Pub Date : 2021-02-25DOI: 10.21136/mb.2022.0026-21
I. Chajda, H. Langer
. We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to study in which posets some of these mappings coincide. We define special mappings determined by two elements and investigate when these are strictly monotone or upper cone preserving. If the considered poset is a semilattice then its monotone mappings coincide with semilattice homomorphisms if and only if the poset is a chain. Similarly, we study posets which need not be semilattices but whose upper cones have a minimal element. We extend this investigation to posets that are direct products of chains or an ordinal sum of an antichain and a finite chain. We characterize equivalence relations induced by strongly monotone mappings and show that the quotient set of a poset by such an equivalence relation is a poset again.
{"title":"Monotone and cone preserving mappings on posets","authors":"I. Chajda, H. Langer","doi":"10.21136/mb.2022.0026-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0026-21","url":null,"abstract":". We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to study in which posets some of these mappings coincide. We define special mappings determined by two elements and investigate when these are strictly monotone or upper cone preserving. If the considered poset is a semilattice then its monotone mappings coincide with semilattice homomorphisms if and only if the poset is a chain. Similarly, we study posets which need not be semilattices but whose upper cones have a minimal element. We extend this investigation to posets that are direct products of chains or an ordinal sum of an antichain and a finite chain. We characterize equivalence relations induced by strongly monotone mappings and show that the quotient set of a poset by such an equivalence relation is a poset again.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42446561","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 : 2021-02-03DOI: 10.21136/MB.2021.0130-20
Prasenjit Ghosh, T. Samanta
Frames for Hilbert spaces were first introduced by Duffin and Schaeffer in 1952 to study some fundamental problems in non-harmonic Fourier series (see [7]). Later on, after some decades, frame theory was popularized by Daubechies, Grossman, Meyer (see [5]). At present, frame theory has been widely used in signal and image processing, filter bank theory, coding and communications, system modeling and so on. Several generalizations of frames, namelyK-frames, g-frames, fusion frames etc. have been introduced in recent times. K-frames were introduced by Gavruta (see [8]) to study the atomic system with respect to a bounded linear operator. Using frame theory techiques, the author also studied the atomic decompositions for operators on reproducing kernel Hilbert spaces, see [9]. Sun in [15] introduced a g-frame and a g-Riesz basis in complex Hilbert spaces and discussed several properties of them. Huang in [12] began to study K-g-frame by combining K-frame and g-frame. Casazza (see [3]) was first to introduce the notion of fusion frames or frames of subspaces and gave various ways to obtain a resolution of the identity operator from a fuison frame. The concept of
{"title":"Generalized atomic subspaces for operators in Hilbert spaces","authors":"Prasenjit Ghosh, T. Samanta","doi":"10.21136/MB.2021.0130-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0130-20","url":null,"abstract":"Frames for Hilbert spaces were first introduced by Duffin and Schaeffer in 1952 to study some fundamental problems in non-harmonic Fourier series (see [7]). Later on, after some decades, frame theory was popularized by Daubechies, Grossman, Meyer (see [5]). At present, frame theory has been widely used in signal and image processing, filter bank theory, coding and communications, system modeling and so on. Several generalizations of frames, namelyK-frames, g-frames, fusion frames etc. have been introduced in recent times. K-frames were introduced by Gavruta (see [8]) to study the atomic system with respect to a bounded linear operator. Using frame theory techiques, the author also studied the atomic decompositions for operators on reproducing kernel Hilbert spaces, see [9]. Sun in [15] introduced a g-frame and a g-Riesz basis in complex Hilbert spaces and discussed several properties of them. Huang in [12] began to study K-g-frame by combining K-frame and g-frame. Casazza (see [3]) was first to introduce the notion of fusion frames or frames of subspaces and gave various ways to obtain a resolution of the identity operator from a fuison frame. The concept of","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44335101","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 : 2021-01-18DOI: 10.21136/MB.2021.0116-19
Gaurav Mittal, R. Sharma
. We characterize the unit group of semisimple group algebras F q G of some non-metabelian groups, where F q is a field with q = p k elements for p prime and a positive integer k . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group (( C 3 × C 3 ) ⋊ C 3 ) ⋊ C 2 of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.
。刻画了一些非亚元群的半单群代数的单位群fqg，其中对于p素数和正整数k, fq是一个有q = p k个元素的域。特别地，我们考虑了所有6个48阶的非平衡群，唯一一个54阶的非平衡群((c3 × c3) c3) c2，以及7个72阶的非平衡群。完成了72阶以上群的半单群代数单位群的研究。
{"title":"On unit group of finite semisimple group algebras of non-metabelian groups up to order 72","authors":"Gaurav Mittal, R. Sharma","doi":"10.21136/MB.2021.0116-19","DOIUrl":"https://doi.org/10.21136/MB.2021.0116-19","url":null,"abstract":". We characterize the unit group of semisimple group algebras F q G of some non-metabelian groups, where F q is a field with q = p k elements for p prime and a positive integer k . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group (( C 3 × C 3 ) ⋊ C 3 ) ⋊ C 2 of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45025053","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.2021.0171-20
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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.2019.0116-18
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":null,"pages":null},"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.2019.0075-18
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":null,"pages":null},"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}
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