OMA – Vol 7 – Issue 1 (2023) – PISRT https://old.pisrt.org Sun, 31 Dec 2023 17:49:51 +0000 en-US hourly 1 https://wordpress.org/?v=6.7 Coefficient bounds for \(p\)-valent functions https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-1-2023/coefficient-bounds-for-p-valent-functions/ Fri, 30 Jun 2023 22:12:16 +0000 https://old.pisrt.org/?p=8074
OMA-Vol. 7 (2023), Issue 1, pp. 83 – 90 Open Access Full-Text PDF
Olusegun Awoyale and Timothy Oloyede Opoola
Abstract: This present paper introduces two new subclasses of p-valent functions. The coefficient bounds and Fekete-Szego inequalities for the functions in these classes are also obtained.]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 83 – 90
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0125

Coefficient bounds for \(p\)-valent functions

Olusegun Awoyale\(^{1,*}\) and Timothy Oloyede Opoola\(^1\)
\(^{1}\) Department of Mathematics, Federal College of Education, Kontagora, Niger State, Nigeria
\(^{2}\) DDepartment of Mathematics, University of Ilorin, P.M.P; 1515 Ilorin, Nigeria

Copyright © 2023 Olusegun Awoyale and Timothy Oloyede Opoola. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 15, 2023 – Accepted: June 20, 2023 – Published: June 30, 2023

Abstract

This present paper introduces two new subclasses of p-valent functions. The coefficient bounds and Fekete-Szego inequalities for the functions in these classes are also obtained.

Keywords:

coefficient bounds; Fekete-Szego inequalities; \(p\)-valent functions
]]> Limit cycles obtained by perturbing a degenerate center https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-1-2023/limit-cycles-obtained-by-perturbing-a-degenerate-center/ Fri, 30 Jun 2023 21:59:26 +0000 https://old.pisrt.org/?p=8070
OMA-Vol. 7 (2023), Issue 1, pp. 56 – 70 Open Access Full-Text PDF
Nabil Rezaiki and Amel Boulfoul
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.]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 71 – 82
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0124

Limit cycles obtained by perturbing a degenerate center

Nabil Rezaiki\(^{1,*}\) and Amel Boulfoul\(^2\)
\(^{1}\) LMA Laboratory , Department of Mathematics, University of Badji Mokhtar, P.O.Box 12, Annaba, 23000, Algeria
\(^{2}\) Department of mathematics, 20 Aout 1955 University, BP26; El Hadaiek 21000, Skikda, Algeria

Copyright © 2023 Nabil Rezaiki and Amel Boulfoul. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 07, 2023 – Accepted: June 23, 2023 – Published: June 30, 2023

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.

Keywords:

Limit cycles; averaging theory; polynomial differential systems; degenerate center
]]> 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 https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-1-2023/expansion-of-the-jensen-gamma_1gamma_2-functional-inequatities-based-on-jensen-type-etalambda-functional-equation-with-3k-variables-in-complex-banach-space/ Fri, 30 Jun 2023 21:52:06 +0000 https://old.pisrt.org/?p=8068
OMA-Vol. 7 (2023), Issue 1, pp. 56 – 70 Open Access Full-Text PDF
Ly Van An
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.]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 56 – 70
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0123

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

Ly Van An\(^{1}\)
\(^{1}\) Faculty of Mathematics Teacher Education, Tay Ninh University, Tay Ninh, Vietnam

Copyright © 2023 Ly Van An. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 17, 2023 – Accepted: June 16, 2023 – Published: June 30, 2023

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.

Keywords:

Generalized Jensen type \((\Gamma_{1},\Gamma_{2})\)-functional inequality; Generalized Jensen type \((\eta,\lambda)\)-functional equations; Hyers-Ulam-Rassias stability; complex Banach space; complex normed vector spaces.
]]> On norms of derivations implemented by self-adjoint operators https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-1-2023/on-norms-of-derivations-implemented-by-self-adjoint-operators/ Fri, 30 Jun 2023 21:50:35 +0000 https://old.pisrt.org/?p=8064
OMA-Vol. 7 (2023), Issue 1, pp. 42 – 55 Open Access Full-Text PDF
Obogi Robert Karieko
Abstract:In this paper, we concentrate on norms of derivations implemented by self-adjoint operators. We determine the upper and lower norm estimates of derivations implemented by self-adjoint operators. The results show that the knowledge of self-adjoint governs the quantum chemical system in which the eigenvalue and eigenvector of a self-adjoint operator represents the ground state energy and the ground state wave function of the system respectively.]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 42 – 55
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0122

On norms of derivations implemented by self-adjoint operators

Obogi Robert Karieko\(^{1}\)
\(^{1}\) Department of Mathematics and Actuarial Science, Kisii University, P.O BOX 408-40200, KISII, KENYA

Copyright © 2023 Obogi Robert Karieko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 17, 2023 – Accepted: June 16, 2023 – Published: June 30, 2023

Abstract

In this paper, we concentrate on norms of derivations implemented by self-adjoint operators. We determine the upper and lower norm estimates of derivations implemented by self-adjoint operators.The results show that the knowledge of self-adjoint governs the quantum chemical system in which the eigenvalue and eigenvector of a self-adjoint operator represents the ground state energy and the ground state wave function of the system respectively.

Keywords:

norm; orthogonality; self-adjoint operator; derivation; linear operator.
]]> A class of power series based modified newton method with high precision for solving nonlinear models https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-1-2023/a-class-of-power-series-based-modified-newton-method-with-high-precision-for-solving-nonlinear-models/ Fri, 30 Jun 2023 21:48:10 +0000 https://old.pisrt.org/?p=8060
OMA-Vol. 7 (2023), Issue 1, pp. 32 – 41 Open Access Full-Text PDF
Oghovese Ogbereyivwe and Salisu Shehu Umar
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.]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 32 – 41
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0121

A class of power series based modified newton method with high precision for solving nonlinear models

Oghovese Ogbereyivwe\(^{1},*\), Salisu Shehu Umar\(^{2}\)
\(^{1}\) Department of Mathematics, Delta State University of Science and Tech., Ozoro, Delta State, Nigeria
\(^{2}\) Department of Statistics, Federal Polytechnic Auchi, Edo State, Nigeria

Copyright © 2023 Oghovese Ogbereyivwe and Salisu Shehu Umar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: August 07, 2022 – Accepted: December 26, 2022 – Published: June 30, 2023

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.

Keywords:

nonlinear models; iterative method; Newton method; power series
]]> Identification of parameters in parabolic partial differential equation from final observations using deep learning https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-1-2023/identification-of-parameters-in-parabolic-partial-differential-equation-from-final-observations-using-deep-learning/ Fri, 30 Jun 2023 10:16:46 +0000 https://old.pisrt.org/?p=8041
OMA-Vol. 7 (2023), Issue 1, pp. 10 – 31 Open Access Full-Text PDF
Khalid Atif, El-Hassan Essouf and Khadija Rizki
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.]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 10 – 31
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0120

Identification of parameters in parabolic partial differential equation from final observations using deep learning

Khalid Atif\(^{1},*\), El-Hassan Essouf\(^{2}\) and Khadija Rizki\(^{2}\)
\(^{1}\) Laboratoire de Mathématiques Appliquées et Informatique (MAI) Université Cadi Ayyad, Marrakech, Morocco
\(^{2}\) Laboratoire de Mathématiques Informatique et Sciences de ´lingenieur (MISI) Université Hassan 1, Settat 26000, ´
Morocco

Copyright © 2023 Khalid Atif, El-Hassan Essouf and Khadija Rizki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 15, 2023 – Accepted: June 20, 2023 – Published: June 30, 2023

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.

Keywords:

deep learning; heat equation; hybrid method; inverse problem; model-driven solution; neural networks; optimization; Tikhonov regularization.
]]> The local fractional natural transform and its applications to differential equations on Cantor sets https://old.pisrt.org/psr-press/journals/oma-vol-7-issue-1-2023/the-local-fractional-natural-transform-and-its-applications-to-differential-equations-on-cantor-sets/ Fri, 30 Jun 2023 09:24:20 +0000 https://old.pisrt.org/?p=8033
OMA-Vol. 7 (2023), Issue 1, pp. 01 – 09 Open Access Full-Text PDF
Djelloul Ziane, and Mountassir Hamdi Cherif
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.]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 01 – 09
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0119

The local fractional natural transform and its applications
to differential equations on Cantor sets

Djelloul Ziane\(^{1,*}\), and Mountassir Hamdi Cherif\(^{2}\)
\(^{1}\) Department of Mathematics, Faculty of Mathematics and Material Sciences, Kasdi Merbah University of Ouargla,
Algeria
\(^{2}\) Hight School of Electrical and Energetics Engineering of Oran (ESGEE-Oran), Oran, Algeria

Copyright © 2023 Djelloul Ziane, and Mountassir Hamdi Cherif. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 06, 2023 – Accepted: June 20, 2023 – Published: June 30, 2023

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.

Keywords:

local fractional calculus; local fractional Laplace transform; natural transform method; local fractional differential equations.
]]>