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Mathematics, Volume 11, Issue 14 (July-2 2023) – 223 articles

Cover Story (view full-size image): Theis’ theory, later improved by Hantush and Jacob and Moench, is a technique designed to study the water level in aquifers. The key formula in this theory is a certain integral transform H[g](r,t) of the pumping function g that depends on the time t and the relative position r to the pumping point, as well as on other physical parameters. In this paper, the analysis of possible analytic approximations of H[g](r,t) is completed by investigating asymptotic expansions of H[g](r,t) in a region of parameters of interest in practical situations. Explicit and/or recursive algorithms for the computation of the coefficients of the expansions and estimates for the remainders are provided. Some numerical examples illustrate the accuracy of the approximations. View this paper
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38 pages, 2427 KiB  
Article
Fuzzy Analytic Network Process with Principal Component Analysis to Establish a Bank Performance Model under the Assumption of Country Risk
Mathematics 2023, 11(14), 3257; https://doi.org/10.3390/math11143257 - 24 Jul 2023
Cited by 2 | Viewed by 1161
Abstract
In recent years, bank-related decision analysis has reflected a relevant research area due to key factors that affect the operating environment of banks. This study’s aim is to develop a model based on the linkages between the performance of banks and their operating [...] Read more.
In recent years, bank-related decision analysis has reflected a relevant research area due to key factors that affect the operating environment of banks. This study’s aim is to develop a model based on the linkages between the performance of banks and their operating context, determined by country risk. For this aim, we propose a multi-analytic methodology using fuzzy analytic network process (fuzzy-ANP) with principal component analysis (PCA) that extends existing mathematical methodologies and decision-making approaches. This method was examined in two studies. The first study focused on determining a model for country risk assessment based on the data extracted from 172 countries. Considering the first study’s scores, the second study established a bank performance model under the assumption of country risk, based on data from 496 banks. Our findings show the importance of country risk as a relevant bank performance dimension for decision makers in establishing efficient strategies with a positive impact on long-term performance. The study offers various contributions. From a mathematic methodology perspective, this research advances an original approach that integrates fuzzy-ANP with PCA, providing a consistent and unbiased framework that overcomes human judgement. From a business and economic analysis perspective, this research establishes novelty based on the performance evaluation of banks considering the operating country’s risk. Full article
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15 pages, 352 KiB  
Article
LPGRI: A Global Relevance-Based Link Prediction Approach for Multiplex Networks
Mathematics 2023, 11(14), 3256; https://doi.org/10.3390/math11143256 - 24 Jul 2023
Viewed by 694
Abstract
The individuals of real-world networks participate in various types of connections, each forming a layer in multiplex networks. Link prediction is an important problem in multiplex network analysis owing to its wide range of practical applications, such as mining drug targets, recommending friends [...] Read more.
The individuals of real-world networks participate in various types of connections, each forming a layer in multiplex networks. Link prediction is an important problem in multiplex network analysis owing to its wide range of practical applications, such as mining drug targets, recommending friends in social networks, and exploring network evolution mechanisms. A key issue of link prediction within multiplex networks is how to estimate the likelihood of potential links in the predicted layer by leveraging both interlayer and intralayer information. Several studies have shown that incorporating interlayer topological information can improve the performance of link prediction in the predicted layer. Therefore, this paper proposes the Link Prediction based on Global Relevance of Interlayer (LPGRI) method to estimate the likelihood of potential links in the predicted layer of multiplex networks, which comprehensively utilizes both types of information. In the LPGRI method, the contribution of interlayer information is determined using the global relevance (GR) index between layers. Experimental studies on six real multiplex networks demonstrate the competitive performance of our method. Full article
(This article belongs to the Section Network Science)
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14 pages, 3404 KiB  
Article
Dual Protection Routing Trees on Graphs
Mathematics 2023, 11(14), 3255; https://doi.org/10.3390/math11143255 - 24 Jul 2023
Viewed by 638
Abstract
In IP networks, packet forwarding is destination-based and hop-by-hop, and routes are built as needed. Kwong et al. introduced a protection routing in which packet delivery to the destination node can proceed uninterrupted in the event of any single node or link failure. [...] Read more.
In IP networks, packet forwarding is destination-based and hop-by-hop, and routes are built as needed. Kwong et al. introduced a protection routing in which packet delivery to the destination node can proceed uninterrupted in the event of any single node or link failure. He then showed that “whether there is a protection routing to the destination” is NP-complete. Tapolcai found that two completely independent spanning trees, abbreviated as CISTs, can be used to configure the protection routing. In this paper, we proposed dual protection routing trees, denoted as dual-PRTs to replace CISTs, which are less restrictive than CISTs. Next, we proposed a transformation algorithm that uses dual-PRTs to configure the protection routing. Taking complete graphs Kn, complete bipartite graphs Km,n, hypercubes Qn, and locally twisted cubes LTQn as examples, we provided a recursive method to construct dual-PRTs on them. This article showed that there are no two CISTs on K3,3, Q3, and LTQ3, but there exist dual-PRTs that can be used to configure the protection routing. As shown in the performance evaluation of simulation results, for both Qn and LTQn, we get the average path length of protection routing configured by dual-PRTs is shorter than that by two CISTs. Full article
(This article belongs to the Special Issue Advances of Computer Algorithms and Data Structures)
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25 pages, 1340 KiB  
Article
Dynamics of a Predator–Prey Model with Impulsive Diffusion and Transient/Nontransient Impulsive Harvesting
Mathematics 2023, 11(14), 3254; https://doi.org/10.3390/math11143254 - 24 Jul 2023
Viewed by 652
Abstract
Harvesting is one of the ways for humans to realize economic interests, while unrestricted harvesting will lead to the extinction of populations. This paper proposes a predator–prey model with impulsive diffusion and transient/nontransient impulsive harvesting. In this model, we consider both impulsive harvesting [...] Read more.
Harvesting is one of the ways for humans to realize economic interests, while unrestricted harvesting will lead to the extinction of populations. This paper proposes a predator–prey model with impulsive diffusion and transient/nontransient impulsive harvesting. In this model, we consider both impulsive harvesting and impulsive diffusion; additionally, predator and prey are harvested simultaneously. First, we obtain the subsystems of the system in prey extinction and predator extinction. We obtain the fixed points of the subsystems by the stroboscopic map theories of impulsive differential equations and analyze their stabilities. Further, we establish the globally asymptotically stable conditions for the prey/predator-extinction periodic solution and the trivial solution of the system, and then the sufficient conditions for the permanence of the system are given. We also perform several numerical simulations to substantiate our results. It is shown that the transient and nontransient impulsive harvesting have strong impacts on the persistence of the predator–prey model. Full article
(This article belongs to the Section Difference and Differential Equations)
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18 pages, 1381 KiB  
Article
Adaptive Tracking Control Schemes for Fuzzy Approximation-Based Noncanonical Nonlinear Systems with Hysteresis Inputs
Mathematics 2023, 11(14), 3253; https://doi.org/10.3390/math11143253 - 24 Jul 2023
Viewed by 561
Abstract
In this paper, the tracking control problem of a class of fuzzy approximation-based noncanonical nonlinear systems with hysteresis inputs is investigated, where the fuzzy weight matrix is not available for measurement, and the hysteresis nonlinearities are modeled by the Prandtl–Ishlinskii operator. Due to [...] Read more.
In this paper, the tracking control problem of a class of fuzzy approximation-based noncanonical nonlinear systems with hysteresis inputs is investigated, where the fuzzy weight matrix is not available for measurement, and the hysteresis nonlinearities are modeled by the Prandtl–Ishlinskii operator. Due to the coupling effects, the plant input containing hysteresis is unknown. To solve the problem, two adaptive control schemes are developed. The first is a Lyapunov-based scheme, and the second is a gradient-based scheme. For convenience, only the relative-degree-one case is taken into account in design and analysis. With the proposed schemes, it can be proved that all signals in the closed-loop system are bounded, and the tracking error converges to a small region around zero. Simulation results show that the maximum steady-state error converges to [0.0131,0.0183]μm and [0.0139,0.0161]μm with two control schemes, which confirms the obtained results. Full article
(This article belongs to the Section Dynamical Systems)
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21 pages, 1266 KiB  
Article
Dissipative Discrete PID Load Frequency Control for Restructured Wind Power Systems via Non-Fragile Design Approach
Mathematics 2023, 11(14), 3252; https://doi.org/10.3390/math11143252 - 24 Jul 2023
Viewed by 743
Abstract
This article proposes a discrete proportional-integral-derivative (PID) load frequency control (LFC) scheme to investigate the dissipative analysis issue of restructured wind power systems via a non-fragile design approach. Firstly, by taking the different power-sharing rates of governors into full consideration, a unified model [...] Read more.
This article proposes a discrete proportional-integral-derivative (PID) load frequency control (LFC) scheme to investigate the dissipative analysis issue of restructured wind power systems via a non-fragile design approach. Firstly, by taking the different power-sharing rates of governors into full consideration, a unified model is constructed for interconnected power systems containing multiple governors. Secondly, unlike existing LFC schemes, a non-fragile discrete PID control scheme is designed, which has the performance of tolerating control gain fluctuation and relieving the huge computational burden. Further, by constructing a discrete-type Lyapunov–Krasovskii functional, improved stability criteria with a strict dissipative performance index are established. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed control method. Full article
(This article belongs to the Section Dynamical Systems)
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25 pages, 2097 KiB  
Article
Breast Cancer Diagnosis Using a Novel Parallel Support Vector Machine with Harris Hawks Optimization
Mathematics 2023, 11(14), 3251; https://doi.org/10.3390/math11143251 - 24 Jul 2023
Cited by 1 | Viewed by 1347
Abstract
Three contributions are proposed. Firstly, a novel hybrid classifier (HHO-SVM) is introduced, which is a combination between the Harris hawks optimization (HHO) and a support vector machine (SVM) is introduced. Second, the performance of the HHO-SVM is enhanced using the conventional normalization method. [...] Read more.
Three contributions are proposed. Firstly, a novel hybrid classifier (HHO-SVM) is introduced, which is a combination between the Harris hawks optimization (HHO) and a support vector machine (SVM) is introduced. Second, the performance of the HHO-SVM is enhanced using the conventional normalization method. The final contribution is to improve the efficiency of the HHO-SVM by adopting a parallel approach that employs the data distribution. The proposed models are evaluated using the Wisconsin Diagnosis Breast Cancer (WDBC) dataset. The results show that the HHO-SVM achieves a 98.24% accuracy rate with the normalization scaling technique, outperforming other related works. On the other hand, the HHO-SVM achieves a 99.47% accuracy rate with the equilibration scaling technique, which is better than other previous works. Finally, to compare the three effective scaling strategies on four CPU cores, the parallel version of the proposed model provides an acceleration of 3.97. Full article
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15 pages, 855 KiB  
Article
Transient Dynamics in Counter-Rotating Stratified Taylor–Couette Flow
Mathematics 2023, 11(14), 3250; https://doi.org/10.3390/math11143250 - 24 Jul 2023
Viewed by 797
Abstract
This study focuses on the investigation of stratified Taylor–Couette flow (STCF) using non-modal analysis, which has received relatively limited attention compared to other shear flows. The dynamics of perturbations under different temperature conditions are explored, and their patterns of amplification are analyzed. The [...] Read more.
This study focuses on the investigation of stratified Taylor–Couette flow (STCF) using non-modal analysis, which has received relatively limited attention compared to other shear flows. The dynamics of perturbations under different temperature conditions are explored, and their patterns of amplification are analyzed. The study highlights the correlation between flow configurations, emphasizing the similarity in transient dynamics despite different speed ratios. The subcritical effects of thermal stratification on disturbance dynamics are examined, considering the interplay between viscous and buoyancy effects counteracted by strong centrifugal forces. It is found that increasing the wall temperature beyond a critical value leads to buoyancy forces dominating, resulting in a linear increase in the amplification factor. The research reveals significant deviations from previous results, indicating the significant role of temperature stratification. Full article
(This article belongs to the Section Probability and Statistics)
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21 pages, 308 KiB  
Article
Solving the Fredholm Integral Equation by Common Fixed Point Results in Bicomplex Valued Metric Spaces
Mathematics 2023, 11(14), 3249; https://doi.org/10.3390/math11143249 - 24 Jul 2023
Viewed by 667
Abstract
The purpose of this research work is to explore the solution of the Fredholm integral equation by common fixed point results in bicomplex valued metric spaces. In this way, we develop some common fixed point theorems for generalized contractions containing point-dependent control functions [...] Read more.
The purpose of this research work is to explore the solution of the Fredholm integral equation by common fixed point results in bicomplex valued metric spaces. In this way, we develop some common fixed point theorems for generalized contractions containing point-dependent control functions in the context of bicomplex valued metric spaces. An illustrative and practical example is also given to show the novelty of the most important result. Full article
20 pages, 481 KiB  
Article
Formulation for Multiple Cracks Problem in Thermoelectric-Bonded Materials Using Hypersingular Integral Equations
Mathematics 2023, 11(14), 3248; https://doi.org/10.3390/math11143248 - 24 Jul 2023
Cited by 1 | Viewed by 630
Abstract
New formulations are produced for problems associated with multiple cracks in the upper part of thermoelectric-bonded materials subjected to remote stress using hypersingular integral equations (HSIEs). The modified complex stress potential function method with the continuity conditions of the resultant electric force and [...] Read more.
New formulations are produced for problems associated with multiple cracks in the upper part of thermoelectric-bonded materials subjected to remote stress using hypersingular integral equations (HSIEs). The modified complex stress potential function method with the continuity conditions of the resultant electric force and displacement electric function, and temperature and resultant heat flux being continuous across the bonded materials’ interface, is used to develop these HSIEs. The unknown crack opening displacement function, electric current density, and energy flux load are mapped into the square root singularity function using the curved length coordinate method. The new HSIEs for multiple cracks in the upper part of thermoelectric-bonded materials can be obtained by applying the superposition principle. The appropriate quadrature formulas are then used to find stress intensity factors, with the traction along the crack as the right-hand term with the help of the curved length coordinate method. The general solutions of HSIEs for crack problems in thermoelectric-bonded materials are demonstrated with two substitutions and it is strictly confirmed with rigorous proof that: (i) the general solutions of HSIEs reduce to infinite materials if G1=G2, K1=K2, and E1=E2, and the values of the electric parts are α1=α2=0 and λ1=λ2=0; (ii) the general solutions of HSIEs reduce to half-plane materials if G2=0, and the values of α1=α2=0, λ1=λ2=0 and κ2=0. These substitutions also partially validate the general solution derived from this study. Full article
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22 pages, 11542 KiB  
Article
A Hybrid Medium and Long-Term Relative Humidity Point and Interval Prediction Method for Intensive Poultry Farming
Mathematics 2023, 11(14), 3247; https://doi.org/10.3390/math11143247 - 24 Jul 2023
Viewed by 855
Abstract
The accurate and reliable relative humidity (RH) prediction holds immense significance in effectively controlling the breeding cycle health and optimizing egg production performance in intensive poultry farming environments. However, current RH prediction research mainly focuses on short-term point predictions, which cannot meet the [...] Read more.
The accurate and reliable relative humidity (RH) prediction holds immense significance in effectively controlling the breeding cycle health and optimizing egg production performance in intensive poultry farming environments. However, current RH prediction research mainly focuses on short-term point predictions, which cannot meet the demand for accurate RH control in poultry houses in intensive farming. To compensate for this deficiency, a hybrid medium and long-term RH prediction model capable of precise point and interval prediction is proposed in this study. Firstly, the complexity of RH is reduced using a data denoising method that combines complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and permutation entropy. Secondly, important environmental factors are selected from feature correlation and change trends. Thirdly, based on the results of data denoising and feature selection, a BiGRU-Attention model incorporating an attention mechanism is established for medium and long-term RH point prediction. Finally, the Gaussian kernel density estimation (KDE-Gaussian) method is used to fit the point prediction error, and the RH prediction interval at different confidence levels is estimated. This method was applied to analyze the actual collection of waterfowl (Magang geese) environmental datasets from October 2022 to March 2023. The results indicate that the CEEMDAN-FS-BiGRU-Attention model proposed in this study has excellent medium and long-term point prediction performance. In comparison to LSTM, the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) are reduced by 57.7%, 48.2%, and 56.6%, respectively. Furthermore, at different confidence levels, the prediction interval formed by the KDE-Gaussian method is reliable and stable, which meets the need for accurate RH control in intensive farming environments. Full article
(This article belongs to the Special Issue Computational Methods and Application in Machine Learning)
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37 pages, 2239 KiB  
Review
A Review of Mathematical Models of Macroeconomics, Microeconomics, and Government Regulation of the Economy
Mathematics 2023, 11(14), 3246; https://doi.org/10.3390/math11143246 - 24 Jul 2023
Cited by 1 | Viewed by 2484
Abstract
This review analyzes articles on the mathematical modeling of economic facts and processes. Mathematical modeling of the economy has rapidly developed in the past and current centuries. This is explained by the fact that, firstly, economics does not tolerate full-scale experiments, secondly, mathematical [...] Read more.
This review analyzes articles on the mathematical modeling of economic facts and processes. Mathematical modeling of the economy has rapidly developed in the past and current centuries. This is explained by the fact that, firstly, economics does not tolerate full-scale experiments, secondly, mathematical modeling significantly improves the accuracy of research results, and, finally, thirdly, economics becomes a science only when it is based on mathematics. The article presents an overview of the main methods of economic modeling used in scientific research over the past twenty years. The review does not claim to cover all areas, methods, and models used in scientific research in the field of economics. This cannot be done in one article. Mathematical modeling of only three sections of economic theory is considered: macroeconomics, microeconomics, and state regulation of the economy. The review of research methods and models in the microeconomics section, which are available in the scientific research toolkit but have already been described in the macroeconomics section, has been omitted. Only effective, practice-tested models are used in the Review. We hope that this review will be useful to scientists involved in the indirect study of economic phenomena and processes. Full article
(This article belongs to the Section Dynamical Systems)
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21 pages, 7185 KiB  
Article
A Novel Light U-Net Model for Left Ventricle Segmentation Using MRI
Mathematics 2023, 11(14), 3245; https://doi.org/10.3390/math11143245 - 24 Jul 2023
Cited by 1 | Viewed by 947
Abstract
MRI segmentation and analysis are significant tasks in clinical cardiac computations. A cardiovascular MR scan with left ventricular segmentation seems necessary to diagnose and further treat the disease. The proposed method for left ventricle segmentation works as a combination of the intelligent histogram-based [...] Read more.
MRI segmentation and analysis are significant tasks in clinical cardiac computations. A cardiovascular MR scan with left ventricular segmentation seems necessary to diagnose and further treat the disease. The proposed method for left ventricle segmentation works as a combination of the intelligent histogram-based image enhancement technique with a Light U-Net model. This technique serves as the basis for choosing the low-contrast image subjected to the stretching technique and produces sharp object contours with good contrast settings for the segmentation process. After enhancement, the images are subjected to the encoder–decoder configuration of U-Net using a novel lightweight processing model. Encoder sampling is supported by a block of three parallel convolutional layers with supporting functions that improve the semantics for segmentation at various levels of resolutions and features. The proposed method finally increased segmentation efficiency, extracting the most relevant image resources from depth-to-depth convolutions, filtering them through each network block, and producing more precise resource maps. The dataset of MICCAI 2009 served as an assessment tool of the proposed methodology and provides a dice coefficient value of 97.7%, accuracy of 92%, and precision of 98.17%. Full article
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25 pages, 3685 KiB  
Article
Optimum Route and Transport Mode Selection of Multimodal Transport with Time Window under Uncertain Conditions
Mathematics 2023, 11(14), 3244; https://doi.org/10.3390/math11143244 - 24 Jul 2023
Viewed by 1409
Abstract
Aiming at the problem of multimodal transport path planning under uncertain environments, this paper establishes a multi-objective fuzzy nonlinear programming model considering mixed-time window constraints by taking cost, time, and carbon emission as optimization objectives. To solve the model, the model is de-fuzzified [...] Read more.
Aiming at the problem of multimodal transport path planning under uncertain environments, this paper establishes a multi-objective fuzzy nonlinear programming model considering mixed-time window constraints by taking cost, time, and carbon emission as optimization objectives. To solve the model, the model is de-fuzzified by the fuzzy expectation value method and fuzzy chance-constrained planning method. Combining the game theory method with the weighted sum method, a cooperative game theory-based multi-objective optimization method is proposed. Finally, the effectiveness of the algorithm is verified in a real intermodal network. The experimental results show that the proposed method can effectively improve the performance of the weighted sum method and obtain the optimal multimodal transport path that satisfies the time window requirement, and the path optimization results are better than MOPSO and NSGA-II, effectively reducing transportation costs and carbon emissions. Meanwhile, the influence of uncertainty factors on the multimodal transport route planning results is analyzed. The results show that the uncertain factors will significantly increase the transportation cost and carbon emissions and affect the choice of route and transportation mode. Considering uncertainty factors can increase the reliability of route planning results and provide a more robust and effective solution for multimodal transportation. Full article
(This article belongs to the Special Issue Game Theory and Artificial Intelligence)
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18 pages, 8052 KiB  
Article
Neural Rendering-Based 3D Scene Style Transfer Method via Semantic Understanding Using a Single Style Image
Mathematics 2023, 11(14), 3243; https://doi.org/10.3390/math11143243 - 24 Jul 2023
Viewed by 1427
Abstract
In the rapidly emerging era of untact (“contact-free”) technologies, the requirement for three-dimensional (3D) virtual environments utilized in virtual reality (VR)/augmented reality (AR) and the metaverse has seen significant growth, owing to their extensive application across various domains. Current research focuses on the [...] Read more.
In the rapidly emerging era of untact (“contact-free”) technologies, the requirement for three-dimensional (3D) virtual environments utilized in virtual reality (VR)/augmented reality (AR) and the metaverse has seen significant growth, owing to their extensive application across various domains. Current research focuses on the automatic transfer of the style of rendering images within a 3D virtual environment using artificial intelligence, which aims to minimize human intervention. However, the prevalent studies on rendering-based 3D environment-style transfers have certain inherent limitations. First, the training of a style transfer network dedicated to 3D virtual environments demands considerable style image data. These data must align with viewpoints that closely resemble those of the virtual environment. Second, there was noticeable inconsistency within the 3D structures. Predominant studies often neglect 3D scene geometry information instead of relying solely on 2D input image features. Finally, style adaptation fails to accommodate the unique characteristics inherent in each object. To address these issues, we propose a novel approach: a neural rendering-based 3D scene-style conversion technique. This methodology employs semantic nearest-neighbor feature matching, thereby facilitating the transfer of style within a 3D scene while considering the distinctive characteristics of each object, even when employing a single style image. The neural radiance field enables the network to comprehend the geometric information of a 3D scene in relation to its viewpoint. Subsequently, it transfers style features by employing the unique features of a single style image via semantic nearest-neighbor feature matching. In an empirical context, our proposed semantic 3D scene style transfer method was applied to 3D scene style transfers for both interior and exterior environments. This application utilizes the replica, 3DFront, and Tanks and Temples datasets for testing. The results illustrate that the proposed methodology surpasses existing style transfer techniques in terms of maintaining 3D viewpoint consistency, style uniformity, and semantic coherence. Full article
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19 pages, 951 KiB  
Article
Robust Reinforcement Learning-Based Multiple Inputs and Multiple Outputs Controller for Wind Turbines
Mathematics 2023, 11(14), 3242; https://doi.org/10.3390/math11143242 - 24 Jul 2023
Viewed by 669
Abstract
The control of variable-speed wind turbines that generate electricity from the kinetic energy of the wind involves subsystems that need to be controlled simultaneously, namely, the blade pitch angle controllers and the generator torque controllers. The presented study solves the control problem with [...] Read more.
The control of variable-speed wind turbines that generate electricity from the kinetic energy of the wind involves subsystems that need to be controlled simultaneously, namely, the blade pitch angle controllers and the generator torque controllers. The presented study solves the control problem with multiple inputs and multiple outputs (MIMO), using the method of reinforcement learning–based Trust Region Policy Optimization, through which the control parameters of both subsystems are simultaneously optimized. In this case, the robust control problem is transformed into a constrained optimal control problem with an appropriate choice of value functions for the nominal system. The study aims to synthesize a robust controller, with the aim of maximizing the generated energy (power) and minimizing unwanted forces (thrust). The innovative control architecture uses an extended input space, which allows fine-tuning of parameters for each operating state. Test calculations carried out in simulation experiments using models of the 5 MW NREL wind turbine and the 4 MW Enercon E-126 EP3 wind turbine are presented to illustrate the performance and practicality of the proposed approach. Full article
(This article belongs to the Special Issue Numerical Simulation and Control in Energy Systems, 2nd Edition)
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15 pages, 318 KiB  
Article
A Novel Inertial Viscosity Algorithm for Bilevel Optimization Problems Applied to Classification Problems
Mathematics 2023, 11(14), 3241; https://doi.org/10.3390/math11143241 - 24 Jul 2023
Cited by 1 | Viewed by 662
Abstract
Fixed-point theory plays many important roles in real-world problems, such as image processing, classification problem, etc. This paper introduces and analyzes a new, accelerated common-fixed-point algorithm using the viscosity approximation method and then employs it to solve convex bilevel optimization problems. The proposed [...] Read more.
Fixed-point theory plays many important roles in real-world problems, such as image processing, classification problem, etc. This paper introduces and analyzes a new, accelerated common-fixed-point algorithm using the viscosity approximation method and then employs it to solve convex bilevel optimization problems. The proposed method was applied to data classification with the Diabetes, Heart Disease UCI and Iris datasets. According to the data classification experiment results, the proposed algorithm outperformed the others in the literature. Full article
11 pages, 4951 KiB  
Article
Optimal Multi-Attribute Auctions Based on Multi-Scale Loss Network
Mathematics 2023, 11(14), 3240; https://doi.org/10.3390/math11143240 - 24 Jul 2023
Viewed by 720
Abstract
There is a strong demand for multi-attribute auctions in real-world scenarios for non-price attributes that allow participants to express their preferences and the item’s value. However, this also makes it difficult to perform calculations with incomplete information, as a single attribute—price—no longer determines [...] Read more.
There is a strong demand for multi-attribute auctions in real-world scenarios for non-price attributes that allow participants to express their preferences and the item’s value. However, this also makes it difficult to perform calculations with incomplete information, as a single attribute—price—no longer determines the revenue. At the same time, the mechanism must satisfy individual rationality (IR) and incentive compatibility (IC). This paper proposes an innovative dual network to solve these problems. A shared MLP module is constructed to extract bidder features, and multiple-scale loss is used to determine network status and update. The method was tested on real and extended cases, showing that the approach effectively improves the auctioneer’s revenue without compromising the bidder. Full article
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19 pages, 349 KiB  
Article
Multi-Key Homomorphic Encryption Scheme with Multi-Output Programmable Bootstrapping
Mathematics 2023, 11(14), 3239; https://doi.org/10.3390/math11143239 - 24 Jul 2023
Viewed by 1267
Abstract
Multi-key Homomorphic Encryption (MKHE) scheme can homomorphically evaluate ciphertexts encrypted by different keys, which can effectively protect the privacy information of data holders in the joint computing of cloud services. Since the first full Homomorphic encryption scheme was proposed, bootstrapping is the only [...] Read more.
Multi-key Homomorphic Encryption (MKHE) scheme can homomorphically evaluate ciphertexts encrypted by different keys, which can effectively protect the privacy information of data holders in the joint computing of cloud services. Since the first full Homomorphic encryption scheme was proposed, bootstrapping is the only way to realize the arbitrary depth homomorphic computation of MKHE schemes. But bootstrap operation is quite expensive. In order to implement fast bootstrapping in MKHE schemes, previous works proposed multi-key TFHE schemes to implement low-latency bootstrapping and output a univariate function of messages after bootstrapping, called Programmable Bootstrapping (PBS). However, these schemes can only encrypt single-bit messages. PBS only outputs a function. And after a homomorphic operation, a bootstrap is required, which undoubtedly results in an increase in the cost of the whole multi-key homomorphic encryption operation. In this paper, we propose a MKHE scheme for multi-output PBS. For this purpose, we study the encryption method and homomorphic operation steps of MKHE, and add BFV homomorphic encryption multiplication and multi-key ciphertext relinearization. We separate the homomorphic operation from bootstrapping. We homomorphically evaluate test polynomials for multiple functions. In contrast to previous MKHE schemes, we support the output of multiple message-related functions with a single bootstrapping operation on the ciphertext. It is no longer limited to encrypting single-bit plaintext, and an effective ciphertext packaging technology is added. According to the analysis given in this paper, it is known that in the scenario of multi-party joint computation, the proposed scheme can be implemented with less bootstrapping when the same number of functions are homomorphically operated. This will effectively reduce the computational overhead. Full article
(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography)
14 pages, 4948 KiB  
Article
Quality Analysis of Natural Gas Using the Structural Reliability of an Analytical Information System
Mathematics 2023, 11(14), 3238; https://doi.org/10.3390/math11143238 - 23 Jul 2023
Viewed by 588
Abstract
In this study, the authors first attempted to evaluate the efficiency of available systems for natural gas quality analysis using various examples. For this purpose, a model for such gas analysis systems was designed and the structural reliability of these systems were calculated. [...] Read more.
In this study, the authors first attempted to evaluate the efficiency of available systems for natural gas quality analysis using various examples. For this purpose, a model for such gas analysis systems was designed and the structural reliability of these systems were calculated. In the following, the main shortcomings of the existing methods for evaluating the reliability of gas analysis systems were discussed. Finally, a new probabilistic approach for the reliability assessment of such systems was proposed. This approach included a subsystem of measuring instruments that depended on the number of measured parameters. Specifically, it was suitable for measuring a single parameter of a gas mixture, but in order to check its effectiveness, a number of criteria were considered to identify and record system failures. For each criterion, various mathematical equations were constructed for reliability indices, including an operating time distribution function, reliability function, and average time to failure function. Finally, the obtained values and the reliability evaluation of gas analysis systems were discussed. Additionally, the main advantages of using the new method compared to the existing methods were enumerated. Furthermore, instead of assessing the standard structural reliability, a probabilistic assessment of reliability based on the accuracy of measurements was proposed. Full article
(This article belongs to the Section Engineering Mathematics)
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12 pages, 802 KiB  
Article
Pattern-Multiplicative Average of Nonnegative Matrices Revisited: Eigenvalue Approximation Is the Best of Versatile Optimization Tools
Mathematics 2023, 11(14), 3237; https://doi.org/10.3390/math11143237 - 23 Jul 2023
Viewed by 581
Abstract
Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern, too. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative (or geometric [...] Read more.
Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern, too. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative (or geometric) nature of averaging. The original concept of PMA was motivated by the practice of matrix population models as a tool to assess the population viability from long-term monitoring data. The task has reduced to searching for an approximate solution to an overdetermined system of polynomial equations for unknown elements of the average matrix (G), and hence to a nonlinear constrained minimization problem for the matrix norm. Former practical solutions faced certain technical problems, which required sophisticated algorithms but returned acceptable estimates. Now, we formulate (for the first time in ecological modeling and nonnegative matrix theory) the PMA problem as an eigenvalue approximation one and reduce it to a standard problem of linear programing (LP). The basic equation of averaging also determines the exact value of λ1(G), the dominant eigenvalue of matrix G, and the corresponding eigenvector. These are bound by the well-known linear equations, which enable an LP formulation of the former nonlinear problem. The LP approach is realized for 13 fixed-pattern matrices gained in a case study of Androsace albana, an alpine short-lived perennial, monitored on permanent plots over 14 years. A standard software routine reveals the unique exact solution, rather than an approximate one, to the PMA problem, which turns the LP approach into ‘’the best of versatile optimization tools”. The exact solution turns out to be peculiar in reaching zero bounds for certain nonnegative entries of G, which deserves modified problem formulation separating the lower bounds from zero. Full article
(This article belongs to the Section Mathematical Biology)
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10 pages, 308 KiB  
Article
Superconvergent Nyström Method Based on Spline Quasi-Interpolants for Nonlinear Urysohn Integral Equations
Mathematics 2023, 11(14), 3236; https://doi.org/10.3390/math11143236 - 23 Jul 2023
Cited by 1 | Viewed by 559
Abstract
Integral equations play an important role for their applications in practical engineering and applied science, and nonlinear Urysohn integral equations can be applied when solving many problems in physics, potential theory and electrostatics, engineering, and economics. The aim of this paper is the [...] Read more.
Integral equations play an important role for their applications in practical engineering and applied science, and nonlinear Urysohn integral equations can be applied when solving many problems in physics, potential theory and electrostatics, engineering, and economics. The aim of this paper is the use of spline quasi-interpolating operators in the space of splines of degree d and of class Cd1 on uniform partitions of a bounded interval for the numerical solution of Urysohn integral equations, by using a superconvergent Nyström method. Firstly, we generate the approximate solution and we obtain outcomes pertaining to the convergence orders. Additionally, we examine the iterative version of the method. In particular, we prove that the convergence order is (2d+2) if d is odd and (2d+3) if d is even. In case of even degrees, we show that the convergence order of the iterated solution increases to (2d+4). Finally, we conduct numerical tests that validate the theoretical findings. Full article
(This article belongs to the Special Issue Approximation Theory and Applications)
30 pages, 814 KiB  
Review
Review on Channel Estimation for Reconfigurable Intelligent Surface Assisted Wireless Communication System
Mathematics 2023, 11(14), 3235; https://doi.org/10.3390/math11143235 - 23 Jul 2023
Cited by 1 | Viewed by 1624
Abstract
With the dramatic increase in the number of mobile users and wireless devices accessing the network, the performance of fifth generation (5G) wireless communication systems has been severely challenged. Reconfigurable intelligent surface (RIS) has received much attention as one of the promising technologies [...] Read more.
With the dramatic increase in the number of mobile users and wireless devices accessing the network, the performance of fifth generation (5G) wireless communication systems has been severely challenged. Reconfigurable intelligent surface (RIS) has received much attention as one of the promising technologies for the sixth generation (6G) due to its ease of deployment, low power consumption, and low price. RIS is an electromagnetic metamaterial that serves to reconfigure the wireless environment by adjusting the phase, amplitude, and frequency of the wireless signal. To maximize channel transmission efficiency and improve the reliability of communication systems, the acquisition of channel state information (CSI) is essential. Therefore, an effective channel estimation method guarantees the achievement of excellent RIS performance. This survey presents a comprehensive study of existing channel estimation methods for RIS. Firstly, channel estimation methods in high and low frequency bands are overviewed and compared. We focus on channel estimation in the high frequency band and analyze the system model. Then, the comprehensive description of the different channel estimation methods is given, with a focus on the application of deep learning. Finally, we conclude the paper and provide an outlook on the future development of RIS channel estimation. Full article
(This article belongs to the Special Issue Mathematical Methods for Pattern Recognition)
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16 pages, 629 KiB  
Article
On Surprise Indices Related to Univariate Discrete and Continuous Distributions: A Survey
Mathematics 2023, 11(14), 3234; https://doi.org/10.3390/math11143234 - 23 Jul 2023
Viewed by 695
Abstract
The notion that the occurrence of an event is surprising has been discussed in the literature without adequate details. By definition, a surprise index is an index by which how surprising an event is may be determined. Since its inception, this index has [...] Read more.
The notion that the occurrence of an event is surprising has been discussed in the literature without adequate details. By definition, a surprise index is an index by which how surprising an event is may be determined. Since its inception, this index has been evaluated for univariate discrete probability models, such as the binomial, negative binomial, and Poisson probability distributions. In this article, we derive and discuss using numerical studies, in addition to the above-mentioned probability models, surprise indices for several other univariate discrete probability models, such as the zero-truncated Poisson, geometric, Hermite, and Skellam distributions, by adopting a established strategy and using the Mathematica, version 12 software. In addition, we provide symbolical expressions for the surprise index for several univariate continuous probability models, which has not been previously discussed. For illustrative purposes, we present some possible real-life applications of this index and potential challenges to extending the notion of the surprise index to bivariate and higher dimensions, which might involve ubiquitous normalizing constants. Full article
(This article belongs to the Special Issue Parametric and Nonparametric Statistics: From Theory to Applications)
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30 pages, 3131 KiB  
Article
The Delay Time Profile of Multistage Networks with Synchronization
Mathematics 2023, 11(14), 3232; https://doi.org/10.3390/math11143232 - 23 Jul 2023
Viewed by 527
Abstract
The interaction between projects and servers has grown significantly in complexity; thus, applying parallel calculations increases dramatically. However, it should not be ignored that parallel processing gives rise to synchronization constraints and delays, generating penalty costs that may overshadow the savings obtained from [...] Read more.
The interaction between projects and servers has grown significantly in complexity; thus, applying parallel calculations increases dramatically. However, it should not be ignored that parallel processing gives rise to synchronization constraints and delays, generating penalty costs that may overshadow the savings obtained from parallel processing. Motivated by this trade-off, this study investigates two special and symmetric systems of split–join structures: (i) parallel structure and (ii) serial structure. In a parallel structure, the project arrives, splits into m parallel groups (subprojects), each comprising n subsequent stages, and ends after all groups are completed. In the serial structure, the project requires synchronization after each stage. Employing a numerical study, we investigates the time profile of the project by focusing on two types of delays: delay due to synchronization overhead (occurring due to the parallel structure), and delay due to overloaded servers (occurring due to the serial structure). In particular, the author studies the effect of the number of stages, the number of groups, and the utilization of the servers on the time profile and performance of the system. Further, this study shows the efficiency of lower and upper bounds for the mean sojourn time. The results show that the added time grows logarithmically with m (parallelism) and linearly with n (seriality) in both structures. However, comparing the two types of split–join structures shows that the synchronization overhead grows logarithmically undr both parallelism and seriality; this yields an unexpected duality property of the added time to the serial system. Full article
(This article belongs to the Special Issue Operations Research and Its Applications)
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16 pages, 325 KiB  
Article
An Improved Dunnett’s Procedure for Comparing Multiple Treatments with a Control in the Presence of Missing Observations
Mathematics 2023, 11(14), 3233; https://doi.org/10.3390/math11143233 - 22 Jul 2023
Viewed by 1106
Abstract
Dunnett’s procedure has been frequently used for multiple comparisons of group means of several treatments with a control, in drug development and other areas. However, in practice, researchers usually face missing observations when performing Dunnett’s procedure. This paper presents an improved Dunnett’s procedure [...] Read more.
Dunnett’s procedure has been frequently used for multiple comparisons of group means of several treatments with a control, in drug development and other areas. However, in practice, researchers usually face missing observations when performing Dunnett’s procedure. This paper presents an improved Dunnett’s procedure that can construct unique ensemble confidence intervals for comparing group means of several treatments with a control, in the presence of missing observations, using a derived multivariate t distribution under the framework of Rubin’s rule. This procedure fills the current research gap that Rubin’s repeated-imputation inferences cannot adjust for multiplicity and, thereby, cannot give a unified confidence interval to control the family-wise error rate (FWER) when dealing with this problem. Simulation results show that the constructed pooled confidence intervals archive nominal joint coverage and the interval estimations preserve comparable precision to Rubin’s repeated-imputation inference as the missing rate increases. The proposed procedure with propensity-score imputation method is shown to produce more accurate interval estimations and control the FWER well. Full article
(This article belongs to the Special Issue Computational Statistics and Data Analysis, 2nd Edition)
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18 pages, 8473 KiB  
Article
Self-Evolving Chebyshev Radial Basis Function Neural Complementary Sliding Mode Control
Mathematics 2023, 11(14), 3231; https://doi.org/10.3390/math11143231 - 22 Jul 2023
Viewed by 598
Abstract
A novel intelligent complementary sliding mode control (ICSMC) method is proposed for nonlinear systems with unknown uncertainties in this paper. A self-evolving Chebyshev radial basis function neural network (RBFNN) (SECRBFNN) with self-learning parameters and structure is proposed and combined with complementary sliding mode [...] Read more.
A novel intelligent complementary sliding mode control (ICSMC) method is proposed for nonlinear systems with unknown uncertainties in this paper. A self-evolving Chebyshev radial basis function neural network (RBFNN) (SECRBFNN) with self-learning parameters and structure is proposed and combined with complementary sliding mode control (CSMC). CSMC not only has the advantages of the strong robustness of traditional SMC but also has certain advantages in reducing chattering and control accuracy. The SECRBFNN, which combines the advantages of the Chebyshev network (CN) and an RBFNN, is used to estimate unknown uncertainties in nonlinear systems. Meanwhile, a node self-evolution mechanism is proposed to avoid redundancy in the number of neurons. Eventually, the detailed simulation results demonstrate the feasibility and superiority of the proposed method. Full article
(This article belongs to the Special Issue Advanced Research in Fuzzy System and Neural Networks)
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19 pages, 375 KiB  
Article
On the Unique Solvability of Inverse Problems of Magnetometry and Gravimetry
Mathematics 2023, 11(14), 3230; https://doi.org/10.3390/math11143230 - 22 Jul 2023
Viewed by 502
Abstract
This article deals with the question of the unique solvability of systems of linear algebraic equations, to the solution of which many inverse problems of geophysics are reduced as a result of discretization when applying the methods of integral equations or integral representations. [...] Read more.
This article deals with the question of the unique solvability of systems of linear algebraic equations, to the solution of which many inverse problems of geophysics are reduced as a result of discretization when applying the methods of integral equations or integral representations. Examples are given of degenerate and nondegenerate systems of different dimensions that arise in the processing of magnetometric and gravimetric data from experimental observations. Conclusions are drawn about the methods for constructing the optimal grid of experimental observation points. Full article
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14 pages, 472 KiB  
Article
A Fast Algorithm for Updating Negative Concept Lattices with Increasing the Granularity Sizes of Attributes
Mathematics 2023, 11(14), 3229; https://doi.org/10.3390/math11143229 - 22 Jul 2023
Viewed by 510
Abstract
In this paper, firstly, we studied the relationship between negative concept lattices with increasing the granularity sizes of the attributes. Aiming to do this, negative concepts and covering relations were both classified into three types, and the sufficient and necessary conditions of distinguishing [...] Read more.
In this paper, firstly, we studied the relationship between negative concept lattices with increasing the granularity sizes of the attributes. Aiming to do this, negative concepts and covering relations were both classified into three types, and the sufficient and necessary conditions of distinguishing these kinds of negative concepts and covering relations are given, respectively. Further, based on the above analysis, an algorithm for updating negative concept lattices after the increase is proposed. Finally, the experimental results demonstrated that our algorithm performed significantly better than the direct construction algorithm. Full article
(This article belongs to the Special Issue Data Mining: Analysis and Applications)
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28 pages, 19499 KiB  
Article
Color Image Encryption Algorithm Based on Cross-Spiral Transformation and Zone Diffusion
Mathematics 2023, 11(14), 3228; https://doi.org/10.3390/math11143228 - 22 Jul 2023
Cited by 1 | Viewed by 1055
Abstract
Due to their rich information, color images are frequently utilized in many different industries, but the network’s security in handling their delivery of images must be taken into account. To improve the security and efficiency of color images, this paper proposed a color [...] Read more.
Due to their rich information, color images are frequently utilized in many different industries, but the network’s security in handling their delivery of images must be taken into account. To improve the security and efficiency of color images, this paper proposed a color image encryption algorithm based on cross-spiral transformation and zone diffusion. The proposed algorithm is based on Chen’s system and the piecewise linear chaotic map, and uses the chaotic sequences generated by them for related operations. Firstly, the R, G and B planes are extracted, and the spiral starting point of each plane is randomly selected by the chaotic sequence to implement the cross-spiral transformation. Secondly, the bit-level image matrix is constructed by the scrambled image matrix, and the bit-level chaotic matrix is constructed by the chaotic sequence. Finally, the three-dimensional matrix is divided into four zones by a dividing line, and partition diffusion is carried out to obtain the encrypted image. Simulation results and algorithm analyses indicate that the proposed algorithm has superior performance and can resist a wide range of attacks. Full article
(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography)
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