Research in the Mathematical Sciences最新文献

{"title":"Identification of unbounded electric potentials through asymptotic boundary spectral data","authors":"Mourad Bellassoued, Yavar Kian, Yosra Mannoubi, Éric Soccorsi","doi":"10.1007/s40687-023-00417-8","DOIUrl":"https://doi.org/10.1007/s40687-023-00417-8","url":null,"abstract":"<p>We prove that the real-valued electric potential <span>(q in L^{max (2,3 n /5)}(Omega ))</span> of the Dirichlet Laplacian <span>(-Delta +q)</span> acting in a bounded domain <span>(Omega subset mathbb {R}^n)</span>, <span>(n ge 3)</span>, is uniquely determined by the asymptotics of the eigenpairs formed by the eigenvalues and the boundary observation of the normal derivative of the eigenfunctions.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"20 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139065603","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":"Analyticity of Steklov eigenvalues of nearly hyperspherical domains in $${mathbb {R}}^{d + 1}$$","authors":"Chee Han Tan, Robert Viator","doi":"10.1007/s40687-023-00415-w","DOIUrl":"https://doi.org/10.1007/s40687-023-00415-w","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"51 40","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946310","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":"Towards the Erdős-Hajnal conjecture for $$P_5$$ -free graphs","authors":"Pablo Blanco, Matija Bucić","doi":"10.1007/s40687-023-00413-y","DOIUrl":"https://doi.org/10.1007/s40687-023-00413-y","url":null,"abstract":"<p>The Erdős-Hajnal conjecture is one of the most classical and well-known problems in extremal and structural combinatorics dating back to 1977. It asserts that in stark contrast to the case of a general <i>n</i>-vertex graph, if one imposes even a little bit of structure on the graph, namely by forbidding a fixed graph <i>H</i> as an induced subgraph, instead of only being able to find a polylogarithmic size clique or an independent set, one can find one of polynomial size. Despite being the focus of considerable attention over the years, the conjecture remains open. In this paper, we improve the best known lower bound of <span>(2^{Omega (sqrt{log n})})</span> on this question, due to Erdős and Hajnal from 1989, in the smallest open case, namely when one forbids a <span>(P_5)</span>, the path on 5 vertices. Namely, we show that any <span>(P_5)</span>-free <i>n</i>-vertex graph contains a clique or an independent set of size at least <span>(2^{Omega (log n)^{2/3}})</span>. We obtain the same improvement for an infinite family of graphs.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"23 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138742679","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":"Estimate for the largest zeros of the D’Arcais polynomials","authors":"Bernhard Heim, Markus Neuhauser","doi":"10.1007/s40687-023-00412-z","DOIUrl":"https://doi.org/10.1007/s40687-023-00412-z","url":null,"abstract":"<p>The zeros of the <i>n</i>th D’Arcais polynomial, also known in combinatorics as the Nekrasov–Okounkov polynomial, dictate the vanishing properties of the <i>n</i>th Fourier coefficients of all complex powers <i>x</i> of the Dedekind <span>(eta )</span>-function. In this paper, we prove that these coefficients are non-vanishing for <span>(vert x vert &gt; kappa , (n-1))</span> and <span>(kappa approx 9.7225)</span>. Numerical computations imply that 9.72245 is a lower bound for <span>(kappa )</span>. This significantly improves previous results by Kostant, Han, and Heim–Neuhauser. The polynomials studied in this paper include Chebyshev polynomials of the second kind, 1-associated Laguerre polynomials, Hermite polynomials, and polynomials associated with overpartitions and plane partitions.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"51 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527794","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":"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}