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.
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.
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(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:
Rishabh Ranjan
,
P.N. Pandey
,
Ajit Paul
Abstract: In this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant. For, the authors have used the notion of conformal transformation and Douglas space. The authors found some results to show that the Douglas space of second kind with certain (α, β)-metrics such as Randers metric, first approximate Matsumoto metric along with some special (α, β)-metrics, is invariant under a conformal change. The authors introduced Douglas space of second kind and established conditions under which it can be transformed to a Douglas space of second kind. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-12-31
DOI: 10.1108/AJMS-08-2021-0189 Issue No:Vol.
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, No.
ahead-of-print
(2021)

Authors:
M'Hamed El-Louh
,
Mohammed El Allali
,
Fatima Ezzaki
Abstract: In this work, the authors are interested in the notion of vector valued and set valued Pettis integrable pramarts. The notion of pramart is more general than that of martingale. Every martingale is a pramart, but the converse is not generally true. In this work, the authors present several properties and convergence theorems for Pettis integrable pramarts with convex weakly compact values in a separable Banach space. The existence of the conditional expectation of Pettis integrable mutifunctions indexed by bounded stopping times is provided. The authors prove the almost sure convergence in Mosco and linear topologies of Pettis integrable pramarts with values in (cwk(E)) the family of convex weakly compact subsets of a separable Banach space. The purpose of the present paper is to present new properties and various new convergence results for convex weakly compact valued Pettis integrable pramarts in Banach space. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-12-29
DOI: 10.1108/AJMS-07-2021-0173 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Farouk Metiri
,
Halim Zeghdoudi
,
Ahmed Saadoun
Abstract: This paper generalizes the quadratic framework introduced by Le Courtois (2016) and Sumpf (2018), to obtain new credibility premiums in the balanced case, i.e. under the balanced squared error loss function. More precisely, the authors construct a quadratic credibility framework under the net quadratic loss function where premiums are estimated based on the values of past observations and of past squared observations under the parametric and the non-parametric approaches, this framework is useful for the practitioner who wants to explicitly take into account higher order (cross) moments of past data. In the actuarial field, credibility theory is an empirical model used to calculate the premium. One of the crucial tasks of the actuary in the insurance company is to design a tariff structure that will fairly distribute the burden of claims among insureds. In this work, the authors use the weighted balanced loss function (WBLF, henceforth) to obtain new credibility premiums, and WBLF is a generalized loss function introduced by Zellner (1994) (see Gupta and Berger (1994), pp. 371-390) which appears also in Dey et al. (1999) and Farsipour and Asgharzadhe (2004). The authors declare that there is no conflict of interest and the funding information is not applicable. This work is motivated by the following: quadratic credibility premium under the balanced loss function is useful for the practitioner who wants to explicitly take into account higher order (cross) moments and new effects such as the clustering effect to finding a premium more credible and more precise, which arranges both parts: the insurer and the insured. Also, it is easy to apply for parametric and non-parametric approaches. In addition, the formulas of the parametric (Poisson–gamma case) and the non-parametric approach are simple in form and may be used to find a more flexible premium in many special cases. On the other hand, this work neglects the semi-parametric approach because it is rarely used by practitioners. There are several examples of actuarial science (credibility). In this paper, the authors used the WBLF and a quadratic adjustment to obtain new credibility premiums. More precisely, the authors construct a quadratic credibility framework under the net quadratic loss function where premiums are estimated based on the values of past observations and of past squared observations under the parametric and the non-parametric approaches, this framework is useful for the practitioner who wants to explicitly take into account higher order (cross) moments of past data. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-12-29
DOI: 10.1108/AJMS-08-2021-0192 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
S. Shivaprasada Nayaka
Abstract: Let b¯2,3(n), which enumerates the number of (2, 3)-regular overcubic bipartition of n. The purpose of the paper is to describe some congruences modulo 8 for b¯2,3(n). For example, for each α ≥ 0 and n ≥ 1, b¯2,3(8n+5)≡0(mod8), b¯2,3(2⋅3α+3n+4⋅3α+2)≡0(mod8). H.C. Chan has studied the congruence properties of cubic partition function a(n), which is defined by ∑n=0∞a(n)qn=1(q;q)∞(q2;q2)∞. To establish several congruence modulo 8 for b¯2,3(n), here the author keeps to the classical spirit of q-series techniques in the proofs. The results established in the work are extension to those proved in ℓ-regular cubic partition pairs. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-12-14
DOI: 10.1108/AJMS-07-2021-0162 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Rabha Ibrahim
Abstract: In this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the LDEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution. The methodology is based on the geometric function theory. The authors present a new analytic function for a class of complex LDEs. The authors introduced a new class of complex differential equation, presented a new technique to indicate the analytic solution and used some special functions. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-11-02
DOI: 10.1108/AJMS-04-2021-0085 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Subramanian Visweswaran
Abstract: The purpose of this article is to determine necessary and sufficient conditions in order that (D, K) to be an S-accr pair, where D is an integral domain and K is a field which contains D as a subring and S is a multiplicatively closed subset of D. The methods used are from the topic multiplicative ideal theory from commutative ring theory. Let S be a strongly multiplicatively closed subset of an integral domain D such that the ring of fractions of D with respect to S is not a field. Then it is shown that (D, K) is an S-accr pair if and only if K is algebraic over D and the integral closure of the ring of fractions of D with respect to S in K is a one-dimensional Prüfer domain. Let D, S, K be as above. If each intermediate domain between D and K satisfies S-strong accr*, then it is shown that K is algebraic over D and the integral closure of the ring of fractions of D with respect to S is a Dedekind domain; the separable degree of K over F is finite and K has finite exponent over F, where F is the quotient field of D. Motivated by the work of some researchers on S-accr, the concept of S-strong accr* is introduced and we determine some necessary conditions in order that (D, K) to be an S-strong accr* pair. This study helps us to understand the behaviour of the rings between D and K. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-10-29
DOI: 10.1108/AJMS-07-2021-0158 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Sakhri Aicha
,
Ahcene Merad
Abstract: This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and uniqueness are proved. The authors divide the proof into two sections for the linear associated problem; the authors derive the a priori bound and demonstrate the operator range density that is generated. The authors solve the nonlinear problem by introducing an iterative process depending on the preceding results. The functional analysis method is the a priori estimate method or energy inequality method. The results show the efficiency of a priori estimate method in the case of time-fractional order differential equations with nonlocal conditions. Our results also illustrate the existence and uniqueness of the continuous dependence of solutions on fractional order differential equations with nonlocal conditions. The authors’ work can be considered a contribution to the development of the functional analysis method that is used to prove well-positioned problems with fractional order. The authors confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-10-14
DOI: 10.1108/AJMS-05-2021-0109 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Mohd Danish Siddiqi
,
Sudhakar Kumar Chaubey
,
Aliya Naaz Siddiqui
Abstract: The central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance this geometrical analysis with some specific cases, namely Clairaut submersion from Lorentzian α-Sasakian manifold, Lorentzian β-Kenmotsu manifold and Lorentzian cosymplectic manifold. Furthermore, the authors discuss some results about Clairaut Lagrangian submersions whose total space is a Lorentzian trans-Sasakian manifolds of type (α, β). Finally, the authors furnished some examples based on this study. This research discourse based on classifications of submersion, mainly Clairaut submersions, whose total manifolds is Lorentzian trans-Sasakian manifolds and its all classes like Lorentzian Sasakian, Lorenztian Kenmotsu and Lorentzian cosymplectic manifolds. In addition, the authors have explored some axioms of Clairaut Lorentzian submersions and illustrates our findings with some non-trivial examples. The major finding of this study is to exhibit a necessary and sufficient condition for a submersions to be a Clairaut submersions and also find a condition for Clairaut Lagrangian submersions from Lorentzian trans-Sasakian manifolds. The results and examples of the present manuscript are original. In addition, more general results with fair value and supportive examples are provided. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-10-07
DOI: 10.1108/AJMS-05-2021-0106 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Aykut Akgün
,
Mehmet Gülbahar
Abstract: Bi-slant submanifolds of S-manifolds are introduced, and some examples of these submanifolds are presented. Some properties of Di-geodesic and Di-umbilical bi-slant submanifolds are examined. The Riemannian curvature invariants of these submanifolds are computed, and some results are discussed with the help of these invariants. The topic is original, and the manuscript has not been submitted to any other journal. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-09-17
DOI: 10.1108/AJMS-04-2021-0073 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Rafik Medjati
,
Hanifi Zoubir
,
Brahim Medjahdi
Abstract: In the Lorentz Heisenberg space H3 endowed with flat metric g3, a translation surface is parametrized by r(x, y) = γ1(x)*γ2(y), where γ1 and γ2 are two planar curves lying in planes, which are not orthogonal. In this article, we classify translation surfaces in H3, which satisfy some algebraic equations in terms of the coordinate functions and the Laplacian operator with respect to the first fundamental form of the surface. In this paper, we classify some type of space-like translation surfaces of H3 endowed with flat metric g3 under the conditionΔri = λiri. We will develop the system which describes surfaces of type finite in H3. For solve the system thus obtained, we will use the calculation variational. Finally, we will try to give performances geometric surfaces that meet the condition imposed. Classification of six types of translation surfaces of finite type in the three-dimensional Lorentz Heisenberg group H3. The subject of this paper lies at the border of geometry differential and spectral analysis on manifolds. Historically, the first research on the study of sub-finite type varieties began around the 1970 by B.Y.Chen. The idea was to find a better estimate of the mean total curvature of a compact subvariety of a Euclidean space. In fact, the notion of finite type subvariety is a natural extension of the notion of a minimal subvariety or surface, a notion directly linked to the calculation of variations. The goal of this work is the classification of surfaces in H3, in other words the surfaces which satisfy the condition/Delta (ri) = /Lambda (ri), such that the Laplacian is associated with the first, fundamental form. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-09-10
DOI: 10.1108/AJMS-03-2021-0071 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Ghodratallah Fasihi-Ramandi
,
Shahroud Azami
Abstract: In this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics. In the first part, we retrieve the geometry of left-invariant Randers metrics on the Heisenberg group H2n+1, of dimension 2n + 1. Considering a left-invariant Randers metric, we give the Levi-Civita connection, curvature tensor, Ricci tensor and scalar curvature and show the Heisenberg groups H2n+1 have constant negative scalar curvature. In the second part, we present our main results. We show that the Heisenberg group H2n+1 cannot admit Randers metric of Berwald and Ricci-quadratic Douglas types. Finally, the flag curvature of Z-Randers metrics in some special directions is obtained which shows that there exist flags of strictly negative and strictly positive curvatures. In this work, we present complete Reimannian geometry of left invarint-metrics on Heisenberg groups. Also, some geometric properties of left-invarainat Randers metrics will be studied. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-08-31
DOI: 10.1108/AJMS-01-2021-0015 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Abdelrachid El Amrouss
,
Omar Hammouti
Abstract: The purpose of this paper is the study of existence and multiplicity of solutions for a nonlinear discrete boundary value problems involving the p-laplacian. The approach is based on variational methods and critical point theory. Theorem 1.1. Theorem 1.2. Theorem 1.3. Theorem 1.4. The paper is original and the authors think the results are new. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-08-20
DOI: 10.1108/AJMS-02-2021-0050 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Omar Benslimane
,
Ahmed Aberqi
,
Jaouad Bennouna
Abstract: In the present paper, the authors will discuss the solvability of a class of nonlinear anisotropic elliptic problems (P), with the presence of a lower-order term and a non-polynomial growth which does not satisfy any sign condition which is described by an N-uplet of N-functions satisfying the Δ2-condition, within the fulfilling of anisotropic Sobolev-Orlicz space. In addition, the resulting analysis requires the development of some new aspects of the theory in this field. The source term is merely integrable. An approximation procedure and some priori estimates are used to solve the problem. The authors prove the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain. The resulting analysis requires the development of some new aspects of the theory in this field. To the best of the authors’ knowledge, this is the first paper that investigates the existence of entropy solutions to unilateral problem in the framework of anisotropic Sobolev-Orlicz space with bounded domain. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-08-18
DOI: 10.1108/AJMS-12-2020-0133 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Mohammed Moussa
,
Abdelqoddous Moussa
,
Hatim Mazan
Abstract: In this paper, the authors give a new version of the sub-super solution method and prove the existence of positive solution for a (p, q)-Laplacian system under weak assumptions than usually made in such systems. In particular, nonlinearities need not be monotone or positive. The authors prove that the sub-super solution method can be proved by the Shcauder fixed-point theorem and use the method to prove the existence of a positive solution in elliptic systems, which appear in some problems of population dynamics. The results complement and generalize some results already published for similar problems. The result is completely new and does not appear elsewhere and will be a reference for this line of research. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-08-17
DOI: 10.1108/AJMS-03-2021-0060 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Mustafa Bojakli
,
Hasan Sankari
Abstract: The authors have determined whether the points fixed by all the full and the partial Atkin–Lehner involutions WQ on X0(N) for N ≤ 50 are Weierstrass points or not. The design is by using Lawittes's and Schoeneberg's theorems. Finding all Weierstrass points on X0(N) fixed by some Atkin–Lehner involutions. Besides, the authors have listed them in a table. The Weierstrass points have played an important role in algebra. For example, in algebraic number theory, they have been used by Schwartz and Hurwitz to determine the group structure of the automorphism groups of compact Riemann surfaces of genus g ≥ 2. Whereas in algebraic geometric coding theory, if one knows a Weierstrass nongap sequence of a Weierstrass point, then one is able to estimate parameters of codes in a concrete way. Finally, the set of Weierstrass points is useful in studying arithmetic and geometric properties of X0(N). Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-08-12
DOI: 10.1108/AJMS-01-2021-0001 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Abhijit Banerjee
,
Arpita Roy
Abstract: The paper aims to build the relationship between an entire function of restricted hyper-order with its linear c-shift operator. Standard methodology for papers in difference and shift operators and value distribution theory have been used. The relation between an entire function of restricted hyper-order with its linear c-shift operator was found under the periphery of sharing a set of two small functions IM (ignoring multiplicities) when exponent of convergence of zeros is strictly less than its order. This research work is an improvement and extension of two previous papers. This is an original research work. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-08-10
DOI: 10.1108/AJMS-10-2020-0099 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Marcos López-García
Abstract: In this work the author gathers several methods and techniques to construct systematically Stieltjes classes for densities defined on R+. The author uses complex integration to obtain integrable functions with vanishing moments sequence, and then the author considers some operators defined on the vanishing moments subspace. The author gather several methods and techniques to construct systematically Stieltjes classes for densities defined on R+. The author constructs explicitly Stieltjes classes with center at well-known probability densities. The author gives a lot of examples, including old cases and new ones. The author computes the Hilbert transform of powers of lnx to construct Stieltjes classes by using a recent result connecting the Krein condition and the Hilbert transform. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-08-06
DOI: 10.1108/AJMS-04-2021-0083 Issue No:Vol.
ahead-of-print
, No.
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(2021)

Authors:
Jihane Abdelli
,
Brahim Brahimi
Abstract: In this paper, the authors applied the empirical likelihood method, which was originally proposed by Owen, to the copula moment based estimation methods to take advantage of its properties, effectiveness, flexibility and reliability of the nonparametric methods, which have limiting chi-square distributions and may be used to obtain tests or confidence intervals. The authors derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result. In this paper we applied the empirical likelihood method which originally proposed by Owen, to the copula moment based estimation methods. We derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result. In this paper we applied the empirical likelihood method which originally proposed by Owen 1988, to the copula moment based estimation methods given by Brahimi and Necir 2012. We derive an new estimator of copula parameters and the asymptotic normality of the empirical likelihood based on copula moment estimation methods. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-07-14
DOI: 10.1108/AJMS-01-2021-0025 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Godwin Amechi Okeke
,
Daniel Francis
Abstract: This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results. The results of this paper are theoretical and analytical in nature. The authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results. Analytical and theoretical results. The results of this paper can be applied in science and engineering. The results of this paper is applicable in certain social sciences. The results of this paper are new and will open up new areas of research in mathematical sciences. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-07-14
DOI: 10.1108/AJMS-02-2021-0037 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Dipankar Dey
,
Dhananjay Mandal
,
Manabendra Nath Mukherjee
Abstract: The present article deals with the initiation and study of a uniformity like notion, captioned μ-uniformity, in the context of a generalized topological space. The existence of uniformity for a completely regular topological space is well-known, and the interrelation of this structure with a proximity is also well-studied. Using this idea, a structure on generalized topological space has been developed, to establish the same type of compatibility in the corresponding frameworks. It is proved, among other things, that a μ-uniformity on a non-empty set X always induces a generalized topology on X, which is μ-completely regular too. In the last theorem of the paper, the authors develop a relation between μ-proximity and μ-uniformity by showing that every μ-uniformity generates a μ-proximity, both giving the same generalized topology on the underlying set. It is an original work influenced by the previous works that have been done on generalized topological spaces. A kind of generalization has been done in this article, that has produced an intermediate structure to the already known generalized topological spaces. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-07-06
DOI: 10.1108/AJMS-03-2021-0058 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
S. Shivaprasada Nayaka
,
T.K. Sreelakshmi
,
Santosh Kumar
Abstract: In this paper, the author defines the function B¯i,jδ,k(n), the number of singular overpartition pairs of n without multiples of k in which no part is divisible by δ and only parts congruent to ± i, ± j modulo δ may be overlined. Andrews introduced to combinatorial objects, which he called singular overpartitions and proved that these singular overpartitions depend on two parameters δ and i can be enumerated by the function C¯δ,i(n), which gives the number of overpartitions of n in which no part divisible by δ and parts ≡ ± i(Mod δ) may be overlined. Using classical spirit of q-series techniques, the author obtains congruences modulo 4 for B¯2,48,3(n), B¯2,48,5 and B¯2,412,3. The results established in this work are extension to those proved in Andrews’ singular overpatition pairs of n. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-07-01
DOI: 10.1108/AJMS-01-2021-0013 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Khadidja Addad
,
Seddik Ouakkas
Abstract: In this paper, we give some properties of the α-connections on statistical manifolds and we study the α-conformal equivalence where we develop an expression of curvature R¯ for ∇¯ in relation to those for ∇ and ∇^. In the first section of this paper, we prove some results about the α-connections of a statistical manifold where we give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds treated in [1, 3], and we construct some examples. We give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples. We give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-06-22
DOI: 10.1108/AJMS-12-2020-0126 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Mushtaq Ali
,
Mohammed Almoaeet
,
Basim Karim Albuohimad
Abstract: This study aims to use new formula derived based on the shifted Jacobi functions have been defined and some theorems of the left- and right-sided fractional derivative for them have been presented. In this article, the authors apply the method of lines (MOL) together with the pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivative (SFPDEs). Then, using the collocation nodes to reduce the SFPDEs to the system of ordinary differential equations, which can be solved by the ode45 MATLAB toolbox. Applying the MOL method together with the pseudospectral discretization method converts the space-dependent on fractional partial differential equations to the system of ordinary differential equations. This paper contributes to gain choosing the shifted Jacobi functions basis with special parameters a, b and give the authors this opportunity to obtain the left- and right-sided fractional differentiation matrices for this basis exactly. The results of the examples are presented in this article. The authors found that the method is efficient and provides accurate results, and the authors found significant implications for success in the science, technology, engineering and mathematics domain. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-06-21
DOI: 10.1108/AJMS-02-2021-0052 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
H. Aruna Kumara
,
V. Venkatesha
,
Devaraja Mallesha Naik
Abstract: Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers. Hence, it deserves special attention to consider the CPE on a certain class of almost contact metric manifolds. In this direction, the authors considered CPE on almost f-cosymplectic manifolds. The paper opted the tensor calculus on manifolds to find the solution of the CPE. In this paper, in particular, the authors obtained that a connected f-cosymplectic manifold satisfying CPE with \lambda=\tilde{f} is Einstein. Next, the authors find that a three dimensional almost f-cosymplectic manifold satisfying the CPE is either Einstein or its scalar curvature vanishes identically if its Ricci tensor is pseudo anti‐commuting. The paper proved that the CPE conjecture is true for almost f-cosymplectic manifolds. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-05-07
DOI: 10.1108/AJMS-10-2020-0094 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Lakehal Belarbi
,
Hichem Elhendi
Abstract: Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature, scalar and sectional curvatures. In this paper the authors introduce a new class of natural metrics called gradient Sasaki metric on tangent bundle. The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature scalar and sectional curvatures. The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature scalar and sectional curvatures. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-05-03
DOI: 10.1108/AJMS-11-2020-0125 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Gauree Shanker
,
Ankit Yadav
Abstract: The purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not. The paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not. The geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds. All results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-04-13
DOI: 10.1108/AJMS-09-2020-0060 Issue No:Vol.
ahead-of-print
, No.
ahead-of-print
(2021)

Authors:
Samuel Ssekajja
Abstract: The author considers an invariant lightlike submanifold M, whose transversal bundle tr(TM) is flat, in an indefinite Sasakian manifold M¯(c) of constant φ¯-sectional curvature c. Under some geometric conditions, the author demonstrates that c=1, that is, M¯ is a space of constant curvature 1. Moreover, M and any leaf M′ of its screen distribution S(TM) are, also, spaces of constant curvature 1. The author has employed the techniques developed by K. L. Duggal and A. Bejancu of reference number 7. The author has discovered that any totally umbilic invariant ligtlike submanifold, whose transversal bundle is flat, in an indefinite Sasakian space form is, in fact, a space of constant curvature 1 (see Theorem 4.4). To the best of the author’s findings, at the time of submission of this paper, the results reported are new and interesting as far as lightlike geometry is concerned. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-04-05
DOI: 10.1108/AJMS-10-2020-0097 Issue No:Vol.
28
, No.
1
(2021)

Authors:
Sudhakar Kumar Chaubey
,
Uday Chand De
Abstract: The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly symmetric trans-Sasakian manifolds. Finally, they give a nontrivial example of three-dimensional proper trans-Sasakian manifold. The authors have used the tensorial approach to achieve the goal. A second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g. The authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-04-05
DOI: 10.1108/AJMS-12-2020-0127 Issue No:Vol.
28
, No.
1
(2021)

Authors:
Habtamu Garoma Debela
Abstract: The purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay. This study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation. The stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points. In this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-03-30
DOI: 10.1108/AJMS-09-2020-0058 Issue No:Vol.
28
, No.
1
(2021)

Authors:
H.M. Manjunatha
,
S.K. Narasimhamurthy
,
Zohreh Nekouee
Abstract: The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties. This paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic. The Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained. The findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-03-26
DOI: 10.1108/AJMS-10-2020-0085 Issue No:Vol.
28
, No.
1
(2021)

Authors:
Md Abu Hanif Sarkar
Abstract: The purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain. For positive and bounded initial data, the authors study the initial zero-boundary value problem. The findings of this study showed the complete extinction of a continuous weak solution at a finite time. The extinction time is studied earlier but for the Laplacian case. The authors presented the finite extinction time for the case of p-Laplacian. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-03-08
DOI: 10.1108/AJMS-08-2020-0042 Issue No:Vol.
28
, No.
1
(2021)

Authors:
Julee Srivastava
Abstract: In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings. Showed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-03-05
DOI: 10.1108/AJMS-08-2020-0044 Issue No:Vol.
28
, No.
1
(2021)

Authors:
Bikash Barman
,
Kukil Kalpa Rajkhowa
Abstract: The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph, denoted by NES(R), of a commutative ring R with unity is an undirected graph whose vertex set is the collection of all nonessential ideals of R and any two vertices are adjacent if and only if their sum is also a nonessential ideal of R. The method is theoretical. The authors obtain some properties of NES(R) related with connectedness, diameter, girth, completeness, cut vertex, r-partition and regular character. The clique number, independence number and domination number of NES(R) are also found. The paper is original. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-02-24
DOI: 10.1108/AJMS-08-2020-0039 Issue No:Vol.
28
, No.
1
(2021)

Authors:
Rim Amami
,
Monique Pontier
,
Hani Abidi
Abstract: The purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem. The main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results. In this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps. In this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem. Citation:
Arab Journal of Mathematical Sciences
PubDate:
2021-02-16
DOI: 10.1108/AJMS-10-2020-0088 Issue No:Vol.
28
, No.
1
(2021)