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Multiplicity of Solutions for the Noncooperative Kirchhoff-Type Variable Exponent Elliptic System with Nonlinear Boundary Conditions 具有非线性边界条件的非合作基尔霍夫型变指数椭圆系统解的多重性
Axioms Pub Date : 2024-05-14 DOI: 10.3390/axioms13050325
Yiying Mao, Yang Yang
{"title":"Multiplicity of Solutions for the Noncooperative Kirchhoff-Type Variable Exponent Elliptic System with Nonlinear Boundary Conditions","authors":"Yiying Mao, Yang Yang","doi":"10.3390/axioms13050325","DOIUrl":"https://doi.org/10.3390/axioms13050325","url":null,"abstract":"Considering the solutions of a class of noncooperative Kirchhoff-type p(x)-Laplacian elliptic systems with nonlinear boundary conditions, we derive a sequence of solutions utilizing both the variational method and limit index theory under certain underlying assumptions. The novelty of this study is that we verify the (PS)c* condition using another method, diverging from the approaches cited in the previous literature.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"1 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140980910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A C0 Nonconforming Virtual Element Method for the Kirchhoff Plate Obstacle Problem 针对基尔霍夫板障碍问题的 C0 不符合虚拟元素法
Axioms Pub Date : 2024-05-13 DOI: 10.3390/axioms13050322
Bangmin Wu, Jiali Qiu
{"title":"A C0 Nonconforming Virtual Element Method for the Kirchhoff Plate Obstacle Problem","authors":"Bangmin Wu, Jiali Qiu","doi":"10.3390/axioms13050322","DOIUrl":"https://doi.org/10.3390/axioms13050322","url":null,"abstract":"This paper investigates a novel C0 nonconforming virtual element method (VEM) for solving the Kirchhoff plate obstacle problem, which is described by a fourth-order variational inequality (VI) of the first kind. In our study, we distinguish our approach by introducing new internal degrees of freedom to the traditional lowest-order C0 nonconforming VEM, which originally lacked such degrees. This addition not only facilitates error estimation but also enhances its intuitiveness. Importantly, our novel C0 nonconforming VEM naturally satisfies the constraints of the obstacle problem. We then establish an a priori error estimate for our novel C0 nonconforming VEM, with the result indicating that the lowest order of our method achieves optimal convergence. Finally, we present a numerical example to validate the theoretical result.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"22 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140982679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum Vision Transformers for Quark–Gluon Classification 用于夸克-胶子分类的量子视觉变换器
Axioms Pub Date : 2024-05-13 DOI: 10.3390/axioms13050323
Marçal Comajoan Cara, Gopal Ramesh Dahale, Zhongtian Dong, Roy T. Forestano, S. Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin T. Matchev, Katia Matcheva, Eyup B. Unlu
{"title":"Quantum Vision Transformers for Quark–Gluon Classification","authors":"Marçal Comajoan Cara, Gopal Ramesh Dahale, Zhongtian Dong, Roy T. Forestano, S. Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin T. Matchev, Katia Matcheva, Eyup B. Unlu","doi":"10.3390/axioms13050323","DOIUrl":"https://doi.org/10.3390/axioms13050323","url":null,"abstract":"We introduce a hybrid quantum-classical vision transformer architecture, notable for its integration of variational quantum circuits within both the attention mechanism and the multi-layer perceptrons. The research addresses the critical challenge of computational efficiency and resource constraints in analyzing data from the upcoming High Luminosity Large Hadron Collider, presenting the architecture as a potential solution. In particular, we evaluate our method by applying the model to multi-detector jet images from CMS Open Data. The goal is to distinguish quark-initiated from gluon-initiated jets. We successfully train the quantum model and evaluate it via numerical simulations. Using this approach, we achieve classification performance almost on par with the one obtained with the completely classical architecture, considering a similar number of parameters.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"96 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140984168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-Configurations Derived by Special Arrangements of Lines 通过特殊线条排列得出的准构图
Axioms Pub Date : 2024-05-11 DOI: 10.3390/axioms13050321
Stefano Innamorati
{"title":"Quasi-Configurations Derived by Special Arrangements of Lines","authors":"Stefano Innamorati","doi":"10.3390/axioms13050321","DOIUrl":"https://doi.org/10.3390/axioms13050321","url":null,"abstract":"A quasi-configuration is a point–line incidence structure in which each point is incident with at least three lines and each line is incident with at least three points. We investigate derived quasi-configurations that arise both by duality and intersecting lines of three special arrangements of lines. Sets with few intersection numbers are provided.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"124 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140987172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strategic Behavior and Optimal Inventory Level in a Make-to-Stock Queueing System with Retrial Customers 有复试客户的从生产到入库排队系统中的战略行为和最佳库存水平
Axioms Pub Date : 2024-05-11 DOI: 10.3390/axioms13050319
Yuejiao Wang, Chenguang Cai
{"title":"Strategic Behavior and Optimal Inventory Level in a Make-to-Stock Queueing System with Retrial Customers","authors":"Yuejiao Wang, Chenguang Cai","doi":"10.3390/axioms13050319","DOIUrl":"https://doi.org/10.3390/axioms13050319","url":null,"abstract":"In this article, we consider a make-to-stock queueing system with retrial customers. Upon their arrival, customers make a decision to either join the system or not based on a reward–cost function. If customers join the retrial queue, they become repeat customers. Each repeat customer repeats their demand after an exponential amount of time until they have been successfully served. We explore the equilibrium strategies of customers in both the almost observable and unobservable cases. Furthermore, we also analyze the expected costs of the entire system based on the customers’ behavior in these two cases. Additionally, we determine the optimal inventory levels in both cases through numerical experiments.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 866","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140989171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of the Borell–Brascamp–Lieb Inequality for Multiple Power Concave Functions 多幂凹函数的 Borell-Brascamp-Lieb 不等式的稳定性
Axioms Pub Date : 2024-05-11 DOI: 10.3390/axioms13050320
Meng Qin, Zhuohua Zhang, Rui Luo, Mengjie Ren, Denghui Wu
{"title":"Stability of the Borell–Brascamp–Lieb Inequality for Multiple Power Concave Functions","authors":"Meng Qin, Zhuohua Zhang, Rui Luo, Mengjie Ren, Denghui Wu","doi":"10.3390/axioms13050320","DOIUrl":"https://doi.org/10.3390/axioms13050320","url":null,"abstract":"In this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establish the stability of the Borell–Brascamp–Lieb inequality for multiple power concave functions via relative asymmetry.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"118 36","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140987647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence Results for History-Dependent Variational Inequalities 历史变量不等式的收敛结果
Axioms Pub Date : 2024-05-10 DOI: 10.3390/axioms13050316
M. Sofonea, D. Tarzia
{"title":"Convergence Results for History-Dependent Variational Inequalities","authors":"M. Sofonea, D. Tarzia","doi":"10.3390/axioms13050316","DOIUrl":"https://doi.org/10.3390/axioms13050316","url":null,"abstract":"We consider a history-dependent variational inequality in a real Hilbert space, for which we recall an existence and uniqueness result. We associate this inequality with a gap function, together with two additional problems: a nonlinear equation and a minimization problem. Then, we prove that solving these problems is equivalent to solving the original history-dependent variational inequality. Next, we state and prove a convergence criterion, i.e., we provide necessary and sufficient conditions which guarantee the convergence of a sequence of functions to the solution of the considered inequality. Based on the equivalence above, we deduce various consequences that present some interest on their own, and, moreover, we obtain convergence results for the two additional problems considered. Finally, we apply our abstract results to the study of an inequality problem in solid mechanics. It concerns the study of a viscoelastic constitutive law with long memory and unilateral constraints, for which we deduce a convergence result and provide the corresponding mechanical interpretations.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 30","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140994029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Basic Computational Algorithms for Representing an Aircraft Flight (Calculation of 3D Displacement and Displaying) 表示飞机飞行的基本计算算法（三维位移计算和显示）
Axioms Pub Date : 2024-05-10 DOI: 10.3390/axioms13050313
Adán Ramírez-López
{"title":"Basic Computational Algorithms for Representing an Aircraft Flight (Calculation of 3D Displacement and Displaying)","authors":"Adán Ramírez-López","doi":"10.3390/axioms13050313","DOIUrl":"https://doi.org/10.3390/axioms13050313","url":null,"abstract":"This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to physical and logical theory. Here, the flight is divided into maneuvers and the aircraft conditions are defined as boundary conditions. Then the aircraft position is calculated using nested loops, which execute the calculation procedure at every step time (Δt). The calculation of the aircraft displacement is obtained as a function of the aircraft speed and heading angles. The simulator was created using the C++ programming language, and each part of the algorithm was compiled independently to reduce the source code, allow easy modification, and improve the programming efficiency. Aerial navigation involves very complex phenomena to be considered for an appropriate representation; moreover, in this manuscript, the influence of the mathematical approach to properly represent the aircraft flight is described in detail. The flight simulator was successfully tested by simulating some basic theoretical flights with different maneuvers, which include stationary position, running along the way, take off, and some movements in the airspace. The maximum aircraft speed tested was 120 km/h, the maximum maneuver time was 12 min, and the space for simulation was assumed to be without obstacles. Here, the geometrical description of path and speed is analyzed according to the symmetric and asymmetric results. Finally, an analysis was conducted to evaluate the approach of the numerical methods used; after that, it was possible to confirm that precision increased as the step time was reduced. According to this analysis, no more than 500 steps are required for a good approach in the calculation of the aircraft displacement.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 28","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140994236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments 特定参数下高斯超几何函数的新封闭式公式
Axioms Pub Date : 2024-05-10 DOI: 10.3390/axioms13050317
Yue-Wu Li, Feng Qi
{"title":"A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments","authors":"Yue-Wu Li, Feng Qi","doi":"10.3390/axioms13050317","DOIUrl":"https://doi.org/10.3390/axioms13050317","url":null,"abstract":"In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some specific arguments, successfully apply a special case of the newly extended closed-form formula to derive an alternative form for the Maclaurin power series expansion of the Wilf function, and discover two novel increasing rational approximations to a quarter of the circular constant.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140992179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-Contraction Maps in Subordinate Semimetric Spaces 从属半对称空间中的准收缩映射
Axioms Pub Date : 2024-05-10 DOI: 10.3390/axioms13050318
Areej Alharbi, Hamed Alsulami, Maha Noorwali
{"title":"Quasi-Contraction Maps in Subordinate Semimetric Spaces","authors":"Areej Alharbi, Hamed Alsulami, Maha Noorwali","doi":"10.3390/axioms13050318","DOIUrl":"https://doi.org/10.3390/axioms13050318","url":null,"abstract":"Throughout this study, we discuss the subordinate Pompeiu–Hausdorff metric (SPHM) in subordinate semimetric spaces. Moreover, we present a well-behaved quasi-contraction (WBQC) to solve quasi-contraction (QC) problems in subordinate semimetric spaces under some local constraints. Furthermore, we provide examples to support our conclusion.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 79","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140991618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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