Bulletin des Sciences Mathematiques最新文献

{"title":"Inequalities for eigenvalues of the poly-Laplacian with arbitrary order on spherical domains","authors":"Yue He,&nbsp;Huan Wang","doi":"10.1016/j.bulsci.2025.103608","DOIUrl":"10.1016/j.bulsci.2025.103608","url":null,"abstract":"<div><div>In this paper, we are devoted to the study of universal inequalities for eigenvalues of the poly-Laplacian with arbitrary order on bounded domains in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mn>1</mn><mo>)</mo></math></span>, respectively, and then establish some new universal inequalities that are different from those already present in the literature. In particular, our results can reveal the relationship between the <span><math><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-th eigenvalue and the first <em>k</em> eigenvalues relatively quickly, and some methods used in this paper might be applied to other eigenvalue problems.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103608"},"PeriodicalIF":1.3,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600544","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":"Weak weak approximation for certain quadric surface bundles","authors":"Nick Rome","doi":"10.1016/j.bulsci.2025.103601","DOIUrl":"10.1016/j.bulsci.2025.103601","url":null,"abstract":"<div><div>We investigate weak approximation away from a finite set of places for a class of biquadratic fourfolds inside <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, some of which appear in the recent work of Hassett–Pirutka–Tschinkel <span><span>[16]</span></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103601"},"PeriodicalIF":1.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the essential norms of Toeplitz operators with symbols in C + H∞ acting on abstract Hardy spaces built upon translation-invariant Banach function spaces","authors":"Oleksiy Karlovych ,&nbsp;Eugene Shargorodsky","doi":"10.1016/j.bulsci.2025.103599","DOIUrl":"10.1016/j.bulsci.2025.103599","url":null,"abstract":"<div><div>Let <em>X</em> be a translation-invariant Banach function space on the unit circle and let <span><math><mi>H</mi><mo>[</mo><mi>X</mi><mo>]</mo></math></span> be the abstract Hardy space built upon <em>X</em>. We suppose the Riesz projection <em>P</em> is bounded on <em>X</em> and estimate the essential norms <span><math><msub><mrow><mo>‖</mo><mi>T</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>‖</mo></mrow><mrow><mi>B</mi><mo>(</mo><mi>H</mi><mo>[</mo><mi>X</mi><mo>]</mo><mo>)</mo><mo>,</mo><mi>e</mi></mrow></msub></math></span> of Toeplitz operators <span><math><mi>T</mi><mo>(</mo><mi>a</mi><mo>)</mo><mi>f</mi><mo>:</mo><mo>=</mo><mi>P</mi><mo>(</mo><mi>a</mi><mi>f</mi><mo>)</mo></math></span> with <span><math><mi>a</mi><mo>∈</mo><mi>C</mi><mo>+</mo><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>. We prove that in this case<span><span><span><math><msub><mrow><mo>‖</mo><mi>a</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></mrow></msub><mo>≤</mo><msub><mrow><mo>‖</mo><mi>T</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>‖</mo></mrow><mrow><mi>B</mi><mo>(</mo><mi>H</mi><mo>[</mo><mi>X</mi><mo>]</mo><mo>)</mo><mo>,</mo><mi>e</mi></mrow></msub><mo>≤</mo><mi>min</mi><mo>⁡</mo><mrow><mo>{</mo><mn>2</mn><mo>,</mo><msub><mrow><mo>‖</mo><mi>P</mi><mo>‖</mo></mrow><mrow><mi>B</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msub><mo>}</mo></mrow><msub><mrow><mo>‖</mo><mi>a</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></mrow></msub><mo>,</mo></math></span></span></span> extending the results by the second author <span><span>[27]</span></span> for classical Hardy spaces <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>=</mo><mi>H</mi><mo>[</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>]</mo></math></span>, <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span>. In contrast to our previous works <span><span>[27]</span></span> and <span><span>[16]</span></span>, we do not assume that <em>X</em> is reflexive or separable, which complicates the matters, but allows us to include the Hardy-Lorentz spaces <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msup><mo>=</mo><mi>H</mi><mo>[</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msup><mo>]</mo></math></span> with <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span> and <span><math><mi>q</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>∞</mo></math></span> into consideration.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103599"},"PeriodicalIF":1.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Schwarz lemma and Schwarz-Pick lemma for solutions of the α-harmonic equation","authors":"Ming Li ,&nbsp;Xiu-Shuang Ma ,&nbsp;Li-Mei Wang","doi":"10.1016/j.bulsci.2025.103598","DOIUrl":"10.1016/j.bulsci.2025.103598","url":null,"abstract":"<div><div>In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of <em>α</em>-harmonic equation (<span><math><mi>α</mi><mo>&gt;</mo><mo>−</mo><mn>1</mn></math></span>) are investigated. By making use of the integral of trigonometric functions, we obtain these two types of inequalities in terms of hypergeometric functions which improve the corresponding results due to Khalfallah et al. (Complex Var. Elliptic Equ., 2023) and Li et al. (Bull. Malays. Math. Sci. Soc., 2022).</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103598"},"PeriodicalIF":1.3,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551791","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":"On the representation of large even integers as the sum of eight primes from positive density sets","authors":"Meng Gao","doi":"10.1016/j.bulsci.2025.103597","DOIUrl":"10.1016/j.bulsci.2025.103597","url":null,"abstract":"<div><div>Let <span><math><mi>P</mi></math></span> denote the set of all primes. We have proved that if <em>A</em> is a subset of <span><math><mi>P</mi></math></span>, and the lower density of <em>A</em> in <span><math><mi>P</mi></math></span> is larger than 1/2, then every sufficiently large even integer <em>n</em> can be expressed in the form <span><math><mi>n</mi><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>8</mn></mrow></msub></math></span>, where <span><math><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>8</mn></mrow></msub><mo>∈</mo><mi>A</mi></math></span>. The constant 1/2 in this statement is the best possible.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103597"},"PeriodicalIF":1.3,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510382","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":"Formal integrability for monodromic nilpotent singular points in R3","authors":"Claudio Pessoa,&nbsp;Lucas Queiroz","doi":"10.1016/j.bulsci.2025.103588","DOIUrl":"10.1016/j.bulsci.2025.103588","url":null,"abstract":"<div><div>Consider analytic three-dimensional differential systems having a singular point at the origin such that its linear part is <span><math><mi>y</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>−</mo><mi>λ</mi><mi>z</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>z</mi></mrow></msub></math></span> for some <span><math><mi>λ</mi><mo>≠</mo><mn>0</mn></math></span>. The restriction of such systems to a center manifold has a nilpotent singular point at the origin. We study the formal and analytic integrability for those types of singular points in the monodromic case. As a byproduct, we obtain some useful results for planar <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> systems having a monodromic nilpotent singularity. We conclude the work by studying issues related to monodromy and formal integrability for the Elsonbaty–El-Sayed system, the Hide–Skeldon–Acheson dynamo system and the Generalized Lorenz system. For this last system, we were able to detect nilpotent centers.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"200 ","pages":"Article 103588"},"PeriodicalIF":1.3,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509436","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":"Direct sums and abstract Kadets–Klee properties","authors":"Tomasz Kiwerski,&nbsp;Paweł Kolwicz","doi":"10.1016/j.bulsci.2025.103587","DOIUrl":"10.1016/j.bulsci.2025.103587","url":null,"abstract":"<div><div>Let <span><math><mi>X</mi><mo>=</mo><msub><mrow><mo>{</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>}</mo></mrow><mrow><mi>γ</mi><mo>∈</mo><mi>Γ</mi></mrow></msub></math></span> be a family of Banach spaces and let <span><math><mi>E</mi></math></span> be a Banach sequence space defined on Γ. The main aim of this work is to investigate the abstract Kadets–Klee properties, that is, the Kadets–Klee type properties in which the weak convergence of sequences is replaced by the convergence with respect to some linear Hausdorff topology, for the direct sum construction <span><math><msub><mrow><mo>(</mo><msub><mrow><mo>⨁</mo></mrow><mrow><mi>γ</mi><mo>∈</mo><mi>Γ</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>E</mi></mrow></msub></math></span>. As we will show, and this seems to be quite atypical behavior when compared to some other geometric properties, to lift the Kadets–Klee properties from the components to whole direct sum it is not enough to assume that all involved spaces have the appropriate Kadets–Klee property. Actually, to complete the picture one must add a dichotomy in the form of the Schur type properties for <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>γ</mi></mrow></msub></math></span>'s supplemented by the variant of strict monotonicity for <span><math><mi>E</mi></math></span>. Back down to earth, this general machinery naturally provides a blue print for other topologies like, for example, the weak topology or the topology of local convergence in measure, that are perhaps more commonly associated with this type of considerations. Furthermore, by limiting ourselves to direct sums in which the family <span><math><mi>X</mi></math></span> is constant, that is, <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>=</mo><mi>X</mi></math></span> for all <span><math><mi>γ</mi><mo>∈</mo><mi>Γ</mi></math></span> and some Banach space <em>X</em>, we return to the well-explored ground of Köthe–Bochner sequence spaces <span><math><mi>E</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. Doing all this, we will reproduce, but sometimes also improve, essentially all existing results about the classical Kadets–Klee properties in Köthe–Bochner sequence spaces.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"200 ","pages":"Article 103587"},"PeriodicalIF":1.3,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509435","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":"Adams-type inequalities with logarithmic weights in fractional dimensions and the existence of extremals","authors":"Rou Jiang ,&nbsp;Wenyan Xu ,&nbsp;Caifeng Zhang ,&nbsp;Maochun Zhu","doi":"10.1016/j.bulsci.2025.103586","DOIUrl":"10.1016/j.bulsci.2025.103586","url":null,"abstract":"<div><div>In this paper, we proved a sharp Adams-type inequality with logarithmic weights <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>r</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mi>β</mi><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span> or <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>r</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mi>β</mi><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>, <span><math><mi>β</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> in the fractional dimensions. Furthermore, we show the existence of extremals for this kind of inequalities.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"200 ","pages":"Article 103586"},"PeriodicalIF":1.3,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509434","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 bounds to the Toeplitz determinants of certain order, Zalcman conjecture and Krushkals inequalities for the functions associated with the lemniscate of Bernoulli","authors":"Winne Bareh ,&nbsp;D. Vamshee Krishna ,&nbsp;Biswajit Rath","doi":"10.1016/j.bulsci.2025.103585","DOIUrl":"10.1016/j.bulsci.2025.103585","url":null,"abstract":"<div><div>The main object of this article is to investigate sharp bounds of the Toeplitz determinants of certain order, Zalcman conjecture and Krushkals inequalities for normalized analytic functions in the open unit disk <span><math><mi>D</mi></math></span>, associated with the familiar subfamily of starlike functions associated with the right half of lemniscate of Bernoulli. The practical tools applied in the derivation of our main results are the coefficient inequalities of the Carathéodory class <span><math><mi>P</mi></math></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103585"},"PeriodicalIF":1.3,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438013","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":"Diagonal property and weak point property of higher rank divisors and certain Hilbert schemes","authors":"Arijit Mukherjee,&nbsp;D.S. Nagaraj","doi":"10.1016/j.bulsci.2024.103541","DOIUrl":"10.1016/j.bulsci.2024.103541","url":null,"abstract":"<div><div>In this paper, we introduce the notion of the diagonal property and the weak point property for an ind-variety. We prove that the ind-varieties of higher rank divisors of integral slopes on a smooth projective curve have the weak point property. Moreover, we show that the ind-variety of <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>)</mo></math></span>-divisors has the diagonal property and is a locally complete linear ind-variety and calculate its Picard group. Furthermore, we obtain that the Hilbert schemes of a curve associated to the good partitions of a constant polynomial satisfy the diagonal property. In the process of obtaining this, we provide the exact number of such Hilbert schemes up to isomorphism by proving that the multi symmetric products associated to two distinct partitions of a positive integer <em>n</em> are not isomorphic.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"198 ","pages":"Article 103541"},"PeriodicalIF":1.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143103542","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}