Journal Description
Mathematics
Mathematics
is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.9 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Sections: published in 13 topical sections.
- Companion journals for Mathematics include: Foundations, AppliedMath, Analytics, International Journal of Topology, Geometry and Logics.
Impact Factor:
2.4 (2022);
5-Year Impact Factor:
2.3 (2022)
Latest Articles
Depth-Optimized Quantum Circuits for ASCON: AEAD and HASH
Mathematics 2024, 12(9), 1337; https://doi.org/10.3390/math12091337 (registering DOI) - 27 Apr 2024
Abstract
Quantum computing advancements pose security challenges for cryptography. Specifically, Grover’s search algorithm affects the reduction in the search complexity of symmetric-key encryption and hash functions. Recent efforts have been made to estimate the complexity of Grover’s search and evaluate post-quantum security. In this
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Quantum computing advancements pose security challenges for cryptography. Specifically, Grover’s search algorithm affects the reduction in the search complexity of symmetric-key encryption and hash functions. Recent efforts have been made to estimate the complexity of Grover’s search and evaluate post-quantum security. In this paper, we propose a depth-optimized quantum circuit implementation for ASCON, including both symmetric-key encryption and hashing algorithms, as a part of the lightweight cryptography standardization by NIST (National Institute of Standards and Technology). As far as we know, this is the first implementation of a quantum circuit for the ASCON AEAD (Authenticated Encryption with Associated Data) scheme, which is a symmetric-key algorithm. Also, our quantum circuit implementation of the ASCON-HASH achieves a reduction of more than 88.9% in the Toffoli depth and more than 80.5% in the full depth compared to the previous work. As per our understanding, the most effective strategy against Grover’s search involves minimizing the depth of the quantum circuit for the target cipher. We showcase the optimal Grover’s search cost for ASCON and introduce a proposed quantum circuit optimized for depth. Furthermore, we utilize the estimated cost to evaluate post-quantum security strength of ASCON, employing the relevant evaluation criteria and the latest advancements in research.
Full article
(This article belongs to the Special Issue Quantum Cryptography and Applications)
Open AccessArticle
Ensemble Approach Using k-Partitioned Isolation Forests for the Detection of Stock Market Manipulation
by
Hugo Núñez Delafuente , César A. Astudillo and David Díaz
Mathematics 2024, 12(9), 1336; https://doi.org/10.3390/math12091336 (registering DOI) - 27 Apr 2024
Abstract
Stock market manipulation, defined as any attempt to artificially influence stock prices, poses significant challenges by causing financial losses and eroding investor trust. The prevalent reliance on supervised learning models for detecting such manipulations, while showing promise, faces notable hurdles due to the
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Stock market manipulation, defined as any attempt to artificially influence stock prices, poses significant challenges by causing financial losses and eroding investor trust. The prevalent reliance on supervised learning models for detecting such manipulations, while showing promise, faces notable hurdles due to the dearth of labeled data and the inability to recognize novel manipulation tactics beyond those explicitly labeled. This study ventures into addressing these gaps by proposing a novel detection framework aimed at identifying suspicious hourly manipulation blocks through an unsupervised learning approach, thereby circumventing the limitations of data labeling and enhancing the adaptability to emerging manipulation strategies.Our methodology involves the innovative creation of features reflecting the behavior of stocks across various time windows followed by the segmentation of the dataset into k subsets. This setup facilitates the identification of potential manipulation instances via a voting ensemble composed of k isolation forest models, which have been chosen for their efficiency in pinpointing anomalies and their linear computational complexity—attributes that are critical for analyzing vast datasets.Evaluated against eight real stocks known to have undergone manipulation, our approach demonstrated a remarkable capability to identify up to 89% of manipulated blocks, thus significantly outperforming previous methods that do not utilize a voting ensemble. This finding not only surpasses the detection rates reported in prior studies but also underscores the enhanced robustness and adaptability of our unsupervised model in uncovering varied manipulation schemes. Through this research, we contribute to the field by offering a scalable and efficient unsupervised learning strategy for stock manipulation detection, thereby marking a substantial advancement over traditional supervised methods and paving the way for more resilient financial markets.
Full article
(This article belongs to the Special Issue Machine Learning and Finance)
Open AccessArticle
Existence of Solutions to a System of Fractional q-Difference Boundary Value Problems
by
Alexandru Tudorache and Rodica Luca
Mathematics 2024, 12(9), 1335; https://doi.org/10.3390/math12091335 (registering DOI) - 27 Apr 2024
Abstract
We are investigating the existence of solutions to a system of two fractional -difference equations containing fractional -integral terms, subject to multi-point boundary conditions that encompass -derivatives and fractional -derivatives of different orders. In our main results, we rely
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We are investigating the existence of solutions to a system of two fractional -difference equations containing fractional -integral terms, subject to multi-point boundary conditions that encompass -derivatives and fractional -derivatives of different orders. In our main results, we rely on various fixed point theorems, such as the Leray–Schauder nonlinear alternative, the Schaefer fixed point theorem, the Krasnosel’skii fixed point theorem for the sum of two operators, and the Banach contraction mapping principle. Finally, several examples are provided to illustrate our findings.
Full article
(This article belongs to the Special Issue Advances in Differential and Difference Equations and Their Applications)
Open AccessArticle
Green Measures for a Class of Non-Markov Processes
by
Herry P. Suryawan and José L. da Silva
Mathematics 2024, 12(9), 1334; https://doi.org/10.3390/math12091334 (registering DOI) - 27 Apr 2024
Abstract
In this paper, we investigate the Green measure for a class of non-Gaussian processes in . These measures are associated with the family of generalized grey Brownian motions , ,
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In this paper, we investigate the Green measure for a class of non-Gaussian processes in . These measures are associated with the family of generalized grey Brownian motions , , . This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability 1 for and . The Green measure then generalizes those measures of all these classes.
Full article
(This article belongs to the Special Issue New Advances in Applied Probability and Stochastic Processes)
Open AccessArticle
µ-Integrable Functions and Weak Convergence of Probability Measures in Complete Paranormed Spaces
by
Renying Zeng
Mathematics 2024, 12(9), 1333; https://doi.org/10.3390/math12091333 (registering DOI) - 27 Apr 2024
Abstract
Abstract: This paper works with functions defined in metric spaces and takes values in complete paranormed vector spaces or in Banach spaces, and proves some necessary and sufficient conditions for weak convergence of probability measures [...]
Full article
(This article belongs to the Special Issue Functional Analysis and Mathematical Optimization)
Open AccessArticle
Embedding Secret Data in a Vector Quantization Codebook Using a Novel Thresholding Scheme
by
Yijie Lin, Jui-Chuan Liu, Ching-Chun Chang and Chin-Chen Chang
Mathematics 2024, 12(9), 1332; https://doi.org/10.3390/math12091332 (registering DOI) - 27 Apr 2024
Abstract
In recent decades, information security has become increasingly valued, including many aspects of privacy protection, copyright protection, and digital forensics. Therefore, many data hiding schemes have been proposed and applied to various carriers such as text, images, audio, and videos. Vector Quantization (VQ)
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In recent decades, information security has become increasingly valued, including many aspects of privacy protection, copyright protection, and digital forensics. Therefore, many data hiding schemes have been proposed and applied to various carriers such as text, images, audio, and videos. Vector Quantization (VQ) compression is a well-known method for compressing images. In previous research, most methods related to VQ compressed images have focused on hiding information in index tables, while only a few of the latest studies have explored embedding data in codebooks. We propose a data hiding scheme for VQ codebooks. With our approach, a sender XORs most of the pixel values in a codebook and then applies a threshold to control data embedding. The auxiliary information generated during this process is embedded alongside secret data in the index reordering phase. Upon receiving the stego codebook and the reordered index table, the recipient can extract the data and reconstruct the VQ-compressed image using the reverse process. Experimental results demonstrate that our scheme significantly improves embedding capacity compared to the most recent codebook-based methods. Specifically, we observe an improvement rate of 223.66% in a small codebook of size 64 and an improvement rate of 85.19% in a codebook of size 1024.
Full article
(This article belongs to the Special Issue Advances in Mathematical Cryptography and Information Security toward Industry 5.0)
Open AccessArticle
Enhanced YOLOX with United Attention Head for Road Detetion When Driving
by
Yuhuan Wu and Yonghong Wu
Mathematics 2024, 12(9), 1331; https://doi.org/10.3390/math12091331 (registering DOI) - 27 Apr 2024
Abstract
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Object detection plays a crucial role in autonomous driving assistance systems. It requires high accuracy for prediction, a small size for deployment on mobile devices, and real-time inference speed to ensure safety. In this paper, we present a compact and efficient algorithm called
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Object detection plays a crucial role in autonomous driving assistance systems. It requires high accuracy for prediction, a small size for deployment on mobile devices, and real-time inference speed to ensure safety. In this paper, we present a compact and efficient algorithm called YOLOX with United Attention Head (UAH-YOLOX) for detection in autonomous driving scenarios. By replacing the backbone network with GhostNet for feature extraction, the model reduces the number of parameters and computational complexity. By adding a united attention head before the YOLO head, the model effectively detects the scale, position, and contour features of targets. In particular, an attention module called Spatial Self-Attention is designed to extract spatial location information, demonstrating great potential in detection. In our network, the IOU Loss (Intersection of Union) has been replaced with CIOU Loss (Complete Intersection of Union). Further experiments demonstrate the effectiveness of our proposed methods on the BDD100k dataset and the Caltech Pedestrian dataset. UAH-YOLOX achieves state-of-the-art results by improving the detection accuracy of the BDD100k dataset by 1.70% and increasing processing speed by 3.37 frames per second (FPS). Visualization provides specific examples in various scenarios.
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Open AccessArticle
Deep-Representation-Learning-Based Classification Strategy for Anticancer Peptides
by
Shujaat Khan
Mathematics 2024, 12(9), 1330; https://doi.org/10.3390/math12091330 (registering DOI) - 27 Apr 2024
Abstract
Cancer, with its complexity and numerous origins, continues to provide a huge challenge in medical research. Anticancer peptides are a potential treatment option, but identifying and synthesizing them on a large scale requires accurate prediction algorithms. This study presents an intuitive classification strategy,
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Cancer, with its complexity and numerous origins, continues to provide a huge challenge in medical research. Anticancer peptides are a potential treatment option, but identifying and synthesizing them on a large scale requires accurate prediction algorithms. This study presents an intuitive classification strategy, named ACP-LSE, based on representation learning, specifically, a deep latent-space encoding scheme. ACP-LSE can demonstrate notable advancements in classification outcomes, particularly in scenarios with limited sample sizes and abundant features. ACP-LSE differs from typical black-box approaches by focusing on representation learning. Utilizing an auto-encoder-inspired network, it embeds high-dimensional features, such as the composition of g-spaced amino acid pairs, into a compressed latent space. In contrast to conventional auto-encoders, ACP-LSE ensures that the learned feature set is both small and effective for classification, giving a transparent alternative. The suggested approach is tested on benchmark datasets and demonstrates higher performance compared to the current methods. The results indicate improved Matthew’s correlation coefficient and balanced accuracy, offering insights into crucial aspects for developing new ACPs. The implementation of the proposed ACP-LSE approach is accessible online, providing a valuable and reproducible resource for researchers in the field.
Full article
(This article belongs to the Special Issue Artificial Intelligence for Biomedical Applications)
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Open AccessFeature PaperArticle
Unraveling the Complexity of Inverting the Sturm–Liouville Boundary Value Problem to Its Canonical Form
by
Natanael Karjanto and Peter Sadhani
Mathematics 2024, 12(9), 1329; https://doi.org/10.3390/math12091329 (registering DOI) - 26 Apr 2024
Abstract
The Sturm–Liouville boundary value problem (SLBVP) stands as a fundamental cornerstone in the realm of mathematical analysis and physical modeling. Also known as the Sturm–Liouville problem (SLP), this paper explores the intricacies of this classical problem, particularly the relationship between its canonical and
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The Sturm–Liouville boundary value problem (SLBVP) stands as a fundamental cornerstone in the realm of mathematical analysis and physical modeling. Also known as the Sturm–Liouville problem (SLP), this paper explores the intricacies of this classical problem, particularly the relationship between its canonical and Liouville normal (Schrödinger) forms. While the conversion from the canonical to Schrödinger form using Liouville’s transformation is well known in the literature, the inverse transformation seems to be neglected. Our study attempts to fill this gap by investigating the inverse of Liouville’s transformation, that is, given any SLP in the Schrödinger form with some invariant function, we seek the SLP in its canonical form. By closely examining the second Paine–de Hoog–Anderson (PdHA) problem, we argue that retrieving the SLP in its canonical form can be notoriously difficult and can even be impossible to achieve in its exact form. Finding the inverse relationship between the two independent variables seems to be the main obstacle. We confirm this claim by considering four different scenarios, depending on the potential and density functions that appear in the corresponding invariant function. In the second PdHA problem, this invariant function takes a reciprocal quadratic binomial form. In some cases, the inverse Liouville transformation produces an exact expression for the SLP in its canonical form. In other situations, however, while an exact canonical form is not possible to obtain, we successfully derived the SLP in its canonical form asymptotically.
Full article
(This article belongs to the Special Issue Differential Equations with Boundary Value Problems: Theory and Applications)
Open AccessArticle
Efficient List Intersection Algorithm for Short Documents by Document Reordering
by
Lianyin Jia, Dongyang Li, Haihe Zhou and Fengling Xia
Mathematics 2024, 12(9), 1328; https://doi.org/10.3390/math12091328 (registering DOI) - 26 Apr 2024
Abstract
List intersection plays a pivotal role in various domains such as search engines, database systems, and social networks. Efficient indexes and query strategies can significantly enhance the efficiency of list intersection. Existing inverted index-based algorithms fail to utilize the length information of documents
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List intersection plays a pivotal role in various domains such as search engines, database systems, and social networks. Efficient indexes and query strategies can significantly enhance the efficiency of list intersection. Existing inverted index-based algorithms fail to utilize the length information of documents and require excessive list intersections, resulting in lower efficiency. To address this issue, in this paper, we propose the LDRpV (Length-based Document Reordering plus Verification) algorithm. LDRpV filters out documents that are unlikely to satisfy the intersection results by reordering documents based on their length, thereby reducing the number of candidates. Additionally, to minimize the number of list intersection operations, an intersection and verification strategy is designed, where only the first lists are intersected, and the resulting candidate set is directly verified. This approach effectively improves the efficiency of list intersection. Experimental results on four real datasets demonstrate that LDRpV can achieve a maximum efficiency improvement of 46.69% compared to the most competitive counterparts.
Full article
(This article belongs to the Special Issue Advances of Computer Algorithms and Data Structures)
Open AccessArticle
Fast Eigenvalue Decomposition of Arrowhead and Diagonal-Plus-Rank-k Matrices of Quaternions
by
Thaniporn Chaysri, Nevena Jakovčević Stor and Ivan Slapničar
Mathematics 2024, 12(9), 1327; https://doi.org/10.3390/math12091327 - 26 Apr 2024
Abstract
Quaternions are a non-commutative associative number system that extends complex numbers, first described by Hamilton in 1843. We present algorithms for solving the eigenvalue problem for arrowhead and DPRk (diagonal-plus-rank-k) matrices of quaternions. The algorithms use the Rayleigh Quotient Iteration with
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Quaternions are a non-commutative associative number system that extends complex numbers, first described by Hamilton in 1843. We present algorithms for solving the eigenvalue problem for arrowhead and DPRk (diagonal-plus-rank-k) matrices of quaternions. The algorithms use the Rayleigh Quotient Iteration with double shifts (RQIds), Wielandt’s deflation technique and the fact that each eigenvector can be computed in operations. The algorithms require floating-point operations, n being the order of the matrix. The algorithms are backward stable in the standard sense and compare well to the standard QR method in terms of speed and accuracy. The algorithms are elegantly implemented in Julia, using its polymorphism feature.
Full article
(This article belongs to the Section Computational and Applied Mathematics)
Open AccessFeature PaperArticle
A Three-Dimensional Velocity Field Related to a Generalized Third-Grade Fluid Model
by
Fernando Carapau, Paulo Correia and Gracino Rodrigues
Mathematics 2024, 12(9), 1326; https://doi.org/10.3390/math12091326 - 26 Apr 2024
Abstract
In this work, we propose a new three-dimensional constitutive equation related to a third-grade fluid. This proposal is based on experimental work for which the viscosity term and the terms related to viscoelasticity may depend on the shear rate, in accordance with a
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In this work, we propose a new three-dimensional constitutive equation related to a third-grade fluid. This proposal is based on experimental work for which the viscosity term and the terms related to viscoelasticity may depend on the shear rate, in accordance with a power-law type model. The numerical implementation of this fluid model is rather demanding in terms of computational calculation and, in this sense, we use the Cosserat theory related to fluid dynamics, which makes the transition from the three-dimensional fluid model to a one-dimensional fluid model for a specific geometry under study which, in this case, is a straight tube with constant circular cross-section. Based on this approximation theory, the one-dimensional fluid model is solved by assuming an ordinary differential equation involving: an unsteady mean pressure gradient; an unsteady volume flow rate; the Womersley number; and the viscosity and viscoelasticity parameters. Consequently, for specific data, and using the Runge–Kutta method, we can obtain the solution for the unsteady volume flow rate and we can present simulations to the three-dimensional velocity field.
Full article
(This article belongs to the Section Mathematical Physics)
Open AccessArticle
Initial Coefficient Bounds Analysis for Novel Subclasses of Bi-Univalent Functions Linked with Lucas-Balancing Polynomials
by
Sondekola Rudra Swamy, Daniel Breaz, Kala Venugopal, Mamatha Paduvalapattana Kempegowda, Luminita-Ioana Cotîrlă and Eleonora Rapeanu
Mathematics 2024, 12(9), 1325; https://doi.org/10.3390/math12091325 - 26 Apr 2024
Abstract
We investigate some subclasses of regular and bi-univalent functions in the open unit disk that are associated with Lucas-Balancing polynomials in this work. For functions that belong to these subclasses, we obtain upper bounds on their initial coefficients. The Fekete–Szegö problem is also
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We investigate some subclasses of regular and bi-univalent functions in the open unit disk that are associated with Lucas-Balancing polynomials in this work. For functions that belong to these subclasses, we obtain upper bounds on their initial coefficients. The Fekete–Szegö problem is also discussed. Along with presenting some new results, we also explore pertinent connections to earlier findings.
Full article
Open AccessArticle
Revolutionary Strategy for Depicting Knowledge Graphs with Temporal Attributes
by
Sihan Li and Qi Li
Mathematics 2024, 12(9), 1324; https://doi.org/10.3390/math12091324 - 26 Apr 2024
Abstract
In practical applications, the temporal completeness of knowledge graphs is of great importance. However, previous studies have mostly focused on static knowledge graphs, generally neglecting the dynamic evolutionary properties of facts. Moreover, the unpredictable and limited availability of temporal knowledge graphs, together with
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In practical applications, the temporal completeness of knowledge graphs is of great importance. However, previous studies have mostly focused on static knowledge graphs, generally neglecting the dynamic evolutionary properties of facts. Moreover, the unpredictable and limited availability of temporal knowledge graphs, together with the complex temporal dependency patterns, make current models inadequate for effectively describing facts that experience temporal transitions. To better represent the evolution of things over time, we provide a learning technique that uses quaternion rotation to describe temporal knowledge graphs. This technique describes the evolution of entities as a temporal rotation change in quaternion space. Compared to the Ermitian inner product in complex number space, the Hamiltonian product in quaternion space is better at showing how things might be connected. This leads to a learning process that is both more effective and more articulate. Experimental results demonstrate that our learning method significantly outperforms existing methods in capturing the dynamic evolution of temporal knowledge graphs, with improved accuracy and robustness across a range of benchmark datasets.
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(This article belongs to the Topic Complex Networks and Social Networks)
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Open AccessArticle
Intellectual Capital Evaluation Index Based on a Hybrid Multi-Criteria Decision-Making Technique
by
Chao Liu, Qichen Liao, Wenyan Gao, Shuxian Li, Peng Jiang and Ding Li
Mathematics 2024, 12(9), 1323; https://doi.org/10.3390/math12091323 - 26 Apr 2024
Abstract
In the context of a burgeoning knowledge economy, enterprise intellectual capital has emerged as a pivotal asset for organizational growth. Evaluating it requires a comprehensive and robust index, yet there is no standard methodology for such assessments. Here, we propose an index for
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In the context of a burgeoning knowledge economy, enterprise intellectual capital has emerged as a pivotal asset for organizational growth. Evaluating it requires a comprehensive and robust index, yet there is no standard methodology for such assessments. Here, we propose an index for evaluating enterprise intellectual capital. We use the Delphi method to delineate a scientific decision structure. A grey-based decision-making trial and evaluation laboratory (DEMATEL) is coupled with an analytic network process (ANP)—i.e., grey DEMATEL-based ANP (GDANP)—to determine the relative weight of indicators. Then, we use the technique for order preference by similarity to an ideal solution to validate the effectiveness and applicability of the proposed evaluation index based on data on thirty new-technology companies in China. This study bridges a critical gap in academic discourse, and we discuss the practical implications for the strategic management of intellectual capital in corporate settings.
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Open AccessArticle
Mathematical Modeling of the Displacement of a Light-Fuel Self-Moving Automobile with an On-Board Liquid Crystal Elastomer Propulsion Device
by
Yunlong Qiu, Jiajing Chen, Yuntong Dai, Lin Zhou, Yong Yu and Kai Li
Mathematics 2024, 12(9), 1322; https://doi.org/10.3390/math12091322 - 26 Apr 2024
Abstract
The achievement and control of desired motions in active machines often involves precise manipulation of artificial muscles in a distributed and sequential manner, which poses significant challenges. A novel motion control strategy based on self-oscillation in active machines offers distinctive benefits, such as
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The achievement and control of desired motions in active machines often involves precise manipulation of artificial muscles in a distributed and sequential manner, which poses significant challenges. A novel motion control strategy based on self-oscillation in active machines offers distinctive benefits, such as direct energy harvesting from the ambient environment and the elimination of complex controllers. Drawing inspiration from automobiles, a self-moving automobile designed for operation under steady illumination is developed, comprising two wheels and a liquid crystal elastomer fiber. To explore the dynamic behavior of this self-moving automobile under steady illumination, a nonlinear theoretical model is proposed, integrating with the established dynamic liquid crystal elastomer model. Numerical simulations are conducted using the Runge-Kutta method based on MATLAB software, and it is observed that the automobile undergoes a supercritical Hopf bifurcation, transitioning from a static state to a self-moving state. The sustained periodic self-moving is facilitated by the interplay between light energy and damping dissipation. Furthermore, the conditions under which the Hopf bifurcation occurs are analyzed in detail. It is worth noting that increasing the light intensity or decreasing rolling resistance coefficient can improve the self-moving average velocity. The innovative design of the self-moving automobile offers advantages such as not requiring an independent power source, possessing a simple structure, and being sustainable. These characteristics make it highly promising for a range of applications including actuators, soft robotics, energy harvesting, and more.
Full article
(This article belongs to the Special Issue Mathematical Modeling, Asymptotic Analysis and Stability of Solutions of Nonlinear Dynamical Systems)
Open AccessFeature PaperArticle
Bifurcation Analysis for an OSN Model with Two Delays
by
Liancheng Wang and Min Wang
Mathematics 2024, 12(9), 1321; https://doi.org/10.3390/math12091321 - 26 Apr 2024
Abstract
In this research, we introduce and analyze a mathematical model for online social networks, incorporating two distinct delays. These delays represent the time it takes for active users within the network to begin disengaging, either with or without contacting non-users of online social
[...] Read more.
In this research, we introduce and analyze a mathematical model for online social networks, incorporating two distinct delays. These delays represent the time it takes for active users within the network to begin disengaging, either with or without contacting non-users of online social platforms. We focus particularly on the user prevailing equilibrium (UPE), denoted as , and explore the role of delays as parameters in triggering Hopf bifurcations. In doing so, we find the conditions under which Hopf bifurcations occur, then establish stable regions based on the two delays. Furthermore, we delineate the boundaries of stability regions wherein bifurcations transpire as the delays cross these thresholds. We present numerical simulations to illustrate and validate our theoretical findings. Through this interdisciplinary approach, we aim to deepen our understanding of the dynamics inherent in online social networks.
Full article
(This article belongs to the Special Issue Advances in Differential and Difference Equations and Their Applications)
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Open AccessArticle
Essential Norm of t-Generalized Composition Operators from F(p, q, s) to Iterated Weighted-Type Banach Space
by
Shams Alyusof and Nacir Hmidouch
Mathematics 2024, 12(9), 1320; https://doi.org/10.3390/math12091320 - 26 Apr 2024
Abstract
In this work, we characterize the boundedness of t-generalized composition operators from spaces to iterated weighted-type Banach space. We also provide estimates of the norm and the essential norm of t-generalized
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In this work, we characterize the boundedness of t-generalized composition operators from spaces to iterated weighted-type Banach space. We also provide estimates of the norm and the essential norm of t-generalized composition operators from spaces to iterated weighted-type Banach space. As corollaries, we obtain approximations of the essential norm of integral operators and generalized composition operators from spaces to iterated weighted-type Banach space. Moreover, we conclude our work by discussing the t-generalized composition operators and the special cases of .
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Open AccessArticle
Neural Network-Based Distributed Consensus Tracking Control for Nonlinear Multi-Agent Systems with Mismatched and Matched Disturbances
by
Linxi Xu and Kaiyu Qin
Mathematics 2024, 12(9), 1319; https://doi.org/10.3390/math12091319 - 26 Apr 2024
Abstract
In practice, disturbances, including model uncertainties and unknown external disturbances, are always widely present and have a significant impact on the cooperative control performance of a networked multi-agent system. In this work, the distributed consensus tracking control problem for a class of multi-agent
[...] Read more.
In practice, disturbances, including model uncertainties and unknown external disturbances, are always widely present and have a significant impact on the cooperative control performance of a networked multi-agent system. In this work, the distributed consensus tracking control problem for a class of multi-agent systems subject to matched and mismatched uncertainties is addressed. In particular, the dynamics of the leader agent are modeled with uncertain terms, i.e., the leader’s higher-order information, such as velocity and acceleration, is unknown to all followers. To solve this problem, a robust consensus tracking control scheme that combines a neural network-based distributed observer, a barrier function-based disturbance observer, and a tracking controller based on the back-stepping method was developed in this study. Firstly, a neural network-based distributed observer is designed, which is able to achieve effective estimation of leader information by all followers. Secondly, a tracking controller was designed utilizing the back-stepping technique, and the boundedness of the closed-loop error system was proved using the Lyapunov-like theorem, which enables the followers to effectively track the leader’s trajectory. Meanwhile, a barrier function-based disturbance observer is proposed, which achieves the effective estimation of matched and mismatched uncertainties of followers. Finally, the effectiveness of the robust consensus tracking control method designed in this study was verified through numerical simulations.
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(This article belongs to the Special Issue Advance in Control Theory and Optimization)
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A Novel Method for Predicting the Behavior of a Sucker Rod Pumping Unit Based on the Polished Rod Velocity
by
Jiaojian Yin and Hongzhang Ma
Mathematics 2024, 12(9), 1318; https://doi.org/10.3390/math12091318 - 25 Apr 2024
Abstract
Fault dynamometer cards are the basis of the diagnosis technique for sucker rod pumping systems. Predicting fault cards with a pumping condition model is an economical and effective method. The usual model is described by a mixed function of the pump displacement and
[...] Read more.
Fault dynamometer cards are the basis of the diagnosis technique for sucker rod pumping systems. Predicting fault cards with a pumping condition model is an economical and effective method. The usual model is described by a mixed function of the pump displacement and pump load, and it is difficult to use in the prediction method based on the analytical solution of the sucker rod string wave equation. In this paper, a normal pumping condition model described by a function of polished rod velocity is proposed. For the analytical solution of the sucker rod wave equation, an iterative prediction algorithm with pumping condition models is proposed, its convergence is analyzed, and then it is validated by classical finite difference method simulated cards and measured surface dynamometer cards. The results show that the proposed algorithm is accurate. The algorithm has a maximum relative error of 0.10% for the classical method simulated card area and 1.45% for the measured card area. The research of this paper provides an effective scheme for the design, prediction, and fault diagnosis of a sucker rod pumping system with an analytical solution.
Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)
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Special Issues
Special Issue in
Mathematics
Advances in the Mathematics of Ecological Modelling
Guest Editors: Dmitrii O. Logofet, Larisa Khanina, Pavel GrabarnikDeadline: 30 April 2024
Special Issue in
Mathematics
Advances in Linear Recurrence System
Guest Editors: Lorentz Jäntschi, Virginia NiculescuDeadline: 15 May 2024
Special Issue in
Mathematics
New Trends on Boundary Value Problems
Guest Editors: Miklós Rontó, András Rontó, Nino Partsvania, Bedřich Půža, Hriczó KrisztiánDeadline: 31 May 2024
Special Issue in
Mathematics
Applications of Fuzzy Modeling in Risk Management
Guest Editors: Edit Toth-Laufer, László PokorádiDeadline: 20 June 2024
Topical Collections
Topical Collection in
Mathematics
Topology and Foundations
Collection Editors: Lorentz Jäntschi, Dušanka Janežič
Topical Collection in
Mathematics
Multiscale Computation and Machine Learning
Collection Editors: Yalchin Efendiev, Eric Chung
Topical Collection in
Mathematics
Theoretical and Mathematical Ecology
Collection Editor: Yuri V. Tyutyunov