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
Numerical Recovering of Space-Dependent Sources in Hyperbolic Transmission Problems
Mathematics 2024, 12(11), 1748; https://doi.org/10.3390/math12111748 (registering DOI) - 4 Jun 2024
Abstract
A body may have a structural, thermal, electromagnetic or optical role. In wave propagation, many models are described for transmission problems, whose solutions are defined in two or more domains. In this paper, we consider an inverse source hyperbolic problem on disconnected intervals,
[...] Read more.
A body may have a structural, thermal, electromagnetic or optical role. In wave propagation, many models are described for transmission problems, whose solutions are defined in two or more domains. In this paper, we consider an inverse source hyperbolic problem on disconnected intervals, using solution point constraints. Applying a transform method, we reduce the inverse problems to direct ones, which are studied for well-posedness in special weighted Sobolev spaces. This means that the inverse problem is said to be well posed in the sense of Tikhonov (or conditionally well posed). The main aim of this study is to develop a finite difference method for solution of the transformed hyperbolic problems with a non-local differential operator and initial conditions. Numerical test examples are also analyzed.
Full article
(This article belongs to the Special Issue Advanced Approaches to Mathematical Physics Problems)
►
Show Figures
Open AccessArticle
An Innovative Method for Wind Load Estimation in High-Rise Buildings Based on Green’s Function
by
Lin Song, Yang Yu, Jianxing Yu, Shibo Wu, Jiandong Ma and Zihang Jin
Mathematics 2024, 12(11), 1747; https://doi.org/10.3390/math12111747 - 4 Jun 2024
Abstract
►▼
Show Figures
High-rise buildings are inherently vulnerable to substantial wind-induced forces. The increasing complexity of building designs has posed challenges in calculating wind loads, while traditional methods involving physical models have proven to be intricate and time-consuming. In order to overcome these obstacles, this paper
[...] Read more.
High-rise buildings are inherently vulnerable to substantial wind-induced forces. The increasing complexity of building designs has posed challenges in calculating wind loads, while traditional methods involving physical models have proven to be intricate and time-consuming. In order to overcome these obstacles, this paper investigates a theoretical methodology aimed at streamlining the computation of wind loads. In the initial theoretical exploration, a simplified mathematical model based on Green’s function is introduced to take into account the interaction between wind loads and building geometry, while the model is not user-friendly and difficult to solve for complex polygonal buildings. To overcome this challenge, the study incorporates numerical simulations to extend the ideas and refine the methodology. To simplify the problem from a three-dimensional to a two-dimensional context, a bold tangential field assumption is made, assuming the wind pressure distribution remains similar across horizontal sections at different heights. The Schwarz–Christoffel formulation is then employed to facilitate the transformation. By integrating Green’s functions and conformal mapping to solve potential flow problems beyond the boundary layer, a comprehensive mathematical derivation is established. The above broadens the applicability of the mathematical theory and provides a new direction for estimations of high-speed wind load on buildings.
Full article
Figure 1
Open AccessArticle
Integrating Uncertainties in a Multi-Criteria Decision Analysis with the Entscheidungsnavi
by
Sven Peters, Mendy Tönsfeuerborn and Rüdiger von Nitzsch
Mathematics 2024, 12(11), 1746; https://doi.org/10.3390/math12111746 (registering DOI) - 4 Jun 2024
Abstract
The Entscheidungsnavi is an open-source decision support system based on multi-attribute utility theory, that offers various methods for dealing with uncertainties. To model decisions with uncertainties, decision-makers can use two categories: Forecast and Parameter Uncertainties. Forecast Uncertainty is modeled with (combined) influence factors
[...] Read more.
The Entscheidungsnavi is an open-source decision support system based on multi-attribute utility theory, that offers various methods for dealing with uncertainties. To model decisions with uncertainties, decision-makers can use two categories: Forecast and Parameter Uncertainties. Forecast Uncertainty is modeled with (combined) influence factors using discrete, user-defined probability distributions or predefined ‘worst-median-best’ distributions. Parameter Uncertainty allows imprecision for utilities, objective weights, and probability distributions. To analyze these uncertainties, the Entscheidungsnavi offers several methods and tools, like a robustness check, based on (Monte Carlo) simulations and a sensitivity analysis. The objective weight analysis provides insights into the effects of different objective weight combinations. Indicator impacts, tornado diagrams, and risk profiles visualize the impact of uncertainties in a decision under risk. Risk profiles also enable a check for stochastic and simulation dominance. This article presents the complete range of methods for dealing with uncertainties in the Entscheidungsnavi using a hypothetical case study.
Full article
(This article belongs to the Special Issue Mathematical Modelling in Decision Making Analysis)
►▼
Show Figures
Figure 1
Open AccessArticle
A Comprehensive Decision-Making Approach for Strategic Product Module Planning in Mass Customization
by
Shuo-Fang Liu, Shi-Yu Wang and Hsueh-Hung Tung
Mathematics 2024, 12(11), 1745; https://doi.org/10.3390/math12111745 - 3 Jun 2024
Abstract
This paper explores the integrated optimization of complex coupled industrial manufacturing systems and production strategies based on user customization needs. Two optimization metrics are considered: one is whether the production process of engineering manufacturing is simplified, and the other is whether it is
[...] Read more.
This paper explores the integrated optimization of complex coupled industrial manufacturing systems and production strategies based on user customization needs. Two optimization metrics are considered: one is whether the production process of engineering manufacturing is simplified, and the other is whether it is based on the customization requirements of the customer. These two metrics are interrelated, and cases may even be conflicting. Considering the interdependence between engineering manufacturing and user requirements, this paper develops an integrated customized modular engineering manufacturing process to minimize production and maintenance costs and improve efficiency while meeting user customization requirements. This paper takes expert evaluation as an important decision indicator and optimizes the production process strategy on this basis. Finally, a case study is given to illustrate the applicability of the proposed process model.
Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
►▼
Show Figures
Figure 1
Open AccessArticle
Linear Combination of Order Statistics Moments from Log-Extended Exponential Geometric Distribution with Applications to Entropy
by
Fatimah E. Almuhayfith, Mahfooz Alam, Hassan S. Bakouch, Sudeep R. Bapat and Olayan Albalawi
Mathematics 2024, 12(11), 1744; https://doi.org/10.3390/math12111744 - 3 Jun 2024
Abstract
Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create the log-extended exponential–geometric (LEEG) distribution, which is bounded in the unit interval
[...] Read more.
Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create the log-extended exponential–geometric (LEEG) distribution, which is bounded in the unit interval (0, 1). In addition to the generalized Stirling numbers of the first kind, a few years ago, the polylogarithm function and the Lerch transcendent function were used to determine the moments of order statistics of the LEEG distributions. As an application based on the L-moments, we expand the features of the LEEG distribution in this work. In terms of the Gauss hypergeometric function, this work presents the precise equations and recurrence relations for the single moments of OSs from the LEEG distribution. Along with recurrence relations between the expectations of function of two OSs from the LEEG distribution, it also displays the truncated and conditional distribution of the OSs. Additionally, we use the L-moments to estimate the parameters of the LEEG distribution. We further fit the LEEG distribution on three practical data sets from medical and environmental sciences areas. It is seen that the estimated parameters through L-moments of the OSs give a superior fit. We finally determine the correspondence between the entropies and the OSs.
Full article
(This article belongs to the Special Issue Advances in Applied Probability and Statistical Inference)
Open AccessArticle
On the Ratio-Type Family of Copulas
by
Farid El Ktaibi, Rachid Bentoumi and Mhamed Mesfioui
Mathematics 2024, 12(11), 1743; https://doi.org/10.3390/math12111743 - 3 Jun 2024
Abstract
Investigating dependence structures across various fields holds paramount importance. Consequently, the creation of new copula families plays a crucial role in developing more flexible stochastic models that address the limitations of traditional and sometimes impractical assumptions. The present article derives some reasonable conditions
[...] Read more.
Investigating dependence structures across various fields holds paramount importance. Consequently, the creation of new copula families plays a crucial role in developing more flexible stochastic models that address the limitations of traditional and sometimes impractical assumptions. The present article derives some reasonable conditions for validating a copula of the ratio-type form . It includes numerous examples and discusses the admissible range of parameter , showcasing the diversity of copulas generated through this framework, such as Archimedean, non-Archimedean, positive dependent, and negative dependent copulas. The exploration extends to the upper bound of a general family of copulas, , and important properties of the copula are discussed, including singularity, measures of association, tail dependence, and monotonicity. Furthermore, an extensive simulation study is presented, comparing the performance of three different estimators based on maximum likelihood, inversion, and the moment copula method.
Full article
(This article belongs to the Special Issue Dependence Modeling with Copulas and Their Applications)
Open AccessArticle
Novel Numerical Investigations of Some Problems Based on the Darcy–Forchheimer Model and Heat Transfer
by
Fahir Talay Akyildiz, Fehaid Salem Alshammari and Cemil Tunç
Mathematics 2024, 12(11), 1742; https://doi.org/10.3390/math12111742 - 3 Jun 2024
Abstract
In this study, we introduced a new type of basis function and subsequently a Chebyshev delta shaped collocation method (CDSC). We then use this method to numerically investigate both the natural convective flow and heat transfer of nanofluids in a vertical rectangular duct
[...] Read more.
In this study, we introduced a new type of basis function and subsequently a Chebyshev delta shaped collocation method (CDSC). We then use this method to numerically investigate both the natural convective flow and heat transfer of nanofluids in a vertical rectangular duct on the basis of a Darcy–Brinkman–Forchheimer model and the electroosmosis-modulated Darcy–Forchheimer flow of Casson nanofluid over stretching sheets with Newtonian heating problems. The approximate solution is represented in terms of Chebyshev delta shaped basis functions. Novel error estimates for interpolating polynomials are derived. Computational experiments were carried out to corroborate the theoretical results and to compare the present method with the existing Chebyshev pseudospectral method. To demonstrate our proposed approach, we also compared the numerical solutions with analytic solutions of the Poisson equation. Computer simulations show that the proposed method is computationally cheap, fast, and spectrally accurate and more importantly the obtained approximate solution can easily be used by researchers in this field.
Full article
(This article belongs to the Section Computational and Applied Mathematics)
Open AccessArticle
Predicting Scientific Breakthroughs Based on Structural Dynamic of Citation Cascades
by
Houqiang Yu, Yian Liang and Yinghua Xie
Mathematics 2024, 12(11), 1741; https://doi.org/10.3390/math12111741 - 3 Jun 2024
Abstract
Predicting breakthrough papers holds great significance; however, prior studies encountered challenges in this task, indicating a need for substantial improvement. We propose that the failure to capture the dynamic structural-evolutionary features of citation networks is one of the major reasons. To overcome this
[...] Read more.
Predicting breakthrough papers holds great significance; however, prior studies encountered challenges in this task, indicating a need for substantial improvement. We propose that the failure to capture the dynamic structural-evolutionary features of citation networks is one of the major reasons. To overcome this limitation, this paper introduces a new method for constructing citation cascades of focus papers, allowing the creation of a time-series-like set of citation cascades. Then, through a thorough review, three types of structural indicators in these citation networks that could reflect breakthroughs are identified, including certain basic topological metrics, PageRank values, and the von Neumann graph entropy. Based on the time-series-like set of citation cascades, the dynamic trajectories of these indicators are calculated and employed as predictors. Using the Nobel Prize-winning papers as a landmark dataset, our prediction method yields approximately a 7% improvement in the ROC-AUC score compared to static-based prior methods. Additionally, our method advances in achieving earlier predictions than other previous methods. The main contribution of this paper is proposing a novel method for creating citation cascades in chronological order and confirming the significance of predicting breakthroughs from a dynamic structural perspective.
Full article
(This article belongs to the Special Issue Application of Machine Learning and Data Mining)
Open AccessArticle
INT-FUP: Intuitionistic Fuzzy Pooling
by
Chaymae Rajafillah, Karim El Moutaouakil, Alina-Mihaela Patriciu, Ali Yahyaouy and Jamal Riffi
Mathematics 2024, 12(11), 1740; https://doi.org/10.3390/math12111740 - 3 Jun 2024
Abstract
Convolutional Neural Networks (CNNs) are a kind of artificial neural network designed to extract features and find out patterns for tasks such as segmentation, recognizing objects, and drawing up classification. Within a CNNs architecture, pooling operations are used until the number of parameters
[...] Read more.
Convolutional Neural Networks (CNNs) are a kind of artificial neural network designed to extract features and find out patterns for tasks such as segmentation, recognizing objects, and drawing up classification. Within a CNNs architecture, pooling operations are used until the number of parameters and the computational complexity are reduced. Numerous papers have focused on investigating the impact of pooling on the performance of Convolutional Neural Networks (CNNs), leading to the development of various pooling models. Recently, a fuzzy pooling operation based on type-1 fuzzy sets was introduced to cope with the local imprecision of the feature maps. However, in fuzzy set theory, it is not always accurate to assume that the degree of non-membership of an element in a fuzzy set is simply the complement of the degree of membership. This is due to the potential existence of a hesitation degree, which implies a certain level of uncertainty. To overcome this limitation, intuitionistic fuzzy sets (IFS) were introduced to incorporate the concept of a degree of hesitation. In this paper, we introduce a novel pooling operation based on intuitionistic fuzzy sets to incorporate the degree of hesitation heretofore neglected by a fuzzy pooling operation based on classical fuzzy sets, and we investigate its performance in the context of image classification. Intuitionistic pooling is performed in four steps: bifuzzification (by the transformation of data through the use of membership and non-membership maps), first aggregation (through the transformation of the IFS into a standard fuzzy set, second aggregation (through the transformation and use of a sum operator), and the defuzzification of feature map neighborhoods by using a max operator. IFS pooling is used for the construction of an intuitionistic pooling layer that can be applied as a drop-in replacement for the current, fuzzy (type-1) and crisp, pooling layers of CNN architectures. Various experiments involving multiple datasets demonstrate that an IFS-based pooling can enhance the classification performance of a CNN. A benchmarking study reveals that this significantly outperforms even the most recent pooling models, especially in stochastic environments.
Full article
(This article belongs to the Special Issue Advanced Methods in Fuzzy Control and Their Applications)
►▼
Show Figures
Figure 1
Open AccessArticle
ARFGCN: Adaptive Receptive Field Graph Convolutional Network for Urban Crowd Flow Prediction
by
Genan Dai, Hu Huang, Xiaojiang Peng, Bowen Zhang and Xianghua Fu
Mathematics 2024, 12(11), 1739; https://doi.org/10.3390/math12111739 - 3 Jun 2024
Abstract
Urban crowd flow prediction is an important task for transportation systems and public safety. While graph convolutional networks (GCNs) have been widely adopted for this task, existing GCN-based methods still face challenges. Firstly, they employ fixed receptive fields, failing to account for urban
[...] Read more.
Urban crowd flow prediction is an important task for transportation systems and public safety. While graph convolutional networks (GCNs) have been widely adopted for this task, existing GCN-based methods still face challenges. Firstly, they employ fixed receptive fields, failing to account for urban region heterogeneity where different functional zones interact distinctly with their surroundings. Secondly, they lack mechanisms to adaptively adjust spatial receptive fields based on temporal dynamics, which limits prediction performance. To address these limitations, we propose an Adaptive Receptive Field Graph Convolutional Network (ARFGCN) for urban crowd flow prediction. ARFGCN allows each region to independently determine its receptive field size, adaptively adjusted and learned in an end-to-end manner during training, enhancing model prediction performance. It comprises a time-aware adaptive receptive field (TARF) gating mechanism, a stacked 3DGCN, and a prediction layer. The TARF aims to leverage gating in neural networks to adapt receptive fields based on temporal dynamics, enabling the predictive network to adapt to urban regional heterogeneity. The TARF can be easily integrated into the stacked 3DGCN, enhancing the prediction. Experimental results demonstrate ARFGCN’s effectiveness compared to other methods.
Full article
(This article belongs to the Section Mathematics and Computer Science)
►▼
Show Figures
Figure 1
Open AccessArticle
A Dual-Competition-Based Particle Swarm Optimizer for Large-Scale Optimization
by
Weijun Gao, Xianjie Peng, Weian Guo and Dongyang Li
Mathematics 2024, 12(11), 1738; https://doi.org/10.3390/math12111738 - 3 Jun 2024
Abstract
►▼
Show Figures
Large-scale particle swarm optimization (PSO) has long been a hot topic due to the following reasons: Swarm diversity preservation is still challenging for current PSO variants for large-scale optimization problems, resulting in difficulties for PSO in balancing its exploration and exploitation. Furthermore, current
[...] Read more.
Large-scale particle swarm optimization (PSO) has long been a hot topic due to the following reasons: Swarm diversity preservation is still challenging for current PSO variants for large-scale optimization problems, resulting in difficulties for PSO in balancing its exploration and exploitation. Furthermore, current PSO variants for large-scale optimization problems often introduce additional operators to improve their ability in diversity preservation, leading to increased algorithm complexity. To address these issues, this paper proposes a dual-competition-based particle update strategy (DCS), which selects the particles to be updated and corresponding exemplars with two rounds of random pairing competitions, which can straightforwardly benefit swarm diversity preservation. Furthermore, DCS confirms the primary and secondary exemplars based on the fitness sorting operation for exploitation and exploration, respectively, leading to a dual-competition-based swarm optimizer. Thanks to the proposed DCS, on the one hand, the proposed algorithm is able to protect more than half of the particles from being updated to benefit diversity preservation at the swarm level. On the other hand, DCS provides an efficient exploration and exploitation exemplar selection mechanism, which is beneficial for balancing exploration and exploitation at the particle update level. Additionally, this paper analyzes the stability conditions and computational complexity of the proposed algorithm. In the experimental section, based on seven state-of-the-art algorithms and a recently proposed large-scale benchmark suite, this paper verifies the competitiveness of the proposed algorithm in large-scale optimization problems.
Full article
Figure 1
Open AccessArticle
Double Exponential Ratio Estimator of a Finite Population Variance under Extreme Values in Simple Random Sampling
by
Umer Daraz, Jinbiao Wu and Olayan Albalawi
Mathematics 2024, 12(11), 1737; https://doi.org/10.3390/math12111737 - 3 Jun 2024
Abstract
This article presents an improved class of efficient estimators aimed at estimating the finite population variance of the study variable. These estimators are especially useful when we have information about the minimum/maximum values of the auxiliary variable within a framework of simple random
[...] Read more.
This article presents an improved class of efficient estimators aimed at estimating the finite population variance of the study variable. These estimators are especially useful when we have information about the minimum/maximum values of the auxiliary variable within a framework of simple random sampling. The characteristics of the proposed class of estimators, including bias and mean squared error ( ) under simple random sampling are derived through a first-order approximation. To assess the performance and validate the theoretical outcomes, we conduct a simulation study. Results indicate that the proposed class of estimators has lower as compared to other existing estimators across all simulation scenarios. Three datasets are used in the application section to emphasize the effectiveness of the proposed class of estimators over conventional unbiased variance estimators, ratio and regression estimators, and other existing estimators.
Full article
(This article belongs to the Special Issue Survey Statistics and Survey Sampling: Challenges and Opportunities)
►▼
Show Figures
Figure 1
Open AccessArticle
A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces
by
Abdelouahed Kouibia, Miguel Pasadas and Loubna Omri
Mathematics 2024, 12(11), 1736; https://doi.org/10.3390/math12111736 - 3 Jun 2024
Abstract
In the study of some real cases, it is possible to encounter well-defined geometric conditions, of an industrial or design type—for example, the case of a specific volume within each of several holes. In most of these cases, it is recommended to fulfil
[...] Read more.
In the study of some real cases, it is possible to encounter well-defined geometric conditions, of an industrial or design type—for example, the case of a specific volume within each of several holes. In most of these cases, it is recommended to fulfil a function defined in a domain in which information is missing in one or more sub-domains (holes) of the global set, where the function data are not known. The problem of filling holes or completing a surface in three dimensions appears in many fields of computing, such as computer-aided geometric design (CAGD). A method to solve the shape-preserving variational spline approximation problem for hole filling in generalized offset surfaces is presented. The existence and uniqueness of the solution of the studied method are established, as well as the computation, and certain convergence results are analyzed. A graphic and numerical example complete this study to demonstrate the effectiveness of the presented method. This manuscript presents the resolution of a complicated problem due to the study of some criteria that can be traduced via an approximation problem related to generalized offset surfaces with holes and also the preservation of the shape of such surfaces.
Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis with Applications in Various Fields)
►▼
Show Figures
Figure 1
Open AccessArticle
A Bi-Starlike Class in a Leaf-like Domain Defined through Subordination via
by
Ala Amourah, Abdullah Alsoboh, Daniel Breaz and Sheza M. El-Deeb
Mathematics 2024, 12(11), 1735; https://doi.org/10.3390/math12111735 - 3 Jun 2024
Abstract
Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with -calculus.
[...] Read more.
Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with -calculus. The class is proved to be not empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on and coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation.
Full article
(This article belongs to the Special Issue Advances in Complex Analysis and Application)
►▼
Show Figures
Figure 1
Open AccessArticle
Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations
by
Hail S. Alrashdi, Wedad Albalawi, Ali Muhib, Osama Moaaz and Elmetwally M. Elabbasy
Mathematics 2024, 12(11), 1734; https://doi.org/10.3390/math12111734 - 3 Jun 2024
Abstract
This paper aims to study the asymptotic properties of nonoscillatory solutions (eventually positive or negative) of a class of third-order canonical neutral differential equations. We use Riccati substitution to reduce the order of the considered equation, and then we use the Philos function
[...] Read more.
This paper aims to study the asymptotic properties of nonoscillatory solutions (eventually positive or negative) of a class of third-order canonical neutral differential equations. We use Riccati substitution to reduce the order of the considered equation, and then we use the Philos function class to obtain new criteria of the Kamenev type, which guarantees that all nonoscillatory solutions converge to zero. This approach is characterized by the possibility of applying its conditions to a wider area of equations. This is not the only aspect that distinguishes our results; we also use improved relationships between the solution and the corresponding function, which in turn is reflected in a direct improvement of the criteria. The findings in this article extend and generalize previous findings in the literature and also improve some of these findings.
Full article
(This article belongs to the Special Issue Advances in Differential and Difference Equations and Their Applications)
Open AccessArticle
Hypergraph-Based Multitask Feature Selection with Temporally Constrained Group Sparsity Learning on fMRI
by
Youzhi Qu, Kai Fu, Linjing Wang, Yu Zhang, Haiyan Wu and Quanying Liu
Mathematics 2024, 12(11), 1733; https://doi.org/10.3390/math12111733 - 2 Jun 2024
Abstract
Localizing the brain regions affected by tasks is crucial to understanding the mechanisms of brain function. However, traditional statistical analysis does not accurately identify the brain regions of interest due to factors such as sample size, task design, and statistical effects. Here, we
[...] Read more.
Localizing the brain regions affected by tasks is crucial to understanding the mechanisms of brain function. However, traditional statistical analysis does not accurately identify the brain regions of interest due to factors such as sample size, task design, and statistical effects. Here, we propose a hypergraph-based multitask feature selection framework, referred to as HMTFS, which we apply to a functional magnetic resonance imaging (fMRI) dataset to extract task-related brain regions. HMTFS is characterized by its ability to construct a hypergraph through correlations between subjects, treating each subject as a node to preserve high-order information of time-varying signals. Additionally, it manages feature selection across different time windows in fMRI data as multiple tasks, facilitating time-constrained group sparse learning with a smoothness constraint. We utilize a large fMRI dataset from the Human Connectome Project (HCP) to validate the performance of HMTFS in feature selection. Experimental results demonstrate that brain regions selected by HMTFS can provide higher accuracy for downstream classification tasks compared to other competing feature selection methods and align with findings from previous neuroscience studies.
Full article
(This article belongs to the Special Issue Advanced Methods and Applications in Medical Informatics)
Open AccessArticle
Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System
by
Haoqing Chen, Guangmei Wei, Yuxin Song and Yaqin Xie
Mathematics 2024, 12(11), 1732; https://doi.org/10.3390/math12111732 - 2 Jun 2024
Abstract
In this paper, a variable-coefficient Davey–Stewartson (vcDS) system is investigated for modeling the evolution of a two-dimensional wave-packet on water of finite depth in inhomogeneous media or nonuniform boundaries, which is where its novelty lies. The Painlevé integrability is tested by the method
[...] Read more.
In this paper, a variable-coefficient Davey–Stewartson (vcDS) system is investigated for modeling the evolution of a two-dimensional wave-packet on water of finite depth in inhomogeneous media or nonuniform boundaries, which is where its novelty lies. The Painlevé integrability is tested by the method of Weiss, Tabor, and Carnevale (WTC) with the simplified form of Krustal. The rational solutions are derived by the Hirota bilinear method, where the formulae of the solutions are represented in terms of determinants. Furthermore the fundamental rogue wave solutions are obtained under certain parameter restrains in rational solutions. Finally the physical characteristics of the influences of the coefficient parameters on the solutions are discussed graphically. These rogue wave solutions have comprehensive implications for two-dimensional surface water waves in the ocean.
Full article
(This article belongs to the Section Mathematical Physics)
►▼
Show Figures
Figure 1
Open AccessArticle
Fault Detection and Diagnosis of Three-Wheeled Omnidirectional Mobile Robot Based on Power Consumption Modeling
by
Bingtao Wang, Liang Zhang and Jongwon Kim
Mathematics 2024, 12(11), 1731; https://doi.org/10.3390/math12111731 - 2 Jun 2024
Abstract
Three-wheeled omnidirectional mobile robots (TOMRs) are widely used to accomplish precise transportation tasks in narrow environments owing to their stability, flexible operation, and heavy loads. However, these robots are susceptible to slippage. For wheeled robots, almost all faults and slippage will directly affect
[...] Read more.
Three-wheeled omnidirectional mobile robots (TOMRs) are widely used to accomplish precise transportation tasks in narrow environments owing to their stability, flexible operation, and heavy loads. However, these robots are susceptible to slippage. For wheeled robots, almost all faults and slippage will directly affect the power consumption. Thus, using the energy consumption model data and encoder data in the healthy condition as a reference to diagnose robot slippage and other system faults is the main issue considered in this paper. We constructed an energy model for the TOMR and analyzed the factors that affect the power consumption in detail, such as the position of the gravity center. The study primarily focuses on the characteristic relationship between power consumption and speed when the robot experiences slippage or common faults, including control system faults. Finally, we present the use of a table-based artificial neural network (ANN) to indicate the type of fault by comparing the modeled data with the measured data. The experiments proved that the method is accurate and effective for diagnosing faults in TOMRs.
Full article
(This article belongs to the Section Engineering Mathematics)
Open AccessArticle
The de Rham Cohomology Classes of Hemi-Slant Submanifolds in Locally Product Riemannian Manifolds
by
Mustafa Gök and Erol Kılıç
Mathematics 2024, 12(11), 1730; https://doi.org/10.3390/math12111730 - 2 Jun 2024
Abstract
This paper aims to discuss the de Rham cohomology of hemi-slant submanifolds in locally product Riemannian manifolds. The integrability and geodesical invariance conditions of the distributions derived from the definition of a hemi-slant submanifold are given. The existence and non-triviality of de Rham
[...] Read more.
This paper aims to discuss the de Rham cohomology of hemi-slant submanifolds in locally product Riemannian manifolds. The integrability and geodesical invariance conditions of the distributions derived from the definition of a hemi-slant submanifold are given. The existence and non-triviality of de Rham cohomology classes of hemi-slant submanifolds are investigated. Finally, an example is presented.
Full article
(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)
Open AccessArticle
Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process
by
Ghada AlNemer, Mohamed Hosny, Ramalingam Udhayakumar and Ahmed M. Elshenhab
Mathematics 2024, 12(11), 1729; https://doi.org/10.3390/math12111729 - 2 Jun 2024
Abstract
Under the effect of the Rosenblatt process, time-delay systems of nonlinear stochastic delay differential equations are considered. Utilizing the delayed matrix functions and exact solutions for these systems, the existence and Hyers–Ulam stability results are derived. First, depending on the fixed point theory,
[...] Read more.
Under the effect of the Rosenblatt process, time-delay systems of nonlinear stochastic delay differential equations are considered. Utilizing the delayed matrix functions and exact solutions for these systems, the existence and Hyers–Ulam stability results are derived. First, depending on the fixed point theory, the existence and uniqueness of solutions are proven. Next, sufficient criteria for the Hyers–Ulam stability are established. Ultimately, to illustrate the importance of the results, an example is provided.
Full article
(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)
Journal Menu
► ▼ Journal Menu-
- Mathematics Home
- Aims & Scope
- Editorial Board
- Reviewer Board
- Topical Advisory Panel
- Instructions for Authors
- Special Issues
- Topics
- Sections & Collections
- Article Processing Charge
- Indexing & Archiving
- Editor’s Choice Articles
- Most Cited & Viewed
- Journal Statistics
- Journal History
- Journal Awards
- Society Collaborations
- Conferences
- Editorial Office
Journal Browser
► ▼ Journal BrowserHighly Accessed Articles
Latest Books
E-Mail Alert
News
Topics
Topic in
Algorithms, Axioms, Fractal Fract, Mathematics, Symmetry
Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems
Topic Editors: Xiaofeng Wang, Fazlollah SoleymaniDeadline: 30 June 2024
Topic in
Algorithms, Computation, Information, Mathematics
Complex Networks and Social Networks
Topic Editors: Jie Meng, Xiaowei Huang, Minghui Qian, Zhixuan XuDeadline: 31 July 2024
Topic in
Algorithms, Future Internet, Information, Mathematics, Symmetry
Research on Data Mining of Electronic Health Records Using Deep Learning Methods
Topic Editors: Dawei Yang, Yu Zhu, Hongyi XinDeadline: 31 August 2024
Topic in
Applied Sciences, Energies, Mathematics, Electronics, Designs
Distributed Optimization for Control
Topic Editors: Honglei Xu, Lingyun WangDeadline: 20 September 2024
Conferences
Special Issues
Special Issue in
Mathematics
Advances and Applications of Soft Computing
Guest Editor: Michael VoskoglouDeadline: 6 June 2024
Special Issue in
Mathematics
Applications of Fuzzy Modeling in Risk Management
Guest Editors: Edit Toth-Laufer, László PokorádiDeadline: 20 June 2024
Special Issue in
Mathematics
Computational Statistical Methods and Extreme Value Theory
Guest Editor: Frederico CaeiroDeadline: 30 June 2024
Special Issue in
Mathematics
Dynamical System and Stochastic Analysis
Guest Editors: Jun Huang, Yueyuan ZhangDeadline: 20 July 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