Journal of Mathematical Analysis and Applications最新文献

{"title":"Wong-Zakai approximation for Landau-Lifshitz-Gilbert equation with anisotropy energy driven by geometric rough paths","authors":"Kistosil Fahim ,&nbsp;Debopriya Mukherjee ,&nbsp;Erika Hausenblas","doi":"10.1016/j.jmaa.2025.129885","DOIUrl":"10.1016/j.jmaa.2025.129885","url":null,"abstract":"<div><div>We investigate the one-dimensional Rough Landau–Lifshitz–Gilbert Equation (RLLGE) in the presence of nonzero exchange and anisotropy energies, using Lyons' rough path theory. The solutions are constrained to lie on the two-dimensional unit sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, and we prove the existence and uniqueness of strong solutions within this geometric setting. Since the equation evolves on a manifold, a central difficulty arises in approximating geometric rough paths in a regular and controlled manner. We conduct a detailed analysis of the limiting equation, the associated correction term, and its convergence rate in the controlled rough path framework. The construction of solutions and the convergence analysis rely on several key techniques: the Doss–Sussmann transformation, maximal regularity results, and the theory of geometric rough paths. Together, these tools ensure a rigorous treatment of the problem and allow us to capture the essential rough structure of the dynamics.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129885"},"PeriodicalIF":1.2,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144670518","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":"Dichotomy gap conditions for the existence of smooth inertial manifolds for non-instantaneous impulsive parabolic equations","authors":"Xuan-Quang Bui","doi":"10.1016/j.jmaa.2025.129880","DOIUrl":"10.1016/j.jmaa.2025.129880","url":null,"abstract":"<div><div>This paper deals with the fully non-autonomous semilinear parabolic equation <span><math><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>+</mo><mi>A</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>x</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></span> under certain non-instantaneous impulsive effects. Using the Lyapunov–Perron method, we provide dichotomy gap conditions, where the dichotomy gap <span><math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is compared to <span><math><msub><mrow><mi>sup</mi></mrow><mrow><mi>t</mi><mo>∈</mo><mi>R</mi></mrow></msub><mo>⁡</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mi>t</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>t</mi></mrow></msubsup><msup><mrow><mo>(</mo><mi>φ</mi><mo>(</mo><mi>τ</mi><mo>)</mo><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>τ</mi></math></span>, for the existence of an inertial manifold for the non-instantaneous impulsive parabolic equations. Moreover, we investigate the regularity of the inertial manifolds under the condition on the regularity of the nonlinear term. We will discuss a consequence of the obtained results for the parabolic equations without impulses. Finally, we apply our abstract results to a nonautonomous reaction-diffusion equation.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129880"},"PeriodicalIF":1.2,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614859","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":"Asymptotic growth of (−1)rΔrlog⁡p‾(n)/nαn and the reverse higher order Turán inequalities for p‾(n)/nαn","authors":"Gargi Mukherjee","doi":"10.1016/j.jmaa.2025.129884","DOIUrl":"10.1016/j.jmaa.2025.129884","url":null,"abstract":"<div><div>Let <span><math><mover><mrow><mi>p</mi></mrow><mo>‾</mo></mover><mo>(</mo><mi>n</mi><mo>)</mo></math></span> denote the overpartition function. In this paper, we study the asymptotic growth of finite difference of logarithm of <span><math><mroot><mrow><mover><mrow><mi>p</mi></mrow><mo>‾</mo></mover><mo>(</mo><mi>n</mi><mo>)</mo><mo>/</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot></math></span> for <em>α</em> being a non-negative real number. Consequently, we retrieve log-convexity of <span><math><mroot><mrow><mover><mrow><mi>p</mi></mrow><mo>‾</mo></mover><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></mroot></math></span> and <span><math><mroot><mrow><mover><mrow><mi>p</mi></mrow><mo>‾</mo></mover><mo>(</mo><mi>n</mi><mo>)</mo><mo>/</mo><mi>n</mi></mrow><mrow><mi>n</mi></mrow></mroot></math></span>, previously studied by the author aligned to the work of Chen and Zheng in context of the partition function <span><math><mi>p</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>. Generalizing the theme of log-convexity, began with the work of Sun, Chen, and Zheng, another main objective of this paper is to prove that <span><math><mroot><mrow><mover><mrow><mi>p</mi></mrow><mo>‾</mo></mover><mo>(</mo><mi>n</mi><mo>)</mo><mo>/</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot></math></span> satisfies the reverse higher order Turán inequalities which depict the non real-rootedness of the Jensen polynomial associated with the sequence presented above.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129884"},"PeriodicalIF":1.2,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632831","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":"Polar factor's representations and approximations","authors":"Abdellatif Bourhim ,&nbsp;Mostafa Mbekhta","doi":"10.1016/j.jmaa.2025.129881","DOIUrl":"10.1016/j.jmaa.2025.129881","url":null,"abstract":"<div><div>Let <em>H</em> be a complex Hilbert space and let <span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> be the algebra of all bounded linear operators on <em>H</em>. The polar decomposition theorem asserts that every operator <span><math><mi>T</mi><mo>∈</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> can be uniquely written as <span><math><mi>T</mi><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>|</mo><mi>T</mi><mo>|</mo></math></span>, where <span><math><mo>|</mo><mi>T</mi><mo>|</mo><mo>:</mo><mo>=</mo><msup><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>T</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math></span> and <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span> is a partial isometry, called the polar factor of <em>T</em>, whose kernel coincides with that of <em>T</em>. In this paper, we obtain various representations and approximations of the polar factors of operators.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129881"},"PeriodicalIF":1.2,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654588","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":"Turing instability of the periodic solutions for a vegetation-water model with cross-diffusion","authors":"Panpan Zhang,&nbsp;Kuilin Wu","doi":"10.1016/j.jmaa.2025.129877","DOIUrl":"10.1016/j.jmaa.2025.129877","url":null,"abstract":"<div><div>In this paper, we focus on a vegetation-water model with cross-diffusion and investigate Turing instability of its periodic solutions. Firstly, we discuss the qualitative properties of the corresponding ODE system without diffusion. By employing center manifold theory and normal form method, we deal with the stability of periodic solutions of the perturbed ODE system. Based on Floquet theory and the change of coefficients of self-diffusion and cross-diffusion, we derive conditions that the stable periodic solution from Hopf bifurcation can become Turing unstable.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129877"},"PeriodicalIF":1.2,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614857","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":"Regular fractional weighted Wiener algebras and invariant subspaces","authors":"Luciano Abadias ,&nbsp;Miguel Monsalve-López","doi":"10.1016/j.jmaa.2025.129875","DOIUrl":"10.1016/j.jmaa.2025.129875","url":null,"abstract":"<div><div>Since the fifties, the interplay between spectral theory, harmonic analysis and a wide variety of techniques based on the functional calculus of operators, has provided useful criteria to find non-trivial closed invariant subspaces for operators acting on complex Banach spaces. In this article, some standard summability methods (mainly the Cesàro summation) are applied to generalize classical results due to Wermer <span><span>[51]</span></span> and Atzmon <span><span>[8]</span></span> regarding the existence of invariant subspaces under growth conditions on the resolvent of an operator. To do so, an extension of Beurling's regularity criterion <span><span>[13]</span></span> is proved for fractional weighted Wiener algebras <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>ρ</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span> related with the Cesàro summation of order <span><math><mi>α</mi><mo>≥</mo><mn>0</mn></math></span>. At the end of the article, other summability methods are considered for the purpose of finding new sufficient criteria which ensure the existence of invariant subspaces, resulting in several open questions on the regularity of fractional weighted Wiener algebras <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>ρ</mi></mrow><mrow><mi>μ</mi></mrow></msubsup></math></span> associated to matrix summation methods defined from non-vanishing complex sequences.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129875"},"PeriodicalIF":1.2,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632891","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":"Dynamics analysis and optimal control of SIR-w infectious disease model under the influence of multidimensional information","authors":"Jianrong Wang ,&nbsp;Xue Yan ,&nbsp;Xinghua Chang","doi":"10.1016/j.jmaa.2025.129855","DOIUrl":"10.1016/j.jmaa.2025.129855","url":null,"abstract":"<div><div>Multidimensional information plays a crucial role in the spread of infectious diseases by facilitating scientific decision-making for prevention and control, enhancing public awareness and participation in preventive measures, optimizing resource allocation to improve treatment efficiency, advancing scientific research to refine prevention and control strategies, as well as guiding public opinion and stabilizing social sentiment. Hence, it is essential to focus on the analysis and utilization of multidimensional information to more effectively tackle the challenges posed by infectious diseases. This paper introduces the SIR-w infectious disease model, which incorporates the influence of multidimensional information. By considering the impact of such information, it examines the interaction mechanisms and the counteracting effects on the spread and control of infectious diseases, and accurately depicts the influence of positive, negative, and legal policies on epidemic spread and control. Employing the next-generation matrix theory, the basic reproduction number is determined. Utilizing stability theory and the Lyapunov function, the dynamical behaviors of the disease-free and endemic equilibrium points are analyzed and discussed. Drawing on the interaction and support mechanisms among multidimensional information such as positive, negative, and legal policies, the study explores how the corresponding parameters affect the compartmental changes. Consequently, an optimal control analysis is conducted for the dissemination rate of positive and negative information generated by confirmed cases, medical resources, and policies and regulations, with numerical solutions for optimal control being obtained. Finally, the four solutions are simulated and verified by numerical simulation, it is found that the simultaneous implementation of the five control measures is the most effective and the least costly.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129855"},"PeriodicalIF":1.2,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614860","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":"Large sums of symmetric power coefficients of holomorphic cusp forms","authors":"Theran Bassett,&nbsp;Alia Hamieh","doi":"10.1016/j.jmaa.2025.129878","DOIUrl":"10.1016/j.jmaa.2025.129878","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Given a non-CM primitive cusp form &lt;em&gt;f&lt;/em&gt; of even weight &lt;em&gt;k&lt;/em&gt; and level &lt;em&gt;N&lt;/em&gt;, we let &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; denote the &lt;em&gt;m&lt;/em&gt;-th symmetric power lift of &lt;em&gt;f&lt;/em&gt;. We denote by &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; the sequence of normalized coefficients of the Dirichlet series associated to the &lt;em&gt;L&lt;/em&gt;-function of &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. In this paper, we investigate the range of &lt;em&gt;x&lt;/em&gt; (in terms of &lt;em&gt;k&lt;/em&gt; and &lt;em&gt;N&lt;/em&gt;) for which there are cancellations in the sum &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. We first prove that &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;log&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;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; implies that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; for some &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. Assuming the Generalized Riemann Hypothesis (GRH) for &lt;span&gt;&lt;math&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, we also show that &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; in the range &lt;span&gt;&lt;math&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129878"},"PeriodicalIF":1.2,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632830","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 exact dimension of Liouville numbers: The Fourier side","authors":"Iván Polasek ,&nbsp;Ezequiel Rela","doi":"10.1016/j.jmaa.2025.129872","DOIUrl":"10.1016/j.jmaa.2025.129872","url":null,"abstract":"<div><div>In this article we study the generalized Fourier dimension of the set of Liouville numbers <span><math><mi>L</mi></math></span>. Being a set of zero Hausdorff dimension, the analysis has to be done at the level of functions with a slow decay at infinity acting as control for the Fourier transform of (Rajchman) measures supported on <span><math><mi>L</mi></math></span>. We give an almost complete characterization of admissible decays for this set in terms of comparison to power-like functions. This work can be seen as the “Fourier side” of the analysis made by Olsen and Renfro regarding the generalized Hausdorff dimension using gauge functions. We also provide an approach to deal with the problem of classifying oscillating candidates for a Fourier decay for <span><math><mi>L</mi></math></span> relying on its translation invariance property.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129872"},"PeriodicalIF":1.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596734","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 general quasilinear elliptic problem with variable exponents and Neumann boundary conditions for image processing","authors":"Bogdan Maxim","doi":"10.1016/j.jmaa.2025.129874","DOIUrl":"10.1016/j.jmaa.2025.129874","url":null,"abstract":"<div><div>The aim of this paper is to state and prove existence and uniqueness results for a general elliptic problem with homogeneous Neumann boundary conditions, often associated with image processing tasks like denoising. The novelty is that we surpass the lack of coercivity of the Euler-Lagrange functional with an innovative technique that has at its core the idea of showing that the minimum of the energy functional over a subset of the space <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> coincides with the global minimum. The obtained existence result applies to multiple-phase elliptic problems under remarkably weak assumptions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129874"},"PeriodicalIF":1.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614858","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}