- Détails du magazine
- Format
- Magazine
- eISSN
- 1844-0835
- Première publication
- 17 May 2013
- Période de publication
- 1 fois par an
- Langues
- Anglais

#### Chercher

- Accès libre

New Curiosity Bivariate Quadratic Quaternionic Polynomials and Their Roots

Pages: 5 - 16

#### Résumé

We consider the second-order linear homogeneous quaternion recurrence solutions for some new curiosity bivariate quadratic quaternionic equations.

#### Mots clés

- Quaternion
- Real quadratic form
- Quadratic quaternionic equation
- Polynomials with mixed quaternion coefficients

#### MSC 2010

- Primary 11R52, 11D09
- Secondary 15A63

- Accès libre

On some new results for the generalised Lucas sequences

Pages: 17 - 36

#### Résumé

In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value

#### Mots clés

- Generalised Lucas sequence
- Generalised Pell-Lucas sequence
- Pell equation
- Special Pell Equation
- Negative Pell equation

#### MSC 2010

- Primary 11B83
- Secondary 26C05

- Accès libre

Univalence Criteria for some General Integral Operators

Pages: 37 - 52

#### Résumé

The main object of this paper is to extend the univalent condition for two general integral operators. A number of known univalent condition would follow upon specializing the parameters involved in our main results.

#### Mots clés

- Integral operator
- analytic and univalent functions
- univalent conditions
- unit disk
- Schwarz Lemma

#### MSC 2010

- Primary 30C45
- Secondary 30C75

- Accès libre

Stochastic orders for a multivariate Pareto distribution

Pages: 53 - 69

#### Résumé

In this article we give some theoretical results for equivalence between different stochastic orders of some kind multivariate Pareto distribution family. Weak multivariate orders are equivalent or imply different stochastic orders between extremal statistics order of two random variables sequences. The random variables in this article are not neccesary independent.

#### Mots clés

- Multivariate stochastic orders
- Multivariate Pareto distribution
- Statistic orders

#### MSC 2010

- Primary 60E15
- Secondary 62G32

- Accès libre

On Quaternion-Gaussian Fibonacci Numbers and Their Properties

Pages: 71 - 82

#### Résumé

We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients. Using the Binet form we prove fundamental relations between these numbers. Moreover, we investigate whether the quaternions newly defined provide existing some important identities such as Cassini’s identity for quaternions.

#### Mots clés

- Fibonacci number
- gaussian number
- quaternion
- recurrence relation

#### MSC 2010

- 11B37
- 11B39
- 11R52

- Accès libre

Invariance property of a five matrix product involving two generalized inverses

Pages: 83 - 92

#### Résumé

Matrix expressions composed by generalized inverses can generally be written as ^{−}_{1}, ^{−}_{2}, . . ., ^{−}_{k}_{1}, _{2}, . . ., _{k}^{−} denotes a generalized inverse of matrix. Once such an expression is given, people are primarily interested in its uniqueness (invariance property) with respect to the choice of the generalized inverses. As such an example, this article describes a general method for deriving necessary and sufficient conditions for the matrix equality _{1}^{−}_{2}_{3}^{−}_{4}_{5} = ^{−}_{2} and ^{−}_{4} of _{2} and _{4} through use of the block matrix representation method and the matrix rank method, and discusses some special cases of the equality for different choices of the five matrices.

#### Mots clés

- Generalized inverse
- matrix product
- matrix equation
- rank formula
- invariance

#### MSC 2010

- Primary 15A09
- 15A24
- Secondary 47A05
- 47A50

#### Résumé

In this paper, we study the reducibility property of special hyper-groups, called Corsini hypergroups, named after the mathematician who introduced them. The concept of reducibility was introduced by Jantosciak, who noticed that it can happen that hyperproduct does not distinguish between a pair of elements. He defined a certain equivalences in order to identify elements which play the same role with respect to the hyperoperation. First we will determine specific conditions under which the Corsini hypergroups are reduced. Next, we will present some properties of these hypergroups necessary for studying the fuzzy reducibility property. The fuzzy reducibility will be considered with respect to the grade fuzzy set μ̃, used for defining the fuzzy grade of a hypergroup. Finally, we will study the reducibility and the fuzzy reducibility of the direct product of Corsini hypergroups.

#### Mots clés

- Hypergroup
- equivalence relations
- reducibility
- Corsini hypergroups

#### MSC 2010

- Primary 20N20

- Accès libre

A Mean Ergodic Theorem for Affine Nonexpansive Mappings in Nonpositive Curvature Metric Spaces

Pages: 111 - 125

#### Résumé

In this paper, we consider the orbits of an affine nonexpansive mapping in Hadamard (nonpositive curvature metric) spaces and prove an ergodic theorem for the inductive mean, which extends the von Neumann linear ergodic theorem. The main result shows that the sequence given by the inductive means of iterations of an affine nonexpansive mapping with a nonempty fixed point set converges strongly to a fixed point of the mapping. A Tauberian theorem is also proved in order to ensure convergence of the iterations.

#### Mots clés

- Ergodic Theorem
- Hadamard Space
- Inductive Mean
- Affine Nonexpansive Mapping
- Tauberian Condition

#### MSC 2010

- Primary: 47H25
- Secondary: 40J05, 40A05

- Accès libre

Qualitative results in thermoelasticity of type III for dipolar bodies

Pages: 127 - 142

#### Résumé

In our study we formulated the mixed initial boundary value problem corresponding to the thermoelasticity of type III for bodies with dipolar structure. In main section we approached four qualitative results regarding the solutions for this problem. In two of these (in the first two theorems) we obtained two results of uniqueness, proved in different ways. Also, we proven two results which show that the solutions of the considered problem depend continuously with respect to the supply terms. We use different procedures in the two theorems on continuous dependence, but we essentially rely on the auxiliary results from Section 3 and Gronwall-type inequalities. It is important to emphasize that all results are obtained by imposing on the basic equations and basic conditions, average constraints that are common in the mechanics of continuous solids.

#### Mots clés

- thermoelasticity of type III
- dipolar body
- uniqueness of solution
- Gronwall inequality
- continuous dependence

#### MSC 2010

- 74F05

- Accès libre

Filters of strong Sheffer stroke non-associative MV-algebras

Pages: 143 - 164

#### Résumé

In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved.

#### Mots clés

- Sheffer stroke
- (Sheffer stroke) NMV-algebra
- filter
- congruence
- homomorphism

#### MSC 2010

- Primary 06F05, 03G25
- Secondary 03G10

- Accès libre

Coincidence and Common Fixed Point Theorems via ϱ-Class Functions in Elliptic Valued Metric Spaces

Pages: 165 - 182

#### Résumé

The main goal of this study is to define a new metric space which is a generalization of complex valued metric spaces introduced by Azam et al. [1] using the set of elliptic numbers

#### Mots clés

- Elliptic valued metric space
- Common fixed point
- ϱ-class Functions
- Weakly Compatible Mappings

#### MSC 2010

- Primary 47H10
- Secondary 54H25

#### Résumé

In this paper, in the spirit of [4], we study a new type of filters in residuated lattices :

#### Mots clés

- Residuated lattice
- Gődel algebra
- Gődel filter
- injective object

#### MSC 2010

- Primary 03B50, 06A06, 03G05
- Secondary 03G25, 08A72, 06D35, 06E05, 06B20, 03C05, 18C05

- Accès libre

Topological Transversality Coincidence Theory for Multivalued Maps with Selections in a Given Class

Pages: 201 - 209

#### Résumé

This paper presents the topological transversality coincidence theorem for general multivalued maps who have selections in a given class of maps.

#### Mots clés

- essential maps
- coincidence points
- topological principles

#### MSC 2010

- Primary 47H10
- Secondary 54H25

#### Résumé

In this article, we are going to look at the convergence properties of the integral

#### Mots clés

- Sophomore’s dream
- upper incomplete gamma function

#### MSC 2010

- 26A06

- Accès libre

Offset Ruled Surface in Euclidean Space with Density

Pages: 219 - 233

#### Résumé

In this paper, offset ruled surfaces in these spaces are defined by using the geometry of ruled surfaces in Euclidean space with density. The mean curvature and Gaussian curvature of these surfaces are studied. In addition, the relationships between the mean curvature and mean curvature with density, and the Gaussian curvature and the Gaussian curvature with density of the offset ruled surfaces in ^{3} with density ^{z}^{−}^{x}^{2−}^{y}^{2} are given.

#### Mots clés

- Ruled surface
- Offset surface
- Space with density

#### MSC 2010

- 53A05
- 14J26
- 14Q10