Pub Date : 2021-01-01DOI: 10.21136/mb.2021.0171-20
Heghine Ghumashyan, J. Guričan
A group G has the endomorphism kernel property (EKP) if every congruence relation θ on G is the kernel of an endomorphism on G. In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian groups which have EKP.
{"title":"Endomorphism kernel property for finite groups","authors":"Heghine Ghumashyan, J. Guričan","doi":"10.21136/mb.2021.0171-20","DOIUrl":"https://doi.org/10.21136/mb.2021.0171-20","url":null,"abstract":"A group G has the endomorphism kernel property (EKP) if every congruence relation θ on G is the kernel of an endomorphism on G. In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian groups which have EKP.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68443267","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 : 2021-01-01DOI: 10.21136/mb.2021.0181-20
R. Shroff
In this paper some results on direct summands of Goldie extending elements are studied in a modular lattice. An element a of a lattice L with 0 is said to be a Goldie extending element if and only if for every b 6 a there exists a direct summand c of a such that b ∧ c is essential in both b and c. Some characterizations of decomposition of a Goldie extending element in a modular lattice are obtained.
{"title":"Direct summands of Goldie extending elements in modular lattices","authors":"R. Shroff","doi":"10.21136/mb.2021.0181-20","DOIUrl":"https://doi.org/10.21136/mb.2021.0181-20","url":null,"abstract":"In this paper some results on direct summands of Goldie extending elements are studied in a modular lattice. An element a of a lattice L with 0 is said to be a Goldie extending element if and only if for every b 6 a there exists a direct summand c of a such that b ∧ c is essential in both b and c. Some characterizations of decomposition of a Goldie extending element in a modular lattice are obtained.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68443361","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 : 2020-11-02DOI: 10.21136/mb.2020.0159-19
S. El-Deeb, G. Oros
We obtain several fuzzy differential subordinations by using a linear operator I n,α m,γf(z) = z + ∞ ∑ k=2 (1 + γ(k − 1))m(m+ k)akz . Using the linear operator I m,γ , we also introduce a class of univalent analytic functions for which we give some properties.
{"title":"Fuzzy differential subordinations connected with the linear operator","authors":"S. El-Deeb, G. Oros","doi":"10.21136/mb.2020.0159-19","DOIUrl":"https://doi.org/10.21136/mb.2020.0159-19","url":null,"abstract":"We obtain several fuzzy differential subordinations by using a linear operator I n,α m,γf(z) = z + ∞ ∑ k=2 (1 + γ(k − 1))m(m+ k)akz . Using the linear operator I m,γ , we also introduce a class of univalent analytic functions for which we give some properties.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46284410","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 : 2020-10-07DOI: 10.21136/mb.2020.0052-18
M. Ashordia
We consider the numerical solvability of the general linear boundary value problem for the systems of linear ordinary differential equations. Along with the continuous boundary value problem we consider the sequence of the general discrete boundary value problems, i.e. the corresponding general difference schemes. We establish the effective necessary and sufficient (and effective sufficient) conditions for the convergence of the schemes. Moreover, we consider the stability of the solutions of general discrete linear boundary value problems, in other words, the continuous dependence of solutions on the small perturbation of the initial dates. In the direction, there are obtained the necessary and sufficient condition, as well. The proofs of the results are based on the concept that both the continuous and discrete boundary value problems can be considered as so called generalized ordinary differential equation in the sense of Kurzweil. Thus, our results follow from the corresponding well-posedness results for the linear boundary value problems for generalized differential equations.
{"title":"On the necessary and sufficient conditions for the convergence of the difference schemes for the general boundary value problem for the linear systems of ordinary differential equations","authors":"M. Ashordia","doi":"10.21136/mb.2020.0052-18","DOIUrl":"https://doi.org/10.21136/mb.2020.0052-18","url":null,"abstract":"We consider the numerical solvability of the general linear boundary value problem for the systems of linear ordinary differential equations. Along with the continuous boundary value problem we consider the sequence of the general discrete boundary value problems, i.e. the corresponding general difference schemes. We establish the effective necessary and sufficient (and effective sufficient) conditions for the convergence of the schemes. Moreover, we consider the stability of the solutions of general discrete linear boundary value problems, in other words, the continuous dependence of solutions on the small perturbation of the initial dates. In the direction, there are obtained the necessary and sufficient condition, as well. The proofs of the results are based on the concept that both the continuous and discrete boundary value problems can be considered as so called generalized ordinary differential equation in the sense of Kurzweil. Thus, our results follow from the corresponding well-posedness results for the linear boundary value problems for generalized differential equations.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45261421","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 : 2020-10-06DOI: 10.21136/mb.2020.0148-19
Samir Cherief, S. Hamouda
. In this paper, we investigate the growth of solutions of a certain class of linear differential equation where the coefficients are analytic functions in the closed complex plane except at a finite singular point. For that, we will use the value distribution theory of meromorphic functions developed by Rolf Nevanlinna with adapted definitions.
{"title":"Finite and infinite order of growth of solutions to linear differential equations near a singular point","authors":"Samir Cherief, S. Hamouda","doi":"10.21136/mb.2020.0148-19","DOIUrl":"https://doi.org/10.21136/mb.2020.0148-19","url":null,"abstract":". In this paper, we investigate the growth of solutions of a certain class of linear differential equation where the coefficients are analytic functions in the closed complex plane except at a finite singular point. For that, we will use the value distribution theory of meromorphic functions developed by Rolf Nevanlinna with adapted definitions.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47076455","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 : 2020-10-01DOI: 10.21136/MB.2019.0075-18
B. L. Ghodadra, V. Fülöp
For a Lebesgue integrable complex-valued function f defined on R := [0,∞) let f̂ be its Walsh-Fourier transform. The Riemann-Lebesgue lemma says that f̂(y)→ 0 as y → ∞. But in general, there is no definite rate at which the Walsh-Fourier transform tends to zero. In fact, the Walsh-Fourier transform of an integrable function can tend to zero as slowly as we wish. Therefore, it is interesting to know for functions of which subclasses of L(R) there is a definite rate at which the Walsh-Fourier transform tends to zero. We determine this rate for functions of bounded variation on R. We also determine such rate of Walsh-Fourier transform for functions of bounded variation in the sense of Vitali defined on (R) , N ∈ N.
{"title":"On the order of magnitude of Walsh-Fourier transform","authors":"B. L. Ghodadra, V. Fülöp","doi":"10.21136/MB.2019.0075-18","DOIUrl":"https://doi.org/10.21136/MB.2019.0075-18","url":null,"abstract":"For a Lebesgue integrable complex-valued function f defined on R := [0,∞) let f̂ be its Walsh-Fourier transform. The Riemann-Lebesgue lemma says that f̂(y)→ 0 as y → ∞. But in general, there is no definite rate at which the Walsh-Fourier transform tends to zero. In fact, the Walsh-Fourier transform of an integrable function can tend to zero as slowly as we wish. Therefore, it is interesting to know for functions of which subclasses of L(R) there is a definite rate at which the Walsh-Fourier transform tends to zero. We determine this rate for functions of bounded variation on R. We also determine such rate of Walsh-Fourier transform for functions of bounded variation in the sense of Vitali defined on (R) , N ∈ N.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48866043","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 : 2020-10-01DOI: 10.21136/MB.2019.0116-18
Driss Lhaimer, M. Moussa, K. Bouras
{"title":"On the class of $text{b}$-L-weakly and order M-weakly compact operators","authors":"Driss Lhaimer, M. Moussa, K. Bouras","doi":"10.21136/MB.2019.0116-18","DOIUrl":"https://doi.org/10.21136/MB.2019.0116-18","url":null,"abstract":"","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49575752","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 : 2020-10-01DOI: 10.21136/MB.2019.0093-18
R. S. Dyavanal, R. V. Desai
{"title":"Uniqueness of $q$-shift difference polynomials of meromorphic functions sharing a small function","authors":"R. S. Dyavanal, R. V. Desai","doi":"10.21136/MB.2019.0093-18","DOIUrl":"https://doi.org/10.21136/MB.2019.0093-18","url":null,"abstract":"","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48952769","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 : 2020-10-01DOI: 10.21136/mb.2019.0084-18
Zakia Benbaziz, S. Djebali
We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel’skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity f = f(t, x, y) which satisfies upper and lower-homogeneity conditions in the space variables x, y may be also singular at time t = 0. Two examples of applications are included to illustrate the existence theorems.
{"title":"On a singular multi-point third-order boundary value problem on the half-line","authors":"Zakia Benbaziz, S. Djebali","doi":"10.21136/mb.2019.0084-18","DOIUrl":"https://doi.org/10.21136/mb.2019.0084-18","url":null,"abstract":"We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel’skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity f = f(t, x, y) which satisfies upper and lower-homogeneity conditions in the space variables x, y may be also singular at time t = 0. Two examples of applications are included to illustrate the existence theorems.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47837579","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 : 2020-10-01DOI: 10.21136/MB.2019.0050-18
M. Petrich
Completely regular semigroups CR are considered here with the unary operation of inversion within the maximal subgroups of the semigroup. This makes CR a variety; its lattice of subvarieties is denoted by L(CR). We study here the relations K,T,L and C relative to a sublattice Ψ of L(CR) constructed in a previous publication. For R being any of these relations, we determine the R-classes of all varieties in the lattice Ψ as well as the restrictions of R to Ψ.
{"title":"Relations on a lattice of varieties of completely regular semigroups","authors":"M. Petrich","doi":"10.21136/MB.2019.0050-18","DOIUrl":"https://doi.org/10.21136/MB.2019.0050-18","url":null,"abstract":"Completely regular semigroups CR are considered here with the unary operation of inversion within the maximal subgroups of the semigroup. This makes CR a variety; its lattice of subvarieties is denoted by L(CR). We study here the relations K,T,L and C relative to a sublattice Ψ of L(CR) constructed in a previous publication. For R being any of these relations, we determine the R-classes of all varieties in the lattice Ψ as well as the restrictions of R to Ψ.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42838562","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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