Pub Date : 2021-03-09DOI: 10.14712/1213-7243.2021.003
D. Donovan, M. Grannell, E. Yazici
We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of $t$ mutually orthogonal Latin squares of order $n$ to construct a set of $2t$ mutually orthogonal Latin squares of order $n^t$.
{"title":"Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results","authors":"D. Donovan, M. Grannell, E. Yazici","doi":"10.14712/1213-7243.2021.003","DOIUrl":"https://doi.org/10.14712/1213-7243.2021.003","url":null,"abstract":"We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of $t$ mutually orthogonal Latin squares of order $n$ to construct a set of $2t$ mutually orthogonal Latin squares of order $n^t$.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46258031","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 : 2021-03-09DOI: 10.14712/1213-7243.2020.041
Gaál Marcell
. The binary operation aba , called Jordan triple product, and its variants (such as e.g. the sequential product √ ab √ a or the inverted Jordan triple product ab − 1 a ) appear in several branches of operator theory and matrix analysis. In this paper we briefly survey some analytic and algebraic properties of these operations, and investigate their intimate connection to Thompson type isometries in different operator algebras.
{"title":"The operation $ABA$ in operator algebras","authors":"Gaál Marcell","doi":"10.14712/1213-7243.2020.041","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.041","url":null,"abstract":". The binary operation aba , called Jordan triple product, and its variants (such as e.g. the sequential product √ ab √ a or the inverted Jordan triple product ab − 1 a ) appear in several branches of operator theory and matrix analysis. In this paper we briefly survey some analytic and algebraic properties of these operations, and investigate their intimate connection to Thompson type isometries in different operator algebras.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44197458","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 : 2021-03-09DOI: 10.14712/1213-7243.2021.001
Smith Jonathan D. H.
. The semisymmetrization of an arbitrary quasigroup builds a semisym-metric quasigroup structure on the cube of the underlying set of the quasigroup. It serves to reduce homotopies to homomorphisms. An alternative semisym-metrization on the square of the underlying set was recently introduced by A. Krapeˇz and Z. Petri´c. Their construction in fact yields a Mendelsohn quasi-group, which is idempotent as well as semisymmetric. We describe it as the Mendelsohnization of the original quasigroup. For quasigroups isotopic to an abelian group, the relation between the semisymmetrization and the Mendel-sohnization is studied. It is shown that the semisymmetrization is the total space for an action of the Mendelsohnization on the abelian group. The Mendel-sohnization of an abelian group isotope is then identified as the idempotent replica of its semisymmetrization, with fibers isomorphic to the abelian group.
{"title":"Semisymmetrization and Mendelsohn quasigroups","authors":" Smith Jonathan D. H.","doi":"10.14712/1213-7243.2021.001","DOIUrl":"https://doi.org/10.14712/1213-7243.2021.001","url":null,"abstract":". The semisymmetrization of an arbitrary quasigroup builds a semisym-metric quasigroup structure on the cube of the underlying set of the quasigroup. It serves to reduce homotopies to homomorphisms. An alternative semisym-metrization on the square of the underlying set was recently introduced by A. Krapeˇz and Z. Petri´c. Their construction in fact yields a Mendelsohn quasi-group, which is idempotent as well as semisymmetric. We describe it as the Mendelsohnization of the original quasigroup. For quasigroups isotopic to an abelian group, the relation between the semisymmetrization and the Mendel-sohnization is studied. It is shown that the semisymmetrization is the total space for an action of the Mendelsohnization on the abelian group. The Mendel-sohnization of an abelian group isotope is then identified as the idempotent replica of its semisymmetrization, with fibers isomorphic to the abelian group.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44236998","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 : 2021-03-09DOI: 10.14712/1213-7243.2020.034
M. Niemenmaa
We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^4$ are centrally nilpotent of class at most two.
证明了具有阶$p^4$的初等阿贝尔内映射群的有限交换逆性质环是中心幂零的。
{"title":"On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^5$","authors":"M. Niemenmaa","doi":"10.14712/1213-7243.2020.034","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.034","url":null,"abstract":"We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^4$ are centrally nilpotent of class at most two.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42388536","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 : 2020-12-21DOI: 10.14712/1213-7243.2020.020
Arriagada Waldo, Huentutripay Jorge
{"title":"Asymptotic properties of a $varphi$-Laplacian and Rayleigh quotient","authors":" Arriagada Waldo, Huentutripay Jorge","doi":"10.14712/1213-7243.2020.020","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.020","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49188692","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 : 2020-12-21DOI: 10.14712/1213-7243.2020.028
Adegbindin Chèfiath A., Togbé Alain
{"title":"Can a Lucas number be a sum of three repdigits?","authors":" Adegbindin Chèfiath A., Togbé Alain","doi":"10.14712/1213-7243.2020.028","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.028","url":null,"abstract":"","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45771897","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 : 2020-12-21DOI: 10.14712/1213-7243.2020.031
Hester Anthony, Morales Claudio H.
. Consider the Mann iteration x n +1 = (1 − α n ) x n + α n Tx n for a nonex-pansive mapping T : K → K defined on some subset K of the normed space X . We present an innovative proof of the Ishikawa almost fixed point principle for nonexpansive mapping that reveals deeper aspects of the behavior of the process. This fact allows us, among other results, to derive convergence of the process under the assumption of existence of an accumulation point of { x n } .
{"title":"Fixed point approximation under Mann iteration beyond Ishikawa","authors":" Hester Anthony, Morales Claudio H.","doi":"10.14712/1213-7243.2020.031","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.031","url":null,"abstract":". Consider the Mann iteration x n +1 = (1 − α n ) x n + α n Tx n for a nonex-pansive mapping T : K → K defined on some subset K of the normed space X . We present an innovative proof of the Ishikawa almost fixed point principle for nonexpansive mapping that reveals deeper aspects of the behavior of the process. This fact allows us, among other results, to derive convergence of the process under the assumption of existence of an accumulation point of { x n } .","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49330604","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 : 2020-11-05DOI: 10.14712/1213-7243.2020.023
Dušek Zdeněk
. The concept of geodesic graph is generalized from Riemannian geometry to Finsler geometry, in particular to homogeneous Randers g.o. manifolds. On modified H-type groups which admit a Riemannian g.o. metric, invariant Randers g.o. metrics are determined and geodesic graphs in these Finsler g.o. manifolds are constructed. New structures of geodesic graphs are observed.
{"title":"Geodesic graphs in Randers g.o. spaces","authors":"Dušek Zdeněk","doi":"10.14712/1213-7243.2020.023","DOIUrl":"https://doi.org/10.14712/1213-7243.2020.023","url":null,"abstract":". The concept of geodesic graph is generalized from Riemannian geometry to Finsler geometry, in particular to homogeneous Randers g.o. manifolds. On modified H-type groups which admit a Riemannian g.o. metric, invariant Randers g.o. metrics are determined and geodesic graphs in these Finsler g.o. manifolds are constructed. New structures of geodesic graphs are observed.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48901121","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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