Research in the Mathematical Sciences最新文献

{"title":"Operator shifting for noisy elliptic systems","authors":"Philip A. Etter, Lexing Ying","doi":"10.1007/s40687-023-00414-x","DOIUrl":"https://doi.org/10.1007/s40687-023-00414-x","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"82 15","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135037343","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}

{"title":"Certain invertible operator-block matrices induced by $$C^{*}$$-algebras and scaled hypercomplex numbers","authors":"Daniel Alpay, Ilwoo Cho","doi":"10.1007/s40687-023-00411-0","DOIUrl":"https://doi.org/10.1007/s40687-023-00411-0","url":null,"abstract":"Abstract The main purposes of this paper are (i) to enlarge scaled hypercomplex structures to operator-valued cases, where the operators are taken from a $$C^{*}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:math> -subalgebra of an operator algebra on a separable Hilbert space, (ii) to characterize the invertibility conditions on the operator-valued scaled-hypercomplex structures of (i), (iii) to study relations between the invertibility of scaled hypercomplex numbers, and that of operator-valued cases of (ii), and (iv) to confirm our invertibility of (ii) and (iii) are equivalent to the general invertibility of $$left( 2times 2right) $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mfenced> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:mfenced> </mml:math> -block operator matrices.","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"44 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510833","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}

{"title":"The tension determination problem for an inextensible interface in 2D Stokes flow","authors":"Po-Chun Kuo, Ming-Chih Lai, Yoichiro Mori, Analise Rodenberg","doi":"10.1007/s40687-023-00406-x","DOIUrl":"https://doi.org/10.1007/s40687-023-00406-x","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570031","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}

{"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":"13 1","pages":"0"},"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}

{"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 $${mathcal {C}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;/mml:math&gt; be the pseudovariety $${mathcal {F}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;/mml:math&gt; of all finite groups or the pseudovariety $${mathcal {S}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;S&lt;/mml:mi&gt; &lt;/mml:math&gt; of all finite solvable groups and let $$Gamma $$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;Γ&lt;/mml:mi&gt; &lt;/mml:math&gt; be either a finitely generated free group or a surface group. The $${mathcal {C}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;/mml:math&gt; -genus of $$Gamma $$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;Γ&lt;/mml:mi&gt; &lt;/mml:math&gt; , denoted by $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;Γ&lt;/mml:mi&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , consists of the isomorphism classes of finitely generated residually- $$mathcal C$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;/mml:math&gt; groups G having the same quotients in $${mathcal {C}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;/mml:math&gt; as $$Gamma $$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;Γ&lt;/mml:mi&gt; &lt;/mml:math&gt; . We show that the groups from $${mathcal {G}}_{{mathcal {C}}}(Gamma )$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;Γ&lt;/mml:mi&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; 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- $${mathcal {C}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;/mml:math&gt; group and $$u:Frightarrow G$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mo&gt;:&lt;/mml:mo&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mo&gt;→&lt;/mml:mo&gt; &lt;mml:mi&gt;G&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; is a homomorphism such that the induced map of pro- $${mathcal {C}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;/mml:math&gt; completions $$u_{widehat{{mathcal {C}}}} : F_{widehat{{mathcal {C}}}}rightarrow G_{widehat{{mathcal {C}}}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mover&gt; &lt;mml:mi&gt;C&lt;/mml:mi&gt; &lt;mml:mo&gt;^&lt;/mml:mo&gt; &lt;/mml:mover&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;:&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;F&lt;/mml:mi&gt; &lt;mml:mover&gt; &lt;mml:mi&gt;C&lt;/","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"439 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":"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}

{"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":"190 1","pages":"0"},"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}

{"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":"9 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":"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}

{"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":"6 1","pages":"0"},"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}

{"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":"106 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":"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}

{"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":"30 1","pages":"0"},"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}