Collectanea Mathematica最新文献

{"title":"On the interior Bernoulli free boundary problem for the fractional Laplacian on an interval","authors":"Tadeusz Kulczycki, Jacek Wszoła","doi":"10.1007/s13348-023-00417-5","DOIUrl":"https://doi.org/10.1007/s13348-023-00417-5","url":null,"abstract":"Abstract We study the structure of solutions of the interior Bernoulli free boundary problem for $$(-Delta )^{alpha /2}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>-</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> on an interval D with parameter $$lambda &gt; 0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . In particular, we show that there exists a constant $$lambda _{alpha ,D} &gt; 0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> (called the Bernoulli constant) such that the problem has no solution for $$lambda in (0,lambda _{alpha ,D})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , at least one solution for $$lambda = lambda _{alpha ,D}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and at least two solutions for $$lambda &gt; lambda _{alpha ,D}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . We also study the interior Bernoulli problem for the fractional Laplacian for an interval with one free boundary point. We discuss the connection of the Bernoulli problem with the corresponding variational problem and present some conjectures. In particular, we show for $$alpha = 1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> that there exists solutions of the interior Bernoulli free boundary problem for $$(-Delta )^{alpha /2}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>-</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> on an interval which are not minimizers of the corresponding variational problem.","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"25 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135391562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Skew derivations of incidence algebras","authors":"Érica Z. Fornaroli, Mykola Khrypchenko","doi":"10.1007/s13348-023-00423-7","DOIUrl":"https://doi.org/10.1007/s13348-023-00423-7","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135773670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Refined two weight estimates for the Bergman projection","authors":"Gianmarco Brocchi","doi":"10.1007/s13348-023-00420-w","DOIUrl":"https://doi.org/10.1007/s13348-023-00420-w","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"31 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Lipschitz numerical index of Banach spaces","authors":"Geunsu Choi, Mingu Jung, Hyung-Joon Tag","doi":"10.1007/s13348-023-00421-9","DOIUrl":"https://doi.org/10.1007/s13348-023-00421-9","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"72 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Attractor for minimal iterated function systems","authors":"Aliasghar Sarizadeh","doi":"10.1007/s13348-023-00422-8","DOIUrl":"https://doi.org/10.1007/s13348-023-00422-8","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Disjoint hypercyclic and supercyclic composition operators on discrete weighted Banach spaces","authors":"Zhiyuan Xu, Ya Wang, Zehua Zhou","doi":"10.1007/s13348-023-00418-4","DOIUrl":"https://doi.org/10.1007/s13348-023-00418-4","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"38 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135512915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Morelli-Włodarczyk cobordism and examples of rooftop flips","authors":"Lorenzo Barban, Alberto Franceschini","doi":"10.1007/s13348-023-00415-7","DOIUrl":"https://doi.org/10.1007/s13348-023-00415-7","url":null,"abstract":"Abstract We introduce the notion of rooftop flip, namely a small modification among normal projective varieties which is modeled by a smooth projective variety of Picard number 2 admitting two projective bundle structures. Examples include the Atiyah flop and the Mukai flop, modeled respectively by $$mathbb {P}^1times mathbb {P}^1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> </mml:math> and by $$mathbb {P}left( T_{mathbb {P}^2}right) $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>T</mml:mi> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:msub> </mml:mfenced> </mml:mrow> </mml:math> . Using the Morelli-Włodarczyk cobordism, we prove that any smooth projective variety of Picard number 1, endowed with a $${mathbb C}^*$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -action with only two fixed point components, induces a rooftop flip.","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":"151 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135060768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The adjoint of an operator on a Banach space","authors":"F. J. García-Pacheco","doi":"10.1007/s13348-023-00414-8","DOIUrl":"https://doi.org/10.1007/s13348-023-00414-8","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43349667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Elliptic curves, ACM bundles and Ulrich bundles on prime Fano threefolds","authors":"C. Ciliberto, F. Flamini, A. L. Knutsen","doi":"10.1007/s13348-023-00413-9","DOIUrl":"https://doi.org/10.1007/s13348-023-00413-9","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45878697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A weak version of the Mond conjecture","authors":"R. Giménez Conejero, J. J. Nuno-Ballesteros","doi":"10.1007/s13348-023-00411-x","DOIUrl":"https://doi.org/10.1007/s13348-023-00411-x","url":null,"abstract":"","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43258965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}