Pub Date : 2022-08-01DOI: 10.46793/kgjmat2204.617y
P. Yiarayong
The purpose of this paper is to introduce the notion of a weakly fuzzy quasi-primary ideals in LA-semigroups, we study fuzzy primary, fuzzy quasi-primary, fuzzy completely primary, weakly fuzzy primary and weakly fuzzy quasi-primary ideals in LA-semigroups. Some characterizations of weakly fuzzy primary and weakly fuzzy quasi-primary ideals are obtained. Moreover, we investigate relationships between fuzzy completely primary and weakly fuzzy quasi-primary ideals in LAsemigroups. Finally we show that a fuzzy left ideal f is a weakly fuzzy quasi-primary ideal of S2 if and only if S1 × f is a weakly fuzzy quasi-primary ideal of S1 × S2.
{"title":"On Fuzzy Primary and Fuzzy Quasi-Primary Ideals in LASemigroups","authors":"P. Yiarayong","doi":"10.46793/kgjmat2204.617y","DOIUrl":"https://doi.org/10.46793/kgjmat2204.617y","url":null,"abstract":"The purpose of this paper is to introduce the notion of a weakly fuzzy quasi-primary ideals in LA-semigroups, we study fuzzy primary, fuzzy quasi-primary, fuzzy completely primary, weakly fuzzy primary and weakly fuzzy quasi-primary ideals in LA-semigroups. Some characterizations of weakly fuzzy primary and weakly fuzzy quasi-primary ideals are obtained. Moreover, we investigate relationships between fuzzy completely primary and weakly fuzzy quasi-primary ideals in LAsemigroups. Finally we show that a fuzzy left ideal f is a weakly fuzzy quasi-primary ideal of S2 if and only if S1 × f is a weakly fuzzy quasi-primary ideal of S1 × S2.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47204238","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 : 2022-08-01DOI: 10.46793/kgjmat2204.595b
Andriy Ivanovych Bandura
In the paper, we present sufficient conditions of boundedness of L-index in joint variables for a sum of entire functions, where L : C n → R n + is a continuous function, R+ = (0, +∞). They are applicable to a very wide class of entire functions because for every entire function F in C n with bounded multiplicities of zero points there exists a positive continuous function L such that F has bounded L-index in joint variables. Our propositions are generalizations of Pugh’s result obtained for entire functions of one variable of bounded index.
本文给出了一类完整函数和在联合变量上L指标有界的充分条件,其中L: C n→R n +是连续函数,R+ =(0, +∞)。它们适用于非常广泛的整函数类因为对于C n中的每一个整函数F具有0点的有界多重度存在一个正的连续函数L使得F在联合变量中有界的L指标。我们的命题推广了Pugh关于单变量有界指标全函数的结论。
{"title":"BOUNDEDNESS OF L-INDEX IN JOINT VARIABLES FOR SUM OF ENTIRE FUNCTIONS","authors":"Andriy Ivanovych Bandura","doi":"10.46793/kgjmat2204.595b","DOIUrl":"https://doi.org/10.46793/kgjmat2204.595b","url":null,"abstract":"In the paper, we present sufficient conditions of boundedness of L-index in joint variables for a sum of entire functions, where L : C n → R n + is a continuous function, R+ = (0, +∞). They are applicable to a very wide class of entire functions because for every entire function F in C n with bounded multiplicities of zero points there exists a positive continuous function L such that F has bounded L-index in joint variables. Our propositions are generalizations of Pugh’s result obtained for entire functions of one variable of bounded index.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48879359","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 : 2022-08-01DOI: 10.46793/kgjmat2204.649t
M. Tahami, A. A. Hemmat
In this study, using a one-dimensionl MRA we constructed a two-dimensional wavelet as well as four masks which are not related to the MRA. Finally, we provide some examples to prove the applicability of our construction in case of finding numerical solution of two-dimensional first kind Fredholm integral equations.
{"title":"Two-Dimensional Wavelet with Matrix Dilation M = 2I and its Application in Solving Integral Equations","authors":"M. Tahami, A. A. Hemmat","doi":"10.46793/kgjmat2204.649t","DOIUrl":"https://doi.org/10.46793/kgjmat2204.649t","url":null,"abstract":"In this study, using a one-dimensionl MRA we constructed a two-dimensional wavelet as well as four masks which are not related to the MRA. Finally, we provide some examples to prove the applicability of our construction in case of finding numerical solution of two-dimensional first kind Fredholm integral equations.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42528868","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 : 2022-06-01DOI: 10.46793/kgjmat2203.433r
J. Rosales, M. Branco
In this paper we give algorithms that allow to compute the set of every elementary numerical semigroups with given genus, Frobenius number and multiplicity. As a consequence we obtain formulas for the cardinality of these sets.
{"title":"On the Enumeration of the Set of Elementary Numerical Semigroups with Fixed Multiplicity, Frobenius Number or Genus","authors":"J. Rosales, M. Branco","doi":"10.46793/kgjmat2203.433r","DOIUrl":"https://doi.org/10.46793/kgjmat2203.433r","url":null,"abstract":"In this paper we give algorithms that allow to compute the set of every elementary numerical semigroups with given genus, Frobenius number and multiplicity. As a consequence we obtain formulas for the cardinality of these sets.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48261016","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 : 2022-06-01DOI: 10.46793/kgjmat2203.407b
B. Benaissa
The aim of this work is to obtain the reverse Minkowski integral inequality. For this aim, we first give a proposition which is important for our main results. Then we establish some reverse Minkowski integral inequalities for parameters 0 < p < 1 and p < 0, respectively.
{"title":"On The Reverse Minkowski’s Integral Inequality","authors":"B. Benaissa","doi":"10.46793/kgjmat2203.407b","DOIUrl":"https://doi.org/10.46793/kgjmat2203.407b","url":null,"abstract":"The aim of this work is to obtain the reverse Minkowski integral inequality. For this aim, we first give a proposition which is important for our main results. Then we establish some reverse Minkowski integral inequalities for parameters 0 < p < 1 and p < 0, respectively.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46288959","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 : 2022-06-01DOI: 10.46793/kgjmat2203.383n
M. F. Nia, A. Z. Bahabadi
In this paper we describe some basic notions of topological dynamical systems for maps of type f : X × X → X named general systems. This is proved that every uniformly expansive general system has the shadowing property and every uniformly contractive general system has the (asymptotic) average shadowing and shadowing properties. In the rest, Devaney chaos for general systems is considered. Also, we show that topological transitivity and density of periodic points of a general systems imply topological ergodicity. We also obtain some results on the topological mixing and sensitivity for general systems.
{"title":"Chaos and Shadowing in General Systems","authors":"M. F. Nia, A. Z. Bahabadi","doi":"10.46793/kgjmat2203.383n","DOIUrl":"https://doi.org/10.46793/kgjmat2203.383n","url":null,"abstract":"In this paper we describe some basic notions of topological dynamical systems for maps of type f : X × X → X named general systems. This is proved that every uniformly expansive general system has the shadowing property and every uniformly contractive general system has the (asymptotic) average shadowing and shadowing properties. In the rest, Devaney chaos for general systems is considered. Also, we show that topological transitivity and density of periodic points of a general systems imply topological ergodicity. We also obtain some results on the topological mixing and sensitivity for general systems.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41766183","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 : 2022-06-01DOI: 10.46793/kgjmat2203.487t
M. Al-Tahan, B. Davvaz
The notion of hypergraphs, introduced around 1960, is a generalization of that of graphs and one of the initial concerns was to extend some classical results of graph theory. In this paper, we present some connections between hypergraph theory and hypergroup theory. In this regard, we construct two hypergroupoids by defining two new hyperoperations on ℍ, the set of all hypergraphs. We prove that our defined hypergroupoids are commutative hypergroups and we define hyperrings on ℍ by using the two defined hyperoperations. Moreover, we study the fundamental group, complete parts, automorphism group and strongly regular relations of one of our hypergroups.
{"title":"Hypergroups Defined on Hypergraphs and their Regular Relations","authors":"M. Al-Tahan, B. Davvaz","doi":"10.46793/kgjmat2203.487t","DOIUrl":"https://doi.org/10.46793/kgjmat2203.487t","url":null,"abstract":"The notion of hypergraphs, introduced around 1960, is a generalization of that of graphs and one of the initial concerns was to extend some classical results of graph theory. In this paper, we present some connections between hypergraph theory and hypergroup theory. In this regard, we construct two hypergroupoids by defining two new hyperoperations on ℍ, the set of all hypergraphs. We prove that our defined hypergroupoids are commutative hypergroups and we define hyperrings on ℍ by using the two defined hyperoperations. Moreover, we study the fundamental group, complete parts, automorphism group and strongly regular relations of one of our hypergroups.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":"77 6","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41315538","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 : 2022-06-01DOI: 10.46793/kgjmat2203.461m
E. Munarini
In this paper, we study the umbral operators J, M and N associated with the generalized rencontres polynomials D(m) n (x). We obtain their representations in terms of the differential operator Dx and the shift operator E. Then, by using these representations, we obtain some combinatorial and differential identities for the generalized rencontres polynomials. Finally, we extend these results to some related polynomials and, in particular, to the generalized permutation polynomials P(m)n (x) and the generalized arrangement polynomials A(m)n (x).
{"title":"An Operational Approach to the Generalized Rencontres Polynomials","authors":"E. Munarini","doi":"10.46793/kgjmat2203.461m","DOIUrl":"https://doi.org/10.46793/kgjmat2203.461m","url":null,"abstract":"In this paper, we study the umbral operators J, M and N associated with the generalized rencontres polynomials D(m) n (x). We obtain their representations in terms of the differential operator Dx and the shift operator E. Then, by using these representations, we obtain some combinatorial and differential identities for the generalized rencontres polynomials. Finally, we extend these results to some related polynomials and, in particular, to the generalized permutation polynomials P(m)n (x) and the generalized arrangement polynomials A(m)n (x).","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42138706","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 : 2022-06-01DOI: 10.46793/kgjmat2203.443b
A. Bagwan, D. Pachpatte
In this paper, the existence results for the solutions to nonlocal initial value problems involving generalized Katugampola derivative are established. Some fixed point theorem techniques are used to derive the existence results. In the sequel, we investigate the generalized Ulam-Hyers-Rassias stability corresponding to our problem. Some examples are given to illustrate our main results.
{"title":"Existence and Stability of Nonlocal Initial Value Problems Involving Generalized Katugampola Derivative","authors":"A. Bagwan, D. Pachpatte","doi":"10.46793/kgjmat2203.443b","DOIUrl":"https://doi.org/10.46793/kgjmat2203.443b","url":null,"abstract":"In this paper, the existence results for the solutions to nonlocal initial value problems involving generalized Katugampola derivative are established. Some fixed point theorem techniques are used to derive the existence results. In the sequel, we investigate the generalized Ulam-Hyers-Rassias stability corresponding to our problem. Some examples are given to illustrate our main results.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47796918","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 : 2022-06-01DOI: 10.46793/kgjmat2203.369m
Sanjay Kumar Mahto, A. Patra, P. Srivastava
The inĄnite lower triangular matrix B(r1, . . . , rl ; s1, . . . , sl ′ ) is considered over the sequence space c0, where l and l ′ are positive integers. The diagonal and sub-diagonal entries of the matrix consist of the oscillatory sequences r = (rk(mod l)+1) and s = (sk(mod l ′)+1), respectively. The rest of the entries of the matrix are zero. It is shown that the matrix represents a bounded linear operator. Then the spectrum of the matrix is evaluated and partitioned into its Ąne structures: point spectrum, continuous spectrum, residual spectrum, etc. In particular, the spectra of the matrix B(r1, . . . , r4; s1, . . . , s6) are determined. Finally, an example is taken in support of the results
{"title":"SPECTRA OF THE LOWER TRIANGULAR MATRIX B(r1, . . . , rl ; s1, . . . , sl ′) OVER c0","authors":"Sanjay Kumar Mahto, A. Patra, P. Srivastava","doi":"10.46793/kgjmat2203.369m","DOIUrl":"https://doi.org/10.46793/kgjmat2203.369m","url":null,"abstract":"The inĄnite lower triangular matrix B(r1, . . . , rl ; s1, . . . , sl ′ ) is considered over the sequence space c0, where l and l ′ are positive integers. The diagonal and sub-diagonal entries of the matrix consist of the oscillatory sequences r = (rk(mod l)+1) and s = (sk(mod l ′)+1), respectively. The rest of the entries of the matrix are zero. It is shown that the matrix represents a bounded linear operator. Then the spectrum of the matrix is evaluated and partitioned into its Ąne structures: point spectrum, continuous spectrum, residual spectrum, etc. In particular, the spectra of the matrix B(r1, . . . , r4; s1, . . . , s6) are determined. Finally, an example is taken in support of the results","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45948675","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}