Pub Date : 2023-09-05DOI: 10.1007/s44007-023-00056-z
Marc Härkönen, Jonas Hirsch, Bernd Sturmfels
Abstract We study linear PDE constraints for vector-valued functions and distributions. Our focus lies on wave solutions, which give rise to distributions with low-dimensional support. Special waves from vector potentials are represented by syzygies. We parametrize all waves by projective varieties derived from the support of the PDE. These include determinantal varieties and Fano varieties, and they generalize wave cones in analysis.
{"title":"Making Waves","authors":"Marc Härkönen, Jonas Hirsch, Bernd Sturmfels","doi":"10.1007/s44007-023-00056-z","DOIUrl":"https://doi.org/10.1007/s44007-023-00056-z","url":null,"abstract":"Abstract We study linear PDE constraints for vector-valued functions and distributions. Our focus lies on wave solutions, which give rise to distributions with low-dimensional support. Special waves from vector potentials are represented by syzygies. We parametrize all waves by projective varieties derived from the support of the PDE. These include determinantal varieties and Fano varieties, and they generalize wave cones in analysis.","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135319687","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 : 2023-09-01DOI: 10.1007/s44007-023-00058-x
Irene Epifanio, Vicent Gimeno, X. Gual-Arnau, M. V. Ibáñez-Gual
{"title":"Archetypal Curves in the Shape and Size Space: Discovering the Salient Features of Curved Big Data by Representative Extremes","authors":"Irene Epifanio, Vicent Gimeno, X. Gual-Arnau, M. V. Ibáñez-Gual","doi":"10.1007/s44007-023-00058-x","DOIUrl":"https://doi.org/10.1007/s44007-023-00058-x","url":null,"abstract":"","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"2 1","pages":"635 - 658"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45779415","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 : 2023-06-14DOI: 10.1007/s44007-023-00051-4
Xander Faber
In the late 19th century, Klein inaugurated a program for describing the finite subgroups of $${text {PGL}}_2(k)$$ by treating the case in which the field k is the complex numbers. Gierster and Moore extended Klein’s arguments to deal with finite fields. In the past century, additional contributions to this problem were made by Serre, Suzuki, and Beauville, among others. We complete this program by giving a classification of the finite subgroups of $${text {PGL}}_2(k)$$ with order divisible by p, up to conjugation, for an arbitrary field k of positive characteristic p.
{"title":"Finite p-Irregular Subgroups of $${text {PGL}}_2(k)$$","authors":"Xander Faber","doi":"10.1007/s44007-023-00051-4","DOIUrl":"https://doi.org/10.1007/s44007-023-00051-4","url":null,"abstract":"In the late 19th century, Klein inaugurated a program for describing the finite subgroups of $${text {PGL}}_2(k)$$ by treating the case in which the field k is the complex numbers. Gierster and Moore extended Klein’s arguments to deal with finite fields. In the past century, additional contributions to this problem were made by Serre, Suzuki, and Beauville, among others. We complete this program by giving a classification of the finite subgroups of $${text {PGL}}_2(k)$$ with order divisible by p, up to conjugation, for an arbitrary field k of positive characteristic p.","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135859925","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 : 2023-05-31DOI: 10.1007/s44007-023-00047-0
Julia Crager, Felicia Flores, Timothy E. Goldberg, L. Rose, Daniel Rose-Levine, Darrion Thornburgh, Raphael Walker
{"title":"How Many Cards Should You Lay Out in a Game of EvenQuads: A Detailed Study of Caps in AG(n,2)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-6","authors":"Julia Crager, Felicia Flores, Timothy E. Goldberg, L. Rose, Daniel Rose-Levine, Darrion Thornburgh, Raphael Walker","doi":"10.1007/s44007-023-00047-0","DOIUrl":"https://doi.org/10.1007/s44007-023-00047-0","url":null,"abstract":"","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"2 1","pages":"382 - 419"},"PeriodicalIF":0.0,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48473659","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 : 2023-05-23DOI: 10.1007/s44007-023-00048-z
Niovi-Paraskevi Pasiou, G. Dassios
{"title":"On the Geometric Sensitivity of the MEG Inversion Algorithm","authors":"Niovi-Paraskevi Pasiou, G. Dassios","doi":"10.1007/s44007-023-00048-z","DOIUrl":"https://doi.org/10.1007/s44007-023-00048-z","url":null,"abstract":"","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"2 1","pages":"362 - 381"},"PeriodicalIF":0.0,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46097206","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 : 2023-04-13DOI: 10.1007/s44007-023-00045-2
B. Choudhury, N. Metiya, S. Kundu
{"title":"A Unified Fixed Point Result Along with Error Estimation and Propagation in the Fixed Point Iteration","authors":"B. Choudhury, N. Metiya, S. Kundu","doi":"10.1007/s44007-023-00045-2","DOIUrl":"https://doi.org/10.1007/s44007-023-00045-2","url":null,"abstract":"","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"1 1","pages":"1-15"},"PeriodicalIF":0.0,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44568652","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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