Journal Description
Mathematics
Mathematics
is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.9 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Sections: published in 13 topical sections.
- Companion journals for Mathematics include: Foundations, AppliedMath, Analytics, International Journal of Topology, Geometry and Logics.
Impact Factor:
2.4 (2022);
5-Year Impact Factor:
2.3 (2022)
Latest Articles
Deformation Prediction Model of Existing Tunnel Structures with Equivalent Layered Method–Peck Coupled under Multiple Factors
Mathematics 2024, 12(10), 1479; https://doi.org/10.3390/math12101479 - 9 May 2024
Abstract
The existing tunnel structure, the new underpass tunnel structure and the rock strata in the area of influence of the crossover tunnel are interacting systems that are affected by various factors, such as dynamic and static excavation loads and dynamic and static train
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The existing tunnel structure, the new underpass tunnel structure and the rock strata in the area of influence of the crossover tunnel are interacting systems that are affected by various factors, such as dynamic and static excavation loads and dynamic and static train loads. The existing theoretical models for the deformation prediction of existing tunnels lack the synergistic analysis of dynamic and static loads on both existing and new tunnels. Based on the theory of the current layer method and Peck’s empirical formula, this paper considers the stiffness of existing tunnels, the stiffness of new tunnels, the loads of excavation methods and the loads of existing tunnels. The results show that a theoretical model for the prediction of the deformation of double-lane highway tunnels underneath existing railroad tunnels with the coupling of the current layer method and Peck under multiple factors is constructed; a modified Peck settlement formula for the base plate of the existing tunnels is put forward; and, through numerical calculations and monitoring data for validation and optimization, it is proved that the theoretical model is applicable to the excavation of tunnels underneath mountainous areas mined by the blasting method.
Full article
Open AccessArticle
Enhancing Robustness in Precast Modular Frame Optimization: Integrating NSGA-II, NSGA-III, and RVEA for Sustainable Infrastructure
by
Andrés Ruiz-Vélez , José García, Julián Alcalá and Víctor Yepes
Mathematics 2024, 12(10), 1478; https://doi.org/10.3390/math12101478 - 9 May 2024
Abstract
The advancement toward sustainable infrastructure presents complex multi-objective optimization (MOO) challenges. This paper expands the current understanding of design frameworks that balance cost, environmental impacts, social factors, and structural integrity. Integrating MOO with multi-criteria decision-making (MCDM), the study targets enhancements in life cycle
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The advancement toward sustainable infrastructure presents complex multi-objective optimization (MOO) challenges. This paper expands the current understanding of design frameworks that balance cost, environmental impacts, social factors, and structural integrity. Integrating MOO with multi-criteria decision-making (MCDM), the study targets enhancements in life cycle sustainability for complex engineering projects using precast modular road frames. Three advanced evolutionary algorithms—NSGA-II, NSGA-III, and RVEA—are optimized and deployed to address sustainability objectives under performance constraints. The efficacy of these algorithms is gauged through a comparative analysis, and a robust MCDM approach is applied to nine non-dominated solutions, employing SAW, FUCA, TOPSIS, PROMETHEE, and VIKOR decision-making techniques. An entropy theory-based method ensures systematic, unbiased criteria weighting, augmenting the framework’s capacity to pinpoint designs balancing life cycle sustainability. The results reveal that NSGA-III is the algorithm converging towards the most cost-effective solutions, surpassing NSGA-II and RVEA by 21.11% and 10.07%, respectively, while maintaining balanced environmental and social impacts. The RVEA achieves up to 15.94% greater environmental efficiency than its counterparts. The analysis of non-dominated solutions identifies the design, utilizing 35 MPa concrete and B500S steel, as the most sustainable alternative across 80% of decision-making algorithms. The ranking correlation coefficients above 0.94 demonstrate consistency among decision-making techniques, underscoring the robustness of the integrated MOO and MCDM framework. The results in this paper expand the understanding of the applicability of novel techniques for enhancing engineering practices and advocate for a comprehensive strategy that employs advanced MOO algorithms and MCDM to enhance sustainable infrastructure development.
Full article
(This article belongs to the Special Issue Combinatorial Optimization and Applications)
Open AccessArticle
Bifurcation Analysis of a Class of Two-Delay Lotka–Volterra Predation Models with Coefficient-Dependent Delay
by
Xiuling Li and Haotian Fan
Mathematics 2024, 12(10), 1477; https://doi.org/10.3390/math12101477 - 9 May 2024
Abstract
In this paper, a class of two-delay differential equations with coefficient-dependent delay is studied. The distribution of the roots of the eigenequation is discussed, and conditions for the stability of the internal equilibrium and the existence of Hopf bifurcation are obtained. Additionally, using
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In this paper, a class of two-delay differential equations with coefficient-dependent delay is studied. The distribution of the roots of the eigenequation is discussed, and conditions for the stability of the internal equilibrium and the existence of Hopf bifurcation are obtained. Additionally, using the normal form method and the central manifold theory, the bifurcation direction and the stability for the periodic solution of Hopf bifurcation are calculated. Finally, the correctness of the theory is verified by numerical simulation.
Full article
Open AccessArticle
Optimal Unmanned Combat System-of-Systems Reconstruction Strategy with Heterogeneous Cost via Deep Reinforcement Learning
by
Ruozhe Li, Hao Yuan, Bangbang Ren, Xiaoxue Zhang, Tao Chen and Xueshan Luo
Mathematics 2024, 12(10), 1476; https://doi.org/10.3390/math12101476 - 9 May 2024
Abstract
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The unmanned combat system-of-systems (UCSoS) in modern warfare is comprised of various interconnected entities that work together to support mission accomplishment. The soaring number of entities makes the UCSoS fragile and susceptible to triggering cascading effects when exposed to uncertain disturbances such as
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The unmanned combat system-of-systems (UCSoS) in modern warfare is comprised of various interconnected entities that work together to support mission accomplishment. The soaring number of entities makes the UCSoS fragile and susceptible to triggering cascading effects when exposed to uncertain disturbances such as attacks or failures. Reconfiguring the UCSoS to restore its effectiveness in a self-coordinated and adaptive manner based on the battlefield situation and operational requirements has attracted increasing attention. In this paper, we focus on the UCSoS reconstruction with heterogeneous costs, where the collaboration nodes may have different reconstruction costs. Specifically, we adopt the heterogeneous network to capture the interdependencies among combat entities and propose a more representative metric to evaluate the UCSoS reconstruction effectiveness. Next, we model the combat network reconstruction problem with heterogeneous costs as a nonlinear optimization problem and prove its NP-hardness. Then, we propose an approach called SoS-Restorer, which is based on deep reinforcement learning (DRL), to address the UCSoS reconstruction problem. The results show that SoS-Restorer can quickly generate reconstruction strategies and improve the operational capabilities of the UCSoS by about 20∼60% compared to the baseline algorithm. Furthermore, even when the size of the UCSoS exceeds that of the training data, SoS-Restorer exhibits robust generalization capability and can efficiently produce satisfactory results in real time.
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Open AccessFeature PaperArticle
An Ad Hoc Procedure for Testing Serial Correlation in Spatial Fixed-Effects Panels
by
Giovanni Millo
Mathematics 2024, 12(10), 1475; https://doi.org/10.3390/math12101475 - 9 May 2024
Abstract
We consider testing for error persistence in spatial panels with (potentially correlated) individual heterogeneity. We propose two variants of an ad hoc testing procedure based on first transforming out the individual effects, either by time-demeaning or by taking forward orthogonal deviations, then estimating
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We consider testing for error persistence in spatial panels with (potentially correlated) individual heterogeneity. We propose two variants of an ad hoc testing procedure based on first transforming out the individual effects, either by time-demeaning or by taking forward orthogonal deviations, then estimating an encompassing spatio-temporal model. The procedure can also be employed under the random effects assumption, in which case, although suboptimal, it can be computationally cheaper and safer than existing tests. We report Monte Carlo simulations demonstrating satisfactory empirical properties.
Full article
(This article belongs to the Special Issue Mathematical Economics and Spatial Econometrics)
Open AccessArticle
Dynamics Behavior of a Predatorg-Prey Diffusion Model Incorporating Hunting Cooperation and Predator-Taxis
by
Huisen Zhang
Mathematics 2024, 12(10), 1474; https://doi.org/10.3390/math12101474 - 9 May 2024
Abstract
In this paper, we consider a predator-prey diffusion model incorporating hunting cooperation and predator-taxis. Firstly, we establish the global existence of a classical solution for the model in any spatial dimension. Secondly, we analyze the stability/instability caused by predator-taxis, and we observe that
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In this paper, we consider a predator-prey diffusion model incorporating hunting cooperation and predator-taxis. Firstly, we establish the global existence of a classical solution for the model in any spatial dimension. Secondly, we analyze the stability/instability caused by predator-taxis, and we observe that predator-taxis play a key role in inducing stability changes. Specifically, if the positive equilibrium is stable for the corresponding reaction-diffusion model, the attractive predator-taxis can further stabilize the system, while the repulsive predator-taxis may lead to a change in spatial stability, if the positive equilibrium is unstable for the corresponding reaction-diffusion model, the attractive predator-taxis makes the model remain unstable, while the repulsive predator-taxis has a stabilizing effect. Finally, numerical simulations are employed to validate the obtained results.
Full article
Open AccessArticle
Kernel-Based Multivariate Nonparametric CUSUM Multi-Chart for Detection of Abrupt Changes
by
Lei Qiao and Bing Wang
Mathematics 2024, 12(10), 1473; https://doi.org/10.3390/math12101473 - 9 May 2024
Abstract
In many cases, it is difficult to obtain precise distributional information on multivariate sequences. Therefore, there is a need to propose nonparametric methods for monitoring multivariate sequences. This article discusses the multivariate change detection problem and utilizes the kernel function as the statistic
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In many cases, it is difficult to obtain precise distributional information on multivariate sequences. Therefore, there is a need to propose nonparametric methods for monitoring multivariate sequences. This article discusses the multivariate change detection problem and utilizes the kernel function as the statistic to construct the nonparametric Multivariate Cumulative Sum multi-chart, under the assumption that there is prior information about the abrupt changes. Through theoretical and numerical analysis, we show that the proposed control chart is more effective compared to other existing control charts. The good monitoring effect of this method demonstrates a strong potential for application.
Full article
(This article belongs to the Special Issue Advances in Statistical Process Monitoring and Wavelet Analysis)
Open AccessArticle
A Net Present Value Analysis of Opportunity-Based Age Replacement Models in Discrete Time
by
Jing Wu, Cunhua Qian and Tadashi Dohi
Mathematics 2024, 12(10), 1472; https://doi.org/10.3390/math12101472 - 9 May 2024
Abstract
Two important opportunistic age replacement models, under replacement first and last disciplines, are generalized in discrete time. The net present value (NPV) is applied to formulate the expected total costs. The priority of multiple replacement options is considered to classify the cost model
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Two important opportunistic age replacement models, under replacement first and last disciplines, are generalized in discrete time. The net present value (NPV) is applied to formulate the expected total costs. The priority of multiple replacement options is considered to classify the cost model with discounting into six cases. Since the NPV method accurately calculates the expected replacement costs over an infinite horizon in an unstable economic environment, we discuss some optimal opportunistic age replacement policies which minimize the expected total discounted costs over an infinite time horizon. Furthermore, we formulate a unified model under each discipline, merging six discrete time replacement models with probabilistic priority. Finally, a case study on optimal replacement first and last policies for pole air switches in a Japanese power company is presented.
Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics)
Open AccessArticle
Fixed-Time Adaptive Event-Triggered Guaranteed Performance Tracking Control of Nonholonomic Mobile Robots under Asymmetric State Constraints
by
Kairui Chen, Yixiang Gu, Weicong Huang, Zhonglin Zhang, Zian Wang and Xiaofeng Wang
Mathematics 2024, 12(10), 1471; https://doi.org/10.3390/math12101471 - 9 May 2024
Abstract
A fixed-time adaptive guaranteed performance tracking control is investigated for a category of nonholonomic mobile robots (NMRs) under asymmetric state constraints. For the sake of favorable transient and steady-state properties of the system, a prescribed performance function (PPF) is introduced and a transform
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A fixed-time adaptive guaranteed performance tracking control is investigated for a category of nonholonomic mobile robots (NMRs) under asymmetric state constraints. For the sake of favorable transient and steady-state properties of the system, a prescribed performance function (PPF) is introduced and a transform function is further constructed. Based on the backstepping technique, an asymmetric barrier Lyapunov function is formulated to ensure the tracking errors converge within a human-specified time. On the foundation of this, the occupation of communication channel is effectively reduced by assigning an event-triggered mechanism (ETM) with relative threshold to the process of controller design. By utilizing the proposed control strategy, the NMR is capable of implementing the enemy dislodging mission while the enemy can always be caught by the NMR and the collision would never be presented. Finally, two simulation experiments are given to verify the effectiveness of the proposed scheme.
Full article
Open AccessArticle
Slime Mould Algorithm Based on a Gaussian Mutation for Solving Constrained Optimization Problems
by
Gauri Thakur, Ashok Pal, Nitin Mittal, Asha Rajiv and Rohit Salgotra
Mathematics 2024, 12(10), 1470; https://doi.org/10.3390/math12101470 - 9 May 2024
Abstract
The slime mould algorithm may not be enough and tends to trap into local optima, low population diversity, and suffers insufficient exploitation when real-world optimization problems become more complex. To overcome the limitations of SMA, the Gaussian mutation (GM) with a novel strategy
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The slime mould algorithm may not be enough and tends to trap into local optima, low population diversity, and suffers insufficient exploitation when real-world optimization problems become more complex. To overcome the limitations of SMA, the Gaussian mutation (GM) with a novel strategy is proposed to enhance SMA and it is named as SMA-GM. The GM is used to increase population diversity, which helps SMA come out of local optima and retain a robust local search capability. Additionally, the oscillatory parameter is updated and incorporated with GM to set the balance between exploration and exploitation. By using a greedy selection technique, this study retains an optimal slime mould position while ensuring the algorithm’s rapid convergence. The SMA-GM performance was evaluated by using unconstrained, constrained, and CEC2022 benchmark functions. The results show that the proposed SMA-GM has a more robust capacity for global search, improved stability, a faster rate of convergence, and the ability to solve constrained optimization problems. Additionally, the Wilcoxon rank sum test illustrates that there is a significant difference between the optimization outcomes of SMA-GM and each compared algorithm. Furthermore, the engineering problem such as industrial refrigeration system (IRS), optimal operation of the alkylation unit problem, welded beam and tension/compression spring design problem are solved, and results prove that the proposed algorithm has a better optimization efficiency to reach the optimum value.
Full article
(This article belongs to the Section Mathematics and Computer Science)
Open AccessArticle
New Properties of Analytic Functions
by
Hatun Özlem Güney and Shigeyoshi Owa
Mathematics 2024, 12(10), 1469; https://doi.org/10.3390/math12101469 - 9 May 2024
Abstract
In the present paper, we consider the class of functions of the form that are analytic in the open unit disc If for then is given by For such functions some interesting properties for subordinations and strongly starlike functions are given. Also, some interesting examples for the results are shown.
Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
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Open AccessArticle
Birth–Death Processes with Two-Type Catastrophes
by
Junping Li
Mathematics 2024, 12(10), 1468; https://doi.org/10.3390/math12101468 - 9 May 2024
Abstract
This paper concentrates on the general birth–death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth–death processes with two-type catastrophes is successfully expressed with the Laplace transform of transition probability function of the birth–death processes without
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This paper concentrates on the general birth–death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth–death processes with two-type catastrophes is successfully expressed with the Laplace transform of transition probability function of the birth–death processes without catastrophe. The first effective catastrophe occurrence time is considered. The Laplace transform of its probability density function, expectation and variance are obtained.
Full article
(This article belongs to the Special Issue Probability, Statistics and Random Processes)
Open AccessArticle
Multi-Camera Multi-Vehicle Tracking Guided by Highway Overlapping FoVs
by
Hongkai Zhang, Ruidi Fang, Suqiang Li, Qiqi Miao, Xinggang Fan, Jie Hu and Sixian Chan
Mathematics 2024, 12(10), 1467; https://doi.org/10.3390/math12101467 - 9 May 2024
Abstract
Multi-Camera Multi-Vehicle Tracking (MCMVT) is a critical task in Intelligent Transportation Systems (ITS). Differently to in urban environments, challenges in highway tunnel MCMVT arise from the changing target scales as vehicles traverse the narrow tunnels, intense light exposure within the tunnels, high similarity
[...] Read more.
Multi-Camera Multi-Vehicle Tracking (MCMVT) is a critical task in Intelligent Transportation Systems (ITS). Differently to in urban environments, challenges in highway tunnel MCMVT arise from the changing target scales as vehicles traverse the narrow tunnels, intense light exposure within the tunnels, high similarity in vehicle appearances, and overlapping camera fields of view, making highway MCMVT more challenging. This paper presents an MCMVT system tailored for highway tunnel roads incorporating road topology structures and the overlapping camera fields of view. The system integrates a Cascade Multi-Level Multi-Target Tracking strategy (CMLM), a trajectory refinement method (HTCF) based on road topology structures, and a spatio-temporal constraint module (HSTC) considering highway entry–exit flow in overlapping fields of view. The CMLM strategy exploits phased vehicle movements within the camera’s fields of view, addressing such challenges as those presented by fast-moving vehicles and appearance variations in long tunnels. The HTCF method filters static traffic signs in the tunnel, compensating for detector imperfections and mitigating the strong lighting effects caused by the tunnel lighting. The HSTC module incorporates spatio-temporal constraints designed for accurate inter-camera trajectory matching within overlapping fields of view. Experiments on the proposed Highway Surveillance Traffic (HST) dataset and CityFlow dataset validate the system’s effectiveness and robustness, achieving an IDF1 score of 81.20% for the HST dataset.
Full article
(This article belongs to the Special Issue Advances in Computer Vision and Machine Learning, 2nd Edition)
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Open AccessArticle
Vehicle Collaborative Partial Offloading Strategy in Vehicular Edge Computing
by
Ruoyu Chen, Yanfang Fan, Shuang Yuan and Yanbo Hao
Mathematics 2024, 12(10), 1466; https://doi.org/10.3390/math12101466 - 9 May 2024
Abstract
Vehicular Edge Computing (VEC) is a crucial application of Mobile Edge Computing (MEC) in vehicular networks. In VEC networks, the computation tasks of vehicle terminals (VTs) can be offloaded to nearby MEC servers, overcoming the limitations of VTs’ processing power and reducing latency
[...] Read more.
Vehicular Edge Computing (VEC) is a crucial application of Mobile Edge Computing (MEC) in vehicular networks. In VEC networks, the computation tasks of vehicle terminals (VTs) can be offloaded to nearby MEC servers, overcoming the limitations of VTs’ processing power and reducing latency caused by distant cloud communication. However, a mismatch between VTs’ demanding tasks and MEC servers’ limited resources can overload MEC servers, impacting Quality of Service (QoS) for computationally intensive tasks. Additionally, vehicle mobility can disrupt communication with static MEC servers, further affecting VTs’ QoS. To address these challenges, this paper proposes a vehicle collaborative partial computation offloading model. This model allows VTs to offload tasks to two types of service nodes: collaborative vehicles and MEC servers. Factors like a vehicle’s mobility, remaining battery power, and available computational power are also considered when evaluating its suitability for collaborative offloading. Furthermore, we design a deep reinforcement learning-based strategy for collaborative partial computation offloading that minimizes overall task delay while meeting individual latency constraints. Experimental results demonstrate that compared to traditional approaches without vehicle collaboration, this scheme significantly reduces latency and achieves a significant reduction (around 2%) in the failure rate under tighter latency constraints.
Full article
(This article belongs to the Special Issue Privacy-Preserving Techniques in AI, Blockchain and Cloud Systems with Formal Mathematical Analysis)
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Open AccessArticle
Asymptotic Analysis of an Elastic Layer under Light Fluid Loading
by
Sheeru Shamsi and Ludmila Prikazchikova
Mathematics 2024, 12(10), 1465; https://doi.org/10.3390/math12101465 - 9 May 2024
Abstract
Asymptotic analysis for an elastic layer under light fluid loading was developed. The ratio of fluid and solid densities was chosen as the main small parameter determining a novel scaling. The leading- and next-order approximations were derived from the full dispersion relation corresponding
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Asymptotic analysis for an elastic layer under light fluid loading was developed. The ratio of fluid and solid densities was chosen as the main small parameter determining a novel scaling. The leading- and next-order approximations were derived from the full dispersion relation corresponding to long-wave, low-frequency, antisymmetric motions. The asymptotic plate models, including the equations of motion and the impenetrability condition, motivated by the aforementioned shortened dispersion equations, were derived for a plane-strain setup. The key findings included, in particular, the necessity of taking into account transverse plate inertia at the leading order, which is not the case for heavy fluid loading. In addition, the transverse shear deformation, rotation inertia, and a number of other corrections appeared at the next order, contrary to the previous asymptotic developments for fluid-loaded plates not assuming a light fluid loading scenario.
Full article
(This article belongs to the Special Issue Multiscale Mathematical Modeling)
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Open AccessArticle
Improved Analytic Learned Iterative Shrinkage Thresholding Algorithm and Its Application to Tomographic Synthetic Aperture Radar Building Object Height Inversion
by
Weiqiu Liang, Jiying Liu and Jubo Zhu
Mathematics 2024, 12(10), 1464; https://doi.org/10.3390/math12101464 - 9 May 2024
Abstract
Tomographic Synthetic Aperture Radar (TomoSAR) building object height inversion is a sparse reconstruction problem that utilizes the data obtained from several spacecraft passes to invert the scatterer position in the height direction. In practical applications, the number of passes is often small, and
[...] Read more.
Tomographic Synthetic Aperture Radar (TomoSAR) building object height inversion is a sparse reconstruction problem that utilizes the data obtained from several spacecraft passes to invert the scatterer position in the height direction. In practical applications, the number of passes is often small, and the observation data are also small due to the objective conditions, so this study focuses on the inversion under the restricted observation data conditions. The Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA) is a kind of deep unfolding network algorithm, which is a combination of the Iterative Shrinkage Thresholding Algorithm (ISTA) and deep learning technology, and it has the advantages of both. The ALISTA is one of the representative algorithms for TomoSAR building object height inversion. However, the structure of the ALISTA algorithm is simple, which has neither the excellent connection structure of a deep learning network nor the acceleration format combined with the ISTA algorithm. Therefore, this study proposes two directions of improvement for the ALISTA algorithm: firstly, an improvement in the inter-layer connection of the network by introducing a connection similar to residual networks obtains the Extragradient Analytic Learned Iterative Shrinkage Thresholding Algorithm (EALISTA) and further proves that the EALISTA achieves linear convergence; secondly, there is an improvement in the iterative format of the intra-layer iteration of the network by introducing the Nesterov momentum acceleration, which obtains the Fast Analytic Learned Iterative Shrinkage Thresholding Algorithm (FALISTA). We first performed inversion experiments on simulated data, which verified the effectiveness of the two proposed algorithms. Then, we conducted TomoSAR building object height inversion experiments on limited measured data and used the deviation metric P to measure the robustness of the algorithms to invert under restricted observation data. The results show that both proposed algorithms have better robustness, which verifies the superior performance of the two algorithms. In addition, we further analyze how to choose the most suitable algorithms for inversion in engineering practice applications based on the results of the experiments on measured data.
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(This article belongs to the Section Engineering Mathematics)
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Open AccessArticle
Automatic Design of Energy-Efficient Dispatching Rules for Multi-Objective Dynamic Flexible Job Shop Scheduling Based on Dual Feature Weight Sets
by
Binzi Xu, Kai Xu, Baolin Fei, Dengchao Huang, Liang Tao and Yan Wang
Mathematics 2024, 12(10), 1463; https://doi.org/10.3390/math12101463 - 9 May 2024
Abstract
Considering the requirements of the actual production scheduling process, the utilization of the genetic programming hyper-heuristic (GPHH) approach to automatically design dispatching rules (DRs) has recently emerged as a popular optimization approach. However, the decision objects and decision environments for routing and sequencing
[...] Read more.
Considering the requirements of the actual production scheduling process, the utilization of the genetic programming hyper-heuristic (GPHH) approach to automatically design dispatching rules (DRs) has recently emerged as a popular optimization approach. However, the decision objects and decision environments for routing and sequencing decisions are different in the dynamic flexible job shop scheduling problem (DFJSSP), leading to different required feature information. Traditional algorithms that allow these two types of scheduling decisions to share one common feature set are not conducive to the further optimization of the evolved DRs, but instead introduce redundant and unnecessary search attempts for algorithm optimization. To address this, some related studies have focused on customizing the feature sets for both routing and sequencing decisions through feature selection when solving single-objective problems. While being effective in reducing the search space, the selected feature sets also diminish the diversity of the obtained DRs, ultimately impacting the optimization performance. Consequently, this paper proposes an improved GPHH with dual feature weight sets for the multi-objective energy-efficient DFJSSP, which includes two novel feature weight measures and one novel hybrid population adjustment strategy. Instead of selecting suitable features, the proposed algorithm assigns appropriate weights to the features based on their multi-objective contribution, which could provide directional guidance to the GPHH while ensuring the search space. Experimental results demonstrate that, compared to existing studies, the proposed algorithm can significantly enhance the optimization performance and interpretability of energy-efficient DRs.
Full article
(This article belongs to the Topic AI and Data-Driven Advancements in Industry 4.0)
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Open AccessArticle
Uniqueness of Single Peak Solutions for a Kirchhoff Equation
by
Junhao Lv, Shichao Yi and Bo Sun
Mathematics 2024, 12(10), 1462; https://doi.org/10.3390/math12101462 - 8 May 2024
Abstract
We deal with the following singular perturbation Kirchhoff equation:
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We deal with the following singular perturbation Kirchhoff equation: where constants and . In this paper, we prove the uniqueness of the concentrated solutions under some suitable assumptions on asymptotic behaviors of and its first derivatives by using a type of Pohozaev identity for a small enough . To some extent, our result exhibits a new phenomenon for a kind of which allows for different orders in different directions.
Full article
(This article belongs to the Section Difference and Differential Equations)
Open AccessArticle
Modeling, Analysis and Evaluation of a Novel Compact 6-DoF 3-RRRS Needle Biopsy Robot
by
Jiangnan Wang, Ruiqi Xiang, Jindong Xiang, Baichuan Wang, Xiyun Wu, Mingzhen Cai, Zhijie Pan, Mengtang Li and Xun Li
Mathematics 2024, 12(10), 1461; https://doi.org/10.3390/math12101461 - 8 May 2024
Abstract
Robot-assisted surgical systems have been widely applied for minimally invasive needle biopsies thanks to their excellent accuracy and superior stability compared to manual surgical operations, which lead to possible fatigue and misoperation due to long procedures. Current needle biopsy robots are normally customed
[...] Read more.
Robot-assisted surgical systems have been widely applied for minimally invasive needle biopsies thanks to their excellent accuracy and superior stability compared to manual surgical operations, which lead to possible fatigue and misoperation due to long procedures. Current needle biopsy robots are normally customed designed for specific application scenarios, and only position-level kinematics are derived, preventing advanced speed control or singularity analysis. As a step forward, this paper aims to design a universal needle biopsy robot platform which features 6 DoF 3-RRRS (Revolute–Revolute–Revolute–Spherical) parallel structure. The analytical solutions to its nonlinear kinematic problems, including forward kinematics, inverse kinematics, and differential kinematics are derived, allowing fast and accurate feedback control calculations. A multibody simulation platform and a first-generation prototype are established next to provide comprehensive verifications for the derived robotic model. Finally, simulated puncture experiments are carried out to illustrate the effectiveness of the proposed method.
Full article
(This article belongs to the Special Issue Mathematical Modeling in Nonlinear Control and Robotics)
Open AccessArticle
Fixed Point Results for Compatible Mappings in Extended Parametric Sb-Metric Spaces
by
Sunil Beniwal, Naveen Mani, Rahul Shukla and Amit Sharma
Mathematics 2024, 12(10), 1460; https://doi.org/10.3390/math12101460 - 8 May 2024
Abstract
This study aims to establish common fixed point theorems for a pair of compatible self-mappings within the framework of extended parametric -metric spaces. To support our assertions, we provide corollaries and examples accompanied with graphical representations. Moreover, we leverage our principal
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This study aims to establish common fixed point theorems for a pair of compatible self-mappings within the framework of extended parametric -metric spaces. To support our assertions, we provide corollaries and examples accompanied with graphical representations. Moreover, we leverage our principal outcome to guarantee the existence of a common solution to a system of integral equations.
Full article
(This article belongs to the Special Issue Novel Approaches in Fuzzy Sets and Metric Spaces)
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New Trends on Boundary Value Problems
Guest Editors: Miklós Rontó, András Rontó, Nino Partsvania, Bedřich Půža, Hriczó KrisztiánDeadline: 31 May 2024
Special Issue in
Mathematics
Applications of Fuzzy Modeling in Risk Management
Guest Editors: Edit Toth-Laufer, László PokorádiDeadline: 20 June 2024
Special Issue in
Mathematics
Computational Statistical Methods and Extreme Value Theory
Guest Editor: Frederico CaeiroDeadline: 30 June 2024
Topical Collections
Topical Collection in
Mathematics
Topology and Foundations
Collection Editors: Lorentz Jäntschi, Dušanka Janežič
Topical Collection in
Mathematics
Multiscale Computation and Machine Learning
Collection Editors: Eric Chung, Yalchin Efendiev
Topical Collection in
Mathematics
Theoretical and Mathematical Ecology
Collection Editor: Yuri V. Tyutyunov