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 17.7 days after submission; acceptance to publication is undertaken in 2.7 days (median values for papers published in this journal in the first 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 and Analytics.
Impact Factor:
2.4 (2022);
5-Year Impact Factor:
2.3 (2022)
Latest Articles
Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion
Mathematics 2023, 11(16), 3447; https://doi.org/10.3390/math11163447 - 08 Aug 2023
Abstract
In the framework of 2D-elasticity, an equilibrium problem for an inhomogeneous body with a curvilinear inclusion located strictly inside the body is considered. The elastic properties of the inclusion are assumed to depend on a small positive parameter characterizing its width and
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In the framework of 2D-elasticity, an equilibrium problem for an inhomogeneous body with a curvilinear inclusion located strictly inside the body is considered. The elastic properties of the inclusion are assumed to depend on a small positive parameter characterizing its width and are assumed to be proportional to . Moreover, it is supposed that the inclusion has a curvilinear rough boundary. Relying on the variational formulation of the equilibrium problem, we perform the asymptotic analysis, as tends to zero. As a result, a variational model of an elastic body containing a thin curvilinear rod is constructed. Numerical calculations give a relative error between the initial and limit problems depending on .
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(This article belongs to the Special Issue Variational Problems and Applications, 2nd Edition)
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Short-Term Prediction of Time-Varying Passenger Flow for Intercity High-Speed Railways: A Neural Network Model Based on Multi-Source Data
Mathematics 2023, 11(16), 3446; https://doi.org/10.3390/math11163446 - 08 Aug 2023
Abstract
The accurate prediction of passenger flow is crucial in improving the quality of the service of intercity high-speed railways. At present, there are a few studies on such predictions for railway origin–destination (O-D) pairs, and usually only a single factor is considered, yielding
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The accurate prediction of passenger flow is crucial in improving the quality of the service of intercity high-speed railways. At present, there are a few studies on such predictions for railway origin–destination (O-D) pairs, and usually only a single factor is considered, yielding a low prediction accuracy. In this paper, we propose a neural network model based on multi-source data (NN-MSD) to predict the O-D passenger flow of intercity high-speed railways at different times in one day in the short term, considering the factors of time, space, and weather. Firstly, the factors that influence time-varying passenger flow are analyzed based on multi-source data. The cyclical characteristics, spatial and temporal fusion characteristics, and weather characteristics are extracted. Secondly, a neural network model including three modules is designed based on the characteristics. A fully connected network (FCN) model is used in the first module to process the classification data. A bi-directional Long Short-Term Memory (Bi-LSTM) model is used in the second module to process the time series data. The results of the first module and the second module are spliced and fused in the third module using an FCN model. Finally, an experimental analysis is performed for the Guangzhou–Zhuhai intercity high-speed railway in China, in which three groups of comparison experiments are designed. The results show that the proposed NN-MSD model can predict many O-D pairs with a high and stable accuracy, which outperforms the baseline models, and multi-source data are very helpful in improving the prediction accuracy.
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(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)
Open AccessArticle
On the Independence Number of Cayley Digraphs of Clifford Semigroups
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and
Mathematics 2023, 11(16), 3445; https://doi.org/10.3390/math11163445 - 08 Aug 2023
Abstract
Let S be a Clifford semigroup and A a subset of S. We write for the Cayley digraph of a Clifford semigroup S relative to A. The (weak, path, weak path) independence number
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Let S be a Clifford semigroup and A a subset of S. We write for the Cayley digraph of a Clifford semigroup S relative to A. The (weak, path, weak path) independence number of a graph is the maximum cardinality of an (weakly, path, weakly path) independent set of vertices in the graph. In this paper, we characterize maximal connected subdigraphs of and apply these results to determine the (weak, path, weak path) independence number of .
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(This article belongs to the Special Issue Algebraic Structures and Graph Theory, 2nd Edition)
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Open AccessArticle
Use of Statistical Process Control for Coking Time Monitoring
Mathematics 2023, 11(16), 3444; https://doi.org/10.3390/math11163444 - 08 Aug 2023
Abstract
Technical and technological developments in recent decades have stimulated the rapid development of methods and tools in the field of statistical process quality control, which also includes control charts. The principle of control charts defined by Dr. W. Shewhart has been known for
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Technical and technological developments in recent decades have stimulated the rapid development of methods and tools in the field of statistical process quality control, which also includes control charts. The principle of control charts defined by Dr. W. Shewhart has been known for more than 100 years. Since then, they have been used in many industries to monitor and control processes. This paper aims to assess the possibilities of use and the selection of the most suitable type of control chart for monitoring the quality of a process depending on its nature. This tool should help operators in monitoring coking time, which is one of the important control variables affecting the quality of coke production. The autoregressive nature of the variable being monitored was considered when selecting a suitable control chart from the group of options considered. In addition to the three traditional types of control charts (Shewhart’s, CUSUM, and EWMA), which were applied to the residuals of individual values of different types of ARIMA models, various statistical tests, and plots, a dynamic EWMA control chart was also used. Its advantage over traditional control charts applied to residuals is that it works with directly measured coking time data. This chart is intended to serve as a method to monitor the process. Its role is only to alert the process operator to the occurrence of problems with the length of the coking time.
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(This article belongs to the Special Issue Statistical Process Control and Application)
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Open AccessFeature PaperArticle
Design of a Port-Hamiltonian Control for an Alt-Azimuth Liquid–Mirror Telescope
Mathematics 2023, 11(16), 3443; https://doi.org/10.3390/math11163443 - 08 Aug 2023
Abstract
In this work, we design a control strategy to be applied in a port-Hamilton representation of a liquid-mirror telescope for an alt-azimuth configuration. Starting from a dynamical model for an alt-azimuth liquid-mirror telescope based on Lagrange mechanics, a transformation to the port-Hamilton form
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In this work, we design a control strategy to be applied in a port-Hamilton representation of a liquid-mirror telescope for an alt-azimuth configuration. Starting from a dynamical model for an alt-azimuth liquid-mirror telescope based on Lagrange mechanics, a transformation to the port-Hamilton form is made. Such a dynamical model is obtained by computing the kinetic and potential energy of the telescope and substituting them in the Euler–Lagrange equation of motion. Then, for the transformation to the port-Hamiltonian form, we obtain the relation between the Hamiltonian and the Lagrangian. The resulting open-loop model based on the Hamiltonian function is controlled using an extension of the interconnection and damping-assignment passivity-based control aiming for a robust and accurate steady behavior in the closed loop while tracking a star’s position. For comparison purposes, two different control strategies are applied to the Lagrangian model, inverse-dynamics control and sliding mode super-twisting control. Since the light is collected by the principal mirror of the telescope while tracking a star, we make a description of the liquid mirror’s behavior. The tracking star’s position is described as a function of the observer’s position and the star’s coordinates as well as the date of observation. The simulations’ results show that the port-Hamilton control has a good transitory and steady response as well as great accuracy competing with that of inverse-dynamics control but with greater robustness and no chattering drawback.
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(This article belongs to the Special Issue Dynamics and Control Theory with Applications)
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Black-Box Solver for Numerical Simulations and Mathematical Modelling in Engineering Physics
Mathematics 2023, 11(16), 3442; https://doi.org/10.3390/math11163442 - 08 Aug 2023
Abstract
This article presents a two-grid approach for developing a black-box iterative solver for a large class of real-life problems in continuum mechanics (heat and mass transfer, fluid dynamics, elasticity, electromagnetism, and others). The main requirements on this (non-)linear black-box solver are: (1) robustness
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This article presents a two-grid approach for developing a black-box iterative solver for a large class of real-life problems in continuum mechanics (heat and mass transfer, fluid dynamics, elasticity, electromagnetism, and others). The main requirements on this (non-)linear black-box solver are: (1) robustness (the lowest number of problem-dependent components), (2) efficiency (close-to-optimal algorithmic complexity), and (3) parallelism (a parallel robust algorithm should be faster than the fastest sequential one). The basic idea is to use the auxiliary structured grid for more computational work, where (non-)linear problems are simpler to solve and to parallelize, i.e., to combine the advantages of unstructured and structured grids: simplicity of generation in complex domain geometry and opportunity to solve (non-)linear (initial-)boundary value problems by using the Robust Multigrid Technique. Topics covered include the description of the two-grid algorithm and estimation of their robustness, convergence, algorithmic complexity, and parallelism. Further development of modern software for solving real-life problems justifies relevance of the research. The proposed two-grid algorithm can be used in black-box parallel software for the reduction in the execution time in solving (initial-)boundary value problems.
Full article
(This article belongs to the Special Issue Numerical Simulations and Mathematical Modelling in Engineering Physics)
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Open AccessArticle
The Predictive Power of Social Media Sentiment: Evidence from Cryptocurrencies and Stock Markets Using NLP and Stochastic ANNs
Mathematics 2023, 11(16), 3441; https://doi.org/10.3390/math11163441 - 08 Aug 2023
Abstract
Cryptocurrencies are nowadays seen as an investment opportunity, since they show some peculiar features, such as high volatility and diversification properties, that are triggering research interest into investigating their differences with traditional assets. In our paper, we address the problem of predictability of
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Cryptocurrencies are nowadays seen as an investment opportunity, since they show some peculiar features, such as high volatility and diversification properties, that are triggering research interest into investigating their differences with traditional assets. In our paper, we address the problem of predictability of cryptocurrency and stock trends by using data from social online communities and platforms to assess their contribution in terms of predictive power. We extend recent developments in the field by exploiting a combination of stochastic neural networks (NNs), an extension of standard NNs, natural language processing (NLP) to extract sentiment from Twitter, and an external evolutionary algorithm for optimal parameter setting to predict the short-term trend direction. Our results point to good and robust accuracy over time and across different market regimes. Furthermore, we propose to exploit recent advances in sentiment analysis to reassess its role in financial forecasting; in this way, we contribute to the empirical literature by showing that predictions based on sentiment analysis are not found to be significantly different from predictions based on historical data. Nonetheless, compared to stock markets, we find that the accuracy of trend predictions with sentiment analysis is on average much higher for cryptocurrencies.
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(This article belongs to the Special Issue Computational Intelligence in Management Science and Finance)
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A Study of Independency on Fuzzy Resolving Sets of Labelling Graphs
Mathematics 2023, 11(16), 3440; https://doi.org/10.3390/math11163440 - 08 Aug 2023
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Considering a fuzzy graph G is simple and can be connected and considered as a subset
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Considering a fuzzy graph G is simple and can be connected and considered as a subset ; then, every two pairs of elements of have a unique depiction with the relation of , and can be termed as a fuzzy resolving set (FRS). The minimal cardinality is regarded as the fuzzy resolving number (FRN), and it is signified by . An independence set is discussed on the FRS, fuzzy resolving domination set (FRDS), and Fuzzy modified antimagic resolving set (FMARS). In this paper, we discuss the independency of FRS and FMARS in which an application has also been developed.
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Open AccessFeature PaperArticle
Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials
Mathematics 2023, 11(16), 3439; https://doi.org/10.3390/math11163439 - 08 Aug 2023
Abstract
A comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions. This paper presents research on a novel family of multivariate Hermite polynomials associated with Apostol-type Frobenius–Euler polynomials. The study derives the generating
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A comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions. This paper presents research on a novel family of multivariate Hermite polynomials associated with Apostol-type Frobenius–Euler polynomials. The study derives the generating expression, operational rule, differential equation, and other defining characteristics for these polynomials. Additionally, the monomiality principle for these polynomials is verified. Moreover, the research establishes series representations, summation formulae, and operational and symmetric identities, as well as recurrence relations satisfied by these polynomials.
Full article
(This article belongs to the Special Issue Orthogonal Polynomials and Special Functions: Recent Trends and Their Applications)
Open AccessArticle
An Improved Mathematical Theory for Designing Membrane Deflection-Based Rain Gauges
Mathematics 2023, 11(16), 3438; https://doi.org/10.3390/math11163438 - 08 Aug 2023
Abstract
This paper is devoted to developing a more refined mathematical theory for designing the previously proposed membrane deflection-based rain gauges. The differential-integral equations governing the large deflection behavior of the membrane are improved by modifying the geometric equations, and more accurate power-series solutions
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This paper is devoted to developing a more refined mathematical theory for designing the previously proposed membrane deflection-based rain gauges. The differential-integral equations governing the large deflection behavior of the membrane are improved by modifying the geometric equations, and more accurate power-series solutions of the large deflection problem are provided, resulting in a new and more refined mathematical theory for designing such rain gauges. Examples are presented to illustrate how to analyze the convergence of the power-series solutions and how to numerically calibrate membrane deflection-based linear rain gauges. In addition, some important issues are demonstrated, analyzed, and discussed, such as the superiority of the new mathematical theory over the old one, the reason why the classical geometric equations cause errors, and the influence of changing design parameters on the input–output relationships of rain gauges.
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(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)
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Open AccessArticle
A Deep Reinforcement Learning Scheme for Spectrum Sensing and Resource Allocation in ITS
Mathematics 2023, 11(16), 3437; https://doi.org/10.3390/math11163437 - 08 Aug 2023
Abstract
In recent years, the Internet of Vehicles (IoV) has been found to be of huge potential value in the promotion of the development of intelligent transportation systems (ITSs) and smart cities. However, the traditional scheme in IoV has difficulty in dealing with an
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In recent years, the Internet of Vehicles (IoV) has been found to be of huge potential value in the promotion of the development of intelligent transportation systems (ITSs) and smart cities. However, the traditional scheme in IoV has difficulty in dealing with an uncertain environment, while reinforcement learning has the advantage of being able to deal with an uncertain environment. Spectrum resource allocation in IoV faces the uncertain environment in most cases. Therefore, this paper investigates the spectrum resource allocation problem by deep reinforcement learning after using spectrum sensing technology in the ITS, including the vehicle-to-infrastructure (V2I) link and the vehicle-to-vehicle (V2V) link. The spectrum resource allocation is modeled as a reinforcement learning-based multi-agent problem which is solved by using the soft actor critic (SAC) algorithm. Considered an agent, each V2V link interacts with the vehicle environment and makes a joint action. After that, each agent receives different observations as well as the same reward, and updates networks through the experiences from the memory. Therefore, during a certain time, each V2V link can optimize its spectrum allocation scheme to maximize the V2I capacity as well as increase the V2V payload delivery transmission rate. However, the number of SAC networks increases linearly as the number of V2V links increases, which means that the networks may have a problem in terms of convergence when there are an excessive number of V2V links. Consequently, a new algorithm, namely parameter sharing soft actor critic (PSSAC), is proposed to reduce the complexity for which the model is easier to converge. The simulation results show that both SAC and PSSAC can improve the V2I capacity and increase the V2V payload transmission success probability within a certain time. Specifically, these novel schemes have a 10 percent performance improvement compared with the existing scheme in the vehicular environment. Additionally, PSSAC has a lower complexity.
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(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)
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Optimal Control Design and Online Controller-Area-Network Bus Data Analysis for a Light Commercial Hybrid Electric Vehicle
Mathematics 2023, 11(15), 3436; https://doi.org/10.3390/math11153436 - 07 Aug 2023
Abstract
In this article, a hybrid powertrain for the Volkswagen (VW) Crafter is designed using the Model-In-The-Loop (MIL) method. An enhanced Proportional-Integral (PI) control technique based on integral cost functions is developed by carrying out a time-based simulation in MATLAB/Simulink software to realize the
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In this article, a hybrid powertrain for the Volkswagen (VW) Crafter is designed using the Model-In-The-Loop (MIL) method. An enhanced Proportional-Integral (PI) control technique based on integral cost functions is developed by carrying out a time-based simulation in MATLAB/Simulink software to realize the optimal fuel economy of the vehicle. Moreover, a comparative study is conducted between the vehicle’s hybrid and pure electric versions to assess the optimal battery energy consumption per unit distance traveled. Communication within our vehicles’ Electronic Control Units (ECUs) is facilitated by a message-based protocol called a Controller Area Network (CAN). Consequently, this paper presents an online CAN Bus data analysis using the Hardware-In-The-Loop (HIL) method. This method uses a standard frame, J1939 CAN protocol, implemented with Net CAN Plus 110 hardware. A graphical user interface is developed on a host Personal Computer (PC) using LabVIEW for decoding the acquired raw CAN data to physical values. The simulation results reveal that the proposed controller is promising and suitable for realizing optimal performance over the HIL method.
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(This article belongs to the Special Issue Dynamics and Control Theory with Applications)
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Fixed Point Results in Controlled Fuzzy Metric Spaces with an Application to the Transformation of Solar Energy to Electric Power
Mathematics 2023, 11(15), 3435; https://doi.org/10.3390/math11153435 - 07 Aug 2023
Abstract
In this manuscript, we give sufficient conditions for a sequence to be Cauchy in the context of controlled fuzzy metric space. Furthermore, we generalize the concept of Banach’s contraction principle by utilizing several new contraction conditions and prove several fixed point results. Furthermore,
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In this manuscript, we give sufficient conditions for a sequence to be Cauchy in the context of controlled fuzzy metric space. Furthermore, we generalize the concept of Banach’s contraction principle by utilizing several new contraction conditions and prove several fixed point results. Furthermore, we provide a number of non-trivial examples to validate the superiority of main results in the existing literature. At the end, we discuss an important application to the transformation of solar energy to electric power by utilizing differential equations.
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(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
Open AccessArticle
Analysis of U-V2X Communications with Non-Clustered and Clustered Jamming in the Presence of Fluctuating UAV Beam Width
by
and
Mathematics 2023, 11(15), 3434; https://doi.org/10.3390/math11153434 - 07 Aug 2023
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Jammers emit strong intentional jamming signals aiming to limit or block legitimate communications. The distribution of jammers, whether in non-clustered or clustered form, significantly influences the performance of vehicle-to-everything (V2X) networks. In addition, the fluctuations in the three-dimensional (3D) antenna beam width of
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Jammers emit strong intentional jamming signals aiming to limit or block legitimate communications. The distribution of jammers, whether in non-clustered or clustered form, significantly influences the performance of vehicle-to-everything (V2X) networks. In addition, the fluctuations in the three-dimensional (3D) antenna beam width of unmanned aerial vehicles (UAVs) can exert a substantial impact on the network’s overall performance. This paper introduces a model for UAV-V2X (U-V2X) communications in mm-Wave bands, considering non-clustered and clustered jammers, as well as the varying 3D antenna beam width. The roads are modeled using a Poisson line process, vehicular nodes (VNs) are modeled using a 1D Poisson point process (PPP), and UAVs are modeled using a 3D PPP. The jammers are distributed in two ways: non-clustered and clustered distributions. Moreover, the fluctuations in the 3D antenna beam width follow a normal distribution. To this end, a typical node’s performance in U-V2X communications is evaluated for various network configurations, including the number of UAVs, VNs, roads, jammers, and jammer’s transmission power. The analytical expressions for the outage probability (OP) of VN to VN connection (i.e., V2V), VN to UAV connection (i.e., V2U2V), and an overall connection (i.e., U-V2X), under non-clustered and clustered jamming, along with the fluctuating antenna beam width, are derived. The results revealed that the performance of the U-V2X communications utilizing mm-Waves is significantly degraded with the non-clustered jamming in comparison with the clustered jamming. The fluctuations in the 3D beam width of the UAV antennas further compromise the network’s performance. Thus, accurate modeling of these fluctuations is crucial, particularly in the presence of non-clustered jammers. Furthermore, the system designers should focus on implementing additional anti-jamming countermeasures specifically targeting non-clustered jammers in U-V2X communications.
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Open AccessFeature PaperArticle
Clustering Methods over the Tropical Projective Torus
by
and
Mathematics 2023, 11(15), 3433; https://doi.org/10.3390/math11153433 - 07 Aug 2023
Abstract
In this paper, we propose clustering methods for use on data described as tropically convex. Our approach is similar to clustering methods used in the Euclidean space, where we identify groupings of similar observations using tropical analogs of K-means and hierarchical clustering in
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In this paper, we propose clustering methods for use on data described as tropically convex. Our approach is similar to clustering methods used in the Euclidean space, where we identify groupings of similar observations using tropical analogs of K-means and hierarchical clustering in the Euclidean space. We provide results from computational experiments on generic simulated data as well as an application to phylogeny using ultrametrics, demonstrating the efficacy of these methods.
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(This article belongs to the Section Algebra, Geometry and Topology)
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Inverse Problem for a Fourth-Order Hyperbolic Equation with a Complex-Valued Coefficient
Mathematics 2023, 11(15), 3432; https://doi.org/10.3390/math11153432 - 07 Aug 2023
Abstract
This paper studies the existence and uniqueness of the classical solution of inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient with Dirichlet and Neumann boundary conditions. Using the method of separation of variables, formal solutions are obtained in the form
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This paper studies the existence and uniqueness of the classical solution of inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient with Dirichlet and Neumann boundary conditions. Using the method of separation of variables, formal solutions are obtained in the form of a Fourier series in terms of the eigenfunctions of a non-self-adjoint fourth-order ordinary differential operator. The proofs of the uniform convergence of the Fourier series are based on estimates of the norms of the derivatives of the eigenfunctions of a fourth-order ordinary differential operator and the uniform boundedness of the Riesz bases of the eigenfunctions.
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(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)
Open AccessArticle
Hybrid Attitude Saturation and Fault-Tolerant Control for Rigid Spacecraft without Unwinding
Mathematics 2023, 11(15), 3431; https://doi.org/10.3390/math11153431 - 07 Aug 2023
Abstract
This paper tackles the saturation and fault-tolerant attitude tracking problem without unwinding for rigid spacecraft with external disturbances and partial loss of actuator effectiveness faults. A hybrid saturation and fault-tolerant attitude control (HSFC) is proposed. The Lyapunov method is employed to prove that
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This paper tackles the saturation and fault-tolerant attitude tracking problem without unwinding for rigid spacecraft with external disturbances and partial loss of actuator effectiveness faults. A hybrid saturation and fault-tolerant attitude control (HSFC) is proposed. The Lyapunov method is employed to prove that the tracking errors of the spacecraft system tend to the equilibrium point asymptotically with HSFC. The advantages of the HSFC are that it is fault-tolerant, anti-unwinding and explicitly upper bounded a priori which means that both actuator saturation and the unwinding phenomenon can be avoided. Simulations verify the effectiveness of the proposed approach.
Full article
(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)
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Open AccessArticle
Investigation of the Product of Random Matrices and Related Evolution Models
Mathematics 2023, 11(15), 3430; https://doi.org/10.3390/math11153430 - 07 Aug 2023
Abstract
In this paper, we study the phase structure of the product of D * D order matrices. In each round, we randomly choose a matrix from a finite set of d matrices and multiply it with the product from the previous round. Initially,
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In this paper, we study the phase structure of the product of D * D order matrices. In each round, we randomly choose a matrix from a finite set of d matrices and multiply it with the product from the previous round. Initially, we derived a functional equation for the case of matrices with real eigenvalues and correlated choice of matrices, which led to the identification of several phases. Subsequently, we explored the case of uncorrelated choice of matrices and derived a simpler functional equation, again identifying multiple phases. In our investigation, we observed a phase with a smooth distribution in steady-state and phases with singularities. For the general case of D-dimensional matrices, we derived a formula for the phase transition point. Additionally, we solved a related evolution model. Moreover, we examined the relaxation dynamics of the considered models. In both the smooth phase and the phase with singularities, the relaxation is exponential. The superiority of relaxation in the smooth phase depends on the specific case.
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(This article belongs to the Section Mathematical Biology)
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On Effective Fine Functions for Inspection—Corruption Games (Evolutionary Approach)
Mathematics 2023, 11(15), 3429; https://doi.org/10.3390/math11153429 - 07 Aug 2023
Abstract
In previous papers of the authors, a generalized evolutionary approach was developed for the analysis of popular inspection and corruption games. Namely, a two-level hierarchy was studied, where a local inspector I of a pool of agents (that may break the law) can
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In previous papers of the authors, a generalized evolutionary approach was developed for the analysis of popular inspection and corruption games. Namely, a two-level hierarchy was studied, where a local inspector I of a pool of agents (that may break the law) can be corrupted and is further controlled by the higher authority A. Here, we extend this two-level modeling by answering the following questions: (i) what levels of illegal profit r of violators and what level of bribes α (fraction of illegal profit asked as a bribe from a violator) of an inspector are feasible, that is, realizable in stable equilibria of generalized replicator dynamics; and (ii) what α can be optimal for a corrupted inspector that aims at maximizing the total profit. Concrete settings that we have in mind are illegal logging, the sales of products with substandard quality, and tax evasion.
Full article
(This article belongs to the Special Issue Multi-Agent Systems of Competitive and Cooperative Interaction)
Open AccessArticle
Anomaly Detection in the Molecular Structure of Gallium Arsenide Using Convolutional Neural Networks
Mathematics 2023, 11(15), 3428; https://doi.org/10.3390/math11153428 - 07 Aug 2023
Abstract
This paper concerns the development of a machine learning tool to detect anomalies in the molecular structure of Gallium Arsenide. We employ a combination of a CNN and a PCA reconstruction to create the model, using real images taken with an electron microscope
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This paper concerns the development of a machine learning tool to detect anomalies in the molecular structure of Gallium Arsenide. We employ a combination of a CNN and a PCA reconstruction to create the model, using real images taken with an electron microscope in training and testing. The methodology developed allows for the creation of a defect detection model, without any labeled images of defects being required for training. The model performed well on all tests under the established assumptions, allowing for reliable anomaly detection. To the best of our knowledge, such methods are not currently available in the open literature; thus, this work fills a gap in current capabilities.
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(This article belongs to the Special Issue Applied Mathematics and Machine Learning)
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Selected Papers from the 19th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2021)
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Advances in Differential and Difference Equations with Applications 2023
Guest Editor: Dumitru BaleanuDeadline: 31 August 2023
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Stochastic Processes Applied to Modelling in Finance: Latest Advances and Prospects
Guest Editors: Peter Lakner, Christoph FreiDeadline: 15 September 2023
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