Authors:
Zagane Abdelkader
,
Osamnia Nada
,
Kaddour Zegga
Abstract: The purpose of this study is to classify harmonic homomorphisms ϕ : (G, g) → (H, h), where G, H are connected and simply connected three-dimensional unimodular Lie groups and g, h are left-invariant Riemannian metrics. This study aims the classification up to conjugation by automorphism of Lie groups of harmonic homomorphism, between twodifferent non-abelian connected and simply connected three-dimensional unimodular Lie groups (G, g) and (H, h), where g and h are two left-invariant Riemannian metrics on G and H, respectively. This study managed to classify some homomorphisms between two different non-abelian connected and simply connected three-dimensional uni-modular Lie groups. The theory of harmonic maps into Lie groups has been extensively studied related homomorphism in compact Lie groups by many mathematicians, harmonic maps into Lie group and harmonics inner automorphisms of compact connected semi-simple Lie groups and intensively study harmonic and biharmonic homomorphisms between Riemannian Lie groups equipped with a left-invariant Riemannian metric. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-11-03
DOI: 10.1108/AJMS-01-2022-0010 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Ramy Shaheen
,
Suhail Mahfud
,
Ali Kassem
Abstract: This paper aims to study Irreversible conversion processes, which examine the spread of a one way change of state (from state 0 to state 1) through a specified society (the spread of disease through populations, the spread of opinion through social networks, etc.) where the conversion rule is determined at the beginning of the study. These processes can be modeled into graph theoretical models where the vertex set V(G) represents the set of individuals on which the conversion is spreading. The irreversible k-threshold conversion process on a graph G=(V,E) is an iterative process which starts by choosing a set S_0'V, and for each step t (t = 1, 2,…,), S_t is obtained from S_(t−1) by adjoining all vertices that have at least k neighbors in S_(t−1). S_0 is called the seed set of the k-threshold conversion process and is called an irreversible k-threshold conversion set (IkCS) of G if S_t = V(G) for some t = 0. The minimum cardinality of all the IkCSs of G is referred to as the irreversible k-threshold conversion number of G and is denoted by C_k (G). In this paper the authors determine C_k (G) for generalized Jahangir graph J_(s,m) for 1 Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-10-18
DOI: 10.1108/AJMS-07-2021-0150 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Anis Elgarna
Abstract: Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based on a complete orthonormal system of Dunkl kernels generalizing the classical exponential system defining the classical Fourier series. Although the difficulties related to the Dunkl settings, the techniques used by K. Sato were still efficient in this case to establish the inequalities which have expected similarities with the classical case, and Hardy and Paley theorems for the Fourier–Bessel expansions due to the fact that the Bessel transform is the even part of the Dunkl transform. Paley's inequality and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions. This work is a participation in extending the harmonic analysis associated with the Dunkl operators and it shows the utility of BMO spaces to establish some analytical results. Dunkl theory is a generalization of Fourier analysis and special function theory related to root systems. Establishing Paley and Hardy's inequalities in these settings is a participation in extending the Dunkl harmonic analysis as it has many applications in mathematical physics and in the framework of vector valued extensions of multipliers. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-09-30
DOI: 10.1108/AJMS-12-2021-0312 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Chems Eddine Berrehail
,
Amar Makhlouf
Abstract: The objective of this work is to study the periodic solutions for a class of sixth-order autonomous ordinary differential equations x(6)+(1+p2+q2)x… .+(p2+q2+p2q2)x¨+p2q2x=εF(x,ẋ,x¨,x…,x… .,x(5)), where p and q are rational numbers different from 1, 0, −1 and p ≠ q, ε is a small enough parameter and F ∈ C2 is a nonlinear autonomous function. The authors shall use the averaging theory to study the periodic solutions for a class of perturbed sixth-order autonomous differential equations (DEs). The averaging theory is a classical tool for the study of the dynamics of nonlinear differential systems with periodic forcing. The averaging theory has a long history that begins with the classical work of Lagrange and Laplace. The averaging theory is used to the study of periodic solutions for second and higher order DEs. All the main results for the periodic solutions for a class of perturbed sixth-order autonomous DEs are presenting in the Theorem 1. The authors present some applications to illustrate the main results. The authors studied Equation 1 which depends explicitly on the independent variable t. Here, the authors studied the autonomous case using a different approach. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-09-16
DOI: 10.1108/AJMS-02-2022-0045 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Gopal Shruthi
,
Murugan Suvinthra
Abstract: The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition. A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work. Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition. The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-08-08
DOI: 10.1108/AJMS-10-2021-0271 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Yahya Alnashri
,
Hasan Alzubaidi
Abstract: The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions. In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions. The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method. This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-06-28
DOI: 10.1108/AJMS-01-2022-0021 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Saida Mancer
,
Abdelhakim Necir
,
Souad Benchaira
Abstract: The purpose of this paper is to propose a semiparametric estimator for the tail index of Pareto-type random truncated data that improves the existing ones in terms of mean square error. Moreover, we establish its consistency and asymptotic normality. To construct a root mean squared error (RMSE)-reduced estimator of the tail index, the authors used the semiparametric estimator of the underlying distribution function given by Wang (1989). This allows us to define the corresponding tail process and provide a weak approximation to this one. By means of a functional representation of the given estimator of the tail index and by using this weak approximation, the authors establish the asymptotic normality of the aforementioned RMSE-reduced estimator. In basis on a semiparametric estimator of the underlying distribution function, the authors proposed a new estimation method to the tail index of Pareto-type distributions for randomly right-truncated data. Compared with the existing ones, this estimator behaves well both in terms of bias and RMSE. A useful weak approximation of the corresponding tail empirical process allowed us to establish both the consistency and asymptotic normality of the proposed estimator. A new tail semiparametric (empirical) process for truncated data is introduced, a new estimator for the tail index of Pareto-type truncated data is introduced and asymptotic normality of the proposed estimator is established. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-06-27
DOI: 10.1108/AJMS-02-2022-0033 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Kwara Nantomah
Abstract: In this paper, the author introduces a degenerate exponential integral function and further studies some of its analytical properties. The new function is a generalization of the classical exponential integral function and the properties established are analogous to those satisfied by the classical function. The methods adopted in establishing the results are theoretical in nature. A degenerate exponential integral function which is a generalization of the classical exponential integral function has been introduced and its properties investigated. Upon taking some limits, the established results reduce to results involving the classical exponential integral function. The results obtained in this paper are new and have the potential of inspiring further research on the subject. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-06-14
DOI: 10.1108/AJMS-09-2021-0230 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Manoj Kumar
Abstract: In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs). The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM). The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations. The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-06-07
DOI: 10.1108/AJMS-11-2021-0282 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Salah Benhiouna
,
Azzeddine Bellour
,
Rachida Amiar
Abstract: A generalization of Ascoli–Arzelá theorem in Banach spaces is established. Schauder's fixed point theorem is used to prove the existence of a solution for a boundary value problem of higher order. The authors’ results are obtained under, rather, general assumptions. First, a generalization of Ascoli–Arzelá theorem in Banach spaces in Cn is established. Second, this new generalization with Schauder's fixed point theorem to prove the existence of a solution for a boundary value problem of higher order is used. Finally, an illustrated example is given. There is no funding. In this work, a new generalization of Ascoli–Arzelá theorem in Banach spaces in Cn is established. To the best of the authors’ knowledge, Ascoli–Arzelá theorem is given only in Banach spaces of continuous functions. In the second part, this new generalization with Schauder's fixed point theorem is used to prove the existence of a solution for a boundary value problem of higher order, where the derivatives appear in the non-linear terms. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-05-31
DOI: 10.1108/AJMS-10-2021-0274 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Mohd Aslam
,
Mohd Danish Siddiqi
,
Aliya Naaz Siddiqui
Abstract: In 1979, P. Wintgen obtained a basic relationship between the extrinsic normal curvature the intrinsic Gauss curvature, and squared mean curvature of any surface in a Euclidean 4-space with the equality holding if and only if the curvature ellipse is a circle. In 1999, P. J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken gave a conjecture of Wintgen inequality, named as the DDVV-conjecture, for general Riemannian submanifolds in real space forms. Later on, this conjecture was proven to be true by Z. Lu and by Ge and Z. Tang independently. Since then, the study of Wintgen’s inequalities and Wintgen ideal submanifolds has attracted many researchers, and a lot of interesting results have been found during the last 15 years. The main purpose of this paper is to extend this conjecture of Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection. The authors used standard technique for obtaining generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection. The authors establish the generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection, and also find conditions under which the equality holds. Some particular cases are also stated. The research may be a challenge for new developments focused on new relationships in terms of various invariants, for different types of submanifolds in that ambient space with several connections. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-03-09
DOI: 10.1108/AJMS-03-2021-0057 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Chems Eddine Berrehail
,
Zineb Bouslah
Abstract: This study aims to provide sufficient conditions for the existence of periodic solutions of the fifth-order differential equation. The authors shall use the averaging theory, more precisely Theorem $6$. The main results on the periodic solutions of the fifth-order differential equation (equation (1)) are given in the statement of Theorem 1 and 2. In this article, the authors provide sufficient conditions for the existence of periodic solutions of the fifth-order differential equation. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-03-08
DOI: 10.1108/AJMS-07-2020-0024 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Riyajur Rahman
,
Nipen Saikia
Abstract: Let p[1,r;t] be defined by ∑n=0∞p[1,r;t](n)qn=(E1Er)t, where t is a non-zero rational number, r ≥ 1 is an integer and Er=∏n=0∞(1−qr(n+1)) for q Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-03-08
DOI: 10.1108/AJMS-09-2021-0235 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Dibakar Dey
,
Pradip Majhi
Abstract: Cotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object of this article is to study the properties of this soliton on certain contact metric manifolds. The authors consider the notion of Cotton soliton on almost Kenmotsu 3-manifolds. The authors use a local basis of the manifold that helps to study this notion in terms of partial differential equations. First the authors consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton. Next the authors assume that the potential vector field is orthogonal to the Reeb vector field. It is proved that such a Cotton soliton on a non-Kenmotsu almost Kenmotsu 3-h-manifold such that the Reeb vector field is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to. The results of this paper are new and interesting. Also, the Proposition 3.2 will be helpful in further study of this space. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-02-04
DOI: 10.1108/AJMS-10-2020-0103 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Alejandro Molano
Abstract: In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials. To do that, the authors use the connection formulas between Sobolev polynomials and classical Laguerre polynomials, as well as the well-known Fourier coefficients for these latter. Then, the authors compute explicit formulas for the Fourier coefficients of some families of Laguerre–Sobolev type orthogonal polynomials over a finite interval. The authors also describe an oscillatory region in each case as a reasonable choice for approximation purposes. In order to take the first step in the study of constructive methods by using Sobolev polynomials, this paper deals with Fourier coefficients for certain families of polynomials orthogonal with respect to the Sobolev type inner product. As far as the authors know, this particular problem has not been addressed in the existing literature. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-01-13
DOI: 10.1108/AJMS-07-2021-0164 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2022)

Authors:
Ryad Ghanam
,
Gerard Thompson
,
Narayana Bandara
Abstract: This study aims to find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1). The authors use Lie Algebra techniques to find all inequivalent subalgebras of so(3,1) in all dimensions. The authors find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1). This paper is an original research idea. It will be a main reference for many applications such as solving partial differential equations. If so(3,1) is part of the symmetry Lie algebra, then the subalgebras listed in this paper will be used to reduce the order of the partial differential equation (PDE) and produce non-equivalent solutions. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-06-02
DOI: 10.1108/AJMS-01-2022-0007 Issue No:Vol.
28
, No.
2
(2022)

Authors:
Mohammed H. Fahmy
,
Ahmed Ageeb Elokl
,
Ramy Abdel-Khalek
Abstract: The aim of this paper is to investigate the relationship between the ring structure of the twisted partial skew generalized power series ring RG,≤;Θ and the corresponding structure of its zero-divisor graph Γ̅RG,≤;Θ. The authors first introduce the history and motivation of this paper. Secondly, the authors give a brief exposition of twisted partial skew generalized power series ring, in addition to presenting some properties of such structure, for instance, a-rigid ring, a-compatible ring and (G,a)-McCoy ring. Finally, the study’s main results are stated and proved. The authors establish the relation between the diameter and girth of the zero-divisor graph of twisted partial skew generalized power series ring RG,≤;Θ and the zero-divisor graph of the ground ring R. The authors also provide counterexamples to demonstrate that some conditions of the results are not redundant. As well the authors indicate that some conditions of recent results can be omitted. The results of the twisted partial skew generalized power series ring embrace a wide range of results of classical ring theoretic extensions, including Laurent (skew Laurent) polynomial ring, Laurent (skew Laurent) power series ring and group (skew group) ring and of course their partial skew versions. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2022-04-04
DOI: 10.1108/AJMS-10-2021-0253 Issue No:Vol.
28
, No.
2
(2022)