Bulletin des Sciences Mathematiques最新文献

{"title":"On the properties of alternating invariant functions","authors":"Haiqing Zhu ,&nbsp;Su Hu ,&nbsp;Min-Soo Kim","doi":"10.1016/j.bulsci.2025.103724","DOIUrl":"10.1016/j.bulsci.2025.103724","url":null,"abstract":"<div><div>Functions satisfying the functional equation<span><span><span><math><munderover><mo>∑</mo><mrow><mi>r</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></munderover><msup><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>r</mi></mrow></msup><mi>f</mi><mo>(</mo><mi>x</mi><mo>+</mo><mi>r</mi><mi>y</mi><mo>,</mo><mi>n</mi><mi>y</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>,</mo><mspace></mspace><mtext>for any positive odd integer</mtext><mspace></mspace><mi>n</mi><mo>,</mo></math></span></span></span> are named the alternating invariant functions. Examples of such functions include Euler polynomials, alternating Hurwitz zeta functions and their associated Gamma functions. In this paper, we systematically investigate the fundamental properties of alternating invariant functions. We prove that the set of such functions is closed under translation, reflection, and differentiation. In addition, we define a convolution operation on alternating invariant functions and derive explicit convolution formulas for Euler polynomials and alternating Hurwitz zeta functions, respectively. Furthermore, using distributional relations, we construct new examples of alternating invariant functions, including suitable combinations of trigonometric, exponential, and logarithmic functions, among others.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103724"},"PeriodicalIF":0.9,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106250","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":"Well-posedness and non-uniform dependence for a generalized two-component Camassa-Holm-type system with high-order nonlinearities and multi-peakons in Besov spaces","authors":"Haiquan Wang","doi":"10.1016/j.bulsci.2025.103725","DOIUrl":"10.1016/j.bulsci.2025.103725","url":null,"abstract":"<div><div>Considered herein is a generalized two-component Camassa-Holm-type system with high-order nonlinearities and multi-peakons, which contains some integrable shallow water wave equations, such as Camassa-Holm equation, Degasperis-Procesi equation, Novikov equation and Geng-Xue system. At first, the results with respect to the local well-posedness of the solutions of Cauchy problem of this system in Besov spaces are demonstrated in detail. Then, the non-uniformly continuous dependence on initial data of the solutions of this problem in Besov spaces on the torus and line is established by constructing new appropriate approximate solutions and initial data. In the process of proof, we need to rely upon Littlewood-Paley decomposition theory and overcome the difficulties resulting from the high-order nonlinearities of the system.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103725"},"PeriodicalIF":0.9,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106251","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":"Sharp inequalities between mean quantities via convexity and applications","authors":"Duong Quoc Huy","doi":"10.1016/j.bulsci.2025.103723","DOIUrl":"10.1016/j.bulsci.2025.103723","url":null,"abstract":"<div><div>The aim of the present paper is to provide a completely new method that allows us to derive the best possible bounds for one-term refinements and reverses of inequalities between mean quantities. These results cover and refine almost all inequalities in the literature. Applications to inequalities for matrix means, the traces and determinants of matrices, as well as inequalities for unitarily invariant norms and numerical radius norms, are also discussed.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103723"},"PeriodicalIF":0.9,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020442","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":"Coarse geometry of free products of metric spaces","authors":"Qin Wang,&nbsp;Jvbin Yao","doi":"10.1016/j.bulsci.2025.103721","DOIUrl":"10.1016/j.bulsci.2025.103721","url":null,"abstract":"<div><div>Recently, a notion of the free product <span><math><mi>X</mi><mo>⁎</mo><mi>Y</mi></math></span> of two metric spaces <em>X</em> and <em>Y</em> has been introduced by T. Fukaya and T. Matsuka in their study of the coarse Baum-Connes conjecture. In this paper, we study coarse geometric permanence properties of the free product <span><math><mi>X</mi><mo>⁎</mo><mi>Y</mi></math></span>. We show that if <em>X</em> and <em>Y</em> satisfy any of the following conditions, then <span><math><mi>X</mi><mo>⁎</mo><mi>Y</mi></math></span> also satisfies that condition: (1) they are coarsely embeddable into a Hilbert space or a uniformly convex Banach space; (2) they have Yu's Property A; (3) they are hyperbolic spaces. These generalize the corresponding results for discrete groups to the case of metric spaces.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103721"},"PeriodicalIF":0.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049124","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 spatial average of solutions to SPDEs is asymptotically independent of the solution","authors":"Ciprian A. Tudor ,&nbsp;Jérémy Zurcher","doi":"10.1016/j.bulsci.2025.103719","DOIUrl":"10.1016/j.bulsci.2025.103719","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> be the solution to the stochastic heat or wave equation driven by a Gaussian noise which is white in time and white or correlated with respect to the spatial variable. We consider the spatial average of the solution <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow></mfrac><msub><mrow><mo>∫</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo><mo>≤</mo><mi>R</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mi>d</mi><mi>x</mi></math></span>, where <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mi>E</mi><msup><mrow><mo>(</mo><msub><mrow><mo>∫</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo><mo>≤</mo><mi>R</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mi>d</mi><mi>x</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>. It is known that, when <em>R</em> goes to infinity, <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> converges in law to a standard Gaussian random variable <em>Z</em>. We show that the spatial average <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> is actually asymptotic independent by the solution itself, at any time and at any point in space, meaning that the random vector <span><math><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>)</mo></math></span> converges in distribution, as <span><math><mi>R</mi><mo>→</mo><mo>∞</mo></math></span>, to <span><math><mo>(</mo><mi>Z</mi><mo>,</mo><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>)</mo></math></span>, where <em>Z</em> is a standard normal random variable independent of <span><math><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span>. By using the Stein-Malliavin calculus, we also obtain the rate of convergence, under the Wasserstein distance, for this limit theorem.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103719"},"PeriodicalIF":0.9,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145009535","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":"Logarithmic connections on principal bundles over normal varieties","authors":"Jyoti Dasgupta ,&nbsp;Bivas Khan ,&nbsp;Mainak Poddar","doi":"10.1016/j.bulsci.2025.103715","DOIUrl":"10.1016/j.bulsci.2025.103715","url":null,"abstract":"<div><div>Let <em>X</em> be a normal projective variety over an algebraically closed field of characteristic zero. Let <em>D</em> be a reduced Weil divisor on <em>X</em>. Let <em>G</em> be a reductive linear algebraic group. We study logarithmic connections on a principal <em>G</em>-bundle over <em>X</em>, which are singular along <em>D</em>. We give necessary and sufficient conditions for the existence of such a connection in terms of connections on associated vector bundles when the logarithmic tangent sheaf of <em>X</em> is locally free. The existence of a logarithmic connection on a principal bundle over a projective toric variety, singular along the boundary divisor, is shown to be equivalent to the existence of a torus equivariant structure on the bundle.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103715"},"PeriodicalIF":0.9,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934292","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":"Equivariant K-theory of cellular toroidal embeddings","authors":"Alexis Tchoudjem ,&nbsp;Vikraman Uma","doi":"10.1016/j.bulsci.2025.103717","DOIUrl":"10.1016/j.bulsci.2025.103717","url":null,"abstract":"<div><div>In this article we describe the <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>m</mi><mi>p</mi></mrow></msub><mo>×</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>m</mi><mi>p</mi></mrow></msub></math></span>-equivariant topological <em>K</em>-ring of a <em>cellular</em> toroidal embedding <span><math><mi>X</mi></math></span> of a complex connected reductive algebraic group <em>G</em>. In particular, our results extend the results in <span><span>[31]</span></span> and <span><span>[32]</span></span> on the regular embeddings of <em>G</em>, to the equivariant topological <em>K</em>-ring of a larger class of (possibly singular) cellular toroidal embeddings. They are also a topological analogue of the results in <span><span>[14]</span></span> on the operational equivariant algebraic <em>K</em>-ring, for cellular toroidal embeddings.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103717"},"PeriodicalIF":0.9,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934293","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":"Semi-hyponormality of commuting pairs of Hilbert space operators","authors":"Raúl E. Curto ,&nbsp;Jasang Yoon","doi":"10.1016/j.bulsci.2025.103718","DOIUrl":"10.1016/j.bulsci.2025.103718","url":null,"abstract":"<div><div>We first find an explicit formula for the square root of positive <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> operator matrices with commuting entries, and then use it to define and study semi-hyponormality for commuting pairs of Hilbert space operators. For the well-known 3–parameter family <span><math><msub><mrow><mi>W</mi></mrow><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></msub><mo>(</mo><mi>a</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> of 2–variable weighted shifts, we completely identify the parametric regions in the open unit cube where <span><math><msub><mrow><mi>W</mi></mrow><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></msub><mo>(</mo><mi>a</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> is subnormal, hyponormal, semi-hyponormal, and weakly hyponormal. As a result, we describe in detail concrete sub-regions where each property holds. For instance, we identify the specific sub-region where weak hyponormality holds but semi-hyponormality does not hold, and vice versa. To accomplish this, we employ a new technique emanating from the homogeneous orthogonal decomposition of <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></math></span>. The technique allows us to reduce the study of semi-hyponormality to positivity considerations of a sequence of <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> scalar matrices. It also requires a specific formula for the square root of <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> scalar and operator matrices, and we obtain that along the way. As an application of our main results, we show that the Drury-Arveson shift is <em>not</em> semi-hyponormal. Taken together, the new results offer a sharp contrast between the above-mentioned properties for unilateral weighted shifts and their 2–variable counterparts.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103718"},"PeriodicalIF":0.9,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018850","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":"Statistics of moduli spaces of vector bundles over hyperelliptic curves","authors":"Arijit Dey ,&nbsp;Sampa Dey ,&nbsp;Anirban Mukhopadhyay","doi":"10.1016/j.bulsci.2025.103716","DOIUrl":"10.1016/j.bulsci.2025.103716","url":null,"abstract":"<div><div>We give an asymptotic formula for the number of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>-rational points over a fixed determinant moduli space of stable vector bundles of rank <em>r</em> and degree <em>d</em> over a smooth, projective curve <em>X</em> of genus <span><math><mi>g</mi><mo>≥</mo><mn>2</mn></math></span> defined over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>. Further, we study the distribution of the error term when <em>X</em> varies over a family of hyperelliptic curves. We then extend the results to the Seshadri desingularisation of the moduli space of semi-stable vector bundles of rank 2 with trivial determinant, and also to the moduli space of rank 2 stable Higgs bundles.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103716"},"PeriodicalIF":0.9,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010732","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":"Oscillation of half-linear second-order difference equations via the adapted Riccati transformation","authors":"Petr Hasil,&nbsp;Jiřina Šišoláková,&nbsp;Michal Veselý","doi":"10.1016/j.bulsci.2025.103711","DOIUrl":"10.1016/j.bulsci.2025.103711","url":null,"abstract":"<div><div>Applying the adapted Riccati technique, we generalize a known oscillation criterion about linear difference equations to the corresponding half-linear version. The criterion covers general classes of difference equations with coefficients which can change sign. This fact gives the novelty of our result, because previously known strongly relevant criteria for the treated half-linear equations are not applicable for such equations. At the same time, the presented criterion does not use any auxiliary sequences which is its undeniable advantage.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103711"},"PeriodicalIF":0.9,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144885566","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}