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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 .

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.

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.

Authors:Nareen Bamerni; Adem Kılıçman Abstract: Publication date: Available online 14 June 2016 Source:Arab Journal of Mathematical Sciences Author(s): Nareen Bamerni, Adem Kılıçman 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.

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.

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.