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On $ p $-Laplacian Kirchhoff-Schrödinger-Poisson type systems with critical growth on the Heisenberg group 关于Heisenberg群上具有临界增长的$p$-Laplaccian-Kirchhoff-Schrödinger-Poisson型系统
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-08-19 DOI: 10.3934/era.2023292
Shujie Bai, Yueqiang Song, Dušan D. Repovš
{"title":"On $ p $-Laplacian Kirchhoff-Schrödinger-Poisson type systems with critical growth on the Heisenberg group","authors":"Shujie Bai, Yueqiang Song, Dušan D. Repovš","doi":"10.3934/era.2023292","DOIUrl":"https://doi.org/10.3934/era.2023292","url":null,"abstract":"In this article, we investigate the Kirchhoff-Schrödinger-Poisson type systems on the Heisenberg group of the following form:\u0000\u0000 begin{document}$ begin{equation*} left{ begin{array}{lll} {-(a+bint_{Omega}|nabla_{H} u|^{p}dxi)Delta_{H, p}u-muphi |u|^{p-2}u} = lambda |u|^{q-2}u+|u|^{Q^{ast}-2}u &mbox{in} Omega, -Delta_{H}phi = |u|^{p} &mbox{in} Omega, u = phi = 0 &mbox{on} partialOmega, end{array} right. end{equation*} $end{document} \u0000where $ a, b $ are positive real numbers, $ Omegasubset mathbb{H}^N $ is a bounded region with smooth boundary, $ 1 < p < Q $, $ Q = 2N + 2 $ is the homogeneous dimension of the Heisenberg group $ mathbb{H}^N $, $ Q^{ast} = frac{pQ}{Q-p} $, $ qin(2p, Q^{ast}) $ and $ Delta_{H, p}u = mbox{div}(|nabla_{H} u|^{p-2}nabla_{H} u) $ is the $ p $-horizontal Laplacian. Under some appropriate conditions for the parameters $ mu $ and $ lambda $, we establish existence and multiplicity results for the system above. To some extent, we generalize the results of An and Liu (Israel J. Math., 2020) and Liu et al. (Adv. Nonlinear Anal., 2022).","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45149796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fredholm inversion around a singularity: Application to autoregressive time series in Banach space 围绕奇点的Fredholm反演:在Banach空间中自回归时间序列中的应用
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-04-08 DOI: 10.3934/era.2023252
Won-Ki Seo
{"title":"Fredholm inversion around a singularity: Application to autoregressive time series in Banach space","authors":"Won-Ki Seo","doi":"10.3934/era.2023252","DOIUrl":"https://doi.org/10.3934/era.2023252","url":null,"abstract":"This paper considers inverting a holomorphic Fredholm operator pencil. Specifically, we provide necessary and sufficient conditions for the inverse of a holomorphic Fredholm operator pencil to have a simple pole and a second order pole. Based on these results, a closed-form expression of the Laurent expansion of the inverse around an isolated singularity is obtained in each case. As an application, we also obtain a suitable extension of the Granger-Johansen representation theorem for random sequences taking values in a separable Banach space. Due to our closed-form expression of the inverse, we may fully characterize solutions to a given autoregressive law of motion except a term that depends on initial values.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43636274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic optimization model for ship inspection planning under uncertainty in maritime transportation 海上运输不确定条件下船舶检验规划的随机优化模型
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023006
Ran Yan, Ying Yang, Yuquan Du
{"title":"Stochastic optimization model for ship inspection planning under uncertainty in maritime transportation","authors":"Ran Yan, Ying Yang, Yuquan Du","doi":"10.3934/era.2023006","DOIUrl":"https://doi.org/10.3934/era.2023006","url":null,"abstract":"Maritime transportation plays a significant role in international trade and global supply chains. Ship navigation safety is the foundation of operating maritime business smoothly. Recently, more and more attention has been paid to marine environmental protection. To enhance maritime safety and reduce pollution in the marine environment, various regulations and conventions are proposed by international organizations and local governments. One of the most efficient ways of ensuring that the related requirements are complied with by ships is ship inspection by port state control (PSC). In the procedure of ship inspection, a critical issue for the port state is how to select ships of higher risk for inspection and how to optimally allocate the limited inspection resources to these ships. In this study, we adopt prediction and optimization approaches to address the above issues. We first predict the number of ship deficiencies based on a k nearest neighbor (kNN) model. Then, we propose three optimization models which aim for a trade-off between the reward for detected deficiencies and the human resource cost of ship inspection. Specifically, we first follow the predict-then-optimize framework and develop a deterministic optimization model. We also establish two stochastic optimization models where the distribution of ship deficiency number is estimated by the predictive prescription method and the global prescriptive analysis method, respectively. Furthermore, we conduct a case study using inspection data at the Hong Kong port to compare the performances of the three optimization models, from which we conclude that the predictive prescription model is more efficient and effective for this problem.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70243576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A priori bounds and existence of smooth solutions to a $ L_p $ Aleksandrov problem for Codazzi tensor with log-convex measure 具有对数凸测度的Codazzi张量$ L_p $ Aleksandrov问题的先验界和光滑解的存在性
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023042
Zhengmao Chen
{"title":"A priori bounds and existence of smooth solutions to a $ L_p $ Aleksandrov problem for Codazzi tensor with log-convex measure","authors":"Zhengmao Chen","doi":"10.3934/era.2023042","DOIUrl":"https://doi.org/10.3934/era.2023042","url":null,"abstract":"In the present paper, we prove the existence of smooth solutions to a $ L_p $ Aleksandrov problem for Codazzi tensor with a log-convex measure in compact Riemannian manifolds $ (M, g) $ with positive constant sectional curvature under suitable conditions. Our proof is based on the solvability of a Monge-Ampère equation on $ (M, g) $ via the method of continuity whose crucial factor is the a priori bounds of smooth solutions to the Monge-Ampère equation mentioned above. It is worth mentioning that our result can be seen as an extension of the classical $ L_p $ Aleksandrov problem in Euclidian space to the frame of Riemannian manifolds with weighted measures and that our result can also be seen as some attempts to get some new results on geometric analysis for Codazzi tensor.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70243967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Regress 3D human pose from 2D skeleton with kinematics knowledge 利用运动学知识从二维骨架回归三维人体姿态
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023075
Longkui Jiang, Yuru Wang, Weijia Li
{"title":"Regress 3D human pose from 2D skeleton with kinematics knowledge","authors":"Longkui Jiang, Yuru Wang, Weijia Li","doi":"10.3934/era.2023075","DOIUrl":"https://doi.org/10.3934/era.2023075","url":null,"abstract":"3D human pose estimation is a hot topic in the field of computer vision. It provides data support for tasks such as pose recognition, human tracking and action recognition. Therefore, it is widely applied in the fields of advanced human-computer interaction, intelligent monitoring and so on. Estimating 3D human pose from a single 2D image is an ill-posed problem and is likely to cause low prediction accuracy, due to the problems of self-occlusion and depth ambiguity. This paper developed two types of human kinematics to improve the estimation accuracy. First, taking the 2D human body skeleton sequence obtained by the 2D human body pose detector as input, a temporal convolutional network is proposed to develop the movement periodicity in temporal domain. Second, geometrical prior knowledge is introduced into the model to constrain the estimated pose to fit the general kinematics knowledge. The experiments are tested on Human3.6M and MPII (Max Planck Institut Informatik) Human Pose (MPI-INF-3DHP) datasets, and the proposed model shows better generalization ability compared with the baseline and the state-of-the-art models.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An improved fixed-time stabilization problem of delayed coupled memristor-based neural networks with pinning control and indefinite derivative approach 基于固定控制和不定导数方法的延迟耦合记忆电阻神经网络的改进定时镇定问题
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023123
Chao Yang, J. Wu, Zhengyang Qiao
{"title":"An improved fixed-time stabilization problem of delayed coupled memristor-based neural networks with pinning control and indefinite derivative approach","authors":"Chao Yang, J. Wu, Zhengyang Qiao","doi":"10.3934/era.2023123","DOIUrl":"https://doi.org/10.3934/era.2023123","url":null,"abstract":"In this brief, we propose a class of generalized memristor-based neural networks with nonlinear coupling. Based on the set-valued mapping theory, novel Lyapunov indefinite derivative and Memristor theory, the coupled memristor-based neural networks (CMNNs) can achieve fixed-time stabilization (FTS) by designing a proper pinning controller, which randomly controls a small number of neuron nodes. Different from the traditional Lyapunov method, this paper uses the implementation method of indefinite derivative to deal with the non-autonomous neural network system with nonlinear coupling topology between different neurons. The system can obtain stabilization in a fixed time and requires fewer conditions. Moreover, the fixed stable setting time estimation of the system is given through a few conditions, which can eliminate the dependence on the initial value. Finally, we give two numerical examples to verify the correctness of our results.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and multiplicity of positive solutions for one-dimensional $ p $-Laplacian problem with sign-changing weight 一维变权$ p $-拉普拉斯问题正解的存在性和多重性
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023156
Liangying Miao, Man Xu, Zhiqian He
{"title":"Existence and multiplicity of positive solutions for one-dimensional $ p $-Laplacian problem with sign-changing weight","authors":"Liangying Miao, Man Xu, Zhiqian He","doi":"10.3934/era.2023156","DOIUrl":"https://doi.org/10.3934/era.2023156","url":null,"abstract":"In this paper, we show the positive solutions set for one-dimensional $ p $-Laplacian problem with sign-changing weight contains a reversed $ S $-shaped continuum. By figuring the shape of unbounded continuum of positive solutions, we identify the interval of bifurcation parameter in which the $ p $-Laplacian problem has one or two or three positive solutions according to the asymptotic behavior of nonlinear term at 0 and $ infty $. The proof of the main result is based upon bifurcation technique.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
EECHS-ARO: Energy-efficient cluster head selection mechanism for livestock industry using artificial rabbits optimization and wireless sensor networks 基于人工兔子优化和无线传感器网络的畜牧业节能簇头选择机制
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023158
Rajakumar Ramalingam, S. B., Shakila Basheer, Prakash Balasubramanian, Mamoon Rashid, Gitanjali Jayaraman
{"title":"EECHS-ARO: Energy-efficient cluster head selection mechanism for livestock industry using artificial rabbits optimization and wireless sensor networks","authors":"Rajakumar Ramalingam, S. B., Shakila Basheer, Prakash Balasubramanian, Mamoon Rashid, Gitanjali Jayaraman","doi":"10.3934/era.2023158","DOIUrl":"https://doi.org/10.3934/era.2023158","url":null,"abstract":"In the livestock industry, wireless sensor networks (WSNs) play a significant role in monitoring many fauna health statuses and behaviors. Energy preservation in WSNs is considered one of the critical, complicated tasks since the sensors are coupled to constrained resources. Therefore, the clustering approach has proved its efficacy in preserving energy in WSNs. In recent studies, various clustering approaches have been introduced that use optimization techniques to improve the network lifespan by decreasing energy depletion. Yet, they take longer to converge and choose the optimal cluster heads in the network. In addition, the energy is exhausted quickly in the network. This paper introduces a novel optimization technique, i.e., an artificial rabbits optimization algorithm-based energy efficient cluster formation (EECHS-ARO) approach in a WSN, to extend the network lifetime by minimizing the energy consumption rate. The EECHS-ARO technique balances the search process in terms of enriched exploration and exploitation while selecting the optimal cluster heads. The experimentation was carried out on a MATLAB 2021a platform with varying sensor nodes. The obtained results of EECHS-ARO are contrasted with other existing approaches via teaching–learning based optimization algorithm (TLBO), ant lion optimizer (ALO) and quasi oppositional butterfly optimization algorithm (QOBOA). The proposed EECHS-ARO enriches the network lifespan by ~15% and improves the packet delivery ratio by ~5%.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Barycentric rational interpolation method for solving KPP equation 求解KPP方程的质心有理插值法
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023152
Jin Li, Yongling Cheng
{"title":"Barycentric rational interpolation method for solving KPP equation","authors":"Jin Li, Yongling Cheng","doi":"10.3934/era.2023152","DOIUrl":"https://doi.org/10.3934/era.2023152","url":null,"abstract":"In this paper, we seek to solve the Kolmogorov-Petrovskii-Piskunov (KPP) equation by the linear barycentric rational interpolation method (LBRIM). As there are non-linear parts in the KPP equation, three kinds of linearization schemes, direct linearization, partial linearization, Newton linearization, are presented to change the KPP equation into linear equations. With the help of barycentric rational interpolation basis function, matrix equations of three kinds of linearization schemes are obtained from the discrete KPP equation. Convergence rate of LBRIM for solving the KPP equation is also proved. At last, two examples are given to prove the theoretical analysis.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A data-driven on-site injury severity assessment model for car-to-electric-bicycle collisions based on positional relationship and random forest 基于位置关系和随机森林的汽车与电动自行车碰撞现场伤害严重程度评估模型
IF 0.8 4区 数学
Electronic Research Archive Pub Date : 2023-01-01 DOI: 10.3934/era.2023173
Ye Yu, Zhiyuan Liu
{"title":"A data-driven on-site injury severity assessment model for car-to-electric-bicycle collisions based on positional relationship and random forest","authors":"Ye Yu, Zhiyuan Liu","doi":"10.3934/era.2023173","DOIUrl":"https://doi.org/10.3934/era.2023173","url":null,"abstract":"Vulnerable road users (VRUs) are usually more susceptible to fatal injuries. Accurate and rapid assessment of VRU injury severity at the accident scene can provide timely support for decision-making in emergency response. However, evaluating VRU injury severity at the accident scene usually requires medical knowledge and medical devices. Few studies have explored the possibility of using on-site positional relationship to assess injury severity, which could provide a new perspective for on-site transportation professionals to assess accident severity. This study proposes a data-driven on-site injury severity assessment model for car-to-electric-bicycle accidents based on the relationship between the final resting positions of the car, electric bicycle and cyclist at the accident scene. Random forest is employed to learn the accident features from the at-scene positional relationship among accident participants, by which injury severity of the cyclist is assessed. Conditional permutation importance, which can account for correlation among predictor variables, is adopted to reflect the importance of predictor variables more accurately. The proposed model is demonstrated using simulated car-to-electric-bicycle collision data. The results show that the proposed model has good performance in terms of overall accuracy and is balanced in recognizing both fatal and non-fatal accidents. Model performance under partial information confirms that the position information of the electric bicycle is more important than the position information of the cyclist in assessing injury severity.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70245719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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