# Arabian Journal of Mathematics

## List of Papers (Total 204)

#### Multipliers on H(p, q, α) spaces

Let f be an analytic function on the unit disc $${\mathbb{D}}$$ and F(a, b; c; z) be the Gaussian hypergeometric function. We consider the operator Ta,b,c on H(p, q, α) defined as Ta, b, cf(z) =  f(z) * F(a, b; c; z), where * denotes the usual Hadamard/convolution product. We prove that the Taylor coefficients of F(a, b; c; z) are a multiplier from H(p, q, α) to H(p, q, α + a + b...

#### Connected Hopf corings and their Dieudonné counterparts

We define coring objects in the category of algebras over a perfect field of characteristic p (with connected underlying Hopf algebra) and the corresponding notion for Dieudonné modules, and prove the equivalence of the two resulting categories, extending thus the methods of Dieudonné theory for Hopf rings from Ravenel (Reunión Sobre Teoría de Homotopía, volume 1 of Serie notas...

#### The descriptive complexity of the family of Banach spaces with the π-property

We show that the set of all separable Banach spaces that have the π-property is a Borel subset of the set of all closed subspaces of C(Δ), where Δ is the Cantor set, equipped with the standard Effros-Borel structure. We show that if α < ω 1, the set of spaces with Szlenk index at most α which have a shrinking FDD is Borel.

#### Norm-minimal Neumann boundary control of the wave equation

We consider the problem to control a vibrating string to rest in a given finite time. The string is fixed at one end and controlled by Neumann boundary control at the other end. We give an explicit representation of the L 2-norm minimal control in terms of the given initial state. We show that if the initial state is sufficiently regular, the same control is also L p -norm...

#### An abstract approach for the study of an elliptic problem in a nonsmooth cylinder

The aim of this work is the resolution of a non-autonomous abstract differential equation of elliptic type set on unbounded domain. The study is performed in the framework of Hölder spaces. An example for a concrete elliptic problem in nonsmooth cylindrical domains will illustrate the theory.Open image in new window

#### Some results on Fredholm and semi-Fredholm perturbations

In this paper, we investigate some properties of semi-Fredholm operators on Banach spaces. These results are applied to the determination of the stability of various essential spectra of closed densely defined linear operators. Also, we generalize some results in the literature and we extend and unify those obtained in Jeribi (J Math Anal Appl 271:343–358, 2002), Jeribi (J Math...

#### On the asymptotic growth rate of the sum of p-adic-valued independent identically distributed random variables

The p-adic semistable laws are characterized as weak limits of scaled summands of p-adic-valued, rotation-symmetric, independent, and identically distributed random variables whose tail probability satisfies some condition. In this article it is verified such scaled sums do not converge in probability, and some more precise estimates, corresponding to the law of iterated...

#### Fredholm pseudo-gradients for the action functional on a sub-manifold of dual Legendrian curves of a three dimensional contact manifold (M3, α)

We prove in this paper that the intersection numbers between periodic orbits have an intrinsic meaning for the variational problem (J,C β ) {Bahri (Pseudo-Orbits of Contact Forms Pitman Research Notes in Mathematics Series No. 173, 1984), Bahri (C R Acad Sci Paris 299, Serie I 15:757–760, 1984), Bahri (Classical and Quantic periodic motions of multiply polarized spin-manifolds...

#### Linking numbers in contact form geometry, with an application to the computation of the intersection operator for the first contact form of J. Gonzalo and F. Varela

We establish in what follows the fact that the linking number between two periodic orbits does not decrease along the decreasing flow-lines of a suitable pseudo-gradient for the action functional of the variational problem (J, C β ) and its extension ( J ∞ , ∪ Γ 2 k ) , [2–4]. This is used to compute almost explicitly the value of the intersection operator for periodic orbits for...

#### Morse relations and Fredholm deformations of v-convex contact forms

We address in this paper the Fredholm and compactness issues for the variational problem (J,C β ), Bahri (Pitman Research Notes in Mathematics Series No. 173. Scientific and Technical, London, 1988), Bahri (C. R. Acad. Sci. Paris 299, Serie I, 15, 757–760, 1984). We prove that the intersection operator restricted to periodic orbits of the Reeb vector-field ∂per does not mix with...

#### On the contact homology of the first exotic contact form of J. Gonzalo and F. Varela

This paper contains a detailed study of the behavior of the first exotic contact structure of J. Gonzalo and F. Varela on S3 along a remarkable vector field v in its kernel found by Martino (Adv Nonlinear Stud, 2011). All contact forms are assumed to verify the condition that reads as follows: d(θ α)(v,.) is a contact form with the same orientation than α. α is the first exotic...

#### A note on bimatrix game maximal Selten subsets

In this paper, we implement automatic procedures to enumerate all Nash maximal subsets of a bimatrix game and compute their dimensions. We propose a linear programming approach to identify extreme perfect Nash equilibria, enumerate all Selten maximal subsets and compute their dimensions. We present the Eχ-MIPerfect and the EEE-Perfect algorithms which enumerate all extreme...

#### Linear subspaces of symmetric tensors whose non-zero elements have at least a prescribed rank

We introduce large vector spaces M of multivariate homogeneous polynomials with a prescribed lower bound for the rank of each non-zero element of M.Open image in new window

#### The chromatic number of the complementary graph to a simple graph associated with a commutative ring

Let R be a Noetherian ring. We denote by G(R) the simple graph whose vertices are elements of R and in which two distinct vertices x and y are joined by an edge if x − y is a zero-divisor of R. Let $${\overline{G}(R)}$$ be the complementary graph to G(R) and $${\overline{\chi}(R)}$$ be the chromatic number of the graph $${\overline{G}(R)}$$. In this paper, we determine the...

#### Irregular multiresolution analysis and associated wavelet

We introduce two generalizations, the first of which generalizes the concept of multiresolution analysis. We define the irregular generalized multiresolution analysis (IGMRA). This structure is defined taking translations on sets that are not necessarily regular lattices, for which certain density requirements are required, and without using dilations, also allows each subspace...

#### Qualitative behavior of solutions of difference equations with several oscillating coefficients

Sufficient conditions which guarantee the convergence of the nonoscillatory solutions or oscillation of all solutions of a difference equation with several deviating arguments and oscillating coefficients are presented. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.

#### Solvability of a fractional boundary value problem with fractional derivative condition

In this paper, we investigate a boundary value problem for fractional differential equations with fractional derivative condition. Some new existence results are obtained using Banach contraction principle and Leray–Schauder nonlinear alternative.

#### Some results concerning n-σ-centralizing mappings in semiprime rings

Let n ≥ 1 be a fixed integer. Let R be a semiprime ring and S an additive subgroup of R, σ, τ two endomorphisms of R and F : R → R an additive mapping of R. In the present paper, we prove that (1) if R is (n + 1)!-torsion free, S is (n + 1)-power closed and [ F ( x ) , σ ( x ) n ] ∈ Z ( R ) for all x ∈ S , then [ F ( x ) , σ ( x ) n ] = 0 for all x ∈ S ;  (2) if R is 3!-torsion...

#### A new algorithm for linear multiobjective programming problems with bounded variables

In this paper, we present a new adapted algorithm for defining the solution set of a multiobjective linear programming problem, where the decision variables are upper and lower bounded. The method is an extension of the direct support method developed by Gabasov and Kirillova in single programming. Its particularity is that it avoids the preliminary transformation of the decision...

#### Some problems of spectral theory of fourth-order differential operators with regular boundary conditions

In this paper, we consider the problem y IV + q x y = λ y , 0 < x < 1 , y ″ ′ 1 - - 1 σ y ″ ′ 0 + α y ′ 0 + γ y 0 = 0 , y ″ 1 - - 1 σ y ″ 0 + β y 0 = 0 , y ′ 1 - - 1 σ y ′ 0 = 0 , y 1 - - 1 σ y 0 = 0 where λ is a spectral parameter; q x ∈ L 1 0 , 1 is a complex-valued function; α , β , γ are arbitrary complex constants and σ = 0 , 1 . The boundary conditions of this problem are...

#### Bayesian inference for exponential distribution based on upper record range

The aim of this paper is to obtain Bayesian estimations of scale parameter of the exponential distribution based on upper record range (R n ). We accomplish this purpose in two steps: point and interval. As the first step, the quadratic, squared error and absolute error, loss functions are considered for obtaining Bayesian-point estimations. Also in the next step, we find the...

#### Iterative approximation of solutions for constrained convex minimization problem

In this paper, we propose a new iterative scheme for finding a minimizer of a constrained convex minimization problem and prove that the sequence generated by our new scheme converges strongly to a solution of the constrained convex minimization problem in a real Hilbert space.

#### A singular perturbation solution of viscous incompressible fluid flow between two eccentric rotating cylinders

The flow inside two concentric cylinders is one dimensional and an exact solution for quantities is easily found. However, when the cylinders axes are displaced by a small distance, two dimensional effects become obvious. In this research, the equations governing an incompressible viscous flow between two rotating cylinders are considered in polar coordinates that can be...

#### G-semipreinvexity and its applications

In this paper, we introduce some new kinds of generalized convexity, which include (semistrict) G-semipreinvexity and (semistrict) G-semipreincavity. Moreover, we establish the relations with common generalized convexity, present properties of (semistrictly) G-semipreinvex and (semistrictly) G-semipreincave functions, and also give characterizations of the classes of G...