{"title":"Functional modelling of Telecommunications Data","authors":"Algimantas Birbilas, A. Račkauskas","doi":"10.3846/mma.2022.14043","DOIUrl":"https://doi.org/10.3846/mma.2022.14043","url":null,"abstract":"","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89903057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Inertial Mann-Krasnoselskii Algorithm with Self adaptive stepsize for Split variational Inclusion Problem and paramonotone Equilibria","authors":"L. Jolaoso, A. A. Mebawondu, O. Mewomo","doi":"10.3846/mma.2022.13949","DOIUrl":"https://doi.org/10.3846/mma.2022.13949","url":null,"abstract":"","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85462619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust numerical method for singularly perturbed convection-diffusion Type Problems with non-Local boundary condition","authors":"H. Debela, M. Woldaregay, G. Duressa","doi":"10.3846/mma.2022.14256","DOIUrl":"https://doi.org/10.3846/mma.2022.14256","url":null,"abstract":"","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76061176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The boundary value problem for the steady Navier–Stokes system is considered in a 2D bounded domain with the boundary having a power cusp singularity at the point O. The case of a boundary value with a nonzero flow rate is studied. In this case there is a source/sink in O and the solution necessarily has an infinite Dirichlet integral. The formal asymptotic expansion of the solution near the singular point is constructed and the existence of a solution having this asymptotic decomposition is proved.
{"title":"On singular solutions of the stationary Navier-Stokes System in Power Cusp Domains","authors":"K. Pileckas, A. Raciene","doi":"10.3846/mma.2021.13836","DOIUrl":"https://doi.org/10.3846/mma.2021.13836","url":null,"abstract":"The boundary value problem for the steady Navier–Stokes system is considered in a 2D bounded domain with the boundary having a power cusp singularity at the point O. The case of a boundary value with a nonzero flow rate is studied. In this case there is a source/sink in O and the solution necessarily has an infinite Dirichlet integral. The formal asymptotic expansion of the solution near the singular point is constructed and the existence of a solution having this asymptotic decomposition is proved.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78583154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. D. Goufo, C. Ravichandran, GUNVANT ACHUTRAO BIRAJDAR
Highly applied in machining, image compressing, network traffic prediction, biological dynamics, nerve dendrite pattern and so on, self-similarity dynamic represents a part of fractal processes where an object is reproduced exactly or approximately exact to a part of itself. These reproduction processes are also very important and captivating in chaos theory. They occur naturally in our environment in the form of growth spirals, romanesco broccoli, trees and so on. Seeking alternative ways to reproduce self-similarity dynamics has called the attention of many authors working in chaos theory since the range of applications is quite wide. In this paper, three combined notions, namely the step series switching process, the Julia’s technique and the fractal-fractional dynamic are used to create various forms of self-similarity dynamics in chaotic systems of attractors, initially with two, five and seven scrolls. In each case, the solvability of the model is addressed via numerical techniques and related graphical simulations are provided. It appears that the initial systems are able to trigger a self-similarity process that generates the exact or approximately exact copy of itself or part of itself. Moreover, the dynamics of the copies are impacted by some model’s parameters involved in the process. Using mathematical concepts to re-create features that usually occur in a natural way proves to be a prowess as related applications are many for engineers.
{"title":"Self-Similarity Techniques for Chaotic attractors with Many Scrolls using Step Series switching","authors":"E. D. Goufo, C. Ravichandran, GUNVANT ACHUTRAO BIRAJDAR","doi":"10.3846/mma.2021.13678","DOIUrl":"https://doi.org/10.3846/mma.2021.13678","url":null,"abstract":"Highly applied in machining, image compressing, network traffic prediction, biological dynamics, nerve dendrite pattern and so on, self-similarity dynamic represents a part of fractal processes where an object is reproduced exactly or approximately exact to a part of itself. These reproduction processes are also very important and captivating in chaos theory. They occur naturally in our environment in the form of growth spirals, romanesco broccoli, trees and so on. Seeking alternative ways to reproduce self-similarity dynamics has called the attention of many authors working in chaos theory since the range of applications is quite wide. In this paper, three combined notions, namely the step series switching process, the Julia’s technique and the fractal-fractional dynamic are used to create various forms of self-similarity dynamics in chaotic systems of attractors, initially with two, five and seven scrolls. In each case, the solvability of the model is addressed via numerical techniques and related graphical simulations are provided. It appears that the initial systems are able to trigger a self-similarity process that generates the exact or approximately exact copy of itself or part of itself. Moreover, the dynamics of the copies are impacted by some model’s parameters involved in the process. Using mathematical concepts to re-create features that usually occur in a natural way proves to be a prowess as related applications are many for engineers.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72435655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.
{"title":"On the Maximum number of period annuli for second order conservative equations","authors":"A. Gritsans, Inara Yermachenko","doi":"10.3846/mma.2021.13979","DOIUrl":"https://doi.org/10.3846/mma.2021.13979","url":null,"abstract":"We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79334010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative. The Cauchy problem for fractional differential equations with this type of derivative is discussed and some existence and uniqueness results are proved. We present a Henry-Gronwall type inequality for an integral inequality with the tempered Ψ−fractional integral. This inequality is applied in the proof of an existence theorem. A result on a representation of solutions of linear systems of Ψ−Caputo fractional differential equations is proved and in the last section an example is presented.
{"title":"Differential equations with tempered ψ-Caputo fractional derivative","authors":"M. Medved', Eva Brestovanská","doi":"10.3846/mma.2021.13252","DOIUrl":"https://doi.org/10.3846/mma.2021.13252","url":null,"abstract":"In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative. The Cauchy problem for fractional differential equations with this type of derivative is discussed and some existence and uniqueness results are proved. We present a Henry-Gronwall type inequality for an integral inequality with the tempered Ψ−fractional integral. This inequality is applied in the proof of an existence theorem. A result on a representation of solutions of linear systems of Ψ−Caputo fractional differential equations is proved and in the last section an example is presented.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87785352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we prove the existence of weak solutions for a class of quasilinear parabolic systems, which correspond to diffusion problems, in the form where Ω is a bounded open domain of be given and The function v belongs to is in a moving and dissolving substance, the dissolution is described by f and the motion by g. We prove the existence result by using Galerkin’s approximation and the theory of Young measures.
{"title":"An existence Result for quasilinear parabolic Systems with Lower order Terms","authors":"Farah Balaadich, E. Azroul","doi":"10.3846/mma.2021.13553","DOIUrl":"https://doi.org/10.3846/mma.2021.13553","url":null,"abstract":"In this paper we prove the existence of weak solutions for a class of quasilinear parabolic systems, which correspond to diffusion problems, in the form where Ω is a bounded open domain of be given and The function v belongs to is in a moving and dissolving substance, the dissolution is described by f and the motion by g. We prove the existence result by using Galerkin’s approximation and the theory of Young measures.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77280907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finite-dimensional space via the functional principal component analysis paradigm in the estimation phase. It is then approximated using the estimated functional principal component functions, and the estimated parameter of the quantile regression model is constructed based on the principal component scores. In addition, we propose a Bayesian information criterion to determine the optimum number of truncation constants used in the functional principal component decomposition. Moreover, a stepwise forward procedure and the Bayesian information criterion are used to determine the significant predictors for including in the model. We employ a nonparametric bootstrap procedure to construct prediction intervals for the response functions. The finite sample performance of the proposed method is evaluated via several Monte Carlo experiments and an empirical data example, and the results produced by the proposed method are compared with the ones from existing models. *Postal address: Department of Statistics, Marmara University, Goztepe Campus, 34722, Istanbul, Turkey; Email: ufuk.beyaztas@marmara.edu.tr 1 ar X iv :2 11 1. 05 37 4v 1 [ st at .M E ] 9 N ov 2 02 1
在这项研究中，我们提出了一个函数对函数线性分位数回归模型，允许多个功能预测器建立一个更灵活和稳健的方法。在估计阶段，首先通过功能主成分分析范式将所提出的模型转换为有限维空间。然后利用估计的功能主成分函数对其进行近似，并根据主成分得分构造分位数回归模型的估计参数。此外，我们提出了一个贝叶斯信息准则，以确定在功能主成分分解中使用的截断常数的最佳数量。此外，采用逐步推进的方法和贝叶斯信息准则来确定需要纳入模型的重要预测因子。我们采用非参数自举过程来构造响应函数的预测区间。通过几个蒙特卡罗实验和一个经验数据算例对所提方法的有限样本性能进行了评价，并将所提方法的结果与已有模型的结果进行了比较。*通讯地址:马尔马拉大学统计学系，戈兹特佩校区，34722，土耳其伊斯坦布尔;电子邮件:ufuk.beyaztas@marmara.edu.tr 1 ar X iv:2 1105 37 4v 1 [st at .M E] 9 N ov 2 02 1
{"title":"Function-on-function linear quantile Regression","authors":"U. Beyaztas, H. Shang","doi":"10.3846/mma.2022.14664","DOIUrl":"https://doi.org/10.3846/mma.2022.14664","url":null,"abstract":"In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a finite-dimensional space via the functional principal component analysis paradigm in the estimation phase. It is then approximated using the estimated functional principal component functions, and the estimated parameter of the quantile regression model is constructed based on the principal component scores. In addition, we propose a Bayesian information criterion to determine the optimum number of truncation constants used in the functional principal component decomposition. Moreover, a stepwise forward procedure and the Bayesian information criterion are used to determine the significant predictors for including in the model. We employ a nonparametric bootstrap procedure to construct prediction intervals for the response functions. The finite sample performance of the proposed method is evaluated via several Monte Carlo experiments and an empirical data example, and the results produced by the proposed method are compared with the ones from existing models. *Postal address: Department of Statistics, Marmara University, Goztepe Campus, 34722, Istanbul, Turkey; Email: ufuk.beyaztas@marmara.edu.tr 1 ar X iv :2 11 1. 05 37 4v 1 [ st at .M E ] 9 N ov 2 02 1","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78290049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we improve the existing results in the literature by presenting weaker sufficient conditions for the solvability of a third-order impulsive problem on the half-line, having generalized impulse effects. More precisely, our nonlinearities do not need to be positive nor sublinear and the monotone assumptions are local ones. Our method makes use of some truncation and perturbed techniques and on the equiconvergence at infinity and the impulsive points. The last section contains an application to a boundary layer flow problem over a stretching sheet with and without heat transfer.
{"title":"Third-order generalized discontinuous impulsive Problems on the half-Line","authors":"F. Minhós, Rui Carapinha","doi":"10.3846/mma.2021.12557","DOIUrl":"https://doi.org/10.3846/mma.2021.12557","url":null,"abstract":"In this paper, we improve the existing results in the literature by presenting weaker sufficient conditions for the solvability of a third-order impulsive problem on the half-line, having generalized impulse effects. More precisely, our nonlinearities do not need to be positive nor sublinear and the monotone assumptions are local ones. Our method makes use of some truncation and perturbed techniques and on the equiconvergence at infinity and the impulsive points. The last section contains an application to a boundary layer flow problem over a stretching sheet with and without heat transfer.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74193634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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