Abstract: Publication date: Available online 2 July 2018Source: Arab Journal of Mathematical SciencesAuthor(s): Aymen Ben Amira, Bechir Chaari, Jamel Dammak, Hamza Si Kaddour Two digraphs G=(V,E) andG′=(V,E′) are isomorphic up to complementation if G′ is isomorphic to G or to the complement G¯≔(V,{(x,y)∈V2:x≠y,(x,y)∉E}) of G. The Boolean sum G+̇G′ is the symmetric digraph U=(V,E(U)) defined by {x,y}∈E(U) if and only if (x,y)∈E and(x,y)∉E′, or (x,y)∉E and(x,y)∈E′. Let k be a nonnegative integer. The digraphs G andG′ are (≤k)-hypomorphic up to complementation if for every t-element subset X of V, with t≤k, the induced subdigraphs G↾X andG↾X...

Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Abdelkader Zagane, Seddik Ouakkas In this paper, we will study the class of biharmonic maps with potential, in the particular case represented by conformal maps between equidimensional manifolds. Some examples are constructed in particular cases (Euclidean space and sphere).

Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Anupam Sharma In this paper we approximate common fixed points of nearly asymptotically nonexpansive mappings under modified SP-iteration process in the setting of CAT(k) spaces and establish strong and Δ-convergence theorems. Our results generalize and improve the corresponding known results of the existing literature.

Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Karim Chaira, Samih Lazaiz In this paper, we formulate best proximity pair theorems for noncyclic relatively ρ-nonexpansive mappings in modular spaces in the setting of proximal ρ-admissible sets. As a companion result, we establish a best proximity pair theorem for pointwise noncyclic contractions in modular spaces. To that end, we provide some examples throughout the paper to illustrate the validity of the obtained results.

Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Kawtar Attas, Abderrahim Boussaïri, Mohamed Zaidi An arc-weighted digraph is a pair (D,ω) where D is a digraph and ω is an arc-weight function that assigns to each arc uv of D a nonzero real number ω(uv). Given an arc-weighted digraph (D,ω) with vertices v1,…,vn, the weighted adjacency matrix of (D,ω) is defined as the n×n matrix A(D,ω)=[aij] where aij=ω(vivj) if vivj is an arc of D, and 0otherwise. Let (D,ω) be a positive arc-weighted digraph and assume that D is loopless and symmetric. A skew-signing of (D,ω) is an arc-weight function ω′ such that ω′(uv)=±ω(uv) and ω′(uv)ω′(vu)

Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): S. Reza Hejazi, Elham Lashkarian In this paper, a (3+1)-dimensional wave equation is studied from the point of view of Lie’s theory in partial differential equations including conservation laws. The symmetry operators are determined to find the reduced form of the considered equation. The non-local conservation theorems and multipliers approach are performed on the (3+1)-dimensional wave equation. We obtain conservation laws by using five methods, such as direct method, Noether’s method, extended Noether’s method, Ibragimov’s method; and finally we can derive infinitely many conservation laws from a known conservation law viewed as the last method. We also derive some exact solutions using some conservation laws Anco and Bluman (2002).

Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): Samuel Azubuike Iyase, Olawale Joshua Adeleke This paper investigates the existence of solutions for higher-order multipoint boundary value problems at resonance. We obtain existence results by using coincidence degree arguments.

Abstract: Publication date: July 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 2Author(s): B. Radhakrishnan, M. Tamilarasi This paper deals with the existence of solutions for quasilinear random impulsive neutral functional differential evolution equation in Banach spaces and the results are derived by using the analytic semigroup theory, fractional powers of operators and the Schauder fixed point approach. An application is provided to illustrate the theory.

Abstract: Publication date: Available online 15 June 2018Source: Arab Journal of Mathematical SciencesAuthor(s): Emmanuel Fouotsa This paper considers the computation of the Ate pairing on the Hessian model of elliptic curves. Due to the many important properties making the model attractive in cryptography, we compute for the first time the Ate pairing on this model and show how both the Tate and the Ate pairings can be parallelized on this curve. We wrote codes in the Sage software to ensure the correctness of formulas in this work.

Abstract: Publication date: Available online 13 March 2018Source: Arab Journal of Mathematical SciencesAuthor(s): Rafik Aguech, Wissem Jedidi We give several new characterizations of completely monotone functions and Bernstein functions via two approaches: the first one is driven algebraically via elementary preserving mappings and the second one is developed in terms of the behavior of their restriction on N0. We give a complete answer to the following question: Can we affirm that a functionfis completely monotone (resp. a Bernstein function) if we know that the sequencef(k)kis completely monotone (resp. alternating)' This approach constitutes a kind of converse to Hausdorff’s moment characterization theorem in the context of completely monotone sequences.

Abstract: Publication date: Available online 8 March 2018Source: Arab Journal of Mathematical SciencesAuthor(s): Hongwu Wu, Julio G. Dix By using iterated estimates involving all delay arguments, we establish an oscillation criterion for first-order linear differential equations with several delay arguments. This criterion is focused on the interaction among the delay arguments, instead of converting the original equation into a single delay equation and using existing results. Several examples illustrate the results obtained.

Abstract: Publication date: January 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 1Author(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.

Abstract: Publication date: January 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 1Author(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.

Abstract: Publication date: January 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 1Author(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.

Abstract: Publication date: January 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 1Author(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∣Fp−p5. We then discuss these results in the context of primality testing.

Abstract: Publication date: January 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 1Author(s): Ahmed Mohammed Cherif, Mustapha 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.

Abstract: Publication date: January 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 1Author(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.

Abstract: Publication date: January 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 1Author(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.

Abstract: Publication date: January 2018Source: Arab Journal of Mathematical Sciences, Volume 24, Issue 1Author(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.