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Multi-type synchronization of impulsive coupled oscillators via topology degree 通过拓扑度实现脉冲耦合振荡器的多类型同步
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-02-19 DOI: 10.21136/AM.2024.0183-23
Yingjie Bi, Zhidan Cai, Shuai Wang
{"title":"Multi-type synchronization of impulsive coupled oscillators via topology degree","authors":"Yingjie Bi,&nbsp;Zhidan Cai,&nbsp;Shuai Wang","doi":"10.21136/AM.2024.0183-23","DOIUrl":"10.21136/AM.2024.0183-23","url":null,"abstract":"<div><p>The existence of synchronization is an important issue in complex dynamical networks. In this paper, we study the synchronization of impulsive coupled oscillator networks with the aid of rotating periodic solutions of impulsive system. The type of synchronization is closely related to the rotating matrix, which gives an insight for finding various types of synchronization in a united way. We transform the synchronization of impulsive coupled oscillators into the existence of rotating periodic solutions in a relevant impulsive system. Some existence theorems about rotating periodic solutions for a non-homogeneous linear impulsive system and a nonlinear perturbation system are established by topology degree theory. Finally, we give two examples to show synchronization behaviors in impulsive coupled oscillator networks.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"185 - 207"},"PeriodicalIF":0.6,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129490","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
Exploring the impact of post-training rounding in regression models 探索回归模型中训练后舍入的影响
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-02-15 DOI: 10.21136/AM.2024.0090-23
Jan Kalina
{"title":"Exploring the impact of post-training rounding in regression models","authors":"Jan Kalina","doi":"10.21136/AM.2024.0090-23","DOIUrl":"10.21136/AM.2024.0090-23","url":null,"abstract":"<div><p>Post-training rounding, also known as quantization, of estimated parameters stands as a widely adopted technique for mitigating energy consumption and latency in machine learning models. This theoretical endeavor delves into the examination of the impact of rounding estimated parameters in key regression methods within the realms of statistics and machine learning. The proposed approach allows for the perturbation of parameters through an additive error with values within a specified interval. This method is elucidated through its application to linear regression and is subsequently extended to encompass radial basis function networks, multilayer perceptrons, regularization networks, and logistic regression, maintaining a consistent approach throughout.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"257 - 271"},"PeriodicalIF":0.6,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2024.0090-23.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139962630","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
Identification of source term in a nonlinear degenerate parabolic equation with memory 带记忆的非线性退化抛物方程中源项的识别
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-02-07 DOI: 10.21136/AM.2024.0049-23
Soufiane Abid, Khalid Atifi, El-Hassan Essoufi, Abderrahim Zafrar
{"title":"Identification of source term in a nonlinear degenerate parabolic equation with memory","authors":"Soufiane Abid,&nbsp;Khalid Atifi,&nbsp;El-Hassan Essoufi,&nbsp;Abderrahim Zafrar","doi":"10.21136/AM.2024.0049-23","DOIUrl":"10.21136/AM.2024.0049-23","url":null,"abstract":"<div><p>In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers’ type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness of this approach.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"209 - 232"},"PeriodicalIF":0.6,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762732","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 balanced finite-element method for an axisymmetrically loaded thin shell 轴对称加载薄壳的平衡有限元法
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-01-30 DOI: 10.21136/AM.2024.0134-23
Norbert Heuer, Torsten Linss
{"title":"A balanced finite-element method for an axisymmetrically loaded thin shell","authors":"Norbert Heuer,&nbsp;Torsten Linss","doi":"10.21136/AM.2024.0134-23","DOIUrl":"10.21136/AM.2024.0134-23","url":null,"abstract":"<div><p>We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"151 - 168"},"PeriodicalIF":0.6,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2024.0134-23.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761989","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
Development of small and large compressive pulses in two-phase flow 两相流中大小压缩脉冲的发展
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-01-23 DOI: 10.21136/AM.2024.0107-23
Nishi Deepa Palo, Jasobanta Jena, Meera Chadha
{"title":"Development of small and large compressive pulses in two-phase flow","authors":"Nishi Deepa Palo,&nbsp;Jasobanta Jena,&nbsp;Meera Chadha","doi":"10.21136/AM.2024.0107-23","DOIUrl":"10.21136/AM.2024.0107-23","url":null,"abstract":"<div><p>The evolutions of small and large compressive pulses are studied in a two-phase flow of gas and dust particles with a variable azimuthal velocity. The method of relatively undistorted waves is used to study the mechanical pulses of different types in a rotational, axisymmetric dusty gas. The results obtained are compared with that of nonrotating medium. Asymptotic expansion procedure is used to discuss the nonlinear theory of geometrical acoustics. The influence of the solid particles and the rotational effect of the medium on the distortion are investigated. In a rotational flow it is observed that with the increase in the value of rotational parameter, the steepening of the pulses also increases. The presence of dust in the rotational flow delays the onset of shock formation thereby increasing the distance where the shock is formed first. The rotational and the dust parameters are observed to have the same effect on the shock strength.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"233 - 255"},"PeriodicalIF":0.6,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139604710","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
Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph 连通单环图描述矩阵的极值逆特征值问题
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-01-10 DOI: 10.21136/AM.2024.0084-23
Bijoya Bardhan, Mausumi Sen, Debashish Sharma
{"title":"Extremal inverse eigenvalue problem for matrices described by a connected unicyclic graph","authors":"Bijoya Bardhan,&nbsp;Mausumi Sen,&nbsp;Debashish Sharma","doi":"10.21136/AM.2024.0084-23","DOIUrl":"10.21136/AM.2024.0084-23","url":null,"abstract":"<div><p>In this paper, we deal with the construction of symmetric matrix whose corresponding graph is connected and unicyclic using some pre-assigned spectral data. Spectral data for the problem consist of the smallest and the largest eigenvalues of each leading principal submatrices. Inverse eigenvalue problem (IEP) with this set of spectral data is generally known as the extremal IEP. We use a standard scheme of labeling the vertices of the graph, which helps in getting a simple relation between the characteristic polynomials of each leading principal submatrix. Sufficient condition for the existence of the solution is obtained. The proof is constructive, hence provides an algorithmic procedure for finding the required matrix. Furthermore, we provide the condition under which the same problem is solvable when two particular entries of the required matrix satisfy a linear relation.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 2","pages":"273 - 286"},"PeriodicalIF":0.6,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440308","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
Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal scales 具有任意数量空间和时间尺度的单调抛物问题的同质化
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2023-12-18 DOI: 10.21136/AM.2023.0269-22
Tatiana Danielsson, Liselott Flodén, Pernilla Johnsen, Marianne Olsson Lindberg
{"title":"Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal scales","authors":"Tatiana Danielsson,&nbsp;Liselott Flodén,&nbsp;Pernilla Johnsen,&nbsp;Marianne Olsson Lindberg","doi":"10.21136/AM.2023.0269-22","DOIUrl":"10.21136/AM.2023.0269-22","url":null,"abstract":"<div><p>We prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of the scale parameter <i>ε</i>. The main tools for the homogenization procedure are multiscale convergence and very weak multiscale convergence, both adapted to evolution problems.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 1","pages":"1 - 24"},"PeriodicalIF":0.6,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030932","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
Strong convergence for weighted sums of WOD random variables and its application in the EV regression model WOD 随机变量加权和的强收敛性及其在 EV 回归模型中的应用
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2023-12-08 DOI: 10.21136/AM.2023.0004-23
Liwang Ding, Caoqing Jiang
{"title":"Strong convergence for weighted sums of WOD random variables and its application in the EV regression model","authors":"Liwang Ding,&nbsp;Caoqing Jiang","doi":"10.21136/AM.2023.0004-23","DOIUrl":"10.21136/AM.2023.0004-23","url":null,"abstract":"<div><p>The strong convergence for weighted sums of widely orthant dependent (WOD) random variables is investigated. As an application, we further investigate the strong consistency of the least squares estimator in EV regression model for WOD random variables. A simulation study is carried out to confirm the theoretical results.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 1","pages":"93 - 111"},"PeriodicalIF":0.6,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588580","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 block triangular preconditioner for three-by-three block saddle-point problem 三乘三块鞍点问题的新块三角形预处理器
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2023-12-07 DOI: 10.21136/AM.2023.0289-22
Jun Li, Xiangtuan Xiong
{"title":"A new block triangular preconditioner for three-by-three block saddle-point problem","authors":"Jun Li,&nbsp;Xiangtuan Xiong","doi":"10.21136/AM.2023.0289-22","DOIUrl":"10.21136/AM.2023.0289-22","url":null,"abstract":"<div><p>In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties are also discussed. Finally, numerical experiments are provided to show the effectiveness of the NBT preconditioner.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 1","pages":"67 - 91"},"PeriodicalIF":0.6,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138594316","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
Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors 半导体全量子流体力学模型全局解的松弛-时间极限
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2023-11-11 DOI: 10.21136/AM.2023.0039-23
Sungjin Ra, Hakho Hong
{"title":"Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors","authors":"Sungjin Ra,&nbsp;Hakho Hong","doi":"10.21136/AM.2023.0039-23","DOIUrl":"10.21136/AM.2023.0039-23","url":null,"abstract":"<div><p>This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in ℝ<sup>3</sup>, we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into that of the simplified quantum energy-transport model and the quantum drift-diffusion model for the moment relaxation limit, and the moment and energy relaxation limit, respectively.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 1","pages":"113 - 137"},"PeriodicalIF":0.6,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030929","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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