Rivista e Edizione

Volume 30 (2022): Edizione 2 (May 2022)

Volume 30 (2022): Edizione 1 (February 2022)

Volume 29 (2021): Edizione 3 (November 2021)

Volume 29 (2021): Edizione 2 (June 2021)

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

Volume 28 (2020): Edizione 3 (December 2020)

Volume 28 (2020): Edizione 2 (July 2020)

Volume 28 (2020): Edizione 1 (March 2020)

Volume 27 (2019): Edizione 3 (December 2019)

Volume 27 (2019): Edizione 2 (June 2019)

Volume 27 (2019): Edizione 1 (March 2019)

Volume 26 (2018): Edizione 3 (December 2018)

Volume 26 (2018): Edizione 2 (July 2018)

Volume 26 (2018): Edizione 1 (March 2018)

Volume 25 (2017): Edizione 3 (December 2017)

Volume 25 (2017): Edizione 2 (July 2017)

Volume 25 (2017): Edizione 1 (January 2017)

Volume 24 (2016): Edizione 3 (November 2016)

Volume 24 (2016): Edizione 2 (June 2016)

Volume 24 (2016): Edizione 1 (January 2016)

Volume 23 (2015): Edizione 3 (November 2015)

Volume 23 (2015): Edizione 2 (June 2015)

Volume 23 (2015): Edizione 1 (January 2015)

Volume 22 (2014): Edizione 3 (September 2014)

Volume 22 (2014): Edizione 2 (June 2014)

Volume 22 (2014): Edizione 1 (March 2014)

Volume 21 (2013): Edizione 3 (November 2013)

Volume 21 (2013): Edizione 2 (June 2013)

Volume 21 (2013): Edizione 1 (March 2013)

Volume 20 (2012): Edizione 3 (December 2012)

Volume 20 (2012): Edizione 2 (June 2012)
Proceedings of the 10th International Workshop on Differential Geometry and its Applications

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

Dettagli della rivista
Formato
Rivista
eISSN
1844-0835
Pubblicato per la prima volta
17 May 2013
Periodo di pubblicazione
1 volta all'anno
Lingue
Inglese

Cerca

Volume 30 (2022): Edizione 1 (February 2022)

Dettagli della rivista
Formato
Rivista
eISSN
1844-0835
Pubblicato per la prima volta
17 May 2013
Periodo di pubblicazione
1 volta all'anno
Lingue
Inglese

Cerca

15 Articoli
Accesso libero

Prime preideals on bounded EQ-algebras

Pubblicato online: 12 Mar 2022
Pagine: 5 - 30

Astratto

Abstract

EQ-algebras were introduced by Novák in [14] as an algebraic structure of truth values for fuzzy type theory (FFT). In [1], Borzooei et. al. introduced the notion of preideal in bounded EQ-algebras. In this paper, we introduce various kinds of preideals on bounded EQ-algebras such as Λ-prime, ⊗-prime, ∩-prime, ∩-irreducible, maximal and then we investigate some properties and the relations among them. Specially, we prove that in a prelinear and involutive bounded EQ-algebra, any proper preideal is included in a Λ-prime preideal. In the following, we show that the set of all Λ-prime preideals in a bounded EQ-algebra is a T0 space and under some conditions, it is compact, connected, and Hausdor. Moreover, we show that the set of all maximal preideals of a prelinear involutive bounded EQ-algebra is an Uryshon (Hausdor) space and for a finite EQ-algebra, it is T3 and T4 space. Finally, we introduce a contravariant functor from the categories of bounded EQ-algebras to the category of topological spaces.

Parole chiave

  • -algebras
  • ideals
  • prime preideals
  • preideals
  • maximal preideals
  • topology

MSC 2010

  • Primary 06E15, 06F99
  • Secondary 06B10, 54F65
Accesso libero

On the sum of the reciprocals of k-generalized Fibonacci numbers

Pubblicato online: 12 Mar 2022
Pagine: 31 - 42

Astratto

Abstract

In this note, we that if { Fn(k) }n0 {\left\{ {F_n^{\left( k \right)}} \right\}_{n \ge 0}} denotes the k-generalized Fibonacci sequence then for n ≥ 2 the closest integer to the reciprocal of mn1/Fm(k) \sum\nolimits_{m \ge n} {1/F_m^{\left( k \right)}} is Fn(k)Fn1(k) F_n^{\left( k \right)} - F_{n - 1}^{\left( k \right)} .

Parole chiave

  • Linearly recurrent sequences

MSC 2010

  • Primary 11B39
Accesso libero

Different approach on elliptic curves mathematical models study and their applications

Pubblicato online: 12 Mar 2022
Pagine: 43 - 56

Astratto

Abstract

In a research project in which a group of mathematical researchers is involved, it was necessary to create a system of nonlinear equations defined over a particular nonsupersingular elliptic space. This paper presents a part of the results obtained in this field, as well as the applications where the built models has been demonstrated their reliability.

Parole chiave

  • Nonlinear system
  • Elliptic space
  • Elliptic curves

MSC 2010

  • Primary 93C10
  • Secondary 11G05, 11G07
Accesso libero

Divisible hypermodules

Pubblicato online: 12 Mar 2022
Pagine: 57 - 74

Astratto

Abstract

The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of the normal injective hypermodules. First we define the concept of zero-divisors over a hypermodule and based on it we introduce a new class of hypermodules, the one of divisible hypermodules. After presenting some of their fundamental properties, we will show that the class of normal injective R-hypermodules M and the class of divisible R-hypermodules M coincide whenever R is a hyperring with no zero-divisors over M. Finally, we answer to an open problem related to canonical hypergroups. In particular, we show that any canonical hypergroup can be endoweded with a ℤ-hypermodule structure and it is a normal injective ℤ-hypermodule if and only if it is a divisible ℤ-hypermodule.

Parole chiave

  • Normal injective hypermodule
  • Zero-divisor
  • Divisible hypermodule
  • Canonical hypergroup

MSC 2010

  • Primary 2020, 16 20
  • Secondary 1399
Accesso libero

On the Upper Bound of the Third Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function

Pubblicato online: 12 Mar 2022
Pagine: 75 - 89

Astratto

Abstract

In the present paper we introduce a new class of analytic functions f in the open unit disk normalized by f(0) = f(0)1 = 0, associated with exponential functions. The aim of the present paper is to investigate the third-order Hankel determinant H3(1) for this function class and obtain the upper bound of the determinant H3(1).

Parole chiave

  • Elementary
  • operators
  • Compact operators
  • orthogonality
  • Gateaux derivative

MSC 2010

  • Primary 46G05, 46L05
  • Secondary 47A30, 47B47
Accesso libero

DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4

Pubblicato online: 12 Mar 2022
Pagine: 89 - 108

Astratto

Abstract

A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established. Using this map the structure of DNA codes over these rings is determined, the length of the code is relatively prime to the characteristic of the residue field of the ring.

Parole chiave

  • Constacyclic codes
  • DNA codes
  • Frobenius local rings
  • Reversible codes

MSC 2010

  • Primary 94B05
  • Secondary 94B15
Accesso libero

Stochastic orders of log-epsilon-skew-normal distributions

Pubblicato online: 12 Mar 2022
Pagine: 109 - 128

Astratto

Abstract

The log-epsilon-skew-normal distributions family is generalized class of log-normal distribution. Is widely used to model non-negative data in many areas of applied research. We give necessary and/or sufficient conditions for some stochastic orders of log-epsilon-skew-normal distributions. Also, we give sufficient conditions for orders of moments and Gini indexes. Finally, it is presented a real data application.

Parole chiave

  • Stochastic order
  • Log-Normal distribution
  • index Gini

MSC 2010

  • Primary 60E15
  • Secondary 62G32
Accesso libero

Generating punctured surface triangulations with degree at least 4

Pubblicato online: 12 Mar 2022
Pagine: 129 - 151

Astratto

Abstract

As a sequel of a previous paper by the authors, we present here a generating theorem for the family of triangulations of an arbitrary punctured surface with vertex degree ≥ 4. The method is based on a series of reversible operations termed reductions which lead to a minimal set of triangulations in such a way that all intermediate triangulations throughout the reduction process remain within the family. Besides contractible edges and octahedra, the reduction operations act on two new configurations near the surface boundary named quasi-octahedra and N-components. It is also observed that another configuration called M-component remains unaltered under any sequence of reduction operations. We show that one gets rid of M-components by flipping appropriate edges.

Parole chiave

  • Punctured surface
  • irreducible triangulation
  • edge contraction
  • vertex splitting
  • removal/addition of octahedra
  • generating theorem

MSC 2010

  • Primary 05C10
  • Secondary 57M20, 57N05
Accesso libero

A Study on Commutative Elliptic Octonion Matrices

Pubblicato online: 12 Mar 2022
Pagine: 151 - 169

Astratto

Abstract

In this study, firstly notions of similarity and consimilarity are given for commutative elliptic octonion matrices. Then the Kalman-Yakubovich s-conjugate equation is solved for the first conjugate of commutative elliptic octonions. Also, the notions of eigenvalue and eigenvector are studied for commutative elliptic octonion matrices. In this regard, the fundamental theorem of algebra and Gershgorin’s Theorem are proved for commutative elliptic octonion matrices. Finally, some examples related to our theorems are provided.

Parole chiave

  • Elliptic octonion matrices
  • consimilarity
  • Gershgorin disk

MSC 2010

  • Primary 12A27, 13A99
  • Secondary 15A18, 15B33
Accesso libero

Nearest neighbor estimates of Kaniadakis entropy

Pubblicato online: 12 Mar 2022
Pagine: 171 - 189

Astratto

Abstract

The aim of this paper is to develop new nonparametric estimators of entropy based on the kth nearest neighbor distances that are considered between n sample points, k ≤ (n − 1) being a positive integer, fixed. The Method consists in using the new estimators which were useful in order to evaluate the entropies for random vectors. As results, using the Kaniadakis entropy measure, the asymptotic unbiasedness and consistency of the estimators are proven.

Parole chiave

  • Kaniadakis entropy
  • estimator
  • k- nearest neighbor
  • variance
  • distribution
Accesso libero

Qualitative Analysis of Coupled Fractional Differential Equations involving Hilfer Derivative

Pubblicato online: 12 Mar 2022
Pagine: 191 - 217

Astratto

Abstract

In this manuscript, we have studied the coupled system of Hilfer fractional differential equations with non-local conditions. We have used the Leray-alternative Schauder’s and the Contraction principle to obtain the results on the existence and uniqueness of the solution of the proposed problem in the weighted space of continuous functions. For the defined problem, sufficient conditions have also been developed to determine the Ulam stability of the solution. The key conclusions are well-illustrated with examples.

Parole chiave

  • Fractional differential equations
  • Couple system
  • Hilfer fractional derivative
  • Non-local conditions
  • Fixed point theorem
  • Ulam’s stability

MSC 2010

  • Primary 39B72, 39B52
  • Secondary 47H10
Accesso libero

Complete parts and subhypergroups in reversible regular hypergroups

Pubblicato online: 12 Mar 2022
Pagine: 219 - 230

Astratto

Abstract

In this paper we analyse the center and centralizer of an element in the context of reversible regular hypergroups, in order to obtain the class equation in regular reversible hypergroups, by using complete parts. After an introduction in which basic notions and results of hypergroup theory are presented, particularly complete parts, then we give several properties, characterisations and also examples for the center and centralizer of an element for two classes of hypergroups. The next paragraph is dedicated to hypergroups associated with binary relations. We establish a connection between several types of equivalence relations, introduced by J. Jantosciak, such as the operational relation, the inseparability and the essential indistin-guishability and the conjugacy relation for complete hypergroups. Finally, we analyse Rosenberg hypergroup associated with a conjugacy relation.

Parole chiave

  • Reversible regular hypergroup
  • Complete part
  • Center
  • Centralizer
  • Conjugacy relation
  • Rosenberg hypergroup

MSC 2010

  • Primary 20N20
Accesso libero

On characterization of finite modules by hypergraphs

Pubblicato online: 12 Mar 2022
Pagine: 231 - 246

Astratto

Abstract

With a finite R-module M we associate a hypergraph 𝒞𝒥ℋR(M) having the set V of vertices being the set of all nontrivial submodules of M. Moreover, a subset Ei of V with at least two elements is a hyperedge if for K, L in Ei there is K ∩ L ≠ = 0 and Ei is maximal with respect to this property. We investigate some general properties of 𝒞𝒥ℋR(M), providing condition under which 𝒞𝒥ℋR(M) is connected, and find its diameter. Besides, we study the form of the hypergraph 𝒞𝒥ℋR(M) when M is semisimple, uniform module and it is a direct sum of its each two nontrivial submodules. Moreover, we characterize finite modules with three nontrivial submodules according to their co-intersection hypergraphs. Finally, we present some illustrative examples for 𝒞𝒥ℋR(M).

Parole chiave

  • Hyperedge
  • hypergraph
  • co-intersection hypergraph

MSC 2010

  • Primary 05C65 05C20, 05C25, 05C69
Accesso libero

Class of Sheffer stroke BCK-algebras

Pubblicato online: 12 Mar 2022
Pagine: 247 - 269

Astratto

Abstract

In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It is indicated that the axioms of a Sheffer stroke BCK-algebra are independent. The relationship between a Sheffer stroke BCK-algebra and a BCK-algebra is stated. After describing a commutative, an implicative and an involutory Sheffer stroke BCK-algebras, some of important properties are proved. The relationship of this structures is demonstrated. A Sheffer stroke BCK-algebra with condition (S) is described and the connection with other structures is shown. Finally, it is proved that for a Sheffer stroke BCK-algebra to be a Boolean lattice, it must be an implicative Sheffer stroke BCK-algebra.

Parole chiave

  • (Sheffer stroke) BCK-algebra
  • (implicative, bounded, involutory, positive implicative, commutative) Sheffer stroke BCK-algebra
  • BCK-lattice

MSC 2010

  • Primary 06F05, 03G25
  • Secondary 03G10
Accesso libero

Algebraic dependence and finiteness problems of differentiably nondegenerate meromorphic mappings on Kähler manifolds

Pubblicato online: 12 Mar 2022
Pagine: 271 - 294

Astratto

Abstract

Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball 𝔹m(R0) in ℂm (0 < R0 +∞). Our first aim in this paper is to study the algebraic dependence problem of differentiably meromorphic mappings. We will show that if k differentibility nonde-generate meromorphic mappings f1, …, fk of M into ℙn(ℂ) (n ≥ 2) satisfying the condition (Cρ) and sharing few hyperplanes in subgeneral position regardless of multiplicity then f1 Λ … Λ fk0. For the second aim, we will show that there are at most two different differentiably nondegenerate meromorphic mappings of M into ℙn(ℂ) sharing q (q ∼ 2N − n + 3 + O(ρ)) hyperplanes in N−subgeneral position regardless of multiplicity. Our results generalize previous finiteness and uniqueness theorems for differentiably meromorphic mappings of ℂm into ℙn(ℂ) and extend some previous results for the case of mappings on Kähler manifold.

Parole chiave

  • Algebraic dependence
  • finiteness theorem
  • Kähler manifold
  • meromorphic mapping

MSC 2010

  • Primary 32H30, 32A22
  • Secondary 30D35
15 Articoli
Accesso libero

Prime preideals on bounded EQ-algebras

Pubblicato online: 12 Mar 2022
Pagine: 5 - 30

Astratto

Abstract

EQ-algebras were introduced by Novák in [14] as an algebraic structure of truth values for fuzzy type theory (FFT). In [1], Borzooei et. al. introduced the notion of preideal in bounded EQ-algebras. In this paper, we introduce various kinds of preideals on bounded EQ-algebras such as Λ-prime, ⊗-prime, ∩-prime, ∩-irreducible, maximal and then we investigate some properties and the relations among them. Specially, we prove that in a prelinear and involutive bounded EQ-algebra, any proper preideal is included in a Λ-prime preideal. In the following, we show that the set of all Λ-prime preideals in a bounded EQ-algebra is a T0 space and under some conditions, it is compact, connected, and Hausdor. Moreover, we show that the set of all maximal preideals of a prelinear involutive bounded EQ-algebra is an Uryshon (Hausdor) space and for a finite EQ-algebra, it is T3 and T4 space. Finally, we introduce a contravariant functor from the categories of bounded EQ-algebras to the category of topological spaces.

Parole chiave

  • -algebras
  • ideals
  • prime preideals
  • preideals
  • maximal preideals
  • topology

MSC 2010

  • Primary 06E15, 06F99
  • Secondary 06B10, 54F65
Accesso libero

On the sum of the reciprocals of k-generalized Fibonacci numbers

Pubblicato online: 12 Mar 2022
Pagine: 31 - 42

Astratto

Abstract

In this note, we that if { Fn(k) }n0 {\left\{ {F_n^{\left( k \right)}} \right\}_{n \ge 0}} denotes the k-generalized Fibonacci sequence then for n ≥ 2 the closest integer to the reciprocal of mn1/Fm(k) \sum\nolimits_{m \ge n} {1/F_m^{\left( k \right)}} is Fn(k)Fn1(k) F_n^{\left( k \right)} - F_{n - 1}^{\left( k \right)} .

Parole chiave

  • Linearly recurrent sequences

MSC 2010

  • Primary 11B39
Accesso libero

Different approach on elliptic curves mathematical models study and their applications

Pubblicato online: 12 Mar 2022
Pagine: 43 - 56

Astratto

Abstract

In a research project in which a group of mathematical researchers is involved, it was necessary to create a system of nonlinear equations defined over a particular nonsupersingular elliptic space. This paper presents a part of the results obtained in this field, as well as the applications where the built models has been demonstrated their reliability.

Parole chiave

  • Nonlinear system
  • Elliptic space
  • Elliptic curves

MSC 2010

  • Primary 93C10
  • Secondary 11G05, 11G07
Accesso libero

Divisible hypermodules

Pubblicato online: 12 Mar 2022
Pagine: 57 - 74

Astratto

Abstract

The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of the normal injective hypermodules. First we define the concept of zero-divisors over a hypermodule and based on it we introduce a new class of hypermodules, the one of divisible hypermodules. After presenting some of their fundamental properties, we will show that the class of normal injective R-hypermodules M and the class of divisible R-hypermodules M coincide whenever R is a hyperring with no zero-divisors over M. Finally, we answer to an open problem related to canonical hypergroups. In particular, we show that any canonical hypergroup can be endoweded with a ℤ-hypermodule structure and it is a normal injective ℤ-hypermodule if and only if it is a divisible ℤ-hypermodule.

Parole chiave

  • Normal injective hypermodule
  • Zero-divisor
  • Divisible hypermodule
  • Canonical hypergroup

MSC 2010

  • Primary 2020, 16 20
  • Secondary 1399
Accesso libero

On the Upper Bound of the Third Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function

Pubblicato online: 12 Mar 2022
Pagine: 75 - 89

Astratto

Abstract

In the present paper we introduce a new class of analytic functions f in the open unit disk normalized by f(0) = f(0)1 = 0, associated with exponential functions. The aim of the present paper is to investigate the third-order Hankel determinant H3(1) for this function class and obtain the upper bound of the determinant H3(1).

Parole chiave

  • Elementary
  • operators
  • Compact operators
  • orthogonality
  • Gateaux derivative

MSC 2010

  • Primary 46G05, 46L05
  • Secondary 47A30, 47B47
Accesso libero

DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4

Pubblicato online: 12 Mar 2022
Pagine: 89 - 108

Astratto

Abstract

A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established. Using this map the structure of DNA codes over these rings is determined, the length of the code is relatively prime to the characteristic of the residue field of the ring.

Parole chiave

  • Constacyclic codes
  • DNA codes
  • Frobenius local rings
  • Reversible codes

MSC 2010

  • Primary 94B05
  • Secondary 94B15
Accesso libero

Stochastic orders of log-epsilon-skew-normal distributions

Pubblicato online: 12 Mar 2022
Pagine: 109 - 128

Astratto

Abstract

The log-epsilon-skew-normal distributions family is generalized class of log-normal distribution. Is widely used to model non-negative data in many areas of applied research. We give necessary and/or sufficient conditions for some stochastic orders of log-epsilon-skew-normal distributions. Also, we give sufficient conditions for orders of moments and Gini indexes. Finally, it is presented a real data application.

Parole chiave

  • Stochastic order
  • Log-Normal distribution
  • index Gini

MSC 2010

  • Primary 60E15
  • Secondary 62G32
Accesso libero

Generating punctured surface triangulations with degree at least 4

Pubblicato online: 12 Mar 2022
Pagine: 129 - 151

Astratto

Abstract

As a sequel of a previous paper by the authors, we present here a generating theorem for the family of triangulations of an arbitrary punctured surface with vertex degree ≥ 4. The method is based on a series of reversible operations termed reductions which lead to a minimal set of triangulations in such a way that all intermediate triangulations throughout the reduction process remain within the family. Besides contractible edges and octahedra, the reduction operations act on two new configurations near the surface boundary named quasi-octahedra and N-components. It is also observed that another configuration called M-component remains unaltered under any sequence of reduction operations. We show that one gets rid of M-components by flipping appropriate edges.

Parole chiave

  • Punctured surface
  • irreducible triangulation
  • edge contraction
  • vertex splitting
  • removal/addition of octahedra
  • generating theorem

MSC 2010

  • Primary 05C10
  • Secondary 57M20, 57N05
Accesso libero

A Study on Commutative Elliptic Octonion Matrices

Pubblicato online: 12 Mar 2022
Pagine: 151 - 169

Astratto

Abstract

In this study, firstly notions of similarity and consimilarity are given for commutative elliptic octonion matrices. Then the Kalman-Yakubovich s-conjugate equation is solved for the first conjugate of commutative elliptic octonions. Also, the notions of eigenvalue and eigenvector are studied for commutative elliptic octonion matrices. In this regard, the fundamental theorem of algebra and Gershgorin’s Theorem are proved for commutative elliptic octonion matrices. Finally, some examples related to our theorems are provided.

Parole chiave

  • Elliptic octonion matrices
  • consimilarity
  • Gershgorin disk

MSC 2010

  • Primary 12A27, 13A99
  • Secondary 15A18, 15B33
Accesso libero

Nearest neighbor estimates of Kaniadakis entropy

Pubblicato online: 12 Mar 2022
Pagine: 171 - 189

Astratto

Abstract

The aim of this paper is to develop new nonparametric estimators of entropy based on the kth nearest neighbor distances that are considered between n sample points, k ≤ (n − 1) being a positive integer, fixed. The Method consists in using the new estimators which were useful in order to evaluate the entropies for random vectors. As results, using the Kaniadakis entropy measure, the asymptotic unbiasedness and consistency of the estimators are proven.

Parole chiave

  • Kaniadakis entropy
  • estimator
  • k- nearest neighbor
  • variance
  • distribution
Accesso libero

Qualitative Analysis of Coupled Fractional Differential Equations involving Hilfer Derivative

Pubblicato online: 12 Mar 2022
Pagine: 191 - 217

Astratto

Abstract

In this manuscript, we have studied the coupled system of Hilfer fractional differential equations with non-local conditions. We have used the Leray-alternative Schauder’s and the Contraction principle to obtain the results on the existence and uniqueness of the solution of the proposed problem in the weighted space of continuous functions. For the defined problem, sufficient conditions have also been developed to determine the Ulam stability of the solution. The key conclusions are well-illustrated with examples.

Parole chiave

  • Fractional differential equations
  • Couple system
  • Hilfer fractional derivative
  • Non-local conditions
  • Fixed point theorem
  • Ulam’s stability

MSC 2010

  • Primary 39B72, 39B52
  • Secondary 47H10
Accesso libero

Complete parts and subhypergroups in reversible regular hypergroups

Pubblicato online: 12 Mar 2022
Pagine: 219 - 230

Astratto

Abstract

In this paper we analyse the center and centralizer of an element in the context of reversible regular hypergroups, in order to obtain the class equation in regular reversible hypergroups, by using complete parts. After an introduction in which basic notions and results of hypergroup theory are presented, particularly complete parts, then we give several properties, characterisations and also examples for the center and centralizer of an element for two classes of hypergroups. The next paragraph is dedicated to hypergroups associated with binary relations. We establish a connection between several types of equivalence relations, introduced by J. Jantosciak, such as the operational relation, the inseparability and the essential indistin-guishability and the conjugacy relation for complete hypergroups. Finally, we analyse Rosenberg hypergroup associated with a conjugacy relation.

Parole chiave

  • Reversible regular hypergroup
  • Complete part
  • Center
  • Centralizer
  • Conjugacy relation
  • Rosenberg hypergroup

MSC 2010

  • Primary 20N20
Accesso libero

On characterization of finite modules by hypergraphs

Pubblicato online: 12 Mar 2022
Pagine: 231 - 246

Astratto

Abstract

With a finite R-module M we associate a hypergraph 𝒞𝒥ℋR(M) having the set V of vertices being the set of all nontrivial submodules of M. Moreover, a subset Ei of V with at least two elements is a hyperedge if for K, L in Ei there is K ∩ L ≠ = 0 and Ei is maximal with respect to this property. We investigate some general properties of 𝒞𝒥ℋR(M), providing condition under which 𝒞𝒥ℋR(M) is connected, and find its diameter. Besides, we study the form of the hypergraph 𝒞𝒥ℋR(M) when M is semisimple, uniform module and it is a direct sum of its each two nontrivial submodules. Moreover, we characterize finite modules with three nontrivial submodules according to their co-intersection hypergraphs. Finally, we present some illustrative examples for 𝒞𝒥ℋR(M).

Parole chiave

  • Hyperedge
  • hypergraph
  • co-intersection hypergraph

MSC 2010

  • Primary 05C65 05C20, 05C25, 05C69
Accesso libero

Class of Sheffer stroke BCK-algebras

Pubblicato online: 12 Mar 2022
Pagine: 247 - 269

Astratto

Abstract

In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It is indicated that the axioms of a Sheffer stroke BCK-algebra are independent. The relationship between a Sheffer stroke BCK-algebra and a BCK-algebra is stated. After describing a commutative, an implicative and an involutory Sheffer stroke BCK-algebras, some of important properties are proved. The relationship of this structures is demonstrated. A Sheffer stroke BCK-algebra with condition (S) is described and the connection with other structures is shown. Finally, it is proved that for a Sheffer stroke BCK-algebra to be a Boolean lattice, it must be an implicative Sheffer stroke BCK-algebra.

Parole chiave

  • (Sheffer stroke) BCK-algebra
  • (implicative, bounded, involutory, positive implicative, commutative) Sheffer stroke BCK-algebra
  • BCK-lattice

MSC 2010

  • Primary 06F05, 03G25
  • Secondary 03G10
Accesso libero

Algebraic dependence and finiteness problems of differentiably nondegenerate meromorphic mappings on Kähler manifolds

Pubblicato online: 12 Mar 2022
Pagine: 271 - 294

Astratto

Abstract

Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball 𝔹m(R0) in ℂm (0 < R0 +∞). Our first aim in this paper is to study the algebraic dependence problem of differentiably meromorphic mappings. We will show that if k differentibility nonde-generate meromorphic mappings f1, …, fk of M into ℙn(ℂ) (n ≥ 2) satisfying the condition (Cρ) and sharing few hyperplanes in subgeneral position regardless of multiplicity then f1 Λ … Λ fk0. For the second aim, we will show that there are at most two different differentiably nondegenerate meromorphic mappings of M into ℙn(ℂ) sharing q (q ∼ 2N − n + 3 + O(ρ)) hyperplanes in N−subgeneral position regardless of multiplicity. Our results generalize previous finiteness and uniqueness theorems for differentiably meromorphic mappings of ℂm into ℙn(ℂ) and extend some previous results for the case of mappings on Kähler manifold.

Parole chiave

  • Algebraic dependence
  • finiteness theorem
  • Kähler manifold
  • meromorphic mapping

MSC 2010

  • Primary 32H30, 32A22
  • Secondary 30D35

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