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Proceedings of the 10th International Workshop on Differential Geometry and its Applications

Volume 20 (2012): Edition 1 (May 2012)

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

Chercher

Volume 29 (2021): Edition 1 (March 2021)

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

Chercher

15 Articles
Accès libre

New Curiosity Bivariate Quadratic Quaternionic Polynomials and Their Roots

Publié en ligne: 13 Apr 2021
Pages: 5 - 16

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 17 - 36

Résumé

Abstract

In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits for them (Theorem 6). We formulate necessary and sufficient arithmetic conditions which can identify the terms of a-Fibonacci and a-Lucas sequences. Finally, using a deep theorem of Siegel, we show that the aforementioned sequences contain only finitely many perfect powers. During the process we also discover some novel integer sequences.

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

Publié en ligne: 13 Apr 2021
Pages: 37 - 52

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 53 - 69

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 71 - 82

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 83 - 92

Résumé

Abstract

Matrix expressions composed by generalized inverses can generally be written as f(A1, A2, . . ., Ak), where A1, A2, . . ., Ak are a family of given matrices of appropriate sizes, and (·) 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 A1A2A3A4A5 = A to always hold for all generalized inverses A2 and A4 of A2 and A4 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
Accès libre

Reducibility in Corsini hypergroups

Publié en ligne: 13 Apr 2021
Pages: 93 - 109

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 111 - 125

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 127 - 142

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 143 - 164

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 165 - 182

Résumé

Abstract

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 numbers𝔼p={=υ+iω:υ,ω,i2=p<0},{\mathbb{E}_p} = \left\{ { \in = \upsilon + i\omega :\upsilon ,\omega \in \mathbb{R},\,\,{i^2} = p < 0} \right\}, and this space is named as an elliptic valued metric space. Some topological properties of this new space are examined. Also, some fixed point results are established in the setting of elliptic valued metric spaces by introducing new classes of mappings which the obtained results are real generalizations of the consequences of several fixed point theorems in the existing literature.

Mots clés

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

MSC 2010

  • Primary 47H10
  • Secondary 54H25
Accès libre

Gődel filters in residuated lattices

Publié en ligne: 13 Apr 2021
Pages: 183 - 200

Résumé

Abstract

In this paper, in the spirit of [4], we study a new type of filters in residuated lattices : Gődel filters. So, we characterize the filters for which the quotient algebra that is constructed via these filters is a Gődel algebra and we establish the connections between these filters and other types of filters. Using Gődel filters we characterize the residuated lattices which are Gődel algebras. Also, we prove that a residuated lattice is a Gődel algebra (divisible residuated lattice, MTL algebra, BL algebra) if and only if every filter is a Gődel filter (divisible filter, MTL filter, BL filter). Finally, we present some results about injective Gődel algebras showing that complete Boolean algebras are injective objects in the category of Gődel algebras.

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

Publié en ligne: 13 Apr 2021
Pages: 201 - 209

Résumé

Abstract

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
Accès libre

Extension of the Sophomore’s Dream

Publié en ligne: 13 Apr 2021
Pages: 211 - 218

Résumé

Abstract

In this article, we are going to look at the convergence properties of the integral 01(ax+b)cx+ddx\int_0^1 {{{\left( {ax + b} \right)}^{cx + d}}dx}, and express it in series form, where a, b, c and d are real parameters.

Mots clés

  • Sophomore’s dream
  • upper incomplete gamma function

MSC 2010

  • 26A06
Accès libre

Offset Ruled Surface in Euclidean Space with Density

Publié en ligne: 13 Apr 2021
Pages: 219 - 233

Résumé

Abstract

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 E3 with density ez and ex2−y2 are given.

Mots clés

  • Ruled surface
  • Offset surface
  • Space with density

MSC 2010

  • 53A05
  • 14J26
  • 14Q10
15 Articles
Accès libre

New Curiosity Bivariate Quadratic Quaternionic Polynomials and Their Roots

Publié en ligne: 13 Apr 2021
Pages: 5 - 16

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 17 - 36

Résumé

Abstract

In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits for them (Theorem 6). We formulate necessary and sufficient arithmetic conditions which can identify the terms of a-Fibonacci and a-Lucas sequences. Finally, using a deep theorem of Siegel, we show that the aforementioned sequences contain only finitely many perfect powers. During the process we also discover some novel integer sequences.

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

Publié en ligne: 13 Apr 2021
Pages: 37 - 52

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 53 - 69

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 71 - 82

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 83 - 92

Résumé

Abstract

Matrix expressions composed by generalized inverses can generally be written as f(A1, A2, . . ., Ak), where A1, A2, . . ., Ak are a family of given matrices of appropriate sizes, and (·) 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 A1A2A3A4A5 = A to always hold for all generalized inverses A2 and A4 of A2 and A4 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
Accès libre

Reducibility in Corsini hypergroups

Publié en ligne: 13 Apr 2021
Pages: 93 - 109

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 111 - 125

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 127 - 142

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 143 - 164

Résumé

Abstract

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

Publié en ligne: 13 Apr 2021
Pages: 165 - 182

Résumé

Abstract

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 numbers𝔼p={=υ+iω:υ,ω,i2=p<0},{\mathbb{E}_p} = \left\{ { \in = \upsilon + i\omega :\upsilon ,\omega \in \mathbb{R},\,\,{i^2} = p < 0} \right\}, and this space is named as an elliptic valued metric space. Some topological properties of this new space are examined. Also, some fixed point results are established in the setting of elliptic valued metric spaces by introducing new classes of mappings which the obtained results are real generalizations of the consequences of several fixed point theorems in the existing literature.

Mots clés

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

MSC 2010

  • Primary 47H10
  • Secondary 54H25
Accès libre

Gődel filters in residuated lattices

Publié en ligne: 13 Apr 2021
Pages: 183 - 200

Résumé

Abstract

In this paper, in the spirit of [4], we study a new type of filters in residuated lattices : Gődel filters. So, we characterize the filters for which the quotient algebra that is constructed via these filters is a Gődel algebra and we establish the connections between these filters and other types of filters. Using Gődel filters we characterize the residuated lattices which are Gődel algebras. Also, we prove that a residuated lattice is a Gődel algebra (divisible residuated lattice, MTL algebra, BL algebra) if and only if every filter is a Gődel filter (divisible filter, MTL filter, BL filter). Finally, we present some results about injective Gődel algebras showing that complete Boolean algebras are injective objects in the category of Gődel algebras.

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

Publié en ligne: 13 Apr 2021
Pages: 201 - 209

Résumé

Abstract

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
Accès libre

Extension of the Sophomore’s Dream

Publié en ligne: 13 Apr 2021
Pages: 211 - 218

Résumé

Abstract

In this article, we are going to look at the convergence properties of the integral 01(ax+b)cx+ddx\int_0^1 {{{\left( {ax + b} \right)}^{cx + d}}dx}, and express it in series form, where a, b, c and d are real parameters.

Mots clés

  • Sophomore’s dream
  • upper incomplete gamma function

MSC 2010

  • 26A06
Accès libre

Offset Ruled Surface in Euclidean Space with Density

Publié en ligne: 13 Apr 2021
Pages: 219 - 233

Résumé

Abstract

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 E3 with density ez and ex2−y2 are given.

Mots clés

  • Ruled surface
  • Offset surface
  • Space with density

MSC 2010

  • 53A05
  • 14J26
  • 14Q10

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