数学最新文献

{"title":"Exploring fractal–fractional integral inequalities: An extensive parametric study","authors":"Pan Gong ,&nbsp;Badreddine Meftah ,&nbsp;Hongyan Xu ,&nbsp;Hüseyin Budak ,&nbsp;Abdelghani Lakhdari","doi":"10.1016/j.chaos.2025.116772","DOIUrl":"10.1016/j.chaos.2025.116772","url":null,"abstract":"<div><div>In this paper, we investigate fractal–fractional integral inequalities for generalized <span><math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>P</mi><mo>)</mo></mrow></math></span>-convex functions, a topic of growing interest in the field of fractional calculus. We begin by establishing a fractal–fractional Hermite–Hadamard inequality, providing a novel perspective on fractal <span><math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>P</mi><mo>)</mo></mrow></math></span>-convexity. Subsequently, we introduce a parameterized identity involving fractal–fractional integrals, which serves as a cornerstone for deriving midpoint-, trapezium-, Bullen-, Milne-, and Simpson-type inequalities. The results are developed for mappings whose fractal derivatives display generalized <span><math><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>P</mi><mo>)</mo></mrow></math></span>-convexity. Additionally, we present a numerical example with graphical representations to validate the theoretical findings. By leveraging improved versions of the Hölder and power mean inequalities, we further extend the applicability of our results. The study concludes by highlighting potential applications and proposing directions for future research, emphasizing the significance of these contributions to the broader field of mathematical analysis and optimization.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic Hopf bifurcation and random chaos of a multi-stable rotational energy harvesting system","authors":"Sengen Hu,&nbsp;Liangqiang Zhou","doi":"10.1016/j.chaos.2025.116850","DOIUrl":"10.1016/j.chaos.2025.116850","url":null,"abstract":"<div><div>This study examines stochastic Hopf bifurcation and random chaos in a multi-stable rotational vibration energy harvester (VEH) for automotive tire applications. The system is modeled as a strongly nonlinear Duffing-van der Pol (DVP) oscillator subject to forced and stochastic Gaussian white noise excitations. Analytical methods, including incomplete elliptic integrals, are used to derive exact solutions for eight possible homoclinic and heteroclinic orbits. Stochastic averaging and three-exponential techniques are employed to analyze Hopf bifurcation, identifying D- and P-bifurcation points and stationary probability density functions (PDFs). The stochastic Melnikov method is applied to derive chaos thresholds for six types of orbital entanglement and establish parameter criteria for four distinct chaos types. Numerical simulations validate the analytical results, demonstrating noise-induced transitions between multiple attractors and intermittent chaotic behavior. The findings provide insights for optimizing VEH performance through controlled chaotic dynamics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":""},"PeriodicalIF":5.3,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal asymptotic lower bound for stability of fractional Sobolev inequality and the global stability of log-Sobolev inequality on the sphere","authors":"Lu Chen ,&nbsp;Guozhen Lu ,&nbsp;Hanli Tang","doi":"10.1016/j.aim.2025.110438","DOIUrl":"10.1016/j.aim.2025.110438","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we establish the optimal asymptotic lower bound for the stability of fractional Sobolev inequality:&lt;span&gt;&lt;span&gt;&lt;span&gt;(0.1)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the set of maximizers of the fractional Sobolev inequality of order &lt;em&gt;s&lt;/em&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; denotes the optimal lower bound of stability. We prove that the optimal lower bound &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; behaves asymptotically at the order of &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt; when &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for any fixed &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. This extends the work by Dolbeault-Esteban-Figalli-Frank-Loss &lt;span&gt;&lt;span&gt;[22]&lt;/span&gt;&lt;/span&gt; on the stability of the first order Sobolev inequality (i.e., &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;) and quantify the asymptotic behavior for lower bound of stability of fractional Sobolev inequality established by the current author's previous work in &lt;span&gt;&lt;span&gt;[15]&lt;/span&gt;&lt;/span&gt; in the case of &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Moreover, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; behaves asymptotically at the order of &lt;em&gt;s&lt;/em&gt; when &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for any given dimension &lt;em&gt;n&lt;/em&gt;. (See &lt;span&gt;&lt;span&gt;Theorem 1.1&lt;/span&gt;&lt;/span&gt; for these asymptotic estimates.) As an important application of this asymptotic estimate as &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, we derive the global stability for the log-Sobolev inequality on the sphere established by Beckner in &lt;span&gt;&lt;span&gt;[3]&lt;/span&gt;&lt;/span&gt;, &lt;span&gt;&lt;span&gt;[5]&lt;/span&gt;&lt;/span&gt; with the optimal asymptotic low","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"479 ","pages":"Article 110438"},"PeriodicalIF":1.5,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Detecting eigenvalues in a fourth-order nonlinear Schrödinger equation with a non-regular Maslov box","authors":"Mitchell Curran ,&nbsp;Robert Marangell","doi":"10.1016/j.jde.2025.113649","DOIUrl":"10.1016/j.jde.2025.113649","url":null,"abstract":"<div><div>We use the Maslov index to study the eigenvalue problem arising from the linearisation about solitons in the fourth-order cubic nonlinear Schrödinger equation (NLSE). Our analysis is motivated by recent work by Bandara et al., in which the fourth-order cubic NLSE was shown to support infinite families of multipulse solitons. Using a homotopy argument, we prove that the Morse indices of two selfadjoint fourth-order operators appearing in the linearisation may be computed by counting conjugate points, as well as a lower bound for the number of real unstable eigenvalues of the linearisation. We also give a Vakhitov-Kolokolov type stability criterion. The interesting aspects of this problem as an application of the Maslov index are the instances of non-regular crossings, which feature crossing forms with varying ranks of degeneracy. We handle such degeneracies directly via higher order crossing forms, using a definition of the Maslov index developed by Piccione and Tausk.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"447 ","pages":"Article 113649"},"PeriodicalIF":2.4,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Graph decomposition via edge edits into a union of regular graphs","authors":"Tony Zeng","doi":"10.1016/j.disc.2025.114686","DOIUrl":"10.1016/j.disc.2025.114686","url":null,"abstract":"<div><div>Suppose a graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> is the union of several (disjoint) regular graphs which are then connected with a few additional edges. <em>G</em> will then have only a small number of vertices <span><math><mi>v</mi><mo>∈</mo><mi>V</mi></math></span> with the property that one of their neighbors <em>w</em> has a higher degree. We prove the converse statement: if a graph has few vertices having a neighbor with higher degree and satisfies a mild regularity condition, then, via adding and removing a few edges, the graph can be turned into a union of disjoint regular graphs. The number of edge edits depends on the maximum degree and number of vertices with a higher degree neighbor but is independent of <span><math><mo>|</mo><mi>V</mi><mo>|</mo></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 1","pages":"Article 114686"},"PeriodicalIF":0.7,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696863","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":"Network classification through random walks","authors":"Gonzalo Travieso,&nbsp;João Merenda,&nbsp;Odemir M. Bruno","doi":"10.1016/j.chaos.2025.116817","DOIUrl":"10.1016/j.chaos.2025.116817","url":null,"abstract":"<div><div>Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based on its structure? This classification problem involves extracting relevant features from the network. Existing literature has proposed various methods that combine structural measurements and dynamical processes for feature extraction. In this study, we introduce an approach to characterize networks using statistics from random walks, which can be particularly informative about network properties. We present the employed statistical metrics and compare their performance on multiple datasets with other state-of-the-art feature extraction methods. Our results demonstrate that the proposed method is effective in many cases, often outperforming existing approaches, although some limitations are observed across certain datasets.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116817"},"PeriodicalIF":5.3,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lifting of locally initial objects and universal (co)acting Hopf algebras","authors":"A.L. Agore ,&nbsp;A.S. Gordienko ,&nbsp;J. Vercruysse","doi":"10.1016/j.aim.2025.110442","DOIUrl":"10.1016/j.aim.2025.110442","url":null,"abstract":"<div><div>The universal (co)acting bi/Hopf algebras introduced by Yu.I. Manin, M. Sweedler and D. Tambara, the universal Hopf algebra of a given (co)module structure, as well as the universal group of a grading, introduced by J. Patera and H. Zassenhaus, find their applications in the classification of quantum symmetries. Typically, universal (co)acting objects are defined as initial or terminal in the corresponding categories and, as such, they do not always exist. In order to ensure their existence, we introduce the support of a given object, which generalizes the support of a grading and is used to restrict the class of objects under consideration. The existence problems for universal objects are formulated and studied in a purely categorical manner by seeing them as particular cases of the lifting problem for a locally initial object. We prove the existence of a lifting and, consequently, of the universal (co)acting objects under some assumptions on the base (braided or symmetric monoidal) category. In contrast to existing constructions, our approach is self-dual in the sense that we can use the same proof to obtain the existence of universal actions and coactions. In particular, when the base category is the category of vector spaces over a field, the category of sets or their duals, we recover known existence results for the aforementioned universal objects. The proposed approach allows us to apply our results not only to the classical categories of sets and vectors spaces and their duals but also to (co)modules over bi/Hopf algebras, differential graded vector spaces, <em>G</em>-sets and graded sets.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"479 ","pages":"Article 110442"},"PeriodicalIF":1.5,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Injectivity radius lower bound of convex sum of tame Riemannian metrics and applications to symplectic topology","authors":"Jaeyoung Choi ,&nbsp;Yong-Geun Oh","doi":"10.1016/j.aim.2025.110443","DOIUrl":"10.1016/j.aim.2025.110443","url":null,"abstract":"<div><div>Motivated by the aspect of large-scale symplectic topology, we prove that for any pair <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> of smooth complete Riemannian metrics of bounded curvature and <em>of injectivity radius bounded away from zero</em>, the convex sum <span><math><msub><mrow><mi>g</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>:</mo><mo>=</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>s</mi><mo>)</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><mi>s</mi><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> also has bounded curvature depending only on the curvature bounds <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>R</mi></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></msub></math></span> of <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, and that the injectivity radii of <span><math><msub><mrow><mi>g</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> have uniform lower bound depending only on the derivative bounds <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>R</mi></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></msub><mo>=</mo><msub><mrow><mo>‖</mo><msub><mrow><mi>R</mi></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></msub><mo>+</mo><msub><mrow><mo>‖</mo><mi>D</mi><msub><mrow><mi>R</mi></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></msub></math></span>. A main technical ingredient to establish the injectivity radius lower bound is an application of the <em>quantitative inverse function theorem</em>. Using these estimates, we prove that each <em>quasi-isometry</em> class of tame metrics is convex <em>for all finite regularity class of</em> <span><math><mn>3</mn><mo>≤</mo><mi>r</mi><mo>&lt;</mo><mo>∞</mo></math></span><em>.</em> Using this Riemannian geometry result, we prove that the set of smooth <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span><em>-tame</em> almost complex structures inside the same quasi-isometry class associated to the symplectic form <em>ω</em> is contractible in strong <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span> topology for all <span><math><mn>0</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>r</mi></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"479 ","pages":"Article 110443"},"PeriodicalIF":1.5,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Steklov vs. Steklov: A fourth-order affair related to the Babuška paradox","authors":"Francesco Ferraresso ,&nbsp;Pier Domenico Lamberti","doi":"10.1016/j.nonrwa.2025.104464","DOIUrl":"10.1016/j.nonrwa.2025.104464","url":null,"abstract":"<div><div>We discuss two fourth-order Steklov problems and highlight a Babuška paradox appearing in their approximations on convex domains via sequences of convex polygons. To do so, we prove that the eigenvalues of one of the two problems depend with continuity upon domain perturbation in the class of convex domains, extending a result known in the literature for the first eigenvalue. This is obtained by examining in detail a nonlocal second order problem for harmonic functions introduced by Ferrero, Gazzola, and Weth. We further review how this result is connected to diverse variants of the classical Babuška paradox for the hinged plate and to a degeneration result by Maz’ya and Nazarov.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104464"},"PeriodicalIF":1.8,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695371","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":"Non-preservation of concavity properties by the Dirichlet heat flow on Riemannian manifolds","authors":"Kazuhiro Ishige,&nbsp;Asuka Takatsu,&nbsp;Haruto Tokunaga","doi":"10.1016/j.aim.2025.110439","DOIUrl":"10.1016/j.aim.2025.110439","url":null,"abstract":"<div><div>We prove that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywhere on the domain.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"479 ","pages":"Article 110439"},"PeriodicalIF":1.5,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}