Pub Date : 2023-12-29DOI: 10.30538/psrp-oma2023.0126
Meas Len
In this work, we establish the existence and uniqueness of solution of Floquet eigenvalue and its adjoint to homogeneous growth-fragmentation equation with positive and periodic coefficients. We study the Floquet exponent, which measures the growth rate of a population. Finally, we establish the long term behavior of solution to the homogeneous growth-fragmentation equation by entropy method [1,2,3].
{"title":"Floquet Exponent of Solution to Homogeneous Growth-Fragmentation Equation","authors":"Meas Len","doi":"10.30538/psrp-oma2023.0126","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0126","url":null,"abstract":"In this work, we establish the existence and uniqueness of solution of Floquet eigenvalue and its adjoint to homogeneous growth-fragmentation equation with positive and periodic coefficients. We study the Floquet exponent, which measures the growth rate of a population. Finally, we establish the long term behavior of solution to the homogeneous growth-fragmentation equation by entropy method [1,2,3].","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139146479","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 : 2023-12-29DOI: 10.30538/psrp-oma2023.0128
Atinuke Ayanfe Amao, T. Opoola
In this work, a new class of bi-univalent functions (I^{n+1}_{Gamma_m,lambda}(x,z)) is defined by means of subordination. Upper bounds for some initial coefficients and the Fekete-Szegö functional of functions in the new class were obtained.
{"title":"Upper Estimates For Initial Coefficients and Fekete-Szegö Functional of A Class of Bi-univalent Functions Defined by Means of Subordination and Associated with Horadam Polynomials","authors":"Atinuke Ayanfe Amao, T. Opoola","doi":"10.30538/psrp-oma2023.0128","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0128","url":null,"abstract":"In this work, a new class of bi-univalent functions (I^{n+1}_{Gamma_m,lambda}(x,z)) is defined by means of subordination. Upper bounds for some initial coefficients and the Fekete-Szegö functional of functions in the new class were obtained.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139147933","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 : 2023-12-29DOI: 10.30538/psrp-oma2023.0130
Shaowen Li
This paper gives sufficient conditions for the existence of positive periodic solutions to general indefinite singular differential equations. Furthermore, under some assumptions we show the existence of two positive periodic solutions. The methods used are Krasnoselski(breve{mbox{i}})'s-Guo fixed point theorem and the positivity of the associated Green's function.
{"title":"Multiplicity results for a class of nonlinear singular differential equation with a parameter","authors":"Shaowen Li","doi":"10.30538/psrp-oma2023.0130","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0130","url":null,"abstract":"This paper gives sufficient conditions for the existence of positive periodic solutions to general indefinite singular differential equations. Furthermore, under some assumptions we show the existence of two positive periodic solutions. The methods used are Krasnoselski(breve{mbox{i}})'s-Guo fixed point theorem and the positivity of the associated Green's function.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139143808","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 : 2023-12-29DOI: 10.30538/psrp-oma2023.0127
Rana Muhammad Kashif Iqbal, A. Qayyum, Tayyaba Nashaiman Atta, Muhammad Moiz Basheer, Ghulam Shabbir
This work is a generalization of Ostrowski type integral inequalities using a special 4-step quadratic kernel. Some new and useful results are obtained. Applications to Quadrature Rules and special Probability distribution are also evaluated.
{"title":"Some new results of ostrowski type inequalities using 4-step quadratic kernel and their applications","authors":"Rana Muhammad Kashif Iqbal, A. Qayyum, Tayyaba Nashaiman Atta, Muhammad Moiz Basheer, Ghulam Shabbir","doi":"10.30538/psrp-oma2023.0127","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0127","url":null,"abstract":"This work is a generalization of Ostrowski type integral inequalities using a special 4-step quadratic kernel. Some new and useful results are obtained. Applications to Quadrature Rules and special Probability distribution are also evaluated.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139146749","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 : 2023-12-29DOI: 10.30538/psrp-oma2023.0129
E. Rahimi, Z. Amiri
Fusion frames and subfusion frames are generalizations of frames in the Hilbert spaces. In this paper, we study subfusion frames and the relations between the fusion frames and subfusion frame operators. Also, we introduce new construction of subfusion frames. In particular, we study atomic resolution of the identity on the Hilbert spaces and derive new results.
{"title":"An Introduction to the Construction of Subfusion Frames","authors":"E. Rahimi, Z. Amiri","doi":"10.30538/psrp-oma2023.0129","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0129","url":null,"abstract":"Fusion frames and subfusion frames are generalizations of frames in the Hilbert spaces. In this paper, we study subfusion frames and the relations between the fusion frames and subfusion frame operators. Also, we introduce new construction of subfusion frames. In particular, we study atomic resolution of the identity on the Hilbert spaces and derive new results.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139147621","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 : 2023-06-30DOI: 10.30538/psrp-oma2023.0120
Khalid Atif, El-Hassan Essouf, Khadija Rizki
In this work, we propose a deep learning approach for identifying parameters (initial condition, a coefficient in the diffusion term and source function) in parabolic partial differential equations (PDEs) from scattered final observations in space and noisy a priori knowledge. In Particular, we approximate the unknown solution and parameters by four deep neural networks trained to satisfy the differential operator, boundary conditions, a priori knowledge and observations. The proposed algorithm is mesh-free, which is key since meshes become infeasible in higher dimensions due to the number of grid points explosion. Instead of forming a mesh, the neural networks are trained on batches of randomly sampled time and space points. This work is devoted to the identification of several parameters of PDEs at the same time. The classical methods require a total a priori knowledge which is not feasible. While they cannot solve this inverse problem given such partial data, the deep learning method allows them to resolve it using minimal a priori knowledge.
{"title":"Identification of parameters in parabolic partial differential equation from final observations using deep learning","authors":"Khalid Atif, El-Hassan Essouf, Khadija Rizki","doi":"10.30538/psrp-oma2023.0120","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0120","url":null,"abstract":"In this work, we propose a deep learning approach for identifying parameters (initial condition, a coefficient in the diffusion term and source function) in parabolic partial differential equations (PDEs) from scattered final observations in space and noisy a priori knowledge. In Particular, we approximate the unknown solution and parameters by four deep neural networks trained to satisfy the differential operator, boundary conditions, a priori knowledge and observations. The proposed algorithm is mesh-free, which is key since meshes become infeasible in higher dimensions due to the number of grid points explosion. Instead of forming a mesh, the neural networks are trained on batches of randomly sampled time and space points. This work is devoted to the identification of several parameters of PDEs at the same time. The classical methods require a total a priori knowledge which is not feasible. While they cannot solve this inverse problem given such partial data, the deep learning method allows them to resolve it using minimal a priori knowledge.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139366910","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 : 2023-06-30DOI: 10.30538/psrp-oma2023.0121
O Ogbereyivwe, S. S. Umar
This manuscript proposed high-precision methods for obtaining solutions for nonlinear models. The method uses the Newton method as its predictor and an iterative function that involves the perturbed Newton method with the quotient of two power series as the corrector function. The theoretical analysis of convergence indicates that the methods class is of convergence order four, requiring three functions evaluation per cycle. The computation performance comparison with some existing methods shows that the developed methods class has perfect precision.
{"title":"A class of power series based modified newton method with high precision for solving nonlinear models","authors":"O Ogbereyivwe, S. S. Umar","doi":"10.30538/psrp-oma2023.0121","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0121","url":null,"abstract":"This manuscript proposed high-precision methods for obtaining solutions for nonlinear models. The method uses the Newton method as its predictor and an iterative function that involves the perturbed Newton method with the quotient of two power series as the corrector function. The theoretical analysis of convergence indicates that the methods class is of convergence order four, requiring three functions evaluation per cycle. The computation performance comparison with some existing methods shows that the developed methods class has perfect precision.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139366650","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 : 2023-06-30DOI: 10.30538/psrp-oma2023.0124
Nabil Rezaiki, A. Boulfoul
This paper deals with the maximum number of limit cycles bifurcating from the degenerate centre [ dot{x}=-y(3x^2+y^2),: dot{y}=x(x^2-y^2), ] when we perturb it inside a class of all homogeneous polynomial differential systems of degree (5). Using averaging theory of second order, we show that, at most, five limit cycles are produced from the periodic orbits surrounding the degenerate centre under quintic perturbation. In addition, we provide six examples that give rise to exactly (5, 4, 3, 2, 1) and (0) limit cycles.
{"title":"Limit cycles obtained by perturbing a degenerate center","authors":"Nabil Rezaiki, A. Boulfoul","doi":"10.30538/psrp-oma2023.0124","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0124","url":null,"abstract":"This paper deals with the maximum number of limit cycles bifurcating from the degenerate centre [ dot{x}=-y(3x^2+y^2),: dot{y}=x(x^2-y^2), ] when we perturb it inside a class of all homogeneous polynomial differential systems of degree (5). Using averaging theory of second order, we show that, at most, five limit cycles are produced from the periodic orbits surrounding the degenerate centre under quintic perturbation. In addition, we provide six examples that give rise to exactly (5, 4, 3, 2, 1) and (0) limit cycles.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139367677","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 : 2023-06-30DOI: 10.30538/psrp-oma2023.0123
Ly Van An
In this paper, we work on expanding the Jensen ((Gamma_{1},Gamma_{2}))-function inequalities by relying on the general Jensen ((eta,lambda))-functional equation with (3k)-variables on the complex Banach space. That is the main result of this.
{"title":"Expansion of the Jensen ((Gamma_{1},Gamma_{2})-)functional inequatities based on Jensen type ((eta,lambda))-functional equation with (3k)-Variables in complex Banach space","authors":"Ly Van An","doi":"10.30538/psrp-oma2023.0123","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0123","url":null,"abstract":"In this paper, we work on expanding the Jensen ((Gamma_{1},Gamma_{2}))-function inequalities by relying on the general Jensen ((eta,lambda))-functional equation with (3k)-variables on the complex Banach space. That is the main result of this.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139367183","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 : 2023-06-30DOI: 10.30538/psrp-oma2023.0119
D. Ziane, M. Cherif
The work that we have done in this paper is the coupling method between the local fractional derivative and the Natural transform (we can call it the local fractional Natural transform), where we have provided some essential results and properties. We have applied this method to some linear local fractional differential equations on Cantor sets to get nondifferentiable solutions. The results show this transform’s effectiveness when we combine it with this operator.
{"title":"The local fractional natural transform and its applications to differential equations on Cantor sets","authors":"D. Ziane, M. Cherif","doi":"10.30538/psrp-oma2023.0119","DOIUrl":"https://doi.org/10.30538/psrp-oma2023.0119","url":null,"abstract":"The work that we have done in this paper is the coupling method between the local fractional derivative and the Natural transform (we can call it the local fractional Natural transform), where we have provided some essential results and properties. We have applied this method to some linear local fractional differential equations on Cantor sets to get nondifferentiable solutions. The results show this transform’s effectiveness when we combine it with this operator.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139367350","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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