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A note on eigenvalue of tensors and its application 张量的特征值及其应用
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-09-16 DOI: 10.21136/AM.2025.0022-25
Snigdhashree Nayak, Krushnachandra Panigrahy, Debasisha Mishra, Nachiketa Mishra
{"title":"A note on eigenvalue of tensors and its application","authors":"Snigdhashree Nayak,&nbsp;Krushnachandra Panigrahy,&nbsp;Debasisha Mishra,&nbsp;Nachiketa Mishra","doi":"10.21136/AM.2025.0022-25","DOIUrl":"10.21136/AM.2025.0022-25","url":null,"abstract":"<div><p>The tensor eigenvalue problem has been widely studied in recent years. In this paper, several new properties of eigenvalues and determinants of tensors are explored. We also proposed a formula to compute the determinant of a tensor as a mimic of the matrix determinant. The Perron-Frobenius theorem, one of the most important results in non-negative matrix theory, is proposed for the class of non-negative tensors in the Einstein product framework. Further, the power method, a widely used matrix iterative method for finding the largest eigenvalue, is framed for tensors using the Einstein product. The proposed higher-order power method is applied to calculate the largest eigenvalue of the Laplacian tensors associated with hyper-stars and hyper-trees. The numerical results show that the higher-order power method with the Einstein product is stable.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 4","pages":"563 - 594"},"PeriodicalIF":0.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271565","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
A weighted hybrid conjugate gradient method for unconstrained multiobjective optimization problems 无约束多目标优化问题的加权混合共轭梯度法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-09-11 DOI: 10.21136/AM.2025.0040-25
Yunchol Jong, Wonchol Hwang, Yungwang Rim
{"title":"A weighted hybrid conjugate gradient method for unconstrained multiobjective optimization problems","authors":"Yunchol Jong,&nbsp;Wonchol Hwang,&nbsp;Yungwang Rim","doi":"10.21136/AM.2025.0040-25","DOIUrl":"10.21136/AM.2025.0040-25","url":null,"abstract":"<div><p>We propose a weighted HS (Hestenes-Stiefel)-FR (Fletcher-Reeves) hybrid conjugate gradient method for unconstrained multiobjective optimization problem, in which a new positive coefficient of the multiobjective steepest descent direction is adaptively updated to keep its positiveness. The method takes advantage of a weighted hybrid of our modified HS and FR parameters and under the Armijo-type backtracking line search, it has global convergence to a Pareto critical point (point satisfying the first-order necessary condition for Pareto optimality) without convexity assumption on the objectives. Numerical experiments show that the practical performance of the method is competitive with the existing methods such as conjugate gradient method, steepest descent method, Newton method, and quasi-Newton method for unconstrained multiobjective optimization.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 4","pages":"537 - 561"},"PeriodicalIF":0.7,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271592","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
Notes on number of one-troughed travelling waves in asymmetrically supported bending beam 非对称支承弯曲梁中单槽行波数的注记
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-08-11 DOI: 10.21136/AM.2025.0035-25
Hana Formánková Levá, Gabriela Holubová
{"title":"Notes on number of one-troughed travelling waves in asymmetrically supported bending beam","authors":"Hana Formánková Levá,&nbsp;Gabriela Holubová","doi":"10.21136/AM.2025.0035-25","DOIUrl":"10.21136/AM.2025.0035-25","url":null,"abstract":"<div><p>We study the boundary value problem for nonlinear fourth-order partial differential equation with jumping nonlinearity which can serve, e.g., as a model of an asymmetrically supported bending beam. We focus on a special type of solutions, the so-called one-troughed travelling waves. The main goal of this paper is to show the existence of at least two different one-troughed travelling waves for particular wave speeds and input parameters of the studied problem. We present the upper bounds for the maximal number of one-troughed solutions together with a visualisation of obtained results and corresponding solutions. Finally, we list several open questions regarding this topic.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 4","pages":"457 - 472"},"PeriodicalIF":0.7,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271562","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
Shape analysis and comparison of audio patterns using divergence measures 形状分析和使用发散测量音频模式的比较
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-08-07 DOI: 10.21136/AM.2025.0093-25
Amit Vishwakarma, K. S. Subrahamanian Moosath
{"title":"Shape analysis and comparison of audio patterns using divergence measures","authors":"Amit Vishwakarma,&nbsp;K. S. Subrahamanian Moosath","doi":"10.21136/AM.2025.0093-25","DOIUrl":"10.21136/AM.2025.0093-25","url":null,"abstract":"<div><p>We represent the point clouds of objects and audio signals as manifolds of Gaussian Mixture Models, and analyze the shape variation and compare the audio patterns using three divergence measures, namely the Kullback-Leibler Divergence, Jensen-Shannon Divergence, and Modified Symmetric Kullback-Leibler Divergence. Experiments are conducted on basic geometric shapes, 3D human body shapes, animal shapes, point clouds of the same object produced from the dense point clouds in the PU-GAN (Point Cloud Upsampling Adversarial Network) dataset. Then, we present a method to generate a point cloud of an audio signal using the Short-Time Fourier Transform. The audio-derived point clouds represent frequency, time, and magnitude relationships, enabling analysis of speech and audio patterns. The results across all datasets show that the Modified Symmetric Kullback-Leibler Divergence provides the most distinct and stable comparison between different point clouds, demonstrating its robustness for point cloud comparison.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 4","pages":"473 - 493"},"PeriodicalIF":0.7,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271563","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
A new numerical method for solving neuro-cognitive models via Chebyshev deep neural network (CDNN) 基于Chebyshev深度神经网络（CDNN）求解神经认知模型的一种新的数值方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-07-14 DOI: 10.21136/AM.2025.0082-24
Kimia Mohammadi Mohammadi, Maryam Babaei, Zeinab Hajimohammadi, Kourosh Parand
{"title":"A new numerical method for solving neuro-cognitive models via Chebyshev deep neural network (CDNN)","authors":"Kimia Mohammadi Mohammadi,&nbsp;Maryam Babaei,&nbsp;Zeinab Hajimohammadi,&nbsp;Kourosh Parand","doi":"10.21136/AM.2025.0082-24","DOIUrl":"10.21136/AM.2025.0082-24","url":null,"abstract":"<div><p>One of the fundamental applications of artificial neural networks is solving Partial Differential Equations (PDEs) which has been considered in this paper. We have created an effective method by combining the spectral methods and multi-layer perceptron to solve Generalized Fitzhugh-Nagumo (GFHN) equation. In this method, we have used Chebyshev polynomials as activation functions of the multi-layer perceptron. In order to solve PDEs, independent variables, which are collocation points, have been used as input dataset. Furthermore, the loss function has been constructed from the residual of the equation and its boundary condition. Minimizing the loss function has adjusted the appropriate values for the parameters of the network. Hence, the network has shown an outstanding performance not only on the training dataset but also on the unseen data. Some numerical examples and a comparison between the results of our proposed method and other existing approaches have been provided to show the efficiency and accuracy of the proposed method. For this purpose different cases such as linear, nonlinear and multi dimensional equations are considered.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 4","pages":"517 - 535"},"PeriodicalIF":0.7,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271566","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
Qualitative analysis of HAART effects on HIV and SARS-CoV-2 coinfection model HAART对HIV和SARS-CoV-2共感染模型的定性分析
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-07-11 DOI: 10.21136/AM.2025.0280-24
João Paulo Simões Maurício de Carvalho
{"title":"Qualitative analysis of HAART effects on HIV and SARS-CoV-2 coinfection model","authors":"João Paulo Simões Maurício de Carvalho","doi":"10.21136/AM.2025.0280-24","DOIUrl":"10.21136/AM.2025.0280-24","url":null,"abstract":"<div><p>HIV is known for causing the destruction of the immune system by affecting different types of cells, while SARS-CoV-2 is an extremely contagious virus that leads to the development of COVID-19. Understanding how these two viruses interact in coinfected individuals is essential, especially in populations under antiretroviral treatment. In this study, we develop and analyze a novel mathematical model capturing the coinfection dynamics of HIV and SARS-CoV-2 under the influence of highly active antiretroviral therapy (HAART). In contrast to previous models, our formulation includes the effect of HAART on both infections and derives the basic reproduction numbers for each virus. We prove that transcritical bifurcations occur when the basic reproduction numbers cross the threshold value of 1, and we establish the conditions for stability of the disease-free equilibria. Numerical simulations show that HAART, although designed to control HIV, also reduces SARS-CoV-2 proliferation in coinfected hosts, which, as far as we know, has not been fully addressed in previous models in the literature. These findings reveal a potentially beneficial indirect effect of antiretroviral therapy on SARS-CoV-2 dynamics, offering new theoretical insights into the control of viral coinfections.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 4","pages":"495 - 516"},"PeriodicalIF":0.7,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2025.0280-24.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145271564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies 负能量Orlicz-Sobolev中涉及临界增长的kirchhoff型方程的无穷多解
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-06-24 DOI: 10.21136/AM.2025.0059-25
Elmostafa Bendib, Mustapha Khiddi
{"title":"Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies","authors":"Elmostafa Bendib,&nbsp;Mustapha Khiddi","doi":"10.21136/AM.2025.0059-25","DOIUrl":"10.21136/AM.2025.0059-25","url":null,"abstract":"<div><p>We investigate a class of Kirchhoff-type equations characterized by critical growth within Orlicz-Sobolev spaces. The main result establishes the existence of infinitely many solutions with negative energy. Using an adapted concentration-compactness principle and advanced variational methods, we overcome key challenges such as non-compactness and non-differentiability to the associated functionals. This work extends existing results to more general functional spaces, offering new insights into nonlocal nonlinear equations.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"441 - 456"},"PeriodicalIF":0.7,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169373","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
H∞ analysis of cooperative multi-agent systems by adaptive interpolation 基于自适应插值的协同多智能体系统H∞分析
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-06-17 DOI: 10.21136/AM.2025.0218-24
Zoran Tomljanović
{"title":"H∞ analysis of cooperative multi-agent systems by adaptive interpolation","authors":"Zoran Tomljanović","doi":"10.21136/AM.2025.0218-24","DOIUrl":"10.21136/AM.2025.0218-24","url":null,"abstract":"<div><p>We consider a projection-based model reduction approach to computing the maximal impact, one agent or a group of agents has on the cooperative system. As a criterion for measuring the agent-team impact on multi-agent systems, we use the <i>H</i><sub>∞</sub> norm, and output synchronization is taken as the underlying cooperative control scheme. We investigate a projection-based model reduction approach that allows efficient <i>H</i><sub>∞</sub> norm calculation. The convergence of this approach depends on initial interpolation points, so we present approaches to their determination. Since the analysis of multi-agent systems is important from different perspectives, several comparisons are presented in the section on numerical experiments. A graph Laplacian matrix of an inter-agent interaction graph is a foundational element in modeling and analyzing multi-agent systems. We consider various graph topology matrices, system parameters, and excitations of different agents. Different strategies for selecting initial interpolation points are also compared with baseline approaches for calculating the <i>H</i><sub>∞</sub> norm.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"367 - 386"},"PeriodicalIF":0.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166458","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
Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part I: L2 stability 网络上交通流的类godunov数值流的不连续伽辽金方法。第一部分：L2稳定性
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-06-12 DOI: 10.21136/AM.2025.0017-25
Lukáš Vacek, Chi-Wang Shu, Václav Kučera
{"title":"Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part I: L2 stability","authors":"Lukáš Vacek,&nbsp;Chi-Wang Shu,&nbsp;Václav Kučera","doi":"10.21136/AM.2025.0017-25","DOIUrl":"10.21136/AM.2025.0017-25","url":null,"abstract":"<div><p>We study the stability of a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks. We discretize the Lighthill-Whitham-Richards equations on each road by DG. At traffic junctions, we consider two types of numerical fluxes that are based on Godunov’s numerical flux derived in a previous work of ours. These fluxes are easily constructible for any number of incoming and outgoing roads, respecting the drivers’ preferences. The analysis is split into two parts: in Part I, contained in this paper, we analyze the stability of the resulting numerical scheme in the <i>L</i><sup>2</sup>-norm. The resulting estimates allow for a linear-in-time growth of the square of the <i>L</i><sup>2</sup>-norm of the DG solution. This is observed in numerical experiments in certain situations with traffic congestions. Next, we prove that under certain assumptions on the junction parameters (number of incoming and outgoing roads and drivers’ preferences) the DG solution satisfies an entropy inequality where the square entropy is nonincreasing in time. Numerical experiments are presented. The work is complemented by the followup paper, Part II, where a maximum principle is proved for the DG scheme with limiters.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"311 - 339"},"PeriodicalIF":0.7,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164618","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
Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part II: Maximum principle 网络上交通流的类godunov数值流的不连续伽辽金方法。第二部分：最大原则
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-06-12 DOI: 10.21136/AM.2025.0018-25
Lukáš Vacek, Chi-Wang Shu, Václav Kučera
{"title":"Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part II: Maximum principle","authors":"Lukáš Vacek,&nbsp;Chi-Wang Shu,&nbsp;Václav Kučera","doi":"10.21136/AM.2025.0018-25","DOIUrl":"10.21136/AM.2025.0018-25","url":null,"abstract":"<div><p>We prove the maximum principle for a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks described by the Lighthill-Whitham-Richards equations. The paper is a followup of the preceding paper, Part I, where <i>L</i><sup><i>2</i></sup> stability of the scheme is analyzed. At traffic junctions, we consider numerical fluxes based on Godunov’s flux derived in our previous work. We also construct a new Godunov-like numerical flux taking into account right of way at the junction to cover a wider variety of scenarios in the analysis. These fluxes are easily constructible for any number of incoming and outgoing roads, respecting the drivers’ preferences. We prove that the explicit Euler or SSP DG scheme with limiters satisfies a maximum principle on general networks. Numerical experiments demonstrate the obtained results.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"341 - 366"},"PeriodicalIF":0.7,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164619","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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