{"title":"Erratum to “Charting the q-Askey scheme. II. The q","authors":"","doi":"10.1016/j.indag.2023.05.006","DOIUrl":"https://doi.org/10.1016/j.indag.2023.05.006","url":null,"abstract":"","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47839650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Beatty primes from fractional powers of almost-primes","authors":"Victor Zhenyu Guo , Jinjiang Li , Min Zhang","doi":"10.1016/j.indag.2023.04.004","DOIUrl":"10.1016/j.indag.2023.04.004","url":null,"abstract":"<div><p>Let <span><math><mrow><mi>α</mi><mo>></mo><mn>1</mn></mrow></math></span> be irrational and of finite type, <span><math><mrow><mi>β</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. In this paper, it is proved that for <span><math><mrow><mi>R</mi><mo>⩾</mo><mn>13</mn></mrow></math></span> and any fixed <span><math><mrow><mi>c</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>, there exist infinitely many primes in the intersection of Beatty sequence <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>α</mi><mo>,</mo><mi>β</mi></mrow></msub></math></span> and <span><math><mrow><mo>⌊</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow></msup><mo>⌋</mo></mrow></math></span>, where <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span> is an explicit constant depending on <span><math><mi>R</mi></math></span> herein, <span><math><mi>n</mi></math></span> is a natural number with at most <span><math><mi>R</mi></math></span> prime factors, counted with multiplicity.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43856784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Heinz type inequality, Bloch type theorem and Lipschitz characteristic of polyharmonic mappings","authors":"Shaolin Chen","doi":"10.1016/j.indag.2023.05.001","DOIUrl":"10.1016/j.indag.2023.05.001","url":null,"abstract":"<div><p>Suppose that <span><math><mi>f</mi></math></span> satisfies the following: <span><math><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math></span> the polyharmonic equation <span><math><mrow><msup><mrow><mi>Δ</mi></mrow><mrow><mi>m</mi></mrow></msup><mi>f</mi><mo>=</mo><mi>Δ</mi><mrow><mo>(</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>f</mi><mo>)</mo></mrow></mrow></math></span>\u0000<span><math><mrow><mo>=</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>m</mi></mrow></msub></mrow></math></span>\u0000<span><math><mrow><mo>(</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>∈</mo><mi>C</mi><mrow><mo>(</mo><mover><mrow><msup><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow><mo>¯</mo></mover><mo>,</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow><mo>)</mo></mrow></math></span>, (2) the boundary conditions <span><math><mrow><msup><mrow><mi>Δ</mi></mrow><mrow><mn>0</mn></mrow></msup><mi>f</mi><mo>=</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>1</mn></mrow></msup><mi>f</mi><mo>=</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mspace></mspace><mo>…</mo><mo>,</mo><mspace></mspace><msup><mrow><mi>Δ</mi></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>f</mi><mo>=</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></math></span> on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>\u0000(<span><math><mrow><msub><mrow><mi>φ</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>∈</mo><mi>C</mi><mrow><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>,</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>j</mi><mo>∈</mo><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>m</mi><mo>−</mo><mn>1</mn><mo>}</mo></mrow></mrow></math></span> and <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> denotes the boundary of the unit ball <span><math><msup><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>), and <span><math><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math></span>\u0000<span><math><mrow><mi>f</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span>, where <span><math><mrow><mi>n</mi><mo>≥</mo><mn>3</mn></mrow></math></span> and <span><math><mrow><mi>m</mi><mo>≥</mo><mn>1</mn></mrow></math></span> are integers. Initially, we prove a Schwarz type lemma and use it to obtain a Heinz type inequality of mappings satisfying the polyharmonic equation with the above Dirichlet boundary value conditions. Furthermore, we establish a Bloch type theorem of mappings satisfying the above polyharmonic equation, which gives an answer to an open problem in Chen an","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47562551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Box and nabla products that are D-spaces","authors":"H.A. Barriga-Acosta , P.M. Gartside","doi":"10.1016/j.indag.2023.04.002","DOIUrl":"https://doi.org/10.1016/j.indag.2023.04.002","url":null,"abstract":"<div><p>A space <span><math><mi>X</mi></math></span> is <span><math><mi>D</mi></math></span> if for every assignment, <span><math><mi>U</mi></math></span><span>, of an open neighborhood to each point </span><span><math><mi>x</mi></math></span> in <span><math><mi>X</mi></math></span> there is a closed discrete <span><math><mi>D</mi></math></span> such that <span><math><mrow><mo>⋃</mo><mrow><mo>{</mo><mi>U</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>:</mo><mi>x</mi><mo>∈</mo><mi>D</mi><mo>}</mo></mrow><mo>=</mo><mi>X</mi></mrow></math></span>. The box product, <span><math><mrow><mo>□</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span>, is <span><math><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></math></span> with topology generated by all <span><math><mrow><msub><mrow><mo>∏</mo></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>, where every <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is open. The nabla product, <span><math><mrow><mo>∇</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span>, is obtained from <span><math><mrow><mo>□</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span> by quotienting out mod-finite. The weight of <span><math><mi>X</mi></math></span>, <span><math><mrow><mi>w</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span>, is the minimal size of a base, while <span><math><mrow><mi>d</mi><mo>=</mo><mo>cof</mo><msup><mrow><mi>ω</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span>.</p><p>It is shown that there are specific compact spaces <span><math><mi>X</mi></math></span> such that <span><math><mrow><mo>□</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span> and <span><math><mrow><mo>∇</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span> are not <span><math><mi>D</mi></math></span>, but in general:</p><p>(1) <span><math><mrow><mo>□</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span> and <span><math><mrow><mo>∇</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span> are hereditarily <span><math><mi>D</mi></math></span> if <span><math><mi>X</mi></math></span> is scattered and either hereditarily paracompact or of finite scattered height, or if <span><math><mi>X</mi></math></span> is metrizable (and <span><math><mrow><mi>w</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>≤</mo><mi>d</mi></mrow></math></span> for <span><math><mrow><mo>□</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span>);</p><p>(2) <span><math><mrow><mo>∇</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>ω</mi></mrow></msup></mrow></math></span> is hereditarily <span><math><mi>D</mi></math></span> if <span><math><mi>X</mi></math></span> is first countable and <span><math>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49838698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Minimal surfaces and Schwarz lemma","authors":"David Kalaj","doi":"10.1016/j.indag.2023.01.002","DOIUrl":"10.1016/j.indag.2023.01.002","url":null,"abstract":"<div><p>We prove a sharp Schwarz lemma type inequality for the Weierstrass–Enneper parameterization of minimal disks. It states the following. If <span><math><mrow><mi>F</mi><mo>:</mo><mi>D</mi><mo>→</mo><mi>Σ</mi></mrow></math></span> is a conformal harmonic parameterization of a minimal disk <span><math><mrow><mi>Σ</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span>, where <span><math><mi>D</mi></math></span> is the unit disk and <span><math><mrow><mrow><mo>|</mo><mi>Σ</mi><mo>|</mo></mrow><mo>=</mo><mi>π</mi><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, then <span><math><mrow><mrow><mo>|</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>x</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>|</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msup><mrow><mrow><mo>|</mo><mi>z</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>≤</mo><mi>R</mi></mrow></math></span>. If for some <span><math><mi>z</mi></math></span> the previous inequality is equality, then the surface is an affine image of a disk, and <span><math><mi>F</mi></math></span><span> is linear up to a Möbius transformation of the unit disk.</span></p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41928826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A decomposition property for an MX/G/","authors":"Igor Kleiner, E. Frostig, David Perry","doi":"10.1016/j.indag.2023.05.002","DOIUrl":"https://doi.org/10.1016/j.indag.2023.05.002","url":null,"abstract":"","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47531744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sums of even powers of k-regulous functions","authors":"Juliusz Banecki, Tomasz Kowalczyk","doi":"10.1016/j.indag.2022.12.004","DOIUrl":"https://doi.org/10.1016/j.indag.2022.12.004","url":null,"abstract":"<div><p>We provide an example of a nonnegative <span><math><mi>k</mi></math></span>-regulous function on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> for <span><math><mrow><mi>k</mi><mo>≥</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></math></span> which cannot be written as a sum of squares of <span><math><mi>k</mi></math></span>-regulous functions. We then obtain lower bounds for Pythagoras numbers <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn><mi>d</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>k</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> of <span><math><mi>k</mi></math></span>-regulous functions on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> for <span><math><mrow><mi>k</mi><mo>≥</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. We also prove that the second Pythagoras number of the ring of 0-regulous functions <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> on an irreducible 0-regulous affine variety <span><math><mi>X</mi></math></span> is finite and bounded from above by <span><math><msup><mrow><mn>2</mn></mrow><mrow><mo>dim</mo><mi>X</mi></mrow></msup></math></span>.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49896146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Box and nabla products that are D-spaces","authors":"H. Barriga-Acosta, P. Gartside","doi":"10.1016/j.indag.2023.04.002","DOIUrl":"https://doi.org/10.1016/j.indag.2023.04.002","url":null,"abstract":"","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44217103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nguyen Xuan Hong , Hoang Van Can , Nguyen Thi Lien , Pham Thi Lieu
{"title":"Complex Monge–Ampère equations for plurifinely plurisubharmonic functions","authors":"Nguyen Xuan Hong , Hoang Van Can , Nguyen Thi Lien , Pham Thi Lieu","doi":"10.1016/j.indag.2022.12.008","DOIUrl":"10.1016/j.indag.2022.12.008","url":null,"abstract":"<div><p>This paper studies the complex Monge–Ampère equations for <span><math><mi>F</mi></math></span>-plurisubharmonic functions in bounded <span><math><mi>F</mi></math></span><span>-hyperconvex domains. We give sufficient conditions<span> for this equation to solve for measures with a singular part.</span></span></p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47391604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Intermittency generated by attracting and weakly repelling fixed points","authors":"Benthen Zeegers","doi":"10.1016/j.indag.2022.12.002","DOIUrl":"10.1016/j.indag.2022.12.002","url":null,"abstract":"<div><p>Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay between a superexponentially attracting fixed point and an exponentially repelling fixed point. In this article we consider a closely related family of random systems with exponentially fast attraction to and polynomially fast repulsion from two fixed points, and show that such a phase transition still exists. The method of the proof however is different and relies on the construction of a suitable invariant set for the transfer operator.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48181565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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