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 Arab Journal of Mathematical Sciences   [3 followers]  Follow       Open Access journal    ISSN (Print) 1319-5166    Published by Elsevier  [3123 journals]
• Classification of derivation algebras in low dimensions

• Authors: Mohammed Guediri; Kholoud Albalawi
Abstract: Publication date: Available online 8 December 2017
Source:Arab Journal of Mathematical Sciences
Author(s): Mohammed Guediri, Kholoud Albalawi
A left-symmetric algebra A is said to be a derivation algebra if all its left and right multiplications are derivations of the Lie algebra associated to A . In this paper, we shall study derivation algebras over R and then classify almost all those of dimensions ≤ 4 .

PubDate: 2017-12-26T21:14:07Z
DOI: 10.1016/j.ajmsc.2017.11.001

• Copula conditional tail expectation for multivariate financial risks

• Authors: Brahimi Brahim; Benatia Fatah; Yahia Djabrane
Abstract: Publication date: Available online 3 November 2017
Source:Arab Journal of Mathematical Sciences
Author(s): Brahimi Brahim, Benatia Fatah, Yahia Djabrane
Our goal in this paper is to propose an alternative risk measure which takes into account the fluctuations of losses and possible correlations between random variables. This new notion of risk measures, that we call Copula Conditional Tail Expectation describes the expected amount of risk that can be experienced given that a potential bivariate risk exceeds a bivariate threshold value, and provides an important measure for right-tail risk. An application to real financial data is given.

PubDate: 2017-11-10T10:25:47Z
DOI: 10.1016/j.ajmsc.2017.10.002

• Some results of the f-biharmonic maps and applications

• Authors: Djelloul Djebbouri; Seddik Ouakkas
Abstract: Publication date: Available online 19 October 2017
Source:Arab Journal of Mathematical Sciences
Author(s): Djelloul Djebbouri, Seddik Ouakkas
In this paper, we give some properties of the f -biharmonic maps, in the particular case represented by conformal maps between equidimensional manifolds. We construct a new example of the f -biharmonic maps and we characterize the p -biharmonicity of some particular cases.

PubDate: 2017-11-10T10:25:47Z
DOI: 10.1016/j.ajmsc.2017.10.001

• Kohn–Vogelius formulation and topological sensitivity analysis based
method for solving geometric inverse problems

• Authors: Maatoug Hassine; Imen Kallel
Abstract: Publication date: Available online 6 October 2017
Source:Arab Journal of Mathematical Sciences
Author(s): Maatoug Hassine, Imen Kallel
In this paper, we propose an alternative approach combining the advantages of the Kohn–Vogelius formulation and the topological sensitivity analysis method for solving geometric inverse problems. The Kohn–Vogelius formulation can rephrase the geometric inverse problem into a shape optimization one minimizing an energy-like function. The sensitivity analysis gives the leading term of the energy-like function variation with respect to the presence of a small geometry perturbation inside the computational domain. The obtained theoretical results lead to build a fast and accurate numerical reconstruction algorithm. The efficiency and accuracy of the proposed algorithm are illustrated by some numerical results.

PubDate: 2017-10-12T20:33:32Z
DOI: 10.1016/j.ajmsc.2017.09.001

• Asymptotic behaviour of a suspension bridge problem

• Authors: Soh Edwin Mukiawa
Abstract: Publication date: Available online 31 July 2017
Source:Arab Journal of Mathematical Sciences
Author(s): Soh Edwin Mukiawa
In this paper, we consider a fourth-order viscoelastic plate equation with infinite memory, and with partially hinged boundary conditions. We investigate the asymptotic behaviour of solutions. This present paper improves earlier results in the literature and allow an extended range of relaxation functions.

PubDate: 2017-08-04T02:49:44Z
DOI: 10.1016/j.ajmsc.2017.07.002

• Oscillation criteria for a class of third order damped differential
equations

• Authors: Osama Moaaz; Elmetwally M. Elabbasy; Ebtesam Shaaban
Abstract: Publication date: Available online 27 July 2017
Source:Arab Journal of Mathematical Sciences
Author(s): Osama Moaaz, Elmetwally M. Elabbasy, Ebtesam Shaaban
The present study concerns the oscillation of a class of third-order nonlinear delay differential equations with middle term. We offer a new description of oscillation of the third-order equations in terms of oscillation of a related well studied second-order linear differential equation without damping. By using the integral averaging technique, we establish new oscillation results for this equation. Some examples are provided to illustrate the main results.

PubDate: 2017-08-04T02:49:44Z
DOI: 10.1016/j.ajmsc.2017.07.001

• On Fibonacci and Lucas sequences modulo a prime and primality testing

• Authors: Dorin Andrica; Vlad Crişan; Fawzi Al-Thukair
Abstract: Publication date: Available online 24 June 2017
Source:Arab Journal of Mathematical Sciences
Author(s): Dorin Andrica, Vlad Crişan, Fawzi Al-Thukair
We prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p ∣ F p − p 5 . We then discuss these results in the context of primality testing.

PubDate: 2017-07-03T20:43:05Z
DOI: 10.1016/j.ajmsc.2017.06.002

• On the bi-harmonic maps with potential

• Authors: A. Mohammed Cherif; M. Djaa
Abstract: Publication date: Available online 15 June 2017
Source:Arab Journal of Mathematical Sciences
Author(s): A. Mohammed Cherif, M. Djaa
In this note we characterize the harmonic maps and biharmonic maps with potential, and we prove that every biharmonic map with potential on a complete manifold satisfying some conditions is a harmonic map with potential.

PubDate: 2017-06-17T18:14:12Z
DOI: 10.1016/j.ajmsc.2017.06.001

• Potential eventual positivity of sign patterns with the underlying broom
graph

• Authors: Ber-Lin Yu; Jie Cui; Hongzhuan Wang; Xingyong Xie
Abstract: Publication date: Available online 30 November 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Ber-Lin Yu, Jie Cui, Hongzhuan Wang, Xingyong Xie
A sign pattern is a matrix whose entries belong to the set { + , − , 0 } . An n -by- n sign pattern A is said to allow an eventually positive matrix or be potentially eventually positive if there exist at least one real matrix A with the same sign pattern as A and a positive integer k 0 such that A k > 0 for all k ≥ k 0 . Identifying the necessary and sufficient conditions for an n -by- n sign pattern to be potentially eventually positive, and classifying the n -by- n sign patterns that allow an eventually positive matrix were posed as two open problems by Berman, Catral, Dealba, et al. In this article, we focus on the potential eventual positivity of a collection of the n -by- n tree sign patterns A n , 4 whose underlying graph G ( A n , 4 ) consists of a path P with 4 vertices, together with ( n − 4 ) pendent vertices all adjacent to the same end vertex of P . Some necessary conditions for the n -by- n tree sign patterns A n , 4 to be potentially eventually positive are established. All the minimal subpatterns of A n , 4 that allow an eventually positive matrix are identified. Consequently, all the potentially eventually positive subpatterns of A n , 4 are classified.

PubDate: 2016-12-04T01:59:30Z
DOI: 10.1016/j.ajmsc.2016.11.002

• Hermite-Hadamard-Fejer type inequalities for p-convex functions

• Authors: Mehmet Kunt
Abstract: Publication date: Available online 17 November 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Mehmet Kunt, İmdat İşcan
In this paper, firstly, Hermite-Hadamard-Fejer type inequalities for p -convex functions are built. Secondly, an integral identity and some Hermite-Hadamard-Fejer type integral inequalities for p -convex functions are obtained. Finally, some Hermite-Hadamard and Hermite-Hadamard-Fejer inequalities for convex, harmonically convex and p -convex functions are given. Some results presented here for p -convex functions provide extensions of others given in earlier works for convex and harmonically convex and p -convex functions.

PubDate: 2016-11-19T18:02:16Z

• Local convergence of a fifth convergence order method in Banach space

• Authors: Ioannis K. Argyros; Santhosh George
Abstract: Publication date: Available online 12 November 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Ioannis K. Argyros, Santhosh George
We provide a local convergence analysis for a fifth convergence order method to find a solution of a nonlinear equation in a Banach space. In our paper the sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative. Previous works use conditions reaching up to the fourth Fréchet-derivative. This way, the applicability of these methods is extended under weaker conditions and less computational cost for the Lipschitz constants appearing in the convergence analysis. Numerical examples are also given in this paper.

PubDate: 2016-11-13T05:55:20Z
DOI: 10.1016/j.ajmsc.2016.10.002

• On the study of Brück conjecture and some non-linear complex
differential equations

• Authors: Dilip Ch.; Pramanik Manab Biswas Rajib Mandal
Abstract: Publication date: Available online 2 November 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Dilip Ch. Pramanik, Manab Biswas, Rajib Mandal
In this paper, we prove the following result: Let f ( z ) and α ( z ) be two non-constant entire functions satisfying σ ( α ) < μ ( f ) and P ( z ) be a polynomial. If f isa non-constant entire solution of the differential equation M [ f ] + β ( z ) − α ( z ) = ( f γ M − α ( z ) ) e P ( z ) , where β ( z ) is an entire function satisfying σ ( β ) < μ ( f ) . Then σ 2 ( f ) = deg P . Our result generalizes the results due to Gundersen and Yang, Chang and Zhu and Li and Cao.

PubDate: 2016-11-06T04:38:36Z

• On the genus of nil-graph of ideals of commutative rings

• Authors: T. Tamizh Chelvam; K. Selvakumar; P. Subbulakshmi
Abstract: Publication date: Available online 2 October 2016
Source:Arab Journal of Mathematical Sciences
Author(s): T. Tamizh Chelvam, K. Selvakumar, P. Subbulakshmi
Let R be a commutative ring with identity and let Nil ( R ) be the ideal of all nilpotent elements of R . Let I ( R ) = { I : I is a non-trivial ideal of R and there exists a non-trivial ideal J such that I J ⊆ Nil ( R ) } . The nil-graph of ideals of R is defined as the simple undirected graph A G N ( R ) whose vertex set is I ( R ) and two distinct vertices I and J are adjacent if and only if I J ⊆ Nil ( R ) . In this paper, we study the planarity and genus of A G N ( R ) . In particular, we have characterized all commutative Artin rings R for which the genus of A G N ( R ) is either zero or one.

PubDate: 2016-10-09T01:22:07Z
DOI: 10.1016/j.ajmsc.2016.09.004

• On the equivalence of two curvature conditions for Lorentzian
hypersurfaces

• Authors: Mohammed Guediri; Norah Alshehri
Abstract: Publication date: Available online 24 September 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Mohammed Guediri, Norah Alshehri
Let n ≥ 3 . We show that semi-symmetry and Ricci-semisymmetry conditions are equivalent for any n -dimensional Lorentzian hypersurface in a Lorentzian space form with nonzero curvature. We also show that these curvature conditions are equivalent for any n -dimensional Lorentzian isoparametric hypersurface in Minkowski space R 1 n + 1 , and we construct an example of a Ricci-semisymmetric 5 -dimensional Lorentzian hypersurface in R 1 6 which is not semi-symmetric.

PubDate: 2016-09-25T08:59:26Z
DOI: 10.1016/j.ajmsc.2016.09.001

• Statistical properties of an estimator for the mean function of a compound
cyclic Poisson process in the presence of linear trend

• Authors: Bonno Andri Wibowo; I Wayan Mangku; Siswadi
Abstract: Publication date: Available online 22 September 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Bonno Andri Wibowo, I. Wayan Mangku, Siswadi
The problem of estimating the mean function of a compound cyclic Poisson process with linear trend is considered. An estimator of this mean function is constructed and investigated. The cyclic component of intensity function of this process is not assumed to have any parametric form, but its period is assumed to be known. The slope of the linear trend is assumed to be positive, but its value is unknown. Moreover, we consider the case when there is only a single realization of the Poisson process is observed in a bounded interval. Asymptotic bias and variance of the proposed estimator are computed, when the size of interval indefinitely expands.

PubDate: 2016-09-25T08:59:26Z
DOI: 10.1016/j.ajmsc.2016.08.004

• Characterizing spheres by an immersion in Euclidean spaces

• Authors: Sharief Deshmukh; Ibrahim Al-Dayel
Abstract: Publication date: Available online 22 September 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Sharief Deshmukh, Ibrahim Al-Dayel
In this paper we study compact immersed orientable hypersurfaces in the Euclidean space R n + 1 and show that suitable restrictions on the tangential and normal components of the immersion give different characterizations of the spheres.

PubDate: 2016-09-25T08:59:26Z
DOI: 10.1016/j.ajmsc.2016.09.002

• Geometry of conformal vector fields

• Authors: Sharief Deshmukh
Abstract: Publication date: Available online 22 September 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Sharief Deshmukh
It is well known that the Euclidean space ( R n , 〈 , 〉 ) , the n -sphere S n ( c ) of constant curvature c and Euclidean complex space form ( C n , J , 〈 , 〉 ) are examples of spaces admitting conformal vector fields and therefore conformal vector fields are used in obtaining characterizations of these spaces. In this article, we study the conformal vector fields on a Riemannian manifold and present the existing results as well as some new results on the characterization of these spaces. Taking clue from the analytic vector fields on a complex manifold, we define φ -analytic conformal vector fields on a Riemannian manifold and study their properties as well as obtain characterizations of the Euclidean space ( R n , 〈 , 〉 ) and the n -sphere S n ( c ) of constant curvature c using these vector fields.

PubDate: 2016-09-25T08:59:26Z
DOI: 10.1016/j.ajmsc.2016.09.003

• A survey on the geometry of production models in economics

• Authors: Alina-Daniela Vîlcu; Gabriel-Eduard Vîlcu
Abstract: Publication date: Available online 24 August 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Alina-Daniela Vîlcu, Gabriel-Eduard Vîlcu
In this article we survey selected recent results on the geometry of production models, focussing on the main production functions that are usually analyzed in economics, namely homogeneous, homothetic, quasi-sum and quasi-product production functions.

PubDate: 2016-08-27T10:55:34Z
DOI: 10.1016/j.ajmsc.2016.08.003

• On connections on principal bundles

• Authors: Indranil Biswas
Abstract: Publication date: Available online 24 August 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Indranil Biswas
A new construction of a universal connection was given in Biswas, Hurtubise & Stasheff (2012). The main aim here is to explain this construction. A theorem of Atiyah and Weil says that a holomorphic vector bundle E over a compact Riemann surface admits a holomorphic connection if and only if the degree of every direct summand of E is degree. In Azad & Biswas (2002), this criterion was generalized to principal bundles on compact Riemann surfaces. This criterion for principal bundles is also explained.

PubDate: 2016-08-27T10:55:34Z
DOI: 10.1016/j.ajmsc.2016.08.002

• Topics in differential geometry associated with position vector fields on
Euclidean submanifolds

• Authors: Bang-Yen Chen
Abstract: Publication date: Available online 13 August 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Bang-Yen Chen
Position vector field is the most elementary and natural geometric object on a Euclidean submanifold. The purpose of this article is to survey six research topics in differential geometry in which the position vector field plays very important roles. In this article we also explain the relationship between position vector fields and mechanics, dynamics, and D’Arcy Thompson’s law of natural growth in biology.

PubDate: 2016-08-17T05:08:50Z
DOI: 10.1016/j.ajmsc.2016.08.001

• Symmetric duality for left and right Riemann–Liouville and Caputo
fractional differences

• Authors: Thabet Abdeljawad; Delfim F.M. Torres
Abstract: Publication date: Available online 18 July 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Thabet Abdeljawad, Delfim F.M. Torres
A discrete version of the symmetric duality of Caputo–Torres, to relate left and right Riemann–Liouville and Caputo fractional differences, is considered. As a corollary, we provide an evidence to the fact that in case of right fractional differences, one has to mix between nabla and delta operators. As an application, we derive right fractional summation by parts formulas and left fractional difference Euler–Lagrange equations for discrete fractional variational problems whose Lagrangians depend on right fractional differences.

PubDate: 2016-07-26T21:46:13Z
DOI: 10.1016/j.ajmsc.2016.07.001

• On the equation Vn=wx2∓1

• Authors: Refik Keskin
Abstract: Publication date: Available online 30 June 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Ümmügülsüm Öğüt, Refik Keskin
Let P ≥ 3 be an integer and ( V n ) denote Lucas sequence of the second kind defined by V 0 = 2 , V 1 = P , and V n + 1 = P V n − V n − 1 for n ≥ 1 . In this study, when P is odd and w ∈ { 10 , 14 , 15 , 21 , 30 , 35 , 42 , 70 , 210 } , we solved the equation V n = w x 2 ∓ 1 . We showed that only V 1 can be of the form w x 2 + 1 and only V 1 or V 2 can be of the form w x 2 − 1 .

PubDate: 2016-07-03T11:14:03Z

• Some explicit and recursive formulas of the large and little Schröder
numbers

• Authors: Feng Qi; Bai-Ni Guo
Abstract: Publication date: Available online 21 June 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Feng Qi, Bai-Ni Guo
In the paper, the authors analytically find some explicit formulas and recursive formulas for the large and little Schröder numbers.

PubDate: 2016-06-28T22:03:13Z
DOI: 10.1016/j.ajmsc.2016.06.002

• Ground state solutions and least energy sign-changing solutions for a
class of fourth order Kirchhoff-type equations in RN

• Authors: Sofiane Khoutir; Haibo Chen
Abstract: Publication date: Available online 21 June 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Sofiane Khoutir, Haibo Chen
In this article we study the problem Δ 2 u − ( 1 + λ ∫ R N ∇ u 2 d x ) Δ u + V ( x ) u = u p − 2 u in  R N , where Δ 2 ≔ Δ ( Δ ) is the biharmonic operator, λ > 0 is a parameter, p ∈ ( 2 , 2 ∗ ) , and V ( x ) ∈ C ( R N , R ) . Under appropriate assumptions on V ( x ) , the existence of ground state solutions and least energy sign-changing solution is obtained by combining the variational methods and the Nehari method.

PubDate: 2016-06-28T22:03:13Z

• On subspace-diskcyclicity

• Authors: Nareen Bamerni; Adem Kılıçman
Abstract: Publication date: Available online 14 June 2016
Source:Arab Journal of Mathematical Sciences
In this paper, we define and study subspace-diskcyclic operators. We show that subspace-diskcyclicity does not imply diskcyclicity. We establish a subspace-diskcyclic criterion and use it to find a subspace-diskcyclic operator that is not subspace-hypercyclic for any subspaces. Also, we show that the inverses of invertible subspace-diskcyclic operators do not need to be subspace-diskcyclic for any subspaces. Finally, we prove that every finite-dimensional Banach space over the complex field supports a subspace-diskcyclic operator.

PubDate: 2016-06-18T20:53:37Z
DOI: 10.1016/j.ajmsc.2016.06.001

• Some congruences modulo 2 and 5 for bipartition with 5-core

• Authors: Nipen Saikia; Chayanika Boruah
Abstract: Publication date: Available online 2 June 2016
Source:Arab Journal of Mathematical Sciences
Author(s): Nipen Saikia, Chayanika Boruah
We find some congruences modulo 2 and 5 for the number of bipartitions with 5-core for a positive integer n in the spirit of Ramanujan.

PubDate: 2016-06-13T06:43:42Z

• On a type of almost Kenmotsu manifolds with nullity distributions

• Authors: U.C. De; Krishanu Mandal
Abstract: Publication date: Available online 27 April 2016
Source:Arab Journal of Mathematical Sciences
Author(s): U.C. De, Krishanu Mandal
The object of the present paper is to characterize Weyl semisymmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to the ( k , μ ) ′ -nullity distribution and ( k , μ ) -nullity distribution respectively. Also we characterize almost Kenmotsu manifolds satisfying the curvature condition C ⋅ S = 0 , where C and S are the Weyl conformal curvature tensor and Ricci tensor respectively with its characteristic vector field ξ belonging to the ( k , μ ) ′ -nullity distribution. As a consequence of the main results we obtain several corollaries. Finally, we present an example to verify our results.

PubDate: 2016-05-04T10:22:41Z
DOI: 10.1016/j.ajmsc.2016.04.001

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