Pub Date : 2023-01-17DOI: 10.21136/mb.2023.0031-22
R. Sharma, A. B. Singh
{"title":"On a theorem of Mchar99Coy","authors":"R. Sharma, A. B. Singh","doi":"10.21136/mb.2023.0031-22","DOIUrl":"https://doi.org/10.21136/mb.2023.0031-22","url":null,"abstract":"","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42733222","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 : 2023-01-10DOI: 10.21136/mb.2023.0008-23
Indrajit Lahiri, Sujoy Majumder
{"title":"Correction to: A power of a meromorphic function sharing two small functions with a derivative of the power","authors":"Indrajit Lahiri, Sujoy Majumder","doi":"10.21136/mb.2023.0008-23","DOIUrl":"https://doi.org/10.21136/mb.2023.0008-23","url":null,"abstract":"","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136327260","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 : 2023-01-02DOI: 10.21136/mb.2023.0047-22
M. Amouch, Hamza Lakrimi
{"title":"Recurrence and mixing recurrence of multiplication operators","authors":"M. Amouch, Hamza Lakrimi","doi":"10.21136/mb.2023.0047-22","DOIUrl":"https://doi.org/10.21136/mb.2023.0047-22","url":null,"abstract":"","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45530783","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 : 2022-12-20DOI: 10.21136/mb.2022.0181-21
A. Berbache
. We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center. We show that when these piecewise differential systems are continuous, they can have at most one limit cycle. However, when the piecewise differential systems are discontinuous, we show that they can have at most two limit cycles, and that there exist such systems with two limit cycles. Therefore, in particular, we have solved the extension of the 16th Hilbert problem to this class of differential systems.
{"title":"On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems","authors":"A. Berbache","doi":"10.21136/mb.2022.0181-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0181-21","url":null,"abstract":". We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center. We show that when these piecewise differential systems are continuous, they can have at most one limit cycle. However, when the piecewise differential systems are discontinuous, we show that they can have at most two limit cycles, and that there exist such systems with two limit cycles. Therefore, in particular, we have solved the extension of the 16th Hilbert problem to this class of differential systems.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45823914","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 : 2022-12-19DOI: 10.21136/mb.2022.0183-21
S. Maity, A. Banerjee
. We study unique range sets of meromorphic functions over an angular domain in the light of weighted sharing. One of our main results generalizes and improves a result of Xu et al. (2014). Most importantly, we have pointed out a gap in the proofs of some main results of Rathod (2021) and subsequently rectifying the gap we have conveniently improved the results.
{"title":"Investigations on unique range sets of meromorphic functions in an angular domain","authors":"S. Maity, A. Banerjee","doi":"10.21136/mb.2022.0183-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0183-21","url":null,"abstract":". We study unique range sets of meromorphic functions over an angular domain in the light of weighted sharing. One of our main results generalizes and improves a result of Xu et al. (2014). Most importantly, we have pointed out a gap in the proofs of some main results of Rathod (2021) and subsequently rectifying the gap we have conveniently improved the results.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49327447","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 : 2022-12-19DOI: 10.21136/mb.2022.0067-22
Gaurav Mittal, R. Sharma
. We consider all the non-metabelian groups G of order 144 that have exponent either 36 or 72 and deduce the unit group U ( F q G ) of semisimple group algebra F q G . Here, q denotes the power of a prime, i.e., q = p r for p prime and a positive integer r . Up to isomorphism, there are 6 groups of order 144 that have exponent either 36 or 72. Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order 144 that are a direct product of two nontrivial groups. In all, this paper covers the unit groups of semisimple group algebras of 17 non-metabelian groups.
{"title":"The unit groups of semisimple group algebras of some non-metabelian groups of order $144$","authors":"Gaurav Mittal, R. Sharma","doi":"10.21136/mb.2022.0067-22","DOIUrl":"https://doi.org/10.21136/mb.2022.0067-22","url":null,"abstract":". We consider all the non-metabelian groups G of order 144 that have exponent either 36 or 72 and deduce the unit group U ( F q G ) of semisimple group algebra F q G . Here, q denotes the power of a prime, i.e., q = p r for p prime and a positive integer r . Up to isomorphism, there are 6 groups of order 144 that have exponent either 36 or 72. Additionally, we also discuss how to simply obtain the unit groups of the semisimple group algebras of those non-metabelian groups of order 144 that are a direct product of two nontrivial groups. In all, this paper covers the unit groups of semisimple group algebras of 17 non-metabelian groups.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43910219","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 : 2022-12-15DOI: 10.21136/mb.2022.0045-22
S. Padhi, J. Graef
. We study the existence of positive solutions to the fourth-order two-point boundary value problem
.我们研究了四阶两点边值问题正解的存在性
{"title":"Positive solutions of a fourth-order differential equation with integral boundary conditions","authors":"S. Padhi, J. Graef","doi":"10.21136/mb.2022.0045-22","DOIUrl":"https://doi.org/10.21136/mb.2022.0045-22","url":null,"abstract":". We study the existence of positive solutions to the fourth-order two-point boundary value problem","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47718327","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 : 2022-12-06DOI: 10.21136/mb.2022.0152-21
Rabah Mecheter, F. Mokhtari
. In this paper, we study the existence results for some parabolic equations with degenerate coercivity, singular lower order term depending on the gradient, and positive initial data in L 1 .
． 本文研究了一类具有退化矫顽力、奇异低阶项依赖于梯度、初始数据为正的抛物方程的存在性结果。
{"title":"Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms","authors":"Rabah Mecheter, F. Mokhtari","doi":"10.21136/mb.2022.0152-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0152-21","url":null,"abstract":". In this paper, we study the existence results for some parabolic equations with degenerate coercivity, singular lower order term depending on the gradient, and positive initial data in L 1 .","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47400855","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 : 2022-12-05DOI: 10.21136/mb.2022.0122-21
NoorA’lawiah Abd Aziz, Nader Jafari Rad, H. Kamarulhaili
. Let G be a 3-connected triangulated disc of order n with the boundary cycle C of the outer face of G . Tokunaga (2013) conjectured that G has a dominating set of cardinality at most 14 ( n +2). This conjecture is proved in Tokunaga (2020) for G − C being a tree. In this paper we prove the above conjecture for G − C being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs.
{"title":"On the domination of triangulated discs","authors":"NoorA’lawiah Abd Aziz, Nader Jafari Rad, H. Kamarulhaili","doi":"10.21136/mb.2022.0122-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0122-21","url":null,"abstract":". Let G be a 3-connected triangulated disc of order n with the boundary cycle C of the outer face of G . Tokunaga (2013) conjectured that G has a dominating set of cardinality at most 14 ( n +2). This conjecture is proved in Tokunaga (2020) for G − C being a tree. In this paper we prove the above conjecture for G − C being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45498339","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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