. In this paper we obtain results on existence of non-constant periodic traveling waves with arbitrary speed c > 0 in infinite system of linearly coupled nonlinear oscillators on a two-dimensional lattice. Sufficient conditions for the existence of such solutions are obtained with the aid of critical point method and linking theorem.
{"title":"Periodic traveling waves in the system of linearly coupled nonlinear oscillators on 2D-lattice","authors":"S. Bak","doi":"10.5817/am2022-1-1","DOIUrl":"https://doi.org/10.5817/am2022-1-1","url":null,"abstract":". In this paper we obtain results on existence of non-constant periodic traveling waves with arbitrary speed c > 0 in infinite system of linearly coupled nonlinear oscillators on a two-dimensional lattice. Sufficient conditions for the existence of such solutions are obtained with the aid of critical point method and linking theorem.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"38 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81633393","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}
Gilbert Mantika, Narcisse Temate-Tangang, D. Tieudjo
. The profinite topology on any abstract group G , is one such that the fundamental system of neighborhoods of the identity is given by all its subgroups of finite index. We say that a group G has the Ribes-Zalesskii property of rank k , or is RZ k with k a natural number, if any product H 1 H 2 ··· H k of finitely generated subgroups H 1 ,H 2 , ··· ,H k is closed in the profinite topology on G . And a group is said to have the Ribes-Zalesskii property or is RZ if it is RZ k for any natural number k . In this paper we characterize groups which are RZ 2 . Consequently, we obtain condition under which a free product with amalgamation of two RZ 2 groups is RZ 2 . After observing that the Baumslag-Solitar groups BS ( m,n ) are RZ 2 and clearly RZ if m = n , we establish some suitable properties on the RZ 2 property for the case when m = − n . Finally, since any group BS ( m,n ) can be viewed as a HNN-extension, then we point out the Ribes-Zalesskii property of rank two on some HNN-extensions.
{"title":"The Ribes-Zalesskii property of some one relator groups","authors":"Gilbert Mantika, Narcisse Temate-Tangang, D. Tieudjo","doi":"10.5817/am2022-1-35","DOIUrl":"https://doi.org/10.5817/am2022-1-35","url":null,"abstract":". The profinite topology on any abstract group G , is one such that the fundamental system of neighborhoods of the identity is given by all its subgroups of finite index. We say that a group G has the Ribes-Zalesskii property of rank k , or is RZ k with k a natural number, if any product H 1 H 2 ··· H k of finitely generated subgroups H 1 ,H 2 , ··· ,H k is closed in the profinite topology on G . And a group is said to have the Ribes-Zalesskii property or is RZ if it is RZ k for any natural number k . In this paper we characterize groups which are RZ 2 . Consequently, we obtain condition under which a free product with amalgamation of two RZ 2 groups is RZ 2 . After observing that the Baumslag-Solitar groups BS ( m,n ) are RZ 2 and clearly RZ if m = n , we establish some suitable properties on the RZ 2 property for the case when m = − n . Finally, since any group BS ( m,n ) can be viewed as a HNN-extension, then we point out the Ribes-Zalesskii property of rank two on some HNN-extensions.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"38 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82678404","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}
. Coherent ideals, strongly coherent ideals, and τ -closed ideals are introduced in pseudo-complemented distributive lattices and their characteri- zation theorems are derived. A set of equivalent conditions is derived for every ideal of a pseudo-complemented distributive lattice to become a coherent ideal. The notion of median prime ideals is introduced and some equivalent conditions are derived for every maximal ideal of a pseudo-complemented distributive lattice to become a median prime ideal which leads to a characterization of Boolean algebras.
{"title":"Median prime ideals of pseudo-complemented distributive lattices","authors":"M. Sambasiva Rao","doi":"10.5817/am2022-4-213","DOIUrl":"https://doi.org/10.5817/am2022-4-213","url":null,"abstract":". Coherent ideals, strongly coherent ideals, and τ -closed ideals are introduced in pseudo-complemented distributive lattices and their characteri- zation theorems are derived. A set of equivalent conditions is derived for every ideal of a pseudo-complemented distributive lattice to become a coherent ideal. The notion of median prime ideals is introduced and some equivalent conditions are derived for every maximal ideal of a pseudo-complemented distributive lattice to become a median prime ideal which leads to a characterization of Boolean algebras.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"68 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89085112","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}
. This note is based on a short talk presented at the “42nd Win-ter School Geometry and Physics” held in Srni, Czech Republic, January 15th–22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational method to determine the cohomology groups induced by sub-superalgebras. In particular, we show as an example the case of osp (1 | 4) and choose osp (1 | 2) × sp (2) as sub-algebra. We finally comment on some physical applications of such new cohomology classes related to super-branes. The note is a compact version of [10].
{"title":"A review of Lie superalgebra cohomology for pseudoforms","authors":"C. Cremonini","doi":"10.5817/am2022-5-269","DOIUrl":"https://doi.org/10.5817/am2022-5-269","url":null,"abstract":". This note is based on a short talk presented at the “42nd Win-ter School Geometry and Physics” held in Srni, Czech Republic, January 15th–22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational method to determine the cohomology groups induced by sub-superalgebras. In particular, we show as an example the case of osp (1 | 4) and choose osp (1 | 2) × sp (2) as sub-algebra. We finally comment on some physical applications of such new cohomology classes related to super-branes. The note is a compact version of [10].","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"8 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78553203","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}
We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3].
{"title":"A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form","authors":"H. D. de Lima","doi":"10.5817/am2022-3-169","DOIUrl":"https://doi.org/10.5817/am2022-3-169","url":null,"abstract":"We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3].","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80969673","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}
. In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators T + S where I − T is Lipschitz invertible and S a k -set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.
{"title":"Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem","authors":"Lydia Bouchal, K. Mebarki, S. Georgiev","doi":"10.5817/am2022-4-199","DOIUrl":"https://doi.org/10.5817/am2022-4-199","url":null,"abstract":". In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators T + S where I − T is Lipschitz invertible and S a k -set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73583334","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}
. Let R and S be commutative rings with unity, f : R → S a ring homomorphism and J an ideal of S . Then the subring R ./ f J := { ( a,f ( a ) + j ) | a ∈ R and j ∈ J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R ./ f J is a (generalized) filter ring.
。设R和S是具有单位的交换环，f: R→S是环同态，J是S的理想。则R × S的子式R ./ f J:= {(a,f (a) + J) | a∈R, J∈J}称为R与S沿J对f的合并。在本文中，我们确定了R ./ f J是一个(广义)滤波环。
{"title":"(Generalized) filter properties of the amalgamated algebra","authors":"Y. Azimi","doi":"10.5817/am2022-3-133","DOIUrl":"https://doi.org/10.5817/am2022-3-133","url":null,"abstract":". Let R and S be commutative rings with unity, f : R → S a ring homomorphism and J an ideal of S . Then the subring R ./ f J := { ( a,f ( a ) + j ) | a ∈ R and j ∈ J } of R × S is called the amalgamation of R with S along J with respect to f . In this paper, we determine when R ./ f J is a (generalized) filter ring.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"23 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82147815","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}
. This is a condensed report from the ongoing project aimed on higher principal connections and their relation with higher differential cohomology theories and generalised short exact sequences of L ∞ algebroids. A historical stem for our project is a paper from sir M. Atiyah who observed a bijective correspondence between data for a horizontal distribution on a fibre bundle and a set of sections for a certain splitting short exact sequence of Lie algebroids, nowadays called the Atiyah sequence . In a meantime there was developed quite firm understanding of the category theory and in the last two decades also the higher category/topos theory. This conceptual framework allows us to examine principal connections and higher principal connections in a prism of differential cohomology theories. In this text we cover mostly the motivational part of the project which resides in searching for a common language of these two successful approaches to connections. From the reasons of conciseness and compactness we have not included computations and several lengthy proofs.
{"title":"Generalised Atiyah’s theory of principal connections","authors":"Jiří Nárožný","doi":"10.5817/am2022-4-241","DOIUrl":"https://doi.org/10.5817/am2022-4-241","url":null,"abstract":". This is a condensed report from the ongoing project aimed on higher principal connections and their relation with higher differential cohomology theories and generalised short exact sequences of L ∞ algebroids. A historical stem for our project is a paper from sir M. Atiyah who observed a bijective correspondence between data for a horizontal distribution on a fibre bundle and a set of sections for a certain splitting short exact sequence of Lie algebroids, nowadays called the Atiyah sequence . In a meantime there was developed quite firm understanding of the category theory and in the last two decades also the higher category/topos theory. This conceptual framework allows us to examine principal connections and higher principal connections in a prism of differential cohomology theories. In this text we cover mostly the motivational part of the project which resides in searching for a common language of these two successful approaches to connections. From the reasons of conciseness and compactness we have not included computations and several lengthy proofs.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"11 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81739017","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}
Amirouche Mouhous a, Svetlin Georgiev Georgiev b, Karima Mebarki c
. In this work, we are interested in the existence of solutions for a class of first order boundary value problems (BVPs for short). We give new sufficient conditions under which the considered problems have at least one solution, one nonnegative solution and two non trivial nonnegative solutions, respectively. To prove our main results we propose a new approach based upon recent theoretical results. The results complement some recent ones.
{"title":"Existence of solutions for a class of first order boundary value problems","authors":"Amirouche Mouhous a, Svetlin Georgiev Georgiev b, Karima Mebarki c","doi":"10.5817/am2022-3-141","DOIUrl":"https://doi.org/10.5817/am2022-3-141","url":null,"abstract":". In this work, we are interested in the existence of solutions for a class of first order boundary value problems (BVPs for short). We give new sufficient conditions under which the considered problems have at least one solution, one nonnegative solution and two non trivial nonnegative solutions, respectively. To prove our main results we propose a new approach based upon recent theoretical results. The results complement some recent ones.","PeriodicalId":45191,"journal":{"name":"Archivum Mathematicum","volume":"77 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83999548","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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