Mathematics

24 pages, 621 KiB

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessFeature PaperReview

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 (registering DOI) - 23 Aug 2024

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, 271 KiB

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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, 922 KiB

Open AccessArticle

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

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)

8 pages, 240 KiB

Open AccessFeature PaperArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessArticle

Relations among the Queue-Length Probabilities in the Pre-Arrival, Random, and Post-Departure Epochs in the GI/M^a,b/c Queue

by Jing Gai and Mohan Chaudhry

Mathematics 2024, 12(17), 2609; https://doi.org/10.3390/math12172609 (registering DOI) - 23 Aug 2024

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/M^{$a, b$}/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

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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

Open AccessArticle

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 (registering DOI) - 23 Aug 2024

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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)

25 pages, 9744 KiB

Open AccessArticle

An Improved Spider-Wasp Optimizer for Obstacle Avoidance Path Planning in Mobile Robots

by Yujie Gao, Zhichun Li, Haorui Wang, Yupeng Hu, Haoze Jiang, Xintong Jiang and Dong Chen

Mathematics 2024, 12(17), 2604; https://doi.org/10.3390/math12172604 (registering DOI) - 23 Aug 2024

Viewed by 162

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 [...] Read more.

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. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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Mathematics, Volume 12, Issue 17 (September-1 2024) – 16 articles

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