Pub Date : 2022-02-07DOI: 10.21136/mb.2022.0200-20
Cholmin Sin, Sin-Il Ri
We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided p(x) > 2n/(n+2). To prove this, we show Poincaréand Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.
{"title":"Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions","authors":"Cholmin Sin, Sin-Il Ri","doi":"10.21136/mb.2022.0200-20","DOIUrl":"https://doi.org/10.21136/mb.2022.0200-20","url":null,"abstract":"We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided p(x) > 2n/(n+2). To prove this, we show Poincaréand Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44867532","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}
{"title":"An inequality for Fibonacci numbers","authors":"H. Alzer, F. Luca","doi":"10.21136/mb.2022.0032-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0032-21","url":null,"abstract":"We extend an inequality for Fibonacci numbers published by P.G.Popescu and J. L.Díaz-Barrero in 2006.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46530009","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 : 2022-01-26DOI: 10.21136/mb.2022.0124-20
S. Ebrahimi Atani
Let L be a lattice with the greatest element 1. Following the concept of generalized small subfilter, we define g-supplemented filters and investigate the basic properties and possible structures of these filters.
{"title":"$G$-supplemented property in the lattices","authors":"S. Ebrahimi Atani","doi":"10.21136/mb.2022.0124-20","DOIUrl":"https://doi.org/10.21136/mb.2022.0124-20","url":null,"abstract":"Let L be a lattice with the greatest element 1. Following the concept of generalized small subfilter, we define g-supplemented filters and investigate the basic properties and possible structures of these filters.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45674188","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 : 2022-01-18DOI: 10.21136/mb.2022.0056-21
A. Azizi, M. M. Chems-Eddin, A. Zekhnini
Let k be a number field with a 2-class group isomorphic to the Klein fourgroup. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields k = Q ( √ d, √ −1 ) , which leads to a correction of some parts in the main results of A.Azizi and A. Zekhini (2020).
{"title":"Note on the Hilbert 2-class field tower","authors":"A. Azizi, M. M. Chems-Eddin, A. Zekhnini","doi":"10.21136/mb.2022.0056-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0056-21","url":null,"abstract":"Let k be a number field with a 2-class group isomorphic to the Klein fourgroup. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields k = Q ( √ d, √ −1 ) , which leads to a correction of some parts in the main results of A.Azizi and A. Zekhini (2020).","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47162081","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 : 2021-11-22DOI: 10.21136/mb.2021.0022-21
A. Naziri-Kordkandi
{"title":"$varphi$-multipliers on a class of topological algebras","authors":"A. Naziri-Kordkandi","doi":"10.21136/mb.2021.0022-21","DOIUrl":"https://doi.org/10.21136/mb.2021.0022-21","url":null,"abstract":"","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48027837","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 : 2021-11-22DOI: 10.21136/mb.2021.0121-20
Lahiri Indrajit, S. Majumder
In connection to a conjecture of W.Lü, Q. Li and C.Yang (2014), we prove a result on small function sharing by a power of a meromorphic function with few poles with a derivative of the power. Our results improve a number of known results.
{"title":"A power of a meromorphic function sharing two small functions with a derivative of the power","authors":"Lahiri Indrajit, S. Majumder","doi":"10.21136/mb.2021.0121-20","DOIUrl":"https://doi.org/10.21136/mb.2021.0121-20","url":null,"abstract":"In connection to a conjecture of W.Lü, Q. Li and C.Yang (2014), we prove a result on small function sharing by a power of a meromorphic function with few poles with a derivative of the power. Our results improve a number of known results.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45132648","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 : 2021-11-16DOI: 10.21136/mb.2021.0122-20
A. Khaldi, Amar Ouaoua, M. Maouni
We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms ut −M ( ∫
我们考虑一类具有变指数和源项ut−M（ξ
{"title":"Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents","authors":"A. Khaldi, Amar Ouaoua, M. Maouni","doi":"10.21136/mb.2021.0122-20","DOIUrl":"https://doi.org/10.21136/mb.2021.0122-20","url":null,"abstract":"We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms ut −M ( ∫","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46343051","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 : 2021-11-15DOI: 10.21136/mb.2021.0172-20
Agus L. Soenjaya
Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven. It is shown that the system is globally well-posed in (u, n) ∈ L × L under some conditions on the nonlinearity (the coupling term), by using the L conservation law for u and controlling the growth of n via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007) for some exponents to other dimensions and in lower regularity spaces.
{"title":"Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling","authors":"Agus L. Soenjaya","doi":"10.21136/mb.2021.0172-20","DOIUrl":"https://doi.org/10.21136/mb.2021.0172-20","url":null,"abstract":"Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven. It is shown that the system is globally well-posed in (u, n) ∈ L × L under some conditions on the nonlinearity (the coupling term), by using the L conservation law for u and controlling the growth of n via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007) for some exponents to other dimensions and in lower regularity spaces.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42106866","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 : 2021-10-18DOI: 10.21136/mb.2021.0058-21
P. Karmakar
The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, ξ-projectively flat, M -projectively flat, ξ-M -projectively flat, pseudo projectively flat and ξ-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, M -projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily.
{"title":"Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold","authors":"P. Karmakar","doi":"10.21136/mb.2021.0058-21","DOIUrl":"https://doi.org/10.21136/mb.2021.0058-21","url":null,"abstract":"The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, ξ-projectively flat, M -projectively flat, ξ-M -projectively flat, pseudo projectively flat and ξ-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, M -projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47982740","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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