Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.13
Mohamed Mellah, A. Hakem
"In this paper we discuss the global existence and the asymptotic behavior of solutions of an initial boundary value problem of a non-linear wave equation of Kirchhoff type. "
"本文讨论了基尔霍夫型非线性波方程初始边界值问题解的全局存在性和渐近行为。"
{"title":"Existence and asymptotic behavior of solutions for non-linear wave equations of Kirchhoff type with viscoelasticity","authors":"Mohamed Mellah, A. Hakem","doi":"10.24193/mathcluj.2023.2.13","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.13","url":null,"abstract":"\"In this paper we discuss the global existence and the asymptotic behavior of solutions of an initial boundary value problem of a non-linear wave equation of Kirchhoff type. \"","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139272977","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}
Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.04
Chabane Bedjguelel, Hacene Gharout, Bakir Farhi
In this work, we study the dynamics of the Weibull model in dimension one, represented by the Weibull function with three parameters. The positive fixed points have been studied and implicitly expressed in terms of the Lambert W-function as well as the existence and stability conditions. We deduce that this Weibull function defines an Allee function for certain parameter values. Numerical simulations have been presented to illustrate the theoretical results.
在这项工作中，我们研究了维度为一的 Weibull 模型的动力学，该模型由带三个参数的 Weibull 函数表示。我们研究了正定点，并用兰伯特 W 函数以及存在性和稳定性条件隐式地表达了这些定点。我们推断出，该 Weibull 函数定义了特定参数值下的阿利函数。为了说明理论结果，我们进行了数值模拟。
{"title":"Dynamics analysis of the Weibull model","authors":"Chabane Bedjguelel, Hacene Gharout, Bakir Farhi","doi":"10.24193/mathcluj.2023.2.04","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.04","url":null,"abstract":"In this work, we study the dynamics of the Weibull model in dimension one, represented by the Weibull function with three parameters. The positive fixed points have been studied and implicitly expressed in terms of the Lambert W-function as well as the existence and stability conditions. We deduce that this Weibull function defines an Allee function for certain parameter values. Numerical simulations have been presented to illustrate the theoretical results.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139271469","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}
Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.02
B. Allahverdiev, H. Tuna
"In this paper, we investigate nonlinear fourth-order dynamic equations on unbounded time scales. The existence and uniqueness of the solutions for these problems are obtained."
"在本文中，我们研究了无界时间尺度上的非线性四阶动态方程。得出了这些问题解的存在性和唯一性"。
{"title":"Nonlinear fourth-order dynamic equations on unbounded time scales","authors":"B. Allahverdiev, H. Tuna","doi":"10.24193/mathcluj.2023.2.02","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.02","url":null,"abstract":"\"In this paper, we investigate nonlinear fourth-order dynamic equations on unbounded time scales. The existence and uniqueness of the solutions for these problems are obtained.\"","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139272641","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}
Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.10
Ahmad Delfan, A. Mirmostafaee
"The aim of this paper is to extend some results on the Baire category in generalized topological spaces. We will apply the Banach-Mazur game to characterize Baireness in generalized topological spaces. Moreover, we will introduce a new separation axiom for generalized topological spaces which provides opportunity to generalize the Banach category theorem for locally compact generalized topological spaces."
{"title":"Some results on Baireness in generalized topological spaces","authors":"Ahmad Delfan, A. Mirmostafaee","doi":"10.24193/mathcluj.2023.2.10","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.10","url":null,"abstract":"\"The aim of this paper is to extend some results on the Baire category in generalized topological spaces. We will apply the Banach-Mazur game to characterize Baireness in generalized topological spaces. Moreover, we will introduce a new separation axiom for generalized topological spaces which provides opportunity to generalize the Banach category theorem for locally compact generalized topological spaces.\"","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139275566","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}
Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.08
Iulia-Elena Chiru, S. Crivei
We use our recent results on von Neumann regular matrices, strongly regular matrices and matrices having a non-zero outer inverse to derive applications to some generalizations of these concepts, called von Neumann local, strongly von Neumann local and outer von Neumann local matrices. Among other properties, we show that the $t^{rm th}$ compound matrix of every matrix of determinantal rank $t$ over a commutative local ring is strongly von Neumann local, and every matrix over an arbitrary semiperfect ring is outer von Neumann local.
{"title":"Von Neumann local matrices","authors":"Iulia-Elena Chiru, S. Crivei","doi":"10.24193/mathcluj.2023.2.08","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.08","url":null,"abstract":"We use our recent results on von Neumann regular matrices, strongly regular matrices and matrices having a non-zero outer inverse to derive applications to some generalizations of these concepts, called von Neumann local, strongly von Neumann local and outer von Neumann local matrices. Among other properties, we show that the $t^{rm th}$ compound matrix of every matrix of determinantal rank $t$ over a commutative local ring is strongly von Neumann local, and every matrix over an arbitrary semiperfect ring is outer von Neumann local.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139274938","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}
Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.09
Subhasis Das
"For a given polynomial p(z) =a_{n}z^{n}+a_{n-1}z^{n-1}+cdots +a_{1}z+a_{0} of degree n with complex coefficients, the Cauchy radius r_{0} is a unique positive root of the equation |a_{n}| t^{n}-(|a_{n-1}|t^{n-1}+|a_{n-2}| t^{n-2}+ ... +|a_{1}| t+ |a_{0}|) =0. It refers to a radius of the circular region |z|<= r_{0} in which all the zeros of p(z) lie. The basic aim has been to determine the smallest radius, thereby, minimizing the area of the circular region. In this present paper, we have obtained a result which gives an improvement of the Cauchy radius. Also, we produce an annular region whose center is different from the origin in which the zeros of p(z) lie. Moreover, in many cases, our results give better approximations for estimating the region of polynomial zeros than that obtained from many other well-known results."
{"title":"An improvement of Cauchy radius for the zeros of a polynomial","authors":"Subhasis Das","doi":"10.24193/mathcluj.2023.2.09","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.09","url":null,"abstract":"\"For a given polynomial p(z) =a_{n}z^{n}+a_{n-1}z^{n-1}+cdots +a_{1}z+a_{0} of degree n with complex coefficients, the Cauchy radius r_{0} is a unique positive root of the equation |a_{n}| t^{n}-(|a_{n-1}|t^{n-1}+|a_{n-2}| t^{n-2}+ ... +|a_{1}| t+ |a_{0}|) =0. It refers to a radius of the circular region |z|<= r_{0} in which all the zeros of p(z) lie. The basic aim has been to determine the smallest radius, thereby, minimizing the area of the circular region. In this present paper, we have obtained a result which gives an improvement of the Cauchy radius. Also, we produce an annular region whose center is different from the origin in which the zeros of p(z) lie. Moreover, in many cases, our results give better approximations for estimating the region of polynomial zeros than that obtained from many other well-known results.\"","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139274164","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}
Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.01
Adimasu Ateneh Tilahun
In this paper we prove that the maximal operator of Cesaro-means for one-dimensional Fourier series on the group of 2-adic integers is of weak type (L^{1}, L^{1}). Moreover, we prove the almost everywhere convergence of Cesaro means of integrable functions.
{"title":"Almost everywhere convergence of varying-parameter setting Cesaro means of Fourier series on the group of 2-adic integers","authors":"Adimasu Ateneh Tilahun","doi":"10.24193/mathcluj.2023.2.01","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.01","url":null,"abstract":"In this paper we prove that the maximal operator of Cesaro-means for one-dimensional Fourier series on the group of 2-adic integers is of weak type (L^{1}, L^{1}). Moreover, we prove the almost everywhere convergence of Cesaro means of integrable functions.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139271376","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}
Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.06
B. Boudine, Soibri Moindze
Let R be a commutative ring with identity. In this paper we investigate the Goldie dimension of finitely generated locally cyclic R-modules. Then, we give a characterization of rings whose finitely generated locally cyclics have finite Goldie dimension.
设 R 是具有同一性的交换环。本文将研究有限生成的局部循环 R 模块的戈尔迪维度。然后，我们给出了有限生成的局部循环具有有限戈尔迪维度的环的特征。
{"title":"On the Goldie dimension of finitely generated locally cyclic modules","authors":"B. Boudine, Soibri Moindze","doi":"10.24193/mathcluj.2023.2.06","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.06","url":null,"abstract":"Let R be a commutative ring with identity. In this paper we investigate the Goldie dimension of finitely generated locally cyclic R-modules. Then, we give a characterization of rings whose finitely generated locally cyclics have finite Goldie dimension.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139272861","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}
Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.11
Ahmed Hamrouni, S. Beloul
"The aim of this study is to prove the existence of solutions for Caputo boundary value problems of nonlinear fractional integro-differential equations with integral boundary conditions, by using the measure of non compactness combined with Mönch's fixed point theorem. Two examples are offered to demonstrate our outcomes."
{"title":"Existence of solutions for fractional integro-differential equations with integral boundary conditions","authors":"Ahmed Hamrouni, S. Beloul","doi":"10.24193/mathcluj.2023.2.11","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.11","url":null,"abstract":"\"The aim of this study is to prove the existence of solutions for Caputo boundary value problems of nonlinear fractional integro-differential equations with integral boundary conditions, by using the measure of non compactness combined with Mönch's fixed point theorem. Two examples are offered to demonstrate our outcomes.\"","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139271156","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}
Pub Date : 2023-11-15DOI: 10.24193/mathcluj.2023.2.14
Ioan Papuc
The flow of Newtonian incompressible fluid inside a two-dimensional lid-driven cavity with two non-adherent porous square blocks was numerically studied. The non-linear governing equations, Darcy-Forchheimer-Brinkman for the porous medium and Navier-Stokes for the free fluid region, were solved using the finite element method. The streamlines and velocity profile of the fluid inside the cavity, as well as the maximum value of the stream function and the coordinates of the main vortex created, are investigated to determine the effect of the Reynolds number, the different combinations of Darcy number and the different placements of the porous squares, on the behaviour of the fluid flow.
{"title":"Lid driven cavity flow with two porous square obstacles","authors":"Ioan Papuc","doi":"10.24193/mathcluj.2023.2.14","DOIUrl":"https://doi.org/10.24193/mathcluj.2023.2.14","url":null,"abstract":"The flow of Newtonian incompressible fluid inside a two-dimensional lid-driven cavity with two non-adherent porous square blocks was numerically studied. The non-linear governing equations, Darcy-Forchheimer-Brinkman for the porous medium and Navier-Stokes for the free fluid region, were solved using the finite element method. The streamlines and velocity profile of the fluid inside the cavity, as well as the maximum value of the stream function and the coordinates of the main vortex created, are investigated to determine the effect of the Reynolds number, the different combinations of Darcy number and the different placements of the porous squares, on the behaviour of the fluid flow.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139271288","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}
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