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Mathematics
Volume 11
Issue 9
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Mathematics, Volume 11, Issue 9 (May-1 2023) – 246 articles

Cover Story (view full-size image): Greedy algorithms are very popular methods for nonlinear sparse approximation with respect to dictionaries. Among others, the vector greedy algorithm can output the approximants simultaneously for a finite set of target elements. The authors introduce a new vector greedy algorithm—the Vector Weak Rescaled Pure Greedy Algorithm in a Hilbert space and a more general Banach space. They study the approximation properties of the new algorithms. The results show that this type of new algorithm is more efficient than other vector greedy algorithms. The results of this paper can be applied to the areas of signal vector processing and multi-task learning. View this paper
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26 pages, 3365 KiB  
Article
A Data-Driven Decision-Making Model for Configuring Surgical Trays Based on the Likelihood of Instrument Usages
by Ehsan Ahmadi, Dale T. Masel and Seth Hostetler
Mathematics 2023, 11(9), 2219; https://doi.org/10.3390/math11092219 - 8 May 2023
Cited by 1 | Viewed by 2007
Abstract
In order to perform a surgical procedure, substantial numbers of sterile instruments should be readily available to surgeons through the containers referred to as surgical trays and peel packs. After the procedure, all instruments in the opened containers, regardless of whether they have [...] Read more.
In order to perform a surgical procedure, substantial numbers of sterile instruments should be readily available to surgeons through the containers referred to as surgical trays and peel packs. After the procedure, all instruments in the opened containers, regardless of whether they have been used or not, must go through the labor-intensive re-sterilization process. Empirical studies have shown that the utilization rate of instruments within trays is very low due to not having optimized tray configurations. Additionally, surgical trays often include instruments that are not likely to be used but are included “just in case”, which imposes an additional cost on hospitals through unnecessary instrument re-sterilization. This study is the first analytical attempt to address the issue of configuring surgical trays based on the likelihood of instrument usage through formulating and solving a probabilistic tray optimization problem (PTOP). The PTOP model can serve as a decision support for surgeons by providing them with the tray’s probability of being used for optimally configured trays and its associated reprocessing costs. The PTOP is constructed upon an integer non-linear programming model. A decomposition-based heuristic and metaheuristic method coupled with two novel local search algorithms are developed to solve the PTOP. The application of this model can be illustrated through a case study. We discuss how hospitals could benefit from our model in reducing the costs associated with opening trays unnecessarily before a procedure. Additionally, we conducted a risk analysis to estimate the level of confidence for the recommended solution. Full article
(This article belongs to the Special Issue New Advance in Operations Research and Analytics)
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12 pages, 2201 KiB  
Article
Improving Mechanical Oscillator Cooling in a Double-Coupled Cavity Optomechanical System with an Optical Parametric Amplifier
by Peipei Pan, Aixi Chen and Li Deng
Mathematics 2023, 11(9), 2218; https://doi.org/10.3390/math11092218 - 8 May 2023
Viewed by 1540
Abstract
We investigate the cooling phenomenon of a mechanical oscillator in a double-coupled cavity optomechanical system. Our model includes two single-mode optical cavities. The left cavity is an optomechanical system with an optical parametric amplifier, and the right cavity is a standard optical cavity. [...] Read more.
We investigate the cooling phenomenon of a mechanical oscillator in a double-coupled cavity optomechanical system. Our model includes two single-mode optical cavities. The left cavity is an optomechanical system with an optical parametric amplifier, and the right cavity is a standard optical cavity. The two optical cavities couple with each other by exchanging photons. The optomechanical system is effectively driven by an input laser field. By solving the linear quantum Langevin equation of the system under a steady-state condition, we can obtain the position fluctuation spectrum and momentum fluctuation spectrum of the mechanical oscillator, and then, the expression of its effective temperature is obtained. Through numerical analysis, we find the change in the effective temperature of the mechanical oscillator under different physical parameters. The results show that the cooling of the mechanical oscillator can be significantly improved in the presence of optical parameter amplification and adjustment of optical cavity parameters. Our cooling solutions have potential applications for the preparation of nonclassical states of mechanical oscillators, high-precision measurements, and quantum information processing. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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31 pages, 18782 KiB  
Article
An Improved Flow Direction Algorithm for Engineering Optimization Problems
by Yuqi Fan, Sheng Zhang, Yaping Wang, Di Xu and Qisong Zhang
Mathematics 2023, 11(9), 2217; https://doi.org/10.3390/math11092217 - 8 May 2023
Cited by 2 | Viewed by 1829
Abstract
Flow Direction Algorithm (FDA) has better searching performance than some traditional optimization algorithms. To give the basic Flow Direction Algorithm more effective searching ability and avoid multiple local minima under the searching space, and enable it to obtain better search results, an improved [...] Read more.
Flow Direction Algorithm (FDA) has better searching performance than some traditional optimization algorithms. To give the basic Flow Direction Algorithm more effective searching ability and avoid multiple local minima under the searching space, and enable it to obtain better search results, an improved FDA based on the Lévy flight strategy and the self-renewable method (LSRFDA) was proposed in this paper. The Lévy flight strategy and the self-renewable approach were added to the basic Flow Direction Algorithm. Random parameters generated by the Lévy flight strategy can increase the algorithm’s diversity of feasible solutions in a short calculation time and greatly enhance the operational efficiency of the algorithm. The self-renewable method lets the algorithm quickly obtain a better possible solution and jump to the local solution space. Then, this paper tested different mathematical testing functions, including low-dimensional and high-dimensional functions, and the test results were compared with those of different algorithms. This paper includes iterative figures, box plots, and search paths to show the different performances of the LSRFDA. Finally, this paper calculated different engineering optimization problems. The test results show that the proposed algorithm in this paper has better searching ability and quicker searching speed than the basic Flow Direction Algorithm. Full article
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17 pages, 504 KiB  
Article
Generalized Data–Driven Predictive Control: Merging Subspace and Hankel Predictors
by M. Lazar and P. C. N. Verheijen
Mathematics 2023, 11(9), 2216; https://doi.org/10.3390/math11092216 - 8 May 2023
Cited by 2 | Viewed by 2174
Abstract
Data–driven predictive control (DPC) is becoming an attractive alternative to model predictive control as it requires less system knowledge for implementation and reliable data is increasingly available in smart engineering systems. Two main approaches exist within DPC: the subspace approach, which estimates prediction [...] Read more.
Data–driven predictive control (DPC) is becoming an attractive alternative to model predictive control as it requires less system knowledge for implementation and reliable data is increasingly available in smart engineering systems. Two main approaches exist within DPC: the subspace approach, which estimates prediction matrices (unbiased for large data) and the behavioral, data-enabled approach, which uses Hankel data matrices for prediction (allows for optimizing the bias/variance trade–off). In this paper we develop a novel, generalized DPC (GDPC) algorithm by merging subspace and Hankel predictors. The predicted input sequence is defined as the sum of a known, baseline input sequence, and an optimized input sequence. The corresponding baseline output sequence is computed using an unbiased, subspace predictor, while the optimized predicted output sequence is computed using a Hankel matrix predictor. By combining these two types of predictors, GDPC can achieve high performance for noisy data even when using a small Hankel matrix, which is computationally more efficient. Simulation results for a benchmark example from the literature show that GDPC with a reduced size Hankel matrix can match the performance of data–enabled predictive control with a larger Hankel matrix in the presence of noisy data. Full article
(This article belongs to the Special Issue Information Theory Applied in Scientific Computing)
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31 pages, 11748 KiB  
Article
Parameter Identification of Lithium-Ion Battery Model Based on African Vultures Optimization Algorithm
by Hend M. Fahmy, Rania A. Sweif, Hany M. Hasanien, Marcos Tostado-Véliz, Mohammed Alharbi and Francisco Jurado
Mathematics 2023, 11(9), 2215; https://doi.org/10.3390/math11092215 - 8 May 2023
Cited by 7 | Viewed by 2512
Abstract
This paper establishes a study for an accurate parameter modeling method for lithium-ion batteries. A precise state space model generated from an equivalent electric circuit is used to carry out the proposed identification process, where parameter identification is a nonlinear optimization process problem. [...] Read more.
This paper establishes a study for an accurate parameter modeling method for lithium-ion batteries. A precise state space model generated from an equivalent electric circuit is used to carry out the proposed identification process, where parameter identification is a nonlinear optimization process problem. The African vultures optimization algorithm (AVOA) is utilized to solve this problem by simulating African vultures’ foraging and navigating habits. The AVOA is used to implement this strategy and improve the quality of the solutions. Four scenarios are considered to take the effect of loading, fading, and dynamic analyses. The fitness function is selected as the integral square error between the estimated and measured voltage in these scenarios. Numerical simulations were executed on a 2600 mAhr Panasonic Li-ion battery to demonstrate the effectiveness of the suggested parameter identification technique. The proposed AVOA was fulfilled with high accuracy, the least error, and high closeness with the experimental data compared with different optimization algorithms, such as the Nelder–Mead simplex algorithm, the quasi-Newton algorithm, the Runge Kutta optimizer, the genetic algorithm, the grey wolf optimizer, and the gorilla troops optimizer. The proposed AVOA achieves the lowest fitness function level of the scenarios studied compared with relative optimization algorithms. Full article
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14 pages, 814 KiB  
Article
Modeling of the Electronic Structure of Semiconductor Nanoparticles
by Vasily B. Novozhilov, Valeria L. Bodneva, Kairat S. Kurmangaleev, Boris V. Lidskii, Vladimir S. Posvyanskii and Leonid I. Trakhtenberg
Mathematics 2023, 11(9), 2214; https://doi.org/10.3390/math11092214 - 8 May 2023
Cited by 1 | Viewed by 1418
Abstract
This paper deals with the mathematical modeling of the electronic structure of semiconductor particles. Mathematically, the task is reduced to a joint solution of the problem of free energy minimization and the set of chemical kinetic equations describing the processes at the surface [...] Read more.
This paper deals with the mathematical modeling of the electronic structure of semiconductor particles. Mathematically, the task is reduced to a joint solution of the problem of free energy minimization and the set of chemical kinetic equations describing the processes at the surface of a nanoparticle. The numerical modeling of the sensor effect is carried out in two steps. First, the number of charged oxygen atoms on the surface of the nanoparticle NO− is determined. This value is found by solving a system of nonlinear algebraic equations, where the unknowns are the stationary points of this system describing the processes on the surface of a nanoparticle. The specific form of such equations is determined by the type of nanoparticles and the mechanism of chemical reactions on the surface. The second step is to calculate the electron density inside the nanoparticle (nc(r)), which gives the minimum free energy. Mathematically, this second step reduces to solving a boundary value problem for a nonlinear integro-differential equation. The calculation results are compared with experimental data on the sensor effect. Full article
(This article belongs to the Special Issue Mathematical Problems in Chemical Physics)
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13 pages, 13982 KiB  
Article
Chaotic States of Transistor-Based Tuned-Collector Oscillator
by Jiri Petrzela
Mathematics 2023, 11(9), 2213; https://doi.org/10.3390/math11092213 - 8 May 2023
Cited by 2 | Viewed by 1234
Abstract
This brief paper shows that robust chaotic behavior can be detected within a tuned-collector single-stage transistor-based oscillator. The content of this work also contributes to the problem of chaos localization in simplified mathematical model of standard analog building block. Searching for chaos is [...] Read more.
This brief paper shows that robust chaotic behavior can be detected within a tuned-collector single-stage transistor-based oscillator. The content of this work also contributes to the problem of chaos localization in simplified mathematical model of standard analog building block. Searching for chaos is performed via numerical optimization routine applied onto the principal schematic of oscillator where generalized bipolar transistor is modelled as a two-port described by impedance as well as admittance matrix. In both cases, the presence of dense chaotic attractor is proved via calculation of the largest Lyapunov exponent, while its structural stability is validated by real measurement, i.e., visualization of captured oscilloscope screenshots. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
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26 pages, 4833 KiB  
Article
Blockchain Transaction Fee Forecasting: A Comparison of Machine Learning Methods
by Conall Butler and Martin Crane
Mathematics 2023, 11(9), 2212; https://doi.org/10.3390/math11092212 - 8 May 2023
Cited by 3 | Viewed by 2704
Abstract
Gas is the transaction-fee metering system of the Ethereum network. Users of the network are required to select a gas price for submission with their transaction, creating a risk of overpaying or delayed/unprocessed transactions involved in this selection. In this work, we investigate [...] Read more.
Gas is the transaction-fee metering system of the Ethereum network. Users of the network are required to select a gas price for submission with their transaction, creating a risk of overpaying or delayed/unprocessed transactions involved in this selection. In this work, we investigate data in the aftermath of the London Hard Fork and shed insight into the transaction dynamics of the network after this major fork. As such, this paper provides an update on work previous to 2019 on the link between EthUSD/BitUSD and gas price. For forecasting, we compare a novel combination of machine learning methods such as Direct-Recursive Hybrid LSTM, CNN-LSTM, and Attention-LSTM. These are combined with wavelet threshold denoising and matrix profile data processing toward the forecasting of block minimum gas price, on a 5-min timescale, over multiple lookaheads. As the first application of the matrix profile being applied to gas price data and forecasting that we are aware of, this study demonstrates that matrix profile data can enhance attention-based models; however, given the hardware constraints, hybrid models outperformed attention and CNN-LSTM models. The wavelet coherence of inputs demonstrates correlation in multiple variables on a 1-day timescale, which is a deviation of base free from gas price. A Direct-Recursive Hybrid LSTM strategy is found to outperform other models, with an average RMSE of 26.08 and R2 of 0.54 over a 50-min lookahead window compared to an RMSE of 26.78 and R2 of 0.452 in the best-performing attention model. Hybrid models are shown to have favorable performance up to a 20-min lookahead with performance being comparable to attention models when forecasting 25–50-min ahead. Forecasts over a range of lookaheads allow users to make an informed decision on gas price selection and the optimal window to submit their transaction in without fear of their transaction being rejected. This, in turn, gives more detailed insight into gas price dynamics than existing recommenders, oracles and forecasting approaches, which provide simple heuristics or limited lookahead horizons. Full article
(This article belongs to the Special Issue Advances in Blockchain Technology)
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15 pages, 3474 KiB  
Article
Three-Dimensional Lidar Localization and Mapping with Loop-Closure Detection Based on Dense Depth Information
by Liang Yang, Zhenbiao Yu, Chunjian Deng and Guanyu Lai
Mathematics 2023, 11(9), 2211; https://doi.org/10.3390/math11092211 - 8 May 2023
Cited by 2 | Viewed by 1588
Abstract
This paper presents a novel lidar SLAM system for localizing a mobile robot to build a map of the environment. To identify the unknown transform matrix, we design a new scan-matching approach, in which a point cloud segmentation algorithm is additionally integrated. Different [...] Read more.
This paper presents a novel lidar SLAM system for localizing a mobile robot to build a map of the environment. To identify the unknown transform matrix, we design a new scan-matching approach, in which a point cloud segmentation algorithm is additionally integrated. Different from the traditional normal distribution transform algorithm for point cloud registration, our newly proposed one additionally incorporates a ground point remover and a point cloud segmentation method. By employing the point cloud segmentation algorithm to divide the point cloud space into different cells, the newly proposed algorithm can guarantee the continuity and convergence of the cost function. To tackle the recognition difficulties that the camera-based loop-closure detection heavily depends on the environment’s appearance, a depth-completion algorithm is introduced to fuse sensor data to ensure the robustness of the algorithm. Moreover, the bags of binary words (DBoW) are adopted to improve the image-matching quality. Finally, experimental results are presented to illustrate the effectiveness of the proposed system. Full article
(This article belongs to the Section Engineering Mathematics)
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5 pages, 882 KiB  
Article
Note on Discovering Doily in PG(2,5)
by Stefano Innamorati
Mathematics 2023, 11(9), 2210; https://doi.org/10.3390/math11092210 - 8 May 2023
Viewed by 1027
Abstract
W. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order 2, GQ(2,2), [...] Read more.
W. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order 2, GQ(2,2), whose representation was dubbed “the doily” by Stan Payne in 1973. In this note, we prove that the external points of a conic in PG(2,5), together with the collinear and non-collinear triples on the non-tangent lines, form the generalized quadrangle of order 2. Full article
(This article belongs to the Special Issue Discrete Mathematics, Graph Theory and Applications)
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12 pages, 766 KiB  
Article
Quarter-Symmetric Metric Connection on a Cosymplectic Manifold
by Miroslav D. Maksimović and Milan Lj. Zlatanović
Mathematics 2023, 11(9), 2209; https://doi.org/10.3390/math11092209 - 8 May 2023
Cited by 1 | Viewed by 1345
Abstract
We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric A-connection, we construct the Weyl projective curvature tensor on a cosymplectic manifold. In this way, we obtain new conditions for [...] Read more.
We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric A-connection, we construct the Weyl projective curvature tensor on a cosymplectic manifold. In this way, we obtain new conditions for the manifold to be projectively flat. At the end of the paper, we define η-Einstein cosymplectic manifolds of the θ-th kind and prove that they coincide with the η-Einstein cosymplectic manifold. Full article
(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Submanifolds)
7 pages, 242 KiB  
Article
Linear Maps Preserving the Set of Semi-Weyl Operators
by Wei-Yan Yu and Xiao-Hong Cao
Mathematics 2023, 11(9), 2208; https://doi.org/10.3390/math11092208 - 8 May 2023
Viewed by 1125
Abstract
Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. In this paper, we characterized the linear maps ϕ:B(H)→B(H) [...] Read more.
Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. In this paper, we characterized the linear maps ϕ:B(H)→B(H), which are surjective up to compact operators preserving the set of left semi-Weyl operators in both directions. As an application, we proved that ϕ preserves the essential approximate point spectrum if and only if the ideal of all compact operators is invariant under ϕ and the induced map φ on the Calkin algebra is an automorphism. Moreover, we have ind(ϕ(T))=ind(T) if both ϕ(T) and T are Fredholm. Full article
1 pages, 154 KiB  
Correction
Correction: Bau, S.; Lei, Y. The Groups of Isometries of Metric Spaces over Vector Groups. Mathematics 2022, 10, 4453
by Sheng Bau and Yiming Lei
Mathematics 2023, 11(9), 2207; https://doi.org/10.3390/math11092207 - 8 May 2023
Viewed by 753
Abstract
Change in Affiliation Numbers [...] Full article
14 pages, 593 KiB  
Article
On Targeted Control over Trajectories of Dynamical Systems Arising in Models of Complex Networks
by Diana Ogorelova, Felix Sadyrbaev and Inna Samuilik
Mathematics 2023, 11(9), 2206; https://doi.org/10.3390/math11092206 - 8 May 2023
Cited by 3 | Viewed by 1489
Abstract
The question of targeted control over trajectories of systems of differential equations encountered in the theory of genetic and neural networks is considered. Examples are given of transferring trajectories corresponding to network states from the basin of attraction of one attractor to the [...] Read more.
The question of targeted control over trajectories of systems of differential equations encountered in the theory of genetic and neural networks is considered. Examples are given of transferring trajectories corresponding to network states from the basin of attraction of one attractor to the basin of attraction of the target attractor. This article considers a system of ordinary differential equations that arises in the theory of gene networks. Each trajectory describes the current and future states of the network. The question of the possibility of reorienting a given trajectory from the initial state to the assigned attractor is considered. This implies an only partial control of the network. The difficulty lies in the selection of parameters, the change of which leads to the goal. Similar problems arise when modeling the response of the body’s gene networks to serious diseases (e.g., leukemia). Solving such problems is the first step in the process of applying mathematical methods in medicine and pharmacology. Full article
(This article belongs to the Special Issue Advances on Complex Systems with Mathematics and Computer Science)
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7 pages, 636 KiB  
Editorial
Advanced Optimization Methods and Applications
by Adrian Marius Deaconu, Daniel Tudor Cotfas and Petru Adrian Cotfas
Mathematics 2023, 11(9), 2205; https://doi.org/10.3390/math11092205 - 8 May 2023
Cited by 2 | Viewed by 1957
Abstract
Optimization methods are finding more applications in all domains, as they play an essential role when dealing with real-life problems [...] Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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8 pages, 256 KiB  
Article
Periodic Solutions for a Neutral System with Two Volterra Terms
by Mouataz Billah Mesmouli, Meshari Alesemi and Wael W. Mohammed
Mathematics 2023, 11(9), 2204; https://doi.org/10.3390/math11092204 - 8 May 2023
Cited by 1 | Viewed by 1145
Abstract
In this paper, we propose a system of equations containing two kernels. In our transformation of the system, we use the integrable dichotomy condition, where we extract the term of the integration matrix from one of the kernels. We then use the fixed-point [...] Read more.
In this paper, we propose a system of equations containing two kernels. In our transformation of the system, we use the integrable dichotomy condition, where we extract the term of the integration matrix from one of the kernels. We then use the fixed-point theory to prove that the system has periodic solutions that are unique under sufficient conditions. An illustrative example at the end of the article is given. Full article
(This article belongs to the Section Difference and Differential Equations)
10 pages, 271 KiB  
Article
Saturated (n, m)-Regular Semigroups
by Amal S. Alali, Sakeena Bano and Muneer Nabi
Mathematics 2023, 11(9), 2203; https://doi.org/10.3390/math11092203 - 7 May 2023
Cited by 1 | Viewed by 1292
Abstract
The aim of this paper is to determine several saturated classes of structurally regular semigroups. First, we show that structurally (n,m)-regular semigroups are saturated in a subclass of semigroups for any pair (n,m) of [...] Read more.
The aim of this paper is to determine several saturated classes of structurally regular semigroups. First, we show that structurally (n,m)-regular semigroups are saturated in a subclass of semigroups for any pair (n,m) of positive integers. We also demonstrate that, for all positive integers n and k with 1≤k≤n, the variety of structurally (0,n)-left seminormal bands is saturated in the variety of structurally (0,k)-bands. As a result, in the category of structurally (0,k)-bands, epis from structurally (0,n)-left seminormal bands is onto. Full article
(This article belongs to the Special Issue New Perspectives in Algebraic Systems Theory)
32 pages, 1040 KiB  
Article
Stability of Traveling Fronts in a Neural Field Model
by Dominick Macaluso and Yixin Guo
Mathematics 2023, 11(9), 2202; https://doi.org/10.3390/math11092202 - 7 May 2023
Viewed by 1340
Abstract
We investigate the stability of traveling front solutions in the neural field model. This model has been studied intensively regarding propagating patterns with saturating Heaviside gain for neuron firing activity. Previous work has shown the existence of traveling fronts in the neural field [...] Read more.
We investigate the stability of traveling front solutions in the neural field model. This model has been studied intensively regarding propagating patterns with saturating Heaviside gain for neuron firing activity. Previous work has shown the existence of traveling fronts in the neural field model in a more complex setting, using a nonsaturating piecewise linear gain. We aimed to study the stability of traveling fronts in the neural field model utilizing the Evans function. We attained the Evans function of traveling fronts using an integration of analytical derivations and a computational approach for the neural field model, with previously uninvestigated piecewise linear gain. Using this approach, we are able to identify both stable and unstable traveling fronts in the neural field model. Full article
(This article belongs to the Section Mathematics and Computer Science)
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24 pages, 1930 KiB  
Article
Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform
by Didar Urynbassarova and Aajaz A. Teali
Mathematics 2023, 11(9), 2201; https://doi.org/10.3390/math11092201 - 7 May 2023
Cited by 4 | Viewed by 1628
Abstract
Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness in analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonical transform (QOLCT), which is the most general form of QFT with additional [...] Read more.
Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness in analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonical transform (QOLCT), which is the most general form of QFT with additional free parameters. We explore the properties of 2D right-sided QOLCT, including inversion and Parseval formulas, besides its relationship with other transforms. We also examine the convolution and correlation theorems of 2D right-sided QOLCT, followed by several uncertainty principles. Additionally, we present an illustrative example of the proposed transform, demonstrating its graphical representation of a given signal and its transformed signal. Finally, we demonstrate an application of QOLCT, where it can be utilized to generalize the treatment of swept-frequency filters. Full article
(This article belongs to the Special Issue Theory and Applications of Fractional Equations and Calculus)
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17 pages, 429 KiB  
Article
Efficient and Effective Directed Minimum Spanning Tree Queries
by Zhuoran Wang, Dian Ouyang, Yikun Wang, Qi Liang and Zhuo Huang
Mathematics 2023, 11(9), 2200; https://doi.org/10.3390/math11092200 - 6 May 2023
Viewed by 2947
Abstract
Computing directed Minimum Spanning Tree (DMST) is a fundamental problem in graph theory. It is applied in a wide spectrum of fields from computer network and communication protocol design to revenue maximization in social networks and syntactic parsing [...] Read more.
Computing directed Minimum Spanning Tree (DMST) is a fundamental problem in graph theory. It is applied in a wide spectrum of fields from computer network and communication protocol design to revenue maximization in social networks and syntactic parsing in Natural Language Processing. State-of-the-art solutions are online algorithms that compute DMST for a given graph and a root. For multi-query requirements, the online algorithm is inefficient. To overcome the drawbacks, in this paper, we propose an indexed approach that reuses the computation result to facilitate single and batch queries. We store all the potential edges of DMST in a hierarchical tree in O(n) space complexity. Furthermore, we answer the DMST query of any root in O(n) time complexity. Experimental results demonstrate that our approach can achieve a speedup of 2–3 orders of magnitude in query processing compared to the state-of-the-art while consuming O(n) index size. Full article
(This article belongs to the Special Issue Advances in Graph Theory: Algorithms and Applications)
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28 pages, 1010 KiB  
Article
Partial Slip Effects for Thermally Radiative Convective Nanofluid Flow
by Remus-Daniel Ene, Nicolina Pop and Rodica Badarau
Mathematics 2023, 11(9), 2199; https://doi.org/10.3390/math11092199 - 6 May 2023
Viewed by 1503
Abstract
The partial slip effects for radiative convective nanofluid flow over a stretching sheet in porous medium are analytically explored in this work. The Navier–Stokes equations, the momentum and the energy equations are converted into a set of non-linear ODEs by the similarity transformation. [...] Read more.
The partial slip effects for radiative convective nanofluid flow over a stretching sheet in porous medium are analytically explored in this work. The Navier–Stokes equations, the momentum and the energy equations are converted into a set of non-linear ODEs by the similarity transformation. Using the modified optimal homotopy asymptotic method (OHAM), the resulting non-linear ODEs are analytically approximately solved. The impact of various parameters, such as: the velocity exponential factor n, the wall thickness parameter γ, the dimensionless velocity slip parameter δ1, the Prandtl number Pr, the radiation parameter R, and the dimensionless temperature jump parameter δ2, on the behaviour of the mass and heat transfer is presented. The influence of these parameters is tabular and graphically presented. An excellent agreement between the approximate analytical solution and the corresponding numerical solution is highlighted. The results obtained confirm that modified OHAM is a useful and competitive mathematical tool to explore a large class of non-linear problems with applications in various fields of science and engineering. Full article
(This article belongs to the Special Issue Nonlinear Vibration Theory and Mechanical Dynamics)
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19 pages, 4727 KiB  
Article
The Gibbons, Ross, and Shanken Test for Portfolio Efficiency: A Note Based on Its Trigonometric Properties
by Pankaj Agrrawal
Mathematics 2023, 11(9), 2198; https://doi.org/10.3390/math11092198 - 6 May 2023
Cited by 2 | Viewed by 6476
Abstract
This study is intended as a note and provides an extension to a much-used and established test for portfolio efficiency, the Gibbons, Ross, and Shanken GRS-Wald test. Tests devised to measure portfolio efficiency are crucial to the theoretical issues related to CAPM (Capital [...] Read more.
This study is intended as a note and provides an extension to a much-used and established test for portfolio efficiency, the Gibbons, Ross, and Shanken GRS-Wald test. Tests devised to measure portfolio efficiency are crucial to the theoretical issues related to CAPM (Capital Asset Pricing Model) testing and have applications for the fund manager who seeks to rank portfolio performance. This study looks at the GRS-Wald test for portfolio efficiency and extends it to make it visually more interpretive without any loss of generality in its structure. The geometrically recast statistic draws upon the trigonometric properties of a portfolio in the mean-variance space and a mathematical proof of the equivalence of the two statistics is provided. The GRS-Wald test is a widely used statistic in studies addressing the issue of portfolio efficiency and CAPM deviations. A simulation demonstrates the use of the recast GRS-Wald test in testing for the mean-variance efficiency of a test portfolio. The study also provides a table of the GRS-Wald test, based on a range of mean-variance locations (cosine of portfolio angles) at which the test portfolio and the efficient market portfolio can be placed. Full article
(This article belongs to the Special Issue Alternate Mathematical Approaches to Estimating Portfolio Efficiency: Incorporating a Multi-Asset Framework)
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23 pages, 15939 KiB  
Article
Bubble Sliding Characteristics and Dynamics of R134a during Subcooled Boiling Flow in a Narrow Gap
by Bo Yu, Jinfeng Wang, Jing Xie, Bingjun Wang, Fei Wang and Meng Deng
Mathematics 2023, 11(9), 2197; https://doi.org/10.3390/math11092197 - 6 May 2023
Cited by 1 | Viewed by 1800
Abstract
The numerical method was used to study bubble sliding characteristics and dynamics of R134a during subcooled flow boiling in a narrow gap. In the numerical method, the volume of fraction (VOF) model, level set method, Lee phase change model and the SST k [...] Read more.
The numerical method was used to study bubble sliding characteristics and dynamics of R134a during subcooled flow boiling in a narrow gap. In the numerical method, the volume of fraction (VOF) model, level set method, Lee phase change model and the SST k − ω turbulent model were adopted for the construction of the subcooled flow boiling model. In order to explore bubble sliding dynamics during subcooled flow boiling, the bubble sliding model was introduced. The bubble velocity, bubble departure diameter, sliding distance and bubble sliding dynamics were investigated at 0.2 to 5 m/s inlet velocities. The simulation results showed that the bubble velocity at the flow direction was the most important contribution to bubble velocity. Additionally, the bubble velocity of 12 bubbles mostly oscillated with time during the sliding process at 0.2 to 0.6 m/s inlet velocities, while the bubble velocity increased during the sliding process due to the bubble having had a certain inertia at 2 to 5 m/s inlet velocities. It was also found that the average bubble velocity in flow direction accounted for about 80% of the mainstream velocities at 0.2 to 5 m/s. In the investigation of bubble sliding distance and departure diameter, it was concluded that the ratio of the maximum sliding distance to the minimum sliding distance was close to two at inlet velocities of 0.3 to 5 m/s. Moreover, with increasing inlet velocity, the average sliding distance increased significantly. The average bubble departure diameter obviously increased from 0.2 to 0.5 m/s inlet velocity and greatly reduced after 0.6 m/s. Finally, the investigations of the bubble sliding dynamics showed that the surface tension dominated the bubble sliding process at 0.2 to 0.6 m/s inlet velocities. However, the drag force dominated the bubble sliding process at 2 to 5 m/s inlet velocities. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)
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16 pages, 4185 KiB  
Article
Dynamic Event-Triggered Consensus Control for Markovian Switched Multi-Agent Systems: A Hybrid Neuroadaptive Method
by Xue Luo, Jingyi Wang, Jianwen Feng, Jiayi Cai and Yi Zhao
Mathematics 2023, 11(9), 2196; https://doi.org/10.3390/math11092196 - 6 May 2023
Cited by 2 | Viewed by 1564
Abstract
This paper presents a solution to the consensus problem for a particular category of uncertain switched multi-agent systems (MASs). In these systems, the communication topologies between agents and the system dynamics are governed by a time-homogeneous Markovian chain in a stochastic manner. To [...] Read more.
This paper presents a solution to the consensus problem for a particular category of uncertain switched multi-agent systems (MASs). In these systems, the communication topologies between agents and the system dynamics are governed by a time-homogeneous Markovian chain in a stochastic manner. To address this issue, we propose a novel neuroadaptive distributed dynamic event-triggered control (DETC) strategy. By leveraging stochastic Lyapunov theory and matrix inequality methodology, we establish sufficient conditions for practical ultimate mean square consensus (UMSBC) of MASs using a combination of neural networks (NNs) adaptive control strategy and DETC method. Our approach employs a distributed adaptive NNs DETC mechanism in MASs with unknown nonlinear dynamics and upgrades it at the moment of event sampling in an aperiodic manner, resulting in significant savings in computation and resources. We also exclude the Zeno phenomenon. Finally, we provide numerical examples to demonstrate the feasibility of our proposed approach, which outperforms existing approaches. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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1 pages, 157 KiB  
Correction
Correction: Ali et al. A Feature Selection Based on Improved Artificial Hummingbird Algorithm Using Random Opposition-Based Learning for Solving Waste Classification Problem. Mathematics 2022, 10, 2675
by Mona A. S. Ali, Fathimathul Rajeena P. P. and Diaa Salama Abd Elminaam
Mathematics 2023, 11(9), 2195; https://doi.org/10.3390/math11092195 - 6 May 2023
Viewed by 855
Abstract
Additional Affiliation(s) [...] Full article
24 pages, 10894 KiB  
Article
Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation
by Nicolae Herisanu, Bogdan Marinca, Livija Cveticanin and Vasile Marinca
Mathematics 2023, 11(9), 2194; https://doi.org/10.3390/math11092194 - 6 May 2023
Cited by 1 | Viewed by 1408
Abstract
In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a [...] Read more.
In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a constant current generating a static force and by an actuation generating a fast alternative force. The deformations between the solids in contact are supposed to be elastic and the contact is maintained. In this study, a single degree of freedom nonlinear damped oscillator under a static normal load is considered. An analytical approximate solution of this problem is obtained using the Optimal Auxiliary Functions Method (OAFM). By means of some auxiliary functions and introducing so-called convergence-control parameters, a very accurate approximate solution of the governing equation can be obtained. We need only the first iteration for this technique, applying a rigorous mathematical procedure in finding the optimal values of the convergence-control parameters. Local stability by means of the Routh-Hurwitz criteria and global stability using the Lyapunov function are also studied. It should be emphasized that the amplitude of AC excitation voltage is not considered much lower than bias voltage (in contrast to other studies). Also, the Hertzian contact coupled with EA is analytically studied for the first time in the present work. The approximate analytical solution is determined with a high accuracy on two domains. Local stability is established in five cases with some cases depending on the trace of the Jacobian matrix and of the discriminant of the characteristic equation. In the study of global stability, the estimate parameters which are components of the Lyapunov function are given in a closed form and a graphical form and therefore the Lyapunov function is well-determined. Full article
(This article belongs to the Special Issue Nonlinear Vibration Theory and Mechanical Dynamics)
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22 pages, 605 KiB  
Article
Finite-Time Adaptive Fuzzy Control for Unmodeled Dynamical Systems with Actuator Faults
by Ruixia Liu, Lei Xing, Hong Deng and Weichao Zhong
Mathematics 2023, 11(9), 2193; https://doi.org/10.3390/math11092193 - 6 May 2023
Cited by 3 | Viewed by 1277
Abstract
This article concentrates upon the issue of finite-time tracking control for a category of nonlinear systems in pure-feedback form with actuator faults and unmodeled dynamics, where the loss of effectiveness and bias fault are considered. Meanwhile, the function approximation method utilizing fuzzy logic [...] Read more.
This article concentrates upon the issue of finite-time tracking control for a category of nonlinear systems in pure-feedback form with actuator faults and unmodeled dynamics, where the loss of effectiveness and bias fault are considered. Meanwhile, the function approximation method utilizing fuzzy logic systems and dynamic surface control approach with first-order filter are implemented to model the unknown nonlinear terms induced from the proposed controller procedure and tackle the “explosion of complexity” issue of the classic backstepping method. The use of the maximal norm of the weight vector estimation method and adaptive approach reduces the computation load induced by fuzzy logic systems. Within the framework of backstepping control, a finite-time adaptive fuzzy fault-tolerant control protocol is derived to guarantee the boundedness of all signals and tracking error of the controlled system within a finite-time. Simulation studies are offered to show the validity of the derived theoretical results of the finite-time control protocol. Full article
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16 pages, 2624 KiB  
Article
The Classification of Application Users Supporting and Facilitating Travel Mobility Using Two-Step Cluster Analysis
by Jaroslav Mašek, Vladimíra Štefancová, Jaroslav Mazanec and Petra Juránková
Mathematics 2023, 11(9), 2192; https://doi.org/10.3390/math11092192 - 6 May 2023
Cited by 2 | Viewed by 1550
Abstract
There is a significant and supported trend toward the achievement of ensuring continuous door-to-door travel in the pan-European transport network. Many innovative programs are dedicated to this topic through assigned projects. This paper is based on the concrete partial results of the H2020 [...] Read more.
There is a significant and supported trend toward the achievement of ensuring continuous door-to-door travel in the pan-European transport network. Many innovative programs are dedicated to this topic through assigned projects. This paper is based on the concrete partial results of the H2020 project Shift2Rail IP4 to support the deployment of mobility as a service (IP4MaaS). Attitudes towards travel for demonstration sites were assessed based on the outputs of a sample of respondents from two countries. Cooperation in working on the IP4MaaS project was also provided by a partner from Slovakia (UNIZA) and the Czech Republic (OLTIS). Mathematical statistical tools were used to evaluate the available data to find a connection with promoting mobility as a service. This paper aims to identify differences in travelers’ needs with a focus on using applications using two-step cluster analysis. The research resulted in the identification of differences in traffic behavior within MaaS activities when comparing different clusters reflecting preferences for using a website or mobile application. Full article
(This article belongs to the Special Issue Big Data Mining and Analytics with Applications)
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19 pages, 2979 KiB  
Article
Optimal Strategy of the Dynamic Mean-Variance Problem for Pairs Trading under a Fast Mean-Reverting Stochastic Volatility Model
by Yaoyuan Zhang and Dewen Xiong
Mathematics 2023, 11(9), 2191; https://doi.org/10.3390/math11092191 - 6 May 2023
Cited by 1 | Viewed by 1610
Abstract
We discuss the dynamic mean-variance (MV) problem for pairs trading with the assumptions that one of the security prices satisfies a stochastic volatility model (SVM) and the corresponding price spread follows an Ornstein–Uhlenbeck (OU) process. We provide a semi-closed-form of the optimal strategy [...] Read more.
We discuss the dynamic mean-variance (MV) problem for pairs trading with the assumptions that one of the security prices satisfies a stochastic volatility model (SVM) and the corresponding price spread follows an Ornstein–Uhlenbeck (OU) process. We provide a semi-closed-form of the optimal strategy based on the solution of a PDE, which is difficult to solve explicitly. Thus, we assume that one of the security prices satisfies the Scott model, a fast-mean-reverting volatility model, and give a closed-form approximation for the optimal strategy. Empirical studies, by using historical data from Chinese security markets, show that the Scott model produces a more stable strategy by better capturing mean-reverting volatility. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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11 pages, 282 KiB  
Article
Generalized Bayes Estimation Based on a Joint Type-II Censored Sample from K-Exponential Populations
by Yahia Abdel-Aty, Mohamed Kayid and Ghadah Alomani
Mathematics 2023, 11(9), 2190; https://doi.org/10.3390/math11092190 - 6 May 2023
Cited by 5 | Viewed by 1229
Abstract
Generalized Bayes is a Bayesian study based on a learning rate parameter. This paper considers a generalized Bayes estimation to study the effect of the learning rate parameter on the estimation results based on a joint censored sample of type-II exponential populations. Squared [...] Read more.
Generalized Bayes is a Bayesian study based on a learning rate parameter. This paper considers a generalized Bayes estimation to study the effect of the learning rate parameter on the estimation results based on a joint censored sample of type-II exponential populations. Squared error, Linex, and general entropy loss functions are used in the Bayesian approach. Monte Carlo simulations were performed to assess how well the different approaches perform. The simulation study compares the Bayesian estimators for different values of the learning rate parameter and different losses. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Process Industries)
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