Pub Date : 2023-10-17DOI: 10.1007/s40687-023-00409-8
Pu-Zhao Kow, Jenn-Nan Wang
{"title":"Inverse problems for some fractional equations with general nonlinearity","authors":"Pu-Zhao Kow, Jenn-Nan Wang","doi":"10.1007/s40687-023-00409-8","DOIUrl":"https://doi.org/10.1007/s40687-023-00409-8","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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/s40687-023-00408-9
Andrei Jaikin-Zapirain
Abstract Let $${mathcal {C}}$$ C be the pseudovariety $${mathcal {F}}$$ F of all finite groups or the pseudovariety $${mathcal {S}}$$ S of all finite solvable groups and let $$Gamma $$ Γ be either a finitely generated free group or a surface group. The $${mathcal {C}}$$ C -genus of $$Gamma $$ Γ , denoted by $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ GC(Γ) , consists of the isomorphism classes of finitely generated residually- $$mathcal C$$ C groups G having the same quotients in $${mathcal {C}}$$ C as $$Gamma $$ Γ . We show that the groups from $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ GC(Γ) are residually- p for all primes p . This answers a question of Gilbert Baumslag and shows that the groups in the genus are residually finite rationally solvable groups. This leads to a positive solution of particular case of a question of Alexander Grothendieck: if F is a free group, G is a finitely generated residually- $${mathcal {C}}$$ C group and $$u:Frightarrow G$$ u:F→G is a homomorphism such that the induced map of pro- $${mathcal {C}}$$ C completions $$u_{widehat{{mathcal {C}}}} : F_{widehat{{mathcal {C}}}}rightarrow G_{widehat{{mathcal {C}}}}$$ uC^:FC
抽象Let $${mathcal {C}}$$ C是伪变种 $${mathcal {F}}$$ 所有有限群的F或伪簇 $${mathcal {S}}$$ 所有有限可解群的S，让 $$Gamma $$ Γ要么是有限生成的自由群，要么是曲面群。The $${mathcal {C}}$$ 的C属 $$Gamma $$ Γ，用表示 $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ gc (Γ)，由有限生成残差的同构类组成 $$mathcal C$$ C组G有相同的商 $${mathcal {C}}$$ 选C。 $$Gamma $$ Γ。我们展示了来自 $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ G C (Γ)对所有素数p都是残差p。这回答了Gilbert Baumslag的一个问题，并证明了属中的群是剩余有限合理可解群。这就得到了Alexander Grothendieck问题的一个特殊情况的正解:如果F是一个自由群，则G是一个有限生成的残差 $${mathcal {C}}$$ C组和 $$u:Frightarrow G$$ u: F→G是一个同态，使得pro-的诱导映射 $${mathcal {C}}$$ C完井 $$u_{widehat{{mathcal {C}}}} : F_{widehat{{mathcal {C}}}}rightarrow G_{widehat{{mathcal {C}}}}$$ u C ^: F C ^→G C ^是同构的，那么u也是同构的。
{"title":"The finite and solvable genus of finitely generated free and surface groups","authors":"Andrei Jaikin-Zapirain","doi":"10.1007/s40687-023-00408-9","DOIUrl":"https://doi.org/10.1007/s40687-023-00408-9","url":null,"abstract":"Abstract Let $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> be the pseudovariety $${mathcal {F}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>F</mml:mi> </mml:math> of all finite groups or the pseudovariety $${mathcal {S}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>S</mml:mi> </mml:math> of all finite solvable groups and let $$Gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Γ</mml:mi> </mml:math> be either a finitely generated free group or a surface group. The $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> -genus of $$Gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Γ</mml:mi> </mml:math> , denoted by $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>C</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Γ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , consists of the isomorphism classes of finitely generated residually- $$mathcal C$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> groups G having the same quotients in $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> as $$Gamma $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Γ</mml:mi> </mml:math> . We show that the groups from $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>C</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Γ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> are residually- p for all primes p . This answers a question of Gilbert Baumslag and shows that the groups in the genus are residually finite rationally solvable groups. This leads to a positive solution of particular case of a question of Alexander Grothendieck: if F is a free group, G is a finitely generated residually- $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> group and $$u:Frightarrow G$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo>:</mml:mo> <mml:mi>F</mml:mi> <mml:mo>→</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> is a homomorphism such that the induced map of pro- $${mathcal {C}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>C</mml:mi> </mml:math> completions $$u_{widehat{{mathcal {C}}}} : F_{widehat{{mathcal {C}}}}rightarrow G_{widehat{{mathcal {C}}}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>u</mml:mi> <mml:mover> <mml:mi>C</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:msub> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>F</mml:mi> <mml:mover> <mml:mi>C</","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135482033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-04DOI: 10.1007/s40687-023-00407-w
Wuchen Li, Siting Liu, Stanley Osher
{"title":"A kernel formula for regularized Wasserstein proximal operators","authors":"Wuchen Li, Siting Liu, Stanley Osher","doi":"10.1007/s40687-023-00407-w","DOIUrl":"https://doi.org/10.1007/s40687-023-00407-w","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135590738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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/s40687-023-00405-y
Fabian Reede
Abstract Let X be a K3 surface. We prove that Addington’s $$mathbb {P}^n$$ Pn -functor between the derived categories of X and the Hilbert scheme of points $$X^{[k]}$$ X[k] maps stable vector bundles on X to stable vector bundles on $$X^{[k]}$$ X[k] , given some numerical conditions are satisfied.
设X是一个K3曲面。在一定的数值条件下，证明了Addington的$$mathbb {P}^n$$ P n -函子在X的衍生范畴和点$$X^{[k]}$$ X [k]的Hilbert格式之间将X上的稳定向量束映射到$$X^{[k]}$$ X [k]上的稳定向量束。
{"title":"Stability and certain $$mathbb {P}^n$$-functors","authors":"Fabian Reede","doi":"10.1007/s40687-023-00405-y","DOIUrl":"https://doi.org/10.1007/s40687-023-00405-y","url":null,"abstract":"Abstract Let X be a K3 surface. We prove that Addington’s $$mathbb {P}^n$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> -functor between the derived categories of X and the Hilbert scheme of points $$X^{[k]}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>k</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> </mml:msup> </mml:math> maps stable vector bundles on X to stable vector bundles on $$X^{[k]}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>X</mml:mi> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>k</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> </mml:msup> </mml:math> , given some numerical conditions are satisfied.","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135695685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1007/s40687-023-00402-1
Cristina Ballantine, Hannah E. Burson, William Craig, Amanda Folsom, Boya Wen
{"title":"Hook length biases and general linear partition inequalities","authors":"Cristina Ballantine, Hannah E. Burson, William Craig, Amanda Folsom, Boya Wen","doi":"10.1007/s40687-023-00402-1","DOIUrl":"https://doi.org/10.1007/s40687-023-00402-1","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135193852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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/s40687-023-00403-0
Bruce C. Berndt, Sun Kim, Alexandru Zaharescu
{"title":"Exact evaluations and reciprocity theorems for finite trigonometric sums","authors":"Bruce C. Berndt, Sun Kim, Alexandru Zaharescu","doi":"10.1007/s40687-023-00403-0","DOIUrl":"https://doi.org/10.1007/s40687-023-00403-0","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135814264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-23DOI: 10.1007/s40687-023-00404-z
Emre Alkan
{"title":"Covering sumsets of a prime field and class numbers","authors":"Emre Alkan","doi":"10.1007/s40687-023-00404-z","DOIUrl":"https://doi.org/10.1007/s40687-023-00404-z","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135959934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-22DOI: 10.1007/s40687-023-00401-2
Soumyarup Banerjee, Atul Dixit, Shivajee Gupta
{"title":"Explicit transformations for generalized Lambert series associated with the divisor function $$sigma _{a}^{(N)}(n)$$ and their applications","authors":"Soumyarup Banerjee, Atul Dixit, Shivajee Gupta","doi":"10.1007/s40687-023-00401-2","DOIUrl":"https://doi.org/10.1007/s40687-023-00401-2","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136011505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-11DOI: 10.1007/s40687-023-00399-7
Yajie Zhang, Zuoqiang Shi
{"title":"A second-order nonlocal approximation for Poisson model with Dirichlet boundary","authors":"Yajie Zhang, Zuoqiang Shi","doi":"10.1007/s40687-023-00399-7","DOIUrl":"https://doi.org/10.1007/s40687-023-00399-7","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79661643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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