# Arabian Journal of Mathematics

## List of Papers (Total 204)

#### Methods of the theory of critical points at infinity on Cauchy Riemann manifolds

Sub-Riemannian spaces are spaces whose metric structure may be viewed as a constrained geometry, where motion is only possible along a given set of directions, changing from point to point. The simplest example of such spaces is given by the so-called Heisenberg group. The characteristic constrained motion of sub-Riemannian spaces has numerous applications in robotic control in...

#### Fractional parts and their relations to the values of the Riemann zeta function

A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the...

#### 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...

#### 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...

#### 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...

#### 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...