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Mathematics
Volume 12
Issue 17
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Mathematics, Volume 12, Issue 17 (September-1 2024) – 31 articles

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22 pages, 3200 KiB  
Article
A Semi-Supervised Active Learning Method for Structured Data Enhancement with Small Samples
by Fangling Leng, Fan Li, Wei Lv, Yubin Bao, Xiaofeng Liu, Tiancheng Zhang and Ge Yu
Mathematics 2024, 12(17), 2634; https://doi.org/10.3390/math12172634 (registering DOI) - 24 Aug 2024
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), [...] Read more.
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. Full article
(This article belongs to the Section Mathematics and Computer Science)
21 pages, 1585 KiB  
Article
Advances in Structural Health Monitoring: Bio-Inspired Optimization Techniques and Vision-Based Monitoring System for Damage Detection Using Natural Frequency
by Minkyu Jung, Jiyeon Koo and Andrew Jaeyong Choi
Mathematics 2024, 12(17), 2633; https://doi.org/10.3390/math12172633 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
(This article belongs to the Section Computational and Applied Mathematics)
17 pages, 1208 KiB  
Article
Optimization Method of Mine Ventilation Network Regulation Based on Mixed-Integer Nonlinear Programming
by Lixue Wen, Deyun Zhong, Lin Bi, Liguan Wang and Yulong Liu
Mathematics 2024, 12(17), 2632; https://doi.org/10.3390/math12172632 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
23 pages, 341 KiB  
Article
On the Equivalence between Differential and Integral Forms of Caputo-Type Fractional Problems on Hölder Spaces
by Mieczysław Cichoń, Hussein A. H. Salem and Wafa Shammakh
Mathematics 2024, 12(17), 2631; https://doi.org/10.3390/math12172631 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Fractional Differential Equations, Inclusions and Inequalities with Applications II)
12 pages, 456 KiB  
Article
Fuzzy Evaluation Model for Operational Performance of Air Cleaning Equipment
by Kuen-Suan Chen, Tsun-Hung Huang, Chun-Min Yu and Hui-E Lee
Mathematics 2024, 12(17), 2630; https://doi.org/10.3390/math12172630 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Numbers, Fuzzy Modeling, and Their Applications in Management and Engineering, 2nd Edition)
21 pages, 491 KiB  
Article
Identification of Time-Wise Thermal Diffusivity, Advection Velocity on the Free-Boundary Inverse Coefficient Problem
by M. S. Hussein, Taysir E. Dyhoum, S. O. Hussein and Mohammed Qassim
Mathematics 2024, 12(17), 2629; https://doi.org/10.3390/math12172629 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
14 pages, 266 KiB  
Article
Hodge Decomposition of Conformal Vector Fields on a Riemannian Manifold and Its Applications
by Hanan Alohali, Sharief Deshmukh, Bang-Yen Chen and Hemangi Madhusudan Shah
Mathematics 2024, 12(17), 2628; https://doi.org/10.3390/math12172628 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)
29 pages, 7553 KiB  
Article
Optimizing Electric Vehicle (EV) Charging with Integrated Renewable Energy Sources: A Cloud-Based Forecasting Approach for Eco-Sustainability
by Mohammad Aldossary, Hatem A. Alharbi and Nasir Ayub
Mathematics 2024, 12(17), 2627; https://doi.org/10.3390/math12172627 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
(This article belongs to the Section Mathematics and Computer Science)
23 pages, 363 KiB  
Article
Operational Calculus for the 1st-Level General Fractional Derivatives and Its Applications
by Maryam Alkandari and Yuri Luchko
Mathematics 2024, 12(17), 2626; https://doi.org/10.3390/math12172626 (registering DOI) - 24 Aug 2024
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, [...] Read more.
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. Full article
22 pages, 1962 KiB  
Article
Quantum-Fuzzy Expert Timeframe Predictor for Post-TAVR Monitoring
by Lilia Tightiz and Joon Yoo
Mathematics 2024, 12(17), 2625; https://doi.org/10.3390/math12172625 (registering DOI) - 24 Aug 2024
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. [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances in Quantum Computing and Applications)
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12 pages, 962 KiB  
Article
An Approximation of the Prime Counting Function and a New Representation of the Riemann Zeta Function
by Timothy Ganesan
Mathematics 2024, 12(17), 2624; https://doi.org/10.3390/math12172624 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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%. Full article
17 pages, 682 KiB  
Article
A Non-Relativistic 2D Quantum System and Its Thermo-Magnetic Properties with a Generalized Pseudo-Harmonic Oscillator
by Haifa I. Alrebdi, Akpan N. Ikot, Ridha Horchani and Uduakobong S. Okorie
Mathematics 2024, 12(17), 2623; https://doi.org/10.3390/math12172623 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
(This article belongs to the Section Mathematical Physics)
20 pages, 4004 KiB  
Article
Study on Ground Motion Amplification in Upper Arch Bridge Due to “W”-Type Deep Canyon Using Boundary-Integral and Peak Frequency Shift Methods
by Yi Liu, Chenhao Zhou and Sihong Huang
Mathematics 2024, 12(17), 2622; https://doi.org/10.3390/math12172622 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
30 pages, 374 KiB  
Article
On General Alternating Tornheim-Type Double Series
by Kwang-Wu Chen
Mathematics 2024, 12(17), 2621; https://doi.org/10.3390/math12172621 (registering DOI) - 24 Aug 2024
Abstract
In this paper, we express ∑n,m≥1ε1nε2mMn(u)Mm(v)nrms(n+m)t as a linear combination of alternating [...] Read more.
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. Full article
15 pages, 297 KiB  
Article
Sorting Permutations on an n − Broom
by Ranjith Rajesh, Rajan Sundaravaradhan and Bhadrachalam Chitturi
Mathematics 2024, 12(17), 2620; https://doi.org/10.3390/math12172620 (registering DOI) - 24 Aug 2024
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Graph Theory: Advanced Algorithms and Applications)
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24 pages, 621 KiB  
Article
The Impact of Digital Economy on TFP of Industries: Empirical Analysis Based on the Extension of Schumpeterian Model to Complex Economic Systems
by Jiaqi Liu, Yiyang Cheng, Yamei Fu and Fei Xue
Mathematics 2024, 12(17), 2619; https://doi.org/10.3390/math12172619 - 23 Aug 2024
Viewed by 188
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advance in Control Theory and Optimization)
20 pages, 566 KiB  
Article
Numerical Solution of the Cauchy Problem for the Helmholtz Equation Using Nesterov’s Accelerated Method
by Syrym E. Kasenov, Aigerim M. Tleulesova, Ainur E. Sarsenbayeva and Almas N. Temirbekov
Mathematics 2024, 12(17), 2618; https://doi.org/10.3390/math12172618 - 23 Aug 2024
Viewed by 181
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 [...] Read more.
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. Full article
(This article belongs to the Section Computational and Applied Mathematics)
29 pages, 633 KiB  
Review
Review about the Permutation Approach in Hypothesis Testing
by Stefano Bonnini, Getnet Melak Assegie and Kamila Trzcinska
Mathematics 2024, 12(17), 2617; https://doi.org/10.3390/math12172617 - 23 Aug 2024
Viewed by 155
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
15 pages, 286 KiB  
Article
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
by Abdelbaki Choucha, Salah Boulaaras, Ali Allahem, Asma Alharbi and Rashid Jan
Mathematics 2024, 12(17), 2616; https://doi.org/10.3390/math12172616 - 23 Aug 2024
Viewed by 182
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 [...] Read more.
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. Full article
21 pages, 2387 KiB  
Article
The Multi-Objective Shortest Path Problem with Multimodal Transportation for Emergency Logistics
by Jinzuo Guo, Hongbin Liu, Tianyu Liu, Guopeng Song and Bo Guo
Mathematics 2024, 12(17), 2615; https://doi.org/10.3390/math12172615 - 23 Aug 2024
Viewed by 167
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 [...] Read more.
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. Full article
58 pages, 553 KiB  
Article
Global Existence of Solutions to a Free Boundary Problem for Viscous Incompressible Magnetohydrodynamics for Small Data
by Piotr Kacprzyk and Wojciech M. Zaja̧czkowski
Mathematics 2024, 12(17), 2614; https://doi.org/10.3390/math12172614 - 23 Aug 2024
Viewed by 174
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics with Applications)
15 pages, 579 KiB  
Article
The Wiener Process with a Random Non-Monotone Hazard Rate-Based Drift
by Luis Alberto Rodríguez-Picón, Luis Carlos Méndez-González, Luis Asunción Pérez-Domínguez and Héctor Eduardo Tovanche-Picón
Mathematics 2024, 12(17), 2613; https://doi.org/10.3390/math12172613 - 23 Aug 2024
Viewed by 186
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Reliability Analysis and Stochastic Models in Reliability Engineering)
14 pages, 1628 KiB  
Article
Integrating Sensor Embeddings with Variant Transformer Graph Networks for Enhanced Anomaly Detection in Multi-Source Data
by Fanjie Meng, Liwei Ma, Yixin Chen, Wangpeng He, Zhaoqiang Wang and Yu Wang
Mathematics 2024, 12(17), 2612; https://doi.org/10.3390/math12172612 (registering DOI) - 23 Aug 2024
Viewed by 184
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Application of Machine Learning and Data Mining, 2nd Edition)
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8 pages, 240 KiB  
Article
Revisiting a Classic Identity That Implies the Rogers–Ramanujan Identities III
by Hei-Chi Chan
Mathematics 2024, 12(17), 2611; https://doi.org/10.3390/math12172611 - 23 Aug 2024
Viewed by 203
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Recent Advances on Ramanujan Theories in Mathematics and Physics)
27 pages, 1997 KiB  
Article
Robust a Posteriori Error Estimates of Time-Dependent Poisson–Nernst–Planck Equations
by Keli Fu and Tingting Hao
Mathematics 2024, 12(17), 2610; https://doi.org/10.3390/math12172610 - 23 Aug 2024
Viewed by 214
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 [...] Read more.
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. Full article
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8 pages, 264 KiB  
Article
Relations among the Queue-Length Probabilities in the Pre-Arrival, Random, and Post-Departure Epochs in the GI/Ma,b/c Queue
by Jing Gai and Mohan Chaudhry
Mathematics 2024, 12(17), 2609; https://doi.org/10.3390/math12172609 - 23 Aug 2024
Viewed by 198
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/M [...] Read more.
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. Full article
(This article belongs to the Special Issue New Advances in Applied Probability and Stochastic Processes)
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21 pages, 851 KiB  
Article
Quasi-Periodic and Periodic Vibration Responses of an Axially Moving Beam under Multiple-Frequency Excitation
by Xinru Fang, Lingdi Huang, Zhimei Lou and Yuanbin Wang
Mathematics 2024, 12(17), 2608; https://doi.org/10.3390/math12172608 - 23 Aug 2024
Viewed by 203
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances in Computational Solid Mechanics and Scientific Computing)
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13 pages, 466 KiB  
Article
EdgePose: An Edge Attention Network for 6D Pose Estimation
by Qi Feng, Jian Nong and Yanyan Liang
Mathematics 2024, 12(17), 2607; https://doi.org/10.3390/math12172607 - 23 Aug 2024
Viewed by 272
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods, Machine Learning and Deep Learning Based Applications, 2nd Edition)
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16 pages, 2312 KiB  
Article
Enhanced Scattering by Wearable Objects in Wireless Power Transfer Links: Case Studies
by Ludovica Tognolatti, Cristina Ponti and Giuseppe Schettini
Mathematics 2024, 12(17), 2606; https://doi.org/10.3390/math12172606 - 23 Aug 2024
Viewed by 241
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 2nd Edition)
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11 pages, 282 KiB  
Article
Majorization Problem for q-General Family of Functions with Bounded Radius Rotations
by Kanwal Jabeen, Afis Saliu, Jianhua Gong and Saqib Hussain
Mathematics 2024, 12(17), 2605; https://doi.org/10.3390/math12172605 - 23 Aug 2024
Viewed by 229
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory)
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