Pub Date : 2023-10-10DOI: 10.1007/s40879-023-00696-z
Lorenz Halbeisen, Pedro Pablo Pérez-Velasco
Abstract In this paper three main results are presented: a bijection between natural sums and natural products, the completion of the axioms of Carruth for natural sums, and a new characterization of the natural sums in terms of Klaua’s integral ordinals. After introducing some preliminary results, we present two lemmas and a proposition for the proof of the existence of a bijection between natural products and natural sums. Then we prove the incompleteness of Carruth’s axioms by providing two counterexamples, and complete Carruth’s axioms by adding a fifth axiom. Finally, we introduce a characterization of natural sums in terms of Klaua’s integral ordinals and present two families of natural sums, which differ from Hessenberg’s sum.
{"title":"On Carruth’s axioms for natural sums and products","authors":"Lorenz Halbeisen, Pedro Pablo Pérez-Velasco","doi":"10.1007/s40879-023-00696-z","DOIUrl":"https://doi.org/10.1007/s40879-023-00696-z","url":null,"abstract":"Abstract In this paper three main results are presented: a bijection between natural sums and natural products, the completion of the axioms of Carruth for natural sums, and a new characterization of the natural sums in terms of Klaua’s integral ordinals. After introducing some preliminary results, we present two lemmas and a proposition for the proof of the existence of a bijection between natural products and natural sums. Then we prove the incompleteness of Carruth’s axioms by providing two counterexamples, and complete Carruth’s axioms by adding a fifth axiom. Finally, we introduce a characterization of natural sums in terms of Klaua’s integral ordinals and present two families of natural sums, which differ from Hessenberg’s sum.","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"2014 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294288","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 : 2023-10-10DOI: 10.1007/s40879-023-00690-5
Sho Ejiri
{"title":"Notes on direct images of pluricanonical bundles","authors":"Sho Ejiri","doi":"10.1007/s40879-023-00690-5","DOIUrl":"https://doi.org/10.1007/s40879-023-00690-5","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136354191","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 : 2023-10-09DOI: 10.1007/s40879-023-00693-2
Guodu Chen
{"title":"Boundedness of n-complements for generalized pairs","authors":"Guodu Chen","doi":"10.1007/s40879-023-00693-2","DOIUrl":"https://doi.org/10.1007/s40879-023-00693-2","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043598","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 : 2023-10-09DOI: 10.1007/s40879-023-00688-z
Kevin Coulembier, Pavel Etingof, Alexander Kleshchev, Victor Ostrik
{"title":"Super invariant theory in positive characteristic","authors":"Kevin Coulembier, Pavel Etingof, Alexander Kleshchev, Victor Ostrik","doi":"10.1007/s40879-023-00688-z","DOIUrl":"https://doi.org/10.1007/s40879-023-00688-z","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135094214","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 : 2023-10-06DOI: 10.1007/s40879-023-00685-2
Vasyl Ustimenko
{"title":"On Eulerian semigroups of multivariate transformations and their cryptographic applications","authors":"Vasyl Ustimenko","doi":"10.1007/s40879-023-00685-2","DOIUrl":"https://doi.org/10.1007/s40879-023-00685-2","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350260","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 : 2023-10-05DOI: 10.1007/s40879-023-00691-4
Victor Monakhov, Irina Sokhor
{"title":"Finite groups with strongly $$textrm{c}$$-reachable second maximal subgroups","authors":"Victor Monakhov, Irina Sokhor","doi":"10.1007/s40879-023-00691-4","DOIUrl":"https://doi.org/10.1007/s40879-023-00691-4","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134975627","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 : 2023-10-03DOI: 10.1007/s40879-023-00686-1
David Favero, Jesse Huang
{"title":"Rouquier dimension is Krull dimension for normal toric varieties","authors":"David Favero, Jesse Huang","doi":"10.1007/s40879-023-00686-1","DOIUrl":"https://doi.org/10.1007/s40879-023-00686-1","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738998","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 : 2023-10-03DOI: 10.1007/s40879-023-00687-0
Oksana Bezushchak
{"title":"Isomorphisms of groups of periodic infinite matrices","authors":"Oksana Bezushchak","doi":"10.1007/s40879-023-00687-0","DOIUrl":"https://doi.org/10.1007/s40879-023-00687-0","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135695683","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 : 2023-10-03DOI: 10.1007/s40879-023-00683-4
Morten Brun, Belén García Pascual, Lars M. Salbu
Abstract The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a subspace X of Euclidean space and a sample A of points in X , we give conditions for the homology of X to be isomorphic to a certain persistent homology group of the intrinsic Čech complex.
{"title":"Determining homology of an unknown space from a sample","authors":"Morten Brun, Belén García Pascual, Lars M. Salbu","doi":"10.1007/s40879-023-00683-4","DOIUrl":"https://doi.org/10.1007/s40879-023-00683-4","url":null,"abstract":"Abstract The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a subspace X of Euclidean space and a sample A of points in X , we give conditions for the homology of X to be isomorphic to a certain persistent homology group of the intrinsic Čech complex.","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135648462","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 : 2023-09-25DOI: 10.1007/s40879-023-00681-6
Behrouz Taji
Abstract We study families of projective manifolds with good minimal models. After constructing a suitable moduli functor for polarized varieties with canonical singularities, we show that, if not birationally isotrivial, the base spaces of such families support subsheaves of log-pluridifferentials with positive Kodaira dimension. Consequently we prove that, over special base schemes, families of this type can only be birationally isotrivial and, as a result, confirm a conjecture of Kebekus and Kovács.
{"title":"Birational geometry of smooth families of varieties admitting good minimal models","authors":"Behrouz Taji","doi":"10.1007/s40879-023-00681-6","DOIUrl":"https://doi.org/10.1007/s40879-023-00681-6","url":null,"abstract":"Abstract We study families of projective manifolds with good minimal models. After constructing a suitable moduli functor for polarized varieties with canonical singularities, we show that, if not birationally isotrivial, the base spaces of such families support subsheaves of log-pluridifferentials with positive Kodaira dimension. Consequently we prove that, over special base schemes, families of this type can only be birationally isotrivial and, as a result, confirm a conjecture of Kebekus and Kovács.","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135768930","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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