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Mathematics
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This is an Open Access Journal

Open Access journal
ISSN (Online) 2227-7390
Published by MDPI

[258 journals]

Mathematics, Vol. 12, Pages 2604: An Improved Spider-Wasp Optimizer for
Obstacle Avoidance Path Planning in Mobile Robots
- Authors: Yujie Gao, Zhichun Li, Haorui Wang, Yupeng Hu, Haoze Jiang, Xintong Jiang, Dong Chen
  First page: 2604
  Abstract: The widespread application of mobile robots holds significant importance for advancing social intelligence. However, as the complexity of the environment increases, existing Obstacle Avoidance Path Planning (OAPP) methods tend to fall into local optimal paths, compromising reliability and practicality. Therefore, based on the Spider-Wasp Optimizer (SWO), this paper proposes an improved OAPP method called the LMBSWO to address these challenges. Firstly, the learning strategy is introduced to enhance the diversity of the algorithm population, thereby improving its global optimization performance. Secondly, the dual-median-point guidance strategy is incorporated to enhance the algorithm’s exploitation capability and increase its path searchability. Lastly, a better guidance strategy is introduced to enhance the algorithm’s ability to escape local optimal paths. Subsequently, the LMBSWO is employed for OAPP in five different map environments. The experimental results show that the LMBSWO achieves an advantage in collision-free path length, with 100% probability, across five maps of different complexity, while obtaining 80% fault tolerance across different maps, compared to nine existing novel OAPP methods with efficient performance. The LMBSWO ranks first in the trade-off between planning time and path length. With these results, the LMBSWO can be considered as a robust OAPP method with efficient solving performance, along with high robustness.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172604
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2605: Majorization Problem for q-General
Family of Functions with Bounded Radius Rotations
- Authors: Kanwal Jabeen, Afis Saliu, Jianhua Gong, Saqib Hussain
  First page: 2605
  Abstract: In this paper, we first prove the q-version of Schwarz Pick’s lemma. This result improved the one presented earlier in the literature without proof. Using this novel result, we study the majorization problem for the q-general class of functions with bounded radius rotations, which we introduce here. In addition, the coefficient bound for majorized functions related to this class is derived. Relaxing the majorized condition on this general family, we obtain the estimate of coefficient bounds associated with the class. Consequently, we present new results as corollaries and point out relevant connections between the main results obtained from the ones in the literature.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172605
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2606: Enhanced Scattering by Wearable Objects
in Wireless Power Transfer Links: Case Studies
- Authors: Ludovica Tognolatti, Cristina Ponti, Giuseppe Schettini
  First page: 2606
  Abstract: Wireless power transfer (WPT) systems have ushered in a new era for wearable and implantable technologies, introducing opportunities for enhanced device functionality. A pivotal aspect in improving these devices is the optimization of electromagnetic transmission. This paper presents several solutions to improve electromagnetic transmission to an implantable/wearable device. Several scatterers are considered to mimic objects that can be easily worn by a patient, such as necklaces and bracelets, or easily integrated into textile fabric. An analytical method is employed to address the scattering by cylindrical objects above a biological tissue, modeled as a multilayer. Expansions into cylindrical waves, also represented through plane-wave spectra, are used to express the scattered fields in each medium. Numerical results for both the case of conducting and of dielectric cylindrical scatterers are presented at a frequency of the Industrial, Scientific and Medical band (f=2.45 GHz), showing possible configurations of worn objects for electromagnetic field intensification.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172606
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2607: EdgePose: An Edge Attention Network for
6D Pose Estimation
- Authors: Qi Feng, Jian Nong, Yanyan Liang
  First page: 2607
  Abstract: We propose a 6D pose estimation method that introduces an edge attention mechanism into the bidirectional feature fusion network. Our method constructs an end-to-end network model by sharing weights between the edge detection encoder and the encoder of the RGB branch in the feature fusion network, effectively utilizing edge information and improving the accuracy and robustness of 6D pose estimation. Experimental results show that this method achieves an accuracy of nearly 100% on the LineMOD dataset, and it also achieves state-of-the-art performance on the YCB-V dataset, especially on objects with significant edge information.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172607
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2608: Quasi-Periodic and Periodic Vibration
Responses of an Axially Moving Beam under Multiple-Frequency Excitation
- Authors: Xinru Fang, Lingdi Huang, Zhimei Lou, Yuanbin Wang
  First page: 2608
  Abstract: In this work, quasi-periodic and periodic vibration responses of an axially moving beam are analytically investigated under multiple-frequency excitation. The governing equation is transformed into a nonlinear differential equation by applying the Galerkin method. A double multiple-scales method is used to study the quasi-periodic and periodic vibrations of an axially moving beam with varying velocity and external excitation. Time traces and phase-plane portraits of quasi-periodic and periodic vibrations are obtained, which are in excellent agreement with those of the direct time integration method. The response frequencies of the axially moving beam are determined through the fast Fourier transform (FFT) method. The frequency–amplitude responses of the beam are analytically obtained and its stability is also determined. Lastly, the effects of system parameters on the quasi-periodic and periodic vibration are analyzed.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172608
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2609: Relations among the Queue-Length
Probabilities in the Pre-Arrival, Random, and Post-Departure Epochs in the
GI/Ma,b/c Queue
- Authors: Jing Gai, Mohan Chaudhry
  First page: 2609
  Abstract: In this paper, we present research results that extend and supplement our article recently published by MDPI. We derive the closed-form relations among the queue-length probabilities observed in the pre-arrival, random, and post-departure epochs for a complex, bulk-service, multi-server queueing system GI/Ma,b/c.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172609
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2610: Robust a Posteriori Error Estimates of
Time-Dependent Poisson–Nernst–Planck Equations
- Authors: Keli Fu, Tingting Hao
  First page: 2610
  Abstract: The paper considers the a posteriori error estimates for fully discrete approximations of time-dependent Poisson–Nernst–Planck (PNP) equations, which provide tools that allow for optimizing the choice of each time step when working with adaptive meshes. The equations are discretized by the Backward Euler scheme in time and conforming finite elements in space. Overcoming the coupling of time and the space with a full discrete solution and dealing with nonlinearity by taking G-derivatives of the nonlinear system, the computable, robust, effective, and reliable space–time a posteriori error estimation is obtained. The adaptive algorithm constructed based on the estimates realizes the parallel adaptations of time steps and mesh refinements, which are verified by numerical experiments with the time singular point and adaptive mesh refinement with boundary layer effects.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172610
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2611: Revisiting a Classic Identity That
Implies the Rogers–Ramanujan Identities III
- Authors: Hei-Chi Chan
  First page: 2611
  Abstract: This is the third installment in a series of papers on a one-parameter extension of the Rogers–Ramanujan identities (this extension was discovered independently by Rogers and Ramanujan). In this paper, we report a new proof of this identity. Our key ingredient is the Bridge Lemma, an identity that connects the both sides of the one-parameter refinement, which differ significantly in terms of their complexity.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172611
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2612: Integrating Sensor Embeddings with
Variant Transformer Graph Networks for Enhanced Anomaly Detection in
Multi-Source Data
- Authors: Fanjie Meng, Liwei Ma, Yixin Chen, Wangpeng He, Zhaoqiang Wang, Yu Wang
  First page: 2612
  Abstract: With the rapid development of sensor technology, the anomaly detection of multi-source time series data becomes more and more important. Traditional anomaly detection methods deal with the temporal and spatial information in the data independently, and fail to make full use of the potential of spatio-temporal information. To address this issue, this paper proposes a novel integration method that combines sensor embeddings and temporal representation networks, effectively exploiting spatio-temporal dynamics. In addition, the graph neural network is introduced to skillfully simulate the complexity of multi-source heterogeneous data. By applying a dual loss function—consisting of a reconstruction loss and a prediction loss—we further improve the accuracy of anomaly detection. This strategy not only promotes the ability to learn normal behavior patterns from historical data, but also significantly improves the predictive ability of the model, making anomaly detection more accurate. Experimental results on four multi-source sensor datasets show that our proposed method performs better than the existing models. In addition, our approach enhances the ability to interpret anomaly detection by analyzing the sensors associated with the detected anomalies.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172612
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2613: The Wiener Process with a Random
Non-Monotone Hazard Rate-Based Drift
- Authors: Luis Alberto Rodríguez-Picón, Luis Carlos Méndez-González, Luis Asunción Pérez-Domínguez, Héctor Eduardo Tovanche-Picón
  First page: 2613
  Abstract: Several variations of stochastic processes have been studied in the literature to obtain reliability estimations of products and systems from degradation data. As the degradation trajectories may have different degradation rates, it is necessary to consider alternatives to characterize their individual behavior. Some stochastic processes have a constant drift parameter, which defines the mean rate of the degradation process. However, for some cases, the mean rate must not be considered as constant, which means that the rate varies in the different stages of the degradation process. This poses an opportunity to study alternative strategies that allow to model this variation in the drift. For this, we consider the Hjorth rate, which is a failure rate that can define different shapes depending on the values of its parameters. In this paper, the integration of this hazard rate with the Wiener process is studied to individually identify the degradation rate of multiple degradation trajectories. Random effects are considered in the model to estimate a parameter of the Hjorth rate for every degradation trajectory, which allows us to identify the type of rate. The reliability functions of the proposed model is obtained through numerical integration as the function results in a complex form. The proposed model is illustrated in two case studies based on a crack propagation and infrared LED datasets. It is found that the proposed approach has better performance for the reliability estimation of products based on information criteria.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172613
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2614: Global Existence of Solutions to a Free
Boundary Problem for Viscous Incompressible Magnetohydrodynamics for Small
Data
- Authors: Piotr Kacprzyk, Wojciech M. Zaja̧czkowski
  First page: 2614
  Abstract: The motion of viscous incompressible magnetohydrodynamics (MHD) is considered in a domain that is bounded by a free surface. The motion interacts through the free surface with an electromagnetic field located in a domain exterior to the free surface and bounded by a given fixed surface. Some electromagnetic fields are prescribed on this fixed boundary. On the free surface, jumps in the magnetic and electric fields are assumed. The global existence of solutions to this problem assuming appropriate smallness conditions on the initial and boundary data is proved.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172614
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2615: The Multi-Objective Shortest Path
Problem with Multimodal Transportation for Emergency Logistics
- Authors: Jinzuo Guo, Hongbin Liu, Tianyu Liu, Guopeng Song, Bo Guo
  First page: 2615
  Abstract: The optimization of emergency logistical transportation is crucial for the timely dispatch of aid and support to affected areas. By incorporating practical constraints into emergency logistics, this study establishes a multi-objective shortest path mixed-integer programming model based on a multimodal transportation network. To solve multi-objective shortest path problems with multimodal transportation, we design an ideal point method and propose a procedure for constructing the complete Pareto frontier based on the k-shortest path multi-objective algorithm. We use modified Dijkstra and Floyd multimodal transportation shortest path algorithms to build a k-shortest path multi-objective algorithm. The effectiveness of the proposed multimodal transportation shortest path algorithm is verified using empirical experiments carried out on test sets of different scales and a comparison of the runtime using a commercial solver. The results show that the modified Dijkstra algorithm has a runtime that is 100 times faster on average than the modified Floyd algorithm, which highlights its greater applicability in large-scale multimodal transportation networks, demonstrating that the proposed method both has practical significance and can generate satisfactory solutions to the multi-objective shortest path problem with multimodal transportation in the context of emergency logistics.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172615
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2616: Results from a Nonlinear Wave Equation
with Acoustic and Fractional Boundary Conditions Coupling by Logarithmic
Source and Delay Terms: Global Existence and Asymptotic Behavior of
Solutions
- Authors: Abdelbaki Choucha, Salah Boulaaras, Ali Allahem, Asma Alharbi, Rashid Jan
  First page: 2616
  Abstract: The nonlinear wave equation with acoustic and fractional boundary conditions, coupled with logarithmic source and delay terms, is significant for its ability to model complex systems, its contribution to the advancement of mathematical theory, and its wide-ranging applicability to real-world problems. This paper examines the global existence and general decay of solutions to a wave equation characterized by coupling with logarithmic source and delay terms, and governed by both fractional and acoustic boundary conditions. The global existence of solutions is analyzed under a range of hypotheses, and the general decay behavior is established through the construction and application of an appropriate Lyapunov function.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172616
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2617: Review about the Permutation Approach in
Hypothesis Testing
- Authors: Stefano Bonnini, Getnet Melak Assegie, Kamila Trzcinska
  First page: 2617
  Abstract: Today, permutation tests represent a powerful and increasingly widespread tool of statistical inference for hypothesis-testing problems. To the best of our knowledge, a review of the application of permutation tests for complex data in practical data analysis for hypothesis testing is missing. In particular, it is essential to review the application of permutation tests in two-sample or multi-sample problems and in regression analysis. The aim of this paper is to consider the main scientific contributions on the subject of permutation methods for hypothesis testing in the mentioned fields. Notes on their use to address the problem of missing data and, in particular, right-censored data, will also be included. This review also tries to highlight the limits and advantages of the works cited with a critical eye and also to provide practical indications to researchers and practitioners who need to identify flexible and distribution-free solutions for the most disparate hypothesis-testing problems.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172617
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2618: Numerical Solution of the Cauchy Problem
for the Helmholtz Equation Using Nesterov’s Accelerated Method
- Authors: Syrym E. Kasenov, Aigerim M. Tleulesova, Ainur E. Sarsenbayeva, Almas N. Temirbekov
  First page: 2618
  Abstract: In this paper, the Cauchy problem for the Helmholtz equation, also known as the continuation problem, is considered. The continuation problem is reduced to a boundary inverse problem for a well-posed direct problem. A generalized solution to the direct problem is obtained and an estimate of its stability is given. The inverse problem is reduced to an optimization problem solved using the gradient method. The convergence of the Landweber method with respect to the functionals is compared with the convergence of the Nesterov method. The calculation of the gradient in discrete form, which is often used in the numerical solutions of the inverse problem, is described. The formulation of the conjugate problem in discrete form is presented. After calculating the gradient, an algorithm for solving the inverse problem using the Nesterov method is constructed. A computational experiment for the boundary inverse problem is carried out, and the results of the comparative analysis of the Landweber and Nesterov methods in a graphical form are presented.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172618
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2619: The Impact of Digital Economy on TFP of
Industries: Empirical Analysis Based on the Extension of Schumpeterian
Model to Complex Economic Systems
- Authors: Jiaqi Liu, Yiyang Cheng, Yamei Fu, Fei Xue
  First page: 2619
  Abstract: The digital economy (DE) is a new driver for enhancing total factor productivity (TFP). Using panel data from 30 provinces in China between 2011 and 2022, this study measures DE and TFP using the entropy-weighted TOPSIS method and the Global Malmquist–Luenberger method and further examines the impact of DE on the TFP of industries. The main findings are as follows: (1) DE can significantly improve TFP, though the extent of improvement varies. DE has the greatest impact on the TFP of the service industry, followed by the manufacturing industry, with the weakest effect on the agricultural industry. (2) The enhancement effect of DE on agriculture and the service industry is more pronounced in the central and western regions, while the improvement effect on manufacturing is more evident in the eastern region. (3) DE has facilitated the improvement of TFP in manufacturing industries such as textiles and special equipment manufacturing, as well as in service industries like wholesale and retail. However, it has not had a significant impact on the TFP of industries such as pharmaceutical manufacturing and real estate. This study has significant theoretical value and policy implications for China and other developing countries in exploring DE and achieving high-quality industrial development.
  Citation: Mathematics
  PubDate: 2024-08-23
  DOI: 10.3390/math12172619
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2620: Sorting Permutations on an n −
Broom
- Authors: Ranjith Rajesh, Rajan Sundaravaradhan, Bhadrachalam Chitturi
  First page: 2620
  Abstract: With applications in computer networks, robotics, genetics, data center network optimization, cryptocurrency exchange, transportation and logistics, cloud computing, and social network analysis, the problem of sorting permutations on transposition trees under various operations is highly relevant. The goal of the problem is to sort or rearrange the markers in a predetermined order by swapping them out at the vertices of a tree in the fewest possible swaps. Only certain classes of transposition trees, like path, star, and broom, have computationally efficient algorithms for sorting permutations. In this paper, we examine the so-called n−broom transposition trees. A single broom or simply a broom is a spanning tree formed by joining the center of the star graph with one end of the path graph. A generalized version of a broom known as an n−broom is created by joining the ends of n brooms to one vertex, known as the n−broom center. By using the idea of clear path markers, we present a novel algorithm for sorting permutations on an n−broom for n>2 that reduces to a novel 2−broom algorithm and that further reduces to two instances of a 1−broom algorithm. Our single-broom algorithm is similar to that of Kawahara et al.; however, our proof of optimality for the same is simpler.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172620
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2621: On General Alternating Tornheim-Type
Double Series
- Authors: Kwang-Wu Chen
  First page: 2621
  Abstract: In this paper, we express ∑n,m≥1ε1nε2mMn(u)Mm(v)nrms(n+m)t as a linear combination of alternating multiple zeta values, where εi∈{1,−1} and Mk(u)∈{Hk(u),H¯k(u)}, with Hk(u) and H¯k(u) being harmonic and alternating harmonic numbers, respectively. These sums include Subbarao and Sitaramachandrarao’s alternating analogues of Tornheim’s double series as a special case. Our method is based on employing two different techniques to evaluate the specific integral associated with a 3-poset Hasse diagram.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172621
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2622: Study on Ground Motion Amplification in
Upper Arch Bridge Due to “W”-Type Deep Canyon Using
Boundary-Integral and Peak Frequency Shift Methods
- Authors: Yi Liu, Chenhao Zhou, Sihong Huang
  First page: 2622
  Abstract: The study of the dynamic response characteristics of “W”-type deep canyon terrain to double-span concrete arch bridges under earthquake action holds great practical significance. In this research, a bridge in Sichuan Province is taken as the object of study. The boundary-integral equation method and peak frequency shift method are combined to apply an embedded linear time–history analysis algorithm to the finite element spatial dynamic calculation model of the entire bridge, resulting in an improved model. By comparing these two methods with model test results, the seismic response characteristics of the middle part of a “W” concrete arch bridge under different foundation depths and seismic intensities are examined. The boundary integral equation method was utilized to calculate ground motion response at any point on site, revealing a significant amplifying effect of increased seismic wave intensity on acceleration response at the top of the arch bridge. When input seismic wave intensity increased from 0.1 g to 0.3 g, maximum acceleration at buried depths of 3 m and 8 m in the middle of the arch bridge foundation increased by 102.63% and 79.16%, respectively, indicating that shallow buried depth structures are more sensitive to seismic wave intensity. Furthermore, using peak frequency shift rules for analyzing seismic wave propagation characteristics in “W”-type deep canyon topography confirms the sensitivity of shallow buried depth structures to seismic wave intensity and reveals the mechanism through which topography influences seismic wave propagation. This study provides a helpful method for understanding the propagation law and energy distribution characteristics of seismic waves in complex terrain. It was observed that the displacement at the top of the arch bridge increased significantly with an increase in seismic intensity. When subjected to 0.1 g, 0.2 g, and 0.3 g EI-Centro seismic waves, the maximum displacement at the top of the arch bridge model with a foundation buried depth of 3 m was 8 mm, 32 mm, and 142 mm, respectively. For arch bridge models with an 8-m foundation buried depth, these displacements were measured at 6.2 mm, 21 mm, and 68 mm, respectively. The results from model tests verified that increasing the depth of foundation burial effectively reduces the displacement at the top of the structure. Furthermore, by combining a boundary-integral equation method and peak-frequency shift method, this study accurately predicted significant influences on W-shaped double deep canyon topography from seismic response, and successfully captured stress concentration and seismic wave amplification/focusing effects on arch foot structures. The calculated results from both methods align well with model test data which confirm their effectiveness and complementarity when analyzing seismic responses under complex terrain conditions for bridge structures.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172622
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2623: A Non-Relativistic 2D Quantum System and
Its Thermo-Magnetic Properties with a Generalized Pseudo-Harmonic
Oscillator
- Authors: Haifa I. Alrebdi, Akpan N. Ikot, Ridha Horchani, Uduakobong S. Okorie
  First page: 2623
  Abstract: In this work, we examine the thermo-magnetic characteristics and energy spectra of a system exposed to both magnetic and Aharonov–Bohm (AB) fields with the existence of an interaction potential that is pseudo-harmonic. Explicit calculations of the eigen-solutions are performed with the expanded Nikiforov–Uvarov formalism. The confluent Heun function is used to represent the equivalent wave functions. If the AB and magnetic fields are gone, quasi-degeneracy in the system’s energy levels is shown by a numerical analysis of the energy spectrum. Additionally, we provided a visual representation of how the AB and magnetic fields affected the system’s thermo-magnetic characteristics. Our results show a strong dependence of thermo-magnetic properties on temperature, screening parameters, external magnetic fields, and AB fields.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172623
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2624: An Approximation of the Prime Counting
Function and a New Representation of the Riemann Zeta Function
- Authors: Timothy Ganesan
  First page: 2624
  Abstract: Determining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuable. These methods also offer avenues for number-theoretic exploration through analytical manipulation. In this work, we introduce a novel approximation function, ϕ(n), which adds to the existing repertoire of approximation methods and provides a fresh perspective for number-theoretic studies. Deeper analytical investigation of ϕ(n) reveals modified representations of the Chebyshev function, prime number theorem, and Riemann zeta function. Computational studies indicate that the difference between ϕ(n) and the logarithmic integral at magnitudes greater than 10100 is less than 1%.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172624
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2625: Quantum-Fuzzy Expert Timeframe Predictor
for Post-TAVR Monitoring
- Authors: Lilia Tightiz, Joon Yoo
  First page: 2625
  Abstract: This paper presents a novel approach to predicting specific monitoring timeframes for Permanent Pacemaker Implantation (PPMI) requirements following a Transcatheter Aortic Valve Replacement (TAVR). The method combines Quantum Ant Colony Optimization (QACO) with the Adaptive Neuro-Fuzzy Inference System (ANFIS) and incorporates expert knowledge. Although this forecast is more precise, it requires a larger number of predictors to achieve this level of accuracy. Our model deploys expert-derived insights to guarantee the clinical relevance and interpretability of the predicted outcomes. Additionally, we employ quantum computing techniques to address this complex and high-dimensional problem. Through extensive assessments, we show that our quantum-enhanced model outperforms traditional methods with notable improvement in evaluation metrics, such as accuracy, precision, recall, and F1 score. Furthermore, with the integration of eXplainable AI (XAI) methods, our solution enhances the transparency and reliability of medical predictive models, hence promoting improved clinical practice decision-making. The findings highlight how quantum computing has the potential to completely transform predictive analytics in the medical field, especially when it comes to improving patient care after TAVR.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172625
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2626: Operational Calculus for the 1st-Level
General Fractional Derivatives and Its Applications
- Authors: Maryam Alkandari, Yuri Luchko
  First page: 2626
  Abstract: The 1st-level General Fractional Derivatives (GFDs) combine in one definition the GFDs of the Riemann–Liouville type and the regularized GFDs (or the GFDs of the Caputo type) that have been recently introduced and actively studied in the fractional calculus literature. In this paper, we first construct an operational calculus of the Mikusiński type for the 1st-level GFDs. In particular, it includes the operational calculi for the GFDs of the Riemann–Liouville type and for the regularized GFDs as its particular cases. In the second part of the paper, this calculus is applied for the derivation of the closed-form solution formulas to the initial-value problems for the linear fractional differential equations with the 1st-level GFDs.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172626
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2627: Optimizing Electric Vehicle (EV)
Charging with Integrated Renewable Energy Sources: A Cloud-Based
Forecasting Approach for Eco-Sustainability
- Authors: Mohammad Aldossary, Hatem A. Alharbi, Nasir Ayub
  First page: 2627
  Abstract: As electric vehicles (EVs) are becoming more common and the need for sustainable energy practices is growing, better management of EV charging station loads is a necessity. The simple act of folding renewable power from solar or wind in an EV charging system presents a huge opportunity to make them even greener as well as improve grid resiliency. This paper proposes an innovative EV charging station energy consumption forecasting approach by incorporating integrated renewable energy data. The optimization is achieved through the application of SARLDNet, which enhances predictive accuracy and reduces forecast errors, thereby allowing for more efficient energy allocation and load management in EV charging stations. The technique leverages comprehensive solar and wind energy statistics alongside detailed EV charging station utilization data collected over 3.5 years from various locations across California. To ensure data integrity, missing data were meticulously addressed, and data quality was enhanced. The Boruta approach was employed for feature selection, identifying critical predictors, and improving the dataset through feature engineering to elucidate energy consumption trends. Empirical mode decomposition (EMD) signal decomposition extracts intrinsic mode functions, revealing temporal patterns and significantly boosting forecasting accuracy. This study introduces a novel stem-auxiliary-reduction-LSTM-dense network (SARLDNet) architecture tailored for robust regression analysis. This architecture combines regularization, dense output layers, LSTM-based temporal context learning, dimensionality reduction, and early feature extraction to mitigate overfitting. The performance of SARLDNet is benchmarked against established models including LSTM, XGBoost, and ARIMA, demonstrating superior accuracy with a mean absolute percentage error (MAPE) of 7.2%, Root Mean Square Error (RMSE) of 22.3 kWh, and R² Score of 0.87. This validation of SARLDNet’s potential for real-world applications, with its enhanced predictive accuracy and reduced error rates across various EV charging stations, is a reason for optimism in the field of renewable energy and EV infrastructure planning. This study also emphasizes the role of cloud infrastructure in enabling real-time forecasting and decision support. By facilitating scalable and efficient data processing, the insights generated support informed energy management and infrastructure planning decisions under dynamic conditions, empowering the audience to adopt sustainable energy practices.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172627
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2628: Hodge Decomposition of Conformal Vector
Fields on a Riemannian Manifold and Its Applications
- Authors: Hanan Alohali, Sharief Deshmukh, Bang-Yen Chen, Hemangi Madhusudan Shah
  First page: 2628
  Abstract: For a compact Riemannian m-manifold (Mm,g),m>1, endowed with a nontrivial conformal vector field ζ with a conformal factor σ, there is an associated skew-symmetric tensor φ called the associated tensor, and also, ζ admits the Hodge decomposition ζ=ζ¯+∇ρ, where ζ¯ satisfies divζ¯=0, which is called the Hodge vector, and ρ is the Hodge potential of ζ. The main purpose of this article is to initiate a study on the impact of the Hodge vector and its potential on Mm. The first result of this article states that a compact Riemannian m-manifold Mm is an m-sphere Sm(c) if and only if (1) for a nonzero constant c, the function −σ/c is a solution of the Poisson equation Δρ=mσ, and (2) the Ricci curvature satisfies Ricζ¯,ζ¯≥φ2. The second result states that if Mm has constant scalar curvature τ=m(m−1)c>0, then it is an Sm(c) if and only if the Ricci curvature satisfies Ricζ¯,ζ¯≥φ2 and the Hodge potential ρ satisfies a certain static perfect fluid equation. The third result provides another new characterization of Sm(c) using the affinity tensor of the Hodge vector ζ¯ of a conformal vector field ζ on a compact Riemannian manifold Mm with positive Ricci curvature. The last result states that a complete, connected Riemannian manifold Mm, m>2, is a Euclidean m-space if and only if it admits a nontrivial conformal vector field ζ whose affinity tensor vanishes identically and ζ annihilates its associated tensor φ.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172628
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2629: Identification of Time-Wise Thermal
Diffusivity, Advection Velocity on the Free-Boundary Inverse Coefficient
Problem
- Authors: M. S. Hussein, Taysir E. Dyhoum, S. O. Hussein, Mohammed Qassim
  First page: 2629
  Abstract: This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172629
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2630: Fuzzy Evaluation Model for Operational
Performance of Air Cleaning Equipment
- Authors: Kuen-Suan Chen, Tsun-Hung Huang, Chun-Min Yu, Hui-E Lee
  First page: 2630
  Abstract: Global warming has led to the continuous deterioration of the living environment, in which air quality directly affects human health. In addition, the severity of the COVID-19 pandemic has further increased the attention to indoor air quality. Indoor clean air quality is not only related to human health but also related to the quality of the manufacturing environment of clean rooms for numerous high-tech processes, such as semiconductors and packaging. This paper proposes a comprehensive model for evaluating, analyzing, and improving the operational performance of air cleaning equipment. Firstly, three operational performance evaluation indexes, such as the number of dust particles, the number of colonies, and microorganisms, were established. Secondly, the 100(1 – α)% upper confidence limits of these three operational performance evaluation indexes were deduced to construct a fuzzy testing model. Meanwhile, the accumulated value of ϕ was used to derive the evaluation decision-making value. The proposed model can help companies identify the key quality characteristics that need to be improved. Furthermore, the competitiveness of cooperative enterprises towards smart manufacturing can be strengthened, so that enterprises can not only fulfill their social responsibilities while developing the economy but also take into account the sustainable development of enterprises and the environment.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172630
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2631: On the Equivalence between Differential
and Integral Forms of Caputo-Type Fractional Problems on Hölder
Spaces
- Authors: Mieczysław Cichoń, Hussein A. H. Salem, Wafa Shammakh
  First page: 2631
  Abstract: As claimed in many papers, the equivalence between the Caputo-type fractional differential problem and the corresponding integral forms may fail outside the spaces of absolutely continuous functions, even in Hölder spaces. To avoid such an equivalence problem, we define a “new” appropriate fractional integral operator, which is the right inverse of the Caputo derivative on some Hölder spaces of critical orders less than 1. A series of illustrative examples and counter-examples substantiate the necessity of our research. As an application, we use our method to discuss the BVP for the Langevin fractional differential equation dψβ,μdtβdψα,μdtα+λx(t)=f(t,x(t)),t∈[a,b],λ∈R, for f∈C[a,b]×R and some critical orders β,α∈(0,1), combined with appropriate initial or boundary conditions, and with general classes of ψ-tempered Hilfer problems with ψ-tempered fractional derivatives. The BVP for fractional differential problems of the Bagley–Torvik type was also studied.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172631
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2632: Optimization Method of Mine Ventilation
Network Regulation Based on Mixed-Integer Nonlinear Programming
- Authors: Lixue Wen, Deyun Zhong, Lin Bi, Liguan Wang, Yulong Liu
  First page: 2632
  Abstract: Mine ventilation is crucial for ensuring safe production in mines, as it is integral to the entire underground mining process. This study addresses the issues of high energy consumption, regulation difficulties, and unreasonable regulation schemes in mine ventilation systems. To this end, we construct an optimization model for mine ventilation network regulation using mixed-integer nonlinear programming (MINLP), focusing on objectives such as minimizing energy consumption, optimal regulation locations and modes, and minimizing the number of regulators. We analyze the construction methods of the mathematical optimization model for both selected and unselected fans. To handle high-order terms in the MINLP model, we propose a variable discretization strategy that introduces 0-1 binary variables to discretize fan branches’ air quantity and frequency regulation ratios. This transformation converts high-order terms in the constraints of fan frequency regulation into quadratic terms, making the model suitable for solvers based on globally accurate algorithms. Example analysis demonstrate that the proposed method can find the optimal solution in all cases, confirming its effectiveness. Finally, we apply the optimization method of ventilation network regulation based on MINLP to a coal mine ventilation network. The results indicate that the power of the main fan after frequency regulation is 71.84 kW, achieving a significant energy savings rate of 65.60% compared to before optimization power levels. Notably, ventilation network can be regulated without adding new regulators, thereby reducing management and maintenance costs. This optimization method provides a solid foundation for the implementation of intelligent ventilation systems.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172632
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2633: Advances in Structural Health
Monitoring: Bio-Inspired Optimization Techniques and Vision-Based
Monitoring System for Damage Detection Using Natural Frequency
- Authors: Minkyu Jung, Jiyeon Koo, Andrew Jaeyong Choi
  First page: 2633
  Abstract: This paper introduces the improvements in natural-frequency-based SHM by applying bio-inspired optimization methods and a vision-based monitoring system for effective damage detection. This paper proposes a natural frequency extraction method using a motion magnification-based vision monitoring system with bio-inspired optimization techniques to estimate the damage location and depth in a cantilever beam. The proposed optimization techniques are inspired by natural processes and biological evolution including genetic algorithms, particle swarm optimization, sea lion optimization, and coral reefs optimization. To verify the performance of each bio-inspired optimization method, the eigenvalues of a two-bay truss structure are used for estimating the damaged elements. Then, using the proposed video motion magnification method, the natural frequency for each undamaged and damaged cantilever beam is extracted and compared with the LDV sensor to verify the proposed vision-based monitoring system. The performance of each bio-inspired optimizer in damage detection is compared. As a result, coral reefs optimization shows the lowest average error, around 1%, in damage detection using the natural frequency.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172633
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2634: A Semi-Supervised Active Learning Method
for Structured Data Enhancement with Small Samples
- Authors: Fangling Leng, Fan Li, Wei Lv, Yubin Bao, Xiaofeng Liu, Tiancheng Zhang, Ge Yu
  First page: 2634
  Abstract: In order to solve the problems of the small capacity of structured data and uneven distribution among classes in machine learning tasks, a supervised generation method for structured data called WAGAN and a cyclic sampling method named SACS (Semi-supervised and Active-learning Cyclic Sampling), based on semi-supervised active learning, are proposed. The loss function and neural network structure are optimized, and the quantity and quality of the small sample set are enhanced. To enhance the reliability of generating pseudo-labels, a Semi-supervised Active learning Framework (SAF) is designed. This framework redistributes class labels to samples, which not only enhances the reliability of generated samples but also reduces the influence of noise and uncertainty on the generation of false labels. To mine the diversity information of generated samples, an uncertain sampling strategy based on spatial overlap is designed. This strategy incorporates the idea of spatial overlap and uses global and local sampling methods to calculate the information content of generated samples. Experimental results show that the proposed method performs better than other data enhancement methods on three different datasets. Compared to the original data, the average F1macro value of the classification model is improved by 11.5%, 16.1%, and 19.6% relative to compared methods.
  Citation: Mathematics
  PubDate: 2024-08-24
  DOI: 10.3390/math12172634
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2635: Detection of Cyber-Attacks in a Discrete
Event System Based on Deep Learning
- Authors: Sichen Ding, Gaiyun Liu, Li Yin, Jianzhou Wang, Zhiwu Li
  First page: 2635
  Abstract: This paper addresses the problem of cyber-attack detection in a discrete event system by proposing a novel model. The model utilizes graph convolutional networks to extract spatial features from event sequences. Subsequently, it employs gated recurrent units to re-extract spatio-temporal features from these spatial features. The obtained spatio-temporal features are then fed into an attention model. This approach enables the model to learn the importance of different event sequences, ensuring that it is sufficiently general for identifying cyber-attacks, obviating the need to specify attack types. Compared with traditional methods that rely on synchronous product computations to synthesize diagnosers, our deep learning-based model circumvents state explosion problems. Our method facilitates real-time and efficient cyber-attack detection, eliminating the necessity to specifically identify system states or distinguish attack types, thereby significantly simplifying the diagnostic process. Additionally, we set an adjustable probability threshold to determine whether an event sequence has been compromised, allowing for customization to meet diverse requirements. Experimental results demonstrate that the proposed method performs well in cyber-attack detection, achieving over 99.9% accuracy at a 1% threshold and a weighted F1-score of 0.8126, validating its superior performance.
  Citation: Mathematics
  PubDate: 2024-08-25
  DOI: 10.3390/math12172635
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2636: Document-Level Event Argument Extraction
with Sparse Representation Attention
- Authors: Mengxi Zhang, Honghui Chen
  First page: 2636
  Abstract: Document-level Event Argument Extraction (DEAE) aims to extract structural event knowledge composed of arguments and roles beyond the sentence level. Existing methods mainly focus on designing prompts and using Abstract Meaning Representation (AMR) graph structure as additional features to enrich event argument representation. However, two challenges still remain: (1) the long-range dependency between event trigger and event arguments and (2) the distracting context in the document towards an event that can mislead the argument classification. To address these issues, we propose a novel document-level event argument extraction model named AMR Parser and Sparse Representation (APSR). Specifically, APSR sets inter- and intra-sentential encoders to capture the contextual information in different scopes. Especially, in the intra-sentential encoder, APSR designs three types of sparse event argument attention mechanisms to extract the long-range dependency. Then, APSR constructs AMR semantic graphs, which capture the interactions among concepts well. Finally, APSR fuses the inter- and intra-sentential representations and predicts what role a candidate span plays. Experimental results on the RAMS and WikiEvents datasets demonstrate that APSR achieves a superior performance compared with competitive baselines in terms of F1 by 1.27% and 3.12%, respectively.
  Citation: Mathematics
  PubDate: 2024-08-25
  DOI: 10.3390/math12172636
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2637: Evaluation and Optimal Design of a
Balanced Diet
- Authors: Zijian Chen, Manyang Cai, Yongshi Cao, Kemeng Zhang, Linchao Hu, Hongpeng Guo
  First page: 2637
  Abstract: Malnutrition has led to growth retardation in many adolescents and health deterioration in adults all over the world. Recently, there has been increasing attention on balanced diets as a preventive measure. This study evaluates the daily diet of a student, aiming to optimize the amino acid score (AAS) across three meals per day. By using balanced diet criteria as constraints, we established a single-objective nonlinear programming model, maximizing AAS as the objective function. The model was solved by using a simulated annealing algorithm, and we obtained a diet that is both balanced and high in AAS. This study helps to raise awareness about individual nutritional needs and provides guidance for dietary structure improvements, thereby contributing to global public health enhancement.
  Citation: Mathematics
  PubDate: 2024-08-25
  DOI: 10.3390/math12172637
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2638: The Proximal Gradient Method for
Composite Optimization Problems on Riemannian Manifolds
- Authors: Xiaobo Li
  First page: 2638
  Abstract: In this paper, the composite optimization problem is studied on Riemannian manifolds. To tackle this problem, the proximal gradient method to solve composite optimization problems is proposed on Riemannian manifolds. Under some reasonable conditions, the convergence of the proximal gradient method with the backtracking procedure in the nonconvex case is presented. Furthermore, a sublinear convergence rate and the complexity result of the proximal gradient method for convex case are also established on Riemannian manifolds.
  Citation: Mathematics
  PubDate: 2024-08-25
  DOI: 10.3390/math12172638
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2639: Sharma–Taneja–Mittal Entropy
and Its Application of Obesity in Saudi Arabia
- Authors: Hanan H. Sakr, Mohamed Said Mohamed
  First page: 2639
  Abstract: This paper presents several nonparametric estimators for the Sharma–Taneja–Mittal entropy measure of a continuous random variable with known support, utilizing spacing, a local linear model, and a kernel function. The properties of these estimators are discussed. Their performance was also examined through real data analysis and Monte Carlo simulations. In the Monte Carlo experiments, the proposed Sharma–Taneja–Mittal entropy estimators were employed to create a test of goodness-of-fit under the standard uniform distribution. The suggested test statistics demonstrate strong performance, as evidenced by a comparison of their power with that of other tests for uniformity. Finally, we examine a classification issue in the recognition of patterns to underscore the significance of these measures.
  Citation: Mathematics
  PubDate: 2024-08-25
  DOI: 10.3390/math12172639
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2640: CL-NOTEARS: Continuous Optimization
Algorithm Based on Curriculum Learning Framework
- Authors: Kaiyue Liu, Lihua Liu, Kaiming Xiao, Xuan Li, Hang Zhang, Yun Zhou, Hongbin Huang
  First page: 2640
  Abstract: Causal structure learning plays a crucial role in the current field of artificial intelligence, yet existing causal structure learning methods are susceptible to interference from data sample noise and often become trapped in local optima. To address these challenges, this paper introduces a continuous optimization algorithm based on the curriculum learning framework: CL-NOTEARS. The model utilizes the curriculum loss function during training as a priority evaluation metric for curriculum selection and formulates the sample learning sequence of the model through task-level curricula, thereby enhancing the model’s learning performance. A curriculum-based sample prioritization strategy is employed that dynamically adjusts the training sequence based on variations in loss function values across different samples throughout the training process. The results demonstrate a significant reduction in the impact of sample noise in the data, leading to improved model training performance.
  Citation: Mathematics
  PubDate: 2024-08-25
  DOI: 10.3390/math12172640
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2641: Hierarchical Learning-Enhanced Chaotic
Crayfish Optimization Algorithm: Improving Extreme Learning Machine
Diagnostics in Breast Cancer
- Authors: Jilong Zhang, Yuan Diao
  First page: 2641
  Abstract: Extreme learning machines (ELMs), single hidden-layer feedforward neural networks, are renowned for their speed and efficiency in classification and regression tasks. However, their generalization ability is often undermined by the random generation of hidden layer weights and biases. To address this issue, this paper introduces a Hierarchical Learning-based Chaotic Crayfish Optimization Algorithm (HLCCOA) aimed at enhancing the generalization ability of ELMs. Initially, to resolve the problems of slow search speed and premature convergence typical of traditional crayfish optimization algorithms (COAs), the HLCCOA utilizes chaotic sequences for population position initialization. The ergodicity of chaos is leveraged to boost population diversity, laying the groundwork for effective global search efforts. Additionally, a hierarchical learning mechanism encourages under-performing individuals to engage in extensive cross-layer learning for enhanced global exploration, while top performers directly learn from elite individuals at the highest layer to improve their local exploitation abilities. Rigorous testing with CEC2019 and CEC2022 suites shows the HLCCOA’s superiority over both the original COA and nine renowned heuristic algorithms. Ultimately, the HLCCOA-optimized extreme learning machine model, the HLCCOA-ELM, exhibits superior performance over reported benchmark models in terms of accuracy, sensitivity, and specificity for UCI breast cancer diagnosis, underscoring the HLCCOA’s practicality and robustness, as well as the HLCCOA-ELM’s commendable generalization performance.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172641
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2642: Analytically Pricing a Vulnerable Option
under a Stochastic Liquidity Risk Model with Stochastic Volatility
- Authors: Junkee Jeon, Geonwoo Kim
  First page: 2642
  Abstract: This paper considers the valuation of a vulnerable option when underlying stock is subject to liquidity risks. That is, it is assumed that the underlying stock is not perfectly liquid. We establish a framework where the stock price follows the stochastic volatility model and the option contains the default risk of the option issuer. In addition, we assume that liquidity risks are caused by stochastic market liquidity, and the default occurs at the first jump time of a stochastic Poisson process, which has a stochastic default intensity process consisting of both idiosyncratic and systematic components. By employing a change of measure, we derive an analytical formula for the value of a vulnerable option. Finally, we present several numerical examples to illustrate the sensitivity of significant parameters.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172642
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2643: Dynamic Byzantine Fault-Tolerant
Consensus Algorithm with Supervised Feedback Mechanisms
- Authors: Anqi Li, Yingbiao Yao, Xin Xu
  First page: 2643
  Abstract: Among the existing consensus algorithms, there are very few low-latency consensus algorithms that can simultaneously take into account node dynamics, fault tolerance, and scalability, and which are applicable to large-scale open scenarios where low latency is required. Therefore, this paper proposes a low-latency scalable dynamic consensus algorithm with high fault tolerance utilizing a combination of layered and threshold signature technologies, known briefly as LTSBFT. Firstly, LTSBFT achieves linear communication complexity through the utilization of threshold signature technology and a two-layer structure. Secondly, the mutual supervision feedback mechanism among nodes enables the attainment of linear complexity for reaching consensus on the faulty upper-layer nodes during the view-change. Lastly, a node dynamic protocol was proposed for the first time to support dynamic changes in the number of nodes during the consensus process. That is to say, consensus can still be reached when the number of nodes dynamically changes without interrupting the client’s request for consensus in the network. The experimental results indicate that LTSBFT exhibits lower communication latency and higher throughput compared to the classic HotStuff and PBFT algorithms. Furthermore, in comparison to double-layer PBFT, the LTSBFT has been demonstrated to have improved fault tolerance.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172643
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2644: Generalized Federated Learning via
Gradient Norm-Aware Minimization and Control Variables
- Authors: Yicheng Xu, Wubin Ma, Chaofan Dai, Yahui Wu, Haohao Zhou
  First page: 2644
  Abstract: Federated Learning (FL) is a promising distributed machine learning framework that emphasizes privacy protection. However, inconsistencies between local optimization objectives and the global objective, commonly referred to as client drift, primarily arise due to non-independently and identically distributed (Non-IID) data, multiple local training steps, and partial client participation in training. The majority of current research tackling this challenge is mainly based on the empirical risk minimization (ERM) principle, while giving little consideration to the connection between the global loss landscape and generalization capability. This study proposes FedGAM, an innovative FL algorithm that incorporates Gradient Norm-Aware Minimization (GAM) to efficiently search for a local flat landscape. FedGAM specifically modifies the client model training objective to simultaneously minimize the loss value and first-order flatness, thereby seeking flat minima. To directly smooth the global flatness, we propose the more significant FedGAM-CV, which employs control variables to correct local updates, guiding each client to train models in a globally flat direction. Experiments on three datasets (CIFAR-10, MNIST, and FashionMNIST) demonstrate that our proposed algorithms outperform existing FL baselines, effectively finding flat minima and addressing the client drift problem.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172644
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2645: Hole Appearance Constraint Method in 2D
Structural Topology Optimization
- Authors: Lei Zhu, Tongxing Zuo, Chong Wang, Qianglong Wang, Zhengdong Yu, Zhenyu Liu
  First page: 2645
  Abstract: A 2D topology optimization algorithm is proposed, which integrates the control of hole shape, hole number, and the minimum scale between holes through the utilization of an appearance target image. The distance between the structure and the appearance target image is defined as the hole appearance constraint. The appearance constraint is organized as inequality constraints to control the performance of the structure in an iterative optimization. Specifically, hole shapes are controlled by matching adaptable equivalent shape templates, the minimum scales between holes are controlled by a hole shrinkage strategy, and the hole number is controlled by a hole number calculation and filling method. Based on the SIMP interpolation topology optimization model, the effectiveness of the proposed method is verified through numerical examples.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172645
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2646: Bounds of Eigenvalues for Complex
q-Sturm–Liouville Problem
- Authors: Xiaoxue Han
  First page: 2646
  Abstract: The eigenvalues of complex q-Sturm–Liouville boundary value problems are the focus of this paper. The coefficients of the corresponding q-Sturm–Liouville equation provide the lower bounds on the real parts of all eigenvalues, and the real part of the eigenvalue and the coefficients of this q-Sturm–Liouville equation provide the bounds on the imaginary part of each eigenvalue.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172646
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2647: Knowledge Distillation for Enhanced Age
and Gender Prediction Accuracy
- Authors: Seunghyun Kim, Yeongje Park, Eui Chul Lee
  First page: 2647
  Abstract: In recent years, the ability to accurately predict age and gender from facial images has gained significant traction across various fields such as personalized marketing, human–computer interaction, and security surveillance. However, the high computational cost of the current models limits their practicality for real-time applications on resource-constrained devices. This study addressed this challenge by leveraging knowledge distillation to develop lightweight age and gender prediction models that maintain a high accuracy. We propose a knowledge distillation method using teacher bounds for the efficient learning of small models for age and gender. This method allows the student model to selectively receive the teacher model’s knowledge, preventing it from unconditionally learning from the teacher in challenging age/gender prediction tasks involving factors like illusions and makeup. Our experiments used MobileNetV3 and EfficientFormer as the student models and Vision Outlooker (VOLO)-D1 as the teacher model, resulting in substantial efficiency improvements. MobileNetV3-Small, one of the student models we experimented with, achieved a 94.27% reduction in parameters and a 99.17% reduction in Giga Floating Point Operations per Second (GFLOPs). Furthermore, the distilled MobileNetV3-Small model improved gender prediction accuracy from 88.11% to 90.78%. Our findings confirm that knowledge distillation can effectively enhance model performance across diverse demographic groups while ensuring efficiency for deployment on embedded devices. This research advances the development of practical, high-performance AI applications in resource-limited environments.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172647
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2648: Modeling the Transmission Dynamics and
Optimal Control Strategy for Huanglongbing
- Authors: Yujiang Liu, Shujing Gao, Di Chen, Bing Liu
  First page: 2648
  Abstract: Huanglongbing (HLB), also known as citrus greening disease, represents a severe and imminent threat to the global citrus industry. With no complete cure currently available, effective control strategies are crucial. This article presents a transmission model of HLB, both with and without nutrient injection, to explore methods for controlling disease spread. By calculating the basic reproduction number (R0) and analyzing threshold dynamics, we demonstrate that the system remains globally stable when R0<1, but persists when R0>1. Sensitivity analyses reveal factors that significantly impact HLB spread on both global and local scales. We also propose a comprehensive optimal control model using the pontryagin minimum principle and validate its feasibility through numerical simulations. Results show that while removing infected trees and spraying insecticides can significantly reduce disease spread, a combination of measures, including the production of disease-free budwood and nursery trees, nutrient solution injection, removal of infected trees, and insecticide application, provides superior control and meets the desired control targets. These findings offer valuable insights for policymakers in understanding and managing HLB outbreaks.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172648
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2649: Cross-Validated Functional Generalized
Partially Linear Single-Functional Index Model
- Authors: Mustapha Rachdi, Mohamed Alahiane, Idir Ouassou, Abdelaziz Alahiane, Lahoucine Hobbad
  First page: 2649
  Abstract: In this paper, we have introduced a functional approach for approximating nonparametric functions and coefficients in the presence of multivariate and functional predictors. By utilizing the Fisher scoring algorithm and the cross-validation technique, we derived the necessary components that allow us to explain scalar responses, including the functional index, the nonlinear regression operator, the single-index component, and the systematic component. This approach effectively addresses the curse of dimensionality and can be applied to the analysis of multivariate and functional random variables in a separable Hilbert space. We employed an iterative Fisher scoring procedure with normalized B-splines to estimate the parameters, and both the theoretical and practical evaluations demonstrated its favorable performance. The results indicate that the nonparametric functions, the coefficients, and the regression operators can be estimated accurately, and our method exhibits strong predictive capabilities when applied to real or simulated data.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172649
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2650: Staged Resource Allocation Optimization
under Heterogeneous Grouping Based on Interval Data: The Case of
China’s Forest Carbon Sequestration
- Authors: Nan Wu, Mengjiao Zhang, Yan Huang, Jiawei Wang
  First page: 2650
  Abstract: In interval data envelopment analysis (DEA), the production possibility set is variable, which causes traditional resource allocation optimization methods to yield results with limited reachability. This study aims to improve existing resource allocation optimization models so that they can produce meaningful results when handling interval data. Addressing this topic can enhance the applicability of existing models and improve decision-making accuracy. We grouped decision-making units (DMUs) based on heterogeneity to form production possibility sets. We then considered the characteristics of the worst and best production possibility sets in the interval DEA to establish multiple benchmark fronts. A staged optimization procedure is proposed; the procedure provides a continuous optimization solution, offering a basis for decision-makers to formulate strategies. To illustrate this, we provide a numerical example analysis and a case study on forest carbon sequestration. Finally, by applying our method to China’s forest carbon sink data, we show that it better meets the practical needs in China. The practical implication of this procedure is that it provides a basis for decision makers to formulate strategies based on interval data. The theoretical implication is that it extends the application of DEA models to interval data.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172650
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2651: ChronoVectors: Mapping Moments through
Enhanced Temporal Representation
- Authors: Qilei Zhang, John H. Mott
  First page: 2651
  Abstract: Time-series data are prevalent across various fields and present unique challenges for deep learning models due to irregular time intervals and missing records, which hinder the ability to capture temporal information effectively. This study proposes ChronoVectors, a novel temporal representation method that addresses these challenges by enabling a more specialized encoding of temporal relationships through the use of learnable parameters tailored to the dataset’s dynamics while maintaining consistent time intervals post-scaling. The theoretical demonstration shows that ChronoVectors allow the transformed encoding tensors to map moments in time to continuous spaces, accommodating potentially infinite extensions of the sequence and preserving temporal consistency. Experimental validation using the Parking Birmingham and Metro Interstate Traffic Volume datasets reveals that ChronoVectors enhanced the predictive capabilities of deep learning models by reducing prediction error for regression tasks compared to conventional time representations, such as vanilla timestamp encoding and Time2Vec. These findings underscore the potential of ChronoVectors in handling irregular time-series data and showcase its ability to improve deep learning model performance in understanding temporal dynamics.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172651
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2652: T2-LSTM-Based AI System for Early
Detection of Motor Failure in Chemical Plants
- Authors: Chien-Chih Wang
  First page: 2652
  Abstract: In the chemical industry, stable reactor operation is essential for consistent production. Motor failures can disrupt operations, resulting in economic losses and safety risks. Traditional monitoring methods, based on human experience and simple current monitoring, often need to be faster and more accurate. The rapid development of artificial intelligence provides powerful tools for early fault detection and maintenance. In this study, the Hotelling T2 index is used to calculate the root mean square values of the normal motor’s x, y, and z axes. A long short-term memory (LSTM) model creates a trend model for the Hotelling T2 index, determining an early warning threshold. Current anomaly detection follows the ISO 10816-1 standard, while future anomaly prediction uses the T2-LSTM trend model. Validated at a chemical plant in Southern Taiwan, the method shows 98% agreement between the predicted and actual anomalies over three months, demonstrating its effectiveness. The T2-LSTM model significantly improves the accuracy of motor fault detection, potentially reducing economic losses and improving safety in the chemical industry. Future research will focus on reducing false alarms and integrating more sensor data.
  Citation: Mathematics
  PubDate: 2024-08-26
  DOI: 10.3390/math12172652
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2653: Preview Control for Cyber–Physical
Systems under Periodic Denial-of-Service Attacks
- Authors: Jiang Wu, Hao Xie, Jinming Liang, Zhiqiang Li
  First page: 2653
  Abstract: In this paper, the preview control problem for cyber–physical systems (CPSs) under denial-of-service (DOS) attacks is studied. First, we employ an attack-tolerant strategy to design an augmented error system (AES) for scenarios where both state and reference signal channels are subject to periodic attacks. We then discuss the stochastic stability conditions for the AES and derive the corresponding controller. Subsequently, the preview controller for the original system is developed. Finally, the effectiveness of the obtained results is demonstrated through a numerical simulation using an unmanned ground vehicle (UGV) model, indicating the practical applicability of the proposed control strategy.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172653
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2654: Dynamic Optimization with Timing Risk
- Authors: Erin Cottle Hunt, Frank N. Caliendo
  First page: 2654
  Abstract: Timing risk refers to a situation in which the timing of an economically important event is unknown (risky) from the perspective of an economic decision maker. While this special class of dynamic stochastic control problems has many applications in economics, the methods used to solve them are not easily accessible within a single, comprehensive survey. We provide a survey of dynamic optimization methods under comprehensive assumptions about the nature of timing risk. We also relax the assumption of full information and summarize optimization with limited information, ambiguity, imperfect hedging, and dynamic inconsistency. Our goal is to provide a concise user guide for specialists and nonspecialists alike.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172654
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2655: Interval Iterative Decreasing Dimension
Method for Interval Linear Systems and Its Implementation to Analog
Circuits
- Authors: Gülnur Çelik Kızılkan, Büşra Yağlıpınar
  First page: 2655
  Abstract: The iterative decreasing dimension method (IDDM) is an iterative method used to solve the linear algebraic system Ax=f. Such systems are important in modeling many problems in applied sciences. For a number of reasons, such as estimated measurements made for modeling, errors arising from floating point calculations, and approximation methods used for solutions, it becomes necessary to study intervals in the solutions of systems of linear equations. The objective of this paper is to utilize IDDM to achieve resolution in the interval linear system (ILS). During the calculations, the Kaucher space is considered an extended classical interval space. The solutions of Barth-Nuding and Hansen interval linear systems, which are commonly used in the literature to test the solutions of ILSs, are obtained with the interval iterative decreasing dimension method for interval linear systems (I-IDDM). Since IDDM is a variation method of Gaussian elimination, a comparative analysis of the results with the interval Gaussian elimination method (I-GEM) is performed. It has been demonstrated that our approach, I-IDDM, produces better outcomes than I-GEM. I-IDDM is also used to investigate the analog circuit problem, where interval analysis is crucial.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172655
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2656: Fuzzy Resilient Control of DC Microgrids
with Constant Power Loads Based on Markov Jump Models
- Authors: Wei Hu, Yu Shen, Fan Yang, Zhen Chang, Shanglin Zhao
  First page: 2656
  Abstract: This paper addresses the fuzzy resilient control of DC microgrids with constant power loads. The DC microgrid is subject to abrupt parameter changes which are described by the Markov jump model. Due to the constant power loads, the DC microgrid exhibits nonlinear dynamics which are characterized by a T-S fuzzy model. According to the parallel distributed compensation principle, mode-dependent fuzzy resilient controllers are designed to stabilize the resultant T-S fuzzy Markov jump DC microgrid. The “resilient” means the controller could cope with the uncertainty caused by the inaccurate execution of the control laws. This uncertainty is governed by a Bernoulli distributed random variable and thus may not occur. Then, the mean square exponential stability is analyzed for the closed-loop system by using the mode-dependent Lyapunov function. Since the stability conditions are not convex, a design algorithm is further derived to calculate the fuzzy resilient controller gains. Finally, simulations are provided to test the effectiveness of the proposed results.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172656
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2657: Second-Order Terminal Sliding Mode
Control for Trajectory Tracking of a Differential Drive Robot
- Authors: Tuan Ngoc Tran Cao, Binh Thanh Pham, No Tan Nguyen, Duc-Lung Vu, Nguyen-Vu Truong
  First page: 2657
  Abstract: This paper proposes a second-order terminal sliding mode (2TSM) approach to the trajectory tracking of the differential drive mobile robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the innermost loop, tracks the robot’s velocity quantities while a kinematic controller, at the outermost loop, regulates the robot’s positions. In this manner, chattering is greatly attenuated, and finite-time convergence is guaranteed by the second-order TSM manifold, which involves higher-order derivatives of the state variables, resulting in an inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172657
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2658: A Dual-Branch Convolutional Neural
Network-Based Bluetooth Low Energy Indoor Positioning Algorithm by Fusing
Received Signal Strength with Angle of Arrival
- Authors: Chunxiang Wu, Yapeng Wang, Wei Ke, Xu Yang
  First page: 2658
  Abstract: Indoor positioning is the key enabling technology for many location-aware applications. As GPS does not work indoors, various solutions are proposed for navigating devices. Among these solutions, Bluetooth low energy (BLE) technology has gained significant attention due to its affordability, low power consumption, and rapid data transmission capabilities, making it highly suitable for indoor positioning. Received signal strength (RSS)-based positioning has been studied intensively for a long time. However, the accuracy of RSS-based positioning can fluctuate due to signal attenuation and environmental factors like crowd density. Angle of arrival (AoA)-based positioning uses angle measurement technology for location devices and can achieve higher precision, but the accuracy may also be affected by radio reflections, diffractions, etc. In this study, a dual-branch convolutional neural network (CNN)-based BLE indoor positioning algorithm integrating RSS and AoA is proposed, which exploits both RSS and AoA to estimate the position of a target. Given the absence of publicly available datasets, we generated our own dataset for this study. Data were collected from each receiver in three different directions, resulting in a total of 2675 records, which included both RSS and AoA measurements. Of these, 1295 records were designated for training purposes. Subsequently, we evaluated our algorithm using the remaining 1380 unseen test records. Our RSS and AoA fusion algorithm yielded a sub-meter accuracy of 0.79 m, which was significantly better than the 1.06 m and 1.67 m obtained when using only the RSS or the AoA method. Compared with the RSS-only and AoA-only solutions, the accuracy was improved by 25.47% and 52.69%, respectively. These results are even close to the latest commercial proprietary system, which represents the state-of-the-art indoor positioning technology.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172658
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2659: Graph Information Vanishing Phenomenon
in Implicit Graph Neural Networks
- Authors: Silu He, Jun Cao, Hongyuan Yuan, Zhe Chen, Shijuan Gao, Haifeng Li
  First page: 2659
  Abstract: Graph neural networks (GNNs) have been highly successful in graph representation learning. The goal of GNNs is to enrich node representations by aggregating information from neighboring nodes. Much work has attempted to improve the quality of aggregation by introducing a variety of graph information with representational capabilities. The class of GNNs that improves the quality of aggregation by encoding graph information with representational capabilities into the weights of neighboring nodes through different learnable transformation structures (LTSs) are referred to as implicit GNNs. However, we argue that LTSs only transform graph information into the weights of neighboring nodes in the direction that minimizes the loss function during the learning process and does not actually utilize the effective properties of graph information, a phenomenon that we refer to as graph information vanishing (GIV). To validate this point, we perform thousands of experiments on seven node classification benchmark datasets. We first replace the graph information utilized by five implicit GNNs with random values and surprisingly observe that the variation range of accuracies is less than ± 0.3%. Then, we quantitatively characterize the similarity of the weights generated from graph information and random values by cosine similarity, and the cosine similarities are greater than 0.99. The empirical experiments show that graph information is equivalent to initializing the input of LTSs. We believe that graph information as an additional supervised signal to constrain the training of GNNs can effectively solve GIV. Here, we propose GinfoNN, which utilizes both labels and discrete graph curvature as supervised signals to jointly constrain the training of the model. The experimental results show that the classification accuracies of GinfoNN improve by two percentage points over baselines on large and dense datasets.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172659
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2660: Width and Local Homology Dimension for
Triangulated Categories
- Authors: Li Wang
  First page: 2660
  Abstract: Let T be a compactly generated triangulated category. In this paper, the width and local homology dimension of an object X with respect to a homogeneous ideal a, widthR(a,X) and hd(a,X), respectively, are introduced. The local nature and some basic properties of widthR(a,X) and hd(a,X) are provided. In addition, we give an upper bound and lower bound of widthR(a,X). What is more, we give the relationship between the local homology dimension hd(a,X) and the arithmetic rank of a and dimR.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172660
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2661: Symmetric ADMM-Based Federated Learning
with a Relaxed Step
- Authors: Jinglei Lu, Ya Zhu, Yazheng Dang
  First page: 2661
  Abstract: Federated learning facilitates the training of global models in a distributed manner without requiring the sharing of raw data. This paper introduces two novel symmetric Alternating Direction Method of Multipliers (ADMM) algorithms for federated learning, Two algorithm utilize a convex combination of current local and global variables to generate relaxed steps to improve computational efficiency. They also integrate two dual-update steps with varying relaxation factors into the ADMM framework to boost the accuracy and the convergence rate. Another key feature is the use of weak parametric assumptions to enhance its computational feasibility. Furthermore, the global update in the second algorithm occurs only at certain steps (e.g., at steps being a multiple of a pre-defined integer) to improve the communication efficiency. Theoretical analysis demonstrates linear convergence under reasonable conditions, and experimental results confirm the superior convergence and heightened efficiency of the proposed algorithms compared to the existing methodologies.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172661
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2662: On Convoluted Forms of Multivariate
Legendre-Hermite Polynomials with Algebraic Matrix Based Approach
- Authors: Mumtaz Riyasat, Amal S. Alali, Shahid Ahmad Wani, Subuhi Khan
  First page: 2662
  Abstract: The main purpose of this article is to construct a new class of multivariate Legendre-Hermite-Apostol type Frobenius-Euler polynomials. A number of significant analytical characterizations of these polynomials using various generating function techniques are provided in a methodical manner. These enactments involve explicit relations comprising Hurwitz-Lerch zeta functions and λ-Stirling numbers of the second kind, recurrence relations, and summation formulae. The symmetry identities for these polynomials are established by connecting generalized integer power sums, double power sums and Hurwitz-Lerch zeta functions. In the end, these polynomials are also characterized Svia an algebraic matrix based approach.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172662
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2663: Reference Architecture for the
Integration of Prescriptive Analytics Use Cases in Smart Factories
- Authors: Julian Weller, Nico Migenda, Yash Naik, Tim Heuwinkel, Arno Kühn, Martin Kohlhase, Wolfram Schenck, Roman Dumitrescu
  First page: 2663
  Abstract: Prescriptive analytics plays an important role in decision making in smart factories by utilizing the available data to gain actionable insights. The planning, integration and development of such use cases still poses manifold challenges. Use cases are still being implemented as standalone versions; the existing IT-infrastructure is not fit for integrative bidirectional decision communication, and implementations only reach low technical readiness levels. We propose a reference architecture for the integration of prescriptive analytics use cases in smart factories. The method for the empirically grounded development of reference architectures by Galster and Avgeriou serves as a blueprint. Through the development and validation of a specific IoT-Factory use case, we demonstrate the efficacy of the proposed reference architecture. We expand the given reference architecture for one use case to the integration of a smart factory and its application to multiple use cases. Moreover, we identify the interdependency among multiple use cases within dynamic environments. Our prescriptive reference architecture provides a structured way to improve operational efficiency and optimize resource allocation.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172663
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2664: Integrated Evaluation Method of Bus Lane
Traffic Benefit Based on Multi-Source Data
- Authors: Wufeng Qiao, Zepeng Yang, Bo Peng, Xiaoyu Cai, Yuanyuan Zhang
  First page: 2664
  Abstract: Bus lanes are an important measure for improving the quality of bus service and the efficiency of transportation systems. A scientific and reasonable evaluation of the overall traffic operation efficiency of the bus priority road section is helpful to fully understand the improvement effect of the introduction of bus lanes on traffic operation. To comprehensively and objectively evaluate the traffic benefits of bus lanes, the Delphi and grey correlation methods were used to construct a comprehensive weight calculation model of the indicators. The weights of eight traffic benefit evaluation indicators at the two levels of buses and general traffic were calculated, and the weights were then optimized using the target optimization model. Combined with different weight indexes, the evaluation of the traffic benefit level of the bus lane was realized using the matter-element extension model based on the improvement in the sticking progress. The bus lanes of the Daping-Yangjiaping, Huanghuayuan interchange-Luneng turntable, and Dashiba-Hongqihegou routes in the main urban area of Chongqing were used for verification. The results show that the traffic benefits of the three case areas have been improved to a certain extent after the construction of bus lanes, but the benefit level has not changed. Through the analysis of various operating indicators, the weaknesses that affect the traffic efficiency can be obtained, and then the decision-making basis for the implementation and improvement of the bus lane optimization scheme can be provided.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172664
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2665: H∞ Differential Game of Nonlinear
Half-Car Active Suspension via Off-Policy Reinforcement Learning
- Authors: Gang Wang, Jiafan Deng, Tingting Zhou, Suqi Liu
  First page: 2665
  Abstract: This paper investigates a parameter-free H∞ differential game approach for nonlinear active vehicle suspensions. The study accounts for the geometric nonlinearity of the half-car active suspension and the cubic nonlinearity of the damping elements. The nonlinear H∞ control problem is reformulated as a zero-sum game between two players, leading to the establishment of the Hamilton–Jacobi–Isaacs (HJI) equation with a Nash equilibrium solution. To minimize reliance on model parameters during the solution process, an actor–critic framework employing neural networks is utilized to approximate the control policy and value function. An off-policy reinforcement learning method is implemented to iteratively solve the HJI equation. In this approach, the disturbance policy is derived directly from the value function, requiring only a limited amount of driving data to approximate the HJI equation’s solution. The primary innovation of this method lies in its capacity to effectively address system nonlinearities without the need for model parameters, making it particularly advantageous for practical engineering applications. Numerical simulations confirm the method’s effectiveness and applicable range. The off-policy reinforcement learning approach ensures the safety of the design process. For low-frequency road disturbances, the designed H∞ control policy enhances both ride comfort and stability.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172665
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2666: Event-Triggered Output Feedback H∞
Control for Markov-Type Networked Control Systems
- Authors: Xuede Zhou, Shanshan Liu, Yan Wang, Yong Zhu
  First page: 2666
  Abstract: This paper studies the output feedback H∞ control problem of event-triggered Markov-type networked control systems. Firstly, a new Lyapunov–Krasovskii functional is constructed, which contains an event-triggered scheme, Markovian jump system, and quantified information. Secondly, the upper bound of the weak infinitesimal generation operator of the Lyapunov–Krasovskii function is estimated by combining Wirtinger’s-based integral inequality and reciprocally convex inequality. Finally, based on the Lyapunov stability theory, the closed-loop stability criterion of event-triggered Markov-type networked control systems and the design method of the output feedback H∞ controller for the disturbance attenuation level γ are given in the terms of linear matrix inequalities. The effectiveness and superiority of the proposed method are verified using three numerical examples.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172666
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2667: Closed-Form Formula for the Conditional
Moment-Generating Function Under a Regime-Switching, Nonlinear Drift CEV
Process, with Applications to Option Pricing
- Authors: Kittisak Chumpong, Khamron Mekchay, Fukiat Nualsri, Phiraphat Sutthimat
  First page: 2667
  Abstract: An analytical derivation of the conditional moment-generating function (MGF) for a regime-switching nonlinear drift constant elasticity of variance process is established. The proposed model incorporates both regime-switching mechanisms and nonlinear drift components to better capture market phenomena such as volatility smiles and leverage effects. Regime-switching models can match the tendency of financial markets to often change their behavior abruptly and the phenomenon that the new behavior of financial variables often persists for several periods after such a change. Closed-form formulas for the MGF under various conditions, which are then applied for option pricing, are also derived. The efficacy and accuracy of the results are validated through a discrete Markov chain simulation. The results obtained from the proposed formulas completely match with those from MC simulations, while requiring significantly less computational time.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172667
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2668: ConvNext as a Basis for Interpretability
in Coffee Leaf Rust Classification
- Authors: Adrian Chavarro, Diego Renza, Ernesto Moya-Albor
  First page: 2668
  Abstract: The increasing complexity of deep learning models can make it difficult to interpret and fit models beyond a purely accuracy-focused evaluation. This is where interpretable and [ eXplainable Artificial Intelligence (XAI)explainable Artificial Intelligence (AI) come into play to facilitate an understanding of the inner workings of models. Consequently, alternatives have emerged, such as [class activation mapping (CAM) techniquesClass Activation Maps (CAM) aimed at identifying regions of importance for an image classification model. However, the behavior of such models can be highly dependent on the type of architecture and the different variants of convolutional neural networks. Accordingly, this paper evaluates three Convolutional Neural Network (CNN) architectures (VGG16, ResNet50, ConvNext-T) against seven CAM models (GradCAM, XGradCAM, HiResCAM, LayerCAM, GradCAM++, GradCAMElementWise, and EigenCAM), indicating that the CAM maps obtained with ConvNext models show less variability among them, i.e., they are less dependent on the selected CAM approach. This study was performed on an image dataset for the classification of coffee leaf rust and evaluated using the RemOve And Debias (ROAD) metric.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172668
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2669: Optimal Dynamic Production Planning for
Supply Network with Random External and Internal Demands
- Authors: Chenglin Hu, Junsong Bian, Daozhi Zhao, Longfei He, Fangqi Dong
  First page: 2669
  Abstract: This paper focuses on joint production/inventory optimization in single and multiple horizons, respectively, within a complicated supply network (CSN) consisting of firm nodes with coupled demands and firm nodes with coupled demands. We first formulate the single-epoch joint optimal output model by allowing the production of extra quantity for stock underage, considering the fixed costs incurred by having inventory over demand and shortfalls. Then, the multi-temporal dynamic joint production model is further investigated to deal with stochastic demand fluctuations among CSN nodes by constructing a dynamic input–output model. The K-convexity defined in Rn space is proved to obtain the optimal control strategy. According to physical flow links, all demands associated to the nodes of CSN are categorized into the inter-node demand inside CSN (intermediate demand) and external demand outside CSN (final demand). We exploit the meliorated input–output matrix to describe demand relations, building dynamic input–output models where demand fluctuates randomly in single-cycle CSN and finite multi-cycle CSN. The novel monocyclic and multicyclic dynamic models have been developed to minimize system-wide operational costs. Unlike existent literature, we consider fixed costs incurred by overdemand and underdemand inventory into system operational cost functions and then demonstrate the convexity of objective functions. The cost function with two fixed penalty costs due to excess and shortage of inventory is developed in a multicycle model, and the K-convexity defined in Rn is proved to find out the optimal strategy for joint dynamic production of CSNs in the case of multi-products and multicycles.
  Citation: Mathematics
  PubDate: 2024-08-27
  DOI: 10.3390/math12172669
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2670: Optimizing Two-Dimensional Irregular
Pattern Packing with Advanced Overlap Optimization Techniques
- Authors: Longhui Meng, Liang Ding, Aqib Mashood Khan, Ray Tahir Mushtaq, Mohammed Alkahtani
  First page: 2670
  Abstract: This research introduces the Iterative Overlap Optimization Placement (IOOP) method, a novel approach designed to enhance the efficiency of irregular pattern packing by dynamically optimizing overlap ratios and pattern placements. Utilizing a modified genetic algorithm, IOOP addresses the complexities of arranging irregular patterns in a given space, focusing on improving spatial and material efficiency. This study demonstrates the method’s superiority over the traditional Size-First Non-Iterative Overlap Optimization Placement technique through comparative analysis, highlighting significant improvements in spatial utilization, flexibility, and material conservation. The effectiveness of IOOP is further validated by its robustness in handling diverse pattern groups and its adaptability in adjusting pattern placements iteratively. This research not only showcases the potential of IOOP in manufacturing and design processes requiring precise spatial planning but also opens avenues for its application across various industries, underscoring the need for further exploration into advanced technological integrations for tackling complex spatial optimization challenges.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172670
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2671: Existence of Solutions for a
Viscoelastic Plate Equation with Variable Exponents and a General Source
Term
- Authors: Youcef Bouizem, Asma Alharbi, Salah Boulaaras
  First page: 2671
  Abstract: The subject of this study is a nonlinear viscoelastic plate equation with variable exponents and a general source term. Through the application of the Faedo–Galerkin approximation method and a fixed point theorem under appropriate assumptions, we proved the existence of weak solutions.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172671
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2672: Multi-Objective Optimized GPSR
Intelligent Routing Protocol for UAV Clusters
- Authors: Hao Chen, Fan Luo, Jianguo Zhou, Yanming Dong
  First page: 2672
  Abstract: Unmanned aerial vehicle (UAV) clusters offer significant potential in civil, military, and commercial fields due to their flexibility and cooperative capabilities. However, characteristics such as dynamic topology and limited energy storage bring challenges to the design of routing protocols for UAV networks. This study leverages the Deep Double Q-Learning Network (DDQN) algorithm to optimize the traditional Greedy Perimeter Stateless Routing (GPSR) protocol, resulting in a multi-objective optimized GPSR routing protocol (DDQN-MTGPSR). By constructing a multi-objective routing optimization model through cross-layer data fusion, the proposed approach aims to enhance UAV network communication performance comprehensively. In addition, this study develops the above DDQN-MTGPSR intelligent routing algorithm based on the NS-3 platform and uses an artificial intelligence framework. In order to verify the effectiveness of the DDQN-MTGPSR algorithm, it is simulated and compared with the traditional ad hoc routing protocols, and the experimental results show that compared with the GPSR protocol, the DDQN-MTGPSR has achieved significant optimization in the key metrics such as the average end-to-end delay, packet delivery rate, node average residual energy variance and percentage of node average residual energy. In high dynamic scenarios, the above indicators were optimized by 20.05%, 12.72%, 0.47%, and 50.15%, respectively, while optimizing 36.31%, 26.26%, 8.709%, and 69.3% in large-scale scenarios, respectively.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172672
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2673: An Enhanced Credit Risk Evaluation by
Incorporating Related Party Transaction in Blockchain Firms of China
- Authors: Ying Chen, Lingjie Liu, Libing Fang
  First page: 2673
  Abstract: Related party transactions (RPTs) can serve as channels for the spread of credit risk events among blockchain firms. However, current credit risk-assessment models typically only consider a firm’s individual characteristics, overlooking the impact of related parties in the blockchain. We suggest incorporating RPT network analysis to improve credit risk evaluation. Our approach begins by representing an RPT network using a weighted adjacency matrix. We then apply DANE, a deep network embedding algorithm, to generate condensed vector representations of the firms within the network. These representations are subsequently used as inputs for credit risk-evaluation models to predict the default distance. Following this, we employ SHAP (Shapley Additive Explanations) to analyze how the network information contributes to the prediction. Lastly, this study demonstrates the enhancing effect of using DANE-based integrated features in credit risk assessment.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172673
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2674: A Penalized Empirical Likelihood
Approach for Estimating Population Sizes under the Negative Binomial
Regression Model
- Authors: Yulu Ji, Yang Liu
  First page: 2674
  Abstract: In capture–recapture experiments, the presence of overdispersion and heterogeneity necessitates the use of the negative binomial regression model for inferring population sizes. However, within this model, existing methods based on likelihood and ratio regression for estimating the dispersion parameter often face boundary and nonidentifiability issues. These problems can result in nonsensically large point estimates and unbounded upper limits of confidence intervals for the population size. We present a penalized empirical likelihood technique for solving these two problems by imposing a half-normal prior on the population size. Based on the proposed approach, a maximum penalized empirical likelihood estimator with asymptotic normality and a penalized empirical likelihood ratio statistic with asymptotic chi-square distribution are derived. To improve numerical performance, we present an effective expectation-maximization (EM) algorithm. In the M-step, optimization for the model parameters could be achieved by fitting a standard negative binomial regression model via the R basic function glm.nb(). This approach ensures the convergence and reliability of the numerical algorithm. Using simulations, we analyze several synthetic datasets to illustrate three advantages of our methods in finite-sample cases: complete mitigation of the boundary problem, more efficient maximum penalized empirical likelihood estimates, and more precise penalized empirical likelihood ratio interval estimates compared to the estimates obtained without penalty. These advantages are further demonstrated in a case study estimating the abundance of black bears (Ursus americanus) at the U.S. Army’s Fort Drum Military Installation in northern New York.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172674
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2675: Weak ψ-Contractions on Directed
Graphs with Applications to Integral Equations
- Authors: Doaa Filali, Mohammad Dilshad, Mohammad Akram
  First page: 2675
  Abstract: This article deals with a few outcomes ensuring the fixed points of a weak (G,ψ)-contraction map of metric spaces comprised with a reflexive and transitive digraph G. To validate our findings, we furnish several examples. The findings we obtain enable us to seek out the unique solution of a nonlinear integral equation. The outcomes presented herewith sharpen, subsume, unify, improve, enrich, and compile a number of existing theorems.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172675
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2676: Game Theory for Predicting
Stocks’ Closing Prices
- Authors: João Costa Freitas, Alberto Adrego Pinto, Óscar Felgueiras
  First page: 2676
  Abstract: We model the financial markets as a game and make predictions using Markov chain estimators. We extract the possible patterns displayed by the financial markets, define a game where one of the players is the speculator, whose strategies depend on his/her risk-to-reward preferences, and the market is the other player, whose strategies are the previously observed patterns. Then, we estimate the market’s mixed probabilities by defining Markov chains and utilizing its transition matrices. Afterwards, we use these probabilities to determine which is the optimal strategy for the speculator. Finally, we apply these models to real-time market data to determine its feasibility. From this, we obtained a model for the financial markets that has a good performance in terms of accuracy and profitability.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172676
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2677: Matching and Rewriting Rules in
Object-Oriented Databases
- Authors: Giacomo Bergami, Oliver Robert Fox, Graham Morgan
  First page: 2677
  Abstract: Graph query languages such as Cypher are widely adopted to match and retrieve data in a graph representation, due to their ability to retrieve and transform information. Even though the most natural way to match and transform information is through rewriting rules, those are scarcely or partially adopted in graph query languages. Their inability to do so has a major impact on the subsequent way the information is structured, as it might then appear more natural to provide major constraints over the data representation to fix the way the information should be represented. On the other hand, recent works are starting to move towards the opposite direction, as the provision of a truly general semistructured model (GSM) allows to both represent all the available data formats (Network-Based, Relational, and Semistructured) as well as support a holistic query language expressing all major queries in such languages. In this paper, we show that the usage of GSM enables the definition of a general rewriting mechanism which can be expressed in current graph query languages only at the cost of adhering the query to the specificity of the underlying data representation. We formalise the proposed query language in terms declarative graph rewriting mechanisms described as a set of production rules L→R while both providing restriction to the characterisation of L, and extending it to support structural graph nesting operations, useful to aggregate similar information around an entry-point of interest. We further achieve our declarative requirements by determining the order in which the data should be rewritten and multiple rules should be applied while ensuring the application of such updates on the GSM database is persisted in subsequent rewriting calls. We discuss how GSM, by fully supporting index-based data representation, allows for a better physical model implementation leveraging the benefits of columnar database storage. Preliminary benchmarks show the scalability of this proposed implementation in comparison with state-of-the-art implementations.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172677
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2678: Quantum Attacks on MIBS Block Cipher
Based on Bernstein–Vazirani Algorithm
- Authors: Huiqin Xie, Zhangmei Zhao, Ke Wang, Yanjun Li, Hongcai Xin
  First page: 2678
  Abstract: Because of the substantial progress in quantum computing technology, the safety of traditional cryptologic schemes is facing serious challenges. In this study, we explore the quantum safety of the lightweight cipher MIBS and propose quantum key-recovery attacks on the MIBS cipher by utilizing Grover’s algorithm and Bernstein–Vazirani algorithm. We first construct linear-structure functions based on the 5-round MIBS cipher according to the characteristics of the linear transformations, and then we obtain a quantum distinguisher of the 5-round MIBS cipher by applying Bernstein–Vazirani algorithm to the constructed functions. Finally, utilizing this distinguisher and Grover’s algorithm, we realize a 7-round key-recovery attack on the MIBS cipher, and then we expand the attack to more rounds of MIBS based on a similar idea. The quantum attack on the 7-round MIBS requires 156 qubits and has a time complexity of 210.5. An 8-round attack requires 179 qubits and has a time complexity of 222. Compared with existing quantum attacks, our attacks have better time complexity when attacking the same number of rounds.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172678
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2679: A Two-Echelon Routing Model for
Sustainable Last-Mile Delivery with an Intermediate Facility: A Case Study
of Pharmaceutical Distribution in Rome
- Authors: Annarita De Maio
  First page: 2679
  Abstract: This paper introduces a two-echelon optimization model for the integrated routing of an electric vehicle (EV) and a traditional internal combustion engine vehicle (ICEV) in an urban environment. The scientific context of this study is sustainable urban logistics. The case study focuses on the distribution of pharmaceuticals in the metropolitan area of Rome. Distributing pharmaceuticals in large cities presents significant challenges, including heavy traffic congestion, the need for strict temperature control, and the maintenance of the integrity and timely delivery of sensitive medications. Furthermore, the complexity of urban logistics and adherence to regulatory requirements introduce additional layers of difficulty. Therefore, the implementation of fast and sustainable distribution mechanisms is crucial in this context. Specifically, the model seeks to minimize both total CO2 emissions and transportation costs while optimizing the use of an EV and an ICEV, all while ensuring that service level requirements are met. Computational results demonstrate the effectiveness of the proposed method in improving the sustainability of pharmaceutical distribution.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172679
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2680: On Spatial Systems of Bars Spherically
Jointed at Their Ends and Having One Common End
- Authors: Valentin Răcășan, Nicolae-Doru Stănescu
  First page: 2680
  Abstract: In this paper we consider a system of linear bars, spherically jointed at their ends. For each bar one end is linked to the origin. We discuss the equations from which one obtains the deviation of the origin, and some possible optimizations concerning the minimum displacement of the origin and the minimum force in one bar, which are the main goals of the paper. The optimization is performed considering that for two bars one end is unknown; that is, the angles between the bars and the axes are unknown. It is proved that it is difficult to obtain an analytical solution in the general case, and the problem can be discussed only by numerical methods. A numerical case is also studied and some comments concerning the results are given.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172680
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2681: Dynamics of Activation and Regulation of
the Immune Response to Attack by Viral Pathogens Using Mathematical
Modeling
- Authors: Ledyz Cuesta-Herrera, Luis Pastenes, Ariel D. Arencibia, Fernando Córdova-Lepe, Cristhian Montoya
  First page: 2681
  Abstract: In this paper, a mathematical model is developed to simulate the activation of regulatory T lymphocytes dynamics. The model considers the adaptive immune response and consists of epithelial cells, infected cells, free virus particles, helper and cytotoxic T lymphocytes, B lymphocytes, and regulatory T lymphocytes. A mathematical analysis was carried out to discuss the conditions of existence and stability of equilibrium solutions in terms of the basic reproductive number. In addition, the definitions and properties necessary to preserve the positivity and stability of the model are shown. The precision of these mathematical models can be affected by numerous sources of uncertainty, partly due to the balance between the complexity of the model and its predictive capacity to depict the biological process accurately. Nevertheless, these models can provide remarkably perspectives on the dynamics of infection and assist in identification specific immunological traits that improve our comprehension of immune mechanisms. The theoretical results are validated by numerical simulations using data reported in the literature. The construction, analysis, and simulation of the developed models demonstrate that the increased induced regulatory T lymphocytes effectively suppress the inflammatory response in contrast to similar cells at lower contents, playing a key role in maintaining self-tolerance and immune homeostasis.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172681
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2682: Bayesian Model Selection for Addressing
Cold-Start Problems in Partitioned Time Series Prediction
- Authors: Jaeseong Yoo, Jihoon Moon
  First page: 2682
  Abstract: How to effectively predict outcomes when initial time series data are limited remains unclear. This study investigated the efficiency of Bayesian model selection to address the lack of initial data for time series analysis, particularly in cold-start scenarios—a common challenge in predictive modeling. We utilized a comprehensive approach that juxtaposed observational data against various candidate models through strategic partitioning. This method contrasted traditional reliance on distance measures like the L2 norm. Instead, it applied statistical tests to validate model efficacy. Notably, the introduction of an interactive visualization tool featuring a slide bar for setting significance levels marked a significant advancement over conventional p-value displays. Our results affirm that when observational data align with a candidate model, effective predictions are possible, albeit with necessary considerations of stationarity and potential structural breaks. These findings underscore the potential of Bayesian methods in predictive analytics, especially when initial data are scarce or incomplete. This research not only enhances our understanding of model selection dynamics but also sets the stage for future investigations into more refined predictive frameworks.
  Citation: Mathematics
  PubDate: 2024-08-28
  DOI: 10.3390/math12172682
  Issue No: Vol. 12, No. 17 (2024)
Mathematics, Vol. 12, Pages 2582: Leveraging ChatGPT and Long Short-Term
Memory in Recommender Algorithm for Self-Management of Cardiovascular Risk
Factors
- Authors: Tatiana V. Afanasieva, Pavel V. Platov, Andrey V. Komolov, Andrey V. Kuzlyakin
  First page: 2582
  Abstract: One of the new trends in the development of recommendation algorithms is the dissemination of their capabilities to support the population in managing their health, in particular cardiovascular health. Cardiovascular diseases (CVDs) affect people in their prime years and remain the main cause of morbidity and mortality worldwide, and their clinical treatment is expensive and time consuming. At the same time, about 80% of them can be prevented, according to the World Federation of Cardiology. The aim of this study is to develop and investigate a knowledge-based recommender algorithm for the self-management of CVD risk factors in adults at home. The proposed algorithm is based on the original user profile, which includes a predictive assessment of the presence of CVD. To obtain a predictive score for CVD presence, AutoML and LSTM models were studied on the Kaggle dataset, and it was shown that the LSTM model, with an accuracy of 0.88, outperformed the AutoML model. The algorithm recommendations generated contain items of three types: targeted, informational, and explanatory. For the first time, large language models, namely ChatGPT-3.5, ChatGPT-4, and ChatGPT-4.o, were leveraged and studied in creating explanations of the recommendations. The experiments show the following: (1) In explaining recommendations, ChatGPT-3.5, ChatGPT-4, and ChatGPT-4.o demonstrate a high accuracy of 71% to 91% and coherence with modern official guidelines of 84% to 92%. (2) The safety properties of ChatGPT-generated explanations estimated by doctors received the highest score of almost 100%. (3) On average, the stability and correctness of the GPT-4.o responses were more acceptable than those of other models for creating explanations. (4) The degree of user satisfaction with the recommendations obtained using the proposed algorithm was 88%, and the rating of the usefulness of the recommendations was 92%.
  Citation: Mathematics
  PubDate: 2024-08-21
  DOI: 10.3390/math12162582
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2584: Convergence Analysis for an Online
Data-Driven Feedback Control Algorithm
- Authors: Siming Liang, Hui Sun, Richard Archibald, Feng Bao
  First page: 2584
  Abstract: This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.
  Citation: Mathematics
  PubDate: 2024-08-21
  DOI: 10.3390/math12162584
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2585: Evaluating Order Allocation
Sustainability Using a Novel Framework Involving Z-Number
- Authors: Kuan-Yu Lin, Cheng-Lu Yeng, Yi-Kuei Lin
  First page: 2585
  Abstract: The United Nations’ sustainable development goals have highlighted the significance of improving supply chain sustainability and ensuring the proper distribution of orders. This study proposes a novel framework involving Z-number, game theory, an indifference threshold-based attribute ratio analysis (ITARA), and a combined compromise solution method (CoCoSo) to evaluate the sustainability of suppliers and order allocations. To better reflect the decision makers’ current choices for the sustainability of assessed suppliers and order allocations and enhance the comprehensiveness of decision-making, the importance parameter of the supplier is obtained through game theory objectively for transforming supplier performance into order allocation performance. The Z-numbers are involved in ITARA (so-called ZITARA) and CoCoSo (so-called ZCoCoSo) to overcome the issue of information uncertainty in the process of expert evaluation. ZITARA and ZCoCoSo are used to determine the objective weights of criteria and to rank the evaluated order allocations, respectively. A case study of a China company is then presented to demonstrate the usefulness of the proposed framework and to inform their decision-making process regarding which suppliers the orders should be assigned to.
  Citation: Mathematics
  PubDate: 2024-08-21
  DOI: 10.3390/math12162585
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2586: Predicting the Performance of Ensemble
Classification Using Conditional Joint Probability
- Authors: Iqbal Murtza, Jin-Young Kim, Muhammad Adnan
  First page: 2586
  Abstract: In many machine learning applications, there are many scenarios when performance is not satisfactory by single classifiers. In this case, an ensemble classification is constructed using several weak base learners to achieve satisfactory performance. Unluckily, the construction of the ensemble classification is empirical, i.e., to try an ensemble classification and if performance is not satisfactory then discard it. In this paper, a challenging analytical problem of the estimation of ensemble classification using the prediction performance of the base learners is considered. The proposed formulation is aimed at estimating the performance of ensemble classification without physically developing it, and it is derived from the perspective of probability theory by manipulating the decision probabilities of the base learners. For this purpose, the output of a base learner (which is either true positive, true negative, false positive, or false negative) is considered as a random variable. Then, the effects of logical disjunction-based and majority voting-based decision combination strategies are analyzed from the perspective of conditional joint probability. To evaluate the forecasted performance of ensemble classifier by the proposed methodology, publicly available standard datasets have been employed. The results show the effectiveness of the derived formulations to estimate the performance of ensemble classification. In addition to this, the theoretical and experimental results show that the logical disjunction-based decision outperforms majority voting in imbalanced datasets and cost-sensitive scenarios.
  Citation: Mathematics
  PubDate: 2024-08-21
  DOI: 10.3390/math12162586
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2587: P-CA: Privacy-Preserving Convolutional
Autoencoder-Based Edge–Cloud Collaborative Computing for Human
Behavior Recognition
- Authors: Haoda Wang, Chen Qiu, Chen Zhang, Jiantao Xu, Chunhua Su
  First page: 2587
  Abstract: With the development of edge computing and deep learning, intelligent human behavior recognition has spawned extensive applications in smart worlds. However, current edge computing technology faces performance bottlenecks due to limited computing resources at the edge, which prevent deploying advanced deep neural networks. In addition, there is a risk of privacy leakage during interactions between the edge and the server. To tackle these problems, we propose an effective, privacy-preserving edge–cloud collaborative interaction scheme based on WiFi, named P-CA, for human behavior sensing. In our scheme, a convolutional autoencoder neural network is split into two parts. The shallow layers are deployed on the edge side for inference and privacy-preserving processing, while the deep layers are deployed on the server side to leverage its computing resources. Experimental results based on datasets collected from real testbeds demonstrate the effectiveness and considerable performance of the P-CA. The recognition accuracy can maintain 88%, although it could achieve about 94.8% without the mixing operation. In addition, the proposed P-CA achieves better recognition accuracy than two state-of-the-art methods, i.e., FedLoc and PPDFL, by 2.7% and 2.1%, respectively, while maintaining privacy.
  Citation: Mathematics
  PubDate: 2024-08-21
  DOI: 10.3390/math12162587
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2588: A U-Statistic for Testing the Lack of
Dependence in Functional Partially Linear Regression Model
- Authors: Fanrong Zhao, Baoxue Zhang
  First page: 2588
  Abstract: The functional partially linear regression model comprises a functional linear part and a non-parametric part. Testing the linear relationship between the response and the functional predictor is of fundamental importance. In cases where functional data cannot be approximated with a few principal components, we develop a second-order U-statistic using a pseudo-estimate for the unknown non-parametric component. Under some regularity conditions, the asymptotic normality of the proposed test statistic is established using the martingale central limit theorem. The proposed test is evaluated for finite sample properties through simulation studies and its application to real data.
  Citation: Mathematics
  PubDate: 2024-08-21
  DOI: 10.3390/math12162588
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2589: Preface to the Special Issue on
“Advances in Machine Learning, Optimization, and Control
Applications”
- Authors: Wanquan Liu, Xianchao Xiu, Xuefang Li
  First page: 2589
  Abstract: Over the past few decades, data science and machine learning have demonstrated tremendous success in many areas of science and engineering, such as large-scale pattern recognition, computer vision, multiagent control, industrial engineering, etc [...]
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162589
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2590: A Bellman–Ford Algorithm for the
Path-Length-Weighted Distance in Graphs
- Authors: Roger Arnau, José M. Calabuig, Luis M. García-Raffi, Enrique A. Sánchez Pérez, Sergi Sanjuan
  First page: 2590
  Abstract: Consider a finite directed graph without cycles in which the arrows are weighted by positive weights. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. The idea is that the new distance explicitly takes into account the size of the paths in the calculations. It has the distinct characteristic that, when calculated along the same path, it may result in a shorter distance between far-apart vertices than between adjacent ones. This property can be particularly useful for modeling scenarios where the connections between vertices are obscured by numerous intermediate vertices, such as in cases of financial fraud. For example, to hide dirty money from financial authorities, fraudsters often use multiple institutions, banks, and intermediaries between the source of the money and its final recipient. Our distance would serve to make such situations explicit. Thus, although our algorithm is based on arguments similar to those at work for the Bellman–Ford and Dijkstra methods, it is in fact essentially different, since the calculation formula contains a weight that explicitly depends on the number of intermediate vertices. This fact totally conditions the algorithm, because longer paths could provide shorter distances—contrary to the classical algorithms mentioned above. We lay out the appropriate framework for its computation, showing the constraints and requirements for its use, along with some illustrative examples.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162590
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2591: Identification of Patterns in CO2
Emissions among 208 Countries: K-Means Clustering Combined with PCA and
Non-Linear t-SNE Visualization
- Authors: Ana Lorena Jiménez-Preciado, Salvador Cruz-Aké, Francisco Venegas-Martínez
  First page: 2591
  Abstract: This paper identifies patterns in total and per capita CO2 emissions among 208 countries considering different emission sources, such as cement, flaring, gas, oil, and coal. This research uses linear and non-linear dimensional reduction techniques, combining K-means clustering with principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE), which allows the identification of distinct emission profiles among nations. This approach allows effective clustering of heterogeneous countries despite the highly dimensional nature of emissions data. The optimal number of clusters is determined using Calinski–Harabasz and Davies–Bouldin scores, of five and six clusters for total and per capita CO2 emissions, respectively. The findings reveal that for total emissions, t-SNE brings together the world’s largest economies and emitters, i.e., China, USA, India, and Russia, into a single cluster, while PCA provides clusters with a single country for China, USA, and Russia. Regarding per capita emissions, PCA generates a cluster with only one country, Qatar, due to its significant flaring emissions, as byproduct of the oil industry, and its low population. This study concludes that international collaboration and coherent global policies are crucial for effectively addressing CO2 emissions and developing targeted climate change mitigation strategies.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162591
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2592: Semi-Discretized Approximation of
Stability of Sine-Gordon System with Average-Central Finite Difference
Scheme
- Authors: Xudong Wang, Sizhe Wang, Xing Qiao, Fu Zheng
  First page: 2592
  Abstract: In this study, the energy control and asymptotic stability of the 1D sine-Gordon equation were investigated from the viewpoint of numerical approximation. An order reduction method was employed to transform the closed-loop system into an equivalent system, and an average-central finite difference scheme was constructed. This scheme is not only energy-preserving but also possesses uniform stability. The discrete multiplier method was utilized to obtain the uniformly asymptotic stability of the discrete systems. Moreover, to cope with the nonlinear term of the model, a discrete Wirtinger inequality suitable for our approximating scheme was established. Finally, several numerical experiments based on the eigenvalue distribution of the linearized approximation systems were conducted to demonstrate the effectiveness of the numerical approximating algorithm.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162592
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2593: Generalized Bertrand Curves of
Non-Light-like Framed Curves in Lorentz–Minkowski 3-Space
- Authors: Linlin Wu, Anjie Zhou, Kaixin Yao, Donghe Pei
  First page: 2593
  Abstract: In this paper, we define the generalized Bertrand curves of non-light-like framed curves in Lorentz–Minkowski 3-space; their study is essential for understanding many classical and modern physics problems. Here, we consider two non-light-like framed curves as generalized Bertrand pairs. Our generalized Bertrand pairs can include Bertrand pairs with either singularities or not, and also include Mannheim pairs with singularities. In addition, we discuss their properties and prove the necessary and sufficient conditions for two non-light-like framed curves to be generalized Bertrand pairs.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162593
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2594: Hirota Bilinear Approach to
Multi-Component Nonlocal Nonlinear Schrödinger Equations
- Authors: Yu-Shan Bai, Li-Na Zheng, Wen-Xiu Ma, Yin-Shan Yun
  First page: 2594
  Abstract: Nonlocal nonlinear Schrödinger equations are among the important models of nonlocal integrable systems. This paper aims to present a general formula for arbitrary-order breather solutions to multi-component nonlocal nonlinear Schrödinger equations by using the Hirota bilinear method. In particular, abundant wave solutions of two- and three-component nonlocal nonlinear Schrödinger equations, including periodic and mixed-wave solutions, are obtained by taking appropriate values for the involved parameters in the general solution formula. Moreover, diverse wave structures of the resulting breather and periodic wave solutions with different parameters are discussed in detail.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162594
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2595: Superconvergence of Modified
Nonconforming Cut Finite Element Method for Elliptic Problems
- Authors: Xiaoxiao He, Fei Song
  First page: 2595
  Abstract: In this work, we aim to explore the superconvergence of a modified nonconforming cut finite element method with rectangular meshes for elliptic problems. Boundary conditions are imposed via the Nitsche’s method. The superclose property is proven for rectangular meshes. Moreover, a postprocessing interpolation operator is introduced, and it is proven that the postprocessed discrete solution converges to the exact solution, with a superconvergence rate O(h3/2). Finally, numerical examples are provided to support the theoretical analysis.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162595
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2596: Fixed-Point Theorems Using
α-Series in F-Metric Spaces
- Authors: Vildan Ozturk, Duran Turkoglu
  First page: 2596
  Abstract: Fixed-point theory, which has been developing since 1922, is widely used. Various contraction principles have been defined in the literature. In this work, we define rational-type contraction and weak Choudhury type contraction using α-series in F-metric spaces and prove common fixed-point theorems for sequences of self-mappings. This method is based on the convergence series of coefficients. Our results are the generalized version of the results in the literature. Finally, we apply our main results to solve an integral equation and a differential equation.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162596
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2597: Approximation of Bivariate Functions by
Generalized Wendland Radial Basis Functions
- Authors: Abdelouahed Kouibia, Pedro González, Miguel Pasadas, Bassim Mustafa, Hossain Oulad Yakhlef, Loubna Omri
  First page: 2597
  Abstract: In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is justified by proving the corresponding convergence result. Likewise, to illustrate this method, some graphical and numerical examples are presented in R2, and a comparison with another work is analyzed.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162597
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2598: Quantum Automated Tools for Finding
Impossible Differentials
- Authors: Huiqin Xie, Qiqing Xia, Ke Wang, Yanjun Li, Li Yang
  First page: 2598
  Abstract: Due to the superiority of quantum computing, traditional cryptography is facing a severe threat. This makes the security evaluation of cryptographic systems in quantum attack models both significant and urgent. For symmetric ciphers, the security analysis heavily relies on cryptanalysis tools. Thus, exploring the use of quantum algorithms in traditional cryptanalysis tools has garnered considerable attention. In this study, we utilize quantum algorithms to improve impossible differential attacks and design two quantum automated tools to search for impossible differentials. The proposed quantum algorithms exploit the idea of miss-in-the-middle and the properties of truncated differentials. We rigorously prove their validity and calculate the quantum resources required for their implementation. Compared to the existing classical automated cryptanalysis, the proposed quantum tools have the advantage of accurately characterizing S-boxes while only requiring polynomial complexity, and can take into consideration the impact of the key schedules in a single-key model.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162598
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2599: Optimality and Duality of
Semi-Preinvariant Convex Multi-Objective Programming Involving Generalized
(F,α,ρ,d)−I−Type Invex Functions
- Authors: Rongbo Wang, Qiang Feng
  First page: 2599
  Abstract: Multiobjective programming refers to a mathematical problem that requires the simultaneous optimization of multiple independent yet interrelated objective functions when solving a problem. It is widely used in various fields, such as engineering design, financial investment, environmental planning, and transportation planning. Research on the theory and application of convex functions and their generalized convexity in multiobjective programming helps us understand the essence of optimization problems, and promotes the development of optimization algorithms and theories. In this paper, we firstly introduces new classes of generalized (F,α,ρ,d)−I functions for semi-preinvariant convex multiobjective programming. Secondly, based on these generalized functions, we derive several sufficient optimality conditions for a feasible solution to be an efficient or weakly efficient solution. Finally, we prove weak duality theorems for mixed-type duality.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162599
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2600: Accurate Forecasting of Global
Horizontal Irradiance in Saudi Arabia: A Comparative Study of Machine
Learning Predictive Models and Feature Selection Techniques
- Authors: Amir A. Imam, Abdullah Abusorrah, Mustafa M. A. Seedahmed, Mousa Marzband
  First page: 2600
  Abstract: The growing interest in solar energy stems from its potential to reduce greenhouse gas emissions. Global horizontal irradiance (GHI) is a crucial determinant of the productivity of solar photovoltaic (PV) systems. Consequently, accurate GHI forecasting is essential for efficient planning, integration, and optimization of solar PV energy systems. This study evaluates the performance of six machine learning (ML) regression models—artificial neural network (ANN), decision tree (DT), elastic net (EN), linear regression (LR), Random Forest (RF), and support vector regression (SVR)—in predicting GHI for a site in northern Saudi Arabia known for its high solar energy potential. Using historical data from the NASA POWER database, covering the period from 1984 to 2022, we employed advanced feature selection techniques to enhance the predictive models. The models were evaluated based on metrics such as R-squared (R2), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute Error (MAE). The DT model demonstrated the highest performance, achieving an R2 of 1.0, MSE of 0.0, RMSE of 0.0, MAPE of 0.0%, and MAE of 0.0. Conversely, the EN model showed the lowest performance with an R2 of 0.8396, MSE of 0.4389, RMSE of 0.6549, MAPE of 9.66%, and MAE of 0.5534. While forward, backward, and exhaustive search feature selection methods generally yielded limited performance improvements for most models, the SVR model experienced significant enhancement. These findings offer valuable insights for selecting optimal forecasting strategies for solar energy projects, contributing to the advancement of renewable energy integration and supporting the global transition towards sustainable energy solutions.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162600
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2601: A Path-Conservative ADER Discontinuous
Galerkin Method for Non-Conservative Hyperbolic Systems: Applications to
Shallow Water Equations
- Authors: Xiaoxu Zhao, Baining Wang, Gang Li, Shouguo Qian
  First page: 2601
  Abstract: In this article, we propose a new path-conservative discontinuous Galerkin (DG) method to solve non-conservative hyperbolic partial differential equations (PDEs). In particular, the method here applies the one-stage ADER (Arbitrary DERivatives in space and time) approach to fulfill the temporal discretization. In addition, this method uses the differential transformation (DT) procedure rather than the traditional Cauchy–Kowalewski (CK) procedure to achieve the local temporal evolution. Compared with the classical ADER methods, the current method is free of solving generalized Riemann problems at inter-cells. In comparison with the Runge–Kutta DG (RKDG) methods, the proposed method needs less computer storage, thanks to the absence of intermediate stages. In brief, this current method is one-step, one-stage, and fully-discrete. Moreover, this method can easily obtain arbitrary high-order accuracy both in space and in time. Numerical results for one- and two-dimensional shallow water equations (SWEs) show that the method enjoys high-order accuracy and keeps good resolution for discontinuous solutions.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162601
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2602: Interdisciplinary Education Promotes
Scientific Research Innovation: Take the Composite Control of the
Permanent Magnet Synchronous Motor as an Example
- Authors: Peng Gao, Liandi Fang, Huihui Pan
  First page: 2602
  Abstract: Intersecting disciplines, as an important trend in the development of modern academic research and education, have exerted a profound and positive influence on scientific research activities. Based on control theory and fractional-order theory, this paper presents a novel approach for the speed regulation of a permanent magnet synchronous motor (PMSM) in the presence of uncertainties and external disturbances. The proposed method is a composite control based on a model-free sliding mode and a fractional-order ultra-local model. The model-free sliding mode is a control strategy that utilizes the sliding mode control methodology without explicitly relying on a mathematical model of the system being controlled. The fractional-order ultra-local model is a mathematical representation of a dynamic system that incorporates the concept of fractional-order derivatives. The core of the controller is a new type of fractional-order fast nonsingular terminal sliding mode surface, which ensures high robustness, quick convergence, while preventing singularity. Moreover, a novel fractional-order nonlinear extended state observer is proposed to estimate both internal and external disturbances of the fractional-order ultra-local model. The stability of the system is analyzed using both the Lyapunov stability theory and the Mittag–Leffler stability theory. The analysis confirms the convergence stability of the closed-loop system under the proposed control scheme. The comparison results indicate that the proposed composite control based on the fractional-order ultra-local model is a promising solution for regulating the speed of PMSMs in the presence of uncertainties and disturbances.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162602
  Issue No: Vol. 12, No. 16 (2024)
Mathematics, Vol. 12, Pages 2603: Defining and Analyzing New Classes
Associated with (λ,γ)-Symmetrical Functions and Quantum
Calculus
- Authors: Hanen Louati, Afrah Y. Al-Rezami, Abdulbasit A. Darem, Fuad Alsarari
  First page: 2603
  Abstract: In this paper, we introduce new classes of functions defined within the open unit disk by integrating the concepts of (λ,γ)-symmetrical functions, generalized Janowski functions, and quantum calculus. We derive a structural formula and a representation theorem for the class Sqλ,γ(x,y,z). Utilizing convolution techniques and quantum calculus, we investigate convolution conditions supported by examples and corollary, establishing sufficient conditions. Additionally, we derive properties related to coefficient estimates, which further elucidate the characteristics of the defined function classes.
  Citation: Mathematics
  PubDate: 2024-08-22
  DOI: 10.3390/math12162603
  Issue No: Vol. 12, No. 16 (2024)

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