For a class of non-symmetric non-local Lévy-type operators $mathcal L^{kappa}$, which include those of the form $$ mathcal L^{kappa}f(x):= int _{mathbb R^d}( f(x+z)-f(x)- mathbf 1_{|z| lt 1} langle z,nabla f(x)rangle )kappa (x,z)J(z), dz, $$
{"title":"Regularity of fundamental solutions for Lévy-type operators","authors":"Karol Szczypkowski","doi":"10.4064/ba230424-12-9","DOIUrl":"https://doi.org/10.4064/ba230424-12-9","url":null,"abstract":"For a class of non-symmetric non-local Lévy-type operators $mathcal L^{kappa}$, which include those of the form $$ mathcal L^{kappa}f(x):= int _{mathbb R^d}( f(x+z)-f(x)- mathbf 1_{|z| lt 1} langle z,nabla f(x)rangle )kappa (x,z)J(z), dz, $$","PeriodicalId":487279,"journal":{"name":"Bulletin of the Polish Academy of Sciences. Mathematics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784801","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}
It is well-known that abelian varieties are projective, and so there exist explicit polynomial and rational functions which define both the variety and its group law. It is however difficult to find any explicit polynomial and rational functions describin
{"title":"Explicit rational group law on hyperelliptic Jacobians of any genus","authors":"David Urbanik","doi":"10.4064/ba230330-7-7","DOIUrl":"https://doi.org/10.4064/ba230330-7-7","url":null,"abstract":"It is well-known that abelian varieties are projective, and so there exist explicit polynomial and rational functions which define both the variety and its group law. It is however difficult to find any explicit polynomial and rational functions describin","PeriodicalId":487279,"journal":{"name":"Bulletin of the Polish Academy of Sciences. Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783632","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 $mathsf {ZFA}$ (Zermelo–Fraenkel set theory with the Axiom of Extensionality weakened to allow the existence of atoms), we prove that the strength of the proposition $mathsf {EDM}$ (“If $G=(V_{G}, E_{G})$ is a graph such that $V_{G}$ is uncountable,
{"title":"On the Erdős–Dushnik–Miller theorem without AC","authors":"Amitayu Banerjee, Alexa Gopaulsingh","doi":"10.4064/ba221221-6-6","DOIUrl":"https://doi.org/10.4064/ba221221-6-6","url":null,"abstract":"In $mathsf {ZFA}$ (Zermelo–Fraenkel set theory with the Axiom of Extensionality weakened to allow the existence of atoms), we prove that the strength of the proposition $mathsf {EDM}$ (“If $G=(V_{G}, E_{G})$ is a graph such that $V_{G}$ is uncountable,","PeriodicalId":487279,"journal":{"name":"Bulletin of the Polish Academy of Sciences. Mathematics","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135828102","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 explore semibounded expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We show that if $mathcal R=langle mathbb R, lt , +, ldots rangle $ is a semibounded o-minimal structure and
{"title":"On semibounded expansions of ordered groups","authors":"Pantelis E. Eleftheriou, Alex Savatovsky","doi":"10.4064/ba230725-27-9","DOIUrl":"https://doi.org/10.4064/ba230725-27-9","url":null,"abstract":"We explore <em>semibounded</em> expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We show that if $mathcal R=langle mathbb R, lt , +, ldots rangle $ is a semibounded o-minimal structure and","PeriodicalId":487279,"journal":{"name":"Bulletin of the Polish Academy of Sciences. Mathematics","volume":"30 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136297296","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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