13(3), 338; https://doi.org/10.3390/math13030338 - 21 Jan 2025

Abstract

In modern warfare, the accurate prediction of the intercept time and intercept point of the interceptor is the key to achieving penetration. Aiming at this problem, firstly, a convolutional neural network (CNN) is used to automatically extract high-level features from the data, and [...] Read more.

In modern warfare, the accurate prediction of the intercept time and intercept point of the interceptor is the key to achieving penetration. Aiming at this problem, firstly, a convolutional neural network (CNN) is used to automatically extract high-level features from the data, and then these features are used as the input of support vector regression (SVR) for regression prediction. The Harris Hawk optimization (HHO) is used to optimize the hyperparameters of SVR, and the HHO-CNN-SVR algorithm is proposed. In order to verify the effectiveness of the algorithm for the prediction of the interception point and interception time, this paper constructs a dataset to test the method of simulating the missile interception maneuvering target. Compared with BP, ELM, SVR, HHO-SVR, and CNN-SVR models, the HHO-CNN-SVR model has outstanding performance in prediction accuracy and stability, especially for the interception time. The error is the smallest, and the error fluctuation is small. The MAE of the prediction result is only 0.0139 s; in the interception point prediction, the error of the range and elevation direction is significantly lower than that of the models used for comparison. The MAE in the range direction is 2.3 m, and the MAE in the elevation direction is 2.01 m, which meet the engineering requirements. The HHO-CNN-SVR model has strong prediction accuracy and stability in interception time and interception point prediction. In addition, different control strategies are used to construct a new prediction set, and noise is added to the prediction set. The HHO-CNN-SVR algorithm can maintain good prediction results. The results show that the HHO-CNN-SVR model proposed in this paper has strong generalization ability and high robustness, which can provide reliable support for penetration decision making and defense system optimization. Full article

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Missile penetration schematic diagram. Full article ">Figure 2
Missle–target relative motion model. Full article ">Figure 3
Missile target engagement diagram. Full article ">Figure 4
CNN model structure diagram. Full article ">Figure 5
Projectile interception point and interception time prediction flow chart. Full article ">Figure 6
Interception time sample point prediction error. Full article ">Figure 7
Interception time prediction error box plot. Full article ">Figure 8
Prediction results of interception point. (a) Prediction error of sample points in x-axis direction; (b) x-axis direction prediction error box plot; (c) prediction error of sample points in y-axis direction; (d) y-axis direction prediction error box plot. Full article ">

23 pages, 315 KiB

Open AccessArticle

Computably Enumerable Semisimple Rings

by Huishan Wu

Mathematics 2025, 13(3), 337; https://doi.org/10.3390/math13030337 - 21 Jan 2025

Abstract

The theory of semisimple rings plays a fundamental role in noncommutative algebra. We study the complexity of the problem of semisimple rings using the tools of computability theory. Following the general idea of computably enumerable (c.e. for short) universal algebras, we define a [...] Read more.

The theory of semisimple rings plays a fundamental role in noncommutative algebra. We study the complexity of the problem of semisimple rings using the tools of computability theory. Following the general idea of computably enumerable (c.e. for short) universal algebras, we define a c.e. ring as the quotient ring of a computable ring modulo a c.e. congruence relation and view such rings as structures in the language of rings, together with a binary relation. We formalize the problem of being semisimple for a c.e. ring by the corresponding index set and prove that the index set of c.e. semisimple rings is

Σ_{3}^{0}

-complete. This reveals that the complexity of the definability of c.e. semisimple rings lies exactly in the

Σ_{3}^{0}

of the arithmetic hierarchy. As applications of the complexity results on semisimple rings, we also obtain the optimal complexity results on other closely connected classes of rings, such as the small class of finite direct products of fields and the more general class of semiperfect rings. Full article

(This article belongs to the Special Issue Mathematical Logic and Foundations of Mathematics)

19 pages, 2948 KiB

Open AccessArticle

Robust Fixed-Time Containment Tracking of Multi-Agent Systems with Unknown External Disturbances

by Ruichi Ren, Zhenbing Luo, Kaiyu Qin, Boxian Lin and Mengji Shi

Mathematics 2025, 13(3), 336; https://doi.org/10.3390/math13030336 - 21 Jan 2025

Abstract

Fixed-time (FXT) containment control, which provides timely protective deployment of heterogeneous agents in non-ideal environments, can be essential in battles or other large dynamic scenarios. With this in mind, this paper comes up with a simplified FXT containment tracking control law making the [...] Read more.

Fixed-time (FXT) containment control, which provides timely protective deployment of heterogeneous agents in non-ideal environments, can be essential in battles or other large dynamic scenarios. With this in mind, this paper comes up with a simplified FXT containment tracking control law making the follower agents under directed communication topologies and unknown external disturbances converge to a dynamic convex hull spanned by a class of fractional-order leaders. Based on FXT theory, a novel simplified FXT containment controller is proposed that consists of two components—a signum function term and a power term—which significantly reduces the complexity of the controller structure. Meanwhile, it remains qualified to achieve the control goal within a fixed settling time, independent of the initial agent states. The proposed containment controller can also be extended to solve the general consensus tracking problem. Finally, some simulation results are presented to demonstrate the effectiveness and conciseness of the proposed FXT containment tracking control scheme. Full article

(This article belongs to the Special Issue Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems, 2nd Edition)

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38 pages, 2581 KiB

Open AccessArticle

Transfinite Patches for Isogeometric Analysis

by Christopher Provatidis

Mathematics 2025, 13(3), 335; https://doi.org/10.3390/math13030335 - 21 Jan 2025

Abstract

This paper extends the well-known transfinite interpolation formula, which was developed in the late 1960s by the applied mathematician William Gordon at the premises of General Motors as an extension of the pre-existing Coons interpolation formula. Here, a conjecture is formulated, which claims [...] Read more.

This paper extends the well-known transfinite interpolation formula, which was developed in the late 1960s by the applied mathematician William Gordon at the premises of General Motors as an extension of the pre-existing Coons interpolation formula. Here, a conjecture is formulated, which claims that the meaning of the involved blending functions can be enhanced, such that it includes any linear independent and complete set of functions, including piecewise-linear, trigonometric functions, Bernstein polynomials, B-splines, and NURBS, among others. In this sense, NURBS-based isogeometric analysis and aspects of T-splines may be considered as special cases. Applications are provided to illustrate the accuracy in the interpolation through the L₂ error norm of closed-formed functions prescribed at the nodal points of the transfinite patch, which represent the solution of partial differential equations under boundary conditions of the Dirichlet type. Full article

(This article belongs to the Special Issue Advanced Numerical and Computational Methods for Engineering and Applied Mathematical Problems, 2nd Edition)

28 pages, 14050 KiB

Open AccessArticle

Hybrid CNN-BiLSTM-MHSA Model for Accurate Fault Diagnosis of Rotor Motor Bearings

by Zizhen Yang, Wei Li, Fang Yuan, Haifeng Zhi, Min Guo, Bo Xin and Zhilong Gao

Mathematics 2025, 13(3), 334; https://doi.org/10.3390/math13030334 - 21 Jan 2025

Abstract

Rotor motor fault diagnosis in Unmanned Aerial Vehicles (UAVs) presents significant challenges under variable speeds. Recent advances in deep learning offer promising solutions. To address challenges in extracting spatial, temporal, and hierarchical features from raw vibration signals, a hybrid CNN-BiLSTM-MHSA model is developed. [...] Read more.

Rotor motor fault diagnosis in Unmanned Aerial Vehicles (UAVs) presents significant challenges under variable speeds. Recent advances in deep learning offer promising solutions. To address challenges in extracting spatial, temporal, and hierarchical features from raw vibration signals, a hybrid CNN-BiLSTM-MHSA model is developed. This model leverages Convolutional Neural Networks (CNNs) to identify spatial patterns, a Bidirectional Long Short-Term Memory (BiLSTM) network to capture long- and short-term temporal dependencies, and a Multi-Head Self-Attention (MHSA) mechanism to highlight essential diagnostic features. Experiments on raw rotor motor vibration data preprocessed with Butterworth band-stop filters were conducted under laboratory and real-world conditions. The proposed model achieves 99.33% accuracy in identifying faulty bearings, outperforming traditional models like CNN (93.33%) and LSTM (62.00%) and recent advances including CNN-LSTM (98.87%), the Attention Recurrent Autoencoder hybrid Model (ARAE) (66.00%), Lightweight Time-focused Model Network (LTFM-Net) (96.67%), and Wavelet Denoising CNN-LSTM (WDCNN-LSTM) (96.00%). The model’s high accuracy and stability under varying conditions underscore its robustness, making it a reliable solution for rolling bearing fault diagnosis in rotor motors, particularly for dynamic UAV applications. Full article

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20 pages, 1078 KiB

Open AccessFeature PaperArticle

Piecewise Analytical Approximation Methods for Initial-Value Problems of Nonlinear Ordinary Differential Equations

by Juan I. Ramos

Mathematics 2025, 13(3), 333; https://doi.org/10.3390/math13030333 - 21 Jan 2025

Abstract

Piecewise analytical solutions to scalar, nonlinear, first-order, ordinary differential equations based on the second-order Taylor series expansion of their right-hand sides that result in Riccati’s equations are presented. Closed-form solutions are obtained if the dependence of the right-hand side on the independent variable [...] Read more.

Piecewise analytical solutions to scalar, nonlinear, first-order, ordinary differential equations based on the second-order Taylor series expansion of their right-hand sides that result in Riccati’s equations are presented. Closed-form solutions are obtained if the dependence of the right-hand side on the independent variable is not considered; otherwise, the solution is given by convergent series. Discrete solutions also based on the second-order Taylor series expansion of the right-hand side and the discretization of the independent variable that result in algebraic quadratic equations are also reported. Both the piecewise analytical and discrete methods are applied to two singularly perturbed initial-value problems and the results are compared with the exact solution and those of linearization procedures, and implicit and explicit Taylor’s methods. It is shown that the accuracy of piecewise analytical techniques depends on the number of terms kept in the series expansion of the solution, whereas that of the discrete methods depends on the location where the coefficients are evaluated. For Riccati equations with constant coefficients, the piecewise analytical method presented here provides the exact solution; it also provides the exact solution for linear, first-order ordinary differential equations with constant coefficients. Full article

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9 pages, 248 KiB

Open AccessArticle

Circular Chromatic Number of Signed Planar Graphs Without Cycles of Length 4 to 9

by Chunyan Wei

Mathematics 2025, 13(3), 332; https://doi.org/10.3390/math13030332 - 21 Jan 2025

Abstract

Given a signed graph

(G, σ)

and a positive real number r, if there exists a vertex mapping

c : V (G) \to [0, r)

satisfying that for every positive edge

w x

, [...] Read more.

Given a signed graph

(G, σ)

and a positive real number r, if there exists a vertex mapping

c : V (G) \to [0, r)

satisfying that for every positive edge

w x

,

1 \leq | c (w) - c (x) | \leq r - 1

and for every negative edge

w x

,

| c (w) - c (x) | \leq \frac{r}{2} - 1

or

| c (w) - c (x) | \geq \frac{r}{2} + 1

, then

(G, σ)

admits a circular r-coloring. We use

χ_{c} (G, σ)

to represent the circular chromatic number of

(G, σ)

, which is the minimum r, such that a circular r-coloring of

(G, σ)

exists. This paper proves that

χ_{c} (G, σ) < 4

, where

(G, σ)

is a simple signed planar graph containing no cycles of length 4 to 9. Moreover, we establish an upper bound for the chromatic number of such a graph to be

4 - \frac{2}{⌊ \frac{v (G) + 1}{2} ⌋}

. Full article

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

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13 pages, 20306 KiB

Open AccessArticle

Clustering-Based Class Hierarchy Modeling for Semantic Segmentation Using Remotely Sensed Imagery

by Lanfa Liu, Song Wang, Zichen Tong and Zhanchuan Cai

Mathematics 2025, 13(3), 331; https://doi.org/10.3390/math13030331 - 21 Jan 2025

Abstract

Land use/land cover (LULC) nomenclature is commonly organized as a tree-like hierarchy, contributing to hierarchical LULC mapping. The hierarchical structure is typically defined by considering natural characteristics or human activities, which may not optimally align with the discriminative features and class relationships present [...] Read more.

Land use/land cover (LULC) nomenclature is commonly organized as a tree-like hierarchy, contributing to hierarchical LULC mapping. The hierarchical structure is typically defined by considering natural characteristics or human activities, which may not optimally align with the discriminative features and class relationships present in remotely sensed imagery. This paper explores a novel cluster-based class hierarchy modeling framework that generates data-driven hierarchical structures for LULC semantic segmentation. First, we perform spectral clustering on confusion matrices generated by a flat model, and then we introduce a hierarchical cluster validity index to obtain the optimal number of clusters to generate initial class hierarchies. We further employ ensemble clustering techniques to yield a refined final class hierarchy. Finally, we conduct comparative experiments on three benchmark datasets. Results demonstrating that the proposed method outperforms predefined hierarchies in both hierarchical LULC segmentation and classification. Full article

(This article belongs to the Special Issue Computing in Image Processing for Remote Sensing and Biomedical Applications)

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31 pages, 550 KiB

Open AccessArticle

On the Extended Simple Equations Method (SEsM) and Its Application for Finding Exact Solutions of the Time-Fractional Diffusive Predator–Prey System Incorporating an Allee Effect

by Elena V. Nikolova

Mathematics 2025, 13(3), 330; https://doi.org/10.3390/math13030330 - 21 Jan 2025

Viewed by 69

Abstract

In this paper, I extend the Simple Equations Method (SEsM) and adapt it to obtain exact solutions of systems of fractional nonlinear partial differential equations (FNPDEs). The novelty in the extended SEsM algorithm is that, in addition to introducing more simple equations in [...] Read more.

In this paper, I extend the Simple Equations Method (SEsM) and adapt it to obtain exact solutions of systems of fractional nonlinear partial differential equations (FNPDEs). The novelty in the extended SEsM algorithm is that, in addition to introducing more simple equations in the construction of the solutions of the studied FNPDEs, it is assumed that the selected simple equations have different independent variables (i.e., different coordinates moving with the wave). As a consequence, nonlinear waves propagating with different wave velocities will be observed. Several scenarios of the extended SEsM are applied to the time-fractional predator–prey model under the Allee effect. Based on this, new analytical solutions are derived. Numerical simulations of some of these solutions are presented, adequately capturing the expected diverse wave dynamics of predator–prey interactions. Full article

(This article belongs to the Section C1: Difference and Differential Equations)

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18 pages, 274 KiB

Open AccessArticle

New Class of Estimators for Finite Population Mean Under Stratified Double Phase Sampling with Simulation and Real-Life Application

by Abdulaziz S. Alghamdi and Hleil Alrweili

Mathematics 2025, 13(3), 329; https://doi.org/10.3390/math13030329 - 21 Jan 2025

Viewed by 77

Abstract

Sampling survey data can sometimes contain outlier observations. When the mean estimator becomes skewed due to the presence of extreme values in the sample, results can be biased. The tendency to remove outliers from sample data is common. However, performing such removal can [...] Read more.

Sampling survey data can sometimes contain outlier observations. When the mean estimator becomes skewed due to the presence of extreme values in the sample, results can be biased. The tendency to remove outliers from sample data is common. However, performing such removal can reduce the accuracy of conventional estimating techniques, particularly with regard to the mean square error (MSE). In order to increase population mean estimation accuracy while taking extreme values into consideration, this study presents an enhanced class of estimators. The method uses extreme values from an auxiliary variable as a source of information rather than eliminating these outliers. Using a first-order approximation, the properties of the suggested class of estimators are investigated within the context of a stratified two-phase sampling framework. A simulation research is conducted to examine the practical performance of these estimators in order to validate the theoretical conclusions. To further demonstrate the superiority of the suggested class of estimators for dealing with extreme values, an analysis of three different datasets demonstrates that they consistently provide higher percent relative efficiency (PRE) when compared to existing estimators. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation: 3rd Edition)

16 pages, 449 KiB

Open AccessArticle

Curvature Control for Plane Curves

by Fatma Karakus, Cristina-Liliana Pripoae and Gabriel-Teodor Pripoae

Mathematics 2025, 13(3), 328; https://doi.org/10.3390/math13030328 - 21 Jan 2025

Viewed by 100

Abstract

We define a family of special functions (the CSI ones), which can be used to write any parameterized plane curve with polynomial curvature explicitly. These special functions generalize the Fresnel integrals, and may have an interest in their own right. We prove that [...] Read more.

We define a family of special functions (the CSI ones), which can be used to write any parameterized plane curve with polynomial curvature explicitly. These special functions generalize the Fresnel integrals, and may have an interest in their own right. We prove that any plane curve with polynomial curvature is asymptotically a pseudo-spiral. Using the CSI functions, we can approximate, locally, any plane curve; this approach provides a useful criterion for a (local) classification of plane curves. In addition, we present a new algorithm for finding an arc-length parametrization for any curve, within a prescribed degree of approximation. Full article

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22 pages, 983 KiB

Open AccessArticle

A Comparative Study of New Ratio-Type Family of Estimators Under Stratified Two-Phase Sampling

by Abdulaziz S. Alghamdi and Hleil Alrweili

Mathematics 2025, 13(3), 327; https://doi.org/10.3390/math13030327 - 21 Jan 2025

Viewed by 131

Abstract

Two-phase sampling is a useful technique for sample surveys, particularly when prior auxiliary data is not accessible. The ranks of the auxiliary variable often coincide with those of the research variable when two variables are correlated. By considering this relationship, we can significantly [...] Read more.

Two-phase sampling is a useful technique for sample surveys, particularly when prior auxiliary data is not accessible. The ranks of the auxiliary variable often coincide with those of the research variable when two variables are correlated. By considering this relationship, we can significantly increase estimator accuracy. In this paper, we use the ranks of the auxiliary variable along with extreme values to estimate the population mean of the study variable. Up to a first-order approximation, we analyze the characteristics of the suggested class of estimators with an emphasis on biases and mean squared errors in stratified two-phase sampling. The theoretical results are verified using different datasets and a simulation study, which demonstrates that the proposed estimators outperform the existing ones in terms of percent relative efficiency. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation: 3rd Edition)

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Mathematics, Volume 13, Issue 3 (February-1 2025) – 15 articles

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