Arabian Journal of Mathematics

List of Papers (Total 204)

On widths of periodic functions in L2

Exact values are obtained of the n-widths of 2π-periodic functions of the form f ( x ) = 1 2 π ∫ 0 2 π K ( x − t ) φ ( t ) d t = ( K ∗ φ ) ( x ) in space L2[0, 2π] and satisfy condition ( ∫ 0 h ω m p ( φ ; t ) sin γ nt d t ) 1 / p ≤ 1 , 0 < h ≤ π / n , γ > 0 , 0 < p ≤ 2 , where ω m (φ; t)−mth order modulus of continuity of function φ(x) ∈ L2[0, 2π]. Some further generalizations...

When every flat ideal is finitely projective

In this paper, we study the class of rings in which every flat ideal is finitely projective. We investigate the stability of this property under localizations and homomorphic images, and its transfer to various contexts of constructions such as direct products, amalgamation of rings \({A \bowtie^{f} J}\), and trivial ring extensions. Our results generate examples which enrich the...

A new algorithm for computing class groups of Zariski surfaces

Let k be an algebraically closed field of characteristic p ≠ 0 and \({X_{g} \subset A_{k}^{3}}\) be a normal surface defined by an equation of the form z p = g(x, y). The two original algorithms for calculating the group of Weil divisors of X g contain key errors. This paper presents an algorithm that corrects and improves upon the earlier attempts.

Another generalization of the gcd-sum function

We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group. We show that the asymptotic properties of this function are closely connected to the Piltz divisor function. A generalization of Menon’s identity is also...

Viscous dissipation, Ohmic heating and radiation effects on MHD flow past a rotating disk embedded in a porous medium with variable properties

The present work investigates the effects of viscous dissipation and Ohmic heating on steady MHD convective flow due to a porous rotating disk taking into account the variable fluid properties (density (ρ) viscosity (μ) and thermal conductivity (κ)) in the presence of Hall current and thermal radiation. These properties are taken to be dependent on temperature. The partial...

Some remarks on multiplicatively closed sets

Rings considered in this article are commutative with identity. A subring of a ring is assumed to contain the identity element of the ring. Let S be a multiplicatively closed subset of a ring R satisfying the following property (P): whenever \({ab \in S}\) with at least one of a, b is in S, then both of them are in S. The (P)-closure of any multiplicatively closed subset of R is...

Chain conditions in amalgamated algebras along an ideal

Let A and B be two rings, let J be an ideal of B and let f : A → B be a ring homomorphism. In this paper, we study when the amalgamation of A with B along J with respect to f is a \({\phi}\)-ring. Hence, we study two different chain conditions over this structure. Namely, the nonnil-Noetherian condition and the Noetherian spectrum condition.

Existence of positive solutions for a quasilinear elliptic system involving critical Sobolev-Hardy exponents and concave-convex nonlinearities

This paper is concerned with a quasilinear elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. The existence and multiplicity results of positive solutions are obtained by variational methods. Open image in new window

Maximax rearrangement optimization related to a homogeneous Dirichlet problem

In this paper we investigate a maximax optimization problem related to a homogeneous Dirichlet problem in two classes of rearrangements. We prove existence and representation of the maximizers. Open image in new window

The set of prime divisors of generalized denominator ideals

Let R be a Noetherian domain with quotient field K. Let A be an integral domain which contains R and whose elements are algebraic over K. We define \({{\rm Eass}_{R}(A/R)}\) to be the set of prime ideals \({\mathfrak{p}}\) ’s of R such that \({\mathfrak{p}}\) is a prime divisor of a generalized denominator ideal I[β] for some \({\beta \in A}\). Assume that \({A = R[\alpha_{1...

The impact of the flatness condition on the prescribed Webster scalar curvature

In this paper, we give existence and multiplicity results for the problem of prescribing the Webster scalar curvature on the three CR sphere of \(\mathbb{C}^{2}\) under mixed conditions: non-degenerancy and flatness. Open image in new window

Symmetric tensor rank over an infinite field

Here we prove two upper bounds (one for bivariate polynomials, one for multivariate ones) for the symmetric tensor rank with respect to an infinite field with characteristic ≠ 2. Open image in new window

Generalized Geraghty type mappings on partial metric spaces and fixed point results

In the present paper, we introduce generalized Geraghty (Proc Am Math Soc 40:604–608, 1973) mappings on partial metric spaces and give a fixed point theorem which generalizes some recent results appearing in the literature. Open image in new window

Unit graphs of rings of polynomials and power series

Let R be a commutative ring. The unit graph of R, denoted by G(R), is a graph with all elements of R as vertices and two distinct vertices x, y ∈ R are adjacent if and only if x + y ∈ U(R) where U(R) denotes the set of all units of R. In this paper, we examine the preservation of the connectedness, diameter, girth, and some other properties, such as chromatic index, clique number...

A characterization of the essential pseudospectra on a Banach space

In this paper, we introduce and study the essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving the definition and we investigate the characterization, the stability and some properties of these essential pseudospectra.

Fekete–Szegö problem for subclasses of analytic functions defined by Komatu integral operator

Using the Komatu integral operator, new subclasses of analytic functions are introduced. For these classes, several Fekete–Szegö type coefficient inequalities are derived.

Complete intersection vanishing ideals on degenerate tori over finite fields

We study the complete intersection property and the algebraic invariants (index of regularity, degree) of vanishing ideals on degenerate tori over finite fields. We establish a correspondence between vanishing ideals and toric ideals associated to numerical semigroups. This correspondence is shown to preserve the complete intersection property, and allows us to use some available...

Energy decay in a Timoshenko-type system of thermoelasticity of type III with different wave-propagation speeds

In this paper, we consider a one-dimensional linear Timoshenko system of thermoelasticity type III and prove a polynomial stability result for the non-equal wave-propagation speed case.

Meromorphic functions that share one value and the solution of Riccati differential equation

In this paper, we shall give new examples on meromorphic functions that share one value with their first derivative and also give the solution for Riccati differential equation.

Hybrid approximation of solutions of integral equations of the Hammerstein type

Let X be a uniformly convex and uniformly smooth real Banach space with dual X*. Let F : X → X* and K : X* → X be continuous monotone operators. Suppose that the Hammerstein equation u + KFu =  0 has a solution in X. It is proved that a hybrid-type approximation sequence converges strongly to u*, where u* is a solution of the equation u +  KFu =  0. In our theorems, the operator...

Some remarks on Dedekind lattices

In this paper, we prove that a principally generated C-lattice L is a Dedekind lattice if and only if L is a WI-lattice in which every invertible element is a finite meet of powers of prime elements.

On differential sandwich theorems of p-valent analytic functions defined by the integral operator

In this paper, we derive some subordination and superordination results for certain p-valent analytic functions in the open unit disc, which are acted upon by an integral operator. Relevant connection of the results, which are presented in this paper with various known results are also considered.

On strongly \({\varphi_{h}}\) -convex functions in inner product spaces

In this paper, we introduce the notion of strongly \({\varphi_{h}}\) -convex functions with respect to c > 0 and present some properties and representation of such functions. We obtain a characterization of inner product spaces involving the notion of strongly \({\varphi_{h}}\) -convex functions. Finally, a version of Hermite–Hadamard-type inequalities for strongly \({\varphi_{h...

Finite groups with some \({\mathcal{F}}\) -supplemented subgroups II

In this paper, we obtain a new characterization of p-nilpotent groups under the assumption that some maximal subgroups of Sylow subgroup are \({\mathcal{F}}\)-supplemented. As its applications, we generalize many known results.

Exponential state estimation for impulsive neural networks with time delay in the leakage term

In this paper, the exponential state estimation problem for impulsive neural networks with both leakage delay and time-varying delays is investigated. Several sufficient conditions which are given in terms of linear matrix inequalities (LMIs) are derived to estimate the neuron states such that the dynamics of the estimation error is globally exponentially stable by constructing...