Arabian Journal of Mathematics

List of Papers (Total 200)

Weakly submaximal spaces and compactifications

In this paper, we characterize spaces such that their one-point compactification (resp., Herrlich compactification) is weakly submaximal. We also establish a necessary and sufficient condition on $$T_{0}$$-spaces in order to get their one-point compactification (resp., Herrlich compactification) $$T_{D}$$-spaces.

Turán type inequalities for the q-exponential functions

In this paper, our aim is to deduce some sharp Turán type inequalities for the remainder q-exponential functions. Our results are shown to be generalizations of results which were obtained by Alzer (Arch Math 55, 462–464, 1990).

Existence of periodic solutions for some quasilinear parabolic problems with variable exponents

In this paper, we prove the existence of at least one periodic solution for some nonlinear parabolic boundary value problems associated with Leray–Lions’s operators with variable exponents under the hypothesis of existence of well-ordered sub- and supersolutions.

Minimal representations of Lie algebras with non-trivial Levi decomposition

We obtain minimal dimension matrix representations for each of the Lie algebras of dimensions five, six, seven and eight obtained by Turkowski that have a non-trivial Levi decomposition. The key technique involves using the invariant subspaces associated to a particular representation of a semi-simple Lie algebra to help in the construction of the radical in the putative Levi...

On representations of the set of supermartingale measures and applications in discrete time

We investigate some new results concerning the m-stability property. We show in particular under the martingale representation property with respect to a bounded martingale S that an m-stable set of probability measures is the set of supermartingale measures for a family of discrete integral processes with respect to S.

Optimal codes from Fibonacci polynomials and secret sharing schemes

In this work, we study cyclic codes that have generators as Fibonacci polynomials over finite fields. We show that these cyclic codes in most cases produce families of maximum distance separable and optimal codes with interesting properties. We explore these relations and present some examples. Also, we present applications of these codes to secret sharing schemes.

(1,1)-Tensor sphere bundle of Cheeger–Gromoll type

We construct a metrical framed $$f(3,-1)$$-structure on the (1, 1)-tensor bundle of a Riemannian manifold equipped with a Cheeger–Gromoll type metric and by restricting this structure to the (1, 1)-tensor sphere bundle, we obtain an almost metrical paracontact structure on the (1, 1)-tensor sphere bundle. Moreover, we show that the (1, 1)-tensor sphere bundles endowed with the...

Conformal metrics of prescribed scalar curvature on 4-manifolds: the degree zero case

In this paper, we consider the problem of existence and multiplicity of conformal metrics on a Riemannian compact 4-dimensional manifold $$(M^4,g_0)$$ with positive scalar curvature. We prove a new existence criterium which provides existence results for a dense subset of positive functions and generalizes Bahri–Coron Euler–Poincaré type criterium. Our argument gives estimates of...

What can be expected from a cubic derivation on finite dimensional algebras?

In this paper, we prove that every rank one cubic derivation on a unital integral domain is identically zero. From this conclusion, under certain conditions, we achieve that the image of a cubic derivation on a commutative algebra is contained in the Jacobson radical of algebra. As the main result of the current study, we prove that every cubic derivation on a finite dimensional...

Expansions of the exponential and the logarithm of power series and applications

In the paper, the authors establish explicit formulas for asymptotic and power series expansions of the exponential and the logarithm of asymptotic and power series expansions. The explicit formulas for the power series expansions of the exponential and the logarithm of a power series expansion are applied to find explicit formulas for the Bell numbers and logarithmic polynomials...

Bahri invariants for fractional Nirenberg-type flows

This paper is concerned with prescribing the fractional Q-curvature on the unit sphere $$\mathbb {S}^{n}$$ endowed with its standard conformal structure $$g_0$$, $$n\ge 4$$. Since the associated variational problem is noncompact, we approach this issue with techniques passed by Abbas Bahri, as the well known theory of critical points at infinity, as well as some lesser known...

Bubbling phenomena in calculus of variations

This paper is a survey on bubbling phenomena occurring in some geometric problems. We present here a few problems from conformal geometry, gauge theory and contact geometry and we give the main ideas of the proofs and important results. We focus in particular on the Yamabe type problems and the Weinstein conjecture, where A. Bahri made a huge contribution by introducing new...

$${\varvec{(k,s)}}$$ -Riemann–Liouville fractional integral inequalities for continuous random variables

In this paper, we introduce some new concepts to the field of probability theory: $$\left( k,s\right)$$-Riemann–Liouville fractional expectation and variance functions. Some generalized integral inequalities are established for $$\left( k,s\right)$$-Riemann–Liouville expectation and variance functions.

Liouville-type theorems for a system governed by degenerate elliptic operators of fractional orders

We study the nonexistence of nontrivial solutions for the nonlinear elliptic system \begin{aligned} \left\{ \begin{array}{lll} (-\Delta _x)^{\alpha /2}u+|x|^{2\delta } (-\Delta _y)^{\beta /2}u+|x|^{2\eta }|y|^{2\theta } (-\Delta _z)^{\gamma /2}u&{}=&{} v^p,\\ \\ (-\Delta _x)^{\mu /2}v+|x|^{2\delta } (-\Delta _y)^{\nu /2}v+|x|^{2\eta }|y|^{2\theta } (-\Delta _z)^{\sigma /2}v...

Rational cohomologies of classifying spaces for homogeneous spaces of small rank

Let a simply-connected homogeneous space $${X}$$ satisfy the condition of $${{\rm dim} \pi_{\rm even}(X)\otimes {\mathbb{Q}}=2}$$ and $${{\rm dim} \pi_{\rm odd}(X)\otimes {\mathbb{Q}}=3}$$ (then, we say it is of (2, 3) type), which is the smallest rank in non-formal pure spaces. Then, we compute the Sullivan minimal model of the Dold–Lashof classifying space \({{\rm Baut}_1 X...

Prescribing the scalar curvature problem on the four-dimensional half sphere

In this paper, we consider the problem of prescribing scalar curvature under minimal boundary conditions on the standard four-dimensional half sphere. We describe the lack of compactness of the associated variational problem and we give new existence and multiplicity results.