Pub Date : 2020-09-29DOI: 10.21136/MB.2020.0096-19
S. Foldes, S. Radeleczki
. Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality and restrictions of the distance to finite chains may or may not coincide with the natural, difference-of-height distance measured in a chain. It is shown that for semilattices the semimodularity ensures the good behaviour of the distances considered. The Jordan-Dedekind chain condition, which is weaker than semimodularity, is equivalent to the basic criterion that the graph-theoretic distance (realized by zig-zagging up and down freely in the poset to connect two points) is compatible with distances measured on chains by the relative height. Semimod-ularity is shown to be equivalent to the validity of the triangle inequality of a restricted graph-theoretic distance, called the up-down distance. The fact that the up-down distance corresponds to the computation of degrees of kinship in family trees leads to the observation that the less familiar canon-law method of computation corresponds also to a mathematically well behaved Chebyshev-type distance on discrete semilattices. For the Chebyshev distance also semimodularity is shown to imply the validity of the triangle inequality. The reverse implication fails, but assuming the validity of the triangle inequality, the semimod-ularity is shown to have a local characterization by a forbidden six-element subsemilattice. Like in the classical case of real spaces, the Chebyshev semilattice distance is shown to be the limit of a converging sequence of distances, all of them verifying the triangle inequality if the semilattice is semimodular.
{"title":"On distances and metrics in discrete ordered sets","authors":"S. Foldes, S. Radeleczki","doi":"10.21136/MB.2020.0096-19","DOIUrl":"https://doi.org/10.21136/MB.2020.0096-19","url":null,"abstract":". Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality and restrictions of the distance to finite chains may or may not coincide with the natural, difference-of-height distance measured in a chain. It is shown that for semilattices the semimodularity ensures the good behaviour of the distances considered. The Jordan-Dedekind chain condition, which is weaker than semimodularity, is equivalent to the basic criterion that the graph-theoretic distance (realized by zig-zagging up and down freely in the poset to connect two points) is compatible with distances measured on chains by the relative height. Semimod-ularity is shown to be equivalent to the validity of the triangle inequality of a restricted graph-theoretic distance, called the up-down distance. The fact that the up-down distance corresponds to the computation of degrees of kinship in family trees leads to the observation that the less familiar canon-law method of computation corresponds also to a mathematically well behaved Chebyshev-type distance on discrete semilattices. For the Chebyshev distance also semimodularity is shown to imply the validity of the triangle inequality. The reverse implication fails, but assuming the validity of the triangle inequality, the semimod-ularity is shown to have a local characterization by a forbidden six-element subsemilattice. Like in the classical case of real spaces, the Chebyshev semilattice distance is shown to be the limit of a converging sequence of distances, all of them verifying the triangle inequality if the semilattice is semimodular.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68443213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.21136/MB.2019.0144-17
Muammer Kula, Samed Özkan
In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point p in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various PreT2, Ti, i = 0, 1, 2, 3, structures at a point p are investigated. Finally, we examine the relationships between the generalized separation properties and the separation properties at a point p in this category.
{"title":"$T_2$ and $T_3$ objects at $p$ in the category of proximity spaces","authors":"Muammer Kula, Samed Özkan","doi":"10.21136/MB.2019.0144-17","DOIUrl":"https://doi.org/10.21136/MB.2019.0144-17","url":null,"abstract":"In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point p in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various PreT2, Ti, i = 0, 1, 2, 3, structures at a point p are investigated. Finally, we examine the relationships between the generalized separation properties and the separation properties at a point p in this category.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47349740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.21136/MB.2019.0140-17
M. Kologani, R. Borzooei
In this paper, we define and characterize the notions of (implicative, maximal, prime) ideals in hoops. Then we investigate the relation between them and prove that every maximal implicative ideal of a $vee $-hoop with double negation property is a prime one. Also, we define a congruence relation on hoops by ideals and study the quotient that is made by it. This notion helps us to show that an ideal is maximal if and only if the quotient hoop is a simple MV-algebra. Also, we investigate the relationship between ideals and filters by exploiting the set of complements.
{"title":"On ideal theory of hoops","authors":"M. Kologani, R. Borzooei","doi":"10.21136/MB.2019.0140-17","DOIUrl":"https://doi.org/10.21136/MB.2019.0140-17","url":null,"abstract":"In this paper, we define and characterize the notions of (implicative, maximal, prime) ideals in hoops. Then we investigate the relation between them and prove that every maximal implicative ideal of a $vee $-hoop with double negation property is a prime one. Also, we define a congruence relation on hoops by ideals and study the quotient that is made by it. This notion helps us to show that an ideal is maximal if and only if the quotient hoop is a simple MV-algebra. Also, we investigate the relationship between ideals and filters by exploiting the set of complements.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42797423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.21136/MB.2019.0054-18
M. Berbiche
We study the existence of global in time and uniform decay of weak solutions to the initial-boundary value problem related to the dynamic behavior of evolution equation accounting for rotational inertial forces along with a linear nonlocal frictional damping arises in viscoelastic materials. By constructing appropriate Lyapunov functional, we show the solution converges to the equilibrium state polynomially in the energy space.
{"title":"Asymptotic behavior of solutions for linear evolutionary boundary value problem of viscoelastic damped wave equation","authors":"M. Berbiche","doi":"10.21136/MB.2019.0054-18","DOIUrl":"https://doi.org/10.21136/MB.2019.0054-18","url":null,"abstract":"We study the existence of global in time and uniform decay of weak solutions to the initial-boundary value problem related to the dynamic behavior of evolution equation accounting for rotational inertial forces along with a linear nonlocal frictional damping arises in viscoelastic materials. By constructing appropriate Lyapunov functional, we show the solution converges to the equilibrium state polynomially in the energy space.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46614333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.21136/MB.2019.0038-18
C. Carpintero, A. Gutiérrez, E. Rosas, J. Sanabria
We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded p-variation in Wiener’s sense coincide. Additional illustrative results are given too.
{"title":"A note on preservation of spectra for two given operators","authors":"C. Carpintero, A. Gutiérrez, E. Rosas, J. Sanabria","doi":"10.21136/MB.2019.0038-18","DOIUrl":"https://doi.org/10.21136/MB.2019.0038-18","url":null,"abstract":"We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded p-variation in Wiener’s sense coincide. Additional illustrative results are given too.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45747660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-01DOI: 10.21136/MB.2019.0055-17
Elham Ilka, A. Mahmoodi, A. Bodaghi
We find some relations between module biprojectivity and module biflatness of Banach algebras A and B and their projective tensor productA ⊗B. For some semigroups S, we study module biprojectivity and module biflatness of semigroup algebras l(S).
{"title":"Some module cohomological properties of Banach algebras","authors":"Elham Ilka, A. Mahmoodi, A. Bodaghi","doi":"10.21136/MB.2019.0055-17","DOIUrl":"https://doi.org/10.21136/MB.2019.0055-17","url":null,"abstract":"We find some relations between module biprojectivity and module biflatness of Banach algebras A and B and their projective tensor productA ⊗B. For some semigroups S, we study module biprojectivity and module biflatness of semigroup algebras l(S).","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44105676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-27DOI: 10.21136/mb.2020.0160-18
Ardavan Najafi, A. Saeid
. We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of n -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type 2 is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that 1-Engel BCI-algebras are exactly the commutative BCI-algebras.
{"title":"Engel BCI-algebras: an application of left and right commutators","authors":"Ardavan Najafi, A. Saeid","doi":"10.21136/mb.2020.0160-18","DOIUrl":"https://doi.org/10.21136/mb.2020.0160-18","url":null,"abstract":". We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of n -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type 2 is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that 1-Engel BCI-algebras are exactly the commutative BCI-algebras.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47439219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-10DOI: 10.21136/MB.2021.0078-20
M. Obradovi'c, N. Tuneski
In this paper we give upper bound of the third order Hankel determinant for two classes of univalent functions with bounded turning. The bounds are not sharp, but the sharp ones are conjectured.
{"title":"Sharp bounds of the third Hankel determinant for classes of univalent functions\u0000 \u0000with bounded turning","authors":"M. Obradovi'c, N. Tuneski","doi":"10.21136/MB.2021.0078-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0078-20","url":null,"abstract":"In this paper we give upper bound of the third order Hankel determinant for two classes of univalent functions with bounded turning. The bounds are not sharp, but the sharp ones are conjectured.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48233207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-01DOI: 10.21136/MB.2019.0104-17
S. Zahiri, A. Saeid
The present study aimed to introduce n-fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of n-fold (positive) implicative IVRL-extended filters and n-fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the n-fold IVRL-extended filters, n-fold (positive) implicative algebras, and the Gödel triangle algebra were discussed.
{"title":"An investigation on the $n$-fold IVRL-filters in triangle algebras","authors":"S. Zahiri, A. Saeid","doi":"10.21136/MB.2019.0104-17","DOIUrl":"https://doi.org/10.21136/MB.2019.0104-17","url":null,"abstract":"The present study aimed to introduce n-fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of n-fold (positive) implicative IVRL-extended filters and n-fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the n-fold IVRL-extended filters, n-fold (positive) implicative algebras, and the Gödel triangle algebra were discussed.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44215061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-01DOI: 10.21136/MB.2019.0051-18
D. Bouafia, T. Moussaoui, D. O’Regan
We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.
{"title":"Multiplicity of positive solutions for second order quasilinear equations","authors":"D. Bouafia, T. Moussaoui, D. O’Regan","doi":"10.21136/MB.2019.0051-18","DOIUrl":"https://doi.org/10.21136/MB.2019.0051-18","url":null,"abstract":"We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41997895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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