Pub Date : 2021-09-09DOI: 10.21136/mb.2021.0079-20
Mimia Benhadri, T. Caraballo
This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.
{"title":"New sufficient conditions for global asymptotic stability of a kind of nonlinear neutral differential equations","authors":"Mimia Benhadri, T. Caraballo","doi":"10.21136/mb.2021.0079-20","DOIUrl":"https://doi.org/10.21136/mb.2021.0079-20","url":null,"abstract":"This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46807442","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 : 2021-08-22DOI: 10.21136/mb.2022.0127-21
D. C. Mayer
. For any number field K with non-elementary 3-class group Cl 3 ( K ) ≃ C 3 e × C 3 , e > 2, the punctured capitulation type κ ( K ) of K in its unramified cyclic cubic extensions L i , 1 6 i 6 4, is an orbit under the action of S 3 × S 3 . By means of Artin’s reciprocity law, the arithmetical invariant κ ( K ) is translated to the punctured transfer kernel type κ ( G 2 ) of the automorphism group G 2 = Gal(F 23 ( K ) /K ) of the second Hilbert 3-class field of K . A classification of finite 3-groups G with low order and bicyclic commutator quotient G/G ′ ≃ C 3 e × C 3 , 2 6 e 6 6, according to the algebraic invariant κ ( G ), admits conclu-sions concerning the length of the Hilbert 3-class field tower F ∞ 3 ( K ) of imaginary quadratic number fields K .
.对于具有非初等3类群Cl3（K）-C3e×C3，e>2的任何数域K，K在其未分支的循环三次扩张L i，16 i 6 4中的穿孔投降型κ（K）是在S3×S3作用下的轨道。利用Artin互易律，将算术不变量κ（K）转化为K的第二个Hilbert 3类域的自同构群G2＝Gal（F23（K）/K）的删截转移核型κ（G2）。根据代数不变量κ（G），给出了具有低阶双环交换商G/G′-C3e×C3，2 6e 6的有限3-群G的一个分类，得到了关于虚二次域K的Hilbert 3-类域塔F∞3（K）的长度的结论。
{"title":"Bicyclic commutator quotients with one non-elementary component","authors":"D. C. Mayer","doi":"10.21136/mb.2022.0127-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0127-21","url":null,"abstract":". For any number field K with non-elementary 3-class group Cl 3 ( K ) ≃ C 3 e × C 3 , e > 2, the punctured capitulation type κ ( K ) of K in its unramified cyclic cubic extensions L i , 1 6 i 6 4, is an orbit under the action of S 3 × S 3 . By means of Artin’s reciprocity law, the arithmetical invariant κ ( K ) is translated to the punctured transfer kernel type κ ( G 2 ) of the automorphism group G 2 = Gal(F 23 ( K ) /K ) of the second Hilbert 3-class field of K . A classification of finite 3-groups G with low order and bicyclic commutator quotient G/G ′ ≃ C 3 e × C 3 , 2 6 e 6 6, according to the algebraic invariant κ ( G ), admits conclu-sions concerning the length of the Hilbert 3-class field tower F ∞ 3 ( K ) of imaginary quadratic number fields K .","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46661907","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 : 2021-07-13DOI: 10.21136/MB.2021.0081-19
J. Graef, D. Beldjerd, M. Remili
The authors establish some new sufficient conditions under which all solutions of a certain class of nonlinear neutral delay differential equations of the third order are stable, bounded, and square integrable. Illustrative examples are given to demonstrate the main results.
{"title":"On stability, boundedness, and square integrability of solutions of certain third order neutral differential equations","authors":"J. Graef, D. Beldjerd, M. Remili","doi":"10.21136/MB.2021.0081-19","DOIUrl":"https://doi.org/10.21136/MB.2021.0081-19","url":null,"abstract":"The authors establish some new sufficient conditions under which all solutions of a certain class of nonlinear neutral delay differential equations of the third order are stable, bounded, and square integrable. Illustrative examples are given to demonstrate the main results.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45129892","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 : 2021-07-12DOI: 10.21136/MB.2021.0109-20
G. Chatzarakis, Ponnuraj Dinakar, S. Selvarangam, E. Thandapani
{"title":"Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms","authors":"G. Chatzarakis, Ponnuraj Dinakar, S. Selvarangam, E. Thandapani","doi":"10.21136/MB.2021.0109-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0109-20","url":null,"abstract":"","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46031461","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 : 2021-07-08DOI: 10.21136/MB.2021.0073-20
B. U. Afsan, Javier Gutiérrez García
In 2005, İ. Tok fuzzified the notion of the topological entropy R.A.Adler et al. (1965) using the notion of fuzzy compactness of C. L.Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R.A.Adler et al. (1965) of continuous mapping ψ : (X, τ)→ (X, τ), where (X, τ) is compact, is equal to the weakly fuzzy topological entropy of ψ : (X,ω(τ))→ (X,ω(τ)). We have also established an example that shows that the fuzzy topological entropy of İ. Tok (2005) cannot give such a bridge result to the topological entropy of Adler et al. (1965). Moreover, our definition of the weakly fuzzy topological entropy can be applied to find the topological entropy (namely weakly fuzzy topological entropy hw(ψ)) of the mapping ψ : X → X (where X is either compact or weakly fuzzy compact), whereas the topological entropy ha(ψ) of Adler does not exist for the mapping ψ : X → X (where X is non-compact weakly fuzzy compact). Finally, a product theorem for the weakly fuzzy topological entropy has been established.
{"title":"Weakly fuzzy topological entropy","authors":"B. U. Afsan, Javier Gutiérrez García","doi":"10.21136/MB.2021.0073-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0073-20","url":null,"abstract":"In 2005, İ. Tok fuzzified the notion of the topological entropy R.A.Adler et al. (1965) using the notion of fuzzy compactness of C. L.Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R.A.Adler et al. (1965) of continuous mapping ψ : (X, τ)→ (X, τ), where (X, τ) is compact, is equal to the weakly fuzzy topological entropy of ψ : (X,ω(τ))→ (X,ω(τ)). We have also established an example that shows that the fuzzy topological entropy of İ. Tok (2005) cannot give such a bridge result to the topological entropy of Adler et al. (1965). Moreover, our definition of the weakly fuzzy topological entropy can be applied to find the topological entropy (namely weakly fuzzy topological entropy hw(ψ)) of the mapping ψ : X → X (where X is either compact or weakly fuzzy compact), whereas the topological entropy ha(ψ) of Adler does not exist for the mapping ψ : X → X (where X is non-compact weakly fuzzy compact). Finally, a product theorem for the weakly fuzzy topological entropy has been established.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46951013","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 : 2021-07-08DOI: 10.21136/MB.2021.0094-20
B. Nam, N. Nhan, L. Ngoc, N. Long
We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.
{"title":"On a system of nonlinear wave equations with the Kirchhoff-Carrier\u0000 \u0000and Balakrishnan-Taylor terms","authors":"B. Nam, N. Nhan, L. Ngoc, N. Long","doi":"10.21136/MB.2021.0094-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0094-20","url":null,"abstract":"We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44010042","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 : 2021-03-08DOI: 10.21136/MB.2021.0104-20
R. Sharma, Gaurav Mittal
. We give the characterization of the unit group of F q SL (2 , Z 5 ), where F q is a finite field with q = p k elements for prime p > 5 , and SL (2 , Z 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group Z 5 .
{"title":"On the unit group of a semisimple group algebra $mathbb{F}_qSL(2, mathbb{Z}_5)$","authors":"R. Sharma, Gaurav Mittal","doi":"10.21136/MB.2021.0104-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0104-20","url":null,"abstract":". We give the characterization of the unit group of F q SL (2 , Z 5 ), where F q is a finite field with q = p k elements for prime p > 5 , and SL (2 , Z 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group Z 5 .","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46787899","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 : 2021-02-25DOI: 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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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}
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